Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(269,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.n (of order \(6\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 359.2 | ||
Root | \(-1.16746 + 0.312819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.359 |
Dual form | 370.2.n.f.269.2 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −1.41240 | − | 0.815449i | −0.815449 | − | 0.470800i | 0.0333957 | − | 0.999442i | \(-0.489368\pi\) |
−0.848844 | + | 0.528643i | \(0.822701\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.60976 | − | 1.55199i | −0.719905 | − | 0.694073i | ||||
\(6\) | 1.63090 | 0.665811 | ||||||||
\(7\) | 0.466951 | + | 0.269594i | 0.176491 | + | 0.101897i | 0.585643 | − | 0.810569i | \(-0.300842\pi\) |
−0.409152 | + | 0.912466i | \(0.634175\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.170086 | − | 0.294598i | −0.0566955 | − | 0.0981995i | ||||
\(10\) | 2.17009 | + | 0.539189i | 0.686242 | + | 0.170506i | ||||
\(11\) | −0.829914 | −0.250228 | −0.125114 | − | 0.992142i | \(-0.539930\pi\) | ||||
−0.125114 | + | 0.992142i | \(0.539930\pi\) | |||||||
\(12\) | −1.41240 | + | 0.815449i | −0.407724 | + | 0.235400i | ||||
\(13\) | 0.945448 | + | 0.545854i | 0.262220 | + | 0.151393i | 0.625347 | − | 0.780347i | \(-0.284958\pi\) |
−0.363127 | + | 0.931740i | \(0.618291\pi\) | |||||||
\(14\) | −0.539189 | −0.144104 | ||||||||
\(15\) | 1.00804 | + | 3.50471i | 0.260276 | + | 0.904912i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.01332 | + | 0.585043i | −0.245767 | + | 0.141894i | −0.617825 | − | 0.786316i | \(-0.711986\pi\) |
0.372057 | + | 0.928210i | \(0.378652\pi\) | |||||||
\(18\) | 0.294598 | + | 0.170086i | 0.0694375 | + | 0.0400898i | ||||
\(19\) | −3.87936 | + | 6.71925i | −0.889987 | + | 1.54150i | −0.0500974 | + | 0.998744i | \(0.515953\pi\) |
−0.839889 | + | 0.542758i | \(0.817380\pi\) | |||||||
\(20\) | −2.14894 | + | 0.618092i | −0.480519 | + | 0.138210i | ||||
\(21\) | −0.439681 | − | 0.761550i | −0.0959462 | − | 0.166184i | ||||
\(22\) | 0.718726 | − | 0.414957i | 0.153233 | − | 0.0884691i | ||||
\(23\) | − | 0.539189i | − | 0.112429i | −0.998419 | − | 0.0562143i | \(-0.982097\pi\) | ||
0.998419 | − | 0.0562143i | \(-0.0179030\pi\) | |||||||
\(24\) | 0.815449 | − | 1.41240i | 0.166453 | − | 0.288305i | ||||
\(25\) | 0.182626 | + | 4.99666i | 0.0365252 | + | 0.999333i | ||||
\(26\) | −1.09171 | −0.214102 | ||||||||
\(27\) | 5.44748i | 1.04837i | ||||||||
\(28\) | 0.466951 | − | 0.269594i | 0.0882455 | − | 0.0509486i | ||||
\(29\) | −9.57531 | −1.77809 | −0.889045 | − | 0.457820i | \(-0.848630\pi\) | ||||
−0.889045 | + | 0.457820i | \(0.848630\pi\) | |||||||
\(30\) | −2.62535 | − | 2.53114i | −0.479321 | − | 0.462122i | ||||
\(31\) | 3.09171 | 0.555287 | 0.277644 | − | 0.960684i | \(-0.410447\pi\) | ||||
0.277644 | + | 0.960684i | \(0.410447\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 1.17217 | + | 0.676752i | 0.204048 | + | 0.117807i | ||||
\(34\) | 0.585043 | − | 1.01332i | 0.100334 | − | 0.173784i | ||||
\(35\) | −0.333268 | − | 1.15869i | −0.0563326 | − | 0.195854i | ||||
\(36\) | −0.340173 | −0.0566955 | ||||||||
\(37\) | −4.29353 | + | 4.30878i | −0.705852 | + | 0.708360i | ||||
\(38\) | − | 7.75872i | − | 1.25863i | ||||||
\(39\) | −0.890233 | − | 1.54193i | −0.142551 | − | 0.246906i | ||||
\(40\) | 1.55199 | − | 1.60976i | 0.245392 | − | 0.254525i | ||||
\(41\) | −0.960811 | + | 1.66417i | −0.150053 | + | 0.259900i | −0.931247 | − | 0.364389i | \(-0.881278\pi\) |
0.781193 | + | 0.624289i | \(0.214611\pi\) | |||||||
\(42\) | 0.761550 | + | 0.439681i | 0.117510 | + | 0.0678442i | ||||
\(43\) | 1.29072i | 0.196834i | 0.995145 | + | 0.0984168i | \(0.0313778\pi\) | ||||
−0.995145 | + | 0.0984168i | \(0.968622\pi\) | |||||||
\(44\) | −0.414957 | + | 0.718726i | −0.0625571 | + | 0.108352i | ||||
\(45\) | −0.183417 | + | 0.738205i | −0.0273423 | + | 0.110045i | ||||
\(46\) | 0.269594 | + | 0.466951i | 0.0397495 | + | 0.0688482i | ||||
\(47\) | − | 5.80098i | − | 0.846160i | −0.906092 | − | 0.423080i | \(-0.860949\pi\) | ||
0.906092 | − | 0.423080i | \(-0.139051\pi\) | |||||||
\(48\) | 1.63090i | 0.235400i | ||||||||
\(49\) | −3.35464 | − | 5.81040i | −0.479234 | − | 0.830058i | ||||
\(50\) | −2.65649 | − | 4.23592i | −0.375685 | − | 0.599050i | ||||
\(51\) | 1.90829 | 0.267214 | ||||||||
\(52\) | 0.945448 | − | 0.545854i | 0.131110 | − | 0.0756964i | ||||
\(53\) | −3.06503 | + | 1.76959i | −0.421014 | + | 0.243072i | −0.695511 | − | 0.718515i | \(-0.744822\pi\) |
0.274497 | + | 0.961588i | \(0.411489\pi\) | |||||||
\(54\) | −2.72374 | − | 4.71766i | −0.370654 | − | 0.641992i | ||||
\(55\) | 1.33596 | + | 1.28802i | 0.180141 | + | 0.173677i | ||||
\(56\) | −0.269594 | + | 0.466951i | −0.0360261 | + | 0.0623990i | ||||
\(57\) | 10.9584 | − | 6.32684i | 1.45148 | − | 0.838011i | ||||
\(58\) | 8.29246 | − | 4.78765i | 1.08885 | − | 0.628650i | ||||
\(59\) | 1.95415 | + | 3.38468i | 0.254408 | + | 0.440648i | 0.964735 | − | 0.263225i | \(-0.0847860\pi\) |
−0.710326 | + | 0.703872i | \(0.751453\pi\) | |||||||
\(60\) | 3.53919 | + | 0.879362i | 0.456907 | + | 0.113525i | ||||
\(61\) | 0.908291 | − | 1.57321i | 0.116295 | − | 0.201428i | −0.802002 | − | 0.597322i | \(-0.796232\pi\) |
0.918297 | + | 0.395893i | \(0.129565\pi\) | |||||||
\(62\) | −2.67750 | + | 1.54585i | −0.340043 | + | 0.196324i | ||||
\(63\) | − | 0.183417i | − | 0.0231084i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.674776 | − | 2.34602i | −0.0836957 | − | 0.290988i | ||||
\(66\) | −1.35350 | −0.166605 | ||||||||
\(67\) | 11.0744 | + | 6.39383i | 1.35296 | + | 0.781130i | 0.988663 | − | 0.150154i | \(-0.0479768\pi\) |
0.364295 | + | 0.931284i | \(0.381310\pi\) | |||||||
\(68\) | 1.17009i | 0.141894i | ||||||||
\(69\) | −0.439681 | + | 0.761550i | −0.0529314 | + | 0.0916798i | ||||
\(70\) | 0.867962 | + | 0.836818i | 0.103741 | + | 0.100019i | ||||
\(71\) | −0.290725 | + | 0.503550i | −0.0345027 | + | 0.0597604i | −0.882761 | − | 0.469822i | \(-0.844318\pi\) |
0.848258 | + | 0.529582i | \(0.177651\pi\) | |||||||
\(72\) | 0.294598 | − | 0.170086i | 0.0347188 | − | 0.0200449i | ||||
\(73\) | − | 5.75154i | − | 0.673166i | −0.941654 | − | 0.336583i | \(-0.890729\pi\) | ||
0.941654 | − | 0.336583i | \(-0.109271\pi\) | |||||||
\(74\) | 1.56391 | − | 5.87828i | 0.181801 | − | 0.683336i | ||||
\(75\) | 3.81658 | − | 7.20620i | 0.440701 | − | 0.832101i | ||||
\(76\) | 3.87936 | + | 6.71925i | 0.444993 | + | 0.770751i | ||||
\(77\) | −0.387529 | − | 0.223740i | −0.0441630 | − | 0.0254975i | ||||
\(78\) | 1.54193 | + | 0.890233i | 0.174589 | + | 0.100799i | ||||
\(79\) | −4.65562 | + | 8.06377i | −0.523798 | + | 0.907245i | 0.475818 | + | 0.879544i | \(0.342152\pi\) |
−0.999616 | + | 0.0277016i | \(0.991181\pi\) | |||||||
\(80\) | −0.539189 | + | 2.17009i | −0.0602831 | + | 0.242623i | ||||
\(81\) | 3.93188 | − | 6.81022i | 0.436876 | − | 0.756691i | ||||
\(82\) | − | 1.92162i | − | 0.212208i | ||||||
\(83\) | −1.86781 | + | 1.07838i | −0.205018 | + | 0.118367i | −0.598994 | − | 0.800753i | \(-0.704433\pi\) |
0.393976 | + | 0.919121i | \(0.371099\pi\) | |||||||
\(84\) | −0.879362 | −0.0959462 | ||||||||
\(85\) | 2.53919 | + | 0.630898i | 0.275414 | + | 0.0684305i | ||||
\(86\) | −0.645362 | − | 1.11780i | −0.0695912 | − | 0.120536i | ||||
\(87\) | 13.5242 | + | 7.80817i | 1.44994 | + | 0.837124i | ||||
\(88\) | − | 0.829914i | − | 0.0884691i | ||||||
\(89\) | −5.39383 | − | 9.34238i | −0.571744 | − | 0.990290i | −0.996387 | − | 0.0849294i | \(-0.972934\pi\) |
0.424643 | − | 0.905361i | \(-0.360400\pi\) | |||||||
\(90\) | −0.210258 | − | 0.731013i | −0.0221632 | − | 0.0770555i | ||||
\(91\) | 0.294319 | + | 0.509775i | 0.0308530 | + | 0.0534389i | ||||
\(92\) | −0.466951 | − | 0.269594i | −0.0486830 | − | 0.0281072i | ||||
\(93\) | −4.36673 | − | 2.52113i | −0.452808 | − | 0.261429i | ||||
\(94\) | 2.90049 | + | 5.02380i | 0.299163 | + | 0.518165i | ||||
\(95\) | 16.6731 | − | 4.79560i | 1.71062 | − | 0.492019i | ||||
\(96\) | −0.815449 | − | 1.41240i | −0.0832264 | − | 0.144152i | ||||
\(97\) | − | 9.17727i | − | 0.931811i | −0.884834 | − | 0.465906i | \(-0.845729\pi\) | ||
0.884834 | − | 0.465906i | \(-0.154271\pi\) | |||||||
\(98\) | 5.81040 | + | 3.35464i | 0.586939 | + | 0.338870i | ||||
\(99\) | 0.141157 | + | 0.244491i | 0.0141868 | + | 0.0245723i | ||||
\(100\) | 4.41855 | + | 2.34017i | 0.441855 | + | 0.234017i | ||||
\(101\) | 11.8999 | 1.18408 | 0.592041 | − | 0.805908i | \(-0.298322\pi\) | ||||
0.592041 | + | 0.805908i | \(0.298322\pi\) | |||||||
\(102\) | −1.65263 | + | 0.954146i | −0.163635 | + | 0.0944745i | ||||
\(103\) | 3.21953i | 0.317230i | 0.987340 | + | 0.158615i | \(0.0507029\pi\) | ||||
−0.987340 | + | 0.158615i | \(0.949297\pi\) | |||||||
\(104\) | −0.545854 | + | 0.945448i | −0.0535254 | + | 0.0927088i | ||||
\(105\) | −0.474142 | + | 1.90829i | −0.0462715 | + | 0.186230i | ||||
\(106\) | 1.76959 | − | 3.06503i | 0.171878 | − | 0.297702i | ||||
\(107\) | −12.3207 | − | 7.11336i | −1.19109 | − | 0.687675i | −0.232534 | − | 0.972588i | \(-0.574702\pi\) |
−0.958553 | + | 0.284914i | \(0.908035\pi\) | |||||||
\(108\) | 4.71766 | + | 2.72374i | 0.453957 | + | 0.262092i | ||||
\(109\) | −4.68035 | − | 8.10660i | −0.448296 | − | 0.776471i | 0.549979 | − | 0.835178i | \(-0.314636\pi\) |
−0.998275 | + | 0.0587070i | \(0.981302\pi\) | |||||||
\(110\) | −1.80098 | − | 0.447480i | −0.171717 | − | 0.0426656i | ||||
\(111\) | 9.57777 | − | 2.58457i | 0.909081 | − | 0.245316i | ||||
\(112\) | − | 0.539189i | − | 0.0509486i | ||||||
\(113\) | −11.4119 | + | 6.58864i | −1.07354 | + | 0.619807i | −0.929146 | − | 0.369714i | \(-0.879456\pi\) |
−0.144391 | + | 0.989521i | \(0.546122\pi\) | |||||||
\(114\) | −6.32684 | + | 10.9584i | −0.592563 | + | 1.02635i | ||||
