Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 30x^{10} + 329x^{8} + 1620x^{6} + 3479x^{4} + 2470x^{2} + 55 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(-2.84623i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.g.151.11 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.84623i | − | 1.42311i | −0.702629 | − | 0.711557i | \(-0.747990\pi\) | ||
0.702629 | − | 0.711557i | \(-0.252010\pi\) | |||||||
\(3\) | − | 2.18419i | − | 0.728063i | −0.931387 | − | 0.364031i | \(-0.881400\pi\) | ||
0.931387 | − | 0.364031i | \(-0.118600\pi\) | |||||||
\(4\) | −4.10101 | −1.02525 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.21669 | −1.03612 | ||||||||
\(7\) | 9.15076 | 1.30725 | 0.653625 | − | 0.756818i | \(-0.273247\pi\) | ||||
0.653625 | + | 0.756818i | \(0.273247\pi\) | |||||||
\(8\) | 0.287487i | 0.0359359i | ||||||||
\(9\) | 4.22932 | 0.469925 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.89207 | 0.899279 | 0.449640 | − | 0.893210i | \(-0.351552\pi\) | ||||
0.449640 | + | 0.893210i | \(0.351552\pi\) | |||||||
\(12\) | 8.95737i | 0.746447i | ||||||||
\(13\) | − | 12.3251i | − | 0.948085i | −0.880502 | − | 0.474042i | \(-0.842794\pi\) | ||
0.880502 | − | 0.474042i | \(-0.157206\pi\) | |||||||
\(14\) | − | 26.0451i | − | 1.86037i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.5858 | −0.974111 | ||||||||
\(17\) | 11.1895 | 0.658206 | 0.329103 | − | 0.944294i | \(-0.393254\pi\) | ||||
0.329103 | + | 0.944294i | \(0.393254\pi\) | |||||||
\(18\) | − | 12.0376i | − | 0.668756i | ||||||
\(19\) | 18.7659 | − | 2.97345i | 0.987678 | − | 0.156497i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 19.9870i | − | 0.951760i | ||||||
\(22\) | − | 28.1551i | − | 1.27978i | ||||||
\(23\) | −20.8666 | −0.907246 | −0.453623 | − | 0.891194i | \(-0.649869\pi\) | ||||
−0.453623 | + | 0.891194i | \(0.649869\pi\) | |||||||
\(24\) | 0.627927 | 0.0261636 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −35.0800 | −1.34923 | ||||||||
\(27\) | − | 28.8953i | − | 1.07020i | ||||||
\(28\) | −37.5273 | −1.34026 | ||||||||
\(29\) | 10.5011i | 0.362107i | 0.983473 | + | 0.181054i | \(0.0579508\pi\) | ||||
−0.983473 | + | 0.181054i | \(0.942049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 52.3075i | 1.68734i | 0.536864 | + | 0.843669i | \(0.319609\pi\) | ||||
−0.536864 | + | 0.843669i | \(0.680391\pi\) | |||||||
\(32\) | 45.5106i | 1.42221i | ||||||||
\(33\) | − | 21.6061i | − | 0.654732i | ||||||
\(34\) | − | 31.8479i | − | 0.936702i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17.3445 | −0.481791 | ||||||||
\(37\) | 10.5041i | 0.283895i | 0.989874 | + | 0.141948i | \(0.0453364\pi\) | ||||
−0.989874 | + | 0.141948i | \(0.954664\pi\) | |||||||
\(38\) | −8.46312 | − | 53.4120i | −0.222714 | − | 1.40558i | ||||
\(39\) | −26.9203 | −0.690265 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 42.6288i | − | 1.03973i | −0.854250 | − | 0.519863i | \(-0.825983\pi\) | ||
0.854250 | − | 0.519863i | \(-0.174017\pi\) | |||||||
\(42\) | −56.8874 | −1.35446 | ||||||||
\(43\) | −45.9768 | −1.06923 | −0.534614 | − | 0.845097i | \(-0.679543\pi\) | ||||
−0.534614 | + | 0.845097i | \(0.679543\pi\) | |||||||
\(44\) | −40.5674 | −0.921987 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 59.3912i | 1.29111i | ||||||||
\(47\) | −4.22163 | −0.0898220 | −0.0449110 | − | 0.998991i | \(-0.514300\pi\) | ||||
−0.0449110 | + | 0.998991i | \(0.514300\pi\) | |||||||
\(48\) | 34.0423i | 0.709214i | ||||||||
\(49\) | 34.7363 | 0.708905 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 24.4400i | − | 0.479215i | ||||||
\(52\) | 50.5453i | 0.972025i | ||||||||
\(53\) | 95.8254i | 1.80803i | 0.427505 | + | 0.904013i | \(0.359393\pi\) | ||||
−0.427505 | + | 0.904013i | \(0.640607\pi\) | |||||||
\(54\) | −82.2427 | −1.52301 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.63073i | 0.0469773i | ||||||||
\(57\) | −6.49458 | − | 40.9882i | −0.113940 | − | 0.719092i | ||||
\(58\) | 29.8886 | 0.515320 | ||||||||
\(59\) | 6.38544i | 0.108228i | 0.998535 | + | 0.0541139i | \(0.0172334\pi\) | ||||
−0.998535 | + | 0.0541139i | \(0.982767\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.8591 | 0.243593 | 0.121796 | − | 0.992555i | \(-0.461135\pi\) | ||||
0.121796 | + | 0.992555i | \(0.461135\pi\) | |||||||
\(62\) | 148.879 | 2.40127 | ||||||||
\(63\) | 38.7015 | 0.614310 | ||||||||
\(64\) | 67.1904 | 1.04985 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −61.4960 | −0.931757 | ||||||||
\(67\) | 38.0693i | 0.568199i | 0.958795 | + | 0.284099i | \(0.0916946\pi\) | ||||
−0.958795 | + | 0.284099i | \(0.908305\pi\) | |||||||
\(68\) | −45.8882 | −0.674827 | ||||||||
\(69\) | 45.5767i | 0.660532i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 125.169i | − | 1.76295i | −0.472230 | − | 0.881475i | \(-0.656551\pi\) | ||
0.472230 | − | 0.881475i | \(-0.343449\pi\) | |||||||
\(72\) | 1.21588i | 0.0168872i | ||||||||
\(73\) | −18.5252 | −0.253769 | −0.126885 | − | 0.991917i | \(-0.540498\pi\) | ||||
−0.126885 | + | 0.991917i | \(0.540498\pi\) | |||||||
\(74\) | 29.8971 | 0.404015 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −76.9590 | + | 12.1941i | −1.01262 | + | 0.160449i | ||||
\(77\) | 90.5199 | 1.17558 | ||||||||
\(78\) | 76.6214i | 0.982325i | ||||||||
\(79\) | 137.419i | 1.73948i | 0.493510 | + | 0.869740i | \(0.335714\pi\) | ||||
−0.493510 | + | 0.869740i | \(0.664286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −25.0489 | −0.309246 | ||||||||
\(82\) | −121.331 | −1.47965 | ||||||||
\(83\) | −127.881 | −1.54073 | −0.770365 | − | 0.637603i | \(-0.779926\pi\) | ||||
−0.770365 | + | 0.637603i | \(0.779926\pi\) | |||||||
\(84\) | 81.9667i | 0.975794i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 130.860i | 1.52163i | ||||||||
\(87\) | 22.9364 | 0.263637 | ||||||||
\(88\) | 2.84385i | 0.0323164i | ||||||||
\(89\) | 19.8059i | 0.222538i | 0.993790 | + | 0.111269i | \(0.0354916\pi\) | ||||
−0.993790 | + | 0.111269i | \(0.964508\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 112.784i | − | 1.23938i | ||||||
\(92\) | 85.5743 | 0.930155 | ||||||||
\(93\) | 114.249 | 1.22849 | ||||||||
\(94\) | 12.0157i | 0.127827i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 99.4037 | 1.03545 | ||||||||
\(97\) | 42.4473i | 0.437601i | 0.975770 | + | 0.218800i | \(0.0702143\pi\) | ||||
−0.975770 | + | 0.218800i | \(0.929786\pi\) | |||||||
\(98\) | − | 98.8675i | − | 1.00885i | ||||||
\(99\) | 41.8368 | 0.422594 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −111.435 | −1.10332 | −0.551660 | − | 0.834069i | \(-0.686005\pi\) | ||||
−0.551660 | + | 0.834069i | \(0.686005\pi\) | |||||||
\(102\) | −69.5617 | −0.681978 | ||||||||
\(103\) | − | 5.71536i | − | 0.0554889i | −0.999615 | − | 0.0277445i | \(-0.991168\pi\) | ||
0.999615 | − | 0.0277445i | \(-0.00883247\pi\) | |||||||
\(104\) | 3.54331 | 0.0340703 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 272.741 | 2.57303 | ||||||||
\(107\) | − | 164.563i | − | 1.53797i | −0.639264 | − | 0.768987i | \(-0.720761\pi\) | ||
0.639264 | − | 0.768987i | \(-0.279239\pi\) | |||||||
\(108\) | 118.500i | 1.09722i | ||||||||
\(109\) | − | 102.267i | − | 0.938227i | −0.883138 | − | 0.469113i | \(-0.844574\pi\) | ||
0.883138 | − | 0.469113i | \(-0.155426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.9430 | 0.206693 | ||||||||
