Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(47,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 59.12 | ||
Character | \(\chi\) | \(=\) | 63.59 |
Dual form | 63.4.s.a.47.12 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.647627 | + | 0.373907i | 0.228971 | + | 0.132196i | 0.610097 | − | 0.792327i | \(-0.291130\pi\) |
−0.381126 | + | 0.924523i | \(0.624464\pi\) | |||||||
\(3\) | 4.16400 | + | 3.10824i | 0.801362 | + | 0.598180i | ||||
\(4\) | −3.72039 | − | 6.44390i | −0.465048 | − | 0.805487i | ||||
\(5\) | 8.70220 | 0.778348 | 0.389174 | − | 0.921164i | \(-0.372760\pi\) | ||||
0.389174 | + | 0.921164i | \(0.372760\pi\) | |||||||
\(6\) | 1.53452 | + | 3.56993i | 0.104411 | + | 0.242903i | ||||
\(7\) | 18.2993 | − | 2.85258i | 0.988067 | − | 0.154025i | ||||
\(8\) | − | 11.5468i | − | 0.510303i | ||||||
\(9\) | 7.67775 | + | 25.8854i | 0.284361 | + | 0.958717i | ||||
\(10\) | 5.63577 | + | 3.25382i | 0.178219 | + | 0.102895i | ||||
\(11\) | 41.5070i | 1.13771i | 0.822437 | + | 0.568856i | \(0.192614\pi\) | ||||
−0.822437 | + | 0.568856i | \(0.807386\pi\) | |||||||
\(12\) | 4.53747 | − | 38.3962i | 0.109155 | − | 0.923669i | ||||
\(13\) | −33.0053 | − | 19.0556i | −0.704155 | − | 0.406544i | 0.104738 | − | 0.994500i | \(-0.466600\pi\) |
−0.808893 | + | 0.587956i | \(0.799933\pi\) | |||||||
\(14\) | 12.9177 | + | 4.99482i | 0.246600 | + | 0.0953516i | ||||
\(15\) | 36.2359 | + | 27.0485i | 0.623738 | + | 0.465592i | ||||
\(16\) | −25.4456 | + | 44.0731i | −0.397588 | + | 0.688643i | ||||
\(17\) | 39.9685 | − | 69.2274i | 0.570222 | − | 0.987654i | −0.426320 | − | 0.904572i | \(-0.640190\pi\) |
0.996543 | − | 0.0830818i | \(-0.0264763\pi\) | |||||||
\(18\) | −4.70642 | + | 19.6348i | −0.0616285 | + | 0.257110i | ||||
\(19\) | −49.4113 | + | 28.5276i | −0.596617 | + | 0.344457i | −0.767710 | − | 0.640798i | \(-0.778604\pi\) |
0.171092 | + | 0.985255i | \(0.445270\pi\) | |||||||
\(20\) | −32.3755 | − | 56.0761i | −0.361969 | − | 0.626949i | ||||
\(21\) | 85.0645 | + | 45.0003i | 0.883933 | + | 0.467613i | ||||
\(22\) | −15.5198 | + | 26.8811i | −0.150401 | + | 0.260503i | ||||
\(23\) | − | 177.014i | − | 1.60478i | −0.596802 | − | 0.802389i | \(-0.703562\pi\) | ||
0.596802 | − | 0.802389i | \(-0.296438\pi\) | |||||||
\(24\) | 35.8903 | − | 48.0810i | 0.305253 | − | 0.408937i | ||||
\(25\) | −49.2718 | −0.394174 | ||||||||
\(26\) | −14.2501 | − | 24.6818i | −0.107487 | − | 0.186173i | ||||
\(27\) | −48.4877 | + | 131.651i | −0.345610 | + | 0.938378i | ||||
\(28\) | −86.4620 | − | 107.306i | −0.583564 | − | 0.724247i | ||||
\(29\) | −60.1430 | + | 34.7236i | −0.385113 | + | 0.222345i | −0.680041 | − | 0.733174i | \(-0.738038\pi\) |
0.294927 | + | 0.955520i | \(0.404705\pi\) | |||||||
\(30\) | 13.3537 | + | 31.0662i | 0.0812682 | + | 0.189063i | ||||
\(31\) | −225.864 | + | 130.403i | −1.30859 | + | 0.755517i | −0.981861 | − | 0.189601i | \(-0.939281\pi\) |
−0.326732 | + | 0.945117i | \(0.605947\pi\) | |||||||
\(32\) | −112.957 | + | 65.2160i | −0.624007 | + | 0.360271i | ||||
\(33\) | −129.014 | + | 172.835i | −0.680557 | + | 0.911720i | ||||
\(34\) | 51.7693 | − | 29.8890i | 0.261128 | − | 0.150762i | ||||
\(35\) | 159.244 | − | 24.8237i | 0.769060 | − | 0.119885i | ||||
\(36\) | 138.238 | − | 145.778i | 0.639993 | − | 0.674899i | ||||
\(37\) | −74.9359 | − | 129.793i | −0.332957 | − | 0.576698i | 0.650134 | − | 0.759820i | \(-0.274713\pi\) |
−0.983090 | + | 0.183122i | \(0.941380\pi\) | |||||||
\(38\) | −42.6668 | −0.182144 | ||||||||
\(39\) | −78.2046 | − | 181.936i | −0.321096 | − | 0.747000i | ||||
\(40\) | − | 100.483i | − | 0.397193i | ||||||
\(41\) | −54.7122 | + | 94.7643i | −0.208405 | + | 0.360968i | −0.951212 | − | 0.308537i | \(-0.900161\pi\) |
0.742807 | + | 0.669505i | \(0.233494\pi\) | |||||||
\(42\) | 38.2641 | + | 60.9496i | 0.140578 | + | 0.223922i | ||||
\(43\) | 124.193 | + | 215.108i | 0.440446 | + | 0.762875i | 0.997723 | − | 0.0674517i | \(-0.0214869\pi\) |
−0.557276 | + | 0.830327i | \(0.688154\pi\) | |||||||
\(44\) | 267.467 | − | 154.422i | 0.916413 | − | 0.529092i | ||||
\(45\) | 66.8133 | + | 225.260i | 0.221332 | + | 0.746216i | ||||
\(46\) | 66.1867 | − | 114.639i | 0.212146 | − | 0.367447i | ||||
\(47\) | 147.528 | − | 255.526i | 0.457855 | − | 0.793029i | −0.540992 | − | 0.841028i | \(-0.681951\pi\) |
0.998847 | + | 0.0479988i | \(0.0152844\pi\) | |||||||
\(48\) | −242.945 | + | 104.429i | −0.730544 | + | 0.314023i | ||||
\(49\) | 326.726 | − | 104.400i | 0.952553 | − | 0.304373i | ||||
\(50\) | −31.9097 | − | 18.4231i | −0.0902543 | − | 0.0521084i | ||||
\(51\) | 381.604 | − | 164.031i | 1.04775 | − | 0.450372i | ||||
\(52\) | 283.577i | 0.756251i | ||||||||
\(53\) | 263.613 | + | 152.197i | 0.683208 | + | 0.394450i | 0.801062 | − | 0.598581i | \(-0.204268\pi\) |
−0.117855 | + | 0.993031i | \(0.537602\pi\) | |||||||
\(54\) | −80.6271 | + | 67.1307i | −0.203185 | + | 0.169173i | ||||
\(55\) | 361.202i | 0.885537i | ||||||||
\(56\) | −32.9382 | − | 211.299i | −0.0785992 | − | 0.504214i | ||||
\(57\) | −294.419 | − | 34.7930i | −0.684154 | − | 0.0808499i | ||||
\(58\) | −51.9336 | −0.117573 | ||||||||
\(59\) | 360.346 | + | 624.138i | 0.795137 | + | 1.37722i | 0.922752 | + | 0.385394i | \(0.125935\pi\) |
−0.127615 | + | 0.991824i | \(0.540732\pi\) | |||||||
\(60\) | 39.4860 | − | 334.131i | 0.0849603 | − | 0.718936i | ||||
\(61\) | −561.494 | − | 324.179i | −1.17856 | − | 0.680440i | −0.222876 | − | 0.974847i | \(-0.571544\pi\) |
−0.955680 | + | 0.294407i | \(0.904878\pi\) | |||||||
\(62\) | −195.034 | −0.399506 | ||||||||
\(63\) | 214.337 | + | 451.782i | 0.428634 | + | 0.903478i | ||||
\(64\) | 309.591 | 0.604671 | ||||||||
\(65\) | −287.218 | − | 165.826i | −0.548078 | − | 0.316433i | ||||
\(66\) | −148.177 | + | 63.6935i | −0.276353 | + | 0.118790i | ||||
\(67\) | 97.4263 | + | 168.747i | 0.177649 | + | 0.307698i | 0.941075 | − | 0.338198i | \(-0.109817\pi\) |
−0.763426 | + | 0.645896i | \(0.776484\pi\) | |||||||
\(68\) | −594.793 | −1.06072 | ||||||||
\(69\) | 550.200 | − | 737.084i | 0.959946 | − | 1.28601i | ||||
\(70\) | 112.412 | + | 43.4659i | 0.191940 | + | 0.0742168i | ||||
\(71\) | 98.7349i | 0.165038i | 0.996590 | + | 0.0825188i | \(0.0262965\pi\) | ||||
−0.996590 | + | 0.0825188i | \(0.973704\pi\) | |||||||
\(72\) | 298.894 | − | 88.6537i | 0.489236 | − | 0.145110i | ||||
\(73\) | 226.289 | + | 130.648i | 0.362809 | + | 0.209468i | 0.670312 | − | 0.742079i | \(-0.266160\pi\) |
−0.307503 | + | 0.951547i | \(0.599493\pi\) | |||||||
\(74\) | − | 112.076i | − | 0.176062i | ||||||
\(75\) | −205.168 | − | 153.148i | −0.315876 | − | 0.235787i | ||||
\(76\) | 367.658 | + | 212.268i | 0.554912 | + | 0.320379i | ||||
\(77\) | 118.402 | + | 759.548i | 0.175236 | + | 1.12414i | ||||
\(78\) | 17.3797 | − | 147.068i | 0.0252290 | − | 0.213489i | ||||
\(79\) | 577.124 | − | 999.608i | 0.821918 | − | 1.42360i | −0.0823344 | − | 0.996605i | \(-0.526238\pi\) |
0.904252 | − | 0.426999i | \(-0.140429\pi\) | |||||||
\(80\) | −221.433 | + | 383.533i | −0.309462 | + | 0.536004i | ||||
\(81\) | −611.104 | + | 397.483i | −0.838278 | + | 0.545244i | ||||
\(82\) | −70.8661 | + | 40.9146i | −0.0954372 | + | 0.0551007i | ||||
\(83\) | −285.406 | − | 494.337i | −0.377438 | − | 0.653741i | 0.613251 | − | 0.789888i | \(-0.289861\pi\) |
−0.990689 | + | 0.136147i | \(0.956528\pi\) | |||||||
\(84\) | −26.4957 | − | 715.566i | −0.0344157 | − | 0.929460i | ||||
\(85\) | 347.813 | − | 602.431i | 0.443831 | − | 0.768739i | ||||
\(86\) | 185.746i | 0.232901i | ||||||||
\(87\) | −358.365 | − | 42.3497i | −0.441617 | − | 0.0521881i | ||||
\(88\) | 479.275 | 0.580578 | ||||||||
\(89\) | 89.5115 | + | 155.038i | 0.106609 | + | 0.184652i | 0.914394 | − | 0.404824i | \(-0.132667\pi\) |
−0.807785 | + | 0.589477i | \(0.799334\pi\) | |||||||
\(90\) | −40.9561 | + | 170.866i | −0.0479684 | + | 0.200121i | ||||
\(91\) | −658.330 | − | 254.553i | −0.758370 | − | 0.293236i | ||||
\(92\) | −1140.66 | + | 658.559i | −1.29263 | + | 0.746299i | ||||
\(93\) | −1345.82 | − | 159.042i | −1.50059 | − | 0.177332i | ||||
\(94\) | 191.086 | − | 110.324i | 0.209671 | − | 0.121054i | ||||
\(95\) | −429.987 | + | 248.253i | −0.464376 | + | 0.268108i | ||||
\(96\) | −673.061 | − | 79.5390i | −0.715562 | − | 0.0845616i | ||||
\(97\) | −956.569 | + | 552.275i | −1.00129 | + | 0.578093i | −0.908629 | − | 0.417605i | \(-0.862870\pi\) |
−0.0926581 | + | 0.995698i | \(0.529536\pi\) | |||||||
\(98\) | 250.632 | + | 54.5529i | 0.258344 | + | 0.0562314i | ||||
\(99\) | −1074.42 | + | 318.681i | −1.09075 | + | 0.323521i | ||||
\(100\) | 183.310 | + | 317.502i | 0.183310 | + | 0.317502i | ||||
\(101\) | −0.750795 | −0.000739672 | −0.000369836 | − | 1.00000i | \(-0.500118\pi\) | ||||
−0.000369836 | 1.00000i | \(0.500118\pi\) | ||||||||
\(102\) | 308.469 | + | 36.4534i | 0.299441 | + | 0.0353865i | ||||
\(103\) | − | 753.027i | − | 0.720369i | −0.932881 | − | 0.360184i | \(-0.882714\pi\) | ||
0.932881 | − | 0.360184i | \(-0.117286\pi\) | |||||||
\(104\) | −220.032 | + | 381.107i | −0.207461 | + | 0.359332i | ||||
\(105\) | 740.248 | + | 391.601i | 0.688008 | + | 0.363965i | ||||
\(106\) | 113.815 | + | 197.134i | 0.104290 | + | 0.180635i | ||||
\(107\) | 1089.54 | − | 629.045i | 0.984388 | − | 0.568337i | 0.0807962 | − | 0.996731i | \(-0.474254\pi\) |
0.903592 | + | 0.428394i | \(0.140920\pi\) | |||||||
\(108\) | 1028.74 | − | 177.342i | 0.916577 | − | 0.158007i | ||||
\(109\) | −110.812 | + | 191.932i | −0.0973748 | + | 0.168658i | −0.910597 | − | 0.413295i | \(-0.864378\pi\) |
0.813222 | + | 0.581953i | \(0.197711\pi\) | |||||||
\(110\) | −135.056 | + | 233.924i | −0.117065 | + | 0.202762i | ||||
\(111\) | 91.3937 | − | 773.376i | 0.0781505 | − | 0.661311i | ||||
\(112\) | −339.914 | + | 879.091i | −0.286776 | + | 0.741664i | ||||
\(113\) | 1345.36 | + | 776.746i | 1.12001 | + | 0.646638i | 0.941404 | − | 0.337282i | \(-0.109508\pi\) |
0.178607 | + | 0.983921i | \(0.442841\pi\) | |||||||
\(114\) | −177.664 | − | 132.618i | −0.145963 | − | 0.108955i | ||||