\(115\) | −0.836818 | + | 0.867962i | −0.0780337 | + | 0.0809379i | ||||
\(116\) | −4.78765 | + | 8.29246i | −0.444522 | + | 0.769935i | ||||
\(117\) | − | 0.371370i | − | 0.0343332i | ||||||
\(118\) | −3.38468 | − | 1.95415i | −0.311585 | − | 0.179894i | ||||
\(119\) | −0.630898 | −0.0578343 | ||||||||
\(120\) | −3.50471 | + | 1.00804i | −0.319935 | + | 0.0920215i | ||||
\(121\) | −10.3112 | −0.937386 | ||||||||
\(122\) | 1.81658i | 0.164466i | ||||||||
\(123\) | 2.71410 | − | 1.56698i | 0.244722 | − | 0.141290i | ||||
\(124\) | 1.54585 | − | 2.67750i | 0.138822 | − | 0.240446i | ||||
\(125\) | 7.46081 | − | 8.32684i | 0.667315 | − | 0.744775i | ||||
\(126\) | 0.0917087 | + | 0.158844i | 0.00817006 | + | 0.0141510i | ||||
\(127\) | 2.73915 | − | 1.58145i | 0.243060 | − | 0.140331i | −0.373522 | − | 0.927621i | \(-0.621850\pi\) |
0.616582 | + | 0.787290i | \(0.288517\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 1.05252 | − | 1.82302i | 0.0926692 | − | 0.160508i | ||||
\(130\) | 1.75738 | + | 1.69433i | 0.154133 | + | 0.148602i | ||||
\(131\) | 2.92162 | + | 5.06040i | 0.255263 | + | 0.442129i | 0.964967 | − | 0.262371i | \(-0.0845045\pi\) |
−0.709704 | + | 0.704500i | \(0.751171\pi\) | |||||||
\(132\) | 1.17217 | − | 0.676752i | 0.102024 | − | 0.0589037i | ||||
\(133\) | −3.62295 | + | 2.09171i | −0.314149 | + | 0.181374i | ||||
\(134\) | −12.7877 | −1.10468 | ||||||||
\(135\) | 8.45446 | − | 8.76911i | 0.727644 | − | 0.754725i | ||||
\(136\) | −0.585043 | − | 1.01332i | −0.0501670 | − | 0.0868919i | ||||
\(137\) | − | 10.9288i | − | 0.933711i | −0.884334 | − | 0.466856i | \(-0.845387\pi\) | ||
0.884334 | − | 0.466856i | \(-0.154613\pi\) | |||||||
\(138\) | − | 0.879362i | − | 0.0748563i | ||||||
\(139\) | 0.124232 | + | 0.215176i | 0.0105372 | + | 0.0182510i | 0.871246 | − | 0.490847i | \(-0.163312\pi\) |
−0.860709 | + | 0.509098i | \(0.829979\pi\) | |||||||
\(140\) | −1.17009 | − | 0.290725i | −0.0988904 | − | 0.0245707i | ||||
\(141\) | −4.73041 | + | 8.19330i | −0.398372 | + | 0.690001i | ||||
\(142\) | − | 0.581449i | − | 0.0487941i | ||||||
\(143\) | −0.784640 | − | 0.453012i | −0.0656149 | − | 0.0378828i | ||||
\(144\) | −0.170086 | + | 0.294598i | −0.0141739 | + | 0.0245499i | ||||
\(145\) | 15.4139 | + | 14.8608i | 1.28005 | + | 1.23412i | ||||
\(146\) | 2.87577 | + | 4.98098i | 0.238000 | + | 0.412229i | ||||
\(147\) | 10.9421i | 0.902493i | ||||||||
\(148\) | 1.58475 | + | 5.87270i | 0.130266 | + | 0.482733i | ||||
\(149\) | −8.99386 | −0.736805 | −0.368403 | − | 0.929666i | \(-0.620095\pi\) | ||||
−0.368403 | + | 0.929666i | \(0.620095\pi\) | |||||||
\(150\) | 0.297844 | + | 8.14905i | 0.0243189 | + | 0.665367i | ||||
\(151\) | −3.49220 | + | 6.04867i | −0.284191 | + | 0.492234i | −0.972413 | − | 0.233267i | \(-0.925058\pi\) |
0.688221 | + | 0.725501i | \(0.258392\pi\) | |||||||
\(152\) | −6.71925 | − | 3.87936i | −0.545003 | − | 0.314658i | ||||
\(153\) | 0.344706 | + | 0.199016i | 0.0278678 | + | 0.0160895i | ||||
\(154\) | 0.447480 | 0.0360590 | ||||||||
\(155\) | −4.97690 | − | 4.79831i | −0.399754 | − | 0.385410i | ||||
\(156\) | −1.78047 | −0.142551 | ||||||||
\(157\) | −7.03268 | + | 4.06032i | −0.561269 | + | 0.324049i | −0.753655 | − | 0.657271i | \(-0.771711\pi\) |
0.192386 | + | 0.981319i | \(0.438378\pi\) | |||||||
\(158\) | − | 9.31124i | − | 0.740763i | ||||||
\(159\) | 5.77205 | 0.457754 | ||||||||
\(160\) | −0.618092 | − | 2.14894i | −0.0488645 | − | 0.169889i | ||||
\(161\) | 0.145362 | − | 0.251775i | 0.0114562 | − | 0.0198426i | ||||
\(162\) | 7.86376i | 0.617836i | ||||||||
\(163\) | −13.1690 | + | 7.60310i | −1.03147 | + | 0.595521i | −0.917406 | − | 0.397952i | \(-0.869721\pi\) |
−0.114066 | + | 0.993473i | \(0.536388\pi\) | |||||||
\(164\) | 0.960811 | + | 1.66417i | 0.0750267 | + | 0.129950i | ||||
\(165\) | −0.836590 | − | 2.90860i | −0.0651284 | − | 0.226435i | ||||
\(166\) | 1.07838 | − | 1.86781i | 0.0836983 | − | 0.144970i | ||||
\(167\) | −16.8170 | − | 9.70928i | −1.30134 | − | 0.751326i | −0.320702 | − | 0.947180i | \(-0.603919\pi\) |
−0.980633 | + | 0.195854i | \(0.937252\pi\) | |||||||
\(168\) | 0.761550 | − | 0.439681i | 0.0587548 | − | 0.0339221i | ||||
\(169\) | −5.90409 | − | 10.2262i | −0.454160 | − | 0.786629i | ||||
\(170\) | −2.51445 | + | 0.723221i | −0.192850 | + | 0.0554685i | ||||
\(171\) | 2.63931 | 0.201833 | ||||||||
\(172\) | 1.11780 | + | 0.645362i | 0.0852315 | + | 0.0492084i | ||||
\(173\) | −20.0293 | + | 11.5639i | −1.52280 | + | 0.879188i | −0.523162 | + | 0.852233i | \(0.675248\pi\) |
−0.999637 | + | 0.0269546i | \(0.991419\pi\) | |||||||
\(174\) | −15.6163 | −1.18387 | ||||||||
\(175\) | −1.26180 | + | 2.38243i | −0.0953828 | + | 0.180095i | ||||
\(176\) | 0.414957 | + | 0.718726i | 0.0312785 | + | 0.0541760i | ||||
\(177\) | − | 6.37402i | − | 0.479101i | ||||||
\(178\) | 9.34238 | + | 5.39383i | 0.700241 | + | 0.404284i | ||||
\(179\) | −11.5174 | −0.860854 | −0.430427 | − | 0.902625i | \(-0.641637\pi\) | ||||
−0.430427 | + | 0.902625i | \(0.641637\pi\) | |||||||
\(180\) | 0.547595 | + | 0.527947i | 0.0408153 | + | 0.0393508i | ||||
\(181\) | 6.56032 | − | 11.3628i | 0.487625 | − | 0.844591i | −0.512274 | − | 0.858822i | \(-0.671197\pi\) |
0.999899 | + | 0.0142313i | \(0.00453012\pi\) | |||||||
\(182\) | −0.509775 | − | 0.294319i | −0.0377870 | − | 0.0218163i | ||||
\(183\) | −2.56574 | + | 1.48133i | −0.189665 | + | 0.109503i | ||||
\(184\) | 0.539189 | 0.0397495 | ||||||||
\(185\) | 13.5987 | − | 0.272555i | 0.999799 | − | 0.0200387i | ||||
\(186\) | 5.04226 | 0.369716 | ||||||||
\(187\) | 0.840972 | − | 0.485535i | 0.0614979 | − | 0.0355059i | ||||
\(188\) | −5.02380 | − | 2.90049i | −0.366398 | − | 0.211540i | ||||
\(189\) | −1.46861 | + | 2.54371i | −0.106826 | + | 0.185028i | ||||
\(190\) | −12.0415 | + | 12.4896i | −0.873582 | + | 0.906094i | ||||
\(191\) | 17.2979 | 1.25163 | 0.625817 | − | 0.779970i | \(-0.284766\pi\) | ||||
0.625817 | + | 0.779970i | \(0.284766\pi\) | |||||||
\(192\) | 1.41240 | + | 0.815449i | 0.101931 | + | 0.0588499i | ||||
\(193\) | 16.6153i | 1.19600i | 0.801498 | + | 0.597998i | \(0.204037\pi\) | ||||
−0.801498 | + | 0.597998i | \(0.795963\pi\) | |||||||
\(194\) | 4.58864 | + | 7.94775i | 0.329445 | + | 0.570615i | ||||
\(195\) | −0.960007 | + | 3.86376i | −0.0687475 | + | 0.276690i | ||||
\(196\) | −6.70928 | −0.479234 | ||||||||
\(197\) | −10.4236 | + | 6.01806i | −0.742650 | + | 0.428769i | −0.823032 | − | 0.567995i | \(-0.807719\pi\) |
0.0803823 | + | 0.996764i | \(0.474386\pi\) | |||||||
\(198\) | −0.244491 | − | 0.141157i | −0.0173752 | − | 0.0100316i | ||||
\(199\) | 18.2195 | 1.29155 | 0.645774 | − | 0.763528i | \(-0.276535\pi\) | ||||
0.645774 | + | 0.763528i | \(0.276535\pi\) | |||||||
\(200\) | −4.99666 | + | 0.182626i | −0.353317 | + | 0.0129136i | ||||
\(201\) | −10.4277 | − | 18.0613i | −0.735512 | − | 1.27394i | ||||
\(202\) | −10.3056 | + | 5.94994i | −0.725099 | + | 0.418636i | ||||
\(203\) | −4.47120 | − | 2.58145i | −0.313817 | − | 0.181182i | ||||
\(204\) | 0.954146 | − | 1.65263i | 0.0668036 | − | 0.115707i | ||||
\(205\) | 4.12946 | − | 1.18774i | 0.288414 | − | 0.0829553i | ||||
\(206\) | −1.60977 | − | 2.78820i | −0.112158 | − | 0.194263i | ||||
\(207\) | −0.158844 | + | 0.0917087i | −0.0110404 | + | 0.00637420i | ||||
\(208\) | − | 1.09171i | − | 0.0756964i | ||||||
\(209\) | 3.21953 | − | 5.57640i | 0.222700 | − | 0.385728i | ||||
\(210\) | −0.543527 | − | 1.88970i | −0.0375069 | − | 0.130402i | ||||
\(211\) | −10.0722 | −0.693401 | −0.346701 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346701 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(212\) | 3.53919i | 0.243072i | ||||||||
\(213\) | 0.821238 | − | 0.474142i | 0.0562703 | − | 0.0324877i | ||||
\(214\) | 14.2267 | 0.972519 | ||||||||
\(215\) | 2.00320 | − | 2.07775i | 0.136617 | − | 0.141701i | ||||
\(216\) | −5.44748 | −0.370654 | ||||||||
\(217\) | 1.44368 | + | 0.833507i | 0.0980032 | + | 0.0565822i | ||||
\(218\) | 8.10660 | + | 4.68035i | 0.549048 | + | 0.316993i | ||||
\(219\) | −4.69008 | + | 8.12346i | −0.316926 | + | 0.548933i | ||||
\(220\) | 1.78344 | − | 0.512963i | 0.120239 | − | 0.0345840i | ||||
\(221\) | −1.27739 | −0.0859268 | ||||||||
\(222\) | −7.00231 | + | 7.02718i | −0.469964 | + | 0.471634i | ||||
\(223\) | − | 23.5597i | − | 1.57767i | −0.614602 | − | 0.788837i | \(-0.710683\pi\) | ||
0.614602 | − | 0.788837i | \(-0.289317\pi\) | |||||||
\(224\) | 0.269594 | + | 0.466951i | 0.0180130 | + | 0.0311995i | ||||
\(225\) | 1.44095 | − | 0.903666i | 0.0960631 | − | 0.0602444i | ||||
\(226\) | 6.58864 | − | 11.4119i | 0.438270 | − | 0.759105i | ||||
\(227\) | −8.40652 | − | 4.85350i | −0.557960 | − | 0.322138i | 0.194366 | − | 0.980929i | \(-0.437735\pi\) |
−0.752326 | + | 0.658791i | \(0.771068\pi\) | |||||||
\(228\) | − | 12.6537i | − | 0.838011i | ||||||
\(229\) | 9.62310 | − | 16.6677i | 0.635912 | − | 1.10143i | −0.350409 | − | 0.936597i | \(-0.613957\pi\) |
0.986321 | − | 0.164835i | \(-0.0527093\pi\) | |||||||
\(230\) | 0.290725 | − | 1.17009i | 0.0191698 | − | 0.0771532i | ||||
\(231\) | 0.364897 | + | 0.632020i | 0.0240085 | + | 0.0415839i | ||||
\(232\) | − | 9.57531i | − | 0.628650i | ||||||
\(233\) | 5.14342i | 0.336957i | 0.985705 | + | 0.168478i | \(0.0538854\pi\) | ||||
−0.985705 | + | 0.168478i | \(0.946115\pi\) | |||||||
\(234\) | 0.185685 | + | 0.321616i | 0.0121386 | + | 0.0210247i | ||||
\(235\) | −9.00310 | + | 9.33817i | −0.587297 | + | 0.609155i | ||||
\(236\) | 3.90829 | 0.254408 | ||||||||
\(237\) | 13.1512 | − | 7.59284i | 0.854262 | − | 0.493208i | ||||
\(238\) | 0.546373 | − | 0.315449i | 0.0354161 | − | 0.0204475i | ||||
\(239\) | 15.1526 | + | 26.2450i | 0.980137 | + | 1.69765i | 0.661820 | + | 0.749663i | \(0.269784\pi\) |
0.318317 | + | 0.947984i | \(0.396882\pi\) | |||||||
\(240\) | 2.53114 | − | 2.62535i | 0.163385 | − | 0.169465i | ||||
