Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2254,2,Mod(2253,2254)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2254, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2254.2253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2254 = 2 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2254.c (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: | \(17.9982806156\) |
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: | \( x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 322) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2253.13 | ||
Root | \(1.52769 + 2.64604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2254.2253 |
Dual form | 2254.2.c.c.2253.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2254\mathbb{Z}\right)^\times\).
\(n\) | \(1473\) | \(1569\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.14817i | 1.24025i | 0.784505 | + | 0.620123i | \(0.212917\pi\) | ||||
−0.784505 | + | 0.620123i | \(0.787083\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.528453 | −0.236332 | −0.118166 | − | 0.992994i | \(-0.537701\pi\) | ||||
−0.118166 | + | 0.992994i | \(0.537701\pi\) | |||||||
\(6\) | 2.14817i | 0.876986i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.61463 | −0.538209 | ||||||||
\(10\) | −0.528453 | −0.167112 | ||||||||
\(11\) | − | 2.05052i | − | 0.618254i | −0.951021 | − | 0.309127i | \(-0.899963\pi\) | ||
0.951021 | − | 0.309127i | \(-0.100037\pi\) | |||||||
\(12\) | 2.14817i | 0.620123i | ||||||||
\(13\) | 3.70082i | 1.02642i | 0.858262 | + | 0.513212i | \(0.171544\pi\) | ||||
−0.858262 | + | 0.513212i | \(0.828456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.13521i | − | 0.293109i | ||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.89954 | −1.67338 | −0.836692 | − | 0.547673i | \(-0.815514\pi\) | ||||
−0.836692 | + | 0.547673i | \(0.815514\pi\) | |||||||
\(18\) | −1.61463 | −0.380571 | ||||||||
\(19\) | −0.528453 | −0.121236 | −0.0606178 | − | 0.998161i | \(-0.519307\pi\) | ||||
−0.0606178 | + | 0.998161i | \(0.519307\pi\) | |||||||
\(20\) | −0.528453 | −0.118166 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.05052i | − | 0.437171i | ||||||
\(23\) | −4.33536 | + | 2.05052i | −0.903986 | + | 0.427562i | ||||
\(24\) | 2.14817i | 0.438493i | ||||||||
\(25\) | −4.72074 | −0.944147 | ||||||||
\(26\) | 3.70082i | 0.725791i | ||||||||
\(27\) | 2.97601i | 0.572734i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.68928 | 0.685082 | 0.342541 | − | 0.939503i | \(-0.388713\pi\) | ||||
0.342541 | + | 0.939503i | \(0.388713\pi\) | |||||||
\(30\) | − | 1.13521i | − | 0.207260i | ||||||
\(31\) | 4.94479i | 0.888110i | 0.896000 | + | 0.444055i | \(0.146460\pi\) | ||||
−0.896000 | + | 0.444055i | \(0.853540\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.40485 | 0.766786 | ||||||||
\(34\) | −6.89954 | −1.18326 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.61463 | −0.269105 | ||||||||
\(37\) | 8.66983i | 1.42531i | 0.701514 | + | 0.712656i | \(0.252508\pi\) | ||||
−0.701514 | + | 0.712656i | \(0.747492\pi\) | |||||||
\(38\) | −0.528453 | −0.0857265 | ||||||||
\(39\) | −7.94999 | −1.27302 | ||||||||
\(40\) | −0.528453 | −0.0835558 | ||||||||
\(41\) | 3.70082i | 0.577972i | 0.957333 | + | 0.288986i | \(0.0933180\pi\) | ||||
−0.957333 | + | 0.288986i | \(0.906682\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.98453i | 1.37013i | 0.728483 | + | 0.685064i | \(0.240226\pi\) | ||||
−0.728483 | + | 0.685064i | \(0.759774\pi\) | |||||||
\(44\) | − | 2.05052i | − | 0.309127i | ||||||
\(45\) | 0.853256 | 0.127196 | ||||||||
\(46\) | −4.33536 | + | 2.05052i | −0.639215 | + | 0.302332i | ||||
\(47\) | − | 1.96877i | − | 0.287175i | −0.989638 | − | 0.143588i | \(-0.954136\pi\) | ||
0.989638 | − | 0.143588i | \(-0.0458639\pi\) | |||||||
\(48\) | 2.14817i | 0.310061i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.72074 | −0.667613 | ||||||||
\(51\) | − | 14.8214i | − | 2.07541i | ||||||
\(52\) | 3.70082i | 0.513212i | ||||||||
\(53\) | − | 13.6862i | − | 1.87994i | −0.341257 | − | 0.939970i | \(-0.610853\pi\) | ||
0.341257 | − | 0.939970i | \(-0.389147\pi\) | |||||||
\(54\) | 2.97601i | 0.404984i | ||||||||
\(55\) | 1.08360i | 0.146113i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.13521i | − | 0.150362i | ||||||
\(58\) | 3.68928 | 0.484426 | ||||||||
\(59\) | 5.77702i | 0.752104i | 0.926599 | + | 0.376052i | \(0.122719\pi\) | ||||
−0.926599 | + | 0.376052i | \(0.877281\pi\) | |||||||
\(60\) | − | 1.13521i | − | 0.146555i | ||||||
\(61\) | −5.84264 | −0.748073 | −0.374036 | − | 0.927414i | \(-0.622026\pi\) | ||||
−0.374036 | + | 0.927414i | \(0.622026\pi\) | |||||||
\(62\) | 4.94479i | 0.627988i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | − | 1.95571i | − | 0.242576i | ||||||
\(66\) | 4.40485 | 0.542200 | ||||||||
\(67\) | 0.820506i | 0.100241i | 0.998743 | + | 0.0501204i | \(0.0159605\pi\) | ||||
−0.998743 | + | 0.0501204i | \(0.984040\pi\) | |||||||
\(68\) | −6.89954 | −0.836692 | ||||||||
\(69\) | −4.40485 | − | 9.31309i | −0.530282 | − | 1.12116i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.03146 | 0.122412 | 0.0612059 | − | 0.998125i | \(-0.480505\pi\) | ||||
0.0612059 | + | 0.998125i | \(0.480505\pi\) | |||||||
\(72\) | −1.61463 | −0.190286 | ||||||||
\(73\) | 4.94479i | 0.578743i | 0.957217 | + | 0.289372i | \(0.0934464\pi\) | ||||
−0.957217 | + | 0.289372i | \(0.906554\pi\) | |||||||
\(74\) | 8.66983i | 1.00785i | ||||||||
\(75\) | − | 10.1409i | − | 1.17097i | ||||||
\(76\) | −0.528453 | −0.0606178 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.94999 | −0.900159 | ||||||||
\(79\) | − | 11.9504i | − | 1.34452i | −0.740315 | − | 0.672260i | \(-0.765324\pi\) | ||
0.740315 | − | 0.672260i | \(-0.234676\pi\) | |||||||
\(80\) | −0.528453 | −0.0590829 | ||||||||
\(81\) | −11.2369 | −1.24854 | ||||||||
\(82\) | 3.70082i | 0.408688i | ||||||||
\(83\) | 16.4544 | 1.80610 | 0.903051 | − | 0.429533i | \(-0.141322\pi\) | ||||
0.903051 | + | 0.429533i | \(0.141322\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.64609 | 0.395474 | ||||||||
\(86\) | 8.98453i | 0.968827i | ||||||||
\(87\) | 7.92519i | 0.849669i | ||||||||
\(88\) | − | 2.05052i | − | 0.218586i | ||||||
\(89\) | 7.63165 | 0.808953 | 0.404476 | − | 0.914548i | \(-0.367454\pi\) | ||||
0.404476 | + | 0.914548i | \(0.367454\pi\) | |||||||
\(90\) | 0.853256 | 0.0899410 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.33536 | + | 2.05052i | −0.451993 | + | 0.213781i | ||||
\(93\) | −10.6222 | −1.10147 | ||||||||
\(94\) | − | 1.96877i | − | 0.203063i | ||||||
\(95\) | 0.279263 | 0.0286518 | ||||||||
\(96\) | 2.14817i | 0.219247i | ||||||||
\(97\) | −11.1402 | −1.13112 | −0.565558 | − | 0.824709i | \(-0.691339\pi\) | ||||
−0.565558 | + | 0.824709i | \(0.691339\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.31082i | 0.332750i | ||||||||
\(100\) | −4.72074 | −0.472074 | ||||||||
\(101\) | 2.98040i | 0.296561i | 0.988945 | + | 0.148281i | \(0.0473739\pi\) | ||||
−0.988945 | + | 0.148281i | \(0.952626\pi\) | |||||||
\(102\) | − | 14.8214i | − | 1.46754i | ||||||
\(103\) | −1.76259 | −0.173673 | −0.0868363 | − | 0.996223i | \(-0.527676\pi\) | ||||
−0.0868363 | + | 0.996223i | \(0.527676\pi\) | |||||||
\(104\) | 3.70082i | 0.362896i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 13.6862i | − | 1.32932i | ||||||
\(107\) | 8.88973i | 0.859403i | 0.902971 | + | 0.429701i | \(0.141381\pi\) | ||||