\(115\) | − | 1540.41i | − | 1.24908i | ||||||
\(116\) | 447.511 | + | 258.370i | 0.358192 | + | 0.206803i | ||||
\(117\) | 239.855 | − | 1000.66i | 0.189527 | − | 0.790691i | ||||
\(118\) | 538.945i | 0.420457i | ||||||||
\(119\) | 533.917 | − | 1380.82i | 0.411295 | − | 1.06370i | ||||
\(120\) | 312.324 | − | 418.410i | 0.237593 | − | 0.318296i | ||||
\(121\) | −391.834 | −0.294391 | ||||||||
\(122\) | −242.426 | − | 419.893i | −0.179903 | − | 0.311601i | ||||
\(123\) | −522.371 | + | 224.540i | −0.382932 | + | 0.164602i | ||||
\(124\) | 1680.60 | + | 970.297i | 1.21712 | + | 0.702703i | ||||
\(125\) | −1516.55 | −1.08515 | ||||||||
\(126\) | −30.1141 | + | 372.728i | −0.0212919 | + | 0.263534i | ||||
\(127\) | 2425.06 | 1.69440 | 0.847202 | − | 0.531271i | \(-0.178285\pi\) | ||||
0.847202 | + | 0.531271i | \(0.178285\pi\) | |||||||
\(128\) | 1104.16 | + | 637.486i | 0.762459 | + | 0.440206i | ||||
\(129\) | −151.468 | + | 1281.73i | −0.103380 | + | 0.874805i | ||||
\(130\) | −124.007 | − | 214.786i | −0.0836624 | − | 0.144908i | ||||
\(131\) | −48.8347 | −0.0325703 | −0.0162851 | − | 0.999867i | \(-0.505184\pi\) | ||||
−0.0162851 | + | 0.999867i | \(0.505184\pi\) | |||||||
\(132\) | 1593.71 | + | 188.337i | 1.05087 | + | 0.124187i | ||||
\(133\) | −822.813 | + | 662.984i | −0.536443 | + | 0.432241i | ||||
\(134\) | 145.714i | 0.0939384i | ||||||||
\(135\) | −421.949 | + | 1145.65i | −0.269005 | + | 0.730385i | ||||
\(136\) | −799.358 | − | 461.510i | −0.504003 | − | 0.290986i | ||||
\(137\) | − | 1532.32i | − | 0.955583i | −0.878473 | − | 0.477792i | \(-0.841437\pi\) | ||
0.878473 | − | 0.477792i | \(-0.158563\pi\) | |||||||
\(138\) | 631.925 | − | 271.631i | 0.389805 | − | 0.167557i | ||||
\(139\) | 638.674 | + | 368.739i | 0.389724 | + | 0.225007i | 0.682040 | − | 0.731314i | \(-0.261093\pi\) |
−0.292317 | + | 0.956322i | \(0.594426\pi\) | |||||||
\(140\) | −752.409 | − | 933.797i | −0.454216 | − | 0.563716i | ||||
\(141\) | 1408.54 | − | 605.459i | 0.841282 | − | 0.361623i | ||||
\(142\) | −36.9177 | + | 63.9433i | −0.0218174 | + | 0.0377888i | ||||
\(143\) | 790.942 | − | 1369.95i | 0.462531 | − | 0.801126i | ||||
\(144\) | −1336.21 | − | 320.287i | −0.773272 | − | 0.185351i | ||||
\(145\) | −523.376 | + | 302.172i | −0.299752 | + | 0.173062i | ||||
\(146\) | 97.7003 | + | 169.222i | 0.0553817 | + | 0.0959240i | ||||
\(147\) | 1684.98 | + | 580.819i | 0.945409 | + | 0.325885i | ||||
\(148\) | −557.581 | + | 965.759i | −0.309682 | + | 0.536385i | ||||
\(149\) | 1475.76i | 0.811400i | 0.914006 | + | 0.405700i | \(0.132972\pi\) | ||||
−0.914006 | + | 0.405700i | \(0.867028\pi\) | |||||||
\(150\) | −75.6087 | − | 175.897i | −0.0411562 | − | 0.0957460i | ||||
\(151\) | −1274.88 | −0.687073 | −0.343536 | − | 0.939139i | \(-0.611625\pi\) | ||||
−0.343536 | + | 0.939139i | \(0.611625\pi\) | |||||||
\(152\) | 329.404 | + | 570.544i | 0.175778 | + | 0.304456i | ||||
\(153\) | 2098.85 | + | 503.088i | 1.10903 | + | 0.265832i | ||||
\(154\) | −207.320 | + | 536.175i | −0.108483 | + | 0.280560i | ||||
\(155\) | −1965.51 | + | 1134.79i | −1.01854 | + | 0.588055i | ||||
\(156\) | −881.423 | + | 1180.81i | −0.452374 | + | 0.606030i | ||||
\(157\) | −1718.19 | + | 991.999i | −0.873418 | + | 0.504268i | −0.868483 | − | 0.495719i | \(-0.834904\pi\) |
−0.00493568 | + | 0.999988i | \(0.501571\pi\) | |||||||
\(158\) | 747.522 | − | 431.582i | 0.376390 | − | 0.217309i | ||||
\(159\) | 624.619 | + | 1453.12i | 0.311544 | + | 0.724778i | ||||
\(160\) | −982.977 | + | 567.522i | −0.485695 | + | 0.280416i | ||||
\(161\) | −504.945 | − | 3239.22i | −0.247175 | − | 1.58563i | ||||
\(162\) | −544.389 | + | 28.9239i | −0.264020 | + | 0.0140276i | ||||
\(163\) | −1836.59 | − | 3181.06i | −0.882532 | − | 1.52859i | −0.848517 | − | 0.529168i | \(-0.822504\pi\) |
−0.0340145 | − | 0.999421i | \(-0.510829\pi\) | |||||||
\(164\) | 814.202 | 0.387674 | ||||||||
\(165\) | −1122.70 | + | 1504.05i | −0.529710 | + | 0.709635i | ||||
\(166\) | − | 426.861i | − | 0.199583i | ||||||
\(167\) | 2007.55 | − | 3477.17i | 0.930231 | − | 1.61121i | 0.147306 | − | 0.989091i | \(-0.452940\pi\) |
0.782925 | − | 0.622116i | \(-0.213727\pi\) | |||||||
\(168\) | 519.611 | − | 982.226i | 0.238624 | − | 0.451074i | ||||
\(169\) | −372.268 | − | 644.787i | −0.169444 | − | 0.293485i | ||||
\(170\) | 450.507 | − | 260.100i | 0.203249 | − | 0.117346i | ||||
\(171\) | −1117.82 | − | 1060.00i | −0.499892 | − | 0.474037i | ||||
\(172\) | 924.089 | − | 1600.57i | 0.409658 | − | 0.709548i | ||||
\(173\) | −1046.75 | + | 1813.03i | −0.460019 | + | 0.796776i | −0.998961 | − | 0.0455667i | \(-0.985491\pi\) |
0.538943 | + | 0.842342i | \(0.318824\pi\) | |||||||
\(174\) | −216.252 | − | 161.422i | −0.0942183 | − | 0.0703297i | ||||
\(175\) | −901.637 | + | 140.552i | −0.389471 | + | 0.0607125i | ||||
\(176\) | −1829.35 | − | 1056.17i | −0.783478 | − | 0.452341i | ||||
\(177\) | −439.487 | + | 3718.95i | −0.186632 | + | 1.57929i | ||||
\(178\) | 133.876i | 0.0563732i | ||||||||
\(179\) | 3194.00 | + | 1844.06i | 1.33369 | + | 0.770008i | 0.985863 | − | 0.167551i | \(-0.0535857\pi\) |
0.347829 | + | 0.937558i | \(0.386919\pi\) | |||||||
\(180\) | 1202.98 | − | 1268.59i | 0.498137 | − | 0.525306i | ||||
\(181\) | 1648.55i | 0.676995i | 0.940967 | + | 0.338497i | \(0.109919\pi\) | ||||
−0.940967 | + | 0.338497i | \(0.890081\pi\) | |||||||
\(182\) | −331.172 | − | 411.010i | −0.134880 | − | 0.167396i | ||||
\(183\) | −1330.44 | − | 3095.13i | −0.537424 | − | 1.25027i | ||||
\(184\) | −2043.95 | −0.818923 | ||||||||
\(185\) | −652.107 | − | 1129.48i | −0.259156 | − | 0.448871i | ||||
\(186\) | −812.122 | − | 606.212i | −0.320149 | − | 0.238976i | ||||
\(187\) | 2873.43 | + | 1658.97i | 1.12367 | + | 0.648749i | ||||
\(188\) | −2195.45 | −0.851700 | ||||||||
\(189\) | −511.745 | + | 2547.43i | −0.196952 | + | 0.980413i | ||||
\(190\) | −371.295 | −0.141771 | ||||||||
\(191\) | 3175.89 | + | 1833.60i | 1.20314 | + | 0.694631i | 0.961251 | − | 0.275674i | \(-0.0889010\pi\) |
0.241885 | + | 0.970305i | \(0.422234\pi\) | |||||||
\(192\) | 1289.14 | + | 962.283i | 0.484560 | + | 0.361702i | ||||
\(193\) | 171.063 | + | 296.289i | 0.0637998 | + | 0.110504i | 0.896161 | − | 0.443729i | \(-0.146345\pi\) |
−0.832361 | + | 0.554234i | \(0.813011\pi\) | |||||||
\(194\) | −825.999 | −0.305687 | ||||||||
\(195\) | −680.551 | − | 1583.24i | −0.249925 | − | 0.581426i | ||||
\(196\) | −1888.29 | − | 1716.98i | −0.688152 | − | 0.625721i | ||||
\(197\) | 468.339i | 0.169380i | 0.996407 | + | 0.0846898i | \(0.0269899\pi\) | ||||
−0.996407 | + | 0.0846898i | \(0.973010\pi\) | |||||||
\(198\) | −814.983 | − | 195.349i | −0.292517 | − | 0.0701155i | ||||
\(199\) | −1359.11 | − | 784.682i | −0.484144 | − | 0.279521i | 0.237998 | − | 0.971266i | \(-0.423509\pi\) |
−0.722142 | + | 0.691745i | \(0.756842\pi\) | |||||||
\(200\) | 568.933i | 0.201148i | ||||||||
\(201\) | −118.823 | + | 1005.49i | −0.0416973 | + | 0.352844i | ||||
\(202\) | −0.486235 | − | 0.280728i | −0.000169363 | − | 9.77818e-5i | ||||
\(203\) | −1001.52 | + | 806.979i | −0.346271 | + | 0.279009i | ||||
\(204\) | −2476.72 | − | 1848.76i | −0.850023 | − | 0.634504i | ||||
\(205\) | −476.116 | + | 824.657i | −0.162212 | + | 0.280959i | ||||
\(206\) | 281.563 | − | 487.681i | 0.0952300 | − | 0.164943i | ||||
\(207\) | 4582.06 | − | 1359.07i | 1.53853 | − | 0.456336i | ||||
\(208\) | 1679.68 | − | 969.764i | 0.559927 | − | 0.323274i | ||||
\(209\) | −1184.10 | − | 2050.92i | −0.391893 | − | 0.678779i | ||||
\(210\) | 332.982 | + | 530.396i | 0.109419 | + | 0.174289i | ||||
\(211\) | 1244.68 | − | 2155.85i | 0.406101 | − | 0.703387i | −0.588348 | − | 0.808608i | \(-0.700222\pi\) |
0.994449 | + | 0.105221i | \(0.0335549\pi\) | |||||||
\(212\) | − | 2264.93i | − | 0.733753i | ||||||
\(213\) | −306.891 | + | 411.132i | −0.0987222 | + | 0.132255i | ||||
\(214\) | 940.818 | 0.300528 | ||||||||
\(215\) | 1080.75 | + | 1871.91i | 0.342821 | + | 0.593783i | ||||
\(216\) | 1520.15 | + | 559.879i | 0.478857 | + | 0.176366i | ||||
\(217\) | −3761.16 | + | 3030.57i | −1.17661 | + | 0.948057i | ||||
\(218\) | −143.530 | + | 82.8668i | −0.0445920 | + | 0.0257452i | ||||
\(219\) | 536.181 | + | 1247.37i | 0.165442 | + | 0.384885i | ||||
\(220\) | 2327.55 | − | 1343.81i | 0.713289 | − | 0.411817i | ||||
\(221\) | −2638.34 | + | 1523.25i | −0.803050 | + | 0.463641i | ||||
\(222\) | 348.360 | − | 466.686i | 0.105317 | − | 0.141090i | ||||
\(223\) | 858.894 | − | 495.883i | 0.257918 | − | 0.148909i | −0.365466 | − | 0.930825i | \(-0.619090\pi\) |
0.623385 | + | 0.781915i | \(0.285757\pi\) | |||||||
\(224\) | −1881.00 | + | 1515.62i | −0.561071 | + | 0.452084i | ||||
\(225\) | −378.296 | − | 1275.42i | −0.112088 | − | 0.377902i | ||||
\(226\) | 580.862 | + | 1006.08i | 0.170966 | + | 0.296122i | ||||
\(227\) | 603.465 | 0.176447 | 0.0882233 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882233 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(228\) | 871.151 | + | 2026.65i | 0.253041 | + | 0.588676i | ||||
\(229\) | 1295.25i | 0.373765i | 0.982382 | + | 0.186883i | \(0.0598384\pi\) | ||||
−0.982382 | + | 0.186883i | \(0.940162\pi\) | |||||||
\(230\) | 575.969 | − | 997.608i | 0.165123 | − | 0.286002i | ||||
\(231\) | −1867.83 | + | 3530.78i | −0.532009 | + | 1.00566i | ||||
\(232\) | 400.948 | + | 694.462i | 0.113463 | + | 0.196524i | ||||
\(233\) | −3699.70 | + | 2136.02i | −1.04024 | + | 0.600581i | −0.919900 | − | 0.392152i | \(-0.871731\pi\) |
−0.120336 | + | 0.992733i | \(0.538397\pi\) | |||||||
\(234\) | 529.490 | − | 558.369i | 0.147922 | − | 0.155990i | ||||
\(235\) | 1283.82 | − | 2223.64i | 0.356371 | − | 0.617253i | ||||
\(236\) | 2681.26 | − | 4644.07i | 0.739555 | − | 1.28095i | ||||
\(237\) | 5510.16 | − | 2368.53i | 1.51022 | − | 0.649166i | ||||
\(238\) | 862.079 | − | 694.623i | 0.234791 | − | 0.189184i | ||||
\(239\) | 2074.66 | + | 1197.80i | 0.561500 | + | 0.324182i | 0.753747 | − | 0.657164i | \(-0.228244\pi\) |
−0.192247 | + | 0.981346i | \(0.561578\pi\) | |||||||
