Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(91,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("690.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.6 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | − | 1.52229i | − | 0.217470i | −0.994071 | − | 0.108735i | \(-0.965320\pi\) | ||
0.994071 | − | 0.108735i | \(-0.0346800\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | 2.20036i | 0.200033i | 0.994986 | + | 0.100016i | \(0.0318896\pi\) | ||||
−0.994986 | + | 0.100016i | \(0.968110\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | −1.82994 | −0.140765 | −0.0703824 | − | 0.997520i | \(-0.522422\pi\) | ||||
−0.0703824 | + | 0.997520i | \(0.522422\pi\) | |||||||
\(14\) | 2.15284i | 0.153774i | ||||||||
\(15\) | − | 3.87298i | − | 0.258199i | ||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 23.2496i | − | 1.36763i | −0.729657 | − | 0.683813i | \(-0.760320\pi\) | ||
0.729657 | − | 0.683813i | \(-0.239680\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 2.85690i | 0.150363i | 0.997170 | + | 0.0751816i | \(0.0239536\pi\) | ||||
−0.997170 | + | 0.0751816i | \(0.976046\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | 2.63668i | 0.125556i | ||||||||
\(22\) | − | 3.11178i | − | 0.141445i | ||||||
\(23\) | −14.5452 | + | 17.8168i | −0.632400 | + | 0.774642i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 2.58793 | 0.0995357 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 3.04458i | − | 0.108735i | ||||||
\(29\) | −7.23088 | −0.249341 | −0.124670 | − | 0.992198i | \(-0.539787\pi\) | ||||
−0.124670 | + | 0.992198i | \(0.539787\pi\) | |||||||
\(30\) | 5.47723i | 0.182574i | ||||||||
\(31\) | 49.9104 | 1.61001 | 0.805007 | − | 0.593266i | \(-0.202162\pi\) | ||||
0.805007 | + | 0.593266i | \(0.202162\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − | 3.81114i | − | 0.115489i | ||||||
\(34\) | 32.8800i | 0.967058i | ||||||||
\(35\) | 3.40394 | 0.0972555 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 9.68006i | 0.261623i | 0.991407 | + | 0.130812i | \(0.0417583\pi\) | ||||
−0.991407 | + | 0.130812i | \(0.958242\pi\) | |||||||
\(38\) | − | 4.04027i | − | 0.106323i | ||||||
\(39\) | 3.16955 | 0.0812706 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | −62.1103 | −1.51489 | −0.757443 | − | 0.652901i | \(-0.773552\pi\) | ||||
−0.757443 | + | 0.652901i | \(0.773552\pi\) | |||||||
\(42\) | − | 3.72883i | − | 0.0887817i | ||||||
\(43\) | − | 76.6308i | − | 1.78211i | −0.453893 | − | 0.891056i | \(-0.649965\pi\) | ||
0.453893 | − | 0.891056i | \(-0.350035\pi\) | |||||||
\(44\) | 4.40073i | 0.100016i | ||||||||
\(45\) | 6.70820i | 0.149071i | ||||||||
\(46\) | 20.5700 | − | 25.1967i | 0.447174 | − | 0.547755i | ||||
\(47\) | 17.1464 | 0.364817 | 0.182408 | − | 0.983223i | \(-0.441611\pi\) | ||||
0.182408 | + | 0.983223i | \(0.441611\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 46.6826 | 0.952707 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | 40.2696i | 0.789599i | ||||||||
\(52\) | −3.65988 | −0.0703824 | ||||||||
\(53\) | 33.9334i | 0.640253i | 0.947375 | + | 0.320127i | \(0.103725\pi\) | ||||
−0.947375 | + | 0.320127i | \(0.896275\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | −4.92016 | −0.0894575 | ||||||||
\(56\) | 4.30569i | 0.0768872i | ||||||||
\(57\) | − | 4.94830i | − | 0.0868122i | ||||||
\(58\) | 10.2260 | 0.176311 | ||||||||
\(59\) | 35.2164 | 0.596889 | 0.298444 | − | 0.954427i | \(-0.403532\pi\) | ||||
0.298444 | + | 0.954427i | \(0.403532\pi\) | |||||||
\(60\) | − | 7.74597i | − | 0.129099i | ||||||
\(61\) | 8.54346i | 0.140057i | 0.997545 | + | 0.0700284i | \(0.0223090\pi\) | ||||
−0.997545 | + | 0.0700284i | \(0.977691\pi\) | |||||||
\(62\) | −70.5840 | −1.13845 | ||||||||
\(63\) | − | 4.56687i | − | 0.0724900i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 4.09187i | − | 0.0629519i | ||||||
\(66\) | 5.38977i | 0.0816631i | ||||||||
\(67\) | − | 78.9586i | − | 1.17849i | −0.807956 | − | 0.589243i | \(-0.799426\pi\) | ||
0.807956 | − | 0.589243i | \(-0.200574\pi\) | |||||||
\(68\) | − | 46.4993i | − | 0.683813i | ||||||
\(69\) | 25.1930 | − | 30.8596i | 0.365116 | − | 0.447240i | ||||
\(70\) | −4.81390 | −0.0687700 | ||||||||
\(71\) | 111.407 | 1.56911 | 0.784554 | − | 0.620061i | \(-0.212892\pi\) | ||||
0.784554 | + | 0.620061i | \(0.212892\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | 134.217 | 1.83858 | 0.919291 | − | 0.393578i | \(-0.128763\pi\) | ||||
0.919291 | + | 0.393578i | \(0.128763\pi\) | |||||||
\(74\) | − | 13.6897i | − | 0.184996i | ||||||
\(75\) | 8.66025 | 0.115470 | ||||||||
\(76\) | 5.71380i | 0.0751816i | ||||||||
\(77\) | 3.34959 | 0.0435012 | ||||||||
\(78\) | −4.48242 | −0.0574670 | ||||||||
\(79\) | − | 72.4039i | − | 0.916505i | −0.888822 | − | 0.458252i | \(-0.848476\pi\) | ||
0.888822 | − | 0.458252i | \(-0.151524\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 87.8373 | 1.07119 | ||||||||
\(83\) | − | 119.919i | − | 1.44481i | −0.691472 | − | 0.722403i | \(-0.743037\pi\) | ||
0.691472 | − | 0.722403i | \(-0.256963\pi\) | |||||||
\(84\) | 5.27337i | 0.0627782i | ||||||||
\(85\) | 51.9878 | 0.611621 | ||||||||
\(86\) | 108.372i | 1.26014i | ||||||||
\(87\) | 12.5243 | 0.143957 | ||||||||
\(88\) | − | 6.22357i | − | 0.0707223i | ||||||
\(89\) | 73.9324i | 0.830701i | 0.909661 | + | 0.415351i | \(0.136341\pi\) | ||||
−0.909661 | + | 0.415351i | \(0.863659\pi\) | |||||||
\(90\) | − | 9.48683i | − | 0.105409i | ||||||
\(91\) | 2.78570i | 0.0306121i | ||||||||
\(92\) | −29.0904 | + | 35.6335i | −0.316200 | + | 0.387321i | ||||
\(93\) | −86.4474 | −0.929542 | ||||||||
\(94\) | −24.2486 | −0.257964 | ||||||||
\(95\) | −6.38822 | −0.0672445 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | − | 178.439i | − | 1.83958i | −0.392408 | − | 0.919791i | \(-0.628358\pi\) | ||
0.392408 | − | 0.919791i | \(-0.371642\pi\) | |||||||
\(98\) | −66.0192 | −0.673665 | ||||||||
\(99\) | 6.60109i | 0.0666777i | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 147.269 | 1.45811 | 0.729053 | − | 0.684457i | \(-0.239961\pi\) | ||||
0.729053 | + | 0.684457i | \(0.239961\pi\) | |||||||
\(102\) | − | 56.9498i | − | 0.558331i | ||||||
\(103\) | − | 58.9552i | − | 0.572380i | −0.958173 | − | 0.286190i | \(-0.907611\pi\) | ||
0.958173 | − | 0.286190i | \(-0.0923889\pi\) | |||||||
\(104\) | 5.17586 | 0.0497679 | ||||||||
\(105\) | −5.89580 | −0.0561505 | ||||||||
\(106\) | − | 47.9891i | − | 0.452727i | ||||||
\(107\) | − | 111.196i | − | 1.03922i | −0.854404 | − | 0.519609i | \(-0.826078\pi\) | ||
0.854404 | − | 0.519609i | \(-0.173922\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | − | 52.7876i | − | 0.484290i | −0.970240 | − | 0.242145i | \(-0.922149\pi\) | ||
0.970240 | − | 0.242145i | \(-0.0778509\pi\) | |||||||
\(110\) | 6.95816 | 0.0632560 | ||||||||
\(111\) | − | 16.7664i | − | 0.151048i | ||||||
\(112\) | − | 6.08916i | − | 0.0543675i | ||||||
\(113\) | 25.4121i | 0.224886i | 0.993658 | + | 0.112443i | \(0.0358676\pi\) | ||||
−0.993658 | + | 0.112443i | \(0.964132\pi\) | |||||||
\(114\) | 6.99795i | 0.0613855i | ||||||||
\(115\) | −39.8395 | − | 32.5240i | −0.346431 | − | 0.282818i | ||||
\(116\) | −14.4618 | −0.124670 | ||||||||
\(117\) | −5.48983 | −0.0469216 | ||||||||
\(118\) | −49.8035 | −0.422064 | ||||||||
\(119\) | −35.3927 | −0.297418 | ||||||||
\(120\) | 10.9545i | 0.0912871i | ||||||||
\(121\) | 116.158 | 0.959987 | ||||||||
\(122\) | − | 12.0823i | − | 0.0990350i | ||||||
\(123\) | 107.578 | 0.874620 | ||||||||
