Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,5,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (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: | \(4.44490841261\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.6 | ||
Root | \(-0.133471i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.5.b.b.42.7 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.133471i | − | 0.0333677i | −0.999861 | − | 0.0166838i | \(-0.994689\pi\) | ||
0.999861 | − | 0.0166838i | \(-0.00531088\pi\) | |||||||
\(3\) | − | 14.8068i | − | 1.64520i | −0.568620 | − | 0.822600i | \(-0.692523\pi\) | ||
0.568620 | − | 0.822600i | \(-0.307477\pi\) | |||||||
\(4\) | 15.9822 | 0.998887 | ||||||||
\(5\) | 26.0324i | 1.04129i | 0.853772 | + | 0.520647i | \(0.174309\pi\) | ||||
−0.853772 | + | 0.520647i | \(0.825691\pi\) | |||||||
\(6\) | −1.97628 | −0.0548965 | ||||||||
\(7\) | − | 87.9232i | − | 1.79435i | −0.441675 | − | 0.897175i | \(-0.645616\pi\) | ||
0.441675 | − | 0.897175i | \(-0.354384\pi\) | |||||||
\(8\) | − | 4.26869i | − | 0.0666982i | ||||||
\(9\) | −138.241 | −1.70668 | ||||||||
\(10\) | 3.47456 | 0.0347456 | ||||||||
\(11\) | −101.658 | −0.840147 | −0.420074 | − | 0.907490i | \(-0.637996\pi\) | ||||
−0.420074 | + | 0.907490i | \(0.637996\pi\) | |||||||
\(12\) | − | 236.645i | − | 1.64337i | ||||||
\(13\) | 190.866 | 1.12939 | 0.564693 | − | 0.825301i | \(-0.308994\pi\) | ||||
0.564693 | + | 0.825301i | \(0.308994\pi\) | |||||||
\(14\) | −11.7352 | −0.0598733 | ||||||||
\(15\) | 385.456 | 1.71314 | ||||||||
\(16\) | 255.145 | 0.996661 | ||||||||
\(17\) | −227.830 | −0.788338 | −0.394169 | − | 0.919038i | \(-0.628968\pi\) | ||||
−0.394169 | + | 0.919038i | \(0.628968\pi\) | |||||||
\(18\) | 18.4512i | 0.0569481i | ||||||||
\(19\) | 304.934i | 0.844693i | 0.906434 | + | 0.422347i | \(0.138793\pi\) | ||||
−0.906434 | + | 0.422347i | \(0.861207\pi\) | |||||||
\(20\) | 416.054i | 1.04014i | ||||||||
\(21\) | −1301.86 | −2.95207 | ||||||||
\(22\) | 13.5683i | 0.0280338i | ||||||||
\(23\) | 797.353 | 1.50728 | 0.753641 | − | 0.657286i | \(-0.228296\pi\) | ||||
0.753641 | + | 0.657286i | \(0.228296\pi\) | |||||||
\(24\) | −63.2056 | −0.109732 | ||||||||
\(25\) | −52.6844 | −0.0842950 | ||||||||
\(26\) | − | 25.4751i | − | 0.0376850i | ||||||
\(27\) | 847.562i | 1.16264i | ||||||||
\(28\) | − | 1405.20i | − | 1.79235i | ||||||
\(29\) | 1084.32i | 1.28932i | 0.764469 | + | 0.644660i | \(0.223001\pi\) | ||||
−0.764469 | + | 0.644660i | \(0.776999\pi\) | |||||||
\(30\) | − | 51.4471i | − | 0.0571635i | ||||||
\(31\) | 433.017 | 0.450590 | 0.225295 | − | 0.974291i | \(-0.427665\pi\) | ||||
0.225295 | + | 0.974291i | \(0.427665\pi\) | |||||||
\(32\) | − | 102.353i | − | 0.0999545i | ||||||
\(33\) | 1505.23i | 1.38221i | ||||||||
\(34\) | 30.4086i | 0.0263050i | ||||||||
\(35\) | 2288.85 | 1.86845 | ||||||||
\(36\) | −2209.40 | −1.70478 | ||||||||
\(37\) | − | 310.044i | − | 0.226475i | −0.993568 | − | 0.113237i | \(-0.963878\pi\) | ||
0.993568 | − | 0.113237i | \(-0.0361220\pi\) | |||||||
\(38\) | 40.6998 | 0.0281855 | ||||||||
\(39\) | − | 2826.12i | − | 1.85807i | ||||||
\(40\) | 111.124 | 0.0694525 | ||||||||
\(41\) | 1339.11 | 0.796618 | 0.398309 | − | 0.917251i | \(-0.369597\pi\) | ||||
0.398309 | + | 0.917251i | \(0.369597\pi\) | |||||||
\(42\) | 173.760i | 0.0985036i | ||||||||
\(43\) | −137.757 | + | 1843.86i | −0.0745034 | + | 0.997221i | ||||
\(44\) | −1624.71 | −0.839212 | ||||||||
\(45\) | − | 3598.75i | − | 1.77716i | ||||||
\(46\) | − | 106.423i | − | 0.0502946i | ||||||
\(47\) | 1003.89 | 0.454456 | 0.227228 | − | 0.973842i | \(-0.427034\pi\) | ||||
0.227228 | + | 0.973842i | \(0.427034\pi\) | |||||||
\(48\) | − | 3777.89i | − | 1.63971i | ||||||
\(49\) | −5329.48 | −2.21969 | ||||||||
\(50\) | 7.03183i | 0.00281273i | ||||||||
\(51\) | 3373.43i | 1.29697i | ||||||||
\(52\) | 3050.46 | 1.12813 | ||||||||
\(53\) | −3648.61 | −1.29890 | −0.649451 | − | 0.760404i | \(-0.725001\pi\) | ||||
−0.649451 | + | 0.760404i | \(0.725001\pi\) | |||||||
\(54\) | 113.125 | 0.0387945 | ||||||||
\(55\) | − | 2646.39i | − | 0.874841i | ||||||
\(56\) | −375.317 | −0.119680 | ||||||||
\(57\) | 4515.10 | 1.38969 | ||||||||
\(58\) | 144.725 | 0.0430217 | ||||||||
\(59\) | −1283.47 | −0.368708 | −0.184354 | − | 0.982860i | \(-0.559019\pi\) | ||||
−0.184354 | + | 0.982860i | \(0.559019\pi\) | |||||||
\(60\) | 6160.43 | 1.71123 | ||||||||
\(61\) | − | 2277.88i | − | 0.612168i | −0.952005 | − | 0.306084i | \(-0.900981\pi\) | ||
0.952005 | − | 0.306084i | \(-0.0990188\pi\) | |||||||
\(62\) | − | 57.7951i | − | 0.0150351i | ||||||
\(63\) | 12154.6i | 3.06239i | ||||||||
\(64\) | 4068.66 | 0.993326 | ||||||||
\(65\) | 4968.70i | 1.17602i | ||||||||
\(66\) | 200.904 | 0.0461212 | ||||||||
\(67\) | −4753.41 | −1.05890 | −0.529451 | − | 0.848340i | \(-0.677602\pi\) | ||||
−0.529451 | + | 0.848340i | \(0.677602\pi\) | |||||||
\(68\) | −3641.22 | −0.787460 | ||||||||
\(69\) | − | 11806.2i | − | 2.47978i | ||||||
\(70\) | − | 305.494i | − | 0.0623458i | ||||||
\(71\) | − | 4258.19i | − | 0.844711i | −0.906430 | − | 0.422356i | \(-0.861203\pi\) | ||
0.906430 | − | 0.422356i | \(-0.138797\pi\) | |||||||
\(72\) | 590.109i | 0.113833i | ||||||||
\(73\) | 3321.32i | 0.623254i | 0.950204 | + | 0.311627i | \(0.100874\pi\) | ||||
−0.950204 | + | 0.311627i | \(0.899126\pi\) | |||||||
\(74\) | −41.3818 | −0.00755693 | ||||||||
\(75\) | 780.087i | 0.138682i | ||||||||
\(76\) | 4873.52i | 0.843753i | ||||||||
\(77\) | 8938.08i | 1.50752i | ||||||||
\(78\) | −377.205 | −0.0619994 | ||||||||
\(79\) | −227.377 | −0.0364328 | −0.0182164 | − | 0.999834i | \(-0.505799\pi\) | ||||