\(240\) | −2114.16 | + | 908.765i | −0.568618 | + | 0.244419i | ||||
\(241\) | 818.126i | 0.218673i | 0.994005 | + | 0.109336i | \(0.0348726\pi\) | ||||
−0.994005 | + | 0.109336i | \(0.965127\pi\) | |||||||
\(242\) | −253.762 | − | 146.510i | −0.0674068 | − | 0.0389174i | ||||
\(243\) | −3780.11 | − | 244.339i | −0.997917 | − | 0.0645036i | ||||
\(244\) | 4824.28i | 1.26575i | ||||||||
\(245\) | 2843.23 | − | 908.509i | 0.741418 | − | 0.236908i | ||||
\(246\) | −422.258 | − | 49.9004i | −0.109440 | − | 0.0129331i | ||||
\(247\) | 2174.44 | 0.560148 | ||||||||
\(248\) | 1505.74 | + | 2608.02i | 0.385542 | + | 0.667779i | ||||
\(249\) | 348.087 | − | 2945.53i | 0.0885910 | − | 0.749659i | ||||
\(250\) | −982.156 | − | 567.048i | −0.248468 | − | 0.143453i | ||||
\(251\) | −7516.24 | −1.89012 | −0.945062 | − | 0.326891i | \(-0.893999\pi\) | ||||
−0.945062 | + | 0.326891i | \(0.893999\pi\) | |||||||
\(252\) | 2113.82 | − | 3061.97i | 0.528405 | − | 0.765420i | ||||
\(253\) | 7347.31 | 1.82578 | ||||||||
\(254\) | 1570.53 | + | 906.748i | 0.387969 | + | 0.223994i | ||||
\(255\) | 3320.79 | − | 1427.43i | 0.815514 | − | 0.350546i | ||||
\(256\) | −761.644 | − | 1319.21i | −0.185948 | − | 0.322072i | ||||
\(257\) | 5548.61 | 1.34674 | 0.673372 | − | 0.739304i | \(-0.264845\pi\) | ||||
0.673372 | + | 0.739304i | \(0.264845\pi\) | |||||||
\(258\) | −577.343 | + | 773.446i | −0.139317 | + | 0.186638i | ||||
\(259\) | −1741.52 | − | 2161.35i | −0.417809 | − | 0.518532i | ||||
\(260\) | 2467.74i | 0.588626i | ||||||||
\(261\) | −1360.60 | − | 1290.23i | −0.322677 | − | 0.305988i | ||||
\(262\) | −31.6267 | − | 18.2597i | −0.00745764 | − | 0.00430567i | ||||
\(263\) | 6373.65i | 1.49436i | 0.664623 | + | 0.747179i | \(0.268592\pi\) | ||||
−0.664623 | + | 0.747179i | \(0.731408\pi\) | |||||||
\(264\) | 1995.70 | + | 1489.70i | 0.465253 | + | 0.347290i | ||||
\(265\) | 2294.01 | + | 1324.45i | 0.531773 | + | 0.307019i | ||||
\(266\) | −780.770 | + | 121.710i | −0.179970 | + | 0.0280546i | ||||
\(267\) | −109.170 | + | 923.802i | −0.0250229 | + | 0.211745i | ||||
\(268\) | 724.927 | − | 1255.61i | 0.165231 | − | 0.286189i | ||||
\(269\) | 2137.07 | − | 3701.52i | 0.484385 | − | 0.838979i | −0.515454 | − | 0.856917i | \(-0.672377\pi\) |
0.999839 | + | 0.0179379i | \(0.00571013\pi\) | |||||||
\(270\) | −701.633 | + | 584.184i | −0.158148 | + | 0.131675i | ||||
\(271\) | −1818.38 | + | 1049.84i | −0.407597 | + | 0.235326i | −0.689757 | − | 0.724041i | \(-0.742283\pi\) |
0.282160 | + | 0.959367i | \(0.408949\pi\) | |||||||
\(272\) | 2034.05 | + | 3523.07i | 0.453427 | + | 0.785359i | ||||
\(273\) | −1950.07 | − | 3106.20i | −0.432321 | − | 0.688630i | ||||
\(274\) | 572.946 | − | 992.371i | 0.126325 | − | 0.218800i | ||||
\(275\) | − | 2045.13i | − | 0.448457i | ||||||
\(276\) | −6796.65 | − | 803.194i | −1.48228 | − | 0.175169i | ||||
\(277\) | 4410.66 | 0.956718 | 0.478359 | − | 0.878164i | \(-0.341232\pi\) | ||||
0.478359 | + | 0.878164i | \(0.341232\pi\) | |||||||
\(278\) | 275.748 | + | 477.610i | 0.0594902 | + | 0.103040i | ||||
\(279\) | −5109.65 | − | 4845.38i | −1.09644 | − | 1.03973i | ||||
\(280\) | −286.635 | − | 1838.76i | −0.0611775 | − | 0.392454i | ||||
\(281\) | −4392.19 | + | 2535.83i | −0.932443 | + | 0.538346i | −0.887583 | − | 0.460647i | \(-0.847617\pi\) |
−0.0448593 | + | 0.998993i | \(0.514284\pi\) | |||||||
\(282\) | 1138.60 | + | 134.554i | 0.240434 | + | 0.0284133i | ||||
\(283\) | 478.561 | − | 276.297i | 0.100521 | − | 0.0580360i | −0.448897 | − | 0.893584i | \(-0.648183\pi\) |
0.549418 | + | 0.835548i | \(0.314850\pi\) | |||||||
\(284\) | 636.238 | − | 367.332i | 0.132936 | − | 0.0767505i | ||||
\(285\) | −2562.09 | − | 302.775i | −0.532510 | − | 0.0629293i | ||||
\(286\) | 1024.47 | − | 591.478i | 0.211812 | − | 0.122290i | ||||
\(287\) | −730.870 | + | 1890.19i | −0.150320 | + | 0.388760i | ||||
\(288\) | −2555.40 | − | 2423.23i | −0.522841 | − | 0.495800i | ||||
\(289\) | −738.458 | − | 1279.05i | −0.150307 | − | 0.260339i | ||||
\(290\) | −451.937 | −0.0915125 | ||||||||
\(291\) | −5699.75 | − | 673.568i | −1.14820 | − | 0.135688i | ||||
\(292\) | − | 1944.24i | − | 0.389651i | ||||||
\(293\) | 496.106 | − | 859.280i | 0.0989174 | − | 0.171330i | −0.812319 | − | 0.583213i | \(-0.801795\pi\) |
0.911237 | + | 0.411883i | \(0.135129\pi\) | |||||||
\(294\) | 874.068 | + | 1006.18i | 0.173390 | + | 0.199598i | ||||
\(295\) | 3135.80 | + | 5431.37i | 0.618894 | + | 1.07196i | ||||
\(296\) | −1498.70 | + | 865.273i | −0.294291 | + | 0.169909i | ||||
\(297\) | −5464.44 | − | 2012.58i | −1.06761 | − | 0.393204i | ||||
\(298\) | −551.796 | + | 955.739i | −0.107264 | + | 0.185787i | ||||
\(299\) | −3373.10 | + | 5842.38i | −0.652413 | + | 1.13001i | ||||
\(300\) | −223.569 | + | 1891.85i | −0.0430259 | + | 0.364087i | ||||
\(301\) | 2886.24 | + | 3582.05i | 0.552692 | + | 0.685933i | ||||
\(302\) | −825.644 | − | 476.686i | −0.157319 | − | 0.0908284i | ||||
\(303\) | −3.12631 | − | 2.33365i | −0.000592745 | − | 0.000442457i | ||||
\(304\) | − | 2903.62i | − | 0.547808i | ||||||
\(305\) | −4886.23 | − | 2821.07i | −0.917327 | − | 0.529619i | ||||
\(306\) | 1171.16 | + | 1110.59i | 0.218793 | + | 0.207477i | ||||
\(307\) | 256.830i | 0.0477462i | 0.999715 | + | 0.0238731i | \(0.00759977\pi\) | ||||
−0.999715 | + | 0.0238731i | \(0.992400\pi\) | |||||||
\(308\) | 4453.95 | − | 3588.78i | 0.823985 | − | 0.663928i | ||||
\(309\) | 2340.59 | − | 3135.60i | 0.430910 | − | 0.577276i | ||||
\(310\) | −1697.22 | −0.310955 | ||||||||
\(311\) | −361.742 | − | 626.556i | −0.0659566 | − | 0.114240i | 0.831161 | − | 0.556031i | \(-0.187677\pi\) |
−0.897118 | + | 0.441791i | \(0.854343\pi\) | |||||||
\(312\) | −2100.78 | + | 903.016i | −0.381197 | + | 0.163856i | ||||
\(313\) | −5961.98 | − | 3442.15i | −1.07665 | − | 0.621604i | −0.146659 | − | 0.989187i | \(-0.546852\pi\) |
−0.929991 | + | 0.367584i | \(0.880185\pi\) | |||||||
\(314\) | −1483.66 | −0.266649 | ||||||||
\(315\) | 1865.20 | + | 3931.49i | 0.333626 | + | 0.703221i | ||||
\(316\) | −8588.50 | −1.52893 | ||||||||
\(317\) | −318.148 | − | 183.683i | −0.0563690 | − | 0.0325447i | 0.471551 | − | 0.881839i | \(-0.343694\pi\) |
−0.527920 | + | 0.849294i | \(0.677028\pi\) | |||||||
\(318\) | −138.812 | + | 1174.63i | −0.0244785 | + | 0.207138i | ||||
\(319\) | −1441.27 | − | 2496.36i | −0.252965 | − | 0.438148i | ||||
\(320\) | 2694.12 | 0.470644 | ||||||||
\(321\) | 6492.05 | + | 767.198i | 1.12882 | + | 0.133398i | ||||
\(322\) | 884.152 | − | 2286.61i | 0.153018 | − | 0.395738i | ||||
\(323\) | 4560.82i | 0.785669i | ||||||||
\(324\) | 4834.88 | + | 2459.11i | 0.829026 | + | 0.421657i | ||||
\(325\) | 1626.23 | + | 938.904i | 0.277560 | + | 0.160249i | ||||
\(326\) | − | 2746.85i | − | 0.466669i | ||||||
\(327\) | −1057.99 | + | 454.774i | −0.178920 | + | 0.0769085i | ||||
\(328\) | 1094.23 | + | 631.753i | 0.184203 | + | 0.106350i | ||||
\(329\) | 1970.75 | − | 5096.78i | 0.330246 | − | 0.854087i | ||||
\(330\) | −1289.47 | + | 554.273i | −0.215099 | + | 0.0924599i | ||||
\(331\) | −1912.88 | + | 3313.20i | −0.317647 | + | 0.550182i | −0.979997 | − | 0.199014i | \(-0.936226\pi\) |
0.662349 | + | 0.749195i | \(0.269560\pi\) | |||||||
\(332\) | −2123.64 | + | 3678.25i | −0.351054 | + | 0.608043i | ||||
\(333\) | 2784.40 | − | 2936.26i | 0.458210 | − | 0.483202i | ||||
\(334\) | 2600.28 | − | 1501.27i | 0.425991 | − | 0.245946i | ||||
\(335\) | 847.823 | + | 1468.47i | 0.138273 | + | 0.239496i | ||||
\(336\) | −4147.83 | + | 2604.00i | −0.673460 | + | 0.422797i | ||||
\(337\) | −477.374 | + | 826.836i | −0.0771639 | + | 0.133652i | −0.902025 | − | 0.431683i | \(-0.857920\pi\) |
0.824861 | + | 0.565335i | \(0.191253\pi\) | |||||||
\(338\) | − | 556.775i | − | 0.0895993i | ||||||
\(339\) | 3187.78 | + | 7416.08i | 0.510727 | + | 1.18816i | ||||
\(340\) | −5176.00 | −0.825612 | ||||||||
\(341\) | −5412.63 | − | 9374.95i | −0.859561 | − | 1.48880i | ||||
\(342\) | −327.585 | − | 1104.44i | −0.0517946 | − | 0.174624i | ||||
\(343\) | 5681.03 | − | 2842.45i | 0.894305 | − | 0.447458i | ||||
\(344\) | 2483.82 | − | 1434.03i | 0.389298 | − | 0.224761i | ||||
\(345\) | 4787.95 | − | 6414.25i | 0.747172 | − | 1.00096i | ||||
\(346\) | −1355.81 | + | 782.778i | −0.210662 | + | 0.121625i | ||||
\(347\) | −4912.79 | + | 2836.40i | −0.760036 | + | 0.438807i | −0.829309 | − | 0.558791i | \(-0.811265\pi\) |
0.0692728 | + | 0.997598i | \(0.477932\pi\) | |||||||
\(348\) | 1060.36 | + | 2466.82i | 0.163337 | + | 0.379987i | ||||
\(349\) | −163.883 | + | 94.6178i | −0.0251360 | + | 0.0145123i | −0.512515 | − | 0.858678i | \(-0.671286\pi\) |
0.487379 | + | 0.873190i | \(0.337953\pi\) | |||||||
\(350\) | −636.478 | − | 246.104i | −0.0972033 | − | 0.0375852i | ||||
\(351\) | 4109.04 | − | 3421.21i | 0.624855 | − | 0.520258i | ||||
\(352\) | −2706.92 | − | 4688.53i | −0.409885 | − | 0.709941i | ||||
\(353\) | −10440.7 | −1.57422 | −0.787110 | − | 0.616812i | \(-0.788424\pi\) | ||||
−0.787110 | + | 0.616812i | \(0.788424\pi\) | |||||||
\(354\) | −1675.17 | + | 2244.16i | −0.251509 | + | 0.336938i | ||||
\(355\) | 859.210i | 0.128457i | ||||||||
\(356\) | 666.035 | − | 1153.61i | 0.0991566 | − | 0.171744i | ||||
\(357\) | 6515.15 | − | 4090.21i | 0.965878 | − | 0.606377i | ||||
\(358\) | 1379.01 | + | 2388.52i | 0.203584 | + | 0.352618i | ||||
\(359\) | 9191.43 | − | 5306.67i | 1.35127 | − | 0.780155i | 0.362840 | − | 0.931851i | \(-0.381807\pi\) |
0.988427 | + | 0.151697i | \(0.0484737\pi\) | |||||||
\(360\) | 2601.04 | − | 771.482i | 0.380796 | − | 0.112946i | ||||
\(361\) | −1801.85 | + | 3120.89i | −0.262698 | + | 0.455007i | ||||
\(362\) | −616.407 | + | 1067.65i | −0.0894962 | + | 0.155012i | ||||
\(363\) | −1631.60 | − | 1217.91i | −0.235914 | − | 0.176099i | ||||
\(364\) | 808.924 | + | 5189.25i | 0.116481 | + | 0.747226i | ||||
\(365\) | 1969.21 | + | 1136.92i | 0.282392 | + | 0.163039i | ||||
\(366\) | 295.668 | − | 2501.95i | 0.0422263 | − | 0.357320i | ||||
\(367\) | 882.734i | 0.125554i | 0.998028 | + | 0.0627770i | \(0.0199957\pi\) | ||||