−0.902971 | + | 0.429701i | \(0.858619\pi\) | |||||||
\(108\) | 2.97601i | 0.286367i | ||||||||
\(109\) | 6.93402i | 0.664159i | 0.943251 | + | 0.332079i | \(0.107750\pi\) | ||||
−0.943251 | + | 0.332079i | \(0.892250\pi\) | |||||||
\(110\) | 1.08360i | 0.103317i | ||||||||
\(111\) | −18.6243 | −1.76774 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.00860i | − | 0.471169i | −0.971854 | − | 0.235585i | \(-0.924299\pi\) | ||
0.971854 | − | 0.235585i | \(-0.0757005\pi\) | |||||||
\(114\) | − | 1.13521i | − | 0.106322i | ||||||
\(115\) | 2.29104 | − | 1.08360i | 0.213640 | − | 0.101046i | ||||
\(116\) | 3.68928 | 0.342541 | ||||||||
\(117\) | − | 5.97545i | − | 0.552431i | ||||||
\(118\) | 5.77702i | 0.531818i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 1.13521i | − | 0.103630i | ||||||
\(121\) | 6.79539 | 0.617762 | ||||||||
\(122\) | −5.84264 | −0.528967 | ||||||||
\(123\) | −7.94999 | −0.716827 | ||||||||
\(124\) | 4.94479i | 0.444055i | ||||||||
\(125\) | 5.13696 | 0.459463 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.31072 | −0.293779 | −0.146890 | − | 0.989153i | \(-0.546926\pi\) | ||||
−0.146890 | + | 0.989153i | \(0.546926\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −19.3003 | −1.69930 | ||||||||
\(130\) | − | 1.95571i | − | 0.171527i | ||||||
\(131\) | − | 16.3341i | − | 1.42711i | −0.700597 | − | 0.713557i | \(-0.747083\pi\) | ||
0.700597 | − | 0.713557i | \(-0.252917\pi\) | |||||||
\(132\) | 4.40485 | 0.383393 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.820506i | 0.0708809i | ||||||||
\(135\) | − | 1.57268i | − | 0.135355i | ||||||
\(136\) | −6.89954 | −0.591631 | ||||||||
\(137\) | 9.80504i | 0.837701i | 0.908055 | + | 0.418851i | \(0.137567\pi\) | ||||
−0.908055 | + | 0.418851i | \(0.862433\pi\) | |||||||
\(138\) | −4.40485 | − | 9.31309i | −0.374966 | − | 0.792783i | ||||
\(139\) | − | 18.4468i | − | 1.56464i | −0.622879 | − | 0.782318i | \(-0.714037\pi\) | ||
0.622879 | − | 0.782318i | \(-0.285963\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.22926 | 0.356168 | ||||||||
\(142\) | 1.03146 | 0.0865582 | ||||||||
\(143\) | 7.58860 | 0.634590 | ||||||||
\(144\) | −1.61463 | −0.134552 | ||||||||
\(145\) | −1.94961 | −0.161906 | ||||||||
\(146\) | 4.94479i | 0.409233i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.66983i | 0.712656i | ||||||||
\(149\) | 4.10103i | 0.335970i | 0.985790 | + | 0.167985i | \(0.0537259\pi\) | ||||
−0.985790 | + | 0.167985i | \(0.946274\pi\) | |||||||
\(150\) | − | 10.1409i | − | 0.828004i | ||||||
\(151\) | 1.77074 | 0.144101 | 0.0720506 | − | 0.997401i | \(-0.477046\pi\) | ||||
0.0720506 | + | 0.997401i | \(0.477046\pi\) | |||||||
\(152\) | −0.528453 | −0.0428632 | ||||||||
\(153\) | 11.1402 | 0.900631 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2.61309i | − | 0.209888i | ||||||
\(156\) | −7.94999 | −0.636509 | ||||||||
\(157\) | 7.46744 | 0.595967 | 0.297983 | − | 0.954571i | \(-0.403686\pi\) | ||||
0.297983 | + | 0.954571i | \(0.403686\pi\) | |||||||
\(158\) | − | 11.9504i | − | 0.950719i | ||||||
\(159\) | 29.4002 | 2.33159 | ||||||||
\(160\) | −0.528453 | −0.0417779 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −11.2369 | −0.882851 | ||||||||
\(163\) | −5.61463 | −0.439772 | −0.219886 | − | 0.975526i | \(-0.570568\pi\) | ||||
−0.219886 | + | 0.975526i | \(0.570568\pi\) | |||||||
\(164\) | 3.70082i | 0.288986i | ||||||||
\(165\) | −2.32776 | −0.181216 | ||||||||
\(166\) | 16.4544 | 1.27711 | ||||||||
\(167\) | − | 4.65513i | − | 0.360225i | −0.983646 | − | 0.180112i | \(-0.942354\pi\) | ||
0.983646 | − | 0.180112i | \(-0.0576461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.696095 | −0.0535458 | ||||||||
\(170\) | 3.64609 | 0.279642 | ||||||||
\(171\) | 0.853256 | 0.0652501 | ||||||||
\(172\) | 8.98453i | 0.685064i | ||||||||
\(173\) | − | 14.7858i | − | 1.12414i | −0.827088 | − | 0.562072i | \(-0.810004\pi\) | ||
0.827088 | − | 0.562072i | \(-0.189996\pi\) | |||||||
\(174\) | 7.92519i | 0.600807i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.05052i | − | 0.154563i | ||||||
\(177\) | −12.4100 | −0.932794 | ||||||||
\(178\) | 7.63165 | 0.572016 | ||||||||
\(179\) | 3.38537 | 0.253035 | 0.126517 | − | 0.991964i | \(-0.459620\pi\) | ||||
0.126517 | + | 0.991964i | \(0.459620\pi\) | |||||||
\(180\) | 0.853256 | 0.0635979 | ||||||||
\(181\) | 10.2869 | 0.764622 | 0.382311 | − | 0.924034i | \(-0.375128\pi\) | ||||
0.382311 | + | 0.924034i | \(0.375128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.5510i | − | 0.927794i | ||||||
\(184\) | −4.33536 | + | 2.05052i | −0.319607 | + | 0.151166i | ||||
\(185\) | − | 4.58160i | − | 0.336846i | ||||||
\(186\) | −10.6222 | −0.778860 | ||||||||
\(187\) | 14.1476i | 1.03458i | ||||||||
\(188\) | − | 1.96877i | − | 0.143588i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.279263 | 0.0202599 | ||||||||
\(191\) | 3.88113i | 0.280829i | 0.990093 | + | 0.140414i | \(0.0448435\pi\) | ||||
−0.990093 | + | 0.140414i | \(0.955157\pi\) | |||||||
\(192\) | 2.14817i | 0.155031i | ||||||||
\(193\) | 13.6954 | 0.985814 | 0.492907 | − | 0.870082i | \(-0.335934\pi\) | ||||
0.492907 | + | 0.870082i | \(0.335934\pi\) | |||||||
\(194\) | −11.1402 | −0.799819 | ||||||||
\(195\) | 4.20120 | 0.300854 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4976 | 1.46039 | 0.730196 | − | 0.683238i | \(-0.239429\pi\) | ||||
0.730196 | + | 0.683238i | \(0.239429\pi\) | |||||||
\(198\) | 3.31082i | 0.235290i | ||||||||
\(199\) | −20.8857 | −1.48054 | −0.740272 | − | 0.672307i | \(-0.765303\pi\) | ||||
−0.740272 | + | 0.672307i | \(0.765303\pi\) | |||||||
\(200\) | −4.72074 | −0.333807 | ||||||||
\(201\) | −1.76259 | −0.124323 | ||||||||
\(202\) | 2.98040i | 0.209700i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 14.8214i | − | 1.03770i | ||||||
\(205\) | − | 1.95571i | − | 0.136593i | ||||||
\(206\) | −1.76259 | −0.122805 | ||||||||
\(207\) | 7.00000 | − | 3.31082i | 0.486534 | − | 0.230118i | ||||
\(208\) | 3.70082i | 0.256606i | ||||||||
\(209\) | 1.08360i | 0.0749543i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0807 | −1.79547 | −0.897736 | − | 0.440533i | \(-0.854789\pi\) | ||||
−0.897736 | + | 0.440533i | \(0.854789\pi\) | |||||||
\(212\) | − | 13.6862i | − | 0.939970i | ||||||
\(213\) | 2.21575i | 0.151821i | ||||||||
\(214\) | 8.88973i | 0.607690i | ||||||||
\(215\) | − | 4.74791i | − | 0.323805i | ||||||
\(216\) | 2.97601i | 0.202492i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.93402i | 0.469631i | ||||||||
\(219\) | −10.6222 | −0.717784 | ||||||||
\(220\) | 1.08360i | 0.0730564i | ||||||||
\(221\) | − | 25.5340i | − | 1.71760i | ||||||
\(222\) | −18.6243 | −1.24998 | ||||||||
\(223\) | 3.15541i | 0.211302i | 0.994403 | + | 0.105651i | \(0.0336926\pi\) | ||||
−0.994403 | + | 0.105651i | \(0.966307\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.62223 | 0.508149 | ||||||||
\(226\) | − | 5.00860i | − | 0.333167i | ||||||
\(227\) | −7.79225 | −0.517190 | −0.258595 | − | 0.965986i | \(-0.583259\pi\) | ||||
−0.258595 | + | 0.965986i | \(0.583259\pi\) | |||||||
\(228\) | − | 1.13521i | − | 0.0751809i | ||||||
\(229\) | 5.67843 | 0.375241 | 0.187621 | − | 0.982242i | \(-0.439922\pi\) | ||||
0.187621 | + | 0.982242i | \(0.439922\pi\) | |||||||
\(230\) | 2.29104 | − | 1.08360i | 0.151067 | − | 0.0714506i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.68928 | 0.242213 | ||||||||