\(112\) | −142.622 | −1.27341 | ||||||||
\(113\) | 24.5050i | 0.216858i | 0.994104 | + | 0.108429i | \(0.0345821\pi\) | ||||
−0.994104 | + | 0.108429i | \(0.965418\pi\) | |||||||
\(114\) | −116.662 | + | 18.4850i | −1.02335 | + | 0.162149i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 43.0651i | − | 0.371251i | ||||||
\(117\) | − | 52.1268i | − | 0.445528i | ||||||
\(118\) | 18.1744 | 0.154021 | ||||||||
\(119\) | 102.392 | 0.860440 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −23.1469 | −0.191297 | ||||||||
\(122\) | − | 42.2925i | − | 0.346660i | ||||||
\(123\) | −93.1093 | −0.756986 | ||||||||
\(124\) | − | 214.513i | − | 1.72995i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 110.153i | − | 0.874232i | ||||||
\(127\) | 58.5427i | 0.460966i | 0.973076 | + | 0.230483i | \(0.0740307\pi\) | ||||
−0.973076 | + | 0.230483i | \(0.925969\pi\) | |||||||
\(128\) | − | 9.19667i | − | 0.0718489i | ||||||
\(129\) | 100.422i | 0.778464i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 223.883 | 1.70903 | 0.854516 | − | 0.519425i | \(-0.173854\pi\) | ||||
0.854516 | + | 0.519425i | \(0.173854\pi\) | |||||||
\(132\) | 88.6069i | 0.671265i | ||||||||
\(133\) | 171.722 | − | 27.2093i | 1.29114 | − | 0.204581i | ||||
\(134\) | 108.354 | 0.808611 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.21684i | 0.0236532i | ||||||||
\(137\) | −6.24728 | −0.0456006 | −0.0228003 | − | 0.999740i | \(-0.507258\pi\) | ||||
−0.0228003 | + | 0.999740i | \(0.507258\pi\) | |||||||
\(138\) | 129.722 | 0.940011 | ||||||||
\(139\) | −204.969 | −1.47460 | −0.737299 | − | 0.675567i | \(-0.763899\pi\) | ||||
−0.737299 | + | 0.675567i | \(0.763899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.22084i | 0.0653960i | ||||||||
\(142\) | −356.261 | −2.50888 | ||||||||
\(143\) | − | 121.921i | − | 0.852593i | ||||||
\(144\) | −65.9173 | −0.457759 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 52.7268i | 0.361143i | ||||||||
\(147\) | − | 75.8707i | − | 0.516127i | ||||||
\(148\) | − | 43.0775i | − | 0.291064i | ||||||
\(149\) | −83.5502 | −0.560740 | −0.280370 | − | 0.959892i | \(-0.590457\pi\) | ||||
−0.280370 | + | 0.959892i | \(0.590457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 189.386i | 1.25421i | 0.778934 | + | 0.627106i | \(0.215761\pi\) | ||||
−0.778934 | + | 0.627106i | \(0.784239\pi\) | |||||||
\(152\) | 0.854830 | + | 5.39496i | 0.00562388 | + | 0.0354931i | ||||
\(153\) | 47.3240 | 0.309307 | ||||||||
\(154\) | − | 257.640i | − | 1.67299i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 110.400 | 0.707695 | ||||||||
\(157\) | 195.060 | 1.24242 | 0.621212 | − | 0.783643i | \(-0.286641\pi\) | ||||
0.621212 | + | 0.783643i | \(0.286641\pi\) | |||||||
\(158\) | 391.126 | 2.47548 | ||||||||
\(159\) | 209.301 | 1.31636 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −190.946 | −1.18600 | ||||||||
\(162\) | 71.2949i | 0.440092i | ||||||||
\(163\) | 171.677 | 1.05323 | 0.526616 | − | 0.850103i | \(-0.323461\pi\) | ||||
0.526616 | + | 0.850103i | \(0.323461\pi\) | |||||||
\(164\) | 174.821i | 1.06598i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 363.977i | 2.19263i | ||||||||
\(167\) | − | 40.7628i | − | 0.244088i | −0.992525 | − | 0.122044i | \(-0.961055\pi\) | ||
0.992525 | − | 0.122044i | \(-0.0389450\pi\) | |||||||
\(168\) | 5.74600 | 0.0342024 | ||||||||
\(169\) | 17.0919 | 0.101136 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 79.3670 | − | 12.5757i | 0.464135 | − | 0.0735420i | ||||
\(172\) | 188.551 | 1.09623 | ||||||||
\(173\) | − | 279.193i | − | 1.61384i | −0.590664 | − | 0.806918i | \(-0.701134\pi\) | ||
0.590664 | − | 0.806918i | \(-0.298866\pi\) | |||||||
\(174\) | − | 65.2822i | − | 0.375185i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −154.176 | −0.875997 | ||||||||
\(177\) | 13.9470 | 0.0787967 | ||||||||
\(178\) | 56.3721 | 0.316697 | ||||||||
\(179\) | − | 308.777i | − | 1.72501i | −0.506048 | − | 0.862505i | \(-0.668894\pi\) | ||
0.506048 | − | 0.862505i | \(-0.331106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 252.084i | 1.39273i | 0.717688 | + | 0.696365i | \(0.245201\pi\) | ||||
−0.717688 | + | 0.696365i | \(0.754799\pi\) | |||||||
\(182\) | −321.009 | −1.76378 | ||||||||
\(183\) | − | 32.4552i | − | 0.177351i | ||||||
\(184\) | − | 5.99890i | − | 0.0326027i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 325.180i | − | 1.74828i | ||||||
\(187\) | 110.687 | 0.591911 | ||||||||
\(188\) | 17.3129 | 0.0920901 | ||||||||
\(189\) | − | 264.414i | − | 1.39902i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 210.693 | 1.10311 | 0.551553 | − | 0.834140i | \(-0.314035\pi\) | ||||
0.551553 | + | 0.834140i | \(0.314035\pi\) | |||||||
\(192\) | − | 146.756i | − | 0.764356i | ||||||
\(193\) | 113.346i | 0.587285i | 0.955915 | + | 0.293643i | \(0.0948676\pi\) | ||||
−0.955915 | + | 0.293643i | \(0.905132\pi\) | |||||||
\(194\) | 120.815 | 0.622755 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −142.454 | −0.726806 | ||||||||
\(197\) | 206.358 | 1.04750 | 0.523752 | − | 0.851871i | \(-0.324532\pi\) | ||||
0.523752 | + | 0.851871i | \(0.324532\pi\) | |||||||
\(198\) | − | 119.077i | − | 0.601399i | ||||||
\(199\) | 181.976 | 0.914450 | 0.457225 | − | 0.889351i | \(-0.348843\pi\) | ||||
0.457225 | + | 0.889351i | \(0.348843\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 83.1505 | 0.413684 | ||||||||
\(202\) | 317.170i | 1.57015i | ||||||||
\(203\) | 96.0931i | 0.473365i | ||||||||
\(204\) | 100.229i | 0.491316i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.2672 | −0.0789670 | ||||||||
\(207\) | −88.2518 | −0.426337 | ||||||||
\(208\) | 192.096i | 0.923539i | ||||||||
\(209\) | 185.633 | − | 29.4136i | 0.888199 | − | 0.140735i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 106.729i | − | 0.505824i | −0.967489 | − | 0.252912i | \(-0.918612\pi\) | ||
0.967489 | − | 0.252912i | \(-0.0813883\pi\) | |||||||
\(212\) | − | 392.981i | − | 1.85368i | ||||||
\(213\) | −273.394 | −1.28354 | ||||||||
\(214\) | −468.384 | −2.18871 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.30704 | 0.0384585 | ||||||||
\(217\) | 478.653i | 2.20577i | ||||||||
\(218\) | −291.074 | −1.33520 | ||||||||
\(219\) | 40.4624i | 0.184760i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 137.912i | − | 0.624035i | ||||||
\(222\) | − | 65.3009i | − | 0.294148i | ||||||
\(223\) | 209.351i | 0.938793i | 0.882987 | + | 0.469397i | \(0.155529\pi\) | ||||
−0.882987 | + | 0.469397i | \(0.844471\pi\) | |||||||
\(224\) | 416.456i | 1.85918i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 69.7467 | 0.308614 | ||||||||
\(227\) | 244.295i | 1.07619i | 0.842885 | + | 0.538094i | \(0.180856\pi\) | ||||
−0.842885 | + | 0.538094i | \(0.819144\pi\) | |||||||
\(228\) | 26.6343 | + | 168.093i | 0.116817 | + | 0.737250i | ||||
\(229\) | 254.372 | 1.11079 | 0.555397 | − | 0.831586i | \(-0.312566\pi\) | ||||
0.555397 | + | 0.831586i | \(0.312566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 197.713i | − | 0.855898i | ||||||
\(232\) | −3.01894 | −0.0130127 | ||||||||
\(233\) | −347.037 | −1.48943 | −0.744714 | − | 0.667384i | \(-0.767414\pi\) | ||||
−0.744714 | + | 0.667384i | \(0.767414\pi\) | |||||||
\(234\) | −148.365 | −0.634038 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 26.1867i | − | 0.110961i | ||||||
\(237\) | 300.149 | 1.26645 | ||||||||
