Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(49,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("570.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.q (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.3 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.a.49.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.917738 | + | 2.03906i | 0.410425 | + | 0.911894i | ||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | 3.00000i | 1.13389i | 0.823754 | + | 0.566947i | \(0.191875\pi\) | ||||
−0.823754 | + | 0.566947i | \(0.808125\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.81431 | + | 1.30701i | 0.573736 | + | 0.413312i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 1.25529 | + | 0.724745i | 0.348156 | + | 0.201008i | 0.663873 | − | 0.747845i | \(-0.268912\pi\) |
−0.315717 | + | 0.948853i | \(0.602245\pi\) | |||||||
\(14\) | 1.50000 | + | 2.59808i | 0.400892 | + | 0.694365i | ||||
\(15\) | 1.81431 | + | 1.30701i | 0.468454 | + | 0.337468i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.24264 | + | 2.44949i | −1.02899 | + | 0.594089i | −0.916696 | − | 0.399586i | \(-0.869154\pi\) |
−0.112296 | + | 0.993675i | \(0.535820\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.00000 | − | 4.24264i | 0.229416 | − | 0.973329i | ||||
\(20\) | 2.22474 | + | 0.224745i | 0.497468 | + | 0.0502545i | ||||
\(21\) | 1.50000 | + | 2.59808i | 0.327327 | + | 0.566947i | ||||
\(22\) | 1.73205 | − | 1.00000i | 0.369274 | − | 0.213201i | ||||
\(23\) | 2.12132 | + | 1.22474i | 0.442326 | + | 0.255377i | 0.704584 | − | 0.709621i | \(-0.251134\pi\) |
−0.262258 | + | 0.964998i | \(0.584467\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −3.31552 | + | 3.74264i | −0.663103 | + | 0.748528i | ||||
\(26\) | 1.44949 | 0.284268 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.59808 | + | 1.50000i | 0.490990 | + | 0.283473i | ||||
\(29\) | 2.67423 | − | 4.63191i | 0.496593 | − | 0.860124i | −0.503399 | − | 0.864054i | \(-0.667918\pi\) |
0.999992 | + | 0.00392972i | \(0.00125087\pi\) | |||||||
\(30\) | 2.22474 | + | 0.224745i | 0.406181 | + | 0.0410326i | ||||
\(31\) | 1.89898 | 0.341067 | 0.170533 | − | 0.985352i | \(-0.445451\pi\) | ||||
0.170533 | + | 0.985352i | \(0.445451\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 1.73205 | − | 1.00000i | 0.301511 | − | 0.174078i | ||||
\(34\) | −2.44949 | + | 4.24264i | −0.420084 | + | 0.727607i | ||||
\(35\) | −6.11717 | + | 2.75321i | −1.03399 | + | 0.465378i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | − | 9.44949i | − | 1.55349i | −0.629817 | − | 0.776743i | \(-0.716870\pi\) | ||
0.629817 | − | 0.776743i | \(-0.283130\pi\) | |||||||
\(38\) | −1.25529 | − | 4.17423i | −0.203636 | − | 0.677150i | ||||
\(39\) | 1.44949 | 0.232104 | ||||||||
\(40\) | 2.03906 | − | 0.917738i | 0.322403 | − | 0.145107i | ||||
\(41\) | 1.22474 | + | 2.12132i | 0.191273 | + | 0.331295i | 0.945672 | − | 0.325121i | \(-0.105405\pi\) |
−0.754399 | + | 0.656416i | \(0.772072\pi\) | |||||||
\(42\) | 2.59808 | + | 1.50000i | 0.400892 | + | 0.231455i | ||||
\(43\) | −4.71940 | + | 2.72474i | −0.719701 | + | 0.415520i | −0.814643 | − | 0.579963i | \(-0.803067\pi\) |
0.0949415 | + | 0.995483i | \(0.469734\pi\) | |||||||
\(44\) | 1.00000 | − | 1.73205i | 0.150756 | − | 0.261116i | ||||
\(45\) | 2.22474 | + | 0.224745i | 0.331645 | + | 0.0335030i | ||||
\(46\) | 2.44949 | 0.361158 | ||||||||
\(47\) | −7.31747 | − | 4.22474i | −1.06736 | − | 0.616242i | −0.139903 | − | 0.990165i | \(-0.544679\pi\) |
−0.927460 | + | 0.373923i | \(0.878012\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | −1.00000 | + | 4.89898i | −0.141421 | + | 0.692820i | ||||
\(51\) | −2.44949 | + | 4.24264i | −0.342997 | + | 0.594089i | ||||
\(52\) | 1.25529 | − | 0.724745i | 0.174078 | − | 0.100504i | ||||
\(53\) | −11.1708 | − | 6.44949i | −1.53443 | − | 0.885906i | −0.999150 | − | 0.0412333i | \(-0.986871\pi\) |
−0.535284 | − | 0.844672i | \(-0.679795\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 1.83548 | + | 4.07812i | 0.247495 | + | 0.549893i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | −1.25529 | − | 4.17423i | −0.166268 | − | 0.552891i | ||||
\(58\) | − | 5.34847i | − | 0.702288i | ||||||
\(59\) | −3.89898 | − | 6.75323i | −0.507604 | − | 0.879196i | −0.999961 | − | 0.00880259i | \(-0.997198\pi\) |
0.492357 | − | 0.870393i | \(-0.336135\pi\) | |||||||
\(60\) | 2.03906 | − | 0.917738i | 0.263241 | − | 0.118479i | ||||
\(61\) | 5.17423 | − | 8.96204i | 0.662493 | − | 1.14747i | −0.317466 | − | 0.948270i | \(-0.602832\pi\) |
0.979959 | − | 0.199202i | \(-0.0638348\pi\) | |||||||
\(62\) | 1.64456 | − | 0.949490i | 0.208860 | − | 0.120585i | ||||
\(63\) | 2.59808 | + | 1.50000i | 0.327327 | + | 0.188982i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.325765 | + | 3.22474i | −0.0404062 | + | 0.399980i | ||||
\(66\) | 1.00000 | − | 1.73205i | 0.123091 | − | 0.213201i | ||||
\(67\) | 2.98735 | + | 1.72474i | 0.364962 | + | 0.210711i | 0.671255 | − | 0.741226i | \(-0.265755\pi\) |
−0.306293 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(68\) | 4.89898i | 0.594089i | ||||||||
\(69\) | 2.44949 | 0.294884 | ||||||||
\(70\) | −3.92102 | + | 5.44294i | −0.468652 | + | 0.650556i | ||||
\(71\) | 4.22474 | + | 7.31747i | 0.501385 | + | 0.868424i | 0.999999 | + | 0.00159997i | \(0.000509286\pi\) |
−0.498614 | + | 0.866824i | \(0.666157\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 1.81954 | − | 1.05051i | 0.212961 | − | 0.122953i | −0.389726 | − | 0.920931i | \(-0.627430\pi\) |
0.602687 | + | 0.797978i | \(0.294097\pi\) | |||||||
\(74\) | −4.72474 | − | 8.18350i | −0.549240 | − | 0.951312i | ||||
\(75\) | −1.00000 | + | 4.89898i | −0.115470 | + | 0.565685i | ||||
\(76\) | −3.17423 | − | 2.98735i | −0.364110 | − | 0.342672i | ||||
\(77\) | 6.00000i | 0.683763i | ||||||||
\(78\) | 1.25529 | − | 0.724745i | 0.142134 | − | 0.0820612i | ||||
\(79\) | −1.39898 | − | 2.42310i | −0.157397 | − | 0.272620i | 0.776532 | − | 0.630078i | \(-0.216977\pi\) |
−0.933929 | + | 0.357457i | \(0.883644\pi\) | |||||||
\(80\) | 1.30701 | − | 1.81431i | 0.146128 | − | 0.202846i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.12132 | + | 1.22474i | 0.234261 | + | 0.135250i | ||||
\(83\) | 13.3485i | 1.46518i | 0.680668 | + | 0.732592i | \(0.261690\pi\) | ||||
−0.680668 | + | 0.732592i | \(0.738310\pi\) | |||||||
\(84\) | 3.00000 | 0.327327 | ||||||||
\(85\) | −8.88828 | − | 6.40300i | −0.964070 | − | 0.694503i | ||||
\(86\) | −2.72474 | + | 4.71940i | −0.293817 | + | 0.508906i | ||||
\(87\) | − | 5.34847i | − | 0.573416i | ||||||
\(88\) | − | 2.00000i | − | 0.213201i | ||||||
\(89\) | −8.22474 | + | 14.2457i | −0.871821 | + | 1.51004i | −0.0117104 | + | 0.999931i | \(0.503728\pi\) |
−0.860111 | + | 0.510107i | \(0.829606\pi\) | |||||||
\(90\) | 2.03906 | − | 0.917738i | 0.214936 | − | 0.0967380i | ||||
\(91\) | −2.17423 | + | 3.76588i | −0.227922 | + | 0.394772i | ||||
\(92\) | 2.12132 | − | 1.22474i | 0.221163 | − | 0.127688i | ||||
\(93\) | 1.64456 | − | 0.949490i | 0.170533 | − | 0.0984575i | ||||
\(94\) | −8.44949 | −0.871498 | ||||||||
\(95\) | 9.56873 | − | 1.85457i | 0.981731 | − | 0.190275i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 9.26382 | − | 5.34847i | 0.940598 | − | 0.543055i | 0.0504506 | − | 0.998727i | \(-0.483934\pi\) |
0.890148 | + | 0.455672i | \(0.150601\pi\) | |||||||
\(98\) | −1.73205 | + | 1.00000i | −0.174964 | + | 0.101015i | ||||
\(99\) | 1.00000 | − | 1.73205i | 0.100504 | − | 0.174078i | ||||
\(100\) | 1.58346 | + | 4.74264i | 0.158346 | + | 0.474264i | ||||
\(101\) | −7.89898 | + | 13.6814i | −0.785978 | + | 1.36135i | 0.142435 | + | 0.989804i | \(0.454507\pi\) |
−0.928413 | + | 0.371549i | \(0.878827\pi\) | |||||||
\(102\) | 4.89898i | 0.485071i | ||||||||
\(103\) | − | 0.101021i | − | 0.00995385i | −0.999988 | − | 0.00497692i | \(-0.998416\pi\) | ||
0.999988 | − | 0.00497692i | \(-0.00158421\pi\) | |||||||
\(104\) | 0.724745 | − | 1.25529i | 0.0710671 | − | 0.123092i | ||||
\(105\) | −3.92102 | + | 5.44294i | −0.382653 | + | 0.531176i | ||||
\(106\) | −12.8990 | −1.25286 | ||||||||
\(107\) | 5.55051i | 0.536588i | 0.963337 | + | 0.268294i | \(0.0864599\pi\) | ||||
−0.963337 | + | 0.268294i | \(0.913540\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −7.00000 | − | 12.1244i | −0.670478 | − | 1.16130i | −0.977769 | − | 0.209687i | \(-0.932756\pi\) |
0.307290 | − | 0.951616i | \(-0.400578\pi\) | |||||||
\(110\) | 3.62863 | + | 2.61401i | 0.345976 | + | 0.249236i | ||||
\(111\) | −4.72474 | − | 8.18350i | −0.448453 | − | 0.776743i | ||||
\(112\) | 2.59808 | − | 1.50000i | 0.245495 | − | 0.141737i | ||||
\(113\) | 5.10102i | 0.479864i | 0.970790 | + | 0.239932i | \(0.0771251\pi\) | ||||
−0.970790 | + | 0.239932i | \(0.922875\pi\) | |||||||
\(114\) | −3.17423 | − | 2.98735i | −0.297294 | − | 0.279791i | ||||
\(115\) | −0.550510 | + | 5.44949i | −0.0513353 | + | 0.508168i | ||||
\(116\) | −2.67423 | − | 4.63191i | −0.248296 | − | 0.430062i | ||||
\(117\) | 1.25529 | − | 0.724745i | 0.116052 | − | 0.0670027i | ||||
\(118\) | −6.75323 | − | 3.89898i | −0.621685 | − | 0.358930i | ||||
\(119\) | −7.34847 | − | 12.7279i | −0.673633 | − | 1.16677i | ||||
\(120\) | 1.30701 | − | 1.81431i | 0.119313 | − | 0.165623i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − | 10.3485i | − | 0.936906i | ||||||
\(123\) | 2.12132 | + | 1.22474i | 0.191273 | + | 0.110432i | ||||
\(124\) | 0.949490 | − | 1.64456i | 0.0852667 | − | 0.147686i | ||||
\(125\) | −10.6742 | − | 3.32577i | −0.954733 | − | 0.297465i | ||||
\(126\) | 3.00000 | 0.267261 | ||||||||
\(127\) | 10.9959 | + | 6.34847i | 0.975726 | + | 0.563336i | 0.900977 | − | 0.433867i | \(-0.142851\pi\) |