−0.998028 | + | 0.0627770i | \(0.980004\pi\) | |||||||
\(368\) | 7801.55 | + | 4504.22i | 1.10512 | + | 0.638041i | ||||
\(369\) | −2873.07 | − | 688.668i | −0.405329 | − | 0.0971562i | ||||
\(370\) | − | 975.311i | − | 0.137038i | ||||||
\(371\) | 5258.07 | + | 2033.11i | 0.735810 | + | 0.284512i | ||||
\(372\) | 3982.12 | + | 9264.02i | 0.555009 | + | 1.29118i | ||||
\(373\) | 2616.16 | 0.363162 | 0.181581 | − | 0.983376i | \(-0.441879\pi\) | ||||
0.181581 | + | 0.983376i | \(0.441879\pi\) | |||||||
\(374\) | 1240.60 | + | 2148.79i | 0.171524 | + | 0.297089i | ||||
\(375\) | −6314.90 | − | 4713.79i | −0.869600 | − | 0.649117i | ||||
\(376\) | −2950.52 | − | 1703.48i | −0.404685 | − | 0.233645i | ||||
\(377\) | 2646.72 | 0.361573 | ||||||||
\(378\) | −1283.92 | + | 1458.44i | −0.174703 | + | 0.198449i | ||||
\(379\) | 636.672 | 0.0862892 | 0.0431446 | − | 0.999069i | \(-0.486262\pi\) | ||||
0.0431446 | + | 0.999069i | \(0.486262\pi\) | |||||||
\(380\) | 3199.43 | + | 1847.19i | 0.431915 | + | 0.249366i | ||||
\(381\) | 10097.9 | + | 7537.66i | 1.35783 | + | 1.01356i | ||||
\(382\) | 1371.19 | + | 2374.97i | 0.183655 | + | 0.318100i | ||||
\(383\) | −7569.77 | −1.00991 | −0.504957 | − | 0.863145i | \(-0.668492\pi\) | ||||
−0.504957 | + | 0.863145i | \(0.668492\pi\) | |||||||
\(384\) | 2616.26 | + | 6086.48i | 0.347683 | + | 0.808852i | ||||
\(385\) | 1030.36 | + | 6609.73i | 0.136394 | + | 0.874970i | ||||
\(386\) | 255.846i | 0.0337364i | ||||||||
\(387\) | −4614.63 | + | 4866.32i | −0.606136 | + | 0.639196i | ||||
\(388\) | 7117.61 | + | 4109.35i | 0.931294 | + | 0.537683i | ||||
\(389\) | − | 11135.5i | − | 1.45139i | −0.688015 | − | 0.725697i | \(-0.741518\pi\) | ||
0.688015 | − | 0.725697i | \(-0.258482\pi\) | |||||||
\(390\) | 151.242 | − | 1279.81i | 0.0196370 | − | 0.166169i | ||||
\(391\) | −12254.2 | − | 7074.96i | −1.58496 | − | 0.915080i | ||||
\(392\) | −1205.49 | − | 3772.65i | −0.155323 | − | 0.486091i | ||||
\(393\) | −203.348 | − | 151.790i | −0.0261006 | − | 0.0194829i | ||||
\(394\) | −175.115 | + | 303.309i | −0.0223913 | + | 0.0387829i | ||||
\(395\) | 5022.24 | − | 8698.78i | 0.639738 | − | 1.10806i | ||||
\(396\) | 6050.82 | + | 5737.87i | 0.767841 | + | 0.728128i | ||||
\(397\) | −777.013 | + | 448.609i | −0.0982297 | + | 0.0567129i | −0.548310 | − | 0.836275i | \(-0.684729\pi\) |
0.450080 | + | 0.892988i | \(0.351395\pi\) | |||||||
\(398\) | −586.797 | − | 1016.36i | −0.0739032 | − | 0.128004i | ||||
\(399\) | −5486.90 | + | 203.167i | −0.688443 | + | 0.0254914i | ||||
\(400\) | 1253.75 | − | 2171.56i | 0.156719 | − | 0.271445i | ||||
\(401\) | − | 4026.51i | − | 0.501432i | −0.968061 | − | 0.250716i | \(-0.919334\pi\) | ||
0.968061 | − | 0.250716i | \(-0.0806660\pi\) | |||||||
\(402\) | −452.912 | + | 606.751i | −0.0561921 | + | 0.0752786i | ||||
\(403\) | 9939.61 | 1.22860 | ||||||||
\(404\) | 2.79325 | + | 4.83804i | 0.000343983 | + | 0.000595796i | ||||
\(405\) | −5317.95 | + | 3458.97i | −0.652472 | + | 0.424389i | ||||
\(406\) | −950.347 | + | 148.145i | −0.116170 | + | 0.0181091i | ||||
\(407\) | 5387.32 | − | 3110.37i | 0.656116 | − | 0.378809i | ||||
\(408\) | −1894.04 | − | 4406.32i | −0.229826 | − | 0.534670i | ||||
\(409\) | −9468.68 | + | 5466.74i | −1.14473 | + | 0.660912i | −0.947598 | − | 0.319464i | \(-0.896497\pi\) |
−0.197135 | + | 0.980376i | \(0.563164\pi\) | |||||||
\(410\) | −616.691 | + | 356.047i | −0.0742834 | + | 0.0428875i | ||||
\(411\) | 4762.81 | − | 6380.58i | 0.571611 | − | 0.765768i | ||||
\(412\) | −4852.43 | + | 2801.55i | −0.580248 | + | 0.335006i | ||||
\(413\) | 8374.47 | + | 10393.4i | 0.997774 | + | 1.23831i | ||||
\(414\) | 3475.63 | + | 833.099i | 0.412604 | + | 0.0989000i | ||||
\(415\) | −2483.66 | − | 4301.82i | −0.293778 | − | 0.508838i | ||||
\(416\) | 4970.92 | 0.585864 | ||||||||
\(417\) | 1513.31 | + | 3520.58i | 0.177715 | + | 0.413437i | ||||
\(418\) | − | 1770.97i | − | 0.207227i | ||||||
\(419\) | −2433.63 | + | 4215.18i | −0.283749 | + | 0.491467i | −0.972305 | − | 0.233716i | \(-0.924912\pi\) |
0.688556 | + | 0.725183i | \(0.258245\pi\) | |||||||
\(420\) | −230.571 | − | 6226.99i | −0.0267874 | − | 0.723443i | ||||
\(421\) | −5868.66 | − | 10164.8i | −0.679385 | − | 1.17673i | −0.975166 | − | 0.221474i | \(-0.928913\pi\) |
0.295781 | − | 0.955256i | \(-0.404420\pi\) | |||||||
\(422\) | 1612.17 | − | 930.789i | 0.185970 | − | 0.107370i | ||||
\(423\) | 7747.08 | + | 1856.96i | 0.890487 | + | 0.213447i | ||||
\(424\) | 1757.39 | − | 3043.89i | 0.201289 | − | 0.348643i | ||||
\(425\) | −1969.32 | + | 3410.96i | −0.224767 | + | 0.389308i | ||||
\(426\) | −352.476 | + | 151.511i | −0.0400881 | + | 0.0172318i | ||||
\(427\) | −11199.7 | − | 4330.52i | −1.26930 | − | 0.490793i | ||||
\(428\) | −8107.00 | − | 4680.58i | −0.915576 | − | 0.528608i | ||||
\(429\) | 7551.61 | − | 3246.04i | 0.849872 | − | 0.365315i | ||||
\(430\) | 1616.40i | 0.181278i | ||||||||
\(431\) | 8093.99 | + | 4673.07i | 0.904580 | + | 0.522260i | 0.878683 | − | 0.477405i | \(-0.158423\pi\) |
0.0258967 | + | 0.999665i | \(0.491756\pi\) | |||||||
\(432\) | −4568.47 | − | 5486.95i | −0.508797 | − | 0.611090i | ||||
\(433\) | 582.680i | 0.0646693i | 0.999477 | + | 0.0323346i | \(0.0102942\pi\) | ||||
−0.999477 | + | 0.0323346i | \(0.989706\pi\) | |||||||
\(434\) | −3568.98 | + | 556.350i | −0.394738 | + | 0.0615337i | ||||
\(435\) | −3118.56 | − | 368.536i | −0.343732 | − | 0.0406205i | ||||
\(436\) | 1649.05 | 0.181136 | ||||||||
\(437\) | 5049.78 | + | 8746.47i | 0.552777 | + | 0.957438i | ||||
\(438\) | −119.158 | + | 1008.32i | −0.0129990 | + | 0.109998i | ||||
\(439\) | 5577.42 | + | 3220.13i | 0.606369 | + | 0.350087i | 0.771543 | − | 0.636177i | \(-0.219485\pi\) |
−0.165174 | + | 0.986264i | \(0.552819\pi\) | |||||||
\(440\) | 4170.75 | 0.451892 | ||||||||
\(441\) | 5210.95 | + | 7655.86i | 0.562677 | + | 0.826677i | ||||
\(442\) | −2278.21 | −0.245166 | ||||||||
\(443\) | −10151.6 | − | 5861.05i | −1.08876 | − | 0.628593i | −0.155511 | − | 0.987834i | \(-0.549702\pi\) |
−0.933245 | + | 0.359241i | \(0.883036\pi\) | |||||||
\(444\) | −5323.57 | + | 2288.32i | −0.569022 | + | 0.244593i | ||||
\(445\) | 778.946 | + | 1349.17i | 0.0829789 | + | 0.143724i | ||||
\(446\) | 741.657 | 0.0787409 | ||||||||
\(447\) | −4587.00 | + | 6145.04i | −0.485364 | + | 0.650225i | ||||
\(448\) | 5665.29 | − | 883.133i | 0.597455 | − | 0.0931341i | ||||
\(449\) | − | 10126.0i | − | 1.06431i | −0.846648 | − | 0.532153i | \(-0.821383\pi\) | ||
0.846648 | − | 0.532153i | \(-0.178617\pi\) | |||||||
\(450\) | 231.894 | − | 967.443i | 0.0242924 | − | 0.101346i | ||||
\(451\) | −3933.38 | − | 2270.94i | −0.410678 | − | 0.237105i | ||||
\(452\) | − | 11559.2i | − | 1.20287i | ||||||
\(453\) | −5308.58 | − | 3962.61i | −0.550594 | − | 0.410993i | ||||
\(454\) | 390.820 | + | 225.640i | 0.0404011 | + | 0.0233256i | ||||
\(455\) | −5728.91 | − | 2215.17i | −0.590276 | − | 0.228239i | ||||
\(456\) | −401.749 | + | 3399.61i | −0.0412579 | + | 0.349126i | ||||
\(457\) | 3527.39 | − | 6109.61i | 0.361059 | − | 0.625373i | −0.627076 | − | 0.778958i | \(-0.715748\pi\) |
0.988135 | + | 0.153585i | \(0.0490818\pi\) | |||||||
\(458\) | −484.302 | + | 838.835i | −0.0494104 | + | 0.0855812i | ||||
\(459\) | 7175.87 | + | 8618.56i | 0.729719 | + | 0.876427i | ||||
\(460\) | −9926.22 | + | 5730.91i | −1.00611 | + | 0.580880i | ||||
\(461\) | 1300.85 | + | 2253.14i | 0.131425 | + | 0.227634i | 0.924226 | − | 0.381846i | \(-0.124712\pi\) |
−0.792801 | + | 0.609480i | \(0.791378\pi\) | |||||||
\(462\) | −2529.84 | + | 1588.23i | −0.254759 | + | 0.159938i | ||||
\(463\) | −4858.94 | + | 8415.93i | −0.487719 | + | 0.844755i | −0.999900 | − | 0.0141228i | \(-0.995504\pi\) |
0.512181 | + | 0.858878i | \(0.328838\pi\) | |||||||
\(464\) | − | 3534.26i | − | 0.353607i | ||||||
\(465\) | −11711.6 | − | 1384.02i | −1.16798 | − | 0.138026i | ||||
\(466\) | −3194.70 | −0.317578 | ||||||||
\(467\) | −4239.34 | − | 7342.76i | −0.420072 | − | 0.727585i | 0.575874 | − | 0.817538i | \(-0.304662\pi\) |
−0.995946 | + | 0.0899527i | \(0.971328\pi\) | |||||||
\(468\) | −7340.49 | + | 2177.23i | −0.725031 | + | 0.215048i | ||||
\(469\) | 2264.19 | + | 2810.03i | 0.222923 | + | 0.276664i | ||||
\(470\) | 1662.87 | − | 960.059i | 0.163197 | − | 0.0942218i | ||||
\(471\) | −10237.9 | − | 1209.87i | −1.00157 | − | 0.118360i | ||||
\(472\) | 7206.82 | − | 4160.86i | 0.702799 | − | 0.405761i | ||||
\(473\) | −8928.49 | + | 5154.87i | −0.867933 | + | 0.501102i | ||||
\(474\) | 4454.14 | + | 526.367i | 0.431614 | + | 0.0510060i | ||||
\(475\) | 2434.58 | − | 1405.61i | 0.235171 | − | 0.135776i | ||||
\(476\) | −10884.3 | + | 1696.69i | −1.04807 | + | 0.163378i | ||||
\(477\) | −1915.72 | + | 7992.24i | −0.183888 | + | 0.767169i | ||||
\(478\) | 895.736 | + | 1551.46i | 0.0857113 | + | 0.148456i | ||||
\(479\) | −19701.4 | −1.87929 | −0.939645 | − | 0.342150i | \(-0.888845\pi\) | ||||
−0.939645 | + | 0.342150i | \(0.888845\pi\) | |||||||
\(480\) | −5857.11 | − | 692.164i | −0.556957 | − | 0.0658183i | ||||
\(481\) | 5711.80i | 0.541446i | ||||||||
\(482\) | −305.903 | + | 529.840i | −0.0289077 | + | 0.0500696i | ||||
\(483\) | 7965.66 | − | 15057.6i | 0.750414 | − | 1.41852i | ||||
\(484\) | 1457.77 | + | 2524.94i | 0.136906 | + | 0.237128i | ||||
\(485\) | −8324.25 | + | 4806.01i | −0.779350 | + | 0.449958i | ||||
\(486\) | −2356.74 | − | 1571.65i | −0.219967 | − | 0.146690i | ||||
\(487\) | −7141.08 | + | 12368.7i | −0.664463 | + | 1.15088i | 0.314968 | + | 0.949102i | \(0.398006\pi\) |
−0.979431 | + | 0.201781i | \(0.935327\pi\) | |||||||
\(488\) | −3743.24 | + | 6483.48i | −0.347230 | + | 0.601421i | ||||
\(489\) | 2239.95 | − | 18954.5i | 0.207145 | − | 1.75287i | ||||
\(490\) | 2181.05 | + | 474.730i | 0.201081 | + | 0.0437676i | ||||
\(491\) | 9090.51 | + | 5248.41i | 0.835537 | + | 0.482398i | 0.855745 | − | 0.517398i | \(-0.173099\pi\) |
−0.0202074 | + | 0.999796i | \(0.506433\pi\) | |||||||
