Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,4,Mod(25,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("168.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.q (of order \(3\), degree \(2\), 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: | \(9.91232088096\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 173x^{6} + 9457x^{4} + 168048x^{2} + 746496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(8.34231i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.121 |
Dual form | 168.4.q.f.25.2 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.363171 | + | 0.629031i | −0.0324830 | + | 0.0562622i | −0.881810 | − | 0.471605i | \(-0.843675\pi\) |
0.849327 | + | 0.527867i | \(0.177008\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.1420 | + | 3.72380i | −0.979578 | + | 0.201066i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 32.2447 | + | 55.8495i | 0.883832 | + | 1.53084i | 0.847046 | + | 0.531519i | \(0.178379\pi\) |
0.0367856 | + | 0.999323i | \(0.488288\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 71.8475 | 1.53284 | 0.766420 | − | 0.642340i | \(-0.222036\pi\) | ||||
0.766420 | + | 0.642340i | \(0.222036\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.17903 | 0.0375081 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −24.4517 | − | 42.3515i | −0.348847 | − | 0.604221i | 0.637198 | − | 0.770700i | \(-0.280093\pi\) |
−0.986045 | + | 0.166479i | \(0.946760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.1984 | + | 29.7885i | −0.207663 | + | 0.359682i | −0.950978 | − | 0.309259i | \(-0.899919\pi\) |
0.743315 | + | 0.668941i | \(0.233252\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 36.8878 | + | 41.5487i | 0.383313 | + | 0.431746i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.451675 | − | 0.782324i | 0.00409482 | − | 0.00709243i | −0.863971 | − | 0.503542i | \(-0.832030\pi\) |
0.868066 | + | 0.496450i | \(0.165363\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 62.2362 | + | 107.796i | 0.497890 | + | 0.862370i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 226.686 | 1.45154 | 0.725769 | − | 0.687939i | \(-0.241484\pi\) | ||||
0.725769 | + | 0.687939i | \(0.241484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 137.898 | + | 238.846i | 0.798940 | + | 1.38380i | 0.920307 | + | 0.391197i | \(0.127939\pi\) |
−0.121367 | + | 0.992608i | \(0.538728\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 96.7342 | − | 167.549i | 0.510281 | − | 0.883832i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.24627 | − | 12.7643i | 0.0205072 | − | 0.0616444i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −147.605 | + | 255.658i | −0.655839 | + | 1.13595i | 0.325844 | + | 0.945423i | \(0.394352\pi\) |
−0.981683 | + | 0.190522i | \(0.938982\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −107.771 | − | 186.665i | −0.442493 | − | 0.766420i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 186.604 | 0.710798 | 0.355399 | − | 0.934715i | \(-0.384345\pi\) | ||||
0.355399 | + | 0.934715i | \(0.384345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −455.317 | −1.61477 | −0.807386 | − | 0.590023i | \(-0.799119\pi\) | ||||
−0.807386 | + | 0.590023i | \(0.799119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.26854 | − | 5.66128i | −0.0108277 | − | 0.0187541i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −141.167 | + | 244.509i | −0.438114 | + | 0.758835i | −0.997544 | − | 0.0700420i | \(-0.977687\pi\) |
0.559430 | + | 0.828877i | \(0.311020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 315.267 | − | 135.115i | 0.919145 | − | 0.393920i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −73.3550 | + | 127.055i | −0.201407 | + | 0.348847i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −178.107 | − | 308.491i | −0.461602 | − | 0.799518i | 0.537439 | − | 0.843303i | \(-0.319392\pi\) |
−0.999041 | + | 0.0437844i | \(0.986059\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −46.8414 | −0.114838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 103.191 | 0.239788 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −364.685 | − | 631.653i | −0.804711 | − | 1.39380i | −0.916486 | − | 0.400066i | \(-0.868987\pi\) |
0.111776 | − | 0.993733i | \(-0.464346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −137.176 | + | 237.596i | −0.287928 | + | 0.498706i | −0.973315 | − | 0.229473i | \(-0.926300\pi\) |
0.685387 | + | 0.728179i | \(0.259633\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 52.6150 | − | 158.160i | 0.105220 | − | 0.316291i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −26.0929 | + | 45.1943i | −0.0497912 | + | 0.0862409i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −96.6361 | − | 167.379i | −0.176209 | − | 0.305202i | 0.764370 | − | 0.644778i | \(-0.223050\pi\) |
−0.940579 | + | 0.339575i | \(0.889717\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.71005 | −0.00472829 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.5277 | 0.0677429 | 0.0338715 | − | 0.999426i | \(-0.489216\pi\) | ||||
0.0338715 | + | 0.999426i | \(0.489216\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 103.236 | + | 178.810i | 0.165519 | + | 0.286687i | 0.936839 | − | 0.349760i | \(-0.113737\pi\) |
−0.771320 | + | 0.636447i | \(0.780403\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 186.709 | − | 323.389i | 0.287457 | − | 0.497890i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −792.958 | − | 893.151i | −1.17358 | − | 1.32187i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −468.870 | + | 812.107i | −0.667747 | + | 1.15657i | 0.310785 | + | 0.950480i | \(0.399408\pi\) |
−0.978533 | + | 0.206092i | \(0.933925\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 911.607 | 1.20556 | 0.602782 | − | 0.797906i | \(-0.294059\pi\) | ||||
0.602782 | + | 0.797906i | \(0.294059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 35.5206 | 0.0453264 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −340.029 | − | 588.948i | −0.419023 | − | 0.725769i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 474.988 | − | 822.703i | 0.565715 | − | 0.979846i | −0.431268 | − | 0.902224i | \(-0.641934\pi\) |
0.996983 | − | 0.0776226i | \(-0.0247329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1303.46 | + | 267.546i | −1.50154 | + | 0.308203i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 413.693 | − | 716.537i | 0.461268 | − | 0.798940i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.4919 | − | 21.6367i | −0.0134910 | − | 0.0233671i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39.4687 | 0.0413138 | 0.0206569 | − | 0.999787i | \(-0.493424\pi\) | ||||
0.0206569 | + | 0.999787i | \(0.493424\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −580.405 | −0.589221 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 158.437 | + | 274.421i | 0.156090 | + | 0.270356i | 0.933455 | − | 0.358694i | \(-0.116778\pi\) |
−0.777365 | + | 0.629049i | \(0.783444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 161.317 | − | 279.409i | 0.154321 | − | 0.267291i | −0.778491 | − | 0.627656i | \(-0.784014\pi\) |
0.932811 | + | 0.360365i | \(0.117348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −39.5320 | + | 8.11426i | −0.0367421 | + | 0.00754163i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −340.726 | + | 590.154i | −0.307843 | + | 0.533200i | −0.977890 | − | 0.209119i | \(-0.932940\pi\) |
0.670047 | + | 0.742318i | \(0.266274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 227.984 | + | 394.879i | 0.200338 | + | 0.346996i | 0.948637 | − | 0.316365i | \(-0.102463\pi\) |
−0.748299 | + | 0.663361i | \(0.769129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 885.627 | 0.757297 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −796.025 | −0.662688 | −0.331344 | − | 0.943510i | \(-0.607502\pi\) | ||||