−0.0182164 | + | 0.999834i | \(0.505799\pi\) | |||||||
\(80\) | 6642.04i | 1.03782i | ||||||||
\(81\) | 1352.14 | 0.206087 | ||||||||
\(82\) | − | 178.733i | − | 0.0265813i | ||||||
\(83\) | −1895.54 | −0.275155 | −0.137577 | − | 0.990491i | \(-0.543932\pi\) | ||||
−0.137577 | + | 0.990491i | \(0.543932\pi\) | |||||||
\(84\) | −20806.6 | −2.94878 | ||||||||
\(85\) | − | 5930.95i | − | 0.820892i | ||||||
\(86\) | 246.102 | + | 18.3865i | 0.0332750 | + | 0.00248601i | ||||
\(87\) | 16055.3 | 2.12119 | ||||||||
\(88\) | 433.945i | 0.0560363i | ||||||||
\(89\) | 10806.3i | 1.36426i | 0.731229 | + | 0.682132i | \(0.238947\pi\) | ||||
−0.731229 | + | 0.682132i | \(0.761053\pi\) | |||||||
\(90\) | −480.328 | −0.0592998 | ||||||||
\(91\) | − | 16781.6i | − | 2.02652i | ||||||
\(92\) | 12743.4 | 1.50560 | ||||||||
\(93\) | − | 6411.60i | − | 0.741311i | ||||||
\(94\) | − | 133.990i | − | 0.0151641i | ||||||
\(95\) | −7938.16 | −0.879575 | ||||||||
\(96\) | −1515.53 | −0.164445 | ||||||||
\(97\) | 10904.7 | 1.15897 | 0.579483 | − | 0.814984i | \(-0.303254\pi\) | ||||
0.579483 | + | 0.814984i | \(0.303254\pi\) | |||||||
\(98\) | 711.330i | 0.0740660i | ||||||||
\(99\) | 14053.3 | 1.43387 | ||||||||
\(100\) | −842.012 | −0.0842012 | ||||||||
\(101\) | 9432.56 | 0.924670 | 0.462335 | − | 0.886705i | \(-0.347012\pi\) | ||||
0.462335 | + | 0.886705i | \(0.347012\pi\) | |||||||
\(102\) | 450.254 | 0.0432770 | ||||||||
\(103\) | −14161.0 | −1.33481 | −0.667406 | − | 0.744694i | \(-0.732596\pi\) | ||||
−0.667406 | + | 0.744694i | \(0.732596\pi\) | |||||||
\(104\) | − | 814.749i | − | 0.0753281i | ||||||
\(105\) | − | 33890.5i | − | 3.07397i | ||||||
\(106\) | 486.983i | 0.0433413i | ||||||||
\(107\) | −6411.74 | −0.560027 | −0.280013 | − | 0.959996i | \(-0.590339\pi\) | ||||
−0.280013 | + | 0.959996i | \(0.590339\pi\) | |||||||
\(108\) | 13545.9i | 1.16134i | ||||||||
\(109\) | −15685.0 | −1.32018 | −0.660088 | − | 0.751188i | \(-0.729481\pi\) | ||||
−0.660088 | + | 0.751188i | \(0.729481\pi\) | |||||||
\(110\) | −353.216 | −0.0291914 | ||||||||
\(111\) | −4590.75 | −0.372596 | ||||||||
\(112\) | − | 22433.2i | − | 1.78836i | ||||||
\(113\) | − | 14798.9i | − | 1.15897i | −0.814982 | − | 0.579487i | \(-0.803253\pi\) | ||
0.814982 | − | 0.579487i | \(-0.196747\pi\) | |||||||
\(114\) | − | 602.634i | − | 0.0463707i | ||||||
\(115\) | 20757.0i | 1.56953i | ||||||||
\(116\) | 17329.8i | 1.28789i | ||||||||
\(117\) | −26385.6 | −1.92751 | ||||||||
\(118\) | 171.306i | 0.0123029i | ||||||||
\(119\) | 20031.5i | 1.41455i | ||||||||
\(120\) | − | 1645.39i | − | 0.114263i | ||||||
\(121\) | −4306.69 | −0.294153 | ||||||||
\(122\) | −304.030 | −0.0204266 | ||||||||
\(123\) | − | 19828.0i | − | 1.31060i | ||||||
\(124\) | 6920.56 | 0.450088 | ||||||||
\(125\) | 14898.7i | 0.953519i | ||||||||
\(126\) | 1622.29 | 0.102185 | ||||||||
\(127\) | 26014.9 | 1.61292 | 0.806462 | − | 0.591286i | \(-0.201379\pi\) | ||||
0.806462 | + | 0.591286i | \(0.201379\pi\) | |||||||
\(128\) | − | 2180.70i | − | 0.133100i | ||||||
\(129\) | 27301.7 | + | 2039.74i | 1.64063 | + | 0.122573i | ||||
\(130\) | 663.177 | 0.0392412 | ||||||||
\(131\) | − | 274.560i | − | 0.0159991i | −0.999968 | − | 0.00799954i | \(-0.997454\pi\) | ||
0.999968 | − | 0.00799954i | \(-0.00254636\pi\) | |||||||
\(132\) | 24056.8i | 1.38067i | ||||||||
\(133\) | 26810.8 | 1.51568 | ||||||||
\(134\) | 634.442i | 0.0353331i | ||||||||
\(135\) | −22064.1 | −1.21065 | ||||||||
\(136\) | 972.534i | 0.0525808i | ||||||||
\(137\) | − | 26627.9i | − | 1.41872i | −0.704849 | − | 0.709358i | \(-0.748985\pi\) | ||
0.704849 | − | 0.709358i | \(-0.251015\pi\) | |||||||
\(138\) | −1575.79 | −0.0827446 | ||||||||
\(139\) | −3210.55 | −0.166169 | −0.0830846 | − | 0.996542i | \(-0.526477\pi\) | ||||
−0.0830846 | + | 0.996542i | \(0.526477\pi\) | |||||||
\(140\) | 36580.8 | 1.86637 | ||||||||
\(141\) | − | 14864.4i | − | 0.747671i | ||||||
\(142\) | −568.344 | −0.0281861 | ||||||||
\(143\) | −19403.1 | −0.948851 | ||||||||
\(144\) | −35271.6 | −1.70099 | ||||||||
\(145\) | −28227.4 | −1.34256 | ||||||||
\(146\) | 443.300 | 0.0207966 | ||||||||
\(147\) | 78912.6i | 3.65184i | ||||||||
\(148\) | − | 4955.17i | − | 0.226222i | ||||||
\(149\) | 22775.1i | 1.02586i | 0.858431 | + | 0.512929i | \(0.171440\pi\) | ||||
−0.858431 | + | 0.512929i | \(0.828560\pi\) | |||||||
\(150\) | 104.119 | 0.00462751 | ||||||||
\(151\) | − | 3692.73i | − | 0.161955i | −0.996716 | − | 0.0809774i | \(-0.974196\pi\) | ||
0.996716 | − | 0.0809774i | \(-0.0258042\pi\) | |||||||
\(152\) | 1301.67 | 0.0563396 | ||||||||
\(153\) | 31495.5 | 1.34544 | ||||||||
\(154\) | 1192.97 | 0.0503024 | ||||||||
\(155\) | 11272.5i | 0.469197i | ||||||||
\(156\) | − | 45167.6i | − | 1.85600i | ||||||
\(157\) | 15232.3i | 0.617967i | 0.951067 | + | 0.308983i | \(0.0999887\pi\) | ||||
−0.951067 | + | 0.308983i | \(0.900011\pi\) | |||||||
\(158\) | 30.3482i | 0.00121568i | ||||||||
\(159\) | 54024.3i | 2.13695i | ||||||||
\(160\) | 2664.50 | 0.104082 | ||||||||
\(161\) | − | 70105.8i | − | 2.70459i | ||||||
\(162\) | − | 180.471i | − | 0.00687664i | ||||||
\(163\) | − | 7069.03i | − | 0.266063i | −0.991112 | − | 0.133031i | \(-0.957529\pi\) | ||
0.991112 | − | 0.133031i | \(-0.0424711\pi\) | |||||||
\(164\) | 21402.0 | 0.795731 | ||||||||
\(165\) | −39184.6 | −1.43929 | ||||||||
\(166\) | 252.999i | 0.00918128i | ||||||||
\(167\) | −33560.8 | −1.20337 | −0.601686 | − | 0.798733i | \(-0.705504\pi\) | ||||
−0.601686 | + | 0.798733i | \(0.705504\pi\) | |||||||
\(168\) | 5557.24i | 0.196898i | ||||||||
\(169\) | 7868.97 | 0.275514 | ||||||||
\(170\) | −791.608 | −0.0273913 | ||||||||
\(171\) | − | 42154.5i | − | 1.44162i | ||||||
