Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (of order \(4\), degree \(2\), not 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.32070 - 0.505727i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.49 |
Dual form | 1600.2.q.h.849.2 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.66366 | − | 1.66366i | −0.960517 | − | 0.960517i | 0.0387330 | − | 0.999250i | \(-0.487668\pi\) |
−0.999250 | + | 0.0387330i | \(0.987668\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.89402 | 1.09384 | 0.546919 | − | 0.837186i | \(-0.315801\pi\) | ||||
0.546919 | + | 0.837186i | \(0.315801\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.53555i | 0.845184i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.84462 | − | 1.84462i | −0.556175 | − | 0.556175i | 0.372041 | − | 0.928216i | \(-0.378658\pi\) |
−0.928216 | + | 0.372041i | \(0.878658\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.08011 | + | 3.08011i | 0.854268 | + | 0.854268i | 0.990656 | − | 0.136388i | \(-0.0435493\pi\) |
−0.136388 | + | 0.990656i | \(0.543549\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.29875i | 1.77021i | 0.465393 | + | 0.885104i | \(0.345913\pi\) | ||||
−0.465393 | + | 0.885104i | \(0.654087\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23593 | + | 1.23593i | −0.283542 | + | 0.283542i | −0.834520 | − | 0.550978i | \(-0.814255\pi\) |
0.550978 | + | 0.834520i | \(0.314255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.81468 | − | 4.81468i | −1.05065 | − | 1.05065i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.60490 | 0.960189 | 0.480094 | − | 0.877217i | \(-0.340602\pi\) | ||||
0.480094 | + | 0.877217i | \(0.340602\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.772683 | + | 0.772683i | −0.148703 | + | 0.148703i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.24680 | + | 4.24680i | −0.788611 | + | 0.788611i | −0.981266 | − | 0.192656i | \(-0.938290\pi\) |
0.192656 | + | 0.981266i | \(0.438290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.06299 | −0.370524 | −0.185262 | − | 0.982689i | \(-0.559313\pi\) | ||||
−0.185262 | + | 0.982689i | \(0.559313\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.13767i | 1.06843i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.17899 | − | 1.17899i | 0.193825 | − | 0.193825i | −0.603522 | − | 0.797346i | \(-0.706236\pi\) |
0.797346 | + | 0.603522i | \(0.206236\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 10.2485i | − | 1.64108i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.61484i | 0.720717i | 0.932814 | + | 0.360359i | \(0.117346\pi\) | ||||
−0.932814 | + | 0.360359i | \(0.882654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.03019 | + | 3.03019i | −0.462099 | + | 0.462099i | −0.899343 | − | 0.437244i | \(-0.855955\pi\) |
0.437244 | + | 0.899343i | \(0.355955\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.7111i | 1.70823i | 0.520081 | + | 0.854117i | \(0.325902\pi\) | ||||
−0.520081 | + | 0.854117i | \(0.674098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.37537 | 0.196481 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.1427 | − | 12.1427i | 1.70031 | − | 1.70031i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.73048 | − | 2.73048i | 0.375061 | − | 0.375061i | −0.494256 | − | 0.869316i | \(-0.664559\pi\) |
0.869316 | + | 0.494256i | \(0.164559\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.11235 | 0.544694 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.11306 | + | 3.11306i | 0.405285 | + | 0.405285i | 0.880091 | − | 0.474805i | \(-0.157482\pi\) |
−0.474805 | + | 0.880091i | \(0.657482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.34962 | − | 2.34962i | 0.300838 | − | 0.300838i | −0.540503 | − | 0.841342i | \(-0.681766\pi\) |
0.841342 | + | 0.540503i | \(0.181766\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.33795i | 0.924495i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.24311 | − | 8.24311i | −1.00706 | − | 1.00706i | −0.999975 | − | 0.00708173i | \(-0.997746\pi\) |
−0.00708173 | − | 0.999975i | \(-0.502254\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.66101 | − | 7.66101i | −0.922277 | − | 0.922277i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.25937i | 0.386816i | 0.981118 | + | 0.193408i | \(0.0619541\pi\) | ||||
−0.981118 | + | 0.193408i | \(0.938046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6877 | 1.48499 | 0.742494 | − | 0.669853i | \(-0.233643\pi\) | ||||
0.742494 | + | 0.669853i | \(0.233643\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.33839 | − | 5.33839i | −0.608365 | − | 0.608365i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.113885 | −0.0128130 | −0.00640652 | − | 0.999979i | \(-0.502039\pi\) | ||||
−0.00640652 | + | 0.999979i | \(0.502039\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1776 | 1.13085 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.76813 | + | 9.76813i | 1.07219 | + | 1.07219i | 0.997183 | + | 0.0750089i | \(0.0238985\pi\) |
0.0750089 | + | 0.997183i | \(0.476101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.1305 | 1.51495 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.74593i | 0.397068i | 0.980094 | + | 0.198534i | \(0.0636180\pi\) | ||||
−0.980094 | + | 0.198534i | \(0.936382\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.91390 | + | 8.91390i | 0.934430 | + | 0.934430i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.43212 | + | 3.43212i | 0.355894 | + | 0.355894i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.9853i | − | 1.41999i | −0.704206 | − | 0.709995i | \(-0.748697\pi\) | ||
0.704206 | − | 0.709995i | \(-0.251303\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.67714 | − | 4.67714i | 0.470071 | − | 0.470071i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.52228 | + | 3.52228i | 0.350480 | + | 0.350480i | 0.860288 | − | 0.509808i | \(-0.170284\pi\) |
−0.509808 | + | 0.860288i | \(0.670284\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.150216 | −0.0148013 | −0.00740063 | − | 0.999973i | \(-0.502356\pi\) | ||||
−0.00740063 | + | 0.999973i | \(0.502356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.75062 | + | 2.75062i | −0.265912 | + | 0.265912i | −0.827451 | − | 0.561539i | \(-0.810210\pi\) |
0.561539 | + | 0.827451i | \(0.310210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.90778 | − | 6.90778i | 0.661646 | − | 0.661646i | −0.294122 | − | 0.955768i | \(-0.595027\pi\) |
0.955768 | + | 0.294122i | \(0.0950273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.92288 | −0.372344 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.49507i | 0.328788i | 0.986395 | + | 0.164394i | \(0.0525669\pi\) | ||||
