Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,5,Mod(97,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.97");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.3907691467\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.97 |
Dual form | 294.5.c.a.97.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82843 | −0.707107 | ||||||||
\(3\) | − 5.19615i | − 0.577350i | ||||||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | 23.9515i | 0.958062i | 0.877798 | + | 0.479031i | \(0.159012\pi\) | ||||
−0.877798 | + | 0.479031i | \(0.840988\pi\) | |||||||
\(6\) | 14.6969i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −22.6274 | −0.353553 | ||||||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | − 67.7452i | − 0.677452i | ||||||||
\(11\) | 97.9706 | 0.809674 | 0.404837 | − | 0.914389i | \(-0.367328\pi\) | ||||
0.404837 | + | 0.914389i | \(0.367328\pi\) | |||||||
\(12\) | − 41.5692i | − 0.288675i | ||||||||
\(13\) | 104.211i | 0.616636i | 0.951283 | + | 0.308318i | \(0.0997661\pi\) | ||||
−0.951283 | + | 0.308318i | \(0.900234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 124.456 | 0.553137 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 107.676i | 0.372580i | 0.982495 | + | 0.186290i | \(0.0596464\pi\) | ||||
−0.982495 | + | 0.186290i | \(0.940354\pi\) | |||||||
\(18\) | 76.3675 | 0.235702 | ||||||||
\(19\) | − 38.3935i | − 0.106353i | −0.998585 | − | 0.0531767i | \(-0.983065\pi\) | ||||
0.998585 | − | 0.0531767i | \(-0.0169346\pi\) | |||||||
\(20\) | 191.612i | 0.479031i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −277.103 | −0.572526 | ||||||||
\(23\) | −1021.50 | −1.93100 | −0.965500 | − | 0.260404i | \(-0.916144\pi\) | ||||
−0.965500 | + | 0.260404i | \(0.916144\pi\) | |||||||
\(24\) | 117.576i | 0.204124i | ||||||||
\(25\) | 51.3238 | 0.0821181 | ||||||||
\(26\) | − 294.755i | − 0.436027i | ||||||||
\(27\) | 140.296i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 621.603 | 0.739124 | 0.369562 | − | 0.929206i | \(-0.379508\pi\) | ||||
0.369562 | + | 0.929206i | \(0.379508\pi\) | |||||||
\(30\) | −352.014 | −0.391127 | ||||||||
\(31\) | − 1519.14i | − 1.58079i | −0.612600 | − | 0.790393i | \(-0.709876\pi\) | ||||
0.612600 | − | 0.790393i | \(-0.290124\pi\) | |||||||
\(32\) | −181.019 | −0.176777 | ||||||||
\(33\) | − 509.070i | − 0.467466i | ||||||||
\(34\) | − 304.553i | − 0.263454i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −216.000 | −0.166667 | ||||||||
\(37\) | −562.235 | −0.410691 | −0.205345 | − | 0.978690i | \(-0.565832\pi\) | ||||
−0.205345 | + | 0.978690i | \(0.565832\pi\) | |||||||
\(38\) | 108.593i | 0.0752031i | ||||||||
\(39\) | 541.499 | 0.356015 | ||||||||
\(40\) | − 541.961i | − 0.338726i | ||||||||
\(41\) | 1023.20i | 0.608684i | 0.952563 | + | 0.304342i | \(0.0984365\pi\) | ||||
−0.952563 | + | 0.304342i | \(0.901563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3382.41 | −1.82932 | −0.914658 | − | 0.404228i | \(-0.867540\pi\) | ||||
−0.914658 | + | 0.404228i | \(0.867540\pi\) | |||||||
\(44\) | 783.765 | 0.404837 | ||||||||
\(45\) | − 646.692i | − 0.319354i | ||||||||
\(46\) | 2889.23 | 1.36542 | ||||||||
\(47\) | 3945.03i | 1.78589i | 0.450165 | + | 0.892945i | \(0.351365\pi\) | ||||
−0.450165 | + | 0.892945i | \(0.648635\pi\) | |||||||
\(48\) | − 332.554i | − 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −145.166 | −0.0580663 | ||||||||
\(51\) | 559.499 | 0.215109 | ||||||||
\(52\) | 833.692i | 0.308318i | ||||||||
\(53\) | 2190.60 | 0.779851 | 0.389925 | − | 0.920846i | \(-0.372501\pi\) | ||||
0.389925 | + | 0.920846i | \(0.372501\pi\) | |||||||
\(54\) | − 396.817i | − 0.136083i | ||||||||
\(55\) | 2346.55i | 0.775718i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −199.499 | −0.0614031 | ||||||||
\(58\) | −1758.16 | −0.522639 | ||||||||
\(59\) | 2934.87i | 0.843111i | 0.906803 | + | 0.421556i | \(0.138516\pi\) | ||||
−0.906803 | + | 0.421556i | \(0.861484\pi\) | |||||||
\(60\) | 995.647 | 0.276569 | ||||||||
\(61\) | − 665.346i | − 0.178809i | −0.995995 | − | 0.0894043i | \(-0.971504\pi\) | ||||
0.995995 | − | 0.0894043i | \(-0.0284963\pi\) | |||||||
\(62\) | 4296.76i | 1.11778i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | −2496.03 | −0.590775 | ||||||||
\(66\) | 1439.87i | 0.330548i | ||||||||
\(67\) | −5925.38 | −1.31998 | −0.659989 | − | 0.751275i | \(-0.729439\pi\) | ||||
−0.659989 | + | 0.751275i | \(0.729439\pi\) | |||||||
\(68\) | 861.405i | 0.186290i | ||||||||
\(69\) | 5307.86i | 1.11486i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4494.41 | −0.891571 | −0.445785 | − | 0.895140i | \(-0.647076\pi\) | ||||
−0.445785 | + | 0.895140i | \(0.647076\pi\) | |||||||
\(72\) | 610.940 | 0.117851 | ||||||||
\(73\) | 8968.93i | 1.68304i | 0.540225 | + | 0.841521i | \(0.318339\pi\) | ||||
−0.540225 | + | 0.841521i | \(0.681661\pi\) | |||||||
\(74\) | 1590.24 | 0.290402 | ||||||||
\(75\) | − 266.686i | − 0.0474109i | ||||||||
\(76\) | − 307.148i | − 0.0531767i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1531.59 | −0.251741 | ||||||||
\(79\) | −10446.8 | −1.67390 | −0.836951 | − | 0.547277i | \(-0.815664\pi\) | ||||
−0.836951 | + | 0.547277i | \(0.815664\pi\) | |||||||
\(80\) | 1532.90i | 0.239515i | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | − 2894.04i | − 0.430405i | ||||||||
\(83\) | − 1269.28i | − 0.184247i | −0.995748 | − | 0.0921234i | \(-0.970635\pi\) | ||||
0.995748 | − | 0.0921234i | \(-0.0293654\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2579.00 | −0.356954 | ||||||||
\(86\) | 9566.89 | 1.29352 | ||||||||
\(87\) | − 3229.94i | − 0.426733i | ||||||||
\(88\) | −2216.82 | −0.286263 | ||||||||
\(89\) | 3604.36i | 0.455038i | 0.973774 | + | 0.227519i | \(0.0730614\pi\) | ||||
−0.973774 | + | 0.227519i | \(0.926939\pi\) | |||||||
\(90\) | 1829.12i | 0.225817i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8171.99 | −0.965500 | ||||||||
\(93\) | −7893.66 | −0.912667 | ||||||||
\(94\) | − 11158.2i | − 1.26282i | ||||||||
\(95\) | 919.584 | 0.101893 | ||||||||
\(96\) | 940.604i | 0.102062i | ||||||||
\(97\) | 1950.53i | 0.207304i | 0.994614 | + | 0.103652i | \(0.0330529\pi\) | ||||
−0.994614 | + | 0.103652i | \(0.966947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2645.21 | −0.269891 | ||||||||
\(100\) | 410.590 | 0.0410590 | ||||||||
\(101\) | 11326.2i | 1.11031i | 0.831748 | + | 0.555153i | \(0.187340\pi\) | ||||
−0.831748 | + | 0.555153i | \(0.812660\pi\) | |||||||
\(102\) | −1582.50 | −0.152105 | ||||||||
\(103\) | 16328.9i | 1.53915i | 0.638555 | + | 0.769576i | \(0.279532\pi\) | ||||
−0.638555 | + | 0.769576i | \(0.720468\pi\) | |||||||
\(104\) | − 2358.04i | − 0.218014i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6195.95 | −0.551438 | ||||||||
\(107\) | 4396.46 | 0.384004 | 0.192002 | − | 0.981395i | \(-0.438502\pi\) | ||||
0.192002 | + | 0.981395i | \(0.438502\pi\) | |||||||
\(108\) | 1122.37i | 0.0962250i | ||||||||
\(109\) | −14697.8 | −1.23708 | −0.618541 | − | 0.785753i | \(-0.712276\pi\) | ||||
−0.618541 | + | 0.785753i | \(0.712276\pi\) | |||||||
\(110\) | − 6637.03i | − 0.548515i | ||||||||
\(111\) | 2921.46i | 0.237112i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2124.36 | 0.166368 | 0.0831842 | − | 0.996534i | \(-0.473491\pi\) | ||||
