Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,3,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), 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: | \(2.01635395627\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 82x^{10} + 2505x^{8} + 34456x^{6} + 196096x^{4} + 262464x^{2} + 69696 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 51.3 | ||
Root | \(4.53867i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.51 |
Dual form | 74.3.g.b.45.3 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | + | 0.366025i | −0.683013 | + | 0.183013i | ||||
\(3\) | 3.93060 | − | 2.26933i | 1.31020 | − | 0.756445i | 0.328072 | − | 0.944653i | \(-0.393601\pi\) |
0.982129 | + | 0.188208i | \(0.0602679\pi\) | |||||||
\(4\) | 1.73205 | − | 1.00000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 0.866025 | + | 0.232051i | 0.173205 | + | 0.0464102i | 0.344379 | − | 0.938831i | \(-0.388089\pi\) |
−0.171174 | + | 0.985241i | \(0.554756\pi\) | |||||||
\(6\) | −4.53867 | + | 4.53867i | −0.756445 | + | 0.756445i | ||||
\(7\) | −2.63849 | − | 4.57000i | −0.376927 | − | 0.652857i | 0.613686 | − | 0.789550i | \(-0.289686\pi\) |
−0.990613 | + | 0.136693i | \(0.956353\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 5.79976 | − | 10.0455i | 0.644417 | − | 1.11616i | ||||
\(10\) | −1.26795 | −0.126795 | ||||||||
\(11\) | 2.58423i | 0.234930i | 0.993077 | + | 0.117465i | \(0.0374768\pi\) | ||||
−0.993077 | + | 0.117465i | \(0.962523\pi\) | |||||||
\(12\) | 4.53867 | − | 7.86120i | 0.378222 | − | 0.655100i | ||||
\(13\) | 14.9302 | + | 4.00055i | 1.14848 | + | 0.307734i | 0.782356 | − | 0.622832i | \(-0.214018\pi\) |
0.366124 | + | 0.930566i | \(0.380684\pi\) | |||||||
\(14\) | 5.27698 | + | 5.27698i | 0.376927 | + | 0.376927i | ||||
\(15\) | 3.93060 | − | 1.05320i | 0.262040 | − | 0.0702134i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.125000 | − | 0.216506i | ||||
\(17\) | 0.861003 | + | 3.21331i | 0.0506472 | + | 0.189018i | 0.986615 | − | 0.163068i | \(-0.0521391\pi\) |
−0.935968 | + | 0.352086i | \(0.885472\pi\) | |||||||
\(18\) | −4.24572 | + | 15.8452i | −0.235873 | + | 0.880291i | ||||
\(19\) | −6.00993 | − | 1.61036i | −0.316312 | − | 0.0847556i | 0.0971699 | − | 0.995268i | \(-0.469021\pi\) |
−0.413482 | + | 0.910512i | \(0.635688\pi\) | |||||||
\(20\) | 1.73205 | − | 0.464102i | 0.0866025 | − | 0.0232051i | ||||
\(21\) | −20.7417 | − | 11.9752i | −0.987700 | − | 0.570249i | ||||
\(22\) | −0.945893 | − | 3.53012i | −0.0429951 | − | 0.160460i | ||||
\(23\) | −31.8083 | + | 31.8083i | −1.38297 | + | 1.38297i | −0.543671 | + | 0.839298i | \(0.682966\pi\) |
−0.839298 | + | 0.543671i | \(0.817034\pi\) | |||||||
\(24\) | −3.32254 | + | 12.3999i | −0.138439 | + | 0.516661i | ||||
\(25\) | −20.9545 | − | 12.0981i | −0.838179 | − | 0.483923i | ||||
\(26\) | −21.8594 | −0.840746 | ||||||||
\(27\) | − | 11.7983i | − | 0.436975i | ||||||
\(28\) | −9.13999 | − | 5.27698i | −0.326428 | − | 0.188463i | ||||
\(29\) | 35.8477 | + | 35.8477i | 1.23613 | + | 1.23613i | 0.961570 | + | 0.274559i | \(0.0885317\pi\) |
0.274559 | + | 0.961570i | \(0.411468\pi\) | |||||||
\(30\) | −4.98380 | + | 2.87740i | −0.166127 | + | 0.0959134i | ||||
\(31\) | −17.4160 | − | 17.4160i | −0.561806 | − | 0.561806i | 0.368014 | − | 0.929820i | \(-0.380038\pi\) |
−0.929820 | + | 0.368014i | \(0.880038\pi\) | |||||||
\(32\) | −1.46410 | + | 5.46410i | −0.0457532 | + | 0.170753i | ||||
\(33\) | 5.86448 | + | 10.1576i | 0.177711 | + | 0.307805i | ||||
\(34\) | −2.35230 | − | 4.07431i | −0.0691854 | − | 0.119833i | ||||
\(35\) | −1.22453 | − | 4.57000i | −0.0349865 | − | 0.130571i | ||||
\(36\) | − | 23.1990i | − | 0.644417i | ||||||
\(37\) | −22.3381 | + | 29.4959i | −0.603732 | + | 0.797187i | ||||
\(38\) | 8.79915 | 0.231557 | ||||||||
\(39\) | 67.7634 | − | 18.1572i | 1.73752 | − | 0.465568i | ||||
\(40\) | −2.19615 | + | 1.26795i | −0.0549038 | + | 0.0316987i | ||||
\(41\) | −21.0885 | + | 12.1755i | −0.514354 | + | 0.296963i | −0.734622 | − | 0.678477i | \(-0.762640\pi\) |
0.220267 | + | 0.975440i | \(0.429307\pi\) | |||||||
\(42\) | 32.7169 | + | 8.76647i | 0.778974 | + | 0.208726i | ||||
\(43\) | 40.1678 | − | 40.1678i | 0.934136 | − | 0.934136i | −0.0638252 | − | 0.997961i | \(-0.520330\pi\) |
0.997961 | + | 0.0638252i | \(0.0203300\pi\) | |||||||
\(44\) | 2.58423 | + | 4.47601i | 0.0587324 | + | 0.101728i | ||||
\(45\) | 7.35380 | − | 7.35380i | 0.163418 | − | 0.163418i | ||||
\(46\) | 31.8083 | − | 55.0936i | 0.691485 | − | 1.19769i | ||||
\(47\) | 14.1710 | 0.301510 | 0.150755 | − | 0.988571i | \(-0.451830\pi\) | ||||
0.150755 | + | 0.988571i | \(0.451830\pi\) | |||||||
\(48\) | − | 18.1547i | − | 0.378222i | ||||||
\(49\) | 10.5768 | − | 18.3195i | 0.215852 | − | 0.373867i | ||||
\(50\) | 33.0526 | + | 8.85641i | 0.661051 | + | 0.177128i | ||||
\(51\) | 10.6763 | + | 10.6763i | 0.209340 | + | 0.209340i | ||||
\(52\) | 29.8605 | − | 8.00109i | 0.574240 | − | 0.153867i | ||||
\(53\) | −26.9625 | + | 46.7005i | −0.508727 | + | 0.881141i | 0.491222 | + | 0.871034i | \(0.336550\pi\) |
−0.999949 | + | 0.0101063i | \(0.996783\pi\) | |||||||
\(54\) | 4.31849 | + | 16.1168i | 0.0799720 | + | 0.298460i | ||||
\(55\) | −0.599672 | + | 2.23801i | −0.0109031 | + | 0.0406910i | ||||
\(56\) | 14.4170 | + | 3.86302i | 0.257446 | + | 0.0689824i | ||||
\(57\) | −27.2771 | + | 7.30888i | −0.478546 | + | 0.128226i | ||||
\(58\) | −62.0901 | − | 35.8477i | −1.07052 | − | 0.618064i | ||||
\(59\) | −21.5652 | − | 80.4823i | −0.365511 | − | 1.36411i | −0.866727 | − | 0.498783i | \(-0.833780\pi\) |
0.501216 | − | 0.865322i | \(-0.332886\pi\) | |||||||
\(60\) | 5.75480 | − | 5.75480i | 0.0959134 | − | 0.0959134i | ||||
\(61\) | −13.1162 | + | 48.9504i | −0.215020 | + | 0.802465i | 0.771140 | + | 0.636666i | \(0.219687\pi\) |
−0.986160 | + | 0.165799i | \(0.946980\pi\) | |||||||
\(62\) | 30.1654 | + | 17.4160i | 0.486538 | + | 0.280903i | ||||
\(63\) | −61.2104 | −0.971593 | ||||||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 12.0016 | + | 6.92915i | 0.184641 | + | 0.106602i | ||||
\(66\) | −11.7290 | − | 11.7290i | −0.177711 | − | 0.177711i | ||||
\(67\) | 23.8908 | − | 13.7933i | 0.356579 | − | 0.205871i | −0.311000 | − | 0.950410i | \(-0.600664\pi\) |
0.667579 | + | 0.744539i | \(0.267331\pi\) | |||||||
\(68\) | 4.70461 | + | 4.70461i | 0.0691854 | + | 0.0691854i | ||||
\(69\) | −52.8421 | + | 197.209i | −0.765828 | + | 2.85811i | ||||
\(70\) | 3.34547 | + | 5.79452i | 0.0477924 | + | 0.0827789i | ||||
\(71\) | −45.4136 | − | 78.6586i | −0.639628 | − | 1.10787i | −0.985514 | − | 0.169591i | \(-0.945755\pi\) |
0.345887 | − | 0.938276i | \(-0.387578\pi\) | |||||||
\(72\) | 8.49143 | + | 31.6905i | 0.117937 | + | 0.440145i | ||||
\(73\) | − | 111.089i | − | 1.52177i | −0.648888 | − | 0.760884i | \(-0.724766\pi\) | ||
0.648888 | − | 0.760884i | \(-0.275234\pi\) | |||||||
\(74\) | 19.7181 | − | 48.4685i | 0.266461 | − | 0.654980i | ||||
\(75\) | −109.818 | −1.46424 | ||||||||
\(76\) | −12.0199 | + | 3.22071i | −0.158156 | + | 0.0423778i | ||||
\(77\) | 11.8099 | − | 6.81845i | 0.153375 | − | 0.0885514i | ||||
\(78\) | −85.9206 | + | 49.6063i | −1.10155 | + | 0.635978i | ||||
\(79\) | 108.969 | + | 29.1982i | 1.37936 | + | 0.369597i | 0.870887 | − | 0.491483i | \(-0.163545\pi\) |
0.508469 | + | 0.861080i | \(0.330212\pi\) | |||||||
\(80\) | 2.53590 | − | 2.53590i | 0.0316987 | − | 0.0316987i | ||||
\(81\) | 25.4235 | + | 44.0347i | 0.313870 | + | 0.543638i | ||||
\(82\) | 24.3509 | − | 24.3509i | 0.296963 | − | 0.296963i | ||||
\(83\) | 1.27819 | − | 2.21389i | 0.0153998 | − | 0.0266733i | −0.858223 | − | 0.513277i | \(-0.828431\pi\) |
0.873623 | + | 0.486604i | \(0.161765\pi\) | |||||||
\(84\) | −47.9009 | −0.570249 | ||||||||
\(85\) | 2.98260i | 0.0350894i | ||||||||
\(86\) | −40.1678 | + | 69.5727i | −0.467068 | + | 0.808985i | ||||
\(87\) | 222.254 | + | 59.5527i | 2.55464 | + | 0.684514i | ||||
\(88\) | −5.16845 | − | 5.16845i | −0.0587324 | − | 0.0587324i | ||||
\(89\) | 129.892 | − | 34.8046i | 1.45947 | − | 0.391063i | 0.560161 | − | 0.828384i | \(-0.310739\pi\) |
0.899305 | + | 0.437321i | \(0.144073\pi\) | |||||||
\(90\) | −7.35380 | + | 12.7372i | −0.0817089 | + | 0.141524i | ||||
\(91\) | −21.1108 | − | 78.7866i | −0.231987 | − | 0.865786i | ||||
\(92\) | −23.2853 | + | 86.9019i | −0.253101 | + | 0.944586i | ||||
\(93\) | −107.978 | − | 28.9326i | −1.16105 | − | 0.311104i | ||||
\(94\) | −19.3579 | + | 5.18694i | −0.205935 | + | 0.0551802i | ||||
\(95\) | −4.83107 | − | 2.78922i | −0.0508534 | − | 0.0293602i | ||||
\(96\) | 6.64507 | + | 24.7997i | 0.0692195 | + | 0.258331i | ||||
\(97\) | −50.8869 | + | 50.8869i | −0.524607 | + | 0.524607i | −0.918959 | − | 0.394352i | \(-0.870969\pi\) |
0.394352 | + | 0.918959i | \(0.370969\pi\) | |||||||
\(98\) | −7.74272 | + | 28.8962i | −0.0790074 | + | 0.294859i | ||||
\(99\) | 25.9598 | + | 14.9879i | 0.262220 | + | 0.151393i | ||||
\(100\) | −48.3923 | −0.483923 | ||||||||
\(101\) | − | 111.442i | − | 1.10339i | −0.834046 | − | 0.551695i | \(-0.813981\pi\) | ||
0.834046 | − | 0.551695i | \(-0.186019\pi\) | |||||||
\(102\) | −18.4919 | − | 10.6763i | −0.181294 | − | 0.104670i | ||||
\(103\) | −93.0692 | − | 93.0692i | −0.903584 | − | 0.903584i | 0.0921599 | − | 0.995744i | \(-0.470623\pi\) |
−0.995744 | + | 0.0921599i | \(0.970623\pi\) | |||||||
\(104\) | −37.8616 | + | 21.8594i | −0.364054 | + | 0.210186i | ||||
\(105\) | −15.1840 | − | 15.1840i | −0.144609 | − | 0.144609i | ||||
\(106\) | 19.7379 | − | 73.6630i | 0.186207 | − | 0.694934i | ||||
\(107\) | −24.5884 | − | 42.5883i | −0.229798 | − | 0.398022i | 0.727950 | − | 0.685630i | \(-0.240473\pi\) |
−0.957748 | + | 0.287608i | \(0.907140\pi\) | |||||||
\(108\) | −11.7983 | − | 20.4353i | −0.109244 | − | 0.189216i | ||||
\(109\) | 15.9102 | + | 59.3778i | 0.145966 | + | 0.544751i | 0.999711 | + | 0.0240595i | \(0.00765911\pi\) |
−0.853745 | + | 0.520691i | \(0.825674\pi\) | |||||||
\(110\) | − | 3.27667i | − | 0.0297879i | ||||||
\(111\) | −20.8660 | + | 166.629i | −0.187982 | + | 1.50117i | ||||