−0.986395 | + | 0.164394i | \(0.947433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.80977 | + | 7.80977i | −0.722014 | + | 0.722014i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.1228i | 1.93632i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 4.19472i | − | 0.381338i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.67755 | − | 7.67755i | 0.692261 | − | 0.692261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.25357i | − | 0.554915i | −0.960738 | − | 0.277458i | \(-0.910508\pi\) | ||
0.960738 | − | 0.277458i | \(-0.0894918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.0824 | 0.887708 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.16490 | − | 5.16490i | 0.451259 | − | 0.451259i | −0.444513 | − | 0.895772i | \(-0.646623\pi\) |
0.895772 | + | 0.444513i | \(0.146623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.57681 | + | 3.57681i | −0.310149 | + | 0.310149i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.9408 | 1.61823 | 0.809113 | − | 0.587654i | \(-0.199948\pi\) | ||||
0.809113 | + | 0.587654i | \(0.199948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.79057 | + | 2.79057i | 0.236693 | + | 0.236693i | 0.815479 | − | 0.578786i | \(-0.196473\pi\) |
−0.578786 | + | 0.815479i | \(0.696473\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.4833 | − | 19.4833i | 1.64079 | − | 1.64079i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.3633i | − | 0.950245i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.28815 | − | 2.28815i | −0.188723 | − | 0.188723i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.60372 | + | 1.60372i | 0.131382 | + | 0.131382i | 0.769740 | − | 0.638358i | \(-0.220386\pi\) |
−0.638358 | + | 0.769740i | \(0.720386\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.53754i | − | 0.206502i | −0.994655 | − | 0.103251i | \(-0.967076\pi\) | ||
0.994655 | − | 0.103251i | \(-0.0329245\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.5064 | −1.49615 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2405 | + | 10.2405i | 0.817278 | + | 0.817278i | 0.985713 | − | 0.168435i | \(-0.0538712\pi\) |
−0.168435 | + | 0.985713i | \(0.553871\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.08521 | −0.720504 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.3267 | 1.05029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.02607 | + | 8.02607i | 0.628650 | + | 0.628650i | 0.947728 | − | 0.319078i | \(-0.103373\pi\) |
−0.319078 | + | 0.947728i | \(0.603373\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.82611 | −0.528221 | −0.264110 | − | 0.964492i | \(-0.585078\pi\) | ||||
−0.264110 | + | 0.964492i | \(0.585078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.97411i | 0.459547i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.13377 | − | 3.13377i | −0.239645 | − | 0.239645i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.08901 | − | 5.08901i | −0.386910 | − | 0.386910i | 0.486674 | − | 0.873584i | \(-0.338210\pi\) |
−0.873584 | + | 0.486674i | \(0.838210\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 10.3582i | − | 0.778567i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.63797 | − | 1.63797i | 0.122428 | − | 0.122428i | −0.643238 | − | 0.765666i | \(-0.722410\pi\) |
0.765666 | + | 0.643238i | \(0.222410\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7757 | − | 16.7757i | −1.24693 | − | 1.24693i | −0.957071 | − | 0.289855i | \(-0.906393\pi\) |
−0.289855 | − | 0.957071i | \(-0.593607\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.81797 | −0.577921 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4635 | − | 13.4635i | 0.984546 | − | 0.984546i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.23616 | + | 2.23616i | −0.162657 | + | 0.162657i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.85815 | −0.423881 | −0.211940 | − | 0.977283i | \(-0.567978\pi\) | ||||
−0.211940 | + | 0.977283i | \(0.567978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.0241155i | 0.00173587i | 1.00000 | 0.000867935i | \(0.000276272\pi\) | |||||
−1.00000 | 0.000867935i | \(0.999724\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9086 | + | 14.9086i | −1.06219 | + | 1.06219i | −0.0642576 | + | 0.997933i | \(0.520468\pi\) |
−0.997933 | + | 0.0642576i | \(0.979532\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6525i | 0.967801i | 0.875123 | + | 0.483900i | \(0.160780\pi\) | ||||
−0.875123 | + | 0.483900i | \(0.839220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.4275i | 1.93459i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.2903 | + | 12.2903i | −0.862612 | + | 0.862612i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.6760i | 0.811537i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.55966 | 0.315398 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.45103 | − | 2.45103i | 0.168736 | − | 0.168736i | −0.617688 | − | 0.786424i | \(-0.711930\pi\) |
0.786424 | + | 0.617688i | \(0.211930\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.42249 | − | 5.42249i | 0.371543 | − | 0.371543i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.97033 | −0.405293 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.1081 | − | 21.1081i | −1.42636 | − | 1.42636i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.4809 | + | 22.4809i | −1.51223 | + | 1.51223i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.9483i | 0.934045i | 0.884245 | + | 0.467023i | \(0.154673\pi\) | ||||
−0.884245 | + | 0.467023i | \(0.845327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.43883 | − | 4.43883i | −0.294616 | − | 0.294616i | 0.544285 | − | 0.838901i | \(-0.316801\pi\) |
−0.838901 | + | 0.544285i | \(0.816801\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.35068 | + | 5.35068i | 0.353583 | + | 0.353583i | 0.861441 | − | 0.507858i | \(-0.169562\pi\) |
−0.507858 | + | 0.861441i | \(0.669562\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.7626i | 1.16869i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.9370 | −0.782019 | −0.391010 | − | 0.920387i | \(-0.627874\pi\) | ||||
−0.391010 | + | 0.920387i | \(0.627874\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.189466 | + | 0.189466i | 0.0123071 | + | 0.0123071i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.7720 | −1.08489 | −0.542445 | − | 0.840091i | \(-0.682501\pi\) | ||||
−0.542445 | + | 0.840091i | \(0.682501\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0294 | −1.41904 | −0.709519 | − | 0.704686i | \(-0.751088\pi\) | ||||