0.0831842 | + | 0.996534i | \(0.473491\pi\) | |||||||
\(114\) | 564.268 | 0.0434186 | ||||||||
\(115\) | − 24466.5i | − 1.85002i | ||||||||
\(116\) | 4972.82 | 0.369562 | ||||||||
\(117\) | − 2813.71i | − 0.205545i | ||||||||
\(118\) | − 8301.07i | − 0.596170i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2816.11 | −0.195563 | ||||||||
\(121\) | −5042.77 | −0.344428 | ||||||||
\(122\) | 1881.88i | 0.126437i | ||||||||
\(123\) | 5316.69 | 0.351424 | ||||||||
\(124\) | − 12153.1i | − 0.790393i | ||||||||
\(125\) | 16199.0i | 1.03674i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8498.07 | 0.526881 | 0.263441 | − | 0.964676i | \(-0.415143\pi\) | ||||
0.263441 | + | 0.964676i | \(0.415143\pi\) | |||||||
\(128\) | −1448.15 | −0.0883883 | ||||||||
\(129\) | 17575.5i | 1.05616i | ||||||||
\(130\) | 7059.83 | 0.417741 | ||||||||
\(131\) | − 14472.3i | − 0.843324i | −0.906753 | − | 0.421662i | \(-0.861447\pi\) | ||||
0.906753 | − | 0.421662i | \(-0.138553\pi\) | |||||||
\(132\) | − 4072.56i | − 0.233733i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 16759.5 | 0.933366 | ||||||||
\(135\) | −3360.31 | −0.184379 | ||||||||
\(136\) | − 2436.42i | − 0.131727i | ||||||||
\(137\) | 12855.2 | 0.684915 | 0.342458 | − | 0.939533i | \(-0.388741\pi\) | ||||
0.342458 | + | 0.939533i | \(0.388741\pi\) | |||||||
\(138\) | − 15012.9i | − 0.788327i | ||||||||
\(139\) | − 5009.46i | − 0.259275i | −0.991561 | − | 0.129638i | \(-0.958619\pi\) | ||||
0.991561 | − | 0.129638i | \(-0.0413814\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20499.0 | 1.03108 | ||||||||
\(142\) | 12712.1 | 0.630436 | ||||||||
\(143\) | 10209.7i | 0.499274i | ||||||||
\(144\) | −1728.00 | −0.0833333 | ||||||||
\(145\) | 14888.3i | 0.708126i | ||||||||
\(146\) | − 25368.0i | − 1.19009i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4497.88 | −0.205345 | ||||||||
\(149\) | 25398.9 | 1.14404 | 0.572022 | − | 0.820238i | \(-0.306159\pi\) | ||||
0.572022 | + | 0.820238i | \(0.306159\pi\) | |||||||
\(150\) | 754.303i | 0.0335246i | ||||||||
\(151\) | −18308.8 | −0.802981 | −0.401491 | − | 0.915863i | \(-0.631508\pi\) | ||||
−0.401491 | + | 0.915863i | \(0.631508\pi\) | |||||||
\(152\) | 868.747i | 0.0376016i | ||||||||
\(153\) | − 2907.24i | − 0.124193i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 36385.6 | 1.51449 | ||||||||
\(156\) | 4331.99 | 0.178007 | ||||||||
\(157\) | − 35244.4i | − 1.42985i | −0.699200 | − | 0.714926i | \(-0.746460\pi\) | ||||
0.699200 | − | 0.714926i | \(-0.253540\pi\) | |||||||
\(158\) | 29548.1 | 1.18363 | ||||||||
\(159\) | − 11382.7i | − 0.450247i | ||||||||
\(160\) | − 4335.69i | − 0.169363i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2061.92 | −0.0785674 | ||||||||
\(163\) | 145.939 | 0.00549281 | 0.00274641 | − | 0.999996i | \(-0.499126\pi\) | ||||
0.00274641 | + | 0.999996i | \(0.499126\pi\) | |||||||
\(164\) | 8185.58i | 0.304342i | ||||||||
\(165\) | 12193.0 | 0.447861 | ||||||||
\(166\) | 3590.05i | 0.130282i | ||||||||
\(167\) | − 31314.1i | − 1.12281i | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||||
0.827541 | − | 0.561405i | \(-0.189739\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17701.0 | 0.619760 | ||||||||
\(170\) | 7294.50 | 0.252405 | ||||||||
\(171\) | 1036.63i | 0.0354511i | ||||||||
\(172\) | −27059.3 | −0.914658 | ||||||||
\(173\) | 40115.8i | 1.34037i | 0.742196 | + | 0.670183i | \(0.233784\pi\) | ||||
−0.742196 | + | 0.670183i | \(0.766216\pi\) | |||||||
\(174\) | 9135.66i | 0.301746i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6270.12 | 0.202419 | ||||||||
\(177\) | 15250.0 | 0.486771 | ||||||||
\(178\) | − 10194.7i | − 0.321760i | ||||||||
\(179\) | −50154.5 | −1.56532 | −0.782661 | − | 0.622448i | \(-0.786138\pi\) | ||||
−0.782661 | + | 0.622448i | \(0.786138\pi\) | |||||||
\(180\) | − 5173.53i | − 0.159677i | ||||||||
\(181\) | − 63974.3i | − 1.95276i | −0.216069 | − | 0.976378i | \(-0.569323\pi\) | ||||
0.216069 | − | 0.976378i | \(-0.430677\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3457.24 | −0.103235 | ||||||||
\(184\) | 23113.9 | 0.682711 | ||||||||
\(185\) | − 13466.4i | − 0.393467i | ||||||||
\(186\) | 22326.6 | 0.645353 | ||||||||
\(187\) | 10549.0i | 0.301668i | ||||||||
\(188\) | 31560.3i | 0.892945i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2600.98 | −0.0720492 | ||||||||
\(191\) | −42768.9 | −1.17236 | −0.586180 | − | 0.810181i | \(-0.699369\pi\) | ||||
−0.586180 | + | 0.810181i | \(0.699369\pi\) | |||||||
\(192\) | − 2660.43i | − 0.0721688i | ||||||||
\(193\) | −8772.58 | −0.235512 | −0.117756 | − | 0.993043i | \(-0.537570\pi\) | ||||
−0.117756 | + | 0.993043i | \(0.537570\pi\) | |||||||
\(194\) | − 5516.92i | − 0.146586i | ||||||||
\(195\) | 12969.7i | 0.341084i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −32825.0 | −0.845808 | −0.422904 | − | 0.906174i | \(-0.638989\pi\) | ||||
−0.422904 | + | 0.906174i | \(0.638989\pi\) | |||||||
\(198\) | 7481.77 | 0.190842 | ||||||||
\(199\) | − 26464.2i | − 0.668271i | −0.942525 | − | 0.334136i | \(-0.891556\pi\) | ||||
0.942525 | − | 0.334136i | \(-0.108444\pi\) | |||||||
\(200\) | −1161.33 | −0.0290331 | ||||||||
\(201\) | 30789.2i | 0.762090i | ||||||||
\(202\) | − 32035.4i | − 0.785106i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4475.99 | 0.107555 | ||||||||
\(205\) | −24507.2 | −0.583157 | ||||||||
\(206\) | − 46185.0i | − 1.08834i | ||||||||
\(207\) | 27580.5 | 0.643666 | ||||||||
\(208\) | 6669.53i | 0.154159i | ||||||||
\(209\) | − 3761.44i | − 0.0861115i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 67056.3 | 1.50617 | 0.753087 | − | 0.657921i | \(-0.228564\pi\) | ||||
0.753087 | + | 0.657921i | \(0.228564\pi\) | |||||||
\(212\) | 17524.8 | 0.389925 | ||||||||
\(213\) | 23353.6i | 0.514749i | ||||||||
\(214\) | −12435.1 | −0.271532 | ||||||||
\(215\) | − 81013.8i | − 1.75260i | ||||||||
\(216\) | − 3174.54i | − 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 41571.6 | 0.874749 | ||||||||
\(219\) | 46603.9 | 0.971705 | ||||||||
\(220\) | 18772.4i | 0.387859i | ||||||||
\(221\) | −11221.0 | −0.229746 | ||||||||
\(222\) | − 8263.14i | − 0.167664i | ||||||||
\(223\) | − 56260.1i | − 1.13133i | −0.824634 | − | 0.565666i | \(-0.808619\pi\) | ||||
0.824634 | − | 0.565666i | \(-0.191381\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1385.74 | −0.0273727 | ||||||||
\(226\) | −6008.59 | −0.117640 | ||||||||
\(227\) | 61148.1i | 1.18667i | 0.804954 | + | 0.593337i | \(0.202190\pi\) | ||||
−0.804954 | + | 0.593337i | \(0.797810\pi\) | |||||||
\(228\) | −1595.99 | −0.0307016 | ||||||||
\(229\) | − 33803.7i | − 0.644605i | −0.946637 | − | 0.322303i | \(-0.895543\pi\) | ||||
0.946637 | − | 0.322303i | \(-0.104457\pi\) | |||||||
\(230\) | 69201.6i | 1.30816i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14065.3 | −0.261320 | ||||||||
\(233\) | 8687.26 | 0.160019 | 0.0800094 | − | 0.996794i | \(-0.474505\pi\) | ||||
0.0800094 | + | 0.996794i | \(0.474505\pi\) | |||||||
\(234\) | 7958.37i | 0.145342i | ||||||||
\(235\) | −94489.6 | −1.71099 | ||||||||
\(236\) | 23479.0i | 0.421556i | ||||||||
\(237\) | 54283.3i | 0.966428i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15715.0 | −0.275118 | −0.137559 | − | 0.990494i | \(-0.543926\pi\) | ||||