−0.331344 | + | 0.943510i | \(0.607502\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.328071 | + | 0.568235i | 0.000266024 | + | 0.000460767i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −323.314 | + | 559.996i | −0.255473 | + | 0.442493i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 601.312 | + | 677.290i | 0.463212 | + | 0.521740i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1413.95 | + | 2449.03i | −1.06232 | + | 1.83999i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −279.907 | − | 484.813i | −0.205190 | − | 0.355399i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −181.202 | −0.129658 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2333.92 | 1.63072 | 0.815362 | − | 0.578952i | \(-0.196538\pi\) | ||||
0.815362 | + | 0.578952i | \(0.196538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 682.976 | + | 1182.95i | 0.466145 | + | 0.807386i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 943.489 | − | 1634.17i | 0.629259 | − | 1.08991i | −0.358441 | − | 0.933552i | \(-0.616692\pi\) |
0.987701 | − | 0.156357i | \(-0.0499750\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 201.088 | − | 604.468i | 0.131102 | − | 0.394091i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.80562 | + | 16.9838i | −0.00625136 | + | 0.0108277i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1473.63 | − | 2552.40i | −0.918983 | − | 1.59173i | −0.800963 | − | 0.598714i | \(-0.795678\pi\) |
−0.118021 | − | 0.993011i | \(-0.537655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 955.433 | 0.583013 | 0.291506 | − | 0.956569i | \(-0.405844\pi\) | ||||
0.291506 | + | 0.956569i | \(0.405844\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 847.003 | 0.505890 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2316.70 | + | 4012.65i | 1.35477 | + | 2.34654i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −82.3259 | + | 142.593i | −0.0471503 | + | 0.0816667i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −823.938 | − | 616.415i | −0.462294 | − | 0.345857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1091.87 | + | 1891.17i | −0.600332 | + | 1.03981i | 0.392439 | + | 0.919778i | \(0.371631\pi\) |
−0.992771 | + | 0.120027i | \(0.961702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −202.360 | − | 350.497i | −0.109058 | − | 0.188894i | 0.806331 | − | 0.591465i | \(-0.201450\pi\) |
−0.915389 | + | 0.402570i | \(0.868117\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 440.130 | 0.232565 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −200.322 | −0.103808 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 464.791 | + | 805.042i | 0.236270 | + | 0.409231i | 0.959641 | − | 0.281228i | \(-0.0907418\pi\) |
−0.723371 | + | 0.690459i | \(0.757408\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −534.322 | + | 925.472i | −0.266506 | + | 0.461602i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.28108 | + | 15.8749i | −0.00258514 | + | 0.00777092i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 712.840 | − | 1234.68i | 0.342540 | − | 0.593296i | −0.642364 | − | 0.766400i | \(-0.722046\pi\) |
0.984904 | + | 0.173104i | \(0.0553796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 70.2621 | + | 121.698i | 0.0331509 | + | 0.0574190i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4185.15 | 1.93926 | 0.969631 | − | 0.244572i | \(-0.0786474\pi\) | ||||
0.969631 | + | 0.244572i | \(0.0786474\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2965.07 | 1.34960 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −154.786 | − | 268.097i | −0.0692209 | − | 0.119894i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1117.78 | + | 1936.05i | −0.491231 | + | 0.850837i | −0.999949 | − | 0.0100961i | \(-0.996786\pi\) |
0.508718 | + | 0.860933i | \(0.330120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1530.50 | − | 1723.89i | −0.661115 | − | 0.744650i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1094.05 | + | 1894.96i | −0.464600 | + | 0.804711i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 470.740 | + | 815.345i | 0.196563 | + | 0.340457i | 0.947412 | − | 0.320017i | \(-0.103689\pi\) |
−0.750849 | + | 0.660474i | \(0.770355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −467.540 | −0.192000 | −0.0960000 | − | 0.995381i | \(-0.530605\pi\) | ||||
−0.0960000 | + | 0.995381i | \(0.530605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 823.058 | 0.332471 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −107.211 | − | 185.696i | −0.0426072 | − | 0.0737979i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1576.88 | − | 2731.23i | 0.616645 | − | 1.06806i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −489.835 | + | 100.543i | −0.188520 | + | 0.0386953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −137.701 | + | 238.506i | −0.0521660 | + | 0.0903542i | −0.890929 | − | 0.454142i | \(-0.849946\pi\) |
0.838763 | + | 0.544496i | \(0.183279\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −820.148 | − | 1420.54i | −0.305884 | − | 0.529806i | 0.671574 | − | 0.740937i | \(-0.265619\pi\) |
−0.977458 | + | 0.211131i | \(0.932285\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 156.558 | 0.0574940 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1303.88 | 0.471560 | 0.235780 | − | 0.971806i | \(-0.424236\pi\) | ||||
0.235780 | + | 0.971806i | \(0.424236\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 663.678 | + | 1149.52i | 0.236417 | + | 0.409485i | 0.959683 | − | 0.281083i | \(-0.0906937\pi\) |
−0.723267 | + | 0.690569i | \(0.757360\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −289.908 | + | 502.136i | −0.101734 | + | 0.176209i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4112.55 | + | 844.135i | −1.42189 | + | 0.291855i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −67.7693 | + | 117.380i | −0.0230889 | + | 0.0399911i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.06508 | + | 7.04092i | 0.00136494 | + | 0.00236414i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2218.23 | −0.734155 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4753.28 | −1.55085 | −0.775426 | − | 0.631439i | \(-0.782465\pi\) | ||||
−0.775426 | + | 0.631439i | \(0.782465\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −60.7915 | − | 105.294i | −0.0195557 | − | 0.0338715i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 165.358 | − | 286.408i | 0.0524527 | − | 0.0908507i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3391.16 | − | 3819.64i | −1.06086 | − | 1.19490i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 309.709 | − | 536.431i | 0.0955624 | − | 0.165519i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1756.79 | − | 3042.85i | −0.534727 | − | 0.926174i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 513.149 | 0.154094 | 0.0770470 | − | 0.997027i | \(-0.475451\pi\) | ||||
0.0770470 | + | 0.997027i | \(0.475451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1120.25 | −0.331926 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1654.67 | − | 2865.97i | −0.483808 | − | 0.837980i | 0.516019 | − | 0.856577i | \(-0.327413\pi\) |
−0.999827 | + | 0.0185972i | \(0.994080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2954.73 | − | 5117.75i | 0.852639 | − | 1.47681i | −0.0261800 | − | 0.999657i | \(-0.508334\pi\) |
0.878819 | − | 0.477156i | \(-0.158332\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1131.04 | + | 3399.89i | −0.322151 | + | 0.968382i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 176.786 | − | 306.202i | 0.0497065 | − | 0.0860943i | −0.840102 | − | 0.542429i | \(-0.817505\pi\) |
0.889808 | + | 0.456335i | \(0.150838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −102.536 | − | 177.597i | −0.0284625 | − | 0.0492985i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2813.22 | 0.771048 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1652.55 | −0.447259 | −0.223629 | − | 0.974674i | \(-0.571791\pi\) | ||||
