Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [592,2,Mod(319,592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(592, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("592.319");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 592 = 2^{4} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 592.be (of order \(12\), degree \(4\), 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: | \(4.72714379966\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 8.0.1234538496.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 24x^{6} - 58x^{5} + 167x^{4} - 242x^{3} + 394x^{2} - 282x + 241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 399.1 | ||
Root | \(0.500000 + 2.27030i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 592.399 |
Dual form | 592.2.be.c.319.1 |
$q$-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 \(\left(\mathbb{Z}/592\mathbb{Z}\right)^\times\).
\(n\) | \(113\) | \(149\) | \(223\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.36603 | − | 2.36603i | 0.788675 | − | 1.36603i | −0.138104 | − | 0.990418i | \(-0.544101\pi\) |
0.926779 | − | 0.375608i | \(-0.122566\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.06816 | − | 3.98644i | −0.477698 | − | 1.78279i | −0.610905 | − | 0.791704i | \(-0.709194\pi\) |
0.133207 | − | 0.991088i | \(-0.457472\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.33847 | − | 1.35012i | −0.883858 | − | 0.510296i | −0.0119294 | − | 0.999929i | \(-0.503797\pi\) |
−0.871928 | + | 0.489633i | \(0.837131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23205 | − | 3.86603i | −0.744017 | − | 1.28868i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.86838 | 1.16636 | 0.583180 | − | 0.812343i | \(-0.301808\pi\) | ||||
0.583180 | + | 0.812343i | \(0.301808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.36603 | + | 5.09808i | 0.378867 | + | 1.41395i | 0.847611 | + | 0.530618i | \(0.178040\pi\) |
−0.468744 | + | 0.883334i | \(0.655293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.8912 | − | 2.91828i | −2.81209 | − | 0.753497i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.70258 | + | 1.79595i | 1.62562 | + | 0.435582i | 0.952644 | − | 0.304086i | \(-0.0983512\pi\) |
0.672971 | + | 0.739669i | \(0.265018\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.48644 | + | 0.934190i | −0.799845 | + | 0.214318i | −0.635516 | − | 0.772088i | \(-0.719213\pi\) |
−0.164329 | + | 0.986406i | \(0.552546\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.38881 | + | 3.68858i | −1.39415 | + | 0.804915i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.40428 | − | 3.40428i | −0.709841 | − | 0.709841i | 0.256661 | − | 0.966502i | \(-0.417378\pi\) |
−0.966502 | + | 0.256661i | \(0.917378\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.4206 | + | 6.01636i | −2.08413 | + | 1.20327i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.545822 | − | 0.545822i | −0.101357 | − | 0.101357i | 0.654610 | − | 0.755967i | \(-0.272833\pi\) |
−0.755967 | + | 0.654610i | \(0.772833\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.98454 | − | 4.98454i | 0.895249 | − | 0.895249i | −0.0997623 | − | 0.995011i | \(-0.531808\pi\) |
0.995011 | + | 0.0997623i | \(0.0318082\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.28431 | − | 9.15268i | 0.919879 | − | 1.59328i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.88429 | + | 10.7643i | −0.487534 | + | 1.81950i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.28621 | + | 5.63677i | 0.375851 | + | 0.926680i | ||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.9282 | + | 3.73205i | 2.23030 | + | 0.597606i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | + | 0.866025i | 0.234261 | + | 0.135250i | 0.612536 | − | 0.790443i | \(-0.290149\pi\) |
−0.378275 | + | 0.925693i | \(0.623483\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.58407 | − | 3.58407i | −0.546566 | − | 0.546566i | 0.378880 | − | 0.925446i | \(-0.376309\pi\) |
−0.925446 | + | 0.378880i | \(0.876309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.0275 | + | 13.0275i | −1.94202 | + | 1.94202i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.03182i | − | 0.588101i | −0.955790 | − | 0.294051i | \(-0.904997\pi\) | ||
0.955790 | − | 0.294051i | \(-0.0950035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.145622 | + | 0.252224i | 0.0208031 | + | 0.0360320i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.4052 | − | 13.4052i | 1.87710 | − | 1.87710i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.700230 | + | 1.21283i | 0.0961840 | + | 0.166596i | 0.910102 | − | 0.414384i | \(-0.136003\pi\) |
−0.813918 | + | 0.580980i | \(0.802670\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.13207 | − | 15.4211i | −0.557168 | − | 2.07938i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.55225 | + | 9.52514i | −0.338054 | + | 1.26164i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.28431 | + | 8.52514i | −0.297391 | + | 1.10988i | 0.641909 | + | 0.766781i | \(0.278143\pi\) |
−0.939300 | + | 0.343098i | \(0.888524\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.30900 | − | 1.42254i | 0.679748 | − | 0.182138i | 0.0976061 | − | 0.995225i | \(-0.468881\pi\) |
0.582142 | + | 0.813087i | \(0.302215\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.0541i | 1.51867i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 18.8641 | − | 10.8912i | 2.33980 | − | 1.35088i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.93419 | − | 8.54627i | 0.602807 | − | 1.04409i | −0.389587 | − | 0.920990i | \(-0.627382\pi\) |
0.992394 | − | 0.123103i | \(-0.0392845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.7049 | + | 3.40428i | −1.52949 | + | 0.409827i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.75058 | − | 2.74275i | −0.563790 | − | 0.325504i | 0.190876 | − | 0.981614i | \(-0.438867\pi\) |
−0.754665 | + | 0.656110i | \(0.772201\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.34916i | − | 0.509031i | −0.967069 | − | 0.254516i | \(-0.918084\pi\) | ||
0.967069 | − | 0.254516i | \(-0.0819160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 32.8740i | 3.79596i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.04608 | − | 5.22276i | −1.03090 | − | 0.595189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.71614 | + | 0.995737i | −0.418098 | + | 0.112029i | −0.461734 | − | 0.887018i | \(-0.652773\pi\) |
0.0436357 | + | 0.999048i | \(0.486106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.23205 | − | 2.13397i | 0.136895 | − | 0.237108i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.945391 | − | 0.545822i | 0.103770 | − | 0.0599117i | −0.447217 | − | 0.894426i | \(-0.647585\pi\) |
0.550987 | + | 0.834514i | \(0.314251\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 28.6379i | − | 3.10621i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.03704 | + | 0.545822i | −0.218393 | + | 0.0585183i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.29048 | + | 4.81613i | −0.136790 | + | 0.510508i | 0.863194 | + | 0.504873i | \(0.168461\pi\) |
−0.999984 | + | 0.00563563i | \(0.998206\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.68858 | − | 13.7660i | 0.386669 | − | 1.44307i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.98454 | − | 18.6025i | −0.516872 | − | 1.92899i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.44819 | + | 12.9006i | 0.764168 | + | 1.32358i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.14276 | − | 1.14276i | 0.116030 | − | 0.116030i | −0.646708 | − | 0.762738i | \(-0.723855\pi\) |
0.762738 | + | 0.646708i | \(0.223855\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.63442 | − | 14.9553i | −0.867792 | − | 1.50306i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.03182i | 0.102670i | 0.998681 | + | 0.0513350i | \(0.0163476\pi\) | ||||
−0.998681 | + | 0.0513350i | \(0.983652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.47575 | + | 6.47575i | −0.638074 | + | 0.638074i | −0.950080 | − | 0.312006i | \(-0.898999\pi\) |