\(112\) | −21.1079 | −0.188463 | ||||||||
\(113\) | −97.3431 | + | 26.0830i | −0.861443 | + | 0.230823i | −0.662384 | − | 0.749164i | \(-0.730455\pi\) |
−0.199059 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(114\) | 34.5860 | − | 19.9682i | 0.303386 | − | 0.175160i | ||||
\(115\) | −34.9279 | + | 20.1657i | −0.303721 | + | 0.175353i | ||||
\(116\) | 97.9378 | + | 26.2424i | 0.844292 | + | 0.226227i | ||||
\(117\) | 126.779 | − | 126.779i | 1.08358 | − | 1.08358i | ||||
\(118\) | 58.9171 | + | 102.047i | 0.499297 | + | 0.864809i | ||||
\(119\) | 12.4131 | − | 12.4131i | 0.104311 | − | 0.104311i | ||||
\(120\) | −5.75480 | + | 9.96761i | −0.0479567 | + | 0.0830634i | ||||
\(121\) | 114.322 | 0.944808 | ||||||||
\(122\) | − | 71.6683i | − | 0.587445i | ||||||
\(123\) | −55.2604 | + | 95.7139i | −0.449272 | + | 0.778161i | ||||
\(124\) | −47.5814 | − | 12.7494i | −0.383721 | − | 0.102818i | ||||
\(125\) | −31.1891 | − | 31.1891i | −0.249513 | − | 0.249513i | ||||
\(126\) | 83.6149 | − | 22.4046i | 0.663611 | − | 0.177814i | ||||
\(127\) | −52.9016 | + | 91.6282i | −0.416548 | + | 0.721482i | −0.995590 | − | 0.0938161i | \(-0.970093\pi\) |
0.579042 | + | 0.815298i | \(0.303427\pi\) | |||||||
\(128\) | 2.92820 | + | 10.9282i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | 66.7296 | − | 249.038i | 0.517283 | − | 1.93053i | ||||
\(130\) | −18.9308 | − | 5.07249i | −0.145621 | − | 0.0390192i | ||||
\(131\) | 136.790 | − | 36.6528i | 1.04420 | − | 0.279792i | 0.304346 | − | 0.952561i | \(-0.401562\pi\) |
0.739852 | + | 0.672769i | \(0.234895\pi\) | |||||||
\(132\) | 20.3151 | + | 11.7290i | 0.153903 | + | 0.0888557i | ||||
\(133\) | 8.49782 | + | 31.7143i | 0.0638934 | + | 0.238453i | ||||
\(134\) | −27.5867 | + | 27.5867i | −0.205871 | + | 0.205871i | ||||
\(135\) | 2.73781 | − | 10.2177i | 0.0202801 | − | 0.0756863i | ||||
\(136\) | −8.14862 | − | 4.70461i | −0.0599163 | − | 0.0345927i | ||||
\(137\) | −76.4553 | −0.558068 | −0.279034 | − | 0.960281i | \(-0.590014\pi\) | ||||
−0.279034 | + | 0.960281i | \(0.590014\pi\) | |||||||
\(138\) | − | 288.735i | − | 2.09228i | ||||||
\(139\) | 39.4004 | + | 22.7479i | 0.283456 | + | 0.163654i | 0.634987 | − | 0.772523i | \(-0.281005\pi\) |
−0.351531 | + | 0.936176i | \(0.614339\pi\) | |||||||
\(140\) | −6.69094 | − | 6.69094i | −0.0477924 | − | 0.0477924i | ||||
\(141\) | 55.7005 | − | 32.1587i | 0.395039 | − | 0.228076i | ||||
\(142\) | 90.8271 | + | 90.8271i | 0.639628 | + | 0.639628i | ||||
\(143\) | −10.3383 | + | 38.5831i | −0.0722960 | + | 0.269812i | ||||
\(144\) | −23.1990 | − | 40.1819i | −0.161104 | − | 0.279041i | ||||
\(145\) | 22.7266 | + | 39.3635i | 0.156735 | + | 0.271473i | ||||
\(146\) | 40.6614 | + | 151.750i | 0.278503 | + | 1.03939i | ||||
\(147\) | − | 96.0088i | − | 0.653121i | ||||||
\(148\) | −9.19478 | + | 73.4265i | −0.0621269 | + | 0.496125i | ||||
\(149\) | 43.2363 | 0.290177 | 0.145088 | − | 0.989419i | \(-0.453653\pi\) | ||||
0.145088 | + | 0.989419i | \(0.453653\pi\) | |||||||
\(150\) | 150.015 | − | 40.1963i | 1.00010 | − | 0.267975i | ||||
\(151\) | −35.9045 | + | 20.7295i | −0.237778 | + | 0.137281i | −0.614155 | − | 0.789185i | \(-0.710503\pi\) |
0.376377 | + | 0.926467i | \(0.377170\pi\) | |||||||
\(152\) | 15.2406 | − | 8.79915i | 0.100267 | − | 0.0578892i | ||||
\(153\) | 37.2728 | + | 9.98721i | 0.243613 | + | 0.0652759i | ||||
\(154\) | −13.6369 | + | 13.6369i | −0.0885514 | + | 0.0885514i | ||||
\(155\) | −11.0413 | − | 19.1241i | −0.0712342 | − | 0.123381i | ||||
\(156\) | 99.2125 | − | 99.2125i | 0.635978 | − | 0.635978i | ||||
\(157\) | 65.0007 | − | 112.585i | 0.414017 | − | 0.717099i | −0.581307 | − | 0.813684i | \(-0.697459\pi\) |
0.995325 | + | 0.0965850i | \(0.0307920\pi\) | |||||||
\(158\) | −159.542 | −1.00976 | ||||||||
\(159\) | 244.748i | 1.53929i | ||||||||
\(160\) | −2.53590 | + | 4.39230i | −0.0158494 | + | 0.0274519i | ||||
\(161\) | 229.290 | + | 61.4380i | 1.42416 | + | 0.381602i | ||||
\(162\) | −50.8469 | − | 50.8469i | −0.313870 | − | 0.313870i | ||||
\(163\) | −137.502 | + | 36.8436i | −0.843572 | + | 0.226035i | −0.654626 | − | 0.755953i | \(-0.727174\pi\) |
−0.188946 | + | 0.981987i | \(0.560507\pi\) | |||||||
\(164\) | −24.3509 | + | 42.1771i | −0.148481 | + | 0.257177i | ||||
\(165\) | 2.72171 | + | 10.1576i | 0.0164952 | + | 0.0615610i | ||||
\(166\) | −0.935698 | + | 3.49207i | −0.00563674 | + | 0.0210366i | ||||
\(167\) | −272.664 | − | 73.0601i | −1.63272 | − | 0.437486i | −0.678016 | − | 0.735047i | \(-0.737160\pi\) |
−0.954703 | + | 0.297561i | \(0.903827\pi\) | |||||||
\(168\) | 65.4339 | − | 17.5329i | 0.389487 | − | 0.104363i | ||||
\(169\) | 60.5495 | + | 34.9583i | 0.358281 | + | 0.206854i | ||||
\(170\) | −1.09171 | − | 4.07431i | −0.00642181 | − | 0.0239665i | ||||
\(171\) | −51.0330 | + | 51.0330i | −0.298438 | + | 0.298438i | ||||
\(172\) | 29.4049 | − | 109.741i | 0.170959 | − | 0.638027i | ||||
\(173\) | −130.152 | − | 75.1434i | −0.752325 | − | 0.434355i | 0.0742087 | − | 0.997243i | \(-0.476357\pi\) |
−0.826533 | + | 0.562888i | \(0.809690\pi\) | |||||||
\(174\) | −325.402 | −1.87013 | ||||||||
\(175\) | 127.683i | 0.729615i | ||||||||
\(176\) | 8.95203 | + | 5.16845i | 0.0508638 | + | 0.0293662i | ||||
\(177\) | −267.405 | − | 267.405i | −1.51076 | − | 1.51076i | ||||
\(178\) | −164.697 | + | 95.0879i | −0.925264 | + | 0.534202i | ||||
\(179\) | −47.9819 | − | 47.9819i | −0.268055 | − | 0.268055i | 0.560261 | − | 0.828316i | \(-0.310701\pi\) |
−0.828316 | + | 0.560261i | \(0.810701\pi\) | |||||||
\(180\) | 5.38335 | − | 20.0909i | 0.0299075 | − | 0.111616i | ||||
\(181\) | 102.624 | + | 177.749i | 0.566981 | + | 0.982040i | 0.996862 | + | 0.0791548i | \(0.0252221\pi\) |
−0.429881 | + | 0.902886i | \(0.641445\pi\) | |||||||
\(182\) | 57.6758 | + | 99.8974i | 0.316900 | + | 0.548887i | ||||
\(183\) | 59.5302 | + | 222.170i | 0.325301 | + | 1.21404i | ||||
\(184\) | − | 127.233i | − | 0.691485i | ||||||
\(185\) | −26.1899 | + | 20.3607i | −0.141567 | + | 0.110058i | ||||
\(186\) | 158.091 | 0.849951 | ||||||||
\(187\) | −8.30391 | + | 2.22503i | −0.0444060 | + | 0.0118985i | ||||
\(188\) | 24.5449 | − | 14.1710i | 0.130558 | − | 0.0753775i | ||||
\(189\) | −53.9183 | + | 31.1298i | −0.285282 | + | 0.164708i | ||||
\(190\) | 7.62029 | + | 2.04185i | 0.0401068 | + | 0.0107466i | ||||
\(191\) | −63.0903 | + | 63.0903i | −0.330316 | + | 0.330316i | −0.852706 | − | 0.522391i | \(-0.825040\pi\) |
0.522391 | + | 0.852706i | \(0.325040\pi\) | |||||||
\(192\) | −18.1547 | − | 31.4448i | −0.0945556 | − | 0.163775i | ||||
\(193\) | −222.820 | + | 222.820i | −1.15451 | + | 1.15451i | −0.168866 | + | 0.985639i | \(0.554011\pi\) |
−0.985639 | + | 0.168866i | \(0.945989\pi\) | |||||||
\(194\) | 50.8869 | − | 88.1387i | 0.262304 | − | 0.454323i | ||||
\(195\) | 62.8982 | 0.322555 | ||||||||
\(196\) | − | 42.3070i | − | 0.215852i | ||||||
\(197\) | 38.6001 | − | 66.8573i | 0.195940 | − | 0.339377i | −0.751269 | − | 0.659997i | \(-0.770558\pi\) |
0.947208 | + | 0.320619i | \(0.103891\pi\) | |||||||
\(198\) | −40.9477 | − | 10.9719i | −0.206806 | − | 0.0554136i | ||||
\(199\) | 119.311 | + | 119.311i | 0.599552 | + | 0.599552i | 0.940193 | − | 0.340641i | \(-0.110644\pi\) |
−0.340641 | + | 0.940193i | \(0.610644\pi\) | |||||||
\(200\) | 66.1051 | − | 17.7128i | 0.330526 | − | 0.0885641i | ||||
\(201\) | 62.6034 | − | 108.432i | 0.311460 | − | 0.539464i | ||||
\(202\) | 40.7907 | + | 152.233i | 0.201934 | + | 0.753629i | ||||
\(203\) | 69.2402 | − | 258.408i | 0.341085 | − | 1.27295i | ||||
\(204\) | 29.1683 | + | 7.81561i | 0.142982 | + | 0.0383118i | ||||
\(205\) | −21.0885 | + | 5.65066i | −0.102871 | + | 0.0275642i | ||||
\(206\) | 161.201 | + | 93.0692i | 0.782527 | + | 0.451792i | ||||
\(207\) | 135.049 | + | 504.010i | 0.652411 | + | 2.43483i | ||||
\(208\) | 43.7188 | − | 43.7188i | 0.210186 | − | 0.210186i | ||||
\(209\) | 4.16153 | − | 15.5310i | 0.0199116 | − | 0.0743112i | ||||
\(210\) | 26.2994 | + | 15.1840i | 0.125235 | + | 0.0723047i | ||||
\(211\) | −137.533 | −0.651815 | −0.325907 | − | 0.945402i | \(-0.605670\pi\) | ||||
−0.325907 | + | 0.945402i | \(0.605670\pi\) | |||||||
\(212\) | 107.850i | 0.508727i | ||||||||
\(213\) | −357.005 | − | 206.117i | −1.67608 | − | 0.967686i | ||||
\(214\) | 49.1768 | + | 49.1768i | 0.229798 | + | 0.229798i | ||||
\(215\) | 44.1074 | − | 25.4654i | 0.205150 | − | 0.118444i | ||||
\(216\) | 23.5967 | + | 23.5967i | 0.109244 | + | 0.109244i | ||||
\(217\) | −33.6391 | + | 125.543i | −0.155019 | + | 0.578539i | ||||
\(218\) | −43.4676 | − | 75.2881i | −0.199393 | − | 0.345358i | ||||
\(219\) | −252.098 | − | 436.647i | −1.15113 | − | 1.99382i | ||||
\(220\) | 1.19934 | + | 4.47601i | 0.00545156 | + | 0.0203455i | ||||
\(221\) | 51.4199i | 0.232669i | ||||||||
\(222\) | −32.4871 | − | 235.257i | −0.146338 | − | 1.05972i | ||||
\(223\) | 413.121 | 1.85256 | 0.926280 | − | 0.376835i | \(-0.122988\pi\) | ||||
0.926280 | + | 0.376835i | \(0.122988\pi\) | |||||||
\(224\) | 28.8339 | − | 7.72603i | 0.128723 | − | 0.0344912i | ||||
\(225\) | −243.062 | + | 140.332i | −1.08027 | + | 0.623697i | ||||
\(226\) | 123.426 | − | 71.2601i | 0.546133 | − | 0.315310i | ||||
\(227\) | −58.6106 | − | 15.7047i | −0.258196 | − | 0.0691835i | 0.127399 | − | 0.991852i | \(-0.459337\pi\) |
−0.385595 | + | 0.922668i | \(0.626004\pi\) | |||||||
\(228\) | −39.9364 | + | 39.9364i | −0.175160 | + | 0.175160i | ||||
\(229\) | −193.773 | − | 335.624i | −0.846169 | − | 1.46561i | −0.884602 | − | 0.466346i | \(-0.845570\pi\) |
0.0384334 | − | 0.999261i | \(-0.487763\pi\) | |||||||
\(230\) | 40.3313 | − | 40.3313i | 0.175353 | − | 0.175353i | ||||
\(231\) | 30.9467 | − | 53.6013i | 0.133968 | − | 0.232040i | ||||
\(232\) | −143.391 | −0.618064 | ||||||||
\(233\) | 300.991i | 1.29181i | 0.763420 | + | 0.645903i | \(0.223519\pi\) | ||||
−0.763420 | + | 0.645903i | \(0.776481\pi\) | |||||||
\(234\) | −126.779 | + | 219.588i | −0.541791 | + | 0.938410i | ||||
\(235\) | 12.2724 | + | 3.28839i | 0.0522231 | + | 0.0139931i | ||||
\(236\) | −117.834 | − | 117.834i | −0.499297 | − | 0.499297i | ||||