−0.223629 | + | 0.974674i | \(0.571791\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1553.47 | + | 2690.69i | 0.415220 | + | 0.719182i | 0.995452 | − | 0.0952696i | \(-0.0303713\pi\) |
−0.580232 | + | 0.814451i | \(0.697038\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −29.5044 | + | 247.382i | −0.00769374 | + | 0.0645088i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1235.66 | + | 2140.23i | −0.318313 | + | 0.551335i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1367.41 | − | 2368.42i | −0.348016 | − | 0.602782i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1771.77 | 0.445551 | 0.222776 | − | 0.974870i | \(-0.428488\pi\) | ||||
0.222776 | + | 0.974870i | \(0.428488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 58.2566 | 0.0144765 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −53.2808 | − | 92.2851i | −0.0130846 | − | 0.0226632i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −739.063 | + | 1280.09i | −0.179383 | + | 0.310701i | −0.941669 | − | 0.336539i | \(-0.890743\pi\) |
0.762286 | + | 0.647240i | \(0.224077\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1725.82 | − | 5187.81i | 0.414044 | − | 1.24461i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1020.09 | + | 1766.84i | −0.241923 | + | 0.419023i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 715.987 | + | 1240.13i | 0.167869 | + | 0.290758i | 0.937671 | − | 0.347525i | \(-0.112978\pi\) |
−0.769801 | + | 0.638284i | \(0.779645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 258.734 | 0.0599769 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2849.93 | −0.653231 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −142.699 | − | 247.162i | −0.0323439 | − | 0.0560213i | 0.849400 | − | 0.527749i | \(-0.176964\pi\) |
−0.881744 | + | 0.471728i | \(0.843631\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2624.66 | − | 4546.05i | 0.588328 | − | 1.01901i | −0.406123 | − | 0.913818i | \(-0.633120\pi\) |
0.994452 | − | 0.105196i | \(-0.0335470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2650.29 | + | 2985.17i | 0.587557 | + | 0.661797i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4013.58 | + | 6951.72i | −0.880102 | + | 1.52438i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3573.93 | − | 6190.24i | −0.775224 | − | 1.34273i | −0.934669 | − | 0.355520i | \(-0.884304\pi\) |
0.159445 | − | 0.987207i | \(-0.449029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2482.16 | −0.532627 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4228.36 | 0.897661 | 0.448831 | − | 0.893617i | \(-0.351841\pi\) | ||||
0.448831 | + | 0.893617i | \(0.351841\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4171.19 | − | 7224.71i | −0.876154 | − | 1.51754i | −0.855528 | − | 0.517756i | \(-0.826768\pi\) |
−0.0206255 | − | 0.999787i | \(-0.506566\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −37.4758 | + | 64.9100i | −0.00778904 | + | 0.0134910i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3385.38 | + | 694.878i | −0.696282 | + | 0.142918i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1260.73 | − | 2183.65i | 0.256611 | − | 0.444464i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −59.2030 | − | 102.543i | −0.0119263 | − | 0.0206569i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5038.84 | 1.00468 | 0.502342 | − | 0.864669i | \(-0.332472\pi\) | ||||
0.502342 | + | 0.864669i | \(0.332472\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 529.772 | 0.104558 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 870.608 | + | 1507.94i | 0.170094 | + | 0.294611i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.4517 | − | 56.2081i | 0.00627670 | − | 0.0108716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8260.38 | − | 1695.51i | 1.58180 | − | 0.324677i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 475.311 | − | 823.263i | 0.0901186 | − | 0.156090i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −99.6369 | − | 172.576i | −0.0187055 | − | 0.0323990i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4869.67 | −0.905300 | −0.452650 | − | 0.891688i | \(-0.649521\pi\) | ||||
−0.452650 | + | 0.891688i | \(0.649521\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −967.901 | −0.178194 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 726.421 | + | 1258.20i | 0.132449 | + | 0.229408i | 0.924620 | − | 0.380891i | \(-0.124383\pi\) |
−0.792171 | + | 0.610299i | \(0.791049\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2848.14 | + | 4933.12i | −0.514333 | + | 0.890850i | 0.485529 | + | 0.874221i | \(0.338627\pi\) |
−0.999862 | + | 0.0166299i | \(0.994706\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 80.3794 | + | 90.5356i | 0.0143774 | + | 0.0161940i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1735.73 | − | 3006.38i | 0.307535 | − | 0.532666i | −0.670288 | − | 0.742101i | \(-0.733829\pi\) |
0.977822 | + | 0.209435i | \(0.0671626\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7309.44 | + | 12660.3i | 1.28291 | + | 2.22207i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2044.35 | 0.355466 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1682.12 | 0.289770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4471.52 | + | 7744.90i | 0.763185 | + | 1.32188i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 683.951 | − | 1184.64i | 0.115665 | − | 0.200338i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1650.56 | − | 4961.56i | 0.276590 | − | 0.831428i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3127.19 | + | 5416.45i | −0.519293 | + | 0.899441i | 0.480456 | + | 0.877019i | \(0.340471\pi\) |
−0.999749 | + | 0.0224223i | \(0.992862\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1328.44 | − | 2300.93i | −0.218613 | − | 0.378649i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 140.382 | 0.0228951 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8006.96 | 1.29426 | 0.647132 | − | 0.762378i | \(-0.275968\pi\) | ||||
0.647132 | + | 0.762378i | \(0.275968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1194.04 | + | 2068.13i | 0.191302 | + | 0.331344i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8892.94 | + | 15403.0i | −1.41226 | + | 2.44610i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5216.44 | + | 3625.25i | −0.821169 | + | 0.570685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.984212 | − | 1.70471i | 0.000153589 | − | 0.000266024i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3817.80 | − | 6612.62i | −0.590634 | − | 1.02301i | −0.994147 | − | 0.108034i | \(-0.965544\pi\) |
0.403513 | − | 0.914974i | \(-0.367789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10358.0 | −1.58869 | −0.794345 | − | 0.607468i | \(-0.792185\pi\) | ||||
−0.794345 | + | 0.607468i | \(0.792185\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1939.88 | 0.294995 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1692.12 | − | 2930.83i | −0.255134 | − | 0.441905i | 0.709798 | − | 0.704405i | \(-0.248786\pi\) |
−0.964932 | + | 0.262500i | \(0.915453\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.7185 | + | 25.4931i | −0.00220049 | + | 0.00381137i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 857.683 | − | 2578.19i | 0.127152 | − | 0.382219i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4097.31 | − | 7096.74i | 0.602361 | − | 1.04332i | −0.390102 | − | 0.920772i | \(-0.627560\pi\) |
0.992463 | − | 0.122548i | \(-0.0391065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2837.93 | + | 4915.44i | 0.413752 | + | 0.716640i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8483.67 | 1.22666 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −149.970 | −0.0215062 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −402.755 | − | 697.592i | −0.0572851 | − | 0.0992208i | 0.835961 | − | 0.548789i | \(-0.184911\pi\) |
