Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(11,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 8]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.j (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 11.12 | ||
Character | \(\chi\) | \(=\) | 75.11 |
Dual form | 75.3.j.a.41.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.733747 | + | 1.00992i | 0.366874 | + | 0.504958i | 0.952048 | − | 0.305949i | \(-0.0989739\pi\) |
−0.585174 | + | 0.810908i | \(0.698974\pi\) | |||||||
\(3\) | 0.0713918 | − | 2.99915i | 0.0237973 | − | 0.999717i | ||||
\(4\) | 0.754522 | − | 2.32218i | 0.188630 | − | 0.580545i | ||||
\(5\) | −3.80815 | − | 3.24006i | −0.761630 | − | 0.648012i | ||||
\(6\) | 3.08127 | − | 2.12852i | 0.513546 | − | 0.354753i | ||||
\(7\) | −0.783313 | −0.111902 | −0.0559509 | − | 0.998434i | \(-0.517819\pi\) | ||||
−0.0559509 | + | 0.998434i | \(0.517819\pi\) | |||||||
\(8\) | 7.64775 | − | 2.48490i | 0.955968 | − | 0.310613i | ||||
\(9\) | −8.98981 | − | 0.428229i | −0.998867 | − | 0.0475811i | ||||
\(10\) | 0.477973 | − | 6.22330i | 0.0477973 | − | 0.622330i | ||||
\(11\) | 6.09322 | + | 8.38660i | 0.553929 | + | 0.762418i | 0.990539 | − | 0.137233i | \(-0.0438210\pi\) |
−0.436610 | + | 0.899651i | \(0.643821\pi\) | |||||||
\(12\) | −6.91070 | − | 2.42871i | −0.575892 | − | 0.202392i | ||||
\(13\) | 18.2529 | + | 13.2615i | 1.40407 | + | 1.02012i | 0.994151 | + | 0.107995i | \(0.0344430\pi\) |
0.409919 | + | 0.912122i | \(0.365557\pi\) | |||||||
\(14\) | −0.574753 | − | 0.791080i | −0.0410538 | − | 0.0565057i | ||||
\(15\) | −9.98930 | + | 11.1899i | −0.665954 | + | 0.745993i | ||||
\(16\) | 0.219602 | + | 0.159550i | 0.0137251 | + | 0.00997187i | ||||
\(17\) | 13.2916 | − | 4.31870i | 0.781859 | − | 0.254041i | 0.109225 | − | 0.994017i | \(-0.465163\pi\) |
0.672634 | + | 0.739976i | \(0.265163\pi\) | |||||||
\(18\) | −6.16377 | − | 9.39316i | −0.342432 | − | 0.521842i | ||||
\(19\) | 0.732695 | + | 2.25500i | 0.0385629 | + | 0.118684i | 0.968485 | − | 0.249073i | \(-0.0801258\pi\) |
−0.929922 | + | 0.367757i | \(0.880126\pi\) | |||||||
\(20\) | −10.3973 | + | 6.39851i | −0.519867 | + | 0.319925i | ||||
\(21\) | −0.0559221 | + | 2.34927i | −0.00266296 | + | 0.111870i | ||||
\(22\) | −3.99888 | + | 12.3073i | −0.181767 | + | 0.559422i | ||||
\(23\) | −13.9453 | − | 19.1940i | −0.606315 | − | 0.834521i | 0.389953 | − | 0.920835i | \(-0.372491\pi\) |
−0.996268 | + | 0.0863135i | \(0.972491\pi\) | |||||||
\(24\) | −6.90661 | − | 23.1141i | −0.287776 | − | 0.963089i | ||||
\(25\) | 4.00400 | + | 24.6773i | 0.160160 | + | 0.987091i | ||||
\(26\) | 28.1645i | 1.08325i | ||||||||
\(27\) | −1.92612 | + | 26.9312i | −0.0713379 | + | 0.997452i | ||||
\(28\) | −0.591026 | + | 1.81899i | −0.0211081 | + | 0.0649640i | ||||
\(29\) | −34.7539 | − | 11.2922i | −1.19841 | − | 0.389387i | −0.359235 | − | 0.933247i | \(-0.616962\pi\) |
−0.839176 | + | 0.543860i | \(0.816962\pi\) | |||||||
\(30\) | −18.6305 | − | 1.87780i | −0.621016 | − | 0.0625935i | ||||
\(31\) | −2.53573 | − | 7.80418i | −0.0817978 | − | 0.251748i | 0.901791 | − | 0.432172i | \(-0.142253\pi\) |
−0.983589 | + | 0.180425i | \(0.942253\pi\) | |||||||
\(32\) | − | 31.8264i | − | 0.994576i | ||||||
\(33\) | 25.5877 | − | 17.6757i | 0.775384 | − | 0.535629i | ||||
\(34\) | 14.1142 | + | 10.2546i | 0.415124 | + | 0.301605i | ||||
\(35\) | 2.98297 | + | 2.53798i | 0.0852277 | + | 0.0725137i | ||||
\(36\) | −7.77743 | + | 20.5528i | −0.216040 | + | 0.570912i | ||||
\(37\) | 25.0115 | + | 18.1719i | 0.675987 | + | 0.491133i | 0.872024 | − | 0.489463i | \(-0.162807\pi\) |
−0.196037 | + | 0.980597i | \(0.562807\pi\) | |||||||
\(38\) | −1.73975 | + | 2.39456i | −0.0457830 | + | 0.0630148i | ||||
\(39\) | 41.0764 | − | 53.7965i | 1.05324 | − | 1.37940i | ||||
\(40\) | −37.1750 | − | 15.3163i | −0.929375 | − | 0.382907i | ||||
\(41\) | −28.4745 | + | 39.1918i | −0.694500 | + | 0.955897i | 0.305493 | + | 0.952194i | \(0.401179\pi\) |
−0.999993 | + | 0.00370304i | \(0.998821\pi\) | |||||||
\(42\) | −2.41360 | + | 1.66730i | −0.0574667 | + | 0.0396975i | ||||
\(43\) | 6.53078 | 0.151879 | 0.0759393 | − | 0.997112i | \(-0.475804\pi\) | ||||
0.0759393 | + | 0.997112i | \(0.475804\pi\) | |||||||
\(44\) | 24.0726 | − | 7.82168i | 0.547106 | − | 0.177765i | ||||
\(45\) | 32.8470 | + | 30.7583i | 0.729934 | + | 0.683518i | ||||
\(46\) | 9.15204 | − | 28.1671i | 0.198957 | − | 0.612328i | ||||
\(47\) | 87.7811 | + | 28.5218i | 1.86768 | + | 0.606847i | 0.992371 | + | 0.123289i | \(0.0393441\pi\) |
0.875312 | + | 0.483558i | \(0.160656\pi\) | |||||||
\(48\) | 0.494192 | − | 0.647228i | 0.0102957 | − | 0.0134839i | ||||
\(49\) | −48.3864 | −0.987478 | ||||||||
\(50\) | −21.9841 | + | 22.1506i | −0.439681 | + | 0.443012i | ||||
\(51\) | −12.0035 | − | 40.1718i | −0.235363 | − | 0.787683i | ||||
\(52\) | 44.5679 | − | 32.3804i | 0.857074 | − | 0.622701i | ||||
\(53\) | −0.900738 | − | 0.292667i | −0.0169950 | − | 0.00552203i | 0.300507 | − | 0.953780i | \(-0.402844\pi\) |
−0.317502 | + | 0.948258i | \(0.602844\pi\) | |||||||
\(54\) | −28.6116 | + | 17.8155i | −0.529844 | + | 0.329916i | ||||
\(55\) | 3.96920 | − | 51.6798i | 0.0721673 | − | 0.939633i | ||||
\(56\) | −5.99058 | + | 1.94646i | −0.106975 | + | 0.0347581i | ||||
\(57\) | 6.81541 | − | 2.03647i | 0.119569 | − | 0.0357276i | ||||
\(58\) | −14.0964 | − | 43.3842i | −0.243041 | − | 0.748004i | ||||
\(59\) | 5.27776 | − | 7.26421i | 0.0894535 | − | 0.123122i | −0.761945 | − | 0.647642i | \(-0.775755\pi\) |
0.851398 | + | 0.524520i | \(0.175755\pi\) | |||||||
\(60\) | 18.4478 | + | 31.6400i | 0.307463 | + | 0.527333i | ||||
\(61\) | −39.4497 | + | 28.6619i | −0.646716 | + | 0.469867i | −0.862151 | − | 0.506651i | \(-0.830883\pi\) |
0.215435 | + | 0.976518i | \(0.430883\pi\) | |||||||
\(62\) | 6.02098 | − | 8.28717i | 0.0971126 | − | 0.133664i | ||||
\(63\) | 7.04183 | + | 0.335438i | 0.111775 | + | 0.00532441i | ||||
\(64\) | 33.0204 | − | 23.9907i | 0.515944 | − | 0.374855i | ||||
\(65\) | −26.5417 | − | 109.642i | −0.408334 | − | 1.68681i | ||||
\(66\) | 36.6259 | + | 12.8719i | 0.554938 | + | 0.195028i | ||||
\(67\) | −14.5905 | − | 44.9050i | −0.217769 | − | 0.670223i | −0.998945 | − | 0.0459134i | \(-0.985380\pi\) |
0.781177 | − | 0.624310i | \(-0.214620\pi\) | |||||||
\(68\) | − | 34.1241i | − | 0.501824i | ||||||
\(69\) | −58.5612 | + | 40.4536i | −0.848714 | + | 0.586284i | ||||
\(70\) | −0.374402 | + | 4.87479i | −0.00534860 | + | 0.0696398i | ||||
\(71\) | 28.0777 | + | 9.12299i | 0.395460 | + | 0.128493i | 0.499995 | − | 0.866028i | \(-0.333335\pi\) |
−0.104534 | + | 0.994521i | \(0.533335\pi\) | |||||||
\(72\) | −69.8159 | + | 19.0638i | −0.969665 | + | 0.264775i | ||||
\(73\) | −75.5255 | + | 54.8725i | −1.03460 | + | 0.751678i | −0.969223 | − | 0.246183i | \(-0.920824\pi\) |
−0.0653725 | + | 0.997861i | \(0.520824\pi\) | |||||||
\(74\) | 38.5931i | 0.521529i | ||||||||
\(75\) | 74.2967 | − | 10.2468i | 0.990623 | − | 0.136625i | ||||
\(76\) | 5.78936 | 0.0761758 | ||||||||
\(77\) | −4.77289 | − | 6.56933i | −0.0619856 | − | 0.0853159i | ||||
\(78\) | 84.4696 | + | 2.01072i | 1.08294 | + | 0.0257784i | ||||
\(79\) | −10.2209 | + | 31.4566i | −0.129378 | + | 0.398185i | −0.994673 | − | 0.103078i | \(-0.967131\pi\) |
0.865295 | + | 0.501263i | \(0.167131\pi\) | |||||||
\(80\) | −0.319324 | − | 1.31911i | −0.00399155 | − | 0.0164889i | ||||
\(81\) | 80.6332 | + | 7.69940i | 0.995472 | + | 0.0950543i | ||||
\(82\) | −60.4735 | −0.737482 | ||||||||
\(83\) | −89.3723 | + | 29.0388i | −1.07678 | + | 0.349865i | −0.793123 | − | 0.609062i | \(-0.791546\pi\) |
−0.283652 | + | 0.958927i | \(0.591546\pi\) | |||||||
\(84\) | 5.41324 | + | 1.90244i | 0.0644433 | + | 0.0226481i | ||||
\(85\) | −64.6093 | − | 26.6194i | −0.760109 | − | 0.313169i | ||||
\(86\) | 4.79194 | + | 6.59554i | 0.0557202 | + | 0.0766923i | ||||
\(87\) | −36.3483 | + | 103.426i | −0.417796 | + | 1.18881i | ||||
\(88\) | 67.4393 | + | 48.9975i | 0.766355 | + | 0.556790i | ||||
\(89\) | 81.8649 | + | 112.677i | 0.919830 | + | 1.26604i | 0.963697 | + | 0.267000i | \(0.0860323\pi\) |
−0.0438667 | + | 0.999037i | \(0.513968\pi\) | |||||||
\(90\) | −6.96188 | + | 55.7416i | −0.0773542 | + | 0.619351i | ||||
\(91\) | −14.2977 | − | 10.3879i | −0.157118 | − | 0.114153i | ||||
\(92\) | −55.0939 | + | 17.9011i | −0.598847 | + | 0.194577i | ||||
\(93\) | −23.5869 | + | 7.04788i | −0.253623 | + | 0.0757837i | ||||
\(94\) | 35.6045 | + | 109.579i | 0.378771 | + | 1.16574i | ||||
\(95\) | 4.51614 | − | 10.9614i | 0.0475383 | − | 0.115383i | ||||
\(96\) | −95.4522 | − | 2.27215i | −0.994294 | − | 0.0236682i | ||||
\(97\) | −16.3457 | + | 50.3068i | −0.168512 | + | 0.518627i | −0.999278 | − | 0.0379953i | \(-0.987903\pi\) |
0.830766 | + | 0.556622i | \(0.187903\pi\) | |||||||
\(98\) | −35.5034 | − | 48.8662i | −0.362280 | − | 0.498635i | ||||
\(99\) | −51.1855 | − | 78.0032i | −0.517025 | − | 0.787911i | ||||
\(100\) | 60.3262 | + | 9.32154i | 0.603262 | + | 0.0932154i | ||||
\(101\) | − | 97.6796i | − | 0.967125i | −0.875310 | − | 0.483562i | \(-0.839343\pi\) | ||
0.875310 | − | 0.483562i | \(-0.160657\pi\) | |||||||
\(102\) | 31.7626 | − | 41.5985i | 0.311398 | − | 0.407829i | ||||
\(103\) | 19.4766 | − | 59.9429i | 0.189093 | − | 0.581970i | −0.810901 | − | 0.585183i | \(-0.801023\pi\) |
0.999995 | + | 0.00321311i | \(0.00102277\pi\) | |||||||
\(104\) | 172.547 | + | 56.0640i | 1.65911 | + | 0.539077i | ||||
\(105\) | 7.82475 | − | 8.76519i | 0.0745214 | − | 0.0834780i | ||||
\(106\) | −0.365344 | − | 1.12441i | −0.00344664 | − | 0.0106077i | ||||
\(107\) | − | 80.9374i | − | 0.756424i | −0.925719 | − | 0.378212i | \(-0.876539\pi\) | ||
0.925719 | − | 0.378212i | \(-0.123461\pi\) | |||||||
\(108\) | 61.0858 | + | 24.7930i | 0.565609 | + | 0.229565i | ||||
\(109\) | −157.177 | − | 114.196i | −1.44200 | − | 1.04767i | −0.987621 | − | 0.156860i | \(-0.949863\pi\) |
−0.454375 | − | 0.890811i | \(-0.650137\pi\) | |||||||
\(110\) | 55.1047 | − | 33.9113i | 0.500952 | − | 0.308285i | ||||
\(111\) | 56.2860 | − | 73.7160i | 0.507081 | − | 0.664108i | ||||
\(112\) | −0.172017 | − | 0.124977i | −0.00153586 | − | 0.00111587i | ||||
\(113\) | −73.2723 | + | 100.851i | −0.648428 | + | 0.892484i | −0.999030 | − | 0.0440402i | \(-0.985977\pi\) |
0.350602 | + | 0.936525i | \(0.385977\pi\) | |||||||
\(114\) | 7.05745 | + | 5.38873i | 0.0619075 | + | 0.0472696i | ||||