\(238\) | − | 291.432i | − | 1.22450i | ||||||
\(239\) | 0.0478766 | 0.000200320 | 0.000100160 | − | 1.00000i | \(-0.499968\pi\) | ||||
0.000100160 | 1.00000i | \(0.499968\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 422.817i | 1.75443i | 0.480100 | + | 0.877214i | \(0.340601\pi\) | ||||
−0.480100 | + | 0.877214i | \(0.659399\pi\) | |||||||
\(242\) | 65.8815i | 0.272237i | ||||||||
\(243\) | − | 205.346i | − | 0.845047i | ||||||
\(244\) | −60.9375 | −0.249744 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 265.010i | 1.07728i | ||||||||
\(247\) | −36.6481 | − | 231.291i | −0.148373 | − | 0.936403i | ||||
\(248\) | −15.0377 | −0.0606361 | ||||||||
\(249\) | 279.315i | 1.12175i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 142.321 | 0.567015 | 0.283507 | − | 0.958970i | \(-0.408502\pi\) | ||||
0.283507 | + | 0.958970i | \(0.408502\pi\) | |||||||
\(252\) | −158.715 | −0.629822 | ||||||||
\(253\) | −206.414 | −0.815867 | ||||||||
\(254\) | 166.626 | 0.656007 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 242.586 | 0.947600 | ||||||||
\(257\) | 198.179i | 0.771123i | 0.922682 | + | 0.385562i | \(0.125992\pi\) | ||||
−0.922682 | + | 0.385562i | \(0.874008\pi\) | |||||||
\(258\) | 285.823 | 1.10784 | ||||||||
\(259\) | 96.1206i | 0.371122i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 44.4126i | 0.170163i | ||||||||
\(262\) | − | 637.223i | − | 2.43215i | ||||||
\(263\) | 149.067 | 0.566794 | 0.283397 | − | 0.959003i | \(-0.408539\pi\) | ||||
0.283397 | + | 0.959003i | \(0.408539\pi\) | |||||||
\(264\) | 6.21149 | 0.0235284 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −77.4439 | − | 488.760i | −0.291143 | − | 1.83744i | ||||
\(267\) | 43.2599 | 0.162022 | ||||||||
\(268\) | − | 156.123i | − | 0.582547i | ||||||
\(269\) | − | 204.113i | − | 0.758785i | −0.925236 | − | 0.379392i | \(-0.876133\pi\) | ||
0.925236 | − | 0.379392i | \(-0.123867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −240.731 | −0.888305 | −0.444152 | − | 0.895951i | \(-0.646495\pi\) | ||||
−0.444152 | + | 0.895951i | \(0.646495\pi\) | |||||||
\(272\) | −174.397 | −0.641166 | ||||||||
\(273\) | −246.341 | −0.902349 | ||||||||
\(274\) | 17.7812i | 0.0648948i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 186.910i | − | 0.677211i | ||||||
\(277\) | −458.745 | −1.65612 | −0.828059 | − | 0.560641i | \(-0.810555\pi\) | ||||
−0.828059 | + | 0.560641i | \(0.810555\pi\) | |||||||
\(278\) | 583.388i | 2.09852i | ||||||||
\(279\) | 221.225i | 0.792922i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 249.476i | − | 0.887816i | −0.896072 | − | 0.443908i | \(-0.853592\pi\) | ||
0.896072 | − | 0.443908i | \(-0.146408\pi\) | |||||||
\(282\) | 26.2446 | 0.0930659 | ||||||||
\(283\) | 365.612 | 1.29192 | 0.645958 | − | 0.763373i | \(-0.276458\pi\) | ||||
0.645958 | + | 0.763373i | \(0.276458\pi\) | |||||||
\(284\) | 513.321i | 1.80747i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −347.014 | −1.21334 | ||||||||
\(287\) | − | 390.086i | − | 1.35918i | ||||||
\(288\) | 192.479i | 0.668330i | ||||||||
\(289\) | −163.795 | −0.566765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 92.7128 | 0.318601 | ||||||||
\(292\) | 75.9718 | 0.260177 | ||||||||
\(293\) | 173.088i | 0.590745i | 0.955382 | + | 0.295373i | \(0.0954438\pi\) | ||||
−0.955382 | + | 0.295373i | \(0.904556\pi\) | |||||||
\(294\) | −215.945 | −0.734507 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.01980 | −0.0102020 | ||||||||
\(297\) | − | 285.835i | − | 0.962406i | ||||||
\(298\) | 237.803i | 0.797996i | ||||||||
\(299\) | 257.184i | 0.860146i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −420.722 | −1.39775 | ||||||||
\(302\) | 539.036 | 1.78489 | ||||||||
\(303\) | 243.396i | 0.803286i | ||||||||
\(304\) | −292.481 | + | 46.3435i | −0.962108 | + | 0.152446i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 134.695i | − | 0.440179i | ||||||
\(307\) | 452.211i | 1.47300i | 0.676438 | + | 0.736500i | \(0.263523\pi\) | ||||
−0.676438 | + | 0.736500i | \(0.736477\pi\) | |||||||
\(308\) | −371.223 | −1.20527 | ||||||||
\(309\) | −12.4834 | −0.0403994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 179.346 | 0.576675 | 0.288337 | − | 0.957529i | \(-0.406898\pi\) | ||||
0.288337 | + | 0.957529i | \(0.406898\pi\) | |||||||
\(312\) | − | 7.73926i | − | 0.0248053i | ||||||
\(313\) | −137.714 | −0.439981 | −0.219990 | − | 0.975502i | \(-0.570603\pi\) | ||||
−0.219990 | + | 0.975502i | \(0.570603\pi\) | |||||||
\(314\) | − | 555.186i | − | 1.76811i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 563.556i | − | 1.78341i | ||||||
\(317\) | 602.099i | 1.89936i | 0.313215 | + | 0.949682i | \(0.398594\pi\) | ||||
−0.313215 | + | 0.949682i | \(0.601406\pi\) | |||||||
\(318\) | − | 595.717i | − | 1.87332i | ||||||
\(319\) | 103.878i | 0.325636i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −359.437 | −1.11974 | ||||||||
\(322\) | 543.474i | 1.68781i | ||||||||
\(323\) | 209.981 | − | 33.2714i | 0.650096 | − | 0.103008i | ||||
\(324\) | 102.726 | 0.317055 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 488.631i | − | 1.49887i | ||||||
\(327\) | −223.370 | −0.683088 | ||||||||
\(328\) | 12.2552 | 0.0373635 | ||||||||
\(329\) | −38.6311 | −0.117420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 190.514i | 0.575571i | 0.957695 | + | 0.287785i | \(0.0929189\pi\) | ||||
−0.957695 | + | 0.287785i | \(0.907081\pi\) | |||||||
\(332\) | 524.439 | 1.57964 | ||||||||
\(333\) | 44.4253i | 0.133409i | ||||||||
\(334\) | −116.020 | −0.347366 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 311.512i | 0.927120i | ||||||||
\(337\) | − | 394.039i | − | 1.16926i | −0.811301 | − | 0.584628i | \(-0.801240\pi\) | ||
0.811301 | − | 0.584628i | \(-0.198760\pi\) | |||||||
\(338\) | − | 48.6475i | − | 0.143927i | ||||||
\(339\) | 53.5235 | 0.157886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 517.429i | 1.51739i | ||||||||
\(342\) | −35.7933 | − | 225.896i | −0.104659 | − | 0.660516i | ||||
\(343\) | −130.523 | −0.380535 | ||||||||
\(344\) | − | 13.2177i | − | 0.0384237i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −794.648 | −2.29667 | ||||||||
\(347\) | −205.061 | −0.590953 | −0.295476 | − | 0.955350i | \(-0.595478\pi\) | ||||
−0.295476 | + | 0.955350i | \(0.595478\pi\) | |||||||
\(348\) | −94.0624 | −0.270294 | ||||||||
\(349\) | −488.832 | −1.40066 | −0.700332 | − | 0.713817i | \(-0.746965\pi\) | ||||
−0.700332 | + | 0.713817i | \(0.746965\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −356.138 | −1.01464 | ||||||||
\(352\) | 450.194i | 1.27896i | ||||||||
\(353\) | −466.761 | −1.32227 | −0.661134 | − | 0.750268i | \(-0.729925\pi\) | ||||
−0.661134 | + | 0.750268i | \(0.729925\pi\) | |||||||
\(354\) | − | 39.6964i | − | 0.112137i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 81.2242i | − | 0.228158i | ||||||
\(357\) | − | 223.644i | − | 0.626455i | ||||||
\(358\) | −878.849 | −2.45489 | ||||||||
\(359\) | 487.730 | 1.35858 | 0.679289 | − | 0.733871i | \(-0.262288\pi\) | ||||
0.679289 | + | 0.733871i | \(0.262288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 343.317 | − | 111.599i | 0.951017 | − | 0.309138i | ||||
\(362\) | 717.489 | 1.98201 | ||||||||
\(363\) | 50.5573i | 0.139276i | ||||||||
\(364\) | 462.528i | 1.27068i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −92.3748 | −0.252390 | ||||||||