\(233\) | 28.5037 | 1.86734 | 0.933669 | − | 0.358138i | \(-0.116588\pi\) | ||||
0.933669 | + | 0.358138i | \(0.116588\pi\) | |||||||
\(234\) | − | 5.97545i | − | 0.390628i | ||||||
\(235\) | 1.04040i | 0.0678685i | ||||||||
\(236\) | 5.77702i | 0.376052i | ||||||||
\(237\) | 25.6714 | 1.66754 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.10460 | 0.136135 | 0.0680676 | − | 0.997681i | \(-0.478317\pi\) | ||||
0.0680676 | + | 0.997681i | \(0.478317\pi\) | |||||||
\(240\) | − | 1.13521i | − | 0.0732773i | ||||||
\(241\) | 15.2072 | 0.979583 | 0.489792 | − | 0.871840i | \(-0.337073\pi\) | ||||
0.489792 | + | 0.871840i | \(0.337073\pi\) | |||||||
\(242\) | 6.79539 | 0.436824 | ||||||||
\(243\) | − | 15.2106i | − | 0.975762i | ||||||
\(244\) | −5.84264 | −0.374036 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.94999 | −0.506873 | ||||||||
\(247\) | − | 1.95571i | − | 0.124439i | ||||||
\(248\) | 4.94479i | 0.313994i | ||||||||
\(249\) | 35.3468i | 2.24001i | ||||||||
\(250\) | 5.13696 | 0.324890 | ||||||||
\(251\) | −21.0463 | −1.32843 | −0.664214 | − | 0.747543i | \(-0.731234\pi\) | ||||
−0.664214 | + | 0.747543i | \(0.731234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.20461 | + | 8.88973i | 0.264342 | + | 0.558893i | ||||
\(254\) | −3.31072 | −0.207733 | ||||||||
\(255\) | 7.83241i | 0.490485i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.3961i | 1.39703i | 0.715594 | + | 0.698517i | \(0.246156\pi\) | ||||
−0.715594 | + | 0.698517i | \(0.753844\pi\) | |||||||
\(258\) | −19.3003 | −1.20158 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.95571i | − | 0.121288i | ||||||
\(261\) | −5.95681 | −0.368717 | ||||||||
\(262\) | − | 16.3341i | − | 1.00912i | ||||||
\(263\) | 9.58514i | 0.591045i | 0.955336 | + | 0.295523i | \(0.0954938\pi\) | ||||
−0.955336 | + | 0.295523i | \(0.904506\pi\) | |||||||
\(264\) | 4.40485 | 0.271100 | ||||||||
\(265\) | 7.23251i | 0.444289i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.3941i | 1.00330i | ||||||||
\(268\) | 0.820506i | 0.0501204i | ||||||||
\(269\) | 17.0691i | 1.04072i | 0.853946 | + | 0.520362i | \(0.174203\pi\) | ||||
−0.853946 | + | 0.520362i | \(0.825797\pi\) | |||||||
\(270\) | − | 1.57268i | − | 0.0957105i | ||||||
\(271\) | 14.9063i | 0.905495i | 0.891639 | + | 0.452747i | \(0.149556\pi\) | ||||
−0.891639 | + | 0.452747i | \(0.850444\pi\) | |||||||
\(272\) | −6.89954 | −0.418346 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.80504i | 0.592344i | ||||||||
\(275\) | 9.67994i | 0.583723i | ||||||||
\(276\) | −4.40485 | − | 9.31309i | −0.265141 | − | 0.560582i | ||||
\(277\) | 29.8814 | 1.79540 | 0.897701 | − | 0.440606i | \(-0.145236\pi\) | ||||
0.897701 | + | 0.440606i | \(0.145236\pi\) | |||||||
\(278\) | − | 18.4468i | − | 1.10637i | ||||||
\(279\) | − | 7.98399i | − | 0.477989i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.7934i | 1.30009i | 0.759897 | + | 0.650044i | \(0.225249\pi\) | ||||
−0.759897 | + | 0.650044i | \(0.774751\pi\) | |||||||
\(282\) | 4.22926 | 0.251848 | ||||||||
\(283\) | 26.7283 | 1.58883 | 0.794416 | − | 0.607374i | \(-0.207777\pi\) | ||||
0.794416 | + | 0.607374i | \(0.207777\pi\) | |||||||
\(284\) | 1.03146 | 0.0612059 | ||||||||
\(285\) | 0.599904i | 0.0355353i | ||||||||
\(286\) | 7.58860 | 0.448723 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.61463 | −0.0951429 | ||||||||
\(289\) | 30.6037 | 1.80022 | ||||||||
\(290\) | −1.94961 | −0.114485 | ||||||||
\(291\) | − | 23.9310i | − | 1.40286i | ||||||
\(292\) | 4.94479i | 0.289372i | ||||||||
\(293\) | −21.3877 | −1.24948 | −0.624741 | − | 0.780832i | \(-0.714795\pi\) | ||||
−0.624741 | + | 0.780832i | \(0.714795\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3.05289i | − | 0.177746i | ||||||
\(296\) | 8.66983i | 0.503924i | ||||||||
\(297\) | 6.10236 | 0.354095 | ||||||||
\(298\) | 4.10103i | 0.237566i | ||||||||
\(299\) | −7.58860 | − | 16.0444i | −0.438860 | − | 0.927873i | ||||
\(300\) | − | 10.1409i | − | 0.585487i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.77074 | 0.101895 | ||||||||
\(303\) | −6.40241 | −0.367809 | ||||||||
\(304\) | −0.528453 | −0.0303089 | ||||||||
\(305\) | 3.08756 | 0.176793 | ||||||||
\(306\) | 11.1402 | 0.636842 | ||||||||
\(307\) | 2.16565i | 0.123600i | 0.998089 | + | 0.0618001i | \(0.0196841\pi\) | ||||
−0.998089 | + | 0.0618001i | \(0.980316\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.78633i | − | 0.215397i | ||||||
\(310\) | − | 2.61309i | − | 0.148413i | ||||||
\(311\) | − | 18.7483i | − | 1.06312i | −0.847022 | − | 0.531558i | \(-0.821607\pi\) | ||
0.847022 | − | 0.531558i | \(-0.178393\pi\) | |||||||
\(312\) | −7.94999 | −0.450080 | ||||||||
\(313\) | −31.3104 | −1.76977 | −0.884883 | − | 0.465813i | \(-0.845762\pi\) | ||||
−0.884883 | + | 0.465813i | \(0.845762\pi\) | |||||||
\(314\) | 7.46744 | 0.421412 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 11.9504i | − | 0.672260i | ||||||
\(317\) | 28.6469 | 1.60897 | 0.804484 | − | 0.593974i | \(-0.202442\pi\) | ||||
0.804484 | + | 0.593974i | \(0.202442\pi\) | |||||||
\(318\) | 29.4002 | 1.64868 | ||||||||
\(319\) | − | 7.56492i | − | 0.423554i | ||||||
\(320\) | −0.528453 | −0.0295414 | ||||||||
\(321\) | −19.0966 | −1.06587 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.64609 | 0.202874 | ||||||||
\(324\) | −11.2369 | −0.624270 | ||||||||
\(325\) | − | 17.4706i | − | 0.969095i | ||||||
\(326\) | −5.61463 | −0.310965 | ||||||||
\(327\) | −14.8954 | −0.823720 | ||||||||
\(328\) | 3.70082i | 0.204344i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.32776 | −0.128139 | ||||||||
\(331\) | 27.3100 | 1.50109 | 0.750547 | − | 0.660817i | \(-0.229790\pi\) | ||||
0.750547 | + | 0.660817i | \(0.229790\pi\) | |||||||
\(332\) | 16.4544 | 0.903051 | ||||||||
\(333\) | − | 13.9986i | − | 0.767116i | ||||||
\(334\) | − | 4.65513i | − | 0.254717i | ||||||
\(335\) | − | 0.433599i | − | 0.0236901i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.09092i | − | 0.168373i | −0.996450 | − | 0.0841866i | \(-0.973171\pi\) | ||
0.996450 | − | 0.0841866i | \(-0.0268292\pi\) | |||||||
\(338\) | −0.696095 | −0.0378626 | ||||||||
\(339\) | 10.7593 | 0.584366 | ||||||||
\(340\) | 3.64609 | 0.197737 | ||||||||
\(341\) | 10.1394 | 0.549077 | ||||||||
\(342\) | 0.853256 | 0.0461388 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 8.98453i | 0.484414i | ||||||||
\(345\) | 2.32776 | + | 4.92154i | 0.125322 | + | 0.264967i | ||||
\(346\) | − | 14.7858i | − | 0.794890i | ||||||
\(347\) | −5.44829 | −0.292480 | −0.146240 | − | 0.989249i | \(-0.546717\pi\) | ||||
−0.146240 | + | 0.989249i | \(0.546717\pi\) | |||||||
\(348\) | 7.92519i | 0.424835i | ||||||||
\(349\) | 7.05311i | 0.377544i | 0.982021 | + | 0.188772i | \(0.0604508\pi\) | ||||
−0.982021 | + | 0.188772i | \(0.939549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.0137 | −0.587868 | ||||||||
\(352\) | − | 2.05052i | − | 0.109293i | ||||||
\(353\) | − | 8.86485i | − | 0.471828i | −0.971774 | − | 0.235914i | \(-0.924192\pi\) | ||
0.971774 | − | 0.235914i | \(-0.0758084\pi\) | |||||||
\(354\) | −12.4100 | −0.659585 | ||||||||
\(355\) | −0.545078 | −0.0289298 | ||||||||
\(356\) | 7.63165 | 0.404476 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.38537 | 0.178922 | ||||||||
\(359\) | 9.62317i | 0.507892i | 0.967218 | + | 0.253946i | \(0.0817285\pi\) | ||||
−0.967218 | + | 0.253946i | \(0.918271\pi\) | |||||||
