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 | 349.2 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | ||||
\(5\) | 1.30701 | + | 1.81431i | 0.584511 | + | 0.811386i | ||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | − | 3.00000i | − | 1.13389i | −0.823754 | − | 0.566947i | \(-0.808125\pi\) | ||
0.823754 | − | 0.566947i | \(-0.191875\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −2.03906 | − | 0.917738i | −0.644807 | − | 0.290214i | ||||
\(11\) | 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 | 0.315717 | − | 0.948853i | \(-0.397755\pi\) |
−0.663873 | + | 0.747845i | \(0.731088\pi\) | |||||||
\(14\) | 1.50000 | + | 2.59808i | 0.400892 | + | 0.694365i | ||||
\(15\) | −2.03906 | − | 0.917738i | −0.526483 | − | 0.236959i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.24264 | − | 2.44949i | 1.02899 | − | 0.594089i | 0.112296 | − | 0.993675i | \(-0.464180\pi\) |
0.916696 | + | 0.399586i | \(0.130846\pi\) | |||||||
\(18\) | 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 | 0.262258 | − | 0.964998i | \(-0.415533\pi\) |
−0.704584 | + | 0.709621i | \(0.748866\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −1.58346 | + | 4.74264i | −0.316693 | + | 0.948528i | ||||
\(26\) | 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 | ||||
\(35\) | 5.44294 | − | 3.92102i | 0.920025 | − | 0.662774i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 9.44949i | 1.55349i | 0.629817 | + | 0.776743i | \(0.283130\pi\) | ||||
−0.629817 | + | 0.776743i | \(0.716870\pi\) | |||||||
\(38\) | 1.25529 | + | 4.17423i | 0.203636 | + | 0.677150i | ||||
\(39\) | 1.44949 | 0.232104 | ||||||||
\(40\) | −1.81431 | + | 1.30701i | −0.286868 | + | 0.206656i | ||||
\(41\) | 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 | −0.0949415 | − | 0.995483i | \(-0.530266\pi\) |
0.814643 | + | 0.579963i | \(0.196933\pi\) | |||||||
\(44\) | 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 | 0.927460 | − | 0.373923i | \(-0.121988\pi\) |
0.139903 | + | 0.990165i | \(0.455321\pi\) | |||||||
\(48\) | 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 | \(0.0131287\pi\) |
0.535284 | + | 0.844672i | \(0.320205\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 2.61401 | + | 3.62863i | 0.352474 | + | 0.489284i | ||||
\(56\) | 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 | \(-0.336135\pi\) | |||||||
\(60\) | −1.81431 | + | 1.30701i | −0.234227 | + | 0.168734i | ||||
\(61\) | 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 | 0.306293 | − | 0.951937i | \(-0.400911\pi\) |
−0.671255 | + | 0.741226i | \(0.734245\pi\) | |||||||
\(68\) | − | 4.89898i | − | 0.594089i | ||||||
\(69\) | 2.44949 | 0.294884 | ||||||||
\(70\) | −2.75321 | + | 6.11717i | −0.329072 | + | 0.731142i | ||||
\(71\) | 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 | −0.602687 | − | 0.797978i | \(-0.705903\pi\) |
0.389726 | + | 0.920931i | \(0.372570\pi\) | |||||||
\(74\) | −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 | \(0.883644\pi\) | |||||||
\(80\) | 0.917738 | − | 2.03906i | 0.102606 | − | 0.227974i | ||||
\(81\) | −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 | \(-0.738310\pi\) | ||
0.680668 | − | 0.732592i | \(-0.261690\pi\) | |||||||
\(84\) | 3.00000 | 0.327327 | ||||||||
\(85\) | 9.98930 | + | 4.49598i | 1.08349 | + | 0.487657i | ||||
\(86\) | −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 | \(0.829606\pi\) | |||||||
\(90\) | −1.81431 | + | 1.30701i | −0.191245 | + | 0.137771i | ||||
\(91\) | −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 | ||||||||
\(95\) | 9.00449 | − | 3.73085i | 0.923841 | − | 0.382777i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −9.26382 | + | 5.34847i | −0.940598 | + | 0.543055i | −0.890148 | − | 0.455672i | \(-0.849399\pi\) |
−0.0504506 | + | 0.998727i | \(0.516066\pi\) | |||||||
\(98\) | 1.73205 | − | 1.00000i | 0.174964 | − | 0.101015i | ||||
\(99\) | 1.00000 | − | 1.73205i | 0.100504 | − | 0.174078i | ||||
\(100\) | 3.31552 | + | 3.74264i | 0.331552 | + | 0.374264i | ||||
\(101\) | −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 | \(0.00158421\pi\) | ||||
−0.999988 | + | 0.00497692i | \(0.998416\pi\) | |||||||
\(104\) | 0.724745 | − | 1.25529i | 0.0710671 | − | 0.123092i | ||||
\(105\) | −2.75321 | + | 6.11717i | −0.268686 | + | 0.596975i | ||||
\(106\) | −12.8990 | −1.25286 | ||||||||
\(107\) | − | 5.55051i | − | 0.536588i | −0.963337 | − | 0.268294i | \(-0.913540\pi\) | ||
0.963337 | − | 0.268294i | \(-0.0864599\pi\) | |||||||
\(108\) | 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 | \(-0.400578\pi\) | |||||||
\(110\) | −4.07812 | − | 1.83548i | −0.388833 | − | 0.175006i | ||||