\(367\) | 63.0494 | 0.171797 | 0.0858983 | − | 0.996304i | \(-0.472624\pi\) | ||||
0.0858983 | + | 0.996304i | \(0.472624\pi\) | |||||||
\(368\) | 325.223 | 0.883758 | ||||||||
\(369\) | − | 180.291i | − | 0.488593i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 876.875i | 2.36354i | ||||||||
\(372\) | −468.537 | −1.25951 | ||||||||
\(373\) | − | 137.833i | − | 0.369526i | −0.982783 | − | 0.184763i | \(-0.940848\pi\) | ||
0.982783 | − | 0.184763i | \(-0.0591517\pi\) | |||||||
\(374\) | − | 315.041i | − | 0.842356i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 1.21367i | − | 0.00322784i | ||||||
\(377\) | 129.427 | 0.343308 | ||||||||
\(378\) | −752.582 | −1.99096 | ||||||||
\(379\) | − | 316.605i | − | 0.835370i | −0.908592 | − | 0.417685i | \(-0.862842\pi\) | ||
0.908592 | − | 0.417685i | \(-0.137158\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 127.868 | 0.335612 | ||||||||
\(382\) | − | 599.681i | − | 1.56985i | ||||||
\(383\) | − | 197.083i | − | 0.514577i | −0.966335 | − | 0.257288i | \(-0.917171\pi\) | ||
0.966335 | − | 0.257288i | \(-0.0828291\pi\) | |||||||
\(384\) | −20.0872 | −0.0523105 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 322.609 | 0.835774 | ||||||||
\(387\) | −194.451 | −0.502456 | ||||||||
\(388\) | − | 174.076i | − | 0.448651i | ||||||
\(389\) | 27.8203 | 0.0715175 | 0.0357587 | − | 0.999360i | \(-0.488615\pi\) | ||||
0.0357587 | + | 0.999360i | \(0.488615\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −233.487 | −0.597155 | ||||||||
\(392\) | 9.98626i | 0.0254751i | ||||||||
\(393\) | − | 489.003i | − | 1.24428i | ||||||
\(394\) | − | 587.343i | − | 1.49072i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −171.573 | −0.433265 | ||||||||
\(397\) | 702.745 | 1.77014 | 0.885069 | − | 0.465459i | \(-0.154111\pi\) | ||||
0.885069 | + | 0.465459i | \(0.154111\pi\) | |||||||
\(398\) | − | 517.944i | − | 1.30137i | ||||||
\(399\) | −59.4303 | − | 375.073i | −0.148948 | − | 0.940033i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 295.297i | 0.736401i | 0.929746 | + | 0.368200i | \(0.120026\pi\) | ||||
−0.929746 | + | 0.368200i | \(0.879974\pi\) | |||||||
\(402\) | − | 236.665i | − | 0.588720i | ||||||
\(403\) | 644.695 | 1.59974 | ||||||||
\(404\) | 456.997 | 1.13118 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 273.503 | 0.673652 | ||||||||
\(407\) | 103.907i | 0.255301i | ||||||||
\(408\) | 7.02619 | 0.0172210 | ||||||||
\(409\) | − | 371.735i | − | 0.908887i | −0.890775 | − | 0.454444i | \(-0.849838\pi\) | ||
0.890775 | − | 0.454444i | \(-0.150162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.6452i | 0.0332001i | ||||||||
\(412\) | 23.4387i | 0.0568901i | ||||||||
\(413\) | 58.4316i | 0.141481i | ||||||||
\(414\) | 251.185i | 0.606726i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 560.923 | 1.34837 | ||||||||
\(417\) | 447.691i | 1.07360i | ||||||||
\(418\) | −83.7177 | − | 528.355i | −0.200282 | − | 1.26401i | ||||
\(419\) | −109.242 | −0.260721 | −0.130360 | − | 0.991467i | \(-0.541613\pi\) | ||||
−0.130360 | + | 0.991467i | \(0.541613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 762.528i | − | 1.81123i | −0.424100 | − | 0.905615i | \(-0.639409\pi\) | ||
0.424100 | − | 0.905615i | \(-0.360591\pi\) | |||||||
\(422\) | −303.774 | −0.719845 | ||||||||
\(423\) | −17.8546 | −0.0422096 | ||||||||
\(424\) | −27.5486 | −0.0649731 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 778.140i | 1.82662i | ||||||||
\(427\) | 135.972 | 0.318437 | ||||||||
\(428\) | 674.875i | 1.57681i | ||||||||
\(429\) | −266.298 | −0.620741 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 131.893i | − | 0.306016i | −0.988225 | − | 0.153008i | \(-0.951104\pi\) | ||
0.988225 | − | 0.153008i | \(-0.0488960\pi\) | |||||||
\(432\) | 450.356i | 1.04249i | ||||||||
\(433\) | 401.234i | 0.926638i | 0.886191 | + | 0.463319i | \(0.153342\pi\) | ||||
−0.886191 | + | 0.463319i | \(0.846658\pi\) | |||||||
\(434\) | 1362.35 | 3.13907 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 419.397i | 0.961919i | ||||||||
\(437\) | −391.581 | + | 62.0460i | −0.896067 | + | 0.141982i | ||||
\(438\) | 115.165 | 0.262934 | ||||||||
\(439\) | 264.338i | 0.602136i | 0.953603 | + | 0.301068i | \(0.0973432\pi\) | ||||
−0.953603 | + | 0.301068i | \(0.902657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 146.911 | 0.333132 | ||||||||
\(442\) | −392.528 | −0.888073 | ||||||||
\(443\) | 451.274 | 1.01868 | 0.509338 | − | 0.860566i | \(-0.329890\pi\) | ||||
0.509338 | + | 0.860566i | \(0.329890\pi\) | |||||||
\(444\) | −94.0893 | −0.211913 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 595.860 | 1.33601 | ||||||||
\(447\) | 182.489i | 0.408254i | ||||||||
\(448\) | 614.843 | 1.37242 | ||||||||
\(449\) | 156.631i | 0.348844i | 0.984671 | + | 0.174422i | \(0.0558057\pi\) | ||||
−0.984671 | + | 0.174422i | \(0.944194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 421.687i | − | 0.935004i | ||||||
\(452\) | − | 100.495i | − | 0.222334i | ||||||
\(453\) | 413.655 | 0.913145 | ||||||||
\(454\) | 695.318 | 1.53154 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.7836 | − | 1.86711i | 0.0258412 | − | 0.00409454i | ||||
\(457\) | −906.098 | −1.98271 | −0.991355 | − | 0.131209i | \(-0.958114\pi\) | ||||
−0.991355 | + | 0.131209i | \(0.958114\pi\) | |||||||
\(458\) | − | 724.000i | − | 1.58078i | ||||||
\(459\) | − | 323.324i | − | 0.704410i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −169.733 | −0.368184 | −0.184092 | − | 0.982909i | \(-0.558934\pi\) | ||||
−0.184092 | + | 0.982909i | \(0.558934\pi\) | |||||||
\(462\) | −562.735 | −1.21804 | ||||||||
\(463\) | −207.991 | −0.449225 | −0.224613 | − | 0.974448i | \(-0.572112\pi\) | ||||
−0.224613 | + | 0.974448i | \(0.572112\pi\) | |||||||
\(464\) | − | 163.668i | − | 0.352733i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 987.745i | 2.11962i | ||||||||
\(467\) | 479.390 | 1.02653 | 0.513266 | − | 0.858230i | \(-0.328435\pi\) | ||||
0.513266 | + | 0.858230i | \(0.328435\pi\) | |||||||
\(468\) | 213.772i | 0.456779i | ||||||||
\(469\) | 348.363i | 0.742778i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 426.049i | − | 0.904562i | ||||||
\(472\) | −1.83573 | −0.00388927 | ||||||||
\(473\) | −454.805 | −0.961534 | ||||||||
\(474\) | − | 854.292i | − | 1.80230i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −419.912 | −0.882168 | ||||||||
\(477\) | 405.277i | 0.849636i | ||||||||
\(478\) | − | 0.136268i | − | 0.000285079i | ||||||
\(479\) | −712.482 | −1.48744 | −0.743718 | − | 0.668493i | \(-0.766940\pi\) | ||||
−0.743718 | + | 0.668493i | \(0.766940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 129.464 | 0.269157 | ||||||||
\(482\) | 1203.43 | 2.49675 | ||||||||
\(483\) | 417.061i | 0.863480i | ||||||||
\(484\) | 94.9258 | 0.196128 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −584.462 | −1.20260 | ||||||||
\(487\) | − | 34.4191i | − | 0.0706757i | −0.999375 | − | 0.0353379i | \(-0.988749\pi\) | ||
0.999375 | − | 0.0353379i | \(-0.0112507\pi\) | |||||||
\(488\) | 4.27182i | 0.00875373i | ||||||||
\(489\) | − | 374.975i | − | 0.766819i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 361.608 | 0.736472 | 0.368236 | − | 0.929732i | \(-0.379962\pi\) | ||||
0.368236 | + | 0.929732i | \(0.379962\pi\) | |||||||
\(492\) | 381.842 | 0.776101 | ||||||||
