Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,3,Mod(321,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1840.321");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.k (of order \(2\), degree \(1\), not 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: | \(50.1363686423\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 321.5 | ||
Character | \(\chi\) | \(=\) | 1840.321 |
Dual form | 1840.3.k.e.321.6 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −4.84326 | −1.61442 | −0.807211 | − | 0.590263i | \(-0.799024\pi\) | ||||
−0.807211 | + | 0.590263i | \(0.799024\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.25633i | − | 0.608047i | −0.952665 | − | 0.304024i | \(-0.901670\pi\) | ||
0.952665 | − | 0.304024i | \(-0.0983302\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 14.4572 | 1.60636 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.80230i | 0.709300i | 0.934999 | + | 0.354650i | \(0.115400\pi\) | ||||
−0.934999 | + | 0.354650i | \(0.884600\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.89073 | −0.760826 | −0.380413 | − | 0.924817i | \(-0.624218\pi\) | ||||
−0.380413 | + | 0.924817i | \(0.624218\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 10.8299i | − | 0.721991i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.5076i | 1.38280i | 0.722471 | + | 0.691401i | \(0.243006\pi\) | ||||
−0.722471 | + | 0.691401i | \(0.756994\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 22.1948i | − | 1.16815i | −0.811700 | − | 0.584075i | \(-0.801457\pi\) | ||
0.811700 | − | 0.584075i | \(-0.198543\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 20.6145i | 0.981644i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.3379 | − | 12.4518i | −0.840777 | − | 0.541381i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.4307 | −0.978915 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 57.8083 | 1.99339 | 0.996694 | − | 0.0812432i | \(-0.0258891\pi\) | ||||
0.996694 | + | 0.0812432i | \(0.0258891\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.0375 | −1.22702 | −0.613508 | − | 0.789688i | \(-0.710242\pi\) | ||||
−0.613508 | + | 0.789688i | \(0.710242\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 37.7886i | − | 1.14511i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.51744 | 0.271927 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.1751i | 0.383112i | 0.981482 | + | 0.191556i | \(0.0613533\pi\) | ||||
−0.981482 | + | 0.191556i | \(0.938647\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 47.9034 | 1.22829 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.7893 | −0.458275 | −0.229137 | − | 0.973394i | \(-0.573590\pi\) | ||||
−0.229137 | + | 0.973394i | \(0.573590\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 56.4998i | 1.31395i | 0.753913 | + | 0.656974i | \(0.228164\pi\) | ||||
−0.753913 | + | 0.656974i | \(0.771836\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 32.3273i | 0.718384i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 62.7323 | 1.33473 | 0.667365 | − | 0.744731i | \(-0.267422\pi\) | ||||
0.667365 | + | 0.744731i | \(0.267422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 30.8837 | 0.630279 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 113.854i | − | 2.23242i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 90.9388i | 1.71583i | 0.513794 | + | 0.857913i | \(0.328239\pi\) | ||||
−0.513794 | + | 0.857913i | \(0.671761\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.4465 | −0.317209 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 107.495i | 1.88589i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −56.2233 | −0.952937 | −0.476469 | − | 0.879191i | \(-0.658083\pi\) | ||||
−0.476469 | + | 0.879191i | \(0.658083\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.12348i | − | 0.0675980i | −0.999429 | − | 0.0337990i | \(-0.989239\pi\) | ||
0.999429 | − | 0.0337990i | \(-0.0107606\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 61.5346i | − | 0.976740i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 22.1164i | − | 0.340252i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 116.768i | 1.74280i | 0.490572 | + | 0.871401i | \(0.336788\pi\) | ||||
−0.490572 | + | 0.871401i | \(0.663212\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 93.6585 | + | 60.3072i | 1.35737 | + | 0.874017i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 84.7000 | 1.19296 | 0.596479 | − | 0.802629i | \(-0.296566\pi\) | ||||
0.596479 | + | 0.802629i | \(0.296566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −105.079 | −1.43944 | −0.719720 | − | 0.694265i | \(-0.755730\pi\) | ||||
−0.719720 | + | 0.694265i | \(0.755730\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 24.2163 | 0.322884 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 33.2092 | 0.431288 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 72.7655i | − | 0.921083i | −0.887638 | − | 0.460541i | \(-0.847655\pi\) | ||
0.887638 | − | 0.460541i | \(-0.152345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.10402 | −0.0259756 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 29.1890i | 0.351675i | 0.984419 | + | 0.175838i | \(0.0562633\pi\) | ||||
−0.984419 | + | 0.175838i | \(0.943737\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −52.5647 | −0.618408 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −279.981 | −3.21817 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 106.120i | − | 1.19236i | −0.802851 | − | 0.596180i | \(-0.796685\pi\) | ||
0.802851 | − | 0.596180i | \(-0.203315\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 42.0982i | 0.462618i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 184.226 | 1.98092 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 49.6292 | 0.522412 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 94.8741i | − | 0.978084i | −0.872260 | − | 0.489042i | \(-0.837346\pi\) | ||
0.872260 | − | 0.489042i | \(-0.162654\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 112.799i | 1.13939i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −28.3320 | −0.280514 | −0.140257 | − | 0.990115i | \(-0.544793\pi\) | ||||
−0.140257 | + | 0.990115i | \(0.544793\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 72.5869i | − | 0.704727i | −0.935863 | − | 0.352363i | \(-0.885378\pi\) | ||
0.935863 | − | 0.352363i | \(-0.114622\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −46.0955 | −0.439005 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.27988i | 0.0399989i | 0.999800 | + | 0.0199994i | \(0.00636644\pi\) | ||||
−0.999800 | + | 0.0199994i | \(0.993634\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 114.253i | 1.04819i | 0.851659 | + | 0.524096i | \(0.175597\pi\) | ||||