0.312006 | + | 0.950080i | \(0.398999\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.5286 | + | 21.5286i | 2.10098 | + | 2.10098i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.721175 | + | 0.416371i | 0.0697187 | + | 0.0402521i | 0.534454 | − | 0.845197i | \(-0.320517\pi\) |
−0.464735 | + | 0.885450i | \(0.653851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.42776 | + | 2.25821i | 0.807233 | + | 0.216297i | 0.638757 | − | 0.769408i | \(-0.279449\pi\) |
0.168476 | + | 0.985706i | \(0.446116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.4598 | + | 2.29074i | 1.56229 | + | 0.217427i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.108326 | − | 0.404278i | 0.0101905 | − | 0.0380313i | −0.960643 | − | 0.277785i | \(-0.910400\pi\) |
0.970834 | + | 0.239753i | \(0.0770665\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.93464 | + | 17.2073i | −0.926410 | + | 1.60459i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.6603 | − | 16.6603i | 1.54024 | − | 1.54024i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.2490 | − | 13.2490i | −1.21454 | − | 1.21454i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.96436 | 0.360397 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.09808 | − | 2.36603i | 0.369511 | − | 0.213337i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 20.5234 | + | 20.5234i | 1.83567 | + | 1.83567i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.20729 | + | 3.00643i | −0.462073 | + | 0.266778i | −0.712915 | − | 0.701250i | \(-0.752626\pi\) |
0.250843 | + | 0.968028i | \(0.419292\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.3759 | + | 3.58407i | −1.17769 | + | 0.315560i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.65033 | + | 2.04990i | 0.668412 | + | 0.179101i | 0.577040 | − | 0.816716i | \(-0.304208\pi\) |
0.0913729 | + | 0.995817i | \(0.470874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.41420 | + | 2.52253i | 0.816315 | + | 0.218731i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.27266 | + | 15.9458i | 0.367732 | + | 1.37239i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.16815 | 0.526981 | 0.263490 | − | 0.964662i | \(-0.415126\pi\) | ||||
0.263490 | + | 0.964662i | \(0.415126\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.722127 | − | 1.25076i | −0.0612500 | − | 0.106088i | 0.833774 | − | 0.552105i | \(-0.186175\pi\) |
−0.895024 | + | 0.446017i | \(0.852842\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.53939 | − | 5.50757i | −0.803362 | − | 0.463821i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.28431 | + | 19.7213i | 0.441896 | + | 1.64918i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.59286 | + | 2.75892i | −0.132280 | + | 0.229116i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.795692 | 0.0656276 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.51350 | 0.123990 | 0.0619952 | − | 0.998076i | \(-0.480254\pi\) | ||||
0.0619952 | + | 0.998076i | \(0.480254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.66198 | + | 6.34273i | −0.298008 | + | 0.516164i | −0.975680 | − | 0.219200i | \(-0.929655\pi\) |
0.677673 | + | 0.735364i | \(0.262989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.01731 | − | 29.9210i | −0.648161 | − | 2.41897i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −25.1949 | − | 14.5463i | −2.02370 | − | 1.16838i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.60406 | − | 6.24242i | −0.287636 | − | 0.498199i | 0.685609 | − | 0.727970i | \(-0.259536\pi\) |
−0.973245 | + | 0.229770i | \(0.926203\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.82613 | 0.303432 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.36463 | + | 12.5570i | 0.265170 | + | 0.989627i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.0921 | + | 3.50801i | 1.02545 | + | 0.274769i | 0.732072 | − | 0.681227i | \(-0.238553\pi\) |
0.293379 | + | 0.955996i | \(0.405220\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −42.1312 | − | 11.2890i | −3.27991 | − | 0.878849i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.1256 | − | 5.39263i | 1.55736 | − | 0.417294i | 0.625536 | − | 0.780195i | \(-0.284880\pi\) |
0.931828 | + | 0.362901i | \(0.118214\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8660 | + | 7.42820i | −0.989694 | + | 0.571400i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.3935 | + | 11.3935i | 0.871284 | + | 0.871284i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9861 | + | 8.65224i | −1.13937 | + | 0.657818i | −0.946275 | − | 0.323362i | \(-0.895187\pi\) |
−0.193098 | + | 0.981179i | \(0.561854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 32.4911 | 2.45610 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.0503 | + | 17.0503i | 1.28158 | + | 1.28158i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1652 | + | 14.1652i | −1.05876 | + | 1.05876i | −0.0605961 | + | 0.998162i | \(0.519300\pi\) |
−0.998162 | + | 0.0605961i | \(0.980700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.37908 | + | 11.0489i | −0.474153 | + | 0.821257i | −0.999562 | − | 0.0295928i | \(-0.990579\pi\) |
0.525409 | + | 0.850850i | \(0.323912\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.88646 | − | 14.5045i | 0.287295 | − | 1.07220i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0286 | − | 15.1349i | 1.47253 | − | 1.11274i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.9281 | + | 6.94742i | 1.89605 | + | 0.508046i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.35387 | + | 5.40046i | 0.680394 | + | 0.392826i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8094 | + | 13.8094i | 0.999217 | + | 0.999217i | 1.00000 | 0.000783154i | \(-0.000249286\pi\) | |
−0.000783154 | 1.00000i | \(0.500249\pi\) | ||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8581 | − | 12.8581i | 0.925548 | − | 0.925548i | −0.0718659 | − | 0.997414i | \(-0.522895\pi\) |
0.997414 | + | 0.0718659i | \(0.0228954\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 59.5104i | − | 4.26163i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.90994 | + | 13.7004i | 0.563560 | + | 0.976114i | 0.997182 | + | 0.0750195i | \(0.0239019\pi\) |
−0.433622 | + | 0.901095i | \(0.642765\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.77641 | − | 9.77641i | 0.693031 | − | 0.693031i | −0.269866 | − | 0.962898i | \(-0.586980\pi\) |
0.962898 | + | 0.269866i | \(0.0869796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.4805 | − | 23.3488i | −0.950838 | − | 1.64690i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.539465 | + | 2.01331i | 0.0378630 | + | 0.141307i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.85012 | − | 6.90472i | 0.129218 | − | 0.482247i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.56250 | + | 20.7595i | −0.386621 | + | 1.44289i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.4869 | + | 3.61380i | −0.932908 | + | 0.249972i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.72823i | 0.394348i | 0.980369 | + | 0.197174i | \(0.0631764\pi\) | ||||
−0.980369 | + | 0.197174i | \(0.936824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.9788 | + | 7.49332i | −0.889294 | + | 0.513434i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.4593 | + | 18.1161i | −0.713321 | + | 1.23551i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.3859 | + | 4.92648i | −1.24811 | + | 0.334431i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.2902 | − | 5.94107i | −0.695349 | − | 0.401460i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 36.6236i | 2.46357i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.45124i | 0.231112i | 0.993301 | + | 0.115556i | \(0.0368650\pi\) | ||||
−0.993301 | + | 0.115556i | \(0.963135\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 46.5188 | + | 26.8576i | 3.10125 | + | 1.79051i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 19.2959 | − | 5.17032i | 1.28071 | − | 0.343166i | 0.446587 | − | 0.894740i | \(-0.352639\pi\) |