\(111\) | −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 | \(-0.922875\pi\) | ||
0.970790 | − | 0.239932i | \(-0.0771251\pi\) | |||||||
\(114\) | −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 | ||||
\(120\) | 0.917738 | − | 2.03906i | 0.0837776 | − | 0.186140i | ||||
\(121\) | −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 | −0.0747488 | − | 0.997202i | \(-0.523815\pi\) |
−0.900977 | + | 0.433867i | \(0.857149\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.72474 | + | 4.71940i | −0.239900 | + | 0.415520i | ||||
\(130\) | 1.89449 | + | 2.62983i | 0.166158 | + | 0.230651i | ||||
\(131\) | 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 | ||||||||
\(135\) | −1.81431 | + | 1.30701i | −0.156151 | + | 0.112489i | ||||
\(136\) | 2.44949 | + | 4.24264i | 0.210042 | + | 0.363803i | ||||
\(137\) | 9.43879 | + | 5.44949i | 0.806411 | + | 0.465581i | 0.845708 | − | 0.533646i | \(-0.179179\pi\) |
−0.0392973 | + | 0.999228i | \(0.512512\pi\) | |||||||
\(138\) | −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 | \(-0.390689\pi\) | |||||||
\(150\) | 3.31552 | + | 3.74264i | 0.270711 | + | 0.305585i | ||||
\(151\) | 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 | ||||
\(155\) | 2.48198 | + | 3.44534i | 0.199357 | + | 0.276737i | ||||
\(156\) | 0.724745 | − | 1.25529i | 0.0580260 | − | 0.100504i | ||||
\(157\) | −0.476756 | + | 0.275255i | −0.0380493 | + | 0.0219678i | −0.518904 | − | 0.854833i | \(-0.673660\pi\) |
0.480855 | + | 0.876800i | \(0.340326\pi\) | |||||||
\(158\) | 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 | \(-0.893979\pi\) | ||
0.945041 | − | 0.326951i | \(-0.106021\pi\) | |||||||
\(164\) | 2.44949 | 0.191273 | ||||||||
\(165\) | −4.07812 | − | 1.83548i | −0.317481 | − | 0.142892i | ||||
\(166\) | 6.67423 | + | 11.5601i | 0.518021 | + | 0.897239i | ||||
\(167\) | 3.28913 | + | 1.89898i | 0.254520 | + | 0.146947i | 0.621832 | − | 0.783150i | \(-0.286389\pi\) |
−0.367312 | + | 0.930098i | \(0.619722\pi\) | |||||||
\(168\) | −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 | −0.485129 | − | 0.874442i | \(-0.661227\pi\) |
0.514725 | + | 0.857355i | \(0.327894\pi\) | |||||||
\(174\) | −2.67423 | − | 4.63191i | −0.202733 | − | 0.351144i | ||||
\(175\) | 14.2279 | + | 4.75039i | 1.07553 | + | 0.359096i | ||||
\(176\) | −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 | \(0.575011\pi\) | |||||||
\(180\) | 0.917738 | − | 2.03906i | 0.0684041 | − | 0.151982i | ||||
\(181\) | 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 | ||||
\(185\) | −17.1443 | + | 12.3506i | −1.26048 | + | 0.908031i | ||||
\(186\) | 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 | ||||||||
\(190\) | −5.93269 | + | 7.73325i | −0.430403 | + | 0.561029i | ||||
\(191\) | 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 | −0.822708 | − | 0.568464i | \(-0.807538\pi\) |
0.0809508 | + | 0.996718i | \(0.474204\pi\) | |||||||
\(194\) | 5.34847 | − | 9.26382i | 0.383998 | − | 0.665104i | ||||
\(195\) | 1.89449 | + | 2.62983i | 0.135667 | + | 0.188326i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | 12.6969i | 0.904619i | 0.891861 | + | 0.452310i | \(0.149400\pi\) | ||||
−0.891861 | + | 0.452310i | \(0.850600\pi\) | |||||||
\(198\) | 2.00000i | 0.142134i | ||||||||
\(199\) | −8.94949 | + | 15.5010i | −0.634413 | + | 1.09883i | 0.352227 | + | 0.935915i | \(0.385425\pi\) |
−0.986639 | + | 0.162920i | \(0.947909\pi\) | |||||||
\(200\) | −4.74264 | − | 1.58346i | −0.335355 | − | 0.111968i | ||||
\(201\) | 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 | ||||
\(205\) | −2.24799 | + | 4.99465i | −0.157006 | + | 0.348842i | ||||
\(206\) | −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 | ||||
\(215\) | 11.1118 | + | 5.00120i | 0.757820 | + | 0.341079i | ||||
\(216\) | −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 | 0.0297846 | − | 0.999556i | \(-0.490518\pi\) |
0.880533 | + | 0.473984i | \(0.157185\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | 3.31552 | + | 3.74264i | 0.221034 | + | 0.249509i | ||||
\(226\) | 2.55051 | + | 4.41761i | 0.169657 | + | 0.293855i | ||||
\(227\) | − | 1.34847i | − | 0.0895010i | −0.998998 | − | 0.0447505i | \(-0.985751\pi\) | ||
0.998998 | − | 0.0447505i | \(-0.0142493\pi\) | |||||||
\(228\) | 4.24264 | + | 1.00000i | 0.280976 | + | 0.0662266i | ||||
\(229\) | 17.0454 | 1.12639 | 0.563196 | − | 0.826323i | \(-0.309572\pi\) | ||||
0.563196 | + | 0.826323i | \(0.309572\pi\) | |||||||
\(230\) | 3.20150 | + | 4.44414i | 0.211101 | + | 0.293038i | ||||
\(231\) | 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 | \(0.744536\pi\) |
−0.970226 | + | 0.242201i | \(0.922131\pi\) | |||||||
\(234\) | 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 | ||||