\(492\) | 3390.33 | + | 2530.73i | 0.310667 | + | 0.231899i | ||||
\(493\) | 5551.40i | 0.507145i | ||||||||
\(494\) | 1408.23 | + | 813.041i | 0.128257 | + | 0.0740495i | ||||
\(495\) | −9349.86 | + | 2773.22i | −0.848979 | + | 0.251812i | ||||
\(496\) | − | 13272.7i | − | 1.20154i | ||||||
\(497\) | 281.649 | + | 1806.77i | 0.0254199 | + | 0.163068i | ||||
\(498\) | 1326.78 | − | 1777.45i | 0.119387 | − | 0.159938i | ||||
\(499\) | 16828.4 | 1.50970 | 0.754850 | − | 0.655897i | \(-0.227710\pi\) | ||||
0.754850 | + | 0.655897i | \(0.227710\pi\) | |||||||
\(500\) | 5642.14 | + | 9772.48i | 0.504649 | + | 0.874077i | ||||
\(501\) | 19167.3 | − | 8239.01i | 1.70924 | − | 0.734714i | ||||
\(502\) | −4867.72 | − | 2810.38i | −0.432783 | − | 0.249867i | ||||
\(503\) | 12335.3 | 1.09344 | 0.546722 | − | 0.837314i | \(-0.315875\pi\) | ||||
0.546722 | + | 0.837314i | \(0.315875\pi\) | |||||||
\(504\) | 5216.65 | − | 2474.92i | 0.461048 | − | 0.218733i | ||||
\(505\) | −6.53356 | −0.000575722 | ||||||||
\(506\) | 4758.31 | + | 2747.21i | 0.418049 | + | 0.241361i | ||||
\(507\) | 454.027 | − | 3841.99i | 0.0397713 | − | 0.336546i | ||||
\(508\) | −9022.16 | − | 15626.8i | −0.787980 | − | 1.36482i | ||||
\(509\) | 14453.1 | 1.25859 | 0.629295 | − | 0.777166i | \(-0.283344\pi\) | ||||
0.629295 | + | 0.777166i | \(0.283344\pi\) | |||||||
\(510\) | 2684.36 | + | 317.224i | 0.233070 | + | 0.0275430i | ||||
\(511\) | 4513.59 | + | 1745.25i | 0.390743 | + | 0.151087i | ||||
\(512\) | − | 11338.9i | − | 0.978739i | ||||||
\(513\) | −1359.85 | − | 7888.28i | −0.117035 | − | 0.678901i | ||||
\(514\) | 3593.43 | + | 2074.67i | 0.308365 | + | 0.178034i | ||||
\(515\) | − | 6552.99i | − | 0.560698i | ||||||
\(516\) | 8822.85 | − | 3792.48i | 0.752721 | − | 0.323555i | ||||
\(517\) | 10606.1 | + | 6123.46i | 0.902239 | + | 0.520908i | ||||
\(518\) | −319.706 | − | 2050.91i | −0.0271179 | − | 0.173961i | ||||
\(519\) | −9994.01 | + | 4295.90i | −0.845257 | + | 0.363332i | ||||
\(520\) | −1914.76 | + | 3316.46i | −0.161477 | + | 0.279686i | ||||
\(521\) | 3797.90 | − | 6578.16i | 0.319365 | − | 0.553156i | −0.660991 | − | 0.750394i | \(-0.729864\pi\) |
0.980356 | + | 0.197238i | \(0.0631971\pi\) | |||||||
\(522\) | −398.733 | − | 1344.32i | −0.0334331 | − | 0.112719i | ||||
\(523\) | 15947.4 | − | 9207.24i | 1.33333 | − | 0.769799i | 0.347522 | − | 0.937672i | \(-0.387023\pi\) |
0.985809 | + | 0.167873i | \(0.0536900\pi\) | |||||||
\(524\) | 181.684 | + | 314.686i | 0.0151468 | + | 0.0262350i | ||||
\(525\) | −4191.28 | − | 2217.24i | −0.348424 | − | 0.184321i | ||||
\(526\) | −2383.15 | + | 4127.74i | −0.197548 | + | 0.342164i | ||||
\(527\) | 20848.0i | 1.72325i | ||||||||
\(528\) | −4334.56 | − | 10083.9i | −0.357268 | − | 0.831150i | ||||
\(529\) | −19166.8 | −1.57531 | ||||||||
\(530\) | 990.441 | + | 1715.49i | 0.0811736 | + | 0.140597i | ||||
\(531\) | −13389.4 | + | 14119.7i | −1.09426 | + | 1.15394i | ||||
\(532\) | 7333.38 | + | 2835.57i | 0.597636 | + | 0.231085i | ||||
\(533\) | 3611.58 | − | 2085.15i | 0.293499 | − | 0.169452i | ||||
\(534\) | −416.118 | + | 557.459i | −0.0337213 | + | 0.0451753i | ||||
\(535\) | 9481.37 | − | 5474.07i | 0.766197 | − | 0.442364i | ||||
\(536\) | 1948.50 | − | 1124.97i | 0.157019 | − | 0.0906551i | ||||
\(537\) | 7568.05 | + | 17606.4i | 0.608167 | + | 1.41484i | ||||
\(538\) | 2768.05 | − | 1598.13i | 0.221820 | − | 0.128068i | ||||
\(539\) | 4333.34 | + | 13561.4i | 0.346289 | + | 1.08373i | ||||
\(540\) | 8952.28 | − | 1543.27i | 0.713416 | − | 0.122985i | ||||
\(541\) | 10525.6 | + | 18230.9i | 0.836474 | + | 1.44882i | 0.892825 | + | 0.450405i | \(0.148720\pi\) |
−0.0563503 | + | 0.998411i | \(0.517946\pi\) | |||||||
\(542\) | −1570.18 | −0.124437 | ||||||||
\(543\) | −5124.09 | + | 6864.58i | −0.404965 | + | 0.542518i | ||||
\(544\) | 10426.3i | 0.821738i | ||||||||
\(545\) | −964.307 | + | 1670.23i | −0.0757915 | + | 0.131275i | ||||
\(546\) | −101.486 | − | 2740.81i | −0.00795455 | − | 0.214827i | ||||
\(547\) | −8242.69 | − | 14276.8i | −0.644300 | − | 1.11596i | −0.984463 | − | 0.175594i | \(-0.943815\pi\) |
0.340163 | − | 0.940367i | \(-0.389518\pi\) | |||||||
\(548\) | −9874.11 | + | 5700.82i | −0.769710 | + | 0.444392i | ||||
\(549\) | 4080.47 | − | 17023.4i | 0.317214 | − | 1.32339i | ||||
\(550\) | 764.688 | − | 1324.48i | 0.0592844 | − | 0.102684i | ||||
\(551\) | 1981.16 | − | 3431.48i | 0.153177 | − | 0.265310i | ||||
\(552\) | −8510.99 | − | 6353.07i | −0.656253 | − | 0.489863i | ||||
\(553\) | 7709.48 | − | 19938.4i | 0.592840 | − | 1.53321i | ||||
\(554\) | 2856.46 | + | 1649.18i | 0.219060 | + | 0.126474i | ||||
\(555\) | 795.325 | − | 6730.07i | 0.0608283 | − | 0.514730i | ||||
\(556\) | − | 5487.40i | − | 0.418557i | ||||||
\(557\) | −5731.63 | − | 3309.16i | −0.436009 | − | 0.251730i | 0.265894 | − | 0.964002i | \(-0.414333\pi\) |
−0.701903 | + | 0.712272i | \(0.747666\pi\) | |||||||
\(558\) | −1497.42 | − | 5048.53i | −0.113604 | − | 0.383013i | ||||
\(559\) | − | 9466.26i | − | 0.716243i | ||||||
\(560\) | −2958.00 | + | 7650.03i | −0.223211 | + | 0.577272i | ||||
\(561\) | 6808.46 | + | 15839.2i | 0.512395 | + | 1.19204i | ||||
\(562\) | −3792.67 | −0.284669 | ||||||||
\(563\) | 8503.32 | + | 14728.2i | 0.636540 | + | 1.10252i | 0.986187 | + | 0.165638i | \(0.0529683\pi\) |
−0.349647 | + | 0.936882i | \(0.613698\pi\) | |||||||
\(564\) | −9141.84 | − | 6823.97i | −0.682520 | − | 0.509470i | ||||
\(565\) | 11707.6 | + | 6759.40i | 0.871758 | + | 0.503310i | ||||
\(566\) | 413.239 | 0.0306885 | ||||||||
\(567\) | −10048.9 | + | 9016.86i | −0.744293 | + | 0.667853i | ||||
\(568\) | 1140.08 | 0.0842192 | ||||||||
\(569\) | −9769.80 | − | 5640.60i | −0.719809 | − | 0.415582i | 0.0948734 | − | 0.995489i | \(-0.469755\pi\) |
−0.814682 | + | 0.579907i | \(0.803089\pi\) | |||||||
\(570\) | −1546.07 | − | 1154.07i | −0.113610 | − | 0.0848047i | ||||
\(571\) | 12233.2 | + | 21188.5i | 0.896571 | + | 1.55291i | 0.831848 | + | 0.555004i | \(0.187283\pi\) |
0.0647233 | + | 0.997903i | \(0.479384\pi\) | |||||||
\(572\) | −11770.4 | −0.860396 | ||||||||
\(573\) | 7525.13 | + | 17506.5i | 0.548633 | + | 1.27634i | ||||
\(574\) | −1180.09 | + | 950.857i | −0.0858115 | + | 0.0691429i | ||||
\(575\) | 8721.78i | 0.632562i | ||||||||
\(576\) | 2376.96 | + | 8013.89i | 0.171945 | + | 0.579708i | ||||
\(577\) | −14445.8 | − | 8340.28i | −1.04226 | − | 0.601751i | −0.121790 | − | 0.992556i | \(-0.538863\pi\) |
−0.920474 | + | 0.390805i | \(0.872197\pi\) | |||||||
\(578\) | − | 1104.46i | − | 0.0794801i | ||||||
\(579\) | −208.632 | + | 1765.45i | −0.0149749 | + | 0.126718i | ||||
\(580\) | 3894.33 | + | 2248.39i | 0.278798 | + | 0.160964i | ||||
\(581\) | −6632.84 | − | 8231.86i | −0.473626 | − | 0.587806i | ||||
\(582\) | −3439.46 | − | 2567.40i | −0.244966 | − | 0.182856i | ||||
\(583\) | −6317.24 | + | 10941.8i | −0.448771 | + | 0.777294i | ||||
\(584\) | 1508.57 | − | 2612.92i | 0.106892 | − | 0.185143i | ||||
\(585\) | 2087.27 | − | 8707.92i | 0.147518 | − | 0.615433i | ||||
\(586\) | 642.582 | − | 370.995i | 0.0452984 | − | 0.0261530i | ||||
\(587\) | 7866.86 | + | 13625.8i | 0.553152 | + | 0.958087i | 0.998045 | + | 0.0625029i | \(0.0199083\pi\) |
−0.444893 | + | 0.895584i | \(0.646758\pi\) | |||||||
\(588\) | −2526.06 | − | 13018.7i | −0.177165 | − | 0.913068i | ||||
\(589\) | 7440.16 | − | 12886.7i | 0.520486 | − | 0.901509i | ||||
\(590\) | 4690.00i | 0.327262i | ||||||||
\(591\) | −1455.71 | + | 1950.16i | −0.101319 | + | 0.135734i | ||||
\(592\) | 7627.17 | 0.529518 | ||||||||
\(593\) | 2335.26 | + | 4044.79i | 0.161716 | + | 0.280101i | 0.935484 | − | 0.353368i | \(-0.114964\pi\) |
−0.773768 | + | 0.633469i | \(0.781630\pi\) | |||||||
\(594\) | −2786.40 | − | 3346.59i | −0.192470 | − | 0.231166i | ||||
\(595\) | 4646.25 | − | 12016.2i | 0.320131 | − | 0.827926i | ||||
\(596\) | 9509.62 | − | 5490.38i | 0.653573 | − | 0.377340i | ||||
\(597\) | −3220.35 | − | 7491.85i | −0.220771 | − | 0.513603i | ||||
\(598\) | −4369.02 | + | 2522.45i | −0.298767 | + | 0.172493i | ||||
\(599\) | −11047.3 | + | 6378.15i | −0.753556 | + | 0.435066i | −0.826977 | − | 0.562235i | \(-0.809941\pi\) |
0.0734215 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(600\) | −1768.38 | + | 2369.04i | −0.120323 | + | 0.161193i | ||||
\(601\) | 17937.2 | − | 10356.0i | 1.21743 | − | 0.702882i | 0.253060 | − | 0.967451i | \(-0.418563\pi\) |
0.964367 | + | 0.264569i | \(0.0852297\pi\) | |||||||
\(602\) | 529.855 | + | 3399.02i | 0.0358725 | + | 0.230122i | ||||
\(603\) | −3620.07 | + | 3817.51i | −0.244479 | + | 0.257813i | ||||
\(604\) | 4743.03 | + | 8215.17i | 0.319522 | + | 0.553428i | ||||
\(605\) | −3409.82 | −0.229139 | ||||||||
\(606\) | −1.15211 | − | 2.68028i | −7.72299e−5 | − | 0.000179668i | ||||
\(607\) | − | 24485.0i | − | 1.63726i | −0.574325 | − | 0.818628i | \(-0.694735\pi\) | ||
0.574325 | − | 0.818628i | \(-0.305265\pi\) | |||||||
\(608\) | 3720.91 | − | 6444.81i | 0.248196 | − | 0.429888i | ||||
\(609\) | −6678.61 | + | 247.293i | −0.444386 | + | 0.0164546i | ||||
\(610\) | −2109.63 | − | 3653.99i | −0.140027 | − | 0.242534i | ||||
\(611\) | −9738.42 | + | 5622.48i | −0.644803 | + | 0.372277i | ||||
\(612\) | −4566.67 | − | 15396.4i | −0.301629 | − | 1.01693i | ||||
\(613\) | −2415.65 | + | 4184.03i | −0.159164 | + | 0.275679i | −0.934567 | − | 0.355786i | \(-0.884213\pi\) |
0.775404 | + | 0.631466i | \(0.217546\pi\) | |||||||
\(614\) | −96.0308 | + | 166.330i | −0.00631187 | + | 0.0109325i | ||||
\(615\) | −4545.77 | + | 1953.99i | −0.298054 | + | 0.128118i | ||||
\(616\) | 8770.38 | − | 1367.17i | 0.573650 | − | 0.0894233i | ||||
\(617\) | −5042.06 | − | 2911.04i | −0.328988 | − | 0.189942i | 0.326404 | − | 0.945231i | \(-0.394163\pi\) |
−0.655392 | + | 0.755289i | \(0.727497\pi\) | |||||||
\(618\) | 2688.25 | − | 1155.54i | 0.174980 | − | 0.0752145i | ||||
\(619\) | 1448.25i | 0.0940388i | 0.998894 | + | 0.0470194i | \(0.0149723\pi\) | ||||
−0.998894 | + | 0.0470194i | \(0.985028\pi\) | |||||||
\(620\) | 14624.9 | + | 8443.71i | 0.947341 | + | 0.546948i | ||||