0.834126 | + | 0.551574i | \(0.185973\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.80665 | + | 6.59331i | −0.251550 | + | 0.435698i | −0.963953 | − | 0.266073i | \(-0.914274\pi\) |
0.712403 | + | 0.701771i | \(0.247607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.7144 | + | 14.2688i | −1.62609 | + | 0.938821i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 28.5956i | − | 1.87336i | −0.350186 | − | 0.936680i | \(-0.613882\pi\) | ||
0.350186 | − | 0.936680i | \(-0.386118\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.0726 | + | 4.30665i | −1.04846 | + | 0.280935i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.72040 | + | 10.1527i | −0.176709 | + | 0.659488i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.92566 | + | 10.9187i | −0.189245 | + | 0.706274i | 0.804436 | + | 0.594039i | \(0.202468\pi\) |
−0.993682 | + | 0.112235i | \(0.964199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.94870 | + | 11.0047i | 0.189943 | + | 0.708876i | 0.993518 | + | 0.113673i | \(0.0362616\pi\) |
−0.803576 | + | 0.595203i | \(0.797072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.36603 | − | 16.2224i | −0.600831 | − | 1.04067i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.849930 | − | 0.849930i | 0.0543000 | − | 0.0543000i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.52514 | − | 16.4980i | −0.606070 | − | 1.04974i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.98243i | − | 0.189004i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8894 | + | 19.8894i | −1.25541 | + | 1.25541i | −0.302150 | + | 0.953260i | \(0.597704\pi\) |
−0.953260 | + | 0.302150i | \(0.902296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1690 | − | 13.1690i | −0.827930 | − | 0.827930i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −67.7579 | − | 39.1200i | −4.24316 | − | 2.44979i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.9904 | − | 5.89230i | −1.37172 | − | 0.367552i | −0.503615 | − | 0.863928i | \(-0.667997\pi\) |
−0.868107 | + | 0.496376i | \(0.834664\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.26406 | − | 16.2681i | 0.140682 | − | 1.01085i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.891859 | + | 3.32846i | −0.0552047 | + | 0.206027i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.6284 | − | 18.4090i | 0.655377 | − | 1.13515i | −0.326422 | − | 0.945224i | \(-0.605843\pi\) |
0.981799 | − | 0.189923i | \(-0.0608237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.08694 | − | 4.08694i | 0.251058 | − | 0.251058i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.63225 | + | 9.63225i | 0.589484 | + | 0.589484i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.33159 | 0.203131 | 0.101565 | − | 0.994829i | \(-0.467615\pi\) | ||||
0.101565 | + | 0.994829i | \(0.467615\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.4771 | − | 7.78100i | 0.818675 | − | 0.472662i | −0.0312846 | − | 0.999511i | \(-0.509960\pi\) |
0.849959 | + | 0.526848i | \(0.176626\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −27.5320 | − | 27.5320i | −1.66631 | − | 1.66631i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −40.3110 | + | 23.2735i | −2.43084 | + | 1.40345i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.2144 | − | 5.41644i | 1.21457 | − | 0.325442i | 0.406014 | − | 0.913867i | \(-0.366918\pi\) |
0.808552 | + | 0.588425i | \(0.200252\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.3961 | − | 8.14460i | −1.81977 | − | 0.487605i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.60972 | + | 0.967222i | 0.215338 | + | 0.0576997i | 0.364875 | − | 0.931056i | \(-0.381112\pi\) |
−0.149537 | + | 0.988756i | \(0.547778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.03641 | − | 3.86793i | −0.0616082 | − | 0.229925i | 0.928256 | − | 0.371942i | \(-0.121308\pi\) |
−0.989864 | + | 0.142017i | \(0.954641\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40.6977 | 2.41072 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.33847 | − | 4.05035i | −0.138035 | − | 0.239084i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.9768 | + | 15.5750i | 1.58687 | + | 0.916179i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.14276 | − | 4.26484i | −0.0669898 | − | 0.250009i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.63588 | + | 8.02959i | −0.270831 | + | 0.469093i | −0.969075 | − | 0.246767i | \(-0.920632\pi\) |
0.698244 | + | 0.715860i | \(0.253965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.4250 | 2.12075 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.4735 | −0.897865 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.7049 | − | 22.0056i | 0.734746 | − | 1.27262i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.54233 | + | 13.2202i | 0.204177 | + | 0.761997i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.44131 | + | 1.40949i | 0.140250 | + | 0.0809733i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.3418 | − | 19.6445i | −0.649428 | − | 1.12484i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3681 | −0.820032 | −0.410016 | − | 0.912078i | \(-0.634477\pi\) | ||||
−0.410016 | + | 0.912078i | \(0.634477\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.47575 | + | 24.1678i | 0.368392 | + | 1.37486i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.8481 | + | 4.51445i | 0.955371 | + | 0.255991i | 0.702640 | − | 0.711546i | \(-0.252005\pi\) |
0.252731 | + | 0.967537i | \(0.418671\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6548 | − | 6.60623i | −1.39357 | − | 0.373406i | −0.517539 | − | 0.855659i | \(-0.673152\pi\) |
−0.876032 | + | 0.482253i | \(0.839819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 48.0530 | − | 12.8758i | 2.70748 | − | 0.725467i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.0054 | − | 10.3954i | 1.01128 | − | 0.583866i | 0.0997172 | − | 0.995016i | \(-0.468206\pi\) |
0.911568 | + | 0.411150i | \(0.134873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.11145 | − | 2.11145i | −0.118218 | − | 0.118218i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.97029 | − | 1.13755i | 0.109971 | − | 0.0634916i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.0459 | −1.39359 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.9067 | − | 44.9067i | −2.49098 | − | 2.49098i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.8555 | − | 16.8555i | 0.932112 | − | 0.932112i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.44342 | + | 9.42828i | −0.300106 | + | 0.519798i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.08089 | + | 11.4980i | −0.169341 | + | 0.631989i | 0.828106 | + | 0.560572i | \(0.189419\pi\) |
−0.997447 | + | 0.0714168i | \(0.977248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.6890 | − | 21.4201i | 0.914550 | − | 1.17382i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.3397 | − | 10.5411i | −2.14936 | − | 0.575919i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.9692 | − | 16.7254i | −1.57805 | − | 0.911089i | −0.995131 | − | 0.0985607i | \(-0.968576\pi\) |
−0.582922 | − | 0.812528i | \(-0.698091\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.808556 | − | 0.808556i | −0.0439147 | − | 0.0439147i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.2821 | − | 19.2821i | 1.04418 | − | 1.04418i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1152i | 0.978128i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 27.1419 | + | 47.0112i | 1.46127 | + | 2.53100i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.38187 | − | 5.38187i | 0.288914 | − | 0.288914i | −0.547737 | − | 0.836651i | \(-0.684510\pi\) |
0.836651 | + | 0.547737i | \(0.184510\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.8712 | − | 30.9538i | −0.956622 | − | 1.65692i | −0.730611 | − | 0.682794i | \(-0.760765\pi\) |
−0.226011 | − | 0.974125i | \(-0.572569\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.46410 | − | 20.3923i | −0.291652 | − | 1.08846i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.10043 | + | 4.10686i | −0.0585700 | + | 0.218586i | −0.989008 | − | 0.147864i | \(-0.952760\pi\) |