\(237\) | 494.575 | − | 132.521i | 2.08681 | − | 0.559160i | ||||
\(238\) | −12.4131 | + | 21.5000i | −0.0521557 | + | 0.0903363i | ||||
\(239\) | −27.4484 | − | 102.439i | −0.114847 | − | 0.428614i | 0.884429 | − | 0.466676i | \(-0.154548\pi\) |
−0.999275 | + | 0.0380612i | \(0.987882\pi\) | |||||||
\(240\) | 4.21281 | − | 15.7224i | 0.0175534 | − | 0.0655100i | ||||
\(241\) | 154.225 | + | 41.3245i | 0.639938 | + | 0.171471i | 0.564175 | − | 0.825655i | \(-0.309194\pi\) |
0.0757627 | + | 0.997126i | \(0.475861\pi\) | |||||||
\(242\) | −156.166 | + | 41.8447i | −0.645316 | + | 0.172912i | ||||
\(243\) | 291.818 | + | 168.481i | 1.20090 | + | 0.693338i | ||||
\(244\) | 26.2324 | + | 97.9008i | 0.107510 | + | 0.401233i | ||||
\(245\) | 13.4108 | − | 13.4108i | 0.0547379 | − | 0.0547379i | ||||
\(246\) | 40.4534 | − | 150.974i | 0.164445 | − | 0.613717i | ||||
\(247\) | −83.2875 | − | 48.0860i | −0.337196 | − | 0.194680i | ||||
\(248\) | 69.6640 | 0.280903 | ||||||||
\(249\) | − | 11.6025i | − | 0.0465965i | ||||||
\(250\) | 54.0211 | + | 31.1891i | 0.216084 | + | 0.124756i | ||||
\(251\) | −171.928 | − | 171.928i | −0.684970 | − | 0.684970i | 0.276145 | − | 0.961116i | \(-0.410943\pi\) |
−0.961116 | + | 0.276145i | \(0.910943\pi\) | |||||||
\(252\) | −106.019 | + | 61.2104i | −0.420712 | + | 0.242898i | ||||
\(253\) | −82.1999 | − | 82.1999i | −0.324901 | − | 0.324901i | ||||
\(254\) | 38.7266 | − | 144.530i | 0.152467 | − | 0.569015i | ||||
\(255\) | 6.76852 | + | 11.7234i | 0.0265432 | + | 0.0459742i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1.31699 | + | 4.91508i | 0.00512448 | + | 0.0191248i | 0.968441 | − | 0.249244i | \(-0.0801821\pi\) |
−0.963316 | + | 0.268369i | \(0.913515\pi\) | |||||||
\(258\) | 364.617i | 1.41324i | ||||||||
\(259\) | 193.735 | + | 24.2603i | 0.748012 | + | 0.0936692i | ||||
\(260\) | 27.7166 | 0.106602 | ||||||||
\(261\) | 568.016 | − | 152.199i | 2.17631 | − | 0.583139i | ||||
\(262\) | −173.443 | + | 100.137i | −0.661995 | + | 0.382203i | ||||
\(263\) | 349.916 | − | 202.024i | 1.33048 | − | 0.768153i | 0.345107 | − | 0.938563i | \(-0.387843\pi\) |
0.985373 | + | 0.170410i | \(0.0545093\pi\) | |||||||
\(264\) | −32.0441 | − | 8.58619i | −0.121379 | − | 0.0325234i | ||||
\(265\) | −34.1871 | + | 34.1871i | −0.129008 | + | 0.129008i | ||||
\(266\) | −23.2165 | − | 40.2121i | −0.0872800 | − | 0.151173i | ||||
\(267\) | 431.572 | − | 431.572i | 1.61638 | − | 1.61638i | ||||
\(268\) | 27.5867 | − | 47.7816i | 0.102935 | − | 0.178289i | ||||
\(269\) | 318.390 | 1.18361 | 0.591803 | − | 0.806083i | \(-0.298416\pi\) | ||||
0.591803 | + | 0.806083i | \(0.298416\pi\) | |||||||
\(270\) | 14.9597i | 0.0554062i | ||||||||
\(271\) | 11.4462 | − | 19.8254i | 0.0422369 | − | 0.0731564i | −0.844134 | − | 0.536132i | \(-0.819885\pi\) |
0.886371 | + | 0.462976i | \(0.153218\pi\) | |||||||
\(272\) | 12.8532 | + | 3.44401i | 0.0472545 | + | 0.0126618i | ||||
\(273\) | −261.771 | − | 261.771i | −0.958869 | − | 0.958869i | ||||
\(274\) | 104.440 | − | 27.9846i | 0.381167 | − | 0.102133i | ||||
\(275\) | 31.2642 | − | 54.1511i | 0.113688 | − | 0.196913i | ||||
\(276\) | 105.684 | + | 394.419i | 0.382914 | + | 1.42905i | ||||
\(277\) | 17.6380 | − | 65.8257i | 0.0636749 | − | 0.237638i | −0.926753 | − | 0.375672i | \(-0.877412\pi\) |
0.990427 | + | 0.138034i | \(0.0440784\pi\) | |||||||
\(278\) | −62.1483 | − | 16.6526i | −0.223555 | − | 0.0599014i | ||||
\(279\) | −275.960 | + | 73.9434i | −0.989105 | + | 0.265030i | ||||
\(280\) | 11.5890 | + | 6.69094i | 0.0413895 | + | 0.0238962i | ||||
\(281\) | 81.9314 | + | 305.772i | 0.291571 | + | 1.08816i | 0.943903 | + | 0.330224i | \(0.107124\pi\) |
−0.652332 | + | 0.757933i | \(0.726209\pi\) | |||||||
\(282\) | −64.3174 | + | 64.3174i | −0.228076 | + | 0.228076i | ||||
\(283\) | 15.3061 | − | 57.1232i | 0.0540852 | − | 0.201849i | −0.933596 | − | 0.358327i | \(-0.883347\pi\) |
0.987681 | + | 0.156478i | \(0.0500140\pi\) | |||||||
\(284\) | −157.317 | − | 90.8271i | −0.553934 | − | 0.319814i | ||||
\(285\) | −25.3187 | −0.0888375 | ||||||||
\(286\) | − | 56.4896i | − | 0.197516i | ||||||
\(287\) | 111.284 | + | 64.2497i | 0.387748 | + | 0.223866i | ||||
\(288\) | 46.3981 | + | 46.3981i | 0.161104 | + | 0.161104i | ||||
\(289\) | 240.697 | − | 138.967i | 0.832863 | − | 0.480854i | ||||
\(290\) | −45.4531 | − | 45.4531i | −0.156735 | − | 0.156735i | ||||
\(291\) | −84.5368 | + | 315.496i | −0.290504 | + | 1.08418i | ||||
\(292\) | −111.089 | − | 192.412i | −0.380442 | − | 0.658945i | ||||
\(293\) | 120.598 | + | 208.882i | 0.411598 | + | 0.712909i | 0.995065 | − | 0.0992280i | \(-0.0316373\pi\) |
−0.583466 | + | 0.812137i | \(0.698304\pi\) | |||||||
\(294\) | 35.1416 | + | 131.150i | 0.119529 | + | 0.446090i | ||||
\(295\) | − | 74.7039i | − | 0.253234i | ||||||
\(296\) | −14.3157 | − | 103.668i | −0.0483638 | − | 0.350230i | ||||
\(297\) | 30.4896 | 0.102658 | ||||||||
\(298\) | −59.0619 | + | 15.8256i | −0.198194 | + | 0.0531060i | ||||
\(299\) | −602.156 | + | 347.655i | −2.01390 | + | 1.16273i | ||||
\(300\) | −190.211 | + | 109.818i | −0.634036 | + | 0.366061i | ||||
\(301\) | −289.549 | − | 77.5845i | −0.961958 | − | 0.257756i | ||||
\(302\) | 41.4590 | − | 41.4590i | 0.137281 | − | 0.137281i | ||||
\(303\) | −252.900 | − | 438.036i | −0.834653 | − | 1.44566i | ||||
\(304\) | −17.5983 | + | 17.5983i | −0.0578892 | + | 0.0578892i | ||||
\(305\) | −22.7179 | + | 39.3486i | −0.0744851 | + | 0.129012i | ||||
\(306\) | −54.5711 | −0.178337 | ||||||||
\(307\) | 341.236i | 1.11152i | 0.831344 | + | 0.555759i | \(0.187572\pi\) | ||||
−0.831344 | + | 0.555759i | \(0.812428\pi\) | |||||||
\(308\) | 13.6369 | − | 23.6198i | 0.0442757 | − | 0.0766877i | ||||
\(309\) | −577.023 | − | 154.613i | −1.86739 | − | 0.500365i | ||||
\(310\) | 22.0826 | + | 22.0826i | 0.0712342 | + | 0.0712342i | ||||
\(311\) | −334.280 | + | 89.5700i | −1.07485 | + | 0.288006i | −0.752486 | − | 0.658608i | \(-0.771146\pi\) |
−0.322368 | + | 0.946614i | \(0.604479\pi\) | |||||||
\(312\) | −99.2125 | + | 171.841i | −0.317989 | + | 0.550773i | ||||
\(313\) | 127.067 | + | 474.220i | 0.405964 | + | 1.51508i | 0.802271 | + | 0.596960i | \(0.203625\pi\) |
−0.396307 | + | 0.918118i | \(0.629708\pi\) | |||||||
\(314\) | −47.5838 | + | 177.585i | −0.151541 | + | 0.565558i | ||||
\(315\) | −53.0097 | − | 14.2039i | −0.168285 | − | 0.0450918i | ||||
\(316\) | 217.938 | − | 58.3964i | 0.689678 | − | 0.184799i | ||||
\(317\) | −26.1348 | − | 15.0889i | −0.0824441 | − | 0.0475991i | 0.458211 | − | 0.888843i | \(-0.348490\pi\) |
−0.540655 | + | 0.841244i | \(0.681824\pi\) | |||||||
\(318\) | −89.5839 | − | 334.332i | −0.281711 | − | 1.05136i | ||||
\(319\) | −92.6387 | + | 92.6387i | −0.290403 | + | 0.290403i | ||||
\(320\) | 1.85641 | − | 6.92820i | 0.00580127 | − | 0.0216506i | ||||
\(321\) | −193.294 | − | 111.599i | −0.602163 | − | 0.347659i | ||||
\(322\) | −335.703 | −1.04256 | ||||||||
\(323\) | − | 20.6983i | − | 0.0640814i | ||||||
\(324\) | 88.0694 | + | 50.8469i | 0.271819 | + | 0.156935i | ||||
\(325\) | −264.457 | − | 264.457i | −0.813713 | − | 0.813713i | ||||
\(326\) | 174.346 | − | 100.659i | 0.534803 | − | 0.308769i | ||||
\(327\) | 197.285 | + | 197.285i | 0.603318 | + | 0.603318i | ||||
\(328\) | 17.8261 | − | 66.5280i | 0.0543479 | − | 0.202829i | ||||
\(329\) | −37.3900 | − | 64.7613i | −0.113647 | − | 0.196843i | ||||
\(330\) | −7.43586 | − | 12.8793i | −0.0225329 | − | 0.0390281i | ||||
\(331\) | 66.7338 | + | 249.054i | 0.201613 | + | 0.752429i | 0.990455 | + | 0.137834i | \(0.0440139\pi\) |
−0.788843 | + | 0.614595i | \(0.789319\pi\) | |||||||
\(332\) | − | 5.11275i | − | 0.0153998i | ||||||
\(333\) | 166.745 | + | 395.466i | 0.500736 | + | 1.18759i | ||||
\(334\) | 399.208 | 1.19523 | ||||||||
\(335\) | 23.8908 | − | 6.40151i | 0.0713157 | − | 0.0191090i | ||||
\(336\) | −82.9668 | + | 47.9009i | −0.246925 | + | 0.142562i | ||||
\(337\) | 375.722 | − | 216.923i | 1.11490 | − | 0.643689i | 0.174808 | − | 0.984603i | \(-0.444070\pi\) |
0.940095 | + | 0.340913i | \(0.110736\pi\) | |||||||
\(338\) | −95.5078 | − | 25.5912i | −0.282567 | − | 0.0757137i | ||||
\(339\) | −323.426 | + | 323.426i | −0.954059 | + | 0.954059i | ||||
\(340\) | 2.98260 | + | 5.16602i | 0.00877236 | + | 0.0151942i | ||||
\(341\) | 45.0069 | − | 45.0069i | 0.131985 | − | 0.131985i | ||||
\(342\) | 51.0330 | − | 88.3917i | 0.149219 | − | 0.258455i | ||||
\(343\) | −370.198 | −1.07930 | ||||||||
\(344\) | 160.671i | 0.467068i | ||||||||
\(345\) | −91.5252 | + | 158.526i | −0.265290 | + | 0.459497i | ||||
\(346\) | 205.296 | + | 55.0088i | 0.593340 | + | 0.158985i | ||||
\(347\) | −338.398 | − | 338.398i | −0.975211 | − | 0.975211i | 0.0244886 | − | 0.999700i | \(-0.492204\pi\) |
−0.999700 | + | 0.0244886i | \(0.992204\pi\) | |||||||
\(348\) | 444.507 | − | 119.105i | 1.27732 | − | 0.342257i | ||||
\(349\) | −28.1189 | + | 48.7033i | −0.0805698 | + | 0.139551i | −0.903495 | − | 0.428599i | \(-0.859007\pi\) |
0.822925 | + | 0.568150i | \(0.192341\pi\) | |||||||
\(350\) | −46.7351 | − | 174.418i | −0.133529 | − | 0.498336i | ||||
\(351\) | 47.1998 | − | 176.152i | 0.134472 | − | 0.501857i | ||||
\(352\) | −14.1205 | − | 3.78357i | −0.0401150 | − | 0.0107488i | ||||
\(353\) | −196.878 | + | 52.7533i | −0.557729 | + | 0.149443i | −0.526663 | − | 0.850074i | \(-0.676557\pi\) |
−0.0310660 | + | 0.999517i | \(0.509890\pi\) | |||||||
\(354\) | 463.159 | + | 267.405i | 1.30836 | + | 0.755382i | ||||
\(355\) | −21.0765 | − | 78.6586i | −0.0593705 | − | 0.221574i | ||||
\(356\) | 190.176 | − | 190.176i | 0.534202 | − | 0.534202i | ||||
\(357\) | 20.6214 | − | 76.9601i | 0.0577630 | − | 0.215575i | ||||
\(358\) | 83.1071 | + | 47.9819i | 0.232143 | + | 0.134028i | ||||
\(359\) | 523.169 | 1.45730 | 0.728648 | − | 0.684889i | \(-0.240149\pi\) | ||||
0.728648 | + | 0.684889i | \(0.240149\pi\) | |||||||
\(360\) | 29.4152i | 0.0817089i | ||||||||
\(361\) | −279.109 | − | 161.144i | −0.773155 | − | 0.446382i | ||||
\(362\) | −205.247 | − | 205.247i | −0.566981 | − | 0.566981i | ||||