\(115\) | −9.08412 | + | 118.277i | −0.0789924 | + | 1.02850i | ||||
\(116\) | −52.4452 | + | 72.1846i | −0.452114 | + | 0.622281i | ||||
\(117\) | −158.411 | − | 127.035i | −1.35394 | − | 1.08577i | ||||
\(118\) | 11.2088 | 0.0949897 | ||||||||
\(119\) | −10.4115 | + | 3.38290i | −0.0874914 | + | 0.0284277i | ||||
\(120\) | −48.5898 | + | 110.400i | −0.404915 | + | 0.920000i | ||||
\(121\) | 4.18338 | − | 12.8751i | 0.0345734 | − | 0.106406i | ||||
\(122\) | −57.8922 | − | 18.8103i | −0.474526 | − | 0.154183i | ||||
\(123\) | 115.509 | + | 88.1973i | 0.939099 | + | 0.717051i | ||||
\(124\) | −20.0360 | −0.161580 | ||||||||
\(125\) | 64.7081 | − | 106.948i | 0.517665 | − | 0.855584i | ||||
\(126\) | 4.82816 | + | 7.35778i | 0.0383187 | + | 0.0583951i | ||||
\(127\) | 60.4323 | − | 43.9067i | 0.475845 | − | 0.345722i | −0.323870 | − | 0.946102i | \(-0.604984\pi\) |
0.799715 | + | 0.600380i | \(0.204984\pi\) | |||||||
\(128\) | −72.6176 | − | 23.5949i | −0.567325 | − | 0.184335i | ||||
\(129\) | 0.466244 | − | 19.5868i | 0.00361430 | − | 0.151836i | ||||
\(130\) | 91.2548 | − | 107.255i | 0.701960 | − | 0.825036i | ||||
\(131\) | −28.0597 | + | 9.11714i | −0.214196 | + | 0.0695965i | −0.414149 | − | 0.910209i | \(-0.635921\pi\) |
0.199953 | + | 0.979805i | \(0.435921\pi\) | |||||||
\(132\) | −21.7398 | − | 72.7559i | −0.164695 | − | 0.551181i | ||||
\(133\) | −0.573929 | − | 1.76637i | −0.00431526 | − | 0.0132810i | ||||
\(134\) | 34.6445 | − | 47.6841i | 0.258541 | − | 0.355851i | ||||
\(135\) | 94.5937 | − | 96.3173i | 0.700694 | − | 0.713462i | ||||
\(136\) | 90.9193 | − | 66.0567i | 0.668524 | − | 0.485711i | ||||
\(137\) | −2.70917 | + | 3.72885i | −0.0197750 | + | 0.0272179i | −0.818790 | − | 0.574093i | \(-0.805355\pi\) |
0.799015 | + | 0.601311i | \(0.205355\pi\) | |||||||
\(138\) | −83.8239 | − | 29.4592i | −0.607420 | − | 0.213473i | ||||
\(139\) | 196.821 | − | 142.999i | 1.41598 | − | 1.02877i | 0.423560 | − | 0.905868i | \(-0.360780\pi\) |
0.992419 | − | 0.122901i | \(-0.0392197\pi\) | |||||||
\(140\) | 8.14436 | − | 5.01203i | 0.0581740 | − | 0.0358002i | ||||
\(141\) | 91.8080 | − | 261.233i | 0.651121 | − | 1.85271i | ||||
\(142\) | 11.3885 | + | 35.0501i | 0.0802004 | + | 0.246832i | ||||
\(143\) | 233.885i | 1.63556i | ||||||||
\(144\) | −1.90585 | − | 1.52836i | −0.0132351 | − | 0.0106136i | ||||
\(145\) | 95.7606 | + | 155.607i | 0.660418 | + | 1.07315i | ||||
\(146\) | −110.833 | − | 36.0119i | −0.759132 | − | 0.246657i | ||||
\(147\) | −3.45439 | + | 145.118i | −0.0234993 | + | 0.987198i | ||||
\(148\) | 61.0702 | − | 44.3701i | 0.412637 | − | 0.299798i | ||||
\(149\) | − | 16.2931i | − | 0.109350i | −0.998504 | − | 0.0546749i | \(-0.982588\pi\) | ||
0.998504 | − | 0.0546749i | \(-0.0174123\pi\) | |||||||
\(150\) | 64.8635 | + | 67.5149i | 0.432423 | + | 0.450099i | ||||
\(151\) | 156.036 | 1.03335 | 0.516675 | − | 0.856181i | \(-0.327169\pi\) | ||||
0.516675 | + | 0.856181i | \(0.327169\pi\) | |||||||
\(152\) | 11.2069 | + | 15.4250i | 0.0737298 | + | 0.101480i | ||||
\(153\) | −121.338 | + | 33.1325i | −0.793061 | + | 0.216552i | ||||
\(154\) | 3.13237 | − | 9.64045i | 0.0203401 | − | 0.0626003i | ||||
\(155\) | −15.6296 | + | 37.9354i | −0.100836 | + | 0.244744i | ||||
\(156\) | −93.9320 | − | 135.977i | −0.602128 | − | 0.871650i | ||||
\(157\) | −149.519 | −0.952349 | −0.476174 | − | 0.879351i | \(-0.657977\pi\) | ||||
−0.476174 | + | 0.879351i | \(0.657977\pi\) | |||||||
\(158\) | −39.2681 | + | 12.7590i | −0.248532 | + | 0.0807530i | ||||
\(159\) | −0.942059 | + | 2.68055i | −0.00592490 | + | 0.0168588i | ||||
\(160\) | −103.120 | + | 121.200i | −0.644497 | + | 0.757498i | ||||
\(161\) | 10.9235 | + | 15.0349i | 0.0678478 | + | 0.0933844i | ||||
\(162\) | 51.3887 | + | 87.0822i | 0.317214 | + | 0.537545i | ||||
\(163\) | −186.417 | − | 135.440i | −1.14366 | − | 0.830917i | −0.156035 | − | 0.987752i | \(-0.549871\pi\) |
−0.987625 | + | 0.156834i | \(0.949871\pi\) | |||||||
\(164\) | 69.5257 | + | 95.6940i | 0.423937 | + | 0.583500i | ||||
\(165\) | −154.712 | − | 15.5938i | −0.937649 | − | 0.0945076i | ||||
\(166\) | −94.9035 | − | 68.9514i | −0.571708 | − | 0.415370i | ||||
\(167\) | 195.782 | − | 63.6135i | 1.17235 | − | 0.380919i | 0.342830 | − | 0.939398i | \(-0.388615\pi\) |
0.829519 | + | 0.558478i | \(0.188615\pi\) | |||||||
\(168\) | 5.41004 | + | 18.1056i | 0.0322026 | + | 0.107771i | ||||
\(169\) | 105.077 | + | 323.394i | 0.621758 | + | 1.91358i | ||||
\(170\) | −20.5236 | − | 84.7818i | −0.120727 | − | 0.498717i | ||||
\(171\) | −5.62113 | − | 20.5858i | −0.0328721 | − | 0.120385i | ||||
\(172\) | 4.92762 | − | 15.1656i | 0.0286489 | − | 0.0881723i | ||||
\(173\) | 33.8072 | + | 46.5316i | 0.195417 | + | 0.268969i | 0.895470 | − | 0.445123i | \(-0.146840\pi\) |
−0.700052 | + | 0.714092i | \(0.746840\pi\) | |||||||
\(174\) | −131.122 | + | 39.1799i | −0.753576 | + | 0.225172i | ||||
\(175\) | −3.13638 | − | 19.3300i | −0.0179222 | − | 0.110457i | ||||
\(176\) | 2.81388i | 0.0159880i | ||||||||
\(177\) | −21.4097 | − | 16.3474i | −0.120959 | − | 0.0923582i | ||||
\(178\) | −53.7265 | + | 165.353i | −0.301835 | + | 0.928951i | ||||
\(179\) | −130.028 | − | 42.2488i | −0.726416 | − | 0.236027i | −0.0776132 | − | 0.996984i | \(-0.524730\pi\) |
−0.648803 | + | 0.760957i | \(0.724730\pi\) | |||||||
\(180\) | 96.2101 | − | 53.0689i | 0.534500 | − | 0.294827i | ||||
\(181\) | 94.7969 | + | 291.755i | 0.523740 | + | 1.61191i | 0.766794 | + | 0.641893i | \(0.221851\pi\) |
−0.243054 | + | 0.970013i | \(0.578149\pi\) | |||||||
\(182\) | − | 22.0616i | − | 0.121218i | ||||||
\(183\) | 83.1449 | + | 120.362i | 0.454344 | + | 0.657715i | ||||
\(184\) | −154.345 | − | 112.138i | −0.838831 | − | 0.609447i | ||||
\(185\) | −36.3694 | − | 150.240i | −0.196591 | − | 0.812110i | ||||
\(186\) | −24.4246 | − | 18.6495i | −0.131315 | − | 0.100266i | ||||
\(187\) | 117.208 | + | 85.1565i | 0.626780 | + | 0.455382i | ||||
\(188\) | 132.466 | − | 182.323i | 0.704604 | − | 0.969804i | ||||
\(189\) | 1.50876 | − | 21.0956i | 0.00798284 | − | 0.111617i | ||||
\(190\) | 14.3838 | − | 3.48195i | 0.0757041 | − | 0.0183261i | ||||
\(191\) | −55.1968 | + | 75.9719i | −0.288988 | + | 0.397758i | −0.928685 | − | 0.370869i | \(-0.879060\pi\) |
0.639697 | + | 0.768627i | \(0.279060\pi\) | |||||||
\(192\) | −69.5945 | − | 100.746i | −0.362471 | − | 0.524719i | ||||
\(193\) | 73.3535 | 0.380070 | 0.190035 | − | 0.981777i | \(-0.439140\pi\) | ||||
0.190035 | + | 0.981777i | \(0.439140\pi\) | |||||||
\(194\) | −62.7992 | + | 20.4047i | −0.323707 | + | 0.105179i | ||||
\(195\) | −330.729 | + | 71.7749i | −1.69605 | + | 0.368077i | ||||
\(196\) | −36.5086 | + | 112.362i | −0.186268 | + | 0.573275i | ||||
\(197\) | −150.723 | − | 48.9727i | −0.765089 | − | 0.248593i | −0.0996278 | − | 0.995025i | \(-0.531765\pi\) |
−0.665461 | + | 0.746432i | \(0.731765\pi\) | |||||||
\(198\) | 41.2195 | − | 108.928i | 0.208179 | − | 0.550140i | ||||
\(199\) | −29.1785 | −0.146626 | −0.0733128 | − | 0.997309i | \(-0.523357\pi\) | ||||
−0.0733128 | + | 0.997309i | \(0.523357\pi\) | |||||||
\(200\) | 91.9422 | + | 178.776i | 0.459711 | + | 0.893880i | ||||
\(201\) | −135.718 | + | 40.5533i | −0.675216 | + | 0.201758i | ||||
\(202\) | 98.6482 | − | 71.6721i | 0.488358 | − | 0.354813i | ||||
\(203\) | 27.2232 | + | 8.84535i | 0.134104 | + | 0.0435732i | ||||
\(204\) | −102.343 | − | 2.43618i | −0.501682 | − | 0.0119420i | ||||
\(205\) | 235.419 | − | 56.9890i | 1.14839 | − | 0.277995i | ||||
\(206\) | 74.8282 | − | 24.3132i | 0.363244 | − | 0.118025i | ||||
\(207\) | 117.146 | + | 178.522i | 0.565921 | + | 0.862425i | ||||
\(208\) | 1.89250 | + | 5.82450i | 0.00909854 | + | 0.0280024i | ||||
\(209\) | −14.4473 | + | 19.8851i | −0.0691260 | + | 0.0951438i | ||||
\(210\) | 14.5935 | + | 1.47091i | 0.0694928 | + | 0.00700432i | ||||
\(211\) | −165.860 | + | 120.505i | −0.786068 | + | 0.571112i | −0.906794 | − | 0.421574i | \(-0.861478\pi\) |
0.120726 | + | 0.992686i | \(0.461478\pi\) | |||||||
\(212\) | −1.35925 | + | 1.87085i | −0.00641157 | + | 0.00882477i | ||||
\(213\) | 29.3657 | − | 83.5579i | 0.137867 | − | 0.392291i | ||||
\(214\) | 81.7400 | − | 59.3876i | 0.381963 | − | 0.277512i | ||||
\(215\) | −24.8702 | − | 21.1601i | −0.115675 | − | 0.0984192i | ||||
\(216\) | 52.1910 | + | 210.749i | 0.241625 | + | 0.975691i | ||||
\(217\) | 1.98627 | + | 6.11311i | 0.00915332 | + | 0.0281710i | ||||
\(218\) | − | 242.527i | − | 1.11251i | ||||||
\(219\) | 159.179 | + | 230.430i | 0.726845 | + | 1.05219i | ||||
\(220\) | −117.015 | − | 48.2107i | −0.531886 | − | 0.219140i | ||||
\(221\) | 299.883 | + | 97.4379i | 1.35694 | + | 0.440896i | ||||
\(222\) | 115.747 | + | 2.75523i | 0.521381 | + | 0.0124110i | ||||
\(223\) | 31.5460 | − | 22.9195i | 0.141462 | − | 0.102778i | −0.514804 | − | 0.857308i | \(-0.672135\pi\) |
0.656265 | + | 0.754530i | \(0.272135\pi\) | |||||||
\(224\) | 24.9300i | 0.111295i | ||||||||
\(225\) | −25.4276 | − | 223.559i | −0.113012 | − | 0.993594i | ||||
\(226\) | −155.614 | −0.688558 | ||||||||
\(227\) | 105.527 | + | 145.245i | 0.464877 | + | 0.639848i | 0.975511 | − | 0.219950i | \(-0.0705895\pi\) |
−0.510635 | + | 0.859798i | \(0.670589\pi\) | |||||||
\(228\) | 0.413313 | − | 17.3632i | 0.00181278 | − | 0.0761542i | ||||
\(229\) | 72.7732 | − | 223.973i | 0.317787 | − | 0.978048i | −0.656805 | − | 0.754060i | \(-0.728093\pi\) |
0.974592 | − | 0.223987i | \(-0.0719075\pi\) | |||||||
\(230\) | −126.115 | + | 77.6113i | −0.548328 | + | 0.337440i | ||||
\(231\) | −20.0431 | + | 13.8456i | −0.0867668 | + | 0.0599378i | ||||
\(232\) | −293.849 | −1.26659 | ||||||||
\(233\) | −46.6227 | + | 15.1486i | −0.200097 | + | 0.0650156i | −0.407351 | − | 0.913272i | \(-0.633547\pi\) |
0.207254 | + | 0.978287i | \(0.433547\pi\) | |||||||
\(234\) | 12.0609 | − | 253.194i | 0.0515422 | − | 1.08202i | ||||
\(235\) | −241.871 | − | 393.031i | −1.02924 | − | 1.67247i | ||||
\(236\) | −12.8866 | − | 17.7369i | −0.0546043 | − | 0.0751564i | ||||
\(237\) | 93.6135 | + | 32.8997i | 0.394994 | + | 0.138817i | ||||
\(238\) | −11.0558 | − | 8.03254i | −0.0464531 | − | 0.0337501i | ||||
\(239\) | −186.865 | − | 257.198i | −0.781864 | − | 1.07614i | −0.995074 | − | 0.0991370i | \(-0.968392\pi\) |
0.213210 | − | 0.977006i | \(-0.431608\pi\) | |||||||
\(240\) | −3.97901 | + | 0.863527i | −0.0165792 | + | 0.00359803i | ||||
\(241\) | −4.60439 | − | 3.34528i | −0.0191053 | − | 0.0138808i | 0.578192 | − | 0.815901i | \(-0.303759\pi\) |
