Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (of order \(2\), degree \(1\), 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: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.12 | ||
Root | \(0.500000 - 0.0286340i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.b.2155.5 |
$q$-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 \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 0.837391i | − | 0.374493i | −0.982313 | − | 0.187246i | \(-0.940044\pi\) | ||
0.982313 | − | 0.187246i | \(-0.0599563\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.837391 | 0.264806 | ||||||||
\(11\) | 0.697189 | − | 3.24252i | 0.210210 | − | 0.977656i | ||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.59370 | 0.719364 | 0.359682 | − | 0.933075i | \(-0.382885\pi\) | ||||
0.359682 | + | 0.933075i | \(0.382885\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.837391 | −0.216214 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.97372 | 1.44884 | 0.724420 | − | 0.689359i | \(-0.242108\pi\) | ||||
0.724420 | + | 0.689359i | \(0.242108\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −3.11181 | −0.713898 | −0.356949 | − | 0.934124i | \(-0.616183\pi\) | ||||
−0.356949 | + | 0.934124i | \(0.616183\pi\) | |||||||
\(20\) | 0.837391i | 0.187246i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.24252 | + | 0.697189i | 0.691307 | + | 0.148641i | ||||
\(23\) | 2.86511 | 0.597418 | 0.298709 | − | 0.954344i | \(-0.403444\pi\) | ||||
0.298709 | + | 0.954344i | \(0.403444\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.29878 | 0.859755 | ||||||||
\(26\) | 2.59370i | 0.508667i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.38769i | − | 1.00047i | −0.865890 | − | 0.500234i | \(-0.833247\pi\) | ||
0.865890 | − | 0.500234i | \(-0.166753\pi\) | |||||||
\(30\) | − | 0.837391i | − | 0.152886i | ||||||
\(31\) | − | 1.05470i | − | 0.189430i | −0.995504 | − | 0.0947151i | \(-0.969806\pi\) | ||
0.995504 | − | 0.0947151i | \(-0.0301940\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −3.24252 | − | 0.697189i | −0.564450 | − | 0.121365i | ||||
\(34\) | 5.97372i | 1.02448i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.9893 | −1.80664 | −0.903319 | − | 0.428970i | \(-0.858877\pi\) | ||||
−0.903319 | + | 0.428970i | \(0.858877\pi\) | |||||||
\(38\) | − | 3.11181i | − | 0.504802i | ||||||
\(39\) | − | 2.59370i | − | 0.415325i | ||||||
\(40\) | −0.837391 | −0.132403 | ||||||||
\(41\) | −11.2350 | −1.75461 | −0.877304 | − | 0.479934i | \(-0.840661\pi\) | ||||
−0.877304 | + | 0.479934i | \(0.840661\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.27527i | 0.194478i | 0.995261 | + | 0.0972388i | \(0.0310010\pi\) | ||||
−0.995261 | + | 0.0972388i | \(0.968999\pi\) | |||||||
\(44\) | −0.697189 | + | 3.24252i | −0.105105 | + | 0.488828i | ||||
\(45\) | 0.837391i | 0.124831i | ||||||||
\(46\) | 2.86511i | 0.422438i | ||||||||
\(47\) | 12.2437i | 1.78593i | 0.450128 | + | 0.892964i | \(0.351378\pi\) | ||||
−0.450128 | + | 0.892964i | \(0.648622\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.29878i | 0.607939i | ||||||||
\(51\) | − | 5.97372i | − | 0.836488i | ||||||
\(52\) | −2.59370 | −0.359682 | ||||||||
\(53\) | 5.17461 | 0.710787 | 0.355394 | − | 0.934717i | \(-0.384347\pi\) | ||||
0.355394 | + | 0.934717i | \(0.384347\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.71526 | − | 0.583820i | −0.366125 | − | 0.0787223i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.11181i | 0.412169i | ||||||||
\(58\) | 5.38769 | 0.707438 | ||||||||
\(59\) | − | 9.68506i | − | 1.26089i | −0.776235 | − | 0.630444i | \(-0.782873\pi\) | ||
0.776235 | − | 0.630444i | \(-0.217127\pi\) | |||||||
\(60\) | 0.837391 | 0.108107 | ||||||||
\(61\) | 4.07048 | 0.521172 | 0.260586 | − | 0.965451i | \(-0.416084\pi\) | ||||
0.260586 | + | 0.965451i | \(0.416084\pi\) | |||||||
\(62\) | 1.05470 | 0.133947 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 2.17195i | − | 0.269397i | ||||||
\(66\) | 0.697189 | − | 3.24252i | 0.0858180 | − | 0.399126i | ||||
\(67\) | 13.0383 | 1.59288 | 0.796442 | − | 0.604715i | \(-0.206713\pi\) | ||||
0.796442 | + | 0.604715i | \(0.206713\pi\) | |||||||
\(68\) | −5.97372 | −0.724420 | ||||||||
\(69\) | − | 2.86511i | − | 0.344919i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0795 | 1.67093 | 0.835467 | − | 0.549541i | \(-0.185197\pi\) | ||||
0.835467 | + | 0.549541i | \(0.185197\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −9.91318 | −1.16025 | −0.580125 | − | 0.814527i | \(-0.696996\pi\) | ||||
−0.580125 | + | 0.814527i | \(0.696996\pi\) | |||||||
\(74\) | − | 10.9893i | − | 1.27749i | ||||||
\(75\) | − | 4.29878i | − | 0.496380i | ||||||
\(76\) | 3.11181 | 0.356949 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.59370 | 0.293679 | ||||||||
\(79\) | − | 13.5121i | − | 1.52023i | −0.649791 | − | 0.760113i | \(-0.725144\pi\) | ||
0.649791 | − | 0.760113i | \(-0.274856\pi\) | |||||||
\(80\) | − | 0.837391i | − | 0.0936232i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 11.2350i | − | 1.24070i | ||||||
\(83\) | 2.99287 | 0.328510 | 0.164255 | − | 0.986418i | \(-0.447478\pi\) | ||||
0.164255 | + | 0.986418i | \(0.447478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 5.00234i | − | 0.542580i | ||||||
\(86\) | −1.27527 | −0.137516 | ||||||||
\(87\) | −5.38769 | −0.577621 | ||||||||
\(88\) | −3.24252 | − | 0.697189i | −0.345654 | − | 0.0743206i | ||||
\(89\) | − | 8.40678i | − | 0.891117i | −0.895253 | − | 0.445559i | \(-0.853005\pi\) | ||
0.895253 | − | 0.445559i | \(-0.146995\pi\) | |||||||
\(90\) | −0.837391 | −0.0882688 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.86511 | −0.298709 | ||||||||
\(93\) | −1.05470 | −0.109368 | ||||||||
\(94\) | −12.2437 | −1.26284 | ||||||||
\(95\) | 2.60580i | 0.267350i | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − | 0.786131i | − | 0.0798195i | −0.999203 | − | 0.0399097i | \(-0.987293\pi\) | ||
0.999203 | − | 0.0399097i | \(-0.0127070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.697189 | + | 3.24252i | −0.0700701 | + | 0.325885i | ||||
\(100\) | −4.29878 | −0.429878 | ||||||||
\(101\) | −6.72227 | −0.668891 | −0.334445 | − | 0.942415i | \(-0.608549\pi\) | ||||
−0.334445 | + | 0.942415i | \(0.608549\pi\) | |||||||
\(102\) | 5.97372 | 0.591486 | ||||||||
\(103\) | 4.07143i | 0.401170i | 0.979676 | + | 0.200585i | \(0.0642842\pi\) | ||||
−0.979676 | + | 0.200585i | \(0.935716\pi\) | |||||||
\(104\) | − | 2.59370i | − | 0.254334i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.17461i | 0.502602i | ||||||||
\(107\) | − | 0.241883i | − | 0.0233837i | −0.999932 | − | 0.0116919i | \(-0.996278\pi\) | ||
0.999932 | − | 0.0116919i | \(-0.00372172\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 17.5252i | − | 1.67861i | −0.543662 | − | 0.839304i | \(-0.682963\pi\) | ||
0.543662 | − | 0.839304i | \(-0.317037\pi\) | |||||||
\(110\) | 0.583820 | − | 2.71526i | 0.0556651 | − | 0.258890i | ||||
\(111\) | 10.9893i | 1.04306i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.08949 | 0.760995 | 0.380498 | − | 0.924782i | \(-0.375753\pi\) | ||||
0.380498 | + | 0.924782i | \(0.375753\pi\) | |||||||
\(114\) | −3.11181 | −0.291448 | ||||||||
\(115\) | − | 2.39922i | − | 0.223729i | ||||||
\(116\) | 5.38769i | 0.500234i | ||||||||
\(117\) | −2.59370 | −0.239788 | ||||||||
\(118\) | 9.68506 | 0.891582 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.837391i | 0.0764430i | ||||||||