\(172\) | −2201.66 | + | 29468.9i | −0.0744205 | + | 0.996110i | ||||
\(173\) | 24263.7 | 0.810707 | 0.405354 | − | 0.914160i | \(-0.367148\pi\) | ||||
0.405354 | + | 0.914160i | \(0.367148\pi\) | |||||||
\(174\) | − | 2142.91i | − | 0.0707793i | ||||||
\(175\) | 4632.18i | 0.151255i | ||||||||
\(176\) | −25937.5 | −0.837342 | ||||||||
\(177\) | 19004.1i | 0.606599i | ||||||||
\(178\) | 1442.33 | 0.0455223 | ||||||||
\(179\) | − | 39627.8i | − | 1.23679i | −0.785869 | − | 0.618393i | \(-0.787784\pi\) | ||
0.785869 | − | 0.618393i | \(-0.212216\pi\) | |||||||
\(180\) | − | 57515.9i | − | 1.77518i | ||||||
\(181\) | 33212.7 | 1.01379 | 0.506893 | − | 0.862009i | \(-0.330794\pi\) | ||||
0.506893 | + | 0.862009i | \(0.330794\pi\) | |||||||
\(182\) | −2239.85 | −0.0676202 | ||||||||
\(183\) | −33728.1 | −1.00714 | ||||||||
\(184\) | − | 3403.65i | − | 0.100533i | ||||||
\(185\) | 8071.17 | 0.235827 | ||||||||
\(186\) | −855.761 | −0.0247358 | ||||||||
\(187\) | 23160.7 | 0.662320 | ||||||||
\(188\) | 16044.4 | 0.453950 | ||||||||
\(189\) | 74520.4 | 2.08618 | ||||||||
\(190\) | 1059.51i | 0.0293494i | ||||||||
\(191\) | − | 24782.3i | − | 0.679321i | −0.940548 | − | 0.339661i | \(-0.889688\pi\) | ||
0.940548 | − | 0.339661i | \(-0.110312\pi\) | |||||||
\(192\) | − | 60243.9i | − | 1.63422i | ||||||
\(193\) | −29341.9 | −0.787723 | −0.393861 | − | 0.919170i | \(-0.628861\pi\) | ||||
−0.393861 | + | 0.919170i | \(0.628861\pi\) | |||||||
\(194\) | − | 1455.46i | − | 0.0386720i | ||||||
\(195\) | 73570.6 | 1.93480 | ||||||||
\(196\) | −85176.8 | −2.21722 | ||||||||
\(197\) | −39758.4 | −1.02446 | −0.512232 | − | 0.858847i | \(-0.671181\pi\) | ||||
−0.512232 | + | 0.858847i | \(0.671181\pi\) | |||||||
\(198\) | − | 1875.71i | − | 0.0478448i | ||||||
\(199\) | − | 2991.17i | − | 0.0755326i | −0.999287 | − | 0.0377663i | \(-0.987976\pi\) | ||
0.999287 | − | 0.0377663i | \(-0.0120242\pi\) | |||||||
\(200\) | 224.893i | 0.00562233i | ||||||||
\(201\) | 70382.9i | 1.74211i | ||||||||
\(202\) | − | 1258.97i | − | 0.0308541i | ||||||
\(203\) | 95336.8 | 2.31349 | ||||||||
\(204\) | 53914.8i | 1.29553i | ||||||||
\(205\) | 34860.3i | 0.829514i | ||||||||
\(206\) | 1890.08i | 0.0445396i | ||||||||
\(207\) | −110227. | −2.57246 | ||||||||
\(208\) | 48698.6 | 1.12562 | ||||||||
\(209\) | − | 30998.9i | − | 0.709667i | ||||||
\(210\) | −4523.40 | −0.102571 | ||||||||
\(211\) | 28641.7i | 0.643331i | 0.946853 | + | 0.321666i | \(0.104243\pi\) | ||||
−0.946853 | + | 0.321666i | \(0.895757\pi\) | |||||||
\(212\) | −58312.8 | −1.29746 | ||||||||
\(213\) | −63050.2 | −1.38972 | ||||||||
\(214\) | 855.781i | 0.0186868i | ||||||||
\(215\) | −48000.1 | − | 3586.14i | −1.03840 | − | 0.0775801i | ||||
\(216\) | 3617.98 | 0.0775458 | ||||||||
\(217\) | − | 38072.2i | − | 0.808516i | ||||||
\(218\) | 2093.49i | 0.0440512i | ||||||||
\(219\) | 49178.2 | 1.02538 | ||||||||
\(220\) | − | 42295.2i | − | 0.873867i | ||||||
\(221\) | −43485.0 | −0.890339 | ||||||||
\(222\) | 612.732i | 0.0124327i | ||||||||
\(223\) | 35376.8i | 0.711393i | 0.934602 | + | 0.355696i | \(0.115756\pi\) | ||||
−0.934602 | + | 0.355696i | \(0.884244\pi\) | |||||||
\(224\) | −8999.24 | −0.179353 | ||||||||
\(225\) | 7283.17 | 0.143865 | ||||||||
\(226\) | −1975.23 | −0.0386723 | ||||||||
\(227\) | 59327.2i | 1.15134i | 0.817684 | + | 0.575668i | \(0.195258\pi\) | ||||
−0.817684 | + | 0.575668i | \(0.804742\pi\) | |||||||
\(228\) | 72161.2 | 1.38814 | ||||||||
\(229\) | −13413.3 | −0.255778 | −0.127889 | − | 0.991788i | \(-0.540820\pi\) | ||||
−0.127889 | + | 0.991788i | \(0.540820\pi\) | |||||||
\(230\) | 2770.45 | 0.0523715 | ||||||||
\(231\) | 132344. | 2.48017 | ||||||||
\(232\) | 4628.62 | 0.0859954 | ||||||||
\(233\) | 39527.8i | 0.728100i | 0.931379 | + | 0.364050i | \(0.118606\pi\) | ||||
−0.931379 | + | 0.364050i | \(0.881394\pi\) | |||||||
\(234\) | 3521.71i | 0.0643165i | ||||||||
\(235\) | 26133.7i | 0.473222i | ||||||||
\(236\) | −20512.7 | −0.368298 | ||||||||
\(237\) | 3366.73i | 0.0599393i | ||||||||
\(238\) | 2673.62 | 0.0472004 | ||||||||
\(239\) | −24573.9 | −0.430208 | −0.215104 | − | 0.976591i | \(-0.569009\pi\) | ||||
−0.215104 | + | 0.976591i | \(0.569009\pi\) | |||||||
\(240\) | 98347.3 | 1.70742 | ||||||||
\(241\) | 21288.0i | 0.366522i | 0.983064 | + | 0.183261i | \(0.0586654\pi\) | ||||
−0.983064 | + | 0.183261i | \(0.941335\pi\) | |||||||
\(242\) | 574.817i | 0.00981520i | ||||||||
\(243\) | 48631.8i | 0.823583i | ||||||||
\(244\) | − | 36405.4i | − | 0.611486i | ||||||
\(245\) | − | 138739.i | − | 2.31136i | ||||||
\(246\) | −2646.46 | −0.0437316 | ||||||||
\(247\) | 58201.7i | 0.953985i | ||||||||
\(248\) | − | 1848.41i | − | 0.0300536i | ||||||
\(249\) | 28066.9i | 0.452685i | ||||||||
\(250\) | 1988.55 | 0.0318167 | ||||||||
\(251\) | 3878.52 | 0.0615628 | 0.0307814 | − | 0.999526i | \(-0.490200\pi\) | ||||
0.0307814 | + | 0.999526i | \(0.490200\pi\) | |||||||
\(252\) | 194257.i | 3.05898i | ||||||||
\(253\) | −81057.1 | −1.26634 | ||||||||
\(254\) | − | 3472.22i | − | 0.0538196i | ||||||
\(255\) | −87818.4 | −1.35053 | ||||||||
\(256\) | 64807.5 | 0.988885 | ||||||||
\(257\) | − | 33269.3i | − | 0.503706i | −0.967765 | − | 0.251853i | \(-0.918960\pi\) | ||
0.967765 | − | 0.251853i | \(-0.0810400\pi\) | |||||||
\(258\) | 272.246 | − | 3643.98i | 0.00408998 | − | 0.0547440i | ||||
\(259\) | −27260.0 | −0.406375 | ||||||||
\(260\) | 79410.8i | 1.17472i | ||||||||
\(261\) | − | 149898.i | − | 2.20046i | ||||||
\(262\) | −36.6457 | −0.000533852 | ||||||||
\(263\) | − | 40367.8i | − | 0.583612i | −0.956478 | − | 0.291806i | \(-0.905744\pi\) | ||
0.956478 | − | 0.291806i | \(-0.0942561\pi\) | |||||||