−0.709519 | + | 0.704686i | \(0.751088\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6141 | − | 14.6141i | −0.937495 | − | 0.937495i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.61360 | −0.484442 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 32.5018i | − | 2.05972i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.63925 | − | 6.63925i | −0.419066 | − | 0.419066i | 0.465816 | − | 0.884882i | \(-0.345761\pi\) |
−0.884882 | + | 0.465816i | \(0.845761\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.49432 | − | 8.49432i | −0.534033 | − | 0.534033i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.25821i | − | 0.452755i | −0.974040 | − | 0.226377i | \(-0.927312\pi\) | ||
0.974040 | − | 0.226377i | \(-0.0726883\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.41202 | − | 3.41202i | 0.212013 | − | 0.212013i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.7680 | − | 10.7680i | −0.666521 | − | 0.666521i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.27431 | 0.571878 | 0.285939 | − | 0.958248i | \(-0.407694\pi\) | ||||
0.285939 | + | 0.958248i | \(0.407694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.23197 | − | 6.23197i | 0.381390 | − | 0.381390i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4195 | − | 13.4195i | 0.818199 | − | 0.818199i | −0.167648 | − | 0.985847i | \(-0.553617\pi\) |
0.985847 | + | 0.167648i | \(0.0536173\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.5999 | −1.37285 | −0.686423 | − | 0.727202i | \(-0.740820\pi\) | ||||
−0.686423 | + | 0.727202i | \(0.740820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 29.6595i | − | 1.79507i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.2015 | + | 16.2015i | −0.973451 | + | 0.973451i | −0.999657 | − | 0.0262056i | \(-0.991658\pi\) |
0.0262056 | + | 0.999657i | \(0.491658\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 5.23082i | − | 0.313161i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.84793i | − | 0.527824i | −0.964547 | − | 0.263912i | \(-0.914987\pi\) | ||
0.964547 | − | 0.263912i | \(-0.0850128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3062 | − | 20.3062i | 1.20708 | − | 1.20708i | 0.235109 | − | 0.971969i | \(-0.424455\pi\) |
0.971969 | − | 0.235109i | \(-0.0755447\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.3555i | 0.788348i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −36.2718 | −2.13364 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.2668 | + | 23.2668i | −1.36392 | + | 1.36392i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.16936 | + | 7.16936i | −0.418839 | + | 0.418839i | −0.884803 | − | 0.465965i | \(-0.845707\pi\) |
0.465965 | + | 0.884803i | \(0.345707\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.85062 | 0.165410 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.1836 | + | 14.1836i | 0.820258 | + | 0.820258i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.76943 | + | 8.76943i | −0.505461 | + | 0.505461i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 11.7198i | − | 0.673284i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.4308 | + | 18.4308i | 1.05190 | + | 1.05190i | 0.998577 | + | 0.0533241i | \(0.0169816\pi\) |
0.0533241 | + | 0.998577i | \(0.483018\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.249910 | + | 0.249910i | 0.0142169 | + | 0.0142169i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 7.08961i | − | 0.402015i | −0.979590 | − | 0.201007i | \(-0.935578\pi\) | ||
0.979590 | − | 0.201007i | \(-0.0644215\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.0477 | 1.24621 | 0.623104 | − | 0.782139i | \(-0.285871\pi\) | ||||
0.623104 | + | 0.782139i | \(0.285871\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.19670 | − | 6.19670i | −0.348042 | − | 0.348042i | 0.511338 | − | 0.859380i | \(-0.329150\pi\) |
−0.859380 | + | 0.511338i | \(0.829150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.6675 | 0.877211 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.15220 | 0.510826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.02076 | − | 9.02076i | −0.501929 | − | 0.501929i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −22.9845 | −1.27104 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.8921i | 1.86853i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6174 | + | 18.6174i | 1.02330 | + | 1.02330i | 0.999722 | + | 0.0235823i | \(0.00750716\pi\) |
0.0235823 | + | 0.999722i | \(0.492493\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.98939 | + | 2.98939i | 0.163818 | + | 0.163818i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.2577i | 0.776666i | 0.921519 | + | 0.388333i | \(0.126949\pi\) | ||||
−0.921519 | + | 0.388333i | \(0.873051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.81462 | − | 5.81462i | 0.315807 | − | 0.315807i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.80544 | + | 3.80544i | 0.206076 | + | 0.206076i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.2778 | −0.878919 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.5395 | + | 23.5395i | −1.26367 | + | 1.26367i | −0.314363 | + | 0.949303i | \(0.601791\pi\) |
−0.949303 | + | 0.314363i | \(0.898209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.56682 | − | 1.56682i | 0.0838701 | − | 0.0838701i | −0.663927 | − | 0.747797i | \(-0.731112\pi\) |
0.747797 | + | 0.663927i | \(0.231112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.75989 | −0.254064 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.44678i | − | 0.502801i | −0.967883 | − | 0.251401i | \(-0.919109\pi\) | ||
0.967883 | − | 0.251401i | \(-0.0808912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.1412 | − | 35.1412i | 1.85987 | − | 1.85987i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.0452i | − | 0.952392i | −0.879339 | − | 0.476196i | \(-0.842015\pi\) | ||
0.879339 | − | 0.476196i | \(-0.157985\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9449i | 0.839208i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.97860 | + | 6.97860i | −0.366282 | + | 0.366282i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 29.1329i | − | 1.52073i | −0.649498 | − | 0.760363i | \(-0.725021\pi\) | ||
0.649498 | − | 0.760363i | \(-0.274979\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.7012 | −0.609139 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.90208 | − | 7.90208i | 0.410255 | − | 0.410255i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.35598 | − | 3.35598i | 0.173766 | − | 0.173766i | −0.614866 | − | 0.788632i | \(-0.710790\pi\) |