\(121\) | −10.0279 | − | 4.52130i | −0.911623 | − | 0.411027i | ||||
\(122\) | 4.07048i | 0.368524i | ||||||||
\(123\) | 11.2350i | 1.01302i | ||||||||
\(124\) | 1.05470i | 0.0947151i | ||||||||
\(125\) | − | 7.78672i | − | 0.696465i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.1313i | − | 1.07648i | −0.842791 | − | 0.538241i | \(-0.819089\pi\) | ||
0.842791 | − | 0.538241i | \(-0.180911\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.27527 | 0.112282 | ||||||||
\(130\) | 2.17195 | 0.190492 | ||||||||
\(131\) | 2.04449 | 0.178628 | 0.0893139 | − | 0.996004i | \(-0.471533\pi\) | ||||
0.0893139 | + | 0.996004i | \(0.471533\pi\) | |||||||
\(132\) | 3.24252 | + | 0.697189i | 0.282225 | + | 0.0606825i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.0383i | 1.12634i | ||||||||
\(135\) | 0.837391 | 0.0720712 | ||||||||
\(136\) | − | 5.97372i | − | 0.512242i | ||||||
\(137\) | −13.2111 | −1.12870 | −0.564351 | − | 0.825535i | \(-0.690874\pi\) | ||||
−0.564351 | + | 0.825535i | \(0.690874\pi\) | |||||||
\(138\) | 2.86511 | 0.243895 | ||||||||
\(139\) | 6.16293 | 0.522733 | 0.261367 | − | 0.965240i | \(-0.415827\pi\) | ||||
0.261367 | + | 0.965240i | \(0.415827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.2437 | 1.03111 | ||||||||
\(142\) | 14.0795i | 1.18153i | ||||||||
\(143\) | 1.80830 | − | 8.41014i | 0.151218 | − | 0.703291i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −4.51160 | −0.374668 | ||||||||
\(146\) | − | 9.91318i | − | 0.820421i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.9893 | 0.903319 | ||||||||
\(149\) | − | 4.39696i | − | 0.360213i | −0.983647 | − | 0.180107i | \(-0.942356\pi\) | ||
0.983647 | − | 0.180107i | \(-0.0576443\pi\) | |||||||
\(150\) | 4.29878 | 0.350994 | ||||||||
\(151\) | − | 10.2407i | − | 0.833380i | −0.909049 | − | 0.416690i | \(-0.863190\pi\) | ||
0.909049 | − | 0.416690i | \(-0.136810\pi\) | |||||||
\(152\) | 3.11181i | 0.252401i | ||||||||
\(153\) | −5.97372 | −0.482947 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.883199 | −0.0709402 | ||||||||
\(156\) | 2.59370i | 0.207663i | ||||||||
\(157\) | − | 15.9861i | − | 1.27583i | −0.770107 | − | 0.637914i | \(-0.779797\pi\) | ||
0.770107 | − | 0.637914i | \(-0.220203\pi\) | |||||||
\(158\) | 13.5121 | 1.07496 | ||||||||
\(159\) | − | 5.17461i | − | 0.410373i | ||||||
\(160\) | 0.837391 | 0.0662016 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | −0.523852 | −0.0410313 | −0.0205156 | − | 0.999790i | \(-0.506531\pi\) | ||||
−0.0205156 | + | 0.999790i | \(0.506531\pi\) | |||||||
\(164\) | 11.2350 | 0.877304 | ||||||||
\(165\) | −0.583820 | + | 2.71526i | −0.0454503 | + | 0.211383i | ||||
\(166\) | 2.99287i | 0.232292i | ||||||||
\(167\) | −17.0544 | −1.31971 | −0.659855 | − | 0.751393i | \(-0.729382\pi\) | ||||
−0.659855 | + | 0.751393i | \(0.729382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.27269 | −0.482515 | ||||||||
\(170\) | 5.00234 | 0.383662 | ||||||||
\(171\) | 3.11181 | 0.237966 | ||||||||
\(172\) | − | 1.27527i | − | 0.0972388i | ||||||
\(173\) | −7.23663 | −0.550191 | −0.275095 | − | 0.961417i | \(-0.588709\pi\) | ||||
−0.275095 | + | 0.961417i | \(0.588709\pi\) | |||||||
\(174\) | − | 5.38769i | − | 0.408440i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.697189 | − | 3.24252i | 0.0525526 | − | 0.244414i | ||||
\(177\) | −9.68506 | −0.727974 | ||||||||
\(178\) | 8.40678 | 0.630115 | ||||||||
\(179\) | 8.06636 | 0.602908 | 0.301454 | − | 0.953481i | \(-0.402528\pi\) | ||||
0.301454 | + | 0.953481i | \(0.402528\pi\) | |||||||
\(180\) | − | 0.837391i | − | 0.0624155i | ||||||
\(181\) | 5.61056i | 0.417030i | 0.978019 | + | 0.208515i | \(0.0668630\pi\) | ||||
−0.978019 | + | 0.208515i | \(0.933137\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.07048i | − | 0.300899i | ||||||
\(184\) | − | 2.86511i | − | 0.211219i | ||||||
\(185\) | 9.20238i | 0.676573i | ||||||||
\(186\) | − | 1.05470i | − | 0.0773345i | ||||||
\(187\) | 4.16481 | − | 19.3699i | 0.304561 | − | 1.41647i | ||||
\(188\) | − | 12.2437i | − | 0.892964i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.60580 | −0.189045 | ||||||||
\(191\) | 11.7841 | 0.852668 | 0.426334 | − | 0.904566i | \(-0.359805\pi\) | ||||
0.426334 | + | 0.904566i | \(0.359805\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 18.0976i | 1.30270i | 0.758779 | + | 0.651348i | \(0.225796\pi\) | ||||
−0.758779 | + | 0.651348i | \(0.774204\pi\) | |||||||
\(194\) | 0.786131 | 0.0564409 | ||||||||
\(195\) | −2.17195 | −0.155536 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.23110i | 0.443948i | 0.975053 | + | 0.221974i | \(0.0712500\pi\) | ||||
−0.975053 | + | 0.221974i | \(0.928750\pi\) | |||||||
\(198\) | −3.24252 | − | 0.697189i | −0.230436 | − | 0.0495471i | ||||
\(199\) | − | 18.2669i | − | 1.29491i | −0.762106 | − | 0.647453i | \(-0.775834\pi\) | ||
0.762106 | − | 0.647453i | \(-0.224166\pi\) | |||||||
\(200\) | − | 4.29878i | − | 0.303969i | ||||||
\(201\) | − | 13.0383i | − | 0.919652i | ||||||
\(202\) | − | 6.72227i | − | 0.472977i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.97372i | 0.418244i | ||||||||
\(205\) | 9.40808i | 0.657088i | ||||||||
\(206\) | −4.07143 | −0.283670 | ||||||||
\(207\) | −2.86511 | −0.199139 | ||||||||
\(208\) | 2.59370 | 0.179841 | ||||||||
\(209\) | −2.16952 | + | 10.0901i | −0.150069 | + | 0.697947i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.2446i | − | 0.705269i | −0.935761 | − | 0.352635i | \(-0.885286\pi\) | ||
0.935761 | − | 0.352635i | \(-0.114714\pi\) | |||||||
\(212\) | −5.17461 | −0.355394 | ||||||||
\(213\) | − | 14.0795i | − | 0.964714i | ||||||
\(214\) | 0.241883 | 0.0165348 | ||||||||
\(215\) | 1.06790 | 0.0728304 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 17.5252 | 1.18696 | ||||||||
\(219\) | 9.91318i | 0.669871i | ||||||||
\(220\) | 2.71526 | + | 0.583820i | 0.183063 | + | 0.0393612i | ||||
\(221\) | 15.4941 | 1.04224 | ||||||||
\(222\) | −10.9893 | −0.737557 | ||||||||
\(223\) | − | 15.6665i | − | 1.04911i | −0.851377 | − | 0.524554i | \(-0.824232\pi\) | ||
0.851377 | − | 0.524554i | \(-0.175768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.29878 | −0.286585 | ||||||||
\(226\) | 8.08949i | 0.538105i | ||||||||
\(227\) | −15.7205 | −1.04341 | −0.521703 | − | 0.853127i | \(-0.674703\pi\) | ||||
−0.521703 | + | 0.853127i | \(0.674703\pi\) | |||||||
\(228\) | − | 3.11181i | − | 0.206085i | ||||||
\(229\) | 2.50417i | 0.165480i | 0.996571 | + | 0.0827400i | \(0.0263671\pi\) | ||||
−0.996571 | + | 0.0827400i | \(0.973633\pi\) | |||||||
\(230\) | 2.39922 | 0.158200 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.38769 | −0.353719 | ||||||||
\(233\) | 0.0553161i | 0.00362388i | 0.999998 | + | 0.00181194i | \(0.000576759\pi\) | ||||
−0.999998 | + | 0.00181194i | \(0.999423\pi\) | |||||||
\(234\) | − | 2.59370i | − | 0.169556i | ||||||
\(235\) | 10.2528 | 0.668817 | ||||||||
\(236\) | 9.68506i | 0.630444i | ||||||||
\(237\) | −13.5121 | −0.877702 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.74465i | − | 0.371591i | −0.982588 | − | 0.185795i | \(-0.940514\pi\) | ||
0.982588 | − | 0.185795i | \(-0.0594861\pi\) | |||||||
\(240\) | −0.837391 | −0.0540534 | ||||||||
\(241\) | 7.34245 | 0.472969 | 0.236484 | − | 0.971635i | \(-0.424005\pi\) | ||||
0.236484 | + | 0.971635i | \(0.424005\pi\) | |||||||
