Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,3,Mod(19,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.l (of order \(4\), degree \(2\), 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: | \(1.30790526893\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 19.2 | ||
Root | \(1.80398 - 0.863518i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.19 |
Dual form | 48.3.l.a.43.2 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80398 | − | 0.863518i | −0.901989 | − | 0.431759i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.50867 | + | 3.11554i | 0.627168 | + | 0.778884i | ||||
\(5\) | 6.49473 | − | 6.49473i | 1.29895 | − | 1.29895i | 0.369856 | − | 0.929089i | \(-0.379407\pi\) |
0.929089 | − | 0.369856i | \(-0.120593\pi\) | |||||||
\(6\) | 3.26700 | − | 1.15182i | 0.544500 | − | 0.191971i | ||||
\(7\) | 3.94273 | 0.563247 | 0.281623 | − | 0.959525i | \(-0.409127\pi\) | ||||
0.281623 | + | 0.959525i | \(0.409127\pi\) | |||||||
\(8\) | −1.83527 | − | 7.78664i | −0.229409 | − | 0.973330i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −17.3247 | + | 6.10803i | −1.73247 | + | 0.610803i | ||||
\(11\) | 4.31091 | + | 4.31091i | 0.391901 | + | 0.391901i | 0.875364 | − | 0.483464i | \(-0.160621\pi\) |
−0.483464 | + | 0.875364i | \(0.660621\pi\) | |||||||
\(12\) | −6.88822 | − | 0.743251i | −0.574018 | − | 0.0619376i | ||||
\(13\) | 4.06281 | + | 4.06281i | 0.312524 | + | 0.312524i | 0.845887 | − | 0.533363i | \(-0.179072\pi\) |
−0.533363 | + | 0.845887i | \(0.679072\pi\) | |||||||
\(14\) | −7.11259 | − | 3.40462i | −0.508042 | − | 0.243187i | ||||
\(15\) | 15.9088i | 1.06058i | ||||||||
\(16\) | −3.41312 | + | 15.6317i | −0.213320 | + | 0.976982i | ||||
\(17\) | −14.5538 | −0.856106 | −0.428053 | − | 0.903754i | \(-0.640800\pi\) | ||||
−0.428053 | + | 0.903754i | \(0.640800\pi\) | |||||||
\(18\) | −2.59055 | + | 5.41193i | −0.143920 | + | 0.300663i | ||||
\(19\) | 4.94805 | − | 4.94805i | 0.260423 | − | 0.260423i | −0.564803 | − | 0.825226i | \(-0.691048\pi\) |
0.825226 | + | 0.564803i | \(0.191048\pi\) | |||||||
\(20\) | 36.5277 | + | 3.94140i | 1.82638 | + | 0.197070i | ||||
\(21\) | −4.82883 | + | 4.82883i | −0.229945 | + | 0.229945i | ||||
\(22\) | −4.05424 | − | 11.4993i | −0.184284 | − | 0.522697i | ||||
\(23\) | −43.6717 | −1.89877 | −0.949385 | − | 0.314115i | \(-0.898292\pi\) | ||||
−0.949385 | + | 0.314115i | \(0.898292\pi\) | |||||||
\(24\) | 11.7844 | + | 7.28891i | 0.491016 | + | 0.303705i | ||||
\(25\) | − | 59.3629i | − | 2.37452i | ||||||
\(26\) | −3.82091 | − | 10.8375i | −0.146958 | − | 0.416828i | ||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | 9.89101 | + | 12.2837i | 0.353250 | + | 0.438704i | ||||
\(29\) | 25.0979 | + | 25.0979i | 0.865445 | + | 0.865445i | 0.991964 | − | 0.126519i | \(-0.0403806\pi\) |
−0.126519 | + | 0.991964i | \(0.540381\pi\) | |||||||
\(30\) | 13.7375 | − | 28.6991i | 0.457917 | − | 0.956635i | ||||
\(31\) | 32.5024i | 1.04846i | 0.851576 | + | 0.524232i | \(0.175648\pi\) | ||||
−0.851576 | + | 0.524232i | \(0.824352\pi\) | |||||||
\(32\) | 19.6555 | − | 25.2520i | 0.614233 | − | 0.789125i | ||||
\(33\) | −10.5595 | −0.319986 | ||||||||
\(34\) | 26.2547 | + | 12.5675i | 0.772198 | + | 0.369631i | ||||
\(35\) | 25.6069 | − | 25.6069i | 0.731627 | − | 0.731627i | ||||
\(36\) | 9.34661 | − | 7.52602i | 0.259628 | − | 0.209056i | ||||
\(37\) | 4.14345 | − | 4.14345i | 0.111985 | − | 0.111985i | −0.648894 | − | 0.760879i | \(-0.724768\pi\) |
0.760879 | + | 0.648894i | \(0.224768\pi\) | |||||||
\(38\) | −13.1989 | + | 4.65344i | −0.347339 | + | 0.122459i | ||||
\(39\) | −9.95180 | −0.255174 | ||||||||
\(40\) | −62.4917 | − | 38.6525i | −1.56229 | − | 0.966313i | ||||
\(41\) | 55.3348i | 1.34963i | 0.737987 | + | 0.674814i | \(0.235776\pi\) | ||||
−0.737987 | + | 0.674814i | \(0.764224\pi\) | |||||||
\(42\) | 12.8809 | − | 4.54133i | 0.306688 | − | 0.108127i | ||||
\(43\) | −16.1189 | − | 16.1189i | −0.374858 | − | 0.374858i | 0.494385 | − | 0.869243i | \(-0.335393\pi\) |
−0.869243 | + | 0.494385i | \(0.835393\pi\) | |||||||
\(44\) | −2.61613 | + | 24.2455i | −0.0594574 | + | 0.551033i | ||||
\(45\) | −19.4842 | − | 19.4842i | −0.432982 | − | 0.432982i | ||||
\(46\) | 78.7828 | + | 37.7113i | 1.71267 | + | 0.819811i | ||||
\(47\) | − | 7.92420i | − | 0.168600i | −0.996440 | − | 0.0843001i | \(-0.973135\pi\) | ||
0.996440 | − | 0.0843001i | \(-0.0268654\pi\) | |||||||
\(48\) | −14.9647 | − | 23.3251i | −0.311764 | − | 0.485939i | ||||
\(49\) | −33.4549 | −0.682753 | ||||||||
\(50\) | −51.2610 | + | 107.089i | −1.02522 | + | 2.14179i | ||||
\(51\) | 17.8247 | − | 17.8247i | 0.349504 | − | 0.349504i | ||||
\(52\) | −2.46556 | + | 22.8501i | −0.0474147 | + | 0.439424i | ||||
\(53\) | −31.5748 | + | 31.5748i | −0.595750 | + | 0.595750i | −0.939179 | − | 0.343429i | \(-0.888412\pi\) |
0.343429 | + | 0.939179i | \(0.388412\pi\) | |||||||
\(54\) | −3.45547 | − | 9.80101i | −0.0639902 | − | 0.181500i | ||||
\(55\) | 55.9964 | 1.01812 | ||||||||
\(56\) | −7.23597 | − | 30.7006i | −0.129214 | − | 0.548225i | ||||
\(57\) | 12.1202i | 0.212635i | ||||||||
\(58\) | −23.6036 | − | 66.9485i | −0.406958 | − | 1.15429i | ||||
\(59\) | −49.7172 | − | 49.7172i | −0.842665 | − | 0.842665i | 0.146540 | − | 0.989205i | \(-0.453186\pi\) |
−0.989205 | + | 0.146540i | \(0.953186\pi\) | |||||||
\(60\) | −49.5643 | + | 39.9099i | −0.826072 | + | 0.665165i | ||||
\(61\) | 44.4711 | + | 44.4711i | 0.729035 | + | 0.729035i | 0.970427 | − | 0.241393i | \(-0.0776043\pi\) |
−0.241393 | + | 0.970427i | \(0.577604\pi\) | |||||||
\(62\) | 28.0664 | − | 58.6336i | 0.452684 | − | 0.945703i | ||||
\(63\) | − | 11.8282i | − | 0.187749i | ||||||
\(64\) | −57.2636 | + | 28.5812i | −0.894743 | + | 0.446581i | ||||
\(65\) | 52.7736 | 0.811902 | ||||||||
\(66\) | 19.0492 | + | 9.11834i | 0.288624 | + | 0.138157i | ||||
\(67\) | −1.64068 | + | 1.64068i | −0.0244878 | + | 0.0244878i | −0.719245 | − | 0.694757i | \(-0.755512\pi\) |
0.694757 | + | 0.719245i | \(0.255512\pi\) | |||||||
\(68\) | −36.5107 | − | 45.3429i | −0.536922 | − | 0.666807i | ||||
\(69\) | 53.4867 | − | 53.4867i | 0.775170 | − | 0.775170i | ||||
\(70\) | −68.3064 | + | 24.0823i | −0.975805 | + | 0.344033i | ||||
\(71\) | 24.1145 | 0.339641 | 0.169821 | − | 0.985475i | \(-0.445681\pi\) | ||||
0.169821 | + | 0.985475i | \(0.445681\pi\) | |||||||
\(72\) | −23.3599 | + | 5.50581i | −0.324443 | + | 0.0764696i | ||||
\(73\) | 10.7741i | 0.147591i | 0.997273 | + | 0.0737955i | \(0.0235112\pi\) | ||||
−0.997273 | + | 0.0737955i | \(0.976489\pi\) | |||||||
\(74\) | −11.0526 | + | 3.89675i | −0.149360 | + | 0.0526588i | ||||
\(75\) | 72.7044 | + | 72.7044i | 0.969392 | + | 0.969392i | ||||
\(76\) | 27.8288 | + | 3.00278i | 0.366169 | + | 0.0395103i | ||||
\(77\) | 16.9967 | + | 16.9967i | 0.220737 | + | 0.220737i | ||||
\(78\) | 17.9528 | + | 8.59356i | 0.230165 | + | 0.110174i | ||||
\(79\) | − | 72.0517i | − | 0.912047i | −0.889968 | − | 0.456024i | \(-0.849273\pi\) | ||
0.889968 | − | 0.456024i | \(-0.150727\pi\) | |||||||
\(80\) | 79.3565 | + | 123.691i | 0.991956 | + | 1.54614i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 47.7826 | − | 99.8227i | 0.582714 | − | 1.21735i | ||||
\(83\) | 42.0499 | − | 42.0499i | 0.506625 | − | 0.506625i | −0.406864 | − | 0.913489i | \(-0.633378\pi\) |
0.913489 | + | 0.406864i | \(0.133378\pi\) | |||||||
\(84\) | −27.1584 | − | 2.93044i | −0.323314 | − | 0.0348861i | ||||
\(85\) | −94.5229 | + | 94.5229i | −1.11203 | + | 1.11203i | ||||
\(86\) | 15.1592 | + | 42.9971i | 0.176269 | + | 0.499966i | ||||
\(87\) | −61.4770 | −0.706633 | ||||||||
\(88\) | 25.6558 | − | 41.4792i | 0.291543 | − | 0.471354i | ||||
\(89\) | − | 28.9853i | − | 0.325677i | −0.986653 | − | 0.162839i | \(-0.947935\pi\) | ||
0.986653 | − | 0.162839i | \(-0.0520650\pi\) | |||||||
\(90\) | 18.3241 | + | 51.9740i | 0.203601 | + | 0.577488i | ||||
\(91\) | 16.0185 | + | 16.0185i | 0.176028 | + | 0.176028i | ||||
\(92\) | −109.558 | − | 136.061i | −1.19085 | − | 1.47892i | ||||
\(93\) | −39.8071 | − | 39.8071i | −0.428034 | − | 0.428034i | ||||
\(94\) | −6.84269 | + | 14.2951i | −0.0727946 | + | 0.152075i | ||||
\(95\) | − | 64.2724i | − | 0.676552i | ||||||
\(96\) | 6.85432 | + | 55.0002i | 0.0713992 | + | 0.572918i | ||||
\(97\) | −54.2698 | −0.559483 | −0.279741 | − | 0.960075i | \(-0.590249\pi\) | ||||
−0.279741 | + | 0.960075i | \(0.590249\pi\) | |||||||
\(98\) | 60.3519 | + | 28.8889i | 0.615836 | + | 0.294785i | ||||
\(99\) | 12.9327 | − | 12.9327i | 0.130634 | − | 0.130634i | ||||
\(100\) | 184.947 | − | 148.922i | 1.84947 | − | 1.48922i | ||||
\(101\) | 57.0829 | − | 57.0829i | 0.565177 | − | 0.565177i | −0.365597 | − | 0.930773i | \(-0.619135\pi\) |
0.930773 | + | 0.365597i | \(0.119135\pi\) | |||||||
\(102\) | −47.5473 | + | 16.7634i | −0.466150 | + | 0.164347i | ||||
\(103\) | 39.3048 | 0.381600 | 0.190800 | − | 0.981629i | \(-0.438892\pi\) | ||||
0.190800 | + | 0.981629i | \(0.438892\pi\) | |||||||
\(104\) | 24.1793 | − | 39.0920i | 0.232493 | − | 0.375884i | ||||
\(105\) | 62.7239i | 0.597371i | ||||||||
\(106\) | 84.2255 | − | 29.6948i | 0.794581 | − | 0.280140i | ||||
\(107\) | 25.6981 | + | 25.6981i | 0.240169 | + | 0.240169i | 0.816920 | − | 0.576751i | \(-0.195680\pi\) |
−0.576751 | + | 0.816920i | \(0.695680\pi\) | |||||||
\(108\) | −2.22975 | + | 20.6647i | −0.0206459 | + | 0.191339i | ||||
\(109\) | −9.66133 | − | 9.66133i | −0.0886360 | − | 0.0886360i | 0.661399 | − | 0.750035i | \(-0.269963\pi\) |
−0.750035 | + | 0.661399i | \(0.769963\pi\) | |||||||
\(110\) | −101.016 | − | 48.3539i | −0.918329 | − | 0.439581i | ||||
\(111\) | 10.1493i | 0.0914355i | ||||||||
\(112\) | −13.4570 | + | 61.6316i | −0.120152 | + | 0.550282i | ||||
\(113\) | 64.2927 | 0.568962 | 0.284481 | − | 0.958682i | \(-0.408179\pi\) | ||||
0.284481 | + | 0.958682i | \(0.408179\pi\) | |||||||
\(114\) | 10.4660 | − | 21.8645i | 0.0918070 | − | 0.191794i | ||||