\(124\) | 99.8208 | 0.805007 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 6.45853i | 0.0512582i | ||||||||
\(127\) | 100.861 | 0.794177 | 0.397089 | − | 0.917780i | \(-0.370021\pi\) | ||||
0.397089 | + | 0.917780i | \(0.370021\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 132.728i | 1.02890i | ||||||||
\(130\) | 5.78678i | 0.0445137i | ||||||||
\(131\) | −28.6539 | −0.218732 | −0.109366 | − | 0.994002i | \(-0.534882\pi\) | ||||
−0.109366 | + | 0.994002i | \(0.534882\pi\) | |||||||
\(132\) | − | 7.62228i | − | 0.0577445i | ||||||
\(133\) | 4.34903 | 0.0326995 | ||||||||
\(134\) | 111.664i | 0.833316i | ||||||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | 65.7599i | 0.483529i | ||||||||
\(137\) | 159.048i | 1.16094i | 0.814282 | + | 0.580469i | \(0.197131\pi\) | ||||
−0.814282 | + | 0.580469i | \(0.802869\pi\) | |||||||
\(138\) | −35.6283 | + | 43.6420i | −0.258176 | + | 0.316246i | ||||
\(139\) | 119.112 | 0.856918 | 0.428459 | − | 0.903561i | \(-0.359057\pi\) | ||||
0.428459 | + | 0.903561i | \(0.359057\pi\) | |||||||
\(140\) | 6.80789 | 0.0486278 | ||||||||
\(141\) | −29.6984 | −0.210627 | ||||||||
\(142\) | −157.553 | −1.10953 | ||||||||
\(143\) | − | 4.02654i | − | 0.0281576i | ||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | − | 16.1687i | − | 0.111509i | ||||||
\(146\) | −189.811 | −1.30007 | ||||||||
\(147\) | −80.8567 | −0.550046 | ||||||||
\(148\) | 19.3601i | 0.130812i | ||||||||
\(149\) | − | 245.833i | − | 1.64989i | −0.565214 | − | 0.824945i | \(-0.691206\pi\) | ||
0.565214 | − | 0.824945i | \(-0.308794\pi\) | |||||||
\(150\) | −12.2474 | −0.0816497 | ||||||||
\(151\) | 209.449 | 1.38708 | 0.693541 | − | 0.720417i | \(-0.256050\pi\) | ||||
0.693541 | + | 0.720417i | \(0.256050\pi\) | |||||||
\(152\) | − | 8.08053i | − | 0.0531614i | ||||||
\(153\) | − | 69.7489i | − | 0.455875i | ||||||
\(154\) | −4.73704 | −0.0307600 | ||||||||
\(155\) | 111.603i | 0.720020i | ||||||||
\(156\) | 6.33911 | 0.0406353 | ||||||||
\(157\) | 211.566i | 1.34755i | 0.738935 | + | 0.673777i | \(0.235329\pi\) | ||||
−0.738935 | + | 0.673777i | \(0.764671\pi\) | |||||||
\(158\) | 102.395i | 0.648067i | ||||||||
\(159\) | − | 58.7744i | − | 0.369650i | ||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | 27.1223 | + | 22.1420i | 0.168461 | + | 0.137528i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −14.1494 | −0.0868061 | −0.0434030 | − | 0.999058i | \(-0.513820\pi\) | ||||
−0.0434030 | + | 0.999058i | \(0.513820\pi\) | |||||||
\(164\) | −124.221 | −0.757443 | ||||||||
\(165\) | 8.52197 | 0.0516483 | ||||||||
\(166\) | 169.591i | 1.02163i | ||||||||
\(167\) | 52.0666 | 0.311776 | 0.155888 | − | 0.987775i | \(-0.450176\pi\) | ||||
0.155888 | + | 0.987775i | \(0.450176\pi\) | |||||||
\(168\) | − | 7.45767i | − | 0.0443909i | ||||||
\(169\) | −165.651 | −0.980185 | ||||||||
\(170\) | −73.5218 | −0.432481 | ||||||||
\(171\) | 8.57070i | 0.0501211i | ||||||||
\(172\) | − | 153.262i | − | 0.891056i | ||||||
\(173\) | −219.256 | −1.26738 | −0.633688 | − | 0.773589i | \(-0.718460\pi\) | ||||
−0.633688 | + | 0.773589i | \(0.718460\pi\) | |||||||
\(174\) | −17.7120 | −0.101793 | ||||||||
\(175\) | 7.61145i | 0.0434940i | ||||||||
\(176\) | 8.80145i | 0.0500082i | ||||||||
\(177\) | −60.9966 | −0.344614 | ||||||||
\(178\) | − | 104.556i | − | 0.587395i | ||||||
\(179\) | −84.3515 | −0.471237 | −0.235619 | − | 0.971846i | \(-0.575712\pi\) | ||||
−0.235619 | + | 0.971846i | \(0.575712\pi\) | |||||||
\(180\) | 13.4164i | 0.0745356i | ||||||||
\(181\) | 272.635i | 1.50627i | 0.657867 | + | 0.753134i | \(0.271459\pi\) | ||||
−0.657867 | + | 0.753134i | \(0.728541\pi\) | |||||||
\(182\) | − | 3.93958i | − | 0.0216460i | ||||||
\(183\) | − | 14.7977i | − | 0.0808618i | ||||||
\(184\) | 41.1400 | − | 50.3934i | 0.223587 | − | 0.273877i | ||||
\(185\) | −21.6453 | −0.117001 | ||||||||
\(186\) | 122.255 | 0.657285 | ||||||||
\(187\) | 51.1577 | 0.273570 | ||||||||
\(188\) | 34.2928 | 0.182408 | ||||||||
\(189\) | 7.91005i | 0.0418521i | ||||||||
\(190\) | 9.03431 | 0.0475490 | ||||||||
\(191\) | 235.645i | 1.23375i | 0.787063 | + | 0.616873i | \(0.211601\pi\) | ||||
−0.787063 | + | 0.616873i | \(0.788399\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | −340.126 | −1.76231 | −0.881155 | − | 0.472828i | \(-0.843233\pi\) | ||||
−0.881155 | + | 0.472828i | \(0.843233\pi\) | |||||||
\(194\) | 252.352i | 1.30078i | ||||||||
\(195\) | 7.08734i | 0.0363453i | ||||||||
\(196\) | 93.3653 | 0.476353 | ||||||||
\(197\) | −221.673 | −1.12524 | −0.562621 | − | 0.826715i | \(-0.690207\pi\) | ||||
−0.562621 | + | 0.826715i | \(0.690207\pi\) | |||||||
\(198\) | − | 9.33535i | − | 0.0471482i | ||||||
\(199\) | − | 198.065i | − | 0.995303i | −0.867377 | − | 0.497651i | \(-0.834196\pi\) | ||
0.867377 | − | 0.497651i | \(-0.165804\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | 136.760i | 0.680400i | ||||||||
\(202\) | −208.269 | −1.03104 | ||||||||
\(203\) | 11.0075i | 0.0542241i | ||||||||
\(204\) | 80.5391i | 0.394800i | ||||||||
\(205\) | − | 138.883i | − | 0.677478i | ||||||
\(206\) | 83.3752i | 0.404734i | ||||||||
\(207\) | −43.6356 | + | 53.4503i | −0.210800 | + | 0.258214i | ||||
\(208\) | −7.31977 | −0.0351912 | ||||||||
\(209\) | −6.28622 | −0.0300776 | ||||||||
\(210\) | 8.33792 | 0.0397044 | ||||||||
\(211\) | −105.845 | −0.501636 | −0.250818 | − | 0.968034i | \(-0.580700\pi\) | ||||
−0.250818 | + | 0.968034i | \(0.580700\pi\) | |||||||
\(212\) | 67.8668i | 0.320127i | ||||||||
\(213\) | −192.962 | −0.905925 | ||||||||
\(214\) | 157.255i | 0.734838i | ||||||||
\(215\) | 171.352 | 0.796985 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | − | 75.9781i | − | 0.350130i | ||||||
\(218\) | 74.6529i | 0.342445i | ||||||||
\(219\) | −232.470 | −1.06151 | ||||||||
\(220\) | −9.84032 | −0.0447287 | ||||||||
\(221\) | 42.5455i | 0.192514i | ||||||||
\(222\) | 23.7112i | 0.106807i | ||||||||
\(223\) | 230.988 | 1.03582 | 0.517910 | − | 0.855435i | \(-0.326710\pi\) | ||||
0.517910 | + | 0.855435i | \(0.326710\pi\) | |||||||
\(224\) | 8.61137i | 0.0384436i | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | − | 35.9382i | − | 0.159019i | ||||||
\(227\) | − | 146.750i | − | 0.646475i | −0.946318 | − | 0.323237i | \(-0.895229\pi\) | ||
0.946318 | − | 0.323237i | \(-0.104771\pi\) | |||||||
\(228\) | − | 9.89659i | − | 0.0434061i | ||||||
\(229\) | − | 203.857i | − | 0.890203i | −0.895480 | − | 0.445102i | \(-0.853168\pi\) | ||
0.895480 | − | 0.445102i | \(-0.146832\pi\) | |||||||
\(230\) | 56.3416 | + | 45.9959i | 0.244963 | + | 0.199982i | ||||
\(231\) | −5.80166 | −0.0251154 | ||||||||
\(232\) | 20.4520 | 0.0881553 | ||||||||
\(233\) | 296.931 | 1.27438 | 0.637191 | − | 0.770706i | \(-0.280096\pi\) | ||||
0.637191 | + | 0.770706i | \(0.280096\pi\) | |||||||
\(234\) | 7.76379 | 0.0331786 | ||||||||
\(235\) | 38.3405i | 0.163151i | ||||||||
\(236\) | 70.4328 | 0.298444 | ||||||||
\(237\) | 125.407i | 0.529144i | ||||||||
\(238\) | 50.0528 | 0.210306 | ||||||||
\(239\) | −266.458 | −1.11488 | −0.557442 | − | 0.830216i | \(-0.688217\pi\) | ||||
−0.557442 | + | 0.830216i | \(0.688217\pi\) | |||||||
\(240\) | − | 15.4919i | − | 0.0645497i | ||||||
\(241\) | 327.615i | 1.35940i | 0.733490 | + | 0.679700i | \(0.237890\pi\) | ||||
−0.733490 | + | 0.679700i | \(0.762110\pi\) | |||||||
\(242\) | −164.273 | −0.678813 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 17.0869i | 0.0700284i | ||||||||
\(245\) | 104.386i | 0.426063i | ||||||||