\(264\) | 6425.34 | 0.0921910 | ||||||||
\(265\) | − | 94982.1i | − | 1.35254i | ||||||
\(266\) | − | 3578.46i | − | 0.0505746i | ||||||
\(267\) | 160007. | 2.24449 | ||||||||
\(268\) | −75970.0 | −1.05772 | ||||||||
\(269\) | 92958.7 | 1.28465 | 0.642326 | − | 0.766432i | \(-0.277970\pi\) | ||||
0.642326 | + | 0.766432i | \(0.277970\pi\) | |||||||
\(270\) | 2944.91i | 0.0403965i | ||||||||
\(271\) | −61813.2 | −0.841671 | −0.420835 | − | 0.907137i | \(-0.638263\pi\) | ||||
−0.420835 | + | 0.907137i | \(0.638263\pi\) | |||||||
\(272\) | −58129.7 | −0.785706 | ||||||||
\(273\) | −248481. | −3.33402 | ||||||||
\(274\) | −3554.04 | −0.0473393 | ||||||||
\(275\) | 5355.78 | 0.0708202 | ||||||||
\(276\) | − | 188690.i | − | 2.47702i | ||||||
\(277\) | 119892.i | 1.56254i | 0.624193 | + | 0.781270i | \(0.285428\pi\) | ||||
−0.624193 | + | 0.781270i | \(0.714572\pi\) | |||||||
\(278\) | 428.515i | 0.00554468i | ||||||||
\(279\) | −59860.9 | −0.769015 | ||||||||
\(280\) | − | 9770.38i | − | 0.124622i | ||||||
\(281\) | 24043.7 | 0.304501 | 0.152250 | − | 0.988342i | \(-0.451348\pi\) | ||||
0.152250 | + | 0.988342i | \(0.451348\pi\) | |||||||
\(282\) | −1983.97 | −0.0249480 | ||||||||
\(283\) | 112052. | 1.39909 | 0.699546 | − | 0.714588i | \(-0.253386\pi\) | ||||
0.699546 | + | 0.714588i | \(0.253386\pi\) | |||||||
\(284\) | − | 68055.2i | − | 0.843771i | ||||||
\(285\) | 117539.i | 1.44708i | ||||||||
\(286\) | 2589.74i | 0.0316610i | ||||||||
\(287\) | − | 117739.i | − | 1.42941i | ||||||
\(288\) | 14149.5i | 0.170591i | ||||||||
\(289\) | −31614.6 | −0.378523 | ||||||||
\(290\) | 3767.53i | 0.0447982i | ||||||||
\(291\) | − | 161464.i | − | 1.90673i | ||||||
\(292\) | 53082.0i | 0.622560i | ||||||||
\(293\) | 19317.9 | 0.225022 | 0.112511 | − | 0.993650i | \(-0.464111\pi\) | ||||
0.112511 | + | 0.993650i | \(0.464111\pi\) | |||||||
\(294\) | 10532.5 | 0.121853 | ||||||||
\(295\) | − | 33411.8i | − | 0.383934i | ||||||
\(296\) | −1323.48 | −0.0151055 | ||||||||
\(297\) | − | 86161.3i | − | 0.976786i | ||||||
\(298\) | 3039.81 | 0.0342305 | ||||||||
\(299\) | 152188. | 1.70231 | ||||||||
\(300\) | 12467.5i | 0.138528i | ||||||||
\(301\) | 162118. | + | 12112.0i | 1.78936 | + | 0.133685i | ||||
\(302\) | −492.872 | −0.00540406 | ||||||||
\(303\) | − | 139666.i | − | 1.52127i | ||||||
\(304\) | 77802.5i | 0.841873i | ||||||||
\(305\) | 59298.5 | 0.637447 | ||||||||
\(306\) | − | 4203.73i | − | 0.0448944i | ||||||
\(307\) | 44232.3 | 0.469313 | 0.234656 | − | 0.972078i | \(-0.424603\pi\) | ||||
0.234656 | + | 0.972078i | \(0.424603\pi\) | |||||||
\(308\) | 142850.i | 1.50584i | ||||||||
\(309\) | 209680.i | 2.19603i | ||||||||
\(310\) | 1504.54 | 0.0156560 | ||||||||
\(311\) | 61470.8 | 0.635547 | 0.317774 | − | 0.948167i | \(-0.397065\pi\) | ||||
0.317774 | + | 0.948167i | \(0.397065\pi\) | |||||||
\(312\) | −12063.8 | −0.123930 | ||||||||
\(313\) | − | 50511.9i | − | 0.515590i | −0.966200 | − | 0.257795i | \(-0.917004\pi\) | ||
0.966200 | − | 0.257795i | \(-0.0829960\pi\) | |||||||
\(314\) | 2033.06 | 0.0206201 | ||||||||
\(315\) | −316414. | −3.18885 | ||||||||
\(316\) | −3633.99 | −0.0363923 | ||||||||
\(317\) | −28664.5 | −0.285250 | −0.142625 | − | 0.989777i | \(-0.545554\pi\) | ||||
−0.142625 | + | 0.989777i | \(0.545554\pi\) | |||||||
\(318\) | 7210.67 | 0.0713052 | ||||||||
\(319\) | − | 110229.i | − | 1.08322i | ||||||
\(320\) | 105917.i | 1.03435i | ||||||||
\(321\) | 94937.4i | 0.921356i | ||||||||
\(322\) | −9357.07 | −0.0902460 | ||||||||
\(323\) | − | 69473.1i | − | 0.665904i | ||||||
\(324\) | 21610.1 | 0.205857 | ||||||||
\(325\) | −10055.7 | −0.0952017 | ||||||||
\(326\) | −943.508 | −0.00887791 | ||||||||
\(327\) | 232245.i | 2.17195i | ||||||||
\(328\) | − | 5716.26i | − | 0.0531330i | ||||||
\(329\) | − | 88265.4i | − | 0.815453i | ||||||
\(330\) | 5230.00i | 0.0480257i | ||||||||
\(331\) | − | 130429.i | − | 1.19047i | −0.803554 | − | 0.595233i | \(-0.797060\pi\) | ||
0.803554 | − | 0.595233i | \(-0.202940\pi\) | |||||||
\(332\) | −30294.9 | −0.274848 | ||||||||
\(333\) | 42860.9i | 0.386520i | ||||||||
\(334\) | 4479.39i | 0.0401538i | ||||||||
\(335\) | − | 123743.i | − | 1.10263i | ||||||
\(336\) | −332164. | −2.94221 | ||||||||
\(337\) | 85348.4 | 0.751511 | 0.375756 | − | 0.926719i | \(-0.377383\pi\) | ||||
0.375756 | + | 0.926719i | \(0.377383\pi\) | |||||||
\(338\) | − | 1050.28i | − | 0.00919328i | ||||||
\(339\) | −219125. | −1.90674 | ||||||||
\(340\) | − | 94789.5i | − | 0.819978i | ||||||
\(341\) | −44019.6 | −0.378562 | ||||||||
\(342\) | −5626.40 | −0.0481037 | ||||||||
\(343\) | 257482.i | 2.18856i | ||||||||
\(344\) | 7870.87 | + | 588.041i | 0.0665129 | + | 0.00496925i | ||||
\(345\) | 307344. | 2.58218 | ||||||||
\(346\) | − | 3238.49i | − | 0.0270514i | ||||||
\(347\) | − | 145539.i | − | 1.20871i | −0.796717 | − | 0.604353i | \(-0.793432\pi\) | ||
0.796717 | − | 0.604353i | \(-0.206568\pi\) | |||||||
\(348\) | 256599. | 2.11883 | ||||||||
\(349\) | 235394.i | 1.93261i | 0.257391 | + | 0.966307i | \(0.417137\pi\) | ||||
−0.257391 | + | 0.966307i | \(0.582863\pi\) | |||||||
\(350\) | 618.261 | 0.00504702 | ||||||||
\(351\) | 161771.i | 1.31307i | ||||||||
\(352\) | 10405.0i | 0.0839765i | ||||||||
\(353\) | −228188. | −1.83123 | −0.915616 | − | 0.402054i | \(-0.868297\pi\) | ||||
−0.915616 | + | 0.402054i | \(0.868297\pi\) | |||||||
\(354\) | 2536.50 | 0.0202408 | ||||||||
\(355\) | 110851. | 0.879593 | ||||||||
\(356\) | 172709.i | 1.36274i | ||||||||
\(357\) | 296603. | 2.32723 | ||||||||
\(358\) | −5289.16 | −0.0412687 | ||||||||
\(359\) | −73217.3 | −0.568100 | −0.284050 | − | 0.958809i | \(-0.591678\pi\) | ||||
