Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (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: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.27793984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{3} + 49x^{2} - 14x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.6 | ||
Root | \(1.79483 - 1.79483i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.b.288.5 |
$q$-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 \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.03251 | 1.77926 | 0.889630 | − | 0.456681i | \(-0.150962\pi\) | ||||
0.889630 | + | 0.456681i | \(0.150962\pi\) | |||||||
\(3\) | 8.47535i | 1.63108i | 0.578699 | + | 0.815541i | \(0.303561\pi\) | ||||
−0.578699 | + | 0.815541i | \(0.696439\pi\) | |||||||
\(4\) | 17.3261 | 2.16577 | ||||||||
\(5\) | 0.885690i | 0.0792185i | 0.999215 | + | 0.0396092i | \(0.0126113\pi\) | ||||
−0.999215 | + | 0.0396092i | \(0.987389\pi\) | |||||||
\(6\) | 42.6523i | 2.90212i | ||||||||
\(7\) | − 3.81828i | − 0.206168i | −0.994673 | − | 0.103084i | \(-0.967129\pi\) | ||||
0.994673 | − | 0.103084i | \(-0.0328711\pi\) | |||||||
\(8\) | 46.9339 | 2.07421 | ||||||||
\(9\) | −44.8316 | −1.66043 | ||||||||
\(10\) | 4.45724i | 0.140950i | ||||||||
\(11\) | 52.3720i | 1.43552i | 0.696289 | + | 0.717761i | \(0.254833\pi\) | ||||
−0.696289 | + | 0.717761i | \(0.745167\pi\) | |||||||
\(12\) | 146.845i | 3.53255i | ||||||||
\(13\) | −8.06025 | −0.171962 | −0.0859811 | − | 0.996297i | \(-0.527402\pi\) | ||||
−0.0859811 | + | 0.996297i | \(0.527402\pi\) | |||||||
\(14\) | − 19.2156i | − 0.366827i | ||||||||
\(15\) | −7.50653 | −0.129212 | ||||||||
\(16\) | 97.5862 | 1.52478 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −225.616 | −2.95434 | ||||||||
\(19\) | 66.5154 | 0.803141 | 0.401570 | − | 0.915828i | \(-0.368465\pi\) | ||||
0.401570 | + | 0.915828i | \(0.368465\pi\) | |||||||
\(20\) | 15.3456i | 0.171569i | ||||||||
\(21\) | 32.3613 | 0.336277 | ||||||||
\(22\) | 263.563i | 2.55417i | ||||||||
\(23\) | − 180.226i | − 1.63390i | −0.576711 | − | 0.816948i | \(-0.695664\pi\) | ||||
0.576711 | − | 0.816948i | \(-0.304336\pi\) | |||||||
\(24\) | 397.782i | 3.38320i | ||||||||
\(25\) | 124.216 | 0.993724 | ||||||||
\(26\) | −40.5633 | −0.305966 | ||||||||
\(27\) | − 151.129i | − 1.07722i | ||||||||
\(28\) | − 66.1562i | − 0.446512i | ||||||||
\(29\) | − 41.2800i | − 0.264328i | −0.991228 | − | 0.132164i | \(-0.957807\pi\) | ||||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(30\) | −37.7767 | −0.229902 | ||||||||
\(31\) | − 34.9114i | − 0.202267i | −0.994873 | − | 0.101133i | \(-0.967753\pi\) | ||||
0.994873 | − | 0.101133i | \(-0.0322469\pi\) | |||||||
\(32\) | 115.632 | 0.638783 | ||||||||
\(33\) | −443.871 | −2.34146 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.38182 | 0.0163323 | ||||||||
\(36\) | −776.759 | −3.59611 | ||||||||
\(37\) | 130.368i | 0.579255i | 0.957139 | + | 0.289627i | \(0.0935314\pi\) | ||||
−0.957139 | + | 0.289627i | \(0.906469\pi\) | |||||||
\(38\) | 334.739 | 1.42900 | ||||||||
\(39\) | − 68.3134i | − 0.280485i | ||||||||
\(40\) | 41.5689i | 0.164315i | ||||||||
\(41\) | 17.9081i | 0.0682142i | 0.999418 | + | 0.0341071i | \(0.0108587\pi\) | ||||
−0.999418 | + | 0.0341071i | \(0.989141\pi\) | |||||||
\(42\) | 162.859 | 0.598325 | ||||||||
\(43\) | −277.620 | −0.984573 | −0.492287 | − | 0.870433i | \(-0.663839\pi\) | ||||
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(44\) | 907.405i | 3.10901i | ||||||||
\(45\) | − 39.7069i | − 0.131537i | ||||||||
\(46\) | − 906.987i | − 2.90713i | ||||||||
\(47\) | 463.789 | 1.43937 | 0.719687 | − | 0.694299i | \(-0.244285\pi\) | ||||
0.719687 | + | 0.694299i | \(0.244285\pi\) | |||||||
\(48\) | 827.078i | 2.48705i | ||||||||
\(49\) | 328.421 | 0.957495 | ||||||||
\(50\) | 625.116 | 1.76809 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −139.653 | −0.372431 | ||||||||
\(53\) | 329.944 | 0.855118 | 0.427559 | − | 0.903987i | \(-0.359374\pi\) | ||||
0.427559 | + | 0.903987i | \(0.359374\pi\) | |||||||
\(54\) | − 760.560i | − 1.91665i | ||||||||
\(55\) | −46.3853 | −0.113720 | ||||||||
\(56\) | − 179.207i | − 0.427635i | ||||||||
\(57\) | 563.741i | 1.30999i | ||||||||
\(58\) | − 207.742i | − 0.470308i | ||||||||
\(59\) | −678.656 | −1.49752 | −0.748759 | − | 0.662843i | \(-0.769350\pi\) | ||||
−0.748759 | + | 0.662843i | \(0.769350\pi\) | |||||||
\(60\) | −130.059 | −0.279843 | ||||||||
\(61\) | − 340.280i | − 0.714237i | −0.934059 | − | 0.357118i | \(-0.883759\pi\) | ||||
0.934059 | − | 0.357118i | \(-0.116241\pi\) | |||||||
\(62\) | − 175.692i | − 0.359885i | ||||||||
\(63\) | 171.180i | 0.342328i | ||||||||
\(64\) | −198.770 | −0.388223 | ||||||||
\(65\) | − 7.13888i | − 0.0136226i | ||||||||
\(66\) | −2233.79 | −4.16606 | ||||||||
\(67\) | 15.3925 | 0.0280671 | 0.0140336 | − | 0.999902i | \(-0.495533\pi\) | ||||
0.0140336 | + | 0.999902i | \(0.495533\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1527.48 | 2.66502 | ||||||||
\(70\) | 17.0190 | 0.0290595 | ||||||||
\(71\) | − 670.203i | − 1.12026i | −0.828405 | − | 0.560130i | \(-0.810751\pi\) | ||||
0.828405 | − | 0.560130i | \(-0.189249\pi\) | |||||||
\(72\) | −2104.12 | −3.44408 | ||||||||
\(73\) | 193.480i | 0.310207i | 0.987898 | + | 0.155103i | \(0.0495711\pi\) | ||||
−0.987898 | + | 0.155103i | \(0.950429\pi\) | |||||||
\(74\) | 656.080i | 1.03065i | ||||||||
\(75\) | 1052.77i | 1.62085i | ||||||||
\(76\) | 1152.46 | 1.73942 | ||||||||
\(77\) | 199.971 | 0.295959 | ||||||||
\(78\) | − 343.788i | − 0.499055i | ||||||||
\(79\) | − 1080.15i | − 1.53831i | −0.639061 | − | 0.769156i | \(-0.720677\pi\) | ||||
0.639061 | − | 0.769156i | \(-0.279323\pi\) | |||||||
\(80\) | 86.4311i | 0.120791i | ||||||||
\(81\) | 70.4207 | 0.0965990 | ||||||||
\(82\) | 90.1229i | 0.121371i | ||||||||
\(83\) | 865.668 | 1.14481 | 0.572406 | − | 0.819970i | \(-0.306010\pi\) | ||||
0.572406 | + | 0.819970i | \(0.306010\pi\) | |||||||
\(84\) | 560.697 | 0.728298 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1397.13 | −1.75181 | ||||||||
\(87\) | 349.863 | 0.431141 | ||||||||
\(88\) | 2458.02i | 2.97757i | ||||||||
\(89\) | 1129.46 | 1.34520 | 0.672599 | − | 0.740008i | \(-0.265178\pi\) | ||||
0.672599 | + | 0.740008i | \(0.265178\pi\) | |||||||
\(90\) | − 199.825i | − 0.234038i | ||||||||
\(91\) | 30.7763i | 0.0354531i | ||||||||
\(92\) | − 3122.61i | − 3.53864i | ||||||||
\(93\) | 295.886 | 0.329914 | ||||||||
\(94\) | 2334.02 | 2.56102 | ||||||||
\(95\) | 58.9120i | 0.0636236i | ||||||||
\(96\) | 980.023i | 1.04191i | ||||||||
\(97\) | − 379.412i | − 0.397149i | −0.980086 | − | 0.198574i | \(-0.936369\pi\) | ||||
0.980086 | − | 0.198574i | \(-0.0636311\pi\) | |||||||
\(98\) | 1652.78 | 1.70363 | ||||||||
\(99\) | − 2347.92i | − 2.38359i | ||||||||
\(100\) | 2152.18 | 2.15218 | ||||||||
\(101\) | 131.732 | 0.129780 | 0.0648902 | − | 0.997892i | \(-0.479330\pi\) | ||||
0.0648902 | + | 0.997892i | \(0.479330\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 195.988 | 0.187488 | 0.0937442 | − | 0.995596i | \(-0.470116\pi\) | ||||
0.0937442 | + | 0.995596i | \(0.470116\pi\) | |||||||
\(104\) | −378.299 | −0.356685 | ||||||||
\(105\) | 28.6621i | 0.0266394i | ||||||||
\(106\) | 1660.45 | 1.52148 | ||||||||
\(107\) | − 485.147i | − 0.438326i | −0.975688 | − | 0.219163i | \(-0.929667\pi\) | ||||
0.975688 | − | 0.219163i | \(-0.0703327\pi\) | |||||||
\(108\) | − 2618.49i | − 2.33300i | ||||||||
