Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3025,2,Mod(1,3025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3025 = 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3025.a (trivial) |
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: | yes |
Analytic conductor: | \(24.1547466114\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.35567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35567 | −0.958606 | −0.479303 | − | 0.877649i | \(-0.659111\pi\) | ||||
−0.479303 | + | 0.877649i | \(0.659111\pi\) | |||||||
\(3\) | −0.575493 | −0.332261 | −0.166131 | − | 0.986104i | \(-0.553127\pi\) | ||||
−0.166131 | + | 0.986104i | \(0.553127\pi\) | |||||||
\(4\) | −0.162147 | −0.0810736 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.780181 | 0.318508 | ||||||||
\(7\) | 3.64941 | 1.37935 | 0.689674 | − | 0.724120i | \(-0.257754\pi\) | ||||
0.689674 | + | 0.724120i | \(0.257754\pi\) | |||||||
\(8\) | 2.93117 | 1.03632 | ||||||||
\(9\) | −2.66881 | −0.889603 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.0933146 | 0.0269376 | ||||||||
\(13\) | 2.83095 | 0.785166 | 0.392583 | − | 0.919717i | \(-0.371582\pi\) | ||||
0.392583 | + | 0.919717i | \(0.371582\pi\) | |||||||
\(14\) | −4.94742 | −1.32225 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.64941 | −0.912353 | ||||||||
\(17\) | −3.69195 | −0.895431 | −0.447715 | − | 0.894176i | \(-0.647762\pi\) | ||||
−0.447715 | + | 0.894176i | \(0.647762\pi\) | |||||||
\(18\) | 3.61803 | 0.852779 | ||||||||
\(19\) | −0.0951243 | −0.0218230 | −0.0109115 | − | 0.999940i | \(-0.503473\pi\) | ||||
−0.0109115 | + | 0.999940i | \(0.503473\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.10021 | −0.458304 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.16215 | −0.242324 | −0.121162 | − | 0.992633i | \(-0.538662\pi\) | ||||
−0.121162 | + | 0.992633i | \(0.538662\pi\) | |||||||
\(24\) | −1.68687 | −0.344330 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.83785 | −0.752665 | ||||||||
\(27\) | 3.26236 | 0.627841 | ||||||||
\(28\) | −0.591742 | −0.111829 | ||||||||
\(29\) | −6.75389 | −1.25417 | −0.627083 | − | 0.778953i | \(-0.715751\pi\) | ||||
−0.627083 | + | 0.778953i | \(0.715751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.77837 | 1.21743 | 0.608716 | − | 0.793388i | \(-0.291685\pi\) | ||||
0.608716 | + | 0.793388i | \(0.291685\pi\) | |||||||
\(32\) | −0.914918 | −0.161736 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.00509 | 0.858366 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.432740 | 0.0721233 | ||||||||
\(37\) | −9.83980 | −1.61765 | −0.808826 | − | 0.588048i | \(-0.799897\pi\) | ||||
−0.808826 | + | 0.588048i | \(0.799897\pi\) | |||||||
\(38\) | 0.128958 | 0.0209197 | ||||||||
\(39\) | −1.62920 | −0.260880 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.31822 | −1.29909 | −0.649544 | − | 0.760324i | \(-0.725040\pi\) | ||||
−0.649544 | + | 0.760324i | \(0.725040\pi\) | |||||||
\(42\) | 2.84720 | 0.439333 | ||||||||
\(43\) | 2.96862 | 0.452710 | 0.226355 | − | 0.974045i | \(-0.427319\pi\) | ||||
0.226355 | + | 0.974045i | \(0.427319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.57549 | 0.232294 | ||||||||
\(47\) | 2.22491 | 0.324536 | 0.162268 | − | 0.986747i | \(-0.448119\pi\) | ||||
0.162268 | + | 0.986747i | \(0.448119\pi\) | |||||||
\(48\) | 2.10021 | 0.303140 | ||||||||
\(49\) | 6.31822 | 0.902603 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.12469 | 0.297517 | ||||||||
\(52\) | −0.459031 | −0.0636562 | ||||||||
\(53\) | −2.99393 | −0.411248 | −0.205624 | − | 0.978631i | \(-0.565922\pi\) | ||||
−0.205624 | + | 0.978631i | \(0.565922\pi\) | |||||||
\(54\) | −4.42270 | −0.601853 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.6970 | 1.42945 | ||||||||
\(57\) | 0.0547434 | 0.00725094 | ||||||||
\(58\) | 9.15607 | 1.20225 | ||||||||
\(59\) | −8.50860 | −1.10773 | −0.553863 | − | 0.832608i | \(-0.686847\pi\) | ||||
−0.553863 | + | 0.832608i | \(0.686847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.48037 | −1.08580 | −0.542900 | − | 0.839797i | \(-0.682674\pi\) | ||||
−0.542900 | + | 0.839797i | \(0.682674\pi\) | |||||||
\(62\) | −9.18926 | −1.16704 | ||||||||
\(63\) | −9.73958 | −1.22707 | ||||||||
\(64\) | 8.53916 | 1.06739 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.4153 | 1.63894 | 0.819469 | − | 0.573123i | \(-0.194268\pi\) | ||||
0.819469 | + | 0.573123i | \(0.194268\pi\) | |||||||
\(68\) | 0.598640 | 0.0725958 | ||||||||
\(69\) | 0.668808 | 0.0805150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.30309 | 0.985396 | 0.492698 | − | 0.870200i | \(-0.336011\pi\) | ||||
0.492698 | + | 0.870200i | \(0.336011\pi\) | |||||||
\(72\) | −7.82272 | −0.921917 | ||||||||
\(73\) | 1.32003 | 0.154498 | 0.0772490 | − | 0.997012i | \(-0.475386\pi\) | ||||
0.0772490 | + | 0.997012i | \(0.475386\pi\) | |||||||
\(74\) | 13.3396 | 1.55069 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0154241 | 0.00176927 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.20866 | 0.250081 | ||||||||
\(79\) | −13.8661 | −1.56006 | −0.780028 | − | 0.625744i | \(-0.784795\pi\) | ||||
−0.780028 | + | 0.625744i | \(0.784795\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.12896 | 0.680995 | ||||||||
\(82\) | 11.2768 | 1.24531 | ||||||||
\(83\) | 10.6445 | 1.16838 | 0.584191 | − | 0.811616i | \(-0.301412\pi\) | ||||
0.584191 | + | 0.811616i | \(0.301412\pi\) | |||||||
\(84\) | 0.340544 | 0.0371564 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.02448 | −0.433971 | ||||||||
\(87\) | 3.88682 | 0.416710 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1612 | −1.28908 | −0.644540 | − | 0.764570i | \(-0.722951\pi\) | ||||
−0.644540 | + | 0.764570i | \(0.722951\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3313 | 1.08302 | ||||||||
\(92\) | 0.188439 | 0.0196461 | ||||||||
\(93\) | −3.90091 | −0.404505 | ||||||||
\(94\) | −3.01625 | −0.311102 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.526529 | 0.0537387 | ||||||||
\(97\) | 4.33133 | 0.439780 | 0.219890 | − | 0.975525i | \(-0.429430\pi\) | ||||
0.219890 | + | 0.975525i | \(0.429430\pi\) | |||||||
\(98\) | −8.56545 | −0.865241 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.90570 | 0.985654 | 0.492827 | − | 0.870127i | \(-0.335964\pi\) | ||||
0.492827 | + | 0.870127i | \(0.335964\pi\) | |||||||
\(102\) | −2.88039 | −0.285201 | ||||||||
\(103\) | −4.06590 | −0.400625 | −0.200313 | − | 0.979732i | \(-0.564196\pi\) | ||||
−0.200313 | + | 0.979732i | \(0.564196\pi\) | |||||||
\(104\) | 8.29800 | 0.813686 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.05879 | 0.394225 | ||||||||
\(107\) | −1.93858 | −0.187409 | −0.0937046 | − | 0.995600i | \(-0.529871\pi\) | ||||
−0.0937046 | + | 0.995600i | \(0.529871\pi\) | |||||||
\(108\) | −0.528983 | −0.0509014 | ||||||||
\(109\) | 6.12664 | 0.586825 | 0.293413 | − | 0.955986i | \(-0.405209\pi\) | ||||