−0.893246 | + | 0.449569i | \(0.851578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −839.720 | + | 1454.44i | −0.118466 | + | 0.205190i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4379.99 | + | 4933.41i | 0.612931 | + | 0.690377i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3952.86 | + | 6846.55i | −0.548716 | + | 0.950404i | 0.449647 | + | 0.893206i | \(0.351550\pi\) |
−0.998363 | + | 0.0571977i | \(0.981783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 271.803 | + | 470.777i | 0.0374290 | + | 0.0648289i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16286.8 | 2.22497 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3324.24 | 0.450540 | 0.225270 | − | 0.974296i | \(-0.427674\pi\) | ||||
0.225270 | + | 0.974296i | \(0.427674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3500.88 | − | 6063.70i | −0.470749 | − | 0.815362i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4235.38 | − | 7335.90i | 0.565060 | − | 0.978712i | −0.431984 | − | 0.901881i | \(-0.642186\pi\) |
0.997044 | − | 0.0768310i | \(-0.0244802\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 849.798 | − | 174.428i | 0.112493 | − | 0.0230901i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2048.93 | − | 3548.85i | 0.269129 | − | 0.466145i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3954.20 | + | 6848.88i | 0.515388 | + | 0.892678i | 0.999840 | + | 0.0178606i | \(0.00568551\pi\) |
−0.484452 | + | 0.874818i | \(0.660981\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.1769 | −0.00571386 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5660.93 | −0.726606 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −340.560 | − | 589.868i | −0.0433809 | − | 0.0751379i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4890.79 | − | 8471.10i | 0.618292 | − | 1.07091i | −0.371506 | − | 0.928431i | \(-0.621158\pi\) |
0.989797 | − | 0.142482i | \(-0.0455083\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1872.09 | + | 384.261i | −0.234891 | + | 0.0482134i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 397.827 | − | 689.056i | 0.0495424 | − | 0.0858100i | −0.840191 | − | 0.542291i | \(-0.817557\pi\) |
0.889733 | + | 0.456481i | \(0.150890\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9907.60 | + | 17160.5i | 1.22465 | + | 2.12115i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 58.8337 | 0.00721844 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19037.9 | −2.31860 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4292.36 | − | 7434.59i | −0.518933 | − | 0.898818i | −0.999758 | − | 0.0220017i | \(-0.992996\pi\) |
0.480825 | − | 0.876817i | \(-0.340337\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4420.89 | + | 7657.21i | −0.530575 | + | 0.918983i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8968.27 | + | 10101.4i | 1.06852 | + | 1.20353i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −331.069 | + | 573.428i | −0.0391603 | + | 0.0678277i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1433.15 | − | 2482.29i | −0.168301 | − | 0.291506i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7447.09 | −0.868292 | −0.434146 | − | 0.900843i | \(-0.642950\pi\) | ||||
−0.434146 | + | 0.900843i | \(0.642950\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4446.76 | −0.514779 | −0.257390 | − | 0.966308i | \(-0.582862\pi\) | ||||
−0.257390 | + | 0.966308i | \(0.582862\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1270.50 | − | 2200.58i | −0.146038 | − | 0.252945i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3043.56 | − | 5271.60i | 0.347375 | − | 0.601671i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1603.89 | − | 4821.30i | 0.181775 | − | 0.546414i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6950.11 | − | 12037.9i | 0.782178 | − | 1.35477i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4481.85 | + | 7762.79i | 0.500889 | + | 0.867565i | 0.999999 | + | 0.00102683i | \(0.000326850\pi\) |
−0.499110 | + | 0.866538i | \(0.666340\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16173.6 | −1.79504 | −0.897520 | − | 0.440973i | \(-0.854633\pi\) | ||||
−0.897520 | + | 0.440973i | \(0.854633\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 493.955 | 0.0544445 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.5362 | + | 26.9095i | 0.00170068 | + | 0.00294567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3149.21 | − | 5454.60i | 0.342378 | − | 0.593015i | −0.642496 | − | 0.766289i | \(-0.722101\pi\) |
0.984874 | + | 0.173274i | \(0.0554345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −365.585 | + | 3065.28i | −0.0394757 | + | 0.330988i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8392.35 | − | 14536.0i | 0.900074 | − | 1.55897i | 0.0726770 | − | 0.997356i | \(-0.476846\pi\) |
0.827397 | − | 0.561618i | \(-0.189821\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 345.004 | + | 597.564i | 0.0367522 | + | 0.0636567i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6551.22 | 0.693203 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2733.88 | 0.287349 | 0.143674 | − | 0.989625i | \(-0.454108\pi\) | ||||
0.143674 | + | 0.989625i | \(0.454108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6017.01 | + | 10421.8i | 0.628226 | + | 1.08812i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −607.079 | + | 1051.49i | −0.0629648 | + | 0.109058i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 305.084 | − | 917.081i | 0.0314342 | − | 0.0944910i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4614.60 | + | 7992.72i | −0.472345 | + | 0.818126i | −0.999499 | − | 0.0316437i | \(-0.989926\pi\) |
0.527154 | + | 0.849770i | \(0.323259\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −660.195 | − | 1143.49i | −0.0671357 | − | 0.116282i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19726.7 | −1.99298 | −0.996491 | − | 0.0837048i | \(-0.973325\pi\) | ||||
−0.996491 | + | 0.0837048i | \(0.973325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 368.924 | 0.0370310 | 0.0185155 | − | 0.999829i | \(-0.494106\pi\) | ||||
0.0185155 | + | 0.999829i | \(0.494106\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 300.482 | + | 520.451i | 0.0299667 | + | 0.0519039i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6654.78 | − | 11526.4i | 0.659414 | − | 1.14214i | −0.321353 | − | 0.946959i | \(-0.604138\pi\) |
0.980768 | − | 0.195179i | \(-0.0625289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2376.46 | + | 2676.73i | 0.233976 | + | 0.263540i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1394.37 | − | 2415.12i | 0.136410 | − | 0.236270i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14681.6 | − | 25429.2i | −1.42719 | − | 2.47196i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4281.46 | −0.413572 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3205.93 | 0.307735 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5781.39 | − | 10013.7i | −0.551479 | − | 0.955189i | −0.998168 | − | 0.0605002i | \(-0.980730\pi\) |
0.446689 | − | 0.894689i | \(-0.352603\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10605.0 | + | 18368.4i | −1.00530 | + | 1.74122i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 49.1658 | − | 10.0917i | 0.00463172 | − | 0.000950700i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.3339 | + | 24.8270i | −0.00134200 | + | 0.00232440i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1314.06 | − | 2276.02i | −0.122271 | − | 0.211779i | 0.798392 | − | 0.602138i | \(-0.205684\pi\) |
−0.920663 | + | 0.390359i | \(0.872351\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4277.04 | −0.395531 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12319.9 | −1.13236 | −0.566181 | − | 0.824281i | \(-0.691580\pi\) | ||||