\(109\) | 1255.12i | 1.10292i | 0.834201 | + | 0.551460i | \(0.185929\pi\) | ||||
−0.834201 | + | 0.551460i | \(0.814071\pi\) | |||||||
\(110\) | −233.435 | −0.202337 | ||||||||
\(111\) | −1104.92 | −0.944812 | ||||||||
\(112\) | − 372.612i | − 0.314362i | ||||||||
\(113\) | 1013.35i | 0.843612i | 0.906686 | + | 0.421806i | \(0.138604\pi\) | ||||
−0.906686 | + | 0.421806i | \(0.861396\pi\) | |||||||
\(114\) | 2837.03i | 2.33081i | ||||||||
\(115\) | 159.624 | 0.129435 | ||||||||
\(116\) | − 715.224i | − 0.572473i | ||||||||
\(117\) | 361.354 | 0.285531 | ||||||||
\(118\) | −3415.34 | −2.66447 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −352.311 | −0.268012 | ||||||||
\(121\) | −1411.83 | −1.06073 | ||||||||
\(122\) | − 1712.46i | − 1.27081i | ||||||||
\(123\) | −151.778 | −0.111263 | ||||||||
\(124\) | − 604.880i | − 0.438063i | ||||||||
\(125\) | 220.728i | 0.157940i | ||||||||
\(126\) | 861.464i | 0.609090i | ||||||||
\(127\) | −1927.72 | −1.34691 | −0.673456 | − | 0.739227i | \(-0.735191\pi\) | ||||
−0.673456 | + | 0.739227i | \(0.735191\pi\) | |||||||
\(128\) | −1925.37 | −1.32953 | ||||||||
\(129\) | − 2352.93i | − 1.60592i | ||||||||
\(130\) | − 35.9265i | − 0.0242381i | ||||||||
\(131\) | − 406.738i | − 0.271274i | −0.990759 | − | 0.135637i | \(-0.956692\pi\) | ||||
0.990759 | − | 0.135637i | \(-0.0433081\pi\) | |||||||
\(132\) | −7690.58 | −5.07105 | ||||||||
\(133\) | − 253.975i | − 0.165582i | ||||||||
\(134\) | 77.4631 | 0.0499387 | ||||||||
\(135\) | 133.854 | 0.0853355 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −130.552 | −0.0814149 | −0.0407074 | − | 0.999171i | \(-0.512961\pi\) | ||||
−0.0407074 | + | 0.999171i | \(0.512961\pi\) | |||||||
\(138\) | 7687.03 | 4.74177 | ||||||||
\(139\) | 2073.54i | 1.26529i | 0.774443 | + | 0.632644i | \(0.218030\pi\) | ||||
−0.774443 | + | 0.632644i | \(0.781970\pi\) | |||||||
\(140\) | 58.5938 | 0.0353720 | ||||||||
\(141\) | 3930.78i | 2.34774i | ||||||||
\(142\) | − 3372.80i | − 1.99323i | ||||||||
\(143\) | − 422.131i | − 0.246856i | ||||||||
\(144\) | −4374.95 | −2.53180 | ||||||||
\(145\) | 36.5613 | 0.0209397 | ||||||||
\(146\) | 973.689i | 0.551939i | ||||||||
\(147\) | 2783.48i | 1.56175i | ||||||||
\(148\) | 2258.78i | 1.25453i | ||||||||
\(149\) | −1852.73 | −1.01867 | −0.509334 | − | 0.860569i | \(-0.670108\pi\) | ||||
−0.509334 | + | 0.860569i | \(0.670108\pi\) | |||||||
\(150\) | 5298.08i | 2.88391i | ||||||||
\(151\) | −2050.86 | −1.10527 | −0.552637 | − | 0.833422i | \(-0.686378\pi\) | ||||
−0.552637 | + | 0.833422i | \(0.686378\pi\) | |||||||
\(152\) | 3121.83 | 1.66588 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1006.36 | 0.526588 | ||||||||
\(155\) | 30.9207 | 0.0160233 | ||||||||
\(156\) | − 1183.61i | − 0.607465i | ||||||||
\(157\) | −262.991 | −0.133688 | −0.0668438 | − | 0.997763i | \(-0.521293\pi\) | ||||
−0.0668438 | + | 0.997763i | \(0.521293\pi\) | |||||||
\(158\) | − 5435.88i | − 2.73706i | ||||||||
\(159\) | 2796.39i | 1.39477i | ||||||||
\(160\) | 102.414i | 0.0506035i | ||||||||
\(161\) | −688.152 | −0.336857 | ||||||||
\(162\) | 354.393 | 0.171875 | ||||||||
\(163\) | 1444.98i | 0.694354i | 0.937800 | + | 0.347177i | \(0.112860\pi\) | ||||
−0.937800 | + | 0.347177i | \(0.887140\pi\) | |||||||
\(164\) | 310.279i | 0.147736i | ||||||||
\(165\) | − 393.132i | − 0.185487i | ||||||||
\(166\) | 4356.48 | 2.03692 | ||||||||
\(167\) | − 501.565i | − 0.232409i | −0.993225 | − | 0.116204i | \(-0.962927\pi\) | ||||
0.993225 | − | 0.116204i | \(-0.0370728\pi\) | |||||||
\(168\) | 1518.84 | 0.697508 | ||||||||
\(169\) | −2132.03 | −0.970429 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2981.99 | −1.33356 | ||||||||
\(172\) | −4810.08 | −2.13236 | ||||||||
\(173\) | − 2590.14i | − 1.13829i | −0.822237 | − | 0.569146i | \(-0.807274\pi\) | ||||
0.822237 | − | 0.569146i | \(-0.192726\pi\) | |||||||
\(174\) | 1760.69 | 0.767112 | ||||||||
\(175\) | − 474.290i | − 0.204874i | ||||||||
\(176\) | 5110.79i | 2.18886i | ||||||||
\(177\) | − 5751.85i | − 2.44257i | ||||||||
\(178\) | 5684.02 | 2.39346 | ||||||||
\(179\) | −2165.65 | −0.904294 | −0.452147 | − | 0.891943i | \(-0.649342\pi\) | ||||
−0.452147 | + | 0.891943i | \(0.649342\pi\) | |||||||
\(180\) | − 687.968i | − 0.284878i | ||||||||
\(181\) | 1925.56i | 0.790750i | 0.918520 | + | 0.395375i | \(0.129385\pi\) | ||||
−0.918520 | + | 0.395375i | \(0.870615\pi\) | |||||||
\(182\) | 154.882i | 0.0630803i | ||||||||
\(183\) | 2884.00 | 1.16498 | ||||||||
\(184\) | − 8458.69i | − 3.38904i | ||||||||
\(185\) | −115.466 | −0.0458877 | ||||||||
\(186\) | 1489.05 | 0.587003 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8035.68 | 3.11735 | ||||||||
\(189\) | −577.055 | −0.222088 | ||||||||
\(190\) | 296.475i | 0.113203i | ||||||||
\(191\) | −2783.52 | −1.05449 | −0.527247 | − | 0.849712i | \(-0.676776\pi\) | ||||
−0.527247 | + | 0.849712i | \(0.676776\pi\) | |||||||
\(192\) | − 1684.65i | − 0.633223i | ||||||||
\(193\) | − 2258.27i | − 0.842246i | −0.907004 | − | 0.421123i | \(-0.861636\pi\) | ||||
0.907004 | − | 0.421123i | \(-0.138364\pi\) | |||||||
\(194\) | − 1909.39i | − 0.706631i | ||||||||
\(195\) | 60.5045 | 0.0222196 | ||||||||
\(196\) | 5690.27 | 2.07371 | ||||||||
\(197\) | 1270.70i | 0.459560i | 0.973243 | + | 0.229780i | \(0.0738007\pi\) | ||||
−0.973243 | + | 0.229780i | \(0.926199\pi\) | |||||||
\(198\) | − 11815.9i | − 4.24102i | ||||||||
\(199\) | − 4794.36i | − 1.70786i | −0.520392 | − | 0.853928i | \(-0.674214\pi\) | ||||
0.520392 | − | 0.853928i | \(-0.325786\pi\) | |||||||
\(200\) | 5829.92 | 2.06119 | ||||||||
\(201\) | 130.457i | 0.0457798i | ||||||||
\(202\) | 662.942 | 0.230913 | ||||||||
\(203\) | −157.619 | −0.0544960 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.8611 | −0.00540383 | ||||||||
\(206\) | 986.313 | 0.333591 | ||||||||
\(207\) | 8079.80i | 2.71297i | ||||||||
\(208\) | −786.569 | −0.262205 | ||||||||
\(209\) | 3483.54i | 1.15293i | ||||||||
\(210\) | 144.242i | 0.0473984i | ||||||||
\(211\) | 2807.00i | 0.915837i | 0.888994 | + | 0.457918i | \(0.151405\pi\) | ||||
−0.888994 | + | 0.457918i | \(0.848595\pi\) | |||||||
\(212\) | 5716.66 | 1.85199 | ||||||||
\(213\) | 5680.21 | 1.82724 | ||||||||
\(214\) | − 2441.50i | − 0.779896i | ||||||||
\(215\) | − 245.885i | − 0.0779964i | ||||||||
\(216\) | − 7093.09i | − 2.23437i | ||||||||
\(217\) | −133.302 | −0.0417009 | ||||||||
\(218\) | 6316.38i | 1.96238i | ||||||||
\(219\) | −1639.81 | −0.505973 | ||||||||
\(220\) | −803.679 | −0.246291 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5560.51 | −1.68107 | ||||||||
\(223\) | −4684.30 | −1.40665 | −0.703327 | − | 0.710866i | \(-0.748303\pi\) | ||||
−0.703327 | + | 0.710866i | \(0.748303\pi\) | |||||||
\(224\) | − 441.516i | − 0.131697i | ||||||||
\(225\) | −5568.79 | −1.65001 | ||||||||
\(226\) | 5099.70i | 1.50101i | ||||||||
\(227\) | 1395.72i | 0.408095i | 0.978961 | + | 0.204047i | \(0.0654096\pi\) | ||||
−0.978961 | + | 0.204047i | \(0.934590\pi\) | |||||||
\(228\) | 9767.47i | 2.83713i | ||||||||
\(229\) | −894.638 | −0.258163 | −0.129082 | − | 0.991634i | \(-0.541203\pi\) | ||||
−0.129082 | + | 0.991634i | \(0.541203\pi\) | |||||||
\(230\) | 803.309 | 0.230298 | ||||||||
\(231\) | 1694.83i | 0.482733i | ||||||||
\(232\) | − 1937.43i | − 0.548270i | ||||||||
\(233\) | 1196.13i | 0.336313i | 0.985760 | + | 0.168156i | \(0.0537814\pi\) | ||||