\(241\) | −4.95774 | + | 8.58706i | −0.319356 | + | 0.553141i | −0.980354 | − | 0.197247i | \(-0.936800\pi\) |
0.660998 | + | 0.750388i | \(0.270133\pi\) | |||||||
\(242\) | 8.92980 | − | 5.15562i | 0.574029 | − | 0.331416i | ||||
\(243\) | 3.04620 | − | 1.75872i | 0.195414 | − | 0.112822i | ||||
\(244\) | −0.908291 | − | 1.57321i | −0.0581474 | − | 0.100714i | ||||
\(245\) | −3.61757 | + | 14.5597i | −0.231118 | + | 0.930186i | ||||
\(246\) | −1.56698 | + | 2.71410i | −0.0999073 | + | 0.173044i | ||||
\(247\) | −7.33547 | + | 4.23513i | −0.466745 | + | 0.269475i | ||||
\(248\) | 3.09171i | 0.196324i | ||||||||
\(249\) | 3.51745 | 0.222909 | ||||||||
\(250\) | −2.29783 | + | 10.9417i | −0.145328 | + | 0.692011i | ||||
\(251\) | −23.0472 | −1.45473 | −0.727363 | − | 0.686253i | \(-0.759254\pi\) | ||||
−0.727363 | + | 0.686253i | \(0.759254\pi\) | |||||||
\(252\) | −0.158844 | − | 0.0917087i | −0.0100062 | − | 0.00577711i | ||||
\(253\) | 0.447480i | 0.0281328i | ||||||||
\(254\) | −1.58145 | + | 2.73915i | −0.0992290 | + | 0.171870i | ||||
\(255\) | −3.07188 | − | 2.96166i | −0.192369 | − | 0.185466i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 5.93797 | − | 3.42829i | 0.370400 | − | 0.213851i | −0.303233 | − | 0.952916i | \(-0.598066\pi\) |
0.673633 | + | 0.739066i | \(0.264733\pi\) | |||||||
\(258\) | 2.10504i | 0.131054i | ||||||||
\(259\) | −3.16649 | + | 0.854480i | −0.196756 | + | 0.0530948i | ||||
\(260\) | −2.36910 | − | 0.588637i | −0.146925 | − | 0.0365057i | ||||
\(261\) | 1.62863 | + | 2.82087i | 0.100810 | + | 0.174607i | ||||
\(262\) | −5.06040 | − | 2.92162i | −0.312632 | − | 0.180498i | ||||
\(263\) | 2.99715 | + | 1.73041i | 0.184812 | + | 0.106701i | 0.589552 | − | 0.807731i | \(-0.299304\pi\) |
−0.404739 | + | 0.914432i | \(0.632638\pi\) | |||||||
\(264\) | −0.676752 | + | 1.17217i | −0.0416512 | + | 0.0721420i | ||||
\(265\) | 7.68035 | + | 1.90829i | 0.471800 | + | 0.117225i | ||||
\(266\) | 2.09171 | − | 3.62295i | 0.128251 | − | 0.222137i | ||||
\(267\) | 17.5936i | 1.07671i | ||||||||
\(268\) | 11.0744 | − | 6.39383i | 0.676479 | − | 0.390565i | ||||
\(269\) | 26.6381 | 1.62415 | 0.812076 | − | 0.583551i | \(-0.198337\pi\) | ||||
0.812076 | + | 0.583551i | \(0.198337\pi\) | |||||||
\(270\) | −2.93722 | + | 11.8215i | −0.178754 | + | 0.719434i | ||||
\(271\) | −5.84377 | − | 10.1217i | −0.354984 | − | 0.614850i | 0.632132 | − | 0.774861i | \(-0.282180\pi\) |
−0.987115 | + | 0.160011i | \(0.948847\pi\) | |||||||
\(272\) | 1.01332 | + | 0.585043i | 0.0614418 | + | 0.0354735i | ||||
\(273\) | − | 0.960007i | − | 0.0581023i | ||||||
\(274\) | 5.46441 | + | 9.46463i | 0.330117 | + | 0.571779i | ||||
\(275\) | −0.151564 | − | 4.14680i | −0.00913965 | − | 0.250061i | ||||
\(276\) | 0.439681 | + | 0.761550i | 0.0264657 | + | 0.0458399i | ||||
\(277\) | −6.06840 | − | 3.50359i | −0.364615 | − | 0.210511i | 0.306488 | − | 0.951874i | \(-0.400846\pi\) |
−0.671103 | + | 0.741364i | \(0.734179\pi\) | |||||||
\(278\) | −0.215176 | − | 0.124232i | −0.0129054 | − | 0.00745095i | ||||
\(279\) | −0.525858 | − | 0.910813i | −0.0314823 | − | 0.0545289i | ||||
\(280\) | 1.15869 | − | 0.333268i | 0.0692448 | − | 0.0199166i | ||||
\(281\) | 11.4535 | + | 19.8381i | 0.683261 | + | 1.18344i | 0.973980 | + | 0.226634i | \(0.0727720\pi\) |
−0.290719 | + | 0.956808i | \(0.593895\pi\) | |||||||
\(282\) | − | 9.46081i | − | 0.563383i | ||||||
\(283\) | 13.9401 | + | 8.04831i | 0.828652 | + | 0.478423i | 0.853391 | − | 0.521271i | \(-0.174542\pi\) |
−0.0247387 | + | 0.999694i | \(0.507875\pi\) | |||||||
\(284\) | 0.290725 | + | 0.503550i | 0.0172513 | + | 0.0298802i | ||||
\(285\) | −27.4596 | − | 6.82273i | −1.62657 | − | 0.404143i | ||||
\(286\) | 0.906024 | 0.0535743 | ||||||||
\(287\) | −0.897304 | + | 0.518059i | −0.0529662 | + | 0.0305800i | ||||
\(288\) | − | 0.340173i | − | 0.0200449i | ||||||
\(289\) | −7.81545 | + | 13.5368i | −0.459732 | + | 0.796280i | ||||
\(290\) | −20.7792 | − | 5.16290i | −1.22020 | − | 0.303176i | ||||
\(291\) | −7.48360 | + | 12.9620i | −0.438696 | + | 0.759844i | ||||
\(292\) | −4.98098 | − | 2.87577i | −0.291490 | − | 0.168292i | ||||
\(293\) | 21.4248 | + | 12.3696i | 1.25165 | + | 0.722641i | 0.971437 | − | 0.237296i | \(-0.0762612\pi\) |
0.280214 | + | 0.959938i | \(0.409595\pi\) | |||||||
\(294\) | −5.47107 | − | 9.47617i | −0.319079 | − | 0.552662i | ||||
\(295\) | 2.10731 | − | 8.48133i | 0.122692 | − | 0.493802i | ||||
\(296\) | −4.30878 | − | 4.29353i | −0.250443 | − | 0.249556i | ||||
\(297\) | − | 4.52094i | − | 0.262331i | ||||||
\(298\) | 7.78891 | − | 4.49693i | 0.451199 | − | 0.260500i | ||||
\(299\) | 0.294319 | − | 0.509775i | 0.0170209 | − | 0.0294810i | ||||
\(300\) | −4.33246 | − | 6.90836i | −0.250135 | − | 0.398854i | ||||
\(301\) | −0.347972 | + | 0.602705i | −0.0200568 | + | 0.0347394i | ||||
\(302\) | − | 6.98440i | − | 0.401907i | ||||||
\(303\) | −16.8074 | − | 9.70374i | −0.965559 | − | 0.557466i | ||||
\(304\) | 7.75872 | 0.444993 | ||||||||
\(305\) | −3.90373 | + | 1.12282i | −0.223527 | + | 0.0642922i | ||||
\(306\) | −0.398032 | −0.0227540 | ||||||||
\(307\) | − | 4.56690i | − | 0.260647i | −0.991472 | − | 0.130323i | \(-0.958398\pi\) | ||
0.991472 | − | 0.130323i | \(-0.0416015\pi\) | |||||||
\(308\) | −0.387529 | + | 0.223740i | −0.0220815 | + | 0.0127488i | ||||
\(309\) | 2.62537 | − | 4.54727i | 0.149352 | − | 0.258685i | ||||
\(310\) | 6.70928 | + | 1.66701i | 0.381061 | + | 0.0946801i | ||||
\(311\) | 5.08084 | + | 8.80027i | 0.288108 | + | 0.499018i | 0.973358 | − | 0.229290i | \(-0.0736405\pi\) |
−0.685250 | + | 0.728308i | \(0.740307\pi\) | |||||||
\(312\) | 1.54193 | − | 0.890233i | 0.0872945 | − | 0.0503995i | ||||
\(313\) | 11.0671 | − | 6.38962i | 0.625552 | − | 0.361163i | −0.153475 | − | 0.988152i | \(-0.549047\pi\) |
0.779028 | + | 0.626990i | \(0.215713\pi\) | |||||||
\(314\) | 4.06032 | − | 7.03268i | 0.229137 | − | 0.396877i | ||||
\(315\) | −0.284663 | + | 0.295257i | −0.0160389 | + | 0.0166359i | ||||
\(316\) | 4.65562 | + | 8.06377i | 0.261899 | + | 0.453623i | ||||
\(317\) | 9.83439 | − | 5.67789i | 0.552354 | − | 0.318902i | −0.197717 | − | 0.980259i | \(-0.563353\pi\) |
0.750071 | + | 0.661357i | \(0.230019\pi\) | |||||||
\(318\) | −4.99875 | + | 2.88603i | −0.280316 | + | 0.161840i | ||||
\(319\) | 7.94668 | 0.444928 | ||||||||
\(320\) | 1.60976 | + | 1.55199i | 0.0899881 | + | 0.0867591i | ||||
\(321\) | 11.6012 | + | 20.0938i | 0.647514 | + | 1.12153i | ||||
\(322\) | 0.290725i | 0.0162015i | ||||||||
\(323\) | − | 9.07838i | − | 0.505134i | ||||||
\(324\) | −3.93188 | − | 6.81022i | −0.218438 | − | 0.378345i | ||||
\(325\) | −2.55479 | + | 4.82377i | −0.141714 | + | 0.267575i | ||||
\(326\) | 7.60310 | − | 13.1690i | 0.421097 | − | 0.729361i | ||||
\(327\) | 15.2663i | 0.844230i | ||||||||
\(328\) | −1.66417 | − | 0.960811i | −0.0918886 | − | 0.0530519i | ||||
\(329\) | 1.56391 | − | 2.70878i | 0.0862213 | − | 0.149340i | ||||
\(330\) | 2.17881 | + | 2.10063i | 0.119940 | + | 0.115636i | ||||
\(331\) | −13.8540 | − | 23.9959i | −0.761486 | − | 1.31893i | −0.942084 | − | 0.335376i | \(-0.891137\pi\) |
0.180598 | − | 0.983557i | \(-0.442197\pi\) | |||||||
\(332\) | 2.15676i | 0.118367i | ||||||||
\(333\) | 1.99963 | + | 0.532001i | 0.109579 | + | 0.0291535i | ||||
\(334\) | 19.4186 | 1.06254 | ||||||||
\(335\) | −7.90395 | − | 27.4800i | −0.431839 | − | 1.50139i | ||||
\(336\) | −0.439681 | + | 0.761550i | −0.0239866 | + | 0.0415459i | ||||
\(337\) | 22.1844 | + | 12.8082i | 1.20846 | + | 0.697706i | 0.962423 | − | 0.271554i | \(-0.0875377\pi\) |
0.246038 | + | 0.969260i | \(0.420871\pi\) | |||||||
\(338\) | 10.2262 | + | 5.90409i | 0.556231 | + | 0.321140i | ||||
\(339\) | 21.4908 | 1.16722 | ||||||||
\(340\) | 1.81597 | − | 1.88355i | 0.0984847 | − | 0.102150i | ||||
\(341\) | −2.56585 | −0.138949 | ||||||||
\(342\) | −2.28571 | + | 1.31965i | −0.123597 | + | 0.0713587i | ||||
\(343\) | − | 7.39189i | − | 0.399124i | ||||||
\(344\) | −1.29072 | −0.0695912 | ||||||||
\(345\) | 1.88970 | − | 0.543527i | 0.101738 | − | 0.0292625i | ||||
\(346\) | 11.5639 | − | 20.0293i | 0.621680 | − | 1.07678i | ||||
\(347\) | − | 18.5464i | − | 0.995622i | −0.867286 | − | 0.497811i | \(-0.834137\pi\) | ||
0.867286 | − | 0.497811i | \(-0.165863\pi\) | |||||||
\(348\) | 13.5242 | − | 7.80817i | 0.724971 | − | 0.418562i | ||||
\(349\) | −4.23513 | − | 7.33547i | −0.226701 | − | 0.392658i | 0.730127 | − | 0.683311i | \(-0.239461\pi\) |
−0.956829 | + | 0.290653i | \(0.906128\pi\) | |||||||
\(350\) | −0.0984700 | − | 2.69415i | −0.00526344 | − | 0.144008i | ||||
\(351\) | −2.97353 | + | 5.15031i | −0.158715 | + | 0.274903i | ||||
\(352\) | −0.718726 | − | 0.414957i | −0.0383082 | − | 0.0221173i | ||||
\(353\) | 18.5051 | − | 10.6839i | 0.984929 | − | 0.568649i | 0.0811740 | − | 0.996700i | \(-0.474133\pi\) |
0.903754 | + | 0.428051i | \(0.140800\pi\) | |||||||
\(354\) | 3.18701 | + | 5.52007i | 0.169388 | + | 0.293388i | ||||
\(355\) | 1.24950 | − | 0.359389i | 0.0663167 | − | 0.0190744i | ||||
\(356\) | −10.7877 | −0.571744 | ||||||||
\(357\) | 0.891079 | + | 0.514465i | 0.0471609 | + | 0.0272284i | ||||
\(358\) | 9.97440 | − | 5.75872i | 0.527164 | − | 0.304358i | ||||
\(359\) | 18.6319 | 0.983356 | 0.491678 | − | 0.870777i | \(-0.336384\pi\) | ||||
0.491678 | + | 0.870777i | \(0.336384\pi\) | |||||||
\(360\) | −0.738205 | − | 0.183417i | −0.0389068 | − | 0.00966695i | ||||
\(361\) | −20.5989 | − | 35.6783i | −1.08415 | − | 1.87781i | ||||
\(362\) | 13.1206i | 0.689605i | ||||||||
\(363\) | 14.5636 | + | 8.40829i | 0.764390 | + | 0.441321i | ||||
\(364\) | 0.588637 | 0.0308530 | ||||||||
\(365\) | −8.92635 | + | 9.25857i | −0.467227 | + | 0.484616i | ||||
\(366\) | 1.48133 | − | 2.56574i | 0.0774304 | − | 0.134113i | ||||