\(621\) | 23304.0 | + | 8582.98i | 1.50589 | + | 0.554626i | ||||
\(622\) | − | 541.032i | − | 0.0348769i | ||||||
\(623\) | 2080.25 | + | 2581.75i | 0.133778 | + | 0.166028i | ||||
\(624\) | 10008.4 | + | 1182.75i | 0.642081 | + | 0.0758779i | ||||
\(625\) | −7038.32 | −0.450452 | ||||||||
\(626\) | −2574.09 | − | 4458.46i | −0.164347 | − | 0.284658i | ||||
\(627\) | 1444.15 | − | 12220.5i | 0.0919839 | − | 0.778371i | ||||
\(628\) | 12784.7 | + | 7381.24i | 0.812363 | + | 0.469018i | ||||
\(629\) | −11980.3 | −0.759437 | ||||||||
\(630\) | −262.059 | + | 3243.55i | −0.0165725 | + | 0.205121i | ||||
\(631\) | −22632.9 | −1.42790 | −0.713948 | − | 0.700199i | \(-0.753095\pi\) | ||||
−0.713948 | + | 0.700199i | \(0.753095\pi\) | |||||||
\(632\) | −11542.3 | − | 6663.96i | −0.726469 | − | 0.419427i | ||||
\(633\) | 11883.7 | − | 5108.19i | 0.746185 | − | 0.320746i | ||||
\(634\) | −137.361 | − | 237.916i | −0.00860456 | − | 0.0149035i | ||||
\(635\) | 21103.4 | 1.31884 | ||||||||
\(636\) | 7039.92 | − | 9431.14i | 0.438917 | − | 0.588002i | ||||
\(637\) | −12773.1 | − | 2780.20i | −0.794486 | − | 0.172929i | ||||
\(638\) | − | 2155.61i | − | 0.133764i | ||||||
\(639\) | −2555.79 | + | 758.062i | −0.158224 | + | 0.0469303i | ||||
\(640\) | 9608.61 | + | 5547.53i | 0.593459 | + | 0.342633i | ||||
\(641\) | − | 15231.9i | − | 0.938571i | −0.883046 | − | 0.469286i | \(-0.844511\pi\) | ||
0.883046 | − | 0.469286i | \(-0.155489\pi\) | |||||||
\(642\) | 3917.56 | + | 2924.28i | 0.240832 | + | 0.179770i | ||||
\(643\) | −12428.6 | − | 7175.65i | −0.762264 | − | 0.440093i | 0.0678441 | − | 0.997696i | \(-0.478388\pi\) |
−0.830108 | + | 0.557603i | \(0.811721\pi\) | |||||||
\(644\) | −18994.6 | + | 15305.0i | −1.16225 | + | 0.936490i | ||||
\(645\) | −1318.11 | + | 11153.9i | −0.0804657 | + | 0.680903i | ||||
\(646\) | −1705.33 | + | 2953.71i | −0.103862 | + | 0.179895i | ||||
\(647\) | 14009.3 | − | 24264.9i | 0.851258 | − | 1.47442i | −0.0288151 | − | 0.999585i | \(-0.509173\pi\) |
0.880073 | − | 0.474838i | \(-0.157493\pi\) | |||||||
\(648\) | 4589.67 | + | 7056.32i | 0.278239 | + | 0.427776i | ||||
\(649\) | −25906.1 | + | 14956.9i | −1.56688 | + | 0.904638i | ||||
\(650\) | 702.126 | + | 1216.12i | 0.0423687 | + | 0.0733847i | ||||
\(651\) | −25081.2 | + | 928.698i | −1.51000 | + | 0.0559117i | ||||
\(652\) | −13665.6 | + | 23669.6i | −0.820840 | + | 1.42174i | ||||
\(653\) | − | 12216.5i | − | 0.732113i | −0.930593 | − | 0.366057i | \(-0.880708\pi\) | ||
0.930593 | − | 0.366057i | \(-0.119292\pi\) | |||||||
\(654\) | −855.226 | − | 101.066i | −0.0511345 | − | 0.00604282i | ||||
\(655\) | −424.969 | −0.0253510 | ||||||||
\(656\) | −2784.37 | − | 4822.67i | −0.165719 | − | 0.287033i | ||||
\(657\) | −1644.48 | + | 6860.64i | −0.0976517 | + | 0.407396i | ||||
\(658\) | 3182.03 | − | 2563.93i | 0.188524 | − | 0.151903i | ||||
\(659\) | 5703.43 | − | 3292.88i | 0.337138 | − | 0.194647i | −0.321868 | − | 0.946785i | \(-0.604311\pi\) |
0.659006 | + | 0.752138i | \(0.270977\pi\) | |||||||
\(660\) | 13868.8 | + | 1638.95i | 0.817943 | + | 0.0966604i | ||||
\(661\) | −6336.72 | + | 3658.51i | −0.372874 | + | 0.215279i | −0.674713 | − | 0.738080i | \(-0.735733\pi\) |
0.301839 | + | 0.953359i | \(0.402399\pi\) | |||||||
\(662\) | −2477.66 | + | 1430.48i | −0.145464 | + | 0.0839836i | ||||
\(663\) | −15720.7 | − | 1857.79i | −0.920874 | − | 0.108824i | ||||
\(664\) | −5708.03 | + | 3295.53i | −0.333606 | + | 0.192608i | ||||
\(665\) | −7160.28 | + | 5769.42i | −0.417539 | + | 0.336434i | ||||
\(666\) | 2901.14 | − | 860.494i | 0.168794 | − | 0.0500653i | ||||
\(667\) | 6146.55 | + | 10646.1i | 0.356815 | + | 0.618021i | ||||
\(668\) | −29875.4 | −1.73041 | ||||||||
\(669\) | 5117.75 | + | 604.790i | 0.295760 | + | 0.0349515i | ||||
\(670\) | 1268.03i | 0.0731167i | ||||||||
\(671\) | 13455.7 | − | 23305.9i | 0.774145 | − | 1.34086i | ||||
\(672\) | −12543.4 | + | 464.453i | −0.720048 | + | 0.0266617i | ||||
\(673\) | 1486.23 | + | 2574.23i | 0.0851263 | + | 0.147443i | 0.905445 | − | 0.424464i | \(-0.139537\pi\) |
−0.820319 | + | 0.571907i | \(0.806204\pi\) | |||||||
\(674\) | −618.320 | + | 356.987i | −0.0353365 | + | 0.0204015i | ||||
\(675\) | 2389.07 | − | 6486.67i | 0.136230 | − | 0.369885i | ||||
\(676\) | −2769.96 | + | 4797.71i | −0.157599 | + | 0.272970i | ||||
\(677\) | 8554.38 | − | 14816.6i | 0.485630 | − | 0.841136i | −0.514233 | − | 0.857650i | \(-0.671923\pi\) |
0.999864 | + | 0.0165140i | \(0.00525681\pi\) | |||||||
\(678\) | −708.433 | + | 5994.78i | −0.0401286 | + | 0.339570i | ||||
\(679\) | −15929.1 | + | 12834.9i | −0.900298 | + | 0.725418i | ||||
\(680\) | −6956.17 | − | 4016.15i | −0.392290 | − | 0.226488i | ||||
\(681\) | 2512.83 | + | 1875.71i | 0.141397 | + | 0.105547i | ||||
\(682\) | − | 8095.29i | − | 0.454523i | ||||||
\(683\) | 4555.42 | + | 2630.07i | 0.255210 | + | 0.147346i | 0.622147 | − | 0.782900i | \(-0.286260\pi\) |
−0.366938 | + | 0.930246i | \(0.619594\pi\) | |||||||
\(684\) | −2671.84 | + | 11146.7i | −0.149357 | + | 0.623107i | ||||
\(685\) | − | 13334.5i | − | 0.743776i | ||||||
\(686\) | 4742.00 | + | 283.330i | 0.263922 | + | 0.0157691i | ||||
\(687\) | −4025.93 | + | 5393.40i | −0.223579 | + | 0.299521i | ||||
\(688\) | −12640.6 | −0.700465 | ||||||||
\(689\) | −5800.41 | − | 10046.6i | −0.320723 | − | 0.555508i | ||||
\(690\) | 5499.14 | − | 2363.79i | 0.303404 | − | 0.130417i | ||||
\(691\) | −16770.2 | − | 9682.26i | −0.923252 | − | 0.533040i | −0.0385810 | − | 0.999255i | \(-0.512284\pi\) |
−0.884671 | + | 0.466216i | \(0.845617\pi\) | |||||||
\(692\) | 15577.3 | 0.855724 | ||||||||
\(693\) | −18752.1 | + | 8896.50i | −1.02790 | + | 0.487662i | ||||
\(694\) | −4242.21 | −0.232034 | ||||||||
\(695\) | 5557.87 | + | 3208.84i | 0.303341 | + | 0.175134i | ||||
\(696\) | −489.005 | + | 4137.98i | −0.0266318 | + | 0.225359i | ||||
\(697\) | 4373.52 | + | 7575.17i | 0.237674 | + | 0.411664i | ||||
\(698\) | −141.513 | −0.00767386 | ||||||||
\(699\) | −22044.8 | − | 2605.14i | −1.19286 | − | 0.140966i | ||||
\(700\) | 4260.14 | + | 5287.15i | 0.230026 | + | 0.285479i | ||||
\(701\) | − | 23797.7i | − | 1.28221i | −0.767455 | − | 0.641103i | \(-0.778477\pi\) | ||
0.767455 | − | 0.641103i | \(-0.221523\pi\) | |||||||
\(702\) | 3940.34 | − | 679.268i | 0.211850 | − | 0.0365204i | ||||
\(703\) | 7405.36 | + | 4275.49i | 0.397295 | + | 0.229379i | ||||
\(704\) | 12850.2i | 0.687942i | ||||||||
\(705\) | 12257.4 | − | 5268.82i | 0.654810 | − | 0.281469i | ||||
\(706\) | −6761.64 | − | 3903.84i | −0.360450 | − | 0.208106i | ||||
\(707\) | −13.7390 | + | 2.14170i | −0.000730845 | + | 0.000113928i | ||||
\(708\) | 25599.6 | − | 11003.9i | 1.35889 | − | 0.584114i | ||||
\(709\) | −7213.51 | + | 12494.2i | −0.382100 | + | 0.661817i | −0.991362 | − | 0.131152i | \(-0.958132\pi\) |
0.609262 | + | 0.792969i | \(0.291466\pi\) | |||||||
\(710\) | −321.265 | + | 556.447i | −0.0169815 | + | 0.0294128i | ||||
\(711\) | 30306.2 | + | 7264.33i | 1.59855 | + | 0.383169i | ||||
\(712\) | 1790.20 | − | 1033.57i | 0.0942285 | − | 0.0544029i | ||||
\(713\) | 23083.0 | + | 39981.0i | 1.21244 | + | 2.10000i | ||||
\(714\) | 5748.75 | − | 212.863i | 0.301318 | − | 0.0111571i | ||||
\(715\) | 6882.93 | − | 11921.6i | 0.360010 | − | 0.623555i | ||||
\(716\) | − | 27442.4i | − | 1.43236i | ||||||
\(717\) | 4915.81 | + | 11436.2i | 0.256045 | + | 0.595665i | ||||
\(718\) | 7936.82 | 0.412534 | ||||||||
\(719\) | 2139.85 | + | 3706.33i | 0.110992 | + | 0.192243i | 0.916170 | − | 0.400789i | \(-0.131264\pi\) |
−0.805179 | + | 0.593032i | \(0.797931\pi\) | |||||||
\(720\) | −11628.0 | − | 2787.20i | −0.601875 | − | 0.144268i | ||||
\(721\) | −2148.07 | − | 13779.8i | −0.110955 | − | 0.711773i | ||||
\(722\) | −2333.85 | + | 1347.45i | −0.120300 | + | 0.0694555i | ||||
\(723\) | −2542.93 | + | 3406.68i | −0.130806 | + | 0.175236i | ||||
\(724\) | 10623.1 | − | 6133.26i | 0.545311 | − | 0.314835i | ||||
\(725\) | 2963.36 | − | 1710.89i | 0.151802 | − | 0.0876428i | ||||
\(726\) | −601.279 | − | 1398.82i | −0.0307377 | − | 0.0715083i | ||||
\(727\) | 8438.47 | − | 4871.95i | 0.430489 | − | 0.248543i | −0.269066 | − | 0.963122i | \(-0.586715\pi\) |
0.699555 | + | 0.714579i | \(0.253382\pi\) | |||||||
\(728\) | −2939.29 | + | 7601.62i | −0.149639 | + | 0.386999i | ||||
\(729\) | −14980.9 | − | 12766.9i | −0.761108 | − | 0.648625i | ||||
\(730\) | 850.207 | + | 1472.60i | 0.0431063 | + | 0.0746623i | ||||
\(731\) | 19855.2 | 1.00461 | ||||||||
\(732\) | −14995.0 | + | 20088.3i | −0.757146 | + | 1.01432i | ||||
\(733\) | 4535.45i | 0.228541i | 0.993450 | + | 0.114271i | \(0.0364531\pi\) | ||||
−0.993450 | + | 0.114271i | \(0.963547\pi\) | |||||||
\(734\) | −330.061 | + | 571.682i | −0.0165978 | + | 0.0287482i | ||||
\(735\) | 14663.1 | + | 5054.40i | 0.735858 | + | 0.253652i | ||||
\(736\) | 11544.1 | + | 19995.0i | 0.578154 | + | 1.00139i | ||||
\(737\) | −7004.20 | + | 4043.88i | −0.350072 | + | 0.202114i | ||||
\(738\) | −1603.18 | − | 1520.26i | −0.0799646 | − | 0.0758288i | ||||
\(739\) | 15942.1 | − | 27612.6i | 0.793561 | − | 1.37449i | −0.130189 | − | 0.991489i | \(-0.541558\pi\) |
0.923749 | − | 0.382998i | \(-0.125108\pi\) | |||||||
\(740\) | −4852.18 | + | 8404.22i | −0.241040 | + | 0.417494i | ||||
\(741\) | 9054.38 | + | 6758.69i | 0.448881 | + | 0.335070i | ||||
\(742\) | 2645.07 | + | 3282.73i | 0.130867 | + | 0.162416i | ||||
\(743\) | −10135.3 | − | 5851.64i | −0.500444 | − | 0.288931i | 0.228453 | − | 0.973555i | \(-0.426633\pi\) |
−0.728897 | + | 0.684624i | \(0.759967\pi\) | |||||||
\(744\) | −1836.43 | + | 15540.0i | −0.0904932 | + | 0.765756i | ||||
\(745\) | 12842.3i | 0.631552i | ||||||||
\(746\) | 1694.29 | + | 978.200i | 0.0831534 | + | 0.0480086i | ||||
\(747\) | 10604.8 | − | 11183.2i | 0.519425 | − | 0.547755i | ||||
\(748\) | − | 24688.1i | − | 1.20680i | ||||||
\(749\) | 18143.3 | − | 14619.0i | 0.885104 | − | 0.713175i | ||||
\(750\) | −2327.18 | − | 5413.96i | −0.113302 | − | 0.263586i | ||||