−0.137559 | + | 0.990494i | \(0.543926\pi\) | |||||||
\(240\) | 7965.17 | 0.138284 | ||||||||
\(241\) | − 5478.82i | − 0.0943307i | −0.998887 | − | 0.0471654i | \(-0.984981\pi\) | ||||
0.998887 | − | 0.0471654i | \(-0.0150188\pi\) | |||||||
\(242\) | 14263.1 | 0.243547 | ||||||||
\(243\) | − 3788.00i | − 0.0641500i | ||||||||
\(244\) | − 5322.77i | − 0.0894043i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15037.9 | −0.248494 | ||||||||
\(247\) | 4001.05 | 0.0655813 | ||||||||
\(248\) | 34374.1i | 0.558892i | ||||||||
\(249\) | −6595.35 | −0.106375 | ||||||||
\(250\) | − 45817.7i | − 0.733083i | ||||||||
\(251\) | 24350.9i | 0.386516i | 0.981148 | + | 0.193258i | \(0.0619054\pi\) | ||||
−0.981148 | + | 0.193258i | \(0.938095\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −100077. | −1.56348 | ||||||||
\(254\) | −24036.2 | −0.372561 | ||||||||
\(255\) | 13400.9i | 0.206088i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | − 11606.7i | − 0.175729i | −0.996132 | − | 0.0878647i | \(-0.971996\pi\) | ||||
0.996132 | − | 0.0878647i | \(-0.0280043\pi\) | |||||||
\(258\) | − 49711.0i | − 0.746815i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −19968.2 | −0.295388 | ||||||||
\(261\) | −16783.3 | −0.246375 | ||||||||
\(262\) | 40933.8i | 0.596320i | ||||||||
\(263\) | 120668. | 1.74453 | 0.872266 | − | 0.489031i | \(-0.162649\pi\) | ||||
0.872266 | + | 0.489031i | \(0.162649\pi\) | |||||||
\(264\) | 11518.9i | 0.165274i | ||||||||
\(265\) | 52468.3i | 0.747145i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18728.8 | 0.262716 | ||||||||
\(268\) | −47403.1 | −0.659989 | ||||||||
\(269\) | − 27246.6i | − 0.376537i | −0.982118 | − | 0.188269i | \(-0.939712\pi\) | ||||
0.982118 | − | 0.188269i | \(-0.0602876\pi\) | |||||||
\(270\) | 9504.39 | 0.130376 | ||||||||
\(271\) | 97043.3i | 1.32138i | 0.750660 | + | 0.660689i | \(0.229736\pi\) | ||||
−0.750660 | + | 0.660689i | \(0.770264\pi\) | |||||||
\(272\) | 6891.24i | 0.0931450i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −36359.9 | −0.484308 | ||||||||
\(275\) | 5028.22 | 0.0664889 | ||||||||
\(276\) | 42462.9i | 0.557432i | ||||||||
\(277\) | 29752.8 | 0.387765 | 0.193882 | − | 0.981025i | \(-0.437892\pi\) | ||||
0.193882 | + | 0.981025i | \(0.437892\pi\) | |||||||
\(278\) | 14168.9i | 0.183335i | ||||||||
\(279\) | 41016.7i | 0.526929i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −122275. | −1.54855 | −0.774276 | − | 0.632849i | \(-0.781886\pi\) | ||||
−0.774276 | + | 0.632849i | \(0.781886\pi\) | |||||||
\(282\) | −57979.9 | −0.729087 | ||||||||
\(283\) | − 60700.7i | − 0.757916i | −0.925414 | − | 0.378958i | \(-0.876282\pi\) | ||||
0.925414 | − | 0.378958i | \(-0.123718\pi\) | |||||||
\(284\) | −35955.3 | −0.445785 | ||||||||
\(285\) | − 4778.30i | − 0.0588280i | ||||||||
\(286\) | − 28877.3i | − 0.353040i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4887.52 | 0.0589256 | ||||||||
\(289\) | 71927.0 | 0.861184 | ||||||||
\(290\) | − 42110.6i | − 0.500721i | ||||||||
\(291\) | 10135.2 | 0.119687 | ||||||||
\(292\) | 71751.4i | 0.841521i | ||||||||
\(293\) | 29557.4i | 0.344296i | 0.985071 | + | 0.172148i | \(0.0550707\pi\) | ||||
−0.985071 | + | 0.172148i | \(0.944929\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −70294.7 | −0.807752 | ||||||||
\(296\) | 12721.9 | 0.145201 | ||||||||
\(297\) | 13744.9i | 0.155822i | ||||||||
\(298\) | −71839.0 | −0.808961 | ||||||||
\(299\) | − 106452.i | − 1.19072i | ||||||||
\(300\) | − 2133.49i | − 0.0237055i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 51785.0 | 0.567794 | ||||||||
\(303\) | 58852.9 | 0.641036 | ||||||||
\(304\) | − 2457.19i | − 0.0265883i | ||||||||
\(305\) | 15936.1 | 0.171310 | ||||||||
\(306\) | 8222.92i | 0.0878179i | ||||||||
\(307\) | 107567.i | 1.14131i | 0.821191 | + | 0.570654i | \(0.193310\pi\) | ||||
−0.821191 | + | 0.570654i | \(0.806690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 84847.3 | 0.888630 | ||||||||
\(310\) | −102914. | −1.07091 | ||||||||
\(311\) | 43371.8i | 0.448421i | 0.974541 | + | 0.224211i | \(0.0719804\pi\) | ||||
−0.974541 | + | 0.224211i | \(0.928020\pi\) | |||||||
\(312\) | −12252.7 | −0.125870 | ||||||||
\(313\) | 107746.i | 1.09980i | 0.835230 | + | 0.549900i | \(0.185334\pi\) | ||||
−0.835230 | + | 0.549900i | \(0.814666\pi\) | |||||||
\(314\) | 99686.3i | 1.01106i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −83574.6 | −0.836951 | ||||||||
\(317\) | −155994. | −1.55235 | −0.776174 | − | 0.630519i | \(-0.782842\pi\) | ||||
−0.776174 | + | 0.630519i | \(0.782842\pi\) | |||||||
\(318\) | 32195.1i | 0.318373i | ||||||||
\(319\) | 60898.8 | 0.598449 | ||||||||
\(320\) | 12263.2i | 0.119758i | ||||||||
\(321\) | − 22844.7i | − 0.221705i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4134.05 | 0.0396251 | ||||||||
\(324\) | 5832.00 | 0.0555556 | ||||||||
\(325\) | 5348.53i | 0.0506370i | ||||||||
\(326\) | −412.776 | −0.00388400 | ||||||||
\(327\) | 76371.9i | 0.714230i | ||||||||
\(328\) | − 23152.3i | − 0.215202i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −34487.0 | −0.316685 | ||||||||
\(331\) | 40218.7 | 0.367090 | 0.183545 | − | 0.983011i | \(-0.441243\pi\) | ||||
0.183545 | + | 0.983011i | \(0.441243\pi\) | |||||||
\(332\) | − 10154.2i | − 0.0921234i | ||||||||
\(333\) | 15180.4 | 0.136897 | ||||||||
\(334\) | 88569.6i | 0.793947i | ||||||||
\(335\) | − 141922.i | − 1.26462i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 90476.4 | 0.796665 | 0.398332 | − | 0.917241i | \(-0.369589\pi\) | ||||
0.398332 | + | 0.917241i | \(0.369589\pi\) | |||||||
\(338\) | −50065.9 | −0.438237 | ||||||||
\(339\) | − 11038.5i | − 0.0960529i | ||||||||
\(340\) | −20632.0 | −0.178477 | ||||||||
\(341\) | − 148831.i | − 1.27992i | ||||||||
\(342\) | − 2932.02i | − 0.0250677i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 76535.1 | 0.646761 | ||||||||
\(345\) | −127131. | −1.06811 | ||||||||
\(346\) | − 113465.i | − 0.947782i | ||||||||
\(347\) | 32074.5 | 0.266379 | 0.133190 | − | 0.991091i | \(-0.457478\pi\) | ||||
0.133190 | + | 0.991091i | \(0.457478\pi\) | |||||||
\(348\) | − 25839.6i | − 0.213367i | ||||||||
\(349\) | 116783.i | 0.958805i | 0.877595 | + | 0.479402i | \(0.159147\pi\) | ||||
−0.877595 | + | 0.479402i | \(0.840853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14620.5 | −0.118672 | ||||||||
\(352\) | −17734.6 | −0.143132 | ||||||||
\(353\) | 124658.i | 1.00039i | 0.865912 | + | 0.500197i | \(0.166739\pi\) | ||||
−0.865912 | + | 0.500197i | \(0.833261\pi\) | |||||||
\(354\) | −43133.6 | −0.344199 | ||||||||
\(355\) | − 107648.i | − 0.854180i | ||||||||
\(356\) | 28834.8i | 0.227519i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 141858. | 1.10685 | ||||||||
\(359\) | 99442.1 | 0.771581 | 0.385790 | − | 0.922587i | \(-0.373929\pi\) | ||||
0.385790 | + | 0.922587i | \(0.373929\pi\) | |||||||
\(360\) | 14633.0i | 0.112909i | ||||||||
\(361\) | 128847. | 0.988689 | ||||||||
\(362\) | 180947.i | 1.38081i | ||||||||
\(363\) | 26203.0i | 0.198856i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −214820. | −1.61246 | ||||||||
\(366\) | 9778.56 | 0.0729983 | ||||||||
\(367\) | 88914.6i | 0.660147i | 0.943955 | + | 0.330074i | \(0.107074\pi\) | ||||