\(245\) | −2.61401 | − | 3.62863i | −0.167003 | − | 0.231824i | ||||
\(246\) | 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 | ||||
\(250\) | 7.58128 | − | 8.21731i | 0.479482 | − | 0.519709i | ||||
\(251\) | −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 | 0.726274 | − | 0.687405i | \(-0.241250\pi\) |
−0.232173 | + | 0.972674i | \(0.574584\pi\) | |||||||
\(258\) | − | 5.44949i | − | 0.339270i | ||||||
\(259\) | 28.3485 | 1.76149 | ||||||||
\(260\) | −2.95559 | − | 1.33025i | −0.183298 | − | 0.0824987i | ||||
\(261\) | −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 | −0.824833 | − | 0.565376i | \(-0.808731\pi\) |
0.0772134 | + | 0.997015i | \(0.475398\pi\) | |||||||
\(264\) | −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 | \(0.592799\pi\) | |||||||
\(270\) | 0.917738 | − | 2.03906i | 0.0558517 | − | 0.124093i | ||||
\(271\) | 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 | ||||||||
\(275\) | −3.16693 | + | 9.48528i | −0.190973 | + | 0.571984i | ||||
\(276\) | 1.22474 | − | 2.12132i | 0.0737210 | − | 0.127688i | ||||
\(277\) | − | 16.4949i | − | 0.991082i | −0.868584 | − | 0.495541i | \(-0.834970\pi\) | ||
0.868584 | − | 0.495541i | \(-0.165030\pi\) | |||||||
\(278\) | 11.4495i | 0.686695i | ||||||||
\(279\) | 0.949490 | − | 1.64456i | 0.0568445 | − | 0.0984575i | ||||
\(280\) | 3.92102 | + | 5.44294i | 0.234326 | + | 0.325278i | ||||
\(281\) | 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 | −0.522961 | − | 0.852357i | \(-0.675173\pi\) |
0.476682 | + | 0.879076i | \(0.341839\pi\) | |||||||
\(284\) | 8.44949 | 0.501385 | ||||||||
\(285\) | −5.93269 | + | 7.73325i | −0.351422 | + | 0.458078i | ||||
\(286\) | 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 | ||||
\(290\) | −9.70380 | + | 6.99049i | −0.569827 | + | 0.410496i | ||||
\(291\) | 5.34847 | − | 9.26382i | 0.313533 | − | 0.543055i | ||||
\(292\) | 2.10102i | 0.122953i | ||||||||
\(293\) | 9.10102i | 0.531687i | 0.964016 | + | 0.265844i | \(0.0856505\pi\) | ||||
−0.964016 | + | 0.265844i | \(0.914350\pi\) | |||||||
\(294\) | −1.00000 | + | 1.73205i | −0.0583212 | + | 0.101015i | ||||
\(295\) | 7.15648 | − | 15.9005i | 0.416666 | − | 0.925762i | ||||
\(296\) | −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 | ||||
\(300\) | −4.74264 | − | 1.58346i | −0.273816 | − | 0.0914214i | ||||
\(301\) | −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 | −0.930194 | − | 0.367068i | \(-0.880362\pi\) |
−0.147207 | + | 0.989106i | \(0.547028\pi\) | |||||||
\(308\) | −5.19615 | − | 3.00000i | −0.296078 | − | 0.170941i | ||||
\(309\) | −0.0505103 | − | 0.0874863i | −0.00287343 | − | 0.00497692i | ||||
\(310\) | −3.87213 | − | 1.74277i | −0.219922 | − | 0.0989824i | ||||
\(311\) | 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 | 0.964666 | − | 0.263477i | \(-0.0848692\pi\) |
0.254155 | + | 0.967163i | \(0.418203\pi\) | |||||||
\(314\) | 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 | −0.0144239 | − | 0.999896i | \(-0.504591\pi\) |
−0.873147 | + | 0.487457i | \(0.837925\pi\) | |||||||
\(318\) | 11.1708 | − | 6.44949i | 0.626430 | − | 0.361669i | ||||
\(319\) | 5.34847 | − | 9.26382i | 0.299457 | − | 0.518674i | ||||
\(320\) | −1.30701 | − | 1.81431i | −0.0730639 | − | 0.101423i | ||||
\(321\) | 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 | ||||||||
\(325\) | 5.42492 | − | 4.80581i | 0.300920 | − | 0.266578i | ||||
\(326\) | 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 | −0.134943 | − | 0.990853i | \(-0.543085\pi\) |
0.790633 | + | 0.612291i | \(0.209752\pi\) | |||||||
\(338\) | 9.43879 | + | 5.44949i | 0.513403 | + | 0.296413i | ||||
\(339\) | 2.55051 | + | 4.41761i | 0.138525 | + | 0.239932i | ||||
\(340\) | 8.88828 | − | 6.40300i | 0.482035 | − | 0.347252i | ||||
\(341\) | 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 | ||||
\(345\) | 3.20150 | + | 4.44414i | 0.172363 | + | 0.239265i | ||||
\(346\) | −0.224745 | + | 0.389270i | −0.0120824 | + | 0.0209273i | ||||
\(347\) | −17.7491 | + | 10.2474i | −0.952822 | + | 0.550112i | −0.893956 | − | 0.448154i | \(-0.852082\pi\) |
−0.0588654 | + | 0.998266i | \(0.518748\pi\) | |||||||
\(348\) | 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 | \(-0.886230\pi\) | ||
0.936803 | − | 0.349857i | \(-0.113770\pi\) | |||||||
\(354\) | −7.79796 | −0.414457 | ||||||||
\(355\) | −7.75442 | + | 17.2290i | −0.411562 | + | 0.914420i | ||||
\(356\) | 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 | ||||
\(365\) | −4.28410 | − | 1.92819i | −0.224240 | − | 0.100926i | ||||
\(366\) | −5.17423 | − | 8.96204i | −0.270462 | − | 0.468453i | ||||
\(367\) | −19.5686 | − | 11.2980i | −1.02147 | − | 0.589749i | −0.106944 | − | 0.994265i | \(-0.534107\pi\) |