\(367\) | 21.5721 | + | 12.4547i | 1.12606 | + | 0.650128i | 0.942940 | − | 0.332963i | \(-0.108048\pi\) |
0.183116 | + | 0.983091i | \(0.441382\pi\) | |||||||
\(368\) | −0.466951 | + | 0.269594i | −0.0243415 | + | 0.0140536i | ||||
\(369\) | 0.653684 | 0.0340294 | ||||||||
\(370\) | −11.6406 | + | 7.03541i | −0.605165 | + | 0.365754i | ||||
\(371\) | −1.90829 | −0.0990735 | ||||||||
\(372\) | −4.36673 | + | 2.52113i | −0.226404 | + | 0.130715i | ||||
\(373\) | −8.36992 | − | 4.83237i | −0.433378 | − | 0.250211i | 0.267407 | − | 0.963584i | \(-0.413833\pi\) |
−0.700785 | + | 0.713373i | \(0.747167\pi\) | |||||||
\(374\) | −0.485535 | + | 0.840972i | −0.0251064 | + | 0.0434856i | ||||
\(375\) | −17.3278 | + | 5.67691i | −0.894801 | + | 0.293154i | ||||
\(376\) | 5.80098 | 0.299163 | ||||||||
\(377\) | −9.05295 | − | 5.22672i | −0.466251 | − | 0.269190i | ||||
\(378\) | − | 2.93722i | − | 0.151074i | ||||||
\(379\) | −6.09530 | − | 10.5574i | −0.313095 | − | 0.542296i | 0.665936 | − | 0.746009i | \(-0.268032\pi\) |
−0.979031 | + | 0.203713i | \(0.934699\pi\) | |||||||
\(380\) | 4.18342 | − | 16.8371i | 0.214605 | − | 0.863725i | ||||
\(381\) | −5.15836 | −0.264271 | ||||||||
\(382\) | −14.9804 | + | 8.64896i | −0.766466 | + | 0.442519i | ||||
\(383\) | 4.52025 | + | 2.60977i | 0.230974 | + | 0.133353i | 0.611021 | − | 0.791614i | \(-0.290759\pi\) |
−0.380047 | + | 0.924967i | \(0.624092\pi\) | |||||||
\(384\) | −1.63090 | −0.0832264 | ||||||||
\(385\) | 0.276584 | + | 0.961610i | 0.0140960 | + | 0.0490082i | ||||
\(386\) | −8.30765 | − | 14.3893i | −0.422848 | − | 0.732395i | ||||
\(387\) | 0.380245 | − | 0.219535i | 0.0193290 | − | 0.0111596i | ||||
\(388\) | −7.94775 | − | 4.58864i | −0.403486 | − | 0.232953i | ||||
\(389\) | −6.37629 | + | 11.0441i | −0.323291 | + | 0.559956i | −0.981165 | − | 0.193172i | \(-0.938123\pi\) |
0.657874 | + | 0.753128i | \(0.271456\pi\) | |||||||
\(390\) | −1.10049 | − | 3.82612i | −0.0557255 | − | 0.193743i | ||||
\(391\) | 0.315449 | + | 0.546373i | 0.0159529 | + | 0.0276313i | ||||
\(392\) | 5.81040 | − | 3.35464i | 0.293470 | − | 0.169435i | ||||
\(393\) | − | 9.52973i | − | 0.480711i | ||||||
\(394\) | 6.01806 | − | 10.4236i | 0.303185 | − | 0.525133i | ||||
\(395\) | 20.0093 | − | 5.75520i | 1.00678 | − | 0.289576i | ||||
\(396\) | 0.282314 | 0.0141868 | ||||||||
\(397\) | − | 25.2895i | − | 1.26924i | −0.772823 | − | 0.634622i | \(-0.781156\pi\) | ||
0.772823 | − | 0.634622i | \(-0.218844\pi\) | |||||||
\(398\) | −15.7786 | + | 9.10977i | −0.790909 | + | 0.456631i | ||||
\(399\) | 6.82273 | 0.341564 | ||||||||
\(400\) | 4.23592 | − | 2.65649i | 0.211796 | − | 0.132825i | ||||
\(401\) | −13.7237 | −0.685326 | −0.342663 | − | 0.939458i | \(-0.611329\pi\) | ||||
−0.342663 | + | 0.939458i | \(0.611329\pi\) | |||||||
\(402\) | 18.0613 | + | 10.4277i | 0.900814 | + | 0.520085i | ||||
\(403\) | 2.92305 | + | 1.68762i | 0.145607 | + | 0.0840665i | ||||
\(404\) | 5.94994 | − | 10.3056i | 0.296021 | − | 0.512723i | ||||
\(405\) | −16.8988 | + | 4.86053i | −0.839708 | + | 0.241522i | ||||
\(406\) | 5.16290 | 0.256230 | ||||||||
\(407\) | 3.56326 | − | 3.57592i | 0.176624 | − | 0.177252i | ||||
\(408\) | 1.90829i | 0.0944745i | ||||||||
\(409\) | 6.02586 | + | 10.4371i | 0.297959 | + | 0.516081i | 0.975669 | − | 0.219249i | \(-0.0703606\pi\) |
−0.677709 | + | 0.735330i | \(0.737027\pi\) | |||||||
\(410\) | −2.98235 | + | 3.09334i | −0.147288 | + | 0.152769i | ||||
\(411\) | −8.91189 | + | 15.4358i | −0.439591 | + | 0.761394i | ||||
\(412\) | 2.78820 | + | 1.60977i | 0.137365 | + | 0.0793075i | ||||
\(413\) | 2.10731i | 0.103694i | ||||||||
\(414\) | 0.0917087 | − | 0.158844i | 0.00450724 | − | 0.00780677i | ||||
\(415\) | 4.68035 | + | 1.16290i | 0.229749 | + | 0.0570844i | ||||
\(416\) | 0.545854 | + | 0.945448i | 0.0267627 | + | 0.0463544i | ||||
\(417\) | − | 0.405220i | − | 0.0198437i | ||||||
\(418\) | 6.43907i | 0.314945i | ||||||||
\(419\) | −8.75513 | − | 15.1643i | −0.427716 | − | 0.740826i | 0.568954 | − | 0.822370i | \(-0.307348\pi\) |
−0.996670 | + | 0.0815436i | \(0.974015\pi\) | |||||||
\(420\) | 1.41556 | + | 1.36476i | 0.0690721 | + | 0.0665937i | ||||
\(421\) | −1.70209 | −0.0829547 | −0.0414773 | − | 0.999139i | \(-0.513206\pi\) | ||||
−0.0414773 | + | 0.999139i | \(0.513206\pi\) | |||||||
\(422\) | 8.72281 | − | 5.03612i | 0.424620 | − | 0.245154i | ||||
\(423\) | −1.70896 | + | 0.986669i | −0.0830925 | + | 0.0479735i | ||||
\(424\) | −1.76959 | − | 3.06503i | −0.0859391 | − | 0.148851i | ||||
\(425\) | −3.10832 | − | 4.95640i | −0.150776 | − | 0.240421i | ||||
\(426\) | −0.474142 | + | 0.821238i | −0.0229723 | + | 0.0397891i | ||||
\(427\) | 0.848255 | − | 0.489741i | 0.0410500 | − | 0.0237002i | ||||
\(428\) | −12.3207 | + | 7.11336i | −0.595544 | + | 0.343837i | ||||
\(429\) | 0.738816 | + | 1.27967i | 0.0356704 | + | 0.0617829i | ||||
\(430\) | −0.695944 | + | 2.80098i | −0.0335614 | + | 0.135075i | ||||
\(431\) | −10.8902 | + | 18.8624i | −0.524564 | + | 0.908572i | 0.475027 | + | 0.879971i | \(0.342438\pi\) |
−0.999591 | + | 0.0286003i | \(0.990895\pi\) | |||||||
\(432\) | 4.71766 | − | 2.72374i | 0.226978 | − | 0.131046i | ||||
\(433\) | 10.6803i | 0.513265i | 0.966509 | + | 0.256632i | \(0.0826129\pi\) | ||||
−0.966509 | + | 0.256632i | \(0.917387\pi\) | |||||||
\(434\) | −1.66701 | −0.0800193 | ||||||||
\(435\) | −9.65234 | − | 33.5587i | −0.462794 | − | 1.60901i | ||||
\(436\) | −9.36069 | −0.448296 | ||||||||
\(437\) | 3.62295 | + | 2.09171i | 0.173309 | + | 0.100060i | ||||
\(438\) | − | 9.38017i | − | 0.448202i | ||||||
\(439\) | −15.4613 | + | 26.7798i | −0.737929 | + | 1.27813i | 0.215497 | + | 0.976504i | \(0.430863\pi\) |
−0.953426 | + | 0.301626i | \(0.902470\pi\) | |||||||
\(440\) | −1.28802 | + | 1.33596i | −0.0614040 | + | 0.0636893i | ||||
\(441\) | −1.14116 | + | 1.97654i | −0.0543408 | + | 0.0941210i | ||||
\(442\) | 1.10626 | − | 0.638697i | 0.0526192 | − | 0.0303797i | ||||
\(443\) | 4.78539i | 0.227361i | 0.993517 | + | 0.113680i | \(0.0362639\pi\) | ||||
−0.993517 | + | 0.113680i | \(0.963736\pi\) | |||||||
\(444\) | 2.55058 | − | 9.58687i | 0.121045 | − | 0.454973i | ||||
\(445\) | −5.81658 | + | 23.4101i | −0.275732 | + | 1.10975i | ||||
\(446\) | 11.7799 | + | 20.4033i | 0.557792 | + | 0.966125i | ||||
\(447\) | 12.7029 | + | 7.33403i | 0.600827 | + | 0.346888i | ||||
\(448\) | −0.466951 | − | 0.269594i | −0.0220614 | − | 0.0127371i | ||||
\(449\) | −9.04831 | + | 15.6721i | −0.427016 | + | 0.739614i | −0.996606 | − | 0.0823149i | \(-0.973769\pi\) |
0.569590 | + | 0.821929i | \(0.307102\pi\) | |||||||
\(450\) | −0.796064 | + | 1.50307i | −0.0375268 | + | 0.0708555i | ||||
\(451\) | 0.797390 | − | 1.38112i | 0.0375476 | − | 0.0650344i | ||||
\(452\) | 13.1773i | 0.619807i | ||||||||
\(453\) | 9.86476 | − | 5.69542i | 0.463487 | − | 0.267594i | ||||
\(454\) | 9.70701 | 0.455572 | ||||||||
\(455\) | 0.317387 | − | 1.27739i | 0.0148793 | − | 0.0598851i | ||||
\(456\) | 6.32684 | + | 10.9584i | 0.296282 | + | 0.513175i | ||||
\(457\) | −33.6965 | − | 19.4547i | −1.57625 | − | 0.910051i | −0.995375 | − | 0.0960611i | \(-0.969376\pi\) |
−0.580879 | − | 0.813990i | \(-0.697291\pi\) | |||||||
\(458\) | 19.2462i | 0.899316i | ||||||||
\(459\) | −3.18701 | − | 5.52007i | −0.148757 | − | 0.257655i | ||||
\(460\) | 0.333268 | + | 1.15869i | 0.0155387 | + | 0.0540241i | ||||
\(461\) | 11.4319 | + | 19.8006i | 0.532436 | + | 0.922206i | 0.999283 | + | 0.0378677i | \(0.0120566\pi\) |
−0.466847 | + | 0.884338i | \(0.654610\pi\) | |||||||
\(462\) | −0.632020 | − | 0.364897i | −0.0294042 | − | 0.0169766i | ||||
\(463\) | −23.7807 | − | 13.7298i | −1.10518 | − | 0.638078i | −0.167605 | − | 0.985854i | \(-0.553603\pi\) |
−0.937577 | + | 0.347777i | \(0.886937\pi\) | |||||||
\(464\) | 4.78765 | + | 8.29246i | 0.222261 | + | 0.384968i | ||||
\(465\) | 3.11658 | + | 10.8355i | 0.144528 | + | 0.502486i | ||||
\(466\) | −2.57171 | − | 4.45434i | −0.119132 | − | 0.206343i | ||||
\(467\) | 29.3896i | 1.35999i | 0.733217 | + | 0.679995i | \(0.238018\pi\) | ||||
−0.733217 | + | 0.679995i | \(0.761982\pi\) | |||||||
\(468\) | −0.321616 | − | 0.185685i | −0.0148667 | − | 0.00858329i | ||||
\(469\) | 3.44748 | + | 5.97121i | 0.159190 | + | 0.275725i | ||||
\(470\) | 3.12783 | − | 12.5886i | 0.144276 | − | 0.580671i | ||||
\(471\) | 13.2439 | 0.610248 | ||||||||
\(472\) | −3.38468 | + | 1.95415i | −0.155793 | + | 0.0899468i | ||||
\(473\) | − | 1.07119i | − | 0.0492534i | ||||||
\(474\) | −7.59284 | + | 13.1512i | −0.348751 | + | 0.604054i | ||||
\(475\) | −34.2823 | − | 18.1568i | −1.57298 | − | 0.833089i | ||||
\(476\) | −0.315449 | + | 0.546373i | −0.0144586 | + | 0.0250430i | ||||
\(477\) | 1.04264 | + | 0.601968i | 0.0477392 | + | 0.0275622i | ||||
\(478\) | −26.2450 | − | 15.1526i | −1.20042 | − | 0.693062i | ||||
\(479\) | −15.5706 | − | 26.9690i | −0.711438 | − | 1.23225i | −0.964317 | − | 0.264749i | \(-0.914711\pi\) |
0.252880 | − | 0.967498i | \(-0.418622\pi\) | |||||||
\(480\) | −0.879362 | + | 3.53919i | −0.0401372 | + | 0.161541i | ||||
\(481\) | −6.41127 | + | 1.73009i | −0.292329 | + | 0.0788852i | ||||
\(482\) | − | 9.91548i | − | 0.451638i | ||||||
\(483\) | −0.410619 | + | 0.237071i | −0.0186838 | + | 0.0107871i | ||||
\(484\) | −5.15562 | + | 8.92980i | −0.234346 | + | 0.405900i | ||||
\(485\) | −14.2431 | + | 14.7732i | −0.646745 | + | 0.670815i | ||||
\(486\) | −1.75872 | + | 3.04620i | −0.0797773 | + | 0.138178i | ||||
\(487\) | 39.1194i | 1.77267i | 0.463045 | + | 0.886335i | \(0.346757\pi\) | ||||
−0.463045 | + | 0.886335i | \(0.653243\pi\) | |||||||
\(488\) | 1.57321 | + | 0.908291i | 0.0712157 | + | 0.0411164i | ||||
\(489\) | 24.7998 | 1.12148 | ||||||||
\(490\) | −4.14695 | − | 14.4179i | −0.187340 | − | 0.651333i | ||||
\(491\) | 5.88163 | 0.265434 | 0.132717 | − | 0.991154i | \(-0.457630\pi\) | ||||