\(493\) | 117.502i | 0.238341i | ||||||||
\(494\) | −658.308 | + | 104.309i | −1.33261 | + | 0.211151i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 815.252i | − | 1.64365i | ||||||
\(497\) | − | 1145.40i | − | 2.30462i | ||||||
\(498\) | 794.994 | 1.59637 | ||||||||
\(499\) | −189.977 | −0.380715 | −0.190358 | − | 0.981715i | \(-0.560965\pi\) | ||||
−0.190358 | + | 0.981715i | \(0.560965\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −89.0336 | −0.177712 | ||||||||
\(502\) | − | 405.077i | − | 0.806926i | ||||||
\(503\) | 687.468 | 1.36674 | 0.683368 | − | 0.730074i | \(-0.260514\pi\) | ||||
0.683368 | + | 0.730074i | \(0.260514\pi\) | |||||||
\(504\) | 11.1262i | 0.0220758i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 587.502i | 1.16107i | ||||||||
\(507\) | − | 37.3319i | − | 0.0736330i | ||||||
\(508\) | − | 240.084i | − | 0.472607i | ||||||
\(509\) | 348.233i | 0.684151i | 0.939672 | + | 0.342076i | \(0.111130\pi\) | ||||
−0.939672 | + | 0.342076i | \(0.888870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −169.519 | −0.331740 | ||||||||
\(512\) | − | 727.241i | − | 1.42039i | ||||||
\(513\) | −85.9189 | − | 542.247i | −0.167483 | − | 1.05701i | ||||
\(514\) | 564.061 | 1.09740 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 411.831i | − | 0.798122i | ||||||
\(517\) | −41.7607 | −0.0807750 | ||||||||
\(518\) | 273.581 | 0.528149 | ||||||||
\(519\) | −609.811 | −1.17497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 222.778i | − | 0.427597i | −0.976878 | − | 0.213798i | \(-0.931416\pi\) | ||
0.976878 | − | 0.213798i | \(-0.0685835\pi\) | |||||||
\(522\) | 126.408 | 0.242162 | ||||||||
\(523\) | − | 45.6247i | − | 0.0872365i | −0.999048 | − | 0.0436182i | \(-0.986111\pi\) | ||
0.999048 | − | 0.0436182i | \(-0.0138885\pi\) | |||||||
\(524\) | −918.147 | −1.75219 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 424.278i | − | 0.806612i | ||||||
\(527\) | 585.295i | 1.11062i | ||||||||
\(528\) | 336.748i | 0.637781i | ||||||||
\(529\) | −93.5830 | −0.176905 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.0061i | 0.0508590i | ||||||||
\(532\) | −704.233 | + | 111.586i | −1.32375 | + | 0.209747i | ||||
\(533\) | −525.404 | −0.985749 | ||||||||
\(534\) | − | 123.127i | − | 0.230576i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −10.9444 | −0.0204187 | ||||||||
\(537\) | −674.427 | −1.25592 | ||||||||
\(538\) | −580.952 | −1.07984 | ||||||||
\(539\) | 343.614 | 0.637503 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 671.919 | 1.24199 | 0.620997 | − | 0.783813i | \(-0.286728\pi\) | ||||
0.620997 | + | 0.783813i | \(0.286728\pi\) | |||||||
\(542\) | 685.174i | 1.26416i | ||||||||
\(543\) | 550.599 | 1.01399 | ||||||||
\(544\) | 509.241i | 0.936105i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 701.143i | 1.28415i | ||||||||
\(547\) | − | 910.710i | − | 1.66492i | −0.554087 | − | 0.832459i | \(-0.686932\pi\) | ||
0.554087 | − | 0.832459i | \(-0.313068\pi\) | |||||||
\(548\) | 25.6201 | 0.0467520 | ||||||||
\(549\) | 62.8441 | 0.114470 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.2246 | + | 197.063i | 0.0566689 | + | 0.357646i | ||||
\(552\) | −13.1027 | −0.0237368 | ||||||||
\(553\) | 1257.49i | 2.27394i | ||||||||
\(554\) | 1305.69i | 2.35684i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 840.579 | 1.51183 | ||||||||
\(557\) | 246.347 | 0.442275 | 0.221138 | − | 0.975243i | \(-0.429023\pi\) | ||||
0.221138 | + | 0.975243i | \(0.429023\pi\) | |||||||
\(558\) | 629.657 | 1.12842 | ||||||||
\(559\) | 566.668i | 1.01372i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 241.762i | − | 0.430948i | ||||||
\(562\) | −710.066 | −1.26346 | ||||||||
\(563\) | − | 772.769i | − | 1.37259i | −0.727322 | − | 0.686296i | \(-0.759235\pi\) | ||
0.727322 | − | 0.686296i | \(-0.240765\pi\) | |||||||
\(564\) | − | 37.8147i | − | 0.0670474i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 1040.61i | − | 1.83854i | ||||||
\(567\) | −229.217 | −0.404262 | ||||||||
\(568\) | 35.9847 | 0.0633533 | ||||||||
\(569\) | 123.962i | 0.217860i | 0.994049 | + | 0.108930i | \(0.0347424\pi\) | ||||
−0.994049 | + | 0.108930i | \(0.965258\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 535.555 | 0.937925 | 0.468963 | − | 0.883218i | \(-0.344628\pi\) | ||||
0.468963 | + | 0.883218i | \(0.344628\pi\) | |||||||
\(572\) | 499.998i | 0.874122i | ||||||||
\(573\) | − | 460.194i | − | 0.803131i | ||||||
\(574\) | −1110.27 | −1.93427 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 284.170 | 0.493350 | ||||||||
\(577\) | 210.295 | 0.364463 | 0.182231 | − | 0.983256i | \(-0.441668\pi\) | ||||
0.182231 | + | 0.983256i | \(0.441668\pi\) | |||||||
\(578\) | 466.198i | 0.806570i | ||||||||
\(579\) | 247.569 | 0.427580 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1170.20 | −2.01412 | ||||||||
\(582\) | − | 263.882i | − | 0.453405i | ||||||
\(583\) | 947.912i | 1.62592i | ||||||||
\(584\) | − | 5.32575i | − | 0.00911944i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 492.649 | 0.840697 | ||||||||
\(587\) | 508.069 | 0.865534 | 0.432767 | − | 0.901506i | \(-0.357537\pi\) | ||||
0.432767 | + | 0.901506i | \(0.357537\pi\) | |||||||
\(588\) | 311.146i | 0.529160i | ||||||||
\(589\) | 155.534 | + | 981.596i | 0.264064 | + | 1.66655i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 450.726i | − | 0.762649i | ||||||
\(592\) | − | 163.715i | − | 0.276545i | ||||||
\(593\) | 32.8735 | 0.0554358 | 0.0277179 | − | 0.999616i | \(-0.491176\pi\) | ||||
0.0277179 | + | 0.999616i | \(0.491176\pi\) | |||||||
\(594\) | −813.550 | −1.36961 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 342.640 | 0.574899 | ||||||||
\(597\) | − | 397.469i | − | 0.665777i | ||||||
\(598\) | 732.003 | 1.22408 | ||||||||
\(599\) | 225.201i | 0.375961i | 0.982173 | + | 0.187981i | \(0.0601942\pi\) | ||||
−0.982173 | + | 0.187981i | \(0.939806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 169.930i | 0.282746i | 0.989956 | + | 0.141373i | \(0.0451517\pi\) | ||||
−0.989956 | + | 0.141373i | \(0.954848\pi\) | |||||||
\(602\) | 1197.47i | 1.98915i | ||||||||
\(603\) | 161.007i | 0.267011i | ||||||||
\(604\) | − | 776.674i | − | 1.28588i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 692.760 | 1.14317 | ||||||||
\(607\) | 522.217i | 0.860325i | 0.902752 | + | 0.430162i | \(0.141544\pi\) | ||||
−0.902752 | + | 0.430162i | \(0.858456\pi\) | |||||||
\(608\) | 135.324 | + | 854.047i | 0.222572 | + | 1.40468i | ||||
\(609\) | 209.885 | 0.344640 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 52.0320i | 0.0851588i | ||||||||
\(612\) | −194.076 | −0.317118 | ||||||||
\(613\) | 639.666 | 1.04350 | 0.521750 | − | 0.853098i | \(-0.325279\pi\) | ||||
0.521750 | + | 0.853098i | \(0.325279\pi\) | |||||||
\(614\) | 1287.09 | 2.09625 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 26.0233i | 0.0422457i | ||||||||
\(617\) | −200.342 | −0.324704 | −0.162352 | − | 0.986733i | \(-0.551908\pi\) | ||||
−0.162352 | + | 0.986733i | \(0.551908\pi\) | |||||||
\(618\) | 35.5306i | 0.0574929i | ||||||||
\(619\) | −347.156 | −0.560833 | −0.280417 | − | 0.959878i | \(-0.590473\pi\) | ||||
−0.280417 | + | 0.959878i | \(0.590473\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 602.949i | 0.970932i | ||||||||
\(622\) | − | 510.459i | − | 0.820674i | ||||||
\(623\) | 181.239i | 0.290914i | ||||||||