\(246\) | −152.139 | −0.618450 | ||||||||
\(247\) | − | 5.22796i | − | 0.0211658i | ||||||
\(248\) | −141.168 | −0.569226 | ||||||||
\(249\) | 207.706i | 0.834160i | ||||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | 5.89337i | 0.0234796i | 0.999931 | + | 0.0117398i | \(0.00373698\pi\) | ||||
−0.999931 | + | 0.0117398i | \(0.996263\pi\) | |||||||
\(252\) | − | 9.13374i | − | 0.0362450i | ||||||
\(253\) | −39.2034 | − | 32.0047i | −0.154954 | − | 0.126501i | ||||
\(254\) | −142.638 | −0.561568 | ||||||||
\(255\) | −90.0455 | −0.353120 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −45.2730 | −0.176160 | −0.0880798 | − | 0.996113i | \(-0.528073\pi\) | ||||
−0.0880798 | + | 0.996113i | \(0.528073\pi\) | |||||||
\(258\) | − | 187.706i | − | 0.727544i | ||||||
\(259\) | 14.7359 | 0.0568952 | ||||||||
\(260\) | − | 8.18375i | − | 0.0314760i | ||||||
\(261\) | −21.6926 | −0.0831136 | ||||||||
\(262\) | 40.5228 | 0.154667 | ||||||||
\(263\) | − | 211.508i | − | 0.804215i | −0.915593 | − | 0.402107i | \(-0.868278\pi\) | ||
0.915593 | − | 0.402107i | \(-0.131722\pi\) | |||||||
\(264\) | 10.7795i | 0.0408316i | ||||||||
\(265\) | −75.8774 | −0.286330 | ||||||||
\(266\) | −6.15046 | −0.0231220 | ||||||||
\(267\) | − | 128.055i | − | 0.479606i | ||||||
\(268\) | − | 157.917i | − | 0.589243i | ||||||
\(269\) | −133.758 | −0.497242 | −0.248621 | − | 0.968601i | \(-0.579977\pi\) | ||||
−0.248621 | + | 0.968601i | \(0.579977\pi\) | |||||||
\(270\) | 16.4317i | 0.0608581i | ||||||||
\(271\) | 186.815 | 0.689353 | 0.344676 | − | 0.938722i | \(-0.387989\pi\) | ||||
0.344676 | + | 0.938722i | \(0.387989\pi\) | |||||||
\(272\) | − | 92.9986i | − | 0.341907i | ||||||
\(273\) | − | 4.82498i | − | 0.0176739i | ||||||
\(274\) | − | 224.929i | − | 0.820907i | ||||||
\(275\) | − | 11.0018i | − | 0.0400066i | ||||||
\(276\) | 50.3860 | − | 61.7191i | 0.182558 | − | 0.223620i | ||||
\(277\) | −128.144 | −0.462615 | −0.231308 | − | 0.972881i | \(-0.574300\pi\) | ||||
−0.231308 | + | 0.972881i | \(0.574300\pi\) | |||||||
\(278\) | −168.449 | −0.605933 | ||||||||
\(279\) | 149.731 | 0.536671 | ||||||||
\(280\) | −9.62781 | −0.0343850 | ||||||||
\(281\) | − | 183.268i | − | 0.652200i | −0.945335 | − | 0.326100i | \(-0.894265\pi\) | ||
0.945335 | − | 0.326100i | \(-0.105735\pi\) | |||||||
\(282\) | 41.9999 | 0.148936 | ||||||||
\(283\) | 436.731i | 1.54322i | 0.636097 | + | 0.771609i | \(0.280548\pi\) | ||||
−0.636097 | + | 0.771609i | \(0.719452\pi\) | |||||||
\(284\) | 222.813 | 0.784554 | ||||||||
\(285\) | 11.0647 | 0.0388236 | ||||||||
\(286\) | 5.69438i | 0.0199104i | ||||||||
\(287\) | 94.5499i | 0.329442i | ||||||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −251.546 | −0.870401 | ||||||||
\(290\) | 22.8661i | 0.0788485i | ||||||||
\(291\) | 309.066i | 1.06208i | ||||||||
\(292\) | 268.433 | 0.919291 | ||||||||
\(293\) | − | 34.4017i | − | 0.117412i | −0.998275 | − | 0.0587060i | \(-0.981303\pi\) | ||
0.998275 | − | 0.0587060i | \(-0.0186974\pi\) | |||||||
\(294\) | 114.349 | 0.388941 | ||||||||
\(295\) | 78.7463i | 0.266937i | ||||||||
\(296\) | − | 27.3793i | − | 0.0924978i | ||||||
\(297\) | − | 11.4334i | − | 0.0384964i | ||||||
\(298\) | 347.661i | 1.16665i | ||||||||
\(299\) | 26.6169 | − | 32.6037i | 0.0890196 | − | 0.109042i | ||||
\(300\) | 17.3205 | 0.0577350 | ||||||||
\(301\) | −116.654 | −0.387556 | ||||||||
\(302\) | −296.206 | −0.980815 | ||||||||
\(303\) | −255.077 | −0.841838 | ||||||||
\(304\) | 11.4276i | 0.0375908i | ||||||||
\(305\) | −19.1038 | −0.0626353 | ||||||||
\(306\) | 98.6399i | 0.322353i | ||||||||
\(307\) | −263.872 | −0.859518 | −0.429759 | − | 0.902944i | \(-0.641401\pi\) | ||||
−0.429759 | + | 0.902944i | \(0.641401\pi\) | |||||||
\(308\) | 6.69918 | 0.0217506 | ||||||||
\(309\) | 102.113i | 0.330464i | ||||||||
\(310\) | − | 157.831i | − | 0.509131i | ||||||
\(311\) | 12.9685 | 0.0416992 | 0.0208496 | − | 0.999783i | \(-0.493363\pi\) | ||||
0.0208496 | + | 0.999783i | \(0.493363\pi\) | |||||||
\(312\) | −8.96485 | −0.0287335 | ||||||||
\(313\) | − | 71.7752i | − | 0.229314i | −0.993405 | − | 0.114657i | \(-0.963423\pi\) | ||
0.993405 | − | 0.114657i | \(-0.0365769\pi\) | |||||||
\(314\) | − | 299.199i | − | 0.952864i | ||||||
\(315\) | 10.2118 | 0.0324185 | ||||||||
\(316\) | − | 144.808i | − | 0.458252i | ||||||
\(317\) | 193.888 | 0.611633 | 0.305816 | − | 0.952090i | \(-0.401071\pi\) | ||||
0.305816 | + | 0.952090i | \(0.401071\pi\) | |||||||
\(318\) | 83.1196i | 0.261382i | ||||||||
\(319\) | − | 15.9106i | − | 0.0498764i | ||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | 192.598i | 0.599993i | ||||||||
\(322\) | −38.3567 | − | 31.3135i | −0.119120 | − | 0.0972469i | ||||
\(323\) | 66.4219 | 0.205641 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 9.14971 | 0.0281530 | ||||||||
\(326\) | 20.0103 | 0.0613812 | ||||||||
\(327\) | 91.4308i | 0.279605i | ||||||||
\(328\) | 175.675 | 0.535593 | ||||||||
\(329\) | − | 26.1018i | − | 0.0793367i | ||||||
\(330\) | −12.0519 | −0.0365209 | ||||||||
\(331\) | 393.325 | 1.18829 | 0.594147 | − | 0.804356i | \(-0.297490\pi\) | ||||
0.594147 | + | 0.804356i | \(0.297490\pi\) | |||||||
\(332\) | − | 239.838i | − | 0.722403i | ||||||
\(333\) | 29.0402i | 0.0872078i | ||||||||
\(334\) | −73.6333 | −0.220459 | ||||||||
\(335\) | 176.557 | 0.527035 | ||||||||
\(336\) | 10.5467i | 0.0313891i | ||||||||
\(337\) | − | 39.3542i | − | 0.116778i | −0.998294 | − | 0.0583891i | \(-0.981404\pi\) | ||
0.998294 | − | 0.0583891i | \(-0.0185964\pi\) | |||||||
\(338\) | 234.266 | 0.693096 | ||||||||
\(339\) | − | 44.0151i | − | 0.129838i | ||||||
\(340\) | 103.976 | 0.305811 | ||||||||
\(341\) | 109.821i | 0.322056i | ||||||||
\(342\) | − | 12.1208i | − | 0.0354409i | ||||||
\(343\) | − | 145.657i | − | 0.424655i | ||||||
\(344\) | 216.745i | 0.630072i | ||||||||
\(345\) | 69.0041 | + | 56.3333i | 0.200012 | + | 0.163285i | ||||
\(346\) | 310.075 | 0.896170 | ||||||||
\(347\) | 309.497 | 0.891922 | 0.445961 | − | 0.895052i | \(-0.352862\pi\) | ||||
0.445961 | + | 0.895052i | \(0.352862\pi\) | |||||||
\(348\) | 25.0485 | 0.0719785 | ||||||||
\(349\) | −328.191 | −0.940375 | −0.470188 | − | 0.882567i | \(-0.655814\pi\) | ||||
−0.470188 | + | 0.882567i | \(0.655814\pi\) | |||||||
\(350\) | − | 10.7642i | − | 0.0307549i | ||||||
\(351\) | 9.50866 | 0.0270902 | ||||||||
\(352\) | − | 12.4471i | − | 0.0353612i | ||||||
\(353\) | −111.495 | −0.315851 | −0.157925 | − | 0.987451i | \(-0.550481\pi\) | ||||
−0.157925 | + | 0.987451i | \(0.550481\pi\) | |||||||
\(354\) | 86.2623 | 0.243679 | ||||||||
\(355\) | 249.113i | 0.701726i | ||||||||
\(356\) | 147.865i | 0.415351i | ||||||||
\(357\) | 61.3020 | 0.171714 | ||||||||
\(358\) | 119.291 | 0.333215 | ||||||||
\(359\) | − | 516.911i | − | 1.43986i | −0.694045 | − | 0.719932i | \(-0.744173\pi\) | ||
0.694045 | − | 0.719932i | \(-0.255827\pi\) | |||||||
\(360\) | − | 18.9737i | − | 0.0527046i | ||||||
\(361\) | 352.838 | 0.977391 | ||||||||
\(362\) | − | 385.564i | − | 1.06509i | ||||||
\(363\) | −201.192 | −0.554249 | ||||||||
\(364\) | 5.57140i | 0.0153061i | ||||||||
\(365\) | 300.117i | 0.822239i | ||||||||
\(366\) | 20.9271i | 0.0571779i | ||||||||
\(367\) | − | 32.4661i | − | 0.0884635i | −0.999021 | − | 0.0442318i | \(-0.985916\pi\) | ||
0.999021 | − | 0.0442318i | \(-0.0140840\pi\) | |||||||
\(368\) | −58.1808 | + | 71.2671i | −0.158100 | + | 0.193661i | ||||
\(369\) | −186.331 | −0.504962 | ||||||||
\(370\) | 30.6110 | 0.0827325 | ||||||||