\(242\) | 4.52130 | − | 10.0279i | 0.290640 | − | 0.644615i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −4.07048 | −0.260586 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.2350 | −0.716316 | ||||||||
\(247\) | −8.07111 | −0.513553 | ||||||||
\(248\) | −1.05470 | −0.0669737 | ||||||||
\(249\) | − | 2.99287i | − | 0.189665i | ||||||
\(250\) | 7.78672 | 0.492475 | ||||||||
\(251\) | − | 4.20803i | − | 0.265608i | −0.991142 | − | 0.132804i | \(-0.957602\pi\) | ||
0.991142 | − | 0.132804i | \(-0.0423981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.99753 | − | 9.29019i | 0.125583 | − | 0.584069i | ||||
\(254\) | 12.1313 | 0.761188 | ||||||||
\(255\) | −5.00234 | −0.313259 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.6466i | 1.53741i | 0.639602 | + | 0.768706i | \(0.279099\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(258\) | 1.27527i | 0.0793951i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.17195i | 0.134698i | ||||||||
\(261\) | 5.38769i | 0.333489i | ||||||||
\(262\) | 2.04449i | 0.126309i | ||||||||
\(263\) | 30.3837i | 1.87354i | 0.349950 | + | 0.936768i | \(0.386198\pi\) | ||||
−0.349950 | + | 0.936768i | \(0.613802\pi\) | |||||||
\(264\) | −0.697189 | + | 3.24252i | −0.0429090 | + | 0.199563i | ||||
\(265\) | − | 4.33317i | − | 0.266185i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.40678 | −0.514487 | ||||||||
\(268\) | −13.0383 | −0.796442 | ||||||||
\(269\) | 19.9737i | 1.21782i | 0.793240 | + | 0.608910i | \(0.208393\pi\) | ||||
−0.793240 | + | 0.608910i | \(0.791607\pi\) | |||||||
\(270\) | 0.837391i | 0.0509620i | ||||||||
\(271\) | 1.61528 | 0.0981212 | 0.0490606 | − | 0.998796i | \(-0.484377\pi\) | ||||
0.0490606 | + | 0.998796i | \(0.484377\pi\) | |||||||
\(272\) | 5.97372 | 0.362210 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 13.2111i | − | 0.798113i | ||||||
\(275\) | 2.99706 | − | 13.9389i | 0.180729 | − | 0.840545i | ||||
\(276\) | 2.86511i | 0.172460i | ||||||||
\(277\) | − | 5.18071i | − | 0.311279i | −0.987814 | − | 0.155639i | \(-0.950256\pi\) | ||
0.987814 | − | 0.155639i | \(-0.0497438\pi\) | |||||||
\(278\) | 6.16293i | 0.369628i | ||||||||
\(279\) | 1.05470i | 0.0631434i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 25.1883i | − | 1.50261i | −0.659956 | − | 0.751304i | \(-0.729425\pi\) | ||
0.659956 | − | 0.751304i | \(-0.270575\pi\) | |||||||
\(282\) | 12.2437i | 0.729102i | ||||||||
\(283\) | 23.0334 | 1.36920 | 0.684598 | − | 0.728921i | \(-0.259978\pi\) | ||||
0.684598 | + | 0.728921i | \(0.259978\pi\) | |||||||
\(284\) | −14.0795 | −0.835467 | ||||||||
\(285\) | 2.60580 | 0.154354 | ||||||||
\(286\) | 8.41014 | + | 1.80830i | 0.497302 | + | 0.106927i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 18.6853 | 1.09914 | ||||||||
\(290\) | − | 4.51160i | − | 0.264930i | ||||||
\(291\) | −0.786131 | −0.0460838 | ||||||||
\(292\) | 9.91318 | 0.580125 | ||||||||
\(293\) | −4.18076 | −0.244242 | −0.122121 | − | 0.992515i | \(-0.538970\pi\) | ||||
−0.122121 | + | 0.992515i | \(0.538970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.11019 | −0.472194 | ||||||||
\(296\) | 10.9893i | 0.638743i | ||||||||
\(297\) | 3.24252 | + | 0.697189i | 0.188150 | + | 0.0404550i | ||||
\(298\) | 4.39696 | 0.254709 | ||||||||
\(299\) | 7.43126 | 0.429761 | ||||||||
\(300\) | 4.29878i | 0.248190i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10.2407 | 0.589288 | ||||||||
\(303\) | 6.72227i | 0.386184i | ||||||||
\(304\) | −3.11181 | −0.178474 | ||||||||
\(305\) | − | 3.40859i | − | 0.195175i | ||||||
\(306\) | − | 5.97372i | − | 0.341495i | ||||||
\(307\) | 10.0657 | 0.574478 | 0.287239 | − | 0.957859i | \(-0.407263\pi\) | ||||
0.287239 | + | 0.957859i | \(0.407263\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.07143 | 0.231615 | ||||||||
\(310\) | − | 0.883199i | − | 0.0501623i | ||||||
\(311\) | 1.42972i | 0.0810718i | 0.999178 | + | 0.0405359i | \(0.0129065\pi\) | ||||
−0.999178 | + | 0.0405359i | \(0.987093\pi\) | |||||||
\(312\) | −2.59370 | −0.146840 | ||||||||
\(313\) | − | 30.3930i | − | 1.71792i | −0.512046 | − | 0.858958i | \(-0.671112\pi\) | ||
0.512046 | − | 0.858958i | \(-0.328888\pi\) | |||||||
\(314\) | 15.9861 | 0.902147 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.5121i | 0.760113i | ||||||||
\(317\) | 10.8522 | 0.609521 | 0.304760 | − | 0.952429i | \(-0.401424\pi\) | ||||
0.304760 | + | 0.952429i | \(0.401424\pi\) | |||||||
\(318\) | 5.17461 | 0.290178 | ||||||||
\(319\) | −17.4697 | − | 3.75624i | −0.978114 | − | 0.210309i | ||||
\(320\) | 0.837391i | 0.0468116i | ||||||||
\(321\) | −0.241883 | −0.0135006 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.5891 | −1.03432 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 11.1498 | 0.618477 | ||||||||
\(326\) | − | 0.523852i | − | 0.0290135i | ||||||
\(327\) | −17.5252 | −0.969145 | ||||||||
\(328\) | 11.2350i | 0.620348i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.71526 | − | 0.583820i | −0.149470 | − | 0.0321382i | ||||
\(331\) | −12.9149 | −0.709870 | −0.354935 | − | 0.934891i | \(-0.615497\pi\) | ||||
−0.354935 | + | 0.934891i | \(0.615497\pi\) | |||||||
\(332\) | −2.99287 | −0.164255 | ||||||||
\(333\) | 10.9893 | 0.602212 | ||||||||
\(334\) | − | 17.0544i | − | 0.933175i | ||||||
\(335\) | − | 10.9182i | − | 0.596523i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.4809i | − | 0.897772i | −0.893589 | − | 0.448886i | \(-0.851821\pi\) | ||
0.893589 | − | 0.448886i | \(-0.148179\pi\) | |||||||
\(338\) | − | 6.27269i | − | 0.341190i | ||||||
\(339\) | − | 8.08949i | − | 0.439361i | ||||||
\(340\) | 5.00234i | 0.271290i | ||||||||
\(341\) | −3.41989 | − | 0.735327i | −0.185198 | − | 0.0398202i | ||||
\(342\) | 3.11181i | 0.168267i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.27527 | 0.0687582 | ||||||||
\(345\) | −2.39922 | −0.129170 | ||||||||
\(346\) | − | 7.23663i | − | 0.389044i | ||||||
\(347\) | 11.4633i | 0.615380i | 0.951487 | + | 0.307690i | \(0.0995560\pi\) | ||||
−0.951487 | + | 0.307690i | \(0.900444\pi\) | |||||||
\(348\) | 5.38769 | 0.288810 | ||||||||
\(349\) | −20.9561 | −1.12176 | −0.560878 | − | 0.827899i | \(-0.689536\pi\) | ||||
−0.560878 | + | 0.827899i | \(0.689536\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.59370i | 0.138442i | ||||||||
\(352\) | 3.24252 | + | 0.697189i | 0.172827 | + | 0.0371603i | ||||
\(353\) | 19.9221i | 1.06035i | 0.847890 | + | 0.530173i | \(0.177873\pi\) | ||||
−0.847890 | + | 0.530173i | \(0.822127\pi\) | |||||||
\(354\) | − | 9.68506i | − | 0.514755i | ||||||
\(355\) | − | 11.7901i | − | 0.625753i | ||||||
\(356\) | 8.40678i | 0.445559i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.06636i | 0.426321i | ||||||||
\(359\) | 3.91431i | 0.206589i | 0.994651 | + | 0.103295i | \(0.0329384\pi\) | ||||
−0.994651 | + | 0.103295i | \(0.967062\pi\) | |||||||
\(360\) | 0.837391 | 0.0441344 | ||||||||
\(361\) | −9.31665 | −0.490350 | ||||||||
\(362\) | −5.61056 | −0.294885 | ||||||||
\(363\) | −4.52130 | + | 10.0279i | −0.237307 | + | 0.526326i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.30121i | 0.434505i | ||||||||
\(366\) | 4.07048 | 0.212768 | ||||||||
\(367\) | 12.0920i | 0.631198i | 0.948893 | + | 0.315599i | \(0.102205\pi\) | ||||
−0.948893 | + | 0.315599i | \(0.897795\pi\) | |||||||
\(368\) | 2.86511 | 0.149354 | ||||||||
\(369\) | 11.2350 | 0.584870 | ||||||||
\(370\) | −9.20238 | −0.478409 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.05470 | 0.0546838 | ||||||||