−0.566181 | + | 0.824281i | \(0.691580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5542.86 | − | 9600.51i | −0.506365 | − | 0.877049i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 210.786 | − | 365.093i | 0.0191397 | − | 0.0331509i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −735.254 | + | 150.917i | −0.0663595 | + | 0.0136208i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1652.90 | − | 2862.91i | 0.148285 | − | 0.256837i | −0.782309 | − | 0.622891i | \(-0.785958\pi\) |
0.930594 | + | 0.366054i | \(0.119291\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6277.73 | − | 10873.3i | −0.559817 | − | 0.969631i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3072.72 | −0.272377 | −0.136189 | − | 0.990683i | \(-0.543485\pi\) | ||||
−0.136189 | + | 0.990683i | \(0.543485\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −230.159 | −0.0202811 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4447.60 | − | 7703.47i | −0.389595 | − | 0.674799i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6784.91 | + | 11751.8i | −0.590836 | + | 1.02336i | 0.403284 | + | 0.915075i | \(0.367869\pi\) |
−0.994120 | + | 0.108284i | \(0.965465\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2538.77 | − | 2859.55i | −0.219782 | − | 0.247552i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −464.357 | + | 804.291i | −0.0399647 | + | 0.0692209i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 117.171 | + | 202.947i | 0.0100256 | + | 0.0173648i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18207.6 | −1.54888 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6706.66 | 0.567225 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5366.68 | + | 9295.36i | 0.451283 | + | 0.781645i | 0.998466 | − | 0.0553681i | \(-0.0176332\pi\) |
−0.547183 | + | 0.837013i | \(0.684300\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4174.07 | + | 7229.71i | −0.348986 | + | 0.604461i | −0.986070 | − | 0.166334i | \(-0.946807\pi\) |
0.637084 | + | 0.770794i | \(0.280140\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2183.04 | + | 6562.20i | −0.181477 | + | 0.545520i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6743.65 | − | 11680.3i | 0.557416 | − | 0.965473i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6083.09 | + | 10536.2i | 0.499966 | + | 0.865967i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6564.33 | 0.536474 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13407.1 | 1.08954 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −247.483 | − | 428.654i | −0.0199993 | − | 0.0346399i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1412.22 | − | 2446.04i | 0.113486 | − | 0.196563i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17711.8 | + | 13250.7i | 1.41540 | + | 1.05891i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11553.6 | − | 20011.5i | 0.918170 | − | 1.59032i | 0.115978 | − | 0.993252i | \(-0.463000\pi\) |
0.802192 | − | 0.597066i | \(-0.203667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 701.310 | + | 1214.71i | 0.0554256 | + | 0.0960000i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −331.188 | −0.0260304 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13935.2 | 1.08926 | 0.544630 | − | 0.838676i | \(-0.316670\pi\) | ||||
0.544630 | + | 0.838676i | \(0.316670\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1234.59 | − | 2138.37i | −0.0959761 | − | 0.166235i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3898.65 | + | 6752.65i | −0.301430 | + | 0.522092i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5482.13 | − | 16479.3i | 0.421562 | − | 1.26721i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −321.634 | + | 557.087i | −0.0245993 | + | 0.0426072i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7523.76 | + | 13031.5i | 0.572337 | + | 0.991317i | 0.996325 | + | 0.0856492i | \(0.0272964\pi\) |
−0.423988 | + | 0.905668i | \(0.639370\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32713.4 | −2.47519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9461.25 | −0.712040 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7721.08 | − | 13373.3i | −0.577983 | − | 1.00110i | −0.995710 | − | 0.0925239i | \(-0.970507\pi\) |
0.417727 | − | 0.908572i | \(-0.362827\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 289.093 | − | 500.724i | 0.0215261 | − | 0.0372843i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 995.970 | + | 1121.81i | 0.0737686 | + | 0.0830895i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6681.06 | − | 11571.9i | 0.492240 | − | 0.852585i | −0.507720 | − | 0.861522i | \(-0.669511\pi\) |
0.999960 | + | 0.00893696i | \(0.00284476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11092.6 | + | 19213.0i | 0.812981 | + | 1.40812i | 0.910769 | + | 0.412917i | \(0.135490\pi\) |
−0.0977876 | + | 0.995207i | \(0.531177\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 826.208 | 0.0602362 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 112.442 | 0.00815507 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9475.68 | + | 16412.4i | 0.683671 | + | 1.18415i | 0.973853 | + | 0.227181i | \(0.0729508\pi\) |
−0.290182 | + | 0.956971i | \(0.593716\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2460.44 | + | 4261.61i | −0.176602 | + | 0.305884i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16538.4 | + | 3394.64i | −1.18094 | + | 0.242399i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11486.0 | − | 19894.4i | 0.815957 | − | 1.41328i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −234.836 | − | 406.749i | −0.0165971 | − | 0.0287470i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19579.5 | 1.37672 | 0.688359 | − | 0.725371i | \(-0.258332\pi\) | ||||
0.688359 | + | 0.725371i | \(0.258332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9486.48 | −0.663640 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1955.81 | − | 3387.57i | −0.136128 | − | 0.235780i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2806.51 | + | 4861.01i | −0.194350 | + | 0.336624i | −0.946687 | − | 0.322154i | \(-0.895593\pi\) |
0.752337 | + | 0.658778i | \(0.228926\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −644.415 | + | 132.272i | −0.0444007 | + | 0.00911362i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1991.03 | − | 3448.57i | 0.136495 | − | 0.236417i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10962.8 | − | 18988.0i | −0.747790 | − | 1.29521i | −0.948880 | − | 0.315637i | \(-0.897782\pi\) |
0.201090 | − | 0.979573i | \(-0.435552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2067.51 | −0.140326 | −0.0701628 | − | 0.997536i | \(-0.522352\pi\) | ||||
−0.0701628 | + | 0.997536i | \(0.522352\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1739.45 | 0.117472 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1027.01 | − | 1778.83i | −0.0690146 | − | 0.119537i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5083.61 | − | 8805.07i | 0.339930 | − | 0.588775i | −0.644490 | − | 0.764613i | \(-0.722930\pi\) |
0.984419 | + | 0.175838i | \(0.0562634\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8361.95 | + | 9418.51i | 0.556393 | + | 0.626695i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10142.5 | + | 17567.3i | −0.671558 | + | 1.16317i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9093.05 | + | 15749.6i | 0.599127 | + | 1.03772i | 0.992950 | + | 0.118532i | \(0.0378188\pi\) |
−0.393824 | + | 0.919186i | \(0.628848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 406.616 | 0.0266607 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6584.41 | 0.429625 | 0.214812 | − | 0.976655i | \(-0.431086\pi\) | ||||
0.214812 | + | 0.976655i | \(0.431086\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3889.86 | + | 6737.43i | 0.252579 | + | 0.437480i | 0.964235 | − | 0.265048i | \(-0.0853878\pi\) |