−0.597297 | + | 0.802020i | \(0.703759\pi\) | |||||||
\(242\) | 16.0723 | − | 5.22222i | 0.0664147 | − | 0.0215794i | ||||
\(243\) | 28.8482 | − | 241.282i | 0.118717 | − | 0.992928i | ||||
\(244\) | 36.7924 | + | 113.235i | 0.150788 | + | 0.464079i | ||||
\(245\) | 184.263 | + | 156.775i | 0.752093 | + | 0.639898i | ||||
\(246\) | −4.31731 | + | 181.369i | −0.0175501 | + | 0.737273i | ||||
\(247\) | −16.5310 | + | 50.8771i | −0.0669270 | + | 0.205980i | ||||
\(248\) | −38.7852 | − | 53.3833i | −0.156392 | − | 0.215255i | ||||
\(249\) | 80.7114 | + | 270.114i | 0.324142 | + | 1.08480i | ||||
\(250\) | 155.488 | − | 13.1230i | 0.621951 | − | 0.0524921i | ||||
\(251\) | 194.851i | 0.776300i | 0.921596 | + | 0.388150i | \(0.126886\pi\) | ||||
−0.921596 | + | 0.388150i | \(0.873114\pi\) | |||||||
\(252\) | 6.09216 | − | 16.0993i | 0.0241752 | − | 0.0638861i | ||||
\(253\) | 76.0008 | − | 233.906i | 0.300398 | − | 0.924531i | ||||
\(254\) | 88.6841 | + | 28.8152i | 0.349150 | + | 0.113446i | ||||
\(255\) | −84.4480 | + | 191.873i | −0.331169 | + | 0.752441i | ||||
\(256\) | −79.9048 | − | 245.922i | −0.312128 | − | 0.960632i | ||||
\(257\) | 69.3384i | 0.269799i | 0.990859 | + | 0.134900i | \(0.0430712\pi\) | ||||
−0.990859 | + | 0.134900i | \(0.956929\pi\) | |||||||
\(258\) | 20.1231 | − | 13.9009i | 0.0779966 | − | 0.0538794i | ||||
\(259\) | −19.5918 | − | 14.2343i | −0.0756442 | − | 0.0549587i | ||||
\(260\) | −274.636 | − | 21.0931i | −1.05629 | − | 0.0811271i | ||||
\(261\) | 307.595 | + | 116.398i | 1.17853 | + | 0.445968i | ||||
\(262\) | −29.7963 | − | 21.6483i | −0.113726 | − | 0.0826269i | ||||
\(263\) | 252.703 | − | 347.816i | 0.960849 | − | 1.32249i | 0.0143124 | − | 0.999898i | \(-0.495444\pi\) |
0.946536 | − | 0.322597i | \(-0.104556\pi\) | |||||||
\(264\) | 151.765 | − | 198.762i | 0.574869 | − | 0.752888i | ||||
\(265\) | 2.48188 | + | 4.03297i | 0.00936559 | + | 0.0152187i | ||||
\(266\) | 1.36277 | − | 1.87569i | 0.00512320 | − | 0.00705147i | ||||
\(267\) | 343.781 | − | 237.481i | 1.28757 | − | 0.889441i | ||||
\(268\) | −115.286 | −0.430173 | ||||||||
\(269\) | −367.408 | + | 119.378i | −1.36583 | + | 0.443785i | −0.897985 | − | 0.440027i | \(-0.854969\pi\) |
−0.467844 | + | 0.883811i | \(0.654969\pi\) | |||||||
\(270\) | 166.680 | + | 24.8592i | 0.617334 | + | 0.0920712i | ||||
\(271\) | 123.124 | − | 378.936i | 0.454331 | − | 1.39829i | −0.417588 | − | 0.908637i | \(-0.637124\pi\) |
0.871919 | − | 0.489651i | \(-0.162876\pi\) | |||||||
\(272\) | 3.60791 | + | 1.17228i | 0.0132644 | + | 0.00430985i | ||||
\(273\) | −32.1757 | + | 42.1395i | −0.117860 | + | 0.154357i | ||||
\(274\) | −5.75368 | −0.0209988 | ||||||||
\(275\) | −182.561 | + | 183.944i | −0.663859 | + | 0.668887i | ||||
\(276\) | 49.7548 | + | 166.513i | 0.180271 | + | 0.603307i | ||||
\(277\) | 168.413 | − | 122.359i | 0.607990 | − | 0.441731i | −0.240716 | − | 0.970596i | \(-0.577382\pi\) |
0.848706 | + | 0.528865i | \(0.177382\pi\) | |||||||
\(278\) | 288.834 | + | 93.8478i | 1.03897 | + | 0.337582i | ||||
\(279\) | 19.4537 | + | 71.2439i | 0.0697267 | + | 0.255354i | ||||
\(280\) | 29.1196 | + | 11.9974i | 0.103999 | + | 0.0428480i | ||||
\(281\) | −228.630 | + | 74.2865i | −0.813632 | + | 0.264365i | −0.686135 | − | 0.727474i | \(-0.740694\pi\) |
−0.127496 | + | 0.991839i | \(0.540694\pi\) | |||||||
\(282\) | 331.187 | − | 98.9602i | 1.17442 | − | 0.350923i | ||||
\(283\) | 28.9769 | + | 89.1818i | 0.102392 | + | 0.315130i | 0.989110 | − | 0.147182i | \(-0.0470201\pi\) |
−0.886718 | + | 0.462312i | \(0.847020\pi\) | |||||||
\(284\) | 42.3705 | − | 58.3179i | 0.149192 | − | 0.205345i | ||||
\(285\) | −32.5524 | − | 14.3271i | −0.114219 | − | 0.0502707i | ||||
\(286\) | −236.204 | + | 171.613i | −0.825890 | + | 0.600044i | ||||
\(287\) | 22.3044 | − | 30.6994i | 0.0777158 | − | 0.106967i | ||||
\(288\) | −13.6290 | + | 286.113i | −0.0473230 | + | 0.993449i | ||||
\(289\) | −75.7903 | + | 55.0649i | −0.262250 | + | 0.190536i | ||||
\(290\) | −86.8864 | + | 210.887i | −0.299608 | + | 0.727196i | ||||
\(291\) | 149.711 | + | 52.6146i | 0.514470 | + | 0.180806i | ||||
\(292\) | 70.4381 | + | 216.786i | 0.241226 | + | 0.742419i | ||||
\(293\) | 90.0043i | 0.307182i | 0.988135 | + | 0.153591i | \(0.0490838\pi\) | ||||
−0.988135 | + | 0.153591i | \(0.950916\pi\) | |||||||
\(294\) | −149.092 | + | 102.991i | −0.507115 | + | 0.350311i | ||||
\(295\) | −43.6350 | + | 10.5629i | −0.147915 | + | 0.0358066i | ||||
\(296\) | 236.437 | + | 76.8231i | 0.798775 | + | 0.259538i | ||||
\(297\) | −237.597 | + | 147.944i | −0.799991 | + | 0.498128i | ||||
\(298\) | 16.4547 | − | 11.9550i | 0.0552171 | − | 0.0401176i | ||||
\(299\) | − | 535.282i | − | 1.79024i | ||||||
\(300\) | 32.2635 | − | 180.262i | 0.107545 | − | 0.600873i | ||||
\(301\) | −5.11564 | −0.0169955 | ||||||||
\(302\) | 114.491 | + | 157.583i | 0.379109 | + | 0.521799i | ||||
\(303\) | −292.956 | − | 6.97352i | −0.966851 | − | 0.0230149i | ||||
\(304\) | −0.198885 | + | 0.612104i | −0.000654226 | + | 0.00201350i | ||||
\(305\) | 243.097 | + | 18.6707i | 0.797038 | + | 0.0612155i | ||||
\(306\) | −122.493 | − | 98.2307i | −0.400303 | − | 0.321015i | ||||
\(307\) | −382.764 | −1.24679 | −0.623394 | − | 0.781908i | \(-0.714247\pi\) | ||||
−0.623394 | + | 0.781908i | \(0.714247\pi\) | |||||||
\(308\) | −18.8564 | + | 6.12682i | −0.0612221 | + | 0.0198923i | ||||
\(309\) | −178.387 | − | 62.6927i | −0.577305 | − | 0.202889i | ||||
\(310\) | −49.7797 | + | 12.0504i | −0.160580 | + | 0.0388723i | ||||
\(311\) | −252.604 | − | 347.680i | −0.812232 | − | 1.11794i | −0.990975 | − | 0.134046i | \(-0.957203\pi\) |
0.178743 | − | 0.983896i | \(-0.442797\pi\) | |||||||
\(312\) | 180.463 | − | 513.493i | 0.578407 | − | 1.64581i | ||||
\(313\) | 131.943 | + | 95.8625i | 0.421544 | + | 0.306270i | 0.778259 | − | 0.627944i | \(-0.216103\pi\) |
−0.356715 | + | 0.934213i | \(0.616103\pi\) | |||||||
\(314\) | −109.709 | − | 151.001i | −0.349392 | − | 0.480896i | ||||
\(315\) | −25.7295 | − | 24.0934i | −0.0816809 | − | 0.0764868i | ||||
\(316\) | 65.3361 | + | 47.4694i | 0.206760 | + | 0.150220i | ||||
\(317\) | 148.427 | − | 48.2269i | 0.468225 | − | 0.152135i | −0.0653959 | − | 0.997859i | \(-0.520831\pi\) |
0.533621 | + | 0.845724i | \(0.320831\pi\) | |||||||
\(318\) | −3.39837 | + | 1.01545i | −0.0106867 | + | 0.00319323i | ||||
\(319\) | −117.060 | − | 360.273i | −0.366959 | − | 1.12938i | ||||
\(320\) | −203.478 | − | 15.6279i | −0.635869 | − | 0.0488372i | ||||
\(321\) | −242.743 | − | 5.77827i | −0.756210 | − | 0.0180008i | ||||
\(322\) | −7.16891 | + | 22.0636i | −0.0222637 | + | 0.0685206i | ||||
\(323\) | 19.4774 | + | 26.8083i | 0.0603015 | + | 0.0829979i | ||||
\(324\) | 78.7189 | − | 181.435i | 0.242960 | − | 0.559986i | ||||
\(325\) | −254.174 | + | 503.531i | −0.782072 | + | 1.54933i | ||||
\(326\) | − | 287.644i | − | 0.882342i | ||||||
\(327\) | −353.713 | + | 463.246i | −1.08169 | + | 1.41666i | ||||
\(328\) | −120.378 | + | 370.485i | −0.367006 | + | 1.12953i | ||||
\(329\) | −68.7600 | − | 22.3415i | −0.208997 | − | 0.0679073i | ||||
\(330\) | −97.7712 | − | 167.688i | −0.296276 | − | 0.508146i | ||||
\(331\) | 39.7004 | + | 122.185i | 0.119941 | + | 0.369140i | 0.992945 | − | 0.118572i | \(-0.0378317\pi\) |
−0.873005 | + | 0.487712i | \(0.837832\pi\) | |||||||
\(332\) | 229.449i | 0.691112i | ||||||||
\(333\) | −217.067 | − | 174.073i | −0.651853 | − | 0.522741i | ||||
\(334\) | 207.899 | + | 151.047i | 0.622452 | + | 0.452238i | ||||
\(335\) | −89.9320 | + | 218.279i | −0.268454 | + | 0.651579i | ||||
\(336\) | −0.387107 | + | 0.506982i | −0.00115210 | + | 0.00150887i | ||||
\(337\) | 214.958 | + | 156.176i | 0.637856 | + | 0.463430i | 0.859113 | − | 0.511786i | \(-0.171016\pi\) |
−0.221257 | + | 0.975216i | \(0.571016\pi\) | |||||||
\(338\) | −249.501 | + | 343.409i | −0.738169 | + | 1.01600i | ||||
\(339\) | 297.235 | + | 226.955i | 0.876801 | + | 0.669483i | ||||
\(340\) | −110.564 | + | 129.949i | −0.325188 | + | 0.382204i | ||||
\(341\) | 49.9997 | − | 68.8187i | 0.146627 | − | 0.201814i | ||||
\(342\) | 16.6655 | − | 20.7817i | 0.0487294 | − | 0.0607651i | ||||
\(343\) | 76.2840 | 0.222402 | ||||||||
\(344\) | 49.9457 | − | 16.2284i | 0.145191 | − | 0.0471755i | ||||
\(345\) | 354.082 | + | 35.6887i | 1.02633 | + | 0.103445i | ||||
\(346\) | −22.1871 | + | 68.2849i | −0.0641246 | + | 0.197355i | ||||
\(347\) | −70.3658 | − | 22.8632i | −0.202783 | − | 0.0658883i | 0.205864 | − | 0.978581i | \(-0.433999\pi\) |
−0.408648 | + | 0.912692i | \(0.633999\pi\) | |||||||
\(348\) | 212.748 | + | 162.444i | 0.611346 | + | 0.466794i | ||||
\(349\) | −224.185 | −0.642364 | −0.321182 | − | 0.947017i | \(-0.604080\pi\) | ||||
−0.321182 | + | 0.947017i | \(0.604080\pi\) | |||||||
\(350\) | 17.2204 | − | 17.3508i | 0.0492011 | − | 0.0495738i | ||||
\(351\) | −392.306 | + | 466.030i | −1.11768 | + | 1.32772i | ||||
\(352\) | 266.915 | − | 193.925i | 0.758282 | − | 0.550924i | ||||
\(353\) | 42.8232 | + | 13.9141i | 0.121312 | + | 0.0394167i | 0.369044 | − | 0.929412i | \(-0.379685\pi\) |
−0.247732 | + | 0.968829i | \(0.579685\pi\) | |||||||
\(354\) | 0.800215 | − | 33.6168i | 0.00226050 | − | 0.0949628i | ||||
\(355\) | −77.3650 | − | 125.715i | −0.217929 | − | 0.354127i | ||||
\(356\) | 323.426 | − | 105.087i | 0.908499 | − | 0.295189i | ||||
\(357\) | 9.40252 | + | 31.4671i | 0.0263376 | + | 0.0881432i | ||||
\(358\) | −52.7402 | − | 162.318i | −0.147319 | − | 0.453402i | ||||
\(359\) | −63.1792 | + | 86.9587i | −0.175987 | + | 0.242225i | −0.887893 | − | 0.460049i | \(-0.847832\pi\) |
0.711907 | + | 0.702274i | \(0.247832\pi\) | |||||||
\(360\) | 327.637 | + | 153.610i | 0.910103 | + | 0.426694i | ||||
\(361\) | 287.507 | − | 208.886i | 0.796418 | − | 0.578632i | ||||
\(362\) | −225.091 | + | 309.811i | −0.621799 | + | 0.855833i | ||||
\(363\) | −38.3158 | − | 13.4658i | −0.105553 | − | 0.0370958i | ||||
\(364\) | −34.9106 | + | 25.3640i | −0.0959081 | + | 0.0696813i | ||||
\(365\) | 465.403 | + | 35.7447i | 1.27508 | + | 0.0979306i | ||||
\(366\) | −60.5480 | + | 172.285i | −0.165432 | + | 0.470723i | ||||
\(367\) | 70.0014 | + | 215.442i | 0.190740 | + | 0.587036i | 1.00000 | 0.000414133i | \(-0.000131823\pi\) | |
−0.809260 | + | 0.587450i | \(0.800132\pi\) | |||||||
\(368\) | − | 6.44000i | − | 0.0175000i | ||||||
\(369\) | 272.763 | − | 340.133i | 0.739196 | − | 0.921770i | ||||