\(360\) | 0.853256 | 0.0449705 | ||||||||
\(361\) | −18.7207 | −0.985302 | ||||||||
\(362\) | 10.2869 | 0.540669 | ||||||||
\(363\) | 14.5976i | 0.766177i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.61309i | − | 0.136775i | ||||||
\(366\) | − | 12.5510i | − | 0.656049i | ||||||
\(367\) | −24.2072 | −1.26360 | −0.631802 | − | 0.775130i | \(-0.717684\pi\) | ||||
−0.631802 | + | 0.775130i | \(0.717684\pi\) | |||||||
\(368\) | −4.33536 | + | 2.05052i | −0.225997 | + | 0.106891i | ||||
\(369\) | − | 5.97545i | − | 0.311070i | ||||||
\(370\) | − | 4.58160i | − | 0.238186i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.6222 | −0.550737 | ||||||||
\(373\) | 0.0567690i | 0.00293939i | 0.999999 | + | 0.00146969i | \(0.000467818\pi\) | ||||
−0.999999 | + | 0.00146969i | \(0.999532\pi\) | |||||||
\(374\) | 14.1476i | 0.731556i | ||||||||
\(375\) | 11.0350i | 0.569848i | ||||||||
\(376\) | − | 1.96877i | − | 0.101532i | ||||||
\(377\) | 13.6534i | 0.703184i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.4003i | − | 1.04789i | −0.851751 | − | 0.523946i | \(-0.824459\pi\) | ||
0.851751 | − | 0.523946i | \(-0.175541\pi\) | |||||||
\(380\) | 0.279263 | 0.0143259 | ||||||||
\(381\) | − | 7.11199i | − | 0.364358i | ||||||
\(382\) | 3.88113i | 0.198576i | ||||||||
\(383\) | 12.9458 | 0.661501 | 0.330750 | − | 0.943718i | \(-0.392698\pi\) | ||||
0.330750 | + | 0.943718i | \(0.392698\pi\) | |||||||
\(384\) | 2.14817i | 0.109623i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.6954 | 0.697076 | ||||||||
\(387\) | − | 14.5067i | − | 0.737416i | ||||||
\(388\) | −11.1402 | −0.565558 | ||||||||
\(389\) | 35.7943i | 1.81484i | 0.420221 | + | 0.907422i | \(0.361952\pi\) | ||||
−0.420221 | + | 0.907422i | \(0.638048\pi\) | |||||||
\(390\) | 4.20120 | 0.212736 | ||||||||
\(391\) | 29.9120 | − | 14.1476i | 1.51272 | − | 0.715476i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 35.0883 | 1.76997 | ||||||||
\(394\) | 20.4976 | 1.03265 | ||||||||
\(395\) | 6.31521i | 0.317753i | ||||||||
\(396\) | 3.31082i | 0.166375i | ||||||||
\(397\) | 21.8641i | 1.09733i | 0.836043 | + | 0.548664i | \(0.184864\pi\) | ||||
−0.836043 | + | 0.548664i | \(0.815136\pi\) | |||||||
\(398\) | −20.8857 | −1.04690 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.72074 | −0.236037 | ||||||||
\(401\) | 17.4345i | 0.870636i | 0.900277 | + | 0.435318i | \(0.143364\pi\) | ||||
−0.900277 | + | 0.435318i | \(0.856636\pi\) | |||||||
\(402\) | −1.76259 | −0.0879098 | ||||||||
\(403\) | −18.2998 | −0.911577 | ||||||||
\(404\) | 2.98040i | 0.148281i | ||||||||
\(405\) | 5.93816 | 0.295069 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.7776 | 0.881204 | ||||||||
\(408\) | − | 14.8214i | − | 0.733768i | ||||||
\(409\) | − | 33.1136i | − | 1.63736i | −0.574250 | − | 0.818680i | \(-0.694706\pi\) | ||
0.574250 | − | 0.818680i | \(-0.305294\pi\) | |||||||
\(410\) | − | 1.95571i | − | 0.0965858i | ||||||
\(411\) | −21.0629 | −1.03896 | ||||||||
\(412\) | −1.76259 | −0.0868363 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.00000 | − | 3.31082i | 0.344031 | − | 0.162718i | ||||
\(415\) | −8.69537 | −0.426839 | ||||||||
\(416\) | 3.70082i | 0.181448i | ||||||||
\(417\) | 39.6268 | 1.94053 | ||||||||
\(418\) | 1.08360i | 0.0530007i | ||||||||
\(419\) | 22.9995 | 1.12360 | 0.561799 | − | 0.827274i | \(-0.310110\pi\) | ||||
0.561799 | + | 0.827274i | \(0.310110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9931i | 0.681984i | 0.940066 | + | 0.340992i | \(0.110763\pi\) | ||||
−0.940066 | + | 0.340992i | \(0.889237\pi\) | |||||||
\(422\) | −26.0807 | −1.26959 | ||||||||
\(423\) | 3.17884i | 0.154560i | ||||||||
\(424\) | − | 13.6862i | − | 0.664659i | ||||||
\(425\) | 32.5709 | 1.57992 | ||||||||
\(426\) | 2.21575i | 0.107353i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.88973i | 0.429701i | ||||||||
\(429\) | 16.3016i | 0.787048i | ||||||||
\(430\) | − | 4.74791i | − | 0.228964i | ||||||
\(431\) | 15.0335i | 0.724140i | 0.932151 | + | 0.362070i | \(0.117930\pi\) | ||||
−0.932151 | + | 0.362070i | \(0.882070\pi\) | |||||||
\(432\) | 2.97601i | 0.143183i | ||||||||
\(433\) | 8.50153 | 0.408557 | 0.204279 | − | 0.978913i | \(-0.434515\pi\) | ||||
0.204279 | + | 0.978913i | \(0.434515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 4.18809i | − | 0.200804i | ||||||
\(436\) | 6.93402i | 0.332079i | ||||||||
\(437\) | 2.29104 | − | 1.08360i | 0.109595 | − | 0.0518357i | ||||
\(438\) | −10.6222 | −0.507550 | ||||||||
\(439\) | 1.78938i | 0.0854023i | 0.999088 | + | 0.0427012i | \(0.0135963\pi\) | ||||
−0.999088 | + | 0.0427012i | \(0.986404\pi\) | |||||||
\(440\) | 1.08360i | 0.0516587i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 25.5340i | − | 1.21453i | ||||||
\(443\) | 14.4229 | 0.685254 | 0.342627 | − | 0.939472i | \(-0.388683\pi\) | ||||
0.342627 | + | 0.939472i | \(0.388683\pi\) | |||||||
\(444\) | −18.6243 | −0.883868 | ||||||||
\(445\) | −4.03297 | −0.191181 | ||||||||
\(446\) | 3.15541i | 0.149413i | ||||||||
\(447\) | −8.80970 | −0.416685 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.65218 | 0.455515 | 0.227757 | − | 0.973718i | \(-0.426861\pi\) | ||||
0.227757 | + | 0.973718i | \(0.426861\pi\) | |||||||
\(450\) | 7.62223 | 0.359315 | ||||||||
\(451\) | 7.58860 | 0.357333 | ||||||||
\(452\) | − | 5.00860i | − | 0.235585i | ||||||
\(453\) | 3.80386i | 0.178721i | ||||||||
\(454\) | −7.79225 | −0.365708 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 1.13521i | − | 0.0531609i | ||||||
\(457\) | 36.1370i | 1.69042i | 0.534437 | + | 0.845208i | \(0.320524\pi\) | ||||
−0.534437 | + | 0.845208i | \(0.679476\pi\) | |||||||
\(458\) | 5.67843 | 0.265336 | ||||||||
\(459\) | − | 20.5331i | − | 0.958404i | ||||||
\(460\) | 2.29104 | − | 1.08360i | 0.106820 | − | 0.0505232i | ||||
\(461\) | − | 27.5367i | − | 1.28251i | −0.767326 | − | 0.641257i | \(-0.778413\pi\) | ||
0.767326 | − | 0.641257i | \(-0.221587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.186065 | −0.00864718 | −0.00432359 | − | 0.999991i | \(-0.501376\pi\) | ||||
−0.00432359 | + | 0.999991i | \(0.501376\pi\) | |||||||
\(464\) | 3.68928 | 0.171270 | ||||||||
\(465\) | 5.61336 | 0.260313 | ||||||||
\(466\) | 28.5037 | 1.32041 | ||||||||
\(467\) | −17.3243 | −0.801671 | −0.400835 | − | 0.916150i | \(-0.631280\pi\) | ||||
−0.400835 | + | 0.916150i | \(0.631280\pi\) | |||||||
\(468\) | − | 5.97545i | − | 0.276215i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.04040i | 0.0479903i | ||||||||
\(471\) | 16.0413i | 0.739145i | ||||||||
\(472\) | 5.77702i | 0.265909i | ||||||||
\(473\) | 18.4229 | 0.847087 | ||||||||
\(474\) | 25.6714 | 1.17913 | ||||||||
\(475\) | 2.49469 | 0.114464 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.0981i | 1.01180i | ||||||||
\(478\) | 2.10460 | 0.0962621 | ||||||||
\(479\) | −32.3673 | −1.47890 | −0.739449 | − | 0.673212i | \(-0.764914\pi\) | ||||
−0.739449 | + | 0.673212i | \(0.764914\pi\) | |||||||
\(480\) | − | 1.13521i | − | 0.0518149i | ||||||
\(481\) | −32.0855 | −1.46297 | ||||||||
\(482\) | 15.2072 | 0.692670 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.79539 | 0.308881 | ||||||||
\(485\) | 5.88707 | 0.267318 | ||||||||
\(486\) | − | 15.2106i | − | 0.689968i | ||||||
\(487\) | 30.0020 | 1.35952 | 0.679759 | − | 0.733435i | \(-0.262084\pi\) | ||||
0.679759 | + | 0.733435i | \(0.262084\pi\) | |||||||
\(488\) | −5.84264 | −0.264484 | ||||||||