−0.851659 | + | 0.524096i | \(0.824403\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 68.6539i | − | 0.618504i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 116.414i | − | 1.03021i | −0.857126 | − | 0.515106i | \(-0.827753\pi\) | ||
0.857126 | − | 0.515106i | \(-0.172247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 27.8430 | − | 43.2408i | 0.242113 | − | 0.376007i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −142.992 | −1.22216 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 100.056 | 0.840809 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.1241 | 0.496894 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 91.0013 | 0.739848 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −168.737 | −1.32864 | −0.664318 | − | 0.747450i | \(-0.731278\pi\) | ||||
−0.664318 | + | 0.747450i | \(0.731278\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 273.643i | − | 2.12127i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 64.8148 | 0.494769 | 0.247385 | − | 0.968917i | \(-0.420429\pi\) | ||||
0.247385 | + | 0.968917i | \(0.420429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −94.4686 | −0.710290 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 59.1008i | − | 0.437784i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 238.587i | − | 1.74151i | −0.491717 | − | 0.870755i | \(-0.663631\pi\) | ||
0.491717 | − | 0.870755i | \(-0.336369\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −124.256 | −0.893929 | −0.446965 | − | 0.894552i | \(-0.647495\pi\) | ||||
−0.446965 | + | 0.894552i | \(0.647495\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −303.829 | −2.15482 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 77.1705i | − | 0.539654i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 129.263i | 0.891470i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −149.578 | −1.01754 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 206.750i | − | 1.38759i | −0.720174 | − | 0.693794i | \(-0.755938\pi\) | ||
0.720174 | − | 0.693794i | \(-0.244062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.4800 | −0.122384 | −0.0611919 | − | 0.998126i | \(-0.519490\pi\) | ||||
−0.0611919 | + | 0.998126i | \(0.519490\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 339.855i | 2.22127i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 85.0545i | − | 0.548739i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 239.367i | − | 1.52463i | −0.647205 | − | 0.762316i | \(-0.724062\pi\) | ||
0.647205 | − | 0.762316i | \(-0.275938\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 440.441i | − | 2.77007i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −52.9988 | + | 82.3084i | −0.329185 | + | 0.511232i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.6526 | 0.108298 | 0.0541489 | − | 0.998533i | \(-0.482755\pi\) | ||||
0.0541489 | + | 0.998533i | \(0.482755\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 84.4979 | 0.512108 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −144.926 | −0.867819 | −0.433909 | − | 0.900956i | \(-0.642866\pi\) | ||||
−0.433909 | + | 0.900956i | \(0.642866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −71.1734 | −0.421144 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 320.875i | − | 1.87646i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.90140 | −0.0456729 | −0.0228364 | − | 0.999739i | \(-0.507270\pi\) | ||||
−0.0228364 | + | 0.999739i | \(0.507270\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.2816i | 0.121609i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 272.304 | 1.53844 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.93306 | −0.0275590 | −0.0137795 | − | 0.999905i | \(-0.504386\pi\) | ||||
−0.0137795 | + | 0.999905i | \(0.504386\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.10508i | 0.0337297i | 0.999858 | + | 0.0168649i | \(0.00536850\pi\) | ||||
−0.999858 | + | 0.0168649i | \(0.994631\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.9711i | 0.109132i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.6966 | −0.171333 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −183.414 | −0.980821 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 112.498i | 0.595226i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 136.948i | − | 0.717004i | −0.933529 | − | 0.358502i | \(-0.883288\pi\) | ||
0.933529 | − | 0.358502i | \(-0.116712\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 63.4162 | 0.328582 | 0.164291 | − | 0.986412i | \(-0.447466\pi\) | ||||
0.164291 | + | 0.986412i | \(0.447466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 107.115i | 0.549309i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 30.3151 | 0.153884 | 0.0769418 | − | 0.997036i | \(-0.475484\pi\) | ||||
0.0769418 | + | 0.997036i | \(0.475484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 170.671i | − | 0.857646i | −0.903389 | − | 0.428823i | \(-0.858928\pi\) | ||
0.903389 | − | 0.428823i | \(-0.141072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 565.537i | − | 2.81362i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 246.051i | − | 1.21207i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 42.0141i | − | 0.204947i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −279.572 | − | 180.018i | −1.35059 | − | 0.869651i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 173.171 | 0.828568 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −70.1721 | −0.332569 | −0.166285 | − | 0.986078i | \(-0.553177\pi\) | ||||
−0.166285 | + | 0.986078i | \(0.553177\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −410.224 | −1.92594 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −126.337 | −0.587616 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 161.900i | 0.746084i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 508.926 | 2.32386 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 232.508i | − | 1.05207i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 42.2122 | 0.189292 | 0.0946461 | − | 0.995511i | \(-0.469828\pi\) | ||||
0.0946461 | + | 0.995511i | \(0.469828\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −72.2860 | −0.321271 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 134.443i | 0.592258i | 0.955148 | + | 0.296129i | \(0.0956958\pi\) | ||||
−0.955148 | + | 0.296129i | \(0.904304\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 329.622i | − | 1.43940i | −0.694288 | − | 0.719698i | \(-0.744280\pi\) | ||
0.694288 | − | 0.719698i | \(-0.255720\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −160.841 | −0.696280 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −205.310 | −0.881157 | −0.440579 | − | 0.897714i | \(-0.645227\pi\) | ||||