\(373\) | − | 17.6936i | − | 0.916141i | −0.888916 | − | 0.458070i | \(-0.848541\pi\) | ||
0.888916 | − | 0.458070i | \(-0.151459\pi\) | |||||||
\(374\) | 19.3699 | + | 4.16481i | 1.00159 | + | 0.215357i | ||||
\(375\) | −7.78672 | −0.402104 | ||||||||
\(376\) | 12.2437 | 0.631421 | ||||||||
\(377\) | − | 13.9741i | − | 0.719701i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.6577 | 1.00975 | 0.504874 | − | 0.863193i | \(-0.331539\pi\) | ||||
0.504874 | + | 0.863193i | \(0.331539\pi\) | |||||||
\(380\) | − | 2.60580i | − | 0.133675i | ||||||
\(381\) | −12.1313 | −0.621507 | ||||||||
\(382\) | 11.7841i | 0.602928i | ||||||||
\(383\) | − | 1.37345i | − | 0.0701800i | −0.999384 | − | 0.0350900i | \(-0.988828\pi\) | ||
0.999384 | − | 0.0350900i | \(-0.0111718\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.0976 | −0.921145 | ||||||||
\(387\) | − | 1.27527i | − | 0.0648258i | ||||||
\(388\) | 0.786131i | 0.0399097i | ||||||||
\(389\) | 31.3793 | 1.59099 | 0.795496 | − | 0.605959i | \(-0.207210\pi\) | ||||
0.795496 | + | 0.605959i | \(0.207210\pi\) | |||||||
\(390\) | − | 2.17195i | − | 0.109981i | ||||||
\(391\) | 17.1154 | 0.865562 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.04449i | − | 0.103131i | ||||||
\(394\) | −6.23110 | −0.313918 | ||||||||
\(395\) | −11.3149 | −0.569313 | ||||||||
\(396\) | 0.697189 | − | 3.24252i | 0.0350351 | − | 0.162943i | ||||
\(397\) | 35.2719i | 1.77025i | 0.465357 | + | 0.885123i | \(0.345926\pi\) | ||||
−0.465357 | + | 0.885123i | \(0.654074\pi\) | |||||||
\(398\) | 18.2669 | 0.915636 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.29878 | 0.214939 | ||||||||
\(401\) | 8.96618 | 0.447750 | 0.223875 | − | 0.974618i | \(-0.428129\pi\) | ||||
0.223875 | + | 0.974618i | \(0.428129\pi\) | |||||||
\(402\) | 13.0383 | 0.650292 | ||||||||
\(403\) | − | 2.73559i | − | 0.136269i | ||||||
\(404\) | 6.72227 | 0.334445 | ||||||||
\(405\) | − | 0.837391i | − | 0.0416103i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.66165 | + | 35.6332i | −0.379774 | + | 1.76627i | ||||
\(408\) | −5.97372 | −0.295743 | ||||||||
\(409\) | −35.9524 | −1.77773 | −0.888867 | − | 0.458166i | \(-0.848506\pi\) | ||||
−0.888867 | + | 0.458166i | \(0.848506\pi\) | |||||||
\(410\) | −9.40808 | −0.464632 | ||||||||
\(411\) | 13.2111i | 0.651657i | ||||||||
\(412\) | − | 4.07143i | − | 0.200585i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 2.86511i | − | 0.140813i | ||||||
\(415\) | − | 2.50620i | − | 0.123025i | ||||||
\(416\) | 2.59370i | 0.127167i | ||||||||
\(417\) | − | 6.16293i | − | 0.301800i | ||||||
\(418\) | −10.0901 | − | 2.16952i | −0.493523 | − | 0.106115i | ||||
\(419\) | 0.724634i | 0.0354007i | 0.999843 | + | 0.0177004i | \(0.00563449\pi\) | ||||
−0.999843 | + | 0.0177004i | \(0.994366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.71423 | 0.181021 | 0.0905103 | − | 0.995896i | \(-0.471150\pi\) | ||||
0.0905103 | + | 0.995896i | \(0.471150\pi\) | |||||||
\(422\) | 10.2446 | 0.498701 | ||||||||
\(423\) | − | 12.2437i | − | 0.595309i | ||||||
\(424\) | − | 5.17461i | − | 0.251301i | ||||||
\(425\) | 25.6797 | 1.24565 | ||||||||
\(426\) | 14.0795 | 0.682156 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.241883i | 0.0116919i | ||||||||
\(429\) | −8.41014 | − | 1.80830i | −0.406045 | − | 0.0873057i | ||||
\(430\) | 1.06790i | 0.0514989i | ||||||||
\(431\) | 4.08478i | 0.196757i | 0.995149 | + | 0.0983784i | \(0.0313656\pi\) | ||||
−0.995149 | + | 0.0983784i | \(0.968634\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 30.3109i | 1.45665i | 0.685232 | + | 0.728325i | \(0.259701\pi\) | ||||
−0.685232 | + | 0.728325i | \(0.740299\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.51160i | 0.216315i | ||||||||
\(436\) | 17.5252i | 0.839304i | ||||||||
\(437\) | −8.91569 | −0.426495 | ||||||||
\(438\) | −9.91318 | −0.473670 | ||||||||
\(439\) | 12.6102 | 0.601854 | 0.300927 | − | 0.953647i | \(-0.402704\pi\) | ||||
0.300927 | + | 0.953647i | \(0.402704\pi\) | |||||||
\(440\) | −0.583820 | + | 2.71526i | −0.0278325 | + | 0.129445i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.4941i | 0.736978i | ||||||||
\(443\) | 15.2372 | 0.723940 | 0.361970 | − | 0.932190i | \(-0.382104\pi\) | ||||
0.361970 | + | 0.932190i | \(0.382104\pi\) | |||||||
\(444\) | − | 10.9893i | − | 0.521531i | ||||||
\(445\) | −7.03977 | −0.333717 | ||||||||
\(446\) | 15.6665 | 0.741831 | ||||||||
\(447\) | −4.39696 | −0.207969 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.2780 | 1.52329 | 0.761647 | − | 0.647993i | \(-0.224391\pi\) | ||||
0.761647 | + | 0.647993i | \(0.224391\pi\) | |||||||
\(450\) | − | 4.29878i | − | 0.202646i | ||||||
\(451\) | −7.83291 | + | 36.4296i | −0.368837 | + | 1.71540i | ||||
\(452\) | −8.08949 | −0.380498 | ||||||||
\(453\) | −10.2407 | −0.481152 | ||||||||
\(454\) | − | 15.7205i | − | 0.737799i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.11181 | 0.145724 | ||||||||
\(457\) | 30.3447i | 1.41947i | 0.704471 | + | 0.709733i | \(0.251184\pi\) | ||||
−0.704471 | + | 0.709733i | \(0.748816\pi\) | |||||||
\(458\) | −2.50417 | −0.117012 | ||||||||
\(459\) | 5.97372i | 0.278829i | ||||||||
\(460\) | 2.39922i | 0.111864i | ||||||||
\(461\) | 4.81402 | 0.224211 | 0.112106 | − | 0.993696i | \(-0.464240\pi\) | ||||
0.112106 | + | 0.993696i | \(0.464240\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.1197 | −1.53920 | −0.769600 | − | 0.638526i | \(-0.779545\pi\) | ||||
−0.769600 | + | 0.638526i | \(0.779545\pi\) | |||||||
\(464\) | − | 5.38769i | − | 0.250117i | ||||||
\(465\) | 0.883199i | 0.0409574i | ||||||||
\(466\) | −0.0553161 | −0.00256247 | ||||||||
\(467\) | 14.3866i | 0.665730i | 0.942974 | + | 0.332865i | \(0.108015\pi\) | ||||
−0.942974 | + | 0.332865i | \(0.891985\pi\) | |||||||
\(468\) | 2.59370 | 0.119894 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 10.2528i | 0.472925i | ||||||||
\(471\) | −15.9861 | −0.736600 | ||||||||
\(472\) | −9.68506 | −0.445791 | ||||||||
\(473\) | 4.13510 | + | 0.889107i | 0.190132 | + | 0.0408812i | ||||
\(474\) | − | 13.5121i | − | 0.620629i | ||||||
\(475\) | −13.3770 | −0.613777 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.17461 | −0.236929 | ||||||||
\(478\) | 5.74465 | 0.262754 | ||||||||
\(479\) | 6.47208 | 0.295717 | 0.147859 | − | 0.989009i | \(-0.452762\pi\) | ||||
0.147859 | + | 0.989009i | \(0.452762\pi\) | |||||||
\(480\) | − | 0.837391i | − | 0.0382215i | ||||||
\(481\) | −28.5031 | −1.29963 | ||||||||
\(482\) | 7.34245i | 0.334440i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.0279 | + | 4.52130i | 0.455812 | + | 0.205514i | ||||
\(485\) | −0.658299 | −0.0298918 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −5.28096 | −0.239303 | −0.119652 | − | 0.992816i | \(-0.538178\pi\) | ||||
−0.119652 | + | 0.992816i | \(0.538178\pi\) | |||||||
\(488\) | − | 4.07048i | − | 0.184262i | ||||||
\(489\) | 0.523852i | 0.0236894i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.3633i | − | 0.512820i | −0.966568 | − | 0.256410i | \(-0.917460\pi\) | ||
0.966568 | − | 0.256410i | \(-0.0825398\pi\) | |||||||
\(492\) | − | 11.2350i | − | 0.506512i | ||||||
\(493\) | − | 32.1845i | − | 1.44952i | ||||||
\(494\) | − | 8.07111i | − | 0.363137i | ||||||
\(495\) | 2.71526 | + | 0.583820i | 0.122042 | + | 0.0262408i | ||||
\(496\) | − | 1.05470i | − | 0.0473575i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.99287 | 0.134114 | ||||||||
\(499\) | −29.1721 | −1.30592 | −0.652961 | − | 0.757392i | \(-0.726473\pi\) | ||||