0.0747488 | + | 0.997202i | \(0.476185\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −2.72474 | + | 4.71940i | −0.239900 | + | 0.415520i | ||||
\(130\) | 1.33025 | + | 2.95559i | 0.116671 | + | 0.259223i | ||||
\(131\) | 5.89898 | + | 10.2173i | 0.515396 | + | 0.892692i | 0.999840 | + | 0.0178702i | \(0.00568857\pi\) |
−0.484444 | + | 0.874822i | \(0.660978\pi\) | |||||||
\(132\) | − | 2.00000i | − | 0.174078i | ||||||
\(133\) | 12.7279 | + | 3.00000i | 1.10365 | + | 0.260133i | ||||
\(134\) | 3.44949 | 0.297991 | ||||||||
\(135\) | 2.03906 | − | 0.917738i | 0.175494 | − | 0.0789863i | ||||
\(136\) | 2.44949 | + | 4.24264i | 0.210042 | + | 0.363803i | ||||
\(137\) | −9.43879 | − | 5.44949i | −0.806411 | − | 0.465581i | 0.0392973 | − | 0.999228i | \(-0.487488\pi\) |
−0.845708 | + | 0.533646i | \(0.820821\pi\) | |||||||
\(138\) | 2.12132 | − | 1.22474i | 0.180579 | − | 0.104257i | ||||
\(139\) | 5.72474 | − | 9.91555i | 0.485567 | − | 0.841026i | −0.514296 | − | 0.857613i | \(-0.671947\pi\) |
0.999862 | + | 0.0165869i | \(0.00528002\pi\) | |||||||
\(140\) | −0.674235 | + | 6.67423i | −0.0569832 | + | 0.564076i | ||||
\(141\) | −8.44949 | −0.711575 | ||||||||
\(142\) | 7.31747 | + | 4.22474i | 0.614069 | + | 0.354533i | ||||
\(143\) | 2.51059 | + | 1.44949i | 0.209946 | + | 0.121212i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 11.8990 | + | 1.20204i | 0.988156 | + | 0.0998241i | ||||
\(146\) | 1.05051 | − | 1.81954i | 0.0869408 | − | 0.150586i | ||||
\(147\) | −1.73205 | + | 1.00000i | −0.142857 | + | 0.0824786i | ||||
\(148\) | −8.18350 | − | 4.72474i | −0.672679 | − | 0.388372i | ||||
\(149\) | −7.89898 | − | 13.6814i | −0.647110 | − | 1.12083i | −0.983810 | − | 0.179215i | \(-0.942644\pi\) |
0.336700 | − | 0.941612i | \(-0.390689\pi\) | |||||||
\(150\) | 1.58346 | + | 4.74264i | 0.129289 | + | 0.387235i | ||||
\(151\) | 0.202041 | 0.0164419 | 0.00822093 | − | 0.999966i | \(-0.497383\pi\) | ||||
0.00822093 | + | 0.999966i | \(0.497383\pi\) | |||||||
\(152\) | −4.24264 | − | 1.00000i | −0.344124 | − | 0.0811107i | ||||
\(153\) | 4.89898i | 0.396059i | ||||||||
\(154\) | 3.00000 | + | 5.19615i | 0.241747 | + | 0.418718i | ||||
\(155\) | 1.74277 | + | 3.87213i | 0.139982 | + | 0.311017i | ||||
\(156\) | 0.724745 | − | 1.25529i | 0.0580260 | − | 0.100504i | ||||
\(157\) | 0.476756 | − | 0.275255i | 0.0380493 | − | 0.0219678i | −0.480855 | − | 0.876800i | \(-0.659674\pi\) |
0.518904 | + | 0.854833i | \(0.326340\pi\) | |||||||
\(158\) | −2.42310 | − | 1.39898i | −0.192772 | − | 0.111297i | ||||
\(159\) | −12.8990 | −1.02296 | ||||||||
\(160\) | 0.224745 | − | 2.22474i | 0.0177676 | − | 0.175882i | ||||
\(161\) | −3.67423 | + | 6.36396i | −0.289570 | + | 0.501550i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 8.34847i | 0.653903i | 0.945041 | + | 0.326951i | \(0.106021\pi\) | ||||
−0.945041 | + | 0.326951i | \(0.893979\pi\) | |||||||
\(164\) | 2.44949 | 0.191273 | ||||||||
\(165\) | 3.62863 | + | 2.61401i | 0.282488 | + | 0.203501i | ||||
\(166\) | 6.67423 | + | 11.5601i | 0.518021 | + | 0.897239i | ||||
\(167\) | −3.28913 | − | 1.89898i | −0.254520 | − | 0.146947i | 0.367312 | − | 0.930098i | \(-0.380278\pi\) |
−0.621832 | + | 0.783150i | \(0.713611\pi\) | |||||||
\(168\) | 2.59808 | − | 1.50000i | 0.200446 | − | 0.115728i | ||||
\(169\) | −5.44949 | − | 9.43879i | −0.419192 | − | 0.726061i | ||||
\(170\) | −10.8990 | − | 1.10102i | −0.835914 | − | 0.0844444i | ||||
\(171\) | −3.17423 | − | 2.98735i | −0.242740 | − | 0.228448i | ||||
\(172\) | 5.44949i | 0.415520i | ||||||||
\(173\) | −0.389270 | + | 0.224745i | −0.0295956 | + | 0.0170870i | −0.514725 | − | 0.857355i | \(-0.672106\pi\) |
0.485129 | + | 0.874442i | \(0.338773\pi\) | |||||||
\(174\) | −2.67423 | − | 4.63191i | −0.202733 | − | 0.351144i | ||||
\(175\) | −11.2279 | − | 9.94655i | −0.848751 | − | 0.751888i | ||||
\(176\) | −1.00000 | − | 1.73205i | −0.0753778 | − | 0.130558i | ||||
\(177\) | −6.75323 | − | 3.89898i | −0.507604 | − | 0.293065i | ||||
\(178\) | 16.4495i | 1.23294i | ||||||||
\(179\) | −6.24745 | −0.466956 | −0.233478 | − | 0.972362i | \(-0.575011\pi\) | ||||
−0.233478 | + | 0.972362i | \(0.575011\pi\) | |||||||
\(180\) | 1.30701 | − | 1.81431i | 0.0974186 | − | 0.135231i | ||||
\(181\) | 10.4495 | − | 18.0990i | 0.776704 | − | 1.34529i | −0.157127 | − | 0.987578i | \(-0.550223\pi\) |
0.933832 | − | 0.357713i | \(-0.116443\pi\) | |||||||
\(182\) | 4.34847i | 0.322330i | ||||||||
\(183\) | − | 10.3485i | − | 0.764981i | ||||||
\(184\) | 1.22474 | − | 2.12132i | 0.0902894 | − | 0.156386i | ||||
\(185\) | 19.2681 | − | 8.67215i | 1.41662 | − | 0.637589i | ||||
\(186\) | 0.949490 | − | 1.64456i | 0.0696200 | − | 0.120585i | ||||
\(187\) | −8.48528 | + | 4.89898i | −0.620505 | + | 0.358249i | ||||
\(188\) | −7.31747 | + | 4.22474i | −0.533682 | + | 0.308121i | ||||
\(189\) | 3.00000 | 0.218218 | ||||||||
\(190\) | 7.35948 | − | 6.39047i | 0.533912 | − | 0.463614i | ||||
\(191\) | 14.6969 | 1.06343 | 0.531717 | − | 0.846922i | \(-0.321547\pi\) | ||||
0.531717 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 10.3048 | − | 5.94949i | 0.741757 | − | 0.428254i | −0.0809508 | − | 0.996718i | \(-0.525796\pi\) |
0.822708 | + | 0.568464i | \(0.192462\pi\) | |||||||
\(194\) | 5.34847 | − | 9.26382i | 0.383998 | − | 0.665104i | ||||
\(195\) | 1.33025 | + | 2.95559i | 0.0952613 | + | 0.211654i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | − | 12.6969i | − | 0.904619i | −0.891861 | − | 0.452310i | \(-0.850600\pi\) | ||
0.891861 | − | 0.452310i | \(-0.149400\pi\) | |||||||
\(198\) | − | 2.00000i | − | 0.142134i | ||||||
\(199\) | −8.94949 | + | 15.5010i | −0.634413 | + | 1.09883i | 0.352227 | + | 0.935915i | \(0.385425\pi\) |
−0.986639 | + | 0.162920i | \(0.947909\pi\) | |||||||
\(200\) | 3.74264 | + | 3.31552i | 0.264645 | + | 0.234442i | ||||
\(201\) | 3.44949 | 0.243308 | ||||||||
\(202\) | 15.7980i | 1.11154i | ||||||||
\(203\) | 13.8957 | + | 8.02270i | 0.975289 | + | 0.563083i | ||||
\(204\) | 2.44949 | + | 4.24264i | 0.171499 | + | 0.297044i | ||||
\(205\) | −3.20150 | + | 4.44414i | −0.223603 | + | 0.310392i | ||||
\(206\) | −0.0505103 | − | 0.0874863i | −0.00351922 | − | 0.00609546i | ||||
\(207\) | 2.12132 | − | 1.22474i | 0.147442 | − | 0.0851257i | ||||
\(208\) | − | 1.44949i | − | 0.100504i | ||||||
\(209\) | 2.00000 | − | 8.48528i | 0.138343 | − | 0.586939i | ||||
\(210\) | −0.674235 | + | 6.67423i | −0.0465266 | + | 0.460566i | ||||
\(211\) | 6.17423 | + | 10.6941i | 0.425052 | + | 0.736211i | 0.996425 | − | 0.0844788i | \(-0.0269225\pi\) |
−0.571373 | + | 0.820690i | \(0.693589\pi\) | |||||||
\(212\) | −11.1708 | + | 6.44949i | −0.767217 | + | 0.442953i | ||||
\(213\) | 7.31747 | + | 4.22474i | 0.501385 | + | 0.289475i | ||||
\(214\) | 2.77526 | + | 4.80688i | 0.189713 | + | 0.328592i | ||||
\(215\) | −9.88708 | − | 7.12252i | −0.674293 | − | 0.485752i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.69694i | 0.386733i | ||||||||
\(218\) | −12.1244 | − | 7.00000i | −0.821165 | − | 0.474100i | ||||
\(219\) | 1.05051 | − | 1.81954i | 0.0709869 | − | 0.122953i | ||||
\(220\) | 4.44949 | + | 0.449490i | 0.299985 | + | 0.0303046i | ||||
\(221\) | −7.10102 | −0.477666 | ||||||||
\(222\) | −8.18350 | − | 4.72474i | −0.549240 | − | 0.317104i | ||||
\(223\) | −13.5939 | + | 7.84847i | −0.910318 | + | 0.525572i | −0.880533 | − | 0.473984i | \(-0.842815\pi\) |
−0.0297846 | + | 0.999556i | \(0.509482\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | 1.58346 | + | 4.74264i | 0.105564 | + | 0.316176i | ||||
\(226\) | 2.55051 | + | 4.41761i | 0.169657 | + | 0.293855i | ||||
\(227\) | 1.34847i | 0.0895010i | 0.998998 | + | 0.0447505i | \(0.0142493\pi\) | ||||
−0.998998 | + | 0.0447505i | \(0.985751\pi\) | |||||||
\(228\) | −4.24264 | − | 1.00000i | −0.280976 | − | 0.0662266i | ||||
\(229\) | 17.0454 | 1.12639 | 0.563196 | − | 0.826323i | \(-0.309572\pi\) | ||||
0.563196 | + | 0.826323i | \(0.309572\pi\) | |||||||
\(230\) | 2.24799 | + | 4.99465i | 0.148228 | + | 0.329338i | ||||
\(231\) | 3.00000 | + | 5.19615i | 0.197386 | + | 0.341882i | ||||
\(232\) | −4.63191 | − | 2.67423i | −0.304100 | − | 0.175572i | ||||
\(233\) | 25.4165 | − | 14.6742i | 1.66509 | − | 0.961341i | 0.694866 | − | 0.719140i | \(-0.255464\pi\) |
0.970226 | − | 0.242201i | \(-0.0778695\pi\) | |||||||
\(234\) | 0.724745 | − | 1.25529i | 0.0473781 | − | 0.0820612i | ||||
\(235\) | 1.89898 | − | 18.7980i | 0.123876 | − | 1.22624i | ||||
\(236\) | −7.79796 | −0.507604 | ||||||||
\(237\) | −2.42310 | − | 1.39898i | −0.157397 | − | 0.0908735i | ||||
\(238\) | −12.7279 | − | 7.34847i | −0.825029 | − | 0.476331i | ||||
\(239\) | −23.3485 | −1.51029 | −0.755143 | − | 0.655560i | \(-0.772433\pi\) | ||||
−0.755143 | + | 0.655560i | \(0.772433\pi\) | |||||||
\(240\) | 0.224745 | − | 2.22474i | 0.0145072 | − | 0.143607i | ||||
\(241\) | −5.50000 | + | 9.52628i | −0.354286 | + | 0.613642i | −0.986996 | − | 0.160748i | \(-0.948609\pi\) |
0.632709 | + | 0.774389i | \(0.281943\pi\) | |||||||
\(242\) | −6.06218 | + | 3.50000i | −0.389692 | + | 0.224989i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | −5.17423 | − | 8.96204i | −0.331246 | − | 0.573736i | ||||
\(245\) | −1.83548 | − | 4.07812i | −0.117264 | − | 0.260541i | ||||
\(246\) | 2.44949 | 0.156174 | ||||||||
\(247\) | 4.33013 | − | 4.60102i | 0.275519 | − | 0.292756i | ||||
\(248\) | − | 1.89898i | − | 0.120585i | ||||||
\(249\) | 6.67423 | + | 11.5601i | 0.422962 | + | 0.732592i | ||||
\(250\) | −10.9070 | + | 2.45692i | −0.689822 | + | 0.155389i | ||||
\(251\) | −4.34847 | + | 7.53177i | −0.274473 | + | 0.475401i | −0.970002 | − | 0.243097i | \(-0.921837\pi\) |