\(115\) | −283.636 | + | 283.636i | −2.46640 | + | 2.46640i | ||||
\(116\) | −15.2310 | + | 141.156i | −0.131301 | + | 1.21686i | ||||
\(117\) | 12.1884 | − | 12.1884i | 0.104175 | − | 0.104175i | ||||
\(118\) | 46.7571 | + | 132.620i | 0.396246 | + | 1.12390i | ||||
\(119\) | −57.3816 | −0.482199 | ||||||||
\(120\) | 123.876 | − | 29.1969i | 1.03230 | − | 0.243307i | ||||
\(121\) | − | 83.8321i | − | 0.692827i | ||||||
\(122\) | −41.8233 | − | 118.627i | −0.342814 | − | 0.972348i | ||||
\(123\) | −67.7710 | − | 67.7710i | −0.550984 | − | 0.550984i | ||||
\(124\) | −101.262 | + | 81.5379i | −0.816632 | + | 0.657563i | ||||
\(125\) | −223.178 | − | 223.178i | −1.78542 | − | 1.78542i | ||||
\(126\) | −10.2138 | + | 21.3378i | −0.0810623 | + | 0.169347i | ||||
\(127\) | 129.668i | 1.02101i | 0.859875 | + | 0.510504i | \(0.170541\pi\) | ||||
−0.859875 | + | 0.510504i | \(0.829459\pi\) | |||||||
\(128\) | 127.983 | − | 2.11172i | 0.999864 | − | 0.0164978i | ||||
\(129\) | 39.4830 | 0.306070 | ||||||||
\(130\) | −95.2025 | − | 45.5710i | −0.732327 | − | 0.350546i | ||||
\(131\) | −118.504 | + | 118.504i | −0.904613 | + | 0.904613i | −0.995831 | − | 0.0912183i | \(-0.970924\pi\) |
0.0912183 | + | 0.995831i | \(0.470924\pi\) | |||||||
\(132\) | −26.4904 | − | 32.8986i | −0.200685 | − | 0.249232i | ||||
\(133\) | 19.5088 | − | 19.5088i | 0.146683 | − | 0.146683i | ||||
\(134\) | 4.37651 | − | 1.54299i | 0.0326605 | − | 0.0115149i | ||||
\(135\) | 47.7263 | 0.353528 | ||||||||
\(136\) | 26.7102 | + | 113.325i | 0.196398 | + | 0.833273i | ||||
\(137\) | 157.472i | 1.14943i | 0.818353 | + | 0.574716i | \(0.194888\pi\) | ||||
−0.818353 | + | 0.574716i | \(0.805112\pi\) | |||||||
\(138\) | −142.676 | + | 50.3021i | −1.03388 | + | 0.364508i | ||||
\(139\) | −118.943 | − | 118.943i | −0.855703 | − | 0.855703i | 0.135125 | − | 0.990829i | \(-0.456856\pi\) |
−0.990829 | + | 0.135125i | \(0.956856\pi\) | |||||||
\(140\) | 144.019 | + | 15.5399i | 1.02871 | + | 0.110999i | ||||
\(141\) | 9.70513 | + | 9.70513i | 0.0688307 | + | 0.0688307i | ||||
\(142\) | −43.5021 | − | 20.8233i | −0.306353 | − | 0.146643i | ||||
\(143\) | 35.0288i | 0.244957i | ||||||||
\(144\) | 46.8952 | + | 10.2394i | 0.325661 | + | 0.0711066i | ||||
\(145\) | 326.008 | 2.24833 | ||||||||
\(146\) | 9.30367 | − | 19.4363i | 0.0637238 | − | 0.133125i | ||||
\(147\) | 40.9737 | − | 40.9737i | 0.278733 | − | 0.278733i | ||||
\(148\) | 23.3036 | + | 2.51450i | 0.157457 | + | 0.0169899i | ||||
\(149\) | 99.5402 | − | 99.5402i | 0.668055 | − | 0.668055i | −0.289210 | − | 0.957266i | \(-0.593393\pi\) |
0.957266 | + | 0.289210i | \(0.0933927\pi\) | |||||||
\(150\) | −68.3756 | − | 193.939i | −0.455837 | − | 1.29293i | ||||
\(151\) | 273.705 | 1.81262 | 0.906308 | − | 0.422618i | \(-0.138889\pi\) | ||||
0.906308 | + | 0.422618i | \(0.138889\pi\) | |||||||
\(152\) | −47.6097 | − | 29.4477i | −0.313221 | − | 0.193735i | ||||
\(153\) | 43.6614i | 0.285369i | ||||||||
\(154\) | −15.9848 | − | 45.3387i | −0.103797 | − | 0.294407i | ||||
\(155\) | 211.094 | + | 211.094i | 1.36190 | + | 1.36190i | ||||
\(156\) | −24.9658 | − | 31.0052i | −0.160037 | − | 0.198751i | ||||
\(157\) | −75.8792 | − | 75.8792i | −0.483307 | − | 0.483307i | 0.422879 | − | 0.906186i | \(-0.361019\pi\) |
−0.906186 | + | 0.422879i | \(0.861019\pi\) | |||||||
\(158\) | −62.2180 | + | 129.980i | −0.393785 | + | 0.822657i | ||||
\(159\) | − | 77.3420i | − | 0.486428i | ||||||
\(160\) | −36.3479 | − | 291.662i | −0.227175 | − | 1.82288i | ||||
\(161\) | −172.186 | −1.06948 | ||||||||
\(162\) | 16.2358 | + | 7.77166i | 0.100221 | + | 0.0479732i | ||||
\(163\) | 177.242 | − | 177.242i | 1.08737 | − | 1.08737i | 0.0915766 | − | 0.995798i | \(-0.470809\pi\) |
0.995798 | − | 0.0915766i | \(-0.0291906\pi\) | |||||||
\(164\) | −172.397 | + | 138.817i | −1.05120 | + | 0.846444i | ||||
\(165\) | −68.5812 | + | 68.5812i | −0.415644 | + | 0.415644i | ||||
\(166\) | −112.168 | + | 39.5462i | −0.675710 | + | 0.238230i | ||||
\(167\) | 61.6774 | 0.369326 | 0.184663 | − | 0.982802i | \(-0.440881\pi\) | ||||
0.184663 | + | 0.982802i | \(0.440881\pi\) | |||||||
\(168\) | 46.4626 | + | 28.7382i | 0.276563 | + | 0.171061i | ||||
\(169\) | − | 135.987i | − | 0.804658i | ||||||
\(170\) | 252.140 | − | 88.8950i | 1.48317 | − | 0.522912i | ||||
\(171\) | −14.8441 | − | 14.8441i | −0.0868078 | − | 0.0868078i | ||||
\(172\) | 9.78193 | − | 90.6560i | 0.0568717 | − | 0.527069i | ||||
\(173\) | 69.7012 | + | 69.7012i | 0.402897 | + | 0.402897i | 0.879253 | − | 0.476355i | \(-0.158042\pi\) |
−0.476355 | + | 0.879253i | \(0.658042\pi\) | |||||||
\(174\) | 110.903 | + | 53.0865i | 0.637375 | + | 0.305095i | ||||
\(175\) | − | 234.052i | − | 1.33744i | ||||||
\(176\) | −82.1006 | + | 52.6733i | −0.466481 | + | 0.299280i | ||||
\(177\) | 121.782 | 0.688033 | ||||||||
\(178\) | −25.0293 | + | 52.2888i | −0.140614 | + | 0.293757i | ||||
\(179\) | 43.6228 | − | 43.6228i | 0.243703 | − | 0.243703i | −0.574677 | − | 0.818380i | \(-0.694872\pi\) |
0.818380 | + | 0.574677i | \(0.194872\pi\) | |||||||
\(180\) | 11.8242 | − | 109.583i | 0.0656900 | − | 0.608795i | ||||
\(181\) | −44.7291 | + | 44.7291i | −0.247122 | + | 0.247122i | −0.819788 | − | 0.572666i | \(-0.805909\pi\) |
0.572666 | + | 0.819788i | \(0.305909\pi\) | |||||||
\(182\) | −15.0648 | − | 42.7294i | −0.0827736 | − | 0.234777i | ||||
\(183\) | −108.932 | −0.595254 | ||||||||
\(184\) | 80.1494 | + | 340.056i | 0.435595 | + | 1.84813i | ||||
\(185\) | − | 53.8211i | − | 0.290925i | ||||||
\(186\) | 37.4370 | + | 106.185i | 0.201274 | + | 0.570889i | ||||
\(187\) | −62.7401 | − | 62.7401i | −0.335509 | − | 0.335509i | ||||
\(188\) | 24.6881 | − | 19.8792i | 0.131320 | − | 0.105741i | ||||
\(189\) | 14.4865 | + | 14.4865i | 0.0766482 | + | 0.0766482i | ||||
\(190\) | −55.5004 | + | 115.946i | −0.292107 | + | 0.610242i | ||||
\(191\) | 171.759i | 0.899263i | 0.893214 | + | 0.449632i | \(0.148445\pi\) | ||||
−0.893214 | + | 0.449632i | \(0.851555\pi\) | |||||||
\(192\) | 35.1286 | − | 105.138i | 0.182961 | − | 0.547593i | ||||
\(193\) | −215.384 | −1.11598 | −0.557989 | − | 0.829848i | \(-0.688427\pi\) | ||||
−0.557989 | + | 0.829848i | \(0.688427\pi\) | |||||||
\(194\) | 97.9016 | + | 46.8630i | 0.504647 | + | 0.241562i | ||||
\(195\) | −64.6342 | + | 64.6342i | −0.331458 | + | 0.331458i | ||||
\(196\) | −83.9274 | − | 104.230i | −0.428201 | − | 0.531785i | ||||
\(197\) | −18.3354 | + | 18.3354i | −0.0930731 | + | 0.0930731i | −0.752110 | − | 0.659037i | \(-0.770964\pi\) |
0.659037 | + | 0.752110i | \(0.270964\pi\) | |||||||
\(198\) | −34.4980 | + | 12.1627i | −0.174232 | + | 0.0614279i | ||||
\(199\) | −227.112 | −1.14127 | −0.570634 | − | 0.821205i | \(-0.693302\pi\) | ||||
−0.570634 | + | 0.821205i | \(0.693302\pi\) | |||||||
\(200\) | −462.238 | + | 108.947i | −2.31119 | + | 0.544735i | ||||
\(201\) | − | 4.01883i | − | 0.0199942i | ||||||
\(202\) | −152.268 | + | 53.6842i | −0.753804 | + | 0.265763i | ||||
\(203\) | 98.9542 | + | 98.9542i | 0.487459 | + | 0.487459i | ||||
\(204\) | 100.250 | + | 10.8171i | 0.491420 | + | 0.0530251i | ||||
\(205\) | 359.384 | + | 359.384i | 1.75309 | + | 1.75309i | ||||
\(206\) | −70.9051 | − | 33.9404i | −0.344199 | − | 0.164759i | ||||
\(207\) | 131.015i | 0.632923i | ||||||||
\(208\) | −77.3755 | + | 49.6418i | −0.371998 | + | 0.238663i | ||||
\(209\) | 42.6612 | 0.204120 | ||||||||
\(210\) | 54.1632 | − | 113.153i | 0.257920 | − | 0.538822i | ||||
\(211\) | 190.206 | − | 190.206i | 0.901451 | − | 0.901451i | −0.0941112 | − | 0.995562i | \(-0.530001\pi\) |
0.995562 | + | 0.0941112i | \(0.0300009\pi\) | |||||||
\(212\) | −177.583 | − | 19.1615i | −0.837656 | − | 0.0903845i | ||||
\(213\) | −29.5342 | + | 29.5342i | −0.138658 | + | 0.138658i | ||||
\(214\) | −24.1680 | − | 68.5496i | −0.112935 | − | 0.320325i | ||||
\(215\) | −209.375 | −0.973839 | ||||||||
\(216\) | 21.8667 | − | 35.3532i | 0.101235 | − | 0.163672i | ||||
\(217\) | 128.148i | 0.590544i | ||||||||
\(218\) | 9.08609 | + | 25.7716i | 0.0416793 | + | 0.118218i | ||||
\(219\) | −13.1956 | − | 13.1956i | −0.0602538 | − | 0.0602538i | ||||
\(220\) | 140.477 | + | 174.459i | 0.638530 | + | 0.792994i | ||||
\(221\) | −59.1293 | − | 59.1293i | −0.267553 | − | 0.267553i | ||||
\(222\) | 8.76414 | − | 18.3092i | 0.0394781 | − | 0.0824738i | ||||
\(223\) | − | 154.401i | − | 0.692379i | −0.938165 | − | 0.346190i | \(-0.887475\pi\) | ||
0.938165 | − | 0.346190i | \(-0.112525\pi\) | |||||||
\(224\) | 77.4961 | − | 99.5617i | 0.345965 | − | 0.444472i | ||||
\(225\) | −178.089 | −0.791506 | ||||||||
\(226\) | −115.983 | − | 55.5179i | −0.513197 | − | 0.245654i | ||||
\(227\) | −36.8204 | + | 36.8204i | −0.162204 | + | 0.162204i | −0.783543 | − | 0.621338i | \(-0.786589\pi\) |
0.621338 | + | 0.783543i | \(0.286589\pi\) | |||||||
\(228\) | −37.7609 | + | 30.4056i | −0.165618 | + | 0.133358i | ||||
\(229\) | 17.9692 | − | 17.9692i | 0.0784683 | − | 0.0784683i | −0.666783 | − | 0.745252i | \(-0.732329\pi\) |
0.745252 | + | 0.666783i | \(0.232329\pi\) | |||||||
\(230\) | 756.597 | − | 266.748i | 3.28955 | − | 1.15977i | ||||
\(231\) | −41.6333 | −0.180231 | ||||||||
\(232\) | 149.367 | − | 241.490i | 0.643823 | − | 1.04090i | ||||
\(233\) | − | 167.669i | − | 0.719608i | −0.933028 | − | 0.359804i | \(-0.882844\pi\) | ||
0.933028 | − | 0.359804i | \(-0.117156\pi\) | |||||||
\(234\) | −32.5126 | + | 11.4627i | −0.138943 | + | 0.0489860i | ||||
\(235\) | −51.4655 | − | 51.4655i | −0.219002 | − | 0.219002i | ||||
\(236\) | 30.1715 | − | 279.620i | 0.127845 | − | 1.18483i | ||||
\(237\) | 88.2450 | + | 88.2450i | 0.372342 | + | 0.372342i | ||||
\(238\) | 103.515 | + | 49.5501i | 0.434938 | + | 0.208194i | ||||
\(239\) | − | 29.7509i | − | 0.124481i | −0.998061 | − | 0.0622403i | \(-0.980175\pi\) | ||
0.998061 | − | 0.0622403i | \(-0.0198245\pi\) | |||||||
\(240\) | −248.681 | − | 54.2985i | −1.03617 | − | 0.226244i | ||||