−0.440579 | + | 0.897714i | \(0.645227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 140.274i | 0.596910i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 352.423i | 1.48702i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −345.287 | −1.44471 | −0.722357 | − | 0.691520i | \(-0.756941\pi\) | ||||
−0.722357 | + | 0.691520i | \(0.756941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 478.152i | 1.98403i | 0.126109 | + | 0.992016i | \(0.459751\pi\) | ||||
−0.126109 | + | 0.992016i | \(0.540249\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 248.067 | 1.02085 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 69.0580i | 0.281869i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 219.523i | 0.888758i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 141.370i | − | 0.567752i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 39.5773i | 0.157679i | 0.996887 | + | 0.0788393i | \(0.0251214\pi\) | ||||
−0.996887 | + | 0.0788393i | \(0.974879\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 97.1524 | − | 150.880i | 0.384001 | − | 0.596363i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 254.585 | 0.998371 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −327.429 | −1.27404 | −0.637022 | − | 0.770846i | \(-0.719834\pi\) | ||||
−0.637022 | + | 0.770846i | \(0.719834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 60.3341 | 0.232950 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 835.746 | 3.20209 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 262.464i | 0.997961i | 0.866613 | + | 0.498980i | \(0.166292\pi\) | ||||
−0.866613 | + | 0.498980i | \(0.833708\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −203.345 | −0.767341 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 513.967i | 1.92497i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −78.9203 | −0.293384 | −0.146692 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146692 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 297.037 | 1.09608 | 0.548039 | − | 0.836453i | \(-0.315375\pi\) | ||||
0.548039 | + | 0.836453i | \(0.315375\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 203.893i | − | 0.746860i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 39.0115i | − | 0.141860i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −522.010 | −1.88451 | −0.942256 | − | 0.334893i | \(-0.891300\pi\) | ||||
−0.942256 | + | 0.334893i | \(0.891300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −549.916 | −1.97103 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 374.374i | − | 1.33229i | −0.745821 | − | 0.666146i | \(-0.767943\pi\) | ||
0.745821 | − | 0.666146i | \(-0.232057\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 561.471i | − | 1.98400i | −0.126255 | − | 0.991998i | \(-0.540296\pi\) | ||
0.126255 | − | 0.991998i | \(-0.459704\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −240.367 | −0.843394 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 79.9733i | 0.278653i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −263.609 | −0.912141 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 459.501i | 1.57904i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 114.848i | − | 0.391972i | −0.980607 | − | 0.195986i | \(-0.937209\pi\) | ||
0.980607 | − | 0.195986i | \(-0.0627907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 125.719i | − | 0.426166i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 206.220i | − | 0.694344i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 191.266 | + | 123.157i | 0.639685 | + | 0.411896i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 240.482 | 0.798943 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 137.219 | 0.452868 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.22038 | 0.0302307 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 204.415 | 0.665848 | 0.332924 | − | 0.942954i | \(-0.391965\pi\) | ||||
0.332924 | + | 0.942954i | \(0.391965\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 351.557i | 1.13773i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −57.5890 | −0.185173 | −0.0925867 | − | 0.995705i | \(-0.529514\pi\) | ||||
−0.0925867 | + | 0.995705i | \(0.529514\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 174.612i | − | 0.557865i | −0.960311 | − | 0.278933i | \(-0.910019\pi\) | ||
0.960311 | − | 0.278933i | \(-0.0899806\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 137.596 | 0.436812 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −302.355 | −0.953802 | −0.476901 | − | 0.878957i | \(-0.658240\pi\) | ||||
−0.476901 | + | 0.878957i | \(0.658240\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 451.037i | 1.41391i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 20.7286i | − | 0.0645750i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 521.748 | 1.61532 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 49.4537 | 0.152165 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 553.357i | − | 1.69222i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 267.009i | − | 0.811579i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −534.227 | −1.61398 | −0.806989 | − | 0.590566i | \(-0.798905\pi\) | ||||
−0.806989 | + | 0.590566i | \(0.798905\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 204.933i | 0.615414i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −261.100 | −0.779404 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 72.7809i | 0.215967i | 0.994153 | + | 0.107984i | \(0.0344394\pi\) | ||||
−0.994153 | + | 0.107984i | \(0.965561\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 563.824i | 1.66320i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 296.780i | − | 0.870323i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 340.011i | − | 0.991286i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −134.851 | + | 209.427i | −0.390872 | + | 0.607034i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −511.199 | −1.47319 | −0.736597 | − | 0.676332i | \(-0.763569\pi\) | ||||
−0.736597 | + | 0.676332i | \(0.763569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 303.181 | 0.868715 | 0.434357 | − | 0.900741i | \(-0.356975\pi\) | ||||
0.434357 | + | 0.900741i | \(0.356975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 261.419 | 0.744783 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 134.926 | 0.382226 | 0.191113 | − | 0.981568i | \(-0.438790\pi\) | ||||
0.191113 | + | 0.981568i | \(0.438790\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 189.395i | 0.533507i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −484.599 | −1.35742 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 697.585i | 1.94313i | 0.236765 | + | 0.971567i | \(0.423913\pi\) | ||||