\(624\) | 419.574 | 0.672395 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 391.965i | 0.626143i | ||||||||
\(627\) | −64.2448 | − | 405.458i | −0.102464 | − | 0.646664i | ||||
\(628\) | −799.944 | −1.27380 | ||||||||
\(629\) | 117.536i | 0.186861i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 204.105 | 0.323463 | 0.161732 | − | 0.986835i | \(-0.448292\pi\) | ||||
0.161732 | + | 0.986835i | \(0.448292\pi\) | |||||||
\(632\) | −39.5062 | −0.0625099 | ||||||||
\(633\) | −233.116 | −0.368271 | ||||||||
\(634\) | 1713.71 | 2.70301 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −858.343 | −1.34960 | ||||||||
\(637\) | − | 428.129i | − | 0.672102i | ||||||
\(638\) | 295.660 | 0.463416 | ||||||||
\(639\) | − | 529.382i | − | 0.828454i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 334.435i | − | 0.521740i | −0.965374 | − | 0.260870i | \(-0.915991\pi\) | ||
0.965374 | − | 0.260870i | \(-0.0840094\pi\) | |||||||
\(642\) | 1023.04i | 1.59352i | ||||||||
\(643\) | 22.8316 | 0.0355079 | 0.0177540 | − | 0.999842i | \(-0.494348\pi\) | ||||
0.0177540 | + | 0.999842i | \(0.494348\pi\) | |||||||
\(644\) | 783.069 | 1.21595 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −94.6981 | − | 597.653i | −0.146591 | − | 0.925160i | ||||
\(647\) | −280.968 | −0.434263 | −0.217131 | − | 0.976142i | \(-0.569670\pi\) | ||||
−0.217131 | + | 0.976142i | \(0.569670\pi\) | |||||||
\(648\) | − | 7.20125i | − | 0.0111130i | ||||||
\(649\) | 63.1653i | 0.0973271i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1045.47 | 1.60594 | ||||||||
\(652\) | −704.048 | −1.07983 | ||||||||
\(653\) | −891.423 | −1.36512 | −0.682559 | − | 0.730830i | \(-0.739133\pi\) | ||||
−0.682559 | + | 0.730830i | \(0.739133\pi\) | |||||||
\(654\) | 635.761i | 0.972112i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 664.402i | 1.01281i | ||||||||
\(657\) | −78.3489 | −0.119253 | ||||||||
\(658\) | 109.953i | 0.167102i | ||||||||
\(659\) | − | 734.584i | − | 1.11470i | −0.830279 | − | 0.557348i | \(-0.811819\pi\) | ||
0.830279 | − | 0.557348i | \(-0.188181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 968.622i | − | 1.46539i | −0.680558 | − | 0.732694i | \(-0.738263\pi\) | ||
0.680558 | − | 0.732694i | \(-0.261737\pi\) | |||||||
\(662\) | 542.246 | 0.819102 | ||||||||
\(663\) | −301.225 | −0.454337 | ||||||||
\(664\) | − | 36.7641i | − | 0.0553676i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 126.445 | 0.189857 | ||||||||
\(667\) | − | 219.123i | − | 0.328520i | ||||||
\(668\) | 167.168i | 0.250252i | ||||||||
\(669\) | 457.262 | 0.683500 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 146.988 | 0.219058 | ||||||||
\(672\) | 909.619 | 1.35360 | ||||||||
\(673\) | − | 948.399i | − | 1.40921i | −0.709599 | − | 0.704606i | \(-0.751124\pi\) | ||
0.709599 | − | 0.704606i | \(-0.248876\pi\) | |||||||
\(674\) | −1121.53 | −1.66398 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −70.0940 | −0.103689 | ||||||||
\(677\) | − | 82.3399i | − | 0.121625i | −0.998149 | − | 0.0608123i | \(-0.980631\pi\) | ||
0.998149 | − | 0.0608123i | \(-0.0193691\pi\) | |||||||
\(678\) | − | 152.340i | − | 0.224690i | ||||||
\(679\) | 388.425i | 0.572054i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 533.586 | 0.783533 | ||||||||
\(682\) | 1472.72 | 2.15941 | ||||||||
\(683\) | 10.8842i | 0.0159359i | 0.999968 | + | 0.00796796i | \(0.00253631\pi\) | ||||
−0.999968 | + | 0.00796796i | \(0.997464\pi\) | |||||||
\(684\) | −325.485 | + | 51.5730i | −0.475855 | + | 0.0753991i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 371.499i | 0.541544i | ||||||||
\(687\) | − | 555.596i | − | 0.808727i | ||||||
\(688\) | 716.583 | 1.04155 | ||||||||
\(689\) | 1181.06 | 1.71416 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 188.047 | 0.272138 | 0.136069 | − | 0.990699i | \(-0.456553\pi\) | ||||
0.136069 | + | 0.990699i | \(0.456553\pi\) | |||||||
\(692\) | 1144.97i | 1.65459i | ||||||||
\(693\) | 382.838 | 0.552436 | ||||||||
\(694\) | 583.649i | 0.840993i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.59393i | 0.00947404i | ||||||||
\(697\) | − | 476.995i | − | 0.684354i | ||||||
\(698\) | 1391.33i | 1.99330i | ||||||||
\(699\) | 757.993i | 1.08440i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1184.52 | −1.68976 | −0.844879 | − | 0.534957i | \(-0.820328\pi\) | ||||
−0.844879 | + | 0.534957i | \(0.820328\pi\) | |||||||
\(702\) | 1013.65i | 1.44394i | ||||||||
\(703\) | 31.2335 | + | 197.119i | 0.0444289 | + | 0.280397i | ||||
\(704\) | 664.652 | 0.944108 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1328.51i | 1.88174i | ||||||||
\(707\) | −1019.72 | −1.44232 | ||||||||
\(708\) | −57.1968 | −0.0807864 | ||||||||
\(709\) | −541.289 | −0.763455 | −0.381727 | − | 0.924275i | \(-0.624671\pi\) | ||||
−0.381727 | + | 0.924275i | \(0.624671\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 581.189i | 0.817425i | ||||||||
\(712\) | −5.69395 | −0.00799713 | ||||||||
\(713\) | − | 1091.48i | − | 1.53083i | ||||||
\(714\) | −636.542 | −0.891516 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1266.30i | 1.76857i | ||||||||
\(717\) | − | 0.104571i | − | 0.000145846i | ||||||
\(718\) | − | 1388.19i | − | 1.93341i | ||||||
\(719\) | −388.854 | −0.540826 | −0.270413 | − | 0.962744i | \(-0.587160\pi\) | ||||
−0.270413 | + | 0.962744i | \(0.587160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 52.2998i | − | 0.0725379i | ||||||
\(722\) | −317.636 | − | 977.159i | −0.439939 | − | 1.35341i | ||||
\(723\) | 923.512 | 1.27733 | ||||||||
\(724\) | − | 1033.80i | − | 1.42790i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 143.897 | 0.198206 | ||||||||
\(727\) | −1450.46 | −1.99513 | −0.997565 | − | 0.0697458i | \(-0.977781\pi\) | ||||
−0.997565 | + | 0.0697458i | \(0.977781\pi\) | |||||||
\(728\) | 32.4240 | 0.0445384 | ||||||||
\(729\) | −673.955 | −0.924493 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −514.457 | −0.703772 | ||||||||
\(732\) | 133.099i | 0.181829i | ||||||||
\(733\) | −873.057 | −1.19107 | −0.595537 | − | 0.803328i | \(-0.703061\pi\) | ||||
−0.595537 | + | 0.803328i | \(0.703061\pi\) | |||||||
\(734\) | − | 179.453i | − | 0.244486i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 949.653i | − | 1.29029i | ||||||
\(737\) | 376.584i | 0.510969i | ||||||||
\(738\) | −513.149 | −0.695323 | ||||||||
\(739\) | −456.992 | −0.618393 | −0.309196 | − | 0.950998i | \(-0.600060\pi\) | ||||
−0.309196 | + | 0.950998i | \(0.600060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −505.184 | + | 80.0463i | −0.681760 | + | 0.108025i | ||||
\(742\) | 2495.78 | 3.36359 | ||||||||
\(743\) | 60.6398i | 0.0816148i | 0.999167 | + | 0.0408074i | \(0.0129930\pi\) | ||||
−0.999167 | + | 0.0408074i | \(0.987007\pi\) | |||||||
\(744\) | 32.8453i | 0.0441468i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −392.304 | −0.525877 | ||||||||
\(747\) | −540.848 | −0.724027 | ||||||||
\(748\) | −453.930 | −0.606858 | ||||||||
\(749\) | − | 1505.88i | − | 2.01052i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1177.72i | − | 1.56821i | −0.620629 | − | 0.784104i | \(-0.713123\pi\) | ||
0.620629 | − | 0.784104i | \(-0.286877\pi\) | |||||||
\(752\) | 65.7974 | 0.0874965 | ||||||||
\(753\) | − | 310.855i | − | 0.412822i | ||||||
\(754\) | − | 368.379i | − | 0.488567i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1084.36i | 1.43434i | ||||||||