−0.652961 | + | 0.757392i | \(0.726473\pi\) | |||||||
\(500\) | 7.78672i | 0.348232i | ||||||||
\(501\) | 17.0544i | 0.761934i | ||||||||
\(502\) | 4.20803 | 0.187813 | ||||||||
\(503\) | 22.4317 | 1.00018 | 0.500090 | − | 0.865973i | \(-0.333300\pi\) | ||||
0.500090 | + | 0.865973i | \(0.333300\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.62917i | 0.250495i | ||||||||
\(506\) | 9.29019 | + | 1.99753i | 0.412999 | + | 0.0888009i | ||||
\(507\) | 6.27269i | 0.278580i | ||||||||
\(508\) | 12.1313i | 0.538241i | ||||||||
\(509\) | 27.3682i | 1.21307i | 0.795055 | + | 0.606537i | \(0.207442\pi\) | ||||
−0.795055 | + | 0.606537i | \(0.792558\pi\) | |||||||
\(510\) | − | 5.00234i | − | 0.221507i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 3.11181i | − | 0.137390i | ||||||
\(514\) | −24.6466 | −1.08711 | ||||||||
\(515\) | 3.40938 | 0.150235 | ||||||||
\(516\) | −1.27527 | −0.0561408 | ||||||||
\(517\) | 39.7005 | + | 8.53618i | 1.74602 | + | 0.375421i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.23663i | 0.317653i | ||||||||
\(520\) | −2.17195 | −0.0952461 | ||||||||
\(521\) | 34.9911i | 1.53299i | 0.642252 | + | 0.766493i | \(0.278000\pi\) | ||||
−0.642252 | + | 0.766493i | \(0.722000\pi\) | |||||||
\(522\) | −5.38769 | −0.235813 | ||||||||
\(523\) | 38.2448 | 1.67233 | 0.836165 | − | 0.548479i | \(-0.184793\pi\) | ||||
0.836165 | + | 0.548479i | \(0.184793\pi\) | |||||||
\(524\) | −2.04449 | −0.0893139 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.3837 | −1.32479 | ||||||||
\(527\) | − | 6.30050i | − | 0.274454i | ||||||
\(528\) | −3.24252 | − | 0.697189i | −0.141113 | − | 0.0303413i | ||||
\(529\) | −14.7911 | −0.643092 | ||||||||
\(530\) | 4.33317 | 0.188221 | ||||||||
\(531\) | 9.68506i | 0.420296i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.1402 | −1.26220 | ||||||||
\(534\) | − | 8.40678i | − | 0.363797i | ||||||
\(535\) | −0.202551 | −0.00875704 | ||||||||
\(536\) | − | 13.0383i | − | 0.563169i | ||||||
\(537\) | − | 8.06636i | − | 0.348089i | ||||||
\(538\) | −19.9737 | −0.861128 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.837391 | −0.0360356 | ||||||||
\(541\) | 3.15324i | 0.135568i | 0.997700 | + | 0.0677842i | \(0.0215929\pi\) | ||||
−0.997700 | + | 0.0677842i | \(0.978407\pi\) | |||||||
\(542\) | 1.61528i | 0.0693821i | ||||||||
\(543\) | 5.61056 | 0.240772 | ||||||||
\(544\) | 5.97372i | 0.256121i | ||||||||
\(545\) | −14.6754 | −0.628627 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.6313i | − | 0.882131i | −0.897475 | − | 0.441065i | \(-0.854601\pi\) | ||
0.897475 | − | 0.441065i | \(-0.145399\pi\) | |||||||
\(548\) | 13.2111 | 0.564351 | ||||||||
\(549\) | −4.07048 | −0.173724 | ||||||||
\(550\) | 13.9389 | + | 2.99706i | 0.594355 | + | 0.127795i | ||||
\(551\) | 16.7655i | 0.714232i | ||||||||
\(552\) | −2.86511 | −0.121947 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.18071 | 0.220107 | ||||||||
\(555\) | 9.20238 | 0.390619 | ||||||||
\(556\) | −6.16293 | −0.261367 | ||||||||
\(557\) | − | 1.27071i | − | 0.0538415i | −0.999638 | − | 0.0269208i | \(-0.991430\pi\) | ||
0.999638 | − | 0.0269208i | \(-0.00857018\pi\) | |||||||
\(558\) | −1.05470 | −0.0446491 | ||||||||
\(559\) | 3.30769i | 0.139900i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.3699 | − | 4.16481i | −0.817798 | − | 0.175839i | ||||
\(562\) | 25.1883 | 1.06250 | ||||||||
\(563\) | 40.3458 | 1.70037 | 0.850187 | − | 0.526481i | \(-0.176489\pi\) | ||||
0.850187 | + | 0.526481i | \(0.176489\pi\) | |||||||
\(564\) | −12.2437 | −0.515553 | ||||||||
\(565\) | − | 6.77407i | − | 0.284987i | ||||||
\(566\) | 23.0334i | 0.968168i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 14.0795i | − | 0.590764i | ||||||
\(569\) | − | 2.78095i | − | 0.116583i | −0.998300 | − | 0.0582917i | \(-0.981435\pi\) | ||
0.998300 | − | 0.0582917i | \(-0.0185653\pi\) | |||||||
\(570\) | 2.60580i | 0.109145i | ||||||||
\(571\) | 38.1829i | 1.59791i | 0.601393 | + | 0.798953i | \(0.294612\pi\) | ||||
−0.601393 | + | 0.798953i | \(0.705388\pi\) | |||||||
\(572\) | −1.80830 | + | 8.41014i | −0.0756089 | + | 0.351645i | ||||
\(573\) | − | 11.7841i | − | 0.492288i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.3165 | 0.513633 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 6.84536i | 0.284976i | 0.989797 | + | 0.142488i | \(0.0455103\pi\) | ||||
−0.989797 | + | 0.142488i | \(0.954490\pi\) | |||||||
\(578\) | 18.6853i | 0.777208i | ||||||||
\(579\) | 18.0976 | 0.752112 | ||||||||
\(580\) | 4.51160 | 0.187334 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 0.786131i | − | 0.0325862i | ||||||
\(583\) | 3.60768 | − | 16.7788i | 0.149415 | − | 0.694905i | ||||
\(584\) | 9.91318i | 0.410210i | ||||||||
\(585\) | 2.17195i | 0.0897989i | ||||||||
\(586\) | − | 4.18076i | − | 0.172705i | ||||||
\(587\) | 22.7050i | 0.937135i | 0.883428 | + | 0.468568i | \(0.155230\pi\) | ||||
−0.883428 | + | 0.468568i | \(0.844770\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.28203i | 0.135234i | ||||||||
\(590\) | − | 8.11019i | − | 0.333891i | ||||||
\(591\) | 6.23110 | 0.256313 | ||||||||
\(592\) | −10.9893 | −0.451659 | ||||||||
\(593\) | 10.1112 | 0.415215 | 0.207608 | − | 0.978212i | \(-0.433432\pi\) | ||||
0.207608 | + | 0.978212i | \(0.433432\pi\) | |||||||
\(594\) | −0.697189 | + | 3.24252i | −0.0286060 | + | 0.133042i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.39696i | 0.180107i | ||||||||
\(597\) | −18.2669 | −0.747614 | ||||||||
\(598\) | 7.43126i | 0.303887i | ||||||||
\(599\) | −2.90438 | −0.118670 | −0.0593349 | − | 0.998238i | \(-0.518898\pi\) | ||||
−0.0593349 | + | 0.998238i | \(0.518898\pi\) | |||||||
\(600\) | −4.29878 | −0.175497 | ||||||||
\(601\) | −8.68237 | −0.354161 | −0.177081 | − | 0.984196i | \(-0.556665\pi\) | ||||
−0.177081 | + | 0.984196i | \(0.556665\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.0383 | −0.530961 | ||||||||
\(604\) | 10.2407i | 0.416690i | ||||||||
\(605\) | −3.78610 | + | 8.39724i | −0.153927 | + | 0.341396i | ||||
\(606\) | −6.72227 | −0.273074 | ||||||||
\(607\) | −23.4682 | −0.952544 | −0.476272 | − | 0.879298i | \(-0.658012\pi\) | ||||
−0.476272 | + | 0.879298i | \(0.658012\pi\) | |||||||
\(608\) | − | 3.11181i | − | 0.126200i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.40859 | 0.138010 | ||||||||
\(611\) | 31.7566i | 1.28473i | ||||||||
\(612\) | 5.97372 | 0.241473 | ||||||||
\(613\) | − | 30.9799i | − | 1.25127i | −0.780117 | − | 0.625633i | \(-0.784841\pi\) | ||
0.780117 | − | 0.625633i | \(-0.215159\pi\) | |||||||
\(614\) | 10.0657i | 0.406217i | ||||||||
\(615\) | 9.40808 | 0.379370 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.35346 | 0.296039 | 0.148020 | − | 0.988984i | \(-0.452710\pi\) | ||||
0.148020 | + | 0.988984i | \(0.452710\pi\) | |||||||
\(618\) | 4.07143i | 0.163777i | ||||||||
\(619\) | − | 3.65678i | − | 0.146978i | −0.997296 | − | 0.0734892i | \(-0.976587\pi\) | ||
0.997296 | − | 0.0734892i | \(-0.0234134\pi\) | |||||||
\(620\) | 0.883199 | 0.0354701 | ||||||||
\(621\) | 2.86511i | 0.114973i | ||||||||
\(622\) | −1.42972 | −0.0573264 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 2.59370i | − | 0.103831i | ||||||
\(625\) | 14.9733 | 0.598934 | ||||||||
\(626\) | 30.3930 | 1.21475 | ||||||||
\(627\) | 10.0901 | + | 2.16952i | 0.402960 | + | 0.0866422i | ||||
\(628\) | 15.9861i | 0.637914i | ||||||||