−0.914531 | + | 0.404516i | \(0.867440\pi\) | |||||||
\(368\) | 2.44949i | 0.127688i | ||||||||
\(369\) | 2.44949 | 0.127515 | ||||||||
\(370\) | 8.67215 | − | 19.2681i | 0.450844 | − | 1.00170i | ||||
\(371\) | 19.3485 | − | 33.5125i | 1.00452 | − | 1.73988i | ||||
\(372\) | 1.89898i | 0.0984575i | ||||||||
\(373\) | 34.8990i | 1.80700i | 0.428587 | + | 0.903500i | \(0.359011\pi\) | ||||
−0.428587 | + | 0.903500i | \(0.640989\pi\) | |||||||
\(374\) | −4.89898 | + | 8.48528i | −0.253320 | + | 0.438763i | ||||
\(375\) | 7.58128 | − | 8.21731i | 0.391495 | − | 0.424340i | ||||
\(376\) | −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 | \(0.825771\pi\) | |||||||
\(380\) | 1.27123 | − | 9.66354i | 0.0652129 | − | 0.495729i | ||||
\(381\) | 12.6969 | 0.650484 | ||||||||
\(382\) | −12.7279 | + | 7.34847i | −0.651217 | + | 0.375980i | ||||
\(383\) | −11.5601 | + | 6.67423i | −0.590694 | + | 0.341037i | −0.765372 | − | 0.643588i | \(-0.777445\pi\) |
0.174678 | + | 0.984626i | \(0.444112\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 10.8859 | − | 7.84204i | 0.554796 | − | 0.399668i | ||||
\(386\) | 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 | \(0.250318\pi\) | |||||||
\(390\) | −2.95559 | − | 1.33025i | −0.149662 | − | 0.0673599i | ||||
\(391\) | −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 | ||||
\(395\) | 2.56779 | − | 5.70520i | 0.129200 | − | 0.287060i | ||||
\(396\) | −1.00000 | − | 1.73205i | −0.0502519 | − | 0.0870388i | ||||
\(397\) | 13.2047 | − | 7.62372i | 0.662724 | − | 0.382624i | −0.130590 | − | 0.991436i | \(-0.541687\pi\) |
0.793314 | + | 0.608813i | \(0.208354\pi\) | |||||||
\(398\) | − | 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 | ||||
\(405\) | 0.917738 | − | 2.03906i | 0.0456028 | − | 0.101322i | ||||
\(406\) | 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 | ||||
\(415\) | 24.2183 | − | 17.4465i | 1.18883 | − | 0.856417i | ||||
\(416\) | −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 | \(0.645301\pi\) | |||||||
\(420\) | 3.92102 | + | 5.44294i | 0.191326 | + | 0.265588i | ||||
\(421\) | −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 | 0.483303 | − | 0.875453i | \(-0.339437\pi\) |
−0.516513 | + | 0.856279i | \(0.672770\pi\) | |||||||
\(434\) | 2.84847 | + | 4.93369i | 0.136731 | + | 0.236825i | ||||
\(435\) | −9.70380 | + | 6.99049i | −0.465262 | + | 0.335168i | ||||
\(436\) | −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 | \(0.562623\pi\) | |||||||
\(440\) | −3.62863 | + | 2.61401i | −0.172988 | + | 0.124618i | ||||
\(441\) | −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 | 0.687841 | − | 0.725861i | \(-0.258558\pi\) |
−0.284693 | + | 0.958619i | \(0.591892\pi\) | |||||||
\(444\) | −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 | \(0.645441\pi\) | |||||||
\(450\) | −4.74264 | − | 1.58346i | −0.223570 | − | 0.0746452i | ||||
\(451\) | 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 | \(-0.811195\pi\) | ||
0.829185 | − | 0.558974i | \(-0.188805\pi\) | |||||||
\(458\) | −14.7618 | + | 8.52270i | −0.689772 | + | 0.398240i | ||||
\(459\) | 2.44949 | + | 4.24264i | 0.114332 | + | 0.198030i | ||||
\(460\) | −4.99465 | − | 2.24799i | −0.232877 | − | 0.104813i | ||||
\(461\) | −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 | \(0.238314\pi\) | ||||
−0.732583 | + | 0.680677i | \(0.761686\pi\) | |||||||
\(464\) | −5.34847 | −0.248296 | ||||||||
\(465\) | −3.87213 | − | 1.74277i | −0.179566 | − | 0.0808188i | ||||
\(466\) | 14.6742 | − | 25.4165i | 0.679771 | − | 1.17740i | ||||
\(467\) | − | 8.44949i | − | 0.390996i | −0.980704 | − | 0.195498i | \(-0.937368\pi\) | ||
0.980704 | − | 0.195498i | \(-0.0626323\pi\) | |||||||
\(468\) | 1.44949i | 0.0670027i | ||||||||
\(469\) | −5.17423 | + | 8.96204i | −0.238924 | + | 0.413828i | ||||
\(470\) | −11.0435 | − | 15.3300i | −0.509401 | − | 0.707121i | ||||
\(471\) | 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 | ||||||||
\(475\) | 18.5379 | + | 11.4607i | 0.850575 | + | 0.525853i | ||||
\(476\) | −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 | \(0.171735\pi\) | |||||||
\(480\) | −1.30701 | − | 1.81431i | −0.0596564 | − | 0.0828117i | ||||
\(481\) | 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 | ||||
\(485\) | −21.8117 | − | 9.81698i | −0.990417 | − | 0.445766i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − | 25.1010i | − | 1.13744i | −0.822533 | − | 0.568718i | \(-0.807440\pi\) | ||
0.822533 | − | 0.568718i | \(-0.192560\pi\) | |||||||
\(488\) | 8.96204 | + | 5.17423i | 0.405692 | + | 0.234227i | ||||
\(489\) | 4.17423 | + | 7.22999i | 0.188765 | + | 0.326951i | ||||
\(490\) | 4.07812 | + | 1.83548i | 0.184231 | + | 0.0829183i | ||||