0.293413 | + | 0.955986i | \(0.405209\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.66273 | 0.537483 | ||||||||
\(112\) | −13.3182 | −1.25845 | ||||||||
\(113\) | −5.78527 | −0.544232 | −0.272116 | − | 0.962264i | \(-0.587724\pi\) | ||||
−0.272116 | + | 0.962264i | \(0.587724\pi\) | |||||||
\(114\) | −0.0742142 | −0.00695080 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.09512 | 0.101680 | ||||||||
\(117\) | −7.55527 | −0.698485 | ||||||||
\(118\) | 11.5349 | 1.06187 | ||||||||
\(119\) | −13.4735 | −1.23511 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 11.4966 | 1.04085 | ||||||||
\(123\) | 4.78708 | 0.431636 | ||||||||
\(124\) | −1.09909 | −0.0987016 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.2037 | 1.17628 | ||||||||
\(127\) | −2.43783 | −0.216322 | −0.108161 | − | 0.994133i | \(-0.534496\pi\) | ||||
−0.108161 | + | 0.994133i | \(0.534496\pi\) | |||||||
\(128\) | −9.74648 | −0.861475 | ||||||||
\(129\) | −1.70842 | −0.150418 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.04156 | 0.615224 | 0.307612 | − | 0.951512i | \(-0.400470\pi\) | ||||
0.307612 | + | 0.951512i | \(0.400470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.347148 | −0.0301016 | ||||||||
\(134\) | −18.1868 | −1.57110 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.8217 | −0.927956 | ||||||||
\(137\) | 9.57286 | 0.817864 | 0.408932 | − | 0.912565i | \(-0.365901\pi\) | ||||
0.408932 | + | 0.912565i | \(0.365901\pi\) | |||||||
\(138\) | −0.906685 | −0.0771822 | ||||||||
\(139\) | 0.515502 | 0.0437243 | 0.0218621 | − | 0.999761i | \(-0.493041\pi\) | ||||
0.0218621 | + | 0.999761i | \(0.493041\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.28042 | −0.107831 | ||||||||
\(142\) | −11.2563 | −0.944607 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 9.73958 | 0.811632 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.78953 | −0.148103 | ||||||||
\(147\) | −3.63609 | −0.299900 | ||||||||
\(148\) | 1.59550 | 0.131149 | ||||||||
\(149\) | −8.15983 | −0.668479 | −0.334240 | − | 0.942488i | \(-0.608479\pi\) | ||||
−0.334240 | + | 0.942488i | \(0.608479\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.94023 | 0.157893 | 0.0789466 | − | 0.996879i | \(-0.474844\pi\) | ||||
0.0789466 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(152\) | −0.278825 | −0.0226157 | ||||||||
\(153\) | 9.85312 | 0.796577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.264169 | 0.0211505 | ||||||||
\(157\) | −21.2745 | −1.69789 | −0.848944 | − | 0.528483i | \(-0.822761\pi\) | ||||
−0.848944 | + | 0.528483i | \(0.822761\pi\) | |||||||
\(158\) | 18.7979 | 1.49548 | ||||||||
\(159\) | 1.72298 | 0.136642 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.24116 | −0.334250 | ||||||||
\(162\) | −8.30887 | −0.652807 | ||||||||
\(163\) | 15.9810 | 1.25173 | 0.625863 | − | 0.779933i | \(-0.284747\pi\) | ||||
0.625863 | + | 0.779933i | \(0.284747\pi\) | |||||||
\(164\) | 1.34878 | 0.105322 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4304 | −1.12002 | ||||||||
\(167\) | −17.7090 | −1.37037 | −0.685183 | − | 0.728371i | \(-0.740278\pi\) | ||||
−0.685183 | + | 0.728371i | \(0.740278\pi\) | |||||||
\(168\) | −6.15607 | −0.474951 | ||||||||
\(169\) | −4.98569 | −0.383515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.253869 | 0.0194138 | ||||||||
\(172\) | −0.481353 | −0.0367029 | ||||||||
\(173\) | −15.8855 | −1.20775 | −0.603875 | − | 0.797079i | \(-0.706378\pi\) | ||||
−0.603875 | + | 0.797079i | \(0.706378\pi\) | |||||||
\(174\) | −5.26926 | −0.399461 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.89664 | 0.368054 | ||||||||
\(178\) | 16.4866 | 1.23572 | ||||||||
\(179\) | −16.8810 | −1.26175 | −0.630874 | − | 0.775885i | \(-0.717304\pi\) | ||||
−0.630874 | + | 0.775885i | \(0.717304\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.0874 | −1.79040 | −0.895200 | − | 0.445664i | \(-0.852968\pi\) | ||||
−0.895200 | + | 0.445664i | \(0.852968\pi\) | |||||||
\(182\) | −14.0059 | −1.03819 | ||||||||
\(183\) | 4.88039 | 0.360769 | ||||||||
\(184\) | −3.40645 | −0.251127 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.28836 | 0.387761 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.360762 | −0.0263113 | ||||||||
\(189\) | 11.9057 | 0.866012 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.38279 | 0.389485 | 0.194743 | − | 0.980854i | \(-0.437613\pi\) | ||||
0.194743 | + | 0.980854i | \(0.437613\pi\) | |||||||
\(192\) | −4.91423 | −0.354654 | ||||||||
\(193\) | −18.2840 | −1.31611 | −0.658057 | − | 0.752968i | \(-0.728622\pi\) | ||||
−0.658057 | + | 0.752968i | \(0.728622\pi\) | |||||||
\(194\) | −5.87187 | −0.421576 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.02448 | −0.0731773 | ||||||||
\(197\) | −2.64566 | −0.188496 | −0.0942478 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942478 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.52800 | 0.462757 | 0.231379 | − | 0.972864i | \(-0.425676\pi\) | ||||
0.231379 | + | 0.972864i | \(0.425676\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.72041 | −0.544555 | ||||||||
\(202\) | −13.4289 | −0.944854 | ||||||||
\(203\) | −24.6477 | −1.72993 | ||||||||
\(204\) | −0.344513 | −0.0241208 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.51204 | 0.384042 | ||||||||
\(207\) | 3.10155 | 0.215572 | ||||||||
\(208\) | −10.3313 | −0.716349 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.4478 | −1.88958 | −0.944792 | − | 0.327671i | \(-0.893736\pi\) | ||||
−0.944792 | + | 0.327671i | \(0.893736\pi\) | |||||||
\(212\) | 0.485457 | 0.0333413 | ||||||||
\(213\) | −4.77837 | −0.327409 | ||||||||
\(214\) | 2.62808 | 0.179652 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 9.56252 | 0.650647 | ||||||||
\(217\) | 24.7371 | 1.67926 | ||||||||
\(218\) | −8.30573 | −0.562535 | ||||||||
\(219\) | −0.759669 | −0.0513337 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4518 | −0.703061 | ||||||||
\(222\) | −7.67682 | −0.515235 | ||||||||
\(223\) | 5.08194 | 0.340312 | 0.170156 | − | 0.985417i | \(-0.445573\pi\) | ||||
0.170156 | + | 0.985417i | \(0.445573\pi\) | |||||||
\(224\) | −3.33892 | −0.223091 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.84294 | 0.521705 | ||||||||
\(227\) | −3.73980 | −0.248219 | −0.124110 | − | 0.992269i | \(-0.539607\pi\) | ||||
−0.124110 | + | 0.992269i | \(0.539607\pi\) | |||||||
\(228\) | −0.00887649 | −0.000587860 0 | ||||||||
\(229\) | 26.9241 | 1.77920 | 0.889598 | − | 0.456745i | \(-0.150985\pi\) | ||||
0.889598 | + | 0.456745i | \(0.150985\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.7968 | −1.29972 | ||||||||
\(233\) | −18.3167 | −1.19997 | −0.599984 | − | 0.800012i | \(-0.704826\pi\) | ||||
−0.599984 | + | 0.800012i | \(0.704826\pi\) | |||||||
\(234\) | 10.2425 | 0.669573 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.37965 | 0.0898073 | ||||||||
\(237\) | 7.97984 | 0.518346 | ||||||||
\(238\) | 18.2656 | 1.18399 | ||||||||
\(239\) | −10.9559 | −0.708676 | −0.354338 | − | 0.935117i | \(-0.615294\pi\) | ||||