\(757\) | 112.664 | 0.148830 | 0.0744151 | − | 0.997227i | \(-0.476291\pi\) | ||||
0.0744151 | + | 0.997227i | \(0.476291\pi\) | |||||||
\(758\) | −901.130 | −1.18883 | ||||||||
\(759\) | 450.848i | 0.594002i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −857.698 | −1.12707 | −0.563534 | − | 0.826093i | \(-0.690558\pi\) | ||||
−0.563534 | + | 0.826093i | \(0.690558\pi\) | |||||||
\(762\) | − | 363.942i | − | 0.477615i | ||||||
\(763\) | − | 935.818i | − | 1.22650i | ||||||
\(764\) | −864.055 | −1.13096 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −560.943 | −0.732301 | ||||||||
\(767\) | 78.7012 | 0.102609 | ||||||||
\(768\) | − | 529.853i | − | 0.689912i | ||||||
\(769\) | −146.990 | −0.191144 | −0.0955719 | − | 0.995423i | \(-0.530468\pi\) | ||||
−0.0955719 | + | 0.995423i | \(0.530468\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 432.859 | 0.561426 | ||||||||
\(772\) | − | 464.833i | − | 0.602115i | ||||||
\(773\) | 624.217i | 0.807525i | 0.914864 | + | 0.403762i | \(0.132298\pi\) | ||||
−0.914864 | + | 0.403762i | \(0.867702\pi\) | |||||||
\(774\) | 553.451i | 0.715052i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.2031 | −0.0157256 | ||||||||
\(777\) | 209.946 | 0.270200 | ||||||||
\(778\) | − | 79.1829i | − | 0.101778i | ||||||
\(779\) | −126.755 | − | 799.967i | −0.162715 | − | 1.02692i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1238.19i | − | 1.58538i | ||||||
\(782\) | 664.558i | 0.849819i | ||||||||
\(783\) | 303.433 | 0.387526 | ||||||||
\(784\) | −541.392 | −0.690552 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1391.81 | −1.77076 | ||||||||
\(787\) | 551.370i | 0.700597i | 0.936638 | + | 0.350298i | \(0.113920\pi\) | ||||
−0.936638 | + | 0.350298i | \(0.886080\pi\) | |||||||
\(788\) | −846.277 | −1.07396 | ||||||||
\(789\) | − | 325.590i | − | 0.412661i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 224.239i | 0.283488i | ||||||||
\(792\) | 12.0275i | 0.0151863i | ||||||||
\(793\) | − | 183.140i | − | 0.230946i | ||||||
\(794\) | − | 2000.17i | − | 2.51911i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −746.283 | −0.937541 | ||||||||
\(797\) | 202.295i | 0.253821i | 0.991914 | + | 0.126911i | \(0.0405061\pi\) | ||||
−0.991914 | + | 0.126911i | \(0.959494\pi\) | |||||||
\(798\) | −1067.54 | + | 169.152i | −1.33777 | + | 0.211970i | ||||
\(799\) | −47.2380 | −0.0591214 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 83.7656i | 0.104576i | ||||||||
\(802\) | 840.481 | 1.04798 | ||||||||
\(803\) | −183.252 | −0.228209 | ||||||||
\(804\) | −341.001 | −0.424130 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1834.95i | − | 2.27661i | ||||||
\(807\) | −445.821 | −0.552443 | ||||||||
\(808\) | − | 32.0363i | − | 0.0396489i | ||||||
\(809\) | −1164.20 | −1.43906 | −0.719531 | − | 0.694461i | \(-0.755643\pi\) | ||||
−0.719531 | + | 0.694461i | \(0.755643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 617.970i | 0.761985i | 0.924578 | + | 0.380993i | \(0.124418\pi\) | ||||
−0.924578 | + | 0.380993i | \(0.875582\pi\) | |||||||
\(812\) | − | 394.079i | − | 0.485318i | ||||||
\(813\) | 525.801i | 0.646741i | ||||||||
\(814\) | 295.744 | 0.363322 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 380.916i | 0.466809i | ||||||||
\(817\) | −862.795 | + | 136.710i | −1.05605 | + | 0.167331i | ||||
\(818\) | −1058.04 | −1.29345 | ||||||||
\(819\) | − | 477.000i | − | 0.582417i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 255.141 | 0.310769 | 0.155384 | − | 0.987854i | \(-0.450338\pi\) | ||||
0.155384 | + | 0.987854i | \(0.450338\pi\) | |||||||
\(822\) | 38.8374 | 0.0472474 | ||||||||
\(823\) | 658.923 | 0.800636 | 0.400318 | − | 0.916376i | \(-0.368900\pi\) | ||||
0.400318 | + | 0.916376i | \(0.368900\pi\) | |||||||
\(824\) | 1.64309 | 0.00199405 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 166.310 | 0.201343 | ||||||||
\(827\) | − | 633.264i | − | 0.765736i | −0.923803 | − | 0.382868i | \(-0.874936\pi\) | ||
0.923803 | − | 0.382868i | \(-0.125064\pi\) | |||||||
\(828\) | 361.921 | 0.437103 | ||||||||
\(829\) | − | 459.961i | − | 0.554838i | −0.960749 | − | 0.277419i | \(-0.910521\pi\) | ||
0.960749 | − | 0.277419i | \(-0.0894790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1001.98i | 1.20576i | ||||||||
\(832\) | − | 828.128i | − | 0.995346i | ||||||
\(833\) | 388.682 | 0.466605 | ||||||||
\(834\) | 1274.23 | 1.52785 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −761.284 | + | 120.625i | −0.910627 | + | 0.144289i | ||||
\(837\) | 1511.44 | 1.80578 | ||||||||
\(838\) | 310.927i | 0.371035i | ||||||||
\(839\) | − | 1033.89i | − | 1.23228i | −0.787635 | − | 0.616142i | \(-0.788695\pi\) | ||
0.787635 | − | 0.616142i | \(-0.211305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 730.727 | 0.868878 | ||||||||
\(842\) | −2170.33 | −2.57759 | ||||||||
\(843\) | −544.903 | −0.646386 | ||||||||
\(844\) | 437.696i | 0.518597i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 50.8184i | 0.0600690i | ||||||||
\(847\) | −211.812 | −0.250073 | ||||||||
\(848\) | − | 1493.51i | − | 1.76122i | ||||||
\(849\) | − | 798.565i | − | 0.940595i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 219.186i | − | 0.257563i | ||||||
\(852\) | 1121.19 | 1.31595 | ||||||||
\(853\) | 333.243 | 0.390671 | 0.195336 | − | 0.980736i | \(-0.437420\pi\) | ||||
0.195336 | + | 0.980736i | \(0.437420\pi\) | |||||||
\(854\) | − | 387.008i | − | 0.453171i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 47.3099 | 0.0552685 | ||||||||
\(857\) | − | 55.2946i | − | 0.0645211i | −0.999479 | − | 0.0322605i | \(-0.989729\pi\) | ||
0.999479 | − | 0.0322605i | \(-0.0102706\pi\) | |||||||
\(858\) | 757.944i | 0.883385i | ||||||||
\(859\) | 417.893 | 0.486488 | 0.243244 | − | 0.969965i | \(-0.421788\pi\) | ||||
0.243244 | + | 0.969965i | \(0.421788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −852.020 | −0.989570 | ||||||||
\(862\) | −375.396 | −0.435495 | ||||||||
\(863\) | − | 1042.76i | − | 1.20830i | −0.796871 | − | 0.604150i | \(-0.793513\pi\) | ||
0.796871 | − | 0.604150i | \(-0.206487\pi\) | |||||||
\(864\) | 1315.04 | 1.52204 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1142.00 | 1.31871 | ||||||||
\(867\) | 357.759i | 0.412640i | ||||||||
\(868\) | − | 1962.96i | − | 2.26147i | ||||||
\(869\) | 1359.36i | 1.56428i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 469.208 | 0.538700 | ||||||||
\(872\) | 29.4004 | 0.0337161 | ||||||||
\(873\) | 179.523i | 0.205639i | ||||||||
\(874\) | 176.597 | + | 1114.53i | 0.202056 | + | 1.27520i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 165.937i | − | 0.189425i | ||||||
\(877\) | − | 143.302i | − | 0.163400i | −0.996657 | − | 0.0817002i | \(-0.973965\pi\) | ||
0.996657 | − | 0.0817002i | \(-0.0260350\pi\) | |||||||
\(878\) | 752.366 | 0.856908 | ||||||||
\(879\) | 378.057 | 0.430099 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −944.916 | −1.07255 | −0.536275 | − | 0.844043i | \(-0.680169\pi\) | ||||
−0.536275 | + | 0.844043i | \(0.680169\pi\) | |||||||
\(882\) | − | 418.142i | − | 0.474084i | ||||||
\(883\) | 1406.88 | 1.59329 | 0.796646 | − | 0.604446i | \(-0.206605\pi\) | ||||
0.796646 | + | 0.604446i | \(0.206605\pi\) | |||||||
\(884\) | 565.577i | 0.639793i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 1284.43i | − | 1.44969i | ||||||