\(491\) | −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 | \(0.590781\pi\) | |||||||
\(500\) | −2.45692 | + | 10.9070i | −0.109877 | + | 0.487778i | ||||
\(501\) | −3.79796 | −0.169680 | ||||||||
\(502\) | − | 8.69694i | − | 0.388163i | ||||||
\(503\) | −11.9494 | − | 6.89898i | −0.532797 | − | 0.307610i | 0.209358 | − | 0.977839i | \(-0.432863\pi\) |
−0.742155 | + | 0.670229i | \(0.766196\pi\) | |||||||
\(504\) | 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 | \(0.234553\pi\) | |||||||
\(510\) | 8.88828 | − | 6.40300i | 0.393580 | − | 0.283530i | ||||
\(511\) | 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 | ||||||||
\(515\) | −0.183283 | + | 0.132035i | −0.00807641 | + | 0.00581814i | ||||
\(516\) | 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 | 0.468403 | − | 0.883515i | \(-0.344829\pi\) |
−0.530945 | + | 0.847407i | \(0.678163\pi\) | |||||||
\(524\) | 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 | ||||
\(530\) | −16.8591 | − | 23.4028i | −0.732311 | − | 1.01655i | ||||
\(531\) | −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 | ||||
\(535\) | 10.0704 | − | 7.25456i | 0.435380 | − | 0.313642i | ||||
\(536\) | 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 | ||||||||
\(545\) | 12.8483 | − | 28.5468i | 0.550362 | − | 1.22281i | ||||
\(546\) | 2.17423 | + | 3.76588i | 0.0930487 | + | 0.161165i | ||||
\(547\) | −17.4473 | − | 10.0732i | −0.745993 | − | 0.430700i | 0.0782510 | − | 0.996934i | \(-0.475066\pi\) |
−0.824244 | + | 0.566234i | \(0.808400\pi\) | |||||||
\(548\) | 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 | ||||
\(555\) | 8.67215 | − | 19.2681i | 0.368112 | − | 0.817884i | ||||
\(556\) | −5.72474 | − | 9.91555i | −0.242783 | − | 0.420513i | ||||
\(557\) | 31.8198 | + | 18.3712i | 1.34825 | + | 0.778412i | 0.988001 | − | 0.154445i | \(-0.0493591\pi\) |
0.360247 | + | 0.932857i | \(0.382692\pi\) | |||||||
\(558\) | 1.89898i | 0.0803902i | ||||||||
\(559\) | −7.89898 | −0.334091 | ||||||||
\(560\) | −6.11717 | − | 2.75321i | −0.258498 | − | 0.116344i | ||||
\(561\) | −4.89898 | + | 8.48528i | −0.206835 | + | 0.358249i | ||||
\(562\) | 21.5505i | 0.909053i | ||||||||
\(563\) | − | 13.5959i | − | 0.573000i | −0.958080 | − | 0.286500i | \(-0.907508\pi\) | ||
0.958080 | − | 0.286500i | \(-0.0924918\pi\) | |||||||
\(564\) | −4.22474 | + | 7.31747i | −0.177894 | + | 0.308121i | ||||
\(565\) | 9.25485 | − | 6.66707i | 0.389354 | − | 0.280486i | ||||
\(566\) | 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 | \(0.339102\pi\) | |||||||
\(570\) | 1.27123 | − | 9.66354i | 0.0532461 | − | 0.404761i | ||||
\(571\) | −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 | ||||
\(575\) | 9.16756 | − | 8.12132i | 0.382314 | − | 0.338682i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 22.0000i | − | 0.915872i | −0.888985 | − | 0.457936i | \(-0.848589\pi\) | ||
0.888985 | − | 0.457936i | \(-0.151411\pi\) | |||||||
\(578\) | 7.00000i | 0.291162i | ||||||||
\(579\) | 5.94949 | − | 10.3048i | 0.247252 | − | 0.428254i | ||||
\(580\) | 4.90849 | − | 10.9058i | 0.203814 | − | 0.452840i | ||||
\(581\) | −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 | ||||
\(585\) | −2.95559 | − | 1.33025i | −0.122199 | − | 0.0549991i | ||||
\(586\) | −4.55051 | − | 7.88171i | −0.187980 | − | 0.325591i | ||||
\(587\) | −31.4305 | + | 18.1464i | −1.29728 | + | 0.748983i | −0.979933 | − | 0.199327i | \(-0.936124\pi\) |
−0.317344 | + | 0.948310i | \(0.602791\pi\) | |||||||
\(588\) | − | 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 | 0.744535 | − | 0.667583i | \(-0.232671\pi\) |
−0.205877 | + | 0.978578i | \(0.566005\pi\) | |||||||
\(594\) | −1.00000 | − | 1.73205i | −0.0410305 | − | 0.0710669i | ||||
\(595\) | 13.4879 | − | 29.9679i | 0.552951 | − | 1.22856i | ||||
\(596\) | −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 | ||||
\(605\) | −9.14905 | − | 12.7002i | −0.371962 | − | 0.516336i | ||||
\(606\) | 7.89898 | + | 13.6814i | 0.320874 | + | 0.555770i | ||||
\(607\) | 27.0000i | 1.09590i | 0.836512 | + | 0.547948i | \(0.184591\pi\) | ||||
−0.836512 | + | 0.547948i | \(0.815409\pi\) | |||||||
\(608\) | 2.98735 | − | 3.17423i | 0.121153 | − | 0.128732i | ||||
\(609\) | 16.0454 | 0.650193 | ||||||||
\(610\) | −18.7754 | + | 13.5255i | −0.760192 | + | 0.547632i | ||||
\(611\) | −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 | −0.0832904 | − | 0.996525i | \(-0.526543\pi\) |
0.821371 | + | 0.570394i | \(0.193210\pi\) | |||||||
\(614\) | 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 | \(0.0265691\pi\) |
0.570462 | + | 0.821324i | \(0.306764\pi\) | |||||||
\(618\) | 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 | ||||