−0.985760 | + | 0.168156i | \(0.946219\pi\) | |||||||
\(234\) | 1818.52 | 0.508035 | ||||||||
\(235\) | 410.773i | 0.114025i | ||||||||
\(236\) | −11758.5 | −3.24328 | ||||||||
\(237\) | 9154.67 | 2.50911 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4948.82 | 1.33938 | 0.669691 | − | 0.742639i | \(-0.266426\pi\) | ||||
0.669691 | + | 0.742639i | \(0.266426\pi\) | |||||||
\(240\) | −732.534 | −0.197020 | ||||||||
\(241\) | − 6702.73i | − 1.79154i | −0.444518 | − | 0.895770i | \(-0.646625\pi\) | ||||
0.444518 | − | 0.895770i | \(-0.353375\pi\) | |||||||
\(242\) | −7105.03 | −1.88731 | ||||||||
\(243\) | − 3483.65i | − 0.919656i | ||||||||
\(244\) | − 5895.75i | − 1.54687i | ||||||||
\(245\) | 290.879i | 0.0758513i | ||||||||
\(246\) | −763.824 | −0.197966 | ||||||||
\(247\) | −536.130 | −0.138110 | ||||||||
\(248\) | − 1638.53i | − 0.419543i | ||||||||
\(249\) | 7336.85i | 1.86728i | ||||||||
\(250\) | 1110.81i | 0.281016i | ||||||||
\(251\) | −4756.08 | −1.19602 | −0.598010 | − | 0.801489i | \(-0.704042\pi\) | ||||
−0.598010 | + | 0.801489i | \(0.704042\pi\) | |||||||
\(252\) | 2965.89i | 0.741402i | ||||||||
\(253\) | 9438.77 | 2.34550 | ||||||||
\(254\) | −9701.29 | −2.39651 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8099.28 | −1.97736 | ||||||||
\(257\) | −2892.84 | −0.702143 | −0.351071 | − | 0.936349i | \(-0.614183\pi\) | ||||
−0.351071 | + | 0.936349i | \(0.614183\pi\) | |||||||
\(258\) | − 11841.1i | − 2.85735i | ||||||||
\(259\) | 497.784 | 0.119424 | ||||||||
\(260\) | − 123.689i | − 0.0295034i | ||||||||
\(261\) | 1850.65i | 0.438898i | ||||||||
\(262\) | − 2046.92i | − 0.482667i | ||||||||
\(263\) | −5415.48 | −1.26971 | −0.634853 | − | 0.772633i | \(-0.718939\pi\) | ||||
−0.634853 | + | 0.772633i | \(0.718939\pi\) | |||||||
\(264\) | −20832.6 | −4.85666 | ||||||||
\(265\) | 292.228i | 0.0677412i | ||||||||
\(266\) | − 1278.13i | − 0.294613i | ||||||||
\(267\) | 9572.58i | 2.19413i | ||||||||
\(268\) | 266.693 | 0.0607869 | ||||||||
\(269\) | 5787.00i | 1.31167i | 0.754904 | + | 0.655835i | \(0.227683\pi\) | ||||
−0.754904 | + | 0.655835i | \(0.772317\pi\) | |||||||
\(270\) | 673.620 | 0.151834 | ||||||||
\(271\) | 5465.13 | 1.22503 | 0.612515 | − | 0.790459i | \(-0.290158\pi\) | ||||
0.612515 | + | 0.790459i | \(0.290158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −260.840 | −0.0578270 | ||||||||
\(274\) | −657.006 | −0.144858 | ||||||||
\(275\) | 6505.42i | 1.42651i | ||||||||
\(276\) | 26465.3 | 5.77182 | ||||||||
\(277\) | − 1207.65i | − 0.261952i | −0.991386 | − | 0.130976i | \(-0.958189\pi\) | ||||
0.991386 | − | 0.130976i | \(-0.0418111\pi\) | |||||||
\(278\) | 10435.1i | 2.25128i | ||||||||
\(279\) | 1565.13i | 0.335850i | ||||||||
\(280\) | 158.722 | 0.0338766 | ||||||||
\(281\) | 1197.18 | 0.254155 | 0.127077 | − | 0.991893i | \(-0.459440\pi\) | ||||
0.127077 | + | 0.991893i | \(0.459440\pi\) | |||||||
\(282\) | 19781.7i | 4.17724i | ||||||||
\(283\) | − 3164.73i | − 0.664748i | −0.943148 | − | 0.332374i | \(-0.892150\pi\) | ||||
0.943148 | − | 0.332374i | \(-0.107850\pi\) | |||||||
\(284\) | − 11612.0i | − 2.42622i | ||||||||
\(285\) | −499.300 | −0.103775 | ||||||||
\(286\) | − 2124.38i | − 0.439221i | ||||||||
\(287\) | 68.3784 | 0.0140636 | ||||||||
\(288\) | −5183.98 | −1.06066 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 183.995 | 0.0372571 | ||||||||
\(291\) | 3215.65 | 0.647782 | ||||||||
\(292\) | 3352.26i | 0.671836i | ||||||||
\(293\) | 7456.21 | 1.48668 | 0.743339 | − | 0.668915i | \(-0.233241\pi\) | ||||
0.743339 | + | 0.668915i | \(0.233241\pi\) | |||||||
\(294\) | 14007.9i | 2.77877i | ||||||||
\(295\) | − 601.079i | − 0.118631i | ||||||||
\(296\) | 6118.70i | 1.20149i | ||||||||
\(297\) | 7914.94 | 1.54637 | ||||||||
\(298\) | −9323.89 | −1.81248 | ||||||||
\(299\) | 1452.66i | 0.280969i | ||||||||
\(300\) | 18240.5i | 3.51038i | ||||||||
\(301\) | 1060.03i | 0.202988i | ||||||||
\(302\) | −10321.0 | −1.96657 | ||||||||
\(303\) | 1116.47i | 0.211683i | ||||||||
\(304\) | 6490.98 | 1.22462 | ||||||||
\(305\) | 301.383 | 0.0565808 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6535.48 | −1.21498 | −0.607491 | − | 0.794327i | \(-0.707824\pi\) | ||||
−0.607491 | + | 0.794327i | \(0.707824\pi\) | |||||||
\(308\) | 3464.73 | 0.640978 | ||||||||
\(309\) | 1661.07i | 0.305809i | ||||||||
\(310\) | 155.608 | 0.0285096 | ||||||||
\(311\) | − 8935.89i | − 1.62928i | −0.579963 | − | 0.814642i | \(-0.696933\pi\) | ||||
0.579963 | − | 0.814642i | \(-0.303067\pi\) | |||||||
\(312\) | − 3206.22i | − 0.581783i | ||||||||
\(313\) | 2628.71i | 0.474707i | 0.971423 | + | 0.237353i | \(0.0762799\pi\) | ||||
−0.971423 | + | 0.237353i | \(0.923720\pi\) | |||||||
\(314\) | −1323.50 | −0.237865 | ||||||||
\(315\) | −151.612 | −0.0271187 | ||||||||
\(316\) | − 18714.9i | − 3.33163i | ||||||||
\(317\) | − 4268.54i | − 0.756293i | −0.925746 | − | 0.378147i | \(-0.876562\pi\) | ||||
0.925746 | − | 0.378147i | \(-0.123438\pi\) | |||||||
\(318\) | 14072.9i | 2.48166i | ||||||||
\(319\) | 2161.92 | 0.379449 | ||||||||
\(320\) | − 176.048i | − 0.0307544i | ||||||||
\(321\) | 4111.79 | 0.714946 | ||||||||
\(322\) | −3463.13 | −0.599357 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1220.12 | 0.209211 | ||||||||
\(325\) | −1001.21 | −0.170883 | ||||||||
\(326\) | 7271.89i | 1.23544i | ||||||||
\(327\) | −10637.5 | −1.79895 | ||||||||
\(328\) | 840.500i | 0.141490i | ||||||||
\(329\) | − 1770.88i | − 0.296753i | ||||||||
\(330\) | − 1978.44i | − 0.330029i | ||||||||
\(331\) | −992.298 | −0.164778 | −0.0823892 | − | 0.996600i | \(-0.526255\pi\) | ||||
−0.0823892 | + | 0.996600i | \(0.526255\pi\) | |||||||
\(332\) | 14998.7 | 2.47940 | ||||||||
\(333\) | − 5844.63i | − 0.961812i | ||||||||
\(334\) | − 2524.13i | − 0.413516i | ||||||||
\(335\) | 13.6330i | 0.00222344i | ||||||||
\(336\) | 3158.02 | 0.512750 | ||||||||
\(337\) | 8042.26i | 1.29997i | 0.759947 | + | 0.649985i | \(0.225225\pi\) | ||||
−0.759947 | + | 0.649985i | \(0.774775\pi\) | |||||||
\(338\) | −10729.5 | −1.72665 | ||||||||
\(339\) | −8588.52 | −1.37600 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1828.38 | 0.290359 | ||||||||
\(342\) | −15006.9 | −2.37275 | ||||||||
\(343\) | − 2563.68i | − 0.403573i | ||||||||
\(344\) | −13029.8 | −2.04221 | ||||||||
\(345\) | 1352.87i | 0.211119i | ||||||||
\(346\) | − 13034.9i | − 2.02532i | ||||||||
\(347\) | 7414.16i | 1.14701i | 0.819202 | + | 0.573506i | \(0.194417\pi\) | ||||
−0.819202 | + | 0.573506i | \(0.805583\pi\) | |||||||
\(348\) | 6061.78 | 0.933751 | ||||||||
\(349\) | 859.194 | 0.131781 | 0.0658905 | − | 0.997827i | \(-0.479011\pi\) | ||||
0.0658905 | + | 0.997827i | \(0.479011\pi\) | |||||||
\(350\) | − 2386.87i | − 0.364525i | ||||||||
\(351\) | 1218.14i | 0.185241i | ||||||||
\(352\) | 6055.89i | 0.916988i | ||||||||
\(353\) | 569.084 | 0.0858053 | 0.0429027 | − | 0.999079i | \(-0.486339\pi\) | ||||
0.0429027 | + | 0.999079i | \(0.486339\pi\) | |||||||
\(354\) | − 28946.3i | − 4.34598i | ||||||||
\(355\) | 593.592 | 0.0887453 | ||||||||
\(356\) | 19569.2 | 2.91339 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10898.7 | −1.60897 | ||||||||
\(359\) | 5005.21 | 0.735835 | 0.367918 | − | 0.929858i | \(-0.380071\pi\) | ||||
0.367918 | + | 0.929858i | \(0.380071\pi\) | |||||||
\(360\) | − 1863.60i | − 0.272834i | ||||||||
\(361\) | −2434.71 | −0.354965 | ||||||||
\(362\) | 9690.40i | 1.40695i | ||||||||
\(363\) | − 11965.7i | − 1.73013i | ||||||||