0.695529 | + | 0.718498i | \(0.255170\pi\) | |||||||
\(252\) | 2.59808 | − | 1.50000i | 0.163663 | − | 0.0944911i | ||||
\(253\) | 4.24264 | + | 2.44949i | 0.266733 | + | 0.153998i | ||||
\(254\) | 12.6969 | 0.796677 | ||||||||
\(255\) | −10.8990 | − | 1.10102i | −0.682521 | − | 0.0689486i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.92104 | − | 4.57321i | −0.494101 | − | 0.285269i | 0.232173 | − | 0.972674i | \(-0.425416\pi\) |
−0.726274 | + | 0.687405i | \(0.758750\pi\) | |||||||
\(258\) | 5.44949i | 0.339270i | ||||||||
\(259\) | 28.3485 | 1.76149 | ||||||||
\(260\) | 2.62983 | + | 1.89449i | 0.163095 | + | 0.117492i | ||||
\(261\) | −2.67423 | − | 4.63191i | −0.165531 | − | 0.286708i | ||||
\(262\) | 10.2173 | + | 5.89898i | 0.631229 | + | 0.364440i | ||||
\(263\) | 12.1244 | − | 7.00000i | 0.747620 | − | 0.431638i | −0.0772134 | − | 0.997015i | \(-0.524602\pi\) |
0.824833 | + | 0.565376i | \(0.191269\pi\) | |||||||
\(264\) | −1.00000 | − | 1.73205i | −0.0615457 | − | 0.106600i | ||||
\(265\) | 2.89898 | − | 28.6969i | 0.178083 | − | 1.76284i | ||||
\(266\) | 12.5227 | − | 3.76588i | 0.767816 | − | 0.230901i | ||||
\(267\) | 16.4495i | 1.00669i | ||||||||
\(268\) | 2.98735 | − | 1.72474i | 0.182481 | − | 0.105356i | ||||
\(269\) | 11.2474 | + | 19.4812i | 0.685769 | + | 1.18779i | 0.973194 | + | 0.229984i | \(0.0738673\pi\) |
−0.287425 | + | 0.957803i | \(0.592799\pi\) | |||||||
\(270\) | 1.30701 | − | 1.81431i | 0.0795419 | − | 0.110416i | ||||
\(271\) | 7.44949 | + | 12.9029i | 0.452524 | + | 0.783795i | 0.998542 | − | 0.0539785i | \(-0.0171903\pi\) |
−0.546018 | + | 0.837774i | \(0.683857\pi\) | |||||||
\(272\) | 4.24264 | + | 2.44949i | 0.257248 | + | 0.148522i | ||||
\(273\) | 4.34847i | 0.263181i | ||||||||
\(274\) | −10.8990 | −0.658431 | ||||||||
\(275\) | −6.63103 | + | 7.48528i | −0.399866 | + | 0.451379i | ||||
\(276\) | 1.22474 | − | 2.12132i | 0.0737210 | − | 0.127688i | ||||
\(277\) | 16.4949i | 0.991082i | 0.868584 | + | 0.495541i | \(0.165030\pi\) | ||||
−0.868584 | + | 0.495541i | \(0.834970\pi\) | |||||||
\(278\) | − | 11.4495i | − | 0.686695i | ||||||
\(279\) | 0.949490 | − | 1.64456i | 0.0568445 | − | 0.0984575i | ||||
\(280\) | 2.75321 | + | 6.11717i | 0.164536 | + | 0.365571i | ||||
\(281\) | 10.7753 | − | 18.6633i | 0.642798 | − | 1.11336i | −0.342008 | − | 0.939697i | \(-0.611107\pi\) |
0.984805 | − | 0.173661i | \(-0.0555598\pi\) | |||||||
\(282\) | −7.31747 | + | 4.22474i | −0.435749 | + | 0.251580i | ||||
\(283\) | 0.778539 | − | 0.449490i | 0.0462793 | − | 0.0267194i | −0.476682 | − | 0.879076i | \(-0.658161\pi\) |
0.522961 | + | 0.852357i | \(0.324827\pi\) | |||||||
\(284\) | 8.44949 | 0.501385 | ||||||||
\(285\) | 7.35948 | − | 6.39047i | 0.435938 | − | 0.378539i | ||||
\(286\) | 2.89898 | 0.171420 | ||||||||
\(287\) | −6.36396 | + | 3.67423i | −0.375653 | + | 0.216883i | ||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | 3.50000 | − | 6.06218i | 0.205882 | − | 0.356599i | ||||
\(290\) | 10.9058 | − | 4.90849i | 0.640413 | − | 0.288237i | ||||
\(291\) | 5.34847 | − | 9.26382i | 0.313533 | − | 0.543055i | ||||
\(292\) | − | 2.10102i | − | 0.122953i | ||||||
\(293\) | − | 9.10102i | − | 0.531687i | −0.964016 | − | 0.265844i | \(-0.914350\pi\) | ||
0.964016 | − | 0.265844i | \(-0.0856505\pi\) | |||||||
\(294\) | −1.00000 | + | 1.73205i | −0.0583212 | + | 0.101015i | ||||
\(295\) | 10.1920 | − | 14.1479i | 0.593401 | − | 0.823725i | ||||
\(296\) | −9.44949 | −0.549240 | ||||||||
\(297\) | − | 2.00000i | − | 0.116052i | ||||||
\(298\) | −13.6814 | − | 7.89898i | −0.792544 | − | 0.457576i | ||||
\(299\) | 1.77526 | + | 3.07483i | 0.102666 | + | 0.177822i | ||||
\(300\) | 3.74264 | + | 3.31552i | 0.216081 | + | 0.191421i | ||||
\(301\) | −8.17423 | − | 14.1582i | −0.471155 | − | 0.816064i | ||||
\(302\) | 0.174973 | − | 0.101021i | 0.0100685 | − | 0.00581308i | ||||
\(303\) | 15.7980i | 0.907569i | ||||||||
\(304\) | −4.17423 | + | 1.25529i | −0.239409 | + | 0.0719961i | ||||
\(305\) | 23.0227 | + | 2.32577i | 1.31828 | + | 0.133173i | ||||
\(306\) | 2.44949 | + | 4.24264i | 0.140028 | + | 0.242536i | ||||
\(307\) | 18.8776 | − | 10.8990i | 1.07740 | − | 0.622038i | 0.147207 | − | 0.989106i | \(-0.452972\pi\) |
0.930194 | + | 0.367068i | \(0.119638\pi\) | |||||||
\(308\) | 5.19615 | + | 3.00000i | 0.296078 | + | 0.170941i | ||||
\(309\) | −0.0505103 | − | 0.0874863i | −0.00287343 | − | 0.00497692i | ||||
\(310\) | 3.44534 | + | 2.48198i | 0.195682 | + | 0.140967i | ||||
\(311\) | 1.10102 | 0.0624331 | 0.0312166 | − | 0.999513i | \(-0.490062\pi\) | ||||
0.0312166 | + | 0.999513i | \(0.490062\pi\) | |||||||
\(312\) | − | 1.44949i | − | 0.0820612i | ||||||
\(313\) | −21.5631 | − | 12.4495i | −1.21882 | − | 0.703687i | −0.254155 | − | 0.967163i | \(-0.581797\pi\) |
−0.964666 | + | 0.263477i | \(0.915131\pi\) | |||||||
\(314\) | 0.275255 | − | 0.476756i | 0.0155335 | − | 0.0269049i | ||||
\(315\) | −0.674235 | + | 6.67423i | −0.0379888 | + | 0.376051i | ||||
\(316\) | −2.79796 | −0.157397 | ||||||||
\(317\) | 15.8028 | + | 9.12372i | 0.887571 | + | 0.512439i | 0.873147 | − | 0.487457i | \(-0.162075\pi\) |
0.0144239 | + | 0.999896i | \(0.495409\pi\) | |||||||
\(318\) | −11.1708 | + | 6.44949i | −0.626430 | + | 0.361669i | ||||
\(319\) | 5.34847 | − | 9.26382i | 0.299457 | − | 0.518674i | ||||
\(320\) | −0.917738 | − | 2.03906i | −0.0513031 | − | 0.113987i | ||||
\(321\) | 2.77526 | + | 4.80688i | 0.154900 | + | 0.268294i | ||||
\(322\) | 7.34847i | 0.409514i | ||||||||
\(323\) | 6.14966 | + | 20.4495i | 0.342176 | + | 1.13784i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −6.87441 | + | 2.29522i | −0.381324 | + | 0.127316i | ||||
\(326\) | 4.17423 | + | 7.22999i | 0.231189 | + | 0.400432i | ||||
\(327\) | −12.1244 | − | 7.00000i | −0.670478 | − | 0.387101i | ||||
\(328\) | 2.12132 | − | 1.22474i | 0.117130 | − | 0.0676252i | ||||
\(329\) | 12.6742 | − | 21.9524i | 0.698753 | − | 1.21028i | ||||
\(330\) | 4.44949 | + | 0.449490i | 0.244936 | + | 0.0247436i | ||||
\(331\) | −1.24745 | −0.0685660 | −0.0342830 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342830 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(332\) | 11.5601 | + | 6.67423i | 0.634444 | + | 0.366296i | ||||
\(333\) | −8.18350 | − | 4.72474i | −0.448453 | − | 0.258914i | ||||
\(334\) | −3.79796 | −0.207815 | ||||||||
\(335\) | −0.775255 | + | 7.67423i | −0.0423567 | + | 0.419288i | ||||
\(336\) | 1.50000 | − | 2.59808i | 0.0818317 | − | 0.141737i | ||||
\(337\) | −12.0369 | + | 6.94949i | −0.655690 | + | 0.378563i | −0.790633 | − | 0.612291i | \(-0.790248\pi\) |
0.134943 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(338\) | −9.43879 | − | 5.44949i | −0.513403 | − | 0.296413i | ||||
\(339\) | 2.55051 | + | 4.41761i | 0.138525 | + | 0.239932i | ||||
\(340\) | −9.98930 | + | 4.49598i | −0.541746 | + | 0.243829i | ||||
\(341\) | 3.79796 | 0.205671 | ||||||||
\(342\) | −4.24264 | − | 1.00000i | −0.229416 | − | 0.0540738i | ||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | 2.72474 | + | 4.71940i | 0.146908 | + | 0.254453i | ||||
\(345\) | 2.24799 | + | 4.99465i | 0.121028 | + | 0.268903i | ||||
\(346\) | −0.224745 | + | 0.389270i | −0.0120824 | + | 0.0209273i | ||||
\(347\) | 17.7491 | − | 10.2474i | 0.952822 | − | 0.550112i | 0.0588654 | − | 0.998266i | \(-0.481252\pi\) |
0.893956 | + | 0.448154i | \(0.147918\pi\) | |||||||
\(348\) | −4.63191 | − | 2.67423i | −0.248296 | − | 0.143354i | ||||
\(349\) | 31.4495 | 1.68345 | 0.841726 | − | 0.539904i | \(-0.181540\pi\) | ||||
0.841726 | + | 0.539904i | \(0.181540\pi\) | |||||||
\(350\) | −14.6969 | − | 3.00000i | −0.785584 | − | 0.160357i | ||||
\(351\) | 0.724745 | − | 1.25529i | 0.0386840 | − | 0.0670027i | ||||
\(352\) | −1.73205 | − | 1.00000i | −0.0923186 | − | 0.0533002i | ||||
\(353\) | 13.1464i | 0.699714i | 0.936803 | + | 0.349857i | \(0.113770\pi\) | ||||
−0.936803 | + | 0.349857i | \(0.886230\pi\) | |||||||
\(354\) | −7.79796 | −0.414457 | ||||||||
\(355\) | −11.0435 | + | 15.3300i | −0.586130 | + | 0.813633i | ||||
\(356\) | 8.22474 | + | 14.2457i | 0.435911 | + | 0.755019i | ||||
\(357\) | −12.7279 | − | 7.34847i | −0.673633 | − | 0.388922i | ||||
\(358\) | −5.41045 | + | 3.12372i | −0.285951 | + | 0.165094i | ||||
\(359\) | 2.12372 | + | 3.67840i | 0.112086 | + | 0.194138i | 0.916611 | − | 0.399780i | \(-0.130913\pi\) |
−0.804525 | + | 0.593918i | \(0.797580\pi\) | |||||||
\(360\) | 0.224745 | − | 2.22474i | 0.0118451 | − | 0.117254i | ||||
\(361\) | −17.0000 | − | 8.48528i | −0.894737 | − | 0.446594i | ||||
\(362\) | − | 20.8990i | − | 1.09843i | ||||||
\(363\) | −6.06218 | + | 3.50000i | −0.318182 | + | 0.183702i | ||||
\(364\) | 2.17423 | + | 3.76588i | 0.113961 | + | 0.197386i | ||||
\(365\) | 3.81191 | + | 2.74605i | 0.199524 | + | 0.143735i | ||||
\(366\) | −5.17423 | − | 8.96204i | −0.270462 | − | 0.468453i | ||||
\(367\) | 19.5686 | + | 11.2980i | 1.02147 | + | 0.589749i | 0.914531 | − | 0.404516i | \(-0.132560\pi\) |
0.106944 | + | 0.994265i | \(0.465893\pi\) | |||||||
\(368\) | − | 2.44949i | − | 0.127688i | ||||||
\(369\) | 2.44949 | 0.127515 | ||||||||
\(370\) | 12.3506 | − | 17.1443i | 0.642075 | − | 0.891291i | ||||
\(371\) | 19.3485 | − | 33.5125i | 1.00452 | − | 1.73988i | ||||
\(372\) | − | 1.89898i | − | 0.0984575i | ||||||
\(373\) | − | 34.8990i | − | 1.80700i | −0.428587 | − | 0.903500i | \(-0.640989\pi\) | ||
0.428587 | − | 0.903500i | \(-0.359011\pi\) | |||||||
\(374\) | −4.89898 | + | 8.48528i | −0.253320 | + | 0.438763i | ||||
\(375\) | −10.9070 | + | 2.45692i | −0.563237 | + | 0.126875i | ||||