0.132717 | + | 0.991154i | \(0.457630\pi\) | |||||||
\(492\) | − | 3.13397i | − | 0.141290i | ||||||
\(493\) | 9.70289 | − | 5.60197i | 0.436996 | − | 0.252300i | ||||
\(494\) | 4.23513 | − | 7.33547i | 0.190548 | − | 0.330038i | ||||
\(495\) | 0.152221 | − | 0.612646i | 0.00684181 | − | 0.0275364i | ||||
\(496\) | −1.54585 | − | 2.67750i | −0.0694109 | − | 0.120223i | ||||
\(497\) | −0.271508 | + | 0.156755i | −0.0121788 | + | 0.00703144i | ||||
\(498\) | −3.04620 | + | 1.75872i | −0.136503 | + | 0.0788103i | ||||
\(499\) | −10.3691 | + | 17.9598i | −0.464185 | + | 0.803992i | −0.999164 | − | 0.0408734i | \(-0.986986\pi\) |
0.534980 | + | 0.844865i | \(0.320319\pi\) | |||||||
\(500\) | −3.48085 | − | 10.6247i | −0.155668 | − | 0.475150i | ||||
\(501\) | 15.8348 | + | 27.4267i | 0.707448 | + | 1.22534i | ||||
\(502\) | 19.9594 | − | 11.5236i | 0.890834 | − | 0.514323i | ||||
\(503\) | −14.2502 | + | 8.22733i | −0.635383 | + | 0.366839i | −0.782834 | − | 0.622231i | \(-0.786227\pi\) |
0.147451 | + | 0.989069i | \(0.452893\pi\) | |||||||
\(504\) | 0.183417 | 0.00817006 | ||||||||
\(505\) | −19.1559 | − | 18.4685i | −0.852426 | − | 0.821840i | ||||
\(506\) | −0.223740 | − | 0.387529i | −0.00994646 | − | 0.0172278i | ||||
\(507\) | 19.2579i | 0.855274i | ||||||||
\(508\) | − | 3.16290i | − | 0.140331i | ||||||
\(509\) | −2.80878 | − | 4.86496i | −0.124497 | − | 0.215635i | 0.797039 | − | 0.603928i | \(-0.206398\pi\) |
−0.921536 | + | 0.388292i | \(0.873065\pi\) | |||||||
\(510\) | 4.14116 | + | 1.02893i | 0.183374 | + | 0.0455618i | ||||
\(511\) | 1.55058 | − | 2.68569i | 0.0685937 | − | 0.118808i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −36.6030 | − | 21.1327i | −1.61606 | − | 0.933034i | ||||
\(514\) | −3.42829 | + | 5.93797i | −0.151215 | + | 0.261913i | ||||
\(515\) | 4.99670 | − | 5.18266i | 0.220181 | − | 0.228375i | ||||
\(516\) | −1.05252 | − | 1.82302i | −0.0463346 | − | 0.0802539i | ||||
\(517\) | 4.81432i | 0.211733i | ||||||||
\(518\) | 2.31502 | − | 2.32325i | 0.101716 | − | 0.102078i | ||||
\(519\) | 37.7191 | 1.65569 | ||||||||
\(520\) | 2.34602 | − | 0.674776i | 0.102880 | − | 0.0295909i | ||||
\(521\) | −10.9433 | + | 18.9543i | −0.479434 | + | 0.830403i | −0.999722 | − | 0.0235874i | \(-0.992491\pi\) |
0.520288 | + | 0.853991i | \(0.325825\pi\) | |||||||
\(522\) | −2.82087 | − | 1.62863i | −0.123466 | − | 0.0712832i | ||||
\(523\) | 26.5021 | + | 15.3010i | 1.15886 | + | 0.669065i | 0.951029 | − | 0.309101i | \(-0.100028\pi\) |
0.207826 | + | 0.978166i | \(0.433361\pi\) | |||||||
\(524\) | 5.84324 | 0.255263 | ||||||||
\(525\) | 3.72491 | − | 2.33602i | 0.162568 | − | 0.101952i | ||||
\(526\) | −3.46081 | −0.150899 | ||||||||
\(527\) | −3.13290 | + | 1.80878i | −0.136471 | + | 0.0787918i | ||||
\(528\) | − | 1.35350i | − | 0.0589037i | ||||||
\(529\) | 22.7093 | 0.987360 | ||||||||
\(530\) | −7.60552 | + | 2.18754i | −0.330363 | + | 0.0950209i | ||||
\(531\) | 0.664748 | − | 1.15138i | 0.0288476 | − | 0.0499655i | ||||
\(532\) | 4.18342i | 0.181374i | ||||||||
\(533\) | −1.81679 | + | 1.04893i | −0.0786940 | + | 0.0454340i | ||||
\(534\) | −8.79678 | − | 15.2365i | −0.380674 | − | 0.659346i | ||||
\(535\) | 8.79342 | + | 30.5724i | 0.380173 | + | 1.32176i | ||||
\(536\) | −6.39383 | + | 11.0744i | −0.276171 | + | 0.478343i | ||||
\(537\) | 16.2672 | + | 9.39189i | 0.701983 | + | 0.405290i | ||||
\(538\) | −23.0693 | + | 13.3190i | −0.994586 | + | 0.574225i | ||||
\(539\) | 2.78406 | + | 4.82213i | 0.119918 | + | 0.207704i | ||||
\(540\) | −3.36704 | − | 11.7063i | −0.144894 | − | 0.503760i | ||||
\(541\) | 1.38735 | 0.0596470 | 0.0298235 | − | 0.999555i | \(-0.490505\pi\) | ||||
0.0298235 | + | 0.999555i | \(0.490505\pi\) | |||||||
\(542\) | 10.1217 | + | 5.84377i | 0.434764 | + | 0.251011i | ||||
\(543\) | −18.5316 | + | 10.6992i | −0.795266 | + | 0.459147i | ||||
\(544\) | −1.17009 | −0.0501670 | ||||||||
\(545\) | −5.04718 | + | 20.3135i | −0.216197 | + | 0.870135i | ||||
\(546\) | 0.480004 | + | 0.831390i | 0.0205423 | + | 0.0355802i | ||||
\(547\) | 4.81658i | 0.205942i | 0.994684 | + | 0.102971i | \(0.0328349\pi\) | ||||
−0.994684 | + | 0.102971i | \(0.967165\pi\) | |||||||
\(548\) | −9.46463 | − | 5.46441i | −0.404309 | − | 0.233428i | ||||
\(549\) | −0.617952 | −0.0263736 | ||||||||
\(550\) | 2.20466 | + | 3.51545i | 0.0940069 | + | 0.149899i | ||||
\(551\) | 37.1461 | − | 64.3389i | 1.58248 | − | 2.74093i | ||||
\(552\) | −0.761550 | − | 0.439681i | −0.0324137 | − | 0.0187141i | ||||
\(553\) | −4.34790 | + | 2.51026i | −0.184891 | + | 0.106747i | ||||
\(554\) | 7.00719 | 0.297707 | ||||||||
\(555\) | −19.4291 | − | 10.7041i | −0.824719 | − | 0.454365i | ||||
\(556\) | 0.248464 | 0.0105372 | ||||||||
\(557\) | 24.3887 | − | 14.0808i | 1.03338 | − | 0.596624i | 0.115431 | − | 0.993315i | \(-0.463175\pi\) |
0.917952 | + | 0.396691i | \(0.129842\pi\) | |||||||
\(558\) | 0.910813 | + | 0.525858i | 0.0385578 | + | 0.0222613i | ||||
\(559\) | −0.704548 | + | 1.22031i | −0.0297992 | + | 0.0516137i | ||||
\(560\) | −0.836818 | + | 0.867962i | −0.0353620 | + | 0.0366781i | ||||
\(561\) | −1.58372 | −0.0668646 | ||||||||
\(562\) | −19.8381 | − | 11.4535i | −0.836820 | − | 0.483138i | ||||
\(563\) | 12.0228i | 0.506700i | 0.967375 | + | 0.253350i | \(0.0815324\pi\) | ||||
−0.967375 | + | 0.253350i | \(0.918468\pi\) | |||||||
\(564\) | 4.73041 | + | 8.19330i | 0.199186 | + | 0.345000i | ||||
\(565\) | 28.5958 | + | 7.10504i | 1.20304 | + | 0.298911i | ||||
\(566\) | −16.0966 | −0.676592 | ||||||||
\(567\) | 3.67199 | − | 2.12003i | 0.154209 | − | 0.0890328i | ||||
\(568\) | −0.503550 | − | 0.290725i | −0.0211285 | − | 0.0121985i | ||||
\(569\) | 30.7009 | 1.28705 | 0.643524 | − | 0.765426i | \(-0.277472\pi\) | ||||
0.643524 | + | 0.765426i | \(0.277472\pi\) | |||||||
\(570\) | 27.1921 | − | 7.82114i | 1.13895 | − | 0.327592i | ||||
\(571\) | −23.1617 | − | 40.1172i | −0.969286 | − | 1.67885i | −0.697630 | − | 0.716458i | \(-0.745762\pi\) |
−0.271656 | − | 0.962394i | \(-0.587571\pi\) | |||||||
\(572\) | −0.784640 | + | 0.453012i | −0.0328074 | + | 0.0189414i | ||||
\(573\) | −24.4316 | − | 14.1056i | −1.02064 | − | 0.589268i | ||||
\(574\) | 0.518059 | − | 0.897304i | 0.0216234 | − | 0.0374527i | ||||
\(575\) | 2.69415 | − | 0.0984700i | 0.112354 | − | 0.00410648i | ||||
\(576\) | 0.170086 | + | 0.294598i | 0.00708694 | + | 0.0122749i | ||||
\(577\) | −15.5677 | + | 8.98800i | −0.648090 | + | 0.374175i | −0.787724 | − | 0.616028i | \(-0.788741\pi\) |
0.139634 | + | 0.990203i | \(0.455407\pi\) | |||||||
\(578\) | − | 15.6309i | − | 0.650160i | ||||||
\(579\) | 13.5489 | − | 23.4674i | 0.563074 | − | 0.975273i | ||||
\(580\) | 20.5768 | − | 5.91842i | 0.854405 | − | 0.245749i | ||||
\(581\) | −1.16290 | −0.0482452 | ||||||||
\(582\) | − | 14.9672i | − | 0.620410i | ||||||
\(583\) | 2.54371 | − | 1.46861i | 0.105350 | − | 0.0608236i | ||||
\(584\) | 5.75154 | 0.238000 | ||||||||
\(585\) | −0.576364 | + | 0.597815i | −0.0238297 | + | 0.0247166i | ||||
\(586\) | −24.7392 | −1.02197 | ||||||||
\(587\) | −18.8489 | − | 10.8824i | −0.777978 | − | 0.449166i | 0.0577349 | − | 0.998332i | \(-0.481612\pi\) |
−0.835713 | + | 0.549166i | \(0.814946\pi\) | |||||||
\(588\) | 9.47617 | + | 5.47107i | 0.390791 | + | 0.225623i | ||||
\(589\) | −11.9939 | + | 20.7740i | −0.494198 | + | 0.855977i | ||||
\(590\) | 2.41568 | + | 8.39870i | 0.0994521 | + | 0.345769i | ||||
\(591\) | 19.6297 | 0.807457 | ||||||||
\(592\) | 5.87828 | + | 1.56391i | 0.241596 | + | 0.0642764i | ||||
\(593\) | 31.7803i | 1.30506i | 0.757763 | + | 0.652530i | \(0.226292\pi\) | ||||
−0.757763 | + | 0.652530i | \(0.773708\pi\) | |||||||
\(594\) | 2.26047 | + | 3.91525i | 0.0927482 | + | 0.160645i | ||||
\(595\) | 1.01559 | + | 0.979150i | 0.0416352 | + | 0.0401412i | ||||
\(596\) | −4.49693 | + | 7.78891i | −0.184201 | + | 0.319046i | ||||
\(597\) | −25.7332 | − | 14.8571i | −1.05319 | − | 0.608061i | ||||
\(598\) | 0.588637i | 0.0240712i | ||||||||
\(599\) | 13.6603 | − | 23.6604i | 0.558147 | − | 0.966739i | −0.439504 | − | 0.898240i | \(-0.644846\pi\) |
0.997651 | − | 0.0684981i | \(-0.0218207\pi\) | |||||||
\(600\) | 7.20620 | + | 3.81658i | 0.294192 | + | 0.155811i | ||||
\(601\) | −10.7176 | − | 18.5634i | −0.437180 | − | 0.757218i | 0.560291 | − | 0.828296i | \(-0.310689\pi\) |
−0.997471 | + | 0.0710781i | \(0.977356\pi\) | |||||||
\(602\) | − | 0.695944i | − | 0.0283646i | ||||||
\(603\) | − | 4.35001i | − | 0.177146i | ||||||
\(604\) | 3.49220 | + | 6.04867i | 0.142096 | + | 0.246117i | ||||
\(605\) | 16.5986 | + | 16.0030i | 0.674828 | + | 0.650614i | ||||
\(606\) | 19.4075 | 0.788375 | ||||||||
\(607\) | 0.993591 | − | 0.573650i | 0.0403286 | − | 0.0232837i | −0.479700 | − | 0.877432i | \(-0.659255\pi\) |
0.520029 | + | 0.854149i | \(0.325921\pi\) | |||||||
\(608\) | −6.71925 | + | 3.87936i | −0.272502 | + | 0.157329i | ||||
\(609\) | 4.21008 | + | 7.29207i | 0.170601 | + | 0.295490i | ||||
\(610\) | 2.81933 | − | 2.92425i | 0.114151 | − | 0.118400i | ||||
\(611\) | 3.16649 | − | 5.48453i | 0.128103 | − | 0.221880i | ||||
\(612\) | 0.344706 | − | 0.199016i | 0.0139339 | − | 0.00804474i | ||||
\(613\) | −14.9115 | + | 8.60916i | −0.602270 | + | 0.347721i | −0.769934 | − | 0.638124i | \(-0.779711\pi\) |
0.167664 | + | 0.985844i | \(0.446378\pi\) | |||||||
\(614\) | 2.28345 | + | 3.95505i | 0.0921525 | + | 0.159613i | ||||
\(615\) | −6.80098 | − | 1.68980i | −0.274242 | − | 0.0681394i | ||||
\(616\) | 0.223740 | − | 0.387529i | 0.00901474 | − | 0.0156140i | ||||
\(617\) | 8.90867 | − | 5.14342i | 0.358650 | − | 0.207066i | −0.309839 | − | 0.950789i | \(-0.600275\pi\) |
0.668488 | + | 0.743723i | \(0.266942\pi\) | |||||||
\(618\) | 5.25073i | 0.211215i | ||||||||
\(619\) | −32.8371 | −1.31983 | −0.659917 | − | 0.751338i | \(-0.729409\pi\) | ||||