−0.354338 | + | 0.935117i | \(0.615294\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.99444 | −0.643798 | −0.321899 | − | 0.946774i | \(-0.604321\pi\) | ||||
−0.321899 | + | 0.946774i | \(0.604321\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.3143 | −0.854110 | ||||||||
\(244\) | 1.37507 | 0.0880297 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.48972 | −0.413769 | ||||||||
\(247\) | −0.269293 | −0.0171347 | ||||||||
\(248\) | 19.8685 | 1.26165 | ||||||||
\(249\) | −6.12581 | −0.388208 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.65743 | 0.609572 | 0.304786 | − | 0.952421i | \(-0.401415\pi\) | ||||
0.304786 | + | 0.952421i | \(0.401415\pi\) | |||||||
\(252\) | 1.57925 | 0.0994832 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.30490 | 0.207368 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.86526 | −0.241579 | ||||||||
\(257\) | −10.4276 | −0.650454 | −0.325227 | − | 0.945636i | \(-0.605441\pi\) | ||||
−0.325227 | + | 0.945636i | \(0.605441\pi\) | |||||||
\(258\) | 2.31606 | 0.144192 | ||||||||
\(259\) | −35.9095 | −2.23131 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.0248 | 1.11571 | ||||||||
\(262\) | −9.54606 | −0.589757 | ||||||||
\(263\) | 10.9619 | 0.675937 | 0.337968 | − | 0.941157i | \(-0.390260\pi\) | ||||
0.337968 | + | 0.941157i | \(0.390260\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.470620 | 0.0288555 | ||||||||
\(267\) | 6.99867 | 0.428311 | ||||||||
\(268\) | −2.17525 | −0.132875 | ||||||||
\(269\) | −0.0893449 | −0.00544746 | −0.00272373 | − | 0.999996i | \(-0.500867\pi\) | ||||
−0.00272373 | + | 0.999996i | \(0.500867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.3996 | −0.813965 | −0.406982 | − | 0.913436i | \(-0.633419\pi\) | ||||
−0.406982 | + | 0.913436i | \(0.633419\pi\) | |||||||
\(272\) | 13.4735 | 0.816949 | ||||||||
\(273\) | −5.94561 | −0.359844 | ||||||||
\(274\) | −12.9777 | −0.784010 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.108445 | −0.00652764 | ||||||||
\(277\) | 3.90669 | 0.234730 | 0.117365 | − | 0.993089i | \(-0.462555\pi\) | ||||
0.117365 | + | 0.993089i | \(0.462555\pi\) | |||||||
\(278\) | −0.698853 | −0.0419144 | ||||||||
\(279\) | −18.0902 | −1.08303 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.53743 | −0.0917155 | −0.0458577 | − | 0.998948i | \(-0.514602\pi\) | ||||
−0.0458577 | + | 0.998948i | \(0.514602\pi\) | |||||||
\(282\) | 1.73583 | 0.103367 | ||||||||
\(283\) | 5.41170 | 0.321692 | 0.160846 | − | 0.986980i | \(-0.448578\pi\) | ||||
0.160846 | + | 0.986980i | \(0.448578\pi\) | |||||||
\(284\) | −1.34632 | −0.0798896 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −30.3566 | −1.79190 | ||||||||
\(288\) | 2.44174 | 0.143881 | ||||||||
\(289\) | −3.36947 | −0.198204 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.49265 | −0.146122 | ||||||||
\(292\) | −0.214039 | −0.0125257 | ||||||||
\(293\) | −11.4165 | −0.666958 | −0.333479 | − | 0.942757i | \(-0.608223\pi\) | ||||
−0.333479 | + | 0.942757i | \(0.608223\pi\) | |||||||
\(294\) | 4.92936 | 0.287486 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −28.8421 | −1.67641 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.0621 | 0.640808 | ||||||||
\(299\) | −3.28999 | −0.190265 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8337 | 0.624445 | ||||||||
\(302\) | −2.63031 | −0.151358 | ||||||||
\(303\) | −5.70066 | −0.327494 | ||||||||
\(304\) | 0.347148 | 0.0199103 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −13.3576 | −0.763604 | ||||||||
\(307\) | 4.25008 | 0.242565 | 0.121282 | − | 0.992618i | \(-0.461299\pi\) | ||||
0.121282 | + | 0.992618i | \(0.461299\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.33990 | 0.133112 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.6195 | −0.942404 | −0.471202 | − | 0.882025i | \(-0.656180\pi\) | ||||
−0.471202 | + | 0.882025i | \(0.656180\pi\) | |||||||
\(312\) | −4.77544 | −0.270356 | ||||||||
\(313\) | 26.5770 | 1.50222 | 0.751109 | − | 0.660178i | \(-0.229519\pi\) | ||||
0.751109 | + | 0.660178i | \(0.229519\pi\) | |||||||
\(314\) | 28.8413 | 1.62761 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.24835 | 0.126479 | ||||||||
\(317\) | −5.79694 | −0.325589 | −0.162794 | − | 0.986660i | \(-0.552051\pi\) | ||||
−0.162794 | + | 0.986660i | \(0.552051\pi\) | |||||||
\(318\) | −2.33581 | −0.130985 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.11564 | 0.0622688 | ||||||||
\(322\) | 5.74963 | 0.320414 | ||||||||
\(323\) | 0.351195 | 0.0195410 | ||||||||
\(324\) | −0.993793 | −0.0552107 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.6650 | −1.19991 | ||||||||
\(327\) | −3.52584 | −0.194979 | ||||||||
\(328\) | −24.3821 | −1.34628 | ||||||||
\(329\) | 8.11961 | 0.447648 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9230 | −0.710311 | −0.355155 | − | 0.934807i | \(-0.615572\pi\) | ||||
−0.355155 | + | 0.934807i | \(0.615572\pi\) | |||||||
\(332\) | −1.72597 | −0.0947249 | ||||||||
\(333\) | 26.2605 | 1.43907 | ||||||||
\(334\) | 24.0077 | 1.31364 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.66454 | 0.418135 | ||||||||
\(337\) | −13.3854 | −0.729148 | −0.364574 | − | 0.931174i | \(-0.618785\pi\) | ||||
−0.364574 | + | 0.931174i | \(0.618785\pi\) | |||||||
\(338\) | 6.75898 | 0.367640 | ||||||||
\(339\) | 3.32938 | 0.180827 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.344163 | −0.0186102 | ||||||||
\(343\) | −2.48809 | −0.134344 | ||||||||
\(344\) | 8.70152 | 0.469155 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.5355 | 1.15776 | ||||||||
\(347\) | 8.44899 | 0.453565 | 0.226783 | − | 0.973945i | \(-0.427179\pi\) | ||||
0.226783 | + | 0.973945i | \(0.427179\pi\) | |||||||
\(348\) | −0.630236 | −0.0337842 | ||||||||
\(349\) | −10.3988 | −0.556636 | −0.278318 | − | 0.960489i | \(-0.589777\pi\) | ||||
−0.278318 | + | 0.960489i | \(0.589777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.23559 | 0.492959 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.1073 | −1.01698 | −0.508489 | − | 0.861069i | \(-0.669796\pi\) | ||||
−0.508489 | + | 0.861069i | \(0.669796\pi\) | |||||||
\(354\) | −6.63825 | −0.352819 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.97190 | 0.104510 | ||||||||
\(357\) | 7.75389 | 0.410379 | ||||||||
\(358\) | 22.8852 | 1.20952 | ||||||||
\(359\) | −4.41417 | −0.232971 | −0.116486 | − | 0.993192i | \(-0.537163\pi\) | ||||
−0.116486 | + | 0.993192i | \(0.537163\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9910 | −0.999524 | ||||||||
\(362\) | 32.6546 | 1.71629 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.67520 | −0.0878041 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.61622 | −0.345836 | ||||||||
\(367\) | 29.3617 | 1.53267 | 0.766335 | − | 0.642442i | \(-0.222078\pi\) | ||||
0.766335 | + | 0.642442i | \(0.222078\pi\) | |||||||
\(368\) | 4.24116 | 0.221086 | ||||||||
\(369\) | 22.1997 | 1.15567 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.9261 | −0.567254 | ||||||||