\(364\) | 533.235i | 0.0767833i | ||||||||
\(365\) | −171.363 | −0.0245741 | ||||||||
\(366\) | 14513.7 | 2.07280 | ||||||||
\(367\) | 10975.3i | 1.56105i | 0.625127 | + | 0.780523i | \(0.285047\pi\) | ||||
−0.625127 | + | 0.780523i | \(0.714953\pi\) | |||||||
\(368\) | − 17587.5i | − 2.49134i | ||||||||
\(369\) | − 802.851i | − 0.113265i | ||||||||
\(370\) | −581.083 | −0.0816462 | ||||||||
\(371\) | − 1259.82i | − 0.176298i | ||||||||
\(372\) | 5126.57 | 0.714517 | ||||||||
\(373\) | −3211.72 | −0.445835 | −0.222918 | − | 0.974837i | \(-0.571558\pi\) | ||||
−0.222918 | + | 0.974837i | \(0.571558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1870.74 | −0.257613 | ||||||||
\(376\) | 21767.4 | 2.98556 | ||||||||
\(377\) | 332.727i | 0.0454544i | ||||||||
\(378\) | −2904.03 | −0.395152 | ||||||||
\(379\) | 8051.48i | 1.09123i | 0.838035 | + | 0.545616i | \(0.183704\pi\) | ||||
−0.838035 | + | 0.545616i | \(0.816296\pi\) | |||||||
\(380\) | 1020.72i | 0.137794i | ||||||||
\(381\) | − 16338.1i | − 2.19692i | ||||||||
\(382\) | −14008.1 | −1.87622 | ||||||||
\(383\) | 2584.16 | 0.344763 | 0.172382 | − | 0.985030i | \(-0.444854\pi\) | ||||
0.172382 | + | 0.985030i | \(0.444854\pi\) | |||||||
\(384\) | − 16318.2i | − 2.16858i | ||||||||
\(385\) | 177.112i | 0.0234454i | ||||||||
\(386\) | − 11364.7i | − 1.49858i | ||||||||
\(387\) | 12446.2 | 1.63482 | ||||||||
\(388\) | − 6573.74i | − 0.860132i | ||||||||
\(389\) | 5174.31 | 0.674417 | 0.337208 | − | 0.941430i | \(-0.390517\pi\) | ||||
0.337208 | + | 0.941430i | \(0.390517\pi\) | |||||||
\(390\) | 304.489 | 0.0395344 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15414.1 | 1.98604 | ||||||||
\(393\) | 3447.25 | 0.442470 | ||||||||
\(394\) | 6394.79i | 0.817677i | ||||||||
\(395\) | 956.680 | 0.121863 | ||||||||
\(396\) | − 40680.4i | − 5.16230i | ||||||||
\(397\) | 5149.36i | 0.650980i | 0.945545 | + | 0.325490i | \(0.105529\pi\) | ||||
−0.945545 | + | 0.325490i | \(0.894471\pi\) | |||||||
\(398\) | − 24127.7i | − 3.03872i | ||||||||
\(399\) | 2152.53 | 0.270078 | ||||||||
\(400\) | 12121.7 | 1.51522 | ||||||||
\(401\) | − 8700.49i | − 1.08350i | −0.840541 | − | 0.541748i | \(-0.817763\pi\) | ||||
0.840541 | − | 0.541748i | \(-0.182237\pi\) | |||||||
\(402\) | 656.527i | 0.0814542i | ||||||||
\(403\) | 281.394i | 0.0347823i | ||||||||
\(404\) | 2282.41 | 0.281074 | ||||||||
\(405\) | 62.3709i | 0.00765243i | ||||||||
\(406\) | −793.219 | −0.0969625 | ||||||||
\(407\) | −6827.65 | −0.831533 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12346.0 | 1.49260 | 0.746299 | − | 0.665611i | \(-0.231829\pi\) | ||||
0.746299 | + | 0.665611i | \(0.231829\pi\) | |||||||
\(410\) | −79.8209 | −0.00961482 | ||||||||
\(411\) | − 1106.48i | − 0.132794i | ||||||||
\(412\) | 3395.72 | 0.406056 | ||||||||
\(413\) | 2591.30i | 0.308740i | ||||||||
\(414\) | 40661.7i | 4.82708i | ||||||||
\(415\) | 766.713i | 0.0906903i | ||||||||
\(416\) | −932.023 | −0.109847 | ||||||||
\(417\) | −17574.0 | −2.06379 | ||||||||
\(418\) | 17531.0i | 2.05136i | ||||||||
\(419\) | 5763.33i | 0.671974i | 0.941867 | + | 0.335987i | \(0.109070\pi\) | ||||
−0.941867 | + | 0.335987i | \(0.890930\pi\) | |||||||
\(420\) | 496.604i | 0.0576947i | ||||||||
\(421\) | −1876.12 | −0.217188 | −0.108594 | − | 0.994086i | \(-0.534635\pi\) | ||||
−0.108594 | + | 0.994086i | \(0.534635\pi\) | |||||||
\(422\) | 14126.2i | 1.62951i | ||||||||
\(423\) | −20792.4 | −2.38998 | ||||||||
\(424\) | 15485.6 | 1.77369 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 28585.7 | 3.25113 | ||||||||
\(427\) | −1299.29 | −0.147253 | ||||||||
\(428\) | − 8405.72i | − 0.949313i | ||||||||
\(429\) | 3577.71 | 0.402642 | ||||||||
\(430\) | − 1237.42i | − 0.138776i | ||||||||
\(431\) | − 83.9299i | − 0.00937996i | −0.999989 | − | 0.00468998i | \(-0.998507\pi\) | ||||
0.999989 | − | 0.00468998i | \(-0.00149287\pi\) | |||||||
\(432\) | − 14748.1i | − 1.64252i | ||||||||
\(433\) | 15345.0 | 1.70308 | 0.851539 | − | 0.524291i | \(-0.175669\pi\) | ||||
0.851539 | + | 0.524291i | \(0.175669\pi\) | |||||||
\(434\) | −670.842 | −0.0741968 | ||||||||
\(435\) | 309.870i | 0.0341543i | ||||||||
\(436\) | 21746.3i | 2.38867i | ||||||||
\(437\) | − 11987.8i | − 1.31225i | ||||||||
\(438\) | −8252.36 | −0.900258 | ||||||||
\(439\) | 3064.74i | 0.333194i | 0.986025 | + | 0.166597i | \(0.0532778\pi\) | ||||
−0.986025 | + | 0.166597i | \(0.946722\pi\) | |||||||
\(440\) | −2177.05 | −0.235879 | ||||||||
\(441\) | −14723.6 | −1.58985 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1792.97 | −0.192295 | −0.0961474 | − | 0.995367i | \(-0.530652\pi\) | ||||
−0.0961474 | + | 0.995367i | \(0.530652\pi\) | |||||||
\(444\) | −19144.0 | −2.04624 | ||||||||
\(445\) | 1000.35i | 0.106564i | ||||||||
\(446\) | −23573.8 | −2.50281 | ||||||||
\(447\) | − 15702.6i | − 1.66153i | ||||||||
\(448\) | 758.960i | 0.0800391i | ||||||||
\(449\) | − 2499.19i | − 0.262681i | −0.991337 | − | 0.131341i | \(-0.958072\pi\) | ||||
0.991337 | − | 0.131341i | \(-0.0419282\pi\) | |||||||
\(450\) | −28025.0 | −2.93580 | ||||||||
\(451\) | −937.885 | −0.0979231 | ||||||||
\(452\) | 17557.5i | 1.82707i | ||||||||
\(453\) | − 17381.7i | − 1.80279i | ||||||||
\(454\) | 7024.00i | 0.726107i | ||||||||
\(455\) | −27.2583 | −0.00280854 | ||||||||
\(456\) | 26458.6i | 2.71719i | ||||||||
\(457\) | −14784.4 | −1.51331 | −0.756656 | − | 0.653813i | \(-0.773168\pi\) | ||||
−0.756656 | + | 0.653813i | \(0.773168\pi\) | |||||||
\(458\) | −4502.28 | −0.459340 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2765.67 | 0.280326 | ||||||||
\(461\) | 17746.9 | 1.79297 | 0.896483 | − | 0.443078i | \(-0.146113\pi\) | ||||
0.896483 | + | 0.443078i | \(0.146113\pi\) | |||||||
\(462\) | 8529.23i | 0.858909i | ||||||||
\(463\) | 18486.4 | 1.85559 | 0.927793 | − | 0.373096i | \(-0.121704\pi\) | ||||
0.927793 | + | 0.373096i | \(0.121704\pi\) | |||||||
\(464\) | − 4028.36i | − 0.403043i | ||||||||
\(465\) | 262.064i | 0.0261353i | ||||||||
\(466\) | 6019.52i | 0.598388i | ||||||||
\(467\) | −7406.57 | −0.733908 | −0.366954 | − | 0.930239i | \(-0.619599\pi\) | ||||
−0.366954 | + | 0.930239i | \(0.619599\pi\) | |||||||
\(468\) | 6260.87 | 0.618395 | ||||||||
\(469\) | − 58.7731i | − 0.00578655i | ||||||||
\(470\) | 2067.22i | 0.202880i | ||||||||
\(471\) | − 2228.94i | − 0.218055i | ||||||||
\(472\) | −31852.0 | −3.10616 | ||||||||
\(473\) | − 14539.5i | − 1.41338i | ||||||||
\(474\) | 46071.0 | 4.46437 | ||||||||
\(475\) | 8262.24 | 0.798101 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14791.9 | −1.41986 | ||||||||
\(478\) | 24905.0 | 2.38311 | ||||||||
\(479\) | − 18550.9i | − 1.76955i | −0.466019 | − | 0.884775i | \(-0.654312\pi\) | ||||
0.466019 | − | 0.884775i | \(-0.345688\pi\) | |||||||
\(480\) | −867.997 | −0.0825384 | ||||||||
\(481\) | − 1050.80i | − 0.0996100i | ||||||||
\(482\) | − 33731.6i | − 3.18762i | ||||||||
\(483\) | − 5832.34i | − 0.549442i | ||||||||
\(484\) | −24461.5 | −2.29729 | ||||||||
\(485\) | 336.041 | 0.0314615 | ||||||||
\(486\) | − 17531.5i | − 1.63631i | ||||||||
\(487\) | − 10203.4i | − 0.949406i | −0.880146 | − | 0.474703i | \(-0.842556\pi\) | ||||
0.880146 | − | 0.474703i | \(-0.157444\pi\) | |||||||
\(488\) | − 15970.7i | − 1.48147i | ||||||||
\(489\) | −12246.7 | −1.13255 | ||||||||
\(490\) | 1463.85i | 0.134959i | ||||||||
\(491\) | 1247.46 | 0.114658 | 0.0573290 | − | 0.998355i | \(-0.481742\pi\) | ||||