\(625\) | −19.9853 | − | 15.0196i | −0.799411 | − | 0.600784i | ||||
\(626\) | −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 | ||||
\(630\) | 3.92102 | + | 5.44294i | 0.156217 | + | 0.216852i | ||||
\(631\) | −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 | ||||||||
\(640\) | 2.03906 | + | 0.917738i | 0.0806008 | + | 0.0362768i | ||||
\(641\) | 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 | −0.821872 | − | 0.569672i | \(-0.807070\pi\) |
0.0824140 | + | 0.996598i | \(0.473737\pi\) | |||||||
\(644\) | 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 | \(0.215287\pi\) | ||||
−0.779866 | + | 0.625946i | \(0.784713\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −7.79796 | − | 13.5065i | −0.306097 | − | 0.530175i | ||||
\(650\) | −2.29522 | + | 6.87441i | −0.0900258 | + | 0.269637i | ||||
\(651\) | 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 | \(-0.984738\pi\) | ||
0.998851 | − | 0.0479280i | \(-0.0152618\pi\) | |||||||
\(654\) | −14.0000 | −0.547443 | ||||||||
\(655\) | −10.8274 | + | 24.0567i | −0.423063 | + | 0.939974i | ||||
\(656\) | 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 | \(0.977876\pi\) | |||||||
\(660\) | −3.62863 | + | 2.61401i | −0.141244 | + | 0.101750i | ||||
\(661\) | −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 | ||||||||
\(665\) | −11.1925 | − | 27.0135i | −0.434028 | − | 1.04754i | ||||
\(666\) | −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 | ||||
\(670\) | 4.50851 | + | 6.25845i | 0.174179 | + | 0.241785i | ||||
\(671\) | 10.3485 | − | 17.9241i | 0.399498 | − | 0.691951i | ||||
\(672\) | 3.00000i | 0.115728i | ||||||||
\(673\) | − | 39.6969i | − | 1.53020i | −0.643909 | − | 0.765102i | \(-0.722688\pi\) | ||
0.643909 | − | 0.765102i | \(-0.277312\pi\) | |||||||
\(674\) | −6.94949 | + | 12.0369i | −0.267684 | + | 0.463643i | ||||
\(675\) | −4.74264 | − | 1.58346i | −0.182544 | − | 0.0609476i | ||||
\(676\) | −10.8990 | −0.419192 | ||||||||
\(677\) | − | 41.1464i | − | 1.58139i | −0.612213 | − | 0.790693i | \(-0.709721\pi\) | ||
0.612213 | − | 0.790693i | \(-0.290279\pi\) | |||||||
\(678\) | −4.41761 | − | 2.55051i | −0.169657 | − | 0.0979518i | ||||
\(679\) | 16.0454 | + | 27.7915i | 0.615766 | + | 1.06654i | ||||
\(680\) | −4.49598 | + | 9.98930i | −0.172413 | + | 0.383072i | ||||
\(681\) | 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 | \(-0.730142\pi\) | ||
0.661645 | − | 0.749817i | \(-0.269858\pi\) | |||||||
\(684\) | −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 | ||||
\(690\) | −4.99465 | − | 2.24799i | −0.190143 | − | 0.0855795i | ||||
\(691\) | 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 | ||||
\(700\) | 11.2279 | − | 9.94655i | 0.424376 | − | 0.375944i | ||||
\(701\) | 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 | ||||||||
\(705\) | −11.0435 | − | 15.3300i | −0.415924 | − | 0.577362i | ||||
\(706\) | 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 | \(0.578865\pi\) | |||||||
\(720\) | −1.30701 | − | 1.81431i | −0.0487093 | − | 0.0676155i | ||||
\(721\) | 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 | ||||
\(725\) | 17.7329 | + | 20.0174i | 0.658585 | + | 0.743428i | ||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | −6.23715 | + | 3.60102i | −0.231323 | + | 0.133554i | −0.611182 | − | 0.791490i | \(-0.709306\pi\) |
0.379859 | + | 0.925044i | \(0.375972\pi\) | |||||||
\(728\) | −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 | \(0.00766082\pi\) | ||||
−0.999710 | + | 0.0240648i | \(0.992339\pi\) | |||||||
\(734\) | 22.5959 | 0.834031 | ||||||||
\(735\) | 4.07812 | + | 1.83548i | 0.150424 | + | 0.0677025i | ||||
\(736\) | −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 | 0.462404 | − | 0.886669i | \(-0.346987\pi\) |
0.999080 | + | 0.0428813i | \(0.0136537\pi\) | |||||||
\(744\) | −0.949490 | − | 1.64456i | −0.0348100 | − | 0.0602927i | ||||
\(745\) | 14.4984 | − | 32.2130i | 0.531180 | − | 1.18019i | ||||
\(746\) | −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 | ||||||||
\(750\) | −2.45692 | + | 10.9070i | −0.0897140 | + | 0.398269i | ||||
\(751\) | 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 | ||||
\(755\) | 0.264069 | + | 0.366566i | 0.00961046 | + | 0.0133407i | ||||
\(756\) | 1.50000 | − | 2.59808i | 0.0545545 | − | 0.0944911i | ||||
\(757\) | −2.03383 | + | 1.17423i | −0.0739210 | + | 0.0426783i | −0.536505 | − | 0.843897i | \(-0.680256\pi\) |
0.462584 | + | 0.886575i | \(0.346922\pi\) | |||||||
\(758\) | 28.7931 | − | 16.6237i | 1.04581 | − | 0.603801i | ||||
\(759\) | 4.89898 | 0.177822 | ||||||||
\(760\) | 3.73085 | + | 9.00449i | 0.135332 | + | 0.326627i | ||||
\(761\) | 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 | ||||