\(372\) | 0.632521 | 0.0327947 | ||||||||
\(373\) | 4.96478 | 0.257067 | 0.128533 | − | 0.991705i | \(-0.458973\pi\) | ||||
0.128533 | + | 0.991705i | \(0.458973\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.52157 | 0.336325 | ||||||||
\(377\) | −19.1200 | −0.984728 | ||||||||
\(378\) | −16.1403 | −0.830165 | ||||||||
\(379\) | 7.92315 | 0.406985 | 0.203492 | − | 0.979077i | \(-0.434771\pi\) | ||||
0.203492 | + | 0.979077i | \(0.434771\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.40295 | 0.0718755 | ||||||||
\(382\) | −7.29731 | −0.373363 | ||||||||
\(383\) | 24.5155 | 1.25268 | 0.626342 | − | 0.779549i | \(-0.284551\pi\) | ||||
0.626342 | + | 0.779549i | \(0.284551\pi\) | |||||||
\(384\) | 5.60903 | 0.286235 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.7872 | 1.26164 | ||||||||
\(387\) | −7.92268 | −0.402732 | ||||||||
\(388\) | −0.702312 | −0.0356545 | ||||||||
\(389\) | 5.46094 | 0.276881 | 0.138440 | − | 0.990371i | \(-0.455791\pi\) | ||||
0.138440 | + | 0.990371i | \(0.455791\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.29059 | 0.216985 | ||||||||
\(392\) | 18.5198 | 0.935389 | ||||||||
\(393\) | −4.05237 | −0.204415 | ||||||||
\(394\) | 3.58665 | 0.180693 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.43455 | 0.322941 | 0.161470 | − | 0.986878i | \(-0.448376\pi\) | ||||
0.161470 | + | 0.986878i | \(0.448376\pi\) | |||||||
\(398\) | −8.84984 | −0.443602 | ||||||||
\(399\) | 0.199781 | 0.0100016 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.7026 | −0.734213 | −0.367107 | − | 0.930179i | \(-0.619652\pi\) | ||||
−0.367107 | + | 0.930179i | \(0.619652\pi\) | |||||||
\(402\) | 10.4664 | 0.522014 | ||||||||
\(403\) | 19.1893 | 0.955885 | ||||||||
\(404\) | −1.60618 | −0.0799105 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 33.4143 | 1.65832 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 6.22784 | 0.308324 | ||||||||
\(409\) | 4.39576 | 0.217356 | 0.108678 | − | 0.994077i | \(-0.465338\pi\) | ||||
0.108678 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.50911 | −0.271745 | ||||||||
\(412\) | 0.659275 | 0.0324802 | ||||||||
\(413\) | −31.0514 | −1.52794 | ||||||||
\(414\) | −4.20469 | −0.206649 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.59009 | −0.126990 | ||||||||
\(417\) | −0.296668 | −0.0145279 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.8526 | 0.872159 | 0.436079 | − | 0.899908i | \(-0.356367\pi\) | ||||
0.436079 | + | 0.899908i | \(0.356367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.82854 | −0.235328 | −0.117664 | − | 0.993053i | \(-0.537541\pi\) | ||||
−0.117664 | + | 0.993053i | \(0.537541\pi\) | |||||||
\(422\) | 37.2103 | 1.81137 | ||||||||
\(423\) | −5.93785 | −0.288708 | ||||||||
\(424\) | −8.77570 | −0.426186 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.47792 | 0.313856 | ||||||||
\(427\) | −30.9484 | −1.49770 | ||||||||
\(428\) | 0.314335 | 0.0151939 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.8739 | −1.19814 | −0.599068 | − | 0.800698i | \(-0.704462\pi\) | ||||
−0.599068 | + | 0.800698i | \(0.704462\pi\) | |||||||
\(432\) | −11.9057 | −0.572813 | ||||||||
\(433\) | 21.2502 | 1.02122 | 0.510611 | − | 0.859812i | \(-0.329419\pi\) | ||||
0.510611 | + | 0.859812i | \(0.329419\pi\) | |||||||
\(434\) | −33.5354 | −1.60975 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.993417 | −0.0475761 | ||||||||
\(437\) | 0.110548 | 0.00528825 | ||||||||
\(438\) | 1.02986 | 0.0492088 | ||||||||
\(439\) | −15.9119 | −0.759434 | −0.379717 | − | 0.925103i | \(-0.623979\pi\) | ||||
−0.379717 | + | 0.925103i | \(0.623979\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.8621 | −0.802958 | ||||||||
\(442\) | 14.1692 | 0.673959 | ||||||||
\(443\) | −26.2876 | −1.24896 | −0.624481 | − | 0.781040i | \(-0.714690\pi\) | ||||
−0.624481 | + | 0.781040i | \(0.714690\pi\) | |||||||
\(444\) | −0.918197 | −0.0435757 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.88945 | −0.326225 | ||||||||
\(447\) | 4.69592 | 0.222110 | ||||||||
\(448\) | 31.1629 | 1.47231 | ||||||||
\(449\) | −8.18961 | −0.386492 | −0.193246 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193246 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.938065 | 0.0441229 | ||||||||
\(453\) | −1.11659 | −0.0524618 | ||||||||
\(454\) | 5.06995 | 0.237945 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.160462 | 0.00751432 | ||||||||
\(457\) | −11.9164 | −0.557425 | −0.278713 | − | 0.960375i | \(-0.589908\pi\) | ||||
−0.278713 | + | 0.960375i | \(0.589908\pi\) | |||||||
\(458\) | −36.5003 | −1.70555 | ||||||||
\(459\) | −12.0445 | −0.562188 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.96172 | 0.324240 | 0.162120 | − | 0.986771i | \(-0.448167\pi\) | ||||
0.162120 | + | 0.986771i | \(0.448167\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4762 | −0.579817 | −0.289909 | − | 0.957054i | \(-0.593625\pi\) | ||||
−0.289909 | + | 0.957054i | \(0.593625\pi\) | |||||||
\(464\) | 24.6477 | 1.14424 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.8315 | 1.15030 | ||||||||
\(467\) | 6.14617 | 0.284411 | 0.142205 | − | 0.989837i | \(-0.454581\pi\) | ||||
0.142205 | + | 0.989837i | \(0.454581\pi\) | |||||||
\(468\) | 1.22507 | 0.0566287 | ||||||||
\(469\) | 48.9579 | 2.26067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.2433 | 0.564142 | ||||||||
\(472\) | −24.9401 | −1.14796 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.8181 | −0.496890 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.18469 | 0.100135 | ||||||||
\(477\) | 7.99022 | 0.365847 | ||||||||
\(478\) | 14.8526 | 0.679341 | ||||||||
\(479\) | 22.1942 | 1.01408 | 0.507039 | − | 0.861923i | \(-0.330740\pi\) | ||||
0.507039 | + | 0.861923i | \(0.330740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.8560 | −1.27013 | ||||||||
\(482\) | 13.5492 | 0.617149 | ||||||||
\(483\) | 2.44076 | 0.111058 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 18.0498 | 0.818755 | ||||||||
\(487\) | 34.2306 | 1.55114 | 0.775569 | − | 0.631263i | \(-0.217463\pi\) | ||||
0.775569 | + | 0.631263i | \(0.217463\pi\) | |||||||
\(488\) | −24.8574 | −1.12524 | ||||||||
\(489\) | −9.19693 | −0.415900 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.9957 | −0.767007 | −0.383503 | − | 0.923539i | \(-0.625283\pi\) | ||||
−0.383503 | + | 0.923539i | \(0.625283\pi\) | |||||||
\(492\) | −0.776212 | −0.0349943 | ||||||||
\(493\) | 24.9351 | 1.12302 | ||||||||
\(494\) | 0.365073 | 0.0164254 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.7371 | −1.11073 | ||||||||
\(497\) | 30.3014 | 1.35920 | ||||||||
\(498\) | 8.30461 | 0.372138 | ||||||||
\(499\) | 5.22946 | 0.234103 | 0.117051 | − | 0.993126i | \(-0.462656\pi\) | ||||
0.117051 | + | 0.993126i | \(0.462656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.1914 | 0.455319 | ||||||||
\(502\) | −13.0923 | −0.584339 | ||||||||