0.788632 | + | 0.614866i | \(0.210790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.1612 | −1.34737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6507 | + | 11.6507i | 0.598457 | + | 0.598457i | 0.939902 | − | 0.341445i | \(-0.110916\pi\) |
−0.341445 | + | 0.939902i | \(0.610916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4038 | + | 10.4038i | −0.533005 | + | 0.533005i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.8044i | − | 1.11415i | −0.830461 | − | 0.557077i | \(-0.811923\pi\) | ||
0.830461 | − | 0.557077i | \(-0.188077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.68320 | − | 7.68320i | −0.390559 | − | 0.390559i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8899 | + | 11.8899i | 0.602842 | + | 0.602842i | 0.941066 | − | 0.338224i | \(-0.109826\pi\) |
−0.338224 | + | 0.941066i | \(0.609826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.6101i | 1.69973i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.1853 | −0.866884 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.23905 | − | 9.23905i | −0.463694 | − | 0.463694i | 0.436170 | − | 0.899864i | \(-0.356335\pi\) |
−0.899864 | + | 0.436170i | \(0.856335\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.9012 | 0.595807 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4744 | −0.722818 | −0.361409 | − | 0.932407i | \(-0.617704\pi\) | ||||
−0.361409 | + | 0.932407i | \(0.617704\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.35422 | − | 6.35422i | −0.316526 | − | 0.316526i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.34958 | −0.215601 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.54117i | 0.471781i | 0.971780 | + | 0.235890i | \(0.0758006\pi\) | ||||
−0.971780 | + | 0.235890i | \(0.924199\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −31.5112 | − | 31.5112i | −1.55433 | − | 1.55433i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.00925 | + | 9.00925i | 0.443316 | + | 0.443316i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.28514i | − | 0.454695i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.837667 | − | 0.837667i | 0.0409227 | − | 0.0409227i | −0.686349 | − | 0.727272i | \(-0.740788\pi\) |
0.727272 | + | 0.686349i | \(0.240788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.9679 | + | 17.9679i | 0.875702 | + | 0.875702i | 0.993087 | − | 0.117385i | \(-0.0374511\pi\) |
−0.117385 | + | 0.993087i | \(0.537451\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.6940 | −1.44377 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.79986 | − | 6.79986i | 0.329068 | − | 0.329068i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.9047 | + | 18.9047i | −0.912726 | + | 0.912726i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.85473 | 0.185676 | 0.0928380 | − | 0.995681i | \(-0.470406\pi\) | ||||
0.0928380 | + | 0.995681i | \(0.470406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.5651i | 1.22858i | 0.789081 | + | 0.614289i | \(0.210557\pi\) | ||||
−0.789081 | + | 0.614289i | \(0.789443\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.69135 | + | 5.69135i | −0.272254 | + | 0.272254i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 30.1311i | − | 1.43808i | −0.694970 | − | 0.719039i | \(-0.744582\pi\) | ||
0.694970 | − | 0.719039i | \(-0.255418\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.48732i | 0.166063i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.1625 | + | 20.1625i | −0.957948 | + | 0.957948i | −0.999151 | − | 0.0412027i | \(-0.986881\pi\) |
0.0412027 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.33610i | − | 0.252389i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.5827 | 1.72644 | 0.863221 | − | 0.504826i | \(-0.168443\pi\) | ||||
0.863221 | + | 0.504826i | \(0.168443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.51265 | − | 8.51265i | 0.400845 | − | 0.400845i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.22161 | + | 4.22161i | −0.198349 | + | 0.198349i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.7340 | 0.782785 | 0.391392 | − | 0.920224i | \(-0.371994\pi\) | ||||
0.391392 | + | 0.920224i | \(0.371994\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.63962 | − | 5.63962i | −0.263235 | − | 0.263235i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.8377 | − | 11.8377i | 0.551335 | − | 0.551335i | −0.375491 | − | 0.926826i | \(-0.622526\pi\) |
0.926826 | + | 0.375491i | \(0.122526\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.2711i | − | 1.49976i | −0.661572 | − | 0.749882i | \(-0.730110\pi\) | ||
0.661572 | − | 0.749882i | \(-0.269890\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.22565 | − | 1.22565i | −0.0567163 | − | 0.0567163i | 0.678180 | − | 0.734896i | \(-0.262769\pi\) |
−0.734896 | + | 0.678180i | \(0.762769\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.8558 | − | 23.8558i | −1.10156 | − | 1.10156i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 34.0734i | − | 1.57002i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.1791 | 0.514016 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.92328 | + | 6.92328i | 0.316995 | + | 0.316995i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.8399 | 1.31773 | 0.658865 | − | 0.752261i | \(-0.271037\pi\) | ||||
0.658865 | + | 0.752261i | \(0.271037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.26282 | 0.331156 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.1711 | − | 22.1711i | −1.00882 | − | 1.00882i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.1668 | 1.45762 | 0.728808 | − | 0.684718i | \(-0.240075\pi\) | ||||
0.728808 | + | 0.684718i | \(0.240075\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 26.7054i | − | 1.20766i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.43607 | + | 5.43607i | 0.245326 | + | 0.245326i | 0.819049 | − | 0.573723i | \(-0.194501\pi\) |
−0.573723 | + | 0.819049i | \(0.694501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.9963 | − | 30.9963i | −1.39600 | − | 1.39600i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.43268i | 0.423114i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1282 | + | 17.1282i | −0.766762 | + | 0.766762i | −0.977535 | − | 0.210773i | \(-0.932402\pi\) |
0.210773 | + | 0.977535i | \(0.432402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.3564 | + | 11.3564i | 0.507365 | + | 0.507365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.5180 | 1.04862 | 0.524308 | − | 0.851529i | \(-0.324324\pi\) | ||||