\(376\) | −4.22474 | + | 7.31747i | −0.217875 | + | 0.377370i | ||||
\(377\) | 6.71391 | − | 3.87628i | 0.345784 | − | 0.199638i | ||||
\(378\) | 2.59808 | − | 1.50000i | 0.133631 | − | 0.0771517i | ||||
\(379\) | −33.2474 | −1.70781 | −0.853903 | − | 0.520432i | \(-0.825771\pi\) | ||||
−0.853903 | + | 0.520432i | \(0.825771\pi\) | |||||||
\(380\) | 3.17826 | − | 9.21405i | 0.163041 | − | 0.472671i | ||||
\(381\) | 12.6969 | 0.650484 | ||||||||
\(382\) | 12.7279 | − | 7.34847i | 0.651217 | − | 0.375980i | ||||
\(383\) | 11.5601 | − | 6.67423i | 0.590694 | − | 0.341037i | −0.174678 | − | 0.984626i | \(-0.555888\pi\) |
0.765372 | + | 0.643588i | \(0.222555\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −12.2343 | + | 5.50643i | −0.623520 | + | 0.280633i | ||||
\(386\) | 5.94949 | − | 10.3048i | 0.302821 | − | 0.524501i | ||||
\(387\) | 5.44949i | 0.277013i | ||||||||
\(388\) | − | 10.6969i | − | 0.543055i | ||||||
\(389\) | −5.12372 | + | 8.87455i | −0.259783 | + | 0.449958i | −0.966184 | − | 0.257855i | \(-0.916984\pi\) |
0.706401 | + | 0.707812i | \(0.250318\pi\) | |||||||
\(390\) | 2.62983 | + | 1.89449i | 0.133167 | + | 0.0959314i | ||||
\(391\) | −12.0000 | −0.606866 | ||||||||
\(392\) | 2.00000i | 0.101015i | ||||||||
\(393\) | 10.2173 | + | 5.89898i | 0.515396 | + | 0.297564i | ||||
\(394\) | −6.34847 | − | 10.9959i | −0.319831 | − | 0.553964i | ||||
\(395\) | 3.65695 | − | 5.07637i | 0.184001 | − | 0.255420i | ||||
\(396\) | −1.00000 | − | 1.73205i | −0.0502519 | − | 0.0870388i | ||||
\(397\) | −13.2047 | + | 7.62372i | −0.662724 | + | 0.382624i | −0.793314 | − | 0.608813i | \(-0.791646\pi\) |
0.130590 | + | 0.991436i | \(0.458313\pi\) | |||||||
\(398\) | 17.8990i | 0.897195i | ||||||||
\(399\) | 12.5227 | − | 3.76588i | 0.626919 | − | 0.188530i | ||||
\(400\) | 4.89898 | + | 1.00000i | 0.244949 | + | 0.0500000i | ||||
\(401\) | 18.1464 | + | 31.4305i | 0.906189 | + | 1.56957i | 0.819313 | + | 0.573347i | \(0.194355\pi\) |
0.0868767 | + | 0.996219i | \(0.472311\pi\) | |||||||
\(402\) | 2.98735 | − | 1.72474i | 0.148995 | − | 0.0860225i | ||||
\(403\) | 2.38378 | + | 1.37628i | 0.118745 | + | 0.0685572i | ||||
\(404\) | 7.89898 | + | 13.6814i | 0.392989 | + | 0.680677i | ||||
\(405\) | 1.30701 | − | 1.81431i | 0.0649457 | − | 0.0901539i | ||||
\(406\) | 16.0454 | 0.796320 | ||||||||
\(407\) | − | 18.8990i | − | 0.936788i | ||||||
\(408\) | 4.24264 | + | 2.44949i | 0.210042 | + | 0.121268i | ||||
\(409\) | −10.4495 | + | 18.0990i | −0.516694 | + | 0.894940i | 0.483118 | + | 0.875555i | \(0.339504\pi\) |
−0.999812 | + | 0.0193851i | \(0.993829\pi\) | |||||||
\(410\) | −0.550510 | + | 5.44949i | −0.0271878 | + | 0.269131i | ||||
\(411\) | −10.8990 | −0.537607 | ||||||||
\(412\) | −0.0874863 | − | 0.0505103i | −0.00431014 | − | 0.00248846i | ||||
\(413\) | 20.2597 | − | 11.6969i | 0.996914 | − | 0.575569i | ||||
\(414\) | 1.22474 | − | 2.12132i | 0.0601929 | − | 0.104257i | ||||
\(415\) | −27.2183 | + | 12.2504i | −1.33609 | + | 0.601348i | ||||
\(416\) | −0.724745 | − | 1.25529i | −0.0355335 | − | 0.0615459i | ||||
\(417\) | − | 11.4495i | − | 0.560684i | ||||||
\(418\) | −2.51059 | − | 8.34847i | −0.122797 | − | 0.408337i | ||||
\(419\) | −18.0454 | −0.881576 | −0.440788 | − | 0.897611i | \(-0.645301\pi\) | ||||
−0.440788 | + | 0.897611i | \(0.645301\pi\) | |||||||
\(420\) | 2.75321 | + | 6.11717i | 0.134343 | + | 0.298488i | ||||
\(421\) | −8.79796 | − | 15.2385i | −0.428786 | − | 0.742680i | 0.567979 | − | 0.823043i | \(-0.307725\pi\) |
−0.996766 | + | 0.0803632i | \(0.974392\pi\) | |||||||
\(422\) | 10.6941 | + | 6.17423i | 0.520580 | + | 0.300557i | ||||
\(423\) | −7.31747 | + | 4.22474i | −0.355788 | + | 0.205414i | ||||
\(424\) | −6.44949 | + | 11.1708i | −0.313215 | + | 0.542504i | ||||
\(425\) | 4.89898 | − | 24.0000i | 0.237635 | − | 1.16417i | ||||
\(426\) | 8.44949 | 0.409379 | ||||||||
\(427\) | 26.8861 | + | 15.5227i | 1.30111 | + | 0.751196i | ||||
\(428\) | 4.80688 | + | 2.77526i | 0.232349 | + | 0.134147i | ||||
\(429\) | 2.89898 | 0.139964 | ||||||||
\(430\) | −12.1237 | − | 1.22474i | −0.584658 | − | 0.0590624i | ||||
\(431\) | −2.87628 | + | 4.98186i | −0.138545 | + | 0.239968i | −0.926946 | − | 0.375194i | \(-0.877576\pi\) |
0.788401 | + | 0.615162i | \(0.210909\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 0.691053 | + | 0.398979i | 0.0332099 | + | 0.0191737i | 0.516513 | − | 0.856279i | \(-0.327230\pi\) |
−0.483303 | + | 0.875453i | \(0.660563\pi\) | |||||||
\(434\) | 2.84847 | + | 4.93369i | 0.136731 | + | 0.236825i | ||||
\(435\) | 10.9058 | − | 4.90849i | 0.522895 | − | 0.235344i | ||||
\(436\) | −14.0000 | −0.670478 | ||||||||
\(437\) | 7.31747 | − | 7.77526i | 0.350042 | − | 0.371941i | ||||
\(438\) | − | 2.10102i | − | 0.100391i | ||||||
\(439\) | 15.7474 | + | 27.2754i | 0.751585 | + | 1.30178i | 0.947054 | + | 0.321073i | \(0.104044\pi\) |
−0.195470 | + | 0.980710i | \(0.562623\pi\) | |||||||
\(440\) | 4.07812 | − | 1.83548i | 0.194417 | − | 0.0875029i | ||||
\(441\) | −1.00000 | + | 1.73205i | −0.0476190 | + | 0.0824786i | ||||
\(442\) | −6.14966 | + | 3.55051i | −0.292510 | + | 0.168881i | ||||
\(443\) | −8.48528 | − | 4.89898i | −0.403148 | − | 0.232758i | 0.284693 | − | 0.958619i | \(-0.408108\pi\) |
−0.687841 | + | 0.725861i | \(0.741442\pi\) | |||||||
\(444\) | −9.44949 | −0.448453 | ||||||||
\(445\) | −36.5959 | − | 3.69694i | −1.73481 | − | 0.175252i | ||||
\(446\) | −7.84847 | + | 13.5939i | −0.371636 | + | 0.643692i | ||||
\(447\) | −13.6814 | − | 7.89898i | −0.647110 | − | 0.373609i | ||||
\(448\) | − | 3.00000i | − | 0.141737i | ||||||
\(449\) | −18.6969 | −0.882363 | −0.441182 | − | 0.897418i | \(-0.645441\pi\) | ||||
−0.441182 | + | 0.897418i | \(0.645441\pi\) | |||||||
\(450\) | 3.74264 | + | 3.31552i | 0.176430 | + | 0.156295i | ||||
\(451\) | 2.44949 | + | 4.24264i | 0.115342 | + | 0.199778i | ||||
\(452\) | 4.41761 | + | 2.55051i | 0.207787 | + | 0.119966i | ||||
\(453\) | 0.174973 | − | 0.101021i | 0.00822093 | − | 0.00474636i | ||||
\(454\) | 0.674235 | + | 1.16781i | 0.0316434 | + | 0.0548080i | ||||
\(455\) | −9.67423 | − | 0.977296i | −0.453535 | − | 0.0458164i | ||||
\(456\) | −4.17423 | + | 1.25529i | −0.195476 | + | 0.0587846i | ||||
\(457\) | 23.8990i | 1.11795i | 0.829185 | + | 0.558974i | \(0.188805\pi\) | ||||
−0.829185 | + | 0.558974i | \(0.811195\pi\) | |||||||
\(458\) | 14.7618 | − | 8.52270i | 0.689772 | − | 0.398240i | ||||
\(459\) | 2.44949 | + | 4.24264i | 0.114332 | + | 0.198030i | ||||
\(460\) | 4.44414 | + | 3.20150i | 0.207209 | + | 0.149271i | ||||
\(461\) | −0.123724 | − | 0.214297i | −0.00576242 | − | 0.00998080i | 0.863130 | − | 0.504982i | \(-0.168501\pi\) |
−0.868892 | + | 0.495001i | \(0.835168\pi\) | |||||||
\(462\) | 5.19615 | + | 3.00000i | 0.241747 | + | 0.139573i | ||||
\(463\) | − | 29.2929i | − | 1.36135i | −0.732583 | − | 0.680677i | \(-0.761686\pi\) | ||
0.732583 | − | 0.680677i | \(-0.238314\pi\) | |||||||
\(464\) | −5.34847 | −0.248296 | ||||||||
\(465\) | 3.44534 | + | 2.48198i | 0.159774 | + | 0.115099i | ||||
\(466\) | 14.6742 | − | 25.4165i | 0.679771 | − | 1.17740i | ||||
\(467\) | 8.44949i | 0.390996i | 0.980704 | + | 0.195498i | \(0.0626323\pi\) | ||||
−0.980704 | + | 0.195498i | \(0.937368\pi\) | |||||||
\(468\) | − | 1.44949i | − | 0.0670027i | ||||||
\(469\) | −5.17423 | + | 8.96204i | −0.238924 | + | 0.413828i | ||||
\(470\) | −7.75442 | − | 17.2290i | −0.357684 | − | 0.794714i | ||||
\(471\) | 0.275255 | − | 0.476756i | 0.0126831 | − | 0.0219678i | ||||
\(472\) | −6.75323 | + | 3.89898i | −0.310843 | + | 0.179465i | ||||
\(473\) | −9.43879 | + | 5.44949i | −0.433996 | + | 0.250568i | ||||
\(474\) | −2.79796 | −0.128515 | ||||||||
\(475\) | 12.5632 | + | 17.8092i | 0.576438 | + | 0.817141i | ||||
\(476\) | −14.6969 | −0.673633 | ||||||||
\(477\) | −11.1708 | + | 6.44949i | −0.511478 | + | 0.295302i | ||||
\(478\) | −20.2204 | + | 11.6742i | −0.924858 | + | 0.533967i | ||||
\(479\) | −0.348469 | + | 0.603566i | −0.0159220 | + | 0.0275777i | −0.873877 | − | 0.486148i | \(-0.838402\pi\) |
0.857955 | + | 0.513725i | \(0.171735\pi\) | |||||||
\(480\) | −0.917738 | − | 2.03906i | −0.0418888 | − | 0.0930698i | ||||
\(481\) | 6.84847 | − | 11.8619i | 0.312263 | − | 0.540856i | ||||
\(482\) | 11.0000i | 0.501036i | ||||||||
\(483\) | 7.34847i | 0.334367i | ||||||||
\(484\) | −3.50000 | + | 6.06218i | −0.159091 | + | 0.275554i | ||||
\(485\) | 19.4076 | + | 13.9810i | 0.881254 | + | 0.634843i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 25.1010i | 1.13744i | 0.822533 | + | 0.568718i | \(0.192560\pi\) | ||||
−0.822533 | + | 0.568718i | \(0.807440\pi\) | |||||||
\(488\) | −8.96204 | − | 5.17423i | −0.405692 | − | 0.234227i | ||||
\(489\) | 4.17423 | + | 7.22999i | 0.188765 | + | 0.326951i | ||||
\(490\) | −3.62863 | − | 2.61401i | −0.163925 | − | 0.118089i | ||||
\(491\) | −17.0227 | − | 29.4842i | −0.768224 | − | 1.33060i | −0.938525 | − | 0.345211i | \(-0.887807\pi\) |
0.170301 | − | 0.985392i | \(-0.445526\pi\) | |||||||
\(492\) | 2.12132 | − | 1.22474i | 0.0956365 | − | 0.0552158i | ||||
\(493\) | 26.2020i | 1.18008i | ||||||||
\(494\) | 1.44949 | − | 6.14966i | 0.0652156 | − | 0.276686i | ||||
\(495\) | 4.44949 | + | 0.449490i | 0.199990 | + | 0.0202031i | ||||
\(496\) | −0.949490 | − | 1.64456i | −0.0426333 | − | 0.0738431i | ||||
\(497\) | −21.9524 | + | 12.6742i | −0.984701 | + | 0.568517i | ||||
\(498\) | 11.5601 | + | 6.67423i | 0.518021 | + | 0.299080i | ||||
\(499\) | 15.4217 | + | 26.7111i | 0.690369 | + | 1.19575i | 0.971717 | + | 0.236149i | \(0.0758853\pi\) |
−0.281348 | + | 0.959606i | \(0.590781\pi\) | |||||||
\(500\) | −8.21731 | + | 7.58128i | −0.367489 | + | 0.339045i | ||||