\(241\) | −107.373 | −0.445531 | −0.222766 | − | 0.974872i | \(-0.571508\pi\) | ||||
−0.222766 | + | 0.974872i | \(0.571508\pi\) | |||||||
\(242\) | −72.3905 | + | 151.231i | −0.299134 | + | 0.624923i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −26.9878 | + | 250.115i | −0.110606 | + | 1.02506i | ||||
\(245\) | −217.280 | + | 217.280i | −0.886859 | + | 0.886859i | ||||
\(246\) | 63.7359 | + | 180.779i | 0.259089 | + | 0.734873i | ||||
\(247\) | 40.2059 | 0.162777 | ||||||||
\(248\) | 253.084 | − | 59.6507i | 1.02050 | − | 0.240527i | ||||
\(249\) | 103.001i | 0.413658i | ||||||||
\(250\) | 209.890 | + | 595.326i | 0.839559 | + | 2.38130i | ||||
\(251\) | −342.946 | − | 342.946i | −1.36632 | − | 1.36632i | −0.865623 | − | 0.500697i | \(-0.833077\pi\) |
−0.500697 | − | 0.865623i | \(-0.666923\pi\) | |||||||
\(252\) | 36.8511 | − | 29.6730i | 0.146235 | − | 0.117750i | ||||
\(253\) | −188.265 | − | 188.265i | −0.744130 | − | 0.744130i | ||||
\(254\) | 111.971 | − | 233.918i | 0.440829 | − | 0.920938i | ||||
\(255\) | − | 231.533i | − | 0.907972i | ||||||
\(256\) | −232.701 | − | 106.706i | −0.908989 | − | 0.416819i | ||||
\(257\) | −393.565 | −1.53138 | −0.765691 | − | 0.643209i | \(-0.777603\pi\) | ||||
−0.765691 | + | 0.643209i | \(0.777603\pi\) | |||||||
\(258\) | −71.2265 | − | 34.0943i | −0.276072 | − | 0.132149i | ||||
\(259\) | 16.3365 | − | 16.3365i | 0.0630753 | − | 0.0630753i | ||||
\(260\) | 132.392 | + | 164.418i | 0.509199 | + | 0.632377i | ||||
\(261\) | 75.2937 | − | 75.2937i | 0.288482 | − | 0.288482i | ||||
\(262\) | 316.110 | − | 111.449i | 1.20653 | − | 0.425376i | ||||
\(263\) | 413.800 | 1.57338 | 0.786692 | − | 0.617346i | \(-0.211792\pi\) | ||||
0.786692 | + | 0.617346i | \(0.211792\pi\) | |||||||
\(264\) | 19.3796 | + | 82.2233i | 0.0734076 | + | 0.311452i | ||||
\(265\) | 410.139i | 1.54769i | ||||||||
\(266\) | −52.0396 | + | 18.3472i | −0.195638 | + | 0.0689746i | ||||
\(267\) | 35.4995 | + | 35.4995i | 0.132957 | + | 0.132957i | ||||
\(268\) | −9.22752 | − | 0.995666i | −0.0344311 | − | 0.00371517i | ||||
\(269\) | 165.389 | + | 165.389i | 0.614830 | + | 0.614830i | 0.944201 | − | 0.329371i | \(-0.106837\pi\) |
−0.329371 | + | 0.944201i | \(0.606837\pi\) | |||||||
\(270\) | −86.0972 | − | 41.2125i | −0.318878 | − | 0.152639i | ||||
\(271\) | 309.821i | 1.14325i | 0.820514 | + | 0.571626i | \(0.193687\pi\) | ||||
−0.820514 | + | 0.571626i | \(0.806313\pi\) | |||||||
\(272\) | 49.6738 | − | 227.501i | 0.182624 | − | 0.836400i | ||||
\(273\) | −39.2372 | −0.143726 | ||||||||
\(274\) | 135.980 | − | 284.076i | 0.496278 | − | 1.03678i | ||||
\(275\) | 255.908 | − | 255.908i | 0.930575 | − | 0.930575i | ||||
\(276\) | 300.820 | + | 32.4590i | 1.08993 | + | 0.117605i | ||||
\(277\) | 157.397 | − | 157.397i | 0.568221 | − | 0.568221i | −0.363409 | − | 0.931630i | \(-0.618387\pi\) |
0.931630 | + | 0.363409i | \(0.118387\pi\) | |||||||
\(278\) | 111.861 | + | 317.279i | 0.402377 | + | 1.14129i | ||||
\(279\) | 97.5071 | 0.349488 | ||||||||
\(280\) | −246.388 | − | 152.396i | −0.879956 | − | 0.544273i | ||||
\(281\) | − | 411.141i | − | 1.46313i | −0.681769 | − | 0.731567i | \(-0.738789\pi\) | ||
0.681769 | − | 0.731567i | \(-0.261211\pi\) | |||||||
\(282\) | −9.12729 | − | 25.8884i | −0.0323663 | − | 0.0918028i | ||||
\(283\) | 343.521 | + | 343.521i | 1.21385 | + | 1.21385i | 0.969748 | + | 0.244106i | \(0.0784946\pi\) |
0.244106 | + | 0.969748i | \(0.421505\pi\) | |||||||
\(284\) | 60.4955 | + | 75.1297i | 0.213012 | + | 0.264541i | ||||
\(285\) | 78.7173 | + | 78.7173i | 0.276201 | + | 0.276201i | ||||
\(286\) | 30.2480 | − | 63.1912i | 0.105762 | − | 0.220948i | ||||
\(287\) | 218.170i | 0.760174i | ||||||||
\(288\) | −75.7560 | − | 58.9664i | −0.263042 | − | 0.204744i | ||||
\(289\) | −77.1870 | −0.267083 | ||||||||
\(290\) | −588.111 | − | 281.514i | −2.02797 | − | 0.970737i | ||||
\(291\) | 66.4667 | − | 66.4667i | 0.228408 | − | 0.228408i | ||||
\(292\) | −33.5672 | + | 27.0288i | −0.114956 | + | 0.0925644i | ||||
\(293\) | 35.1386 | − | 35.1386i | 0.119927 | − | 0.119927i | −0.644596 | − | 0.764523i | \(-0.722975\pi\) |
0.764523 | + | 0.644596i | \(0.222975\pi\) | |||||||
\(294\) | −109.297 | + | 38.5341i | −0.371759 | + | 0.131069i | ||||
\(295\) | −645.799 | −2.18915 | ||||||||
\(296\) | −39.8679 | − | 24.6592i | −0.134689 | − | 0.0833081i | ||||
\(297\) | 31.6786i | 0.106662i | ||||||||
\(298\) | −265.523 | + | 93.6136i | −0.891017 | + | 0.314140i | ||||
\(299\) | −177.430 | − | 177.430i | −0.593410 | − | 0.593410i | ||||
\(300\) | −44.1215 | + | 408.905i | −0.147072 | + | 1.36302i | ||||
\(301\) | −63.5524 | − | 63.5524i | −0.211137 | − | 0.211137i | ||||
\(302\) | −493.758 | − | 236.349i | −1.63496 | − | 0.782613i | ||||
\(303\) | 139.824i | 0.461465i | ||||||||
\(304\) | 60.4582 | + | 94.2347i | 0.198876 | + | 0.309983i | ||||
\(305\) | 577.655 | 1.89395 | ||||||||
\(306\) | 37.7024 | − | 78.7642i | 0.123210 | − | 0.257399i | ||||
\(307\) | −16.4432 | + | 16.4432i | −0.0535609 | + | 0.0535609i | −0.733380 | − | 0.679819i | \(-0.762058\pi\) |
0.679819 | + | 0.733380i | \(0.262058\pi\) | |||||||
\(308\) | −10.3147 | + | 95.5932i | −0.0334892 | + | 0.310368i | ||||
\(309\) | −48.1384 | + | 48.1384i | −0.155788 | + | 0.155788i | ||||
\(310\) | −198.526 | − | 563.093i | −0.640405 | − | 1.81643i | ||||
\(311\) | 39.8016 | 0.127980 | 0.0639898 | − | 0.997951i | \(-0.479618\pi\) | ||||
0.0639898 | + | 0.997951i | \(0.479618\pi\) | |||||||
\(312\) | 18.2643 | + | 77.4911i | 0.0585393 | + | 0.248369i | ||||
\(313\) | − | 431.885i | − | 1.37982i | −0.723894 | − | 0.689911i | \(-0.757649\pi\) | ||
0.723894 | − | 0.689911i | \(-0.242351\pi\) | |||||||
\(314\) | 71.3613 | + | 202.407i | 0.227265 | + | 0.644610i | ||||
\(315\) | −76.8208 | − | 76.8208i | −0.243876 | − | 0.243876i | ||||
\(316\) | 224.480 | − | 180.754i | 0.710379 | − | 0.572007i | ||||
\(317\) | 255.063 | + | 255.063i | 0.804615 | + | 0.804615i | 0.983813 | − | 0.179198i | \(-0.0573503\pi\) |
−0.179198 | + | 0.983813i | \(0.557350\pi\) | |||||||
\(318\) | −66.7862 | + | 139.523i | −0.210020 | + | 0.438753i | ||||
\(319\) | 216.390i | 0.678337i | ||||||||
\(320\) | −186.284 | + | 557.538i | −0.582138 | + | 1.74231i | ||||
\(321\) | −62.9472 | −0.196097 | ||||||||
\(322\) | 310.619 | + | 148.685i | 0.964656 | + | 0.461756i | ||||
\(323\) | −72.0128 | + | 72.0128i | −0.222950 | + | 0.222950i | ||||
\(324\) | −22.5781 | − | 28.0398i | −0.0696854 | − | 0.0865426i | ||||
\(325\) | 241.180 | − | 241.180i | 0.742092 | − | 0.742092i | ||||
\(326\) | −472.792 | + | 166.689i | −1.45028 | + | 0.511316i | ||||
\(327\) | 23.6653 | 0.0723710 | ||||||||
\(328\) | 430.872 | − | 101.554i | 1.31363 | − | 0.309617i | ||||
\(329\) | − | 31.2430i | − | 0.0949635i | ||||||
\(330\) | 182.940 | − | 64.4979i | 0.554364 | − | 0.195448i | ||||
\(331\) | 205.897 | + | 205.897i | 0.622045 | + | 0.622045i | 0.946054 | − | 0.324009i | \(-0.105031\pi\) |
−0.324009 | + | 0.946054i | \(0.605031\pi\) | |||||||
\(332\) | 236.497 | + | 25.5185i | 0.712341 | + | 0.0768628i | ||||
\(333\) | −12.4303 | − | 12.4303i | −0.0373284 | − | 0.0373284i | ||||
\(334\) | −111.265 | − | 53.2596i | −0.333128 | − | 0.159460i | ||||
\(335\) | 21.3115i | 0.0636165i | ||||||||
\(336\) | −59.0016 | − | 91.9644i | −0.175600 | − | 0.273703i | ||||
\(337\) | 45.7312 | 0.135701 | 0.0678504 | − | 0.997696i | \(-0.478386\pi\) | ||||
0.0678504 | + | 0.997696i | \(0.478386\pi\) | |||||||
\(338\) | −117.427 | + | 245.318i | −0.347418 | + | 0.725793i | ||||
\(339\) | −78.7421 | + | 78.7421i | −0.232278 | + | 0.232278i | ||||
\(340\) | −531.617 | − | 57.3623i | −1.56358 | − | 0.168713i | ||||
\(341\) | −140.115 | + | 140.115i | −0.410894 | + | 0.410894i | ||||
\(342\) | 13.9603 | + | 39.5967i | 0.0408196 | + | 0.115780i | ||||
\(343\) | −325.097 | −0.947805 | ||||||||
\(344\) | −95.9294 | + | 155.094i | −0.278865 | + | 0.450856i | ||||
\(345\) | − | 694.763i | − | 2.01381i | ||||||
\(346\) | −65.5512 | − | 185.928i | −0.189454 | − | 0.537363i | ||||
\(347\) | 296.512 | + | 296.512i | 0.854500 | + | 0.854500i | 0.990684 | − | 0.136183i | \(-0.0434836\pi\) |
−0.136183 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(348\) | −154.226 | − | 191.534i | −0.443178 | − | 0.550385i | ||||
\(349\) | −198.107 | − | 198.107i | −0.567641 | − | 0.567641i | 0.363826 | − | 0.931467i | \(-0.381470\pi\) |
−0.931467 | + | 0.363826i | \(0.881470\pi\) | |||||||
\(350\) | −202.108 | + | 422.224i | −0.577451 | + | 1.20636i | ||||
\(351\) | 29.8554i | 0.0850581i | ||||||||
\(352\) | 193.592 | − | 24.1261i | 0.549977 | − | 0.0685402i | ||||
\(353\) | 85.4490 | 0.242065 | 0.121033 | − | 0.992649i | \(-0.461379\pi\) | ||||
0.121033 | + | 0.992649i | \(0.461379\pi\) | |||||||
\(354\) | −219.692 | − | 105.161i | −0.620598 | − | 0.297064i | ||||
\(355\) | 156.617 | − | 156.617i | 0.441176 | − | 0.441176i | ||||
\(356\) | 90.3046 | − | 72.7145i | 0.253665 | − | 0.204254i | ||||
\(357\) | 70.2779 | − | 70.2779i | 0.196857 | − | 0.196857i | ||||
\(358\) | −116.364 | + | 41.0255i | −0.325038 | + | 0.114596i | ||||
\(359\) | −302.214 | −0.841823 | −0.420911 | − | 0.907102i | \(-0.638290\pi\) | ||||
−0.420911 | + | 0.907102i | \(0.638290\pi\) | |||||||
\(360\) | −115.958 | + | 187.475i | −0.322104 | + | 0.520764i | ||||
\(361\) | 312.034i | 0.864359i | ||||||||
\(362\) | 119.315 | − | 42.0659i | 0.329599 | − | 0.116204i | ||||
\(363\) | 102.673 | + | 102.673i | 0.282846 | + | 0.282846i | ||||
\(364\) | −9.72104 | + | 90.0916i | −0.0267061 | + | 0.247504i | ||||
\(365\) | 69.9751 | + | 69.9751i | 0.191713 | + | 0.191713i | ||||
\(366\) | 196.510 | + | 94.0643i | 0.536913 | + | 0.257006i | ||||
\(367\) | 372.554i | 1.01513i | 0.861612 | + | 0.507567i | \(0.169455\pi\) | ||||
−0.861612 | + | 0.507567i | \(0.830545\pi\) | |||||||
\(368\) | 149.057 | − | 682.664i | 0.405045 | − | 1.85507i | ||||