\(751\) | −16580.5 | −0.805635 | −0.402817 | − | 0.915280i | \(-0.631969\pi\) | ||||
−0.402817 | + | 0.915280i | \(0.631969\pi\) | |||||||
\(752\) | 7507.90 | + | 13004.1i | 0.364076 | + | 0.630598i | ||||
\(753\) | −31297.6 | − | 23362.3i | −1.51467 | − | 1.13063i | ||||
\(754\) | 1714.08 | + | 989.627i | 0.0827895 | + | 0.0477985i | ||||
\(755\) | −11094.2 | −0.534782 | ||||||||
\(756\) | 18319.3 | − | 6179.78i | 0.881303 | − | 0.297297i | ||||
\(757\) | −16410.7 | −0.787923 | −0.393962 | − | 0.919127i | \(-0.628896\pi\) | ||||
−0.393962 | + | 0.919127i | \(0.628896\pi\) | |||||||
\(758\) | 412.325 | + | 238.056i | 0.0197577 | + | 0.0114071i | ||||
\(759\) | 30594.2 | + | 22837.2i | 1.46311 | + | 1.09214i | ||||
\(760\) | 2866.54 | + | 4964.99i | 0.136816 | + | 0.236972i | ||||
\(761\) | 21191.0 | 1.00943 | 0.504713 | − | 0.863287i | \(-0.331598\pi\) | ||||
0.504713 | + | 0.863287i | \(0.331598\pi\) | |||||||
\(762\) | 3721.31 | + | 8657.29i | 0.176915 | + | 0.411575i | ||||
\(763\) | −1480.28 | + | 3828.31i | −0.0702354 | + | 0.181644i | ||||
\(764\) | − | 27286.8i | − | 1.29215i | ||||||
\(765\) | 18264.6 | + | 4377.97i | 0.863211 | + | 0.206910i | ||||
\(766\) | −4902.38 | − | 2830.39i | −0.231241 | − | 0.133507i | ||||
\(767\) | − | 27466.5i | − | 1.29303i | ||||||
\(768\) | 928.919 | − | 7860.54i | 0.0436451 | − | 0.369326i | ||||
\(769\) | −4457.86 | − | 2573.75i | −0.209044 | − | 0.120691i | 0.391823 | − | 0.920041i | \(-0.371844\pi\) |
−0.600867 | + | 0.799349i | \(0.705178\pi\) | |||||||
\(770\) | −1804.14 | + | 4665.90i | −0.0844374 | + | 0.218373i | ||||
\(771\) | 23104.4 | + | 17246.4i | 1.07923 | + | 0.805595i | ||||
\(772\) | 1272.84 | − | 2204.62i | 0.0593400 | − | 0.102780i | ||||
\(773\) | −13537.8 | + | 23448.2i | −0.629912 | + | 1.09104i | 0.357657 | + | 0.933853i | \(0.383576\pi\) |
−0.987569 | + | 0.157187i | \(0.949758\pi\) | |||||||
\(774\) | −4808.11 | + | 1426.11i | −0.223287 | + | 0.0662281i | ||||
\(775\) | 11128.7 | − | 6425.17i | 0.515814 | − | 0.297805i | ||||
\(776\) | 6377.03 | + | 11045.3i | 0.295003 | + | 0.510960i | ||||
\(777\) | −533.676 | − | 14412.9i | −0.0246403 | − | 0.665457i | ||||
\(778\) | 4163.64 | − | 7211.64i | 0.191869 | − | 0.332326i | ||||
\(779\) | − | 6243.23i | − | 0.287146i | ||||||
\(780\) | −7670.32 | + | 10275.7i | −0.352104 | + | 0.471702i | ||||
\(781\) | −4098.19 | −0.187765 | ||||||||
\(782\) | −5290.76 | − | 9163.87i | −0.241940 | − | 0.419053i | ||||
\(783\) | −1655.19 | − | 9601.55i | −0.0755451 | − | 0.438227i | ||||
\(784\) | −3712.51 | + | 17056.4i | −0.169119 | + | 0.776984i | ||||
\(785\) | −14952.0 | + | 8632.57i | −0.679823 | + | 0.392496i | ||||
\(786\) | −74.9380 | − | 174.336i | −0.00340070 | − | 0.00791141i | ||||
\(787\) | −9407.72 | + | 5431.55i | −0.426110 | + | 0.246015i | −0.697688 | − | 0.716401i | \(-0.745788\pi\) |
0.271578 | + | 0.962416i | \(0.412455\pi\) | |||||||
\(788\) | 3017.93 | − | 1742.40i | 0.136433 | − | 0.0787697i | ||||
\(789\) | −19810.8 | + | 26539.8i | −0.893895 | + | 1.19752i | ||||
\(790\) | 6505.08 | − | 3755.71i | 0.292962 | − | 0.169142i | ||||
\(791\) | 26834.9 | + | 10376.1i | 1.20624 | + | 0.466413i | ||||
\(792\) | 3679.75 | + | 12406.2i | 0.165094 | + | 0.556610i | ||||
\(793\) | 12354.8 | + | 21399.2i | 0.553257 | + | 0.958270i | ||||
\(794\) | −670.953 | −0.0299889 | ||||||||
\(795\) | 5435.56 | + | 12645.3i | 0.242490 | + | 0.564130i | ||||
\(796\) | 11677.3i | 0.519963i | ||||||||
\(797\) | 3869.66 | − | 6702.44i | 0.171983 | − | 0.297883i | −0.767130 | − | 0.641491i | \(-0.778316\pi\) |
0.939113 | + | 0.343608i | \(0.111649\pi\) | |||||||
\(798\) | −3629.43 | − | 1920.02i | −0.161003 | − | 0.0851727i | ||||
\(799\) | −11793.0 | − | 20426.0i | −0.522159 | − | 0.904406i | ||||
\(800\) | 5565.61 | − | 3213.31i | 0.245968 | − | 0.142010i | ||||
\(801\) | −3325.98 | + | 3507.38i | −0.146714 | + | 0.154716i | ||||
\(802\) | 1505.54 | − | 2607.67i | 0.0662874 | − | 0.114813i | ||||
\(803\) | −5422.80 | + | 9392.57i | −0.238314 | + | 0.412773i | ||||
\(804\) | 6921.33 | − | 2975.11i | 0.303602 | − | 0.130503i | ||||
\(805\) | −4394.13 | − | 28188.3i | −0.192388 | − | 1.23417i | ||||
\(806\) | 6437.15 | + | 3716.49i | 0.281314 | + | 0.162417i | ||||
\(807\) | 20403.9 | − | 8770.58i | 0.890028 | − | 0.382576i | ||||
\(808\) | 8.66930i | 0.000377457i | ||||||||
\(809\) | −18111.7 | − | 10456.8i | −0.787114 | − | 0.454440i | 0.0518317 | − | 0.998656i | \(-0.483494\pi\) |
−0.838945 | + | 0.544215i | \(0.816827\pi\) | |||||||
\(810\) | −4737.38 | + | 251.702i | −0.205499 | + | 0.0109184i | ||||
\(811\) | 31359.1i | 1.35779i | 0.734235 | + | 0.678895i | \(0.237541\pi\) | ||||
−0.734235 | + | 0.678895i | \(0.762459\pi\) | |||||||
\(812\) | 8926.13 | + | 3451.43i | 0.385771 | + | 0.149164i | ||||
\(813\) | −10834.9 | − | 1280.41i | −0.467400 | − | 0.0552350i | ||||
\(814\) | 4651.96 | 0.200308 | ||||||||
\(815\) | −15982.3 | − | 27682.2i | −0.686917 | − | 1.18977i | ||||
\(816\) | −2480.77 | + | 20992.4i | −0.106427 | + | 0.900588i | ||||
\(817\) | −12273.0 | − | 7085.84i | −0.525556 | − | 0.303430i | ||||
\(818\) | −8176.22 | −0.349480 | ||||||||
\(819\) | 1534.72 | − | 18995.5i | 0.0654791 | − | 0.810447i | ||||
\(820\) | 7085.34 | 0.301745 | ||||||||
\(821\) | 16357.5 | + | 9444.03i | 0.695349 | + | 0.401460i | 0.805613 | − | 0.592442i | \(-0.201836\pi\) |
−0.110264 | + | 0.993902i | \(0.535169\pi\) | |||||||
\(822\) | 5470.27 | − | 2351.38i | 0.232114 | − | 0.0997735i | ||||
\(823\) | 6742.64 | + | 11678.6i | 0.285582 | + | 0.494642i | 0.972750 | − | 0.231856i | \(-0.0744799\pi\) |
−0.687168 | + | 0.726498i | \(0.741147\pi\) | |||||||
\(824\) | −8695.09 | −0.367606 | ||||||||
\(825\) | 6356.73 | − | 8515.90i | 0.268258 | − | 0.359376i | ||||
\(826\) | 1537.38 | + | 9862.29i | 0.0647607 | + | 0.415439i | ||||
\(827\) | 17296.9i | 0.727292i | 0.931537 | + | 0.363646i | \(0.118468\pi\) | ||||
−0.931537 | + | 0.363646i | \(0.881532\pi\) | |||||||
\(828\) | −25804.7 | − | 24470.1i | −1.08306 | − | 1.02705i | ||||
\(829\) | −4067.89 | − | 2348.59i | −0.170426 | − | 0.0983957i | 0.412360 | − | 0.911021i | \(-0.364704\pi\) |
−0.582787 | + | 0.812625i | \(0.698038\pi\) | |||||||
\(830\) | − | 3714.63i | − | 0.155345i | ||||||
\(831\) | 18366.0 | + | 13709.4i | 0.766677 | + | 0.572290i | ||||
\(832\) | −10218.1 | − | 5899.45i | −0.425782 | − | 0.245825i | ||||
\(833\) | 5831.38 | − | 26791.1i | 0.242551 | − | 1.11435i | ||||
\(834\) | −336.309 | + | 2845.86i | −0.0139633 | + | 0.118158i | ||||
\(835\) | 17470.1 | − | 30259.0i | 0.724043 | − | 1.25408i | ||||
\(836\) | −8810.60 | + | 15260.4i | −0.364499 | + | 0.631330i | ||||
\(837\) | −6216.00 | − | 36058.1i | −0.256698 | − | 1.48907i | ||||
\(838\) | −3152.17 | + | 1819.91i | −0.129940 | + | 0.0750210i | ||||
\(839\) | 1606.27 | + | 2782.14i | 0.0660960 | + | 0.114482i | 0.897180 | − | 0.441666i | \(-0.145612\pi\) |
−0.831084 | + | 0.556147i | \(0.812279\pi\) | |||||||
\(840\) | 4521.76 | − | 8547.53i | 0.185733 | − | 0.351092i | ||||
\(841\) | −9783.04 | + | 16944.7i | −0.401125 | + | 0.694769i | ||||
\(842\) | − | 8777.35i | − | 0.359249i | ||||||
\(843\) | −26171.1 | − | 3092.76i | −1.06925 | − | 0.126359i | ||||
\(844\) | −18522.7 | −0.755425 | ||||||||
\(845\) | −3239.55 | − | 5611.06i | −0.131886 | − | 0.228434i | ||||
\(846\) | 4322.89 | + | 4099.30i | 0.175678 | + | 0.166592i | ||||
\(847\) | −7170.28 | + | 1117.74i | −0.290878 | + | 0.0453434i | ||||
\(848\) | −13415.6 | + | 7745.50i | −0.543270 | + | 0.313657i | ||||
\(849\) | 2851.52 | + | 336.979i | 0.115270 | + | 0.0136220i | ||||
\(850\) | −2550.77 | + | 1472.69i | −0.102930 | + | 0.0594267i | ||||
\(851\) | −22975.1 | + | 13264.7i | −0.925471 | + | 0.534321i | ||||
\(852\) | 3791.05 | + | 448.007i | 0.152440 | + | 0.0180146i | ||||
\(853\) | −34142.7 | + | 19712.3i | −1.37048 | + | 0.791249i | −0.990989 | − | 0.133945i | \(-0.957235\pi\) |
−0.379495 | + | 0.925194i | \(0.623902\pi\) | |||||||
\(854\) | −5633.99 | − | 6992.20i | −0.225751 | − | 0.280173i | ||||
\(855\) | −9727.45 | − | 9224.34i | −0.389090 | − | 0.368966i | ||||
\(856\) | −7263.48 | − | 12580.7i | −0.290024 | − | 0.502336i | ||||
\(857\) | −1759.78 | −0.0701435 | −0.0350718 | − | 0.999385i | \(-0.511166\pi\) | ||||
−0.0350718 | + | 0.999385i | \(0.511166\pi\) | |||||||
\(858\) | 6104.34 | + | 721.380i | 0.242889 | + | 0.0287034i | ||||
\(859\) | − | 5140.46i | − | 0.204179i | −0.994775 | − | 0.102090i | \(-0.967447\pi\) | ||
0.994775 | − | 0.102090i | \(-0.0325529\pi\) | |||||||
\(860\) | 8041.60 | − | 13928.5i | 0.318856 | − | 0.552275i | ||||
\(861\) | −8918.48 | + | 5599.01i | −0.353009 | + | 0.221619i | ||||
\(862\) | 3494.59 | + | 6052.81i | 0.138081 | + | 0.239164i | ||||
\(863\) | −30321.8 | + | 17506.3i | −1.19602 | + | 0.690523i | −0.959666 | − | 0.281144i | \(-0.909286\pi\) |
−0.236355 | + | 0.971667i | \(0.575953\pi\) | |||||||
\(864\) | −3108.70 | − | 18033.1i | −0.122407 | − | 0.710068i | ||||
\(865\) | −9109.06 | + | 15777.4i | −0.358055 | + | 0.620169i | ||||
\(866\) | −217.868 | + | 377.359i | −0.00854903 | + | 0.0148074i | ||||
\(867\) | 900.641 | − | 7621.25i | 0.0352796 | − | 0.298537i | ||||
\(868\) | 33521.6 | + | 12961.7i | 1.31083 | + | 0.506852i | ||||
\(869\) | 41490.8 | + | 23954.7i | 1.61965 | + | 0.935107i | ||||
\(870\) | −1881.86 | − | 1404.73i | −0.0733346 | − | 0.0547410i | ||||
\(871\) | − | 7426.07i | − | 0.288889i | ||||||
\(872\) | 2216.21 | + | 1279.53i | 0.0860668 | + | 0.0496907i | ||||
\(873\) | −21640.1 | − | 20520.9i | −0.838955 | − | 0.795564i | ||||
\(874\) | 7552.60i | 0.292300i | ||||||||
\(875\) | −27751.7 | + | 4326.07i | −1.07220 | + | 0.167140i | ||||
\(876\) | 6043.16 | − | 8095.81i | 0.233081 | − | 0.312251i | ||||
\(877\) | 17341.8 | 0.667721 | 0.333860 | − | 0.942623i | \(-0.391649\pi\) | ||||
0.333860 | + | 0.942623i | \(0.391649\pi\) | |||||||
\(878\) | 2408.06 | + | 4170.88i | 0.0925604 | + | 0.160319i | ||||
\(879\) | 4736.63 | − | 2036.03i | 0.181755 | − | 0.0781268i | ||||
\(880\) | −15919.3 | − | 9191.03i | −0.609819 | − | 0.352079i | ||||