0.0573290 | + | 0.998355i | \(0.481742\pi\) | |||||||
\(492\) | −2629.73 | −0.240970 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2698.08 | −0.245734 | ||||||||
\(495\) | 2079.53 | 0.188824 | ||||||||
\(496\) | − 3406.87i | − 0.308413i | ||||||||
\(497\) | −2559.03 | −0.230962 | ||||||||
\(498\) | 36922.7i | 3.32238i | ||||||||
\(499\) | − 70.0303i | − 0.00628254i | −0.999995 | − | 0.00314127i | \(-0.999000\pi\) | ||||
0.999995 | − | 0.00314127i | \(-0.000999898\pi\) | |||||||
\(500\) | 3824.36i | 0.342061i | ||||||||
\(501\) | 4250.94 | 0.379078 | ||||||||
\(502\) | −23935.0 | −2.12803 | ||||||||
\(503\) | − 1444.29i | − 0.128028i | −0.997949 | − | 0.0640138i | \(-0.979610\pi\) | ||||
0.997949 | − | 0.0640138i | \(-0.0203902\pi\) | |||||||
\(504\) | 8034.15i | 0.710058i | ||||||||
\(505\) | 116.674i | 0.0102810i | ||||||||
\(506\) | 47500.7 | 4.17325 | ||||||||
\(507\) | − 18069.7i | − 1.58285i | ||||||||
\(508\) | −33400.0 | −2.91710 | ||||||||
\(509\) | 14272.8 | 1.24289 | 0.621445 | − | 0.783458i | \(-0.286546\pi\) | ||||
0.621445 | + | 0.783458i | \(0.286546\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 738.761 | 0.0639547 | ||||||||
\(512\) | −25356.7 | −2.18871 | ||||||||
\(513\) | − 10052.4i | − 0.865157i | ||||||||
\(514\) | −14558.3 | −1.24929 | ||||||||
\(515\) | 173.585i | 0.0148525i | ||||||||
\(516\) | − 40767.2i | − 3.47805i | ||||||||
\(517\) | 24289.6i | 2.06625i | ||||||||
\(518\) | 2505.10 | 0.212486 | ||||||||
\(519\) | 21952.3 | 1.85665 | ||||||||
\(520\) | − 335.055i | − 0.0282561i | ||||||||
\(521\) | − 14874.0i | − 1.25075i | −0.780324 | − | 0.625376i | \(-0.784946\pi\) | ||||
0.780324 | − | 0.625376i | \(-0.215054\pi\) | |||||||
\(522\) | 9313.42i | 0.780914i | ||||||||
\(523\) | −8142.90 | −0.680811 | −0.340406 | − | 0.940279i | \(-0.610564\pi\) | ||||
−0.340406 | + | 0.940279i | \(0.610564\pi\) | |||||||
\(524\) | − 7047.21i | − 0.587517i | ||||||||
\(525\) | 4019.78 | 0.334167 | ||||||||
\(526\) | −27253.4 | −2.25914 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −43315.7 | −3.57022 | ||||||||
\(529\) | −20314.2 | −1.66962 | ||||||||
\(530\) | 1470.64i | 0.120529i | ||||||||
\(531\) | 30425.3 | 2.48652 | ||||||||
\(532\) | − 4400.40i | − 0.358612i | ||||||||
\(533\) | − 144.344i | − 0.0117303i | ||||||||
\(534\) | 48174.1i | 3.90393i | ||||||||
\(535\) | 429.689 | 0.0347235 | ||||||||
\(536\) | 722.432 | 0.0582170 | ||||||||
\(537\) | − 18354.7i | − 1.47498i | ||||||||
\(538\) | 29123.1i | 2.33380i | ||||||||
\(539\) | 17200.0i | 1.37451i | ||||||||
\(540\) | 2319.17 | 0.184817 | ||||||||
\(541\) | 3179.67i | 0.252689i | 0.991986 | + | 0.126344i | \(0.0403244\pi\) | ||||
−0.991986 | + | 0.126344i | \(0.959676\pi\) | |||||||
\(542\) | 27503.3 | 2.17965 | ||||||||
\(543\) | −16319.8 | −1.28978 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1111.64 | −0.0873716 | ||||||||
\(546\) | −1312.68 | −0.102889 | ||||||||
\(547\) | 2107.07i | 0.164702i | 0.996603 | + | 0.0823509i | \(0.0262428\pi\) | ||||
−0.996603 | + | 0.0823509i | \(0.973757\pi\) | |||||||
\(548\) | −2261.97 | −0.176326 | ||||||||
\(549\) | 15255.3i | 1.18594i | ||||||||
\(550\) | 32738.6i | 2.53814i | ||||||||
\(551\) | − 2745.76i | − 0.212292i | ||||||||
\(552\) | 71690.4 | 5.52780 | ||||||||
\(553\) | −4124.33 | −0.317151 | ||||||||
\(554\) | − 6077.51i | − 0.466081i | ||||||||
\(555\) | − 978.614i | − 0.0748466i | ||||||||
\(556\) | 35926.4i | 2.74032i | ||||||||
\(557\) | 467.382 | 0.0355540 | 0.0177770 | − | 0.999842i | \(-0.494341\pi\) | ||||
0.0177770 | + | 0.999842i | \(0.494341\pi\) | |||||||
\(558\) | 7876.55i | 0.597565i | ||||||||
\(559\) | 2237.69 | 0.169309 | ||||||||
\(560\) | 330.019 | 0.0249033 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6024.80 | 0.452208 | ||||||||
\(563\) | −14612.6 | −1.09387 | −0.546935 | − | 0.837175i | \(-0.684206\pi\) | ||||
−0.546935 | + | 0.837175i | \(0.684206\pi\) | |||||||
\(564\) | 68105.2i | 5.08466i | ||||||||
\(565\) | −897.515 | −0.0668297 | ||||||||
\(566\) | − 15926.5i | − 1.18276i | ||||||||
\(567\) | − 268.886i | − 0.0199156i | ||||||||
\(568\) | − 31455.3i | − 2.32365i | ||||||||
\(569\) | −11602.3 | −0.854821 | −0.427410 | − | 0.904058i | \(-0.640574\pi\) | ||||
−0.427410 | + | 0.904058i | \(0.640574\pi\) | |||||||
\(570\) | −2512.73 | −0.184643 | ||||||||
\(571\) | 10534.9i | 0.772104i | 0.922477 | + | 0.386052i | \(0.126161\pi\) | ||||
−0.922477 | + | 0.386052i | \(0.873839\pi\) | |||||||
\(572\) | − 7313.91i | − 0.534633i | ||||||||
\(573\) | − 23591.3i | − 1.71997i | ||||||||
\(574\) | 344.115 | 0.0250228 | ||||||||
\(575\) | − 22386.8i | − 1.62364i | ||||||||
\(576\) | 8911.18 | 0.644617 | ||||||||
\(577\) | 14404.7 | 1.03930 | 0.519650 | − | 0.854379i | \(-0.326062\pi\) | ||||
0.519650 | + | 0.854379i | \(0.326062\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19139.6 | 1.37377 | ||||||||
\(580\) | 633.466 | 0.0453504 | ||||||||
\(581\) | − 3305.37i | − 0.236024i | ||||||||
\(582\) | 16182.8 | 1.15257 | ||||||||
\(583\) | 17279.8i | 1.22754i | ||||||||
\(584\) | 9080.77i | 0.643433i | ||||||||
\(585\) | 320.047i | 0.0226194i | ||||||||
\(586\) | 37523.5 | 2.64519 | ||||||||
\(587\) | 11004.9 | 0.773799 | 0.386900 | − | 0.922122i | \(-0.373546\pi\) | ||||
0.386900 | + | 0.922122i | \(0.373546\pi\) | |||||||
\(588\) | 48227.0i | 3.38240i | ||||||||
\(589\) | − 2322.14i | − 0.162449i | ||||||||
\(590\) | − 3024.94i | − 0.211076i | ||||||||
\(591\) | −10769.6 | −0.749581 | ||||||||
\(592\) | 12722.2i | 0.883239i | ||||||||
\(593\) | −1853.59 | −0.128361 | −0.0641804 | − | 0.997938i | \(-0.520443\pi\) | ||||
−0.0641804 | + | 0.997938i | \(0.520443\pi\) | |||||||
\(594\) | 39832.0 | 2.75139 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32100.7 | −2.20620 | ||||||||
\(597\) | 40633.9 | 2.78565 | ||||||||
\(598\) | 7310.53i | 0.499916i | ||||||||
\(599\) | 19074.7 | 1.30112 | 0.650559 | − | 0.759456i | \(-0.274535\pi\) | ||||
0.650559 | + | 0.759456i | \(0.274535\pi\) | |||||||
\(600\) | 49410.7i | 3.36197i | ||||||||
\(601\) | 27776.0i | 1.88520i | 0.333923 | + | 0.942600i | \(0.391627\pi\) | ||||
−0.333923 | + | 0.942600i | \(0.608373\pi\) | |||||||
\(602\) | 5334.62i | 0.361168i | ||||||||
\(603\) | −690.073 | −0.0466035 | ||||||||
\(604\) | −35533.4 | −2.39377 | ||||||||
\(605\) | − 1250.44i | − 0.0840291i | ||||||||
\(606\) | 5618.67i | 0.376638i | ||||||||
\(607\) | 18728.3i | 1.25232i | 0.779695 | + | 0.626159i | \(0.215374\pi\) | ||||
−0.779695 | + | 0.626159i | \(0.784626\pi\) | |||||||
\(608\) | 7691.32 | 0.513033 | ||||||||
\(609\) | − 1335.88i | − 0.0888874i | ||||||||
\(610\) | 1516.71 | 0.100672 | ||||||||
\(611\) | −3738.25 | −0.247518 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24405.3 | −1.60802 | −0.804012 | − | 0.594613i | \(-0.797305\pi\) | ||||
−0.804012 | + | 0.594613i | \(0.797305\pi\) | |||||||
\(614\) | −32889.8 | −2.16177 | ||||||||
\(615\) | − 134.428i | − 0.00881409i | ||||||||
\(616\) | 9385.43 | 0.613880 | ||||||||
\(617\) | − 22516.4i | − 1.46917i | −0.678518 | − | 0.734584i | \(-0.737377\pi\) | ||||
0.678518 | − | 0.734584i | \(-0.262623\pi\) | |||||||
\(618\) | 8359.35i | 0.544114i | ||||||||
\(619\) | 5146.53i | 0.334179i | 0.985942 | + | 0.167089i | \(0.0534369\pi\) | ||||
−0.985942 | + | 0.167089i | \(0.946563\pi\) | |||||||
\(620\) | 535.736 | 0.0347027 | ||||||||
\(621\) | −27237.4 | −1.76006 | ||||||||