\(370\) | 125.044 | − | 146.968i | 0.337957 | − | 0.397212i | ||||
\(371\) | 0.705559 | + | 0.229250i | 0.00190178 | + | 0.000617925i | ||||
\(372\) | −1.43040 | + | 60.0909i | −0.00384517 | + | 0.161535i | ||||
\(373\) | 74.9836 | − | 54.4788i | 0.201029 | − | 0.146056i | −0.482717 | − | 0.875777i | \(-0.660350\pi\) |
0.683745 | + | 0.729721i | \(0.260350\pi\) | |||||||
\(374\) | 180.854i | 0.483566i | ||||||||
\(375\) | −316.133 | − | 201.704i | −0.843022 | − | 0.537879i | ||||
\(376\) | 742.202 | 1.97394 | ||||||||
\(377\) | −484.608 | − | 667.006i | −1.28543 | − | 1.76925i | ||||
\(378\) | 22.4118 | − | 13.9551i | 0.0592905 | − | 0.0369182i | ||||
\(379\) | −143.626 | + | 442.035i | −0.378960 | + | 1.16632i | 0.561808 | + | 0.827268i | \(0.310106\pi\) |
−0.940768 | + | 0.339051i | \(0.889894\pi\) | |||||||
\(380\) | −22.0467 | − | 18.7579i | −0.0580178 | − | 0.0493629i | ||||
\(381\) | −127.368 | − | 184.380i | −0.334300 | − | 0.483938i | ||||
\(382\) | −117.226 | −0.306874 | ||||||||
\(383\) | 473.836 | − | 153.959i | 1.23717 | − | 0.401981i | 0.383863 | − | 0.923390i | \(-0.374594\pi\) |
0.853307 | + | 0.521410i | \(0.174594\pi\) | |||||||
\(384\) | −75.9489 | + | 216.107i | −0.197784 | + | 0.562778i | ||||
\(385\) | −3.10913 | + | 40.4814i | −0.00807566 | + | 0.105147i | ||||
\(386\) | 53.8229 | + | 74.0809i | 0.139438 | + | 0.191919i | ||||
\(387\) | −58.7104 | − | 2.79667i | −0.151707 | − | 0.00722654i | ||||
\(388\) | 104.488 | + | 75.9152i | 0.269300 | + | 0.195658i | ||||
\(389\) | 257.580 | + | 354.529i | 0.662160 | + | 0.911386i | 0.999551 | − | 0.0299793i | \(-0.00954413\pi\) |
−0.337390 | + | 0.941365i | \(0.609544\pi\) | |||||||
\(390\) | −315.158 | − | 281.344i | −0.808098 | − | 0.721395i | ||||
\(391\) | −268.248 | − | 194.894i | −0.686056 | − | 0.498449i | ||||
\(392\) | −370.047 | + | 120.236i | −0.943998 | + | 0.306723i | ||||
\(393\) | 25.3405 | + | 84.8061i | 0.0644795 | + | 0.215792i | ||||
\(394\) | −61.1339 | − | 188.151i | −0.155162 | − | 0.477540i | ||||
\(395\) | 140.844 | − | 86.6752i | 0.356567 | − | 0.219431i | ||||
\(396\) | −219.758 | + | 60.0067i | −0.554944 | + | 0.151532i | ||||
\(397\) | 230.685 | − | 709.976i | 0.581071 | − | 1.78835i | −0.0334362 | − | 0.999441i | \(-0.510645\pi\) |
0.614507 | − | 0.788911i | \(-0.289355\pi\) | |||||||
\(398\) | −21.4096 | − | 29.4679i | −0.0537931 | − | 0.0740398i | ||||
\(399\) | −5.33859 | + | 1.59520i | −0.0133799 | + | 0.00399799i | ||||
\(400\) | −3.05797 | + | 6.05801i | −0.00764493 | + | 0.0151450i | ||||
\(401\) | − | 382.778i | − | 0.954558i | −0.878752 | − | 0.477279i | \(-0.841623\pi\) | ||
0.878752 | − | 0.477279i | \(-0.158377\pi\) | |||||||
\(402\) | −140.538 | − | 107.308i | −0.349598 | − | 0.266936i | ||||
\(403\) | 57.2108 | − | 176.077i | 0.141962 | − | 0.436915i | ||||
\(404\) | −226.830 | − | 73.7014i | −0.561459 | − | 0.182429i | ||||
\(405\) | −282.117 | − | 290.577i | −0.696585 | − | 0.717474i | ||||
\(406\) | 11.0419 | + | 33.9834i | 0.0271967 | + | 0.0837030i | ||||
\(407\) | 320.487i | 0.787437i | ||||||||
\(408\) | −191.623 | − | 277.396i | −0.469665 | − | 0.679893i | ||||
\(409\) | 308.404 | + | 224.069i | 0.754044 | + | 0.547845i | 0.897078 | − | 0.441873i | \(-0.145686\pi\) |
−0.143034 | + | 0.989718i | \(0.545686\pi\) | |||||||
\(410\) | 230.292 | + | 195.938i | 0.561688 | + | 0.477897i | ||||
\(411\) | 10.9900 | + | 8.39142i | 0.0267396 | + | 0.0204171i | ||||
\(412\) | −124.503 | − | 90.4564i | −0.302191 | − | 0.219554i | ||||
\(413\) | −4.13413 | + | 5.69015i | −0.0100100 | + | 0.0137776i | ||||
\(414\) | −94.3370 | + | 249.297i | −0.227867 | + | 0.602168i | ||||
\(415\) | 434.431 | + | 178.988i | 1.04682 | + | 0.431296i | ||||
\(416\) | 422.067 | − | 580.925i | 1.01458 | − | 1.39645i | ||||
\(417\) | −414.824 | − | 600.505i | −0.994781 | − | 1.44006i | ||||
\(418\) | −30.6829 | −0.0734041 | ||||||||
\(419\) | 570.619 | − | 185.405i | 1.36186 | − | 0.442495i | 0.465196 | − | 0.885208i | \(-0.345984\pi\) |
0.896663 | + | 0.442713i | \(0.145984\pi\) | |||||||
\(420\) | −14.4504 | − | 24.7840i | −0.0344057 | − | 0.0590095i | ||||
\(421\) | 115.877 | − | 356.632i | 0.275242 | − | 0.847108i | −0.713913 | − | 0.700234i | \(-0.753079\pi\) |
0.989155 | − | 0.146874i | \(-0.0469211\pi\) | |||||||
\(422\) | −243.399 | − | 79.0852i | −0.576776 | − | 0.187406i | ||||
\(423\) | −776.921 | − | 293.996i | −1.83669 | − | 0.695026i | ||||
\(424\) | −7.61586 | −0.0179619 | ||||||||
\(425\) | 159.793 | + | 310.709i | 0.375985 | + | 0.731079i | ||||
\(426\) | 105.934 | − | 31.6534i | 0.248670 | − | 0.0743038i | ||||
\(427\) | 30.9014 | − | 22.4512i | 0.0723687 | − | 0.0525790i | ||||
\(428\) | −187.951 | − | 61.0690i | −0.439138 | − | 0.142685i | ||||
\(429\) | 701.457 | + | 16.6975i | 1.63510 | + | 0.0389219i | ||||
\(430\) | 3.12153 | − | 40.6430i | 0.00725938 | − | 0.0945186i | ||||
\(431\) | −292.960 | + | 95.1885i | −0.679722 | + | 0.220855i | −0.628474 | − | 0.777831i | \(-0.716320\pi\) |
−0.0512482 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(432\) | −4.71985 | + | 5.60683i | −0.0109256 | + | 0.0129788i | ||||
\(433\) | 117.801 | + | 362.555i | 0.272058 | + | 0.837310i | 0.989983 | + | 0.141189i | \(0.0450924\pi\) |
−0.717924 | + | 0.696121i | \(0.754908\pi\) | |||||||
\(434\) | −4.71631 | + | 6.49144i | −0.0108671 | + | 0.0149572i | ||||
\(435\) | 473.527 | − | 276.091i | 1.08857 | − | 0.634693i | ||||
\(436\) | −383.778 | + | 278.831i | −0.880224 | + | 0.639520i | ||||
\(437\) | 33.0649 | − | 45.5100i | 0.0756634 | − | 0.104142i | ||||
\(438\) | −115.918 | + | 329.835i | −0.264652 | + | 0.753047i | ||||
\(439\) | −169.776 | + | 123.349i | −0.386733 | + | 0.280978i | −0.764115 | − | 0.645080i | \(-0.776824\pi\) |
0.377383 | + | 0.926057i | \(0.376824\pi\) | |||||||
\(440\) | −98.0639 | − | 405.097i | −0.222872 | − | 0.920675i | ||||
\(441\) | 434.985 | + | 20.7205i | 0.986360 | + | 0.0469852i | ||||
\(442\) | 121.634 | + | 374.352i | 0.275191 | + | 0.846950i | ||||
\(443\) | 441.307i | 0.996178i | 0.867126 | + | 0.498089i | \(0.165965\pi\) | ||||
−0.867126 | + | 0.498089i | \(0.834035\pi\) | |||||||
\(444\) | −128.713 | − | 186.326i | −0.289894 | − | 0.419654i | ||||
\(445\) | 53.3279 | − | 694.339i | 0.119838 | − | 1.56031i | ||||
\(446\) | 46.2935 | + | 15.0417i | 0.103797 | + | 0.0337257i | ||||
\(447\) | −48.8655 | − | 1.16320i | −0.109319 | − | 0.00260223i | ||||
\(448\) | −25.8653 | + | 18.7923i | −0.0577351 | + | 0.0419470i | ||||
\(449\) | 421.696i | 0.939190i | 0.882882 | + | 0.469595i | \(0.155600\pi\) | ||||
−0.882882 | + | 0.469595i | \(0.844400\pi\) | |||||||
\(450\) | 207.118 | − | 189.715i | 0.460262 | − | 0.421589i | ||||
\(451\) | −502.187 | −1.11350 | ||||||||
\(452\) | 178.908 | + | 246.246i | 0.395814 | + | 0.544791i | ||||
\(453\) | 11.1397 | − | 467.975i | 0.0245909 | − | 1.03306i | ||||
\(454\) | −69.2556 | + | 213.147i | −0.152545 | + | 0.469486i | ||||
\(455\) | 20.7904 | + | 85.8843i | 0.0456933 | + | 0.188757i | ||||
\(456\) | 47.0621 | − | 32.5101i | 0.103206 | − | 0.0712940i | ||||
\(457\) | 326.638 | 0.714743 | 0.357372 | − | 0.933962i | \(-0.383673\pi\) | ||||
0.357372 | + | 0.933962i | \(0.383673\pi\) | |||||||
\(458\) | 279.591 | − | 90.8447i | 0.610461 | − | 0.198351i | ||||
\(459\) | 90.7067 | + | 366.277i | 0.197618 | + | 0.797990i | ||||
\(460\) | 267.806 | + | 110.338i | 0.582188 | + | 0.239864i | ||||
\(461\) | −245.381 | − | 337.737i | −0.532279 | − | 0.732619i | 0.455197 | − | 0.890391i | \(-0.349569\pi\) |
−0.987476 | + | 0.157772i | \(0.949569\pi\) | |||||||
\(462\) | −28.6895 | − | 10.0827i | −0.0620985 | − | 0.0218240i | ||||
\(463\) | 269.448 | + | 195.765i | 0.581961 | + | 0.422820i | 0.839431 | − | 0.543467i | \(-0.182889\pi\) |
−0.257469 | + | 0.966286i | \(0.582889\pi\) | |||||||
\(464\) | −5.83035 | − | 8.02478i | −0.0125654 | − | 0.0172948i | ||||
\(465\) | 112.658 | + | 49.5837i | 0.242275 | + | 0.106632i | ||||
\(466\) | −49.5081 | − | 35.9698i | −0.106241 | − | 0.0771883i | ||||
\(467\) | −791.562 | + | 257.194i | −1.69499 | + | 0.550736i | −0.987724 | − | 0.156209i | \(-0.950073\pi\) |
−0.707269 | + | 0.706945i | \(0.750073\pi\) | |||||||
\(468\) | −414.523 | + | 272.009i | −0.885732 | + | 0.581215i | ||||
\(469\) | 11.4289 | + | 35.1746i | 0.0243687 | + | 0.0749992i | ||||
\(470\) | 219.457 | − | 532.655i | 0.466929 | − | 1.13331i | ||||
\(471\) | −10.6744 | + | 448.429i | −0.0226633 | + | 0.952079i | ||||
\(472\) | 22.3121 | − | 68.6696i | 0.0472714 | − | 0.145486i | ||||
\(473\) | 39.7935 | + | 54.7710i | 0.0841299 | + | 0.115795i | ||||
\(474\) | 35.4627 | + | 118.682i | 0.0748158 | + | 0.250384i | ||||
\(475\) | −52.7137 | + | 27.1100i | −0.110976 | + | 0.0570736i | ||||
\(476\) | 26.7298i | 0.0561550i | ||||||||
\(477\) | 7.97213 | + | 3.01675i | 0.0167131 | + | 0.00632441i | ||||
\(478\) | 122.637 | − | 377.437i | 0.256562 | − | 0.789617i | ||||
\(479\) | −516.203 | − | 167.725i | −1.07767 | − | 0.350156i | −0.284199 | − | 0.958765i | \(-0.591728\pi\) |
−0.793470 | + | 0.608610i | \(0.791728\pi\) | |||||||
\(480\) | 356.134 | + | 317.924i | 0.741947 | + | 0.662341i | ||||
\(481\) | 215.546 | + | 663.382i | 0.448120 | + | 1.37917i | ||||
\(482\) | − | 7.10464i | − | 0.0147399i | ||||||
\(483\) | 45.8718 | − | 31.6878i | 0.0949726 | − | 0.0656063i | ||||
\(484\) | −26.7419 | − | 19.4291i | −0.0552519 | − | 0.0401428i | ||||
\(485\) | 225.244 | − | 138.615i | 0.464420 | − | 0.285804i | ||||
\(486\) | 264.841 | − | 147.905i | 0.544941 | − | 0.304332i | ||||
\(487\) | −404.480 | − | 293.872i | −0.830554 | − | 0.603433i | 0.0891618 | − | 0.996017i | \(-0.471581\pi\) |
−0.919716 | + | 0.392584i | \(0.871581\pi\) | |||||||
\(488\) | −230.479 | + | 317.228i | −0.472294 | + | 0.650056i | ||||
\(489\) | −419.512 | + | 549.422i | −0.857898 | + | 1.12356i | ||||
\(490\) | −23.1274 | + | 301.123i | −0.0471988 | + | 0.614537i | ||||
\(491\) | −394.868 | + | 543.489i | −0.804211 | + | 1.10690i | 0.187980 | + | 0.982173i | \(0.439806\pi\) |
−0.992191 | + | 0.124729i | \(0.960194\pi\) | |||||||
\(492\) | 291.964 | − | 201.686i | 0.593423 | − | 0.409932i | ||||
\(493\) | −510.703 | −1.03591 | ||||||||
\(494\) | −63.5111 | + | 20.6360i | −0.128565 | + | 0.0417733i | ||||
\(495\) | −57.8132 | + | 462.892i | −0.116794 | + | 0.935135i | ||||
\(496\) | 0.688305 | − | 2.11839i | 0.00138771 | − | 0.00427094i | ||||
\(497\) | −21.9936 | − | 7.14616i | −0.0442527 | − | 0.0143786i | ||||