0.930438 | + | 0.366450i | \(0.119427\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.85941 | + | 21.8676i | −0.310985 | + | 1.16061i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −49.4461 | + | 13.2490i | −2.61696 | + | 0.701213i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.17190 | + | 2.98600i | −0.272205 | + | 0.157158i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.41542 | − | 9.37978i | 0.284236 | − | 0.492311i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −17.3377 | + | 4.64562i | −0.907497 | + | 0.243163i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.9788 | − | 17.8856i | −1.61708 | − | 0.933622i | −0.987670 | − | 0.156549i | \(-0.949963\pi\) |
−0.629411 | − | 0.777073i | \(-0.716704\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.73205i | − | 0.402514i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.78157i | − | 0.196329i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.5018 | + | 11.8367i | 1.06155 | + | 0.612883i | 0.925859 | − | 0.377869i | \(-0.123343\pi\) |
0.135686 | + | 0.990752i | \(0.456676\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 76.5944 | − | 20.5234i | 3.95532 | − | 1.05982i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.03704 | − | 3.52825i | 0.104913 | − | 0.181714i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.85214 | + | 5.68814i | −0.506071 | + | 0.292180i | −0.731217 | − | 0.682145i | \(-0.761047\pi\) |
0.225146 | + | 0.974325i | \(0.427714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.4275i | 0.841604i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.2959 | + | 3.56262i | −0.679388 | + | 0.182042i | −0.581980 | − | 0.813203i | \(-0.697722\pi\) |
−0.0974081 | + | 0.995245i | \(0.531055\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.1575 | + | 41.6405i | −0.568640 | + | 2.12219i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.85629 | + | 21.8560i | −0.297692 | + | 1.11100i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.37818 | − | 20.0717i | −0.272685 | − | 1.01767i | −0.957377 | − | 0.288841i | \(-0.906730\pi\) |
0.684692 | − | 0.728832i | \(-0.259937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.7035 | − | 28.9314i | −0.844734 | − | 1.46312i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.3007 | − | 15.3007i | 0.771816 | − | 0.771816i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.93890 | + | 13.7506i | 0.399449 | + | 0.691867i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5724i | 0.831746i | 0.909423 | + | 0.415873i | \(0.136524\pi\) | ||||
−0.909423 | + | 0.415873i | \(0.863476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.8284 | − | 18.8284i | 0.942599 | − | 0.942599i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.1810 | + | 21.1810i | 1.05773 | + | 1.05773i | 0.998228 | + | 0.0595011i | \(0.0189510\pi\) |
0.0595011 | + | 0.998228i | \(0.481049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.2205 | + | 18.6025i | 1.60502 | + | 0.926658i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.82300 | − | 2.63207i | −0.488109 | − | 0.130788i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.84394 | + | 21.8052i | 0.438378 | + | 1.08084i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.877999 | + | 3.27674i | −0.0434142 | + | 0.162024i | −0.984230 | − | 0.176895i | \(-0.943395\pi\) |
0.940815 | + | 0.338919i | \(0.110061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.42585 | − | 14.5940i | 0.415616 | − | 0.719869i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.8517 | − | 16.8517i | 0.829218 | − | 0.829218i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.18572 | − | 3.18572i | −0.156381 | − | 0.156381i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.94578 | −0.193225 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.6496 | + | 6.72588i | −0.569119 | + | 0.328581i | −0.756797 | − | 0.653650i | \(-0.773237\pi\) |
0.187678 | + | 0.982231i | \(0.439904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.3386 | + | 20.3386i | 0.991242 | + | 0.991242i | 0.999962 | − | 0.00871988i | \(-0.00277566\pi\) |
−0.00871988 | + | 0.999962i | \(0.502776\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.5871 | + | 8.99923i | −0.757872 | + | 0.437557i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −80.6503 | + | 21.6102i | −3.91211 | + | 1.04825i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3355 | − | 3.84119i | −0.693745 | − | 0.185888i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 53.8796 | + | 14.4370i | 2.60133 | + | 0.697024i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.28824 | + | 19.7360i | 0.254726 | + | 0.950649i | 0.968243 | + | 0.250011i | \(0.0804344\pi\) |
−0.713517 | + | 0.700638i | \(0.752899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.6189 | 1.75979 | 0.879896 | − | 0.475167i | \(-0.157612\pi\) | ||||
0.879896 | + | 0.475167i | \(0.157612\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.35178 | + | 7.53750i | 0.208652 | + | 0.361395i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.0491 | + | 8.68858i | 0.719895 | + | 0.415631i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1763 | + | 37.9785i | 0.485689 | + | 1.81261i | 0.576940 | + | 0.816786i | \(0.304247\pi\) |
−0.0912516 | + | 0.995828i | \(0.529087\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.650070 | − | 1.12595i | 0.0309557 | − | 0.0536169i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.7449 | 0.510506 | 0.255253 | − | 0.966874i | \(-0.417841\pi\) | ||||
0.255253 | + | 0.966874i | \(0.417841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.5777 | 0.975474 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.06747 | − | 3.58097i | 0.0977881 | − | 0.169374i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.32969 | + | 23.6227i | 0.298716 | + | 1.11482i | 0.938221 | + | 0.346037i | \(0.112473\pi\) |
−0.639504 | + | 0.768787i | \(0.720860\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.80257 | + | 3.35012i | 0.273232 | + | 0.157751i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.0047 | + | 17.3287i | 0.470062 | + | 0.814172i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −58.8173 | −2.75740 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.76101 | − | 25.2324i | −0.316267 | − | 1.18032i | −0.922804 | − | 0.385269i | \(-0.874109\pi\) |
0.606538 | − | 0.795055i | \(-0.292558\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.8103 | − | 7.18381i | −1.25140 | − | 0.335311i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.95221 | + | 1.86284i | 0.323797 | + | 0.0867610i | 0.417056 | − | 0.908881i | \(-0.363062\pi\) |
−0.0932593 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.8365 | − | 5.58312i | 0.968354 | − | 0.259470i | 0.260221 | − | 0.965549i | \(-0.416204\pi\) |
0.708133 | + | 0.706079i | \(0.249538\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −68.8337 | + | 39.7411i | −3.19209 | + | 1.84295i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.4165 | + | 22.4165i | 1.03731 | + | 1.03731i | 0.999276 | + | 0.0380351i | \(0.0121099\pi\) |
0.0380351 | + | 0.999276i | \(0.487890\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −23.0769 | + | 13.3234i | −1.06559 | + | 0.615220i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.6930 | −0.907404 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8646 | − | 13.8646i | −0.637493 | − | 0.637493i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.7105 | − | 30.7105i | 1.40910 | − | 1.40910i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.12590 | − | 5.41422i | 0.143125 | − | 0.247900i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.44113 | − | 31.5027i | 0.385685 | − | 1.43940i | −0.451399 | − | 0.892322i | \(-0.649075\pi\) |
0.837084 | − | 0.547075i | \(-0.184259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.6137 | + | 19.3553i | −1.16788 | + | 0.882524i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 34.3063 | + | 9.19233i | 1.56099 | + | 0.418266i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.77621 | − | 3.33490i | −0.262284 | − | 0.151430i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.6246 | − | 19.6246i | −0.889276 | − | 0.889276i | 0.105177 | − | 0.994453i | \(-0.466459\pi\) |