0.524308 | + | 0.851529i | \(0.324324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.93890 | − | 9.93890i | 0.441402 | − | 0.441402i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3147 | + | 20.3147i | −0.900434 | + | 0.900434i | −0.995474 | − | 0.0950391i | \(-0.969702\pi\) |
0.0950391 | + | 0.995474i | \(0.469702\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.7186 | 1.62434 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.90997i | − | 0.0843271i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.6025 | − | 21.6025i | 0.950077 | − | 0.950077i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.9328i | 0.743268i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 35.5082i | − | 1.55564i | −0.628487 | − | 0.777820i | \(-0.716325\pi\) | ||
0.628487 | − | 0.777820i | \(-0.283675\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.677766 | + | 0.677766i | −0.0296366 | + | 0.0296366i | −0.721770 | − | 0.692133i | \(-0.756671\pi\) |
0.692133 | + | 0.721770i | \(0.256671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 15.0572i | − | 0.655904i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.79485 | −0.0780371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.89332 | + | 7.89332i | −0.342541 | + | 0.342541i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.2142 | + | 14.2142i | −0.615686 | + | 0.615686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.45007 | −0.235188 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.53704 | − | 2.53704i | −0.109278 | − | 0.109278i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.37099 | − | 5.37099i | 0.230917 | − | 0.230917i | −0.582158 | − | 0.813075i | \(-0.697792\pi\) |
0.813075 | + | 0.582158i | \(0.197792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 55.8181i | 2.39539i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.86782 | − | 8.86782i | −0.379161 | − | 0.379161i | 0.491639 | − | 0.870799i | \(-0.336398\pi\) |
−0.870799 | + | 0.491639i | \(0.836398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.95760 | + | 5.95760i | 0.254264 | + | 0.254264i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.4975i | − | 0.447209i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.329585 | −0.0140154 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.8089 | − | 22.8089i | −0.966446 | − | 0.966446i | 0.0330091 | − | 0.999455i | \(-0.489491\pi\) |
−0.999455 | + | 0.0330091i | \(0.989491\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.6666 | −0.789513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −44.7973 | −1.89135 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.9711 | + | 20.9711i | 0.883826 | + | 0.883826i | 0.993921 | − | 0.110095i | \(-0.0351156\pi\) |
−0.110095 | + | 0.993921i | \(0.535116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.4543 | 1.23696 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.05295i | 0.337597i | 0.985651 | + | 0.168799i | \(0.0539888\pi\) | ||||
−0.985651 | + | 0.168799i | \(0.946011\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5040 | + | 22.5040i | 0.941762 | + | 0.941762i | 0.998395 | − | 0.0566333i | \(-0.0180366\pi\) |
−0.0566333 | + | 0.998395i | \(0.518037\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.74599 | + | 9.74599i | 0.407144 | + | 0.407144i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.9819i | 0.665334i | 0.943044 | + | 0.332667i | \(0.107949\pi\) | ||||
−0.943044 | + | 0.332667i | \(0.892051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.0401200 | − | 0.0401200i | 0.00166733 | − | 0.00166733i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.2692 | + | 28.2692i | 1.17280 | + | 1.17280i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0734 | −0.417199 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.25752 | + | 5.25752i | −0.217001 | + | 0.217001i | −0.807233 | − | 0.590232i | \(-0.799036\pi\) |
0.590232 | + | 0.807233i | \(0.299036\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.54971 | − | 2.54971i | 0.105059 | − | 0.105059i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.6057 | 2.04050 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.96571i | − | 0.162852i | −0.996679 | − | 0.0814260i | \(-0.974053\pi\) | ||
0.996679 | − | 0.0814260i | \(-0.0259474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.7132 | − | 22.7132i | 0.929589 | − | 0.929589i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.31600i | 0.339783i | 0.985463 | + | 0.169891i | \(0.0543417\pi\) | ||||
−0.985463 | + | 0.169891i | \(0.945658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 46.0550i | − | 1.87862i | −0.343068 | − | 0.939310i | \(-0.611466\pi\) | ||
0.343068 | − | 0.939310i | \(-0.388534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.9009 | − | 20.9009i | 0.851149 | − | 0.851149i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.05760i | 0.205282i | 0.994718 | + | 0.102641i | \(0.0327292\pi\) | ||||
−0.994718 | + | 0.102641i | \(0.967271\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 40.8940 | 1.65711 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.0713 | + | 36.0713i | −1.45929 | + | 1.45929i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.2000 | − | 31.2000i | 1.26016 | − | 1.26016i | 0.309141 | − | 0.951016i | \(-0.399958\pi\) |
0.951016 | − | 0.309141i | \(-0.100042\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.7412 | −1.23759 | −0.618796 | − | 0.785551i | \(-0.712379\pi\) | ||||
−0.618796 | + | 0.785551i | \(0.712379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.8766 | − | 16.8766i | −0.678329 | − | 0.678329i | 0.281293 | − | 0.959622i | \(-0.409237\pi\) |
−0.959622 | + | 0.281293i | \(0.909237\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.55813 | + | 3.55813i | −0.142783 | + | 0.142783i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.8408i | 0.434328i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.58574 | − | 7.58574i | −0.302945 | − | 0.302945i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.60515 | + | 8.60515i | 0.343110 | + | 0.343110i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.7318i | − | 1.22342i | −0.791084 | − | 0.611708i | \(-0.790483\pi\) | ||
0.791084 | − | 0.611708i | \(-0.209517\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.15539 | −0.324147 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.23628 | + | 4.23628i | 0.167848 | + | 0.167848i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.26430 | −0.326931 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.1658 | 0.875496 | 0.437748 | − | 0.899098i | \(-0.355776\pi\) | ||||
0.437748 | + | 0.899098i | \(0.355776\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.975773 | + | 0.975773i | 0.0384807 | + | 0.0384807i | 0.726085 | − | 0.687605i | \(-0.241338\pi\) |