\(363\) | 449.353 | − | 259.434i | 1.23789 | − | 0.714695i | ||||
\(364\) | −115.352 | − | 115.352i | −0.316900 | − | 0.316900i | ||||
\(365\) | 25.7783 | − | 96.2059i | 0.0706255 | − | 0.263578i | ||||
\(366\) | −162.639 | − | 281.700i | −0.444370 | − | 0.769671i | ||||
\(367\) | 235.671 | + | 408.195i | 0.642156 | + | 1.11225i | 0.984950 | + | 0.172837i | \(0.0552933\pi\) |
−0.342794 | + | 0.939411i | \(0.611373\pi\) | |||||||
\(368\) | 46.5706 | + | 173.804i | 0.126550 | + | 0.472293i | ||||
\(369\) | 282.459i | 0.765472i | ||||||||
\(370\) | 28.3236 | − | 37.3993i | 0.0765502 | − | 0.101079i | ||||
\(371\) | 284.561 | 0.767011 | ||||||||
\(372\) | −215.956 | + | 57.8653i | −0.580527 | + | 0.155552i | ||||
\(373\) | −51.7992 | + | 29.9063i | −0.138872 | + | 0.0801776i | −0.567826 | − | 0.823148i | \(-0.692215\pi\) |
0.428954 | + | 0.903326i | \(0.358882\pi\) | |||||||
\(374\) | 10.5289 | − | 6.07889i | 0.0281522 | − | 0.0162537i | ||||
\(375\) | −193.371 | − | 51.8135i | −0.515655 | − | 0.138169i | ||||
\(376\) | −28.3420 | + | 28.3420i | −0.0753775 | + | 0.0753775i | ||||
\(377\) | 391.805 | + | 678.626i | 1.03927 | + | 1.80007i | ||||
\(378\) | 62.2595 | − | 62.2595i | 0.164708 | − | 0.164708i | ||||
\(379\) | 212.159 | − | 367.470i | 0.559787 | − | 0.969579i | −0.437727 | − | 0.899108i | \(-0.644216\pi\) |
0.997514 | − | 0.0704710i | \(-0.0224502\pi\) | |||||||
\(380\) | −11.1569 | −0.0293602 | ||||||||
\(381\) | 480.205i | 1.26038i | ||||||||
\(382\) | 63.0903 | − | 109.276i | 0.165158 | − | 0.286062i | ||||
\(383\) | 207.328 | + | 55.5535i | 0.541327 | + | 0.145048i | 0.519114 | − | 0.854705i | \(-0.326262\pi\) |
0.0222134 | + | 0.999753i | \(0.492929\pi\) | |||||||
\(384\) | 36.3093 | + | 36.3093i | 0.0945556 | + | 0.0945556i | ||||
\(385\) | 11.8099 | − | 3.16446i | 0.0306751 | − | 0.00821937i | ||||
\(386\) | 222.820 | − | 385.935i | 0.577253 | − | 0.999831i | ||||
\(387\) | −170.541 | − | 636.469i | −0.440675 | − | 1.64462i | ||||
\(388\) | −37.2518 | + | 139.026i | −0.0960098 | + | 0.358313i | ||||
\(389\) | 428.270 | + | 114.755i | 1.10095 | + | 0.294999i | 0.763152 | − | 0.646219i | \(-0.223651\pi\) |
0.337800 | + | 0.941218i | \(0.390317\pi\) | |||||||
\(390\) | −85.9206 | + | 23.0224i | −0.220309 | + | 0.0590317i | ||||
\(391\) | −129.597 | − | 74.8228i | −0.331450 | − | 0.191363i | ||||
\(392\) | 15.4854 | + | 57.7925i | 0.0395037 | + | 0.147430i | ||||
\(393\) | 454.490 | − | 454.490i | 1.15646 | − | 1.15646i | ||||
\(394\) | −28.2572 | + | 105.457i | −0.0717189 | + | 0.267658i | ||||
\(395\) | 87.5945 | + | 50.5727i | 0.221758 | + | 0.128032i | ||||
\(396\) | 59.9516 | 0.151393 | ||||||||
\(397\) | 104.624i | 0.263536i | 0.991281 | + | 0.131768i | \(0.0420655\pi\) | ||||
−0.991281 | + | 0.131768i | \(0.957935\pi\) | |||||||
\(398\) | −206.652 | − | 119.311i | −0.519227 | − | 0.299776i | ||||
\(399\) | 105.372 | + | 105.372i | 0.264090 | + | 0.264090i | ||||
\(400\) | −83.8179 | + | 48.3923i | −0.209545 | + | 0.120981i | ||||
\(401\) | −466.509 | − | 466.509i | −1.16336 | − | 1.16336i | −0.983735 | − | 0.179629i | \(-0.942510\pi\) |
−0.179629 | − | 0.983735i | \(-0.557490\pi\) | |||||||
\(402\) | −45.8289 | + | 171.036i | −0.114002 | + | 0.425462i | ||||
\(403\) | −190.352 | − | 329.698i | −0.472336 | − | 0.818110i | ||||
\(404\) | −111.442 | − | 193.024i | −0.275847 | − | 0.477782i | ||||
\(405\) | 11.7991 | + | 44.0347i | 0.0291335 | + | 0.108728i | ||||
\(406\) | 378.335i | 0.931861i | ||||||||
\(407\) | −76.2242 | − | 57.7267i | −0.187283 | − | 0.141835i | ||||
\(408\) | −42.7053 | −0.104670 | ||||||||
\(409\) | −133.745 | + | 35.8368i | −0.327004 | + | 0.0876205i | −0.418586 | − | 0.908177i | \(-0.637474\pi\) |
0.0915821 | + | 0.995798i | \(0.470808\pi\) | |||||||
\(410\) | 26.7392 | − | 15.4379i | 0.0652175 | − | 0.0376534i | ||||
\(411\) | −300.515 | + | 173.503i | −0.731181 | + | 0.422147i | ||||
\(412\) | −254.270 | − | 68.1314i | −0.617160 | − | 0.165367i | ||||
\(413\) | −310.904 | + | 310.904i | −0.752795 | + | 0.752795i | ||||
\(414\) | −368.961 | − | 639.059i | −0.891210 | − | 1.54362i | ||||
\(415\) | 1.62068 | − | 1.62068i | 0.00390524 | − | 0.00390524i | ||||
\(416\) | −43.7188 | + | 75.7232i | −0.105093 | + | 0.182027i | ||||
\(417\) | 206.490 | 0.495180 | ||||||||
\(418\) | 22.7390i | 0.0543996i | ||||||||
\(419\) | −316.954 | + | 548.981i | −0.756454 | + | 1.31022i | 0.188195 | + | 0.982132i | \(0.439736\pi\) |
−0.944648 | + | 0.328084i | \(0.893597\pi\) | |||||||
\(420\) | −41.4834 | − | 11.1154i | −0.0987700 | − | 0.0264653i | ||||
\(421\) | −383.928 | − | 383.928i | −0.911942 | − | 0.911942i | 0.0844826 | − | 0.996425i | \(-0.473076\pi\) |
−0.996425 | + | 0.0844826i | \(0.973076\pi\) | |||||||
\(422\) | 187.873 | − | 50.3405i | 0.445198 | − | 0.119290i | ||||
\(423\) | 82.1882 | − | 142.354i | 0.194298 | − | 0.336535i | ||||
\(424\) | −39.4759 | − | 147.326i | −0.0931035 | − | 0.347467i | ||||
\(425\) | 20.8330 | − | 77.7496i | 0.0490187 | − | 0.182940i | ||||
\(426\) | 563.123 | + | 150.888i | 1.32188 | + | 0.354198i | ||||
\(427\) | 258.310 | − | 69.2140i | 0.604942 | − | 0.162094i | ||||
\(428\) | −85.1767 | − | 49.1768i | −0.199011 | − | 0.114899i | ||||
\(429\) | 46.9222 | + | 175.116i | 0.109376 | + | 0.408196i | ||||
\(430\) | −50.9308 | + | 50.9308i | −0.118444 | + | 0.118444i | ||||
\(431\) | −182.634 | + | 681.599i | −0.423744 | + | 1.58144i | 0.342905 | + | 0.939370i | \(0.388589\pi\) |
−0.766650 | + | 0.642066i | \(0.778078\pi\) | |||||||
\(432\) | −40.8706 | − | 23.5967i | −0.0946079 | − | 0.0546219i | ||||
\(433\) | −260.578 | −0.601797 | −0.300898 | − | 0.953656i | \(-0.597286\pi\) | ||||
−0.300898 | + | 0.953656i | \(0.597286\pi\) | |||||||
\(434\) | − | 183.808i | − | 0.423520i | ||||||
\(435\) | 178.658 | + | 103.148i | 0.410708 | + | 0.237123i | ||||
\(436\) | 86.9352 | + | 86.9352i | 0.199393 | + | 0.199393i | ||||
\(437\) | 242.388 | − | 139.943i | 0.554665 | − | 0.320236i | ||||
\(438\) | 504.196 | + | 504.196i | 1.15113 | + | 1.15113i | ||||
\(439\) | 170.599 | − | 636.684i | 0.388608 | − | 1.45031i | −0.443792 | − | 0.896130i | \(-0.646367\pi\) |
0.832400 | − | 0.554175i | \(-0.186966\pi\) | |||||||
\(440\) | −3.27667 | − | 5.67536i | −0.00744697 | − | 0.0128985i | ||||
\(441\) | −122.685 | − | 212.497i | −0.278198 | − | 0.481853i | ||||
\(442\) | −18.8210 | − | 70.2409i | −0.0425814 | − | 0.158916i | ||||
\(443\) | − | 472.541i | − | 1.06668i | −0.845900 | − | 0.533342i | \(-0.820936\pi\) | ||
0.845900 | − | 0.533342i | \(-0.179064\pi\) | |||||||
\(444\) | 130.488 | + | 309.477i | 0.293893 | + | 0.697019i | ||||
\(445\) | 120.567 | 0.270936 | ||||||||
\(446\) | −564.334 | + | 151.213i | −1.26532 | + | 0.339042i | ||||
\(447\) | 169.945 | − | 98.1177i | 0.380190 | − | 0.219503i | ||||
\(448\) | −36.5600 | + | 21.1079i | −0.0816071 | + | 0.0471159i | ||||
\(449\) | 733.716 | + | 196.599i | 1.63411 | + | 0.437859i | 0.955104 | − | 0.296272i | \(-0.0957435\pi\) |
0.679008 | + | 0.734131i | \(0.262410\pi\) | |||||||
\(450\) | 280.664 | − | 280.664i | 0.623697 | − | 0.623697i | ||||
\(451\) | −31.4642 | − | 54.4976i | −0.0697654 | − | 0.120837i | ||||
\(452\) | −142.520 | + | 142.520i | −0.315310 | + | 0.315310i | ||||
\(453\) | −94.0843 | + | 162.959i | −0.207692 | + | 0.359732i | ||||
\(454\) | 85.8118 | 0.189013 | ||||||||
\(455\) | − | 73.1299i | − | 0.160725i | ||||||
\(456\) | 39.9364 | − | 69.1720i | 0.0875799 | − | 0.151693i | ||||
\(457\) | 355.673 | + | 95.3022i | 0.778277 | + | 0.208539i | 0.626025 | − | 0.779803i | \(-0.284681\pi\) |
0.152252 | + | 0.988342i | \(0.451347\pi\) | |||||||
\(458\) | 387.545 | + | 387.545i | 0.846169 | + | 0.846169i | ||||
\(459\) | 37.9117 | − | 10.1584i | 0.0825962 | − | 0.0221316i | ||||
\(460\) | −40.3313 | + | 69.8559i | −0.0876767 | + | 0.151861i | ||||
\(461\) | 45.9133 | + | 171.351i | 0.0995950 | + | 0.371694i | 0.997676 | − | 0.0681364i | \(-0.0217053\pi\) |
−0.898081 | + | 0.439830i | \(0.855039\pi\) | |||||||
\(462\) | −22.6546 | + | 84.5480i | −0.0490358 | + | 0.183004i | ||||
\(463\) | −286.206 | − | 76.6887i | −0.618156 | − | 0.165634i | −0.0638667 | − | 0.997958i | \(-0.520343\pi\) |
−0.554289 | + | 0.832324i | \(0.687010\pi\) | |||||||
\(464\) | 195.876 | − | 52.4847i | 0.422146 | − | 0.113114i | ||||
\(465\) | −86.7979 | − | 50.1128i | −0.186662 | − | 0.107769i | ||||
\(466\) | −110.170 | − | 411.161i | −0.236417 | − | 0.882320i | ||||
\(467\) | −55.7642 | + | 55.7642i | −0.119409 | + | 0.119409i | −0.764286 | − | 0.644877i | \(-0.776909\pi\) |
0.644877 | + | 0.764286i | \(0.276909\pi\) | |||||||
\(468\) | 92.8088 | − | 346.367i | 0.198309 | − | 0.740101i | ||||
\(469\) | −126.071 | − | 72.7872i | −0.268808 | − | 0.155197i | ||||
\(470\) | −17.9681 | −0.0382300 | ||||||||
\(471\) | − | 590.033i | − | 1.25272i | ||||||
\(472\) | 204.095 | + | 117.834i | 0.432404 | + | 0.249649i | ||||
\(473\) | 103.803 | + | 103.803i | 0.219456 | + | 0.219456i | ||||
\(474\) | −627.096 | + | 362.054i | −1.32299 | + | 0.763827i | ||||
\(475\) | 106.453 | + | 106.453i | 0.224111 | + | 0.224111i | ||||
\(476\) | 9.08698 | − | 33.9131i | 0.0190903 | − | 0.0712460i | ||||
\(477\) | 312.752 | + | 541.703i | 0.655665 | + | 1.13564i | ||||
\(478\) | 74.9904 | + | 129.887i | 0.156884 | + | 0.271731i | ||||
\(479\) | −83.2380 | − | 310.648i | −0.173774 | − | 0.648535i | −0.996757 | − | 0.0804687i | \(-0.974358\pi\) |
0.822983 | − | 0.568067i | \(-0.192308\pi\) | |||||||
\(480\) | 23.0192i | 0.0479567i | ||||||||
\(481\) | −451.513 | + | 351.017i | −0.938696 | + | 0.729765i | ||||
\(482\) | −225.801 | −0.468467 | ||||||||
\(483\) | 1040.67 | − | 278.847i | 2.15460 | − | 0.577322i | ||||
\(484\) | 198.011 | − | 114.322i | 0.409114 | − | 0.236202i | ||||
\(485\) | −55.8777 | + | 32.2610i | −0.115212 | + | 0.0665175i | ||||
\(486\) | −460.299 | − | 123.337i | −0.947117 | − | 0.253779i | ||||
\(487\) | −89.8601 | + | 89.8601i | −0.184518 | + | 0.184518i | −0.793321 | − | 0.608803i | \(-0.791650\pi\) |
0.608803 | + | 0.793321i | \(0.291650\pi\) | |||||||