\(629\) | −65.6473 | −2.61753 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5757 | 0.898724 | 0.449362 | − | 0.893350i | \(-0.351651\pi\) | ||||
0.449362 | + | 0.893350i | \(0.351651\pi\) | |||||||
\(632\) | −13.5121 | −0.537481 | ||||||||
\(633\) | −10.2446 | −0.407187 | ||||||||
\(634\) | 10.8522i | 0.430996i | ||||||||
\(635\) | −10.1587 | −0.403135 | ||||||||
\(636\) | 5.17461i | 0.205187i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.75624 | − | 17.4697i | 0.148711 | − | 0.691631i | ||||
\(639\) | −14.0795 | −0.556978 | ||||||||
\(640\) | −0.837391 | −0.0331008 | ||||||||
\(641\) | −44.5605 | −1.76003 | −0.880017 | − | 0.474943i | \(-0.842469\pi\) | ||||
−0.880017 | + | 0.474943i | \(0.842469\pi\) | |||||||
\(642\) | − | 0.241883i | − | 0.00954637i | ||||||
\(643\) | − | 14.8587i | − | 0.585968i | −0.956117 | − | 0.292984i | \(-0.905352\pi\) | ||
0.956117 | − | 0.292984i | \(-0.0946483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1.06790i | − | 0.0420487i | ||||||
\(646\) | − | 18.5891i | − | 0.731377i | ||||||
\(647\) | 47.9408i | 1.88475i | 0.334565 | + | 0.942373i | \(0.391411\pi\) | ||||
−0.334565 | + | 0.942373i | \(0.608589\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −31.4040 | − | 6.75232i | −1.23271 | − | 0.265052i | ||||
\(650\) | 11.1498i | 0.437329i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.523852 | 0.0205156 | ||||||||
\(653\) | 25.8319 | 1.01088 | 0.505440 | − | 0.862862i | \(-0.331330\pi\) | ||||
0.505440 | + | 0.862862i | \(0.331330\pi\) | |||||||
\(654\) | − | 17.5252i | − | 0.685289i | ||||||
\(655\) | − | 1.71204i | − | 0.0668948i | ||||||
\(656\) | −11.2350 | −0.438652 | ||||||||
\(657\) | 9.91318 | 0.386750 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 28.7951i | − | 1.12170i | −0.827918 | − | 0.560850i | \(-0.810475\pi\) | ||
0.827918 | − | 0.560850i | \(-0.189525\pi\) | |||||||
\(660\) | 0.583820 | − | 2.71526i | 0.0227252 | − | 0.105691i | ||||
\(661\) | − | 26.6354i | − | 1.03600i | −0.855381 | − | 0.517999i | \(-0.826677\pi\) | ||
0.855381 | − | 0.517999i | \(-0.173323\pi\) | |||||||
\(662\) | − | 12.9149i | − | 0.501954i | ||||||
\(663\) | − | 15.4941i | − | 0.601740i | ||||||
\(664\) | − | 2.99287i | − | 0.116146i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.9893i | 0.425829i | ||||||||
\(667\) | − | 15.4363i | − | 0.597697i | ||||||
\(668\) | 17.0544 | 0.659855 | ||||||||
\(669\) | −15.6665 | −0.605703 | ||||||||
\(670\) | 10.9182 | 0.421806 | ||||||||
\(671\) | 2.83790 | − | 13.1986i | 0.109556 | − | 0.509527i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.3054i | 0.474337i | 0.971469 | + | 0.237168i | \(0.0762193\pi\) | ||||
−0.971469 | + | 0.237168i | \(0.923781\pi\) | |||||||
\(674\) | 16.4809 | 0.634820 | ||||||||
\(675\) | 4.29878i | 0.165460i | ||||||||
\(676\) | 6.27269 | 0.241257 | ||||||||
\(677\) | −11.4608 | −0.440476 | −0.220238 | − | 0.975446i | \(-0.570683\pi\) | ||||
−0.220238 | + | 0.975446i | \(0.570683\pi\) | |||||||
\(678\) | 8.08949 | 0.310675 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.00234 | −0.191831 | ||||||||
\(681\) | 15.7205i | 0.602411i | ||||||||
\(682\) | 0.735327 | − | 3.41989i | 0.0281571 | − | 0.130954i | ||||
\(683\) | −7.56002 | −0.289276 | −0.144638 | − | 0.989485i | \(-0.546202\pi\) | ||||
−0.144638 | + | 0.989485i | \(0.546202\pi\) | |||||||
\(684\) | −3.11181 | −0.118983 | ||||||||
\(685\) | 11.0629i | 0.422691i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.50417 | 0.0955399 | ||||||||
\(688\) | 1.27527i | 0.0486194i | ||||||||
\(689\) | 13.4214 | 0.511315 | ||||||||
\(690\) | − | 2.39922i | − | 0.0913368i | ||||||
\(691\) | 19.0094i | 0.723152i | 0.932343 | + | 0.361576i | \(0.117761\pi\) | ||||
−0.932343 | + | 0.361576i | \(0.882239\pi\) | |||||||
\(692\) | 7.23663 | 0.275095 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.4633 | −0.435140 | ||||||||
\(695\) | − | 5.16079i | − | 0.195760i | ||||||
\(696\) | 5.38769i | 0.204220i | ||||||||
\(697\) | −67.1146 | −2.54215 | ||||||||
\(698\) | − | 20.9561i | − | 0.793201i | ||||||
\(699\) | 0.0553161 | 0.00209225 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.6349i | − | 1.23260i | −0.787510 | − | 0.616302i | \(-0.788630\pi\) | ||
0.787510 | − | 0.616302i | \(-0.211370\pi\) | |||||||
\(702\) | −2.59370 | −0.0978931 | ||||||||
\(703\) | 34.1967 | 1.28975 | ||||||||
\(704\) | −0.697189 | + | 3.24252i | −0.0262763 | + | 0.122207i | ||||
\(705\) | − | 10.2528i | − | 0.386142i | ||||||
\(706\) | −19.9221 | −0.749778 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.68506 | 0.363987 | ||||||||
\(709\) | 15.1506 | 0.568994 | 0.284497 | − | 0.958677i | \(-0.408173\pi\) | ||||
0.284497 | + | 0.958677i | \(0.408173\pi\) | |||||||
\(710\) | 11.7901 | 0.442474 | ||||||||
\(711\) | 13.5121i | 0.506742i | ||||||||
\(712\) | −8.40678 | −0.315057 | ||||||||
\(713\) | − | 3.02184i | − | 0.113169i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.04258 | − | 1.51426i | −0.263377 | − | 0.0566300i | ||||
\(716\) | −8.06636 | −0.301454 | ||||||||
\(717\) | −5.74465 | −0.214538 | ||||||||
\(718\) | −3.91431 | −0.146081 | ||||||||
\(719\) | − | 5.15470i | − | 0.192238i | −0.995370 | − | 0.0961189i | \(-0.969357\pi\) | ||
0.995370 | − | 0.0961189i | \(-0.0306429\pi\) | |||||||
\(720\) | 0.837391i | 0.0312077i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 9.31665i | − | 0.346730i | ||||||
\(723\) | − | 7.34245i | − | 0.273069i | ||||||
\(724\) | − | 5.61056i | − | 0.208515i | ||||||
\(725\) | − | 23.1605i | − | 0.860158i | ||||||
\(726\) | −10.0279 | − | 4.52130i | −0.372169 | − | 0.167801i | ||||
\(727\) | 24.1329i | 0.895041i | 0.894274 | + | 0.447520i | \(0.147693\pi\) | ||||
−0.894274 | + | 0.447520i | \(0.852307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −8.30121 | −0.307242 | ||||||||
\(731\) | 7.61813i | 0.281767i | ||||||||
\(732\) | 4.07048i | 0.150449i | ||||||||
\(733\) | −52.1041 | −1.92451 | −0.962254 | − | 0.272153i | \(-0.912264\pi\) | ||||
−0.962254 | + | 0.272153i | \(0.912264\pi\) | |||||||
\(734\) | −12.0920 | −0.446324 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.86511i | 0.105609i | ||||||||
\(737\) | 9.09017 | − | 42.2770i | 0.334841 | − | 1.55729i | ||||
\(738\) | 11.2350i | 0.413565i | ||||||||
\(739\) | − | 5.54673i | − | 0.204040i | −0.994782 | − | 0.102020i | \(-0.967469\pi\) | ||
0.994782 | − | 0.102020i | \(-0.0325305\pi\) | |||||||
\(740\) | − | 9.20238i | − | 0.338286i | ||||||
\(741\) | 8.07111i | 0.296500i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.2750i | 0.670443i | 0.942139 | + | 0.335222i | \(0.108811\pi\) | ||||
−0.942139 | + | 0.335222i | \(0.891189\pi\) | |||||||
\(744\) | 1.05470i | 0.0386673i | ||||||||
\(745\) | −3.68198 | −0.134897 | ||||||||
\(746\) | 17.6936 | 0.647809 | ||||||||
\(747\) | −2.99287 | −0.109503 | ||||||||
\(748\) | −4.16481 | + | 19.3699i | −0.152281 | + | 0.708234i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 7.78672i | − | 0.284331i | ||||||
\(751\) | −14.7153 | −0.536968 | −0.268484 | − | 0.963284i | \(-0.586523\pi\) | ||||
−0.268484 | + | 0.963284i | \(0.586523\pi\) | |||||||
\(752\) | 12.2437i | 0.446482i | ||||||||
\(753\) | −4.20803 | −0.153349 | ||||||||
\(754\) | 13.9741 | 0.508906 | ||||||||
\(755\) | −8.57551 | −0.312095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.8890 | −1.70421 | −0.852105 | − | 0.523371i | \(-0.824674\pi\) | ||||
−0.852105 | + | 0.523371i | \(0.824674\pi\) | |||||||
\(758\) | 19.6577i | 0.713999i | ||||||||