\(498\) | −213.571 | + | 279.707i | −0.428857 | + | 0.561661i | ||||
\(499\) | 352.874 | 0.707163 | 0.353581 | − | 0.935404i | \(-0.384964\pi\) | ||||
0.353581 | + | 0.935404i | \(0.384964\pi\) | |||||||
\(500\) | −199.529 | − | 230.958i | −0.399057 | − | 0.461917i | ||||
\(501\) | −176.809 | − | 591.722i | −0.352913 | − | 1.18108i | ||||
\(502\) | −196.784 | + | 142.972i | −0.391999 | + | 0.284804i | ||||
\(503\) | 831.466 | + | 270.160i | 1.65301 | + | 0.537097i | 0.979390 | − | 0.201977i | \(-0.0647366\pi\) |
0.673624 | + | 0.739074i | \(0.264737\pi\) | |||||||
\(504\) | 54.6877 | − | 14.9329i | 0.108507 | − | 0.0296288i | ||||
\(505\) | −316.488 | + | 371.978i | −0.626709 | + | 0.736591i | ||||
\(506\) | 291.991 | − | 94.8737i | 0.577058 | − | 0.187497i | ||||
\(507\) | 977.410 | − | 292.055i | 1.92783 | − | 0.576044i | ||||
\(508\) | −56.3616 | − | 173.463i | −0.110948 | − | 0.341463i | ||||
\(509\) | 71.2318 | − | 98.0421i | 0.139945 | − | 0.192617i | −0.733292 | − | 0.679914i | \(-0.762017\pi\) |
0.873236 | + | 0.487297i | \(0.162017\pi\) | |||||||
\(510\) | −255.739 | + | 55.5005i | −0.501448 | + | 0.108825i | ||||
\(511\) | 59.1601 | − | 42.9823i | 0.115773 | − | 0.0841141i | ||||
\(512\) | 10.2099 | − | 14.0527i | 0.0199412 | − | 0.0274466i | ||||
\(513\) | −62.1413 | + | 15.3890i | −0.121133 | + | 0.0299980i | ||||
\(514\) | −70.0260 | + | 50.8768i | −0.136237 | + | 0.0989822i | ||||
\(515\) | −268.388 | + | 165.166i | −0.521143 | + | 0.320711i | ||||
\(516\) | −45.1323 | − | 15.8614i | −0.0874656 | − | 0.0307391i | ||||
\(517\) | 295.669 | + | 909.974i | 0.571893 | + | 1.76010i | ||||
\(518\) | − | 30.2305i | − | 0.0583600i | ||||||
\(519\) | 141.969 | − | 98.0709i | 0.273543 | − | 0.188961i | ||||
\(520\) | −475.435 | − | 772.564i | −0.914298 | − | 1.48570i | ||||
\(521\) | −381.495 | − | 123.955i | −0.732237 | − | 0.237918i | −0.0809163 | − | 0.996721i | \(-0.525785\pi\) |
−0.651320 | + | 0.758803i | \(0.725785\pi\) | |||||||
\(522\) | 108.145 | + | 396.052i | 0.207175 | + | 0.758721i | ||||
\(523\) | −589.147 | + | 428.040i | −1.12648 | + | 0.818433i | −0.985178 | − | 0.171535i | \(-0.945127\pi\) |
−0.141298 | + | 0.989967i | \(0.545127\pi\) | |||||||
\(524\) | 72.0387i | 0.137478i | ||||||||
\(525\) | −58.1976 | + | 8.02648i | −0.110852 | + | 0.0152885i | ||||
\(526\) | 536.685 | 1.02031 | ||||||||
\(527\) | −67.4079 | − | 92.7790i | −0.127909 | − | 0.176051i | ||||
\(528\) | 8.43926 | + | 0.200888i | 0.0159834 | + | 0.000380470i | ||||
\(529\) | −10.4693 | + | 32.2212i | −0.0197907 | + | 0.0609096i | ||||
\(530\) | −2.25188 | + | 5.46567i | −0.00424884 | + | 0.0103126i | ||||
\(531\) | −50.5568 | + | 63.0438i | −0.0952105 | + | 0.118726i | ||||
\(532\) | −4.53488 | −0.00852421 | ||||||||
\(533\) | −1039.49 | + | 337.749i | −1.95025 | + | 0.633676i | ||||
\(534\) | 492.084 | + | 172.939i | 0.921505 | + | 0.323856i | ||||
\(535\) | −262.242 | + | 308.222i | −0.490172 | + | 0.576115i | ||||
\(536\) | −223.169 | − | 307.166i | −0.416360 | − | 0.573071i | ||||
\(537\) | −135.993 | + | 386.959i | −0.253247 | + | 0.720593i | ||||
\(538\) | −390.146 | − | 283.458i | −0.725179 | − | 0.526873i | ||||
\(539\) | −294.829 | − | 405.797i | −0.546993 | − | 0.752871i | ||||
\(540\) | −152.293 | − | 292.337i | −0.282024 | − | 0.541365i | ||||
\(541\) | −340.439 | − | 247.344i | −0.629278 | − | 0.457197i | 0.226872 | − | 0.973925i | \(-0.427150\pi\) |
−0.856150 | + | 0.516728i | \(0.827150\pi\) | |||||||
\(542\) | 473.035 | − | 153.698i | 0.872759 | − | 0.283577i | ||||
\(543\) | 881.785 | − | 263.481i | 1.62391 | − | 0.485233i | ||||
\(544\) | −137.449 | − | 423.024i | −0.252663 | − | 0.777618i | ||||
\(545\) | 228.553 | + | 944.141i | 0.419363 | + | 1.73237i | ||||
\(546\) | −66.1661 | − | 1.57502i | −0.121183 | − | 0.00288465i | ||||
\(547\) | 181.922 | − | 559.898i | 0.332581 | − | 1.02358i | −0.635320 | − | 0.772249i | \(-0.719132\pi\) |
0.967901 | − | 0.251331i | \(-0.0808682\pi\) | |||||||
\(548\) | 6.61494 | + | 9.10468i | 0.0120711 | + | 0.0166144i | ||||
\(549\) | 366.919 | − | 240.771i | 0.668341 | − | 0.438563i | ||||
\(550\) | −319.722 | − | 49.4031i | −0.581312 | − | 0.0898238i | ||||
\(551\) | − | 86.6440i | − | 0.157249i | ||||||
\(552\) | −347.338 | + | 454.898i | −0.629236 | + | 0.824091i | ||||
\(553\) | 8.00614 | − | 24.6404i | 0.0144777 | − | 0.0445576i | ||||
\(554\) | 247.146 | + | 80.3024i | 0.446111 | + | 0.144950i | ||||
\(555\) | −453.190 | + | 98.3514i | −0.816558 | + | 0.177210i | ||||
\(556\) | −183.563 | − | 564.950i | −0.330150 | − | 1.01610i | ||||
\(557\) | − | 676.919i | − | 1.21529i | −0.794207 | − | 0.607647i | \(-0.792113\pi\) | ||
0.794207 | − | 0.607647i | \(-0.207887\pi\) | |||||||
\(558\) | −57.6762 | + | 71.9217i | −0.103362 | + | 0.128892i | ||||
\(559\) | 119.206 | + | 86.6081i | 0.213248 | + | 0.154934i | ||||
\(560\) | 0.250131 | + | 1.03328i | 0.000446662 | + | 0.00184514i | ||||
\(561\) | 263.765 | − | 345.445i | 0.470169 | − | 0.615766i | ||||
\(562\) | −242.780 | − | 176.390i | −0.431993 | − | 0.313861i | ||||
\(563\) | 244.412 | − | 336.404i | 0.434124 | − | 0.597520i | −0.534770 | − | 0.844998i | \(-0.679602\pi\) |
0.968894 | + | 0.247478i | \(0.0796017\pi\) | |||||||
\(564\) | −537.358 | − | 410.300i | −0.952762 | − | 0.727483i | ||||
\(565\) | 605.795 | − | 146.648i | 1.07220 | − | 0.259553i | ||||
\(566\) | −68.8044 | + | 94.7012i | −0.121563 | + | 0.167317i | ||||
\(567\) | −63.1610 | − | 6.03104i | −0.111395 | − | 0.0106367i | ||||
\(568\) | 237.401 | 0.417959 | ||||||||
\(569\) | 304.385 | − | 98.9007i | 0.534947 | − | 0.173815i | −0.0290708 | − | 0.999577i | \(-0.509255\pi\) |
0.564018 | + | 0.825762i | \(0.309255\pi\) | |||||||
\(570\) | −9.41601 | − | 43.3877i | −0.0165193 | − | 0.0761187i | ||||
\(571\) | 38.0039 | − | 116.964i | 0.0665567 | − | 0.204841i | −0.912247 | − | 0.409640i | \(-0.865654\pi\) |
0.978804 | + | 0.204800i | \(0.0656543\pi\) | |||||||
\(572\) | 543.123 | + | 176.471i | 0.949516 | + | 0.308517i | ||||
\(573\) | 223.910 | + | 170.967i | 0.390769 | + | 0.298372i | ||||
\(574\) | 47.3697 | 0.0825255 | ||||||||
\(575\) | 417.819 | − | 420.984i | 0.726641 | − | 0.732145i | ||||
\(576\) | −307.121 | + | 201.532i | −0.533196 | + | 0.349882i | ||||
\(577\) | −65.6670 | + | 47.7099i | −0.113808 | + | 0.0826861i | −0.643233 | − | 0.765670i | \(-0.722407\pi\) |
0.529426 | + | 0.848356i | \(0.322407\pi\) | |||||||
\(578\) | −111.222 | − | 36.1382i | −0.192425 | − | 0.0625228i | ||||
\(579\) | 5.23684 | − | 219.998i | 0.00904462 | − | 0.379962i | ||||
\(580\) | 433.602 | − | 104.964i | 0.747589 | − | 0.180973i | ||||
\(581\) | 70.0065 | − | 22.7465i | 0.120493 | − | 0.0391506i | ||||
\(582\) | 56.7134 | + | 189.801i | 0.0974458 | + | 0.326119i | ||||
\(583\) | −3.03391 | − | 9.33741i | −0.00520396 | − | 0.0160161i | ||||
\(584\) | −441.247 | + | 607.324i | −0.755560 | + | 1.03994i | ||||
\(585\) | 191.652 | + | 997.030i | 0.327611 | + | 1.70432i | ||||
\(586\) | −90.8968 | + | 66.0404i | −0.155114 | + | 0.112697i | ||||
\(587\) | 355.132 | − | 488.797i | 0.604995 | − | 0.832704i | −0.391159 | − | 0.920323i | \(-0.627926\pi\) |
0.996154 | + | 0.0876189i | \(0.0279258\pi\) | |||||||
\(588\) | 334.384 | + | 117.517i | 0.568680 | + | 0.199858i | ||||
\(589\) | 15.7405 | − | 11.4362i | 0.0267242 | − | 0.0194162i | ||||
\(590\) | −42.6847 | − | 36.3172i | −0.0723470 | − | 0.0615545i | ||||
\(591\) | −157.637 | + | 448.543i | −0.266729 | + | 0.758957i | ||||
\(592\) | 2.59324 | + | 7.98117i | 0.00438047 | + | 0.0134817i | ||||
\(593\) | − | 293.240i | − | 0.494503i | −0.968951 | − | 0.247251i | \(-0.920473\pi\) | ||
0.968951 | − | 0.247251i | \(-0.0795273\pi\) | |||||||
\(594\) | −323.748 | − | 131.400i | −0.545030 | − | 0.221212i | ||||
\(595\) | 50.6093 | + | 20.8513i | 0.0850576 | + | 0.0350442i | ||||
\(596\) | −37.8356 | − | 12.2935i | −0.0634825 | − | 0.0206267i | ||||
\(597\) | −2.08311 | + | 87.5107i | −0.00348929 | + | 0.146584i | ||||
\(598\) | 540.590 | − | 392.761i | 0.903996 | − | 0.656791i | ||||
\(599\) | − | 47.1673i | − | 0.0787434i | −0.999225 | − | 0.0393717i | \(-0.987464\pi\) | ||
0.999225 | − | 0.0393717i | \(-0.0125356\pi\) | |||||||
\(600\) | 542.740 | − | 262.985i | 0.904567 | − | 0.438309i | ||||
\(601\) | −185.793 | −0.309140 | −0.154570 | − | 0.987982i | \(-0.549399\pi\) | ||||
−0.154570 | + | 0.987982i | \(0.549399\pi\) | |||||||
\(602\) | −3.75359 | − | 5.16637i | −0.00623520 | − | 0.00858201i | ||||
\(603\) | 111.936 | + | 409.935i | 0.185632 | + | 0.679826i | ||||
\(604\) | 117.733 | − | 362.344i | 0.194921 | − | 0.599907i | ||||
\(605\) | −57.6472 | + | 35.4760i | −0.0952846 | + | 0.0586380i | ||||
\(606\) | −207.913 | − | 300.978i | −0.343090 | − | 0.496663i | ||||
\(607\) | −365.126 | −0.601525 | −0.300763 | − | 0.953699i | \(-0.597241\pi\) | ||||
−0.300763 | + | 0.953699i | \(0.597241\pi\) | |||||||
\(608\) | 71.7687 | − | 23.3191i | 0.118041 | − | 0.0383537i | ||||
\(609\) | 28.4721 | − | 81.0150i | 0.0467521 | − | 0.133029i | ||||
\(610\) | 159.516 | + | 259.207i | 0.261501 | + | 0.424929i | ||||
\(611\) | 1224.02 | + | 1684.72i | 2.00330 | + | 2.75731i | ||||
\(612\) | −14.6129 | + | 306.769i | −0.0238773 | + | 0.501256i | ||||
\(613\) | −490.076 | − | 356.061i | −0.799471 | − | 0.580850i | 0.111288 | − | 0.993788i | \(-0.464502\pi\) |
−0.910759 | + | 0.412938i | \(0.864502\pi\) | |||||||
\(614\) | −280.852 | − | 386.560i | −0.457414 | − | 0.629576i | ||||
\(615\) | −154.112 | − | 710.125i | −0.250588 | − | 1.15468i | ||||
\(616\) | −52.8260 | − | 38.3804i | −0.0857565 | − | 0.0623058i | ||||
\(617\) | 68.2082 | − | 22.1622i | 0.110548 | − | 0.0359192i | −0.253221 | − | 0.967409i | \(-0.581490\pi\) |
0.363769 | + | 0.931489i | \(0.381490\pi\) | |||||||
\(618\) | −67.5767 | − | 226.157i | −0.109347 | − | 0.365950i | ||||
\(619\) | −368.101 | − | 1132.90i | −0.594671 | − | 1.83021i | −0.556357 | − | 0.830943i | \(-0.687801\pi\) |
−0.0383140 | − | 0.999266i | \(-0.512199\pi\) | |||||||
\(620\) | 76.2999 | + | 64.9177i | 0.123064 | + | 0.104706i | ||||
\(621\) | 543.778 | − | 338.592i | 0.875648 | − | 0.545238i | ||||
\(622\) | 165.780 | − | 510.218i | 0.266527 | − | 0.820287i | ||||
\(623\) | −64.1258 | − | 88.2616i | −0.102931 | − | 0.141672i | ||||
\(624\) | 17.6037 | − | 5.26006i | 0.0282110 | − | 0.00842958i | ||||
\(625\) | −592.936 | + | 197.616i | −0.948698 | + | 0.316185i | ||||
\(626\) | 203.591i | 0.325225i | ||||||||