\(765\) | 8.88828 | − | 6.40300i | 0.321357 | − | 0.231501i | ||||
\(766\) | 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 | \(0.921671\pi\) | |||||||
\(770\) | −5.50643 | + | 12.2343i | −0.198438 | + | 0.440895i | ||||
\(771\) | −9.14643 | −0.329401 | ||||||||
\(772\) | 11.8990i | 0.428254i | ||||||||
\(773\) | −25.2022 | − | 14.5505i | −0.906461 | − | 0.523345i | −0.0271702 | − | 0.999631i | \(-0.508650\pi\) |
−0.879291 | + | 0.476285i | \(0.841983\pi\) | |||||||
\(774\) | 2.72474 | + | 4.71940i | 0.0979389 | + | 0.169635i | ||||
\(775\) | −3.00697 | + | 9.00618i | −0.108013 | + | 0.323511i | ||||
\(776\) | −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 | ||||
\(785\) | −1.12252 | − | 0.505224i | −0.0400645 | − | 0.0180322i | ||||
\(786\) | 11.7980 | 0.420819 | ||||||||
\(787\) | 35.9444i | 1.28128i | 0.767842 | + | 0.640640i | \(0.221331\pi\) | ||||
−0.767842 | + | 0.640640i | \(0.778669\pi\) | |||||||
\(788\) | 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 | ||||
\(795\) | −16.8591 | − | 23.4028i | −0.597929 | − | 0.830011i | ||||
\(796\) | 8.94949 | + | 15.5010i | 0.317206 | + | 0.549417i | ||||
\(797\) | − | 1.10102i | − | 0.0390001i | −0.999810 | − | 0.0195001i | \(-0.993793\pi\) | ||
0.999810 | − | 0.0195001i | \(-0.00620746\pi\) | |||||||
\(798\) | −8.96204 | + | 9.52270i | −0.317253 | + | 0.337100i | ||||
\(799\) | 41.3939 | 1.46441 | ||||||||
\(800\) | −3.74264 | + | 3.31552i | −0.132322 | + | 0.117221i | ||||
\(801\) | 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 | ||||
\(815\) | 15.1467 | − | 10.9115i | 0.530567 | − | 0.382214i | ||||
\(816\) | 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 | ||||
\(820\) | 3.20150 | + | 4.44414i | 0.111801 | + | 0.155196i | ||||
\(821\) | −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 | \(0.0175180\pi\) |
0.546880 | + | 0.837211i | \(0.315815\pi\) | |||||||
\(824\) | −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 | \(-0.932576\pi\) |
−0.670897 | − | 0.741551i | \(-0.734091\pi\) | |||||||
\(828\) | 2.44949i | 0.0851257i | ||||||||
\(829\) | 51.4495 | 1.78691 | 0.893457 | − | 0.449148i | \(-0.148272\pi\) | ||||
0.893457 | + | 0.449148i | \(0.148272\pi\) | |||||||
\(830\) | −12.2504 | + | 27.2183i | −0.425217 | + | 0.944761i | ||||
\(831\) | 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 | \(-0.344433\pi\) | |||||||
\(840\) | −6.11717 | − | 2.75321i | −0.211063 | − | 0.0949949i | ||||
\(841\) | 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 | ||||||||
\(845\) | 10.0024 | − | 22.2237i | 0.344093 | − | 0.764517i | ||||
\(846\) | −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 | ||||
\(850\) | −16.2426 | − | 18.3351i | −0.557118 | − | 0.628889i | ||||
\(851\) | 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 | −0.679614 | − | 0.733570i | \(-0.737853\pi\) |
0.295483 | + | 0.955348i | \(0.404519\pi\) | |||||||
\(854\) | 31.0454 | 1.06235 | ||||||||
\(855\) | 1.27123 | − | 9.66354i | 0.0434753 | − | 0.330486i | ||||
\(856\) | 5.55051 | 0.189713 | ||||||||
\(857\) | −9.65309 | + | 5.57321i | −0.329743 | + | 0.190377i | −0.655727 | − | 0.754998i | \(-0.727638\pi\) |
0.325984 | + | 0.945375i | \(0.394304\pi\) | |||||||
\(858\) | −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 | \(-0.211102\pi\) | |||||||
\(860\) | 9.88708 | − | 7.12252i | 0.337147 | − | 0.242876i | ||||
\(861\) | −3.67423 | + | 6.36396i | −0.125218 | + | 0.216883i | ||||
\(862\) | − | 5.75255i | − | 0.195933i | ||||||
\(863\) | 27.7980i | 0.946254i | 0.880994 | + | 0.473127i | \(0.156875\pi\) | ||||
−0.880994 | + | 0.473127i | \(0.843125\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 0.916536 | + | 0.412514i | 0.0311631 | + | 0.0140259i | ||||
\(866\) | 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 | ||||
\(870\) | 4.90849 | − | 10.9058i | 0.166413 | − | 0.369743i | ||||
\(871\) | 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 | −0.995752 | − | 0.0920805i | \(-0.970648\pi\) |
−0.418132 | + | 0.908386i | \(0.637315\pi\) | |||||||
\(878\) | −27.2754 | − | 15.7474i | −0.920500 | − | 0.531451i | ||||
\(879\) | −4.55051 | − | 7.88171i | −0.153485 | − | 0.265844i | ||||
\(880\) | 1.83548 | − | 4.07812i | 0.0618739 | − | 0.137473i | ||||
\(881\) | 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 | 0.0340728 | − | 0.999419i | \(-0.489152\pi\) |
−0.848486 | + | 0.529218i | \(0.822486\pi\) | |||||||
\(884\) | −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 | 0.766929 | − | 0.641733i | \(-0.221784\pi\) |
−0.172292 | + | 0.985046i | \(0.555117\pi\) | |||||||
\(888\) | 8.18350 | − | 4.72474i | 0.274620 | − | 0.158552i | ||||
\(889\) | −19.0454 | + | 32.9876i | −0.638762 | + | 1.10637i | ||||