\(369\) | 166.004 | 0.449876 | ||||||||
\(370\) | −46.4755 | + | 97.0921i | −0.125610 | + | 0.262411i | ||||
\(371\) | −124.491 | + | 124.491i | −0.335554 | + | 0.335554i | ||||
\(372\) | 24.1574 | − | 223.884i | 0.0649393 | − | 0.601838i | ||||
\(373\) | −407.130 | + | 407.130i | −1.09150 | + | 1.09150i | −0.0961318 | + | 0.995369i | \(0.530647\pi\) |
−0.995369 | + | 0.0961318i | \(0.969353\pi\) | |||||||
\(374\) | 59.0046 | + | 167.359i | 0.157766 | + | 0.447484i | ||||
\(375\) | 546.672 | 1.45779 | ||||||||
\(376\) | −61.7029 | + | 14.5431i | −0.164104 | + | 0.0386784i | ||||
\(377\) | 203.936i | 0.540944i | ||||||||
\(378\) | −13.6240 | − | 38.6427i | −0.0360423 | − | 0.102229i | ||||
\(379\) | −117.854 | − | 117.854i | −0.310961 | − | 0.310961i | 0.534321 | − | 0.845282i | \(-0.320567\pi\) |
−0.845282 | + | 0.534321i | \(0.820567\pi\) | |||||||
\(380\) | 200.243 | − | 161.238i | 0.526955 | − | 0.424312i | ||||
\(381\) | −158.810 | − | 158.810i | −0.416825 | − | 0.416825i | ||||
\(382\) | 148.317 | − | 309.850i | 0.388265 | − | 0.811126i | ||||
\(383\) | − | 407.983i | − | 1.06523i | −0.846357 | − | 0.532615i | \(-0.821209\pi\) | ||
0.846357 | − | 0.532615i | \(-0.178791\pi\) | |||||||
\(384\) | −154.160 | + | 159.332i | −0.401458 | + | 0.414928i | ||||
\(385\) | 220.778 | 0.573450 | ||||||||
\(386\) | 388.548 | + | 185.988i | 1.00660 | + | 0.481834i | ||||
\(387\) | −48.3566 | + | 48.3566i | −0.124953 | + | 0.124953i | ||||
\(388\) | −136.145 | − | 169.080i | −0.350890 | − | 0.435772i | ||||
\(389\) | 458.508 | − | 458.508i | 1.17868 | − | 1.17868i | 0.198605 | − | 0.980080i | \(-0.436359\pi\) |
0.980080 | − | 0.198605i | \(-0.0636411\pi\) | |||||||
\(390\) | 172.412 | − | 60.7859i | 0.442081 | − | 0.155861i | ||||
\(391\) | 635.589 | 1.62555 | ||||||||
\(392\) | 61.3988 | + | 260.501i | 0.156630 | + | 0.664544i | ||||
\(393\) | − | 290.275i | − | 0.738613i | ||||||
\(394\) | 48.9096 | − | 17.2437i | 0.124136 | − | 0.0437658i | ||||
\(395\) | −467.956 | − | 467.956i | −1.18470 | − | 1.18470i | ||||
\(396\) | 72.7364 | + | 7.84838i | 0.183678 | + | 0.0198191i | ||||
\(397\) | −259.865 | − | 259.865i | −0.654573 | − | 0.654573i | 0.299518 | − | 0.954091i | \(-0.403174\pi\) |
−0.954091 | + | 0.299518i | \(0.903174\pi\) | |||||||
\(398\) | 409.705 | + | 196.115i | 1.02941 | + | 0.492752i | ||||
\(399\) | 47.7866i | 0.119766i | ||||||||
\(400\) | 927.944 | + | 202.613i | 2.31986 | + | 0.506531i | ||||
\(401\) | −499.197 | −1.24488 | −0.622441 | − | 0.782667i | \(-0.713859\pi\) | ||||
−0.622441 | + | 0.782667i | \(0.713859\pi\) | |||||||
\(402\) | −3.47033 | + | 7.24988i | −0.00863266 | + | 0.0180345i | ||||
\(403\) | −132.051 | + | 132.051i | −0.327670 | + | 0.327670i | ||||
\(404\) | 321.046 | + | 34.6414i | 0.794668 | + | 0.0857461i | ||||
\(405\) | −58.4525 | + | 58.4525i | −0.144327 | + | 0.144327i | ||||
\(406\) | −93.0624 | − | 263.960i | −0.229218 | − | 0.650147i | ||||
\(407\) | 35.7241 | 0.0877741 | ||||||||
\(408\) | −171.508 | − | 106.081i | −0.420362 | − | 0.260003i | ||||
\(409\) | 494.949i | 1.21014i | 0.796171 | + | 0.605072i | \(0.206856\pi\) | ||||
−0.796171 | + | 0.605072i | \(0.793144\pi\) | |||||||
\(410\) | −337.986 | − | 958.656i | −0.824357 | − | 2.33819i | ||||
\(411\) | −192.863 | − | 192.863i | −0.469254 | − | 0.469254i | ||||
\(412\) | 98.6030 | + | 122.456i | 0.239328 | + | 0.297222i | ||||
\(413\) | −196.021 | − | 196.021i | −0.474628 | − | 0.474628i | ||||
\(414\) | 113.134 | − | 236.348i | 0.273270 | − | 0.570890i | ||||
\(415\) | − | 546.205i | − | 1.31616i | ||||||
\(416\) | 182.450 | − | 22.7376i | 0.438582 | − | 0.0546577i | ||||
\(417\) | 291.349 | 0.698679 | ||||||||
\(418\) | −76.9598 | − | 36.8387i | −0.184114 | − | 0.0881308i | ||||
\(419\) | −560.555 | + | 560.555i | −1.33784 | + | 1.33784i | −0.439693 | + | 0.898148i | \(0.644913\pi\) |
−0.898148 | + | 0.439693i | \(0.855087\pi\) | |||||||
\(420\) | −195.419 | + | 157.354i | −0.465282 | + | 0.374652i | ||||
\(421\) | 397.946 | − | 397.946i | 0.945239 | − | 0.945239i | −0.0533373 | − | 0.998577i | \(-0.516986\pi\) |
0.998577 | + | 0.0533373i | \(0.0169858\pi\) | |||||||
\(422\) | −507.374 | + | 178.881i | −1.20231 | + | 0.423889i | ||||
\(423\) | −23.7726 | −0.0562000 | ||||||||
\(424\) | 303.810 | + | 187.913i | 0.716532 | + | 0.443191i | ||||
\(425\) | 863.956i | 2.03284i | ||||||||
\(426\) | 78.7823 | − | 27.7757i | 0.184935 | − | 0.0652012i | ||||
\(427\) | 175.337 | + | 175.337i | 0.410626 | + | 0.410626i | ||||
\(428\) | −15.5952 | + | 144.531i | −0.0364374 | + | 0.337690i | ||||
\(429\) | −42.9013 | − | 42.9013i | −0.100003 | − | 0.100003i | ||||
\(430\) | 377.709 | + | 180.799i | 0.878392 | + | 0.420464i | ||||
\(431\) | − | 662.874i | − | 1.53799i | −0.639255 | − | 0.768995i | \(-0.720757\pi\) | ||
0.639255 | − | 0.768995i | \(-0.279243\pi\) | |||||||
\(432\) | −69.9752 | + | 44.8940i | −0.161980 | + | 0.103921i | ||||
\(433\) | −338.800 | −0.782448 | −0.391224 | − | 0.920296i | \(-0.627948\pi\) | ||||
−0.391224 | + | 0.920296i | \(0.627948\pi\) | |||||||
\(434\) | 110.658 | − | 231.176i | 0.254973 | − | 0.532664i | ||||
\(435\) | −399.277 | + | 399.277i | −0.917877 | + | 0.917877i | ||||
\(436\) | 5.86309 | − | 54.3373i | 0.0134475 | − | 0.124627i | ||||
\(437\) | −216.090 | + | 216.090i | −0.494484 | + | 0.494484i | ||||
\(438\) | 12.4099 | + | 35.1992i | 0.0283331 | + | 0.0803634i | ||||
\(439\) | −234.566 | −0.534319 | −0.267160 | − | 0.963652i | \(-0.586085\pi\) | ||||
−0.267160 | + | 0.963652i | \(0.586085\pi\) | |||||||
\(440\) | −102.768 | − | 436.024i | −0.233565 | − | 0.990963i | ||||
\(441\) | 100.365i | 0.227584i | ||||||||
\(442\) | 55.6087 | + | 157.727i | 0.125812 | + | 0.356849i | ||||
\(443\) | 421.096 | + | 421.096i | 0.950555 | + | 0.950555i | 0.998834 | − | 0.0482792i | \(-0.0153737\pi\) |
−0.0482792 | + | 0.998834i | \(0.515374\pi\) | |||||||
\(444\) | −31.6206 | + | 25.4614i | −0.0712176 | + | 0.0573454i | ||||
\(445\) | −188.251 | − | 188.251i | −0.423037 | − | 0.423037i | ||||
\(446\) | −133.328 | + | 278.535i | −0.298941 | + | 0.624518i | ||||
\(447\) | 243.823i | 0.545465i | ||||||||
\(448\) | −225.775 | + | 112.688i | −0.503961 | + | 0.251535i | ||||
\(449\) | 492.636 | 1.09718 | 0.548592 | − | 0.836090i | \(-0.315164\pi\) | ||||
0.548592 | + | 0.836090i | \(0.315164\pi\) | |||||||
\(450\) | 321.268 | + | 153.783i | 0.713929 | + | 0.341740i | ||||
\(451\) | −238.543 | + | 238.543i | −0.528921 | + | 0.528921i | ||||
\(452\) | 161.289 | + | 200.306i | 0.356835 | + | 0.443155i | ||||
\(453\) | −335.219 | + | 335.219i | −0.739997 | + | 0.739997i | ||||
\(454\) | 98.2182 | − | 34.6281i | 0.216340 | − | 0.0762733i | ||||
\(455\) | 208.072 | 0.457301 | ||||||||
\(456\) | 94.3755 | − | 22.2438i | 0.206964 | − | 0.0487803i | ||||
\(457\) | 516.831i | 1.13092i | 0.824775 | + | 0.565461i | \(0.191302\pi\) | ||||
−0.824775 | + | 0.565461i | \(0.808698\pi\) | |||||||
\(458\) | −47.9329 | + | 16.8994i | −0.104657 | + | 0.0368981i | ||||
\(459\) | −53.4741 | − | 53.4741i | −0.116501 | − | 0.116501i | ||||
\(460\) | −1595.23 | − | 172.128i | −3.46788 | − | 0.374191i | ||||
\(461\) | −27.5260 | − | 27.5260i | −0.0597093 | − | 0.0597093i | 0.676622 | − | 0.736331i | \(-0.263443\pi\) |
−0.736331 | + | 0.676622i | \(0.763443\pi\) | |||||||
\(462\) | 75.1056 | + | 35.9511i | 0.162566 | + | 0.0778163i | ||||
\(463\) | − | 122.111i | − | 0.263740i | −0.991267 | − | 0.131870i | \(-0.957902\pi\) | ||
0.991267 | − | 0.131870i | \(-0.0420981\pi\) | |||||||
\(464\) | −477.985 | + | 306.661i | −1.03014 | + | 0.660908i | ||||
\(465\) | −517.073 | −1.11198 | ||||||||
\(466\) | −144.785 | + | 302.471i | −0.310697 | + | 0.649079i | ||||
\(467\) | 267.964 | − | 267.964i | 0.573798 | − | 0.573798i | −0.359390 | − | 0.933188i | \(-0.617015\pi\) |
0.933188 | + | 0.359390i | \(0.117015\pi\) | |||||||
\(468\) | 68.5502 | + | 7.39669i | 0.146475 | + | 0.0158049i | ||||
\(469\) | −6.46875 | + | 6.46875i | −0.0137926 | + | 0.0137926i | ||||
\(470\) | 48.4013 | + | 137.284i | 0.102981 | + | 0.292094i | ||||
\(471\) | 185.865 | 0.394618 | ||||||||
\(472\) | −295.886 | + | 478.375i | −0.626876 | + | 1.01351i | ||||
\(473\) | − | 138.974i | − | 0.293814i | ||||||
\(474\) | −82.9909 | − | 235.393i | −0.175086 | − | 0.496610i | ||||
\(475\) | −293.730 | − | 293.730i | −0.618380 | − | 0.618380i | ||||
\(476\) | −143.952 | − | 178.775i | −0.302420 | − | 0.375577i | ||||
\(477\) | 94.7243 | + | 94.7243i | 0.198583 | + | 0.198583i | ||||
\(478\) | −25.6904 | + | 53.6699i | −0.0537456 | + | 0.112280i | ||||
\(479\) | − | 419.084i | − | 0.874915i | −0.899239 | − | 0.437457i | \(-0.855879\pi\) | ||
0.899239 | − | 0.437457i | \(-0.144121\pi\) | |||||||
\(480\) | 401.728 | + | 312.694i | 0.836933 | + | 0.651446i | ||||
\(481\) | 33.6681 | 0.0699960 | ||||||||
\(482\) | 193.699 | + | 92.7186i | 0.401864 | + | 0.192362i | ||||
\(483\) | 210.883 | − | 210.883i | 0.436612 | − | 0.436612i | ||||
\(484\) | 261.182 | − | 210.307i | 0.539632 | − | 0.434519i | ||||
\(485\) | −352.468 | + | 352.468i | −0.726738 | + | 0.726738i | ||||
\(486\) | −29.4030 | + | 10.3664i | −0.0605000 | + | 0.0213301i | ||||
\(487\) | −57.2378 | −0.117531 | −0.0587657 | − | 0.998272i | \(-0.518716\pi\) | ||||
−0.0587657 | + | 0.998272i | \(0.518716\pi\) | |||||||
\(488\) | 264.664 | − | 427.897i | 0.542344 | − | 0.876838i | ||||
\(489\) | 434.153i | 0.887838i | ||||||||
\(490\) | 579.595 | − | 204.344i | 1.18285 | − | 0.417028i | ||||
\(491\) | −301.955 | − | 301.955i | −0.614979 | − | 0.614979i | 0.329260 | − | 0.944239i | \(-0.393201\pi\) |
−0.944239 | + | 0.329260i | \(0.893201\pi\) | |||||||
\(492\) | 41.1276 | − | 381.158i | 0.0835927 | − | 0.774712i | ||||
\(493\) | −365.270 | − | 365.270i | −0.740912 | − | 0.740912i | ||||
\(494\) | −72.5306 | − | 34.7185i | −0.146823 | − | 0.0702804i | ||||
\(495\) | − | 167.989i | − | 0.339372i | ||||||
\(496\) | −508.068 | − | 110.934i | −1.02433 | − | 0.223658i | ||||