−0.284050 | + | 0.958809i | \(0.591678\pi\) | |||||||
\(360\) | −15361.9 | −0.118534 | ||||||||
\(361\) | 37336.1 | 0.286493 | ||||||||
\(362\) | − | 4432.92i | − | 0.0338277i | ||||||
\(363\) | 63768.3i | 0.483940i | ||||||||
\(364\) | − | 268206.i | − | 2.02426i | ||||||
\(365\) | −86461.9 | −0.648992 | ||||||||
\(366\) | 4501.71i | 0.0336059i | ||||||||
\(367\) | 77952.5 | 0.578759 | 0.289380 | − | 0.957214i | \(-0.406551\pi\) | ||||
0.289380 | + | 0.957214i | \(0.406551\pi\) | |||||||
\(368\) | 203441. | 1.50225 | ||||||||
\(369\) | −185121. | −1.35958 | ||||||||
\(370\) | − | 1077.27i | − | 0.00786900i | ||||||
\(371\) | 320798.i | 2.33068i | ||||||||
\(372\) | − | 102471.i | − | 0.740485i | ||||||
\(373\) | − | 141224.i | − | 1.01506i | −0.861635 | − | 0.507529i | \(-0.830559\pi\) | ||
0.861635 | − | 0.507529i | \(-0.169441\pi\) | |||||||
\(374\) | − | 3091.27i | − | 0.0221001i | ||||||
\(375\) | 220603. | 1.56873 | ||||||||
\(376\) | − | 4285.30i | − | 0.0303114i | ||||||
\(377\) | 206960.i | 1.45614i | ||||||||
\(378\) | − | 9946.29i | − | 0.0696110i | ||||||
\(379\) | −223694. | −1.55731 | −0.778657 | − | 0.627450i | \(-0.784099\pi\) | ||||
−0.778657 | + | 0.627450i | \(0.784099\pi\) | |||||||
\(380\) | −126869. | −0.878595 | ||||||||
\(381\) | − | 385197.i | − | 2.65358i | ||||||
\(382\) | −3307.71 | −0.0226674 | ||||||||
\(383\) | − | 59491.5i | − | 0.405562i | −0.979224 | − | 0.202781i | \(-0.935002\pi\) | ||
0.979224 | − | 0.202781i | \(-0.0649980\pi\) | |||||||
\(384\) | −32289.2 | −0.218975 | ||||||||
\(385\) | −232679. | −1.56977 | ||||||||
\(386\) | 3916.28i | 0.0262845i | ||||||||
\(387\) | 19043.7 | − | 254898.i | 0.127154 | − | 1.70194i | ||||
\(388\) | 174281. | 1.15768 | ||||||||
\(389\) | 273729.i | 1.80893i | 0.426546 | + | 0.904466i | \(0.359730\pi\) | ||||
−0.426546 | + | 0.904466i | \(0.640270\pi\) | |||||||
\(390\) | − | 9819.53i | − | 0.0645597i | ||||||
\(391\) | −181661. | −1.18825 | ||||||||
\(392\) | 22749.9i | 0.148050i | ||||||||
\(393\) | −4065.36 | −0.0263217 | ||||||||
\(394\) | 5306.59i | 0.0341840i | ||||||||
\(395\) | − | 5919.17i | − | 0.0379373i | ||||||
\(396\) | 224603. | 1.43227 | ||||||||
\(397\) | 188678. | 1.19713 | 0.598564 | − | 0.801075i | \(-0.295738\pi\) | ||||
0.598564 | + | 0.801075i | \(0.295738\pi\) | |||||||
\(398\) | −399.233 | −0.00252035 | ||||||||
\(399\) | − | 396982.i | − | 2.49359i | ||||||
\(400\) | −13442.2 | −0.0840136 | ||||||||
\(401\) | −27975.8 | −0.173978 | −0.0869889 | − | 0.996209i | \(-0.527724\pi\) | ||||
−0.0869889 | + | 0.996209i | \(0.527724\pi\) | |||||||
\(402\) | 9394.06 | 0.0581301 | ||||||||
\(403\) | 82648.4 | 0.508890 | ||||||||
\(404\) | 150753. | 0.923641 | ||||||||
\(405\) | 35199.3i | 0.214597i | ||||||||
\(406\) | − | 12724.7i | − | 0.0771959i | ||||||
\(407\) | 31518.4i | 0.190272i | ||||||||
\(408\) | 14400.1 | 0.0865059 | ||||||||
\(409\) | − | 22322.2i | − | 0.133441i | −0.997772 | − | 0.0667207i | \(-0.978746\pi\) | ||
0.997772 | − | 0.0667207i | \(-0.0212536\pi\) | |||||||
\(410\) | 4652.84 | 0.0276790 | ||||||||
\(411\) | −394274. | −2.33407 | ||||||||
\(412\) | −226324. | −1.33333 | ||||||||
\(413\) | 112847.i | 0.661592i | ||||||||
\(414\) | 14712.1i | 0.0858369i | ||||||||
\(415\) | − | 49345.4i | − | 0.286517i | ||||||
\(416\) | − | 19535.8i | − | 0.112887i | ||||||
\(417\) | 47538.0i | 0.273382i | ||||||||
\(418\) | −4137.45 | −0.0236799 | ||||||||
\(419\) | − | 160113.i | − | 0.912006i | −0.889978 | − | 0.456003i | \(-0.849281\pi\) | ||
0.889978 | − | 0.456003i | \(-0.150719\pi\) | |||||||
\(420\) | − | 541645.i | − | 3.07055i | ||||||
\(421\) | − | 289642.i | − | 1.63417i | −0.576517 | − | 0.817085i | \(-0.695589\pi\) | ||
0.576517 | − | 0.817085i | \(-0.304411\pi\) | |||||||
\(422\) | 3822.84 | 0.0214665 | ||||||||
\(423\) | −138780. | −0.775612 | ||||||||
\(424\) | 15574.8i | 0.0866344i | ||||||||
\(425\) | 12003.1 | 0.0664530 | ||||||||
\(426\) | 8415.35i | 0.0463717i | ||||||||
\(427\) | −200278. | −1.09844 | ||||||||
\(428\) | −102474. | −0.559403 | ||||||||
\(429\) | 287297.i | 1.56105i | ||||||||
\(430\) | −478.645 | + | 6406.61i | −0.00258867 | + | 0.0346490i | ||||
\(431\) | −6996.04 | −0.0376615 | −0.0188308 | − | 0.999823i | \(-0.505994\pi\) | ||||
−0.0188308 | + | 0.999823i | \(0.505994\pi\) | |||||||
\(432\) | 216252.i | 1.15876i | ||||||||
\(433\) | 190817.i | 1.01775i | 0.860841 | + | 0.508875i | \(0.169938\pi\) | ||||
−0.860841 | + | 0.508875i | \(0.830062\pi\) | |||||||
\(434\) | −5081.53 | −0.0269783 | ||||||||
\(435\) | 417957.i | 2.20879i | ||||||||
\(436\) | −250681. | −1.31871 | ||||||||
\(437\) | 243140.i | 1.27319i | ||||||||
\(438\) | − | 6563.85i | − | 0.0342145i | ||||||
\(439\) | 284875. | 1.47818 | 0.739088 | − | 0.673609i | \(-0.235257\pi\) | ||||
0.739088 | + | 0.673609i | \(0.235257\pi\) | |||||||
\(440\) | −11296.6 | −0.0583503 | ||||||||
\(441\) | 736755. | 3.78832 | ||||||||
\(442\) | 5803.98i | 0.0297085i | ||||||||
\(443\) | 278521. | 1.41922 | 0.709610 | − | 0.704594i | \(-0.248871\pi\) | ||||
0.709610 | + | 0.704594i | \(0.248871\pi\) | |||||||
\(444\) | −73370.3 | −0.372181 | ||||||||
\(445\) | −281314. | −1.42060 | ||||||||
\(446\) | 4721.78 | 0.0237375 | ||||||||
\(447\) | 337226. | 1.68774 | ||||||||
\(448\) | − | 357730.i | − | 1.78237i | ||||||
\(449\) | 14484.9i | 0.0718495i | 0.999354 | + | 0.0359248i | \(0.0114377\pi\) | ||||
−0.999354 | + | 0.0359248i | \(0.988562\pi\) | |||||||
\(450\) | − | 972.090i | − | 0.00480044i | ||||||
\(451\) | −136131. | −0.669276 | ||||||||
\(452\) | − | 236519.i | − | 1.15768i | ||||||
\(453\) | −54677.6 | −0.266448 | ||||||||
\(454\) | 7918.45 | 0.0384174 | ||||||||