−0.236765 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −131.611 | −0.364573 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −291.197 | −0.802196 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 234.964i | − | 0.643737i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 0.324838i | − | 0.000885116i | −1.00000 | 0.000442558i | \(-0.999859\pi\) | |||
1.00000 | 0.000442558i | \(-0.000140871\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −271.640 | −0.736152 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 387.066 | 1.04330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 458.513i | − | 1.22926i | −0.788817 | − | 0.614629i | \(-0.789306\pi\) | ||
0.788817 | − | 0.614629i | \(-0.210694\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 54.1493i | 0.144398i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −571.766 | −1.51662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 336.529i | − | 0.887940i | −0.896042 | − | 0.443970i | \(-0.853570\pi\) | ||
0.896042 | − | 0.443970i | \(-0.146430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 817.237 | 2.14498 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.7590i | 0.0672558i | 0.999434 | + | 0.0336279i | \(0.0107061\pi\) | ||||
−0.999434 | + | 0.0336279i | \(0.989294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 74.2579i | 0.192878i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 816.829i | 2.11067i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 236.383i | 0.607669i | 0.952725 | + | 0.303834i | \(0.0982669\pi\) | ||||
−0.952725 | + | 0.303834i | \(0.901733\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 292.711 | − | 454.588i | 0.748622 | − | 1.16263i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −313.915 | −0.798766 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 162.709 | 0.411921 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 231.062 | 0.582021 | 0.291010 | − | 0.956720i | \(-0.406009\pi\) | ||||
0.291010 | + | 0.956720i | \(0.406009\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 457.536 | 1.14671 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 391.881i | − | 0.977260i | −0.872491 | − | 0.488630i | \(-0.837497\pi\) | ||
0.872491 | − | 0.488630i | \(-0.162503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 376.219 | 0.933546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 4.70474i | − | 0.0116166i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −110.599 | −0.271741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.5445 | 0.0502309 | 0.0251155 | − | 0.999685i | \(-0.492005\pi\) | ||||
0.0251155 | + | 0.999685i | \(0.492005\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1155.54i | 2.81153i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 239.305i | 0.579431i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −65.2687 | −0.157274 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 601.805 | 1.44318 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 70.9780i | − | 0.169399i | −0.996407 | − | 0.0846993i | \(-0.973007\pi\) | ||
0.996407 | − | 0.0846993i | \(-0.0269930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 218.160i | − | 0.518195i | −0.965851 | − | 0.259098i | \(-0.916575\pi\) | ||
0.965851 | − | 0.259098i | \(-0.0834252\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 906.934 | 2.14405 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 117.538i | − | 0.276560i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.5509 | −0.0411028 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 373.757i | 0.871228i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.6479i | 0.0316658i | 0.999875 | + | 0.0158329i | \(0.00503997\pi\) | ||||
−0.999875 | + | 0.0158329i | \(0.994960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 596.772i | − | 1.37823i | −0.724654 | − | 0.689113i | \(-0.758000\pi\) | ||
0.724654 | − | 0.689113i | \(-0.242000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 626.056i | − | 1.43921i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −276.365 | + | 429.201i | −0.632414 | + | 0.982154i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 395.203 | 0.900234 | 0.450117 | − | 0.892970i | \(-0.351382\pi\) | ||||
0.450117 | + | 0.892970i | \(0.351382\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 446.491 | 1.01245 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 641.179 | 1.44736 | 0.723678 | − | 0.690137i | \(-0.242450\pi\) | ||||
0.723678 | + | 0.690137i | \(0.242450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 237.292 | 0.533240 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1001.35i | 2.24015i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 457.160 | 1.01817 | 0.509087 | − | 0.860715i | \(-0.329983\pi\) | ||||
0.509087 | + | 0.860715i | \(0.329983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 146.599i | − | 0.325054i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 89.5033 | 0.197579 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −94.1345 | −0.206889 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 478.890i | 1.04790i | 0.851749 | + | 0.523949i | \(0.175542\pi\) | ||||
−0.851749 | + | 0.523949i | \(0.824458\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 621.323i | − | 1.35364i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 734.375 | 1.59300 | 0.796502 | − | 0.604636i | \(-0.206681\pi\) | ||||
0.796502 | + | 0.604636i | \(0.206681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −500.834 | −1.08171 | −0.540857 | − | 0.841115i | \(-0.681900\pi\) | ||||
−0.540857 | + | 0.841115i | \(0.681900\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 411.941i | 0.885895i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.4457i | 0.0459223i | 0.999736 | + | 0.0229612i | \(0.00730941\pi\) | ||||
−0.999736 | + | 0.0229612i | \(0.992691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 497.002 | 1.05971 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1159.32i | 2.46140i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −440.828 | −0.931984 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 110.974i | 0.233630i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1314.72i | 2.75623i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 333.257i | − | 0.695735i | −0.937544 | − | 0.347867i | \(-0.886906\pi\) | ||
0.937544 | − | 0.347867i | \(-0.113094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 140.202i | − | 0.291481i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 256.687 | − | 398.641i | 0.531443 | − | 0.825344i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 212.145 | 0.437412 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 522.920 | 1.07376 | 0.536879 | − | 0.843659i | \(-0.319603\pi\) | ||||