\(501\) | −3.79796 | −0.169680 | ||||||||
\(502\) | 8.69694i | 0.388163i | ||||||||
\(503\) | 11.9494 | + | 6.89898i | 0.532797 | + | 0.307610i | 0.742155 | − | 0.670229i | \(-0.233804\pi\) |
−0.209358 | + | 0.977839i | \(0.567137\pi\) | |||||||
\(504\) | 1.50000 | − | 2.59808i | 0.0668153 | − | 0.115728i | ||||
\(505\) | −35.1464 | − | 3.55051i | −1.56400 | − | 0.157996i | ||||
\(506\) | 4.89898 | 0.217786 | ||||||||
\(507\) | −9.43879 | − | 5.44949i | −0.419192 | − | 0.242020i | ||||
\(508\) | 10.9959 | − | 6.34847i | 0.487863 | − | 0.281668i | ||||
\(509\) | −4.77526 | + | 8.27098i | −0.211659 | + | 0.366605i | −0.952234 | − | 0.305369i | \(-0.901220\pi\) |
0.740575 | + | 0.671974i | \(0.234553\pi\) | |||||||
\(510\) | −9.98930 | + | 4.49598i | −0.442334 | + | 0.199085i | ||||
\(511\) | 3.15153 | + | 5.45861i | 0.139416 | + | 0.241475i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.24264 | − | 1.00000i | −0.187317 | − | 0.0441511i | ||||
\(514\) | −9.14643 | −0.403432 | ||||||||
\(515\) | 0.205987 | − | 0.0927103i | 0.00907686 | − | 0.00408531i | ||||
\(516\) | 2.72474 | + | 4.71940i | 0.119950 | + | 0.207760i | ||||
\(517\) | −14.6349 | − | 8.44949i | −0.643644 | − | 0.371608i | ||||
\(518\) | 24.5505 | − | 14.1742i | 1.07869 | − | 0.622780i | ||||
\(519\) | −0.224745 | + | 0.389270i | −0.00986520 | + | 0.0170870i | ||||
\(520\) | 3.22474 | + | 0.325765i | 0.141414 | + | 0.0142858i | ||||
\(521\) | −6.24745 | −0.273706 | −0.136853 | − | 0.990591i | \(-0.543699\pi\) | ||||
−0.136853 | + | 0.990591i | \(0.543699\pi\) | |||||||
\(522\) | −4.63191 | − | 2.67423i | −0.202733 | − | 0.117048i | ||||
\(523\) | 1.43027 | + | 0.825765i | 0.0625412 | + | 0.0361082i | 0.530945 | − | 0.847407i | \(-0.321837\pi\) |
−0.468403 | + | 0.883515i | \(0.655171\pi\) | |||||||
\(524\) | 11.7980 | 0.515396 | ||||||||
\(525\) | −14.6969 | − | 3.00000i | −0.641427 | − | 0.130931i | ||||
\(526\) | 7.00000 | − | 12.1244i | 0.305215 | − | 0.528647i | ||||
\(527\) | −8.05669 | + | 4.65153i | −0.350955 | + | 0.202624i | ||||
\(528\) | −1.73205 | − | 1.00000i | −0.0753778 | − | 0.0435194i | ||||
\(529\) | −8.50000 | − | 14.7224i | −0.369565 | − | 0.640106i | ||||
\(530\) | −11.8379 | − | 26.3018i | −0.514205 | − | 1.14248i | ||||
\(531\) | −7.79796 | −0.338403 | ||||||||
\(532\) | 8.96204 | − | 9.52270i | 0.388554 | − | 0.412862i | ||||
\(533\) | 3.55051i | 0.153790i | ||||||||
\(534\) | 8.22474 | + | 14.2457i | 0.355920 | + | 0.616471i | ||||
\(535\) | −11.3178 | + | 5.09391i | −0.489312 | + | 0.220229i | ||||
\(536\) | 1.72474 | − | 2.98735i | 0.0744976 | − | 0.129034i | ||||
\(537\) | −5.41045 | + | 3.12372i | −0.233478 | + | 0.134799i | ||||
\(538\) | 19.4812 | + | 11.2474i | 0.839892 | + | 0.484912i | ||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0.224745 | − | 2.22474i | 0.00967148 | − | 0.0957378i | ||||
\(541\) | −0.174235 | + | 0.301783i | −0.00749093 | + | 0.0129747i | −0.869747 | − | 0.493499i | \(-0.835718\pi\) |
0.862256 | + | 0.506473i | \(0.169051\pi\) | |||||||
\(542\) | 12.9029 | + | 7.44949i | 0.554227 | + | 0.319983i | ||||
\(543\) | − | 20.8990i | − | 0.896861i | ||||||
\(544\) | 4.89898 | 0.210042 | ||||||||
\(545\) | 18.2981 | − | 25.4004i | 0.783805 | − | 1.08803i | ||||
\(546\) | 2.17423 | + | 3.76588i | 0.0930487 | + | 0.161165i | ||||
\(547\) | 17.4473 | + | 10.0732i | 0.745993 | + | 0.430700i | 0.824244 | − | 0.566234i | \(-0.191600\pi\) |
−0.0782510 | + | 0.996934i | \(0.524934\pi\) | |||||||
\(548\) | −9.43879 | + | 5.44949i | −0.403205 | + | 0.232791i | ||||
\(549\) | −5.17423 | − | 8.96204i | −0.220831 | − | 0.382490i | ||||
\(550\) | −2.00000 | + | 9.79796i | −0.0852803 | + | 0.417786i | ||||
\(551\) | −16.9773 | − | 15.9777i | −0.723257 | − | 0.680674i | ||||
\(552\) | − | 2.44949i | − | 0.104257i | ||||||
\(553\) | 7.26931 | − | 4.19694i | 0.309123 | − | 0.178472i | ||||
\(554\) | 8.24745 | + | 14.2850i | 0.350401 | + | 0.606912i | ||||
\(555\) | 12.3506 | − | 17.1443i | 0.524252 | − | 0.727736i | ||||
\(556\) | −5.72474 | − | 9.91555i | −0.242783 | − | 0.420513i | ||||
\(557\) | −31.8198 | − | 18.3712i | −1.34825 | − | 0.778412i | −0.360247 | − | 0.932857i | \(-0.617308\pi\) |
−0.988001 | + | 0.154445i | \(0.950641\pi\) | |||||||
\(558\) | − | 1.89898i | − | 0.0803902i | ||||||
\(559\) | −7.89898 | −0.334091 | ||||||||
\(560\) | 5.44294 | + | 3.92102i | 0.230006 | + | 0.165693i | ||||
\(561\) | −4.89898 | + | 8.48528i | −0.206835 | + | 0.358249i | ||||
\(562\) | − | 21.5505i | − | 0.909053i | ||||||
\(563\) | 13.5959i | 0.573000i | 0.958080 | + | 0.286500i | \(0.0924918\pi\) | ||||
−0.958080 | + | 0.286500i | \(0.907508\pi\) | |||||||
\(564\) | −4.22474 | + | 7.31747i | −0.177894 | + | 0.308121i | ||||
\(565\) | −10.4013 | + | 4.68140i | −0.437585 | + | 0.196948i | ||||
\(566\) | 0.449490 | − | 0.778539i | 0.0188935 | − | 0.0327244i | ||||
\(567\) | 2.59808 | − | 1.50000i | 0.109109 | − | 0.0629941i | ||||
\(568\) | 7.31747 | − | 4.22474i | 0.307034 | − | 0.177266i | ||||
\(569\) | 23.1010 | 0.968445 | 0.484223 | − | 0.874945i | \(-0.339102\pi\) | ||||
0.484223 | + | 0.874945i | \(0.339102\pi\) | |||||||
\(570\) | 3.17826 | − | 9.21405i | 0.133123 | − | 0.385934i | ||||
\(571\) | −25.4495 | −1.06503 | −0.532514 | − | 0.846421i | \(-0.678753\pi\) | ||||
−0.532514 | + | 0.846421i | \(0.678753\pi\) | |||||||
\(572\) | 2.51059 | − | 1.44949i | 0.104973 | − | 0.0606062i | ||||
\(573\) | 12.7279 | − | 7.34847i | 0.531717 | − | 0.306987i | ||||
\(574\) | −3.67423 | + | 6.36396i | −0.153360 | + | 0.265627i | ||||
\(575\) | −11.6170 | + | 3.87868i | −0.484464 | + | 0.161752i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 22.0000i | 0.915872i | 0.888985 | + | 0.457936i | \(0.151411\pi\) | ||||
−0.888985 | + | 0.457936i | \(0.848589\pi\) | |||||||
\(578\) | − | 7.00000i | − | 0.291162i | ||||||
\(579\) | 5.94949 | − | 10.3048i | 0.247252 | − | 0.428254i | ||||
\(580\) | 6.99049 | − | 9.70380i | 0.290264 | − | 0.402928i | ||||
\(581\) | −40.0454 | −1.66136 | ||||||||
\(582\) | − | 10.6969i | − | 0.443402i | ||||||
\(583\) | −22.3417 | − | 12.8990i | −0.925298 | − | 0.534221i | ||||
\(584\) | −1.05051 | − | 1.81954i | −0.0434704 | − | 0.0752930i | ||||
\(585\) | 2.62983 | + | 1.89449i | 0.108730 | + | 0.0783277i | ||||
\(586\) | −4.55051 | − | 7.88171i | −0.187980 | − | 0.325591i | ||||
\(587\) | 31.4305 | − | 18.1464i | 1.29728 | − | 0.748983i | 0.317344 | − | 0.948310i | \(-0.397209\pi\) |
0.979933 | + | 0.199327i | \(0.0638757\pi\) | |||||||
\(588\) | 2.00000i | 0.0824786i | ||||||||
\(589\) | 1.89898 | − | 8.05669i | 0.0782461 | − | 0.331970i | ||||
\(590\) | 1.75255 | − | 17.3485i | 0.0721514 | − | 0.714225i | ||||
\(591\) | −6.34847 | − | 10.9959i | −0.261141 | − | 0.452310i | ||||
\(592\) | −8.18350 | + | 4.72474i | −0.336340 | + | 0.194186i | ||||
\(593\) | −13.1172 | − | 7.57321i | −0.538658 | − | 0.310995i | 0.205877 | − | 0.978578i | \(-0.433995\pi\) |
−0.744535 | + | 0.667583i | \(0.767329\pi\) | |||||||
\(594\) | −1.00000 | − | 1.73205i | −0.0410305 | − | 0.0710669i | ||||
\(595\) | 19.2090 | − | 26.6648i | 0.787492 | − | 1.09315i | ||||
\(596\) | −15.7980 | −0.647110 | ||||||||
\(597\) | 17.8990i | 0.732556i | ||||||||
\(598\) | 3.07483 | + | 1.77526i | 0.125739 | + | 0.0725956i | ||||
\(599\) | −2.87628 | + | 4.98186i | −0.117521 | + | 0.203553i | −0.918785 | − | 0.394759i | \(-0.870828\pi\) |
0.801263 | + | 0.598312i | \(0.204162\pi\) | |||||||
\(600\) | 4.89898 | + | 1.00000i | 0.200000 | + | 0.0408248i | ||||
\(601\) | −15.0000 | −0.611863 | −0.305931 | − | 0.952054i | \(-0.598968\pi\) | ||||
−0.305931 | + | 0.952054i | \(0.598968\pi\) | |||||||
\(602\) | −14.1582 | − | 8.17423i | −0.577045 | − | 0.333157i | ||||
\(603\) | 2.98735 | − | 1.72474i | 0.121654 | − | 0.0702370i | ||||
\(604\) | 0.101021 | − | 0.174973i | 0.00411047 | − | 0.00711954i | ||||
\(605\) | −6.42416 | − | 14.2734i | −0.261179 | − | 0.580296i | ||||
\(606\) | 7.89898 | + | 13.6814i | 0.320874 | + | 0.555770i | ||||
\(607\) | − | 27.0000i | − | 1.09590i | −0.836512 | − | 0.547948i | \(-0.815409\pi\) | ||
0.836512 | − | 0.547948i | \(-0.184591\pi\) | |||||||
\(608\) | −2.98735 | + | 3.17423i | −0.121153 | + | 0.128732i | ||||
\(609\) | 16.0454 | 0.650193 | ||||||||
\(610\) | 21.1011 | − | 9.49718i | 0.854360 | − | 0.384530i | ||||
\(611\) | −6.12372 | − | 10.6066i | −0.247739 | − | 0.429097i | ||||
\(612\) | 4.24264 | + | 2.44949i | 0.171499 | + | 0.0990148i | ||||
\(613\) | −18.2740 | + | 10.5505i | −0.738081 | + | 0.426131i | −0.821371 | − | 0.570394i | \(-0.806790\pi\) |
0.0832904 | + | 0.996525i | \(0.473457\pi\) | |||||||
\(614\) | 10.8990 | − | 18.8776i | 0.439847 | − | 0.761837i | ||||
\(615\) | −0.550510 | + | 5.44949i | −0.0221987 | + | 0.219745i | ||||
\(616\) | 6.00000 | 0.241747 | ||||||||
\(617\) | −38.9230 | − | 22.4722i | −1.56698 | − | 0.904696i | −0.996518 | − | 0.0833723i | \(-0.973431\pi\) |
−0.570462 | − | 0.821324i | \(-0.693236\pi\) | |||||||
\(618\) | −0.0874863 | − | 0.0505103i | −0.00351922 | − | 0.00203182i | ||||
\(619\) | −33.0454 | −1.32821 | −0.664104 | − | 0.747641i | \(-0.731187\pi\) | ||||
−0.664104 | + | 0.747641i | \(0.731187\pi\) | |||||||
\(620\) | 4.22474 | + | 0.426786i | 0.169670 | + | 0.0171401i | ||||
\(621\) | 1.22474 | − | 2.12132i | 0.0491473 | − | 0.0851257i | ||||
\(622\) | 0.953512 | − | 0.550510i | 0.0382323 | − | 0.0220735i | ||||
\(623\) | −42.7370 | − | 24.6742i | −1.71222 | − | 0.988552i | ||||
\(624\) | −0.724745 | − | 1.25529i | −0.0290130 | − | 0.0502520i | ||||
\(625\) | −3.01472 | − | 24.8176i | −0.120589 | − | 0.992703i | ||||
\(626\) | −24.8990 | −0.995163 | ||||||||