\(371\) | 51.6565 | 0.139236 | ||||||||
\(372\) | −172.895 | −0.464771 | ||||||||
\(373\) | 153.444i | 0.411377i | 0.978617 | + | 0.205689i | \(0.0659434\pi\) | ||||
−0.978617 | + | 0.205689i | \(0.934057\pi\) | |||||||
\(374\) | −72.3478 | −0.193443 | ||||||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | −48.4973 | −0.128982 | ||||||||
\(377\) | 13.2321 | 0.0350984 | ||||||||
\(378\) | − | 11.1865i | − | 0.0295939i | ||||||
\(379\) | − | 597.537i | − | 1.57662i | −0.615281 | − | 0.788308i | \(-0.710958\pi\) | ||
0.615281 | − | 0.788308i | \(-0.289042\pi\) | |||||||
\(380\) | −12.7764 | −0.0336222 | ||||||||
\(381\) | −174.696 | −0.458518 | ||||||||
\(382\) | − | 333.253i | − | 0.872390i | ||||||
\(383\) | 309.730i | 0.808694i | 0.914606 | + | 0.404347i | \(0.132501\pi\) | ||||
−0.914606 | + | 0.404347i | \(0.867499\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | 7.48991i | 0.0194543i | ||||||||
\(386\) | 481.010 | 1.24614 | ||||||||
\(387\) | − | 229.892i | − | 0.594037i | ||||||
\(388\) | − | 356.879i | − | 0.919791i | ||||||
\(389\) | − | 295.042i | − | 0.758461i | −0.925302 | − | 0.379231i | \(-0.876189\pi\) | ||
0.925302 | − | 0.379231i | \(-0.123811\pi\) | |||||||
\(390\) | − | 10.0230i | − | 0.0257000i | ||||||
\(391\) | 414.234 | + | 338.171i | 1.05942 | + | 0.864886i | ||||
\(392\) | −132.038 | −0.336833 | ||||||||
\(393\) | 49.6301 | 0.126285 | ||||||||
\(394\) | 313.492 | 0.795666 | ||||||||
\(395\) | 161.900 | 0.409873 | ||||||||
\(396\) | 13.2022i | 0.0333388i | ||||||||
\(397\) | 45.4461 | 0.114474 | 0.0572368 | − | 0.998361i | \(-0.481771\pi\) | ||||
0.0572368 | + | 0.998361i | \(0.481771\pi\) | |||||||
\(398\) | 280.107i | 0.703785i | ||||||||
\(399\) | −7.53274 | −0.0188791 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 51.4990i | 0.128427i | 0.997936 | + | 0.0642133i | \(0.0204538\pi\) | ||||
−0.997936 | + | 0.0642133i | \(0.979546\pi\) | |||||||
\(402\) | − | 193.408i | − | 0.481115i | ||||||
\(403\) | −91.3332 | −0.226633 | ||||||||
\(404\) | 294.537 | 0.729053 | ||||||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | − | 15.5669i | − | 0.0383422i | ||||||
\(407\) | −21.2996 | −0.0523333 | ||||||||
\(408\) | − | 113.900i | − | 0.279166i | ||||||
\(409\) | −507.527 | −1.24090 | −0.620449 | − | 0.784247i | \(-0.713050\pi\) | ||||
−0.620449 | + | 0.784247i | \(0.713050\pi\) | |||||||
\(410\) | 196.410i | 0.479049i | ||||||||
\(411\) | − | 275.480i | − | 0.670268i | ||||||
\(412\) | − | 117.910i | − | 0.286190i | ||||||
\(413\) | − | 53.6096i | − | 0.129805i | ||||||
\(414\) | 61.7100 | − | 75.5902i | 0.149058 | − | 0.182585i | ||||
\(415\) | 268.147 | 0.646137 | ||||||||
\(416\) | 10.3517 | 0.0248839 | ||||||||
\(417\) | −206.307 | −0.494742 | ||||||||
\(418\) | 8.89005 | 0.0212681 | ||||||||
\(419\) | − | 471.677i | − | 1.12572i | −0.826552 | − | 0.562861i | \(-0.809701\pi\) | ||
0.826552 | − | 0.562861i | \(-0.190299\pi\) | |||||||
\(420\) | −11.7916 | −0.0280753 | ||||||||
\(421\) | 760.247i | 1.80581i | 0.429838 | + | 0.902906i | \(0.358570\pi\) | ||||
−0.429838 | + | 0.902906i | \(0.641430\pi\) | |||||||
\(422\) | 149.688 | 0.354711 | ||||||||
\(423\) | 51.4391 | 0.121606 | ||||||||
\(424\) | − | 95.9782i | − | 0.226364i | ||||||
\(425\) | 116.248i | 0.273525i | ||||||||
\(426\) | 272.889 | 0.640585 | ||||||||
\(427\) | 13.0056 | 0.0304581 | ||||||||
\(428\) | − | 222.393i | − | 0.519609i | ||||||
\(429\) | 6.97417i | 0.0162568i | ||||||||
\(430\) | −242.328 | −0.563553 | ||||||||
\(431\) | − | 601.309i | − | 1.39515i | −0.716512 | − | 0.697575i | \(-0.754262\pi\) | ||
0.716512 | − | 0.697575i | \(-0.245738\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | − | 466.438i | − | 1.07722i | −0.842554 | − | 0.538612i | \(-0.818949\pi\) | ||
0.842554 | − | 0.538612i | \(-0.181051\pi\) | |||||||
\(434\) | 107.449i | 0.247579i | ||||||||
\(435\) | 28.0051i | 0.0643795i | ||||||||
\(436\) | − | 105.575i | − | 0.242145i | ||||||
\(437\) | −50.9007 | − | 41.5542i | −0.116478 | − | 0.0950896i | ||||
\(438\) | 328.762 | 0.750598 | ||||||||
\(439\) | −294.320 | −0.670432 | −0.335216 | − | 0.942141i | \(-0.608809\pi\) | ||||
−0.335216 | + | 0.942141i | \(0.608809\pi\) | |||||||
\(440\) | 13.9163 | 0.0316280 | ||||||||
\(441\) | 140.048 | 0.317569 | ||||||||
\(442\) | − | 60.1684i | − | 0.136128i | ||||||
\(443\) | 642.170 | 1.44959 | 0.724797 | − | 0.688962i | \(-0.241934\pi\) | ||||
0.724797 | + | 0.688962i | \(0.241934\pi\) | |||||||
\(444\) | − | 33.5327i | − | 0.0755241i | ||||||
\(445\) | −165.318 | −0.371501 | ||||||||
\(446\) | −326.666 | −0.732435 | ||||||||
\(447\) | 425.796i | 0.952564i | ||||||||
\(448\) | − | 12.1783i | − | 0.0271837i | ||||||
\(449\) | 663.924 | 1.47867 | 0.739337 | − | 0.673336i | \(-0.235139\pi\) | ||||
0.739337 | + | 0.673336i | \(0.235139\pi\) | |||||||
\(450\) | 21.2132 | 0.0471405 | ||||||||
\(451\) | − | 136.665i | − | 0.303027i | ||||||
\(452\) | 50.8243i | 0.112443i | ||||||||
\(453\) | −362.777 | −0.800832 | ||||||||
\(454\) | 207.536i | 0.457127i | ||||||||
\(455\) | −6.22902 | −0.0136902 | ||||||||
\(456\) | 13.9959i | 0.0306928i | ||||||||
\(457\) | 22.1190i | 0.0484005i | 0.999707 | + | 0.0242002i | \(0.00770393\pi\) | ||||
−0.999707 | + | 0.0242002i | \(0.992296\pi\) | |||||||
\(458\) | 288.297i | 0.629469i | ||||||||
\(459\) | 120.809i | 0.263200i | ||||||||
\(460\) | −79.6790 | − | 65.0481i | −0.173215 | − | 0.141409i | ||||
\(461\) | −332.992 | −0.722325 | −0.361162 | − | 0.932503i | \(-0.617620\pi\) | ||||
−0.361162 | + | 0.932503i | \(0.617620\pi\) | |||||||
\(462\) | 8.20479 | 0.0177593 | ||||||||
\(463\) | −58.4021 | −0.126139 | −0.0630693 | − | 0.998009i | \(-0.520089\pi\) | ||||
−0.0630693 | + | 0.998009i | \(0.520089\pi\) | |||||||
\(464\) | −28.9235 | −0.0623352 | ||||||||
\(465\) | − | 193.302i | − | 0.415704i | ||||||
\(466\) | −419.924 | −0.901124 | ||||||||
\(467\) | 609.288i | 1.30469i | 0.757924 | + | 0.652343i | \(0.226214\pi\) | ||||
−0.757924 | + | 0.652343i | \(0.773786\pi\) | |||||||
\(468\) | −10.9797 | −0.0234608 | ||||||||
\(469\) | −120.198 | −0.256285 | ||||||||
\(470\) | − | 54.2216i | − | 0.115365i | ||||||
\(471\) | − | 366.443i | − | 0.778010i | ||||||
\(472\) | −99.6071 | −0.211032 | ||||||||
\(473\) | 168.616 | 0.356481 | ||||||||
\(474\) | − | 177.353i | − | 0.374161i | ||||||
\(475\) | − | 14.2845i | − | 0.0300726i | ||||||
\(476\) | −70.7854 | −0.148709 | ||||||||
\(477\) | 101.800i | 0.213418i | ||||||||
\(478\) | 376.828 | 0.788343 | ||||||||
\(479\) | 200.294i | 0.418150i | 0.977900 | + | 0.209075i | \(0.0670453\pi\) | ||||
−0.977900 | + | 0.209075i | \(0.932955\pi\) | |||||||
\(480\) | 21.9089i | 0.0456435i | ||||||||
\(481\) | − | 17.7140i | − | 0.0368273i | ||||||
\(482\) | − | 463.318i | − | 0.961241i | ||||||
\(483\) | −46.9772 | − | 38.3511i | −0.0972613 | − | 0.0794018i | ||||
\(484\) | 232.317 | 0.479993 | ||||||||
\(485\) | 399.003 | 0.822686 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 136.133 | 0.279534 | 0.139767 | − | 0.990184i | \(-0.455365\pi\) | ||||
0.139767 | + | 0.990184i | \(0.455365\pi\) | |||||||
\(488\) | − | 24.1646i | − | 0.0495175i | ||||||
\(489\) | 24.5075 | 0.0501175 | ||||||||
\(490\) | − | 147.623i | − | 0.301272i | ||||||
\(491\) | −217.319 | −0.442604 | −0.221302 | − | 0.975205i | \(-0.571031\pi\) | ||||
−0.221302 | + | 0.975205i | \(0.571031\pi\) | |||||||
\(492\) | 215.156 | 0.437310 | ||||||||
\(493\) | 168.115i | 0.341005i | ||||||||
\(494\) | 7.39345i | 0.0149665i | ||||||||