−0.659917 | + | 0.751338i | \(0.729409\pi\) | |||||||
\(620\) | −6.64391 | + | 1.91096i | −0.266826 | + | 0.0767460i | ||||
\(621\) | 2.93722 | 0.117867 | ||||||||
\(622\) | −8.80027 | − | 5.08084i | −0.352859 | − | 0.203723i | ||||
\(623\) | − | 5.81658i | − | 0.233036i | ||||||
\(624\) | −0.890233 | + | 1.54193i | −0.0356378 | + | 0.0617265i | ||||
\(625\) | −24.9333 | + | 1.82504i | −0.997332 | + | 0.0730017i | ||||
\(626\) | −6.38962 | + | 11.0671i | −0.255381 | + | 0.442332i | ||||
\(627\) | −9.09453 | + | 5.25073i | −0.363201 | + | 0.209694i | ||||
\(628\) | 8.12064i | 0.324049i | ||||||||
\(629\) | 1.82991 | − | 6.87810i | 0.0729634 | − | 0.274248i | ||||
\(630\) | 0.0988967 | − | 0.398032i | 0.00394014 | − | 0.0158580i | ||||
\(631\) | 13.0405 | + | 22.5868i | 0.519135 | + | 0.899168i | 0.999753 | + | 0.0222376i | \(0.00707905\pi\) |
−0.480618 | + | 0.876930i | \(0.659588\pi\) | |||||||
\(632\) | −8.06377 | − | 4.65562i | −0.320760 | − | 0.185191i | ||||
\(633\) | 14.2260 | + | 8.21339i | 0.565433 | + | 0.326453i | ||||
\(634\) | −5.67789 | + | 9.83439i | −0.225498 | + | 0.390573i | ||||
\(635\) | −6.86376 | − | 1.70540i | −0.272380 | − | 0.0676767i | ||||
\(636\) | 2.88603 | − | 4.99875i | 0.114438 | − | 0.198213i | ||||
\(637\) | − | 7.32457i | − | 0.290210i | ||||||
\(638\) | −6.88202 | + | 3.97334i | −0.272462 | + | 0.157306i | ||||
\(639\) | 0.197793 | 0.00782458 | ||||||||
\(640\) | −2.17009 | − | 0.539189i | −0.0857802 | − | 0.0213133i | ||||
\(641\) | 0.461945 | + | 0.800112i | 0.0182457 | + | 0.0316025i | 0.875004 | − | 0.484116i | \(-0.160859\pi\) |
−0.856758 | + | 0.515718i | \(0.827525\pi\) | |||||||
\(642\) | −20.0938 | − | 11.6012i | −0.793039 | − | 0.457861i | ||||
\(643\) | 9.24128i | 0.364440i | 0.983258 | + | 0.182220i | \(0.0583284\pi\) | ||||
−0.983258 | + | 0.182220i | \(0.941672\pi\) | |||||||
\(644\) | −0.145362 | − | 0.251775i | −0.00572808 | − | 0.00992132i | ||||
\(645\) | −4.52361 | + | 1.30111i | −0.178117 | + | 0.0512311i | ||||
\(646\) | 4.53919 | + | 7.86211i | 0.178592 | + | 0.309330i | ||||
\(647\) | 38.7299 | + | 22.3607i | 1.52263 | + | 0.879090i | 0.999642 | + | 0.0267479i | \(0.00851514\pi\) |
0.522985 | + | 0.852342i | \(0.324818\pi\) | |||||||
\(648\) | 6.81022 | + | 3.93188i | 0.267531 | + | 0.154459i | ||||
\(649\) | −1.62177 | − | 2.80899i | −0.0636601 | − | 0.110263i | ||||
\(650\) | −0.199375 | − | 5.45490i | −0.00782011 | − | 0.213959i | ||||
\(651\) | −1.35937 | − | 2.35449i | −0.0532777 | − | 0.0922797i | ||||
\(652\) | 15.2062i | 0.595521i | ||||||||
\(653\) | −5.01848 | − | 2.89742i | −0.196388 | − | 0.113385i | 0.398581 | − | 0.917133i | \(-0.369503\pi\) |
−0.594970 | + | 0.803748i | \(0.702836\pi\) | |||||||
\(654\) | −7.63317 | − | 13.2210i | −0.298480 | − | 0.516983i | ||||
\(655\) | 3.15061 | − | 12.6803i | 0.123105 | − | 0.495462i | ||||
\(656\) | 1.92162 | 0.0750267 | ||||||||
\(657\) | −1.69439 | + | 0.978259i | −0.0661046 | + | 0.0381655i | ||||
\(658\) | 3.12783i | 0.121935i | ||||||||
\(659\) | −3.66701 | + | 6.35146i | −0.142847 | + | 0.247418i | −0.928567 | − | 0.371164i | \(-0.878959\pi\) |
0.785721 | + | 0.618581i | \(0.212292\pi\) | |||||||
\(660\) | −2.93722 | − | 0.729794i | −0.114331 | − | 0.0284072i | ||||
\(661\) | 20.7870 | − | 36.0042i | 0.808522 | − | 1.40040i | −0.105365 | − | 0.994434i | \(-0.533601\pi\) |
0.913887 | − | 0.405968i | \(-0.133066\pi\) | |||||||
\(662\) | 23.9959 | + | 13.8540i | 0.932626 | + | 0.538452i | ||||
\(663\) | 1.80419 | + | 1.04165i | 0.0700689 | + | 0.0404543i | ||||
\(664\) | −1.07838 | − | 1.86781i | −0.0418492 | − | 0.0724849i | ||||
\(665\) | 9.07838 | + | 2.25565i | 0.352044 | + | 0.0874704i | ||||
\(666\) | −1.99773 | + | 0.539090i | −0.0774106 | + | 0.0208893i | ||||
\(667\) | 5.16290i | 0.199908i | ||||||||
\(668\) | −16.8170 | + | 9.70928i | −0.650668 | + | 0.375663i | ||||
\(669\) | −19.2117 | + | 33.2757i | −0.742769 | + | 1.28651i | ||||
\(670\) | 20.5850 | + | 19.8464i | 0.795268 | + | 0.766732i | ||||
\(671\) | −0.753803 | + | 1.30563i | −0.0291002 | + | 0.0504031i | ||||
\(672\) | − | 0.879362i | − | 0.0339221i | ||||||
\(673\) | −27.2780 | − | 15.7490i | −1.05149 | − | 0.607079i | −0.128425 | − | 0.991719i | \(-0.540992\pi\) |
−0.923066 | + | 0.384640i | \(0.874325\pi\) | |||||||
\(674\) | −25.6163 | −0.986705 | ||||||||
\(675\) | −27.2192 | + | 0.994852i | −1.04767 | + | 0.0382919i | ||||
\(676\) | −11.8082 | −0.454160 | ||||||||
\(677\) | − | 21.2351i | − | 0.816132i | −0.912952 | − | 0.408066i | \(-0.866203\pi\) | ||
0.912952 | − | 0.408066i | \(-0.133797\pi\) | |||||||
\(678\) | −18.6116 | + | 10.7454i | −0.714773 | + | 0.412674i | ||||
\(679\) | 2.47414 | − | 4.28534i | 0.0949489 | − | 0.164456i | ||||
\(680\) | −0.630898 | + | 2.53919i | −0.0241938 | + | 0.0973734i | ||||
\(681\) | 7.91557 | + | 13.7102i | 0.303325 | + | 0.525375i | ||||
\(682\) | 2.22209 | − | 1.28293i | 0.0850883 | − | 0.0491258i | ||||
\(683\) | 37.1124 | − | 21.4269i | 1.42007 | − | 0.819876i | 0.423764 | − | 0.905773i | \(-0.360709\pi\) |
0.996304 | + | 0.0858963i | \(0.0273754\pi\) | |||||||
\(684\) | 1.31965 | − | 2.28571i | 0.0504582 | − | 0.0873962i | ||||
\(685\) | −16.9615 | + | 17.5927i | −0.648064 | + | 0.672183i | ||||
\(686\) | 3.69594 | + | 6.40156i | 0.141112 | + | 0.244413i | ||||
\(687\) | −27.1833 | + | 15.6943i | −1.03711 | + | 0.598774i | ||||
\(688\) | 1.11780 | − | 0.645362i | 0.0426157 | − | 0.0246042i | ||||
\(689\) | −3.86376 | −0.147198 | ||||||||
\(690\) | −1.36476 | + | 1.41556i | −0.0519557 | + | 0.0538894i | ||||
\(691\) | −15.9480 | − | 27.6228i | −0.606691 | − | 1.05082i | −0.991782 | − | 0.127940i | \(-0.959163\pi\) |
0.385091 | − | 0.922879i | \(-0.374170\pi\) | |||||||
\(692\) | 23.1278i | 0.879188i | ||||||||
\(693\) | 0.152221i | 0.00578238i | ||||||||
\(694\) | 9.27319 | + | 16.0616i | 0.352005 | + | 0.609691i | ||||
\(695\) | 0.133969 | − | 0.539189i | 0.00508174 | − | 0.0204526i | ||||
\(696\) | −7.80817 | + | 13.5242i | −0.295968 | + | 0.512632i | ||||
\(697\) | − | 2.24846i | − | 0.0851667i | ||||||
\(698\) | 7.33547 | + | 4.23513i | 0.277651 | + | 0.160302i | ||||
\(699\) | 4.19420 | − | 7.26457i | 0.158639 | − | 0.274771i | ||||
\(700\) | 1.43235 | + | 2.28396i | 0.0541377 | + | 0.0863257i | ||||
\(701\) | 9.63809 | + | 16.6937i | 0.364025 | + | 0.630511i | 0.988619 | − | 0.150439i | \(-0.0480688\pi\) |
−0.624594 | + | 0.780950i | \(0.714735\pi\) | |||||||
\(702\) | − | 5.94706i | − | 0.224457i | ||||||
\(703\) | −12.2956 | − | 45.5646i | −0.463739 | − | 1.71850i | ||||
\(704\) | 0.829914 | 0.0312785 | ||||||||
\(705\) | 20.3308 | − | 5.84765i | 0.765701 | − | 0.220235i | ||||
\(706\) | −10.6839 | + | 18.5051i | −0.402095 | + | 0.696450i | ||||
\(707\) | 5.55666 | + | 3.20814i | 0.208980 | + | 0.120655i | ||||
\(708\) | −5.52007 | − | 3.18701i | −0.207457 | − | 0.119775i | ||||
\(709\) | 31.4740 | 1.18203 | 0.591015 | − | 0.806661i | \(-0.298727\pi\) | ||||
0.591015 | + | 0.806661i | \(0.298727\pi\) | |||||||
\(710\) | −0.902406 | + | 0.935991i | −0.0338667 | + | 0.0351271i | ||||
\(711\) | 3.16743 | 0.118788 | ||||||||
\(712\) | 9.34238 | − | 5.39383i | 0.350121 | − | 0.202142i | ||||
\(713\) | − | 1.66701i | − | 0.0624302i | ||||||
\(714\) | −1.02893 | −0.0385067 | ||||||||
\(715\) | 0.560006 | + | 1.94699i | 0.0209430 | + | 0.0728135i | ||||
\(716\) | −5.75872 | + | 9.97440i | −0.215214 | + | 0.372761i | ||||
\(717\) | − | 49.4245i | − | 1.84579i | ||||||
\(718\) | −16.1357 | + | 9.31597i | −0.602180 | + | 0.347669i | ||||
\(719\) | −9.23041 | − | 15.9875i | −0.344236 | − | 0.596234i | 0.640979 | − | 0.767559i | \(-0.278529\pi\) |
−0.985215 | + | 0.171324i | \(0.945195\pi\) | |||||||
\(720\) | 0.731013 | − | 0.210258i | 0.0272432 | − | 0.00783586i | ||||
\(721\) | −0.867969 | + | 1.50337i | −0.0323248 | + | 0.0559883i | ||||
\(722\) | 35.6783 | + | 20.5989i | 1.32781 | + | 0.766612i | ||||
\(723\) | 14.0046 | − | 8.08557i | 0.520837 | − | 0.300705i | ||||
\(724\) | −6.56032 | − | 11.3628i | −0.243812 | − | 0.422295i | ||||
\(725\) | −1.74870 | − | 47.8446i | −0.0649451 | − | 1.77690i | ||||
\(726\) | −16.8166 | −0.624122 | ||||||||
\(727\) | −37.0479 | − | 21.3896i | −1.37403 | − | 0.793297i | −0.382598 | − | 0.923915i | \(-0.624971\pi\) |
−0.991433 | + | 0.130618i | \(0.958304\pi\) | |||||||
\(728\) | −0.509775 | + | 0.294319i | −0.0188935 | + | 0.0109082i | ||||
\(729\) | −29.3279 | −1.08622 | ||||||||
\(730\) | 3.10116 | − | 12.4813i | 0.114779 | − | 0.461955i | ||||
\(731\) | −0.755130 | − | 1.30792i | −0.0279295 | − | 0.0483753i | ||||
\(732\) | 2.96266i | 0.109503i | ||||||||
\(733\) | 28.3770 | + | 16.3835i | 1.04813 | + | 0.605138i | 0.922125 | − | 0.386892i | \(-0.126451\pi\) |
0.126004 | + | 0.992030i | \(0.459785\pi\) | |||||||
\(734\) | −24.9093 | −0.919420 | ||||||||
\(735\) | 16.9821 | − | 17.6142i | 0.626396 | − | 0.649709i | ||||
\(736\) | 0.269594 | − | 0.466951i | 0.00993738 | − | 0.0172121i | ||||
\(737\) | −9.19082 | − | 5.30632i | −0.338548 | − | 0.195461i | ||||
\(738\) | −0.566107 | + | 0.326842i | −0.0208387 | + | 0.0120312i | ||||
\(739\) | −32.9965 | −1.21380 | −0.606898 | − | 0.794780i | \(-0.707586\pi\) | ||||
−0.606898 | + | 0.794780i | \(0.707586\pi\) | |||||||
\(740\) | 6.56333 | − | 11.9131i | 0.241273 | − | 0.437935i | ||||
\(741\) | 13.8141 | 0.507475 | ||||||||
\(742\) | 1.65263 | − | 0.954146i | 0.0606699 | − | 0.0350278i | ||||
\(743\) | 34.2722 | + | 19.7870i | 1.25732 | + | 0.725916i | 0.972553 | − | 0.232680i | \(-0.0747494\pi\) |
0.284770 | + | 0.958596i | \(0.408083\pi\) | |||||||
\(744\) | 2.52113 | − | 4.36673i | 0.0924291 | − | 0.160092i | ||||
\(745\) | 14.4779 | + | 13.9584i | 0.530430 | + | 0.511397i | ||||
\(746\) | 9.66475 | 0.353852 | ||||||||
\(747\) | 0.635377 | + | 0.366835i | 0.0232472 | + | 0.0134218i | ||||