−0.711656 | + | 0.702528i | \(0.752054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.1952 | − | 21.1228i | 0.000788048 | − | 0.00136494i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5553.66 | + | 16694.3i | −0.357147 | + | 1.07358i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7713.72 | + | 13360.6i | −0.493678 | + | 0.855075i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3327.35 | + | 5763.14i | 0.211932 | + | 0.367078i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14436.7 | 0.915150 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3787.78 | 0.238969 | 0.119484 | − | 0.992836i | \(-0.461876\pi\) | ||||
0.119484 | + | 0.992836i | \(0.461876\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7129.93 | + | 12349.4i | 0.447692 | + | 0.775426i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −847.612 | + | 1468.11i | −0.0529708 | + | 0.0917481i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22651.1 | − | 9707.66i | 1.40890 | − | 0.603817i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −182.374 | + | 315.882i | −0.0112905 | + | 0.0195557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9965.44 | + | 17260.6i | 0.614058 | + | 1.06358i | 0.990549 | + | 0.137159i | \(0.0437973\pi\) |
−0.376491 | + | 0.926420i | \(0.622869\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3185.18 | 0.195352 | 0.0976759 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976759 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −992.148 | −0.0605671 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8471.50 | + | 14673.1i | 0.514759 | + | 0.891589i | 0.999853 | + | 0.0171270i | \(0.00545198\pi\) |
−0.485094 | + | 0.874462i | \(0.661215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23518.3 | − | 40734.9i | 1.42246 | − | 2.46377i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4836.98 | + | 14539.9i | −0.291208 | + | 0.875369i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10039.4 | − | 17388.7i | 0.601640 | − | 1.04207i | −0.390932 | − | 0.920419i | \(-0.627847\pi\) |
0.992573 | − | 0.121652i | \(-0.0388193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 685.295 | + | 1186.97i | 0.0408805 | + | 0.0708070i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1858.25 | −0.110346 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9442.46 | −0.558158 | −0.279079 | − | 0.960268i | \(-0.590029\pi\) | ||||
−0.279079 | + | 0.960268i | \(0.590029\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −380.995 | − | 659.902i | −0.0224190 | − | 0.0388309i | 0.854598 | − | 0.519290i | \(-0.173803\pi\) |
−0.877017 | + | 0.480459i | \(0.840470\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5270.38 | + | 9128.56i | −0.308725 | + | 0.534727i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 307.200 | + | 346.016i | 0.0179138 | + | 0.0201773i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 102.389 | − | 177.342i | 0.00594378 | − | 0.0102949i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −769.723 | − | 1333.20i | −0.0444831 | − | 0.0770470i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17692.8 | −1.01792 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16111.6 | −0.922818 | −0.461409 | − | 0.887188i | \(-0.652656\pi\) | ||||
−0.461409 | + | 0.887188i | \(0.652656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1680.38 | + | 2910.50i | 0.0958189 | + | 0.165963i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15620.7 | + | 27055.9i | −0.886786 | + | 1.53596i | −0.0431329 | + | 0.999069i | \(0.513734\pi\) |
−0.843653 | + | 0.536889i | \(0.819599\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −716.042 | + | 146.974i | −0.0404700 | + | 0.00830682i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4964.01 | + | 8597.92i | −0.279327 | + | 0.483808i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15056.8 | + | 26079.1i | 0.843530 | + | 1.46104i | 0.886892 | + | 0.461978i | \(0.152860\pi\) |
−0.0433614 | + | 0.999059i | \(0.513807\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2140.72 | 0.119405 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17728.4 | −0.984542 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12796.6 | − | 22164.3i | −0.707562 | − | 1.22553i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4875.43 | − | 8444.49i | 0.268408 | − | 0.464896i | −0.700043 | − | 0.714101i | \(-0.746836\pi\) |
0.968451 | + | 0.249204i | \(0.0801691\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10529.7 | − | 2161.31i | 0.577188 | − | 0.118473i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −346.986 | + | 600.997i | −0.0189380 | + | 0.0328016i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4562.79 | − | 7902.99i | −0.247960 | − | 0.429479i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1060.71 | −0.0573962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11851.6 | 0.638559 | 0.319280 | − | 0.947661i | \(-0.396559\pi\) | ||||
0.319280 | + | 0.947661i | \(0.396559\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5077.13 | − | 8793.85i | −0.272386 | − | 0.471787i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −307.607 | + | 532.791i | −0.0164328 | + | 0.0284625i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3896.26 | − | 4388.57i | −0.207262 | − | 0.233450i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −661.196 | + | 1145.22i | −0.0350236 | + | 0.0606627i | −0.883006 | − | 0.469362i | \(-0.844484\pi\) |
0.847982 | + | 0.530025i | \(0.177817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4219.83 | − | 7308.96i | −0.222582 | − | 0.385524i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 249.140 | 0.0130861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3365.44 | −0.176028 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2478.83 | + | 4293.46i | 0.129112 | + | 0.223629i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3650.78 | + | 6323.33i | −0.189362 | + | 0.327984i | −0.945038 | − | 0.326962i | \(-0.893975\pi\) |
0.755676 | + | 0.654946i | \(0.227309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1886.15 | + | 5669.76i | −0.0974257 | + | 0.292861i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4660.42 | − | 8072.08i | 0.239727 | − | 0.415220i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14108.1 | + | 24435.9i | 0.722705 | + | 1.25176i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6088.72 | −0.310616 | −0.155308 | − | 0.987866i | \(-0.549637\pi\) | ||||
−0.155308 | + | 0.987866i | \(0.549637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11133.3 | + | 19283.4i | 0.563309 | + | 0.975680i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13289.2 | − | 23017.6i | 0.669644 | − | 1.15986i | −0.308360 | − | 0.951270i | \(-0.599780\pi\) |
0.978004 | − | 0.208587i | \(-0.0668865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 686.974 | − | 294.418i | 0.0344754 | − | 0.0147752i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6232.01 | − | 10794.2i | 0.311478 | − | 0.539495i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12609.9 | − | 21841.0i | −0.627689 | − | 1.08719i | −0.988014 | − | 0.154363i | \(-0.950668\pi\) |
0.360325 | − | 0.932827i | \(-0.382666\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7413.98 | 0.367557 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2634.28 | 0.130071 | 0.0650353 | − | 0.997883i | \(-0.479284\pi\) | ||||
0.0650353 | + | 0.997883i | \(0.479284\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −793.071 | − | 1373.64i | −0.0390012 | − | 0.0675520i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4102.23 | + | 7105.27i | −0.200927 | + | 0.348016i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3983.84 | − | 11975.4i | 0.194347 | − | 0.584207i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2883.64 | + | 4994.62i | −0.140114 | + | 0.242685i | −0.927539 | − | 0.373725i | \(-0.878080\pi\) |