\(489\) | − | 12.0612i | − | 0.545425i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.9761 | −0.540476 | −0.270238 | − | 0.962794i | \(-0.587102\pi\) | ||||
−0.270238 | + | 0.962794i | \(0.587102\pi\) | |||||||
\(492\) | −7.94999 | −0.358413 | ||||||||
\(493\) | −25.4543 | −1.14641 | ||||||||
\(494\) | − | 1.95571i | − | 0.0879917i | ||||||
\(495\) | − | 1.74961i | − | 0.0786393i | ||||||
\(496\) | 4.94479i | 0.222027i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 35.3468i | 1.58393i | ||||||||
\(499\) | −40.2744 | −1.80293 | −0.901465 | − | 0.432852i | \(-0.857507\pi\) | ||||
−0.901465 | + | 0.432852i | \(0.857507\pi\) | |||||||
\(500\) | 5.13696 | 0.229732 | ||||||||
\(501\) | 10.0000 | 0.446767 | ||||||||
\(502\) | −21.0463 | −0.939340 | ||||||||
\(503\) | 19.6812 | 0.877540 | 0.438770 | − | 0.898599i | \(-0.355414\pi\) | ||||
0.438770 | + | 0.898599i | \(0.355414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.57500i | − | 0.0700868i | ||||||
\(506\) | 4.20461 | + | 8.88973i | 0.186918 | + | 0.395197i | ||||
\(507\) | − | 1.49533i | − | 0.0664099i | ||||||
\(508\) | −3.31072 | −0.146890 | ||||||||
\(509\) | 28.9509i | 1.28323i | 0.767028 | + | 0.641613i | \(0.221735\pi\) | ||||
−0.767028 | + | 0.641613i | \(0.778265\pi\) | |||||||
\(510\) | 7.83241i | 0.346825i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | − | 1.57268i | − | 0.0694357i | ||||||
\(514\) | 22.3961i | 0.987852i | ||||||||
\(515\) | 0.931444 | 0.0410443 | ||||||||
\(516\) | −19.3003 | −0.849648 | ||||||||
\(517\) | −4.03700 | −0.177547 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.7624 | 1.39422 | ||||||||
\(520\) | − | 1.95571i | − | 0.0857637i | ||||||
\(521\) | 29.1571 | 1.27740 | 0.638698 | − | 0.769458i | \(-0.279473\pi\) | ||||
0.638698 | + | 0.769458i | \(0.279473\pi\) | |||||||
\(522\) | −5.95681 | −0.260722 | ||||||||
\(523\) | 16.7397 | 0.731977 | 0.365989 | − | 0.930619i | \(-0.380731\pi\) | ||||
0.365989 | + | 0.930619i | \(0.380731\pi\) | |||||||
\(524\) | − | 16.3341i | − | 0.713557i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.58514i | 0.417932i | ||||||||
\(527\) | − | 34.1168i | − | 1.48615i | ||||||
\(528\) | 4.40485 | 0.191697 | ||||||||
\(529\) | 14.5908 | − | 17.7795i | 0.634381 | − | 0.773020i | ||||
\(530\) | 7.23251i | 0.314160i | ||||||||
\(531\) | − | 9.32774i | − | 0.404789i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.6961 | −0.593244 | ||||||||
\(534\) | 16.3941i | 0.709441i | ||||||||
\(535\) | − | 4.69781i | − | 0.203104i | ||||||
\(536\) | 0.820506i | 0.0354405i | ||||||||
\(537\) | 7.27235i | 0.313825i | ||||||||
\(538\) | 17.0691i | 0.735903i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 1.57268i | − | 0.0676776i | ||||||
\(541\) | −27.8890 | −1.19904 | −0.599522 | − | 0.800358i | \(-0.704643\pi\) | ||||
−0.599522 | + | 0.800358i | \(0.704643\pi\) | |||||||
\(542\) | 14.9063i | 0.640282i | ||||||||
\(543\) | 22.0981i | 0.948319i | ||||||||
\(544\) | −6.89954 | −0.295815 | ||||||||
\(545\) | − | 3.66431i | − | 0.156962i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.2861 | −1.25219 | −0.626093 | − | 0.779749i | \(-0.715347\pi\) | ||||
−0.626093 | + | 0.779749i | \(0.715347\pi\) | |||||||
\(548\) | 9.80504i | 0.418851i | ||||||||
\(549\) | 9.43368 | 0.402620 | ||||||||
\(550\) | 9.67994i | 0.412754i | ||||||||
\(551\) | −1.94961 | −0.0830562 | ||||||||
\(552\) | −4.40485 | − | 9.31309i | −0.187483 | − | 0.396392i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 29.8814 | 1.26954 | ||||||||
\(555\) | 9.84206 | 0.417772 | ||||||||
\(556\) | − | 18.4468i | − | 0.782318i | ||||||
\(557\) | 26.5215i | 1.12375i | 0.827221 | + | 0.561877i | \(0.189921\pi\) | ||||
−0.827221 | + | 0.561877i | \(0.810079\pi\) | |||||||
\(558\) | − | 7.98399i | − | 0.337989i | ||||||
\(559\) | −33.2502 | −1.40633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.3915 | −1.28313 | ||||||||
\(562\) | 21.7934i | 0.919300i | ||||||||
\(563\) | −22.5007 | −0.948290 | −0.474145 | − | 0.880447i | \(-0.657243\pi\) | ||||
−0.474145 | + | 0.880447i | \(0.657243\pi\) | |||||||
\(564\) | 4.22926 | 0.178084 | ||||||||
\(565\) | 2.64681i | 0.111352i | ||||||||
\(566\) | 26.7283 | 1.12347 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.03146 | 0.0432791 | ||||||||
\(569\) | − | 46.1239i | − | 1.93361i | −0.255508 | − | 0.966807i | \(-0.582243\pi\) | ||
0.255508 | − | 0.966807i | \(-0.417757\pi\) | |||||||
\(570\) | 0.599904i | 0.0251272i | ||||||||
\(571\) | − | 9.64191i | − | 0.403501i | −0.979437 | − | 0.201751i | \(-0.935337\pi\) | ||
0.979437 | − | 0.201751i | \(-0.0646631\pi\) | |||||||
\(572\) | 7.58860 | 0.317295 | ||||||||
\(573\) | −8.33733 | −0.348297 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4661 | − | 9.67994i | 0.853496 | − | 0.403682i | ||||
\(576\) | −1.61463 | −0.0672762 | ||||||||
\(577\) | 6.43834i | 0.268032i | 0.990979 | + | 0.134016i | \(0.0427873\pi\) | ||||
−0.990979 | + | 0.134016i | \(0.957213\pi\) | |||||||
\(578\) | 30.6037 | 1.27295 | ||||||||
\(579\) | 29.4200i | 1.22265i | ||||||||
\(580\) | −1.94961 | −0.0809532 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 23.9310i | − | 0.991972i | ||||||
\(583\) | −28.0637 | −1.16228 | ||||||||
\(584\) | 4.94479i | 0.204617i | ||||||||
\(585\) | 3.15775i | 0.130557i | ||||||||
\(586\) | −21.3877 | −0.883517 | ||||||||
\(587\) | − | 23.4844i | − | 0.969303i | −0.874707 | − | 0.484652i | \(-0.838946\pi\) | ||
0.874707 | − | 0.484652i | \(-0.161054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.61309i | − | 0.107670i | ||||||
\(590\) | − | 3.05289i | − | 0.125685i | ||||||
\(591\) | 44.0322i | 1.81124i | ||||||||
\(592\) | 8.66983i | 0.356328i | ||||||||
\(593\) | − | 5.34187i | − | 0.219364i | −0.993967 | − | 0.109682i | \(-0.965017\pi\) | ||
0.993967 | − | 0.109682i | \(-0.0349833\pi\) | |||||||
\(594\) | 6.10236 | 0.250383 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.10103i | 0.167985i | ||||||||
\(597\) | − | 44.8659i | − | 1.83624i | ||||||
\(598\) | −7.58860 | − | 16.0444i | −0.310321 | − | 0.656105i | ||||
\(599\) | 14.0576 | 0.574378 | 0.287189 | − | 0.957874i | \(-0.407279\pi\) | ||||
0.287189 | + | 0.957874i | \(0.407279\pi\) | |||||||
\(600\) | − | 10.1409i | − | 0.414002i | ||||||
\(601\) | − | 13.0270i | − | 0.531383i | −0.964058 | − | 0.265691i | \(-0.914400\pi\) | ||
0.964058 | − | 0.265691i | \(-0.0856002\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.32481i | − | 0.0539505i | ||||||
\(604\) | 1.77074 | 0.0720506 | ||||||||
\(605\) | −3.59105 | −0.145997 | ||||||||
\(606\) | −6.40241 | −0.260080 | ||||||||
\(607\) | 39.6771i | 1.61044i | 0.592973 | + | 0.805222i | \(0.297954\pi\) | ||||
−0.592973 | + | 0.805222i | \(0.702046\pi\) | |||||||
\(608\) | −0.528453 | −0.0214316 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.08756 | 0.125012 | ||||||||
\(611\) | 7.28608 | 0.294763 | ||||||||
\(612\) | 11.1402 | 0.450316 | ||||||||
\(613\) | 26.3700i | 1.06507i | 0.846407 | + | 0.532537i | \(0.178761\pi\) | ||||
−0.846407 | + | 0.532537i | \(0.821239\pi\) | |||||||
\(614\) | 2.16565i | 0.0873985i | ||||||||
\(615\) | 4.20120 | 0.169409 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.7491i | 0.432744i | 0.976311 | + | 0.216372i | \(0.0694224\pi\) | ||||
−0.976311 | + | 0.216372i | \(0.930578\pi\) | |||||||
\(618\) | − | 3.78633i | − | 0.152309i | ||||||