0.536879 | + | 0.843659i | \(0.319603\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −85.4960 | −0.174838 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −107.040 | −0.218005 | −0.109002 | − | 0.994041i | \(-0.534766\pi\) | ||||
−0.109002 | + | 0.994041i | \(0.534766\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1358.94i | 2.75646i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −252.227 | −0.509550 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 360.511i | − | 0.725374i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −655.185 | −1.31300 | −0.656498 | − | 0.754328i | \(-0.727963\pi\) | ||||
−0.656498 | + | 0.754328i | \(0.727963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 701.914 | 1.40103 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 241.825i | 0.480766i | 0.970678 | + | 0.240383i | \(0.0772731\pi\) | ||||
−0.970678 | + | 0.240383i | \(0.922727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 63.3522i | − | 0.125450i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 344.712 | 0.679905 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −432.806 | −0.850307 | −0.425153 | − | 0.905121i | \(-0.639780\pi\) | ||||
−0.425153 | + | 0.905121i | \(0.639780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 447.251i | 0.875247i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 586.625i | 1.14352i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 162.309 | 0.315163 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 489.456i | 0.946724i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 38.2686 | 0.0737352 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 49.2636i | 0.0945558i | 0.998882 | + | 0.0472779i | \(0.0150546\pi\) | ||||
−0.998882 | + | 0.0472779i | \(0.984945\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 184.254i | 0.352303i | 0.984363 | + | 0.176151i | \(0.0563649\pi\) | ||||
−0.984363 | + | 0.176151i | \(0.943635\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 103.073i | − | 0.196329i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 894.172i | − | 1.69672i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 218.907 | + | 481.581i | 0.413813 | + | 0.910362i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −812.832 | −1.53076 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 185.840 | 0.348667 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.57010 | −0.0178880 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23.8921 | 0.0444918 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 240.963i | 0.447057i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 411.725 | 0.761044 | 0.380522 | − | 0.924772i | \(-0.375744\pi\) | ||||
0.380522 | + | 0.924772i | \(0.375744\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 29.5685i | − | 0.0544540i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −255.477 | −0.468765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 388.425 | 0.710101 | 0.355050 | − | 0.934847i | \(-0.384464\pi\) | ||||
0.355050 | + | 0.934847i | \(0.384464\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 59.6140i | − | 0.108586i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1283.05i | − | 2.32858i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −309.714 | −0.560062 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 153.515 | 0.276603 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 87.2673i | − | 0.156674i | −0.996927 | − | 0.0783369i | \(-0.975039\pi\) | ||
0.996927 | − | 0.0783369i | \(-0.0249610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 558.824i | − | 0.999686i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 888.320 | 1.58346 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1061.94i | − | 1.88621i | −0.332495 | − | 0.943105i | \(-0.607891\pi\) | ||
0.332495 | − | 0.943105i | \(-0.392109\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 260.310 | 0.460725 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.95542i | 0.0157944i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 89.2879i | − | 0.156921i | −0.996917 | − | 0.0784604i | \(-0.975000\pi\) | ||
0.996917 | − | 0.0784604i | \(-0.0250004\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 378.800i | 0.663398i | 0.943385 | + | 0.331699i | \(0.107622\pi\) | ||||
−0.943385 | + | 0.331699i | \(0.892378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 663.274i | 1.15755i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 96.6894 | + | 62.2588i | 0.168155 | + | 0.108276i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 512.166 | 0.887635 | 0.443818 | − | 0.896117i | \(-0.353624\pi\) | ||||
0.443818 | + | 0.896117i | \(0.353624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −307.142 | −0.530469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 124.238 | 0.213835 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −709.532 | −1.21704 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 319.741i | − | 0.546565i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −915.337 | −1.55935 | −0.779674 | − | 0.626186i | \(-0.784615\pi\) | ||||
−0.779674 | + | 0.626186i | \(0.784615\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 844.237i | 1.43334i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −146.824 | −0.248433 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −522.001 | −0.880272 | −0.440136 | − | 0.897931i | \(-0.645070\pi\) | ||||
−0.440136 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 223.733i | 0.376021i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 826.607i | 1.38460i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 431.271 | 0.719985 | 0.359993 | − | 0.932955i | \(-0.382779\pi\) | ||||
0.359993 | + | 0.932955i | \(0.382779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3935 | −0.0405882 | −0.0202941 | − | 0.999794i | \(-0.506460\pi\) | ||||
−0.0202941 | + | 0.999794i | \(0.506460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1688.13i | 2.79956i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 134.442i | 0.222218i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −618.034 | −1.01818 | −0.509089 | − | 0.860714i | \(-0.670018\pi\) | ||||
−0.509089 | + | 0.860714i | \(0.670018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1191.69i | 1.95680i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −620.469 | −1.01550 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 997.907i | 1.62791i | 0.580930 | + | 0.813954i | \(0.302689\pi\) | ||||
−0.580930 | + | 0.813954i | \(0.697311\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 203.485i | 0.330870i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 797.346i | − | 1.29230i | −0.763212 | − | 0.646148i | \(-0.776379\pi\) | ||