−0.687605 | + | 0.726085i | \(0.741338\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.2610 | −0.914484 | −0.457242 | − | 0.889342i | \(-0.651163\pi\) | ||||
−0.457242 | + | 0.889342i | \(0.651163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.4848i | − | 0.450819i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.93263 | + | 9.93263i | 0.389290 | + | 0.389290i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.9372 | + | 23.9372i | 0.936735 | + | 0.936735i | 0.998115 | − | 0.0613792i | \(-0.0195499\pi\) |
−0.0613792 | + | 0.998115i | \(0.519550\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32.1704i | 1.25509i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.1064 | + | 14.1064i | −0.549508 | + | 0.549508i | −0.926299 | − | 0.376790i | \(-0.877028\pi\) |
0.376790 | + | 0.926299i | \(0.377028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.04121 | − | 3.04121i | −0.118289 | − | 0.118289i | 0.645484 | − | 0.763774i | \(-0.276656\pi\) |
−0.763774 | + | 0.645484i | \(0.776656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 74.8014 | 2.90505 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5561 | + | 19.5561i | −0.757215 | + | 0.757215i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.2052 | − | 23.2052i | 0.897166 | − | 0.897166i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.66835 | −0.334638 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.3628i | 0.977662i | 0.872378 | + | 0.488831i | \(0.162577\pi\) | ||||
−0.872378 | + | 0.488831i | \(0.837423\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.36526 | + | 9.36526i | −0.359936 | + | 0.359936i | −0.863789 | − | 0.503853i | \(-0.831915\pi\) |
0.503853 | + | 0.863789i | \(0.331915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 40.4737i | − | 1.55324i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.7695i | 0.565967i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.20530 | + | 4.20530i | −0.160911 | + | 0.160911i | −0.782970 | − | 0.622059i | \(-0.786296\pi\) |
0.622059 | + | 0.782970i | \(0.286296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 17.8035i | − | 0.679245i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.8204 | 0.640804 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.79295 | + | 5.79295i | −0.220374 | + | 0.220374i | −0.808656 | − | 0.588282i | \(-0.799805\pi\) |
0.588282 | + | 0.808656i | \(0.299805\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.5358 | − | 13.5358i | 0.514181 | − | 0.514181i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −33.6826 | −1.27582 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8592 | + | 19.8592i | 0.751142 | + | 0.751142i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.258991 | + | 0.258991i | −0.00978196 | + | 0.00978196i | −0.711981 | − | 0.702199i | \(-0.752202\pi\) |
0.702199 | + | 0.711981i | \(0.252202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.91430i | 0.109915i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.1936 | + | 10.1936i | 0.383368 | + | 0.383368i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.751674 | + | 0.751674i | 0.0282297 | + | 0.0282297i | 0.721081 | − | 0.692851i | \(-0.243646\pi\) |
−0.692851 | + | 0.721081i | \(0.743646\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 0.288761i | − | 0.0108294i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.49986 | −0.355773 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.9029 | + | 27.9029i | 1.04205 | + | 1.04205i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.6557 | 1.47891 | 0.739455 | − | 0.673206i | \(-0.235083\pi\) | ||||
0.739455 | + | 0.673206i | \(0.235083\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.434730 | −0.0161902 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.6495 | + | 36.6495i | 1.36301 | + | 1.36301i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.2952 | 0.826881 | 0.413441 | − | 0.910531i | \(-0.364327\pi\) | ||||
0.413441 | + | 0.910531i | \(0.364327\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.0930i | 0.670112i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.1166 | − | 22.1166i | −0.818011 | − | 0.818011i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.2309 | − | 28.2309i | −1.04273 | − | 1.04273i | −0.999045 | − | 0.0436851i | \(-0.986090\pi\) |
−0.0436851 | − | 0.999045i | \(-0.513910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.4109i | 1.12020i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.45140 | + | 5.45140i | −0.200533 | + | 0.200533i | −0.800228 | − | 0.599695i | \(-0.795288\pi\) |
0.599695 | + | 0.800228i | \(0.295288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.6665 | + | 12.6665i | 0.465314 | + | 0.465314i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.5667 | −1.92849 | −0.964243 | − | 0.265020i | \(-0.914621\pi\) | ||||
−0.964243 | + | 0.265020i | \(0.914621\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −24.7676 | + | 24.7676i | −0.906200 | + | 0.906200i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.96035 | + | 7.96035i | −0.290865 | + | 0.290865i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.0189 | −1.13190 | −0.565948 | − | 0.824441i | \(-0.691490\pi\) | ||||
−0.565948 | + | 0.824441i | \(0.691490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.0910i | 0.805040i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.47389 | − | 2.47389i | 0.0899152 | − | 0.0899152i | −0.660719 | − | 0.750634i | \(-0.729748\pi\) |
0.750634 | + | 0.660719i | \(0.229748\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.2634i | 1.02590i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.48375i | − | 0.0900358i | −0.998986 | − | 0.0450179i | \(-0.985666\pi\) | ||
0.998986 | − | 0.0450179i | \(-0.0143345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.9913 | − | 19.9913i | 0.723733 | − | 0.723733i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.1771i | 0.692444i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.4690 | −1.56753 | −0.783767 | − | 0.621055i | \(-0.786704\pi\) | ||||
−0.783767 | + | 0.621055i | \(0.786704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0752 | + | 12.0752i | −0.434879 | + | 0.434879i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.297026 | − | 0.297026i | 0.0106833 | − | 0.0106833i | −0.701745 | − | 0.712428i | \(-0.747595\pi\) |