−0.943955 | + | 0.330074i | \(0.892926\pi\) | |||||||
\(368\) | −65375.9 | −0.482750 | ||||||||
\(369\) | − 27626.3i | − 0.202895i | ||||||||
\(370\) | 38088.7i | 0.278223i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −63149.3 | −0.456334 | ||||||||
\(373\) | −91352.9 | −0.656606 | −0.328303 | − | 0.944573i | \(-0.606477\pi\) | ||||
−0.328303 | + | 0.944573i | \(0.606477\pi\) | |||||||
\(374\) | − 29837.2i | − 0.213312i | ||||||||
\(375\) | 84172.5 | 0.598560 | ||||||||
\(376\) | − 89265.9i | − 0.631408i | ||||||||
\(377\) | 64778.2i | 0.455770i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6328.51 | 0.0440578 | 0.0220289 | − | 0.999757i | \(-0.492987\pi\) | ||||
0.0220289 | + | 0.999757i | \(0.492987\pi\) | |||||||
\(380\) | 7356.68 | 0.0509465 | ||||||||
\(381\) | − 44157.2i | − 0.304195i | ||||||||
\(382\) | 120969. | 0.828984 | ||||||||
\(383\) | 13436.0i | 0.0915949i | 0.998951 | + | 0.0457974i | \(0.0145829\pi\) | ||||
−0.998951 | + | 0.0457974i | \(0.985417\pi\) | |||||||
\(384\) | 7524.83i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24812.6 | 0.166532 | ||||||||
\(387\) | 91325.0 | 0.609772 | ||||||||
\(388\) | 15604.2i | 0.103652i | ||||||||
\(389\) | 88296.3 | 0.583503 | 0.291752 | − | 0.956494i | \(-0.405762\pi\) | ||||
0.291752 | + | 0.956494i | \(0.405762\pi\) | |||||||
\(390\) | − 36683.9i | − 0.241183i | ||||||||
\(391\) | − 109990.i | − 0.719451i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −75200.2 | −0.486894 | ||||||||
\(394\) | 92843.0 | 0.598077 | ||||||||
\(395\) | − 250218.i | − 1.60370i | ||||||||
\(396\) | −21161.6 | −0.134946 | ||||||||
\(397\) | − 216587.i | − 1.37421i | −0.726560 | − | 0.687103i | \(-0.758882\pi\) | ||||
0.726560 | − | 0.687103i | \(-0.241118\pi\) | |||||||
\(398\) | 74852.1i | 0.472539i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3284.72 | 0.0205295 | ||||||||
\(401\) | −5166.84 | −0.0321319 | −0.0160659 | − | 0.999871i | \(-0.505114\pi\) | ||||
−0.0160659 | + | 0.999871i | \(0.505114\pi\) | |||||||
\(402\) | − 87085.0i | − 0.538879i | ||||||||
\(403\) | 158311. | 0.974769 | ||||||||
\(404\) | 90609.9i | 0.555153i | ||||||||
\(405\) | 17460.7i | 0.106451i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −55082.5 | −0.332526 | ||||||||
\(408\) | −12660.0 | −0.0760525 | ||||||||
\(409\) | 38910.7i | 0.232607i | 0.993214 | + | 0.116303i | \(0.0371045\pi\) | ||||
−0.993214 | + | 0.116303i | \(0.962896\pi\) | |||||||
\(410\) | 69316.7 | 0.412354 | ||||||||
\(411\) | − 66797.4i | − 0.395436i | ||||||||
\(412\) | 130631.i | 0.769576i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −78009.3 | −0.455141 | ||||||||
\(415\) | 30401.1 | 0.176520 | ||||||||
\(416\) | − 18864.3i | − 0.109007i | ||||||||
\(417\) | −26029.9 | −0.149693 | ||||||||
\(418\) | 10639.0i | 0.0608900i | ||||||||
\(419\) | − 263425.i | − 1.50048i | −0.661167 | − | 0.750239i | \(-0.729938\pi\) | ||||
0.661167 | − | 0.750239i | \(-0.270062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16375.1 | −0.0923889 | −0.0461944 | − | 0.998932i | \(-0.514709\pi\) | ||||
−0.0461944 | + | 0.998932i | \(0.514709\pi\) | |||||||
\(422\) | −189664. | −1.06503 | ||||||||
\(423\) | − 106516.i | − 0.595297i | ||||||||
\(424\) | −49567.6 | −0.275719 | ||||||||
\(425\) | 5526.32i | 0.0305955i | ||||||||
\(426\) | − 66054.0i | − 0.363982i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 35171.7 | 0.192002 | ||||||||
\(429\) | 53050.9 | 0.288256 | ||||||||
\(430\) | 229142.i | 1.23927i | ||||||||
\(431\) | −250416. | −1.34806 | −0.674028 | − | 0.738705i | \(-0.735437\pi\) | ||||
−0.674028 | + | 0.738705i | \(0.735437\pi\) | |||||||
\(432\) | 8978.95i | 0.0481125i | ||||||||
\(433\) | 91495.1i | 0.488002i | 0.969775 | + | 0.244001i | \(0.0784601\pi\) | ||||
−0.969775 | + | 0.244001i | \(0.921540\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 77362.1 | 0.408837 | ||||||||
\(436\) | −117582. | −0.618541 | ||||||||
\(437\) | 39219.0i | 0.205368i | ||||||||
\(438\) | −131816. | −0.687099 | ||||||||
\(439\) | − 8859.37i | − 0.0459699i | −0.999736 | − | 0.0229850i | \(-0.992683\pi\) | ||||
0.999736 | − | 0.0229850i | \(-0.00731699\pi\) | |||||||
\(440\) | − 53096.3i | − 0.274258i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31737.9 | 0.162455 | ||||||||
\(443\) | 300209. | 1.52974 | 0.764868 | − | 0.644187i | \(-0.222804\pi\) | ||||
0.764868 | + | 0.644187i | \(0.222804\pi\) | |||||||
\(444\) | 23371.7i | 0.118556i | ||||||||
\(445\) | −86329.9 | −0.435954 | ||||||||
\(446\) | 159127.i | 0.799973i | ||||||||
\(447\) | − 131977.i | − 0.660514i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 116866. | 0.579691 | 0.289846 | − | 0.957073i | \(-0.406396\pi\) | ||||
0.289846 | + | 0.957073i | \(0.406396\pi\) | |||||||
\(450\) | 3919.47 | 0.0193554 | ||||||||
\(451\) | 100243.i | 0.492836i | ||||||||
\(452\) | 16994.9 | 0.0831842 | ||||||||
\(453\) | 95135.2i | 0.463601i | ||||||||
\(454\) | − 172953.i | − 0.839105i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4514.14 | 0.0217093 | ||||||||
\(457\) | 73745.8 | 0.353106 | 0.176553 | − | 0.984291i | \(-0.443505\pi\) | ||||
0.176553 | + | 0.984291i | \(0.443505\pi\) | |||||||
\(458\) | 95611.4i | 0.455805i | ||||||||
\(459\) | −15106.5 | −0.0717030 | ||||||||
\(460\) | − 195732.i | − 0.925008i | ||||||||
\(461\) | 88219.1i | 0.415108i | 0.978224 | + | 0.207554i | \(0.0665502\pi\) | ||||
−0.978224 | + | 0.207554i | \(0.933450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 297880. | 1.38957 | 0.694784 | − | 0.719219i | \(-0.255500\pi\) | ||||
0.694784 | + | 0.719219i | \(0.255500\pi\) | |||||||
\(464\) | 39782.6 | 0.184781 | ||||||||
\(465\) | − 189065.i | − 0.874391i | ||||||||
\(466\) | −24571.3 | −0.113150 | ||||||||
\(467\) | 187470.i | 0.859601i | 0.902924 | + | 0.429801i | \(0.141416\pi\) | ||||
−0.902924 | + | 0.429801i | \(0.858584\pi\) | |||||||
\(468\) | − 22509.7i | − 0.102773i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 267257. | 1.20985 | ||||||||
\(471\) | −183135. | −0.825526 | ||||||||
\(472\) | − 66408.5i | − 0.298085i | ||||||||
\(473\) | −331376. | −1.48115 | ||||||||
\(474\) | − 153536.i | − 0.683368i | ||||||||
\(475\) | − 1970.50i | − 0.00873353i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −59146.2 | −0.259950 | ||||||||
\(478\) | 44448.8 | 0.194538 | ||||||||
\(479\) | − 120489.i | − 0.525142i | −0.964913 | − | 0.262571i | \(-0.915430\pi\) | ||||
0.964913 | − | 0.262571i | \(-0.0845703\pi\) | |||||||
\(480\) | −22528.9 | −0.0977817 | ||||||||
\(481\) | − 58591.4i | − 0.253247i | ||||||||
\(482\) | 15496.4i | 0.0667019i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −40342.2 | −0.172214 | ||||||||
\(485\) | −46718.1 | −0.198610 | ||||||||
\(486\) | 10714.1i | 0.0453609i | ||||||||
\(487\) | −267394. | −1.12744 | −0.563721 | − | 0.825966i | \(-0.690631\pi\) | ||||
−0.563721 | + | 0.825966i | \(0.690631\pi\) | |||||||
\(488\) | 15055.1i | 0.0632184i | ||||||||
\(489\) | − 758.319i | − 0.00317128i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 178364. | 0.739851 | 0.369926 | − | 0.929061i | \(-0.379383\pi\) | ||||
0.369926 | + | 0.929061i | \(0.379383\pi\) | |||||||
\(492\) | 42533.5 | 0.175712 | ||||||||
\(493\) | 66931.5i | 0.275383i | ||||||||