\(497\) | 95.0771 | 0.191302 | ||||||||
\(498\) | 88.9430 | − | 185.811i | 0.178600 | − | 0.373115i | ||||
\(499\) | 619.990 | − | 619.990i | 1.24247 | − | 1.24247i | 0.283491 | − | 0.958975i | \(-0.408507\pi\) |
0.958975 | − | 0.283491i | \(-0.0914925\pi\) | |||||||
\(500\) | 135.438 | − | 1255.20i | 0.270876 | − | 2.51040i | ||||
\(501\) | −75.5391 | + | 75.5391i | −0.150777 | + | 0.150777i | ||||
\(502\) | 322.527 | + | 914.808i | 0.642484 | + | 1.82233i | ||||
\(503\) | 222.446 | 0.442239 | 0.221120 | − | 0.975247i | \(-0.429029\pi\) | ||||
0.221120 | + | 0.975247i | \(0.429029\pi\) | |||||||
\(504\) | −92.1018 | + | 21.7079i | −0.182742 | + | 0.0430713i | ||||
\(505\) | − | 741.475i | − | 1.46827i | ||||||
\(506\) | 177.056 | + | 502.196i | 0.349912 | + | 0.992482i | ||||
\(507\) | 166.550 | + | 166.550i | 0.328500 | + | 0.328500i | ||||
\(508\) | −403.985 | + | 325.295i | −0.795246 | + | 0.640344i | ||||
\(509\) | 489.873 | + | 489.873i | 0.962421 | + | 0.962421i | 0.999319 | − | 0.0368976i | \(-0.0117475\pi\) |
−0.0368976 | + | 0.999319i | \(0.511748\pi\) | |||||||
\(510\) | −199.933 | + | 417.680i | −0.392025 | + | 0.818981i | ||||
\(511\) | 42.4795i | 0.0831302i | ||||||||
\(512\) | 327.646 | + | 393.437i | 0.639933 | + | 0.768431i | ||||
\(513\) | 36.3606 | 0.0708783 | ||||||||
\(514\) | 709.983 | + | 339.850i | 1.38129 | + | 0.661188i | ||||
\(515\) | 255.274 | − | 255.274i | 0.495678 | − | 0.495678i | ||||
\(516\) | 99.0500 | + | 123.011i | 0.191957 | + | 0.238393i | ||||
\(517\) | 34.1605 | − | 34.1605i | 0.0660745 | − | 0.0660745i | ||||
\(518\) | −43.5775 | + | 15.3638i | −0.0841265 | + | 0.0296599i | ||||
\(519\) | −170.732 | −0.328964 | ||||||||
\(520\) | −96.8539 | − | 410.929i | −0.186257 | − | 0.790249i | ||||
\(521\) | − | 197.152i | − | 0.378412i | −0.981937 | − | 0.189206i | \(-0.939409\pi\) | ||
0.981937 | − | 0.189206i | \(-0.0605913\pi\) | |||||||
\(522\) | −200.846 | + | 70.8107i | −0.384762 | + | 0.135653i | ||||
\(523\) | 621.874 | + | 621.874i | 1.18905 | + | 1.18905i | 0.977330 | + | 0.211721i | \(0.0679067\pi\) |
0.211721 | + | 0.977330i | \(0.432093\pi\) | |||||||
\(524\) | −666.493 | − | 71.9157i | −1.27193 | − | 0.137244i | ||||
\(525\) | 286.654 | + | 286.654i | 0.546007 | + | 0.546007i | ||||
\(526\) | −746.486 | − | 357.324i | −1.41918 | − | 0.679323i | ||||
\(527\) | − | 473.033i | − | 0.897596i | ||||||
\(528\) | 36.0409 | − | 165.064i | 0.0682593 | − | 0.312620i | ||||
\(529\) | 1378.22 | 2.60533 | ||||||||
\(530\) | 354.162 | − | 739.881i | 0.668231 | − | 1.39600i | ||||
\(531\) | −149.152 | + | 149.152i | −0.280888 | + | 0.280888i | ||||
\(532\) | 109.722 | + | 11.8391i | 0.206243 | + | 0.0222540i | ||||
\(533\) | −224.815 | + | 224.815i | −0.421791 | + | 0.421791i | ||||
\(534\) | −33.3859 | − | 94.6949i | −0.0625204 | − | 0.177331i | ||||
\(535\) | 333.804 | 0.623933 | ||||||||
\(536\) | 15.7865 | + | 9.76429i | 0.0294524 | + | 0.0182170i | ||||
\(537\) | 106.854i | 0.198983i | ||||||||
\(538\) | −155.542 | − | 441.175i | −0.289111 | − | 0.820028i | ||||
\(539\) | −144.221 | − | 144.221i | −0.267572 | − | 0.267572i | ||||
\(540\) | 119.730 | + | 148.693i | 0.221722 | + | 0.275357i | ||||
\(541\) | 423.563 | + | 423.563i | 0.782925 | + | 0.782925i | 0.980323 | − | 0.197398i | \(-0.0632492\pi\) |
−0.197398 | + | 0.980323i | \(0.563249\pi\) | |||||||
\(542\) | 267.536 | − | 558.911i | 0.493609 | − | 1.03120i | ||||
\(543\) | − | 109.563i | − | 0.201774i | ||||||
\(544\) | −286.062 | + | 367.512i | −0.525848 | + | 0.675574i | ||||
\(545\) | −125.495 | −0.230267 | ||||||||
\(546\) | 70.7831 | + | 33.8821i | 0.129639 | + | 0.0620551i | ||||
\(547\) | −14.5553 | + | 14.5553i | −0.0266093 | + | 0.0266093i | −0.720286 | − | 0.693677i | \(-0.755990\pi\) |
0.693677 | + | 0.720286i | \(0.255990\pi\) | |||||||
\(548\) | −490.610 | + | 395.046i | −0.895274 | + | 0.720888i | ||||
\(549\) | 133.413 | − | 133.413i | 0.243012 | − | 0.243012i | ||||
\(550\) | −682.634 | + | 240.671i | −1.24115 | + | 0.437584i | ||||
\(551\) | 248.371 | 0.450764 | ||||||||
\(552\) | −514.644 | − | 318.319i | −0.932327 | − | 0.576665i | ||||
\(553\) | − | 284.080i | − | 0.513708i | ||||||
\(554\) | −419.856 | + | 148.026i | −0.757863 | + | 0.267194i | ||||
\(555\) | 65.9172 | + | 65.9172i | 0.118770 | + | 0.118770i | ||||
\(556\) | 72.1818 | − | 668.959i | 0.129823 | − | 1.20316i | ||||
\(557\) | −351.991 | − | 351.991i | −0.631941 | − | 0.631941i | 0.316614 | − | 0.948554i | \(-0.397454\pi\) |
−0.948554 | + | 0.316614i | \(0.897454\pi\) | |||||||
\(558\) | −175.901 | − | 84.1992i | −0.315234 | − | 0.150895i | ||||
\(559\) | − | 130.976i | − | 0.234304i | ||||||
\(560\) | 312.881 | + | 487.680i | 0.558716 | + | 0.870857i | ||||
\(561\) | 153.681 | 0.273942 | ||||||||
\(562\) | −355.027 | + | 741.689i | −0.631721 | + | 1.31973i | ||||
\(563\) | −150.902 | + | 150.902i | −0.268031 | + | 0.268031i | −0.828307 | − | 0.560275i | \(-0.810695\pi\) |
0.560275 | + | 0.828307i | \(0.310695\pi\) | |||||||
\(564\) | −5.88967 | + | 54.5837i | −0.0104427 | + | 0.0967796i | ||||
\(565\) | 417.563 | − | 417.563i | 0.739050 | − | 0.739050i | ||||
\(566\) | −323.068 | − | 916.341i | −0.570791 | − | 1.61898i | ||||
\(567\) | −35.4845 | −0.0625830 | ||||||||
\(568\) | −44.2567 | − | 187.771i | −0.0779168 | − | 0.330583i | ||||
\(569\) | − | 113.300i | − | 0.199121i | −0.995032 | − | 0.0995603i | \(-0.968256\pi\) | ||
0.995032 | − | 0.0995603i | \(-0.0317436\pi\) | |||||||
\(570\) | −74.0305 | − | 209.978i | −0.129878 | − | 0.368383i | ||||
\(571\) | −207.486 | − | 207.486i | −0.363373 | − | 0.363373i | 0.501680 | − | 0.865053i | \(-0.332715\pi\) |
−0.865053 | + | 0.501680i | \(0.832715\pi\) | |||||||
\(572\) | −109.133 | + | 87.8758i | −0.190793 | + | 0.153629i | ||||
\(573\) | −210.361 | − | 210.361i | −0.367123 | − | 0.367123i | ||||
\(574\) | 188.394 | − | 393.574i | 0.328212 | − | 0.685669i | ||||
\(575\) | 2592.48i | 4.50866i | ||||||||
\(576\) | 85.7436 | + | 171.791i | 0.148860 | + | 0.298248i | ||||
\(577\) | −484.715 | −0.840061 | −0.420031 | − | 0.907510i | \(-0.637981\pi\) | ||||
−0.420031 | + | 0.907510i | \(0.637981\pi\) | |||||||
\(578\) | 139.244 | + | 66.6524i | 0.240906 | + | 0.115316i | ||||
\(579\) | 263.790 | − | 263.790i | 0.455596 | − | 0.455596i | ||||
\(580\) | 817.847 | + | 1015.69i | 1.41008 | + | 1.75119i | ||||
\(581\) | 165.791 | − | 165.791i | 0.285355 | − | 0.285355i | ||||
\(582\) | −177.300 | + | 62.5093i | −0.304639 | + | 0.107404i | ||||
\(583\) | −272.232 | −0.466950 | ||||||||
\(584\) | 83.8944 | − | 19.7735i | 0.143655 | − | 0.0338587i | ||||
\(585\) | − | 158.321i | − | 0.270634i | ||||||
\(586\) | −93.7320 | + | 33.0464i | −0.159952 | + | 0.0563932i | ||||
\(587\) | −540.404 | − | 540.404i | −0.920619 | − | 0.920619i | 0.0764537 | − | 0.997073i | \(-0.475640\pi\) |
−0.997073 | + | 0.0764537i | \(0.975640\pi\) | |||||||
\(588\) | 230.445 | + | 24.8654i | 0.391913 | + | 0.0422881i | ||||
\(589\) | 160.823 | + | 160.823i | 0.273045 | + | 0.273045i | ||||
\(590\) | 1165.01 | + | 557.659i | 1.97459 | + | 0.945185i | ||||
\(591\) | − | 44.9124i | − | 0.0759939i | ||||||
\(592\) | 50.6272 | + | 78.9113i | 0.0855189 | + | 0.133296i | ||||
\(593\) | 411.176 | 0.693383 | 0.346692 | − | 0.937979i | \(-0.387305\pi\) | ||||
0.346692 | + | 0.937979i | \(0.387305\pi\) | |||||||
\(594\) | 27.3550 | − | 57.1475i | 0.0460522 | − | 0.0962079i | ||||
\(595\) | −372.678 | + | 372.678i | −0.626350 | + | 0.626350i | ||||
\(596\) | 559.835 | + | 60.4072i | 0.939320 | + | 0.101354i | ||||
\(597\) | 278.154 | − | 278.154i | 0.465920 | − | 0.465920i | ||||
\(598\) | 166.866 | + | 473.293i | 0.279039 | + | 0.791460i | ||||
\(599\) | −552.839 | −0.922936 | −0.461468 | − | 0.887157i | \(-0.652677\pi\) | ||||
−0.461468 | + | 0.887157i | \(0.652677\pi\) | |||||||
\(600\) | 432.691 | − | 699.556i | 0.721152 | − | 1.16593i | ||||
\(601\) | 881.159i | 1.46615i | 0.680145 | + | 0.733077i | \(0.261917\pi\) | ||||
−0.680145 | + | 0.733077i | \(0.738083\pi\) | |||||||
\(602\) | 59.7684 | + | 169.526i | 0.0992831 | + | 0.281604i | ||||
\(603\) | 4.92204 | + | 4.92204i | 0.00816259 | + | 0.00816259i | ||||
\(604\) | 686.637 | + | 852.738i | 1.13682 | + | 1.41182i | ||||
\(605\) | −544.467 | − | 544.467i | −0.899945 | − | 0.899945i | ||||
\(606\) | 120.740 | − | 252.239i | 0.199242 | − | 0.416236i | ||||
\(607\) | − | 1175.08i | − | 1.93588i | −0.251186 | − | 0.967939i | \(-0.580820\pi\) | ||
0.251186 | − | 0.967939i | \(-0.419180\pi\) | |||||||
\(608\) | −27.6919 | − | 222.204i | −0.0455459 | − | 0.365467i | ||||
\(609\) | −242.387 | −0.398009 | ||||||||
\(610\) | −1042.08 | − | 498.816i | −1.70832 | − | 0.817731i | ||||
\(611\) | 32.1945 | − | 32.1945i | 0.0526915 | − | 0.0526915i | ||||
\(612\) | −136.029 | + | 109.532i | −0.222269 | + | 0.178974i | ||||
\(613\) | −496.928 | + | 496.928i | −0.810649 | + | 0.810649i | −0.984731 | − | 0.174082i | \(-0.944304\pi\) |
0.174082 | + | 0.984731i | \(0.444304\pi\) | |||||||
\(614\) | 43.8622 | − | 15.4642i | 0.0714367 | − | 0.0251859i | ||||
\(615\) | −880.308 | −1.43140 | ||||||||
\(616\) | 101.154 | − | 163.541i | 0.164211 | − | 0.265489i | ||||
\(617\) | − | 623.301i | − | 1.01021i | −0.863057 | − | 0.505106i | \(-0.831453\pi\) | ||
0.863057 | − | 0.505106i | \(-0.168547\pi\) | |||||||
\(618\) | 128.409 | − | 45.2722i | 0.207781 | − | 0.0732560i | ||||
\(619\) | 7.45302 | + | 7.45302i | 0.0120404 | + | 0.0120404i | 0.713101 | − | 0.701061i | \(-0.247290\pi\) |
−0.701061 | + | 0.713101i | \(0.747290\pi\) | |||||||
\(620\) | −128.105 | + | 1187.24i | −0.206621 | + | 1.91490i | ||||
\(621\) | −160.460 | − | 160.460i | −0.258390 | − | 0.258390i | ||||
\(622\) | −71.8013 | − | 34.3694i | −0.115436 | − | 0.0552563i | ||||
\(623\) | − | 114.281i | − | 0.183437i | ||||||
\(624\) | 33.9667 | − | 155.564i | 0.0544338 | − | 0.249301i | ||||
\(625\) | −1414.88 | −2.26381 | ||||||||