0.712428 | + | 0.701745i | \(0.247595\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.3529 | −0.407283 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.70363 | − | 5.70363i | −0.204354 | − | 0.204354i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.01231 | − | 6.01231i | 0.215137 | − | 0.215137i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.56286i | − | 0.234537i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6931 | + | 23.6931i | 0.844567 | + | 0.844567i | 0.989449 | − | 0.144882i | \(-0.0462802\pi\) |
−0.144882 | + | 0.989449i | \(0.546280\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.4293 | − | 15.4293i | −0.549299 | − | 0.549299i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1148i | 0.359641i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.4742 | 0.513993 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.2292 | + | 38.2292i | 1.35415 | + | 1.35415i | 0.880963 | + | 0.473186i | \(0.156896\pi\) |
0.473186 | + | 0.880963i | \(0.343104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −85.4762 | −3.02393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.49801 | −0.335596 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.4041 | − | 23.4041i | −0.825913 | − | 0.825913i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −44.6509 | −1.57179 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 53.8310i | − | 1.89260i | −0.323296 | − | 0.946298i | \(-0.604791\pi\) | ||
0.323296 | − | 0.946298i | \(-0.395209\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.0549 | − | 27.0549i | −0.950025 | − | 0.950025i | 0.0487847 | − | 0.998809i | \(-0.484465\pi\) |
−0.998809 | + | 0.0487847i | \(0.984465\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.5986 | + | 37.5986i | 1.31864 | + | 1.31864i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.49020i | − | 0.262049i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.6017 | + | 22.6017i | −0.789766 | + | 0.789766i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.2170 | − | 24.2170i | −0.845180 | − | 0.845180i | 0.144347 | − | 0.989527i | \(-0.453892\pi\) |
−0.989527 | + | 0.144347i | \(0.953892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.3013 | 1.43967 | 0.719836 | − | 0.694144i | \(-0.244217\pi\) | ||||
0.719836 | + | 0.694144i | \(0.244217\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.7264 | − | 15.7264i | 0.546862 | − | 0.546862i | −0.378670 | − | 0.925532i | \(-0.623618\pi\) |
0.925532 | + | 0.378670i | \(0.123618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.7323 | − | 20.7323i | 0.720061 | − | 0.720061i | −0.248556 | − | 0.968618i | \(-0.579956\pi\) |
0.968618 | + | 0.248556i | \(0.0799560\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 53.9075 | 1.87003 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0385i | 0.347813i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.59404 | − | 1.59404i | 0.0550980 | − | 0.0550980i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.6919i | 1.50841i | 0.656638 | + | 0.754206i | \(0.271978\pi\) | ||||
−0.656638 | + | 0.754206i | \(0.728022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.07060i | − | 0.243814i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.7200 | + | 14.7200i | −0.506983 | + | 0.506983i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 12.1396i | − | 0.417122i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −67.5654 | −2.31884 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.42913 | − | 5.42913i | 0.186108 | − | 0.186108i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.0610 | + | 35.0610i | −1.20046 | + | 1.20046i | −0.226439 | + | 0.974025i | \(0.572708\pi\) |
−0.974025 | + | 0.226439i | \(0.927292\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.3397 | 1.54878 | 0.774388 | − | 0.632711i | \(-0.218058\pi\) | ||||
0.774388 | + | 0.632711i | \(0.218058\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.1229 | + | 32.1229i | 1.09602 | + | 1.09602i | 0.994871 | + | 0.101147i | \(0.0322514\pi\) |
0.101147 | + | 0.994871i | \(0.467749\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.2190 | − | 22.2190i | 0.757221 | − | 0.757221i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 36.9142i | 1.25657i | 0.777981 | + | 0.628287i | \(0.216244\pi\) | ||||
−0.777981 | + | 0.628287i | \(0.783756\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 60.3441 | + | 60.3441i | 2.04939 | + | 2.04939i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.210075 | + | 0.210075i | 0.00712630 | + | 0.00712630i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 50.7793i | − | 1.72059i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.4604 | 1.20015 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7178 | − | 15.7178i | −0.530753 | − | 0.530753i | 0.390044 | − | 0.920796i | \(-0.372460\pi\) |
−0.920796 | + | 0.390044i | \(0.872460\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.8548 | 0.804603 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.16748 | 0.0393335 | 0.0196667 | − | 0.999807i | \(-0.493739\pi\) | ||||
0.0196667 | + | 0.999807i | \(0.493739\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.2410 | + | 32.2410i | 1.08500 | + | 1.08500i | 0.996035 | + | 0.0889621i | \(0.0283550\pi\) |
0.0889621 | + | 0.996035i | \(0.471645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.7282 | −1.43467 | −0.717336 | − | 0.696728i | \(-0.754639\pi\) | ||||
−0.717336 | + | 0.696728i | \(0.754639\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 18.0980i | − | 0.606987i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.7739 | − | 18.7739i | −0.628949 | − | 0.628949i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.4741 | − | 14.4741i | −0.484356 | − | 0.484356i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 47.1935i | − | 1.57574i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.76109 | − | 8.76109i | 0.292199 | − | 0.292199i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.9291 | + | 19.9291i | 0.663935 | + | 0.663935i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.1788 | 0.971008 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.23335 | − | 1.23335i | 0.0409528 | − | 0.0409528i | −0.686334 | − | 0.727287i | \(-0.740781\pi\) |
0.727287 | + | 0.686334i | \(0.240781\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.93093 | + | 8.93093i | −0.296220 | + | 0.296220i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.9284 | −0.792785 | −0.396392 | − | 0.918081i | \(-0.629738\pi\) | ||||
−0.396392 | + | 0.918081i | \(0.629738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 36.0371i | − | 1.19265i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.9473 | − | 14.9473i | 0.493605 | − | 0.493605i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 45.3844i | − | 1.49709i | −0.663082 | − | 0.748546i | \(-0.730752\pi\) | ||