\(627\) | −2.51059 | − | 8.34847i | −0.100263 | − | 0.333406i | ||||
\(628\) | − | 0.550510i | − | 0.0219678i | ||||||
\(629\) | 23.1464 | + | 40.0908i | 0.922909 | + | 1.59852i | ||||
\(630\) | 2.75321 | + | 6.11717i | 0.109691 | + | 0.243714i | ||||
\(631\) | −16.0505 | + | 27.8003i | −0.638961 | + | 1.10671i | 0.346700 | + | 0.937976i | \(0.387302\pi\) |
−0.985661 | + | 0.168737i | \(0.946031\pi\) | |||||||
\(632\) | −2.42310 | + | 1.39898i | −0.0963859 | + | 0.0556484i | ||||
\(633\) | 10.6941 | + | 6.17423i | 0.425052 | + | 0.245404i | ||||
\(634\) | 18.2474 | 0.724699 | ||||||||
\(635\) | −2.85357 | + | 28.2474i | −0.113241 | + | 1.12097i | ||||
\(636\) | −6.44949 | + | 11.1708i | −0.255739 | + | 0.442953i | ||||
\(637\) | −2.51059 | − | 1.44949i | −0.0994732 | − | 0.0574309i | ||||
\(638\) | − | 10.6969i | − | 0.423496i | ||||||
\(639\) | 8.44949 | 0.334257 | ||||||||
\(640\) | −1.81431 | − | 1.30701i | −0.0717170 | − | 0.0516640i | ||||
\(641\) | 8.87628 | + | 15.3742i | 0.350592 | + | 0.607243i | 0.986353 | − | 0.164643i | \(-0.0526471\pi\) |
−0.635761 | + | 0.771886i | \(0.719314\pi\) | |||||||
\(642\) | 4.80688 | + | 2.77526i | 0.189713 | + | 0.109531i | ||||
\(643\) | 18.7508 | − | 10.8258i | 0.739458 | − | 0.426927i | −0.0824140 | − | 0.996598i | \(-0.526263\pi\) |
0.821872 | + | 0.569672i | \(0.192930\pi\) | |||||||
\(644\) | 3.67423 | + | 6.36396i | 0.144785 | + | 0.250775i | ||||
\(645\) | −12.1237 | − | 1.22474i | −0.477371 | − | 0.0482243i | ||||
\(646\) | 15.5505 | + | 14.6349i | 0.611827 | + | 0.575804i | ||||
\(647\) | − | 31.8434i | − | 1.25189i | −0.779866 | − | 0.625946i | \(-0.784713\pi\) | ||
0.779866 | − | 0.625946i | \(-0.215287\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | −7.79796 | − | 13.5065i | −0.306097 | − | 0.530175i | ||||
\(650\) | −4.80581 | + | 5.42492i | −0.188499 | + | 0.212783i | ||||
\(651\) | 2.84847 | + | 4.93369i | 0.111640 | + | 0.193367i | ||||
\(652\) | 7.22999 | + | 4.17423i | 0.283148 | + | 0.163476i | ||||
\(653\) | 2.44949i | 0.0958559i | 0.998851 | + | 0.0479280i | \(0.0152618\pi\) | ||||
−0.998851 | + | 0.0479280i | \(0.984738\pi\) | |||||||
\(654\) | −14.0000 | −0.547443 | ||||||||
\(655\) | −15.4200 | + | 21.4052i | −0.602510 | + | 0.836370i | ||||
\(656\) | 1.22474 | − | 2.12132i | 0.0478183 | − | 0.0828236i | ||||
\(657\) | − | 2.10102i | − | 0.0819686i | ||||||
\(658\) | − | 25.3485i | − | 0.988186i | ||||||
\(659\) | −14.3485 | + | 24.8523i | −0.558937 | + | 0.968107i | 0.438649 | + | 0.898659i | \(0.355457\pi\) |
−0.997586 | + | 0.0694486i | \(0.977876\pi\) | |||||||
\(660\) | 4.07812 | − | 1.83548i | 0.158740 | − | 0.0714458i | ||||
\(661\) | −1.44949 | + | 2.51059i | −0.0563786 | + | 0.0976506i | −0.892837 | − | 0.450379i | \(-0.851289\pi\) |
0.836459 | + | 0.548030i | \(0.184622\pi\) | |||||||
\(662\) | −1.08032 | + | 0.623724i | −0.0419879 | + | 0.0242417i | ||||
\(663\) | −6.14966 | + | 3.55051i | −0.238833 | + | 0.137890i | ||||
\(664\) | 13.3485 | 0.518021 | ||||||||
\(665\) | 5.56372 | + | 28.7062i | 0.215752 | + | 1.11318i | ||||
\(666\) | −9.44949 | −0.366160 | ||||||||
\(667\) | 11.3458 | − | 6.55051i | 0.439312 | − | 0.253637i | ||||
\(668\) | −3.28913 | + | 1.89898i | −0.127260 | + | 0.0734737i | ||||
\(669\) | −7.84847 | + | 13.5939i | −0.303439 | + | 0.525572i | ||||
\(670\) | 3.16573 | + | 7.03371i | 0.122303 | + | 0.271736i | ||||
\(671\) | 10.3485 | − | 17.9241i | 0.399498 | − | 0.691951i | ||||
\(672\) | − | 3.00000i | − | 0.115728i | ||||||
\(673\) | 39.6969i | 1.53020i | 0.643909 | + | 0.765102i | \(0.277312\pi\) | ||||
−0.643909 | + | 0.765102i | \(0.722688\pi\) | |||||||
\(674\) | −6.94949 | + | 12.0369i | −0.267684 | + | 0.463643i | ||||
\(675\) | 3.74264 | + | 3.31552i | 0.144054 | + | 0.127614i | ||||
\(676\) | −10.8990 | −0.419192 | ||||||||
\(677\) | 41.1464i | 1.58139i | 0.612213 | + | 0.790693i | \(0.290279\pi\) | ||||
−0.612213 | + | 0.790693i | \(0.709721\pi\) | |||||||
\(678\) | 4.41761 | + | 2.55051i | 0.169657 | + | 0.0979518i | ||||
\(679\) | 16.0454 | + | 27.7915i | 0.615766 | + | 1.06654i | ||||
\(680\) | −6.40300 | + | 8.88828i | −0.245544 | + | 0.340850i | ||||
\(681\) | 0.674235 | + | 1.16781i | 0.0258367 | + | 0.0447505i | ||||
\(682\) | 3.28913 | − | 1.89898i | 0.125947 | − | 0.0727157i | ||||
\(683\) | 39.1918i | 1.49963i | 0.661645 | + | 0.749817i | \(0.269858\pi\) | ||||
−0.661645 | + | 0.749817i | \(0.730142\pi\) | |||||||
\(684\) | −4.17423 | + | 1.25529i | −0.159606 | + | 0.0479974i | ||||
\(685\) | 2.44949 | − | 24.2474i | 0.0935902 | − | 0.926447i | ||||
\(686\) | 7.50000 | + | 12.9904i | 0.286351 | + | 0.495975i | ||||
\(687\) | 14.7618 | − | 8.52270i | 0.563196 | − | 0.325161i | ||||
\(688\) | 4.71940 | + | 2.72474i | 0.179925 | + | 0.103880i | ||||
\(689\) | −9.34847 | − | 16.1920i | −0.356148 | − | 0.616867i | ||||
\(690\) | 4.44414 | + | 3.20150i | 0.169186 | + | 0.121879i | ||||
\(691\) | 39.5959 | 1.50630 | 0.753150 | − | 0.657849i | \(-0.228534\pi\) | ||||
0.753150 | + | 0.657849i | \(0.228534\pi\) | |||||||
\(692\) | 0.449490i | 0.0170870i | ||||||||
\(693\) | 5.19615 | + | 3.00000i | 0.197386 | + | 0.113961i | ||||
\(694\) | 10.2474 | − | 17.7491i | 0.388988 | − | 0.673747i | ||||
\(695\) | 25.4722 | + | 2.57321i | 0.966215 | + | 0.0976076i | ||||
\(696\) | −5.34847 | −0.202733 | ||||||||
\(697\) | −10.3923 | − | 6.00000i | −0.393637 | − | 0.227266i | ||||
\(698\) | 27.2361 | − | 15.7247i | 1.03090 | − | 0.595190i | ||||
\(699\) | 14.6742 | − | 25.4165i | 0.555031 | − | 0.961341i | ||||
\(700\) | −14.2279 | + | 4.75039i | −0.537765 | + | 0.179548i | ||||
\(701\) | 18.8990 | + | 32.7340i | 0.713805 | + | 1.23635i | 0.963419 | + | 0.268000i | \(0.0863629\pi\) |
−0.249614 | + | 0.968345i | \(0.580304\pi\) | |||||||
\(702\) | − | 1.44949i | − | 0.0547075i | ||||||
\(703\) | −40.0908 | − | 9.44949i | −1.51205 | − | 0.356394i | ||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | −7.75442 | − | 17.2290i | −0.292048 | − | 0.648882i | ||||
\(706\) | 6.57321 | + | 11.3851i | 0.247386 | + | 0.428485i | ||||
\(707\) | −41.0443 | − | 23.6969i | −1.54363 | − | 0.891215i | ||||
\(708\) | −6.75323 | + | 3.89898i | −0.253802 | + | 0.146533i | ||||
\(709\) | −8.37628 | + | 14.5081i | −0.314578 | + | 0.544864i | −0.979348 | − | 0.202184i | \(-0.935196\pi\) |
0.664770 | + | 0.747048i | \(0.268530\pi\) | |||||||
\(710\) | −1.89898 | + | 18.7980i | −0.0712674 | + | 0.705475i | ||||
\(711\) | −2.79796 | −0.104932 | ||||||||
\(712\) | 14.2457 | + | 8.22474i | 0.533879 | + | 0.308235i | ||||
\(713\) | 4.02834 | + | 2.32577i | 0.150863 | + | 0.0871006i | ||||
\(714\) | −14.6969 | −0.550019 | ||||||||
\(715\) | −0.651531 | + | 6.44949i | −0.0243659 | + | 0.241197i | ||||
\(716\) | −3.12372 | + | 5.41045i | −0.116739 | + | 0.202198i | ||||
\(717\) | −20.2204 | + | 11.6742i | −0.755143 | + | 0.435982i | ||||
\(718\) | 3.67840 | + | 2.12372i | 0.137277 | + | 0.0792567i | ||||
\(719\) | 19.2247 | + | 33.2982i | 0.716962 | + | 1.24181i | 0.962198 | + | 0.272351i | \(0.0878012\pi\) |
−0.245236 | + | 0.969463i | \(0.578865\pi\) | |||||||
\(720\) | −0.917738 | − | 2.03906i | −0.0342021 | − | 0.0759912i | ||||
\(721\) | 0.303062 | 0.0112866 | ||||||||
\(722\) | −18.9651 | + | 1.15153i | −0.705807 | + | 0.0428555i | ||||
\(723\) | 11.0000i | 0.409094i | ||||||||
\(724\) | −10.4495 | − | 18.0990i | −0.388352 | − | 0.672646i | ||||
\(725\) | 8.46911 | + | 25.3659i | 0.314535 | + | 0.942065i | ||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | 6.23715 | − | 3.60102i | 0.231323 | − | 0.133554i | −0.379859 | − | 0.925044i | \(-0.624028\pi\) |
0.611182 | + | 0.791490i | \(0.290694\pi\) | |||||||
\(728\) | 3.76588 | + | 2.17423i | 0.139573 | + | 0.0805825i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 4.67423 | + | 0.472194i | 0.173001 | + | 0.0174767i | ||||
\(731\) | 13.3485 | − | 23.1202i | 0.493711 | − | 0.855132i | ||||
\(732\) | −8.96204 | − | 5.17423i | −0.331246 | − | 0.191245i | ||||
\(733\) | − | 1.30306i | − | 0.0481297i | −0.999710 | − | 0.0240648i | \(-0.992339\pi\) | ||
0.999710 | − | 0.0240648i | \(-0.00766082\pi\) | |||||||
\(734\) | 22.5959 | 0.834031 | ||||||||
\(735\) | −3.62863 | − | 2.61401i | −0.133844 | − | 0.0964194i | ||||
\(736\) | −1.22474 | − | 2.12132i | −0.0451447 | − | 0.0781929i | ||||
\(737\) | 5.97469 | + | 3.44949i | 0.220081 | + | 0.127064i | ||||
\(738\) | 2.12132 | − | 1.22474i | 0.0780869 | − | 0.0450835i | ||||
\(739\) | 18.1742 | + | 31.4787i | 0.668550 | + | 1.15796i | 0.978310 | + | 0.207148i | \(0.0664181\pi\) |
−0.309760 | + | 0.950815i | \(0.600249\pi\) | |||||||
\(740\) | 2.12372 | − | 21.0227i | 0.0780697 | − | 0.772810i | ||||
\(741\) | 1.44949 | − | 6.14966i | 0.0532483 | − | 0.225914i | ||||
\(742\) | − | 38.6969i | − | 1.42061i | ||||||
\(743\) | −39.8372 | + | 23.0000i | −1.46148 | + | 0.843788i | −0.999080 | − | 0.0428813i | \(-0.986346\pi\) |
−0.462404 | + | 0.886669i | \(0.653013\pi\) | |||||||
\(744\) | −0.949490 | − | 1.64456i | −0.0348100 | − | 0.0602927i | ||||
\(745\) | 20.6480 | − | 28.6624i | 0.756486 | − | 1.05011i | ||||
\(746\) | −17.4495 | − | 30.2234i | −0.638871 | − | 1.10656i | ||||
\(747\) | 11.5601 | + | 6.67423i | 0.422962 | + | 0.244197i | ||||
\(748\) | 9.79796i | 0.358249i | ||||||||
\(749\) | −16.6515 | −0.608434 | ||||||||
\(750\) | −8.21731 | + | 7.58128i | −0.300054 | + | 0.276829i | ||||
\(751\) | 24.8485 | − | 43.0388i | 0.906734 | − | 1.57051i | 0.0881603 | − | 0.996106i | \(-0.471901\pi\) |
0.818573 | − | 0.574402i | \(-0.194765\pi\) | |||||||
\(752\) | 8.44949i | 0.308121i | ||||||||
\(753\) | 8.69694i | 0.316934i | ||||||||
\(754\) | 3.87628 | − | 6.71391i | 0.141166 | − | 0.244506i | ||||