\(488\) | −71.6683 | − | 124.133i | −0.146861 | − | 0.254371i | ||||
\(489\) | −456.856 | + | 456.856i | −0.934267 | + | 0.934267i | ||||
\(490\) | −13.4108 | + | 23.2282i | −0.0273690 | + | 0.0474044i | ||||
\(491\) | −503.090 | −1.02462 | −0.512312 | − | 0.858799i | \(-0.671211\pi\) | ||||
−0.512312 | + | 0.858799i | \(0.671211\pi\) | |||||||
\(492\) | 221.042i | 0.449272i | ||||||||
\(493\) | −84.3248 | + | 146.055i | −0.171044 | + | 0.296257i | ||||
\(494\) | 131.374 | + | 35.2014i | 0.265938 | + | 0.0712579i | ||||
\(495\) | 19.0039 | + | 19.0039i | 0.0383917 | + | 0.0383917i | ||||
\(496\) | −95.1627 | + | 25.4988i | −0.191860 | + | 0.0514088i | ||||
\(497\) | −239.646 | + | 415.080i | −0.482186 | + | 0.835170i | ||||
\(498\) | 4.24682 | + | 15.8494i | 0.00852776 | + | 0.0318260i | ||||
\(499\) | 233.400 | − | 871.060i | 0.467735 | − | 1.74561i | −0.179923 | − | 0.983681i | \(-0.557585\pi\) |
0.647658 | − | 0.761931i | \(-0.275749\pi\) | |||||||
\(500\) | −85.2102 | − | 22.8320i | −0.170420 | − | 0.0456640i | ||||
\(501\) | −1237.53 | + | 331.596i | −2.47012 | + | 0.661868i | ||||
\(502\) | 297.787 | + | 171.928i | 0.593202 | + | 0.342485i | ||||
\(503\) | 56.0079 | + | 209.024i | 0.111348 | + | 0.415555i | 0.998988 | − | 0.0449826i | \(-0.0143232\pi\) |
−0.887640 | + | 0.460538i | \(0.847657\pi\) | |||||||
\(504\) | 122.421 | − | 122.421i | 0.242898 | − | 0.242898i | ||||
\(505\) | 25.8603 | − | 96.5119i | 0.0512085 | − | 0.191113i | ||||
\(506\) | 142.374 | + | 82.1999i | 0.281372 | + | 0.162450i | ||||
\(507\) | 317.328 | 0.625894 | ||||||||
\(508\) | 211.606i | 0.416548i | ||||||||
\(509\) | −120.914 | − | 69.8096i | −0.237552 | − | 0.137151i | 0.376499 | − | 0.926417i | \(-0.377128\pi\) |
−0.614051 | + | 0.789266i | \(0.710461\pi\) | |||||||
\(510\) | −13.5370 | − | 13.5370i | −0.0265432 | − | 0.0265432i | ||||
\(511\) | −507.676 | + | 293.107i | −0.993496 | + | 0.573595i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −18.9995 | + | 70.9072i | −0.0370361 | + | 0.138221i | ||||
\(514\) | −3.59809 | − | 6.23208i | −0.00700018 | − | 0.0121247i | ||||
\(515\) | −59.0035 | − | 102.197i | −0.114570 | − | 0.198441i | ||||
\(516\) | −133.459 | − | 498.076i | −0.258642 | − | 0.965264i | ||||
\(517\) | 36.6210i | 0.0708337i | ||||||||
\(518\) | −273.527 | + | 37.7718i | −0.528044 | + | 0.0729185i | ||||
\(519\) | −682.102 | −1.31426 | ||||||||
\(520\) | −37.8616 | + | 10.1450i | −0.0728107 | + | 0.0195096i | ||||
\(521\) | 364.584 | − | 210.493i | 0.699778 | − | 0.404017i | −0.107487 | − | 0.994206i | \(-0.534280\pi\) |
0.807265 | + | 0.590190i | \(0.200947\pi\) | |||||||
\(522\) | −720.215 | + | 415.816i | −1.37972 | + | 0.796583i | ||||
\(523\) | 963.060 | + | 258.051i | 1.84142 | + | 0.493406i | 0.998970 | − | 0.0453753i | \(-0.0144484\pi\) |
0.842446 | + | 0.538781i | \(0.181115\pi\) | |||||||
\(524\) | 200.274 | − | 200.274i | 0.382203 | − | 0.382203i | ||||
\(525\) | 289.754 | + | 501.869i | 0.551913 | + | 0.955942i | ||||
\(526\) | −404.049 | + | 404.049i | −0.768153 | + | 0.768153i | ||||
\(527\) | 40.9677 | − | 70.9581i | 0.0777376 | − | 0.134645i | ||||
\(528\) | 46.9158 | 0.0888557 | ||||||||
\(529\) | − | 1494.54i | − | 2.82521i | ||||||
\(530\) | 34.1871 | − | 59.2138i | 0.0645040 | − | 0.111724i | ||||
\(531\) | −933.555 | − | 250.145i | −1.75811 | − | 0.471083i | ||||
\(532\) | 46.4329 | + | 46.4329i | 0.0872800 | + | 0.0872800i | ||||
\(533\) | −363.565 | + | 97.4171i | −0.682112 | + | 0.182771i | ||||
\(534\) | −431.572 | + | 747.505i | −0.808188 | + | 1.39982i | ||||
\(535\) | −11.4115 | − | 42.5883i | −0.0213299 | − | 0.0796044i | ||||
\(536\) | −20.1949 | + | 75.3682i | −0.0376770 | + | 0.140612i | ||||
\(537\) | −297.485 | − | 79.7108i | −0.553975 | − | 0.148437i | ||||
\(538\) | −434.929 | + | 116.539i | −0.808417 | + | 0.216615i | ||||
\(539\) | 47.3417 | + | 27.3327i | 0.0878324 | + | 0.0507101i | ||||
\(540\) | −5.47562 | − | 20.4353i | −0.0101400 | − | 0.0378432i | ||||
\(541\) | 475.702 | − | 475.702i | 0.879301 | − | 0.879301i | −0.114161 | − | 0.993462i | \(-0.536418\pi\) |
0.993462 | + | 0.114161i | \(0.0364180\pi\) | |||||||
\(542\) | −8.37920 | + | 31.2716i | −0.0154598 | + | 0.0576967i | ||||
\(543\) | 806.745 | + | 465.775i | 1.48572 | + | 0.857780i | ||||
\(544\) | −18.8184 | −0.0345927 | ||||||||
\(545\) | 55.1147i | 0.101128i | ||||||||
\(546\) | 453.401 | + | 261.771i | 0.830405 | + | 0.479434i | ||||
\(547\) | 381.426 | + | 381.426i | 0.697304 | + | 0.697304i | 0.963828 | − | 0.266524i | \(-0.0858751\pi\) |
−0.266524 | + | 0.963828i | \(0.585875\pi\) | |||||||
\(548\) | −132.424 | + | 76.4553i | −0.241650 | + | 0.139517i | ||||
\(549\) | 415.659 | + | 415.659i | 0.757120 | + | 0.757120i | ||||
\(550\) | −22.8870 | + | 85.4153i | −0.0416127 | + | 0.155301i | ||||
\(551\) | −157.715 | − | 273.170i | −0.286234 | − | 0.495772i | ||||
\(552\) | −288.735 | − | 500.103i | −0.523070 | − | 0.905984i | ||||
\(553\) | −154.078 | − | 575.028i | −0.278622 | − | 1.03983i | ||||
\(554\) | 96.3756i | 0.173963i | ||||||||
\(555\) | −56.7370 | + | 139.463i | −0.102229 | + | 0.251285i | ||||
\(556\) | 90.9914 | 0.163654 | ||||||||
\(557\) | −91.2573 | + | 24.4523i | −0.163837 | + | 0.0439000i | −0.339805 | − | 0.940496i | \(-0.610361\pi\) |
0.175968 | + | 0.984396i | \(0.443694\pi\) | |||||||
\(558\) | 349.904 | − | 202.017i | 0.627068 | − | 0.362038i | ||||
\(559\) | 760.409 | − | 439.022i | 1.36030 | − | 0.785371i | ||||
\(560\) | −18.2800 | − | 4.89811i | −0.0326428 | − | 0.00874662i | ||||
\(561\) | −27.5901 | + | 27.5901i | −0.0491801 | + | 0.0491801i | ||||
\(562\) | −223.841 | − | 387.703i | −0.398293 | − | 0.689864i | ||||
\(563\) | −346.836 | + | 346.836i | −0.616049 | + | 0.616049i | −0.944516 | − | 0.328467i | \(-0.893468\pi\) |
0.328467 | + | 0.944516i | \(0.393468\pi\) | |||||||
\(564\) | 64.3174 | − | 111.401i | 0.114038 | − | 0.197519i | ||||
\(565\) | −90.3542 | −0.159919 | ||||||||
\(566\) | 83.6342i | 0.147764i | ||||||||
\(567\) | 134.159 | − | 232.370i | 0.236612 | − | 0.409824i | ||||
\(568\) | 248.144 | + | 66.4901i | 0.436874 | + | 0.117060i | ||||
\(569\) | 100.632 | + | 100.632i | 0.176858 | + | 0.176858i | 0.789985 | − | 0.613127i | \(-0.210089\pi\) |
−0.613127 | + | 0.789985i | \(0.710089\pi\) | |||||||
\(570\) | 34.5860 | − | 9.26728i | 0.0606772 | − | 0.0162584i | ||||
\(571\) | 67.9181 | − | 117.638i | 0.118946 | − | 0.206020i | −0.800404 | − | 0.599461i | \(-0.795382\pi\) |
0.919350 | + | 0.393440i | \(0.128715\pi\) | |||||||
\(572\) | 20.6766 | + | 77.1663i | 0.0361480 | + | 0.134906i | ||||
\(573\) | −104.810 | + | 391.156i | −0.182914 | + | 0.682645i | ||||
\(574\) | −175.533 | − | 47.0340i | −0.305807 | − | 0.0819408i | ||||
\(575\) | 1051.35 | − | 281.707i | 1.82843 | − | 0.489926i | ||||
\(576\) | −80.3638 | − | 46.3981i | −0.139520 | − | 0.0805522i | ||||
\(577\) | −181.182 | − | 676.182i | −0.314008 | − | 1.17189i | −0.924910 | − | 0.380186i | \(-0.875860\pi\) |
0.610902 | − | 0.791706i | \(-0.290807\pi\) | |||||||
\(578\) | −277.933 | + | 277.933i | −0.480854 | + | 0.480854i | ||||
\(579\) | −370.163 | + | 1381.47i | −0.639314 | + | 2.38595i | ||||
\(580\) | 78.7271 | + | 45.4531i | 0.135736 | + | 0.0783674i | ||||
\(581\) | −13.4899 | −0.0232185 | ||||||||
\(582\) | − | 461.918i | − | 0.793673i | ||||||
\(583\) | −120.685 | − | 69.6773i | −0.207006 | − | 0.119515i | ||||
\(584\) | 222.178 | + | 222.178i | 0.380442 | + | 0.380442i | ||||
\(585\) | 139.213 | − | 80.3748i | 0.237971 | − | 0.137393i | ||||
\(586\) | −241.197 | − | 241.197i | −0.411598 | − | 0.411598i | ||||
\(587\) | 24.2262 | − | 90.4132i | 0.0412711 | − | 0.154026i | −0.942215 | − | 0.335008i | \(-0.891261\pi\) |
0.983486 | + | 0.180982i | \(0.0579276\pi\) | |||||||
\(588\) | −96.0088 | − | 166.292i | −0.163280 | − | 0.282810i | ||||
\(589\) | 76.6230 | + | 132.715i | 0.130090 | + | 0.225322i | ||||
\(590\) | 27.3435 | + | 102.047i | 0.0463449 | + | 0.172962i | ||||
\(591\) | − | 350.386i | − | 0.592870i | ||||||
\(592\) | 57.5007 | + | 136.373i | 0.0971296 | + | 0.230360i | ||||
\(593\) | 951.626 | 1.60477 | 0.802383 | − | 0.596810i | \(-0.203565\pi\) | ||||
0.802383 | + | 0.596810i | \(0.203565\pi\) | |||||||
\(594\) | −41.6495 | + | 11.1600i | −0.0701170 | + | 0.0187878i | ||||
\(595\) | 13.6305 | − | 7.86956i | 0.0229084 | − | 0.0132262i | ||||
\(596\) | 74.8875 | − | 43.2363i | 0.125650 | − | 0.0725442i | ||||
\(597\) | 739.720 | + | 198.207i | 1.23906 | + | 0.332005i | ||||
\(598\) | 695.310 | − | 695.310i | 1.16273 | − | 1.16273i | ||||
\(599\) | 123.946 | + | 214.681i | 0.206922 | + | 0.358399i | 0.950743 | − | 0.309979i | \(-0.100322\pi\) |
−0.743822 | + | 0.668378i | \(0.766989\pi\) | |||||||
\(600\) | 219.637 | − | 219.637i | 0.366061 | − | 0.366061i | ||||
\(601\) | 383.142 | − | 663.622i | 0.637508 | − | 1.10420i | −0.348470 | − | 0.937320i | \(-0.613299\pi\) |
0.985978 | − | 0.166876i | \(-0.0533680\pi\) | |||||||
\(602\) | 423.930 | 0.704202 | ||||||||
\(603\) | − | 319.992i | − | 0.530667i | ||||||
\(604\) | −41.4590 | + | 71.8090i | −0.0686407 | + | 0.118889i | ||||
\(605\) | 99.0056 | + | 26.5285i | 0.163646 | + | 0.0438487i | ||||
\(606\) | 505.800 | + | 505.800i | 0.834653 | + | 0.834653i | ||||
\(607\) | −574.672 | + | 153.983i | −0.946741 | + | 0.253678i | −0.698979 | − | 0.715142i | \(-0.746362\pi\) |
−0.247762 | + | 0.968821i | \(0.579695\pi\) | |||||||
\(608\) | 17.5983 | − | 30.4812i | 0.0289446 | − | 0.0501335i | ||||
\(609\) | −314.258 | − | 1172.83i | −0.516023 | − | 1.92583i | ||||
\(610\) | 16.6307 | − | 62.0666i | 0.0272634 | − | 0.101749i | ||||
\(611\) | 211.576 | + | 56.6917i | 0.346278 | + | 0.0927850i | ||||
\(612\) | 74.5456 | − | 19.9744i | 0.121806 | − | 0.0326380i | ||||
\(613\) | −855.706 | − | 494.042i | −1.39593 | − | 0.805941i | −0.401968 | − | 0.915654i | \(-0.631674\pi\) |
−0.993963 | + | 0.109712i | \(0.965007\pi\) | |||||||
\(614\) | −124.901 | − | 466.137i | −0.203422 | − | 0.759181i | ||||
\(615\) | −70.0674 | + | 70.0674i | −0.113931 | + | 0.113931i | ||||
\(616\) | −9.98291 | + | 37.2567i | −0.0162060 | + | 0.0604817i | ||||