\(881\) | −38797.9 | −1.48369 | −0.741846 | − | 0.670570i | \(-0.766050\pi\) | ||||
−0.741846 | + | 0.670570i | \(0.766050\pi\) | |||||||
\(882\) | 512.169 | + | 6906.55i | 0.0195529 | + | 0.263668i | ||||
\(883\) | 27338.7 | 1.04193 | 0.520963 | − | 0.853579i | \(-0.325573\pi\) | ||||
0.520963 | + | 0.853579i | \(0.325573\pi\) | |||||||
\(884\) | 19631.3 | + | 11334.1i | 0.746914 | + | 0.431231i | ||||
\(885\) | −3824.50 | + | 32363.0i | −0.145265 | + | 1.22923i | ||||
\(886\) | −4382.98 | − | 7591.54i | −0.166195 | − | 0.287859i | ||||
\(887\) | −43410.3 | −1.64326 | −0.821631 | − | 0.570019i | \(-0.806936\pi\) | ||||
−0.821631 | + | 0.570019i | \(0.806936\pi\) | |||||||
\(888\) | −8930.04 | − | 1055.31i | −0.337469 | − | 0.0398804i | ||||
\(889\) | 44376.8 | − | 6917.67i | 1.67418 | − | 0.260980i | ||||
\(890\) | 1165.02i | 0.0438780i | ||||||||
\(891\) | −16498.3 | − | 25365.1i | −0.620331 | − | 0.953719i | ||||
\(892\) | −6390.83 | − | 3689.75i | −0.239889 | − | 0.138500i | ||||
\(893\) | 16834.5i | 0.630847i | ||||||||
\(894\) | −5268.34 | + | 2264.58i | −0.197091 | + | 0.0847192i | ||||
\(895\) | 27794.8 | + | 16047.4i | 1.03808 | + | 0.599334i | ||||
\(896\) | 22023.8 | + | 8515.83i | 0.821163 | + | 0.317516i | ||||
\(897\) | −32205.1 | + | 13843.3i | −1.19877 | + | 0.515288i | ||||
\(898\) | 3786.17 | − | 6557.84i | 0.140697 | − | 0.243695i | ||||
\(899\) | 9056.10 | − | 15685.6i | 0.335971 | − | 0.581919i | ||||
\(900\) | −6811.26 | + | 7182.75i | −0.252269 | + | 0.266028i | ||||
\(901\) | 21072.4 | − | 12166.2i | 0.779160 | − | 0.449848i | ||||
\(902\) | −1698.24 | − | 2941.44i | −0.0626888 | − | 0.108580i | ||||
\(903\) | 884.471 | + | 23886.8i | 0.0325951 | + | 0.880289i | ||||
\(904\) | 8968.96 | − | 15534.7i | 0.329981 | − | 0.571545i | ||||
\(905\) | 14346.0i | 0.526938i | ||||||||
\(906\) | −1956.33 | − | 4551.21i | −0.0717380 | − | 0.166892i | ||||
\(907\) | −5130.22 | −0.187813 | −0.0939064 | − | 0.995581i | \(-0.529935\pi\) | ||||
−0.0939064 | + | 0.995581i | \(0.529935\pi\) | |||||||
\(908\) | −2245.12 | − | 3888.67i | −0.0820562 | − | 0.142125i | ||||
\(909\) | −5.76441 | − | 19.4346i | −0.000210334 | − | 0.000709136i | ||||
\(910\) | −2881.93 | − | 3576.69i | −0.104983 | − | 0.130292i | ||||
\(911\) | 20476.8 | − | 11822.3i | 0.744707 | − | 0.429957i | −0.0790715 | − | 0.996869i | \(-0.525196\pi\) |
0.823778 | + | 0.566912i | \(0.191862\pi\) | |||||||
\(912\) | 9025.12 | − | 12090.6i | 0.327688 | − | 0.438993i | ||||
\(913\) | 20518.5 | − | 11846.3i | 0.743770 | − | 0.429416i | ||||
\(914\) | 4568.86 | − | 2637.83i | 0.165344 | − | 0.0954614i | ||||
\(915\) | −11577.7 | − | 26934.5i | −0.418303 | − | 0.973143i | ||||
\(916\) | 8346.43 | − | 4818.81i | 0.301063 | − | 0.173819i | ||||
\(917\) | −893.639 | + | 139.305i | −0.0321816 | + | 0.00501663i | ||||
\(918\) | 1424.74 | + | 8264.72i | 0.0512238 | + | 0.297142i | ||||
\(919\) | −22890.0 | − | 39646.7i | −0.821623 | − | 1.42309i | −0.904473 | − | 0.426531i | \(-0.859735\pi\) |
0.0828494 | − | 0.996562i | \(-0.473598\pi\) | |||||||
\(920\) | −17786.8 | −0.637407 | ||||||||
\(921\) | −798.290 | + | 1069.44i | −0.0285608 | + | 0.0382620i | ||||
\(922\) | 1945.59i | 0.0694953i | ||||||||
\(923\) | 1881.45 | − | 3258.77i | 0.0670951 | − | 0.116212i | ||||
\(924\) | 29701.0 | − | 1099.76i | 1.05746 | − | 0.0391552i | ||||
\(925\) | 3692.23 | + | 6395.13i | 0.131243 | + | 0.227319i | ||||
\(926\) | −6293.56 | + | 3633.59i | −0.223347 | + | 0.128949i | ||||
\(927\) | 19492.4 | − | 5781.55i | 0.690630 | − | 0.204845i | ||||
\(928\) | 4529.07 | − | 7844.57i | 0.160209 | − | 0.277490i | ||||
\(929\) | −14332.6 | + | 24824.8i | −0.506176 | + | 0.876723i | 0.493798 | + | 0.869577i | \(0.335608\pi\) |
−0.999974 | + | 0.00714671i | \(0.997725\pi\) | |||||||
\(930\) | −7067.24 | − | 5275.37i | −0.249187 | − | 0.186007i | ||||
\(931\) | −13165.7 | + | 14479.2i | −0.463466 | + | 0.509708i | ||||
\(932\) | 27528.6 | + | 15893.6i | 0.967521 | + | 0.558598i | ||||
\(933\) | 441.189 | − | 3733.36i | 0.0154811 | − | 0.131002i | ||||
\(934\) | − | 6340.49i | − | 0.222128i | ||||||
\(935\) | 25005.1 | + | 14436.7i | 0.874604 | + | 0.504953i | ||||
\(936\) | −11554.4 | − | 2769.57i | −0.403492 | − | 0.0967160i | ||||
\(937\) | 20013.0i | 0.697754i | 0.937168 | + | 0.348877i | \(0.113437\pi\) | ||||
−0.937168 | + | 0.348877i | \(0.886563\pi\) | |||||||
\(938\) | 415.659 | + | 2666.45i | 0.0144688 | + | 0.0928174i | ||||
\(939\) | −14126.7 | − | 32864.4i | −0.490954 | − | 1.14216i | ||||
\(940\) | −19105.2 | −0.662919 | ||||||||
\(941\) | 11943.4 | + | 20686.6i | 0.413757 | + | 0.716647i | 0.995297 | − | 0.0968701i | \(-0.0308831\pi\) |
−0.581540 | + | 0.813517i | \(0.697550\pi\) | |||||||
\(942\) | −6177.97 | − | 4611.57i | −0.213683 | − | 0.159504i | ||||
\(943\) | 16774.6 | + | 9684.80i | 0.579273 | + | 0.334444i | ||||
\(944\) | −36677.0 | −1.26455 | ||||||||
\(945\) | −4453.30 | + | 22168.2i | −0.153297 | + | 0.763103i | ||||
\(946\) | −7709.77 | −0.264975 | ||||||||
\(947\) | 8161.37 | + | 4711.97i | 0.280052 | + | 0.161688i | 0.633447 | − | 0.773786i | \(-0.281640\pi\) |
−0.353395 | + | 0.935474i | \(0.614973\pi\) | |||||||
\(948\) | −35762.5 | − | 26695.1i | −1.22522 | − | 0.914573i | ||||
\(949\) | −4979.14 | − | 8624.13i | −0.170316 | − | 0.294996i | ||||
\(950\) | 2102.27 | 0.0717964 | ||||||||
\(951\) | −753.838 | − | 1753.73i | −0.0257044 | − | 0.0597988i | ||||
\(952\) | −15944.1 | − | 6165.05i | −0.542808 | − | 0.209885i | ||||
\(953\) | 42523.4i | 1.44540i | 0.691161 | + | 0.722701i | \(0.257100\pi\) | ||||
−0.691161 | + | 0.722701i | \(0.742900\pi\) | |||||||
\(954\) | −4229.03 | + | 4459.69i | −0.143522 | + | 0.151350i | ||||
\(955\) | 27637.2 | + | 15956.3i | 0.936459 | + | 0.540665i | ||||
\(956\) | − | 17825.2i | − | 0.603041i | ||||||
\(957\) | 1757.81 | − | 14874.7i | 0.0593751 | − | 0.502434i | ||||
\(958\) | −12759.2 | − | 7366.50i | −0.430302 | − | 0.248435i | ||||
\(959\) | −4371.06 | − | 28040.3i | −0.147183 | − | 0.944180i | ||||
\(960\) | 11218.3 | + | 8373.97i | 0.377156 | + | 0.281530i | ||||
\(961\) | 19114.2 | − | 33106.8i | 0.641611 | − | 1.11130i | ||||
\(962\) | −2135.68 | + | 3699.11i | −0.0715771 | + | 0.123975i | ||||
\(963\) | 24648.2 | + | 23373.4i | 0.824796 | + | 0.782137i | ||||
\(964\) | 5271.92 | − | 3043.75i | 0.176138 | − | 0.101693i | ||||
\(965\) | 1488.62 | + | 2578.37i | 0.0496584 | + | 0.0860109i | ||||
\(966\) | 10788.9 | − | 6773.27i | 0.359345 | − | 0.225597i | ||||
\(967\) | −2110.16 | + | 3654.91i | −0.0701739 | + | 0.121545i | −0.898977 | − | 0.437995i | \(-0.855689\pi\) |
0.828803 | + | 0.559540i | \(0.189022\pi\) | |||||||
\(968\) | 4524.45i | 0.150229i | ||||||||
\(969\) | −14176.1 | + | 18991.3i | −0.469971 | + | 0.629605i | ||||
\(970\) | −7188.01 | −0.237931 | ||||||||
\(971\) | 5026.42 | + | 8706.01i | 0.166123 | + | 0.287733i | 0.937054 | − | 0.349186i | \(-0.113542\pi\) |
−0.770931 | + | 0.636919i | \(0.780208\pi\) | |||||||
\(972\) | 12489.0 | + | 25267.7i | 0.412123 | + | 0.833807i | ||||
\(973\) | 12739.1 | + | 4925.78i | 0.419730 | + | 0.162295i | ||||
\(974\) | −9249.51 | + | 5340.21i | −0.304285 | + | 0.175679i | ||||
\(975\) | 3853.28 | + | 8964.29i | 0.126568 | + | 0.294448i | ||||
\(976\) | 28575.1 | − | 16497.9i | 0.937160 | − | 0.541070i | ||||
\(977\) | −18918.6 | + | 10922.7i | −0.619509 | + | 0.357674i | −0.776678 | − | 0.629898i | \(-0.783097\pi\) |
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(978\) | 8537.87 | − | 11437.9i | 0.279152 | − | 0.373971i | ||||
\(979\) | −6435.19 | + | 3715.36i | −0.210081 | + | 0.121290i | ||||
\(980\) | −16432.3 | − | 14941.5i | −0.535622 | − | 0.487029i | ||||
\(981\) | −5819.01 | − | 1394.80i | −0.189385 | − | 0.0453951i | ||||
\(982\) | 3924.84 | + | 6798.02i | 0.127542 | + | 0.220910i | ||||
\(983\) | 44724.2 | 1.45115 | 0.725575 | − | 0.688143i | \(-0.241574\pi\) | ||||
0.725575 | + | 0.688143i | \(0.241574\pi\) | |||||||
\(984\) | 2592.73 | + | 6031.73i | 0.0839970 | + | 0.195411i | ||||
\(985\) | 4075.58i | 0.131836i | ||||||||
\(986\) | −2075.71 | + | 3595.23i | −0.0670426 | + | 0.116121i | ||||
\(987\) | 24048.2 | − | 15097.4i | 0.775544 | − | 0.486886i | ||||
\(988\) | −8089.78 | − | 14011.9i | −0.260496 | − | 0.451192i | ||||
\(989\) | 38077.0 | − | 21983.8i | 1.22425 | − | 0.706818i | ||||
\(990\) | −7092.14 | − | 1699.97i | −0.227680 | − | 0.0545743i | ||||
\(991\) | −8670.77 | + | 15018.2i | −0.277937 | + | 0.481402i | −0.970872 | − | 0.239599i | \(-0.922984\pi\) |
0.692935 | + | 0.721000i | \(0.256317\pi\) | |||||||
\(992\) | 17008.7 | − | 29459.9i | 0.544381 | − | 0.942896i | ||||
\(993\) | −18263.4 | + | 7850.49i | −0.583658 | + | 0.250884i | ||||
\(994\) | −493.163 | + | 1275.43i | −0.0157366 | + | 0.0406982i | ||||
\(995\) | −11827.2 | − | 6828.46i | −0.376833 | − | 0.217565i | ||||
\(996\) | −20275.7 | + | 8715.45i | −0.645040 | + | 0.277269i | ||||
\(997\) | 56296.2i | 1.78828i | 0.447783 | + | 0.894142i | \(0.352214\pi\) | ||||
−0.447783 | + | 0.894142i | \(0.647786\pi\) | |||||||
\(998\) | 10898.5 | + | 6292.25i | 0.345677 | + | 0.199577i | ||||
\(999\) | 20720.8 | − | 3572.03i | 0.656234 | − | 0.113127i |
(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 | 63.4.s.a.59.12 | yes | 44 | |
3.2 | odd | 2 | 189.4.s.a.17.11 | 44 | |||
7.5 | odd | 6 | 63.4.i.a.5.11 | ✓ | 44 | ||
9.2 | odd | 6 | 63.4.i.a.38.12 | yes | 44 | ||
9.7 | even | 3 | 189.4.i.a.143.11 | 44 | |||
21.5 | even | 6 | 189.4.i.a.152.12 | 44 | |||
63.47 | even | 6 | inner | 63.4.s.a.47.12 | yes | 44 | |
63.61 | odd | 6 | 189.4.s.a.89.11 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.11 | ✓ | 44 | 7.5 | odd | 6 | ||
63.4.i.a.38.12 | yes | 44 | 9.2 | odd | 6 | ||
63.4.s.a.47.12 | yes | 44 | 63.47 | even | 6 | inner | |
63.4.s.a.59.12 | yes | 44 | 1.1 | even | 1 | trivial | |
189.4.i.a.143.11 | 44 | 9.7 | even | 3 | |||
189.4.i.a.152.12 | 44 | 21.5 | even | 6 | |||
189.4.s.a.17.11 | 44 | 3.2 | odd | 2 | |||
189.4.s.a.89.11 | 44 | 63.61 | odd | 6 |