\(494\) | −11316.7 | −0.0463730 | ||||||||
\(495\) | − 63356.7i | − 0.258573i | ||||||||
\(496\) | − 97224.7i | − 0.395196i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 18654.5 | 0.0752184 | ||||||||
\(499\) | 263747. | 1.05922 | 0.529610 | − | 0.848241i | \(-0.322338\pi\) | ||||
0.529610 | + | 0.848241i | \(0.322338\pi\) | |||||||
\(500\) | 129592.i | 0.518368i | ||||||||
\(501\) | −162713. | −0.648255 | ||||||||
\(502\) | − 68874.7i | − 0.273308i | ||||||||
\(503\) | − 480056.i | − 1.89739i | −0.316197 | − | 0.948694i | \(-0.602406\pi\) | ||||
0.316197 | − | 0.948694i | \(-0.397594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −271281. | −1.06374 | ||||||||
\(506\) | 283060. | 1.10555 | ||||||||
\(507\) | − 91976.9i | − 0.357819i | ||||||||
\(508\) | 67984.5 | 0.263441 | ||||||||
\(509\) | 60266.8i | 0.232618i | 0.993213 | + | 0.116309i | \(0.0371062\pi\) | ||||
−0.993213 | + | 0.116309i | \(0.962894\pi\) | |||||||
\(510\) | − 37903.3i | − 0.145726i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11585.2 | −0.0441942 | ||||||||
\(513\) | 5386.46 | 0.0204677 | ||||||||
\(514\) | 32828.8i | 0.124259i | ||||||||
\(515\) | −391101. | −1.47460 | ||||||||
\(516\) | 140604.i | 0.528078i | ||||||||
\(517\) | 386497.i | 1.44599i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 208448. | 0.773861 | ||||||||
\(520\) | 56478.6 | 0.208871 | ||||||||
\(521\) | 287316.i | 1.05848i | 0.848471 | + | 0.529242i | \(0.177524\pi\) | ||||
−0.848471 | + | 0.529242i | \(0.822476\pi\) | |||||||
\(522\) | 47470.3 | 0.174213 | ||||||||
\(523\) | 276444.i | 1.01066i | 0.862927 | + | 0.505328i | \(0.168629\pi\) | ||||
−0.862927 | + | 0.505328i | \(0.831371\pi\) | |||||||
\(524\) | − 115778.i | − 0.421662i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −341300. | −1.23357 | ||||||||
\(527\) | 163574. | 0.588969 | ||||||||
\(528\) | − 32580.5i | − 0.116866i | ||||||||
\(529\) | 763619. | 2.72876 | ||||||||
\(530\) | − 148403.i | − 0.528311i | ||||||||
\(531\) | − 79241.5i | − 0.281037i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −106629. | −0.375336 | ||||||||
\(534\) | −52973.0 | −0.185768 | ||||||||
\(535\) | 105302.i | 0.367900i | ||||||||
\(536\) | 134076. | 0.466683 | ||||||||
\(537\) | 260610.i | 0.903739i | ||||||||
\(538\) | 77065.1i | 0.266252i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −26882.5 | −0.0921895 | ||||||||
\(541\) | −59664.0 | −0.203853 | −0.101927 | − | 0.994792i | \(-0.532501\pi\) | ||||
−0.101927 | + | 0.994792i | \(0.532501\pi\) | |||||||
\(542\) | − 274480.i | − 0.934355i | ||||||||
\(543\) | −332420. | −1.12742 | ||||||||
\(544\) | − 19491.4i | − 0.0658634i | ||||||||
\(545\) | − 352034.i | − 1.18520i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 489585. | 1.63627 | 0.818133 | − | 0.575030i | \(-0.195010\pi\) | ||||
0.818133 | + | 0.575030i | \(0.195010\pi\) | |||||||
\(548\) | 102841. | 0.342458 | ||||||||
\(549\) | 17964.4i | 0.0596028i | ||||||||
\(550\) | −14222.0 | −0.0470147 | ||||||||
\(551\) | − 23865.5i | − 0.0786082i | ||||||||
\(552\) | − 120103.i | − 0.394164i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −84153.6 | −0.274191 | ||||||||
\(555\) | −69973.5 | −0.227168 | ||||||||
\(556\) | − 40075.7i | − 0.129638i | ||||||||
\(557\) | 508534. | 1.63912 | 0.819558 | − | 0.572996i | \(-0.194219\pi\) | ||||
0.819558 | + | 0.572996i | \(0.194219\pi\) | |||||||
\(558\) | − 116013.i | − 0.372595i | ||||||||
\(559\) | − 352486.i | − 1.12802i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 54814.4 | 0.174168 | ||||||||
\(562\) | 345846. | 1.09499 | ||||||||
\(563\) | 119817.i | 0.378009i | 0.981976 | + | 0.189004i | \(0.0605260\pi\) | ||||
−0.981976 | + | 0.189004i | \(0.939474\pi\) | |||||||
\(564\) | 163992. | 0.515542 | ||||||||
\(565\) | 50881.7i | 0.159391i | ||||||||
\(566\) | 171688.i | 0.535927i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 101697. | 0.315218 | ||||||||
\(569\) | −97659.4 | −0.301640 | −0.150820 | − | 0.988561i | \(-0.548191\pi\) | ||||
−0.150820 | + | 0.988561i | \(0.548191\pi\) | |||||||
\(570\) | 13515.1i | 0.0415976i | ||||||||
\(571\) | 47651.4 | 0.146151 | 0.0730757 | − | 0.997326i | \(-0.476719\pi\) | ||||
0.0730757 | + | 0.997326i | \(0.476719\pi\) | |||||||
\(572\) | 81677.3i | 0.249637i | ||||||||
\(573\) | 222234.i | 0.676863i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −52427.2 | −0.158570 | ||||||||
\(576\) | −13824.0 | −0.0416667 | ||||||||
\(577\) | − 131457.i | − 0.394849i | −0.980318 | − | 0.197425i | \(-0.936742\pi\) | ||||
0.980318 | − | 0.197425i | \(-0.0632578\pi\) | |||||||
\(578\) | −203440. | −0.608949 | ||||||||
\(579\) | 45583.7i | 0.135973i | ||||||||
\(580\) | 119107.i | 0.354063i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −28666.8 | −0.0846316 | ||||||||
\(583\) | 214614. | 0.631425 | ||||||||
\(584\) | − 202944.i | − 0.595045i | ||||||||
\(585\) | 67392.7 | 0.196925 | ||||||||
\(586\) | − 83601.0i | − 0.243454i | ||||||||
\(587\) | 135493.i | 0.393224i | 0.980481 | + | 0.196612i | \(0.0629940\pi\) | ||||
−0.980481 | + | 0.196612i | \(0.937006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −58325.0 | −0.168122 | ||||||||
\(590\) | 198823. | 0.571167 | ||||||||
\(591\) | 170564.i | 0.488328i | ||||||||
\(592\) | −35983.1 | −0.102673 | ||||||||
\(593\) | − 188208.i | − 0.535216i | −0.963528 | − | 0.267608i | \(-0.913767\pi\) | ||||
0.963528 | − | 0.267608i | \(-0.0862332\pi\) | |||||||
\(594\) | − 38876.4i | − 0.110183i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 203191. | 0.572022 | ||||||||
\(597\) | −137512. | −0.385827 | ||||||||
\(598\) | 301091.i | 0.841969i | ||||||||
\(599\) | −78404.8 | −0.218519 | −0.109259 | − | 0.994013i | \(-0.534848\pi\) | ||||
−0.109259 | + | 0.994013i | \(0.534848\pi\) | |||||||
\(600\) | 6034.42i | 0.0167623i | ||||||||
\(601\) | 254898.i | 0.705695i | 0.935681 | + | 0.352848i | \(0.114787\pi\) | ||||
−0.935681 | + | 0.352848i | \(0.885213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 159985. | 0.439993 | ||||||||
\(604\) | −146470. | −0.401491 | ||||||||
\(605\) | − 120782.i | − 0.329983i | ||||||||
\(606\) | −166461. | −0.453281 | ||||||||
\(607\) | − 565684.i | − 1.53531i | −0.640863 | − | 0.767655i | \(-0.721423\pi\) | ||||
0.640863 | − | 0.767655i | \(-0.278577\pi\) | |||||||
\(608\) | 6949.97i | 0.0188008i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −45074.0 | −0.121134 | ||||||||
\(611\) | −411118. | −1.10124 | ||||||||
\(612\) | − 23257.9i | − 0.0620966i | ||||||||
\(613\) | −414221. | −1.10233 | −0.551164 | − | 0.834397i | \(-0.685816\pi\) | ||||
−0.551164 | + | 0.834397i | \(0.685816\pi\) | |||||||
\(614\) | − 304246.i | − 0.807026i | ||||||||
\(615\) | 127343.i | 0.336686i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22896.0 | 0.0601435 | 0.0300717 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300717 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(618\) | −239984. | −0.628356 | ||||||||
\(619\) | 161155.i | 0.420593i | 0.977638 | + | 0.210296i | \(0.0674429\pi\) | ||||
−0.977638 | + | 0.210296i | \(0.932557\pi\) | |||||||
\(620\) | 291085. | 0.757245 | ||||||||
\(621\) | − 143312.i | − 0.371621i | ||||||||
\(622\) | − 122674.i | − 0.317082i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 34655.9 | 0.0890037 | ||||||||