\(890\) | 29.8445 | − | 21.4996i | 1.00039 | − | 0.720668i | ||||
\(891\) | −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 | ||||||||
\(895\) | −8.16546 | − | 11.3348i | −0.272941 | − | 0.378882i | ||||
\(896\) | −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 | 0.0189790 | − | 0.999820i | \(-0.493958\pi\) |
0.875359 | + | 0.483474i | \(0.160625\pi\) | |||||||
\(908\) | −1.16781 | − | 0.674235i | −0.0387551 | − | 0.0223753i | ||||
\(909\) | 7.89898 | + | 13.6814i | 0.261993 | + | 0.453785i | ||||
\(910\) | 7.88948 | − | 5.68348i | 0.261534 | − | 0.188406i | ||||
\(911\) | −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 | ||||
\(915\) | −18.7754 | + | 13.5255i | −0.620694 | + | 0.447140i | ||||
\(916\) | 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 | ||||||||
\(925\) | −44.8155 | − | 14.9629i | −1.47353 | − | 0.491978i | ||||
\(926\) | −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 | ||||
\(935\) | 19.9786 | + | 8.99196i | 0.653370 | + | 0.294068i | ||||
\(936\) | −0.724745 | − | 1.25529i | −0.0236890 | − | 0.0410306i | ||||
\(937\) | −5.28364 | − | 3.05051i | −0.172609 | − | 0.0996558i | 0.411207 | − | 0.911542i | \(-0.365108\pi\) |
−0.583815 | + | 0.811886i | \(0.698441\pi\) | |||||||
\(938\) | − | 10.3485i | − | 0.337889i | ||||||
\(939\) | −24.8990 | −0.812547 | ||||||||
\(940\) | 17.2290 | + | 7.75442i | 0.561948 | + | 0.252921i | ||||
\(941\) | 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 | ||||
\(945\) | 3.92102 | + | 5.44294i | 0.127551 | + | 0.177059i | ||||
\(946\) | −5.44949 | + | 9.43879i | −0.177178 | + | 0.306882i | ||||
\(947\) | −40.2658 | + | 23.2474i | −1.30846 | + | 0.755441i | −0.981839 | − | 0.189714i | \(-0.939244\pi\) |
−0.326622 | + | 0.945155i | \(0.605910\pi\) | |||||||
\(948\) | 2.42310 | − | 1.39898i | 0.0786987 | − | 0.0454367i | ||||
\(949\) | 3.04541 | 0.0988581 | ||||||||
\(950\) | −21.7846 | − | 0.656339i | −0.706786 | − | 0.0212944i | ||||
\(951\) | 18.2474 | 0.591714 | ||||||||
\(952\) | 12.7279 | − | 7.34847i | 0.412514 | − | 0.238165i | ||||
\(953\) | 4.98186 | − | 2.87628i | 0.161378 | − | 0.0931717i | −0.417136 | − | 0.908844i | \(-0.636966\pi\) |
0.578514 | + | 0.815672i | \(0.303633\pi\) | |||||||
\(954\) | −6.44949 | + | 11.1708i | −0.208810 | + | 0.361669i | ||||
\(955\) | 19.2090 | + | 26.6648i | 0.621589 | + | 0.862854i | ||||
\(956\) | −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 | ||||
\(960\) | 2.03906 | + | 0.917738i | 0.0658103 | + | 0.0296199i | ||||
\(961\) | −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 | ||||
\(965\) | −24.2627 | − | 10.9201i | −0.781044 | − | 0.351532i | ||||
\(966\) | 3.67423 | + | 6.36396i | 0.118217 | + | 0.204757i | ||||
\(967\) | −33.8536 | + | 19.5454i | −1.08866 | + | 0.628538i | −0.933219 | − | 0.359307i | \(-0.883013\pi\) |
−0.155440 | + | 0.987845i | \(0.549680\pi\) | |||||||
\(968\) | − | 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 | ||||
\(975\) | −2.29522 | + | 6.87441i | −0.0735057 | + | 0.220157i | ||||
\(976\) | −10.3485 | −0.331246 | ||||||||
\(977\) | − | 20.2929i | − | 0.649226i | −0.945847 | − | 0.324613i | \(-0.894766\pi\) | ||
0.945847 | − | 0.324613i | \(-0.105234\pi\) | |||||||
\(978\) | −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 | −0.365301 | − | 0.930890i | \(-0.619034\pi\) |
0.623524 | + | 0.781805i | \(0.285701\pi\) | |||||||
\(984\) | 1.22474 | − | 2.12132i | 0.0390434 | − | 0.0676252i | ||||
\(985\) | −23.0362 | + | 16.5950i | −0.733995 | + | 0.528760i | ||||
\(986\) | 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 | ||||||||
\(990\) | −3.62863 | + | 2.61401i | −0.115325 | + | 0.0830788i | ||||
\(991\) | −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 | 0.321005 | − | 0.947077i | \(-0.395979\pi\) |
−0.659690 | + | 0.751537i | \(0.729313\pi\) | |||||||
\(998\) | −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.349.2 | yes | 8 | |
3.2 | odd | 2 | 1710.2.t.a.919.3 | 8 | |||
5.4 | even | 2 | inner | 570.2.q.a.349.3 | yes | 8 | |
15.14 | odd | 2 | 1710.2.t.a.919.2 | 8 | |||
19.11 | even | 3 | inner | 570.2.q.a.49.3 | yes | 8 | |
57.11 | odd | 6 | 1710.2.t.a.1189.2 | 8 | |||
95.49 | even | 6 | inner | 570.2.q.a.49.2 | ✓ | 8 | |
285.239 | odd | 6 | 1710.2.t.a.1189.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.a.49.2 | ✓ | 8 | 95.49 | even | 6 | inner | |
570.2.q.a.49.3 | yes | 8 | 19.11 | even | 3 | inner | |
570.2.q.a.349.2 | yes | 8 | 1.1 | even | 1 | trivial | |
570.2.q.a.349.3 | yes | 8 | 5.4 | even | 2 | inner | |
1710.2.t.a.919.2 | 8 | 15.14 | odd | 2 | |||
1710.2.t.a.919.3 | 8 | 3.2 | odd | 2 | |||
1710.2.t.a.1189.2 | 8 | 57.11 | odd | 6 | |||
1710.2.t.a.1189.3 | 8 | 285.239 | odd | 6 |