0.787425 | + | 0.616410i | \(0.211414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2657.66 | − | 4603.20i | −0.128619 | − | 0.222776i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 293.965 | 0.0141702 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33378.7 | 1.60260 | 0.801302 | − | 0.598260i | \(-0.204141\pi\) | ||||
0.801302 | + | 0.598260i | \(0.204141\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −87.3849 | − | 151.355i | −0.00417901 | − | 0.00723826i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1813.04 | + | 3140.28i | −0.0863637 | + | 0.149586i | −0.905971 | − | 0.423339i | \(-0.860858\pi\) |
0.819608 | + | 0.572925i | \(0.194191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5606.54 | − | 6314.95i | −0.266016 | − | 0.299628i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −159.843 | + | 276.855i | −0.00755440 | + | 0.0130846i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26201.7 | − | 45382.7i | −1.23349 | − | 2.13647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3426.15 | 0.160663 | 0.0803316 | − | 0.996768i | \(-0.474402\pi\) | ||||
0.0803316 | + | 0.996768i | \(0.474402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4434.38 | 0.207134 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6554.09 | − | 11352.0i | −0.304960 | − | 0.528207i | 0.672292 | − | 0.740286i | \(-0.265310\pi\) |
−0.977252 | + | 0.212079i | \(0.931976\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17164.4 | + | 29729.7i | −0.795568 | + | 1.37796i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16067.1 | + | 3297.90i | −0.741831 | + | 0.152267i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3209.30 | + | 5558.67i | −0.147606 | + | 0.255661i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1306.80 | + | 2263.45i | 0.0598734 | + | 0.103704i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6120.53 | 0.279348 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −675.194 | −0.0306990 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19659.9 | − | 34051.9i | −0.890468 | − | 1.54234i | −0.839315 | − | 0.543646i | \(-0.817043\pi\) |
−0.0511538 | − | 0.998691i | \(-0.516290\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2147.96 | − | 3720.38i | 0.0969195 | − | 0.167869i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14441.5 | − | 2964.24i | 0.649154 | − | 0.133244i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9855.77 | + | 17070.7i | −0.441348 | + | 0.764437i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −388.100 | − | 672.209i | −0.0173138 | − | 0.0299884i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14597.8 | −0.648785 | −0.324393 | − | 0.945923i | \(-0.605160\pi\) | ||||
−0.324393 | + | 0.945923i | \(0.605160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13807.1 | 0.611339 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4274.89 | + | 7404.33i | 0.188572 | + | 0.326615i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6657.65 | + | 11531.4i | −0.292582 | + | 0.506767i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.06786 | − | 9.08727i | −0.000353236 | − | 0.000397868i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −428.097 | + | 741.486i | −0.0186738 | + | 0.0323439i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13413.7 | − | 23233.2i | −0.582943 | − | 1.00969i | −0.995128 | − | 0.0985870i | \(-0.968568\pi\) |
0.412185 | − | 0.911100i | \(-0.364766\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5177.09 | −0.224158 | −0.112079 | − | 0.993699i | \(-0.535751\pi\) | ||||
−0.112079 | + | 0.993699i | \(0.535751\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15748.0 | −0.679343 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 517.766 | + | 896.796i | 0.0222534 | + | 0.0385441i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7830.74 | − | 13563.2i | 0.335328 | − | 0.580805i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3780.25 | − | 11363.4i | 0.161285 | − | 0.484823i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10178.4 | + | 17629.5i | −0.432678 | + | 0.749420i | −0.997103 | − | 0.0760646i | \(-0.975764\pi\) |
0.564425 | + | 0.825484i | \(0.309098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.7869 | − | 49.8603i | −0.00121926 | − | 0.00211181i | 0.865415 | − | 0.501056i | \(-0.167055\pi\) |
−0.866634 | + | 0.498944i | \(0.833721\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 24081.5 | 1.01625 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12296.6 | −0.517044 | −0.258522 | − | 0.966005i | \(-0.583235\pi\) | ||||
−0.258522 | + | 0.966005i | \(0.583235\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11435.9 | − | 19807.5i | −0.479112 | − | 0.829846i | 0.520601 | − | 0.853800i | \(-0.325708\pi\) |
−0.999713 | + | 0.0239540i | \(0.992374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10721.8 | + | 18570.7i | −0.447576 | + | 0.775224i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13431.1 | − | 10048.2i | −0.558656 | − | 0.417948i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1519.93 | + | 2632.59i | −0.0629931 | + | 0.109107i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3723.23 | + | 6448.83i | 0.153756 | + | 0.266313i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37571.3 | 1.54601 | 0.773007 | − | 0.634398i | \(-0.218752\pi\) | ||||
0.773007 | + | 0.634398i | \(0.218752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26997.6 | 1.10696 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6342.54 | − | 10985.6i | −0.259132 | − | 0.448831i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1076.83 | + | 1865.12i | −0.0438390 | + | 0.0759313i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16532.2 | − | 49695.6i | 0.670663 | − | 2.01601i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12513.6 | + | 21674.1i | −0.505848 | + | 0.876154i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 133.339 | + | 230.949i | 0.00537108 | + | 0.00930298i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38354.5 | −1.53955 | −0.769774 | − | 0.638317i | \(-0.779631\pi\) | ||||
−0.769774 | + | 0.638317i | \(0.779631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 224.855 | 0.00899401 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18272.8 | − | 31649.5i | −0.728341 | − | 1.26152i | −0.957584 | − | 0.288154i | \(-0.906958\pi\) |
0.229243 | − | 0.973369i | \(-0.426375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9282.13 | − | 16077.1i | 0.368687 | − | 0.638585i | −0.620673 | − | 0.784069i | \(-0.713141\pi\) |
0.989361 | + | 0.145484i | \(0.0464740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6883.42 | + | 7753.17i | 0.272458 | + | 0.306884i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18728.9 | + | 32439.3i | −0.738746 | + | 1.27955i | 0.214314 | + | 0.976765i | \(0.431248\pi\) |
−0.953060 | + | 0.302781i | \(0.902085\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −811.888 | − | 1406.23i | −0.0319133 | − | 0.0552755i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7564.39 | −0.296309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −60474.4 | −2.36071 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6943.06 | − | 12025.7i | −0.270100 | − | 0.467826i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −177.609 | + | 307.628i | −0.00688563 | + | 0.0119263i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3287.38 | − | 674.762i | 0.127010 | − | 0.0260698i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13564.4 | − | 23494.2i | 0.522277 | − | 0.904611i | −0.477387 | − | 0.878693i | \(-0.658416\pi\) |
0.999664 | − | 0.0259177i | \(-0.00825080\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7558.27 | − | 13091.3i | −0.290027 | − | 0.502342i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23647.8 | 0.904329 | 0.452165 | − | 0.891935i | \(-0.350652\pi\) | ||||
0.452165 | + | 0.891935i | \(0.350652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4488.47 | −0.171063 | −0.0855316 | − | 0.996335i | \(-0.527259\pi\) | ||||