\(619\) | 35.8758 | 1.44197 | 0.720985 | − | 0.692950i | \(-0.243689\pi\) | ||||
0.720985 | + | 0.692950i | \(0.243689\pi\) | |||||||
\(620\) | − | 2.61309i | − | 0.104944i | ||||||
\(621\) | −6.10236 | − | 12.9021i | −0.244879 | − | 0.517744i | ||||
\(622\) | − | 18.7483i | − | 0.751737i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.94999 | −0.318254 | ||||||||
\(625\) | 20.8890 | 0.835562 | ||||||||
\(626\) | −31.3104 | −1.25141 | ||||||||
\(627\) | −2.32776 | −0.0929618 | ||||||||
\(628\) | 7.46744 | 0.297983 | ||||||||
\(629\) | − | 59.8179i | − | 2.38510i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 33.2092i | − | 1.32204i | −0.750370 | − | 0.661018i | \(-0.770124\pi\) | ||
0.750370 | − | 0.661018i | \(-0.229876\pi\) | |||||||
\(632\) | − | 11.9504i | − | 0.475360i | ||||||
\(633\) | − | 56.0258i | − | 2.22683i | ||||||
\(634\) | 28.6469 | 1.13771 | ||||||||
\(635\) | 1.74956 | 0.0694293 | ||||||||
\(636\) | 29.4002 | 1.16579 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 7.56492i | − | 0.299498i | ||||||
\(639\) | −1.66542 | −0.0658831 | ||||||||
\(640\) | −0.528453 | −0.0208890 | ||||||||
\(641\) | 5.45614i | 0.215504i | 0.994178 | + | 0.107752i | \(0.0343653\pi\) | ||||
−0.994178 | + | 0.107752i | \(0.965635\pi\) | |||||||
\(642\) | −19.0966 | −0.753684 | ||||||||
\(643\) | 19.3950 | 0.764865 | 0.382432 | − | 0.923983i | \(-0.375086\pi\) | ||||
0.382432 | + | 0.923983i | \(0.375086\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.1993 | 0.401597 | ||||||||
\(646\) | 3.64609 | 0.143453 | ||||||||
\(647\) | 37.9892i | 1.49351i | 0.665099 | + | 0.746755i | \(0.268389\pi\) | ||||
−0.665099 | + | 0.746755i | \(0.731611\pi\) | |||||||
\(648\) | −11.2369 | −0.441426 | ||||||||
\(649\) | 11.8459 | 0.464991 | ||||||||
\(650\) | − | 17.4706i | − | 0.685254i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.61463 | −0.219886 | ||||||||
\(653\) | −6.65782 | −0.260541 | −0.130270 | − | 0.991479i | \(-0.541585\pi\) | ||||
−0.130270 | + | 0.991479i | \(0.541585\pi\) | |||||||
\(654\) | −14.8954 | −0.582458 | ||||||||
\(655\) | 8.63180i | 0.337272i | ||||||||
\(656\) | 3.70082i | 0.144493i | ||||||||
\(657\) | − | 7.98399i | − | 0.311485i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7.65972i | − | 0.298380i | −0.988809 | − | 0.149190i | \(-0.952333\pi\) | ||
0.988809 | − | 0.149190i | \(-0.0476667\pi\) | |||||||
\(660\) | −2.32776 | −0.0906079 | ||||||||
\(661\) | 23.3705 | 0.909009 | 0.454504 | − | 0.890745i | \(-0.349816\pi\) | ||||
0.454504 | + | 0.890745i | \(0.349816\pi\) | |||||||
\(662\) | 27.3100 | 1.06143 | ||||||||
\(663\) | 54.8513 | 2.13025 | ||||||||
\(664\) | 16.4544 | 0.638554 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 13.9986i | − | 0.542433i | ||||||
\(667\) | −15.9944 | + | 7.56492i | −0.619304 | + | 0.292915i | ||||
\(668\) | − | 4.65513i | − | 0.180112i | ||||||
\(669\) | −6.77835 | −0.262066 | ||||||||
\(670\) | − | 0.433599i | − | 0.0167514i | ||||||
\(671\) | 11.9804i | 0.462499i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.0944 | −1.23715 | −0.618575 | − | 0.785726i | \(-0.712290\pi\) | ||||
−0.618575 | + | 0.785726i | \(0.712290\pi\) | |||||||
\(674\) | − | 3.09092i | − | 0.119058i | ||||||
\(675\) | − | 14.0490i | − | 0.540745i | ||||||
\(676\) | −0.696095 | −0.0267729 | ||||||||
\(677\) | 10.6117 | 0.407842 | 0.203921 | − | 0.978987i | \(-0.434631\pi\) | ||||
0.203921 | + | 0.978987i | \(0.434631\pi\) | |||||||
\(678\) | 10.7593 | 0.413209 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.64609 | 0.139821 | ||||||||
\(681\) | − | 16.7391i | − | 0.641442i | ||||||
\(682\) | 10.1394 | 0.388256 | ||||||||
\(683\) | −41.4737 | −1.58695 | −0.793474 | − | 0.608604i | \(-0.791730\pi\) | ||||
−0.793474 | + | 0.608604i | \(0.791730\pi\) | |||||||
\(684\) | 0.853256 | 0.0326250 | ||||||||
\(685\) | − | 5.18151i | − | 0.197975i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.1982i | 0.465392i | ||||||||
\(688\) | 8.98453i | 0.342532i | ||||||||
\(689\) | 50.6501 | 1.92962 | ||||||||
\(690\) | 2.32776 | + | 4.92154i | 0.0886163 | + | 0.187360i | ||||
\(691\) | − | 4.32846i | − | 0.164663i | −0.996605 | − | 0.0823313i | \(-0.973763\pi\) | ||
0.996605 | − | 0.0823313i | \(-0.0262365\pi\) | |||||||
\(692\) | − | 14.7858i | − | 0.562072i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.44829 | −0.206814 | ||||||||
\(695\) | 9.74827i | 0.369773i | ||||||||
\(696\) | 7.92519i | 0.300404i | ||||||||
\(697\) | − | 25.5340i | − | 0.967169i | ||||||
\(698\) | 7.05311i | 0.266964i | ||||||||
\(699\) | 61.2307i | 2.31596i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.85553i | 0.183391i | 0.995787 | + | 0.0916954i | \(0.0292286\pi\) | ||||
−0.995787 | + | 0.0916954i | \(0.970771\pi\) | |||||||
\(702\) | −11.0137 | −0.415685 | ||||||||
\(703\) | − | 4.58160i | − | 0.172798i | ||||||
\(704\) | − | 2.05052i | − | 0.0772817i | ||||||
\(705\) | −2.23496 | −0.0841736 | ||||||||
\(706\) | − | 8.86485i | − | 0.333633i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −12.4100 | −0.466397 | ||||||||
\(709\) | − | 14.0086i | − | 0.526104i | −0.964782 | − | 0.263052i | \(-0.915271\pi\) | ||
0.964782 | − | 0.263052i | \(-0.0847292\pi\) | |||||||
\(710\) | −0.545078 | −0.0204564 | ||||||||
\(711\) | 19.2954i | 0.723633i | ||||||||
\(712\) | 7.63165 | 0.286008 | ||||||||
\(713\) | −10.1394 | − | 21.4374i | −0.379722 | − | 0.802839i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.01022 | −0.149974 | ||||||||
\(716\) | 3.38537 | 0.126517 | ||||||||
\(717\) | 4.52103i | 0.168841i | ||||||||
\(718\) | 9.62317i | 0.359134i | ||||||||
\(719\) | − | 34.5763i | − | 1.28948i | −0.764403 | − | 0.644739i | \(-0.776966\pi\) | ||
0.764403 | − | 0.644739i | \(-0.223034\pi\) | |||||||
\(720\) | 0.853256 | 0.0317990 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.7207 | −0.696714 | ||||||||
\(723\) | 32.6677i | 1.21492i | ||||||||
\(724\) | 10.2869 | 0.382311 | ||||||||
\(725\) | −17.4161 | −0.646818 | ||||||||
\(726\) | 14.5976i | 0.541769i | ||||||||
\(727\) | −29.9681 | −1.11146 | −0.555728 | − | 0.831364i | \(-0.687560\pi\) | ||||
−0.555728 | + | 0.831364i | \(0.687560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.03559 | −0.0383550 | ||||||||
\(730\) | − | 2.61309i | − | 0.0967148i | ||||||
\(731\) | − | 61.9892i | − | 2.29275i | ||||||
\(732\) | − | 12.5510i | − | 0.463897i | ||||||
\(733\) | −47.6700 | −1.76073 | −0.880366 | − | 0.474295i | \(-0.842703\pi\) | ||||
−0.880366 | + | 0.474295i | \(0.842703\pi\) | |||||||
\(734\) | −24.2072 | −0.893503 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.33536 | + | 2.05052i | −0.159804 | + | 0.0755830i | ||||
\(737\) | 1.68246 | 0.0619742 | ||||||||
\(738\) | − | 5.97545i | − | 0.219959i | ||||||
\(739\) | −0.345584 | −0.0127125 | −0.00635626 | − | 0.999980i | \(-0.502023\pi\) | ||||
−0.00635626 | + | 0.999980i | \(0.502023\pi\) | |||||||
\(740\) | − | 4.58160i | − | 0.168423i | ||||||
\(741\) | 4.20120 | 0.154335 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14.5735i | − | 0.534650i | −0.963606 | − | 0.267325i | \(-0.913860\pi\) | ||
0.963606 | − | 0.267325i | \(-0.0861397\pi\) | |||||||
\(744\) | −10.6222 | −0.389430 | ||||||||
\(745\) | − | 2.16720i | − | 0.0794002i | ||||||
\(746\) | 0.0567690i | 0.00207846i | ||||||||
\(747\) | −26.5677 | −0.972061 | ||||||||
\(748\) | 14.1476i | 0.517288i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.0350i | 0.402943i | ||||||||