\(755\) | 0.185421 | + | 0.411973i | 0.00674815 | + | 0.0149932i | ||||
\(756\) | 1.50000 | − | 2.59808i | 0.0545545 | − | 0.0944911i | ||||
\(757\) | 2.03383 | − | 1.17423i | 0.0739210 | − | 0.0426783i | −0.462584 | − | 0.886575i | \(-0.653078\pi\) |
0.536505 | + | 0.843897i | \(0.319744\pi\) | |||||||
\(758\) | −28.7931 | + | 16.6237i | −1.04581 | + | 0.603801i | ||||
\(759\) | 4.89898 | 0.177822 | ||||||||
\(760\) | −1.85457 | − | 9.56873i | −0.0672724 | − | 0.347094i | ||||
\(761\) | 25.1010 | 0.909911 | 0.454956 | − | 0.890514i | \(-0.349655\pi\) | ||||
0.454956 | + | 0.890514i | \(0.349655\pi\) | |||||||
\(762\) | 10.9959 | − | 6.34847i | 0.398338 | − | 0.229981i | ||||
\(763\) | 36.3731 | − | 21.0000i | 1.31679 | − | 0.760251i | ||||
\(764\) | 7.34847 | − | 12.7279i | 0.265858 | − | 0.460480i | ||||
\(765\) | −9.98930 | + | 4.49598i | −0.361164 | + | 0.162552i | ||||
\(766\) | 6.67423 | − | 11.5601i | 0.241150 | − | 0.417684i | ||||
\(767\) | − | 11.3031i | − | 0.408130i | ||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −19.2980 | + | 33.4250i | −0.695902 | + | 1.20534i | 0.273973 | + | 0.961737i | \(0.411662\pi\) |
−0.969876 | + | 0.243601i | \(0.921671\pi\) | |||||||
\(770\) | −7.84204 | + | 10.8859i | −0.282608 | + | 0.392300i | ||||
\(771\) | −9.14643 | −0.329401 | ||||||||
\(772\) | − | 11.8990i | − | 0.428254i | ||||||
\(773\) | 25.2022 | + | 14.5505i | 0.906461 | + | 0.523345i | 0.879291 | − | 0.476285i | \(-0.158017\pi\) |
0.0271702 | + | 0.999631i | \(0.491350\pi\) | |||||||
\(774\) | 2.72474 | + | 4.71940i | 0.0979389 | + | 0.169635i | ||||
\(775\) | −6.29610 | + | 7.10720i | −0.226162 | + | 0.255298i | ||||
\(776\) | −5.34847 | − | 9.26382i | −0.191999 | − | 0.332552i | ||||
\(777\) | 24.5505 | − | 14.1742i | 0.880744 | − | 0.508498i | ||||
\(778\) | 10.2474i | 0.367389i | ||||||||
\(779\) | 10.2247 | − | 3.07483i | 0.366340 | − | 0.110167i | ||||
\(780\) | 3.22474 | + | 0.325765i | 0.115464 | + | 0.0116643i | ||||
\(781\) | 8.44949 | + | 14.6349i | 0.302347 | + | 0.523680i | ||||
\(782\) | −10.3923 | + | 6.00000i | −0.371628 | + | 0.214560i | ||||
\(783\) | −4.63191 | − | 2.67423i | −0.165531 | − | 0.0955693i | ||||
\(784\) | 1.00000 | + | 1.73205i | 0.0357143 | + | 0.0618590i | ||||
\(785\) | 0.998798 | + | 0.719521i | 0.0356486 | + | 0.0256808i | ||||
\(786\) | 11.7980 | 0.420819 | ||||||||
\(787\) | − | 35.9444i | − | 1.28128i | −0.767842 | − | 0.640640i | \(-0.778669\pi\) | ||
0.767842 | − | 0.640640i | \(-0.221331\pi\) | |||||||
\(788\) | −10.9959 | − | 6.34847i | −0.391712 | − | 0.226155i | ||||
\(789\) | 7.00000 | − | 12.1244i | 0.249207 | − | 0.431638i | ||||
\(790\) | 0.628827 | − | 6.22474i | 0.0223727 | − | 0.221466i | ||||
\(791\) | −15.3031 | −0.544114 | ||||||||
\(792\) | −1.73205 | − | 1.00000i | −0.0615457 | − | 0.0355335i | ||||
\(793\) | 12.9904 | − | 7.50000i | 0.461302 | − | 0.266333i | ||||
\(794\) | −7.62372 | + | 13.2047i | −0.270556 | + | 0.468616i | ||||
\(795\) | −11.8379 | − | 26.3018i | −0.419846 | − | 0.932828i | ||||
\(796\) | 8.94949 | + | 15.5010i | 0.317206 | + | 0.549417i | ||||
\(797\) | 1.10102i | 0.0390001i | 0.999810 | + | 0.0195001i | \(0.00620746\pi\) | ||||
−0.999810 | + | 0.0195001i | \(0.993793\pi\) | |||||||
\(798\) | 8.96204 | − | 9.52270i | 0.317253 | − | 0.337100i | ||||
\(799\) | 41.3939 | 1.46441 | ||||||||
\(800\) | 4.74264 | − | 1.58346i | 0.167678 | − | 0.0559839i | ||||
\(801\) | 8.22474 | + | 14.2457i | 0.290607 | + | 0.503346i | ||||
\(802\) | 31.4305 | + | 18.1464i | 1.10985 | + | 0.640773i | ||||
\(803\) | 3.63907 | − | 2.10102i | 0.128420 | − | 0.0741434i | ||||
\(804\) | 1.72474 | − | 2.98735i | 0.0608271 | − | 0.105356i | ||||
\(805\) | −16.3485 | − | 1.65153i | −0.576208 | − | 0.0582088i | ||||
\(806\) | 2.75255 | 0.0969545 | ||||||||
\(807\) | 19.4812 | + | 11.2474i | 0.685769 | + | 0.395929i | ||||
\(808\) | 13.6814 | + | 7.89898i | 0.481311 | + | 0.277885i | ||||
\(809\) | −3.34847 | −0.117726 | −0.0588630 | − | 0.998266i | \(-0.518747\pi\) | ||||
−0.0588630 | + | 0.998266i | \(0.518747\pi\) | |||||||
\(810\) | 0.224745 | − | 2.22474i | 0.00789673 | − | 0.0781696i | ||||
\(811\) | −13.7980 | + | 23.8988i | −0.484512 | + | 0.839199i | −0.999842 | − | 0.0177928i | \(-0.994336\pi\) |
0.515330 | + | 0.856992i | \(0.327669\pi\) | |||||||
\(812\) | 13.8957 | − | 8.02270i | 0.487645 | − | 0.281542i | ||||
\(813\) | 12.9029 | + | 7.44949i | 0.452524 | + | 0.261265i | ||||
\(814\) | −9.44949 | − | 16.3670i | −0.331204 | − | 0.573663i | ||||
\(815\) | −17.0230 | + | 7.66170i | −0.596290 | + | 0.268378i | ||||
\(816\) | 4.89898 | 0.171499 | ||||||||
\(817\) | 6.84072 | + | 22.7474i | 0.239326 | + | 0.795832i | ||||
\(818\) | 20.8990i | 0.730716i | ||||||||
\(819\) | 2.17423 | + | 3.76588i | 0.0759739 | + | 0.131591i | ||||
\(820\) | 2.24799 | + | 4.99465i | 0.0785032 | + | 0.174421i | ||||
\(821\) | −3.32577 | + | 5.76039i | −0.116070 | + | 0.201039i | −0.918207 | − | 0.396101i | \(-0.870363\pi\) |
0.802137 | + | 0.597140i | \(0.203696\pi\) | |||||||
\(822\) | −9.43879 | + | 5.44949i | −0.329216 | + | 0.190073i | ||||
\(823\) | −44.3334 | − | 25.5959i | −1.54537 | − | 0.892218i | −0.998486 | − | 0.0550068i | \(-0.982482\pi\) |
−0.546880 | − | 0.837211i | \(-0.684185\pi\) | |||||||
\(824\) | −0.101021 | −0.00351922 | ||||||||
\(825\) | −2.00000 | + | 9.79796i | −0.0696311 | + | 0.341121i | ||||
\(826\) | 11.6969 | − | 20.2597i | 0.406989 | − | 0.704925i | ||||
\(827\) | 47.4083 | + | 27.3712i | 1.64855 | + | 0.951789i | 0.977650 | + | 0.210238i | \(0.0674239\pi\) |
0.670897 | + | 0.741551i | \(0.265909\pi\) | |||||||
\(828\) | − | 2.44949i | − | 0.0851257i | ||||||
\(829\) | 51.4495 | 1.78691 | 0.893457 | − | 0.449148i | \(-0.148272\pi\) | ||||
0.893457 | + | 0.449148i | \(0.148272\pi\) | |||||||
\(830\) | −17.4465 | + | 24.2183i | −0.605578 | + | 0.840630i | ||||
\(831\) | 8.24745 | + | 14.2850i | 0.286101 | + | 0.495541i | ||||
\(832\) | −1.25529 | − | 0.724745i | −0.0435195 | − | 0.0251260i | ||||
\(833\) | 8.48528 | − | 4.89898i | 0.293998 | − | 0.169740i | ||||
\(834\) | −5.72474 | − | 9.91555i | −0.198232 | − | 0.343347i | ||||
\(835\) | 0.853572 | − | 8.44949i | 0.0295391 | − | 0.292407i | ||||
\(836\) | −6.34847 | − | 5.97469i | −0.219566 | − | 0.206639i | ||||
\(837\) | − | 1.89898i | − | 0.0656383i | ||||||
\(838\) | −15.6278 | + | 9.02270i | −0.539853 | + | 0.311684i | ||||
\(839\) | −15.3485 | − | 26.5843i | −0.529888 | − | 0.917793i | −0.999392 | − | 0.0348627i | \(-0.988901\pi\) |
0.469504 | − | 0.882930i | \(-0.344433\pi\) | |||||||
\(840\) | 5.44294 | + | 3.92102i | 0.187799 | + | 0.135288i | ||||
\(841\) | 0.196938 | + | 0.341107i | 0.00679098 | + | 0.0117623i | ||||
\(842\) | −15.2385 | − | 8.79796i | −0.525154 | − | 0.303198i | ||||
\(843\) | − | 21.5505i | − | 0.742239i | ||||||
\(844\) | 12.3485 | 0.425052 | ||||||||
\(845\) | 14.2450 | − | 19.7742i | 0.490044 | − | 0.680252i | ||||
\(846\) | −4.22474 | + | 7.31747i | −0.145250 | + | 0.251580i | ||||
\(847\) | − | 21.0000i | − | 0.721569i | ||||||
\(848\) | 12.8990i | 0.442953i | ||||||||
\(849\) | 0.449490 | − | 0.778539i | 0.0154264 | − | 0.0267194i | ||||
\(850\) | −7.75736 | − | 23.2341i | −0.266075 | − | 0.796923i | ||||
\(851\) | 11.5732 | − | 20.0454i | 0.396725 | − | 0.687147i | ||||
\(852\) | 7.31747 | − | 4.22474i | 0.250692 | − | 0.144737i | ||||
\(853\) | 11.2190 | − | 6.47730i | 0.384131 | − | 0.221778i | −0.295483 | − | 0.955348i | \(-0.595481\pi\) |
0.679614 | + | 0.733570i | \(0.262147\pi\) | |||||||
\(854\) | 31.0454 | 1.06235 | ||||||||
\(855\) | 3.17826 | − | 9.21405i | 0.108694 | − | 0.315114i | ||||
\(856\) | 5.55051 | 0.189713 | ||||||||
\(857\) | 9.65309 | − | 5.57321i | 0.329743 | − | 0.190377i | −0.325984 | − | 0.945375i | \(-0.605696\pi\) |
0.655727 | + | 0.754998i | \(0.272362\pi\) | |||||||
\(858\) | 2.51059 | − | 1.44949i | 0.0857101 | − | 0.0494848i | ||||
\(859\) | 27.1742 | − | 47.0672i | 0.927173 | − | 1.60591i | 0.139144 | − | 0.990272i | \(-0.455565\pi\) |
0.788029 | − | 0.615638i | \(-0.211102\pi\) | |||||||
\(860\) | −11.1118 | + | 5.00120i | −0.378910 | + | 0.170540i | ||||
\(861\) | −3.67423 | + | 6.36396i | −0.125218 | + | 0.216883i | ||||
\(862\) | 5.75255i | 0.195933i | ||||||||
\(863\) | − | 27.7980i | − | 0.946254i | −0.880994 | − | 0.473127i | \(-0.843125\pi\) | ||
0.880994 | − | 0.473127i | \(-0.156875\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −0.815515 | − | 0.587486i | −0.0277283 | − | 0.0199751i | ||||
\(866\) | 0.797959 | 0.0271157 | ||||||||
\(867\) | − | 7.00000i | − | 0.237732i | ||||||
\(868\) | 4.93369 | + | 2.84847i | 0.167460 | + | 0.0966833i | ||||
\(869\) | −2.79796 | − | 4.84621i | −0.0949143 | − | 0.164396i | ||||
\(870\) | 6.99049 | − | 9.70380i | 0.237000 | − | 0.328990i | ||||
\(871\) | 2.50000 | + | 4.33013i | 0.0847093 | + | 0.146721i | ||||
\(872\) | −12.1244 | + | 7.00000i | −0.410582 | + | 0.237050i | ||||
\(873\) | − | 10.6969i | − | 0.362037i | ||||||
\(874\) | 2.44949 | − | 10.3923i | 0.0828552 | − | 0.351525i | ||||
\(875\) | 9.97730 | − | 32.0227i | 0.337294 | − | 1.08256i | ||||
\(876\) | −1.05051 | − | 1.81954i | −0.0354935 | − | 0.0614765i | ||||
\(877\) | 41.8710 | − | 24.1742i | 1.41388 | − | 0.816306i | 0.418132 | − | 0.908386i | \(-0.362685\pi\) |
0.995752 | + | 0.0920805i | \(0.0293517\pi\) | |||||||
\(878\) | 27.2754 | + | 15.7474i | 0.920500 | + | 0.531451i | ||||
\(879\) | −4.55051 | − | 7.88171i | −0.153485 | − | 0.265844i | ||||
\(880\) | 2.61401 | − | 3.62863i | 0.0881184 | − | 0.122321i | ||||
\(881\) | 21.5505 | 0.726055 | 0.363028 | − | 0.931778i | \(-0.381743\pi\) | ||||
0.363028 | + | 0.931778i | \(0.381743\pi\) | |||||||