\(617\) | 162.062 | + | 93.5667i | 0.262662 | + | 0.151648i | 0.625548 | − | 0.780186i | \(-0.284875\pi\) |
−0.362886 | + | 0.931833i | \(0.618209\pi\) | |||||||
\(618\) | 844.820 | 1.36702 | ||||||||
\(619\) | 1130.11i | 1.82570i | 0.408296 | + | 0.912850i | \(0.366123\pi\) | ||||
−0.408296 | + | 0.912850i | \(0.633877\pi\) | |||||||
\(620\) | −38.2482 | − | 22.0826i | −0.0616906 | − | 0.0356171i | ||||
\(621\) | 375.285 | + | 375.285i | 0.604323 | + | 0.604323i | ||||
\(622\) | 423.850 | − | 244.710i | 0.681431 | − | 0.393424i | ||||
\(623\) | −501.777 | − | 501.777i | −0.805420 | − | 0.805420i | ||||
\(624\) | 72.6286 | − | 271.054i | 0.116392 | − | 0.434381i | ||||
\(625\) | 282.679 | + | 489.614i | 0.452286 | + | 0.783382i | ||||
\(626\) | −347.153 | − | 601.286i | −0.554557 | − | 0.960521i | ||||
\(627\) | −18.8878 | − | 70.4902i | −0.0301241 | − | 0.112425i | ||||
\(628\) | − | 260.003i | − | 0.414017i | ||||||
\(629\) | −114.013 | − | 46.3830i | −0.181260 | − | 0.0737409i | ||||
\(630\) | 77.6116 | 0.123193 | ||||||||
\(631\) | −355.653 | + | 95.2968i | −0.563633 | + | 0.151025i | −0.529375 | − | 0.848388i | \(-0.677574\pi\) |
−0.0342582 | + | 0.999413i | \(0.510907\pi\) | |||||||
\(632\) | −276.335 | + | 159.542i | −0.437238 | + | 0.252440i | ||||
\(633\) | −540.587 | + | 312.108i | −0.854008 | + | 0.493062i | ||||
\(634\) | 41.2237 | + | 11.0459i | 0.0650216 | + | 0.0174225i | ||||
\(635\) | −67.0765 | + | 67.0765i | −0.105632 | + | 0.105632i | ||||
\(636\) | 244.748 | + | 423.916i | 0.384824 | + | 0.666534i | ||||
\(637\) | 231.201 | − | 231.201i | 0.362954 | − | 0.362954i | ||||
\(638\) | 92.6387 | − | 160.455i | 0.145202 | − | 0.251497i | ||||
\(639\) | −1053.55 | −1.64875 | ||||||||
\(640\) | 10.1436i | 0.0158494i | ||||||||
\(641\) | 53.5878 | − | 92.8168i | 0.0836003 | − | 0.144800i | −0.821194 | − | 0.570650i | \(-0.806691\pi\) |
0.904794 | + | 0.425850i | \(0.140025\pi\) | |||||||
\(642\) | 304.893 | + | 81.6958i | 0.474911 | + | 0.127252i | ||||
\(643\) | 582.588 | + | 582.588i | 0.906046 | + | 0.906046i | 0.995950 | − | 0.0899044i | \(-0.0286562\pi\) |
−0.0899044 | + | 0.995950i | \(0.528656\pi\) | |||||||
\(644\) | 458.579 | − | 122.876i | 0.712080 | − | 0.190801i | ||||
\(645\) | 115.579 | − | 200.189i | 0.179192 | − | 0.310370i | ||||
\(646\) | 7.57610 | + | 28.2744i | 0.0117277 | + | 0.0437684i | ||||
\(647\) | −189.200 | + | 706.104i | −0.292427 | + | 1.09135i | 0.650813 | + | 0.759238i | \(0.274428\pi\) |
−0.943240 | + | 0.332113i | \(0.892238\pi\) | |||||||
\(648\) | −138.916 | − | 37.2225i | −0.214377 | − | 0.0574422i | ||||
\(649\) | 207.984 | − | 55.7293i | 0.320469 | − | 0.0858694i | ||||
\(650\) | 458.052 | + | 264.457i | 0.704696 | + | 0.406856i | ||||
\(651\) | 152.677 | + | 569.798i | 0.234527 | + | 0.875265i | ||||
\(652\) | −201.317 | + | 201.317i | −0.308769 | + | 0.308769i | ||||
\(653\) | 39.6903 | − | 148.126i | 0.0607814 | − | 0.226839i | −0.928853 | − | 0.370448i | \(-0.879204\pi\) |
0.989635 | + | 0.143609i | \(0.0458708\pi\) | |||||||
\(654\) | −341.708 | − | 197.285i | −0.522489 | − | 0.301659i | ||||
\(655\) | 126.969 | 0.193846 | ||||||||
\(656\) | 97.4038i | 0.148481i | ||||||||
\(657\) | −1115.94 | − | 644.289i | −1.69854 | − | 0.980653i | ||||
\(658\) | 74.7799 | + | 74.7799i | 0.113647 | + | 0.113647i | ||||
\(659\) | −730.438 | + | 421.719i | −1.10840 | + | 0.639937i | −0.938416 | − | 0.345509i | \(-0.887706\pi\) |
−0.169989 | + | 0.985446i | \(0.554373\pi\) | |||||||
\(660\) | 14.8717 | + | 14.8717i | 0.0225329 | + | 0.0225329i | ||||
\(661\) | −192.641 | + | 718.947i | −0.291439 | + | 1.08767i | 0.652565 | + | 0.757732i | \(0.273693\pi\) |
−0.944004 | + | 0.329933i | \(0.892974\pi\) | |||||||
\(662\) | −182.320 | − | 315.788i | −0.275408 | − | 0.477021i | ||||
\(663\) | 116.689 | + | 202.111i | 0.176002 | + | 0.304844i | ||||
\(664\) | 1.87140 | + | 6.98415i | 0.00281837 | + | 0.0105183i | ||||
\(665\) | 29.4373i | 0.0442666i | ||||||||
\(666\) | −372.529 | − | 479.184i | −0.559352 | − | 0.719495i | ||||
\(667\) | −2280.51 | −3.41906 | ||||||||
\(668\) | −545.328 | + | 146.120i | −0.816360 | + | 0.218743i | ||||
\(669\) | 1623.81 | − | 937.510i | 2.42723 | − | 1.40136i | ||||
\(670\) | −30.2923 | + | 17.4893i | −0.0452124 | + | 0.0261034i | ||||
\(671\) | −126.499 | − | 33.8953i | −0.188523 | − | 0.0505146i | ||||
\(672\) | 95.8018 | − | 95.8018i | 0.142562 | − | 0.142562i | ||||
\(673\) | 269.525 | + | 466.831i | 0.400483 | + | 0.693656i | 0.993784 | − | 0.111324i | \(-0.0355091\pi\) |
−0.593301 | + | 0.804980i | \(0.702176\pi\) | |||||||
\(674\) | −433.847 | + | 433.847i | −0.643689 | + | 0.643689i | ||||
\(675\) | −142.737 | + | 247.228i | −0.211462 | + | 0.366264i | ||||
\(676\) | 139.833 | 0.206854 | ||||||||
\(677\) | − | 733.532i | − | 1.08350i | −0.840538 | − | 0.541752i | \(-0.817761\pi\) | ||
0.840538 | − | 0.541752i | \(-0.182239\pi\) | |||||||
\(678\) | 323.426 | − | 560.190i | 0.477029 | − | 0.826239i | ||||
\(679\) | 366.818 | + | 98.2885i | 0.540232 | + | 0.144755i | ||||
\(680\) | −5.96520 | − | 5.96520i | −0.00877236 | − | 0.00877236i | ||||
\(681\) | −266.014 | + | 71.2782i | −0.390623 | + | 0.104667i | ||||
\(682\) | −45.0069 | + | 77.9542i | −0.0659925 | + | 0.114302i | ||||
\(683\) | 5.60855 | + | 20.9314i | 0.00821164 | + | 0.0306463i | 0.969910 | − | 0.243463i | \(-0.0782836\pi\) |
−0.961698 | + | 0.274110i | \(0.911617\pi\) | |||||||
\(684\) | −37.3587 | + | 139.425i | −0.0546180 | + | 0.203837i | ||||
\(685\) | −66.2122 | − | 17.7415i | −0.0966602 | − | 0.0259000i | ||||
\(686\) | 505.701 | − | 135.502i | 0.737173 | − | 0.197525i | ||||
\(687\) | −1523.29 | − | 879.470i | −2.21730 | − | 1.28016i | ||||
\(688\) | −58.8098 | − | 219.481i | −0.0854794 | − | 0.319013i | ||||
\(689\) | −589.384 | + | 589.384i | −0.855420 | + | 0.855420i | ||||
\(690\) | 67.0011 | − | 250.052i | 0.0971031 | − | 0.362394i | ||||
\(691\) | 681.718 | + | 393.590i | 0.986568 | + | 0.569595i | 0.904247 | − | 0.427011i | \(-0.140433\pi\) |
0.0823212 | + | 0.996606i | \(0.473767\pi\) | |||||||
\(692\) | −300.573 | −0.434355 | ||||||||
\(693\) | − | 158.182i | − | 0.228256i | ||||||
\(694\) | 586.123 | + | 338.398i | 0.844558 | + | 0.487606i | ||||
\(695\) | 28.8431 | + | 28.8431i | 0.0415009 | + | 0.0415009i | ||||
\(696\) | −563.613 | + | 325.402i | −0.809789 | + | 0.467532i | ||||
\(697\) | −57.2808 | − | 57.2808i | −0.0821819 | − | 0.0821819i | ||||
\(698\) | 20.5844 | − | 76.8221i | 0.0294906 | − | 0.110060i | ||||
\(699\) | 683.049 | + | 1183.08i | 0.977180 | + | 1.69253i | ||||
\(700\) | 127.683 | + | 221.153i | 0.182404 | + | 0.315932i | ||||
\(701\) | 65.5540 | + | 244.651i | 0.0935150 | + | 0.349003i | 0.996790 | − | 0.0800591i | \(-0.0255109\pi\) |
−0.903275 | + | 0.429062i | \(0.858844\pi\) | |||||||
\(702\) | 257.904i | 0.367385i | ||||||||
\(703\) | 181.749 | − | 141.296i | 0.258534 | − | 0.200990i | ||||
\(704\) | 20.6738 | 0.0293662 | ||||||||
\(705\) | 55.7005 | − | 14.9249i | 0.0790078 | − | 0.0211701i | ||||
\(706\) | 249.632 | − | 144.125i | 0.353586 | − | 0.204143i | ||||
\(707\) | −509.291 | + | 294.039i | −0.720355 | + | 0.415897i | ||||
\(708\) | −730.565 | − | 195.754i | −1.03187 | − | 0.276489i | ||||
\(709\) | −560.020 | + | 560.020i | −0.789873 | + | 0.789873i | −0.981473 | − | 0.191600i | \(-0.938632\pi\) |
0.191600 | + | 0.981473i | \(0.438632\pi\) | |||||||
\(710\) | 57.5821 | + | 99.7351i | 0.0811015 | + | 0.140472i | ||||
\(711\) | 925.304 | − | 925.304i | 1.30141 | − | 1.30141i | ||||
\(712\) | −190.176 | + | 329.394i | −0.267101 | + | 0.462632i | ||||
\(713\) | 1107.95 | 1.55392 | ||||||||
\(714\) | 112.677i | 0.157812i | ||||||||
\(715\) | −17.9065 | + | 31.0150i | −0.0250441 | + | 0.0433776i | ||||
\(716\) | −131.089 | − | 35.1252i | −0.183085 | − | 0.0490575i | ||||
\(717\) | −340.357 | − | 340.357i | −0.474696 | − | 0.474696i | ||||
\(718\) | −714.662 | + | 191.493i | −0.995352 | + | 0.266704i | ||||
\(719\) | 10.6725 | − | 18.4853i | 0.0148435 | − | 0.0257097i | −0.858508 | − | 0.512800i | \(-0.828608\pi\) |
0.873352 | + | 0.487090i | \(0.161942\pi\) | |||||||
\(720\) | −10.7667 | − | 40.1819i | −0.0149538 | − | 0.0558082i | ||||
\(721\) | −179.764 | + | 670.888i | −0.249326 | + | 0.930496i | ||||
\(722\) | 440.253 | + | 117.965i | 0.609768 | + | 0.163387i | ||||
\(723\) | 699.977 | − | 187.558i | 0.968156 | − | 0.259417i | ||||
\(724\) | 355.499 | + | 205.247i | 0.491020 | + | 0.283491i | ||||
\(725\) | −317.482 | − | 1184.86i | −0.437906 | − | 1.63429i | ||||
\(726\) | −518.869 | + | 518.869i | −0.714695 | + | 0.714695i | ||||
\(727\) | −230.014 | + | 858.425i | −0.316388 | + | 1.18078i | 0.606302 | + | 0.795235i | \(0.292652\pi\) |
−0.922690 | + | 0.385543i | \(0.874014\pi\) | |||||||
\(728\) | 199.795 | + | 115.352i | 0.274443 | + | 0.158450i | ||||
\(729\) | 1071.74 | 1.47015 | ||||||||
\(730\) | 140.855i | 0.192952i | ||||||||
\(731\) | 163.656 | + | 94.4869i | 0.223880 | + | 0.129257i | ||||
\(732\) | 325.279 | + | 325.279i | 0.444370 | + | 0.444370i | ||||
\(733\) | 234.846 | − | 135.588i | 0.320390 | − | 0.184977i | −0.331176 | − | 0.943569i | \(-0.607446\pi\) |
0.651566 | + | 0.758592i | \(0.274112\pi\) | |||||||
\(734\) | −471.343 | − | 471.343i | −0.642156 | − | 0.642156i | ||||
\(735\) | 22.2789 | − | 83.1460i | 0.0303114 | − | 0.113124i | ||||
\(736\) | −127.233 | − | 220.374i | −0.172871 | − | 0.299422i | ||||
\(737\) | 35.6451 | + | 61.7392i | 0.0483652 | + | 0.0837709i | ||||
\(738\) | −103.387 | − | 385.846i | −0.140091 | − | 0.522827i | ||||
\(739\) | 126.877i | 0.171688i | 0.996309 | + | 0.0858439i | \(0.0273586\pi\) | ||||
−0.996309 | + | 0.0858439i | \(0.972641\pi\) | |||||||
\(740\) | −25.0016 | + | 61.4556i | −0.0337859 | + | 0.0830481i | ||||
\(741\) | −436.493 | −0.589060 | ||||||||
\(742\) | −388.718 | + | 104.157i | −0.523879 | + | 0.140373i | ||||
\(743\) | −196.167 | + | 113.257i | −0.264020 | + | 0.152432i | −0.626167 | − | 0.779689i | \(-0.715377\pi\) |
0.362147 | + | 0.932121i | \(0.382044\pi\) | |||||||
\(744\) | 273.821 | − | 158.091i | 0.368039 | − | 0.212488i | ||||