\(625\) | −355913. | −0.911139 | ||||||||
\(626\) | − 304753.i | − 0.777676i | ||||||||
\(627\) | −19545.0 | −0.0497165 | ||||||||
\(628\) | − 281956.i | − 0.714926i | ||||||||
\(629\) | − 60539.0i | − 0.153015i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 489038. | 1.22824 | 0.614121 | − | 0.789212i | \(-0.289511\pi\) | ||||
0.614121 | + | 0.789212i | \(0.289511\pi\) | |||||||
\(632\) | 236385. | 0.591814 | ||||||||
\(633\) | − 348435.i | − 0.869590i | ||||||||
\(634\) | 441217. | 1.09768 | ||||||||
\(635\) | 203542.i | 0.504785i | ||||||||
\(636\) | − 91061.5i | − 0.225123i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −172248. | −0.423168 | ||||||||
\(639\) | 121349. | 0.297190 | ||||||||
\(640\) | − 34685.5i | − 0.0846815i | ||||||||
\(641\) | 119340. | 0.290448 | 0.145224 | − | 0.989399i | \(-0.453610\pi\) | ||||
0.145224 | + | 0.989399i | \(0.453610\pi\) | |||||||
\(642\) | 64614.5i | 0.156769i | ||||||||
\(643\) | 324224.i | 0.784194i | 0.919924 | + | 0.392097i | \(0.128250\pi\) | ||||
−0.919924 | + | 0.392097i | \(0.871750\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −420960. | −1.01186 | ||||||||
\(646\) | −11692.9 | −0.0280192 | ||||||||
\(647\) | − 460781.i | − 1.10074i | −0.834920 | − | 0.550372i | \(-0.814486\pi\) | ||||
0.834920 | − | 0.550372i | \(-0.185514\pi\) | |||||||
\(648\) | −16495.4 | −0.0392837 | ||||||||
\(649\) | 287531.i | 0.682645i | ||||||||
\(650\) | − 15127.9i | − 0.0358057i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1167.51 | 0.00274641 | ||||||||
\(653\) | −559124. | −1.31124 | −0.655620 | − | 0.755091i | \(-0.727593\pi\) | ||||
−0.655620 | + | 0.755091i | \(0.727593\pi\) | |||||||
\(654\) | − 216012.i | − 0.505037i | ||||||||
\(655\) | 346634. | 0.807957 | ||||||||
\(656\) | 65484.6i | 0.152171i | ||||||||
\(657\) | − 242161.i | − 0.561014i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −184372. | −0.424546 | −0.212273 | − | 0.977210i | \(-0.568087\pi\) | ||||
−0.212273 | + | 0.977210i | \(0.568087\pi\) | |||||||
\(660\) | 97544.1 | 0.223930 | ||||||||
\(661\) | 79226.4i | 0.181329i | 0.995881 | + | 0.0906645i | \(0.0288991\pi\) | ||||
−0.995881 | + | 0.0906645i | \(0.971101\pi\) | |||||||
\(662\) | −113756. | −0.259572 | ||||||||
\(663\) | 58306.2i | 0.132644i | ||||||||
\(664\) | 28720.4i | 0.0651411i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −42936.5 | −0.0968007 | ||||||||
\(667\) | −634967. | −1.42725 | ||||||||
\(668\) | − 250513.i | − 0.561405i | ||||||||
\(669\) | −292336. | −0.653175 | ||||||||
\(670\) | 401416.i | 0.894222i | ||||||||
\(671\) | − 65184.4i | − 0.144777i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −482896. | −1.06616 | −0.533082 | − | 0.846064i | \(-0.678966\pi\) | ||||
−0.533082 | + | 0.846064i | \(0.678966\pi\) | |||||||
\(674\) | −255906. | −0.563327 | ||||||||
\(675\) | 7200.53i | 0.0158036i | ||||||||
\(676\) | 141608. | 0.309880 | ||||||||
\(677\) | 380329.i | 0.829817i | 0.909863 | + | 0.414908i | \(0.136186\pi\) | ||||
−0.909863 | + | 0.414908i | \(0.863814\pi\) | |||||||
\(678\) | 31221.6i | 0.0679196i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 58356.0 | 0.126202 | ||||||||
\(681\) | 317735. | 0.685127 | ||||||||
\(682\) | 420956.i | 0.905041i | ||||||||
\(683\) | −342069. | −0.733283 | −0.366642 | − | 0.930362i | \(-0.619493\pi\) | ||||
−0.366642 | + | 0.930362i | \(0.619493\pi\) | |||||||
\(684\) | 8293.01i | 0.0177256i | ||||||||
\(685\) | 307901.i | 0.656191i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −175649. | −0.372163 | ||||||||
\(688\) | −216474. | −0.457329 | ||||||||
\(689\) | 228286.i | 0.480884i | ||||||||
\(690\) | 359582. | 0.755266 | ||||||||
\(691\) | − 73062.6i | − 0.153017i | −0.997069 | − | 0.0765084i | \(-0.975623\pi\) | ||||
0.997069 | − | 0.0765084i | \(-0.0243772\pi\) | |||||||
\(692\) | 320927.i | 0.670183i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −90720.3 | −0.188359 | ||||||||
\(695\) | 119984. | 0.248402 | ||||||||
\(696\) | 73085.3i | 0.150873i | ||||||||
\(697\) | −110173. | −0.226783 | ||||||||
\(698\) | − 330313.i | − 0.677977i | ||||||||
\(699\) | − 45140.3i | − 0.0923869i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −288287. | −0.586664 | −0.293332 | − | 0.956011i | \(-0.594764\pi\) | ||||
−0.293332 | + | 0.956011i | \(0.594764\pi\) | |||||||
\(702\) | 41352.9 | 0.0839135 | ||||||||
\(703\) | 21586.2i | 0.0436783i | ||||||||
\(704\) | 50160.9 | 0.101209 | ||||||||
\(705\) | 490982.i | 0.987842i | ||||||||
\(706\) | − 352586.i | − 0.707386i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 122000. | 0.243385 | ||||||||
\(709\) | −310512. | −0.617711 | −0.308856 | − | 0.951109i | \(-0.599946\pi\) | ||||
−0.308856 | + | 0.951109i | \(0.599946\pi\) | |||||||
\(710\) | 304475.i | 0.603996i | ||||||||
\(711\) | 282064. | 0.557968 | ||||||||
\(712\) | − 81557.3i | − 0.160880i | ||||||||
\(713\) | 1.55179e6i | 3.05250i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −244537. | −0.478335 | ||||||||
\(716\) | −401236. | −0.782661 | ||||||||
\(717\) | 81657.7i | 0.158840i | ||||||||
\(718\) | −281265. | −0.545590 | ||||||||
\(719\) | − 10084.7i | − 0.0195077i | −0.999952 | − | 0.00975383i | \(-0.996895\pi\) | ||||
0.999952 | − | 0.00975383i | \(-0.00310479\pi\) | |||||||
\(720\) | − 41388.3i | − 0.0798385i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −364434. | −0.699109 | ||||||||
\(723\) | −28468.8 | −0.0544619 | ||||||||
\(724\) | − 511794.i | − 0.976378i | ||||||||
\(725\) | 31903.0 | 0.0606954 | ||||||||
\(726\) | − 74113.3i | − 0.140612i | ||||||||
\(727\) | 638552.i | 1.20817i | 0.796921 | + | 0.604084i | \(0.206461\pi\) | ||||
−0.796921 | + | 0.604084i | \(0.793539\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 607602. | 1.14018 | ||||||||
\(731\) | − 364203.i | − 0.681567i | ||||||||
\(732\) | −27657.9 | −0.0516176 | ||||||||
\(733\) | 826084.i | 1.53750i | 0.639547 | + | 0.768752i | \(0.279122\pi\) | ||||
−0.639547 | + | 0.768752i | \(0.720878\pi\) | |||||||
\(734\) | − 251488.i | − 0.466795i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 184911. | 0.341356 | ||||||||
\(737\) | −580513. | −1.06875 | ||||||||
\(738\) | 78139.1i | 0.143468i | ||||||||
\(739\) | 769990. | 1.40992 | 0.704962 | − | 0.709245i | \(-0.250964\pi\) | ||||
0.704962 | + | 0.709245i | \(0.250964\pi\) | |||||||
\(740\) | − 107731.i | − 0.196733i | ||||||||
\(741\) | − 20790.1i | − 0.0378634i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −611777. | −1.10819 | −0.554097 | − | 0.832452i | \(-0.686936\pi\) | ||||
−0.554097 | + | 0.832452i | \(0.686936\pi\) | |||||||
\(744\) | 178613. | 0.322677 | ||||||||
\(745\) | 608343.i | 1.09606i | ||||||||
\(746\) | 258385. | 0.464290 | ||||||||
\(747\) | 34270.4i | 0.0614156i | ||||||||
\(748\) | 84392.3i | 0.150834i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −238076. | −0.423246 | ||||||||
\(751\) | 370622. | 0.657129 | 0.328565 | − | 0.944481i | \(-0.393435\pi\) | ||||
0.328565 | + | 0.944481i | \(0.393435\pi\) | |||||||
\(752\) | 252482.i | 0.446473i | ||||||||
\(753\) | 126531. | 0.223155 | ||||||||
\(754\) | − 183220.i | − 0.322278i | ||||||||