\(622\) | − 44969.9i | − 2.89892i | ||||||||
\(623\) | − 4312.60i | − 0.277337i | ||||||||
\(624\) | − 6666.45i | − 0.427679i | ||||||||
\(625\) | 15331.4 | 0.981213 | ||||||||
\(626\) | 13229.0i | 0.844627i | ||||||||
\(627\) | −29524.3 | −1.88052 | ||||||||
\(628\) | −4556.62 | −0.289536 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −762.990 | −0.0482512 | ||||||||
\(631\) | 3858.77 | 0.243447 | 0.121724 | − | 0.992564i | \(-0.461158\pi\) | ||||
0.121724 | + | 0.992564i | \(0.461158\pi\) | |||||||
\(632\) | − 50695.8i | − 3.19078i | ||||||||
\(633\) | −23790.3 | −1.49381 | ||||||||
\(634\) | − 21481.5i | − 1.34564i | ||||||||
\(635\) | − 1707.36i | − 0.106700i | ||||||||
\(636\) | 48450.7i | 3.02075i | ||||||||
\(637\) | −2647.15 | −0.164653 | ||||||||
\(638\) | 10879.9 | 0.675138 | ||||||||
\(639\) | 30046.3i | 1.86011i | ||||||||
\(640\) | − 1705.28i | − 0.105324i | ||||||||
\(641\) | 18689.3i | 1.15161i | 0.817587 | + | 0.575805i | \(0.195311\pi\) | ||||
−0.817587 | + | 0.575805i | \(0.804689\pi\) | |||||||
\(642\) | 20692.6 | 1.27208 | ||||||||
\(643\) | 26473.5i | 1.62366i | 0.583893 | + | 0.811831i | \(0.301529\pi\) | ||||
−0.583893 | + | 0.811831i | \(0.698471\pi\) | |||||||
\(644\) | −11923.0 | −0.729555 | ||||||||
\(645\) | 2083.96 | 0.127219 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14397.7 | 0.874855 | 0.437427 | − | 0.899254i | \(-0.355890\pi\) | ||||
0.437427 | + | 0.899254i | \(0.355890\pi\) | |||||||
\(648\) | 3305.12 | 0.200366 | ||||||||
\(649\) | − 35542.6i | − 2.14972i | ||||||||
\(650\) | −5038.59 | −0.304046 | ||||||||
\(651\) | − 1129.78i | − 0.0680177i | ||||||||
\(652\) | 25036.0i | 1.50381i | ||||||||
\(653\) | − 20939.5i | − 1.25486i | −0.778672 | − | 0.627431i | \(-0.784107\pi\) | ||||
0.778672 | − | 0.627431i | \(-0.215893\pi\) | |||||||
\(654\) | −53533.6 | −3.20081 | ||||||||
\(655\) | 360.244 | 0.0214899 | ||||||||
\(656\) | 1747.59i | 0.104012i | ||||||||
\(657\) | − 8674.02i | − 0.515077i | ||||||||
\(658\) | − 8911.96i | − 0.528001i | ||||||||
\(659\) | 4031.76 | 0.238323 | 0.119162 | − | 0.992875i | \(-0.461979\pi\) | ||||
0.119162 | + | 0.992875i | \(0.461979\pi\) | |||||||
\(660\) | − 6811.47i | − 0.401721i | ||||||||
\(661\) | −6691.52 | −0.393752 | −0.196876 | − | 0.980428i | \(-0.563080\pi\) | ||||
−0.196876 | + | 0.980428i | \(0.563080\pi\) | |||||||
\(662\) | −4993.75 | −0.293184 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 40629.2 | 2.37458 | ||||||||
\(665\) | 224.943 | 0.0131171 | ||||||||
\(666\) | − 29413.1i | − 1.71131i | ||||||||
\(667\) | −7439.71 | −0.431884 | ||||||||
\(668\) | − 8690.19i | − 0.503344i | ||||||||
\(669\) | − 39701.1i | − 2.29437i | ||||||||
\(670\) | 68.6083i | 0.00395607i | ||||||||
\(671\) | 17821.2 | 1.02530 | ||||||||
\(672\) | 3742.01 | 0.214808 | ||||||||
\(673\) | − 10319.2i | − 0.591048i | −0.955335 | − | 0.295524i | \(-0.904506\pi\) | ||||
0.955335 | − | 0.295524i | \(-0.0954942\pi\) | |||||||
\(674\) | 40472.7i | 2.31298i | ||||||||
\(675\) | − 18772.6i | − 1.07046i | ||||||||
\(676\) | −36939.9 | −2.10172 | ||||||||
\(677\) | − 19813.3i | − 1.12480i | −0.826866 | − | 0.562398i | \(-0.809879\pi\) | ||||
0.826866 | − | 0.562398i | \(-0.190121\pi\) | |||||||
\(678\) | −43221.8 | −2.44826 | ||||||||
\(679\) | −1448.70 | −0.0818793 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11829.3 | −0.665636 | ||||||||
\(682\) | 9201.33 | 0.516624 | ||||||||
\(683\) | 5924.61i | 0.331916i | 0.986133 | + | 0.165958i | \(0.0530717\pi\) | ||||
−0.986133 | + | 0.165958i | \(0.946928\pi\) | |||||||
\(684\) | −51666.4 | −2.88818 | ||||||||
\(685\) | − 115.629i | − 0.00644957i | ||||||||
\(686\) | − 12901.7i | − 0.718061i | ||||||||
\(687\) | − 7582.38i | − 0.421085i | ||||||||
\(688\) | −27091.9 | −1.50126 | ||||||||
\(689\) | −2659.43 | −0.147048 | ||||||||
\(690\) | 6808.33i | 0.375636i | ||||||||
\(691\) | − 1973.16i | − 0.108629i | −0.998524 | − | 0.0543143i | \(-0.982703\pi\) | ||||
0.998524 | − | 0.0543143i | \(-0.0172973\pi\) | |||||||
\(692\) | − 44877.1i | − 2.46528i | ||||||||
\(693\) | −8965.03 | −0.491419 | ||||||||
\(694\) | 37311.8i | 2.04083i | ||||||||
\(695\) | −1836.51 | −0.100234 | ||||||||
\(696\) | 16420.4 | 0.894274 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 4323.90 | 0.234473 | ||||||||
\(699\) | −10137.6 | −0.548554 | ||||||||
\(700\) | − 8217.63i | − 0.443710i | ||||||||
\(701\) | −12840.1 | −0.691815 | −0.345907 | − | 0.938269i | \(-0.612429\pi\) | ||||
−0.345907 | + | 0.938269i | \(0.612429\pi\) | |||||||
\(702\) | 6130.30i | 0.329591i | ||||||||
\(703\) | 8671.50i | 0.465223i | ||||||||
\(704\) | − 10410.0i | − 0.557302i | ||||||||
\(705\) | −3481.45 | −0.185984 | ||||||||
\(706\) | 2863.92 | 0.152670 | ||||||||
\(707\) | − 502.990i | − 0.0267566i | ||||||||
\(708\) | − 99657.5i | − 5.29005i | ||||||||
\(709\) | − 27749.7i | − 1.46990i | −0.678119 | − | 0.734952i | \(-0.737204\pi\) | ||||
0.678119 | − | 0.734952i | \(-0.262796\pi\) | |||||||
\(710\) | 2987.26 | 0.157901 | ||||||||
\(711\) | 48425.0i | 2.55426i | ||||||||
\(712\) | 53010.0 | 2.79022 | ||||||||
\(713\) | −6291.92 | −0.330483 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 373.877 | 0.0195555 | ||||||||
\(716\) | −37522.4 | −1.95849 | ||||||||
\(717\) | 41943.0i | 2.18464i | ||||||||
\(718\) | 25188.8 | 1.30924 | ||||||||
\(719\) | 16888.3i | 0.875979i | 0.898980 | + | 0.437989i | \(0.144309\pi\) | ||||
−0.898980 | + | 0.437989i | \(0.855691\pi\) | |||||||
\(720\) | − 3874.85i | − 0.200565i | ||||||||
\(721\) | − 748.339i | − 0.0386541i | ||||||||
\(722\) | −12252.7 | −0.631575 | ||||||||
\(723\) | 56808.0 | 2.92215 | ||||||||
\(724\) | 33362.6i | 1.71258i | ||||||||
\(725\) | − 5127.62i | − 0.262669i | ||||||||
\(726\) | − 60217.6i | − 3.07835i | ||||||||
\(727\) | 2135.25 | 0.108930 | 0.0544649 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544649 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(728\) | 1444.45i | 0.0735371i | ||||||||
\(729\) | 31426.5 | 1.59663 | ||||||||
\(730\) | −862.386 | −0.0437238 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 49968.6 | 2.52308 | ||||||||
\(733\) | −4795.27 | −0.241633 | −0.120817 | − | 0.992675i | \(-0.538551\pi\) | ||||
−0.120817 | + | 0.992675i | \(0.538551\pi\) | |||||||
\(734\) | 55233.1i | 2.77751i | ||||||||
\(735\) | −2465.30 | −0.123720 | ||||||||
\(736\) | − 20839.9i | − 1.04371i | ||||||||
\(737\) | 806.138i | 0.0402910i | ||||||||
\(738\) | − 4040.36i | − 0.201528i | ||||||||
\(739\) | 32747.6 | 1.63010 | 0.815048 | − | 0.579393i | \(-0.196710\pi\) | ||||
0.815048 | + | 0.579393i | \(0.196710\pi\) | |||||||
\(740\) | −2000.58 | −0.0993821 | ||||||||
\(741\) | − 4543.89i | − 0.225269i | ||||||||
\(742\) | − 6340.05i | − 0.313680i | ||||||||
\(743\) | 12299.4i | 0.607298i | 0.952784 | + | 0.303649i | \(0.0982050\pi\) | ||||
−0.952784 | + | 0.303649i | \(0.901795\pi\) | |||||||
\(744\) | 13887.1 | 0.684309 | ||||||||
\(745\) | − 1640.94i | − 0.0806974i | ||||||||
\(746\) | −16163.0 | −0.793257 | ||||||||
\(747\) | −38809.3 | −1.90088 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1852.43 | −0.0903688 | ||||||||
\(750\) | −9414.54 | −0.458361 | ||||||||
\(751\) | 30102.6i | 1.46266i | 0.682021 | + | 0.731332i | \(0.261101\pi\) | ||||
−0.682021 | + | 0.731332i | \(0.738899\pi\) | |||||||
\(752\) | 45259.4 | 2.19474 | ||||||||
\(753\) | − 40309.4i | − 1.95081i | ||||||||
\(754\) | 1674.45i | 0.0808753i | ||||||||