\(751\) | − | 46.2645i | − | 1.68821i | −0.536175 | − | 0.844107i | \(-0.680131\pi\) | ||
0.536175 | − | 0.844107i | \(-0.319869\pi\) | |||||||
\(752\) | − | 1.96877i | − | 0.0717938i | ||||||
\(753\) | − | 45.2109i | − | 1.64758i | ||||||
\(754\) | 13.6534i | 0.497226i | ||||||||
\(755\) | −0.935756 | −0.0340557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 5.74054i | − | 0.208644i | −0.994544 | − | 0.104322i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104322i | \(-0.0332672\pi\) | |||||||
\(758\) | − | 20.4003i | − | 0.740972i | ||||||
\(759\) | −19.0966 | + | 9.03222i | −0.693164 | + | 0.327849i | ||||
\(760\) | 0.279263 | 0.0101299 | ||||||||
\(761\) | − | 44.7232i | − | 1.62121i | −0.585591 | − | 0.810607i | \(-0.699138\pi\) | ||
0.585591 | − | 0.810607i | \(-0.300862\pi\) | |||||||
\(762\) | − | 7.11199i | − | 0.257640i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.88113i | 0.140414i | ||||||||
\(765\) | −5.88707 | −0.212848 | ||||||||
\(766\) | 12.9458 | 0.467752 | ||||||||
\(767\) | −21.3797 | −0.771978 | ||||||||
\(768\) | 2.14817i | 0.0775154i | ||||||||
\(769\) | 30.7425 | 1.10860 | 0.554301 | − | 0.832316i | \(-0.312986\pi\) | ||||
0.554301 | + | 0.832316i | \(0.312986\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −48.1107 | −1.73266 | ||||||||
\(772\) | 13.6954 | 0.492907 | ||||||||
\(773\) | 28.3038 | 1.01802 | 0.509009 | − | 0.860761i | \(-0.330012\pi\) | ||||
0.509009 | + | 0.860761i | \(0.330012\pi\) | |||||||
\(774\) | − | 14.5067i | − | 0.521432i | ||||||
\(775\) | − | 23.3430i | − | 0.838506i | ||||||
\(776\) | −11.1402 | −0.399910 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.7943i | 1.28329i | ||||||||
\(779\) | − | 1.95571i | − | 0.0700707i | ||||||
\(780\) | 4.20120 | 0.150427 | ||||||||
\(781\) | − | 2.11502i | − | 0.0756815i | ||||||
\(782\) | 29.9120 | − | 14.1476i | 1.06965 | − | 0.505918i | ||||
\(783\) | 10.9793i | 0.392370i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.94620 | −0.140846 | ||||||||
\(786\) | 35.0883 | 1.25156 | ||||||||
\(787\) | −3.75165 | −0.133732 | −0.0668659 | − | 0.997762i | \(-0.521300\pi\) | ||||
−0.0668659 | + | 0.997762i | \(0.521300\pi\) | |||||||
\(788\) | 20.4976 | 0.730196 | ||||||||
\(789\) | −20.5905 | −0.733041 | ||||||||
\(790\) | 6.31521i | 0.224685i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.31082i | 0.117645i | ||||||||
\(793\) | − | 21.6226i | − | 0.767840i | ||||||
\(794\) | 21.8641i | 0.775929i | ||||||||
\(795\) | −15.5366 | −0.551028 | ||||||||
\(796\) | −20.8857 | −0.740272 | ||||||||
\(797\) | −14.8394 | −0.525637 | −0.262819 | − | 0.964845i | \(-0.584652\pi\) | ||||
−0.262819 | + | 0.964845i | \(0.584652\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5836i | 0.480554i | ||||||||
\(800\) | −4.72074 | −0.166903 | ||||||||
\(801\) | −12.3223 | −0.435386 | ||||||||
\(802\) | 17.4345i | 0.615632i | ||||||||
\(803\) | 10.1394 | 0.357810 | ||||||||
\(804\) | −1.76259 | −0.0621616 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.2998 | −0.644582 | ||||||||
\(807\) | −36.6674 | −1.29075 | ||||||||
\(808\) | 2.98040i | 0.104850i | ||||||||
\(809\) | 46.6720 | 1.64090 | 0.820450 | − | 0.571719i | \(-0.193723\pi\) | ||||
0.820450 | + | 0.571719i | \(0.193723\pi\) | |||||||
\(810\) | 5.93816 | 0.208646 | ||||||||
\(811\) | − | 10.5200i | − | 0.369409i | −0.982794 | − | 0.184704i | \(-0.940867\pi\) | ||
0.982794 | − | 0.184704i | \(-0.0591328\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.0213 | −1.12304 | ||||||||
\(814\) | 17.7776 | 0.623105 | ||||||||
\(815\) | 2.96707 | 0.103932 | ||||||||
\(816\) | − | 14.8214i | − | 0.518852i | ||||||
\(817\) | − | 4.74791i | − | 0.166108i | ||||||
\(818\) | − | 33.1136i | − | 1.15779i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 1.95571i | − | 0.0682965i | ||||||
\(821\) | −14.0561 | −0.490561 | −0.245281 | − | 0.969452i | \(-0.578880\pi\) | ||||
−0.245281 | + | 0.969452i | \(0.578880\pi\) | |||||||
\(822\) | −21.0629 | −0.734652 | ||||||||
\(823\) | −6.99436 | −0.243808 | −0.121904 | − | 0.992542i | \(-0.538900\pi\) | ||||
−0.121904 | + | 0.992542i | \(0.538900\pi\) | |||||||
\(824\) | −1.76259 | −0.0614026 | ||||||||
\(825\) | −20.7941 | −0.723959 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.9598i | 1.28522i | 0.766194 | + | 0.642609i | \(0.222148\pi\) | ||||
−0.766194 | + | 0.642609i | \(0.777852\pi\) | |||||||
\(828\) | 7.00000 | − | 3.31082i | 0.243267 | − | 0.115059i | ||||
\(829\) | − | 3.55072i | − | 0.123322i | −0.998097 | − | 0.0616608i | \(-0.980360\pi\) | ||
0.998097 | − | 0.0616608i | \(-0.0196397\pi\) | |||||||
\(830\) | −8.69537 | −0.301821 | ||||||||
\(831\) | 64.1904i | 2.22674i | ||||||||
\(832\) | 3.70082i | 0.128303i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 39.6268 | 1.37216 | ||||||||
\(835\) | 2.46002i | 0.0851325i | ||||||||
\(836\) | 1.08360i | 0.0374772i | ||||||||
\(837\) | −14.7157 | −0.508651 | ||||||||
\(838\) | 22.9995 | 0.794503 | ||||||||
\(839\) | −4.89386 | −0.168955 | −0.0844774 | − | 0.996425i | \(-0.526922\pi\) | ||||
−0.0844774 | + | 0.996425i | \(0.526922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3892 | −0.530663 | ||||||||
\(842\) | 13.9931i | 0.482235i | ||||||||
\(843\) | −46.8160 | −1.61243 | ||||||||
\(844\) | −26.0807 | −0.897736 | ||||||||
\(845\) | 0.367854 | 0.0126546 | ||||||||
\(846\) | 3.17884i | 0.109291i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 13.6862i | − | 0.469985i | ||||||
\(849\) | 57.4169i | 1.97054i | ||||||||
\(850\) | 32.5709 | 1.11717 | ||||||||
\(851\) | −17.7776 | − | 37.5869i | −0.609409 | − | 1.28846i | ||||
\(852\) | 2.21575i | 0.0759103i | ||||||||
\(853\) | 15.0374i | 0.514871i | 0.966296 | + | 0.257435i | \(0.0828774\pi\) | ||||
−0.966296 | + | 0.257435i | \(0.917123\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.450906 | −0.0154207 | ||||||||
\(856\) | 8.88973i | 0.303845i | ||||||||
\(857\) | 24.4456i | 0.835045i | 0.908666 | + | 0.417523i | \(0.137102\pi\) | ||||
−0.908666 | + | 0.417523i | \(0.862898\pi\) | |||||||
\(858\) | 16.3016i | 0.556527i | ||||||||
\(859\) | − | 45.4187i | − | 1.54967i | −0.632166 | − | 0.774833i | \(-0.717834\pi\) | ||
0.632166 | − | 0.774833i | \(-0.282166\pi\) | |||||||
\(860\) | − | 4.74791i | − | 0.161902i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.0335i | 0.512044i | ||||||||
\(863\) | −31.0376 | −1.05653 | −0.528265 | − | 0.849079i | \(-0.677157\pi\) | ||||
−0.528265 | + | 0.849079i | \(0.677157\pi\) | |||||||
\(864\) | 2.97601i | 0.101246i | ||||||||
\(865\) | 7.81361i | 0.265671i | ||||||||
\(866\) | 8.50153 | 0.288894 | ||||||||
\(867\) | 65.7419i | 2.23271i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24.5044 | −0.831255 | ||||||||
\(870\) | − | 4.18809i | − | 0.141990i | ||||||
\(871\) | −3.03655 | −0.102889 | ||||||||
\(872\) | 6.93402i | 0.234816i | ||||||||
\(873\) | 17.9873 | 0.608777 | ||||||||
\(874\) | 2.29104 | − | 1.08360i | 0.0774955 | − | 0.0366534i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.6222 | −0.358892 | ||||||||
\(877\) | −26.9940 | −0.911522 | −0.455761 | − | 0.890102i | \(-0.650633\pi\) | ||||
−0.455761 | + | 0.890102i | \(0.650633\pi\) | |||||||
\(878\) | 1.78938i | 0.0603885i | ||||||||
\(879\) | − | 45.9443i | − | 1.54966i | ||||||
\(880\) | 1.08360i | 0.0365282i | ||||||||
\(881\) | 41.9616 | 1.41372 | 0.706860 | − | 0.707353i | \(-0.250111\pi\) | ||||