\(503\) | −41.9448 | −1.87023 | −0.935113 | − | 0.354350i | \(-0.884702\pi\) | ||||
−0.935113 | + | 0.354350i | \(0.884702\pi\) | |||||||
\(504\) | −28.5484 | −1.27164 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.86923 | 0.127427 | ||||||||
\(508\) | 0.395287 | 0.0175380 | ||||||||
\(509\) | 20.3678 | 0.902787 | 0.451393 | − | 0.892325i | \(-0.350927\pi\) | ||||
0.451393 | + | 0.892325i | \(0.350927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.81734 | 0.213107 | ||||||||
\(512\) | 24.7330 | 1.09305 | ||||||||
\(513\) | −0.310330 | −0.0137014 | ||||||||
\(514\) | 14.1364 | 0.623529 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.277016 | 0.0121949 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 48.6816 | 2.13895 | ||||||||
\(519\) | 9.14199 | 0.401289 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.4779 | 0.634287 | 0.317143 | − | 0.948378i | \(-0.397276\pi\) | ||||
0.317143 | + | 0.948378i | \(0.397276\pi\) | |||||||
\(522\) | −24.4358 | −1.06953 | ||||||||
\(523\) | −11.1601 | −0.487998 | −0.243999 | − | 0.969775i | \(-0.578459\pi\) | ||||
−0.243999 | + | 0.969775i | \(0.578459\pi\) | |||||||
\(524\) | −1.14177 | −0.0498784 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.8607 | −0.647958 | ||||||||
\(527\) | −25.0254 | −1.09013 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6494 | −0.941279 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.7078 | 0.985436 | ||||||||
\(532\) | 0.0562891 | 0.00244044 | ||||||||
\(533\) | −23.5485 | −1.02000 | ||||||||
\(534\) | −9.48791 | −0.410582 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 39.3225 | 1.69847 | ||||||||
\(537\) | 9.71492 | 0.419230 | ||||||||
\(538\) | 0.121123 | 0.00522197 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6808 | 0.459203 | 0.229602 | − | 0.973285i | \(-0.426258\pi\) | ||||
0.229602 | + | 0.973285i | \(0.426258\pi\) | |||||||
\(542\) | 18.1654 | 0.780272 | ||||||||
\(543\) | 13.8621 | 0.594880 | ||||||||
\(544\) | 3.37784 | 0.144824 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.06031 | 0.344949 | ||||||||
\(547\) | −1.74760 | −0.0747220 | −0.0373610 | − | 0.999302i | \(-0.511895\pi\) | ||||
−0.0373610 | + | 0.999302i | \(0.511895\pi\) | |||||||
\(548\) | −1.55221 | −0.0663072 | ||||||||
\(549\) | 22.6325 | 0.965930 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.642459 | 0.0273697 | ||||||||
\(552\) | 1.96039 | 0.0834396 | ||||||||
\(553\) | −50.6031 | −2.15186 | ||||||||
\(554\) | −5.29619 | −0.225014 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0835872 | −0.00354489 | ||||||||
\(557\) | 19.4844 | 0.825579 | 0.412790 | − | 0.910826i | \(-0.364554\pi\) | ||||
0.412790 | + | 0.910826i | \(0.364554\pi\) | |||||||
\(558\) | 24.5244 | 1.03820 | ||||||||
\(559\) | 8.40403 | 0.355453 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.08426 | 0.0879191 | ||||||||
\(563\) | 14.6892 | 0.619074 | 0.309537 | − | 0.950887i | \(-0.399826\pi\) | ||||
0.309537 | + | 0.950887i | \(0.399826\pi\) | |||||||
\(564\) | 0.207616 | 0.00874222 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.33650 | −0.308376 | ||||||||
\(567\) | 22.3671 | 0.939330 | ||||||||
\(568\) | 24.3377 | 1.02119 | ||||||||
\(569\) | 19.9335 | 0.835658 | 0.417829 | − | 0.908526i | \(-0.362791\pi\) | ||||
0.417829 | + | 0.908526i | \(0.362791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.24422 | 0.219464 | 0.109732 | − | 0.993961i | \(-0.465001\pi\) | ||||
0.109732 | + | 0.993961i | \(0.465001\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.09776 | −0.129411 | ||||||||
\(574\) | 41.1537 | 1.71772 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −22.7894 | −0.949557 | ||||||||
\(577\) | −37.6004 | −1.56533 | −0.782663 | − | 0.622446i | \(-0.786139\pi\) | ||||
−0.782663 | + | 0.622446i | \(0.786139\pi\) | |||||||
\(578\) | 4.56790 | 0.190000 | ||||||||
\(579\) | 10.5223 | 0.437294 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.8460 | 1.61161 | ||||||||
\(582\) | 3.37922 | 0.140073 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.86923 | 0.160110 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.4770 | 0.639351 | ||||||||
\(587\) | −25.5711 | −1.05543 | −0.527716 | − | 0.849421i | \(-0.676952\pi\) | ||||
−0.527716 | + | 0.849421i | \(0.676952\pi\) | |||||||
\(588\) | 0.589582 | 0.0243140 | ||||||||
\(589\) | −0.644788 | −0.0265680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.52256 | 0.0626297 | ||||||||
\(592\) | 35.9095 | 1.47587 | ||||||||
\(593\) | −40.2260 | −1.65188 | −0.825942 | − | 0.563754i | \(-0.809356\pi\) | ||||
−0.825942 | + | 0.563754i | \(0.809356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.32309 | 0.0541960 | ||||||||
\(597\) | −3.75682 | −0.153756 | ||||||||
\(598\) | 4.46015 | 0.182389 | ||||||||
\(599\) | 4.92997 | 0.201433 | 0.100716 | − | 0.994915i | \(-0.467886\pi\) | ||||
0.100716 | + | 0.994915i | \(0.467886\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.0896 | 1.88003 | 0.940017 | − | 0.341127i | \(-0.110809\pi\) | ||||
0.940017 | + | 0.341127i | \(0.110809\pi\) | |||||||
\(602\) | −14.6870 | −0.598597 | ||||||||
\(603\) | −35.8028 | −1.45800 | ||||||||
\(604\) | −0.314602 | −0.0128010 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.72824 | 0.313938 | ||||||||
\(607\) | 45.1365 | 1.83203 | 0.916016 | − | 0.401141i | \(-0.131386\pi\) | ||||
0.916016 | + | 0.401141i | \(0.131386\pi\) | |||||||
\(608\) | 0.0870310 | 0.00352957 | ||||||||
\(609\) | 14.1846 | 0.574789 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.29861 | 0.254815 | ||||||||
\(612\) | −1.59766 | −0.0645814 | ||||||||
\(613\) | −4.73418 | −0.191212 | −0.0956059 | − | 0.995419i | \(-0.530479\pi\) | ||||
−0.0956059 | + | 0.995419i | \(0.530479\pi\) | |||||||
\(614\) | −5.76172 | −0.232524 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.8468 | −0.718486 | −0.359243 | − | 0.933244i | \(-0.616965\pi\) | ||||
−0.359243 | + | 0.933244i | \(0.616965\pi\) | |||||||
\(618\) | −3.17214 | −0.127602 | ||||||||
\(619\) | 0.356952 | 0.0143471 | 0.00717356 | − | 0.999974i | \(-0.497717\pi\) | ||||
0.00717356 | + | 0.999974i | \(0.497717\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.79134 | −0.152141 | ||||||||
\(622\) | 22.5306 | 0.903394 | ||||||||
\(623\) | −44.3811 | −1.77809 | ||||||||
\(624\) | 5.94561 | 0.238015 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −36.0297 | −1.44004 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.44960 | 0.137654 | ||||||||
\(629\) | 36.3281 | 1.44850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.9922 | −1.27359 | −0.636795 | − | 0.771033i | \(-0.719740\pi\) | ||||
−0.636795 | + | 0.771033i | \(0.719740\pi\) | |||||||
\(632\) | −40.6438 | −1.61672 | ||||||||
\(633\) | 15.7960 | 0.627835 | ||||||||
\(634\) | 7.85876 | 0.312111 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.279377 | −0.0110780 | ||||||||
\(637\) | 17.8866 | 0.708693 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.1594 | −0.876610 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.01285 | 0.0400050 | 0.0200025 | − | 0.999800i | \(-0.493633\pi\) | ||||