0.763212 | − | 0.646148i | \(-0.223621\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 667.584i | − | 1.07849i | −0.842150 | − | 0.539244i | \(-0.818710\pi\) | ||
0.842150 | − | 0.539244i | \(-0.181290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 511.114 | + | 329.109i | 0.823049 | + | 0.529966i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −451.682 | −0.725011 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −838.712 | −1.33766 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −333.224 | −0.529768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.47756i | − | 0.00392641i | −0.999998 | − | 0.00196320i | \(-0.999375\pi\) | ||
0.999998 | − | 0.00196320i | \(-0.000624908\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 339.862 | 0.536907 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 377.307i | − | 0.594184i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −305.462 | −0.479532 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1224.53 | 1.91631 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 171.378i | 0.267361i | 0.991024 | + | 0.133680i | \(0.0426796\pi\) | ||||
−0.991024 | + | 0.133680i | \(0.957320\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 879.530i | − | 1.36785i | −0.729551 | − | 0.683927i | \(-0.760271\pi\) | ||
0.729551 | − | 0.683927i | \(-0.239729\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 611.885 | 0.948660 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 465.470 | 0.719428 | 0.359714 | − | 0.933063i | \(-0.382874\pi\) | ||||
0.359714 | + | 0.933063i | \(0.382874\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 438.671i | − | 0.675918i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 784.126i | − | 1.20449i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −868.579 | −1.33014 | −0.665068 | − | 0.746782i | \(-0.731598\pi\) | ||||
−0.665068 | + | 0.746782i | \(0.731598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 144.930i | 0.221268i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1519.15 | −2.31225 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 216.285i | − | 0.328202i | −0.986444 | − | 0.164101i | \(-0.947528\pi\) | ||
0.986444 | − | 0.164101i | \(-0.0524723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 650.905i | − | 0.984727i | −0.870390 | − | 0.492363i | \(-0.836133\pi\) | ||
0.870390 | − | 0.492363i | \(-0.163867\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1126.10i | 1.69849i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 211.238i | − | 0.317651i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1117.89 | − | 719.815i | −1.67600 | − | 1.07918i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −204.445 | −0.305597 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.1726 | 0.0479473 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −431.470 | −0.641114 | −0.320557 | − | 0.947229i | \(-0.603870\pi\) | ||||
−0.320557 | + | 0.947229i | \(0.603870\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 132.153 | 0.195783 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 912.137i | − | 1.34732i | −0.739041 | − | 0.673661i | \(-0.764721\pi\) | ||
0.739041 | − | 0.673661i | \(-0.235279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −403.816 | −0.594721 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 651.141i | − | 0.956154i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 635.519 | 0.930481 | 0.465241 | − | 0.885184i | \(-0.345968\pi\) | ||||
0.465241 | + | 0.885184i | \(0.345968\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 533.496 | 0.778827 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1596.44i | 2.32379i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 899.452i | − | 1.30544i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 157.061 | 0.227295 | 0.113648 | − | 0.993521i | \(-0.463747\pi\) | ||||
0.113648 | + | 0.993521i | \(0.463747\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 480.112 | 0.692802 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 277.845i | − | 0.399777i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 441.691i | − | 0.633703i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 994.369 | 1.42256 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 458.204i | 0.653643i | 0.945086 | + | 0.326821i | \(0.105978\pi\) | ||||
−0.945086 | + | 0.326821i | \(0.894022\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 314.615 | 0.447532 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 679.383i | − | 0.963664i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 120.590i | 0.170566i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 745.366i | − | 1.05129i | −0.850703 | − | 0.525646i | \(-0.823824\pi\) | ||
0.850703 | − | 0.525646i | \(-0.176176\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1051.99i | − | 1.47959i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 735.565 | + | 473.634i | 1.03165 | + | 0.664283i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 172.558 | 0.241340 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1672.31 | 2.33238 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −308.243 | −0.428711 | −0.214355 | − | 0.976756i | \(-0.568765\pi\) | ||||
−0.214355 | + | 0.976756i | \(0.568765\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −308.954 | −0.428507 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2315.82i | − | 3.20307i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −289.041 | −0.398678 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 221.410i | − | 0.304553i | −0.988338 | − | 0.152276i | \(-0.951340\pi\) | ||
0.988338 | − | 0.152276i | \(-0.0486604\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1182.52 | −1.62211 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1328.18 | −1.81693 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1103.22i | 1.50508i | 0.658548 | + | 0.752539i | \(0.271171\pi\) | ||||
−0.658548 | + | 0.752539i | \(0.728829\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 334.466i | − | 0.455056i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −911.056 | −1.23617 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1170.21 | −1.58351 | −0.791754 | − | 0.610841i | \(-0.790832\pi\) | ||||
−0.791754 | + | 0.610841i | \(0.790832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 1063.21i | − | 1.43483i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1463.99i | 1.97038i | 0.171460 | + | 0.985191i | \(0.445151\pi\) | ||||