\(755\) | − 1816.42i | − 0.0875581i | ||||||||
\(756\) | −9998.14 | −0.480990 | ||||||||
\(757\) | −38826.3 | −1.86416 | −0.932078 | − | 0.362257i | \(-0.882006\pi\) | ||||
−0.932078 | + | 0.362257i | \(0.882006\pi\) | |||||||
\(758\) | 40519.2i | 1.94159i | ||||||||
\(759\) | 79996.9i | 3.82570i | ||||||||
\(760\) | 2764.97i | 0.131968i | ||||||||
\(761\) | 19981.6 | 0.951815 | 0.475907 | − | 0.879495i | \(-0.342120\pi\) | ||||
0.475907 | + | 0.879495i | \(0.342120\pi\) | |||||||
\(762\) | − 82221.8i | − 3.90890i | ||||||||
\(763\) | 4792.39 | 0.227387 | ||||||||
\(764\) | −48227.7 | −2.28379 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13004.8 | 0.613424 | ||||||||
\(767\) | 5470.14 | 0.257517 | ||||||||
\(768\) | − 68644.2i | − 3.22524i | ||||||||
\(769\) | −22407.7 | −1.05077 | −0.525384 | − | 0.850865i | \(-0.676078\pi\) | ||||
−0.525384 | + | 0.850865i | \(0.676078\pi\) | |||||||
\(770\) | 891.320i | 0.0417155i | ||||||||
\(771\) | − 24517.9i | − 1.14525i | ||||||||
\(772\) | − 39127.0i | − 1.82411i | ||||||||
\(773\) | 6902.77 | 0.321184 | 0.160592 | − | 0.987021i | \(-0.448660\pi\) | ||||
0.160592 | + | 0.987021i | \(0.448660\pi\) | |||||||
\(774\) | 62635.4 | 2.90876 | ||||||||
\(775\) | − 4336.54i | − 0.200997i | ||||||||
\(776\) | − 17807.3i | − 0.823768i | ||||||||
\(777\) | 4218.89i | 0.194790i | ||||||||
\(778\) | 26039.8 | 1.19996 | ||||||||
\(779\) | 1191.17i | 0.0547856i | ||||||||
\(780\) | 1048.31 | 0.0481225 | ||||||||
\(781\) | 35099.9 | 1.60816 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6238.62 | −0.284738 | ||||||||
\(784\) | 32049.3 | 1.45997 | ||||||||
\(785\) | − 232.928i | − 0.0105905i | ||||||||
\(786\) | 17348.3 | 0.787270 | ||||||||
\(787\) | − 22185.9i | − 1.00488i | −0.864611 | − | 0.502442i | \(-0.832435\pi\) | ||||
0.864611 | − | 0.502442i | \(-0.167565\pi\) | |||||||
\(788\) | 22016.3i | 0.995301i | ||||||||
\(789\) | − 45898.1i | − 2.07099i | ||||||||
\(790\) | 4814.50 | 0.216826 | ||||||||
\(791\) | 3869.27 | 0.173926 | ||||||||
\(792\) | − 110197.i | − 4.94405i | ||||||||
\(793\) | 2742.74i | 0.122822i | ||||||||
\(794\) | 25914.2i | 1.15826i | ||||||||
\(795\) | −2476.73 | −0.110491 | ||||||||
\(796\) | − 83067.8i | − 3.69882i | ||||||||
\(797\) | 16291.1 | 0.724040 | 0.362020 | − | 0.932170i | \(-0.382087\pi\) | ||||
0.362020 | + | 0.932170i | \(0.382087\pi\) | |||||||
\(798\) | 10832.6 | 0.480539 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 14363.3 | 0.634775 | ||||||||
\(801\) | −50635.5 | −2.23361 | ||||||||
\(802\) | − 43785.3i | − 1.92782i | ||||||||
\(803\) | −10132.9 | −0.445309 | ||||||||
\(804\) | 2260.32i | 0.0991485i | ||||||||
\(805\) | − 609.489i | − 0.0266853i | ||||||||
\(806\) | 1416.12i | 0.0618867i | ||||||||
\(807\) | −49046.8 | −2.13944 | ||||||||
\(808\) | 6182.70 | 0.269191 | ||||||||
\(809\) | − 17696.8i | − 0.769082i | −0.923108 | − | 0.384541i | \(-0.874360\pi\) | ||||
0.923108 | − | 0.384541i | \(-0.125640\pi\) | |||||||
\(810\) | 313.882i | 0.0136157i | ||||||||
\(811\) | − 3095.34i | − 0.134022i | −0.997752 | − | 0.0670111i | \(-0.978654\pi\) | ||||
0.997752 | − | 0.0670111i | \(-0.0213463\pi\) | |||||||
\(812\) | −2730.93 | −0.118026 | ||||||||
\(813\) | 46318.9i | 1.99812i | ||||||||
\(814\) | −34360.2 | −1.47951 | ||||||||
\(815\) | −1279.81 | −0.0550057 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18466.0 | −0.790751 | ||||||||
\(818\) | 62131.5 | 2.65572 | ||||||||
\(819\) | − 1379.75i | − 0.0588674i | ||||||||
\(820\) | −274.811 | −0.0117034 | ||||||||
\(821\) | 12323.5i | 0.523864i | 0.965086 | + | 0.261932i | \(0.0843597\pi\) | ||||
−0.965086 | + | 0.261932i | \(0.915640\pi\) | |||||||
\(822\) | − 5568.36i | − 0.236276i | ||||||||
\(823\) | 34436.5i | 1.45854i | 0.684225 | + | 0.729271i | \(0.260140\pi\) | ||||
−0.684225 | + | 0.729271i | \(0.739860\pi\) | |||||||
\(824\) | 9198.50 | 0.388889 | ||||||||
\(825\) | −55135.7 | −2.32676 | ||||||||
\(826\) | 13040.8i | 0.549329i | ||||||||
\(827\) | − 18761.6i | − 0.788880i | −0.918922 | − | 0.394440i | \(-0.870939\pi\) | ||||
0.918922 | − | 0.394440i | \(-0.129061\pi\) | |||||||
\(828\) | 139992.i | 5.87567i | ||||||||
\(829\) | 22423.8 | 0.939457 | 0.469728 | − | 0.882811i | \(-0.344352\pi\) | ||||
0.469728 | + | 0.882811i | \(0.344352\pi\) | |||||||
\(830\) | 3858.49i | 0.161362i | ||||||||
\(831\) | 10235.3 | 0.427265 | ||||||||
\(832\) | 1602.13 | 0.0667596 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −88441.1 | −3.67202 | ||||||||
\(835\) | 444.231 | 0.0184111 | ||||||||
\(836\) | 60356.4i | 2.49697i | ||||||||
\(837\) | −5276.13 | −0.217885 | ||||||||
\(838\) | 29004.0i | 1.19562i | ||||||||
\(839\) | − 9128.63i | − 0.375632i | −0.982204 | − | 0.187816i | \(-0.939859\pi\) | ||||
0.982204 | − | 0.187816i | \(-0.0601409\pi\) | |||||||
\(840\) | 1345.22i | 0.0552555i | ||||||||
\(841\) | 22685.0 | 0.930131 | ||||||||
\(842\) | −9441.58 | −0.386435 | ||||||||
\(843\) | 10146.5i | 0.414547i | ||||||||
\(844\) | 48634.4i | 1.98349i | ||||||||
\(845\) | − 1888.32i | − 0.0768759i | ||||||||
\(846\) | −104638. | −4.25240 | ||||||||
\(847\) | 5390.75i | 0.218688i | ||||||||
\(848\) | 32198.0 | 1.30387 | ||||||||
\(849\) | 26822.2 | 1.08426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23495.7 | 0.946442 | ||||||||
\(852\) | 98416.1 | 3.95737 | ||||||||
\(853\) | 27204.8i | 1.09200i | 0.837786 | + | 0.545999i | \(0.183850\pi\) | ||||
−0.837786 | + | 0.545999i | \(0.816150\pi\) | |||||||
\(854\) | −6538.68 | −0.262001 | ||||||||
\(855\) | − 2641.12i | − 0.105643i | ||||||||
\(856\) | − 22769.8i | − 0.909179i | ||||||||
\(857\) | 38060.0i | 1.51704i | 0.651649 | + | 0.758520i | \(0.274077\pi\) | ||||
−0.651649 | + | 0.758520i | \(0.725923\pi\) | |||||||
\(858\) | 18004.9 | 0.716405 | ||||||||
\(859\) | 33326.2 | 1.32372 | 0.661860 | − | 0.749627i | \(-0.269767\pi\) | ||||
0.661860 | + | 0.749627i | \(0.269767\pi\) | |||||||
\(860\) | − 4260.24i | − 0.168922i | ||||||||
\(861\) | 579.531i | 0.0229389i | ||||||||
\(862\) | − 422.378i | − 0.0166894i | ||||||||
\(863\) | −41724.2 | −1.64578 | −0.822890 | − | 0.568201i | \(-0.807640\pi\) | ||||
−0.822890 | + | 0.568201i | \(0.807640\pi\) | |||||||
\(864\) | − 17475.4i | − 0.688108i | ||||||||
\(865\) | 2294.06 | 0.0901737 | ||||||||
\(866\) | 77223.8 | 3.03022 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2309.60 | −0.0903146 | ||||||||
\(869\) | 56569.7 | 2.20828 | ||||||||
\(870\) | 1559.42i | 0.0607694i | ||||||||
\(871\) | −124.068 | −0.00482649 | ||||||||
\(872\) | 58907.5i | 2.28768i | ||||||||
\(873\) | 17009.6i | 0.659438i | ||||||||
\(874\) | − 60328.6i | − 2.33483i | ||||||||
\(875\) | 842.801 | 0.0325621 | ||||||||
\(876\) | −28411.6 | −1.09582 | ||||||||
\(877\) | 49337.3i | 1.89966i | 0.312767 | + | 0.949830i | \(0.398744\pi\) | ||||
−0.312767 | + | 0.949830i | \(0.601256\pi\) | |||||||
\(878\) | 15423.3i | 0.592838i | ||||||||
\(879\) | 63194.0i | 2.42489i | ||||||||
\(880\) | −4526.57 | −0.173398 | ||||||||
\(881\) | 8845.46i | 0.338265i | 0.985593 | + | 0.169132i | \(0.0540965\pi\) | ||||
−0.985593 | + | 0.169132i | \(0.945903\pi\) | |||||||
\(882\) | −74096.8 | −2.82876 | ||||||||
\(883\) | 14724.2 | 0.561165 | 0.280582 | − | 0.959830i | \(-0.409472\pi\) | ||||
0.280582 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5094.36 | 0.193497 | ||||||||
\(886\) | −9023.14 | −0.342143 | ||||||||
\(887\) | 3864.38i | 0.146283i | 0.997322 | + | 0.0731415i | \(0.0233025\pi\) | ||||