\(755\) | − 438523.i | − 0.769305i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 298778. | 0.521384 | 0.260692 | − | 0.965422i | \(-0.416049\pi\) | ||||
0.260692 | + | 0.965422i | \(0.416049\pi\) | |||||||
\(758\) | −17899.7 | −0.0311536 | ||||||||
\(759\) | 520014.i | 0.902676i | ||||||||
\(760\) | −20807.8 | −0.0360246 | ||||||||
\(761\) | − 803142.i | − 1.38683i | −0.720539 | − | 0.693414i | \(-0.756106\pi\) | ||||
0.720539 | − | 0.693414i | \(-0.243894\pi\) | |||||||
\(762\) | 124896.i | 0.215098i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −342151. | −0.586180 | ||||||||
\(765\) | 69632.9 | 0.118985 | ||||||||
\(766\) | − 38002.6i | − 0.0647674i | ||||||||
\(767\) | −305847. | −0.519893 | ||||||||
\(768\) | − 21283.4i | − 0.0360844i | ||||||||
\(769\) | − 452541.i | − 0.765253i | −0.923903 | − | 0.382626i | \(-0.875020\pi\) | ||||
0.923903 | − | 0.382626i | \(-0.124980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −60310.4 | −0.101457 | ||||||||
\(772\) | −70180.7 | −0.117756 | ||||||||
\(773\) | 1.04853e6i | 1.75478i | 0.479774 | + | 0.877392i | \(0.340719\pi\) | ||||
−0.479774 | + | 0.877392i | \(0.659281\pi\) | |||||||
\(774\) | −258306. | −0.431174 | ||||||||
\(775\) | − 77967.8i | − 0.129811i | ||||||||
\(776\) | − 44135.4i | − 0.0732932i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −249740. | −0.412599 | ||||||||
\(779\) | 39284.2 | 0.0647355 | ||||||||
\(780\) | 103758.i | 0.170542i | ||||||||
\(781\) | −440320. | −0.721882 | ||||||||
\(782\) | 311100.i | 0.508729i | ||||||||
\(783\) | 87208.5i | 0.142244i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 844159. | 1.36989 | ||||||||
\(786\) | 212698. | 0.344286 | ||||||||
\(787\) | 195967.i | 0.316398i | 0.987407 | + | 0.158199i | \(0.0505687\pi\) | ||||
−0.987407 | + | 0.158199i | \(0.949431\pi\) | |||||||
\(788\) | −262600. | −0.422904 | ||||||||
\(789\) | − 627007.i | − 1.00721i | ||||||||
\(790\) | 707722.i | 1.13399i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 59854.2 | 0.0954210 | ||||||||
\(793\) | 69336.7 | 0.110260 | ||||||||
\(794\) | 612601.i | 0.971710i | ||||||||
\(795\) | 272633. | 0.431364 | ||||||||
\(796\) | − 211714.i | − 0.334136i | ||||||||
\(797\) | − 66453.8i | − 0.104617i | −0.998631 | − | 0.0523086i | \(-0.983342\pi\) | ||||
0.998631 | − | 0.0523086i | \(-0.0166579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −424784. | −0.665387 | ||||||||
\(800\) | −9290.60 | −0.0145166 | ||||||||
\(801\) | − 97317.6i | − 0.151679i | ||||||||
\(802\) | 14614.0 | 0.0227207 | ||||||||
\(803\) | 878691.i | 1.36272i | ||||||||
\(804\) | 246314.i | 0.381045i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −447772. | −0.689266 | ||||||||
\(807\) | −141578. | −0.217394 | ||||||||
\(808\) | − 256284.i | − 0.392553i | ||||||||
\(809\) | 82304.6 | 0.125755 | 0.0628777 | − | 0.998021i | \(-0.479972\pi\) | ||||
0.0628777 | + | 0.998021i | \(0.479972\pi\) | |||||||
\(810\) | − 49386.2i | − 0.0752724i | ||||||||
\(811\) | − 469097.i | − 0.713215i | −0.934254 | − | 0.356608i | \(-0.883933\pi\) | ||||
0.934254 | − | 0.356608i | \(-0.116067\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 504252. | 0.762898 | ||||||||
\(814\) | 155797. | 0.235131 | ||||||||
\(815\) | 3495.45i | 0.00526245i | ||||||||
\(816\) | 35807.9 | 0.0537773 | ||||||||
\(817\) | 129863.i | 0.194554i | ||||||||
\(818\) | − 110056.i | − 0.164478i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −196057. | −0.291578 | ||||||||
\(821\) | −5379.52 | −0.00798099 | −0.00399050 | − | 0.999992i | \(-0.501270\pi\) | ||||
−0.00399050 | + | 0.999992i | \(0.501270\pi\) | |||||||
\(822\) | 188932.i | 0.279615i | ||||||||
\(823\) | −969806. | −1.43181 | −0.715905 | − | 0.698198i | \(-0.753986\pi\) | ||||
−0.715905 | + | 0.698198i | \(0.753986\pi\) | |||||||
\(824\) | − 369480.i | − 0.544172i | ||||||||
\(825\) | − 26127.4i | − 0.0383874i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 838747. | 1.22637 | 0.613183 | − | 0.789941i | \(-0.289889\pi\) | ||||
0.613183 | + | 0.789941i | \(0.289889\pi\) | |||||||
\(828\) | 220644. | 0.321833 | ||||||||
\(829\) | − 883703.i | − 1.28587i | −0.765920 | − | 0.642935i | \(-0.777716\pi\) | ||||
0.765920 | − | 0.642935i | \(-0.222284\pi\) | |||||||
\(830\) | −85987.3 | −0.124818 | ||||||||
\(831\) | − 154600.i | − 0.223876i | ||||||||
\(832\) | 53356.3i | 0.0770795i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 73623.7 | 0.105849 | ||||||||
\(835\) | 750020. | 1.07572 | ||||||||
\(836\) | − 30091.5i | − 0.0430558i | ||||||||
\(837\) | 213129. | 0.304222 | ||||||||
\(838\) | 745080.i | 1.06100i | ||||||||
\(839\) | 1.12626e6i | 1.59998i | 0.600011 | + | 0.799992i | \(0.295163\pi\) | ||||
−0.600011 | + | 0.799992i | \(0.704837\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −320891. | −0.453696 | ||||||||
\(842\) | 46315.8 | 0.0653288 | ||||||||
\(843\) | 635360.i | 0.894056i | ||||||||
\(844\) | 536451. | 0.753087 | ||||||||
\(845\) | 423965.i | 0.593768i | ||||||||
\(846\) | 301272.i | 0.420938i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 140198. | 0.194963 | ||||||||
\(849\) | −315410. | −0.437583 | ||||||||
\(850\) | − 15630.8i | − 0.0216343i | ||||||||
\(851\) | 574323. | 0.793043 | ||||||||
\(852\) | 186829.i | 0.257374i | ||||||||
\(853\) | − 805486.i | − 1.10703i | −0.832839 | − | 0.553516i | \(-0.813286\pi\) | ||||
0.832839 | − | 0.553516i | \(-0.186714\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24828.8 | −0.0339643 | ||||||||
\(856\) | −99480.6 | −0.135766 | ||||||||
\(857\) | − 980477.i | − 1.33498i | −0.744618 | − | 0.667491i | \(-0.767368\pi\) | ||||
0.744618 | − | 0.667491i | \(-0.232632\pi\) | |||||||
\(858\) | −150051. | −0.203828 | ||||||||
\(859\) | 433780.i | 0.587873i | 0.955825 | + | 0.293936i | \(0.0949654\pi\) | ||||
−0.955825 | + | 0.293936i | \(0.905035\pi\) | |||||||
\(860\) | − 648111.i | − 0.876299i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 708284. | 0.953220 | ||||||||
\(863\) | −303157. | −0.407048 | −0.203524 | − | 0.979070i | \(-0.565240\pi\) | ||||
−0.203524 | + | 0.979070i | \(0.565240\pi\) | |||||||
\(864\) | − 25396.3i | − 0.0340207i | ||||||||
\(865\) | −960836. | −1.28415 | ||||||||
\(866\) | − 258787.i | − 0.345070i | ||||||||
\(867\) | − 373744.i | − 0.497205i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.02348e6 | −1.35532 | ||||||||
\(870\) | −218813. | −0.289091 | ||||||||
\(871\) | − 617493.i | − 0.813946i | ||||||||
\(872\) | 332573. | 0.437375 | ||||||||
\(873\) | − 52664.2i | − 0.0691015i | ||||||||
\(874\) | − 110928.i | − 0.145217i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 372831. | 0.485852 | ||||||||
\(877\) | 355000. | 0.461562 | 0.230781 | − | 0.973006i | \(-0.425872\pi\) | ||||
0.230781 | + | 0.973006i | \(0.425872\pi\) | |||||||
\(878\) | 25058.1i | 0.0325057i | ||||||||
\(879\) | 153585. | 0.198779 | ||||||||
\(880\) | 150179.i | 0.193929i | ||||||||
\(881\) | 320002.i | 0.412288i | 0.978522 | + | 0.206144i | \(0.0660915\pi\) | ||||
−0.978522 | + | 0.206144i | \(0.933909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.08605e6 | −1.39293 | −0.696467 | − | 0.717589i | \(-0.745246\pi\) | ||||
−0.696467 | + | 0.717589i | \(0.745246\pi\) | |||||||
\(884\) | −89768.2 | −0.114873 | ||||||||
\(885\) | 365262.i | 0.466356i | ||||||||
\(886\) | −849120. | −1.08169 | ||||||||