\(748\) | − | 0.971071i | − | 0.0355059i | ||||||
\(749\) | −3.83545 | − | 6.64319i | −0.140144 | − | 0.242737i | ||||
\(750\) | 12.1678 | − | 13.5802i | 0.444306 | − | 0.495880i | ||||
\(751\) | −47.1699 | −1.72125 | −0.860627 | − | 0.509236i | \(-0.829928\pi\) | ||||
−0.860627 | + | 0.509236i | \(0.829928\pi\) | |||||||
\(752\) | −5.02380 | + | 2.90049i | −0.183199 | + | 0.105770i | ||||
\(753\) | 32.5518 | + | 18.7938i | 1.18625 | + | 0.684884i | ||||
\(754\) | 10.4534 | 0.380692 | ||||||||
\(755\) | 15.0091 | − | 4.31700i | 0.546237 | − | 0.157112i | ||||
\(756\) | 1.46861 | + | 2.54371i | 0.0534128 | + | 0.0925138i | ||||
\(757\) | 42.0005 | − | 24.2490i | 1.52653 | − | 0.881344i | 0.527029 | − | 0.849847i | \(-0.323306\pi\) |
0.999504 | − | 0.0314974i | \(-0.0100276\pi\) | |||||||
\(758\) | 10.5574 | + | 6.09530i | 0.383461 | + | 0.221391i | ||||
\(759\) | 0.364897 | − | 0.632020i | 0.0132449 | − | 0.0229409i | ||||
\(760\) | 4.79560 | + | 16.6731i | 0.173955 | + | 0.604796i | ||||
\(761\) | −13.7607 | − | 23.8342i | −0.498824 | − | 0.863988i | 0.501175 | − | 0.865346i | \(-0.332901\pi\) |
−0.999999 | + | 0.00135787i | \(0.999568\pi\) | |||||||
\(762\) | 4.46727 | − | 2.57918i | 0.161832 | − | 0.0934339i | ||||
\(763\) | − | 5.04718i | − | 0.182720i | ||||||
\(764\) | 8.64896 | − | 14.9804i | 0.312908 | − | 0.541973i | ||||
\(765\) | −0.246020 | − | 0.855348i | −0.00889488 | − | 0.0309252i | ||||
\(766\) | −5.21953 | −0.188589 | ||||||||
\(767\) | 4.26672i | 0.154062i | ||||||||
\(768\) | 1.41240 | − | 0.815449i | 0.0509656 | − | 0.0294250i | ||||
\(769\) | −5.24354 | −0.189087 | −0.0945435 | − | 0.995521i | \(-0.530139\pi\) | ||||
−0.0945435 | + | 0.995521i | \(0.530139\pi\) | |||||||
\(770\) | −0.720334 | − | 0.694487i | −0.0259590 | − | 0.0250276i | ||||
\(771\) | −11.1824 | −0.402723 | ||||||||
\(772\) | 14.3893 | + | 8.30765i | 0.517881 | + | 0.298999i | ||||
\(773\) | 20.6604 | + | 11.9283i | 0.743103 | + | 0.429031i | 0.823196 | − | 0.567757i | \(-0.192189\pi\) |
−0.0800935 | + | 0.996787i | \(0.525522\pi\) | |||||||
\(774\) | −0.219535 | + | 0.380245i | −0.00789102 | + | 0.0136676i | ||||
\(775\) | 0.564627 | + | 15.4482i | 0.0202820 | + | 0.554917i | ||||
\(776\) | 9.17727 | 0.329445 | ||||||||
\(777\) | 5.16914 | + | 1.37525i | 0.185442 | + | 0.0493367i | ||||
\(778\) | − | 12.7526i | − | 0.457202i | ||||||
\(779\) | −7.45467 | − | 12.9119i | −0.267091 | − | 0.462616i | ||||
\(780\) | 2.86611 | + | 2.76327i | 0.102623 | + | 0.0989410i | ||||
\(781\) | 0.241276 | − | 0.417903i | 0.00863355 | − | 0.0149537i | ||||
\(782\) | −0.546373 | − | 0.315449i | −0.0195383 | − | 0.0112804i | ||||
\(783\) | − | 52.1613i | − | 1.86409i | ||||||
\(784\) | −3.35464 | + | 5.81040i | −0.119808 | + | 0.207514i | ||||
\(785\) | 17.6225 | + | 4.37856i | 0.628974 | + | 0.156277i | ||||
\(786\) | 4.76487 | + | 8.25299i | 0.169957 | + | 0.294374i | ||||
\(787\) | 29.1894i | 1.04049i | 0.854017 | + | 0.520245i | \(0.174159\pi\) | ||||
−0.854017 | + | 0.520245i | \(0.825841\pi\) | |||||||
\(788\) | 12.0361i | 0.428769i | ||||||||
\(789\) | −2.82211 | − | 4.88805i | −0.100470 | − | 0.174019i | ||||
\(790\) | −14.4510 | + | 14.9888i | −0.514143 | + | 0.533279i | ||||
\(791\) | −7.10504 | −0.252626 | ||||||||
\(792\) | −0.244491 | + | 0.141157i | −0.00868762 | + | 0.00501580i | ||||
\(793\) | 1.71748 | − | 0.991590i | 0.0609896 | − | 0.0352124i | ||||
\(794\) | 12.6448 | + | 21.9014i | 0.448745 | + | 0.777250i | ||||
\(795\) | −9.29160 | − | 8.95820i | −0.329539 | − | 0.317715i | ||||
\(796\) | 9.10977 | − | 15.7786i | 0.322887 | − | 0.559257i | ||||
\(797\) | −7.49857 | + | 4.32930i | −0.265613 | + | 0.153352i | −0.626892 | − | 0.779106i | \(-0.715673\pi\) |
0.361279 | + | 0.932458i | \(0.382340\pi\) | |||||||
\(798\) | −5.90865 | + | 3.41136i | −0.209164 | + | 0.120761i | ||||
\(799\) | 3.39383 | + | 5.87828i | 0.120065 | + | 0.207959i | ||||
\(800\) | −2.34017 | + | 4.41855i | −0.0827376 | + | 0.156219i | ||||
\(801\) | −1.83483 | + | 3.17803i | −0.0648307 | + | 0.112290i | ||||
\(802\) | 11.8850 | − | 6.86183i | 0.419675 | − | 0.242299i | ||||
\(803\) | 4.77328i | 0.168445i | ||||||||
\(804\) | −20.8554 | −0.735512 | ||||||||
\(805\) | −0.624751 | + | 0.179695i | −0.0220196 | + | 0.00633340i | ||||
\(806\) | −3.37525 | −0.118888 | ||||||||
\(807\) | −37.6236 | − | 21.7220i | −1.32441 | − | 0.764650i | ||||
\(808\) | 11.8999i | 0.418636i | ||||||||
\(809\) | −18.9885 | + | 32.8891i | −0.667601 | + | 1.15632i | 0.310972 | + | 0.950419i | \(0.399345\pi\) |
−0.978573 | + | 0.205899i | \(0.933988\pi\) | |||||||
\(810\) | 12.2045 | − | 12.6587i | 0.428823 | − | 0.444783i | ||||
\(811\) | −3.39576 | + | 5.88164i | −0.119241 | + | 0.206532i | −0.919467 | − | 0.393167i | \(-0.871380\pi\) |
0.800226 | + | 0.599699i | \(0.204713\pi\) | |||||||
\(812\) | −4.47120 | + | 2.58145i | −0.156908 | + | 0.0905911i | ||||
\(813\) | 19.0612i | 0.668504i | ||||||||
\(814\) | −1.29791 | + | 4.87846i | −0.0454918 | + | 0.170990i | ||||
\(815\) | 32.9988 | + | 8.19902i | 1.15590 | + | 0.287199i | ||||
\(816\) | −0.954146 | − | 1.65263i | −0.0334018 | − | 0.0578536i | ||||
\(817\) | −8.67270 | − | 5.00719i | −0.303420 | − | 0.175179i | ||||
\(818\) | −10.4371 | − | 6.02586i | −0.364924 | − | 0.210689i | ||||
\(819\) | 0.100119 | − | 0.173412i | 0.00349845 | − | 0.00605949i | ||||
\(820\) | 1.03612 | − | 4.17009i | 0.0361828 | − | 0.145626i | ||||
\(821\) | 24.3545 | − | 42.1833i | 0.849980 | − | 1.47221i | −0.0312459 | − | 0.999512i | \(-0.509947\pi\) |
0.881225 | − | 0.472696i | \(-0.156719\pi\) | |||||||
\(822\) | − | 17.8238i | − | 0.621675i | ||||||
\(823\) | 22.4300 | − | 12.9499i | 0.781859 | − | 0.451407i | −0.0552297 | − | 0.998474i | \(-0.517589\pi\) |
0.837089 | + | 0.547067i | \(0.184256\pi\) | |||||||
\(824\) | −3.21953 | −0.112158 | ||||||||
\(825\) | −3.16743 | + | 5.98053i | −0.110276 | + | 0.208215i | ||||
\(826\) | −1.05365 | − | 1.82498i | −0.0366613 | − | 0.0634992i | ||||
\(827\) | −7.49767 | − | 4.32878i | −0.260719 | − | 0.150526i | 0.363943 | − | 0.931421i | \(-0.381430\pi\) |
−0.624663 | + | 0.780895i | \(0.714764\pi\) | |||||||
\(828\) | 0.183417i | 0.00637420i | ||||||||
\(829\) | −4.23348 | − | 7.33260i | −0.147035 | − | 0.254672i | 0.783095 | − | 0.621901i | \(-0.213640\pi\) |
−0.930130 | + | 0.367230i | \(0.880306\pi\) | |||||||
\(830\) | −4.63475 | + | 1.33307i | −0.160874 | + | 0.0462716i | ||||
\(831\) | 5.71400 | + | 9.89694i | 0.198217 | + | 0.343321i | ||||
\(832\) | −0.945448 | − | 0.545854i | −0.0327775 | − | 0.0189241i | ||||
\(833\) | 6.79867 | + | 3.92522i | 0.235560 | + | 0.136001i | ||||
\(834\) | 0.202610 | + | 0.350931i | 0.00701581 | + | 0.0121517i | ||||
\(835\) | 12.0025 | + | 41.7294i | 0.415362 | + | 1.44410i | ||||
\(836\) | −3.21953 | − | 5.57640i | −0.111350 | − | 0.192864i | ||||
\(837\) | 16.8420i | 0.582145i | ||||||||
\(838\) | 15.1643 | + | 8.75513i | 0.523843 | + | 0.302441i | ||||
\(839\) | −7.72313 | − | 13.3769i | −0.266632 | − | 0.461820i | 0.701358 | − | 0.712809i | \(-0.252578\pi\) |
−0.967990 | + | 0.250989i | \(0.919244\pi\) | |||||||
\(840\) | −1.90829 | − | 0.474142i | −0.0658423 | − | 0.0163595i | ||||
\(841\) | 62.6865 | 2.16160 | ||||||||
\(842\) | 1.47405 | − | 0.851044i | 0.0507992 | − | 0.0293289i | ||||
\(843\) | − | 37.3591i | − | 1.28672i | ||||||
\(844\) | −5.03612 | + | 8.72281i | −0.173350 | + | 0.300252i | ||||
\(845\) | −6.36683 | + | 25.6248i | −0.219026 | + | 0.881518i | ||||
\(846\) | 0.986669 | − | 1.70896i | 0.0339224 | − | 0.0587553i | ||||
\(847\) | −4.81485 | − | 2.77985i | −0.165440 | − | 0.0955169i | ||||
\(848\) | 3.06503 | + | 1.76959i | 0.105253 | + | 0.0607681i | ||||
\(849\) | −13.1260 | − | 22.7349i | −0.450482 | − | 0.780258i | ||||
\(850\) | 5.17009 | + | 2.73820i | 0.177333 | + | 0.0939196i | ||||
\(851\) | 2.32325 | + | 2.31502i | 0.0796399 | + | 0.0793580i | ||||
\(852\) | − | 0.948284i | − | 0.0324877i | ||||||
\(853\) | 41.9200 | − | 24.2025i | 1.43531 | − | 0.828679i | 0.437794 | − | 0.899075i | \(-0.355760\pi\) |
0.997519 | + | 0.0703967i | \(0.0224265\pi\) | |||||||
\(854\) | −0.489741 | + | 0.848255i | −0.0167586 | + | 0.0290267i | ||||
\(855\) | −4.24864 | − | 4.09619i | −0.145300 | − | 0.140087i | ||||
\(856\) | 7.11336 | − | 12.3207i | 0.243130 | − | 0.421113i | ||||
\(857\) | 12.9821i | 0.443461i | 0.975108 | + | 0.221731i | \(0.0711706\pi\) | ||||
−0.975108 | + | 0.221731i | \(0.928829\pi\) | |||||||
\(858\) | −1.27967 | − | 0.738816i | −0.0436871 | − | 0.0252228i | ||||
\(859\) | 15.0061 | 0.512003 | 0.256001 | − | 0.966676i | \(-0.417595\pi\) | ||||
0.256001 | + | 0.966676i | \(0.417595\pi\) | |||||||
\(860\) | −0.797787 | − | 2.77370i | −0.0272043 | − | 0.0945822i | ||||
\(861\) | 1.68980 | 0.0575883 | ||||||||
\(862\) | − | 21.7805i | − | 0.741846i | ||||||
\(863\) | 2.27114 | − | 1.31124i | 0.0773105 | − | 0.0446352i | −0.460846 | − | 0.887480i | \(-0.652454\pi\) |
0.538157 | + | 0.842845i | \(0.319121\pi\) | |||||||
\(864\) | −2.72374 | + | 4.71766i | −0.0926635 | + | 0.160498i | ||||
\(865\) | 50.1894 | + | 12.4703i | 1.70649 | + | 0.424002i | ||||
\(866\) | −5.34017 | − | 9.24945i | −0.181466 | − | 0.314309i | ||||
\(867\) | 22.0771 | − | 12.7462i | 0.749776 | − | 0.432884i | ||||
\(868\) | 1.44368 | − | 0.833507i | 0.0490016 | − | 0.0282911i | ||||
\(869\) | 3.86376 | − | 6.69223i | 0.131069 | − | 0.227019i | ||||
\(870\) | 25.1385 | + | 24.2365i | 0.852275 | + | 0.821694i | ||||
\(871\) | 6.98020 | + | 12.0901i | 0.236515 | + | 0.409656i | ||||
\(872\) | 8.10660 | − | 4.68035i | 0.274524 | − | 0.158497i | ||||
\(873\) | −2.70361 | + | 1.56093i | −0.0915034 | + | 0.0528295i | ||||
\(874\) | −4.18342 | −0.141506 | ||||||||
\(875\) | 5.72871 | − | 1.87684i | 0.193666 | − | 0.0634486i | ||||
\(876\) | 4.69008 | + | 8.12346i | 0.158463 | + | 0.274466i | ||||