−0.171460 | + | 0.985191i | \(0.554849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 462.308 | 0.620548 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 421.992i | 0.564916i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.2166 | 0.0243212 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 127.395i | − | 0.169633i | −0.996397 | − | 0.0848166i | \(-0.972970\pi\) | ||
0.996397 | − | 0.0848166i | \(-0.0270304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 191.683i | − | 0.254560i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 41.3224i | − | 0.0547317i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 896.048i | 1.18368i | 0.806055 | + | 0.591841i | \(0.201599\pi\) | ||||
−0.806055 | + | 0.591841i | \(0.798401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −470.535 | + | 730.751i | −0.619940 | + | 0.962782i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1141.19 | −1.49959 | −0.749797 | − | 0.661667i | \(-0.769849\pi\) | ||||
−0.749797 | + | 0.661667i | \(0.769849\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 486.298 | 0.637350 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −759.938 | −0.993383 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 556.090 | 0.725019 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 15.1581i | − | 0.0197115i | −0.999951 | − | 0.00985575i | \(-0.996863\pi\) | ||
0.999951 | − | 0.00985575i | \(-0.00313723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1585.83 | 2.05684 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 923.266i | − | 1.19439i | −0.802095 | − | 0.597197i | \(-0.796281\pi\) | ||
0.802095 | − | 0.597197i | \(-0.203719\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 190.188 | 0.245403 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −292.214 | −0.376079 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 417.025i | 0.535333i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 660.855i | 0.846165i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1527.91 | −1.95136 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 535.241 | 0.681836 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 679.117i | − | 0.862919i | −0.902132 | − | 0.431459i | \(-0.857999\pi\) | ||
0.902132 | − | 0.431459i | \(-0.142001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1271.18i | − | 1.61113i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −495.496 | −0.626417 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.7842i | 0.0514303i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 984.855 | 1.23881 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 962.620i | 1.20780i | 0.797059 | + | 0.603902i | \(0.206388\pi\) | ||||
−0.797059 | + | 0.603902i | \(0.793612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1474.69i | 1.84567i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1534.20i | − | 1.91535i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 819.858i | − | 1.02099i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −184.047 | − | 118.509i | −0.228630 | − | 0.147216i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 382.232 | 0.473645 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 263.301 | 0.325464 | 0.162732 | − | 0.986670i | \(-0.447969\pi\) | ||||
0.162732 | + | 0.986670i | \(0.447969\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −352.086 | −0.434139 | −0.217069 | − | 0.976156i | \(-0.569650\pi\) | ||||
−0.217069 | + | 0.976156i | \(0.569650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1438.63 | −1.76953 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.4723i | 0.0484323i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1254.00 | 1.53489 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 608.623i | 0.743129i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 134.116 | 0.163357 | 0.0816786 | − | 0.996659i | \(-0.473972\pi\) | ||||
0.0816786 | + | 0.996659i | \(0.473972\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −526.603 | −0.639858 | −0.319929 | − | 0.947441i | \(-0.603659\pi\) | ||||
−0.319929 | + | 0.947441i | \(0.603659\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 188.943i | 0.229022i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 533.202i | − | 0.644743i | −0.946613 | − | 0.322371i | \(-0.895520\pi\) | ||
0.946613 | − | 0.322371i | \(-0.104480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 208.483 | 0.251487 | 0.125744 | − | 0.992063i | \(-0.459868\pi\) | ||||
0.125744 | + | 0.992063i | \(0.459868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2528.23 | 3.04240 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 726.002i | 0.871550i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 324.064i | − | 0.388100i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1005.36 | 1.20114 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 470.155i | 0.560376i | 0.959945 | + | 0.280188i | \(0.0903968\pi\) | ||||
−0.959945 | + | 0.280188i | \(0.909603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2500.80 | 2.97360 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1813.19i | 2.15088i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 159.149i | − | 0.188341i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 255.908i | − | 0.302135i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2719.35i | 3.20301i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 176.505 | − | 274.117i | 0.207409 | − | 0.322112i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −808.878 | −0.948275 | −0.474137 | − | 0.880451i | \(-0.657240\pi\) | ||||
−0.474137 | + | 0.880451i | \(0.657240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 717.499 | 0.839180 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −416.626 | −0.486145 | −0.243072 | − | 0.970008i | \(-0.578155\pi\) | ||||
−0.243072 | + | 0.970008i | \(0.578155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −710.886 | −0.827574 | −0.413787 | − | 0.910374i | \(-0.635794\pi\) | ||||
−0.413787 | + | 0.910374i | \(0.635794\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 387.332i | − | 0.449863i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 903.225 | 1.04661 | 0.523306 | − | 0.852145i | \(-0.324699\pi\) | ||||
0.523306 | + | 0.852145i | \(0.324699\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 17.6681i | − | 0.0204255i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1276.73 | 1.47258 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 567.739 | 0.653324 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1154.92i | − | 1.32597i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1371.62i | − | 1.57115i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −47.5872 | −0.0543854 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 812.051 | 0.925941 | 0.462971 | − | 0.886374i | \(-0.346784\pi\) | ||||