\(495\) | −14.7605 | −0.0298192 | ||||||||
\(496\) | 199.642 | 0.402503 | ||||||||
\(497\) | − | 169.593i | − | 0.341234i | ||||||
\(498\) | − | 293.740i | − | 0.589840i | ||||||
\(499\) | −620.672 | −1.24383 | −0.621916 | − | 0.783084i | \(-0.713646\pi\) | ||||
−0.621916 | + | 0.783084i | \(0.713646\pi\) | |||||||
\(500\) | − | 22.3607i | − | 0.0447214i | ||||||
\(501\) | −90.1821 | −0.180004 | ||||||||
\(502\) | − | 8.33449i | − | 0.0166026i | ||||||
\(503\) | − | 165.943i | − | 0.329906i | −0.986301 | − | 0.164953i | \(-0.947253\pi\) | ||
0.986301 | − | 0.164953i | \(-0.0527473\pi\) | |||||||
\(504\) | 12.9171i | 0.0256291i | ||||||||
\(505\) | 329.303i | 0.652085i | ||||||||
\(506\) | 55.4419 | + | 45.2615i | 0.109569 | + | 0.0894496i | ||||
\(507\) | 286.916 | 0.565910 | ||||||||
\(508\) | 201.721 | 0.397089 | ||||||||
\(509\) | −376.623 | −0.739928 | −0.369964 | − | 0.929046i | \(-0.620630\pi\) | ||||
−0.369964 | + | 0.929046i | \(0.620630\pi\) | |||||||
\(510\) | 127.344 | 0.249693 | ||||||||
\(511\) | − | 204.316i | − | 0.399836i | ||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | − | 14.8449i | − | 0.0289374i | ||||||
\(514\) | 64.0257 | 0.124564 | ||||||||
\(515\) | 131.828 | 0.255976 | ||||||||
\(516\) | 265.457i | 0.514452i | ||||||||
\(517\) | 37.7283i | 0.0729754i | ||||||||
\(518\) | −20.8397 | −0.0402310 | ||||||||
\(519\) | 379.762 | 0.731720 | ||||||||
\(520\) | 11.5736i | 0.0222569i | ||||||||
\(521\) | − | 675.726i | − | 1.29698i | −0.761223 | − | 0.648490i | \(-0.775401\pi\) | ||
0.761223 | − | 0.648490i | \(-0.224599\pi\) | |||||||
\(522\) | 30.6780 | 0.0587702 | ||||||||
\(523\) | − | 53.9295i | − | 0.103116i | −0.998670 | − | 0.0515578i | \(-0.983581\pi\) | ||
0.998670 | − | 0.0515578i | \(-0.0164186\pi\) | |||||||
\(524\) | −57.3079 | −0.109366 | ||||||||
\(525\) | − | 13.1834i | − | 0.0251113i | ||||||
\(526\) | 299.118i | 0.568666i | ||||||||
\(527\) | − | 1160.40i | − | 2.20190i | ||||||
\(528\) | − | 15.2446i | − | 0.0288723i | ||||||
\(529\) | −105.875 | − | 518.297i | −0.200141 | − | 0.979767i | ||||
\(530\) | 107.307 | 0.202466 | ||||||||
\(531\) | 105.649 | 0.198963 | ||||||||
\(532\) | 8.69806 | 0.0163497 | ||||||||
\(533\) | 113.658 | 0.213243 | ||||||||
\(534\) | 181.097i | 0.339132i | ||||||||
\(535\) | 248.643 | 0.464752 | ||||||||
\(536\) | 223.329i | 0.416658i | ||||||||
\(537\) | 146.101 | 0.272069 | ||||||||
\(538\) | 189.163 | 0.351604 | ||||||||
\(539\) | 102.719i | 0.190573i | ||||||||
\(540\) | − | 23.2379i | − | 0.0430331i | ||||||
\(541\) | 32.6654 | 0.0603797 | 0.0301899 | − | 0.999544i | \(-0.490389\pi\) | ||||
0.0301899 | + | 0.999544i | \(0.490389\pi\) | |||||||
\(542\) | −264.196 | −0.487446 | ||||||||
\(543\) | − | 472.217i | − | 0.869645i | ||||||
\(544\) | 131.520i | 0.241764i | ||||||||
\(545\) | 118.037 | 0.216581 | ||||||||
\(546\) | 6.82355i | 0.0124973i | ||||||||
\(547\) | 125.227 | 0.228934 | 0.114467 | − | 0.993427i | \(-0.463484\pi\) | ||||
0.114467 | + | 0.993427i | \(0.463484\pi\) | |||||||
\(548\) | 318.097i | 0.580469i | ||||||||
\(549\) | 25.6304i | 0.0466856i | ||||||||
\(550\) | 15.5589i | 0.0282889i | ||||||||
\(551\) | − | 20.6579i | − | 0.0374917i | ||||||
\(552\) | −71.2566 | + | 87.2840i | −0.129088 | + | 0.158123i | ||||
\(553\) | −110.220 | −0.199312 | ||||||||
\(554\) | 181.224 | 0.327118 | ||||||||
\(555\) | 37.4907 | 0.0675508 | ||||||||
\(556\) | 238.223 | 0.428459 | ||||||||
\(557\) | − | 18.9083i | − | 0.0339466i | −0.999856 | − | 0.0169733i | \(-0.994597\pi\) | ||
0.999856 | − | 0.0169733i | \(-0.00540303\pi\) | |||||||
\(558\) | −211.752 | −0.379484 | ||||||||
\(559\) | 140.230i | 0.250859i | ||||||||
\(560\) | 13.6158 | 0.0243139 | ||||||||
\(561\) | −88.6077 | −0.157946 | ||||||||
\(562\) | 259.181i | 0.461175i | ||||||||
\(563\) | 663.769i | 1.17899i | 0.807774 | + | 0.589493i | \(0.200672\pi\) | ||||
−0.807774 | + | 0.589493i | \(0.799328\pi\) | |||||||
\(564\) | −59.3968 | −0.105313 | ||||||||
\(565\) | −56.8233 | −0.100572 | ||||||||
\(566\) | − | 617.630i | − | 1.09122i | ||||||
\(567\) | − | 13.7006i | − | 0.0241633i | ||||||
\(568\) | −315.105 | −0.554763 | ||||||||
\(569\) | 491.805i | 0.864332i | 0.901794 | + | 0.432166i | \(0.142251\pi\) | ||||
−0.901794 | + | 0.432166i | \(0.857749\pi\) | |||||||
\(570\) | −15.6479 | −0.0274524 | ||||||||
\(571\) | 880.062i | 1.54126i | 0.637280 | + | 0.770632i | \(0.280060\pi\) | ||||
−0.637280 | + | 0.770632i | \(0.719940\pi\) | |||||||
\(572\) | − | 8.05307i | − | 0.0140788i | ||||||
\(573\) | − | 408.150i | − | 0.712303i | ||||||
\(574\) | − | 133.714i | − | 0.232951i | ||||||
\(575\) | 72.7260 | − | 89.0839i | 0.126480 | − | 0.154928i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | −4.02697 | −0.00697914 | −0.00348957 | − | 0.999994i | \(-0.501111\pi\) | ||||
−0.00348957 | + | 0.999994i | \(0.501111\pi\) | |||||||
\(578\) | 355.740 | 0.615467 | ||||||||
\(579\) | 589.115 | 1.01747 | ||||||||
\(580\) | − | 32.3375i | − | 0.0557543i | ||||||
\(581\) | −182.551 | −0.314202 | ||||||||
\(582\) | − | 437.086i | − | 0.751006i | ||||||
\(583\) | −74.6658 | −0.128072 | ||||||||
\(584\) | −379.622 | −0.650037 | ||||||||
\(585\) | − | 12.2756i | − | 0.0209840i | ||||||
\(586\) | 48.6513i | 0.0830228i | ||||||||
\(587\) | −313.115 | −0.533415 | −0.266708 | − | 0.963778i | \(-0.585936\pi\) | ||||
−0.266708 | + | 0.963778i | \(0.585936\pi\) | |||||||
\(588\) | −161.713 | −0.275023 | ||||||||
\(589\) | 142.589i | 0.242087i | ||||||||
\(590\) | − | 111.364i | − | 0.188753i | ||||||
\(591\) | 383.948 | 0.649659 | ||||||||
\(592\) | 38.7202i | 0.0654058i | ||||||||
\(593\) | 643.656 | 1.08542 | 0.542712 | − | 0.839919i | \(-0.317398\pi\) | ||||
0.542712 | + | 0.839919i | \(0.317398\pi\) | |||||||
\(594\) | 16.1693i | 0.0272210i | ||||||||
\(595\) | − | 79.1405i | − | 0.133009i | ||||||
\(596\) | − | 491.667i | − | 0.824945i | ||||||
\(597\) | 343.059i | 0.574638i | ||||||||
\(598\) | −37.6419 | + | 46.1085i | −0.0629464 | + | 0.0771046i | ||||
\(599\) | 482.724 | 0.805884 | 0.402942 | − | 0.915226i | \(-0.367988\pi\) | ||||
0.402942 | + | 0.915226i | \(0.367988\pi\) | |||||||
\(600\) | −24.4949 | −0.0408248 | ||||||||
\(601\) | −510.476 | −0.849377 | −0.424689 | − | 0.905340i | \(-0.639616\pi\) | ||||
−0.424689 | + | 0.905340i | \(0.639616\pi\) | |||||||
\(602\) | 164.974 | 0.274043 | ||||||||
\(603\) | − | 236.876i | − | 0.392829i | ||||||
\(604\) | 418.899 | 0.693541 | ||||||||
\(605\) | 259.738i | 0.429319i | ||||||||
\(606\) | 360.733 | 0.595269 | ||||||||
\(607\) | −719.184 | −1.18482 | −0.592409 | − | 0.805638i | \(-0.701823\pi\) | ||||
−0.592409 | + | 0.805638i | \(0.701823\pi\) | |||||||
\(608\) | − | 16.1611i | − | 0.0265807i | ||||||
\(609\) | − | 19.0655i | − | 0.0313063i | ||||||
\(610\) | 27.0168 | 0.0442898 | ||||||||
\(611\) | −31.3769 | −0.0513533 | ||||||||
\(612\) | − | 139.498i | − | 0.227938i | ||||||
\(613\) | 672.054i | 1.09634i | 0.836368 | + | 0.548168i | \(0.184675\pi\) | ||||
−0.836368 | + | 0.548168i | \(0.815325\pi\) | |||||||
\(614\) | 373.171 | 0.607771 | ||||||||
\(615\) | 240.552i | 0.391142i | ||||||||
\(616\) | −9.47407 | −0.0153800 | ||||||||
\(617\) | 295.731i | 0.479305i | 0.970859 | + | 0.239653i | \(0.0770336\pi\) | ||||
−0.970859 | + | 0.239653i | \(0.922966\pi\) | |||||||
\(618\) | − | 144.410i | − | 0.233673i | ||||||
\(619\) | − | 823.442i | − | 1.33028i | −0.746720 | − | 0.665139i | \(-0.768372\pi\) | ||
0.746720 | − | 0.665139i | \(-0.231628\pi\) | |||||||