0.663082 | − | 0.748546i | \(-0.269248\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 61.3253i | − | 2.02074i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.0392 | + | 10.0392i | −0.330444 | + | 0.330444i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 0.380882i | − | 0.0125098i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.51036 | 0.213598 | 0.106799 | − | 0.994281i | \(-0.465940\pi\) | ||||
0.106799 | + | 0.994281i | \(0.465940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.69986 | + | 1.69986i | −0.0557107 | + | 0.0557107i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.7947 | + | 11.7947i | −0.386142 | + | 0.386142i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.2986 | 1.31650 | 0.658248 | − | 0.752801i | \(-0.271298\pi\) | ||||
0.658248 | + | 0.752801i | \(0.271298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −36.6799 | − | 36.6799i | −1.19700 | − | 1.19700i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.10649 | − | 1.10649i | 0.0360705 | − | 0.0360705i | −0.688841 | − | 0.724912i | \(-0.741880\pi\) |
0.724912 | + | 0.688841i | \(0.241880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.2509i | 0.692025i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.83833 | + | 8.83833i | 0.287207 | + | 0.287207i | 0.835975 | − | 0.548768i | \(-0.184903\pi\) |
−0.548768 | + | 0.835975i | \(0.684903\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.0796 | + | 39.0796i | 1.26858 | + | 1.26858i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.6185i | 0.668600i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.9610 | 0.484636 | 0.242318 | − | 0.970197i | \(-0.422092\pi\) | ||||
0.242318 | + | 0.970197i | \(0.422092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −26.0654 | − | 26.0654i | −0.842576 | − | 0.842576i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 54.8152 | 1.77008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7441 | −0.862712 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.97433 | − | 6.97433i | −0.224745 | − | 0.224745i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.95287 | −0.127116 | −0.0635578 | − | 0.997978i | \(-0.520245\pi\) | ||||
−0.0635578 | + | 0.997978i | \(0.520245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.0150i | 0.964221i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.0538 | + | 29.0538i | 0.932380 | + | 0.932380i | 0.997854 | − | 0.0654740i | \(-0.0208560\pi\) |
−0.0654740 | + | 0.997854i | \(0.520856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.07597 | + | 8.07597i | 0.258904 | + | 0.258904i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8962i | 0.828494i | 0.910164 | + | 0.414247i | \(0.135955\pi\) | ||||
−0.910164 | + | 0.414247i | \(0.864045\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.90984 | − | 6.90984i | 0.220839 | − | 0.220839i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.5151 | + | 17.5151i | 0.559213 | + | 0.559213i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.0151 | −0.702173 | −0.351087 | − | 0.936343i | \(-0.614188\pi\) | ||||
−0.351087 | + | 0.936343i | \(0.614188\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 56.3850 | − | 56.3850i | 1.79476 | − | 1.79476i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.9537 | + | 13.9537i | −0.443702 | + | 0.443702i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.3207 | 1.72556 | 0.862778 | − | 0.505583i | \(-0.168723\pi\) | ||||
0.862778 | + | 0.505583i | \(0.168723\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 61.9461i | − | 1.96580i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.14405 | + | 8.14405i | −0.257925 | + | 0.257925i | −0.824210 | − | 0.566285i | \(-0.808380\pi\) |
0.566285 | + | 0.824210i | \(0.308380\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.82197i | 0.0576446i |
(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 | 1600.2.q.h.49.2 | 16 | ||
4.3 | odd | 2 | 400.2.q.g.149.2 | 16 | |||
5.2 | odd | 4 | 1600.2.l.i.1201.2 | 16 | |||
5.3 | odd | 4 | 320.2.l.a.241.7 | 16 | |||
5.4 | even | 2 | 1600.2.q.g.49.7 | 16 | |||
15.8 | even | 4 | 2880.2.t.c.2161.6 | 16 | |||
16.3 | odd | 4 | 400.2.q.h.349.7 | 16 | |||
16.13 | even | 4 | 1600.2.q.g.849.7 | 16 | |||
20.3 | even | 4 | 80.2.l.a.21.4 | ✓ | 16 | ||
20.7 | even | 4 | 400.2.l.h.101.5 | 16 | |||
20.19 | odd | 2 | 400.2.q.h.149.7 | 16 | |||
40.3 | even | 4 | 640.2.l.b.481.7 | 16 | |||
40.13 | odd | 4 | 640.2.l.a.481.2 | 16 | |||
60.23 | odd | 4 | 720.2.t.c.181.5 | 16 | |||
80.3 | even | 4 | 80.2.l.a.61.4 | yes | 16 | ||
80.13 | odd | 4 | 320.2.l.a.81.7 | 16 | |||
80.19 | odd | 4 | 400.2.q.g.349.2 | 16 | |||
80.29 | even | 4 | inner | 1600.2.q.h.849.2 | 16 | ||
80.43 | even | 4 | 640.2.l.b.161.7 | 16 | |||
80.53 | odd | 4 | 640.2.l.a.161.2 | 16 | |||
80.67 | even | 4 | 400.2.l.h.301.5 | 16 | |||
80.77 | odd | 4 | 1600.2.l.i.401.2 | 16 | |||
160.3 | even | 8 | 5120.2.a.v.1.1 | 8 | |||
160.13 | odd | 8 | 5120.2.a.u.1.1 | 8 | |||
160.83 | even | 8 | 5120.2.a.s.1.8 | 8 | |||
160.93 | odd | 8 | 5120.2.a.t.1.8 | 8 | |||
240.83 | odd | 4 | 720.2.t.c.541.5 | 16 | |||
240.173 | even | 4 | 2880.2.t.c.721.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.4 | ✓ | 16 | 20.3 | even | 4 | ||
80.2.l.a.61.4 | yes | 16 | 80.3 | even | 4 | ||
320.2.l.a.81.7 | 16 | 80.13 | odd | 4 | |||
320.2.l.a.241.7 | 16 | 5.3 | odd | 4 | |||
400.2.l.h.101.5 | 16 | 20.7 | even | 4 | |||
400.2.l.h.301.5 | 16 | 80.67 | even | 4 | |||
400.2.q.g.149.2 | 16 | 4.3 | odd | 2 | |||
400.2.q.g.349.2 | 16 | 80.19 | odd | 4 | |||
400.2.q.h.149.7 | 16 | 20.19 | odd | 2 | |||
400.2.q.h.349.7 | 16 | 16.3 | odd | 4 | |||
640.2.l.a.161.2 | 16 | 80.53 | odd | 4 | |||
640.2.l.a.481.2 | 16 | 40.13 | odd | 4 | |||
640.2.l.b.161.7 | 16 | 80.43 | even | 4 | |||
640.2.l.b.481.7 | 16 | 40.3 | even | 4 | |||
720.2.t.c.181.5 | 16 | 60.23 | odd | 4 | |||
720.2.t.c.541.5 | 16 | 240.83 | odd | 4 | |||
1600.2.l.i.401.2 | 16 | 80.77 | odd | 4 | |||
1600.2.l.i.1201.2 | 16 | 5.2 | odd | 4 | |||
1600.2.q.g.49.7 | 16 | 5.4 | even | 2 | |||
1600.2.q.g.849.7 | 16 | 16.13 | even | 4 | |||
1600.2.q.h.49.2 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.q.h.849.2 | 16 | 80.29 | even | 4 | inner | ||
2880.2.t.c.721.7 | 16 | 240.173 | even | 4 | |||
2880.2.t.c.2161.6 | 16 | 15.8 | even | 4 | |||
5120.2.a.s.1.8 | 8 | 160.83 | even | 8 | |||
5120.2.a.t.1.8 | 8 | 160.93 | odd | 8 | |||
5120.2.a.u.1.1 | 8 | 160.13 | odd | 8 | |||
5120.2.a.v.1.1 | 8 | 160.3 | even | 8 |