0.0200025 | + | 0.999800i | \(0.493633\pi\) | |||||||
\(642\) | −1.51244 | −0.0596912 | ||||||||
\(643\) | 14.9724 | 0.590455 | 0.295228 | − | 0.955427i | \(-0.404605\pi\) | ||||
0.295228 | + | 0.955427i | \(0.404605\pi\) | |||||||
\(644\) | 0.687692 | 0.0270988 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.476106 | −0.0187321 | ||||||||
\(647\) | −17.8873 | −0.703224 | −0.351612 | − | 0.936146i | \(-0.614366\pi\) | ||||
−0.351612 | + | 0.936146i | \(0.614366\pi\) | |||||||
\(648\) | 17.9650 | 0.705732 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.2360 | −0.557954 | ||||||||
\(652\) | −2.59127 | −0.101482 | ||||||||
\(653\) | −45.7642 | −1.79089 | −0.895446 | − | 0.445169i | \(-0.853144\pi\) | ||||
−0.895446 | + | 0.445169i | \(0.853144\pi\) | |||||||
\(654\) | 4.77989 | 0.186908 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 30.3566 | 1.18523 | ||||||||
\(657\) | −3.52291 | −0.137442 | ||||||||
\(658\) | −11.0075 | −0.429119 | ||||||||
\(659\) | −9.54036 | −0.371640 | −0.185820 | − | 0.982584i | \(-0.559494\pi\) | ||||
−0.185820 | + | 0.982584i | \(0.559494\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.7769 | 0.613651 | 0.306825 | − | 0.951766i | \(-0.400733\pi\) | ||||
0.306825 | + | 0.951766i | \(0.400733\pi\) | |||||||
\(662\) | 17.5193 | 0.680908 | ||||||||
\(663\) | 6.01491 | 0.233600 | ||||||||
\(664\) | 31.2007 | 1.21082 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −35.6007 | −1.37950 | ||||||||
\(667\) | 7.84901 | 0.303915 | ||||||||
\(668\) | 2.87147 | 0.111100 | ||||||||
\(669\) | −2.92462 | −0.113072 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.92152 | 0.0741243 | ||||||||
\(673\) | −47.3031 | −1.82340 | −0.911700 | − | 0.410856i | \(-0.865230\pi\) | ||||
−0.911700 | + | 0.410856i | \(0.865230\pi\) | |||||||
\(674\) | 18.1462 | 0.698966 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.808416 | 0.0310929 | ||||||||
\(677\) | −27.5431 | −1.05857 | −0.529284 | − | 0.848445i | \(-0.677539\pi\) | ||||
−0.529284 | + | 0.848445i | \(0.677539\pi\) | |||||||
\(678\) | −4.51356 | −0.173342 | ||||||||
\(679\) | 15.8068 | 0.606609 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.15223 | 0.0824736 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.1617 | 1.03931 | 0.519656 | − | 0.854375i | \(-0.326060\pi\) | ||||
0.519656 | + | 0.854375i | \(0.326060\pi\) | |||||||
\(684\) | −0.0411641 | −0.00157395 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.37304 | 0.128783 | ||||||||
\(687\) | −15.4946 | −0.591157 | ||||||||
\(688\) | −10.8337 | −0.413032 | ||||||||
\(689\) | −8.47567 | −0.322897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.52680 | −0.286333 | −0.143166 | − | 0.989699i | \(-0.545728\pi\) | ||||
−0.143166 | + | 0.989699i | \(0.545728\pi\) | |||||||
\(692\) | 2.57579 | 0.0979167 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.4541 | −0.434791 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.3929 | 0.431847 | ||||||||
\(697\) | 30.7105 | 1.16324 | ||||||||
\(698\) | 14.0974 | 0.533595 | ||||||||
\(699\) | 10.5411 | 0.398702 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.8207 | −1.20185 | −0.600926 | − | 0.799305i | \(-0.705201\pi\) | ||||
−0.600926 | + | 0.799305i | \(0.705201\pi\) | |||||||
\(702\) | −12.5205 | −0.472554 | ||||||||
\(703\) | 0.936004 | 0.0353021 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.9032 | 0.974882 | ||||||||
\(707\) | 36.1500 | 1.35956 | ||||||||
\(708\) | −0.793977 | −0.0298395 | ||||||||
\(709\) | −14.4381 | −0.542235 | −0.271118 | − | 0.962546i | \(-0.587393\pi\) | ||||
−0.271118 | + | 0.962546i | \(0.587393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 37.0059 | 1.38783 | ||||||||
\(712\) | −35.6464 | −1.33591 | ||||||||
\(713\) | −7.87747 | −0.295013 | ||||||||
\(714\) | −10.5117 | −0.393392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.73721 | 0.102294 | ||||||||
\(717\) | 6.30503 | 0.235465 | ||||||||
\(718\) | 5.98418 | 0.223328 | ||||||||
\(719\) | 5.41004 | 0.201761 | 0.100880 | − | 0.994899i | \(-0.467834\pi\) | ||||
0.100880 | + | 0.994899i | \(0.467834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.8382 | −0.552602 | ||||||||
\(722\) | 25.7455 | 0.958150 | ||||||||
\(723\) | 5.75173 | 0.213909 | ||||||||
\(724\) | 3.90570 | 0.145154 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.7753 | 0.622161 | 0.311080 | − | 0.950384i | \(-0.399309\pi\) | ||||
0.311080 | + | 0.950384i | \(0.399309\pi\) | |||||||
\(728\) | 30.2828 | 1.12236 | ||||||||
\(729\) | −10.7246 | −0.397208 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.9600 | −0.405371 | ||||||||
\(732\) | −0.791342 | −0.0292488 | ||||||||
\(733\) | 14.0851 | 0.520243 | 0.260122 | − | 0.965576i | \(-0.416237\pi\) | ||||
0.260122 | + | 0.965576i | \(0.416237\pi\) | |||||||
\(734\) | −39.8049 | −1.46923 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.06327 | 0.0391926 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −30.0956 | −1.10783 | ||||||||
\(739\) | −36.3457 | −1.33700 | −0.668499 | − | 0.743713i | \(-0.733063\pi\) | ||||
−0.668499 | + | 0.743713i | \(0.733063\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.154976 | 0.00569319 | ||||||||
\(742\) | 14.8122 | 0.543773 | ||||||||
\(743\) | 1.95716 | 0.0718012 | 0.0359006 | − | 0.999355i | \(-0.488570\pi\) | ||||
0.0359006 | + | 0.999355i | \(0.488570\pi\) | |||||||
\(744\) | −11.4342 | −0.419198 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.73063 | −0.246426 | ||||||||
\(747\) | −28.4080 | −1.03939 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.07466 | −0.258503 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7106 | 0.682759 | 0.341379 | − | 0.939926i | \(-0.389106\pi\) | ||||
0.341379 | + | 0.939926i | \(0.389106\pi\) | |||||||
\(752\) | −8.11961 | −0.296092 | ||||||||
\(753\) | −5.55778 | −0.202537 | ||||||||
\(754\) | 25.9204 | 0.943967 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.93048 | −0.0702107 | ||||||||
\(757\) | 14.5470 | 0.528721 | 0.264361 | − | 0.964424i | \(-0.414839\pi\) | ||||
0.264361 | + | 0.964424i | \(0.414839\pi\) | |||||||
\(758\) | −10.7412 | −0.390138 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.1406 | 0.476345 | 0.238173 | − | 0.971223i | \(-0.423452\pi\) | ||||
0.238173 | + | 0.971223i | \(0.423452\pi\) | |||||||
\(762\) | −1.90195 | −0.0689003 | ||||||||
\(763\) | 22.3586 | 0.809437 | ||||||||
\(764\) | −0.872805 | −0.0315770 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.2350 | −1.20083 | ||||||||
\(767\) | −24.0875 | −0.869748 | ||||||||
\(768\) | 2.22443 | 0.0802673 | ||||||||
\(769\) | 38.9767 | 1.40554 | 0.702768 | − | 0.711419i | \(-0.251947\pi\) | ||||
0.702768 | + | 0.711419i | \(0.251947\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00099 | 0.216121 | ||||||||
\(772\) | 2.96471 | 0.106702 | ||||||||