\(620\) | 223.206i | 0.360010i | ||||||||
\(621\) | 75.5790 | − | 92.5787i | 0.121705 | − | 0.149080i | ||||
\(622\) | −18.3402 | −0.0294858 | ||||||||
\(623\) | 112.547 | 0.180653 | ||||||||
\(624\) | 12.6782 | 0.0203176 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 101.505i | 0.162149i | ||||||||
\(627\) | 10.8880 | 0.0173653 | ||||||||
\(628\) | 423.132i | 0.673777i | ||||||||
\(629\) | 225.058 | 0.357803 | ||||||||
\(630\) | −14.4417 | −0.0229233 | ||||||||
\(631\) | 471.460i | 0.747163i | 0.927597 | + | 0.373582i | \(0.121870\pi\) | ||||
−0.927597 | + | 0.373582i | \(0.878130\pi\) | |||||||
\(632\) | 204.789i | 0.324033i | ||||||||
\(633\) | 183.329 | 0.289620 | ||||||||
\(634\) | −274.199 | −0.432490 | ||||||||
\(635\) | 225.531i | 0.355167i | ||||||||
\(636\) | − | 117.549i | − | 0.184825i | ||||||
\(637\) | −85.4265 | −0.134108 | ||||||||
\(638\) | 22.5009i | 0.0352679i | ||||||||
\(639\) | 334.220 | 0.523036 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | − | 1114.03i | − | 1.73796i | −0.494850 | − | 0.868979i | \(-0.664777\pi\) | ||
0.494850 | − | 0.868979i | \(-0.335223\pi\) | |||||||
\(642\) | − | 272.374i | − | 0.424259i | ||||||
\(643\) | − | 182.160i | − | 0.283298i | −0.989917 | − | 0.141649i | \(-0.954760\pi\) | ||
0.989917 | − | 0.141649i | \(-0.0452404\pi\) | |||||||
\(644\) | 54.2446 | + | 44.2840i | 0.0842307 | + | 0.0687640i | ||||
\(645\) | −296.790 | −0.460139 | ||||||||
\(646\) | −93.9348 | −0.145410 | ||||||||
\(647\) | 231.496 | 0.357799 | 0.178899 | − | 0.983867i | \(-0.442746\pi\) | ||||
0.178899 | + | 0.983867i | \(0.442746\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | 77.4889i | 0.119397i | ||||||||
\(650\) | −12.9396 | −0.0199071 | ||||||||
\(651\) | 131.598i | 0.202147i | ||||||||
\(652\) | −28.2988 | −0.0434030 | ||||||||
\(653\) | 961.708 | 1.47275 | 0.736377 | − | 0.676572i | \(-0.236535\pi\) | ||||
0.736377 | + | 0.676572i | \(0.236535\pi\) | |||||||
\(654\) | − | 129.303i | − | 0.197710i | ||||||
\(655\) | − | 64.0722i | − | 0.0978201i | ||||||
\(656\) | −248.441 | −0.378721 | ||||||||
\(657\) | 402.650 | 0.612861 | ||||||||
\(658\) | 36.9135i | 0.0560995i | ||||||||
\(659\) | 482.196i | 0.731709i | 0.930672 | + | 0.365854i | \(0.119223\pi\) | ||||
−0.930672 | + | 0.365854i | \(0.880777\pi\) | |||||||
\(660\) | 17.0439 | 0.0258241 | ||||||||
\(661\) | − | 514.781i | − | 0.778792i | −0.921070 | − | 0.389396i | \(-0.872684\pi\) | ||
0.921070 | − | 0.389396i | \(-0.127316\pi\) | |||||||
\(662\) | −556.246 | −0.840251 | ||||||||
\(663\) | − | 73.6910i | − | 0.111148i | ||||||
\(664\) | 339.182i | 0.510816i | ||||||||
\(665\) | 9.72473i | 0.0146236i | ||||||||
\(666\) | − | 41.0690i | − | 0.0616652i | ||||||
\(667\) | 105.175 | − | 128.831i | 0.157683 | − | 0.193150i | ||||
\(668\) | 104.133 | 0.155888 | ||||||||
\(669\) | −400.083 | −0.598031 | ||||||||
\(670\) | −249.689 | −0.372670 | ||||||||
\(671\) | −18.7987 | −0.0280160 | ||||||||
\(672\) | − | 14.9153i | − | 0.0221954i | ||||||
\(673\) | −1100.79 | −1.63565 | −0.817824 | − | 0.575468i | \(-0.804820\pi\) | ||||
−0.817824 | + | 0.575468i | \(0.804820\pi\) | |||||||
\(674\) | 55.6553i | 0.0825746i | ||||||||
\(675\) | 25.9808 | 0.0384900 | ||||||||
\(676\) | −331.303 | −0.490093 | ||||||||
\(677\) | − | 155.504i | − | 0.229695i | −0.993383 | − | 0.114848i | \(-0.963362\pi\) | ||
0.993383 | − | 0.114848i | \(-0.0366380\pi\) | |||||||
\(678\) | 62.2468i | 0.0918094i | ||||||||
\(679\) | −271.637 | −0.400054 | ||||||||
\(680\) | −147.044 | −0.216241 | ||||||||
\(681\) | 254.178i | 0.373242i | ||||||||
\(682\) | − | 155.310i | − | 0.227728i | ||||||
\(683\) | −1077.79 | −1.57803 | −0.789014 | − | 0.614376i | \(-0.789408\pi\) | ||||
−0.789014 | + | 0.614376i | \(0.789408\pi\) | |||||||
\(684\) | 17.1414i | 0.0250605i | ||||||||
\(685\) | −355.643 | −0.519187 | ||||||||
\(686\) | 205.990i | 0.300276i | ||||||||
\(687\) | 353.090i | 0.513959i | ||||||||
\(688\) | − | 306.523i | − | 0.445528i | ||||||
\(689\) | − | 62.0962i | − | 0.0901251i | ||||||
\(690\) | −97.5865 | − | 79.6673i | −0.141430 | − | 0.115460i | ||||
\(691\) | −884.748 | −1.28039 | −0.640194 | − | 0.768214i | \(-0.721146\pi\) | ||||
−0.640194 | + | 0.768214i | \(0.721146\pi\) | |||||||
\(692\) | −438.512 | −0.633688 | ||||||||
\(693\) | 10.0488 | 0.0145004 | ||||||||
\(694\) | −437.695 | −0.630684 | ||||||||
\(695\) | 266.342i | 0.383225i | ||||||||
\(696\) | −35.4239 | −0.0508965 | ||||||||
\(697\) | 1444.04i | 2.07180i | ||||||||
\(698\) | 464.132 | 0.664946 | ||||||||
\(699\) | −514.299 | −0.735765 | ||||||||
\(700\) | 15.2229i | 0.0217470i | ||||||||
\(701\) | − | 666.703i | − | 0.951074i | −0.879696 | − | 0.475537i | \(-0.842254\pi\) | ||
0.879696 | − | 0.475537i | \(-0.157746\pi\) | |||||||
\(702\) | −13.4473 | −0.0191557 | ||||||||
\(703\) | −27.6550 | −0.0393385 | ||||||||
\(704\) | 17.6029i | 0.0250041i | ||||||||
\(705\) | − | 66.4076i | − | 0.0941952i | ||||||
\(706\) | 157.678 | 0.223340 | ||||||||
\(707\) | − | 224.186i | − | 0.317094i | ||||||
\(708\) | −121.993 | −0.172307 | ||||||||
\(709\) | 967.418i | 1.36448i | 0.731127 | + | 0.682241i | \(0.238995\pi\) | ||||
−0.731127 | + | 0.682241i | \(0.761005\pi\) | |||||||
\(710\) | − | 352.299i | − | 0.496195i | ||||||
\(711\) | − | 217.212i | − | 0.305502i | ||||||
\(712\) | − | 209.112i | − | 0.293697i | ||||||
\(713\) | −725.957 | + | 889.242i | −1.01817 | + | 1.24718i | ||||
\(714\) | −86.6941 | −0.121420 | ||||||||
\(715\) | 9.00361 | 0.0125925 | ||||||||
\(716\) | −168.703 | −0.235619 | ||||||||
\(717\) | 461.518 | 0.643679 | ||||||||
\(718\) | 731.023i | 1.01814i | ||||||||
\(719\) | −216.266 | −0.300787 | −0.150393 | − | 0.988626i | \(-0.548054\pi\) | ||||
−0.150393 | + | 0.988626i | \(0.548054\pi\) | |||||||
\(720\) | 26.8328i | 0.0372678i | ||||||||
\(721\) | −89.7469 | −0.124476 | ||||||||
\(722\) | −498.988 | −0.691120 | ||||||||
\(723\) | − | 567.447i | − | 0.784850i | ||||||
\(724\) | 545.269i | 0.753134i | ||||||||
\(725\) | 36.1544 | 0.0498681 | ||||||||
\(726\) | 284.529 | 0.391913 | ||||||||
\(727\) | − | 113.587i | − | 0.156240i | −0.996944 | − | 0.0781200i | \(-0.975108\pi\) | ||
0.996944 | − | 0.0781200i | \(-0.0248917\pi\) | |||||||
\(728\) | − | 7.87916i | − | 0.0108230i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 424.430i | − | 0.581411i | ||||||
\(731\) | −1781.64 | −2.43726 | ||||||||
\(732\) | − | 29.5954i | − | 0.0404309i | ||||||
\(733\) | − | 104.468i | − | 0.142522i | −0.997458 | − | 0.0712608i | \(-0.977298\pi\) | ||
0.997458 | − | 0.0712608i | \(-0.0227023\pi\) | |||||||
\(734\) | 45.9140i | 0.0625531i | ||||||||
\(735\) | − | 180.801i | − | 0.245988i | ||||||
\(736\) | 82.2800 | − | 100.787i | 0.111794 | − | 0.136939i | ||||
\(737\) | 173.738 | 0.235736 | ||||||||
\(738\) | 263.512 | 0.357062 | ||||||||
\(739\) | 828.795 | 1.12151 | 0.560755 | − | 0.827982i | \(-0.310511\pi\) | ||||
0.560755 | + | 0.827982i | \(0.310511\pi\) | |||||||
\(740\) | −43.2905 | −0.0585007 | ||||||||
\(741\) | 9.05510i | 0.0122201i | ||||||||
\(742\) | −73.0533 | −0.0984546 | ||||||||
\(743\) | 1067.78i | 1.43712i | 0.695465 | + | 0.718560i | \(0.255198\pi\) | ||||
−0.695465 | + | 0.718560i | \(0.744802\pi\) | |||||||
\(744\) | 244.510 | 0.328643 | ||||||||
\(745\) | 549.700 | 0.737853 | ||||||||
\(746\) | − | 217.002i | − | 0.290888i | ||||||
\(747\) | − | 359.757i | − | 0.481602i | ||||||
\(748\) | 102.315 | 0.136785 | ||||||||
\(749\) | −169.273 | −0.225999 | ||||||||
\(750\) | − | 27.3861i | − | 0.0365148i | ||||||