−0.997322 | + | 0.0731415i | \(0.976698\pi\) | |||||||
\(888\) | −51858.1 | −1.95974 | ||||||||
\(889\) | 7360.60i | 0.277690i | ||||||||
\(890\) | 5034.28i | 0.189606i | ||||||||
\(891\) | 3688.07i | 0.138670i | ||||||||
\(892\) | −81160.9 | −3.04649 | ||||||||
\(893\) | 30849.1 | 1.15602 | ||||||||
\(894\) | − 79023.2i | − 2.95630i | ||||||||
\(895\) | − 1918.10i | − 0.0716368i | ||||||||
\(896\) | 7351.61i | 0.274107i | ||||||||
\(897\) | −12311.8 | −0.458283 | ||||||||
\(898\) | − 12577.2i | − 0.467379i | ||||||||
\(899\) | −1441.14 | −0.0534648 | ||||||||
\(900\) | −96485.6 | −3.57354 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4719.92 | −0.174231 | ||||||||
\(903\) | −8984.15 | −0.331089 | ||||||||
\(904\) | 47560.6i | 1.74982i | ||||||||
\(905\) | −1705.45 | −0.0626421 | ||||||||
\(906\) | − 87473.7i | − 3.20764i | ||||||||
\(907\) | 743.409i | 0.0272155i | 0.999907 | + | 0.0136078i | \(0.00433162\pi\) | ||||
−0.999907 | + | 0.0136078i | \(0.995668\pi\) | |||||||
\(908\) | 24182.5i | 0.883839i | ||||||||
\(909\) | −5905.76 | −0.215491 | ||||||||
\(910\) | −137.177 | −0.00499713 | ||||||||
\(911\) | − 16291.0i | − 0.592475i | −0.955114 | − | 0.296238i | \(-0.904268\pi\) | ||||
0.955114 | − | 0.296238i | \(-0.0957320\pi\) | |||||||
\(912\) | 55013.4i | 1.99745i | ||||||||
\(913\) | 45336.8i | 1.64340i | ||||||||
\(914\) | −74402.5 | −2.69258 | ||||||||
\(915\) | 2554.33i | 0.0922879i | ||||||||
\(916\) | −15500.6 | −0.559122 | ||||||||
\(917\) | −1553.04 | −0.0559280 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6188.99 | −0.222150 | −0.111075 | − | 0.993812i | \(-0.535429\pi\) | ||||
−0.111075 | + | 0.993812i | \(0.535429\pi\) | |||||||
\(920\) | 7491.78 | 0.268474 | ||||||||
\(921\) | − 55390.5i | − 1.98174i | ||||||||
\(922\) | 89311.6 | 3.19015 | ||||||||
\(923\) | 5402.00i | 0.192643i | ||||||||
\(924\) | 29364.8i | 1.04549i | ||||||||
\(925\) | 16193.8i | 0.575620i | ||||||||
\(926\) | 93033.0 | 3.30157 | ||||||||
\(927\) | −8786.47 | −0.311311 | ||||||||
\(928\) | − 4773.30i | − 0.168848i | ||||||||
\(929\) | 31661.7i | 1.11818i | 0.829108 | + | 0.559089i | \(0.188849\pi\) | ||||
−0.829108 | + | 0.559089i | \(0.811151\pi\) | |||||||
\(930\) | 1318.84i | 0.0465015i | ||||||||
\(931\) | 21845.0 | 0.769003 | ||||||||
\(932\) | 20724.3i | 0.728376i | ||||||||
\(933\) | 75734.8 | 2.65750 | ||||||||
\(934\) | −37273.6 | −1.30581 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16959.8 | 0.592251 | ||||||||
\(937\) | −35010.5 | −1.22064 | −0.610322 | − | 0.792153i | \(-0.708960\pi\) | ||||
−0.610322 | + | 0.792153i | \(0.708960\pi\) | |||||||
\(938\) | − 295.776i | − 0.0102958i | ||||||||
\(939\) | −22279.2 | −0.774286 | ||||||||
\(940\) | 7117.12i | 0.246952i | ||||||||
\(941\) | 45625.8i | 1.58061i | 0.612711 | + | 0.790307i | \(0.290079\pi\) | ||||
−0.612711 | + | 0.790307i | \(0.709921\pi\) | |||||||
\(942\) | − 11217.2i | − 0.387977i | ||||||||
\(943\) | 3227.51 | 0.111455 | ||||||||
\(944\) | −66227.5 | −2.28339 | ||||||||
\(945\) | − 511.092i | − 0.0175934i | ||||||||
\(946\) | − 73170.2i | − 2.51477i | ||||||||
\(947\) | − 21508.4i | − 0.738044i | −0.929421 | − | 0.369022i | \(-0.879693\pi\) | ||||
0.929421 | − | 0.369022i | \(-0.120307\pi\) | |||||||
\(948\) | 158615. | 5.43416 | ||||||||
\(949\) | − 1559.50i | − 0.0533439i | ||||||||
\(950\) | 41579.8 | 1.42003 | ||||||||
\(951\) | 36177.4 | 1.23358 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35686.7 | 1.21302 | 0.606509 | − | 0.795076i | \(-0.292569\pi\) | ||||
0.606509 | + | 0.795076i | \(0.292569\pi\) | |||||||
\(954\) | −74440.5 | −2.52631 | ||||||||
\(955\) | − 2465.34i | − 0.0835355i | ||||||||
\(956\) | 85744.0 | 2.90079 | ||||||||
\(957\) | 18323.0i | 0.618912i | ||||||||
\(958\) | − 93357.8i | − 3.14849i | ||||||||
\(959\) | 498.486i | 0.0167851i | ||||||||
\(960\) | 1492.07 | 0.0501630 | ||||||||
\(961\) | 28572.2 | 0.959088 | ||||||||
\(962\) | − 5288.17i | − 0.177232i | ||||||||
\(963\) | 21749.9i | 0.727810i | ||||||||
\(964\) | − 116133.i | − 3.88006i | ||||||||
\(965\) | 2000.12 | 0.0667215 | ||||||||
\(966\) | − 29351.3i | − 0.977600i | ||||||||
\(967\) | 3731.33 | 0.124086 | 0.0620432 | − | 0.998073i | \(-0.480238\pi\) | ||||
0.0620432 | + | 0.998073i | \(0.480238\pi\) | |||||||
\(968\) | −66262.5 | −2.20016 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1691.13 | 0.0559782 | ||||||||
\(971\) | −17645.1 | −0.583171 | −0.291585 | − | 0.956545i | \(-0.594183\pi\) | ||||
−0.291585 | + | 0.956545i | \(0.594183\pi\) | |||||||
\(972\) | − 60358.3i | − 1.99176i | ||||||||
\(973\) | 7917.35 | 0.260862 | ||||||||
\(974\) | − 51348.7i | − 1.68924i | ||||||||
\(975\) | − 8485.59i | − 0.278725i | ||||||||
\(976\) | − 33206.7i | − 1.08906i | ||||||||
\(977\) | −24941.2 | −0.816723 | −0.408362 | − | 0.912820i | \(-0.633900\pi\) | ||||
−0.408362 | + | 0.912820i | \(0.633900\pi\) | |||||||
\(978\) | −61631.8 | −2.01510 | ||||||||
\(979\) | 59152.1i | 1.93106i | ||||||||
\(980\) | 5039.81i | 0.164276i | ||||||||
\(981\) | − 56268.9i | − 1.83132i | ||||||||
\(982\) | 6277.85 | 0.204006 | ||||||||
\(983\) | − 22506.2i | − 0.730252i | −0.930958 | − | 0.365126i | \(-0.881026\pi\) | ||||
0.930958 | − | 0.365126i | \(-0.118974\pi\) | |||||||
\(984\) | −7123.53 | −0.230782 | ||||||||
\(985\) | −1125.44 | −0.0364057 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15008.8 | 0.484029 | ||||||||
\(988\) | −9289.07 | −0.299114 | ||||||||
\(989\) | 50034.2i | 1.60869i | ||||||||
\(990\) | 10465.3 | 0.335967 | ||||||||
\(991\) | 32694.1i | 1.04799i | 0.851720 | + | 0.523997i | \(0.175560\pi\) | ||||
−0.851720 | + | 0.523997i | \(0.824440\pi\) | |||||||
\(992\) | − 4036.88i | − 0.129205i | ||||||||
\(993\) | − 8410.08i | − 0.268767i | ||||||||
\(994\) | −12878.3 | −0.410941 | ||||||||
\(995\) | 4246.32 | 0.135294 | ||||||||
\(996\) | 127119.i | 4.04410i | ||||||||
\(997\) | − 18248.8i | − 0.579686i | −0.957074 | − | 0.289843i | \(-0.906397\pi\) | ||||
0.957074 | − | 0.289843i | \(-0.0936030\pi\) | |||||||
\(998\) | − 352.428i | − 0.0111783i | ||||||||
\(999\) | 19702.5 | 0.623983 |
(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 | 289.4.b.b.288.6 | 6 | ||
17.4 | even | 4 | 17.4.a.b.1.1 | ✓ | 3 | ||
17.13 | even | 4 | 289.4.a.b.1.1 | 3 | |||
17.16 | even | 2 | inner | 289.4.b.b.288.5 | 6 | ||
51.38 | odd | 4 | 153.4.a.g.1.3 | 3 | |||
68.55 | odd | 4 | 272.4.a.h.1.1 | 3 | |||
85.4 | even | 4 | 425.4.a.g.1.3 | 3 | |||
85.38 | odd | 4 | 425.4.b.f.324.6 | 6 | |||
85.72 | odd | 4 | 425.4.b.f.324.1 | 6 | |||
119.55 | odd | 4 | 833.4.a.d.1.1 | 3 | |||
136.21 | even | 4 | 1088.4.a.v.1.1 | 3 | |||
136.123 | odd | 4 | 1088.4.a.x.1.3 | 3 | |||
187.21 | odd | 4 | 2057.4.a.e.1.3 | 3 | |||
204.191 | even | 4 | 2448.4.a.bi.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.1 | ✓ | 3 | 17.4 | even | 4 | ||
153.4.a.g.1.3 | 3 | 51.38 | odd | 4 | |||
272.4.a.h.1.1 | 3 | 68.55 | odd | 4 | |||
289.4.a.b.1.1 | 3 | 17.13 | even | 4 | |||
289.4.b.b.288.5 | 6 | 17.16 | even | 2 | inner | ||
289.4.b.b.288.6 | 6 | 1.1 | even | 1 | trivial | ||
425.4.a.g.1.3 | 3 | 85.4 | even | 4 | |||
425.4.b.f.324.1 | 6 | 85.72 | odd | 4 | |||
425.4.b.f.324.6 | 6 | 85.38 | odd | 4 | |||
833.4.a.d.1.1 | 3 | 119.55 | odd | 4 | |||
1088.4.a.v.1.1 | 3 | 136.21 | even | 4 | |||
1088.4.a.x.1.3 | 3 | 136.123 | odd | 4 | |||
2057.4.a.e.1.3 | 3 | 187.21 | odd | 4 | |||
2448.4.a.bi.1.2 | 3 | 204.191 | even | 4 |