\(627\) | 58.6068 | + | 44.7494i | 0.0934718 | + | 0.0713706i | ||||
\(628\) | −112.815 | + | 347.209i | −0.179642 | + | 0.552881i | ||||
\(629\) | 410.922 | + | 133.517i | 0.653295 | + | 0.212268i | ||||
\(630\) | 5.45333 | − | 43.6631i | 0.00865608 | − | 0.0693065i | ||||
\(631\) | 268.802 | + | 827.286i | 0.425993 | + | 1.31107i | 0.902040 | + | 0.431652i | \(0.142069\pi\) |
−0.476047 | + | 0.879420i | \(0.657931\pi\) | |||||||
\(632\) | 265.970i | 0.420839i | ||||||||
\(633\) | 349.571 | + | 506.043i | 0.552244 | + | 0.799437i | ||||
\(634\) | 157.613 | + | 114.513i | 0.248601 | + | 0.180619i | ||||
\(635\) | −372.396 | − | 28.6014i | −0.586450 | − | 0.0450416i | ||||
\(636\) | 5.51392 | + | 4.21017i | 0.00866969 | + | 0.00661976i | ||||
\(637\) | −883.193 | − | 641.677i | −1.38649 | − | 1.00734i | ||||
\(638\) | 277.953 | − | 382.570i | 0.435664 | − | 0.599640i | ||||
\(639\) | −248.506 | − | 94.0376i | −0.388899 | − | 0.147164i | ||||
\(640\) | 200.090 | + | 325.138i | 0.312640 | + | 0.508029i | ||||
\(641\) | −11.2775 | + | 15.5222i | −0.0175936 | + | 0.0242155i | −0.817723 | − | 0.575612i | \(-0.804764\pi\) |
0.800130 | + | 0.599827i | \(0.204764\pi\) | |||||||
\(642\) | −172.277 | − | 249.390i | −0.268344 | − | 0.388458i | ||||
\(643\) | 729.610 | 1.13470 | 0.567349 | − | 0.823478i | \(-0.307969\pi\) | ||||
0.567349 | + | 0.823478i | \(0.307969\pi\) | |||||||
\(644\) | 43.1557 | − | 14.0221i | 0.0670120 | − | 0.0217735i | ||||
\(645\) | −65.2379 | + | 73.0788i | −0.101144 | + | 0.113300i | ||||
\(646\) | −12.7827 | + | 39.3411i | −0.0197874 | + | 0.0608995i | ||||
\(647\) | 486.460 | + | 158.060i | 0.751870 | + | 0.244298i | 0.659786 | − | 0.751454i | \(-0.270647\pi\) |
0.0920846 | + | 0.995751i | \(0.470647\pi\) | |||||||
\(648\) | 635.795 | − | 141.483i | 0.981165 | − | 0.218338i | ||||
\(649\) | 93.0805 | 0.143421 | ||||||||
\(650\) | −695.024 | + | 112.771i | −1.06927 | + | 0.173493i | ||||
\(651\) | 18.4759 | − | 5.52069i | 0.0283809 | − | 0.00848033i | ||||
\(652\) | −455.170 | + | 330.701i | −0.698114 | + | 0.507209i | ||||
\(653\) | −1084.62 | − | 352.415i | −1.66098 | − | 0.539686i | −0.679905 | − | 0.733300i | \(-0.737979\pi\) |
−0.981078 | + | 0.193614i | \(0.937979\pi\) | |||||||
\(654\) | −727.376 | − | 17.3145i | −1.11220 | − | 0.0264747i | ||||
\(655\) | 136.396 | + | 56.1957i | 0.208237 | + | 0.0857949i | ||||
\(656\) | −12.5061 | + | 4.06348i | −0.0190642 | + | 0.00619432i | ||||
\(657\) | 702.458 | − | 460.951i | 1.06919 | − | 0.701599i | ||||
\(658\) | −27.8894 | − | 85.8349i | −0.0423852 | − | 0.130448i | ||||
\(659\) | 566.935 | − | 780.319i | 0.860295 | − | 1.18410i | −0.121204 | − | 0.992628i | \(-0.538675\pi\) |
0.981499 | − | 0.191467i | \(-0.0613246\pi\) | |||||||
\(660\) | −152.945 | + | 347.504i | −0.231735 | + | 0.526521i | ||||
\(661\) | −171.448 | + | 124.565i | −0.259377 | + | 0.188449i | −0.709872 | − | 0.704330i | \(-0.751247\pi\) |
0.450495 | + | 0.892779i | \(0.351247\pi\) | |||||||
\(662\) | −94.2669 | + | 129.747i | −0.142397 | + | 0.195993i | ||||
\(663\) | 313.640 | − | 892.438i | 0.473062 | − | 1.34606i | ||||
\(664\) | −611.338 | + | 444.163i | −0.920690 | + | 0.668921i | ||||
\(665\) | −3.53755 | + | 8.58618i | −0.00531962 | + | 0.0129115i | ||||
\(666\) | 16.5267 | − | 346.945i | 0.0248149 | − | 0.520938i | ||||
\(667\) | 267.909 | + | 824.540i | 0.401663 | + | 1.23619i | ||||
\(668\) | − | 502.639i | − | 0.752454i | ||||||
\(669\) | −66.4869 | − | 96.2473i | −0.0993824 | − | 0.143867i | ||||
\(670\) | −286.431 | + | 69.3377i | −0.427509 | + | 0.103489i | ||||
\(671\) | −480.751 | − | 156.206i | −0.716470 | − | 0.232795i | ||||
\(672\) | 74.7689 | + | 1.77980i | 0.111263 | + | 0.00264851i | ||||
\(673\) | 461.073 | − | 334.989i | 0.685102 | − | 0.497755i | −0.189945 | − | 0.981795i | \(-0.560831\pi\) |
0.875046 | + | 0.484039i | \(0.160831\pi\) | |||||||
\(674\) | 331.683i | 0.492111i | ||||||||
\(675\) | −672.301 | + | 60.3011i | −0.996002 | + | 0.0893349i | ||||
\(676\) | 830.263 | 1.22820 | ||||||||
\(677\) | 276.422 | + | 380.463i | 0.408305 | + | 0.561983i | 0.962804 | − | 0.270201i | \(-0.0870901\pi\) |
−0.554499 | + | 0.832184i | \(0.687090\pi\) | |||||||
\(678\) | −11.1096 | + | 466.710i | −0.0163858 | + | 0.688363i | ||||
\(679\) | 12.8038 | − | 39.4059i | 0.0188568 | − | 0.0580353i | ||||
\(680\) | −560.262 | − | 43.0302i | −0.823915 | − | 0.0632797i | ||||
\(681\) | 443.147 | − | 306.122i | 0.650729 | − | 0.449518i | ||||
\(682\) | 106.188 | 0.155701 | ||||||||
\(683\) | 920.493 | − | 299.086i | 1.34772 | − | 0.437901i | 0.455796 | − | 0.890084i | \(-0.349355\pi\) |
0.891925 | + | 0.452183i | \(0.149355\pi\) | |||||||
\(684\) | −52.0452 | − | 2.47917i | −0.0760895 | − | 0.00362452i | ||||
\(685\) | 22.3986 | − | 5.42215i | 0.0326988 | − | 0.00791555i | ||||
\(686\) | 55.9732 | + | 77.0405i | 0.0815936 | + | 0.112304i | ||||
\(687\) | −666.533 | − | 234.248i | −0.970208 | − | 0.340972i | ||||
\(688\) | 1.43417 | + | 1.04199i | 0.00208455 | + | 0.00151451i | ||||
\(689\) | −12.5599 | − | 17.2872i | −0.0182291 | − | 0.0250902i | ||||
\(690\) | 223.764 | + | 383.780i | 0.324296 | + | 0.556203i | ||||
\(691\) | −513.593 | − | 373.147i | −0.743260 | − | 0.540010i | 0.150471 | − | 0.988614i | \(-0.451921\pi\) |
−0.893730 | + | 0.448605i | \(0.851921\pi\) | |||||||
\(692\) | 133.563 | − | 43.3973i | 0.193010 | − | 0.0627128i | ||||
\(693\) | 40.0942 | + | 61.1009i | 0.0578560 | + | 0.0881686i | ||||
\(694\) | −28.5408 | − | 87.8394i | −0.0411250 | − | 0.126570i | ||||
\(695\) | −1212.85 | − | 93.1514i | −1.74511 | − | 0.134031i | ||||
\(696\) | −20.9784 | + | 881.299i | −0.0301414 | + | 1.26623i | ||||
\(697\) | −209.214 | + | 643.895i | −0.300164 | + | 0.923809i | ||||
\(698\) | −164.495 | − | 226.408i | −0.235666 | − | 0.324367i | ||||
\(699\) | 42.1045 | + | 140.910i | 0.0602354 | + | 0.201588i | ||||
\(700\) | −47.2542 | − | 7.30168i | −0.0675061 | − | 0.0104310i | ||||
\(701\) | 890.825i | 1.27079i | 0.772187 | + | 0.635396i | \(0.219163\pi\) | ||||
−0.772187 | + | 0.635396i | \(0.780837\pi\) | |||||||
\(702\) | −758.505 | − | 54.2483i | −1.08049 | − | 0.0772768i | ||||
\(703\) | −22.6520 | + | 69.7156i | −0.0322219 | + | 0.0991687i | ||||
\(704\) | 402.401 | + | 130.748i | 0.571593 | + | 0.185722i | ||||
\(705\) | −1196.03 | + | 697.349i | −1.69649 | + | 0.989147i | ||||
\(706\) | 17.3693 | + | 53.4572i | 0.0246024 | + | 0.0757185i | ||||
\(707\) | 76.5137i | 0.108223i | ||||||||
\(708\) | −54.1157 | + | 37.3826i | −0.0764345 | + | 0.0528003i | ||||
\(709\) | 434.163 | + | 315.438i | 0.612360 | + | 0.444905i | 0.850244 | − | 0.526388i | \(-0.176454\pi\) |
−0.237885 | + | 0.971293i | \(0.576454\pi\) | |||||||
\(710\) | 70.1955 | − | 170.375i | 0.0988669 | − | 0.239965i | ||||
\(711\) | 105.354 | − | 278.412i | 0.148178 | − | 0.391578i | ||||
\(712\) | 906.074 | + | 658.301i | 1.27258 | + | 0.924580i | ||||
\(713\) | −114.432 | + | 157.502i | −0.160494 | + | 0.220900i | ||||
\(714\) | −24.8801 | + | 32.5847i | −0.0348460 | + | 0.0456368i | ||||
\(715\) | 757.802 | − | 890.670i | 1.05986 | − | 1.24569i | ||||
\(716\) | −196.219 | + | 270.072i | −0.274048 | + | 0.377195i | ||||
\(717\) | −784.717 | + | 542.076i | −1.09444 | + | 0.756033i | ||||
\(718\) | −134.179 | −0.186878 | ||||||||
\(719\) | −714.198 | + | 232.057i | −0.993321 | + | 0.322749i | −0.760193 | − | 0.649697i | \(-0.774896\pi\) |
−0.233127 | + | 0.972446i | \(0.574896\pi\) | |||||||
\(720\) | 2.30578 | + | 11.9953i | 0.00320247 | + | 0.0166602i | ||||
\(721\) | −15.2563 | + | 46.9540i | −0.0211599 | + | 0.0651234i | ||||
\(722\) | 421.915 | + | 137.088i | 0.584370 | + | 0.189873i | ||||
\(723\) | −10.3617 | + | 13.5704i | −0.0143316 | + | 0.0187696i | ||||
\(724\) | 749.034 | 1.03458 | ||||||||
\(725\) | 139.507 | − | 902.847i | 0.192423 | − | 1.24531i | ||||
\(726\) | −14.5148 | − | 48.5762i | −0.0199928 | − | 0.0669094i | ||||
\(727\) | 254.046 | − | 184.575i | 0.349444 | − | 0.253886i | −0.399192 | − | 0.916867i | \(-0.630709\pi\) |
0.748636 | + | 0.662981i | \(0.230709\pi\) | |||||||
\(728\) | −135.158 | − | 43.9156i | −0.185657 | − | 0.0603237i | ||||
\(729\) | −721.580 | − | 103.746i | −0.989822 | − | 0.142312i | ||||
\(730\) | 305.389 | + | 496.245i | 0.418341 | + | 0.679788i | ||||
\(731\) | 86.8045 | − | 28.2045i | 0.118748 | − | 0.0385835i | ||||
\(732\) | 342.236 | − | 102.262i | 0.467536 | − | 0.139702i | ||||
\(733\) | 314.346 | + | 967.459i | 0.428849 | + | 1.31986i | 0.899260 | + | 0.437415i | \(0.144106\pi\) |
−0.470411 | + | 0.882448i | \(0.655894\pi\) | |||||||
\(734\) | −166.215 | + | 228.776i | −0.226451 | + | 0.311684i | ||||
\(735\) | 483.347 | − | 541.439i | 0.657614 | − | 0.736652i | ||||
\(736\) | −610.876 | + | 443.827i | −0.829995 | + | 0.603026i | ||||
\(737\) | 287.697 | − | 395.980i | 0.390362 | − | 0.537287i | ||||
\(738\) | 543.645 | + | 25.8965i | 0.736647 | + | 0.0350902i | ||||
\(739\) | −883.041 | + | 641.567i | −1.19491 | + | 0.868156i | −0.993775 | − | 0.111407i | \(-0.964464\pi\) |
−0.201139 | + | 0.979563i | \(0.564464\pi\) | |||||||
\(740\) | −376.326 | − | 28.9033i | −0.508549 | − | 0.0390585i | ||||
\(741\) | 151.408 | + | 53.2110i | 0.204329 | + | 0.0718098i | ||||
\(742\) | 0.286179 | + | 0.880767i | 0.000385685 | + | 0.00118702i | ||||
\(743\) | − | 356.015i | − | 0.479159i | −0.970877 | − | 0.239579i | \(-0.922990\pi\) | ||
0.970877 | − | 0.239579i | \(-0.0770096\pi\) | |||||||
\(744\) | −162.874 | + | 112.512i | −0.218916 | + | 0.151225i | ||||
\(745\) | −52.7907 | + | 62.0467i | −0.0708601 | + | 0.0832841i | ||||
\(746\) | 110.038 | + | 35.7535i | 0.147504 | + | 0.0479270i | ||||
\(747\) | 815.875 | − | 222.782i | 1.09220 | − | 0.298235i | ||||
\(748\) | 286.185 | − | 207.925i | 0.382600 | − | 0.277975i | ||||
\(749\) | 63.3993i | 0.0846452i | ||||||||
\(750\) | −28.2573 | − | 467.268i | −0.0376765 | − | 0.623024i | ||||
\(751\) | −367.946 | −0.489941 | −0.244971 | − | 0.969530i | \(-0.578778\pi\) | ||||
−0.244971 | + | 0.969530i | \(0.578778\pi\) | |||||||
\(752\) | 14.7262 | + | 20.2689i | 0.0195827 | + | 0.0269533i | ||||
\(753\) | 584.388 | + | 13.9108i | 0.776080 | + | 0.0184738i | ||||
\(754\) | 318.040 | − | 978.828i | 0.421804 | − | 1.29818i | ||||
\(755\) | −594.208 | − | 505.566i | −0.787031 | − | 0.669624i | ||||
\(756\) | −47.8493 | − | 19.4207i | −0.0632927 | − | 0.0256887i | ||||
\(757\) | −945.980 | −1.24964 | −0.624822 | − | 0.780768i | \(-0.714828\pi\) | ||||