\(626\) | −372.940 | + | 779.110i | −0.595751 | + | 1.24458i | ||||
\(627\) | −52.2490 | + | 52.2490i | −0.0833318 | + | 0.0833318i | ||||
\(628\) | 46.0482 | − | 426.760i | 0.0733251 | − | 0.679555i | ||||
\(629\) | −60.3029 | + | 60.3029i | −0.0958711 | + | 0.0958711i | ||||
\(630\) | 72.2469 | + | 204.919i | 0.114678 | + | 0.325268i | ||||
\(631\) | 147.833 | 0.234284 | 0.117142 | − | 0.993115i | \(-0.462627\pi\) | ||||
0.117142 | + | 0.993115i | \(0.462627\pi\) | |||||||
\(632\) | −561.041 | + | 132.234i | −0.887723 | + | 0.209232i | ||||
\(633\) | 465.908i | 0.736031i | ||||||||
\(634\) | −239.877 | − | 680.379i | −0.378354 | − | 1.07315i | ||||
\(635\) | 842.158 | + | 842.158i | 1.32623 | + | 1.32623i | ||||
\(636\) | 240.962 | − | 194.026i | 0.378871 | − | 0.305072i | ||||
\(637\) | −135.921 | − | 135.921i | −0.213376 | − | 0.213376i | ||||
\(638\) | 186.856 | − | 390.362i | 0.292878 | − | 0.611853i | ||||
\(639\) | − | 72.3436i | − | 0.113214i | ||||||
\(640\) | 817.497 | − | 844.927i | 1.27734 | − | 1.32020i | ||||
\(641\) | −782.691 | −1.22105 | −0.610523 | − | 0.791998i | \(-0.709041\pi\) | ||||
−0.610523 | + | 0.791998i | \(0.709041\pi\) | |||||||
\(642\) | 113.555 | + | 54.3561i | 0.176878 | + | 0.0846668i | ||||
\(643\) | 126.760 | − | 126.760i | 0.197138 | − | 0.197138i | −0.601634 | − | 0.798772i | \(-0.705483\pi\) |
0.798772 | + | 0.601634i | \(0.205483\pi\) | |||||||
\(644\) | −431.958 | − | 536.450i | −0.670741 | − | 0.832998i | ||||
\(645\) | 256.431 | − | 256.431i | 0.397568 | − | 0.397568i | ||||
\(646\) | 192.094 | − | 67.7252i | 0.297359 | − | 0.104838i | ||||
\(647\) | 1226.09 | 1.89504 | 0.947520 | − | 0.319697i | \(-0.103581\pi\) | ||||
0.947520 | + | 0.319697i | \(0.103581\pi\) | |||||||
\(648\) | 16.5174 | + | 70.0798i | 0.0254899 | + | 0.108148i | ||||
\(649\) | − | 428.653i | − | 0.660482i | ||||||
\(650\) | −643.347 | + | 226.820i | −0.989764 | + | 0.348954i | ||||
\(651\) | −156.949 | − | 156.949i | −0.241089 | − | 0.241089i | ||||
\(652\) | 996.846 | + | 107.561i | 1.52891 | + | 0.164972i | ||||
\(653\) | 326.300 | + | 326.300i | 0.499694 | + | 0.499694i | 0.911343 | − | 0.411649i | \(-0.135047\pi\) |
−0.411649 | + | 0.911343i | \(0.635047\pi\) | |||||||
\(654\) | −42.6917 | − | 20.4354i | −0.0652779 | − | 0.0312468i | ||||
\(655\) | 1539.31i | 2.35008i | ||||||||
\(656\) | −864.978 | − | 188.864i | −1.31856 | − | 0.287903i | ||||
\(657\) | 32.3224 | 0.0491970 | ||||||||
\(658\) | −26.9789 | + | 56.3616i | −0.0410013 | + | 0.0856560i | ||||
\(659\) | −574.901 | + | 574.901i | −0.872384 | + | 0.872384i | −0.992732 | − | 0.120347i | \(-0.961599\pi\) |
0.120347 | + | 0.992732i | \(0.461599\pi\) | |||||||
\(660\) | −385.715 | − | 41.6193i | −0.584417 | − | 0.0630596i | ||||
\(661\) | 52.8795 | − | 52.8795i | 0.0799993 | − | 0.0799993i | −0.665975 | − | 0.745974i | \(-0.731984\pi\) |
0.745974 | + | 0.665975i | \(0.231984\pi\) | |||||||
\(662\) | −193.638 | − | 549.229i | −0.292504 | − | 0.829651i | ||||
\(663\) | 144.837 | 0.218456 | ||||||||
\(664\) | −404.600 | − | 250.254i | −0.609338 | − | 0.376889i | ||||
\(665\) | − | 253.409i | − | 0.381065i | ||||||
\(666\) | 11.6902 | + | 33.1579i | 0.0175529 | + | 0.0497866i | ||||
\(667\) | −1096.07 | − | 1096.07i | −1.64328 | − | 1.64328i | ||||
\(668\) | 154.729 | + | 192.158i | 0.231630 | + | 0.287662i | ||||
\(669\) | 189.101 | + | 189.101i | 0.282663 | + | 0.282663i | ||||
\(670\) | 18.4029 | − | 38.4455i | 0.0274670 | − | 0.0573814i | ||||
\(671\) | 383.422i | 0.571419i | ||||||||
\(672\) | 27.0247 | + | 216.851i | 0.0402154 | + | 0.322694i | ||||
\(673\) | 342.318 | 0.508645 | 0.254322 | − | 0.967119i | \(-0.418148\pi\) | ||||
0.254322 | + | 0.967119i | \(0.418148\pi\) | |||||||
\(674\) | −82.4981 | − | 39.4897i | −0.122401 | − | 0.0585901i | ||||
\(675\) | 218.113 | − | 218.113i | 0.323131 | − | 0.323131i | ||||
\(676\) | 423.673 | − | 341.147i | 0.626735 | − | 0.504656i | ||||
\(677\) | 107.154 | − | 107.154i | 0.158278 | − | 0.158278i | −0.623525 | − | 0.781803i | \(-0.714300\pi\) |
0.781803 | + | 0.623525i | \(0.214300\pi\) | |||||||
\(678\) | 210.044 | − | 74.0538i | 0.309800 | − | 0.109224i | ||||
\(679\) | −213.971 | −0.315127 | ||||||||
\(680\) | 909.491 | + | 562.541i | 1.33749 | + | 0.827266i | ||||
\(681\) | − | 90.1911i | − | 0.132439i | ||||||
\(682\) | 373.756 | − | 131.772i | 0.548029 | − | 0.193215i | ||||
\(683\) | 724.233 | + | 724.233i | 1.06037 | + | 1.06037i | 0.998057 | + | 0.0623142i | \(0.0198481\pi\) |
0.0623142 | + | 0.998057i | \(0.480152\pi\) | |||||||
\(684\) | 9.00834 | − | 83.4865i | 0.0131701 | − | 0.122056i | ||||
\(685\) | 1022.74 | + | 1022.74i | 1.49305 | + | 1.49305i | ||||
\(686\) | 586.468 | + | 280.727i | 0.854910 | + | 0.409223i | ||||
\(687\) | 44.0155i | 0.0640691i | ||||||||
\(688\) | 306.981 | − | 196.950i | 0.446194 | − | 0.286265i | ||||
\(689\) | −256.564 | −0.372372 | ||||||||
\(690\) | −599.940 | + | 1253.34i | −0.869479 | + | 1.81643i | ||||
\(691\) | 162.528 | − | 162.528i | 0.235207 | − | 0.235207i | −0.579655 | − | 0.814862i | \(-0.696813\pi\) |
0.814862 | + | 0.579655i | \(0.196813\pi\) | |||||||
\(692\) | −42.2990 | + | 392.014i | −0.0611257 | + | 0.566495i | ||||
\(693\) | 50.9902 | − | 50.9902i | 0.0735790 | − | 0.0735790i | ||||
\(694\) | −278.857 | − | 790.943i | −0.401812 | − | 1.13969i | ||||
\(695\) | −1545.00 | −2.22302 | ||||||||
\(696\) | 112.827 | + | 478.700i | 0.162108 | + | 0.687787i | ||||
\(697\) | − | 805.331i | − | 1.15543i | ||||||
\(698\) | 186.312 | + | 528.449i | 0.266922 | + | 0.757090i | ||||
\(699\) | 205.351 | + | 205.351i | 0.293779 | + | 0.293779i | ||||
\(700\) | 729.197 | − | 587.159i | 1.04171 | − | 0.838799i | ||||
\(701\) | −301.659 | − | 301.659i | −0.430327 | − | 0.430327i | 0.458412 | − | 0.888740i | \(-0.348418\pi\) |
−0.888740 | + | 0.458412i | \(0.848418\pi\) | |||||||
\(702\) | 25.7807 | − | 53.8585i | 0.0367246 | − | 0.0767215i | ||||
\(703\) | − | 41.0040i | − | 0.0583271i | ||||||
\(704\) | −370.069 | − | 123.647i | −0.525666 | − | 0.175635i | ||||
\(705\) | 126.064 | 0.178815 | ||||||||
\(706\) | −154.148 | − | 73.7867i | −0.218340 | − | 0.104514i | ||||
\(707\) | 225.062 | − | 225.062i | 0.318334 | − | 0.318334i | ||||
\(708\) | 305.511 | + | 379.415i | 0.431512 | + | 0.535898i | ||||
\(709\) | −629.100 | + | 629.100i | −0.887306 | + | 0.887306i | −0.994264 | − | 0.106958i | \(-0.965889\pi\) |
0.106958 | + | 0.994264i | \(0.465889\pi\) | |||||||
\(710\) | −417.776 | + | 147.292i | −0.588417 | + | 0.207454i | ||||
\(711\) | −216.155 | −0.304016 | ||||||||
\(712\) | −225.698 | + | 53.1958i | −0.316991 | + | 0.0747132i | ||||
\(713\) | − | 1419.43i | − | 1.99079i | ||||||
\(714\) | −187.466 | + | 66.0935i | −0.262557 | + | 0.0925680i | ||||
\(715\) | 227.502 | + | 227.502i | 0.318185 | + | 0.318185i | ||||
\(716\) | 245.344 | + | 26.4730i | 0.342659 | + | 0.0369735i | ||||
\(717\) | 36.4372 | + | 36.4372i | 0.0508190 | + | 0.0508190i | ||||
\(718\) | 545.188 | + | 260.968i | 0.759315 | + | 0.363465i | ||||
\(719\) | 145.542i | 0.202422i | 0.994865 | + | 0.101211i | \(0.0322718\pi\) | ||||
−0.994865 | + | 0.101211i | \(0.967728\pi\) | |||||||
\(720\) | 371.073 | − | 238.069i | 0.515379 | − | 0.330652i | ||||
\(721\) | 154.968 | 0.214935 | ||||||||
\(722\) | 269.447 | − | 562.902i | 0.373195 | − | 0.779643i | ||||
\(723\) | 131.505 | − | 131.505i | 0.181887 | − | 0.181887i | ||||
\(724\) | −251.566 | − | 27.1444i | −0.347466 | − | 0.0374922i | ||||
\(725\) | 1489.88 | − | 1489.88i | 2.05501 | − | 2.05501i | ||||
\(726\) | −96.5598 | − | 273.880i | −0.133002 | − | 0.377245i | ||||
\(727\) | −938.214 | −1.29053 | −0.645264 | − | 0.763960i | \(-0.723253\pi\) | ||||
−0.645264 | + | 0.763960i | \(0.723253\pi\) | |||||||
\(728\) | 95.3322 | − | 154.129i | 0.130951 | − | 0.211716i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −65.8088 | − | 186.658i | −0.0901490 | − | 0.255696i | ||||
\(731\) | 234.591 | + | 234.591i | 0.320918 | + | 0.320918i | ||||
\(732\) | −273.274 | − | 339.380i | −0.373325 | − | 0.463634i | ||||
\(733\) | 692.101 | + | 692.101i | 0.944203 | + | 0.944203i | 0.998524 | − | 0.0543203i | \(-0.0172992\pi\) |
−0.0543203 | + | 0.998524i | \(0.517299\pi\) | |||||||
\(734\) | 321.707 | − | 672.080i | 0.438294 | − | 0.915640i | ||||
\(735\) | − | 532.226i | − | 0.724117i | ||||||
\(736\) | −858.388 | + | 1102.80i | −1.16629 | + | 1.49837i | ||||
\(737\) | −14.1456 | −0.0191935 | ||||||||
\(738\) | −299.468 | − | 143.348i | −0.405783 | − | 0.194238i | ||||
\(739\) | −440.389 | + | 440.389i | −0.595926 | + | 0.595926i | −0.939226 | − | 0.343300i | \(-0.888455\pi\) |
0.343300 | + | 0.939226i | \(0.388455\pi\) | |||||||
\(740\) | 167.682 | − | 135.020i | 0.226597 | − | 0.182459i | ||||
\(741\) | −49.2420 | + | 49.2420i | −0.0664534 | + | 0.0664534i | ||||
\(742\) | 332.078 | − | 117.078i | 0.447545 | − | 0.157788i | ||||
\(743\) | −1010.54 | −1.36008 | −0.680039 | − | 0.733176i | \(-0.738037\pi\) | ||||
−0.680039 | + | 0.733176i | \(0.738037\pi\) | |||||||
\(744\) | −236.907 | + | 383.021i | −0.318423 | + | 0.514813i | ||||
\(745\) | − | 1292.97i | − | 1.73553i | ||||||
\(746\) | 1086.02 | − | 382.889i | 1.45579 | − | 0.513256i | ||||
\(747\) | −126.150 | − | 126.150i | −0.168875 | − | 0.168875i | ||||
\(748\) | 38.0746 | − | 352.863i | 0.0509018 | − | 0.471743i | ||||
\(749\) | 101.321 | + | 101.321i | 0.135275 | + | 0.135275i | ||||
\(750\) | −986.183 | − | 472.061i | −1.31491 | − | 0.629414i | ||||
\(751\) | 776.971i | 1.03458i | 0.855810 | + | 0.517291i | \(0.173060\pi\) | ||||
−0.855810 | + | 0.517291i | \(0.826940\pi\) | |||||||
\(752\) | 123.869 | + | 27.0462i | 0.164719 | + | 0.0359657i | ||||
\(753\) | 840.043 | 1.11560 | ||||||||
\(754\) | 176.102 | − | 367.896i | 0.233557 | − | 0.487925i | ||||
\(755\) | 1777.64 | − | 1777.64i | 2.35449 | − | 2.35449i | ||||
\(756\) | −8.79131 | + | 81.4751i | −0.0116287 | + | 0.107771i | ||||