\(455\) | 436864. | 2.11020 | ||||||||
\(456\) | − | 19273.6i | − | 0.0926898i | ||||||
\(457\) | − | 352890.i | − | 1.68969i | −0.535012 | − | 0.844844i | \(-0.679693\pi\) | ||
0.535012 | − | 0.844844i | \(-0.320307\pi\) | |||||||
\(458\) | 1790.28i | 0.00853473i | ||||||||
\(459\) | − | 193100.i | − | 0.916551i | ||||||
\(460\) | 331742.i | 1.56778i | ||||||||
\(461\) | −183860. | −0.865138 | −0.432569 | − | 0.901601i | \(-0.642393\pi\) | ||||
−0.432569 | + | 0.901601i | \(0.642393\pi\) | |||||||
\(462\) | − | 17664.1i | − | 0.0827575i | ||||||
\(463\) | 33276.3i | 0.155229i | 0.996983 | + | 0.0776145i | \(0.0247303\pi\) | ||||
−0.996983 | + | 0.0776145i | \(0.975270\pi\) | |||||||
\(464\) | 276659.i | 1.28502i | ||||||||
\(465\) | 166909. | 0.771923 | ||||||||
\(466\) | 5275.81 | 0.0242950 | ||||||||
\(467\) | 16400.1i | 0.0751992i | 0.999293 | + | 0.0375996i | \(0.0119711\pi\) | ||||
−0.999293 | + | 0.0375996i | \(0.988029\pi\) | |||||||
\(468\) | −421700. | −1.92536 | ||||||||
\(469\) | 417935.i | 1.90004i | ||||||||
\(470\) | 3488.09 | 0.0157903 | ||||||||
\(471\) | 225541. | 1.01668 | ||||||||
\(472\) | 5478.75i | 0.0245922i | ||||||||
\(473\) | 14004.1 | − | 187443.i | 0.0625939 | − | 0.837812i | ||||
\(474\) | 449.360 | 0.00200004 | ||||||||
\(475\) | − | 16065.3i | − | 0.0712034i | ||||||
\(476\) | 320147.i | 1.41298i | ||||||||
\(477\) | 504390. | 2.21681 | ||||||||
\(478\) | 3279.90i | 0.0143551i | ||||||||
\(479\) | −400012. | −1.74342 | −0.871711 | − | 0.490020i | \(-0.836989\pi\) | ||||
−0.871711 | + | 0.490020i | \(0.836989\pi\) | |||||||
\(480\) | − | 39452.8i | − | 0.171236i | ||||||
\(481\) | − | 59176.9i | − | 0.255777i | ||||||
\(482\) | 2841.32 | 0.0122300 | ||||||||
\(483\) | −1.03804e6 | −4.44960 | ||||||||
\(484\) | −68830.3 | −0.293825 | ||||||||
\(485\) | 283876.i | 1.20683i | ||||||||
\(486\) | 6490.92 | 0.0274811 | ||||||||
\(487\) | 166088. | 0.700293 | 0.350146 | − | 0.936695i | \(-0.386132\pi\) | ||||
0.350146 | + | 0.936695i | \(0.386132\pi\) | |||||||
\(488\) | −9723.54 | −0.0408305 | ||||||||
\(489\) | −104670. | −0.437727 | ||||||||
\(490\) | −18517.6 | −0.0771246 | ||||||||
\(491\) | 320840.i | 1.33084i | 0.746470 | + | 0.665419i | \(0.231747\pi\) | ||||
−0.746470 | + | 0.665419i | \(0.768253\pi\) | |||||||
\(492\) | − | 316895.i | − | 1.30914i | ||||||
\(493\) | − | 247040.i | − | 1.01642i | ||||||
\(494\) | 7768.23 | 0.0318323 | ||||||||
\(495\) | 365841.i | 1.49308i | ||||||||
\(496\) | 110482. | 0.449085 | ||||||||
\(497\) | −374393. | −1.51571 | ||||||||
\(498\) | 3746.11 | 0.0151050 | ||||||||
\(499\) | − | 56730.2i | − | 0.227831i | −0.993490 | − | 0.113916i | \(-0.963661\pi\) | ||
0.993490 | − | 0.113916i | \(-0.0363393\pi\) | |||||||
\(500\) | 238114.i | 0.952457i | ||||||||
\(501\) | 496929.i | 1.97979i | ||||||||
\(502\) | − | 517.669i | − | 0.00205421i | ||||||
\(503\) | − | 331332.i | − | 1.30957i | −0.755817 | − | 0.654783i | \(-0.772760\pi\) | ||
0.755817 | − | 0.654783i | \(-0.227240\pi\) | |||||||
\(504\) | 51884.3 | 0.204256 | ||||||||
\(505\) | 245552.i | 0.962854i | ||||||||
\(506\) | 10818.8i | 0.0422548i | ||||||||
\(507\) | − | 116514.i | − | 0.453276i | ||||||
\(508\) | 415774. | 1.61113 | ||||||||
\(509\) | −68886.4 | −0.265887 | −0.132944 | − | 0.991124i | \(-0.542443\pi\) | ||||
−0.132944 | + | 0.991124i | \(0.542443\pi\) | |||||||
\(510\) | 11721.2i | 0.0450642i | ||||||||
\(511\) | 292021. | 1.11834 | ||||||||
\(512\) | − | 43541.2i | − | 0.166096i | ||||||
\(513\) | −258451. | −0.982072 | ||||||||
\(514\) | −4440.48 | −0.0168075 | ||||||||
\(515\) | − | 368645.i | − | 1.38993i | ||||||
\(516\) | 436341. | + | 32599.5i | 1.63880 | + | 0.122437i | ||||
\(517\) | −102054. | −0.381810 | ||||||||
\(518\) | 3638.42i | 0.0135598i | ||||||||
\(519\) | − | 359267.i | − | 1.33378i | ||||||
\(520\) | 21209.8 | 0.0784388 | ||||||||
\(521\) | − | 480907.i | − | 1.77168i | −0.463990 | − | 0.885841i | \(-0.653582\pi\) | ||
0.463990 | − | 0.885841i | \(-0.346418\pi\) | |||||||
\(522\) | −20007.0 | −0.0734244 | ||||||||
\(523\) | 140709.i | 0.514423i | 0.966355 | + | 0.257211i | \(0.0828036\pi\) | ||||
−0.966355 | + | 0.257211i | \(0.917196\pi\) | |||||||
\(524\) | − | 4388.07i | − | 0.0159813i | ||||||
\(525\) | 68587.8 | 0.248844 | ||||||||
\(526\) | −5387.93 | −0.0194738 | ||||||||
\(527\) | −98654.1 | −0.355217 | ||||||||
\(528\) | 384051.i | 1.37760i | ||||||||
\(529\) | 355930. | 1.27190 | ||||||||
\(530\) | −12677.3 | −0.0451311 | ||||||||
\(531\) | 177429. | 0.629268 | ||||||||
\(532\) | 428495. | 1.51399 | ||||||||
\(533\) | 255592. | 0.899690 | ||||||||
\(534\) | − | 21356.3i | − | 0.0748934i | ||||||
\(535\) | − | 166913.i | − | 0.583153i | ||||||
\(536\) | 20290.8i | 0.0706269i | ||||||||
\(537\) | −586761. | −2.03476 | ||||||||
\(538\) | − | 12407.3i | − | 0.0428659i | ||||||
\(539\) | 541784. | 1.86487 | ||||||||
\(540\) | −352632. | −1.20930 | ||||||||
\(541\) | −227082. | −0.775869 | −0.387935 | − | 0.921687i | \(-0.626811\pi\) | ||||
−0.387935 | + | 0.921687i | \(0.626811\pi\) | |||||||
\(542\) | 8250.25i | 0.0280846i | ||||||||
\(543\) | − | 491773.i | − | 1.66788i | ||||||
\(544\) | 23319.2i | 0.0787980i | ||||||||
\(545\) | − | 408318.i | − | 1.37469i | ||||||
\(546\) | 33165.0i | 0.111249i | ||||||||
\(547\) | −203039. | −0.678587 | −0.339294 | − | 0.940681i | \(-0.610188\pi\) | ||||
−0.339294 | + | 0.940681i | \(0.610188\pi\) | |||||||
\(548\) | − | 425572.i | − | 1.41714i | ||||||
\(549\) | 314897.i | 1.04478i | ||||||||
\(550\) | − | 714.840i | − | 0.00236311i | ||||||
\(551\) | −330646. | −1.08908 | ||||||||
\(552\) | −50397.2 | −0.165397 | ||||||||
\(553\) | 19991.7i | 0.0653733i | ||||||||