\(751\) | − | 116.437i | − | 0.155043i | −0.996991 | − | 0.0775213i | \(-0.975299\pi\) | ||
0.996991 | − | 0.0775213i | \(-0.0247006\pi\) | |||||||
\(752\) | 68.5855 | 0.0912042 | ||||||||
\(753\) | − | 10.2076i | − | 0.0135559i | ||||||
\(754\) | −18.7130 | −0.0248183 | ||||||||
\(755\) | 468.343i | 0.620322i | ||||||||
\(756\) | 15.8201i | 0.0209261i | ||||||||
\(757\) | 893.537i | 1.18037i | 0.807269 | + | 0.590183i | \(0.200944\pi\) | ||||
−0.807269 | + | 0.590183i | \(0.799056\pi\) | |||||||
\(758\) | 845.045i | 1.11484i | ||||||||
\(759\) | 67.9022 | + | 55.4338i | 0.0894627 | + | 0.0730353i | ||||
\(760\) | 18.0686 | 0.0237745 | ||||||||
\(761\) | −80.0115 | −0.105140 | −0.0525700 | − | 0.998617i | \(-0.516741\pi\) | ||||
−0.0525700 | + | 0.998617i | \(0.516741\pi\) | |||||||
\(762\) | 247.057 | 0.324221 | ||||||||
\(763\) | −80.3580 | −0.105318 | ||||||||
\(764\) | 471.291i | 0.616873i | ||||||||
\(765\) | 155.963 | 0.203874 | ||||||||
\(766\) | − | 438.024i | − | 0.571833i | ||||||
\(767\) | −64.4440 | −0.0840209 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 890.267i | 1.15769i | 0.815436 | + | 0.578847i | \(0.196497\pi\) | ||||
−0.815436 | + | 0.578847i | \(0.803503\pi\) | |||||||
\(770\) | − | 10.5923i | − | 0.0137563i | ||||||
\(771\) | 78.4151 | 0.101706 | ||||||||
\(772\) | −680.251 | −0.881155 | ||||||||
\(773\) | − | 619.222i | − | 0.801063i | −0.916283 | − | 0.400531i | \(-0.868826\pi\) | ||
0.916283 | − | 0.400531i | \(-0.131174\pi\) | |||||||
\(774\) | 325.117i | 0.420048i | ||||||||
\(775\) | −249.552 | −0.322003 | ||||||||
\(776\) | 504.703i | 0.650391i | ||||||||
\(777\) | −25.5233 | −0.0328485 | ||||||||
\(778\) | 417.252i | 0.536313i | ||||||||
\(779\) | − | 177.443i | − | 0.227783i | ||||||
\(780\) | 14.1747i | 0.0181727i | ||||||||
\(781\) | 245.135i | 0.313873i | ||||||||
\(782\) | −585.815 | − | 478.245i | −0.749124 | − | 0.611567i | ||||
\(783\) | 37.5728 | 0.0479856 | ||||||||
\(784\) | 186.731 | 0.238177 | ||||||||
\(785\) | −473.076 | −0.602644 | ||||||||
\(786\) | −70.1875 | −0.0892971 | ||||||||
\(787\) | − | 375.043i | − | 0.476548i | −0.971198 | − | 0.238274i | \(-0.923418\pi\) | ||
0.971198 | − | 0.238274i | \(-0.0765816\pi\) | |||||||
\(788\) | −443.345 | −0.562621 | ||||||||
\(789\) | 366.343i | 0.464314i | ||||||||
\(790\) | −228.961 | −0.289824 | ||||||||
\(791\) | 38.6846 | 0.0489060 | ||||||||
\(792\) | − | 18.6707i | − | 0.0235741i | ||||||
\(793\) | − | 15.6340i | − | 0.0197151i | ||||||
\(794\) | −64.2704 | −0.0809451 | ||||||||
\(795\) | 131.424 | 0.165313 | ||||||||
\(796\) | − | 396.131i | − | 0.497651i | ||||||
\(797\) | 493.978i | 0.619797i | 0.950770 | + | 0.309898i | \(0.100295\pi\) | ||||
−0.950770 | + | 0.309898i | \(0.899705\pi\) | |||||||
\(798\) | 10.6529 | 0.0133495 | ||||||||
\(799\) | − | 398.647i | − | 0.498933i | ||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | 221.797i | 0.276900i | ||||||||
\(802\) | − | 72.8306i | − | 0.0908113i | ||||||
\(803\) | 295.325i | 0.367777i | ||||||||
\(804\) | 273.521i | 0.340200i | ||||||||
\(805\) | −49.5110 | + | 60.6473i | −0.0615044 | + | 0.0753382i | ||||
\(806\) | 129.165 | 0.160254 | ||||||||
\(807\) | 231.676 | 0.287083 | ||||||||
\(808\) | −416.539 | −0.515518 | ||||||||
\(809\) | −132.182 | −0.163389 | −0.0816946 | − | 0.996657i | \(-0.526033\pi\) | ||||
−0.0816946 | + | 0.996657i | \(0.526033\pi\) | |||||||
\(810\) | − | 28.4605i | − | 0.0351364i | ||||||
\(811\) | −158.090 | −0.194932 | −0.0974659 | − | 0.995239i | \(-0.531074\pi\) | ||||
−0.0974659 | + | 0.995239i | \(0.531074\pi\) | |||||||
\(812\) | 22.0150i | 0.0271121i | ||||||||
\(813\) | −323.572 | −0.397998 | ||||||||
\(814\) | 30.1222 | 0.0370052 | ||||||||
\(815\) | − | 31.6390i | − | 0.0388209i | ||||||
\(816\) | 161.078i | 0.197400i | ||||||||
\(817\) | 218.927 | 0.267964 | ||||||||
\(818\) | 717.752 | 0.877448 | ||||||||
\(819\) | 8.35711i | 0.0102040i | ||||||||
\(820\) | − | 277.766i | − | 0.338739i | ||||||
\(821\) | −218.188 | −0.265759 | −0.132879 | − | 0.991132i | \(-0.542422\pi\) | ||||
−0.132879 | + | 0.991132i | \(0.542422\pi\) | |||||||
\(822\) | 389.588i | 0.473951i | ||||||||
\(823\) | 147.052 | 0.178678 | 0.0893391 | − | 0.996001i | \(-0.471525\pi\) | ||||
0.0893391 | + | 0.996001i | \(0.471525\pi\) | |||||||
\(824\) | 166.750i | 0.202367i | ||||||||
\(825\) | 19.0557i | 0.0230978i | ||||||||
\(826\) | 75.8154i | 0.0917862i | ||||||||
\(827\) | − | 942.783i | − | 1.14000i | −0.821644 | − | 0.570002i | \(-0.806943\pi\) | ||
0.821644 | − | 0.570002i | \(-0.193057\pi\) | |||||||
\(828\) | −87.2712 | + | 106.901i | −0.105400 | + | 0.129107i | ||||
\(829\) | 110.053 | 0.132754 | 0.0663771 | − | 0.997795i | \(-0.478856\pi\) | ||||
0.0663771 | + | 0.997795i | \(0.478856\pi\) | |||||||
\(830\) | −379.217 | −0.456888 | ||||||||
\(831\) | 221.953 | 0.267091 | ||||||||
\(832\) | −14.6395 | −0.0175956 | ||||||||
\(833\) | − | 1085.35i | − | 1.30295i | ||||||
\(834\) | 291.763 | 0.349835 | ||||||||
\(835\) | 116.425i | 0.139431i | ||||||||
\(836\) | −12.5724 | −0.0150388 | ||||||||
\(837\) | −259.342 | −0.309847 | ||||||||
\(838\) | 667.052i | 0.796005i | ||||||||
\(839\) | 724.729i | 0.863800i | 0.901921 | + | 0.431900i | \(0.142157\pi\) | ||||
−0.901921 | + | 0.431900i | \(0.857843\pi\) | |||||||
\(840\) | 16.6758 | 0.0198522 | ||||||||
\(841\) | −788.714 | −0.937829 | ||||||||
\(842\) | − | 1075.15i | − | 1.27690i | ||||||
\(843\) | 317.430i | 0.376548i | ||||||||
\(844\) | −211.691 | −0.250818 | ||||||||
\(845\) | − | 370.408i | − | 0.438352i | ||||||
\(846\) | −72.7459 | −0.0859881 | ||||||||
\(847\) | − | 176.827i | − | 0.208768i | ||||||
\(848\) | 135.734i | 0.160063i | ||||||||
\(849\) | − | 756.440i | − | 0.890977i | ||||||
\(850\) | − | 164.400i | − | 0.193412i | ||||||
\(851\) | −172.467 | − | 140.798i | −0.202664 | − | 0.165450i | ||||
\(852\) | −385.924 | −0.452962 | ||||||||
\(853\) | −1575.08 | −1.84652 | −0.923261 | − | 0.384172i | \(-0.874487\pi\) | ||||
−0.923261 | + | 0.384172i | \(0.874487\pi\) | |||||||
\(854\) | −18.3927 | −0.0215371 | ||||||||
\(855\) | −19.1647 | −0.0224148 | ||||||||
\(856\) | 314.511i | 0.367419i | ||||||||
\(857\) | 190.678 | 0.222495 | 0.111247 | − | 0.993793i | \(-0.464515\pi\) | ||||
0.111247 | + | 0.993793i | \(0.464515\pi\) | |||||||
\(858\) | − | 9.86296i | − | 0.0114953i | ||||||
\(859\) | 81.9616 | 0.0954151 | 0.0477076 | − | 0.998861i | \(-0.484808\pi\) | ||||
0.0477076 | + | 0.998861i | \(0.484808\pi\) | |||||||
\(860\) | 342.704 | 0.398492 | ||||||||
\(861\) | − | 163.765i | − | 0.190204i | ||||||
\(862\) | 850.380i | 0.986520i | ||||||||
\(863\) | 1544.93 | 1.79019 | 0.895093 | − | 0.445878i | \(-0.147109\pi\) | ||||
0.895093 | + | 0.445878i | \(0.147109\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | − | 490.271i | − | 0.566788i | ||||||
\(866\) | 659.642i | 0.761712i | ||||||||
\(867\) | 435.690 | 0.502526 | ||||||||
\(868\) | − | 151.956i | − | 0.175065i | ||||||
\(869\) | 159.315 | 0.183331 | ||||||||
\(870\) | − | 39.6052i | − | 0.0455232i | ||||||
\(871\) | 144.490i | 0.165889i | ||||||||
\(872\) | 149.306i | 0.171222i | ||||||||
\(873\) | − | 535.318i | − | 0.613194i | ||||||
\(874\) | 71.9845 | + | 58.7665i | 0.0823621 | + | 0.0672385i | ||||
\(875\) | −17.0197 | −0.0194511 | ||||||||
\(876\) | −464.940 | −0.530753 | ||||||||
\(877\) | 277.527 | 0.316450 | 0.158225 | − | 0.987403i | \(-0.449423\pi\) | ||||
0.158225 | + | 0.987403i | \(0.449423\pi\) | |||||||