\(757\) | 375.481 | − | 375.481i | 0.496012 | − | 0.496012i | −0.414182 | − | 0.910194i | \(-0.635932\pi\) |
0.910194 | + | 0.414182i | \(0.135932\pi\) | |||||||
\(758\) | 110.837 | + | 314.376i | 0.146223 | + | 0.414744i | ||||
\(759\) | 461.153 | 0.607579 | ||||||||
\(760\) | −500.466 | + | 117.957i | −0.658508 | + | 0.155207i | ||||
\(761\) | 1502.22i | 1.97400i | 0.160711 | + | 0.987001i | \(0.448621\pi\) | ||||
−0.160711 | + | 0.987001i | \(0.551379\pi\) | |||||||
\(762\) | 149.355 | + | 423.626i | 0.196003 | + | 0.555939i | ||||
\(763\) | −38.0920 | − | 38.0920i | −0.0499239 | − | 0.0499239i | ||||
\(764\) | −535.122 | + | 430.888i | −0.700421 | + | 0.563989i | ||||
\(765\) | 283.569 | + | 283.569i | 0.370678 | + | 0.370678i | ||||
\(766\) | −352.301 | + | 735.993i | −0.459923 | + | 0.960827i | ||||
\(767\) | − | 403.983i | − | 0.526705i | ||||||
\(768\) | 415.687 | − | 154.312i | 0.541259 | − | 0.200928i | ||||
\(769\) | −293.930 | −0.382223 | −0.191112 | − | 0.981568i | \(-0.561209\pi\) | ||||
−0.191112 | + | 0.981568i | \(0.561209\pi\) | |||||||
\(770\) | −398.279 | − | 190.646i | −0.517246 | − | 0.247592i | ||||
\(771\) | 482.017 | − | 482.017i | 0.625184 | − | 0.625184i | ||||
\(772\) | −540.328 | − | 671.036i | −0.699906 | − | 0.869218i | ||||
\(773\) | −748.271 | + | 748.271i | −0.968009 | + | 0.968009i | −0.999504 | − | 0.0314945i | \(-0.989973\pi\) |
0.0314945 | + | 0.999504i | \(0.489973\pi\) | |||||||
\(774\) | 128.991 | − | 45.4775i | 0.166655 | − | 0.0587564i | ||||
\(775\) | 1929.44 | 2.48960 | ||||||||
\(776\) | 99.5999 | + | 422.580i | 0.128350 | + | 0.544562i | ||||
\(777\) | 40.0161i | 0.0515007i | ||||||||
\(778\) | −1223.07 | + | 431.209i | −1.57207 | + | 0.554253i | ||||
\(779\) | 273.799 | + | 273.799i | 0.351475 | + | 0.351475i | ||||
\(780\) | −363.516 | − | 39.2240i | −0.466047 | − | 0.0502872i | ||||
\(781\) | 103.956 | + | 103.956i | 0.133106 | + | 0.133106i | ||||
\(782\) | −1146.59 | − | 548.843i | −1.46623 | − | 0.701845i | ||||
\(783\) | 184.431i | 0.235544i | ||||||||
\(784\) | 114.185 | − | 522.958i | 0.145645 | − | 0.667038i | ||||
\(785\) | −985.629 | −1.25558 | ||||||||
\(786\) | −250.658 | + | 523.650i | −0.318903 | + | 0.666221i | ||||
\(787\) | −735.839 | + | 735.839i | −0.934992 | + | 0.934992i | −0.998012 | − | 0.0630203i | \(-0.979927\pi\) |
0.0630203 | + | 0.998012i | \(0.479927\pi\) | |||||||
\(788\) | −103.122 | − | 11.1271i | −0.130866 | − | 0.0141206i | ||||
\(789\) | −506.799 | + | 506.799i | −0.642331 | + | 0.642331i | ||||
\(790\) | 440.094 | + | 1248.27i | 0.557081 | + | 1.58009i | ||||
\(791\) | 253.488 | 0.320466 | ||||||||
\(792\) | −124.438 | − | 76.9675i | −0.157118 | − | 0.0971811i | ||||
\(793\) | 361.355i | 0.455681i | ||||||||
\(794\) | 244.393 | + | 693.190i | 0.307800 | + | 0.873035i | ||||
\(795\) | −502.315 | − | 502.315i | −0.631843 | − | 0.631843i | ||||
\(796\) | −569.750 | − | 707.576i | −0.715767 | − | 0.888914i | ||||
\(797\) | 212.043 | + | 212.043i | 0.266051 | + | 0.266051i | 0.827507 | − | 0.561455i | \(-0.189758\pi\) |
−0.561455 | + | 0.827507i | \(0.689758\pi\) | |||||||
\(798\) | 41.2646 | − | 86.2060i | 0.0517100 | − | 0.108028i | ||||
\(799\) | 115.327i | 0.144340i | ||||||||
\(800\) | −1499.03 | − | 1166.81i | −1.87379 | − | 1.45851i | ||||
\(801\) | −86.9558 | −0.108559 | ||||||||
\(802\) | 900.541 | + | 431.066i | 1.12287 | + | 0.537489i | ||||
\(803\) | −46.4464 | + | 46.4464i | −0.0578411 | + | 0.0578411i | ||||
\(804\) | 12.5208 | − | 10.0819i | 0.0155731 | − | 0.0125397i | ||||
\(805\) | −1118.30 | + | 1118.30i | −1.38919 | + | 1.38919i | ||||
\(806\) | 352.245 | − | 124.189i | 0.437029 | − | 0.154080i | ||||
\(807\) | −405.119 | −0.502006 | ||||||||
\(808\) | −549.246 | − | 339.721i | −0.679760 | − | 0.420447i | ||||
\(809\) | 827.491i | 1.02286i | 0.859326 | + | 0.511428i | \(0.170883\pi\) | ||||
−0.859326 | + | 0.511428i | \(0.829117\pi\) | |||||||
\(810\) | 155.922 | − | 54.9723i | 0.192496 | − | 0.0678670i | ||||
\(811\) | 112.908 | + | 112.908i | 0.139221 | + | 0.139221i | 0.773283 | − | 0.634062i | \(-0.218613\pi\) |
−0.634062 | + | 0.773283i | \(0.718613\pi\) | |||||||
\(812\) | −60.0515 | + | 556.539i | −0.0739550 | + | 0.685393i | ||||
\(813\) | −379.452 | − | 379.452i | −0.466731 | − | 0.466731i | ||||
\(814\) | −64.4454 | − | 30.8484i | −0.0791713 | − | 0.0378973i | ||||
\(815\) | − | 2302.28i | − | 2.82488i | ||||||
\(816\) | 217.793 | + | 339.468i | 0.266903 | + | 0.416015i | ||||
\(817\) | −159.514 | −0.195243 | ||||||||
\(818\) | 427.397 | − | 892.877i | 0.522491 | − | 1.09154i | ||||
\(819\) | 48.0556 | − | 48.0556i | 0.0586760 | − | 0.0586760i | ||||
\(820\) | −218.097 | + | 2021.25i | −0.265971 | + | 2.46494i | ||||
\(821\) | 555.298 | − | 555.298i | 0.676368 | − | 0.676368i | −0.282808 | − | 0.959176i | \(-0.591266\pi\) |
0.959176 | + | 0.282808i | \(0.0912661\pi\) | |||||||
\(822\) | 181.380 | + | 514.462i | 0.220657 | + | 0.625866i | ||||
\(823\) | 763.799 | 0.928067 | 0.464034 | − | 0.885818i | \(-0.346402\pi\) | ||||
0.464034 | + | 0.885818i | \(0.346402\pi\) | |||||||
\(824\) | −72.1350 | − | 306.053i | −0.0875425 | − | 0.371423i | ||||
\(825\) | 626.844i | 0.759812i | ||||||||
\(826\) | 184.350 | + | 522.886i | 0.223184 | + | 0.633034i | ||||
\(827\) | 116.947 | + | 116.947i | 0.141411 | + | 0.141411i | 0.774268 | − | 0.632858i | \(-0.218118\pi\) |
−0.632858 | + | 0.774268i | \(0.718118\pi\) | |||||||
\(828\) | −408.182 | + | 328.674i | −0.492974 | + | 0.396949i | ||||
\(829\) | 181.419 | + | 181.419i | 0.218841 | + | 0.218841i | 0.808010 | − | 0.589169i | \(-0.200545\pi\) |
−0.589169 | + | 0.808010i | \(0.700545\pi\) | |||||||
\(830\) | −471.658 | + | 985.341i | −0.568262 | + | 1.18716i | ||||
\(831\) | 385.543i | 0.463950i | ||||||||
\(832\) | −348.771 | − | 116.531i | −0.419195 | − | 0.140061i | ||||
\(833\) | 486.896 | 0.584509 | ||||||||
\(834\) | −525.587 | − | 251.585i | −0.630201 | − | 0.301661i | ||||
\(835\) | 400.578 | − | 400.578i | 0.479734 | − | 0.479734i | ||||
\(836\) | 107.023 | + | 132.912i | 0.128018 | + | 0.158986i | ||||
\(837\) | −119.421 | + | 119.421i | −0.142678 | + | 0.142678i | ||||
\(838\) | 1495.28 | − | 527.180i | 1.78434 | − | 0.629093i | ||||
\(839\) | 521.472 | 0.621540 | 0.310770 | − | 0.950485i | \(-0.399413\pi\) | ||||
0.310770 | + | 0.950485i | \(0.399413\pi\) | |||||||
\(840\) | 488.409 | − | 115.115i | 0.581439 | − | 0.137042i | ||||
\(841\) | 418.809i | 0.497989i | ||||||||
\(842\) | −1061.52 | + | 374.252i | −1.26071 | + | 0.444480i | ||||
\(843\) | 503.542 | + | 503.542i | 0.597322 | + | 0.597322i | ||||
\(844\) | 1069.76 | + | 115.429i | 1.26749 | + | 0.136764i | ||||
\(845\) | −883.200 | − | 883.200i | −1.04521 | − | 1.04521i | ||||
\(846\) | 42.8853 | + | 20.5281i | 0.0506918 | + | 0.0242649i | ||||
\(847\) | − | 330.527i | − | 0.390233i | ||||||
\(848\) | −385.799 | − | 601.336i | −0.454952 | − | 0.709123i | ||||
\(849\) | −841.451 | −0.991108 | ||||||||
\(850\) | 746.041 | − | 1558.56i | 0.877696 | − | 1.83360i | ||||
\(851\) | −180.952 | + | 180.952i | −0.212634 | + | 0.212634i | ||||
\(852\) | −166.106 | − | 17.9232i | −0.194960 | − | 0.0210366i | ||||
\(853\) | −644.278 | + | 644.278i | −0.755309 | + | 0.755309i | −0.975465 | − | 0.220156i | \(-0.929343\pi\) |
0.220156 | + | 0.975465i | \(0.429343\pi\) | |||||||
\(854\) | −164.898 | − | 467.712i | −0.193089 | − | 0.547672i | ||||
\(855\) | −192.817 | −0.225517 | ||||||||
\(856\) | 152.939 | − | 247.265i | 0.178667 | − | 0.288861i | ||||
\(857\) | 757.190i | 0.883536i | 0.897129 | + | 0.441768i | \(0.145649\pi\) | ||||
−0.897129 | + | 0.441768i | \(0.854351\pi\) | |||||||
\(858\) | 40.3470 | + | 114.439i | 0.0470245 | + | 0.133379i | ||||
\(859\) | −1011.32 | − | 1011.32i | −1.17732 | − | 1.17732i | −0.980425 | − | 0.196894i | \(-0.936915\pi\) |
−0.196894 | − | 0.980425i | \(-0.563085\pi\) | |||||||
\(860\) | −525.255 | − | 652.316i | −0.610761 | − | 0.758508i | ||||
\(861\) | −267.203 | − | 267.203i | −0.310340 | − | 0.310340i | ||||
\(862\) | −572.403 | + | 1195.81i | −0.664041 | + | 1.38725i | ||||
\(863\) | 598.188i | 0.693149i | 0.938022 | + | 0.346575i | \(0.112655\pi\) | ||||
−0.938022 | + | 0.346575i | \(0.887345\pi\) | |||||||
\(864\) | 165.000 | − | 20.5630i | 0.190973 | − | 0.0237997i | ||||
\(865\) | 905.381 | 1.04668 | ||||||||
\(866\) | 611.187 | + | 292.560i | 0.705759 | + | 0.337829i | ||||
\(867\) | 94.5344 | − | 94.5344i | 0.109036 | − | 0.109036i | ||||
\(868\) | −399.250 | + | 321.482i | −0.459965 | + | 0.370370i | ||||
\(869\) | 310.609 | − | 310.609i | 0.357432 | − | 0.357432i | ||||
\(870\) | 1065.07 | − | 375.504i | 1.22422 | − | 0.431613i | ||||
\(871\) | −13.3315 | −0.0153060 | ||||||||
\(872\) | −57.4981 | + | 92.9604i | −0.0659382 | + | 0.106606i | ||||
\(873\) | 162.810i | 0.186494i | ||||||||
\(874\) | 576.418 | − | 203.224i | 0.659517 | − | 0.232521i | ||||
\(875\) | −879.929 | − | 879.929i | −1.00563 | − | 1.00563i | ||||
\(876\) | 8.00789 | − | 74.2147i | 0.00914143 | − | 0.0847200i | ||||
\(877\) | −664.587 | − | 664.587i | −0.757796 | − | 0.757796i | 0.218125 | − | 0.975921i | \(-0.430006\pi\) |
−0.975921 | + | 0.218125i | \(0.930006\pi\) | |||||||
\(878\) | 423.152 | + | 202.552i | 0.481950 | + | 0.230697i | ||||
\(879\) | 86.0716i | 0.0979199i | ||||||||
\(880\) | −191.122 | + | 875.319i | −0.217184 | + | 0.994681i | ||||
\(881\) | 772.898 | 0.877296 | 0.438648 | − | 0.898659i | \(-0.355458\pi\) | ||||
0.438648 | + | 0.898659i | \(0.355458\pi\) | |||||||
\(882\) | 86.6667 | − | 181.056i | 0.0982616 | − | 0.205279i | ||||
\(883\) | −321.603 | + | 321.603i | −0.364216 | + | 0.364216i | −0.865363 | − | 0.501146i | \(-0.832912\pi\) |
0.501146 | + | 0.865363i | \(0.332912\pi\) | |||||||
\(884\) | 35.8833 | − | 332.555i | 0.0405920 | − | 0.376194i | ||||
\(885\) | 790.939 | − | 790.939i | 0.893717 | − | 0.893717i | ||||
\(886\) | −396.024 | − | 1123.27i | −0.446979 | − | 1.26780i | ||||