\(882\) | 2.00000i | 0.0673435i | ||||||||
\(883\) | 24.2005 | + | 13.9722i | 0.814413 | + | 0.470202i | 0.848486 | − | 0.529218i | \(-0.177514\pi\) |
−0.0340728 | + | 0.999419i | \(0.510848\pi\) | |||||||
\(884\) | −3.55051 | + | 6.14966i | −0.119417 | + | 0.206836i | ||||
\(885\) | 1.75255 | − | 17.3485i | 0.0589114 | − | 0.583162i | ||||
\(886\) | −9.79796 | −0.329169 | ||||||||
\(887\) | −17.7098 | − | 10.2247i | −0.594636 | − | 0.343313i | 0.172292 | − | 0.985046i | \(-0.444883\pi\) |
−0.766929 | + | 0.641733i | \(0.778216\pi\) | |||||||
\(888\) | −8.18350 | + | 4.72474i | −0.274620 | + | 0.158552i | ||||
\(889\) | −19.0454 | + | 32.9876i | −0.638762 | + | 1.10637i | ||||
\(890\) | −33.5415 | + | 15.0963i | −1.12431 | + | 0.506030i | ||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 15.6969i | 0.525572i | ||||||||
\(893\) | −25.2415 | + | 26.8207i | −0.844676 | + | 0.897519i | ||||
\(894\) | −15.7980 | −0.528363 | ||||||||
\(895\) | −5.73352 | − | 12.7389i | −0.191650 | − | 0.425815i | ||||
\(896\) | −1.50000 | − | 2.59808i | −0.0501115 | − | 0.0867956i | ||||
\(897\) | 3.07483 | + | 1.77526i | 0.102666 | + | 0.0592740i | ||||
\(898\) | −16.1920 | + | 9.34847i | −0.540335 | + | 0.311962i | ||||
\(899\) | 5.07832 | − | 8.79590i | 0.169371 | − | 0.293360i | ||||
\(900\) | 4.89898 | + | 1.00000i | 0.163299 | + | 0.0333333i | ||||
\(901\) | 63.1918 | 2.10523 | ||||||||
\(902\) | 4.24264 | + | 2.44949i | 0.141264 | + | 0.0815591i | ||||
\(903\) | −14.1582 | − | 8.17423i | −0.471155 | − | 0.272021i | ||||
\(904\) | 5.10102 | 0.169657 | ||||||||
\(905\) | 46.4949 | + | 4.69694i | 1.54554 | + | 0.156132i | ||||
\(906\) | 0.101021 | − | 0.174973i | 0.00335618 | − | 0.00581308i | ||||
\(907\) | −26.9343 | + | 15.5505i | −0.894338 | + | 0.516346i | −0.875359 | − | 0.483474i | \(-0.839375\pi\) |
−0.0189790 | + | 0.999820i | \(0.506042\pi\) | |||||||
\(908\) | 1.16781 | + | 0.674235i | 0.0387551 | + | 0.0223753i | ||||
\(909\) | 7.89898 | + | 13.6814i | 0.261993 | + | 0.453785i | ||||
\(910\) | −8.86678 | + | 3.99075i | −0.293931 | + | 0.132292i | ||||
\(911\) | −50.4495 | −1.67147 | −0.835733 | − | 0.549136i | \(-0.814957\pi\) | ||||
−0.835733 | + | 0.549136i | \(0.814957\pi\) | |||||||
\(912\) | −2.98735 | + | 3.17423i | −0.0989209 | + | 0.105109i | ||||
\(913\) | 26.6969i | 0.883540i | ||||||||
\(914\) | 11.9495 | + | 20.6971i | 0.395254 | + | 0.684600i | ||||
\(915\) | 21.1011 | − | 9.49718i | 0.697582 | − | 0.313967i | ||||
\(916\) | 8.52270 | − | 14.7618i | 0.281598 | − | 0.487742i | ||||
\(917\) | −30.6520 | + | 17.6969i | −1.01222 | + | 0.584404i | ||||
\(918\) | 4.24264 | + | 2.44949i | 0.140028 | + | 0.0808452i | ||||
\(919\) | 1.20204 | 0.0396517 | 0.0198258 | − | 0.999803i | \(-0.493689\pi\) | ||||
0.0198258 | + | 0.999803i | \(0.493689\pi\) | |||||||
\(920\) | 5.44949 | + | 0.550510i | 0.179664 | + | 0.0181498i | ||||
\(921\) | 10.8990 | − | 18.8776i | 0.359134 | − | 0.622038i | ||||
\(922\) | −0.214297 | − | 0.123724i | −0.00705749 | − | 0.00407464i | ||||
\(923\) | 12.2474i | 0.403130i | ||||||||
\(924\) | 6.00000 | 0.197386 | ||||||||
\(925\) | 35.3660 | + | 31.3299i | 1.16283 | + | 1.03012i | ||||
\(926\) | −14.6464 | − | 25.3684i | −0.481311 | − | 0.833656i | ||||
\(927\) | −0.0874863 | − | 0.0505103i | −0.00287343 | − | 0.00165897i | ||||
\(928\) | −4.63191 | + | 2.67423i | −0.152050 | + | 0.0877861i | ||||
\(929\) | 3.55051 | + | 6.14966i | 0.116488 | + | 0.201764i | 0.918374 | − | 0.395714i | \(-0.129503\pi\) |
−0.801885 | + | 0.597478i | \(0.796170\pi\) | |||||||
\(930\) | 4.22474 | + | 0.426786i | 0.138535 | + | 0.0139949i | ||||
\(931\) | −2.00000 | + | 8.48528i | −0.0655474 | + | 0.278094i | ||||
\(932\) | − | 29.3485i | − | 0.961341i | ||||||
\(933\) | 0.953512 | − | 0.550510i | 0.0312166 | − | 0.0180229i | ||||
\(934\) | 4.22474 | + | 7.31747i | 0.138238 | + | 0.239435i | ||||
\(935\) | −17.7766 | − | 12.8060i | −0.581356 | − | 0.418801i | ||||
\(936\) | −0.724745 | − | 1.25529i | −0.0236890 | − | 0.0410306i | ||||
\(937\) | 5.28364 | + | 3.05051i | 0.172609 | + | 0.0996558i | 0.583815 | − | 0.811886i | \(-0.301559\pi\) |
−0.411207 | + | 0.911542i | \(0.634892\pi\) | |||||||
\(938\) | 10.3485i | 0.337889i | ||||||||
\(939\) | −24.8990 | −0.812547 | ||||||||
\(940\) | −15.3300 | − | 11.0435i | −0.500010 | − | 0.360201i | ||||
\(941\) | 18.0227 | − | 31.2162i | 0.587523 | − | 1.01762i | −0.407032 | − | 0.913414i | \(-0.633436\pi\) |
0.994556 | − | 0.104207i | \(-0.0332303\pi\) | |||||||
\(942\) | − | 0.550510i | − | 0.0179366i | ||||||
\(943\) | 6.00000i | 0.195387i | ||||||||
\(944\) | −3.89898 | + | 6.75323i | −0.126901 | + | 0.219799i | ||||
\(945\) | 2.75321 | + | 6.11717i | 0.0895620 | + | 0.198992i | ||||
\(946\) | −5.44949 | + | 9.43879i | −0.177178 | + | 0.306882i | ||||
\(947\) | 40.2658 | − | 23.2474i | 1.30846 | − | 0.755441i | 0.326622 | − | 0.945155i | \(-0.394090\pi\) |
0.981839 | + | 0.189714i | \(0.0607562\pi\) | |||||||
\(948\) | −2.42310 | + | 1.39898i | −0.0786987 | + | 0.0454367i | ||||
\(949\) | 3.04541 | 0.0988581 | ||||||||
\(950\) | 19.7846 | + | 9.14162i | 0.641898 | + | 0.296593i | ||||
\(951\) | 18.2474 | 0.591714 | ||||||||
\(952\) | −12.7279 | + | 7.34847i | −0.412514 | + | 0.238165i | ||||
\(953\) | −4.98186 | + | 2.87628i | −0.161378 | + | 0.0931717i | −0.578514 | − | 0.815672i | \(-0.696367\pi\) |
0.417136 | + | 0.908844i | \(0.363034\pi\) | |||||||
\(954\) | −6.44949 | + | 11.1708i | −0.208810 | + | 0.361669i | ||||
\(955\) | 13.4879 | + | 29.9679i | 0.436459 | + | 0.969739i | ||||
\(956\) | −11.6742 | + | 20.2204i | −0.377572 | + | 0.653973i | ||||
\(957\) | − | 10.6969i | − | 0.345783i | ||||||
\(958\) | 0.696938i | 0.0225171i | ||||||||
\(959\) | 16.3485 | − | 28.3164i | 0.527920 | − | 0.914384i | ||||
\(960\) | −1.81431 | − | 1.30701i | −0.0585567 | − | 0.0421835i | ||||
\(961\) | −27.3939 | −0.883673 | ||||||||
\(962\) | − | 13.6969i | − | 0.441607i | ||||||
\(963\) | 4.80688 | + | 2.77526i | 0.154900 | + | 0.0894313i | ||||
\(964\) | 5.50000 | + | 9.52628i | 0.177143 | + | 0.306821i | ||||
\(965\) | 21.5885 | + | 15.5521i | 0.694958 | + | 0.500638i | ||||
\(966\) | 3.67423 | + | 6.36396i | 0.118217 | + | 0.204757i | ||||
\(967\) | 33.8536 | − | 19.5454i | 1.08866 | − | 0.628538i | 0.155440 | − | 0.987845i | \(-0.450320\pi\) |
0.933219 | + | 0.359307i | \(0.116987\pi\) | |||||||
\(968\) | 7.00000i | 0.224989i | ||||||||
\(969\) | 15.5505 | + | 14.6349i | 0.499554 | + | 0.470142i | ||||
\(970\) | 23.7980 | + | 2.40408i | 0.764106 | + | 0.0771904i | ||||
\(971\) | 7.87628 | + | 13.6421i | 0.252762 | + | 0.437796i | 0.964285 | − | 0.264866i | \(-0.0853278\pi\) |
−0.711523 | + | 0.702662i | \(0.751994\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | 29.7466 | + | 17.1742i | 0.953634 | + | 0.550581i | ||||
\(974\) | 12.5505 | + | 21.7381i | 0.402144 | + | 0.696534i | ||||
\(975\) | −4.80581 | + | 5.42492i | −0.153909 | + | 0.173736i | ||||
\(976\) | −10.3485 | −0.331246 | ||||||||
\(977\) | 20.2929i | 0.649226i | 0.945847 | + | 0.324613i | \(0.105234\pi\) | ||||
−0.945847 | + | 0.324613i | \(0.894766\pi\) | |||||||
\(978\) | 7.22999 | + | 4.17423i | 0.231189 | + | 0.133477i | ||||
\(979\) | −16.4495 | + | 28.4914i | −0.525728 | + | 0.910588i | ||||
\(980\) | −4.44949 | − | 0.449490i | −0.142134 | − | 0.0143584i | ||||
\(981\) | −14.0000 | −0.446986 | ||||||||
\(982\) | −29.4842 | − | 17.0227i | −0.940878 | − | 0.543216i | ||||
\(983\) | −8.09601 | + | 4.67423i | −0.258223 | + | 0.149085i | −0.623524 | − | 0.781805i | \(-0.714299\pi\) |
0.365301 | + | 0.930890i | \(0.380966\pi\) | |||||||
\(984\) | 1.22474 | − | 2.12132i | 0.0390434 | − | 0.0676252i | ||||
\(985\) | 25.8898 | − | 11.6525i | 0.824917 | − | 0.371278i | ||||
\(986\) | 13.1010 | + | 22.6916i | 0.417221 | + | 0.722649i | ||||
\(987\) | − | 25.3485i | − | 0.806851i | ||||||
\(988\) | −1.81954 | − | 6.05051i | −0.0578872 | − | 0.192492i | ||||
\(989\) | −13.3485 | −0.424457 | ||||||||
\(990\) | 4.07812 | − | 1.83548i | 0.129611 | − | 0.0583352i | ||||
\(991\) | −3.15153 | − | 5.45861i | −0.100112 | − | 0.173399i | 0.811619 | − | 0.584187i | \(-0.198587\pi\) |
−0.911731 | + | 0.410789i | \(0.865253\pi\) | |||||||
\(992\) | −1.64456 | − | 0.949490i | −0.0522150 | − | 0.0301463i | ||||
\(993\) | −1.08032 | + | 0.623724i | −0.0342830 | + | 0.0197933i | ||||
\(994\) | −12.6742 | + | 21.9524i | −0.402002 | + | 0.696288i | ||||
\(995\) | −39.8207 | − | 4.02270i | −1.26240 | − | 0.127528i | ||||
\(996\) | 13.3485 | 0.422962 | ||||||||
\(997\) | 10.6941 | + | 6.17423i | 0.338685 | + | 0.195540i | 0.659690 | − | 0.751537i | \(-0.270687\pi\) |
−0.321005 | + | 0.947077i | \(0.604021\pi\) | |||||||
\(998\) | 26.7111 | + | 15.4217i | 0.845526 | + | 0.488165i | ||||
\(999\) | −9.44949 | −0.298969 |
(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 | 570.2.q.a.349.3 | yes | 8 | |
3.2 | odd | 2 | 1710.2.t.a.919.2 | 8 | |||
5.4 | even | 2 | inner | 570.2.q.a.349.2 | yes | 8 | |
15.14 | odd | 2 | 1710.2.t.a.919.3 | 8 | |||
19.11 | even | 3 | inner | 570.2.q.a.49.2 | ✓ | 8 | |
57.11 | odd | 6 | 1710.2.t.a.1189.3 | 8 | |||
95.49 | even | 6 | inner | 570.2.q.a.49.3 | yes | 8 | |
285.239 | odd | 6 | 1710.2.t.a.1189.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.a.49.2 | ✓ | 8 | 19.11 | even | 3 | inner | |
570.2.q.a.49.3 | yes | 8 | 95.49 | even | 6 | inner | |
570.2.q.a.349.2 | yes | 8 | 5.4 | even | 2 | inner | |
570.2.q.a.349.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1710.2.t.a.919.2 | 8 | 3.2 | odd | 2 | |||
1710.2.t.a.919.3 | 8 | 15.14 | odd | 2 | |||
1710.2.t.a.1189.2 | 8 | 285.239 | odd | 6 | |||
1710.2.t.a.1189.3 | 8 | 57.11 | odd | 6 |