\(759\) | −9.29019 | − | 1.99753i | −0.337212 | − | 0.0725056i | ||||
\(760\) | 2.60580 | 0.0945224 | ||||||||
\(761\) | −37.0413 | −1.34275 | −0.671373 | − | 0.741120i | \(-0.734295\pi\) | ||||
−0.671373 | + | 0.741120i | \(0.734295\pi\) | |||||||
\(762\) | − | 12.1313i | − | 0.439472i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −11.7841 | −0.426334 | ||||||||
\(765\) | 5.00234i | 0.180860i | ||||||||
\(766\) | 1.37345 | 0.0496248 | ||||||||
\(767\) | − | 25.1202i | − | 0.907038i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −10.3666 | −0.373830 | −0.186915 | − | 0.982376i | \(-0.559849\pi\) | ||||
−0.186915 | + | 0.982376i | \(0.559849\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.6466 | 0.887625 | ||||||||
\(772\) | − | 18.0976i | − | 0.651348i | ||||||
\(773\) | − | 21.6146i | − | 0.777423i | −0.921359 | − | 0.388712i | \(-0.872920\pi\) | ||
0.921359 | − | 0.388712i | \(-0.127080\pi\) | |||||||
\(774\) | 1.27527 | 0.0458388 | ||||||||
\(775\) | − | 4.53393i | − | 0.162864i | ||||||
\(776\) | −0.786131 | −0.0282204 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.3793i | 1.12500i | ||||||||
\(779\) | 34.9611 | 1.25261 | ||||||||
\(780\) | 2.17195 | 0.0777682 | ||||||||
\(781\) | 9.81610 | − | 45.6532i | 0.351248 | − | 1.63360i | ||||
\(782\) | 17.1154i | 0.612045i | ||||||||
\(783\) | 5.38769 | 0.192540 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.3866 | −0.477789 | ||||||||
\(786\) | 2.04449 | 0.0729245 | ||||||||
\(787\) | 48.6910 | 1.73565 | 0.867824 | − | 0.496871i | \(-0.165518\pi\) | ||||
0.867824 | + | 0.496871i | \(0.165518\pi\) | |||||||
\(788\) | − | 6.23110i | − | 0.221974i | ||||||
\(789\) | 30.3837 | 1.08169 | ||||||||
\(790\) | − | 11.3149i | − | 0.402565i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.24252 | + | 0.697189i | 0.115218 | + | 0.0247735i | ||||
\(793\) | 10.5576 | 0.374913 | ||||||||
\(794\) | −35.2719 | −1.25175 | ||||||||
\(795\) | −4.33317 | −0.153682 | ||||||||
\(796\) | 18.2669i | 0.647453i | ||||||||
\(797\) | − | 36.0374i | − | 1.27651i | −0.769825 | − | 0.638255i | \(-0.779657\pi\) | ||
0.769825 | − | 0.638255i | \(-0.220343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73.1405i | 2.58752i | ||||||||
\(800\) | 4.29878i | 0.151985i | ||||||||
\(801\) | 8.40678i | 0.297039i | ||||||||
\(802\) | 8.96618i | 0.316607i | ||||||||
\(803\) | −6.91136 | + | 32.1437i | −0.243897 | + | 1.13433i | ||||
\(804\) | 13.0383i | 0.459826i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.73559 | 0.0963569 | ||||||||
\(807\) | 19.9737 | 0.703108 | ||||||||
\(808\) | 6.72227i | 0.236489i | ||||||||
\(809\) | 29.9102i | 1.05159i | 0.850613 | + | 0.525793i | \(0.176231\pi\) | ||||
−0.850613 | + | 0.525793i | \(0.823769\pi\) | |||||||
\(810\) | 0.837391 | 0.0294229 | ||||||||
\(811\) | 18.1295 | 0.636611 | 0.318306 | − | 0.947988i | \(-0.396886\pi\) | ||||
0.318306 | + | 0.947988i | \(0.396886\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.61528i | − | 0.0566503i | ||||||
\(814\) | −35.6332 | − | 7.66165i | −1.24894 | − | 0.268541i | ||||
\(815\) | 0.438669i | 0.0153659i | ||||||||
\(816\) | − | 5.97372i | − | 0.209122i | ||||||
\(817\) | − | 3.96841i | − | 0.138837i | ||||||
\(818\) | − | 35.9524i | − | 1.25705i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 9.40808i | − | 0.328544i | ||||||
\(821\) | 19.4780i | 0.679786i | 0.940464 | + | 0.339893i | \(0.110391\pi\) | ||||
−0.940464 | + | 0.339893i | \(0.889609\pi\) | |||||||
\(822\) | −13.2111 | −0.460791 | ||||||||
\(823\) | 28.1862 | 0.982510 | 0.491255 | − | 0.871016i | \(-0.336538\pi\) | ||||
0.491255 | + | 0.871016i | \(0.336538\pi\) | |||||||
\(824\) | 4.07143 | 0.141835 | ||||||||
\(825\) | −13.9389 | − | 2.99706i | −0.485289 | − | 0.104344i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7981i | 0.897089i | 0.893761 | + | 0.448544i | \(0.148057\pi\) | ||||
−0.893761 | + | 0.448544i | \(0.851943\pi\) | |||||||
\(828\) | 2.86511 | 0.0995696 | ||||||||
\(829\) | 36.9176i | 1.28220i | 0.767457 | + | 0.641100i | \(0.221522\pi\) | ||||
−0.767457 | + | 0.641100i | \(0.778478\pi\) | |||||||
\(830\) | 2.50620 | 0.0869915 | ||||||||
\(831\) | −5.18071 | −0.179717 | ||||||||
\(832\) | −2.59370 | −0.0899205 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.16293 | 0.213405 | ||||||||
\(835\) | 14.2812i | 0.494222i | ||||||||
\(836\) | 2.16952 | − | 10.0901i | 0.0750344 | − | 0.348973i | ||||
\(837\) | 1.05470 | 0.0364559 | ||||||||
\(838\) | −0.724634 | −0.0250321 | ||||||||
\(839\) | − | 6.71611i | − | 0.231866i | −0.993257 | − | 0.115933i | \(-0.963014\pi\) | ||
0.993257 | − | 0.115933i | \(-0.0369858\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.0271771 | −0.000937142 | ||||||||
\(842\) | 3.71423i | 0.128001i | ||||||||
\(843\) | −25.1883 | −0.867531 | ||||||||
\(844\) | 10.2446i | 0.352635i | ||||||||
\(845\) | 5.25270i | 0.180698i | ||||||||
\(846\) | 12.2437 | 0.420947 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.17461 | 0.177697 | ||||||||
\(849\) | − | 23.0334i | − | 0.790506i | ||||||
\(850\) | 25.6797i | 0.880806i | ||||||||
\(851\) | −31.4857 | −1.07932 | ||||||||
\(852\) | 14.0795i | 0.482357i | ||||||||
\(853\) | 39.8993 | 1.36613 | 0.683063 | − | 0.730360i | \(-0.260648\pi\) | ||||
0.683063 | + | 0.730360i | \(0.260648\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 2.60580i | − | 0.0891165i | ||||||
\(856\) | −0.241883 | −0.00826740 | ||||||||
\(857\) | −15.7093 | −0.536621 | −0.268310 | − | 0.963332i | \(-0.586465\pi\) | ||||
−0.268310 | + | 0.963332i | \(0.586465\pi\) | |||||||
\(858\) | 1.80830 | − | 8.41014i | 0.0617344 | − | 0.287117i | ||||
\(859\) | − | 19.2809i | − | 0.657854i | −0.944355 | − | 0.328927i | \(-0.893313\pi\) | ||
0.944355 | − | 0.328927i | \(-0.106687\pi\) | |||||||
\(860\) | −1.06790 | −0.0364152 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.08478 | −0.139128 | ||||||||
\(863\) | 38.1522 | 1.29872 | 0.649358 | − | 0.760483i | \(-0.275038\pi\) | ||||
0.649358 | + | 0.760483i | \(0.275038\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 6.05989i | 0.206042i | ||||||||
\(866\) | −30.3109 | −1.03001 | ||||||||
\(867\) | − | 18.6853i | − | 0.634587i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.8131 | − | 9.42046i | −1.48626 | − | 0.319567i | ||||
\(870\) | −4.51160 | −0.152958 | ||||||||
\(871\) | 33.8175 | 1.14586 | ||||||||
\(872\) | −17.5252 | −0.593478 | ||||||||
\(873\) | 0.786131i | 0.0266065i | ||||||||
\(874\) | − | 8.91569i | − | 0.301578i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 9.91318i | − | 0.334935i | ||||||
\(877\) | − | 9.15113i | − | 0.309012i | −0.987992 | − | 0.154506i | \(-0.950621\pi\) | ||
0.987992 | − | 0.154506i | \(-0.0493785\pi\) | |||||||
\(878\) | 12.6102i | 0.425575i | ||||||||
\(879\) | 4.18076i | 0.141013i | ||||||||
\(880\) | −2.71526 | − | 0.583820i | −0.0915313 | − | 0.0196806i | ||||
\(881\) | 47.7019i | 1.60712i | 0.595225 | + | 0.803559i | \(0.297063\pi\) | ||||
−0.595225 | + | 0.803559i | \(0.702937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.7932 | 1.47376 | 0.736879 | − | 0.676025i | \(-0.236299\pi\) | ||||
0.736879 | + | 0.676025i | \(0.236299\pi\) | |||||||
\(884\) | −15.4941 | −0.521122 | ||||||||
\(885\) | 8.11019i | 0.272621i | ||||||||
\(886\) | 15.2372i | 0.511903i | ||||||||
\(887\) | 50.5792 | 1.69828 | 0.849142 | − | 0.528165i | \(-0.177120\pi\) | ||||
0.849142 | + | 0.528165i | \(0.177120\pi\) | |||||||