\(887\) | − | 437.734i | − | 0.493500i | −0.969079 | − | 0.246750i | \(-0.920637\pi\) | ||
0.969079 | − | 0.246750i | \(-0.0793626\pi\) | |||||||
\(888\) | 6.59582i | 0.00742772i | ||||||||
\(889\) | 535.710i | 0.602599i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −247.786 | −0.278098 | ||||||||
\(892\) | − | 858.549i | − | 0.962499i | ||||||
\(893\) | −79.2227 | + | 12.5528i | −0.0887152 | + | 0.0140569i | ||||
\(894\) | 519.406 | 0.580991 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 84.1564i | − | 0.0939246i | ||||||
\(897\) | 561.737 | 0.626240 | ||||||||
\(898\) | 445.807 | 0.496445 | ||||||||
\(899\) | −549.287 | −0.610998 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1072.24i | 1.19005i | ||||||||
\(902\) | −1200.22 | −1.33062 | ||||||||
\(903\) | 918.936i | 1.01765i | ||||||||
\(904\) | −7.04488 | −0.00779300 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 1177.36i | − | 1.29951i | ||||||
\(907\) | 174.898i | 0.192832i | 0.995341 | + | 0.0964158i | \(0.0307378\pi\) | ||||
−0.995341 | + | 0.0964158i | \(0.969262\pi\) | |||||||
\(908\) | − | 1001.85i | − | 1.10336i | ||||||
\(909\) | −471.296 | −0.518478 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 475.064i | 0.521476i | 0.965410 | + | 0.260738i | \(0.0839658\pi\) | ||||
−0.965410 | + | 0.260738i | \(0.916034\pi\) | |||||||
\(912\) | 101.223 | + | 638.833i | 0.110990 | + | 0.700475i | ||||
\(913\) | −1265.00 | −1.38555 | ||||||||
\(914\) | 2578.96i | 2.82162i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1043.18 | −1.13884 | ||||||||
\(917\) | 2048.70 | 2.23413 | ||||||||
\(918\) | −920.254 | −1.00246 | ||||||||
\(919\) | 456.862 | 0.497130 | 0.248565 | − | 0.968615i | \(-0.420041\pi\) | ||||
0.248565 | + | 0.968615i | \(0.420041\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 987.714 | 1.07244 | ||||||||
\(922\) | 483.098i | 0.523967i | ||||||||
\(923\) | −1542.73 | −1.67143 | ||||||||
\(924\) | 810.820i | 0.877511i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 591.991i | 0.639299i | ||||||||
\(927\) | − | 24.1721i | − | 0.0260756i | ||||||
\(928\) | −477.912 | −0.514991 | ||||||||
\(929\) | 714.272 | 0.768861 | 0.384430 | − | 0.923154i | \(-0.374398\pi\) | ||||
0.384430 | + | 0.923154i | \(0.374398\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 651.858 | − | 103.287i | 0.700170 | − | 0.110942i | ||||
\(932\) | 1423.20 | 1.52704 | ||||||||
\(933\) | − | 391.725i | − | 0.419855i | ||||||
\(934\) | − | 1364.45i | − | 1.46087i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14.9858 | 0.0160105 | ||||||||
\(937\) | −711.794 | −0.759652 | −0.379826 | − | 0.925058i | \(-0.624016\pi\) | ||||
−0.379826 | + | 0.925058i | \(0.624016\pi\) | |||||||
\(938\) | 991.520 | 1.05706 | ||||||||
\(939\) | 300.793i | 0.320334i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1055.43i | − | 1.12161i | −0.827950 | − | 0.560803i | \(-0.810493\pi\) | ||
0.827950 | − | 0.560803i | \(-0.189507\pi\) | |||||||
\(942\) | −1212.63 | −1.28729 | ||||||||
\(943\) | 889.520i | 0.943287i | ||||||||
\(944\) | − | 99.5221i | − | 0.105426i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1294.48i | 1.36837i | ||||||||
\(947\) | 611.188 | 0.645394 | 0.322697 | − | 0.946502i | \(-0.395411\pi\) | ||||
0.322697 | + | 0.946502i | \(0.395411\pi\) | |||||||
\(948\) | −1230.91 | −1.29843 | ||||||||
\(949\) | 228.324i | 0.240595i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1315.10 | 1.38286 | ||||||||
\(952\) | 29.4365i | 0.0309207i | ||||||||
\(953\) | 847.554i | 0.889354i | 0.895691 | + | 0.444677i | \(0.146682\pi\) | ||||
−0.895691 | + | 0.444677i | \(0.853318\pi\) | |||||||
\(954\) | 1153.51 | 1.20913 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.196342 | −0.000205379 | ||||||||
\(957\) | 226.889 | 0.237083 | ||||||||
\(958\) | 2027.89i | 2.11679i | ||||||||
\(959\) | −57.1673 | −0.0596114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1775.07 | −1.84711 | ||||||||
\(962\) | − | 368.485i | − | 0.383040i | ||||||
\(963\) | − | 695.991i | − | 0.722732i | ||||||
\(964\) | − | 1733.98i | − | 1.79873i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1187.05 | 1.22883 | ||||||||
\(967\) | 293.882 | 0.303911 | 0.151955 | − | 0.988387i | \(-0.451443\pi\) | ||||
0.151955 | + | 0.988387i | \(0.451443\pi\) | |||||||
\(968\) | − | 6.65446i | − | 0.00687444i | ||||||
\(969\) | −72.6711 | − | 458.638i | −0.0749960 | − | 0.473311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1289.96i | 1.32849i | 0.747517 | + | 0.664243i | \(0.231246\pi\) | ||||
−0.747517 | + | 0.664243i | \(0.768754\pi\) | |||||||
\(972\) | 842.127i | 0.866386i | ||||||||
\(973\) | −1875.62 | −1.92767 | ||||||||
\(974\) | −97.9645 | −0.100580 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −231.591 | −0.237286 | ||||||||
\(977\) | − | 362.429i | − | 0.370961i | −0.982648 | − | 0.185481i | \(-0.940616\pi\) | ||
0.982648 | − | 0.185481i | \(-0.0593842\pi\) | |||||||
\(978\) | −1067.26 | −1.09127 | ||||||||
\(979\) | 195.922i | 0.200124i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 432.519i | − | 0.440896i | ||||||
\(982\) | − | 1029.22i | − | 1.04808i | ||||||
\(983\) | 236.553i | 0.240644i | 0.992735 | + | 0.120322i | \(0.0383927\pi\) | ||||
−0.992735 | + | 0.120322i | \(0.961607\pi\) | |||||||
\(984\) | − | 26.7677i | − | 0.0272030i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 334.438 | 0.339187 | ||||||||
\(987\) | 84.3776i | 0.0854890i | ||||||||
\(988\) | 150.294 | + | 948.528i | 0.152119 | + | 0.960048i | ||||
\(989\) | 959.381 | 0.970052 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 328.650i | 0.331635i | 0.986156 | + | 0.165817i | \(0.0530262\pi\) | ||||
−0.986156 | + | 0.165817i | \(0.946974\pi\) | |||||||
\(992\) | −2380.54 | −2.39974 | ||||||||
\(993\) | 416.118 | 0.419051 | ||||||||
\(994\) | −3260.06 | −3.27973 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 1145.47i | − | 1.15007i | ||||||
\(997\) | 537.051 | 0.538667 | 0.269333 | − | 0.963047i | \(-0.413197\pi\) | ||||
0.269333 | + | 0.963047i | \(0.413197\pi\) | |||||||
\(998\) | 540.718i | 0.541801i | ||||||||
\(999\) | 303.520 | 0.303824 |
(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 | 475.3.c.g.151.2 | 12 | ||
5.2 | odd | 4 | 475.3.d.c.474.21 | 24 | |||
5.3 | odd | 4 | 475.3.d.c.474.4 | 24 | |||
5.4 | even | 2 | 95.3.c.a.56.11 | yes | 12 | ||
15.14 | odd | 2 | 855.3.e.a.721.2 | 12 | |||
19.18 | odd | 2 | inner | 475.3.c.g.151.11 | 12 | ||
20.19 | odd | 2 | 1520.3.h.a.721.5 | 12 | |||
95.18 | even | 4 | 475.3.d.c.474.22 | 24 | |||
95.37 | even | 4 | 475.3.d.c.474.3 | 24 | |||
95.94 | odd | 2 | 95.3.c.a.56.2 | ✓ | 12 | ||
285.284 | even | 2 | 855.3.e.a.721.11 | 12 | |||
380.379 | even | 2 | 1520.3.h.a.721.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.3.c.a.56.2 | ✓ | 12 | 95.94 | odd | 2 | ||
95.3.c.a.56.11 | yes | 12 | 5.4 | even | 2 | ||
475.3.c.g.151.2 | 12 | 1.1 | even | 1 | trivial | ||
475.3.c.g.151.11 | 12 | 19.18 | odd | 2 | inner | ||
475.3.d.c.474.3 | 24 | 95.37 | even | 4 | |||
475.3.d.c.474.4 | 24 | 5.3 | odd | 4 | |||
475.3.d.c.474.21 | 24 | 5.2 | odd | 4 | |||
475.3.d.c.474.22 | 24 | 95.18 | even | 4 | |||
855.3.e.a.721.2 | 12 | 15.14 | odd | 2 | |||
855.3.e.a.721.11 | 12 | 285.284 | even | 2 | |||
1520.3.h.a.721.5 | 12 | 20.19 | odd | 2 | |||
1520.3.h.a.721.8 | 12 | 380.379 | even | 2 |