\(554\) | 16002.1 | 0.0521384 | ||||||||
\(555\) | − | 119508.i | − | 0.387982i | ||||||
\(556\) | −51311.7 | −0.165984 | ||||||||
\(557\) | −578004. | −1.86303 | −0.931517 | − | 0.363699i | \(-0.881514\pi\) | ||||
−0.931517 | + | 0.363699i | \(0.881514\pi\) | |||||||
\(558\) | 7989.68i | 0.0256603i | ||||||||
\(559\) | −26293.2 | + | 351931.i | −0.0841432 | + | 1.12625i | ||||
\(560\) | 583989. | 1.86221 | ||||||||
\(561\) | − | 342935.i | − | 1.08965i | ||||||
\(562\) | − | 3209.13i | − | 0.0101605i | ||||||
\(563\) | 263355. | 0.830855 | 0.415428 | − | 0.909626i | \(-0.363632\pi\) | ||||
0.415428 | + | 0.909626i | \(0.363632\pi\) | |||||||
\(564\) | − | 237566.i | − | 0.746838i | ||||||
\(565\) | 385251. | 1.20683 | ||||||||
\(566\) | − | 14955.6i | − | 0.0466845i | ||||||
\(567\) | − | 118884.i | − | 0.369792i | ||||||
\(568\) | −18176.9 | −0.0563407 | ||||||||
\(569\) | 233303. | 0.720603 | 0.360302 | − | 0.932836i | \(-0.382674\pi\) | ||||
0.360302 | + | 0.932836i | \(0.382674\pi\) | |||||||
\(570\) | 15688.0 | 0.0482856 | ||||||||
\(571\) | − | 348145.i | − | 1.06779i | −0.845549 | − | 0.533897i | \(-0.820727\pi\) | ||
0.845549 | − | 0.533897i | \(-0.179273\pi\) | |||||||
\(572\) | −310103. | −0.947795 | ||||||||
\(573\) | −366947. | −1.11762 | ||||||||
\(574\) | −15714.7 | −0.0476962 | ||||||||
\(575\) | −42008.0 | −0.127056 | ||||||||
\(576\) | −562458. | −1.69529 | ||||||||
\(577\) | 217612.i | 0.653628i | 0.945089 | + | 0.326814i | \(0.105975\pi\) | ||||
−0.945089 | + | 0.326814i | \(0.894025\pi\) | |||||||
\(578\) | 4219.63i | 0.0126304i | ||||||||
\(579\) | 434460.i | 1.29596i | ||||||||
\(580\) | −451135. | −1.34107 | ||||||||
\(581\) | 166662.i | 0.493724i | ||||||||
\(582\) | −21550.7 | −0.0636233 | ||||||||
\(583\) | 370910. | 1.09127 | ||||||||
\(584\) | 14177.7 | 0.0415700 | ||||||||
\(585\) | − | 686881.i | − | 2.00710i | ||||||
\(586\) | − | 2578.38i | − | 0.00750848i | ||||||
\(587\) | − | 368118.i | − | 1.06834i | −0.845376 | − | 0.534172i | \(-0.820624\pi\) | ||
0.845376 | − | 0.534172i | \(-0.179376\pi\) | |||||||
\(588\) | 1.26120e6i | 3.64777i | ||||||||
\(589\) | 132042.i | 0.380610i | ||||||||
\(590\) | −4459.51 | −0.0128110 | ||||||||
\(591\) | 588696.i | 1.68545i | ||||||||
\(592\) | − | 79106.1i | − | 0.225718i | ||||||
\(593\) | 216642.i | 0.616073i | 0.951374 | + | 0.308037i | \(0.0996720\pi\) | ||||
−0.951374 | + | 0.308037i | \(0.900328\pi\) | |||||||
\(594\) | −11500.0 | −0.0325931 | ||||||||
\(595\) | −521468. | −1.47297 | ||||||||
\(596\) | 363996.i | 1.02472i | ||||||||
\(597\) | −44289.6 | −0.124266 | ||||||||
\(598\) | − | 20312.6i | − | 0.0568020i | ||||||
\(599\) | −119963. | −0.334345 | −0.167173 | − | 0.985928i | \(-0.553464\pi\) | ||||
−0.167173 | + | 0.985928i | \(0.553464\pi\) | |||||||
\(600\) | 3329.95 | 0.00924986 | ||||||||
\(601\) | − | 128663.i | − | 0.356207i | −0.984012 | − | 0.178104i | \(-0.943004\pi\) | ||
0.984012 | − | 0.178104i | \(-0.0569963\pi\) | |||||||
\(602\) | 1616.60 | − | 21638.0i | 0.00446077 | − | 0.0597069i | ||||
\(603\) | 657119. | 1.80721 | ||||||||
\(604\) | − | 59018.0i | − | 0.161775i | ||||||
\(605\) | − | 112113.i | − | 0.306300i | ||||||
\(606\) | −18641.3 | −0.0507612 | ||||||||
\(607\) | − | 44121.9i | − | 0.119750i | −0.998206 | − | 0.0598751i | \(-0.980930\pi\) | ||
0.998206 | − | 0.0598751i | \(-0.0190703\pi\) | |||||||
\(608\) | 31211.1 | 0.0844309 | ||||||||
\(609\) | − | 1.41163e6i | − | 3.80616i | ||||||
\(610\) | − | 7914.62i | − | 0.0212701i | ||||||
\(611\) | 191609. | 0.513256 | ||||||||
\(612\) | 503367. | 1.34395 | ||||||||
\(613\) | −130644. | −0.347671 | −0.173836 | − | 0.984775i | \(-0.555616\pi\) | ||||
−0.173836 | + | 0.984775i | \(0.555616\pi\) | |||||||
\(614\) | − | 5903.72i | − | 0.0156599i | ||||||
\(615\) | 516170. | 1.36472 | ||||||||
\(616\) | 38153.9 | 0.100549 | ||||||||
\(617\) | −6618.63 | −0.0173859 | −0.00869296 | − | 0.999962i | \(-0.502767\pi\) | ||||
−0.00869296 | + | 0.999962i | \(0.502767\pi\) | |||||||
\(618\) | 27986.1 | 0.0732766 | ||||||||
\(619\) | 294513. | 0.768641 | 0.384320 | − | 0.923200i | \(-0.374436\pi\) | ||||
0.384320 | + | 0.923200i | \(0.374436\pi\) | |||||||
\(620\) | 180159.i | 0.468675i | ||||||||
\(621\) | 675806.i | 1.75242i | ||||||||
\(622\) | − | 8204.55i | − | 0.0212068i | ||||||
\(623\) | 950127. | 2.44797 | ||||||||
\(624\) | − | 721071.i | − | 1.85186i | ||||||
\(625\) | −420777. | −1.07719 | ||||||||
\(626\) | −6741.86 | −0.0172041 | ||||||||
\(627\) | −458995. | −1.16754 | ||||||||
\(628\) | 243445.i | 0.617279i | ||||||||
\(629\) | 70637.2i | 0.178539i | ||||||||
\(630\) | 42232.0i | 0.106405i | ||||||||
\(631\) | 493017.i | 1.23824i | 0.785298 | + | 0.619118i | \(0.212510\pi\) | ||||
−0.785298 | + | 0.619118i | \(0.787490\pi\) | |||||||
\(632\) | 970.603i | 0.00243001i | ||||||||
\(633\) | 424093. | 1.05841 | ||||||||
\(634\) | 3825.88i | 0.00951815i | ||||||||
\(635\) | 677228.i | 1.67953i | ||||||||
\(636\) | 863426.i | 2.13457i | ||||||||
\(637\) | −1.01722e6 | −2.50689 | ||||||||
\(638\) | −14712.4 | −0.0361445 | ||||||||
\(639\) | 588658.i | 1.44165i | ||||||||
\(640\) | 56768.9 | 0.138596 | ||||||||
\(641\) | 212494.i | 0.517167i | 0.965989 | + | 0.258584i | \(0.0832557\pi\) | ||||
−0.965989 | + | 0.258584i | \(0.916744\pi\) | |||||||
\(642\) | 12671.4 | 0.0307435 | ||||||||
\(643\) | 332186. | 0.803451 | 0.401725 | − | 0.915760i | \(-0.368411\pi\) | ||||
0.401725 | + | 0.915760i | \(0.368411\pi\) | |||||||
\(644\) | − | 1.12044e6i | − | 2.70158i | ||||||
\(645\) | −53099.2 | + | 710728.i | −0.127635 | + | 1.70838i | ||||
\(646\) | −9272.63 | −0.0222197 | ||||||||