\(888\) | 10.9893 | 0.368778 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.03977i | − | 0.235974i | ||||||
\(891\) | 0.697189 | − | 3.24252i | 0.0233567 | − | 0.108628i | ||||
\(892\) | 15.6665i | 0.524554i | ||||||||
\(893\) | − | 38.1001i | − | 1.27497i | ||||||
\(894\) | − | 4.39696i | − | 0.147056i | ||||||
\(895\) | − | 6.75470i | − | 0.225785i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 7.43126i | − | 0.248123i | ||||||
\(898\) | 32.2780i | 1.07713i | ||||||||
\(899\) | −5.68241 | −0.189519 | ||||||||
\(900\) | 4.29878 | 0.143293 | ||||||||
\(901\) | 30.9117 | 1.02982 | ||||||||
\(902\) | −36.4296 | − | 7.83291i | −1.21297 | − | 0.260807i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.08949i | − | 0.269053i | ||||||
\(905\) | 4.69824 | 0.156175 | ||||||||
\(906\) | − | 10.2407i | − | 0.340226i | ||||||
\(907\) | −57.8688 | −1.92150 | −0.960752 | − | 0.277410i | \(-0.910524\pi\) | ||||
−0.960752 | + | 0.277410i | \(0.910524\pi\) | |||||||
\(908\) | 15.7205 | 0.521703 | ||||||||
\(909\) | 6.72227 | 0.222964 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.4860 | 0.844389 | 0.422195 | − | 0.906505i | \(-0.361260\pi\) | ||||
0.422195 | + | 0.906505i | \(0.361260\pi\) | |||||||
\(912\) | 3.11181i | 0.103042i | ||||||||
\(913\) | 2.08659 | − | 9.70443i | 0.0690562 | − | 0.321170i | ||||
\(914\) | −30.3447 | −1.00371 | ||||||||
\(915\) | −3.40859 | −0.112684 | ||||||||
\(916\) | − | 2.50417i | − | 0.0827400i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.97372 | −0.197162 | ||||||||
\(919\) | − | 12.9898i | − | 0.428494i | −0.976779 | − | 0.214247i | \(-0.931270\pi\) | ||
0.976779 | − | 0.214247i | \(-0.0687298\pi\) | |||||||
\(920\) | −2.39922 | −0.0791000 | ||||||||
\(921\) | − | 10.0657i | − | 0.331675i | ||||||
\(922\) | 4.81402i | 0.158541i | ||||||||
\(923\) | 36.5182 | 1.20201 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −47.2407 | −1.55327 | ||||||||
\(926\) | − | 33.1197i | − | 1.08838i | ||||||
\(927\) | − | 4.07143i | − | 0.133723i | ||||||
\(928\) | 5.38769 | 0.176860 | ||||||||
\(929\) | 21.8047i | 0.715389i | 0.933839 | + | 0.357695i | \(0.116437\pi\) | ||||
−0.933839 | + | 0.357695i | \(0.883563\pi\) | |||||||
\(930\) | −0.883199 | −0.0289612 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 0.0553161i | − | 0.00181194i | ||||||
\(933\) | 1.42972 | 0.0468068 | ||||||||
\(934\) | −14.3866 | −0.470742 | ||||||||
\(935\) | −16.2202 | − | 3.48758i | −0.530457 | − | 0.114056i | ||||
\(936\) | 2.59370i | 0.0847779i | ||||||||
\(937\) | 31.2647 | 1.02137 | 0.510686 | − | 0.859767i | \(-0.329391\pi\) | ||||
0.510686 | + | 0.859767i | \(0.329391\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.3930 | −0.991839 | ||||||||
\(940\) | −10.2528 | −0.334409 | ||||||||
\(941\) | −18.7756 | −0.612066 | −0.306033 | − | 0.952021i | \(-0.599002\pi\) | ||||
−0.306033 | + | 0.952021i | \(0.599002\pi\) | |||||||
\(942\) | − | 15.9861i | − | 0.520855i | ||||||
\(943\) | −32.1895 | −1.04823 | ||||||||
\(944\) | − | 9.68506i | − | 0.315222i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.889107 | + | 4.13510i | −0.0289074 | + | 0.134444i | ||||
\(947\) | −39.5459 | −1.28507 | −0.642534 | − | 0.766257i | \(-0.722117\pi\) | ||||
−0.642534 | + | 0.766257i | \(0.722117\pi\) | |||||||
\(948\) | 13.5121 | 0.438851 | ||||||||
\(949\) | −25.7119 | −0.834643 | ||||||||
\(950\) | − | 13.3770i | − | 0.434006i | ||||||
\(951\) | − | 10.8522i | − | 0.351907i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.98673i | 0.0967495i | 0.998829 | + | 0.0483748i | \(0.0154042\pi\) | ||||
−0.998829 | + | 0.0483748i | \(0.984596\pi\) | |||||||
\(954\) | − | 5.17461i | − | 0.167534i | ||||||
\(955\) | − | 9.86792i | − | 0.319318i | ||||||
\(956\) | 5.74465i | 0.185795i | ||||||||
\(957\) | −3.75624 | + | 17.4697i | −0.121422 | + | 0.564714i | ||||
\(958\) | 6.47208i | 0.209104i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.837391 | 0.0270267 | ||||||||
\(961\) | 29.8876 | 0.964116 | ||||||||
\(962\) | − | 28.5031i | − | 0.918977i | ||||||
\(963\) | 0.241883i | 0.00779458i | ||||||||
\(964\) | −7.34245 | −0.236484 | ||||||||
\(965\) | 15.1548 | 0.487850 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 3.61655i | − | 0.116300i | −0.998308 | − | 0.0581502i | \(-0.981480\pi\) | ||
0.998308 | − | 0.0581502i | \(-0.0185202\pi\) | |||||||
\(968\) | −4.52130 | + | 10.0279i | −0.145320 | + | 0.322307i | ||||
\(969\) | 18.5891i | 0.597167i | ||||||||
\(970\) | − | 0.658299i | − | 0.0211367i | ||||||
\(971\) | − | 27.6549i | − | 0.887488i | −0.896154 | − | 0.443744i | \(-0.853650\pi\) | ||
0.896154 | − | 0.443744i | \(-0.146350\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 5.28096i | − | 0.169213i | ||||||
\(975\) | − | 11.1498i | − | 0.357078i | ||||||
\(976\) | 4.07048 | 0.130293 | ||||||||
\(977\) | 34.8349 | 1.11447 | 0.557234 | − | 0.830356i | \(-0.311863\pi\) | ||||
0.557234 | + | 0.830356i | \(0.311863\pi\) | |||||||
\(978\) | −0.523852 | −0.0167509 | ||||||||
\(979\) | −27.2591 | − | 5.86112i | −0.871206 | − | 0.187322i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.5252i | 0.559536i | ||||||||
\(982\) | 11.3633 | 0.362619 | ||||||||
\(983\) | 22.2764i | 0.710507i | 0.934770 | + | 0.355254i | \(0.115605\pi\) | ||||
−0.934770 | + | 0.355254i | \(0.884395\pi\) | |||||||
\(984\) | 11.2350 | 0.358158 | ||||||||
\(985\) | 5.21787 | 0.166255 | ||||||||
\(986\) | 32.1845 | 1.02496 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.07111 | 0.256776 | ||||||||
\(989\) | 3.65381i | 0.116184i | ||||||||
\(990\) | −0.583820 | + | 2.71526i | −0.0185550 | + | 0.0862965i | ||||
\(991\) | 54.6176 | 1.73499 | 0.867493 | − | 0.497449i | \(-0.165730\pi\) | ||||
0.867493 | + | 0.497449i | \(0.165730\pi\) | |||||||
\(992\) | 1.05470 | 0.0334868 | ||||||||
\(993\) | 12.9149i | 0.409843i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.2965 | −0.484933 | ||||||||
\(996\) | 2.99287i | 0.0948326i | ||||||||
\(997\) | −16.9182 | −0.535806 | −0.267903 | − | 0.963446i | \(-0.586331\pi\) | ||||
−0.267903 | + | 0.963446i | \(0.586331\pi\) | |||||||
\(998\) | − | 29.1721i | − | 0.923426i | ||||||
\(999\) | − | 10.9893i | − | 0.347688i |
(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 | 3234.2.e.b.2155.12 | 16 | ||
7.4 | even | 3 | 462.2.p.b.439.2 | yes | 16 | ||
7.5 | odd | 6 | 462.2.p.a.241.6 | ✓ | 16 | ||
7.6 | odd | 2 | 3234.2.e.a.2155.13 | 16 | |||
11.10 | odd | 2 | 3234.2.e.a.2155.4 | 16 | |||
21.5 | even | 6 | 1386.2.bk.a.703.3 | 16 | |||
21.11 | odd | 6 | 1386.2.bk.b.901.7 | 16 | |||
77.32 | odd | 6 | 462.2.p.a.439.6 | yes | 16 | ||
77.54 | even | 6 | 462.2.p.b.241.2 | yes | 16 | ||
77.76 | even | 2 | inner | 3234.2.e.b.2155.5 | 16 | ||
231.32 | even | 6 | 1386.2.bk.a.901.3 | 16 | |||
231.131 | odd | 6 | 1386.2.bk.b.703.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.6 | ✓ | 16 | 7.5 | odd | 6 | ||
462.2.p.a.439.6 | yes | 16 | 77.32 | odd | 6 | ||
462.2.p.b.241.2 | yes | 16 | 77.54 | even | 6 | ||
462.2.p.b.439.2 | yes | 16 | 7.4 | even | 3 | ||
1386.2.bk.a.703.3 | 16 | 21.5 | even | 6 | |||
1386.2.bk.a.901.3 | 16 | 231.32 | even | 6 | |||
1386.2.bk.b.703.7 | 16 | 231.131 | odd | 6 | |||
1386.2.bk.b.901.7 | 16 | 21.11 | odd | 6 | |||
3234.2.e.a.2155.4 | 16 | 11.10 | odd | 2 | |||
3234.2.e.a.2155.13 | 16 | 7.6 | odd | 2 | |||
3234.2.e.b.2155.5 | 16 | 77.76 | even | 2 | inner | ||
3234.2.e.b.2155.12 | 16 | 1.1 | even | 1 | trivial |