−0.624822 | + | 0.780768i | \(0.714828\pi\) | |||||||
\(758\) | −551.803 | + | 179.292i | −0.727972 | + | 0.236533i | ||||
\(759\) | −696.095 | − | 244.637i | −0.917121 | − | 0.322315i | ||||
\(760\) | 7.30035 | − | 95.0520i | 0.00960572 | − | 0.125068i | ||||
\(761\) | −220.345 | − | 303.279i | −0.289546 | − | 0.398527i | 0.639320 | − | 0.768941i | \(-0.279216\pi\) |
−0.928867 | + | 0.370414i | \(0.879216\pi\) | |||||||
\(762\) | 92.7525 | − | 263.920i | 0.121722 | − | 0.346352i | ||||
\(763\) | 123.119 | + | 89.4513i | 0.161362 | + | 0.117236i | ||||
\(764\) | 134.773 | + | 185.499i | 0.176405 | + | 0.242800i | ||||
\(765\) | 569.426 | + | 266.970i | 0.744347 | + | 0.348981i | ||||
\(766\) | 503.161 | + | 365.568i | 0.656868 | + | 0.477243i | ||||
\(767\) | 192.669 | − | 62.6019i | 0.251198 | − | 0.0816192i | ||||
\(768\) | −743.261 | + | 222.090i | −0.967788 | + | 0.289179i | ||||
\(769\) | 92.1558 | + | 283.626i | 0.119838 | + | 0.368825i | 0.992925 | − | 0.118740i | \(-0.0378854\pi\) |
−0.873087 | + | 0.487565i | \(0.837885\pi\) | |||||||
\(770\) | −43.1642 | + | 26.5632i | −0.0560574 | + | 0.0344976i | ||||
\(771\) | 207.956 | + | 4.95019i | 0.269723 | + | 0.00642048i | ||||
\(772\) | 55.3468 | − | 170.340i | 0.0716927 | − | 0.220648i | ||||
\(773\) | 250.281 | + | 344.482i | 0.323779 | + | 0.445643i | 0.939616 | − | 0.342230i | \(-0.111182\pi\) |
−0.615838 | + | 0.787873i | \(0.711182\pi\) | |||||||
\(774\) | −40.2542 | − | 61.3447i | −0.0520080 | − | 0.0792567i | ||||
\(775\) | 182.433 | − | 93.8228i | 0.235397 | − | 0.121062i | ||||
\(776\) | 425.351i | 0.548133i | ||||||||
\(777\) | −44.0895 | + | 57.7427i | −0.0567433 | + | 0.0743149i | ||||
\(778\) | −169.046 | + | 520.269i | −0.217282 | + | 0.668727i | ||||
\(779\) | −109.241 | − | 35.4945i | −0.140232 | − | 0.0455642i | ||||
\(780\) | −82.8680 | + | 822.168i | −0.106241 | + | 1.05406i | ||||
\(781\) | 94.5726 | + | 291.065i | 0.121092 | + | 0.372682i | ||||
\(782\) | − | 413.911i | − | 0.529297i | ||||||
\(783\) | 371.054 | − | 914.215i | 0.473888 | − | 1.16758i | ||||
\(784\) | −10.6257 | − | 7.72005i | −0.0135532 | − | 0.00984700i | ||||
\(785\) | 569.390 | + | 484.450i | 0.725337 | + | 0.617134i | ||||
\(786\) | −67.0536 | + | 87.8180i | −0.0853099 | + | 0.111728i | ||||
\(787\) | 7.07372 | + | 5.13936i | 0.00898821 | + | 0.00653032i | 0.592270 | − | 0.805739i | \(-0.298232\pi\) |
−0.583282 | + | 0.812270i | \(0.698232\pi\) | |||||||
\(788\) | −227.447 | + | 313.054i | −0.288638 | + | 0.397277i | ||||
\(789\) | −1025.11 | − | 782.726i | −1.29925 | − | 0.992048i | ||||
\(790\) | 190.879 | + | 78.6430i | 0.241619 | + | 0.0995481i | ||||
\(791\) | 57.3952 | − | 78.9976i | 0.0725602 | − | 0.0998706i | ||||
\(792\) | −585.284 | − | 469.358i | −0.738995 | − | 0.592623i | ||||
\(793\) | −1100.17 | −1.38735 | ||||||||
\(794\) | 886.281 | − | 287.970i | 1.11622 | − | 0.362683i | ||||
\(795\) | 12.2727 | − | 7.15562i | 0.0154373 | − | 0.00900078i | ||||
\(796\) | −22.0158 | + | 67.7577i | −0.0276581 | + | 0.0851228i | ||||
\(797\) | 893.619 | + | 290.354i | 1.12123 | + | 0.364309i | 0.810236 | − | 0.586104i | \(-0.199339\pi\) |
0.310992 | + | 0.950413i | \(0.399339\pi\) | |||||||
\(798\) | −5.52819 | − | 4.22106i | −0.00692756 | − | 0.00528955i | ||||
\(799\) | 1289.93 | 1.61443 | ||||||||
\(800\) | 785.389 | − | 127.433i | 0.981737 | − | 0.159291i | ||||
\(801\) | −687.697 | − | 1048.00i | −0.858549 | − | 1.30837i | ||||
\(802\) | 386.573 | − | 280.862i | 0.482012 | − | 0.350202i | ||||
\(803\) | −920.387 | − | 299.052i | −1.14619 | − | 0.372418i | ||||
\(804\) | −8.23049 | + | 345.761i | −0.0102369 | + | 0.430051i | ||||
\(805\) | 7.11571 | − | 92.6479i | 0.00883939 | − | 0.115091i | ||||
\(806\) | 219.801 | − | 71.4176i | 0.272706 | − | 0.0886075i | ||||
\(807\) | 331.803 | + | 1110.43i | 0.411156 | + | 1.37600i | ||||
\(808\) | −242.724 | − | 747.029i | −0.300401 | − | 0.924541i | ||||
\(809\) | −531.193 | + | 731.124i | −0.656604 | + | 0.903738i | −0.999363 | − | 0.0356851i | \(-0.988639\pi\) |
0.342759 | + | 0.939423i | \(0.388639\pi\) | |||||||
\(810\) | 86.4562 | − | 498.125i | 0.106736 | − | 0.614969i | ||||
\(811\) | 191.442 | − | 139.090i | 0.236056 | − | 0.171505i | −0.463468 | − | 0.886114i | \(-0.653395\pi\) |
0.699524 | + | 0.714609i | \(0.253395\pi\) | |||||||
\(812\) | 41.0810 | − | 56.5431i | 0.0505924 | − | 0.0696344i | ||||
\(813\) | −1127.70 | − | 396.320i | −1.38708 | − | 0.487478i | ||||
\(814\) | −323.665 | + | 235.156i | −0.397623 | + | 0.288890i | ||||
\(815\) | 271.069 | + | 1119.78i | 0.332601 | + | 1.37396i | ||||
\(816\) | 3.77342 | − | 10.7370i | 0.00462429 | − | 0.0131580i | ||||
\(817\) | 4.78507 | + | 14.7269i | 0.00585688 | + | 0.0180256i | ||||
\(818\) | 475.872i | 0.581751i | ||||||||
\(819\) | 124.085 | + | 99.5081i | 0.151509 | + | 0.121499i | ||||
\(820\) | 45.2900 | − | 589.685i | 0.0552317 | − | 0.719128i | ||||
\(821\) | −482.696 | − | 156.837i | −0.587937 | − | 0.191032i | −8.36507e−5 | − | 1.00000i | \(-0.500027\pi\) |
−0.587853 | + | 0.808968i | \(0.700027\pi\) | |||||||
\(822\) | −0.410765 | + | 17.2561i | −0.000499715 | + | 0.0209929i | ||||
\(823\) | −257.610 | + | 187.165i | −0.313014 | + | 0.227418i | −0.733189 | − | 0.680025i | \(-0.761969\pi\) |
0.420175 | + | 0.907443i | \(0.361969\pi\) | |||||||
\(824\) | − | 506.825i | − | 0.615079i | ||||||
\(825\) | 538.642 | + | 560.660i | 0.652900 | + | 0.679588i | ||||
\(826\) | −8.77998 | −0.0106295 | ||||||||
\(827\) | −86.3255 | − | 118.817i | −0.104384 | − | 0.143672i | 0.753629 | − | 0.657300i | \(-0.228301\pi\) |
−0.858013 | + | 0.513627i | \(0.828301\pi\) | |||||||
\(828\) | 502.949 | − | 137.335i | 0.607427 | − | 0.165863i | ||||
\(829\) | 189.199 | − | 582.294i | 0.228225 | − | 0.702406i | −0.769723 | − | 0.638378i | \(-0.779606\pi\) |
0.997948 | − | 0.0640274i | \(-0.0203945\pi\) | |||||||
\(830\) | 138.000 | + | 570.070i | 0.166265 | + | 0.686832i | ||||
\(831\) | −354.951 | − | 513.832i | −0.427137 | − | 0.618330i | ||||
\(832\) | 920.873 | 1.10682 | ||||||||
\(833\) | −643.133 | + | 208.967i | −0.772069 | + | 0.250860i | ||||
\(834\) | 302.084 | − | 859.556i | 0.362211 | − | 1.03064i | ||||
\(835\) | −951.680 | − | 392.097i | −1.13974 | − | 0.469577i | ||||
\(836\) | 35.2758 | + | 48.5530i | 0.0421960 | + | 0.0580778i | ||||
\(837\) | 215.060 | − | 53.2585i | 0.256941 | − | 0.0636302i | ||||
\(838\) | 605.934 | + | 440.237i | 0.723072 | + | 0.525342i | ||||
\(839\) | 605.208 | + | 832.997i | 0.721344 | + | 0.992845i | 0.999478 | + | 0.0323026i | \(0.0102840\pi\) |
−0.278134 | + | 0.960542i | \(0.589716\pi\) | |||||||
\(840\) | 38.0610 | − | 86.4777i | 0.0453108 | − | 0.102950i | ||||
\(841\) | 399.938 | + | 290.572i | 0.475550 | + | 0.345508i | ||||
\(842\) | 445.193 | − | 144.652i | 0.528733 | − | 0.171796i | ||||
\(843\) | 206.474 | + | 691.001i | 0.244928 | + | 0.819692i | ||||
\(844\) | 154.688 | + | 476.081i | 0.183280 | + | 0.564077i | ||||
\(845\) | 647.668 | − | 1571.99i | 0.766471 | − | 1.86034i | ||||
\(846\) | −273.152 | − | 1000.34i | −0.322875 | − | 1.18244i | ||||
\(847\) | −3.27690 | + | 10.0853i | −0.00386883 | + | 0.0119070i | ||||
\(848\) | −0.151108 | − | 0.207983i | −0.000178194 | − | 0.000245263i | ||||
\(849\) | 269.538 | − | 80.5393i | 0.317478 | − | 0.0948638i | ||||
\(850\) | −196.542 | + | 389.360i | −0.231225 | + | 0.458070i | ||||
\(851\) | − | 733.483i | − | 0.861907i | ||||||
\(852\) | −171.879 | − | 131.239i | −0.201736 | − | 0.154036i | ||||
\(853\) | 300.002 | − | 923.312i | 0.351703 | − | 1.08243i | −0.606194 | − | 0.795317i | \(-0.707305\pi\) |
0.957897 | − | 0.287113i | \(-0.0926954\pi\) | |||||||
\(854\) | 45.3477 | + | 14.7344i | 0.0531003 | + | 0.0172533i | ||||
\(855\) | −45.2932 | + | 96.6067i | −0.0529745 | + | 0.112990i | ||||
\(856\) | −201.122 | − | 618.989i | −0.234955 | − | 0.723118i | ||||
\(857\) | − | 684.027i | − | 0.798164i | −0.916915 | − | 0.399082i | \(-0.869329\pi\) | ||
0.916915 | − | 0.399082i | \(-0.130671\pi\) | |||||||
\(858\) | 497.829 | + | 720.664i | 0.580220 | + | 0.839935i | ||||
\(859\) | 580.595 | + | 421.827i | 0.675896 | + | 0.491067i | 0.871994 | − | 0.489517i | \(-0.162827\pi\) |
−0.196098 | + | 0.980584i | \(0.562827\pi\) | |||||||
\(860\) | −67.9027 | + | 41.7872i | −0.0789566 | + | 0.0485898i | ||||
\(861\) | −90.4798 | − | 69.0860i | −0.105087 | − | 0.0802393i | ||||
\(862\) | −311.091 | − | 226.021i | −0.360894 | − | 0.262205i | ||||
\(863\) | −268.475 | + | 369.524i | −0.311095 | + | 0.428186i | −0.935722 | − | 0.352737i | \(-0.885251\pi\) |
0.624627 | + | 0.780923i | \(0.285251\pi\) | |||||||
\(864\) | 857.124 | + | 61.3016i | 0.992042 | + | 0.0709509i | ||||
\(865\) | 22.0225 | − | 286.737i | 0.0254595 | − | 0.331488i | ||||
\(866\) | −279.714 | + | 384.993i | −0.322995 | + | 0.444565i | ||||
\(867\) | 159.737 | + | 231.238i | 0.184241 | + | 0.266710i | ||||
\(868\) | 15.6944 | 0.0180811 | ||||||||
\(869\) | −326.092 | + | 105.954i | −0.375250 | + | 0.121926i | ||||
\(870\) | 626.278 | + | 275.641i | 0.719860 | + | 0.316829i | ||||
\(871\) | 329.189 | − | 1013.14i | 0.377944 | − | 1.16319i | ||||
\(872\) | −1485.82 | − | 482.772i | −1.70392 | − | 0.553638i | ||||
\(873\) | 168.487 | − | 445.249i | 0.192998 | − | 0.510021i | ||||
\(874\) | 70.2225 | 0.0803461 | ||||||||
\(875\) | −50.6866 | + | 83.7737i | −0.0579276 | + | 0.0957413i | ||||
\(876\) | 655.203 | − | 195.778i | 0.747949 | − | 0.223491i | ||||
\(877\) | 544.210 | − | 395.392i | 0.620536 | − | 0.450846i | −0.232573 | − | 0.972579i | \(-0.574714\pi\) |
0.853109 | + | 0.521733i | \(0.174714\pi\) | |||||||
\(878\) | −249.145 | − | 80.9520i | −0.283764 | − | 0.0922005i | ||||
\(879\) | 269.937 | + | 6.42557i | 0.307095 | + | 0.00731009i | ||||
\(880\) | 9.11715 | − | 10.7157i | 0.0103604 | − | 0.0121769i | ||||
\(881\) | −951.535 | + | 309.172i | −1.08006 | + | 0.350933i | −0.794399 | − | 0.607397i | \(-0.792214\pi\) |
−0.285663 | + | 0.958330i | \(0.592214\pi\) | |||||||
\(882\) | 298.243 | + | 454.502i | 0.338144 | + | 0.515308i | ||||
\(883\) | −153.020 | − | 470.946i | −0.173295 | − | 0.533347i | 0.826256 | − | 0.563294i | \(-0.190466\pi\) |
−0.999551 | + | 0.0299468i | \(0.990466\pi\) | |||||||
\(884\) | 452.537 | − | 622.863i | 0.511919 | − | 0.704597i | ||||
\(885\) | 28.5647 | + | 131.622i | 0.0322764 | + | 0.148725i | ||||
\(886\) | −445.683 | + | 323.808i | −0.503028 | + | 0.365472i | ||||