\(878\) | 416.231 | 0.474067 | ||||||||
\(879\) | 59.5855i | 0.0677878i | ||||||||
\(880\) | −19.6806 | −0.0223644 | ||||||||
\(881\) | 946.407i | 1.07424i | 0.843505 | + | 0.537121i | \(0.180488\pi\) | ||||
−0.843505 | + | 0.537121i | \(0.819512\pi\) | |||||||
\(882\) | −198.058 | −0.224555 | ||||||||
\(883\) | 1235.93 | 1.39969 | 0.699845 | − | 0.714295i | \(-0.253252\pi\) | ||||
0.699845 | + | 0.714295i | \(0.253252\pi\) | |||||||
\(884\) | 85.0910i | 0.0962568i | ||||||||
\(885\) | − | 136.393i | − | 0.154116i | ||||||
\(886\) | −908.166 | −1.02502 | ||||||||
\(887\) | −243.464 | −0.274480 | −0.137240 | − | 0.990538i | \(-0.543823\pi\) | ||||
−0.137240 | + | 0.990538i | \(0.543823\pi\) | |||||||
\(888\) | 47.4224i | 0.0534036i | ||||||||
\(889\) | − | 153.539i | − | 0.172710i | ||||||
\(890\) | 233.795 | 0.262691 | ||||||||
\(891\) | 19.8033i | 0.0222259i | ||||||||
\(892\) | 461.976 | 0.517910 | ||||||||
\(893\) | 48.9855i | 0.0548550i | ||||||||
\(894\) | − | 602.167i | − | 0.673564i | ||||||
\(895\) | − | 188.616i | − | 0.210744i | ||||||
\(896\) | 17.2227i | 0.0192218i | ||||||||
\(897\) | −46.1018 | + | 56.4712i | −0.0513955 | + | 0.0629556i | ||||
\(898\) | −938.931 | −1.04558 | ||||||||
\(899\) | −360.896 | −0.401442 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | 788.940 | 0.875627 | ||||||||
\(902\) | 193.274i | 0.214273i | ||||||||
\(903\) | 202.051 | 0.223756 | ||||||||
\(904\) | − | 71.8764i | − | 0.0795093i | ||||||
\(905\) | −609.630 | −0.673624 | ||||||||
\(906\) | 513.044 | 0.566274 | ||||||||
\(907\) | 1671.67i | 1.84307i | 0.388292 | + | 0.921536i | \(0.373065\pi\) | ||||
−0.388292 | + | 0.921536i | \(0.626935\pi\) | |||||||
\(908\) | − | 293.500i | − | 0.323237i | ||||||
\(909\) | 441.806 | 0.486035 | ||||||||
\(910\) | 8.80916 | 0.00968040 | ||||||||
\(911\) | − | 1179.25i | − | 1.29445i | −0.762297 | − | 0.647227i | \(-0.775929\pi\) | ||
0.762297 | − | 0.647227i | \(-0.224071\pi\) | |||||||
\(912\) | − | 19.7932i | − | 0.0217031i | ||||||
\(913\) | 263.865 | 0.289009 | ||||||||
\(914\) | − | 31.2810i | − | 0.0342243i | ||||||
\(915\) | 33.0887 | 0.0361625 | ||||||||
\(916\) | − | 407.713i | − | 0.445102i | ||||||
\(917\) | 43.6196i | 0.0475677i | ||||||||
\(918\) | − | 170.849i | − | 0.186110i | ||||||
\(919\) | − | 734.211i | − | 0.798924i | −0.916750 | − | 0.399462i | \(-0.869197\pi\) | ||
0.916750 | − | 0.399462i | \(-0.130803\pi\) | |||||||
\(920\) | 112.683 | + | 91.9919i | 0.122482 | + | 0.0999912i | ||||
\(921\) | 457.040 | 0.496243 | ||||||||
\(922\) | 470.921 | 0.510761 | ||||||||
\(923\) | −203.868 | −0.220875 | ||||||||
\(924\) | −11.6033 | −0.0125577 | ||||||||
\(925\) | − | 48.4003i | − | 0.0523247i | ||||||
\(926\) | 82.5931 | 0.0891934 | ||||||||
\(927\) | − | 176.866i | − | 0.190793i | ||||||
\(928\) | 40.9040 | 0.0440776 | ||||||||
\(929\) | −43.9814 | −0.0473427 | −0.0236714 | − | 0.999720i | \(-0.507536\pi\) | ||||
−0.0236714 | + | 0.999720i | \(0.507536\pi\) | |||||||
\(930\) | 273.371i | 0.293947i | ||||||||
\(931\) | 133.368i | 0.143252i | ||||||||
\(932\) | 593.862 | 0.637191 | ||||||||
\(933\) | −22.4620 | −0.0240751 | ||||||||
\(934\) | − | 861.664i | − | 0.922552i | ||||||
\(935\) | 114.392i | 0.122344i | ||||||||
\(936\) | 15.5276 | 0.0165893 | ||||||||
\(937\) | − | 393.511i | − | 0.419969i | −0.977705 | − | 0.209984i | \(-0.932659\pi\) | ||
0.977705 | − | 0.209984i | \(-0.0673413\pi\) | |||||||
\(938\) | 169.985 | 0.181221 | ||||||||
\(939\) | 124.318i | 0.132394i | ||||||||
\(940\) | 76.6809i | 0.0815755i | ||||||||
\(941\) | − | 330.827i | − | 0.351569i | −0.984429 | − | 0.175785i | \(-0.943754\pi\) | ||
0.984429 | − | 0.175785i | \(-0.0562463\pi\) | |||||||
\(942\) | 518.228i | 0.550136i | ||||||||
\(943\) | 903.407 | − | 1106.61i | 0.958013 | − | 1.17349i | ||||
\(944\) | 140.866 | 0.149222 | ||||||||
\(945\) | −17.6874 | −0.0187168 | ||||||||
\(946\) | −238.459 | −0.252070 | ||||||||
\(947\) | −251.483 | −0.265557 | −0.132779 | − | 0.991146i | \(-0.542390\pi\) | ||||
−0.132779 | + | 0.991146i | \(0.542390\pi\) | |||||||
\(948\) | 250.814i | 0.264572i | ||||||||
\(949\) | −245.608 | −0.258808 | ||||||||
\(950\) | 20.2013i | 0.0212646i | ||||||||
\(951\) | −335.823 | −0.353126 | ||||||||
\(952\) | 100.106 | 0.105153 | ||||||||
\(953\) | 1263.57i | 1.32589i | 0.748670 | + | 0.662943i | \(0.230693\pi\) | ||||
−0.748670 | + | 0.662943i | \(0.769307\pi\) | |||||||
\(954\) | − | 143.967i | − | 0.150909i | ||||||
\(955\) | −526.919 | −0.551748 | ||||||||
\(956\) | −532.915 | −0.557442 | ||||||||
\(957\) | 27.5579i | 0.0287961i | ||||||||
\(958\) | − | 283.259i | − | 0.295677i | ||||||
\(959\) | 242.118 | 0.252469 | ||||||||
\(960\) | − | 30.9839i | − | 0.0322749i | ||||||
\(961\) | 1530.05 | 1.59214 | ||||||||
\(962\) | 25.0513i | 0.0260409i | ||||||||
\(963\) | − | 333.589i | − | 0.346406i | ||||||
\(964\) | 655.231i | 0.679700i | ||||||||
\(965\) | − | 760.544i | − | 0.788129i | ||||||
\(966\) | 66.4358 | + | 54.2366i | 0.0687741 | + | 0.0561455i | ||||
\(967\) | −717.203 | −0.741678 | −0.370839 | − | 0.928697i | \(-0.620930\pi\) | ||||
−0.370839 | + | 0.928697i | \(0.620930\pi\) | |||||||
\(968\) | −328.546 | −0.339407 | ||||||||
\(969\) | −115.046 | −0.118727 | ||||||||
\(970\) | −564.275 | −0.581727 | ||||||||
\(971\) | − | 1232.61i | − | 1.26943i | −0.772748 | − | 0.634713i | \(-0.781118\pi\) | ||
0.772748 | − | 0.634713i | \(-0.218882\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | − | 181.322i | − | 0.186354i | ||||||
\(974\) | −192.521 | −0.197661 | ||||||||
\(975\) | −15.8478 | −0.0162541 | ||||||||
\(976\) | 34.1738i | 0.0350142i | ||||||||
\(977\) | 1365.57i | 1.39771i | 0.715262 | + | 0.698857i | \(0.246307\pi\) | ||||
−0.715262 | + | 0.698857i | \(0.753693\pi\) | |||||||
\(978\) | −34.6588 | −0.0354384 | ||||||||
\(979\) | −162.678 | −0.166168 | ||||||||
\(980\) | 208.771i | 0.213032i | ||||||||
\(981\) | − | 158.363i | − | 0.161430i | ||||||
\(982\) | 307.335 | 0.312968 | ||||||||
\(983\) | 1879.04i | 1.91154i | 0.294119 | + | 0.955769i | \(0.404974\pi\) | ||||
−0.294119 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(984\) | −304.277 | −0.309225 | ||||||||
\(985\) | − | 495.675i | − | 0.503223i | ||||||
\(986\) | − | 237.751i | − | 0.241127i | ||||||
\(987\) | 45.2096i | 0.0458050i | ||||||||
\(988\) | − | 10.4559i | − | 0.0105829i | ||||||
\(989\) | 1365.31 | + | 1114.61i | 1.38050 | + | 1.12701i | ||||
\(990\) | 20.8745 | 0.0210853 | ||||||||
\(991\) | 1192.84 | 1.20367 | 0.601837 | − | 0.798619i | \(-0.294436\pi\) | ||||
0.601837 | + | 0.798619i | \(0.294436\pi\) | |||||||
\(992\) | −282.336 | −0.284613 | ||||||||
\(993\) | −681.260 | −0.686062 | ||||||||
\(994\) | 239.841i | 0.241289i | ||||||||
\(995\) | 442.887 | 0.445113 | ||||||||
\(996\) | 415.411i | 0.417080i | ||||||||
\(997\) | 1855.93 | 1.86152 | 0.930758 | − | 0.365637i | \(-0.119149\pi\) | ||||
0.930758 | + | 0.365637i | \(0.119149\pi\) | |||||||
\(998\) | 877.763 | 0.879522 | ||||||||
\(999\) | − | 50.2991i | − | 0.0503494i |
(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 | 690.3.c.a.91.6 | yes | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.19 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.3 | ✓ | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.30 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.3 | ✓ | 32 | 23.22 | odd | 2 | inner | |
690.3.c.a.91.6 | yes | 32 | 1.1 | even | 1 | trivial | |
2070.3.c.b.91.19 | 32 | 3.2 | odd | 2 | |||
2070.3.c.b.91.30 | 32 | 69.68 | even | 2 |