−0.994453 | + | 0.105177i | \(0.966459\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.1842 | − | 26.1842i | 1.18409 | − | 1.18409i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.9356i | 1.53149i | 0.643143 | + | 0.765746i | \(0.277630\pi\) | ||||
−0.643143 | + | 0.765746i | \(0.722370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.67815 | − | 4.63869i | −0.120618 | − | 0.208916i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −50.3953 | + | 50.3953i | −2.26510 | + | 2.26510i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.40605 | + | 12.8276i | 0.332207 | + | 0.575399i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.01820 | − | 22.4602i | −0.269412 | − | 1.00546i | −0.959494 | − | 0.281727i | \(-0.909093\pi\) |
0.690083 | − | 0.723730i | \(-0.257574\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.7329 | − | 54.9841i | 0.658219 | − | 2.45651i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.05589 | + | 11.4047i | −0.136255 | + | 0.508511i | 0.863734 | + | 0.503947i | \(0.168119\pi\) |
−0.999990 | + | 0.00456409i | \(0.998547\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.11329 | − | 1.10215i | 0.183039 | − | 0.0490452i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 40.5885i | 1.80260i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0225 | − | 7.51852i | 0.577211 | − | 0.333253i | −0.182813 | − | 0.983148i | \(-0.558520\pi\) |
0.760024 | + | 0.649895i | \(0.225187\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.87187 | + | 10.1704i | −0.259756 | + | 0.449911i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.9458 | − | 3.73676i | 0.615721 | − | 0.164982i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 32.7324 | + | 18.8980i | 1.44236 | + | 0.832747i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.5966i | − | 0.685938i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 47.2767i | 2.07522i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.7281 | − | 6.77119i | −0.513815 | − | 0.296651i | 0.220585 | − | 0.975368i | \(-0.429203\pi\) |
−0.734401 | + | 0.678716i | \(0.762537\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.8098 | + | 7.45162i | −1.21604 | + | 0.325837i | −0.809129 | − | 0.587631i | \(-0.800061\pi\) |
−0.406910 | + | 0.913468i | \(0.633394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 44.3837 | − | 76.8747i | 1.93706 | − | 3.35509i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 42.3613 | − | 24.4573i | 1.84529 | − | 1.06538i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.178219i | 0.00774866i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 38.0571 | − | 10.1974i | 1.65154 | − | 0.442528i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.36603 | + | 8.83013i | −0.102484 | + | 0.382475i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.889505 | − | 3.31968i | 0.0384567 | − | 0.143522i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.1652 | + | 52.8653i | 0.611274 | + | 2.28131i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.563320 | + | 0.975699i | 0.0242639 | + | 0.0420263i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.1395 | + | 28.1395i | −1.20981 | + | 1.20981i | −0.238725 | + | 0.971087i | \(0.576729\pi\) |
−0.971087 | + | 0.238725i | \(0.923271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.4280 | + | 30.1861i | 0.747905 | + | 1.29541i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 36.0089i | − | 1.54245i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.54373 | − | 6.54373i | 0.279790 | − | 0.279790i | −0.553235 | − | 0.833025i | \(-0.686607\pi\) |
0.833025 | + | 0.553235i | \(0.186607\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.3495 | − | 17.3495i | −0.740461 | − | 0.740461i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.41288 | + | 1.39308i | 0.102792 | + | 0.0593471i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.0344 | + | 2.68872i | 0.426708 | + | 0.114336i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.44985 | − | 68.0629i | −0.358676 | − | 2.88911i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.57261 | + | 5.86907i | −0.0666337 | + | 0.248681i | −0.991206 | − | 0.132325i | \(-0.957756\pi\) |
0.924573 | + | 0.381006i | \(0.124422\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.3759 | − | 23.1678i | 0.565742 | − | 0.979895i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 51.8563 | − | 51.8563i | 2.18937 | − | 2.18937i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.05703 | + | 8.05703i | 0.339563 | + | 0.339563i | 0.856203 | − | 0.516640i | \(-0.172817\pi\) |
−0.516640 | + | 0.856203i | \(0.672817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.72734 | −0.0726698 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.76222 | + | 3.32682i | −0.241991 | + | 0.139713i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.0590 | + | 19.0590i | 0.798994 | + | 0.798994i | 0.982937 | − | 0.183943i | \(-0.0588860\pi\) |
−0.183943 | + | 0.982937i | \(0.558886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.439400 | + | 0.253687i | −0.0183883 | + | 0.0106165i | −0.509166 | − | 0.860668i | \(-0.670046\pi\) |
0.490778 | + | 0.871285i | \(0.336713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 51.5376 | − | 13.8094i | 2.15301 | − | 0.576898i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 55.9561 | + | 14.9934i | 2.33353 | + | 0.625267i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.31613 | + | 0.620604i | 0.0964216 | + | 0.0258361i | 0.306707 | − | 0.951804i | \(-0.400773\pi\) |
−0.210286 | + | 0.977640i | \(0.567439\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.8581 | − | 47.9872i | −0.534366 | − | 1.99428i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.94769 | −0.122291 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.70876 | + | 4.69170i | 0.112185 | + | 0.194311i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −84.2111 | − | 48.6193i | −3.48170 | − | 2.01016i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.80557 | − | 14.2026i | −0.157073 | − | 0.586203i | −0.998919 | − | 0.0464859i | \(-0.985198\pi\) |
0.841846 | − | 0.539717i | \(-0.181469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.7218 | + | 22.0348i | −0.524193 | + | 0.907928i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 43.2207 | 1.77786 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.490191 | −0.0201297 | −0.0100649 | − | 0.999949i | \(-0.503204\pi\) | ||||
−0.0100649 | + | 0.999949i | \(0.503204\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38.6644 | + | 66.9687i | −1.58509 | + | 2.74545i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.77641 | − | 36.4861i | −0.400122 | − | 1.49327i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.1651 | − | 9.33293i | −0.660488 | − | 0.381333i | 0.131975 | − | 0.991253i | \(-0.457868\pi\) |
−0.792463 | + | 0.609920i | \(0.791202\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.37863 | − | 12.7802i | −0.300981 | − | 0.521314i | 0.675378 | − | 0.737472i | \(-0.263981\pi\) |
−0.976358 | + | 0.216158i | \(0.930647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −44.0534 | −1.79400 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.23459 | − | 15.8037i | −0.172161 | − | 0.642512i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.5032 | − | 8.70920i | −1.31926 | − | 0.353496i | −0.470562 | − | 0.882367i | \(-0.655949\pi\) |
−0.848702 | + | 0.528872i | \(0.822615\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.50046 | + | 1.47385i | 0.222890 | + | 0.0597232i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.5545 | − | 5.50757i | 0.831547 | − | 0.222812i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.44411 | − | 4.29786i | 0.300665 | − | 0.173589i | −0.342077 | − | 0.939672i | \(-0.611130\pi\) |