\(877\) | 5.18673i | 0.175143i | 0.996158 | + | 0.0875717i | \(0.0279107\pi\) | ||||
−0.996158 | + | 0.0875717i | \(0.972089\pi\) | |||||||
\(878\) | − | 30.9227i | − | 1.04359i | ||||||
\(879\) | −20.1736 | − | 34.9417i | −0.680438 | − | 1.17855i | ||||
\(880\) | 0.447480 | − | 1.80098i | 0.0150846 | − | 0.0607112i | ||||
\(881\) | −13.9402 | + | 24.1451i | −0.469657 | + | 0.813470i | −0.999398 | − | 0.0346892i | \(-0.988956\pi\) |
0.529741 | + | 0.848160i | \(0.322289\pi\) | |||||||
\(882\) | − | 2.28231i | − | 0.0768495i | ||||||
\(883\) | 4.30311 | + | 2.48440i | 0.144811 | + | 0.0836068i | 0.570655 | − | 0.821190i | \(-0.306689\pi\) |
−0.425844 | + | 0.904797i | \(0.640023\pi\) | |||||||
\(884\) | −0.638697 | + | 1.10626i | −0.0214817 | + | 0.0372074i | ||||
\(885\) | −9.89245 | + | 10.2606i | −0.332531 | + | 0.344907i | ||||
\(886\) | −2.39269 | − | 4.14427i | −0.0803841 | − | 0.139229i | ||||
\(887\) | 18.4969i | 0.621066i | 0.950563 | + | 0.310533i | \(0.100508\pi\) | ||||
−0.950563 | + | 0.310533i | \(0.899492\pi\) | |||||||
\(888\) | 2.58457 | + | 9.57777i | 0.0867324 | + | 0.321409i | ||||
\(889\) | 1.70540 | 0.0571973 | ||||||||
\(890\) | −6.66776 | − | 23.1821i | −0.223504 | − | 0.777065i | ||||
\(891\) | −3.26312 | + | 5.65189i | −0.109319 | + | 0.189346i | ||||
\(892\) | −20.4033 | − | 11.7799i | −0.683153 | − | 0.394419i | ||||
\(893\) | 38.9783 | + | 22.5041i | 1.30436 | + | 0.753072i | ||||
\(894\) | −14.6681 | −0.490573 | ||||||||
\(895\) | 18.5403 | + | 17.8750i | 0.619733 | + | 0.597496i | ||||
\(896\) | 0.539189 | 0.0180130 | ||||||||
\(897\) | −0.831390 | + | 0.480004i | −0.0277593 | + | 0.0160269i | ||||
\(898\) | − | 18.0966i | − | 0.603892i | ||||||
\(899\) | −29.6041 | −0.987351 | ||||||||
\(900\) | −0.0621245 | − | 1.69973i | −0.00207082 | − | 0.0566577i | ||||
\(901\) | 2.07058 | − | 3.58635i | 0.0689810 | − | 0.119479i | ||||
\(902\) | 1.59478i | 0.0531004i | ||||||||
\(903\) | 0.982951 | − | 0.567507i | 0.0327106 | − | 0.0188855i | ||||
\(904\) | −6.58864 | − | 11.4119i | −0.219135 | − | 0.379553i | ||||
\(905\) | −28.1955 | + | 8.10976i | −0.937251 | + | 0.269578i | ||||
\(906\) | −5.69542 | + | 9.86476i | −0.189218 | + | 0.327735i | ||||
\(907\) | −22.9898 | − | 13.2732i | −0.763365 | − | 0.440729i | 0.0671376 | − | 0.997744i | \(-0.478613\pi\) |
−0.830503 | + | 0.557015i | \(0.811947\pi\) | |||||||
\(908\) | −8.40652 | + | 4.85350i | −0.278980 | + | 0.161069i | ||||
\(909\) | −2.02401 | − | 3.50569i | −0.0671321 | − | 0.116276i | ||||
\(910\) | 0.363832 | + | 1.26495i | 0.0120609 | + | 0.0419326i | ||||
\(911\) | 33.2095 | 1.10028 | 0.550140 | − | 0.835072i | \(-0.314574\pi\) | ||||
0.550140 | + | 0.835072i | \(0.314574\pi\) | |||||||
\(912\) | −10.9584 | − | 6.32684i | −0.362869 | − | 0.209503i | ||||
\(913\) | 1.55012 | − | 0.894960i | 0.0513014 | − | 0.0296189i | ||||
\(914\) | 38.9093 | 1.28701 | ||||||||
\(915\) | 6.42923 | + | 1.59743i | 0.212544 | + | 0.0528095i | ||||
\(916\) | −9.62310 | − | 16.6677i | −0.317956 | − | 0.550716i | ||||
\(917\) | 3.15061i | 0.104042i | ||||||||
\(918\) | 5.52007 | + | 3.18701i | 0.182189 | + | 0.105187i | ||||
\(919\) | −2.65368 | −0.0875370 | −0.0437685 | − | 0.999042i | \(-0.513936\pi\) | ||||
−0.0437685 | + | 0.999042i | \(0.513936\pi\) | |||||||
\(920\) | −0.867962 | − | 0.836818i | −0.0286159 | − | 0.0275891i | ||||
\(921\) | −3.72407 | + | 6.45028i | −0.122712 | + | 0.212544i | ||||
\(922\) | −19.8006 | − | 11.4319i | −0.652098 | − | 0.376489i | ||||
\(923\) | −0.549730 | + | 0.317387i | −0.0180946 | + | 0.0104469i | ||||
\(924\) | 0.729794 | 0.0240085 | ||||||||
\(925\) | −22.3137 | − | 20.6664i | −0.733668 | − | 0.679508i | ||||
\(926\) | 27.4596 | 0.902378 | ||||||||
\(927\) | 0.948470 | − | 0.547599i | 0.0311518 | − | 0.0179855i | ||||
\(928\) | −8.29246 | − | 4.78765i | −0.272213 | − | 0.157162i | ||||
\(929\) | −26.9101 | + | 46.6097i | −0.882893 | + | 1.52922i | −0.0347834 | + | 0.999395i | \(0.511074\pi\) |
−0.848110 | + | 0.529821i | \(0.822259\pi\) | |||||||
\(930\) | −8.11681 | − | 7.82556i | −0.266161 | − | 0.256610i | ||||
\(931\) | 52.0554 | 1.70605 | ||||||||
\(932\) | 4.45434 | + | 2.57171i | 0.145907 | + | 0.0842392i | ||||
\(933\) | − | 16.5727i | − | 0.542564i | ||||||
\(934\) | −14.6948 | − | 25.4522i | −0.480829 | − | 0.832820i | ||||
\(935\) | −2.10731 | − | 0.523590i | −0.0689163 | − | 0.0171232i | ||||
\(936\) | 0.371370 | 0.0121386 | ||||||||
\(937\) | 23.2416 | − | 13.4186i | 0.759270 | − | 0.438365i | −0.0697634 | − | 0.997564i | \(-0.522224\pi\) |
0.829034 | + | 0.559199i | \(0.188891\pi\) | |||||||
\(938\) | −5.97121 | − | 3.44748i | −0.194967 | − | 0.112564i | ||||
\(939\) | −20.8416 | −0.680141 | ||||||||
\(940\) | 3.58554 | + | 12.4660i | 0.116947 | + | 0.406596i | ||||
\(941\) | −6.66536 | − | 11.5447i | −0.217284 | − | 0.376348i | 0.736692 | − | 0.676228i | \(-0.236387\pi\) |
−0.953977 | + | 0.299880i | \(0.903053\pi\) | |||||||
\(942\) | −11.4696 | + | 6.62196i | −0.373699 | + | 0.215755i | ||||
\(943\) | 0.897304 | + | 0.518059i | 0.0292202 | + | 0.0168703i | ||||
\(944\) | 1.95415 | − | 3.38468i | 0.0636020 | − | 0.110162i | ||||
\(945\) | 6.31192 | − | 1.81547i | 0.205327 | − | 0.0590573i | ||||
\(946\) | 0.535595 | + | 0.927678i | 0.0174137 | + | 0.0301614i | ||||
\(947\) | −44.4671 | + | 25.6731i | −1.44499 | + | 0.834263i | −0.998176 | − | 0.0603667i | \(-0.980773\pi\) |
−0.446809 | + | 0.894629i | \(0.647440\pi\) | |||||||
\(948\) | − | 15.1857i | − | 0.493208i | ||||||
\(949\) | 3.13950 | − | 5.43778i | 0.101913 | − | 0.176518i | ||||
\(950\) | 38.7677 | − | 1.41695i | 1.25779 | − | 0.0459718i | ||||
\(951\) | −18.5201 | −0.600555 | ||||||||
\(952\) | − | 0.630898i | − | 0.0204475i | ||||||
\(953\) | 38.3288 | − | 22.1292i | 1.24159 | − | 0.716834i | 0.272174 | − | 0.962248i | \(-0.412257\pi\) |
0.969418 | + | 0.245415i | \(0.0789241\pi\) | |||||||
\(954\) | −1.20394 | −0.0389789 | ||||||||
\(955\) | −27.8454 | − | 26.8463i | −0.901056 | − | 0.868725i | ||||
\(956\) | 30.3051 | 0.980137 | ||||||||
\(957\) | −11.2239 | − | 6.48011i | −0.362816 | − | 0.209472i | ||||
\(958\) | 26.9690 | + | 15.5706i | 0.871330 | + | 0.503063i | ||||
\(959\) | 2.94635 | − | 5.10322i | 0.0951425 | − | 0.164792i | ||||
\(960\) | −1.00804 | − | 3.50471i | −0.0325345 | − | 0.113114i | ||||
\(961\) | −21.4413 | −0.691656 | ||||||||
\(962\) | 4.68728 | − | 4.70394i | 0.151124 | − | 0.151661i | ||||
\(963\) | 4.83955i | 0.155952i | ||||||||
\(964\) | 4.95774 | + | 8.58706i | 0.159678 | + | 0.276570i | ||||
\(965\) | 25.7869 | − | 26.7466i | 0.830108 | − | 0.861003i | ||||
\(966\) | 0.237071 | − | 0.410619i | 0.00762764 | − | 0.0132115i | ||||
\(967\) | 20.4062 | + | 11.7815i | 0.656218 | + | 0.378868i | 0.790835 | − | 0.612030i | \(-0.209647\pi\) |
−0.134616 | + | 0.990898i | \(0.542980\pi\) | |||||||
\(968\) | − | 10.3112i | − | 0.331416i | ||||||
\(969\) | −7.40295 | + | 12.8223i | −0.237817 | + | 0.411911i | ||||
\(970\) | 4.94828 | − | 19.9155i | 0.158880 | − | 0.639447i | ||||
\(971\) | 30.2147 | + | 52.3334i | 0.969636 | + | 1.67946i | 0.696606 | + | 0.717454i | \(0.254693\pi\) |
0.273031 | + | 0.962005i | \(0.411974\pi\) | |||||||
\(972\) | − | 3.51745i | − | 0.112822i | ||||||
\(973\) | 0.133969i | 0.00429485i | ||||||||
\(974\) | −19.5597 | − | 33.8784i | −0.626733 | − | 1.08553i | ||||
\(975\) | 7.54192 | − | 4.72979i | 0.241535 | − | 0.151474i | ||||
\(976\) | −1.81658 | −0.0581474 | ||||||||
\(977\) | −22.3347 | + | 12.8950i | −0.714551 | + | 0.412546i | −0.812744 | − | 0.582621i | \(-0.802027\pi\) |
0.0981927 | + | 0.995167i | \(0.468694\pi\) | |||||||
\(978\) | −21.4772 | + | 12.3999i | −0.686766 | + | 0.396504i | ||||
\(979\) | 4.47641 | + | 7.75337i | 0.143067 | + | 0.247799i | ||||
\(980\) | 10.8003 | + | 10.4128i | 0.345003 | + | 0.332623i | ||||
\(981\) | −1.59213 | + | 2.75765i | −0.0508327 | + | 0.0880448i | ||||
\(982\) | −5.09364 | + | 2.94081i | −0.162545 | + | 0.0938452i | ||||
\(983\) | −28.0700 | + | 16.2062i | −0.895293 | + | 0.516898i | −0.875670 | − | 0.482910i | \(-0.839580\pi\) |
−0.0196229 | + | 0.999807i | \(0.506247\pi\) | |||||||
\(984\) | 1.56698 | + | 2.71410i | 0.0499536 | + | 0.0865222i | ||||
\(985\) | 26.1194 | + | 6.48974i | 0.832234 | + | 0.206780i | ||||
\(986\) | −5.60197 | + | 9.70289i | −0.178403 | + | 0.309003i | ||||
\(987\) | −4.41774 | + | 2.55058i | −0.140618 | + | 0.0811859i | ||||
\(988\) | 8.47027i | 0.269475i | ||||||||
\(989\) | 0.695944 | 0.0221297 | ||||||||
\(990\) | 0.174496 | + | 0.606677i | 0.00554585 | + | 0.0192815i | ||||
\(991\) | −3.46308 | −0.110008 | −0.0550042 | − | 0.998486i | \(-0.517517\pi\) | ||||
−0.0550042 | + | 0.998486i | \(0.517517\pi\) | |||||||
\(992\) | 2.67750 | + | 1.54585i | 0.0850107 | + | 0.0490809i | ||||
\(993\) | 45.1890i | 1.43403i | ||||||||
\(994\) | 0.156755 | − | 0.271508i | 0.00497198 | − | 0.00861173i | ||||
\(995\) | −29.3290 | − | 28.2766i | −0.929792 | − | 0.896429i | ||||
\(996\) | 1.75872 | − | 3.04620i | 0.0557273 | − | 0.0965225i | ||||
\(997\) | 4.96837 | − | 2.86849i | 0.157350 | − | 0.0908460i | −0.419258 | − | 0.907867i | \(-0.637710\pi\) |
0.576607 | + | 0.817021i | \(0.304376\pi\) | |||||||
\(998\) | − | 20.7382i | − | 0.656456i | ||||||
\(999\) | −23.4720 | − | 23.3889i | −0.742622 | − | 0.739992i |
(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 | 370.2.n.f.359.2 | yes | 12 | |
5.4 | even | 2 | inner | 370.2.n.f.359.5 | yes | 12 | |
37.10 | even | 3 | inner | 370.2.n.f.269.5 | yes | 12 | |
185.84 | even | 6 | inner | 370.2.n.f.269.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.n.f.269.2 | ✓ | 12 | 185.84 | even | 6 | inner | |
370.2.n.f.269.5 | yes | 12 | 37.10 | even | 3 | inner | |
370.2.n.f.359.2 | yes | 12 | 1.1 | even | 1 | trivial | |
370.2.n.f.359.5 | yes | 12 | 5.4 | even | 2 | inner |