\(773\) | 38.7539 | 1.39388 | 0.696940 | − | 0.717129i | \(-0.254544\pi\) | ||||
0.696940 | + | 0.717129i | \(0.254544\pi\) | |||||||
\(774\) | 10.7406 | 0.386062 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.6958 | 0.455754 | ||||||||
\(777\) | 20.6657 | 0.741377 | ||||||||
\(778\) | −7.40326 | −0.265420 | ||||||||
\(779\) | 0.791265 | 0.0283500 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.81665 | −0.208003 | ||||||||
\(783\) | −22.0336 | −0.787417 | ||||||||
\(784\) | −23.0578 | −0.823493 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.49369 | 0.195953 | ||||||||
\(787\) | 21.3842 | 0.762265 | 0.381132 | − | 0.924521i | \(-0.375534\pi\) | ||||
0.381132 | + | 0.924521i | \(0.375534\pi\) | |||||||
\(788\) | 0.428986 | 0.0152820 | ||||||||
\(789\) | −6.30847 | −0.224588 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.1128 | −0.750686 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0075 | −0.852533 | ||||||||
\(794\) | −8.72315 | −0.309573 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.05850 | −0.0375174 | ||||||||
\(797\) | 2.22456 | 0.0787978 | 0.0393989 | − | 0.999224i | \(-0.487456\pi\) | ||||
0.0393989 | + | 0.999224i | \(0.487456\pi\) | |||||||
\(798\) | −0.270838 | −0.00958757 | ||||||||
\(799\) | −8.21426 | −0.290599 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.4558 | 1.14677 | ||||||||
\(802\) | 19.9319 | 0.703821 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.25184 | 0.0441491 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.0144 | −0.916318 | ||||||||
\(807\) | 0.0514174 | 0.00180998 | ||||||||
\(808\) | 29.0353 | 1.02146 | ||||||||
\(809\) | 21.1682 | 0.744234 | 0.372117 | − | 0.928186i | \(-0.378632\pi\) | ||||
0.372117 | + | 0.928186i | \(0.378632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.7172 | −1.28932 | −0.644658 | − | 0.764471i | \(-0.723000\pi\) | ||||
−0.644658 | + | 0.764471i | \(0.723000\pi\) | |||||||
\(812\) | 3.99656 | 0.140252 | ||||||||
\(813\) | 7.71135 | 0.270449 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.75389 | −0.271440 | ||||||||
\(817\) | −0.282388 | −0.00987951 | ||||||||
\(818\) | −5.95922 | −0.208359 | ||||||||
\(819\) | −27.5723 | −0.963455 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.6693 | −1.38447 | −0.692235 | − | 0.721673i | \(-0.743374\pi\) | ||||
−0.692235 | + | 0.721673i | \(0.743374\pi\) | |||||||
\(822\) | 7.46856 | 0.260496 | ||||||||
\(823\) | 45.9283 | 1.60096 | 0.800480 | − | 0.599359i | \(-0.204578\pi\) | ||||
0.800480 | + | 0.599359i | \(0.204578\pi\) | |||||||
\(824\) | −11.9178 | −0.415178 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 42.0956 | 1.46469 | ||||||||
\(827\) | 39.6949 | 1.38033 | 0.690164 | − | 0.723653i | \(-0.257538\pi\) | ||||
0.690164 | + | 0.723653i | \(0.257538\pi\) | |||||||
\(828\) | −0.502907 | −0.0174772 | ||||||||
\(829\) | 7.65584 | 0.265898 | 0.132949 | − | 0.991123i | \(-0.457555\pi\) | ||||
0.132949 | + | 0.991123i | \(0.457555\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.24827 | −0.0779916 | ||||||||
\(832\) | 24.1740 | 0.838082 | ||||||||
\(833\) | −23.3266 | −0.808218 | ||||||||
\(834\) | 0.402185 | 0.0139265 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.1135 | 0.764354 | ||||||||
\(838\) | −24.2024 | −0.836057 | ||||||||
\(839\) | 27.5886 | 0.952465 | 0.476233 | − | 0.879319i | \(-0.342002\pi\) | ||||
0.476233 | + | 0.879319i | \(0.342002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.6150 | 0.572932 | ||||||||
\(842\) | 6.54592 | 0.225587 | ||||||||
\(843\) | 0.884781 | 0.0304735 | ||||||||
\(844\) | 4.45058 | 0.153195 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.04979 | 0.276757 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.9261 | 0.375203 | ||||||||
\(849\) | −3.11439 | −0.106886 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4353 | 0.391997 | ||||||||
\(852\) | 0.774800 | 0.0265442 | ||||||||
\(853\) | −42.1496 | −1.44318 | −0.721588 | − | 0.692323i | \(-0.756587\pi\) | ||||
−0.721588 | + | 0.692323i | \(0.756587\pi\) | |||||||
\(854\) | 41.9559 | 1.43570 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.68229 | −0.194217 | ||||||||
\(857\) | 45.0850 | 1.54008 | 0.770038 | − | 0.637998i | \(-0.220237\pi\) | ||||
0.770038 | + | 0.637998i | \(0.220237\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.8257 | −0.403488 | −0.201744 | − | 0.979438i | \(-0.564661\pi\) | ||||
−0.201744 | + | 0.979438i | \(0.564661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.4700 | 0.595377 | ||||||||
\(862\) | 33.7210 | 1.14854 | ||||||||
\(863\) | −27.8713 | −0.948750 | −0.474375 | − | 0.880323i | \(-0.657326\pi\) | ||||
−0.474375 | + | 0.880323i | \(0.657326\pi\) | |||||||
\(864\) | −2.98479 | −0.101545 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −28.8084 | −0.978950 | ||||||||
\(867\) | 1.93911 | 0.0658555 | ||||||||
\(868\) | −4.01105 | −0.136144 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.9781 | 1.28684 | ||||||||
\(872\) | 17.9582 | 0.608141 | ||||||||
\(873\) | −11.5595 | −0.391229 | ||||||||
\(874\) | −0.149868 | −0.00506935 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.123178 | 0.00416181 | ||||||||
\(877\) | 11.4471 | 0.386543 | 0.193271 | − | 0.981145i | \(-0.438090\pi\) | ||||
0.193271 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(878\) | 21.5714 | 0.727998 | ||||||||
\(879\) | 6.57011 | 0.221604 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.0037 | 1.58360 | 0.791798 | − | 0.610783i | \(-0.209145\pi\) | ||||
0.791798 | + | 0.610783i | \(0.209145\pi\) | |||||||
\(882\) | 22.8595 | 0.769721 | ||||||||
\(883\) | 46.9146 | 1.57880 | 0.789401 | − | 0.613877i | \(-0.210391\pi\) | ||||
0.789401 | + | 0.613877i | \(0.210391\pi\) | |||||||
\(884\) | 1.69472 | 0.0569997 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.6374 | 1.19726 | ||||||||
\(887\) | 27.8427 | 0.934866 | 0.467433 | − | 0.884029i | \(-0.345179\pi\) | ||||
0.467433 | + | 0.884029i | \(0.345179\pi\) | |||||||
\(888\) | 16.5984 | 0.557007 | ||||||||
\(889\) | −8.89664 | −0.298384 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.824022 | −0.0275903 | ||||||||
\(893\) | −0.211643 | −0.00708236 | ||||||||
\(894\) | −6.36614 | −0.212916 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −35.5689 | −1.18828 | ||||||||
\(897\) | 1.89336 | 0.0632176 | ||||||||
\(898\) | 11.1024 | 0.370494 | ||||||||
\(899\) | −45.7804 | −1.52686 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0534 | 0.368244 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.23473 | −0.207479 | ||||||||
\(904\) | −16.9576 | −0.564001 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.51373 | 0.0502902 | ||||||||
\(907\) | 28.6233 | 0.950421 | 0.475210 | − | 0.879872i | \(-0.342372\pi\) | ||||
0.475210 | + | 0.879872i | \(0.342372\pi\) | |||||||
\(908\) | 0.606398 | 0.0201240 | ||||||||
\(909\) | −26.4364 | −0.876840 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.12823 | 0.169906 | 0.0849529 | − | 0.996385i | \(-0.472926\pi\) | ||||