0.642742 | + | 0.766083i | \(0.277797\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.8094 | − | 13.8094i | −0.556851 | − | 0.556851i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.1177 | − | 20.8526i | 1.45405 | − | 0.839494i | 0.455338 | − | 0.890319i | \(-0.349518\pi\) |
0.998708 | + | 0.0508250i | \(0.0161851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.8957 | −0.920257 | −0.460129 | − | 0.887852i | \(-0.652197\pi\) | ||||
−0.460129 | + | 0.887852i | \(0.652197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.6171 | + | 13.6171i | 0.546436 | + | 0.546436i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.52006 | − | 9.52006i | 0.381413 | − | 0.381413i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 29.8113 | − | 51.6347i | 1.19245 | − | 2.06539i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.87309 | + | 36.8469i | −0.394293 | + | 1.47152i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.20016 | + | 41.8869i | 0.207344 | + | 1.67014i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6095 | − | 3.37870i | −0.501975 | − | 0.134504i | −0.00105844 | − | 0.999999i | \(-0.500337\pi\) |
−0.500916 | + | 0.865496i | \(0.667004\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.5531 | + | 7.82491i | 0.538689 | + | 0.311012i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.5472 | + | 17.5472i | 0.696340 | + | 0.696340i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.08694 | + | 1.08694i | −0.0430659 | + | 0.0430659i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.4878i | 0.968722i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.3593 | − | 24.8711i | −0.567160 | − | 0.982350i | −0.996845 | − | 0.0793713i | \(-0.974709\pi\) |
0.429685 | − | 0.902979i | \(-0.358625\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.43666 | − | 9.43666i | 0.372146 | − | 0.372146i | −0.496113 | − | 0.868258i | \(-0.665240\pi\) |
0.868258 | + | 0.496113i | \(0.165240\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.5754 | + | 49.4941i | 1.12516 | + | 1.94883i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.14982 | − | 26.6835i | −0.281088 | − | 1.04904i | −0.951651 | − | 0.307183i | \(-0.900614\pi\) |
0.670562 | − | 0.741853i | \(-0.266053\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.83656 | + | 32.9785i | −0.346865 | + | 1.29452i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.4594 | + | 50.2311i | −0.527515 | + | 1.96871i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.8729 | − | 3.18133i | 0.464623 | − | 0.124495i | −0.0189108 | − | 0.999821i | \(-0.506020\pi\) |
0.483533 | + | 0.875326i | \(0.339353\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 32.6872i | − | 1.27720i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.8140 | + | 9.70755i | −0.655976 | + | 0.378728i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.6942 | + | 21.9870i | −0.494495 | + | 0.856491i | −0.999980 | − | 0.00634482i | \(-0.997980\pi\) |
0.505485 | + | 0.862836i | \(0.331314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5227 | + | 4.69520i | −0.681555 | + | 0.182622i | −0.582954 | − | 0.812505i | \(-0.698103\pi\) |
−0.0986008 | + | 0.995127i | \(0.531437\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 86.6524 | + | 50.0288i | 3.36530 | + | 1.94296i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 40.2237i | − | 1.55981i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.71626i | 0.143894i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.16572 | + | 4.71448i | 0.315705 | + | 0.182272i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.5372 | − | 5.50294i | 0.792831 | − | 0.212438i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7479 | + | 29.0082i | −0.645584 | + | 1.11818i | 0.338582 | + | 0.940937i | \(0.390053\pi\) |
−0.984166 | + | 0.177248i | \(0.943281\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 41.6825 | − | 24.0654i | 1.60436 | − | 0.926279i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.7324i | 0.489347i | 0.969606 | + | 0.244673i | \(0.0786807\pi\) | ||||
−0.969606 | + | 0.244673i | \(0.921319\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.21517 | + | 1.12945i | −0.161763 | + | 0.0433444i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.1256 | − | 52.7174i | 0.541293 | − | 2.02013i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.95125 | − | 18.4783i | 0.189454 | − | 0.707053i | −0.804179 | − | 0.594387i | \(-0.797395\pi\) |
0.993633 | − | 0.112665i | \(-0.0359387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.58860 | − | 24.5890i | −0.251737 | − | 0.939497i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.4000 | + | 18.0132i | 0.396783 | + | 0.687248i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.22659 | + | 5.22659i | −0.199117 | + | 0.199117i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.4804 | − | 40.6692i | −0.893236 | − | 1.54713i | −0.835972 | − | 0.548772i | \(-0.815096\pi\) |
−0.0572642 | − | 0.998359i | \(-0.518238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.6298i | 1.77132i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.21474 | + | 4.21474i | −0.159874 | + | 0.159874i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.49854 | + | 8.49854i | 0.321905 | + | 0.321905i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −67.6579 | − | 39.0623i | −2.55906 | − | 1.47747i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.3713 | + | 11.8893i | 1.67588 | + | 0.449051i | 0.966687 | − | 0.255962i | \(-0.0823923\pi\) |
0.709194 | + | 0.705013i | \(0.249059\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.2366 | − | 17.5165i | −0.499227 | − | 0.660649i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11.7660 | + | 43.9112i | −0.443132 | + | 1.65379i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.39308 | − | 2.41288i | 0.0523920 | − | 0.0907457i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.0066 | + | 11.0066i | −0.413362 | + | 0.413362i | −0.882908 | − | 0.469546i | \(-0.844418\pi\) |
0.469546 | + | 0.882908i | \(0.344418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.1442 | + | 12.1442i | 0.455442 | + | 0.455442i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.9375 | −1.27097 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 72.9733 | − | 42.1312i | 2.72905 | − | 1.57562i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.8375 | + | 21.8375i | 0.815535 | + | 0.815535i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.36448 | + | 3.09719i | −0.200061 | + | 0.115506i | −0.596684 | − | 0.802476i | \(-0.703515\pi\) |
0.396623 | + | 0.917982i | \(0.370182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.8863 | − | 6.40032i | 0.889574 | − | 0.238361i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.0654 | + | 8.05601i | 1.11815 | + | 0.299606i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.97167 | + | 2.40395i | 0.333199 | + | 0.0892805i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.6413 | + | 39.7140i | 0.394666 | + | 1.47291i | 0.822349 | + | 0.568983i | \(0.192663\pi\) |
−0.427684 | + | 0.903929i | \(0.640670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.5857 | − | 30.4594i | −0.650432 | − | 1.12658i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.84732 | − | 1.64390i | −0.105168 | − | 0.0607188i | 0.446493 | − | 0.894787i | \(-0.352673\pi\) |
−0.551661 | + | 0.834068i | \(0.686006\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.849930 | − | 3.17198i | −0.0313501 | − | 0.117000i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.0873 | − | 33.0602i | 0.703090 | − | 1.21779i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.0393 | −1.17859 | −0.589293 | − | 0.807919i | \(-0.700594\pi\) | ||||
−0.589293 | + | 0.807919i | \(0.700594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −52.0463 | −1.91197 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.5574 | + | 40.8026i | −0.864237 | + | 1.49690i | 0.00356481 | + | 0.999994i | \(0.498865\pi\) |