\(745\) | 37.4437 | + | 10.0330i | 0.0502601 | + | 0.0134671i | ||||
\(746\) | 59.8125 | − | 59.8125i | 0.0801776 | − | 0.0801776i | ||||
\(747\) | −14.8264 | − | 25.6800i | −0.0198479 | − | 0.0343775i | ||||
\(748\) | −12.1578 | + | 12.1578i | −0.0162537 | + | 0.0162537i | ||||
\(749\) | −129.752 | + | 224.738i | −0.173234 | + | 0.300050i | ||||
\(750\) | 283.114 | 0.377485 | ||||||||
\(751\) | 844.287i | 1.12422i | 0.827064 | + | 0.562108i | \(0.190010\pi\) | ||||
−0.827064 | + | 0.562108i | \(0.809990\pi\) | |||||||
\(752\) | 28.3420 | − | 49.0897i | 0.0376888 | − | 0.0652789i | ||||
\(753\) | −1065.94 | − | 285.618i | −1.41559 | − | 0.379307i | ||||
\(754\) | −783.610 | − | 783.610i | −1.03927 | − | 1.03927i | ||||
\(755\) | −35.9045 | + | 9.62059i | −0.0475557 | + | 0.0127425i | ||||
\(756\) | −62.2595 | + | 107.837i | −0.0823539 | + | 0.142641i | ||||
\(757\) | 121.331 | + | 452.814i | 0.160279 | + | 0.598169i | 0.998595 | + | 0.0529848i | \(0.0168735\pi\) |
−0.838317 | + | 0.545184i | \(0.816460\pi\) | |||||||
\(758\) | −155.311 | + | 579.629i | −0.204896 | + | 0.764683i | ||||
\(759\) | −509.634 | − | 136.556i | −0.671454 | − | 0.179916i | ||||
\(760\) | 15.2406 | − | 4.08370i | 0.0200534 | − | 0.00537329i | ||||
\(761\) | −482.112 | − | 278.348i | −0.633524 | − | 0.365765i | 0.148591 | − | 0.988899i | \(-0.452526\pi\) |
−0.782116 | + | 0.623133i | \(0.785859\pi\) | |||||||
\(762\) | −175.767 | − | 655.973i | −0.230666 | − | 0.860856i | ||||
\(763\) | 229.378 | − | 229.378i | 0.300626 | − | 0.300626i | ||||
\(764\) | −46.1853 | + | 172.366i | −0.0604519 | + | 0.225610i | ||||
\(765\) | 29.9616 | + | 17.2984i | 0.0391655 | + | 0.0226122i | ||||
\(766\) | −303.550 | −0.396279 | ||||||||
\(767\) | − | 1287.89i | − | 1.67913i | ||||||
\(768\) | −62.8896 | − | 36.3093i | −0.0818876 | − | 0.0472778i | ||||
\(769\) | 101.249 | + | 101.249i | 0.131664 | + | 0.131664i | 0.769867 | − | 0.638204i | \(-0.220322\pi\) |
−0.638204 | + | 0.769867i | \(0.720322\pi\) | |||||||
\(770\) | −14.9744 | + | 8.64545i | −0.0194472 | + | 0.0112279i | ||||
\(771\) | 16.3305 | + | 16.3305i | 0.0211810 | + | 0.0211810i | ||||
\(772\) | −163.115 | + | 608.754i | −0.211289 | + | 0.788542i | ||||
\(773\) | −430.845 | − | 746.245i | −0.557367 | − | 0.965388i | −0.997715 | − | 0.0675609i | \(-0.978478\pi\) |
0.440348 | − | 0.897827i | \(-0.354855\pi\) | |||||||
\(774\) | 465.927 | + | 807.010i | 0.601973 | + | 1.04265i | ||||
\(775\) | 154.243 | + | 575.643i | 0.199023 | + | 0.742765i | ||||
\(776\) | − | 203.548i | − | 0.262304i | ||||||
\(777\) | 816.550 | − | 344.292i | 1.05090 | − | 0.443104i | ||||
\(778\) | −627.031 | −0.805953 | ||||||||
\(779\) | 146.348 | − | 39.2137i | 0.187866 | − | 0.0503385i | ||||
\(780\) | 108.943 | − | 62.8982i | 0.139670 | − | 0.0806388i | ||||
\(781\) | 203.272 | − | 117.359i | 0.260271 | − | 0.150268i | ||||
\(782\) | 204.420 | + | 54.7741i | 0.261406 | + | 0.0700436i | ||||
\(783\) | 422.944 | − | 422.944i | 0.540158 | − | 0.540158i | ||||
\(784\) | −42.3070 | − | 73.2779i | −0.0539630 | − | 0.0934667i | ||||
\(785\) | 82.4176 | − | 82.4176i | 0.104991 | − | 0.104991i | ||||
\(786\) | −454.490 | + | 787.199i | −0.578231 | + | 1.00153i | ||||
\(787\) | 445.900 | 0.566582 | 0.283291 | − | 0.959034i | \(-0.408574\pi\) | ||||
0.283291 | + | 0.959034i | \(0.408574\pi\) | |||||||
\(788\) | − | 154.400i | − | 0.195940i | ||||||
\(789\) | 916.921 | − | 1588.15i | 1.16213 | − | 2.01287i | ||||
\(790\) | −138.167 | − | 37.0218i | −0.174895 | − | 0.0468631i | ||||
\(791\) | 376.038 | + | 376.038i | 0.475396 | + | 0.475396i | ||||
\(792\) | −81.8954 | + | 21.9438i | −0.103403 | + | 0.0277068i | ||||
\(793\) | −391.657 | + | 678.369i | −0.493892 | + | 0.855446i | ||||
\(794\) | −38.2950 | − | 142.919i | −0.0482305 | − | 0.179999i | ||||
\(795\) | −56.7939 | + | 211.958i | −0.0714389 | + | 0.266614i | ||||
\(796\) | 325.963 | + | 87.3416i | 0.409502 | + | 0.109726i | ||||
\(797\) | −864.985 | + | 231.772i | −1.08530 | + | 0.290806i | −0.756766 | − | 0.653686i | \(-0.773222\pi\) |
−0.328535 | + | 0.944492i | \(0.606555\pi\) | |||||||
\(798\) | −182.509 | − | 105.372i | −0.228709 | − | 0.132045i | ||||
\(799\) | 12.2013 | + | 45.5357i | 0.0152707 | + | 0.0569909i | ||||
\(800\) | 96.7846 | − | 96.7846i | 0.120981 | − | 0.120981i | ||||
\(801\) | 403.716 | − | 1506.69i | 0.504015 | − | 1.88101i | ||||
\(802\) | 808.017 | + | 466.509i | 1.00750 | + | 0.581682i | ||||
\(803\) | 287.079 | 0.357508 | ||||||||
\(804\) | − | 250.414i | − | 0.311460i | ||||||
\(805\) | 184.314 | + | 106.414i | 0.228961 | + | 0.132191i | ||||
\(806\) | 380.703 | + | 380.703i | 0.472336 | + | 0.472336i | ||||
\(807\) | 1251.46 | − | 722.533i | 1.55076 | − | 0.895332i | ||||
\(808\) | 222.885 | + | 222.885i | 0.275847 | + | 0.275847i | ||||
\(809\) | 207.204 | − | 773.295i | 0.256123 | − | 0.955865i | −0.711339 | − | 0.702849i | \(-0.751911\pi\) |
0.967462 | − | 0.253016i | \(-0.0814224\pi\) | |||||||
\(810\) | −32.2356 | − | 55.8338i | −0.0397971 | − | 0.0689306i | ||||
\(811\) | 523.200 | + | 906.209i | 0.645130 | + | 1.11740i | 0.984272 | + | 0.176662i | \(0.0565301\pi\) |
−0.339142 | + | 0.940735i | \(0.610137\pi\) | |||||||
\(812\) | −138.480 | − | 516.816i | −0.170542 | − | 0.636473i | ||||
\(813\) | − | 103.901i | − | 0.127800i | ||||||
\(814\) | 125.254 | + | 50.9561i | 0.153874 | + | 0.0625997i | ||||
\(815\) | −127.630 | −0.156601 | ||||||||
\(816\) | 58.3365 | − | 15.6312i | 0.0714908 | − | 0.0191559i | ||||
\(817\) | −306.091 | + | 176.722i | −0.374652 | + | 0.216305i | ||||
\(818\) | 169.582 | − | 97.9079i | 0.207312 | − | 0.119692i | ||||
\(819\) | −913.886 | − | 244.875i | −1.11586 | − | 0.298993i | ||||
\(820\) | −30.8758 | + | 30.8758i | −0.0376534 | + | 0.0376534i | ||||
\(821\) | 584.120 | + | 1011.73i | 0.711474 | + | 1.23231i | 0.964304 | + | 0.264798i | \(0.0853054\pi\) |
−0.252830 | + | 0.967511i | \(0.581361\pi\) | |||||||
\(822\) | 347.005 | − | 347.005i | 0.422147 | − | 0.422147i | ||||
\(823\) | 12.5640 | − | 21.7615i | 0.0152661 | − | 0.0264417i | −0.858291 | − | 0.513163i | \(-0.828474\pi\) |
0.873558 | + | 0.486721i | \(0.161807\pi\) | |||||||
\(824\) | 372.277 | 0.451792 | ||||||||
\(825\) | − | 283.795i | − | 0.343995i | ||||||
\(826\) | 310.904 | − | 538.502i | 0.376397 | − | 0.651939i | ||||
\(827\) | 113.895 | + | 30.5180i | 0.137720 | + | 0.0369021i | 0.327021 | − | 0.945017i | \(-0.393955\pi\) |
−0.189300 | + | 0.981919i | \(0.560622\pi\) | |||||||
\(828\) | 737.922 | + | 737.922i | 0.891210 | + | 0.891210i | ||||
\(829\) | −150.428 | + | 40.3071i | −0.181457 | + | 0.0486214i | −0.348403 | − | 0.937345i | \(-0.613276\pi\) |
0.166946 | + | 0.985966i | \(0.446609\pi\) | |||||||
\(830\) | −1.62068 | + | 2.80709i | −0.00195262 | + | 0.00338204i | ||||
\(831\) | −80.0528 | − | 298.761i | −0.0963331 | − | 0.359520i | ||||
\(832\) | 32.0044 | − | 119.442i | 0.0384668 | − | 0.143560i | ||||
\(833\) | 67.9727 | + | 18.2132i | 0.0815999 | + | 0.0218646i | ||||
\(834\) | −282.071 | + | 75.5806i | −0.338214 | + | 0.0906242i | ||||
\(835\) | −219.180 | − | 126.544i | −0.262491 | − | 0.151550i | ||||
\(836\) | −8.32306 | − | 31.0621i | −0.00995581 | − | 0.0371556i | ||||
\(837\) | −205.480 | + | 205.480i | −0.245495 | + | 0.245495i | ||||
\(838\) | 232.027 | − | 865.935i | 0.276881 | − | 1.03333i | ||||
\(839\) | −716.872 | − | 413.886i | −0.854436 | − | 0.493309i | 0.00770908 | − | 0.999970i | \(-0.497546\pi\) |
−0.862145 | + | 0.506661i | \(0.830879\pi\) | |||||||
\(840\) | 60.7359 | 0.0723047 | ||||||||
\(841\) | 1729.12i | 2.05603i | ||||||||
\(842\) | 664.982 | + | 383.928i | 0.789765 | + | 0.455971i | ||||
\(843\) | 1015.94 | + | 1015.94i | 1.20515 | + | 1.20515i | ||||
\(844\) | −238.214 | + | 137.533i | −0.282244 | + | 0.162954i | ||||
\(845\) | 44.3253 | + | 44.3253i | 0.0524560 | + | 0.0524560i | ||||
\(846\) | −60.1660 | + | 224.542i | −0.0711182 | + | 0.265417i | ||||
\(847\) | −301.637 | − | 522.450i | −0.356124 | − | 0.616824i | ||||
\(848\) | 107.850 | + | 186.802i | 0.127182 | + | 0.220285i | ||||
\(849\) | −69.4694 | − | 259.263i | −0.0818250 | − | 0.305375i | ||||
\(850\) | 113.833i | 0.133922i | ||||||||
\(851\) | −227.679 | − | 1648.75i | −0.267542 | − | 1.93743i | ||||
\(852\) | −824.469 | −0.967686 | ||||||||
\(853\) | 156.425 | − | 41.9140i | 0.183382 | − | 0.0491371i | −0.165959 | − | 0.986133i | \(-0.553072\pi\) |
0.349341 | + | 0.936996i | \(0.386405\pi\) | |||||||
\(854\) | −327.524 | + | 189.096i | −0.383518 | + | 0.221424i | ||||
\(855\) | −56.0381 | + | 32.3536i | −0.0655416 | + | 0.0378405i | ||||
\(856\) | 134.353 | + | 35.9999i | 0.156955 | + | 0.0420560i | ||||
\(857\) | 284.490 | − | 284.490i | 0.331961 | − | 0.331961i | −0.521370 | − | 0.853331i | \(-0.674579\pi\) |
0.853331 | + | 0.521370i | \(0.174579\pi\) | |||||||
\(858\) | −128.194 | − | 222.038i | −0.149410 | − | 0.258786i | ||||
\(859\) | 71.6633 | − | 71.6633i | 0.0834265 | − | 0.0834265i | −0.664162 | − | 0.747589i | \(-0.731212\pi\) |
0.747589 | + | 0.664162i | \(0.231212\pi\) | |||||||
\(860\) | 50.9308 | − | 88.2147i | 0.0592218 | − | 0.102575i | ||||
\(861\) | 583.216 | 0.677371 | ||||||||
\(862\) | − | 997.930i | − | 1.15769i | ||||||
\(863\) | 306.166 | − | 530.295i | 0.354770 | − | 0.614479i | −0.632309 | − | 0.774716i | \(-0.717893\pi\) |
0.987079 | + | 0.160237i | \(0.0512260\pi\) | |||||||
\(864\) | 64.4673 | + | 17.2740i | 0.0746149 | + | 0.0199930i | ||||
\(865\) | −95.2780 | − | 95.2780i | −0.110148 | − | 0.110148i | ||||
\(866\) | 355.956 | − | 95.3781i | 0.411035 | − | 0.110136i | ||||
\(867\) | 630.724 | − | 1092.45i | 0.727478 | − | 1.26003i | ||||
\(868\) | 67.2782 | + | 251.086i | 0.0775095 | + | 0.289269i | ||||
\(869\) | −75.4547 | + | 281.601i | −0.0868294 | + | 0.324052i | ||||
\(870\) | −281.806 | − | 75.5098i | −0.323915 | − | 0.0867929i | ||||
\(871\) | 411.876 | − | 110.362i | 0.472877 | − | 0.126707i | ||||
\(872\) | −150.576 | − | 86.9352i | −0.172679 | − | 0.0996963i | ||||
\(873\) | 216.051 | + | 806.315i | 0.247482 | + | 0.923614i | ||||