−0.0855316 | + | 0.996335i | \(0.527259\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −794.658 | − | 1376.39i | −0.0301832 | − | 0.0522788i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20513.4 | − | 35530.3i | 0.776520 | − | 1.34497i | −0.157417 | − | 0.987532i | \(-0.550317\pi\) |
0.933936 | − | 0.357439i | \(-0.116350\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −42342.0 | + | 8691.06i | −1.59742 | + | 0.327884i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2611.82 | − | 4523.81i | 0.0982036 | − | 0.170094i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4855.71 | − | 8410.33i | −0.181960 | − | 0.315163i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −683.836 | −0.0255398 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −194.710 | −0.00724771 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31259.5 | + | 54143.0i | 1.15969 | + | 2.00864i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8710.04 | + | 15086.2i | −0.322057 | + | 0.557819i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16795.6 | − | 18917.8i | −0.618963 | − | 0.697171i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 169.797 | − | 294.097i | 0.00623673 | − | 0.0108023i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 368.152 | + | 637.659i | 0.0134777 | + | 0.0233441i | 0.872686 | − | 0.488283i | \(-0.162376\pi\) |
−0.859208 | + | 0.511627i | \(0.829043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2851.87 | −0.104060 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1287.54 | 0.0468256 | 0.0234128 | − | 0.999726i | \(-0.492547\pi\) | ||||
0.0234128 | + | 0.999726i | \(0.492547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29394.5 | + | 50912.8i | 1.06552 | + | 1.84553i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −298.911 | + | 517.728i | −0.0107997 | + | 0.0187055i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11031.5 | + | 33160.5i | −0.397264 | + | 1.19417i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17140.0 | + | 29687.3i | −0.615230 | + | 1.06561i | 0.375114 | + | 0.926979i | \(0.377603\pi\) |
−0.990344 | + | 0.138631i | \(0.955730\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7304.51 | + | 12651.8i | 0.261337 | + | 0.452650i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2911.81 | 0.103839 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36745.4 | −1.30614 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1451.85 | + | 2514.68i | 0.0514402 | + | 0.0890971i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15737.9 | − | 27258.9i | 0.555806 | − | 0.962685i | −0.442034 | − | 0.896998i | \(-0.645743\pi\) |
0.997840 | − | 0.0656866i | \(-0.0209238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1397.22 | + | 11715.1i | −0.0491858 | + | 0.412402i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2179.26 | − | 3774.59i | 0.0764693 | − | 0.132449i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1145.35 | + | 1983.81i | 0.0400609 | + | 0.0693876i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52560.6 | 1.83253 | 0.916264 | − | 0.400575i | \(-0.131190\pi\) | ||||
0.916264 | + | 0.400575i | \(0.131190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17088.8 | 0.593900 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7988.37 | − | 13836.3i | −0.276741 | − | 0.479330i | 0.693832 | − | 0.720137i | \(-0.255921\pi\) |
−0.970573 | + | 0.240807i | \(0.922588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 84.2846 | − | 145.985i | 0.00291059 | − | 0.00504129i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 114.649 | − | 344.635i | 0.00394661 | − | 0.0118635i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4252.22 | − | 7365.06i | 0.145912 | − | 0.252727i | −0.783801 | − | 0.621012i | \(-0.786722\pi\) |
0.929713 | + | 0.368285i | \(0.120055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7417.27 | + | 12847.1i | 0.253714 | + | 0.439446i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10414.4 | −0.355111 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29417.5 | 0.999923 | 0.499961 | − | 0.866048i | \(-0.333348\pi\) | ||||
0.499961 | + | 0.866048i | \(0.333348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −100.018 | − | 173.237i | −0.00338902 | − | 0.00586995i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21928.3 | − | 37980.9i | 0.740691 | − | 1.28291i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36239.3 | + | 40818.2i | 1.22026 | + | 1.37444i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23136.0 | + | 40072.7i | −0.776610 | + | 1.34513i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3066.53 | − | 5311.39i | −0.102614 | − | 0.177733i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1191.42 | 0.0397441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3461.97 | 0.115129 | 0.0575643 | − | 0.998342i | \(-0.481667\pi\) | ||||
0.0575643 | + | 0.998342i | \(0.481667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2523.18 | − | 4370.28i | −0.0836494 | − | 0.144885i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21779.4 | − | 37723.0i | 0.719809 | − | 1.24675i | −0.241266 | − | 0.970459i | \(-0.577563\pi\) |
0.961075 | − | 0.276287i | \(-0.0891039\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17333.5 | + | 3557.84i | −0.571106 | + | 0.117224i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13414.6 | − | 23234.7i | 0.440625 | − | 0.763185i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2752.47 | + | 4767.42i | 0.0901325 | + | 0.156114i | 0.907567 | − | 0.419908i | \(-0.137938\pi\) |
−0.817434 | + | 0.576022i | \(0.804604\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61263.4 | 1.99999 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4103.71 | −0.133559 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15394.9 | + | 26664.7i | 0.499511 | + | 0.865179i | 1.00000 | 0.000564108i | \(-0.000179561\pi\) | |
−0.500488 | + | 0.865743i | \(0.666846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −473.530 | + | 820.178i | −0.0153177 | + | 0.0265310i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15366.4 | + | 3154.07i | −0.495559 | + | 0.101718i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −205.655 | + | 356.206i | −0.00661220 | + | 0.0114527i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10814.6 | + | 18731.4i | 0.346656 | + | 0.600426i | 0.985653 | − | 0.168783i | \(-0.0539838\pi\) |
−0.638997 | + | 0.769209i | \(0.720650\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18763.1 | 0.599627 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −964.114 | −0.0307181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19097.9 | + | 33078.5i | 0.606656 | + | 1.05076i | 0.991787 | + | 0.127898i | \(0.0408229\pi\) |
−0.385131 | + | 0.922862i | \(0.625844\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3985.32 | + | 6902.78i | −0.126216 | + | 0.218613i |
(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 | 168.4.q.f.121.2 | yes | 8 | |
3.2 | odd | 2 | 504.4.s.j.289.3 | 8 | |||
4.3 | odd | 2 | 336.4.q.m.289.2 | 8 | |||
7.2 | even | 3 | 1176.4.a.bd.1.3 | 4 | |||
7.4 | even | 3 | inner | 168.4.q.f.25.2 | ✓ | 8 | |
7.5 | odd | 6 | 1176.4.a.ba.1.2 | 4 | |||
21.11 | odd | 6 | 504.4.s.j.361.3 | 8 | |||
28.11 | odd | 6 | 336.4.q.m.193.2 | 8 | |||
28.19 | even | 6 | 2352.4.a.cp.1.2 | 4 | |||
28.23 | odd | 6 | 2352.4.a.cm.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.q.f.25.2 | ✓ | 8 | 7.4 | even | 3 | inner | |
168.4.q.f.121.2 | yes | 8 | 1.1 | even | 1 | trivial | |
336.4.q.m.193.2 | 8 | 28.11 | odd | 6 | |||
336.4.q.m.289.2 | 8 | 4.3 | odd | 2 | |||
504.4.s.j.289.3 | 8 | 3.2 | odd | 2 | |||
504.4.s.j.361.3 | 8 | 21.11 | odd | 6 | |||
1176.4.a.ba.1.2 | 4 | 7.5 | odd | 6 | |||
1176.4.a.bd.1.3 | 4 | 7.2 | even | 3 | |||
2352.4.a.cm.1.3 | 4 | 28.23 | odd | 6 | |||
2352.4.a.cp.1.2 | 4 | 28.19 | even | 6 |