−0.867802 | + | 0.496910i | \(0.834468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.61666 | − | 6.03346i | −0.0592299 | − | 0.221049i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.22032 | − | 2.43660i | −0.154414 | − | 0.0891507i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.12430 | − | 1.94734i | −0.0410809 | − | 0.0711542i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.11583 | −0.259660 | −0.129830 | − | 0.991536i | \(-0.541443\pi\) | ||||
−0.129830 | + | 0.991536i | \(0.541443\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.8894 | + | 74.2284i | 0.724812 | + | 2.70503i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29.1965 | + | 7.82319i | 1.06257 | + | 0.284715i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.5502 | + | 8.72181i | 1.18306 | + | 0.316999i | 0.796139 | − | 0.605114i | \(-0.206873\pi\) |
0.386919 | + | 0.922114i | \(0.373539\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −49.1475 | + | 13.1690i | −1.78394 | + | 0.478006i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.84330 | − | 4.52833i | 0.284319 | − | 0.164152i | −0.351058 | − | 0.936354i | \(-0.614178\pi\) |
0.635377 | + | 0.772202i | \(0.280845\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.6592 | − | 16.6592i | −0.603103 | − | 0.603103i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −110.715 | + | 63.9211i | −4.00290 | + | 2.31107i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46.5822 | −1.68199 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.0988 | − | 24.0988i | −0.869024 | − | 0.869024i | 0.123340 | − | 0.992364i | \(-0.460639\pi\) |
−0.992364 | + | 0.123340i | \(0.960639\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.9808 | + | 43.9808i | −1.58393 | + | 1.58393i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.5615 | + | 20.0251i | −0.415838 | + | 0.720252i | −0.995516 | − | 0.0945933i | \(-0.969845\pi\) |
0.579678 | + | 0.814845i | \(0.303178\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.9533 | + | 81.9308i | −0.788585 | + | 2.94304i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.3979 | − | 27.5794i | −1.26989 | − | 0.989406i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.03870 | − | 1.61806i | −0.216359 | − | 0.0579732i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.3770 | − | 10.6100i | −0.657582 | − | 0.379655i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.18329 | + | 2.18329i | 0.0780244 | + | 0.0780244i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.0353 | + | 21.0353i | −0.750783 | + | 0.750783i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 53.8467i | 1.91943i | 0.280977 | + | 0.959715i | \(0.409342\pi\) | ||||
−0.280977 | + | 0.959715i | \(0.590658\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.0374 | − | 50.2943i | −1.03376 | − | 1.79052i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.799139 | + | 0.799139i | −0.0284141 | + | 0.0284141i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.5045 | + | 25.1225i | 0.515069 | + | 0.892125i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.08694 | − | 15.2527i | −0.144949 | − | 0.540956i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.41765 | + | 16.4869i | −0.156481 | + | 0.583996i | 0.842493 | + | 0.538708i | \(0.181087\pi\) |
−0.998974 | + | 0.0452880i | \(0.985579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.24096 | − | 27.0236i | 0.256167 | − | 0.956027i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.4997 | − | 5.76082i | 0.759654 | − | 0.203549i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 16.8242i | − | 0.593714i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 46.4637 | − | 26.8258i | 1.63763 | − | 0.945485i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.55104 | − | 7.88263i | 0.160204 | − | 0.277482i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.7820 | + | 9.58776i | −1.25803 | + | 0.337088i | −0.825433 | − | 0.564500i | \(-0.809069\pi\) |
−0.432596 | + | 0.901588i | \(0.642402\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.9181 | + | 13.2318i | 0.804765 | + | 0.464631i | 0.845134 | − | 0.534554i | \(-0.179520\pi\) |
−0.0403699 | + | 0.999185i | \(0.512854\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 42.5162i | − | 1.49111i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 55.9380i | − | 1.95942i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.8439 | + | 9.14747i | 0.554307 | + | 0.320029i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −61.4527 | + | 16.4662i | −2.14733 | + | 0.575376i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.25681 | + | 7.37301i | −0.148564 | + | 0.257320i | −0.930697 | − | 0.365792i | \(-0.880798\pi\) |
0.782133 | + | 0.623111i | \(0.214132\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.3469 | − | 24.4490i | 1.47612 | − | 0.852239i | 0.476485 | − | 0.879183i | \(-0.341911\pi\) |
0.999637 | + | 0.0269434i | \(0.00857738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 127.169i | 4.42746i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.1669 | − | 5.13576i | 0.666500 | − | 0.178588i | 0.0903220 | − | 0.995913i | \(-0.471210\pi\) |
0.576177 | + | 0.817325i | \(0.304544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.02246 | + | 3.81588i | −0.0355116 | + | 0.132531i | −0.981406 | − | 0.191944i | \(-0.938521\pi\) |
0.945894 | + | 0.324475i | \(0.105188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.7980 | − | 55.2268i | 0.513336 | − | 1.91580i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.523059 | + | 1.95208i | 0.0181229 | + | 0.0676357i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.9948 | − | 74.4693i | −1.48790 | − | 2.57711i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.9381 | + | 19.9381i | −0.689163 | + | 0.689163i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.2817 | − | 17.8084i | −0.354963 | − | 0.614815i | 0.632148 | − | 0.774847i | \(-0.282173\pi\) |
−0.987112 | + | 0.160033i | \(0.948840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.4042i | − | 0.979454i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.21945 | − | 7.21945i | 0.248651 | − | 0.248651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 43.3551 | + | 43.3551i | 1.49146 | + | 1.49146i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.27053 | − | 5.35234i | −0.318539 | − | 0.183909i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.5674 | − | 2.83152i | −0.362672 | − | 0.0971777i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4062 | − | 26.9721i | 0.391001 | − | 0.924590i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.64958 | − | 9.88837i | 0.0907199 | − | 0.338571i | −0.905616 | − | 0.424099i | \(-0.860591\pi\) |
0.996336 | + | 0.0855276i | \(0.0272576\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.2495 | − | 57.5898i | 1.13711 | − | 1.96953i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.7841 | − | 21.7841i | 0.744129 | − | 0.744129i | −0.229241 | − | 0.973370i | \(-0.573624\pi\) |
0.973370 | + | 0.229241i | \(0.0736242\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.6297 | + | 35.6297i | 1.21567 | + | 1.21567i | 0.969134 | + | 0.246534i | \(0.0792916\pi\) |
0.246534 | + | 0.969134i | \(0.420708\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.7776 | −0.435460 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.8209 | + | 9.71155i | −0.572590 | + | 0.330585i | −0.758183 | − | 0.652042i | \(-0.773913\pi\) |
0.185593 | + | 0.982627i | \(0.440579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.4993 | + | 50.4993i | 1.71703 | + | 1.71703i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 73.7019 | − | 42.5518i | 2.50305 | − | 1.44514i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.3754 | + | 3.85189i | −0.487653 | + | 0.130666i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.3098 | + | 13.4805i | 1.70468 | + | 0.456768i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.96864 | − | 1.86724i | −0.235853 | − | 0.0631966i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.2844 | − | 75.7023i | −0.685737 | − | 2.55921i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.3984 | 0.384897 | 0.192448 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192448 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.6655 | + | 21.9372i | 0.427196 | + | 0.739925i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.8685 | − | 15.5125i | −0.905223 | − | 0.522631i | −0.0263319 | − | 0.999653i | \(-0.508383\pi\) |