\(874\) | −279.886 | + | 279.886i | −0.320236 | + | 0.320236i | ||||
\(875\) | −60.2420 | + | 224.826i | −0.0688480 | + | 0.256944i | ||||
\(876\) | −873.294 | − | 504.196i | −0.996910 | − | 0.575566i | ||||
\(877\) | −360.322 | −0.410857 | −0.205429 | − | 0.978672i | \(-0.565859\pi\) | ||||
−0.205429 | + | 0.978672i | \(0.565859\pi\) | |||||||
\(878\) | 932.170i | 1.06170i | ||||||||
\(879\) | 948.048 | + | 547.356i | 1.07855 | + | 0.622703i | ||||
\(880\) | 6.55334 | + | 6.55334i | 0.00744697 | + | 0.00744697i | ||||
\(881\) | 173.512 | − | 100.177i | 0.196949 | − | 0.113709i | −0.398282 | − | 0.917263i | \(-0.630394\pi\) |
0.595232 | + | 0.803554i | \(0.297060\pi\) | |||||||
\(882\) | 245.370 | + | 245.370i | 0.278198 | + | 0.278198i | ||||
\(883\) | 10.7749 | − | 40.2125i | 0.0122026 | − | 0.0455407i | −0.959556 | − | 0.281517i | \(-0.909162\pi\) |
0.971759 | + | 0.235977i | \(0.0758289\pi\) | |||||||
\(884\) | 51.4199 | + | 89.0619i | 0.0581673 | + | 0.100749i | ||||
\(885\) | −169.528 | − | 293.631i | −0.191557 | − | 0.331787i | ||||
\(886\) | 172.962 | + | 645.502i | 0.195217 | + | 0.728558i | ||||
\(887\) | − | 299.625i | − | 0.337796i | −0.985634 | − | 0.168898i | \(-0.945979\pi\) | ||
0.985634 | − | 0.168898i | \(-0.0540209\pi\) | |||||||
\(888\) | −291.527 | − | 374.991i | −0.328296 | − | 0.422287i | ||||
\(889\) | 558.321 | 0.628032 | ||||||||
\(890\) | −164.697 | + | 44.1304i | −0.185053 | + | 0.0495848i | ||||
\(891\) | −113.796 | + | 65.7000i | −0.127717 | + | 0.0737373i | ||||
\(892\) | 715.547 | − | 413.121i | 0.802182 | − | 0.463140i | ||||
\(893\) | −85.1666 | − | 22.8203i | −0.0953714 | − | 0.0255547i | ||||
\(894\) | −196.235 | + | 196.235i | −0.219503 | + | 0.219503i | ||||
\(895\) | −30.4193 | − | 52.6878i | −0.0339880 | − | 0.0588690i | ||||
\(896\) | 42.2158 | − | 42.2158i | 0.0471159 | − | 0.0471159i | ||||
\(897\) | −1577.89 | + | 2732.99i | −1.75908 | + | 3.04681i | ||||
\(898\) | −1074.24 | −1.19625 | ||||||||
\(899\) | − | 1248.65i | − | 1.38893i | ||||||
\(900\) | −280.664 | + | 486.124i | −0.311848 | + | 0.540137i | ||||
\(901\) | −173.278 | − | 46.4296i | −0.192317 | − | 0.0515312i | ||||
\(902\) | 62.9284 | + | 62.9284i | 0.0697654 | + | 0.0697654i | ||||
\(903\) | −1314.17 | + | 352.130i | −1.45534 | + | 0.389956i | ||||
\(904\) | 142.520 | − | 246.852i | 0.157655 | − | 0.273067i | ||||
\(905\) | 47.6278 | + | 177.749i | 0.0526274 | + | 0.196408i | ||||
\(906\) | 68.8745 | − | 257.043i | 0.0760204 | − | 0.283712i | ||||
\(907\) | 403.168 | + | 108.028i | 0.444507 | + | 0.119105i | 0.474128 | − | 0.880456i | \(-0.342763\pi\) |
−0.0296211 | + | 0.999561i | \(0.509430\pi\) | |||||||
\(908\) | −117.221 | + | 31.4093i | −0.129098 | + | 0.0345918i | ||||
\(909\) | −1119.49 | − | 646.339i | −1.23156 | − | 0.711044i | ||||
\(910\) | 26.7674 | + | 99.8974i | 0.0294147 | + | 0.109777i | ||||
\(911\) | −90.2042 | + | 90.2042i | −0.0990167 | + | 0.0990167i | −0.754880 | − | 0.655863i | \(-0.772305\pi\) |
0.655863 | + | 0.754880i | \(0.272305\pi\) | |||||||
\(912\) | −29.2355 | + | 109.108i | −0.0320565 | + | 0.119636i | ||||
\(913\) | 5.72118 | + | 3.30313i | 0.00626636 | + | 0.00361788i | ||||
\(914\) | −520.741 | −0.569738 | ||||||||
\(915\) | 206.218i | 0.225375i | ||||||||
\(916\) | −671.248 | − | 387.545i | −0.732804 | − | 0.423084i | ||||
\(917\) | −528.422 | − | 528.422i | −0.576251 | − | 0.576251i | ||||
\(918\) | −48.0700 | + | 27.7533i | −0.0523639 | + | 0.0302323i | ||||
\(919\) | −416.984 | − | 416.984i | −0.453737 | − | 0.453737i | 0.442856 | − | 0.896593i | \(-0.353965\pi\) |
−0.896593 | + | 0.442856i | \(0.853965\pi\) | |||||||
\(920\) | 29.5246 | − | 110.187i | 0.0320919 | − | 0.119769i | ||||
\(921\) | 774.378 | + | 1341.26i | 0.840802 | + | 1.45631i | ||||
\(922\) | −125.437 | − | 217.264i | −0.136049 | − | 0.235644i | ||||
\(923\) | −363.358 | − | 1356.07i | −0.393671 | − | 1.46920i | ||||
\(924\) | − | 123.787i | − | 0.133968i | ||||||
\(925\) | 824.927 | − | 347.824i | 0.891813 | − | 0.376026i | ||||
\(926\) | 419.035 | 0.452522 | ||||||||
\(927\) | −1474.70 | + | 395.145i | −1.59083 | + | 0.426263i | ||||
\(928\) | −248.360 | + | 143.391i | −0.267630 | + | 0.154516i | ||||
\(929\) | −225.210 | + | 130.025i | −0.242422 | + | 0.139962i | −0.616289 | − | 0.787520i | \(-0.711365\pi\) |
0.373868 | + | 0.927482i | \(0.378031\pi\) | |||||||
\(930\) | 136.911 | + | 36.6851i | 0.147216 | + | 0.0394463i | ||||
\(931\) | −93.0665 | + | 93.0665i | −0.0999640 | + | 0.0999640i | ||||
\(932\) | 300.991 | + | 521.331i | 0.322951 | + | 0.559368i | ||||
\(933\) | −1110.66 | + | 1110.66i | −1.19041 | + | 1.19041i | ||||
\(934\) | 55.7642 | − | 96.5864i | 0.0597047 | − | 0.103412i | ||||
\(935\) | −7.70772 | −0.00824355 | ||||||||
\(936\) | 507.117i | 0.541791i | ||||||||
\(937\) | −886.119 | + | 1534.80i | −0.945698 | + | 1.63800i | −0.191350 | + | 0.981522i | \(0.561287\pi\) |
−0.754348 | + | 0.656475i | \(0.772047\pi\) | |||||||
\(938\) | 198.858 | + | 53.2839i | 0.212002 | + | 0.0568059i | ||||
\(939\) | 1575.61 | + | 1575.61i | 1.67797 | + | 1.67797i | ||||
\(940\) | 24.5449 | − | 6.57677i | 0.0261115 | − | 0.00699657i | ||||
\(941\) | 827.078 | − | 1432.54i | 0.878935 | − | 1.52236i | 0.0264237 | − | 0.999651i | \(-0.491588\pi\) |
0.852511 | − | 0.522709i | \(-0.175079\pi\) | |||||||
\(942\) | 215.967 | + | 806.001i | 0.229265 | + | 0.855627i | ||||
\(943\) | 283.509 | − | 1058.07i | 0.300646 | − | 1.12203i | ||||
\(944\) | −321.929 | − | 86.2606i | −0.341026 | − | 0.0913778i | ||||
\(945\) | −53.9183 | + | 14.4474i | −0.0570564 | + | 0.0152882i | ||||
\(946\) | −179.792 | − | 103.803i | −0.190055 | − | 0.109728i | ||||
\(947\) | 312.818 | + | 1167.45i | 0.330325 | + | 1.23279i | 0.908849 | + | 0.417125i | \(0.136962\pi\) |
−0.578524 | + | 0.815666i | \(0.696371\pi\) | |||||||
\(948\) | 724.108 | − | 724.108i | 0.763827 | − | 0.763827i | ||||
\(949\) | 444.417 | − | 1658.59i | 0.468300 | − | 1.74772i | ||||
\(950\) | −184.382 | − | 106.453i | −0.194086 | − | 0.112056i | ||||
\(951\) | −136.967 | −0.144024 | ||||||||
\(952\) | 49.6522i | 0.0521557i | ||||||||
\(953\) | −654.673 | − | 377.976i | −0.686960 | − | 0.396616i | 0.115512 | − | 0.993306i | \(-0.463149\pi\) |
−0.802472 | + | 0.596690i | \(0.796482\pi\) | |||||||
\(954\) | −625.504 | − | 625.504i | −0.655665 | − | 0.655665i | ||||
\(955\) | −69.2779 | + | 39.9976i | −0.0725423 | + | 0.0418823i | ||||
\(956\) | −149.981 | − | 149.981i | −0.156884 | − | 0.156884i | ||||
\(957\) | −153.898 | + | 574.354i | −0.160813 | + | 0.600161i | ||||
\(958\) | 227.410 | + | 393.886i | 0.237380 | + | 0.411155i | ||||
\(959\) | 201.726 | + | 349.400i | 0.210351 | + | 0.364338i | ||||
\(960\) | −8.42561 | − | 31.4448i | −0.00877668 | − | 0.0327550i | ||||
\(961\) | − | 354.367i | − | 0.368748i | ||||||
\(962\) | 488.297 | − | 644.763i | 0.507585 | − | 0.670232i | ||||
\(963\) | −570.427 | −0.592344 | ||||||||
\(964\) | 308.450 | − | 82.6490i | 0.319969 | − | 0.0857354i | ||||
\(965\) | −244.673 | + | 141.262i | −0.253547 | + | 0.146385i | ||||
\(966\) | −1319.52 | + | 761.823i | −1.36596 | + | 0.788637i | ||||
\(967\) | −49.8356 | − | 13.3534i | −0.0515363 | − | 0.0138091i | 0.232959 | − | 0.972487i | \(-0.425159\pi\) |
−0.284495 | + | 0.958677i | \(0.591826\pi\) | |||||||
\(968\) | −228.644 | + | 228.644i | −0.236202 | + | 0.236202i | ||||
\(969\) | −46.9713 | − | 81.3567i | −0.0484740 | − | 0.0839594i | ||||
\(970\) | 64.5220 | − | 64.5220i | 0.0665175 | − | 0.0665175i | ||||
\(971\) | −238.604 | + | 413.274i | −0.245730 | + | 0.425617i | −0.962337 | − | 0.271861i | \(-0.912361\pi\) |
0.716607 | + | 0.697477i | \(0.245694\pi\) | |||||||
\(972\) | 673.924 | 0.693338 | ||||||||
\(973\) | − | 240.080i | − | 0.246742i | ||||||
\(974\) | 89.8601 | − | 155.642i | 0.0922588 | − | 0.159797i | ||||
\(975\) | −1639.61 | − | 439.333i | −1.68166 | − | 0.450598i | ||||
\(976\) | 143.337 | + | 143.337i | 0.146861 | + | 0.146861i | ||||
\(977\) | −137.157 | + | 36.7511i | −0.140386 | + | 0.0376163i | −0.328328 | − | 0.944564i | \(-0.606485\pi\) |
0.187942 | + | 0.982180i | \(0.439818\pi\) | |||||||
\(978\) | 456.856 | − | 791.298i | 0.467133 | − | 0.809099i | ||||
\(979\) | 89.9430 | + | 335.672i | 0.0918723 | + | 0.342872i | ||||
\(980\) | 9.81738 | − | 36.6389i | 0.0100177 | − | 0.0373867i | ||||
\(981\) | 688.754 | + | 184.551i | 0.702094 | + | 0.188125i | ||||
\(982\) | 687.234 | − | 184.144i | 0.699831 | − | 0.187519i | ||||
\(983\) | 1683.97 | + | 972.239i | 1.71309 | + | 0.989053i | 0.930325 | + | 0.366737i | \(0.119525\pi\) |
0.782766 | + | 0.622316i | \(0.213808\pi\) | |||||||
\(984\) | −80.9069 | − | 301.949i | −0.0822224 | − | 0.306858i | ||||
\(985\) | 48.9430 | − | 48.9430i | 0.0496883 | − | 0.0496883i | ||||
\(986\) | 61.7300 | − | 230.380i | 0.0626065 | − | 0.233651i | ||||
\(987\) | −293.930 | − | 169.701i | −0.297802 | − | 0.171936i | ||||
\(988\) | −192.344 | −0.194680 | ||||||||
\(989\) | 2555.34i | 2.58376i | ||||||||
\(990\) | −32.9157 | − | 19.0039i | −0.0332482 | − | 0.0191958i | ||||
\(991\) | −795.632 | − | 795.632i | −0.802857 | − | 0.802857i | 0.180684 | − | 0.983541i | \(-0.442169\pi\) |
−0.983541 | + | 0.180684i | \(0.942169\pi\) | |||||||
\(992\) | 120.662 | − | 69.6640i | 0.121635 | − | 0.0702258i | ||||
\(993\) | 827.490 | + | 827.490i | 0.833324 | + | 0.833324i | ||||
\(994\) | 175.433 | − | 654.726i | 0.176492 | − | 0.658678i | ||||
\(995\) | 75.6400 | + | 131.012i | 0.0760201 | + | 0.131671i | ||||
\(996\) | −11.6025 | − | 20.0962i | −0.0116491 | − | 0.0201769i | ||||
\(997\) | −171.784 | − | 641.107i | −0.172301 | − | 0.643036i | −0.996996 | − | 0.0774580i | \(-0.975320\pi\) |
0.824695 | − | 0.565578i | \(-0.191347\pi\) | |||||||
\(998\) | 1275.32i | 1.27788i | ||||||||
\(999\) | 348.003 | + | 263.552i | 0.348351 | + | 0.263816i |
(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 | 74.3.g.b.51.3 | yes | 12 | |
37.8 | odd | 12 | inner | 74.3.g.b.45.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.3.g.b.45.3 | ✓ | 12 | 37.8 | odd | 12 | inner | |
74.3.g.b.51.3 | yes | 12 | 1.1 | even | 1 | trivial |