\(887\) | − 1.28423e6i | − 1.63229i | −0.577848 | − | 0.816144i | \(-0.696107\pi\) | ||||
0.577848 | − | 0.816144i | \(-0.303893\pi\) | |||||||
\(888\) | − 66105.1i | − 0.0838319i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 244178. | 0.308266 | ||||||||
\(891\) | 71420.5 | 0.0899638 | ||||||||
\(892\) | − 450080.i | − 0.565666i | ||||||||
\(893\) | 151464. | 0.189935 | ||||||||
\(894\) | 373286.i | 0.467054i | ||||||||
\(895\) | − 1.20128e6i | − 1.49967i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −553140. | −0.687465 | ||||||||
\(898\) | −330548. | −0.409904 | ||||||||
\(899\) | − 944299.i | − 1.16840i | ||||||||
\(900\) | −11085.9 | −0.0136863 | ||||||||
\(901\) | 235874.i | 0.290557i | ||||||||
\(902\) | − 283531.i | − 0.348487i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −48068.7 | −0.0588201 | ||||||||
\(905\) | 1.53228e6 | 1.87086 | ||||||||
\(906\) | − 269083.i | − 0.327816i | ||||||||
\(907\) | 48435.5 | 0.0588775 | 0.0294388 | − | 0.999567i | \(-0.490628\pi\) | ||||
0.0294388 | + | 0.999567i | \(0.490628\pi\) | |||||||
\(908\) | 489185.i | 0.593337i | ||||||||
\(909\) | − 305808.i | − 0.370102i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 727675. | 0.876801 | 0.438400 | − | 0.898780i | \(-0.355545\pi\) | ||||
0.438400 | + | 0.898780i | \(0.355545\pi\) | |||||||
\(912\) | −12767.9 | −0.0153508 | ||||||||
\(913\) | − 124352.i | − 0.149180i | ||||||||
\(914\) | −208584. | −0.249683 | ||||||||
\(915\) | − 82806.3i | − 0.0989056i | ||||||||
\(916\) | − 270430.i | − 0.322303i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 42727.5 | 0.0507017 | ||||||||
\(919\) | 87715.9 | 0.103860 | 0.0519299 | − | 0.998651i | \(-0.483463\pi\) | ||||
0.0519299 | + | 0.998651i | \(0.483463\pi\) | |||||||
\(920\) | 553613.i | 0.654080i | ||||||||
\(921\) | 558935. | 0.658934 | ||||||||
\(922\) | − 249521.i | − 0.293526i | ||||||||
\(923\) | − 468369.i | − 0.549775i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28856.1 | −0.0337251 | ||||||||
\(926\) | −842533. | −0.982573 | ||||||||
\(927\) | − 440879.i | − 0.513051i | ||||||||
\(928\) | −112522. | −0.130660 | ||||||||
\(929\) | − 901913.i | − 1.04504i | −0.852627 | − | 0.522520i | \(-0.824992\pi\) | ||||
0.852627 | − | 0.522520i | \(-0.175008\pi\) | |||||||
\(930\) | 534757.i | 0.618288i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 69498.1 | 0.0800094 | ||||||||
\(933\) | 225366. | 0.258896 | ||||||||
\(934\) | − 530244.i | − 0.607830i | ||||||||
\(935\) | −252666. | −0.289017 | ||||||||
\(936\) | 63667.0i | 0.0726712i | ||||||||
\(937\) | − 1.24186e6i | − 1.41447i | −0.706978 | − | 0.707236i | \(-0.749942\pi\) | ||||
0.706978 | − | 0.707236i | \(-0.250058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 559867. | 0.634970 | ||||||||
\(940\) | −755917. | −0.855496 | ||||||||
\(941\) | 426245.i | 0.481371i | 0.970603 | + | 0.240685i | \(0.0773722\pi\) | ||||
−0.970603 | + | 0.240685i | \(0.922628\pi\) | |||||||
\(942\) | 517985. | 0.583735 | ||||||||
\(943\) | − 1.04520e6i | − 1.17537i | ||||||||
\(944\) | 187832.i | 0.210778i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 937274. | 1.04733 | ||||||||
\(947\) | 27330.4 | 0.0304752 | 0.0152376 | − | 0.999884i | \(-0.495150\pi\) | ||||
0.0152376 | + | 0.999884i | \(0.495150\pi\) | |||||||
\(948\) | 434266.i | 0.483214i | ||||||||
\(949\) | −934665. | −1.03782 | ||||||||
\(950\) | 5573.42i | 0.00617554i | ||||||||
\(951\) | 810568.i | 0.896248i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.30093e6 | 1.43242 | 0.716208 | − | 0.697887i | \(-0.245876\pi\) | ||||
0.716208 | + | 0.697887i | \(0.245876\pi\) | |||||||
\(954\) | 167291. | 0.183813 | ||||||||
\(955\) | − 1.02438e6i | − 1.12319i | ||||||||
\(956\) | −125720. | −0.137559 | ||||||||
\(957\) | − 316439.i | − 0.345515i | ||||||||
\(958\) | 340794.i | 0.371331i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 63721.4 | 0.0691421 | ||||||||
\(961\) | −1.38425e6 | −1.49888 | ||||||||
\(962\) | 165721.i | 0.179072i | ||||||||
\(963\) | −118705. | −0.128001 | ||||||||
\(964\) | − 43830.6i | − 0.0471654i | ||||||||
\(965\) | − 210117.i | − 0.225635i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 463079. | 0.495225 | 0.247612 | − | 0.968859i | \(-0.420354\pi\) | ||||
0.247612 | + | 0.968859i | \(0.420354\pi\) | |||||||
\(968\) | 114105. | 0.121774 | ||||||||
\(969\) | − 21481.1i | − 0.0228776i | ||||||||
\(970\) | 132139. | 0.140439 | ||||||||
\(971\) | − 63188.7i | − 0.0670195i | −0.999438 | − | 0.0335098i | \(-0.989332\pi\) | ||||
0.999438 | − | 0.0335098i | \(-0.0106685\pi\) | |||||||
\(972\) | − 30304.0i | − 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 756305. | 0.797221 | ||||||||
\(975\) | 27791.8 | 0.0292353 | ||||||||
\(976\) | − 42582.2i | − 0.0447021i | ||||||||
\(977\) | 1.43899e6 | 1.50754 | 0.753772 | − | 0.657136i | \(-0.228232\pi\) | ||||
0.753772 | + | 0.657136i | \(0.228232\pi\) | |||||||
\(978\) | 2144.85i | 0.00224243i | ||||||||
\(979\) | 353121.i | 0.368432i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 396840. | 0.412361 | ||||||||
\(982\) | −504490. | −0.523154 | ||||||||
\(983\) | 400596.i | 0.414572i | 0.978280 | + | 0.207286i | \(0.0664630\pi\) | ||||
−0.978280 | + | 0.207286i | \(0.933537\pi\) | |||||||
\(984\) | −120303. | −0.124247 | ||||||||
\(985\) | − 786209.i | − 0.810336i | ||||||||
\(986\) | − 189311.i | − 0.194725i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 32008.4 | 0.0327906 | ||||||||
\(989\) | 3.45512e6 | 3.53241 | ||||||||
\(990\) | 179200.i | 0.182838i | ||||||||
\(991\) | 198549. | 0.202172 | 0.101086 | − | 0.994878i | \(-0.467768\pi\) | ||||
0.101086 | + | 0.994878i | \(0.467768\pi\) | |||||||
\(992\) | 274993.i | 0.279446i | ||||||||
\(993\) | − 208983.i | − 0.211939i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 633858. | 0.640245 | ||||||||
\(996\) | −52762.8 | −0.0531875 | ||||||||
\(997\) | 914786.i | 0.920299i | 0.887841 | + | 0.460150i | \(0.152204\pi\) | ||||
−0.887841 | + | 0.460150i | \(0.847796\pi\) | |||||||
\(998\) | −745988. | −0.748981 | ||||||||
\(999\) | − 78879.5i | − 0.0790375i |
(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 | 294.5.c.a.97.1 | 4 | ||
3.2 | odd | 2 | 882.5.c.a.685.3 | 4 | |||
7.2 | even | 3 | 294.5.g.c.31.2 | 4 | |||
7.3 | odd | 6 | 294.5.g.c.19.2 | 4 | |||
7.4 | even | 3 | 42.5.g.a.19.2 | ✓ | 4 | ||
7.5 | odd | 6 | 42.5.g.a.31.2 | yes | 4 | ||
7.6 | odd | 2 | inner | 294.5.c.a.97.2 | 4 | ||
21.5 | even | 6 | 126.5.n.b.73.1 | 4 | |||
21.11 | odd | 6 | 126.5.n.b.19.1 | 4 | |||
21.20 | even | 2 | 882.5.c.a.685.4 | 4 | |||
28.11 | odd | 6 | 336.5.bh.d.145.1 | 4 | |||
28.19 | even | 6 | 336.5.bh.d.241.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.5.g.a.19.2 | ✓ | 4 | 7.4 | even | 3 | ||
42.5.g.a.31.2 | yes | 4 | 7.5 | odd | 6 | ||
126.5.n.b.19.1 | 4 | 21.11 | odd | 6 | |||
126.5.n.b.73.1 | 4 | 21.5 | even | 6 | |||
294.5.c.a.97.1 | 4 | 1.1 | even | 1 | trivial | ||
294.5.c.a.97.2 | 4 | 7.6 | odd | 2 | inner | ||
294.5.g.c.19.2 | 4 | 7.3 | odd | 6 | |||
294.5.g.c.31.2 | 4 | 7.2 | even | 3 | |||
336.5.bh.d.145.1 | 4 | 28.11 | odd | 6 | |||
336.5.bh.d.241.1 | 4 | 28.19 | even | 6 | |||
882.5.c.a.685.3 | 4 | 3.2 | odd | 2 | |||
882.5.c.a.685.4 | 4 | 21.20 | even | 2 |