−0.878891 | + | 0.477023i | \(0.841716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.9708 | + | 40.9436i | 0.369197 | + | 1.37786i | 0.861642 | + | 0.507517i | \(0.169437\pi\) |
−0.492445 | + | 0.870343i | \(0.663897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 49.7575 | − | 86.1825i | 1.67258 | − | 2.89699i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.9296 | −1.10567 | −0.552834 | − | 0.833291i | \(-0.686454\pi\) | ||||
−0.552834 | + | 0.833291i | \(0.686454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.2361 | 0.544542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.76604 | − | 8.25502i | 0.159668 | − | 0.276554i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.76649 | + | 14.0567i | 0.126041 | + | 0.470390i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 71.5997 | + | 41.3381i | 2.39331 | + | 1.38178i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.7105 | − | 60.1204i | −1.15895 | − | 2.00736i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.44134 | −0.181479 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.51516 | + | 9.38671i | 0.0837921 | + | 0.312716i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.1181 | + | 9.67783i | 1.20194 | + | 0.322058i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.8597 | + | 13.6278i | 1.69063 | + | 0.453003i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.1853 | + | 8.62403i | −1.06870 | + | 0.286356i | −0.749957 | − | 0.661486i | \(-0.769926\pi\) |
−0.318739 | + | 0.947842i | \(0.603259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.98904 | − | 2.30308i | 0.132308 | − | 0.0763882i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.5509 | + | 12.5509i | 0.415830 | + | 0.415830i | 0.883764 | − | 0.467933i | \(-0.155001\pi\) |
−0.467933 | + | 0.883764i | \(0.655001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.65713 | − | 2.11145i | 0.121033 | − | 0.0698787i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −61.9726 | −2.04875 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.1225 | − | 15.1225i | −0.499387 | − | 0.499387i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0943 | + | 24.0943i | −0.794798 | + | 0.794798i | −0.982270 | − | 0.187472i | \(-0.939971\pi\) |
0.187472 | + | 0.982270i | \(0.439971\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.6272 | + | 33.9953i | −0.646739 | + | 1.12018i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.49332 | − | 27.9655i | 0.246646 | − | 0.920494i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −57.7366 | − | 44.9841i | −1.89837 | − | 1.47907i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39.4896 | + | 10.5812i | 1.29701 | + | 0.347532i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −31.6174 | − | 18.2543i | −1.03733 | − | 0.598905i | −0.118257 | − | 0.992983i | \(-0.537731\pi\) |
−0.919077 | + | 0.394078i | \(0.871064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.743327 | − | 0.743327i | −0.0243616 | − | 0.0243616i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.6963 | − | 33.6963i | 1.10317 | − | 1.10317i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 110.782i | − | 3.62296i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.89492 | − | 8.47825i | −0.159910 | − | 0.276972i | 0.774926 | − | 0.632052i | \(-0.217787\pi\) |
−0.934836 | + | 0.355080i | \(0.884454\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −49.3096 | + | 49.3096i | −1.60916 | + | 1.60916i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.53106 | − | 16.5083i | −0.310704 | − | 0.538155i | 0.667811 | − | 0.744331i | \(-0.267231\pi\) |
−0.978515 | + | 0.206176i | \(0.933898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.15823 | − | 8.05461i | −0.0702815 | − | 0.262294i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.5372 | − | 43.0573i | 0.375304 | − | 1.40065i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.82962 | − | 29.2205i | 0.254428 | − | 0.949540i | −0.713979 | − | 0.700167i | \(-0.753109\pi\) |
0.968408 | − | 0.249373i | \(-0.0802245\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.1724 | − | 5.94107i | 0.719745 | − | 0.192855i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 56.8017i | − | 1.84192i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.4413 | + | 6.60565i | −0.370621 | + | 0.213978i | −0.673730 | − | 0.738978i | \(-0.735309\pi\) |
0.303109 | + | 0.952956i | \(0.401975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.2998 | − | 69.8014i | 1.30407 | − | 2.25872i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.88003 | + | 2.11145i | −0.254725 | + | 0.0682534i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.4240 | − | 8.32771i | −0.465776 | − | 0.268916i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 18.6912i | − | 0.602941i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 3.71744i | − | 0.119793i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −64.9928 | − | 37.5236i | −2.09219 | − | 1.20793i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.7681 | + | 6.63659i | −0.796488 | + | 0.213418i | −0.634041 | − | 0.773299i | \(-0.718605\pi\) |
−0.162447 | + | 0.986717i | \(0.551938\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.2134 | + | 59.2593i | −1.09909 | + | 1.90368i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.8530 | + | 20.6997i | −1.15058 | + | 0.664286i | −0.949028 | − | 0.315193i | \(-0.897931\pi\) |
−0.201549 | + | 0.979478i | \(0.564598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.89982i | 0.125022i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −167.594 | + | 44.9067i | −5.36731 | + | 1.43817i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.55575 | + | 17.0023i | −0.145751 | + | 0.543951i | 0.853970 | + | 0.520323i | \(0.174188\pi\) |
−0.999721 | + | 0.0236280i | \(0.992478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.99205 | + | 18.6306i | −0.159547 | + | 0.595437i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0809 | − | 37.6224i | −0.321858 | − | 1.20119i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.2243 | + | 45.4218i | 0.836424 | + | 1.44873i | 0.892865 | + | 0.450324i | \(0.148691\pi\) |
−0.0564409 | + | 0.998406i | \(0.517975\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.1668 | − | 46.1668i | 1.47100 | − | 1.47100i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.8717 | + | 25.7585i | 0.473372 | + | 0.819904i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.4024i | 0.775950i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.5355 | + | 29.5355i | −0.938225 | + | 0.938225i | −0.998200 | − | 0.0599753i | \(-0.980898\pi\) |
0.0599753 | + | 0.998200i | \(0.480898\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.9961 | + | 22.9961i | 0.729758 | + | 0.729758i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.4159 | − | 28.5303i | −1.56659 | − | 0.904471i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.2520 | + | 5.42650i | 0.641387 | + | 0.171859i | 0.564831 | − | 0.825206i | \(-0.308941\pi\) |
0.0765552 | + | 0.997065i | \(0.475608\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.14486 | − | 22.5471i | −0.289330 | − | 0.713359i |
(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 | 592.2.be.c.399.1 | yes | 8 | |
4.3 | odd | 2 | 592.2.be.b.399.1 | yes | 8 | ||
37.23 | odd | 12 | 592.2.be.b.319.1 | ✓ | 8 | ||
148.23 | even | 12 | inner | 592.2.be.c.319.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
592.2.be.b.319.1 | ✓ | 8 | 37.23 | odd | 12 | ||
592.2.be.b.399.1 | yes | 8 | 4.3 | odd | 2 | ||
592.2.be.c.319.1 | yes | 8 | 148.23 | even | 12 | inner | |
592.2.be.c.399.1 | yes | 8 | 1.1 | even | 1 | trivial |