\(887\) | −154.724 | + | 212.960i | −0.174435 | + | 0.240090i | −0.887279 | − | 0.461233i | \(-0.847407\pi\) |
0.712843 | + | 0.701323i | \(0.247407\pi\) | |||||||
\(888\) | 247.284 | − | 703.626i | 0.278473 | − | 0.792372i | ||||
\(889\) | −47.3374 | + | 34.3926i | −0.0532479 | + | 0.0386869i | ||||
\(890\) | 740.354 | − | 455.613i | 0.831858 | − | 0.511924i | ||||
\(891\) | 426.744 | + | 723.152i | 0.478950 | + | 0.811619i | ||||
\(892\) | −29.4210 | − | 90.5486i | −0.0329832 | − | 0.101512i | ||||
\(893\) | 218.845i | 0.245067i | ||||||||
\(894\) | −34.6802 | − | 50.2036i | −0.0387922 | − | 0.0561562i | ||||
\(895\) | 358.279 | + | 582.190i | 0.400312 | + | 0.650492i | ||||
\(896\) | 56.8823 | + | 18.4822i | 0.0634847 | + | 0.0206274i | ||||
\(897\) | −1605.39 | − | 38.2147i | −1.78973 | − | 0.0426028i | ||||
\(898\) | −425.878 | + | 309.418i | −0.474252 | + | 0.344564i | ||||
\(899\) | 299.860i | 0.333548i | ||||||||
\(900\) | −538.329 | − | 109.632i | −0.598143 | − | 0.121814i | ||||
\(901\) | −13.2362 | −0.0146906 | ||||||||
\(902\) | −368.478 | − | 507.167i | −0.408513 | − | 0.562269i | ||||
\(903\) | −0.365215 | + | 15.3426i | −0.000404446 | + | 0.0169907i | ||||
\(904\) | −309.764 | + | 953.356i | −0.342659 | + | 1.05460i | ||||
\(905\) | 584.303 | − | 1418.19i | 0.645639 | − | 1.56707i | ||||
\(906\) | 480.790 | − | 332.125i | 0.530673 | − | 0.366584i | ||||
\(907\) | 2.24647 | 0.00247682 | 0.00123841 | − | 0.999999i | \(-0.499606\pi\) | ||||
0.00123841 | + | 0.999999i | \(0.499606\pi\) | |||||||
\(908\) | 416.908 | − | 135.462i | 0.459150 | − | 0.149187i | ||||
\(909\) | −41.8293 | + | 878.121i | −0.0460168 | + | 0.966029i | ||||
\(910\) | −71.4810 | + | 84.0140i | −0.0785506 | + | 0.0923230i | ||||
\(911\) | −151.462 | − | 208.469i | −0.166259 | − | 0.228836i | 0.717756 | − | 0.696295i | \(-0.245169\pi\) |
−0.884015 | + | 0.467459i | \(0.845169\pi\) | |||||||
\(912\) | 1.82159 | + | 0.640184i | 0.00199736 | + | 0.000701957i | ||||
\(913\) | −788.102 | − | 572.590i | −0.863201 | − | 0.627152i | ||||
\(914\) | 239.669 | + | 329.877i | 0.262220 | + | 0.360915i | ||||
\(915\) | 73.3514 | − | 727.750i | 0.0801655 | − | 0.795356i | ||||
\(916\) | −465.196 | − | 337.985i | −0.507856 | − | 0.368979i | ||||
\(917\) | 21.9795 | − | 7.14157i | 0.0239689 | − | 0.00778797i | ||||
\(918\) | −303.354 | + | 360.361i | −0.330451 | + | 0.392550i | ||||
\(919\) | −137.952 | − | 424.572i | −0.150111 | − | 0.461993i | 0.847522 | − | 0.530760i | \(-0.178094\pi\) |
−0.997633 | + | 0.0687669i | \(0.978094\pi\) | |||||||
\(920\) | 224.434 | + | 927.126i | 0.243950 | + | 1.00775i | ||||
\(921\) | −27.3262 | + | 1147.97i | −0.0296702 | + | 1.24644i | ||||
\(922\) | 161.039 | − | 495.628i | 0.174663 | − | 0.537557i | ||||
\(923\) | 391.515 | + | 538.874i | 0.424176 | + | 0.583829i | ||||
\(924\) | 17.0291 | + | 56.9906i | 0.0184297 | + | 0.0616781i | ||||
\(925\) | −348.288 | + | 689.977i | −0.376527 | + | 0.745921i | ||||
\(926\) | 415.762i | 0.448987i | ||||||||
\(927\) | −200.760 | + | 530.534i | −0.216570 | + | 0.572313i | ||||
\(928\) | −359.391 | + | 1106.09i | −0.387275 | + | 1.19191i | ||||
\(929\) | 1652.02 | + | 536.774i | 1.77828 | + | 0.577797i | 0.998816 | − | 0.0486535i | \(-0.0154930\pi\) |
0.779461 | + | 0.626451i | \(0.215493\pi\) | |||||||
\(930\) | 32.5872 | + | 150.157i | 0.0350400 | + | 0.161459i | ||||
\(931\) | −35.4525 | − | 109.112i | −0.0380800 | − | 0.117198i | ||||
\(932\) | 119.696i | 0.128429i | ||||||||
\(933\) | −1060.78 | + | 732.777i | −1.13695 | + | 0.785398i | ||||
\(934\) | −840.550 | − | 610.696i | −0.899947 | − | 0.653850i | ||||
\(935\) | −170.433 | − | 704.049i | −0.182281 | − | 0.752994i | ||||
\(936\) | −1527.16 | − | 577.894i | −1.63158 | − | 0.617409i | ||||
\(937\) | 307.252 | + | 223.232i | 0.327911 | + | 0.238241i | 0.739544 | − | 0.673109i | \(-0.235041\pi\) |
−0.411633 | + | 0.911350i | \(0.635041\pi\) | |||||||
\(938\) | −27.1375 | + | 37.3515i | −0.0289312 | + | 0.0398204i | ||||
\(939\) | 296.926 | − | 388.874i | 0.316215 | − | 0.414137i | ||||
\(940\) | −1095.19 | + | 265.117i | −1.16509 | + | 0.282040i | ||||
\(941\) | 482.778 | − | 664.487i | 0.513048 | − | 0.706150i | −0.471382 | − | 0.881929i | \(-0.656245\pi\) |
0.984430 | + | 0.175779i | \(0.0562445\pi\) | |||||||
\(942\) | −460.708 | + | 318.253i | −0.489075 | + | 0.337849i | ||||
\(943\) | 1149.33 | 1.21880 | ||||||||
\(944\) | 2.31801 | − | 0.753167i | 0.00245552 | − | 0.000797846i | ||||
\(945\) | −74.0965 | + | 75.4466i | −0.0784090 | + | 0.0798376i | ||||
\(946\) | −26.1158 | + | 80.3761i | −0.0276065 | + | 0.0849642i | ||||
\(947\) | −340.488 | − | 110.631i | −0.359544 | − | 0.116823i | 0.123674 | − | 0.992323i | \(-0.460532\pi\) |
−0.483218 | + | 0.875500i | \(0.660532\pi\) | |||||||
\(948\) | 147.032 | − | 192.564i | 0.155097 | − | 0.203126i | ||||
\(949\) | −2106.25 | −2.21944 | ||||||||
\(950\) | −66.0573 | − | 33.3445i | −0.0695340 | − | 0.0350995i | ||||
\(951\) | −134.043 | − | 448.599i | −0.140950 | − | 0.471713i | ||||
\(952\) | −71.2182 | + | 51.7431i | −0.0748090 | + | 0.0543520i | ||||
\(953\) | 678.525 | + | 220.466i | 0.711989 | + | 0.231339i | 0.642546 | − | 0.766247i | \(-0.277878\pi\) |
0.0694423 | + | 0.997586i | \(0.477878\pi\) | |||||||
\(954\) | 2.80287 | + | 10.2647i | 0.00293801 | + | 0.0107597i | ||||
\(955\) | 456.351 | − | 110.471i | 0.477855 | − | 0.115677i | ||||
\(956\) | −738.255 | + | 239.873i | −0.772233 | + | 0.250914i | ||||
\(957\) | −1088.87 | + | 325.360i | −1.13780 | + | 0.339979i | ||||
\(958\) | −209.375 | − | 644.390i | −0.218554 | − | 0.672641i | ||||
\(959\) | 2.12213 | − | 2.92086i | 0.00221286 | − | 0.00304573i | ||||
\(960\) | −61.3971 | + | 609.146i | −0.0639553 | + | 0.634527i | ||||
\(961\) | 722.990 | − | 525.283i | 0.752331 | − | 0.546600i | ||||
\(962\) | −511.804 | + | 704.437i | −0.532021 | + | 0.732263i | ||||
\(963\) | −34.6598 | + | 727.611i | −0.0359915 | + | 0.755567i | ||||
\(964\) | −11.2425 | + | 8.16813i | −0.0116623 | + | 0.00847316i | ||||
\(965\) | −279.341 | − | 237.670i | −0.289472 | − | 0.246290i | ||||
\(966\) | 65.6603 | + | 23.0758i | 0.0679714 | + | 0.0238880i | ||||
\(967\) | −36.1744 | − | 111.333i | −0.0374089 | − | 0.115133i | 0.930608 | − | 0.366017i | \(-0.119279\pi\) |
−0.968017 | + | 0.250884i | \(0.919279\pi\) | |||||||
\(968\) | − | 108.861i | − | 0.112460i | ||||||
\(969\) | 81.7928 | − | 56.5017i | 0.0844094 | − | 0.0583093i | ||||
\(970\) | 305.261 | + | 125.769i | 0.314702 | + | 0.129659i | ||||
\(971\) | 842.108 | + | 273.617i | 0.867258 | + | 0.281789i | 0.708657 | − | 0.705553i | \(-0.249301\pi\) |
0.158602 | + | 0.987343i | \(0.449301\pi\) | |||||||
\(972\) | −538.532 | − | 249.043i | −0.554046 | − | 0.256217i | ||||
\(973\) | −154.172 | + | 112.013i | −0.158451 | + | 0.115121i | ||||
\(974\) | − | 624.119i | − | 0.640779i | ||||||
\(975\) | 1492.02 | + | 798.253i | 1.53028 | + | 0.818721i | ||||
\(976\) | −13.2362 | −0.0135617 | ||||||||
\(977\) | 335.629 | + | 461.954i | 0.343531 | + | 0.472829i | 0.945468 | − | 0.325714i | \(-0.105605\pi\) |
−0.601938 | + | 0.798543i | \(0.705605\pi\) | |||||||
\(978\) | −862.686 | − | 20.5354i | −0.882092 | − | 0.0209973i | ||||
\(979\) | −446.159 | + | 1373.13i | −0.455729 | + | 1.40259i | ||||
\(980\) | 503.090 | − | 309.601i | 0.513357 | − | 0.315919i | ||||
\(981\) | 1364.09 | + | 1093.91i | 1.39051 | + | 1.11510i | ||||
\(982\) | −838.611 | −0.853983 | ||||||||
\(983\) | −259.544 | + | 84.3309i | −0.264033 | + | 0.0857894i | −0.438042 | − | 0.898955i | \(-0.644328\pi\) |
0.174009 | + | 0.984744i | \(0.444328\pi\) | |||||||
\(984\) | 1102.55 | + | 387.481i | 1.12047 | + | 0.393782i | ||||
\(985\) | 415.299 | + | 674.846i | 0.421624 | + | 0.685123i | ||||
\(986\) | −374.727 | − | 515.768i | −0.380048 | − | 0.523091i | ||||
\(987\) | −71.9144 | + | 204.627i | −0.0728616 | + | 0.207322i | ||||
\(988\) | 105.673 | + | 76.7757i | 0.106956 | + | 0.0777082i | ||||
\(989\) | −91.0734 | − | 125.352i | −0.0920863 | − | 0.126746i | ||||
\(990\) | −509.902 | + | 281.259i | −0.515053 | + | 0.284100i | ||||
\(991\) | 681.309 | + | 495.000i | 0.687497 | + | 0.499496i | 0.875836 | − | 0.482608i | \(-0.160311\pi\) |
−0.188340 | + | 0.982104i | \(0.560311\pi\) | |||||||
\(992\) | −248.379 | + | 80.7032i | −0.250382 | + | 0.0813540i | ||||
\(993\) | 369.286 | − | 110.344i | 0.371890 | − | 0.111122i | ||||
\(994\) | −8.92073 | − | 27.4552i | −0.00897457 | − | 0.0276209i | ||||
\(995\) | 111.116 | + | 94.5402i | 0.111674 | + | 0.0950152i | ||||
\(996\) | 688.152 | + | 16.3808i | 0.690916 | + | 0.0164466i | ||||
\(997\) | 74.6597 | − | 229.779i | 0.0748844 | − | 0.230470i | −0.906607 | − | 0.421975i | \(-0.861337\pi\) |
0.981492 | + | 0.191505i | \(0.0613368\pi\) | |||||||
\(998\) | 258.920 | + | 356.373i | 0.259439 | + | 0.357088i | ||||
\(999\) | −537.567 | + | 638.589i | −0.538105 | + | 0.639228i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.3.j.a.11.12 | yes | 72 | |
3.2 | odd | 2 | inner | 75.3.j.a.11.7 | ✓ | 72 | |
5.2 | odd | 4 | 375.3.h.b.74.13 | 144 | |||
5.3 | odd | 4 | 375.3.h.b.74.24 | 144 | |||
5.4 | even | 2 | 375.3.j.a.176.7 | 72 | |||
15.2 | even | 4 | 375.3.h.b.74.23 | 144 | |||
15.8 | even | 4 | 375.3.h.b.74.14 | 144 | |||
15.14 | odd | 2 | 375.3.j.a.176.12 | 72 | |||
25.9 | even | 10 | 375.3.j.a.326.12 | 72 | |||
25.12 | odd | 20 | 375.3.h.b.299.14 | 144 | |||
25.13 | odd | 20 | 375.3.h.b.299.23 | 144 | |||
25.16 | even | 5 | inner | 75.3.j.a.41.7 | yes | 72 | |
75.38 | even | 20 | 375.3.h.b.299.13 | 144 | |||
75.41 | odd | 10 | inner | 75.3.j.a.41.12 | yes | 72 | |
75.59 | odd | 10 | 375.3.j.a.326.7 | 72 | |||
75.62 | even | 20 | 375.3.h.b.299.24 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.j.a.11.7 | ✓ | 72 | 3.2 | odd | 2 | inner | |
75.3.j.a.11.12 | yes | 72 | 1.1 | even | 1 | trivial | |
75.3.j.a.41.7 | yes | 72 | 25.16 | even | 5 | inner | |
75.3.j.a.41.12 | yes | 72 | 75.41 | odd | 10 | inner | |
375.3.h.b.74.13 | 144 | 5.2 | odd | 4 | |||
375.3.h.b.74.14 | 144 | 15.8 | even | 4 | |||
375.3.h.b.74.23 | 144 | 15.2 | even | 4 | |||
375.3.h.b.74.24 | 144 | 5.3 | odd | 4 | |||
375.3.h.b.299.13 | 144 | 75.38 | even | 20 | |||
375.3.h.b.299.14 | 144 | 25.12 | odd | 20 | |||
375.3.h.b.299.23 | 144 | 25.13 | odd | 20 | |||
375.3.h.b.299.24 | 144 | 75.62 | even | 20 | |||
375.3.j.a.176.7 | 72 | 5.4 | even | 2 | |||
375.3.j.a.176.12 | 72 | 15.14 | odd | 2 | |||
375.3.j.a.326.7 | 72 | 75.59 | odd | 10 | |||
375.3.j.a.326.12 | 72 | 25.9 | even | 10 |