0.462971 | + | 0.886374i | \(0.346784\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 556.238i | 0.632808i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 530.228i | 0.601848i | 0.953648 | + | 0.300924i | \(0.0972951\pi\) | ||||
−0.953648 | + | 0.300924i | \(0.902705\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −92.2733 | −0.104500 | −0.0522499 | − | 0.998634i | \(-0.516639\pi\) | ||||
−0.0522499 | + | 0.998634i | \(0.516639\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 608.891i | 0.688012i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1234.24 | 1.39147 | 0.695737 | − | 0.718296i | \(-0.255078\pi\) | ||||
0.695737 | + | 0.718296i | \(0.255078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 718.199i | 0.807873i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 16.4162i | − | 0.0184245i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1392.33i | − | 1.55916i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11.0307i | − | 0.0123248i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −926.351 | − | 596.482i | −1.03272 | − | 0.664974i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2198.88 | −2.44592 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2137.76 | −2.37265 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1164.72 | −1.28983 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.6514 | −0.0150844 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 138.686i | 0.152906i | 0.997073 | + | 0.0764530i | \(0.0243595\pi\) | ||||
−0.997073 | + | 0.0764530i | \(0.975640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −409.601 | −0.450606 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1075.06i | 1.18009i | 0.807371 | + | 0.590044i | \(0.200890\pi\) | ||||
−0.807371 | + | 0.590044i | \(0.799110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −227.742 | −0.249443 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −44.6567 | −0.0488052 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 275.873i | − | 0.300843i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 924.661i | − | 1.00616i | −0.864240 | − | 0.503080i | \(-0.832200\pi\) | ||
0.864240 | − | 0.503080i | \(-0.167800\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −990.037 | −1.07496 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −837.745 | −0.907633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 70.8757i | − | 0.0766224i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1049.40i | − | 1.13204i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −804.685 | −0.866184 | −0.433092 | − | 0.901350i | \(-0.642577\pi\) | ||||
−0.433092 | + | 0.901350i | \(0.642577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 685.458i | − | 0.736260i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 278.919 | 0.298948 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 410.125i | − | 0.438637i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1026.35i | 1.09536i | 0.836689 | + | 0.547678i | \(0.184488\pi\) | ||||
−0.836689 | + | 0.547678i | \(0.815512\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 845.691i | 0.900629i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1639.31i | 1.74210i | 0.491196 | + | 0.871049i | \(0.336560\pi\) | ||||
−0.491196 | + | 0.871049i | \(0.663440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 363.344 | + | 233.959i | 0.385307 | + | 0.248101i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −251.553 | −0.266193 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1301.61 | −1.37446 | −0.687228 | − | 0.726442i | \(-0.741173\pi\) | ||||
−0.687228 | + | 0.726442i | \(0.741173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1039.31 | 1.09516 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1464.39 | 1.53984 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1341.73i | − | 1.40790i | −0.710248 | − | 0.703951i | \(-0.751417\pi\) | ||
0.710248 | − | 0.703951i | \(-0.248583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 306.224 | 0.320654 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 2184.49i | − | 2.28265i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1015.50 | −1.05892 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 485.853 | 0.505570 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 61.8751i | 0.0642524i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 141.803i | 0.146946i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1308.76 | −1.35342 | −0.676709 | − | 0.736250i | \(-0.736595\pi\) | ||||
−0.676709 | + | 0.736250i | \(0.736595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2526.96 | −2.60781 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1483.52i | 1.52783i | 0.645316 | + | 0.763916i | \(0.276726\pi\) | ||||
−0.645316 | + | 0.763916i | \(0.723274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 528.875i | 0.543551i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −239.517 | −0.245659 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 518.336i | 0.530538i | 0.964174 | + | 0.265269i | \(0.0854608\pi\) | ||||
−0.964174 | + | 0.265269i | \(0.914539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 827.980 | 0.845741 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1651.78i | 1.68377i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1079.22i | 1.09789i | 0.835859 | + | 0.548944i | \(0.184970\pi\) | ||||
−0.835859 | + | 0.548944i | \(0.815030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 67.7866i | 0.0688189i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1293.20i | 1.31023i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 703.522 | − | 1092.59i | 0.711347 | − | 1.10474i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1431.19 | 1.44419 | 0.722094 | − | 0.691795i | \(-0.243180\pi\) | ||||
0.722094 | + | 0.691795i | \(0.243180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2587.40 | 2.60564 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 381.633 | 0.383551 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −582.437 | −0.584189 | −0.292095 | − | 0.956389i | \(-0.594352\pi\) | ||||
−0.292095 | + | 0.956389i | \(0.594352\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 374.659i | − | 0.375034i |
(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 | 1840.3.k.e.321.5 | 48 | ||
4.3 | odd | 2 | 920.3.k.a.321.43 | ✓ | 48 | ||
23.22 | odd | 2 | inner | 1840.3.k.e.321.6 | 48 | ||
92.91 | even | 2 | 920.3.k.a.321.44 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.3.k.a.321.43 | ✓ | 48 | 4.3 | odd | 2 | ||
920.3.k.a.321.44 | yes | 48 | 92.91 | even | 2 | ||
1840.3.k.e.321.5 | 48 | 1.1 | even | 1 | trivial | ||
1840.3.k.e.321.6 | 48 | 23.22 | odd | 2 | inner |