0.706860 | + | 0.707353i | \(0.250111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.3346 | −0.347786 | −0.173893 | − | 0.984765i | \(-0.555635\pi\) | ||||
−0.173893 | + | 0.984765i | \(0.555635\pi\) | |||||||
\(884\) | − | 25.5340i | − | 0.858801i | ||||||
\(885\) | 6.55812 | 0.220449 | ||||||||
\(886\) | 14.4229 | 0.484548 | ||||||||
\(887\) | − | 34.6999i | − | 1.16511i | −0.812792 | − | 0.582554i | \(-0.802053\pi\) | ||
0.812792 | − | 0.582554i | \(-0.197947\pi\) | |||||||
\(888\) | −18.6243 | −0.624989 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.03297 | −0.135185 | ||||||||
\(891\) | 23.0414i | 0.771914i | ||||||||
\(892\) | 3.15541i | 0.105651i | ||||||||
\(893\) | 1.04040i | 0.0348158i | ||||||||
\(894\) | −8.80970 | −0.294641 | ||||||||
\(895\) | −1.78901 | −0.0598001 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.4661 | − | 16.3016i | 1.15079 | − | 0.544294i | ||||
\(898\) | 9.65218 | 0.322097 | ||||||||
\(899\) | 18.2427i | 0.608428i | ||||||||
\(900\) | 7.62223 | 0.254074 | ||||||||
\(901\) | 94.4283i | 3.14586i | ||||||||
\(902\) | 7.58860 | 0.252673 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 5.00860i | − | 0.166584i | ||||||
\(905\) | −5.43617 | −0.180704 | ||||||||
\(906\) | 3.80386i | 0.126375i | ||||||||
\(907\) | 31.8184i | 1.05651i | 0.849085 | + | 0.528256i | \(0.177154\pi\) | ||||
−0.849085 | + | 0.528256i | \(0.822846\pi\) | |||||||
\(908\) | −7.79225 | −0.258595 | ||||||||
\(909\) | − | 4.81224i | − | 0.159612i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.68229i | − | 0.122000i | −0.998138 | − | 0.0609998i | \(-0.980571\pi\) | ||
0.998138 | − | 0.0609998i | \(-0.0194289\pi\) | |||||||
\(912\) | − | 1.13521i | − | 0.0375905i | ||||||
\(913\) | − | 33.7399i | − | 1.11663i | ||||||
\(914\) | 36.1370i | 1.19531i | ||||||||
\(915\) | 6.63260i | 0.219267i | ||||||||
\(916\) | 5.67843 | 0.187621 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 20.5331i | − | 0.677694i | ||||||
\(919\) | 52.4083i | 1.72879i | 0.502814 | + | 0.864395i | \(0.332298\pi\) | ||||
−0.502814 | + | 0.864395i | \(0.667702\pi\) | |||||||
\(920\) | 2.29104 | − | 1.08360i | 0.0755333 | − | 0.0357253i | ||||
\(921\) | −4.65218 | −0.153295 | ||||||||
\(922\) | − | 27.5367i | − | 0.906874i | ||||||
\(923\) | 3.81725i | 0.125646i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 40.9280i | − | 1.34570i | ||||||
\(926\) | −0.186065 | −0.00611448 | ||||||||
\(927\) | 2.84592 | 0.0934722 | ||||||||
\(928\) | 3.68928 | 0.121106 | ||||||||
\(929\) | − | 1.70276i | − | 0.0558658i | −0.999610 | − | 0.0279329i | \(-0.991108\pi\) | ||
0.999610 | − | 0.0279329i | \(-0.00889247\pi\) | |||||||
\(930\) | 5.61336 | 0.184069 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28.5037 | 0.933669 | ||||||||
\(933\) | 40.2744 | 1.31853 | ||||||||
\(934\) | −17.3243 | −0.566867 | ||||||||
\(935\) | − | 7.47636i | − | 0.244503i | ||||||
\(936\) | − | 5.97545i | − | 0.195314i | ||||||
\(937\) | 17.8589 | 0.583425 | 0.291713 | − | 0.956506i | \(-0.405775\pi\) | ||||
0.291713 | + | 0.956506i | \(0.405775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 67.2599i | − | 2.19495i | ||||||
\(940\) | 1.04040i | 0.0339343i | ||||||||
\(941\) | −57.3232 | −1.86868 | −0.934341 | − | 0.356380i | \(-0.884011\pi\) | ||||
−0.934341 | + | 0.356380i | \(0.884011\pi\) | |||||||
\(942\) | 16.0413i | 0.522655i | ||||||||
\(943\) | −7.58860 | − | 16.0444i | −0.247119 | − | 0.522478i | ||||
\(944\) | 5.77702i | 0.188026i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.4229 | 0.598981 | ||||||||
\(947\) | 2.45851 | 0.0798909 | 0.0399454 | − | 0.999202i | \(-0.487282\pi\) | ||||
0.0399454 | + | 0.999202i | \(0.487282\pi\) | |||||||
\(948\) | 25.6714 | 0.833768 | ||||||||
\(949\) | −18.2998 | −0.594036 | ||||||||
\(950\) | 2.49469 | 0.0809384 | ||||||||
\(951\) | 61.5383i | 1.99552i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 22.3180i | − | 0.722950i | −0.932382 | − | 0.361475i | \(-0.882273\pi\) | ||
0.932382 | − | 0.361475i | \(-0.117727\pi\) | |||||||
\(954\) | 22.0981i | 0.715452i | ||||||||
\(955\) | − | 2.05100i | − | 0.0663687i | ||||||
\(956\) | 2.10460 | 0.0680676 | ||||||||
\(957\) | 16.2507 | 0.525311 | ||||||||
\(958\) | −32.3673 | −1.04574 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 1.13521i | − | 0.0366387i | ||||||
\(961\) | 6.54909 | 0.211261 | ||||||||
\(962\) | −32.0855 | −1.03448 | ||||||||
\(963\) | − | 14.3536i | − | 0.462539i | ||||||
\(964\) | 15.2072 | 0.489792 | ||||||||
\(965\) | −7.23737 | −0.232979 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.7700 | 1.69697 | 0.848485 | − | 0.529220i | \(-0.177515\pi\) | ||||
0.848485 | + | 0.529220i | \(0.177515\pi\) | |||||||
\(968\) | 6.79539 | 0.218412 | ||||||||
\(969\) | 7.83241i | 0.251613i | ||||||||
\(970\) | 5.88707 | 0.189023 | ||||||||
\(971\) | 3.50893 | 0.112607 | 0.0563034 | − | 0.998414i | \(-0.482069\pi\) | ||||
0.0563034 | + | 0.998414i | \(0.482069\pi\) | |||||||
\(972\) | − | 15.2106i | − | 0.487881i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.0020 | 0.961325 | ||||||||
\(975\) | 37.5298 | 1.20192 | ||||||||
\(976\) | −5.84264 | −0.187018 | ||||||||
\(977\) | 30.2053i | 0.966354i | 0.875523 | + | 0.483177i | \(0.160517\pi\) | ||||
−0.875523 | + | 0.483177i | \(0.839483\pi\) | |||||||
\(978\) | − | 12.0612i | − | 0.385674i | ||||||
\(979\) | − | 15.6488i | − | 0.500138i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 11.1959i | − | 0.357456i | ||||||
\(982\) | −11.9761 | −0.382174 | ||||||||
\(983\) | −21.1876 | −0.675780 | −0.337890 | − | 0.941186i | \(-0.609713\pi\) | ||||
−0.337890 | + | 0.941186i | \(0.609713\pi\) | |||||||
\(984\) | −7.94999 | −0.253437 | ||||||||
\(985\) | −10.8320 | −0.345137 | ||||||||
\(986\) | −25.4543 | −0.810631 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 1.95571i | − | 0.0622195i | ||||||
\(989\) | −18.4229 | − | 38.9512i | −0.585815 | − | 1.23858i | ||||
\(990\) | − | 1.74961i | − | 0.0556064i | ||||||
\(991\) | −55.6132 | −1.76661 | −0.883305 | − | 0.468798i | \(-0.844687\pi\) | ||||
−0.883305 | + | 0.468798i | \(0.844687\pi\) | |||||||
\(992\) | 4.94479i | 0.156997i | ||||||||
\(993\) | 58.6665i | 1.86172i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.0371 | 0.349899 | ||||||||
\(996\) | 35.3468i | 1.12001i | ||||||||
\(997\) | − | 6.48719i | − | 0.205451i | −0.994710 | − | 0.102726i | \(-0.967244\pi\) | ||
0.994710 | − | 0.102726i | \(-0.0327564\pi\) | |||||||
\(998\) | −40.2744 | −1.27486 | ||||||||
\(999\) | −25.8015 | −0.816324 |
(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 | 2254.2.c.c.2253.13 | 16 | ||
7.2 | even | 3 | 322.2.g.a.45.2 | yes | 16 | ||
7.3 | odd | 6 | 322.2.g.a.229.1 | yes | 16 | ||
7.6 | odd | 2 | inner | 2254.2.c.c.2253.4 | 16 | ||
23.22 | odd | 2 | inner | 2254.2.c.c.2253.14 | 16 | ||
161.45 | even | 6 | 322.2.g.a.229.2 | yes | 16 | ||
161.114 | odd | 6 | 322.2.g.a.45.1 | ✓ | 16 | ||
161.160 | even | 2 | inner | 2254.2.c.c.2253.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.2.g.a.45.1 | ✓ | 16 | 161.114 | odd | 6 | ||
322.2.g.a.45.2 | yes | 16 | 7.2 | even | 3 | ||
322.2.g.a.229.1 | yes | 16 | 7.3 | odd | 6 | ||
322.2.g.a.229.2 | yes | 16 | 161.45 | even | 6 | ||
2254.2.c.c.2253.3 | 16 | 161.160 | even | 2 | inner | ||
2254.2.c.c.2253.4 | 16 | 7.6 | odd | 2 | inner | ||
2254.2.c.c.2253.13 | 16 | 1.1 | even | 1 | trivial | ||
2254.2.c.c.2253.14 | 16 | 23.22 | odd | 2 | inner |