\(887\) | 762.665 | 0.859825 | 0.429912 | − | 0.902871i | \(-0.358544\pi\) | ||||
0.429912 | + | 0.902871i | \(0.358544\pi\) | |||||||
\(888\) | 79.0292 | − | 18.6268i | 0.0889969 | − | 0.0209761i | ||||
\(889\) | 511.245i | 0.575079i | ||||||||
\(890\) | 177.043 | + | 502.160i | 0.198925 | + | 0.564224i | ||||
\(891\) | −38.7982 | − | 38.7982i | −0.0435445 | − | 0.0435445i | ||||
\(892\) | 481.040 | − | 387.341i | 0.539283 | − | 0.434238i | ||||
\(893\) | −39.2093 | − | 39.2093i | −0.0439074 | − | 0.0439074i | ||||
\(894\) | 210.545 | − | 439.851i | 0.235509 | − | 0.492003i | ||||
\(895\) | − | 566.637i | − | 0.633114i | ||||||
\(896\) | 504.600 | − | 8.32594i | 0.563170 | − | 0.00929234i | ||||
\(897\) | 434.612 | 0.484518 | ||||||||
\(898\) | −888.704 | − | 425.400i | −0.989648 | − | 0.473719i | ||||
\(899\) | −815.741 | + | 815.741i | −0.907388 | + | 0.907388i | ||||
\(900\) | −446.767 | − | 554.842i | −0.496407 | − | 0.616491i | ||||
\(901\) | 459.533 | − | 459.533i | 0.510025 | − | 0.510025i | ||||
\(902\) | 636.313 | − | 224.340i | 0.705447 | − | 0.248714i | ||||
\(903\) | 155.671 | 0.172393 | ||||||||
\(904\) | −117.994 | − | 500.624i | −0.130525 | − | 0.553787i | ||||
\(905\) | 581.006i | 0.641996i | ||||||||
\(906\) | 894.195 | − | 315.260i | 0.986970 | − | 0.347969i | ||||
\(907\) | −729.007 | − | 729.007i | −0.803756 | − | 0.803756i | 0.179924 | − | 0.983680i | \(-0.442415\pi\) |
−0.983680 | + | 0.179924i | \(0.942415\pi\) | |||||||
\(908\) | −207.086 | − | 22.3449i | −0.228068 | − | 0.0246089i | ||||
\(909\) | −171.249 | − | 171.249i | −0.188392 | − | 0.188392i | ||||
\(910\) | −375.357 | − | 179.674i | −0.412481 | − | 0.197444i | ||||
\(911\) | 885.541i | 0.972054i | 0.873944 | + | 0.486027i | \(0.161554\pi\) | ||||
−0.873944 | + | 0.486027i | \(0.838446\pi\) | |||||||
\(912\) | −189.459 | − | 41.3676i | −0.207741 | − | 0.0453592i | ||||
\(913\) | 362.546 | 0.397094 | ||||||||
\(914\) | 446.293 | − | 932.352i | 0.488286 | − | 1.02008i | ||||
\(915\) | −707.480 | + | 707.480i | −0.773203 | + | 0.773203i | ||||
\(916\) | 101.063 | + | 10.9048i | 0.110331 | + | 0.0119049i | ||||
\(917\) | −467.230 | + | 467.230i | −0.509520 | + | 0.509520i | ||||
\(918\) | 50.2902 | + | 142.642i | 0.0547824 | + | 0.155383i | ||||
\(919\) | 714.964 | 0.777980 | 0.388990 | − | 0.921242i | \(-0.372824\pi\) | ||||
0.388990 | + | 0.921242i | \(0.372824\pi\) | |||||||
\(920\) | 2729.12 | + | 1688.02i | 2.96643 | + | 1.83481i | ||||
\(921\) | − | 40.2774i | − | 0.0437323i | ||||||
\(922\) | 25.8871 | + | 73.4255i | 0.0280771 | + | 0.0796371i | ||||
\(923\) | 97.9727 | + | 97.9727i | 0.106146 | + | 0.106146i | ||||
\(924\) | −104.444 | − | 129.710i | −0.113035 | − | 0.140379i | ||||
\(925\) | −245.967 | − | 245.967i | −0.265911 | − | 0.265911i | ||||
\(926\) | −105.445 | + | 220.286i | −0.113872 | + | 0.237890i | ||||
\(927\) | − | 117.914i | − | 0.127200i | ||||||
\(928\) | 1127.08 | − | 140.461i | 1.21453 | − | 0.151359i | ||||
\(929\) | 585.585 | 0.630339 | 0.315170 | − | 0.949035i | \(-0.397939\pi\) | ||||
0.315170 | + | 0.949035i | \(0.397939\pi\) | |||||||
\(930\) | 932.788 | + | 446.502i | 1.00300 | + | 0.480109i | ||||
\(931\) | −165.536 | + | 165.536i | −0.177805 | + | 0.177805i | ||||
\(932\) | 522.378 | − | 420.626i | 0.560491 | − | 0.451315i | ||||
\(933\) | −48.7468 | + | 48.7468i | −0.0522474 | + | 0.0522474i | ||||
\(934\) | −714.792 | + | 252.009i | −0.765302 | + | 0.269817i | ||||
\(935\) | −814.960 | −0.871614 | ||||||||
\(936\) | −117.276 | − | 72.5378i | −0.125295 | − | 0.0774977i | ||||
\(937\) | − | 1423.91i | − | 1.51965i | −0.650129 | − | 0.759824i | \(-0.725285\pi\) | ||
0.650129 | − | 0.759824i | \(-0.274715\pi\) | |||||||
\(938\) | 17.2554 | − | 6.08360i | 0.0183959 | − | 0.00648572i | ||||
\(939\) | 528.948 | + | 528.948i | 0.563310 | + | 0.563310i | ||||
\(940\) | 31.2325 | − | 289.453i | 0.0332260 | − | 0.307929i | ||||
\(941\) | 142.471 | + | 142.471i | 0.151404 | + | 0.151404i | 0.778745 | − | 0.627341i | \(-0.215857\pi\) |
−0.627341 | + | 0.778745i | \(0.715857\pi\) | |||||||
\(942\) | −335.297 | − | 160.498i | −0.355941 | − | 0.170380i | ||||
\(943\) | − | 2416.56i | − | 2.56264i | ||||||
\(944\) | 946.856 | − | 607.475i | 1.00303 | − | 0.643511i | ||||
\(945\) | 188.172 | 0.199124 | ||||||||
\(946\) | −120.007 | + | 250.706i | −0.126857 | + | 0.265017i | ||||
\(947\) | 174.352 | − | 174.352i | 0.184110 | − | 0.184110i | −0.609034 | − | 0.793144i | \(-0.708443\pi\) |
0.793144 | + | 0.609034i | \(0.208443\pi\) | |||||||
\(948\) | −53.5525 | + | 496.308i | −0.0564900 | + | 0.523532i | ||||
\(949\) | −43.7733 | + | 43.7733i | −0.0461257 | + | 0.0461257i | ||||
\(950\) | 276.242 | + | 783.525i | 0.290781 | + | 0.824763i | ||||
\(951\) | −624.774 | −0.656965 | ||||||||
\(952\) | 105.311 | + | 446.810i | 0.110621 | + | 0.469339i | ||||
\(953\) | − | 66.9080i | − | 0.0702078i | −0.999384 | − | 0.0351039i | \(-0.988824\pi\) | ||
0.999384 | − | 0.0351039i | \(-0.0111762\pi\) | |||||||
\(954\) | −89.0844 | − | 252.677i | −0.0933799 | − | 0.264860i | ||||
\(955\) | 1115.53 | + | 1115.53i | 1.16809 | + | 1.16809i | ||||
\(956\) | 92.6899 | − | 74.6352i | 0.0969559 | − | 0.0780703i | ||||
\(957\) | −265.022 | − | 265.022i | −0.276930 | − | 0.276930i | ||||
\(958\) | −361.887 | + | 756.019i | −0.377752 | + | 0.789163i | ||||
\(959\) | 620.870i | 0.647414i | ||||||||
\(960\) | −454.691 | − | 910.992i | −0.473637 | − | 0.948950i | ||||
\(961\) | −95.4048 | −0.0992766 | ||||||||
\(962\) | −60.7365 | − | 29.0730i | −0.0631356 | − | 0.0302214i | ||||
\(963\) | 77.0943 | − | 77.0943i | 0.0800564 | − | 0.0800564i | ||||
\(964\) | −269.364 | − | 334.525i | −0.279423 | − | 0.347017i | ||||
\(965\) | −1398.86 | + | 1398.86i | −1.44959 | + | 1.44959i | ||||
\(966\) | −562.531 | + | 198.327i | −0.582330 | + | 0.205308i | ||||
\(967\) | −128.892 | −0.133290 | −0.0666451 | − | 0.997777i | \(-0.521230\pi\) | ||||
−0.0666451 | + | 0.997777i | \(0.521230\pi\) | |||||||
\(968\) | −652.771 | + | 153.855i | −0.674350 | + | 0.158941i | ||||
\(969\) | − | 176.395i | − | 0.182038i | ||||||
\(970\) | 940.206 | − | 331.482i | 0.969285 | − | 0.341734i | ||||
\(971\) | −801.089 | − | 801.089i | −0.825015 | − | 0.825015i | 0.161808 | − | 0.986822i | \(-0.448268\pi\) |
−0.986822 | + | 0.161808i | \(0.948268\pi\) | |||||||
\(972\) | 61.9940 | + | 6.68926i | 0.0637798 | + | 0.00688195i | ||||
\(973\) | −468.959 | − | 468.959i | −0.481972 | − | 0.481972i | ||||
\(974\) | 103.256 | + | 49.4258i | 0.106012 | + | 0.0507452i | ||||
\(975\) | 590.768i | 0.605916i | ||||||||
\(976\) | −846.945 | + | 543.375i | −0.867771 | + | 0.556736i | ||||
\(977\) | −1591.49 | −1.62896 | −0.814479 | − | 0.580194i | \(-0.802977\pi\) | ||||
−0.814479 | + | 0.580194i | \(0.802977\pi\) | |||||||
\(978\) | 374.899 | − | 783.202i | 0.383332 | − | 0.800820i | ||||
\(979\) | 124.953 | − | 124.953i | 0.127633 | − | 0.127633i | ||||
\(980\) | −1222.03 | − | 131.859i | −1.24697 | − | 0.134550i | ||||
\(981\) | −28.9840 | + | 28.9840i | −0.0295453 | + | 0.0295453i | ||||
\(982\) | 283.976 | + | 805.463i | 0.289182 | + | 0.820227i | ||||
\(983\) | −1699.86 | −1.72926 | −0.864631 | − | 0.502408i | \(-0.832448\pi\) | ||||
−0.864631 | + | 0.502408i | \(0.832448\pi\) | |||||||
\(984\) | −403.330 | + | 652.087i | −0.409889 | + | 0.662690i | ||||
\(985\) | 238.167i | 0.241794i | ||||||||
\(986\) | 343.522 | + | 974.355i | 0.348399 | + | 0.988190i | ||||
\(987\) | 38.2647 | + | 38.2647i | 0.0387687 | + | 0.0387687i | ||||
\(988\) | 100.863 | + | 125.263i | 0.102089 | + | 0.126784i | ||||
\(989\) | 703.939 | + | 703.939i | 0.711769 | + | 0.711769i | ||||
\(990\) | −145.062 | + | 303.049i | −0.146527 | + | 0.306110i | ||||
\(991\) | − | 228.875i | − | 0.230954i | −0.993310 | − | 0.115477i | \(-0.963160\pi\) | ||
0.993310 | − | 0.115477i | \(-0.0368397\pi\) | |||||||
\(992\) | 820.750 | + | 638.849i | 0.827369 | + | 0.644001i | ||||
\(993\) | −504.342 | −0.507898 | ||||||||
\(994\) | −171.517 | − | 82.1008i | −0.172552 | − | 0.0825963i | ||||
\(995\) | −1475.03 | + | 1475.03i | −1.48244 | + | 1.48244i | ||||
\(996\) | −320.902 | + | 258.395i | −0.322191 | + | 0.259433i | ||||
\(997\) | 1020.63 | − | 1020.63i | 1.02370 | − | 1.02370i | 0.0239926 | − | 0.999712i | \(-0.492362\pi\) |
0.999712 | − | 0.0239926i | \(-0.00763781\pi\) | |||||||
\(998\) | −1653.82 | + | 583.076i | −1.65714 | + | 0.584245i | ||||
\(999\) | 30.4480 | 0.0304785 |
(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 | 48.3.l.a.19.2 | ✓ | 16 | |
3.2 | odd | 2 | 144.3.m.c.19.7 | 16 | |||
4.3 | odd | 2 | 192.3.l.a.175.8 | 16 | |||
8.3 | odd | 2 | 384.3.l.b.223.1 | 16 | |||
8.5 | even | 2 | 384.3.l.a.223.5 | 16 | |||
12.11 | even | 2 | 576.3.m.c.559.1 | 16 | |||
16.3 | odd | 4 | 384.3.l.a.31.5 | 16 | |||
16.5 | even | 4 | 192.3.l.a.79.8 | 16 | |||
16.11 | odd | 4 | inner | 48.3.l.a.43.2 | yes | 16 | |
16.13 | even | 4 | 384.3.l.b.31.1 | 16 | |||
24.5 | odd | 2 | 1152.3.m.f.991.8 | 16 | |||
24.11 | even | 2 | 1152.3.m.c.991.8 | 16 | |||
48.5 | odd | 4 | 576.3.m.c.271.1 | 16 | |||
48.11 | even | 4 | 144.3.m.c.91.7 | 16 | |||
48.29 | odd | 4 | 1152.3.m.c.415.8 | 16 | |||
48.35 | even | 4 | 1152.3.m.f.415.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
48.3.l.a.43.2 | yes | 16 | 16.11 | odd | 4 | inner | |
144.3.m.c.19.7 | 16 | 3.2 | odd | 2 | |||
144.3.m.c.91.7 | 16 | 48.11 | even | 4 | |||
192.3.l.a.79.8 | 16 | 16.5 | even | 4 | |||
192.3.l.a.175.8 | 16 | 4.3 | odd | 2 | |||
384.3.l.a.31.5 | 16 | 16.3 | odd | 4 | |||
384.3.l.a.223.5 | 16 | 8.5 | even | 2 | |||
384.3.l.b.31.1 | 16 | 16.13 | even | 4 | |||
384.3.l.b.223.1 | 16 | 8.3 | odd | 2 | |||
576.3.m.c.271.1 | 16 | 48.5 | odd | 4 | |||
576.3.m.c.559.1 | 16 | 12.11 | even | 2 | |||
1152.3.m.c.415.8 | 16 | 48.29 | odd | 4 | |||
1152.3.m.c.991.8 | 16 | 24.11 | even | 2 | |||
1152.3.m.f.415.8 | 16 | 48.35 | even | 4 | |||
1152.3.m.f.991.8 | 16 | 24.5 | odd | 2 |