0.0849529 | + | 0.996385i | \(0.472926\pi\) | |||||||
\(912\) | −0.199781 | −0.00661542 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 16.1547 | 0.534351 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.36567 | −0.144246 | ||||||||
\(917\) | 25.6976 | 0.848608 | ||||||||
\(918\) | 16.3284 | 0.538917 | ||||||||
\(919\) | 35.2810 | 1.16381 | 0.581906 | − | 0.813256i | \(-0.302307\pi\) | ||||
0.581906 | + | 0.813256i | \(0.302307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.44589 | −0.0805949 | ||||||||
\(922\) | −9.43783 | −0.310818 | ||||||||
\(923\) | 23.5057 | 0.773699 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.9136 | 0.555817 | ||||||||
\(927\) | 10.8511 | 0.356397 | ||||||||
\(928\) | 6.17926 | 0.202844 | ||||||||
\(929\) | −59.1427 | −1.94041 | −0.970204 | − | 0.242289i | \(-0.922102\pi\) | ||||
−0.970204 | + | 0.242289i | \(0.922102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.601017 | −0.0196975 | ||||||||
\(932\) | 2.97000 | 0.0972857 | ||||||||
\(933\) | 9.56439 | 0.313124 | ||||||||
\(934\) | −8.33220 | −0.272638 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.1458 | −0.723857 | ||||||||
\(937\) | −14.4425 | −0.471817 | −0.235909 | − | 0.971775i | \(-0.575807\pi\) | ||||
−0.235909 | + | 0.971775i | \(0.575807\pi\) | |||||||
\(938\) | −66.3710 | −2.16709 | ||||||||
\(939\) | −15.2949 | −0.499129 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.6591 | −0.608269 | −0.304135 | − | 0.952629i | \(-0.598367\pi\) | ||||
−0.304135 | + | 0.952629i | \(0.598367\pi\) | |||||||
\(942\) | −16.5979 | −0.540790 | ||||||||
\(943\) | 9.66700 | 0.314801 | ||||||||
\(944\) | 31.0514 | 1.01064 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.991391 | 0.0322159 | 0.0161079 | − | 0.999870i | \(-0.494872\pi\) | ||||
0.0161079 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(948\) | −1.29391 | −0.0420242 | ||||||||
\(949\) | 3.73695 | 0.121306 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.33610 | 0.108180 | ||||||||
\(952\) | −39.4930 | −1.27998 | ||||||||
\(953\) | 8.26404 | 0.267699 | 0.133849 | − | 0.991002i | \(-0.457266\pi\) | ||||
0.133849 | + | 0.991002i | \(0.457266\pi\) | |||||||
\(954\) | −10.8321 | −0.350703 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.77646 | 0.0574549 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.0881 | −0.972101 | ||||||||
\(959\) | 34.9353 | 1.12812 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.9463 | 0.482139 | ||||||||
\(962\) | 37.7637 | 1.21755 | ||||||||
\(963\) | 5.17368 | 0.166720 | ||||||||
\(964\) | 1.62057 | 0.0521950 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.30887 | −0.106461 | ||||||||
\(967\) | −7.36029 | −0.236691 | −0.118345 | − | 0.992972i | \(-0.537759\pi\) | ||||
−0.118345 | + | 0.992972i | \(0.537759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.202110 | −0.00649271 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.97733 | −0.159730 | −0.0798650 | − | 0.996806i | \(-0.525449\pi\) | ||||
−0.0798650 | + | 0.996806i | \(0.525449\pi\) | |||||||
\(972\) | 2.15887 | 0.0692457 | ||||||||
\(973\) | 1.88128 | 0.0603111 | ||||||||
\(974\) | −46.4056 | −1.48693 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.9484 | 0.990633 | ||||||||
\(977\) | −10.3368 | −0.330704 | −0.165352 | − | 0.986235i | \(-0.552876\pi\) | ||||
−0.165352 | + | 0.986235i | \(0.552876\pi\) | |||||||
\(978\) | 12.4680 | 0.398684 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.3508 | −0.522041 | ||||||||
\(982\) | 23.0407 | 0.735258 | ||||||||
\(983\) | 29.0614 | 0.926913 | 0.463457 | − | 0.886120i | \(-0.346609\pi\) | ||||
0.463457 | + | 0.886120i | \(0.346609\pi\) | |||||||
\(984\) | 14.0317 | 0.447315 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −33.8038 | −1.07653 | ||||||||
\(987\) | −4.67278 | −0.148736 | ||||||||
\(988\) | 0.0436651 | 0.00138917 | ||||||||
\(989\) | −3.44997 | −0.109703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.70381 | 0.244719 | 0.122360 | − | 0.992486i | \(-0.460954\pi\) | ||||
0.122360 | + | 0.992486i | \(0.460954\pi\) | |||||||
\(992\) | −6.20166 | −0.196903 | ||||||||
\(993\) | 7.43708 | 0.236009 | ||||||||
\(994\) | −41.0788 | −1.30294 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.993283 | 0.0314734 | ||||||||
\(997\) | 2.86418 | 0.0907095 | 0.0453547 | − | 0.998971i | \(-0.485558\pi\) | ||||
0.0453547 | + | 0.998971i | \(0.485558\pi\) | |||||||
\(998\) | −7.08945 | −0.224413 | ||||||||
\(999\) | −32.1010 | −1.01563 |
(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 | 3025.2.a.bd.1.1 | 4 | ||
5.4 | even | 2 | 605.2.a.j.1.4 | 4 | |||
11.5 | even | 5 | 275.2.h.a.201.2 | 8 | |||
11.9 | even | 5 | 275.2.h.a.26.2 | 8 | |||
11.10 | odd | 2 | 3025.2.a.w.1.4 | 4 | |||
15.14 | odd | 2 | 5445.2.a.bp.1.1 | 4 | |||
20.19 | odd | 2 | 9680.2.a.cn.1.2 | 4 | |||
55.4 | even | 10 | 605.2.g.m.511.2 | 8 | |||
55.9 | even | 10 | 55.2.g.b.26.1 | ✓ | 8 | ||
55.14 | even | 10 | 605.2.g.m.251.2 | 8 | |||
55.19 | odd | 10 | 605.2.g.e.251.1 | 8 | |||
55.24 | odd | 10 | 605.2.g.k.81.2 | 8 | |||
55.27 | odd | 20 | 275.2.z.a.124.4 | 16 | |||
55.29 | odd | 10 | 605.2.g.e.511.1 | 8 | |||
55.38 | odd | 20 | 275.2.z.a.124.1 | 16 | |||
55.39 | odd | 10 | 605.2.g.k.366.2 | 8 | |||
55.42 | odd | 20 | 275.2.z.a.224.1 | 16 | |||
55.49 | even | 10 | 55.2.g.b.36.1 | yes | 8 | ||
55.53 | odd | 20 | 275.2.z.a.224.4 | 16 | |||
55.54 | odd | 2 | 605.2.a.k.1.1 | 4 | |||
165.104 | odd | 10 | 495.2.n.e.91.2 | 8 | |||
165.119 | odd | 10 | 495.2.n.e.136.2 | 8 | |||
165.164 | even | 2 | 5445.2.a.bi.1.4 | 4 | |||
220.119 | odd | 10 | 880.2.bo.h.81.1 | 8 | |||
220.159 | odd | 10 | 880.2.bo.h.641.1 | 8 | |||
220.219 | even | 2 | 9680.2.a.cm.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.26.1 | ✓ | 8 | 55.9 | even | 10 | ||
55.2.g.b.36.1 | yes | 8 | 55.49 | even | 10 | ||
275.2.h.a.26.2 | 8 | 11.9 | even | 5 | |||
275.2.h.a.201.2 | 8 | 11.5 | even | 5 | |||
275.2.z.a.124.1 | 16 | 55.38 | odd | 20 | |||
275.2.z.a.124.4 | 16 | 55.27 | odd | 20 | |||
275.2.z.a.224.1 | 16 | 55.42 | odd | 20 | |||
275.2.z.a.224.4 | 16 | 55.53 | odd | 20 | |||
495.2.n.e.91.2 | 8 | 165.104 | odd | 10 | |||
495.2.n.e.136.2 | 8 | 165.119 | odd | 10 | |||
605.2.a.j.1.4 | 4 | 5.4 | even | 2 | |||
605.2.a.k.1.1 | 4 | 55.54 | odd | 2 | |||
605.2.g.e.251.1 | 8 | 55.19 | odd | 10 | |||
605.2.g.e.511.1 | 8 | 55.29 | odd | 10 | |||
605.2.g.k.81.2 | 8 | 55.24 | odd | 10 | |||
605.2.g.k.366.2 | 8 | 55.39 | odd | 10 | |||
605.2.g.m.251.2 | 8 | 55.14 | even | 10 | |||
605.2.g.m.511.2 | 8 | 55.4 | even | 10 | |||
880.2.bo.h.81.1 | 8 | 220.119 | odd | 10 | |||
880.2.bo.h.641.1 | 8 | 220.159 | odd | 10 | |||
3025.2.a.w.1.4 | 4 | 11.10 | odd | 2 | |||
3025.2.a.bd.1.1 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.bi.1.4 | 4 | 165.164 | even | 2 | |||
5445.2.a.bp.1.1 | 4 | 15.14 | odd | 2 | |||
9680.2.a.cm.1.2 | 4 | 220.219 | even | 2 | |||
9680.2.a.cn.1.2 | 4 | 20.19 | odd | 2 |