\(647\) | − | 672018.i | − | 1.60536i | −0.596410 | − | 0.802680i | \(-0.703407\pi\) | ||
0.596410 | − | 0.802680i | \(-0.296593\pi\) | |||||||
\(648\) | − | 5771.84i | − | 0.0137456i | ||||||
\(649\) | 130475. | 0.309769 | ||||||||
\(650\) | 1342.14i | 0.00317666i | ||||||||
\(651\) | −563728. | −1.33017 | ||||||||
\(652\) | − | 112978.i | − | 0.265767i | ||||||
\(653\) | − | 471578.i | − | 1.10593i | −0.833205 | − | 0.552965i | \(-0.813496\pi\) | ||
0.833205 | − | 0.552965i | \(-0.186504\pi\) | |||||||
\(654\) | 30997.9 | 0.0724731 | ||||||||
\(655\) | 7147.45 | 0.0166598 | ||||||||
\(656\) | 341669. | 0.793958 | ||||||||
\(657\) | − | 459144.i | − | 1.06370i | ||||||
\(658\) | −11780.9 | −0.0272098 | ||||||||
\(659\) | −140481. | −0.323479 | −0.161739 | − | 0.986834i | \(-0.551710\pi\) | ||||
−0.161739 | + | 0.986834i | \(0.551710\pi\) | |||||||
\(660\) | −626256. | −1.43769 | ||||||||
\(661\) | −426152. | −0.975353 | −0.487676 | − | 0.873024i | \(-0.662155\pi\) | ||||
−0.487676 | + | 0.873024i | \(0.662155\pi\) | |||||||
\(662\) | −17408.4 | −0.0397231 | ||||||||
\(663\) | 643874.i | 1.46479i | ||||||||
\(664\) | 8091.47i | 0.0183523i | ||||||||
\(665\) | 697948.i | 1.57827i | ||||||||
\(666\) | 5720.67 | 0.0128973 | ||||||||
\(667\) | 864584.i | 1.94337i | ||||||||
\(668\) | −536376. | −1.20203 | ||||||||
\(669\) | 523818. | 1.17038 | ||||||||
\(670\) | −16516.0 | −0.0367922 | ||||||||
\(671\) | 231564.i | 0.514311i | ||||||||
\(672\) | 133250.i | 0.295072i | ||||||||
\(673\) | − | 183510.i | − | 0.405163i | −0.979265 | − | 0.202582i | \(-0.935067\pi\) | ||
0.979265 | − | 0.202582i | \(-0.0649332\pi\) | |||||||
\(674\) | − | 11391.5i | − | 0.0250762i | ||||||
\(675\) | − | 44653.3i | − | 0.0980045i | ||||||
\(676\) | 125763. | 0.275208 | ||||||||
\(677\) | − | 331953.i | − | 0.724269i | −0.932126 | − | 0.362134i | \(-0.882048\pi\) | ||
0.932126 | − | 0.362134i | \(-0.117952\pi\) | |||||||
\(678\) | 29246.8i | 0.0636237i | ||||||||
\(679\) | − | 958777.i | − | 2.07959i | ||||||
\(680\) | −25317.4 | −0.0547521 | ||||||||
\(681\) | 878446. | 1.89418 | ||||||||
\(682\) | 5875.32i | 0.0126317i | ||||||||
\(683\) | −801639. | −1.71845 | −0.859226 | − | 0.511596i | \(-0.829054\pi\) | ||||
−0.859226 | + | 0.511596i | \(0.829054\pi\) | |||||||
\(684\) | − | 673722.i | − | 1.44002i | ||||||
\(685\) | 693187. | 1.47730 | ||||||||
\(686\) | 34366.3 | 0.0730271 | ||||||||
\(687\) | 198608.i | 0.420807i | ||||||||
\(688\) | −35148.0 | + | 470452.i | −0.0742547 | + | 0.993891i | ||||
\(689\) | −696398. | −1.46696 | ||||||||
\(690\) | − | 41021.5i | − | 0.0861615i | ||||||
\(691\) | 54538.3i | 0.114221i | 0.998368 | + | 0.0571105i | \(0.0181887\pi\) | ||||
−0.998368 | + | 0.0571105i | \(0.981811\pi\) | |||||||
\(692\) | 387786. | 0.809805 | ||||||||
\(693\) | − | 1.23561e6i | − | 2.57286i | ||||||
\(694\) | −19425.2 | −0.0403317 | ||||||||
\(695\) | − | 83578.3i | − | 0.173031i | ||||||
\(696\) | − | 68535.0i | − | 0.141480i | ||||||
\(697\) | −305090. | −0.628004 | ||||||||
\(698\) | 31418.3 | 0.0644869 | ||||||||
\(699\) | 585281. | 1.19787 | ||||||||
\(700\) | 74032.3i | 0.151086i | ||||||||
\(701\) | −830004. | −1.68906 | −0.844528 | − | 0.535511i | \(-0.820119\pi\) | ||||
−0.844528 | + | 0.535511i | \(0.820119\pi\) | |||||||
\(702\) | 21591.7 | 0.0438140 | ||||||||
\(703\) | 94542.9 | 0.191301 | ||||||||
\(704\) | −413611. | −0.834540 | ||||||||
\(705\) | 386957. | 0.778546 | ||||||||
\(706\) | 30456.4i | 0.0611040i | ||||||||
\(707\) | − | 829341.i | − | 1.65918i | ||||||
\(708\) | 303728.i | 0.605923i | ||||||||
\(709\) | 539592. | 1.07343 | 0.536715 | − | 0.843764i | \(-0.319665\pi\) | ||||
0.536715 | + | 0.843764i | \(0.319665\pi\) | |||||||
\(710\) | − | 14795.3i | − | 0.0293500i | ||||||
\(711\) | 31433.0 | 0.0621793 | ||||||||
\(712\) | 46128.9 | 0.0909940 | ||||||||
\(713\) | 345267. | 0.679166 | ||||||||
\(714\) | − | 39587.8i | − | 0.0776542i | ||||||
\(715\) | − | 505108.i | − | 0.988034i | ||||||
\(716\) | − | 633339.i | − | 1.23541i | ||||||
\(717\) | 363861.i | 0.707779i | ||||||||
\(718\) | 9772.37i | 0.0189562i | ||||||||
\(719\) | −707898. | −1.36935 | −0.684673 | − | 0.728851i | \(-0.740055\pi\) | ||||
−0.684673 | + | 0.728851i | \(0.740055\pi\) | |||||||
\(720\) | − | 918204.i | − | 1.77123i | ||||||
\(721\) | 1.24508e6i | 2.39512i | ||||||||
\(722\) | − | 4983.28i | − | 0.00955962i | ||||||
\(723\) | 315207. | 0.603003 | ||||||||
\(724\) | 530811. | 1.01266 | ||||||||
\(725\) | − | 57126.7i | − | 0.108683i | ||||||
\(726\) | 8511.21 | 0.0161480 | ||||||||
\(727\) | 182701.i | 0.345679i | 0.984950 | + | 0.172839i | \(0.0552942\pi\) | ||||
−0.984950 | + | 0.172839i | \(0.944706\pi\) | |||||||
\(728\) | −71635.3 | −0.135165 | ||||||||
\(729\) | 829604. | 1.56105 | ||||||||
\(730\) | 11540.1i | 0.0216554i | ||||||||
\(731\) | 31385.1 | − | 420086.i | 0.0587339 | − | 0.786147i | ||||
\(732\) | −539048. | −1.00602 | ||||||||
\(733\) | − | 928539.i | − | 1.72819i | −0.503326 | − | 0.864097i | \(-0.667890\pi\) | ||
0.503326 | − | 0.864097i | \(-0.332110\pi\) | |||||||
\(734\) | − | 10404.4i | − | 0.0193119i | ||||||
\(735\) | −2.05428e6 | −3.80264 | ||||||||
\(736\) | − | 81611.8i | − | 0.150660i | ||||||
\(737\) | 483222. | 0.889634 | ||||||||
\(738\) | 24708.3i | 0.0453659i | ||||||||
\(739\) | 177700.i | 0.325386i | 0.986677 | + | 0.162693i | \(0.0520180\pi\) | ||||
−0.986677 | + | 0.162693i | \(0.947982\pi\) | |||||||
\(740\) | 128995. | 0.235564 | ||||||||
\(741\) | 861781. | 1.56950 | ||||||||
\(742\) | 42817.1 | 0.0777696 | ||||||||
\(743\) | 576694.i | 1.04464i | 0.852748 | + | 0.522322i | \(0.174934\pi\) | ||||
−0.852748 | + | 0.522322i | \(0.825066\pi\) | |||||||
\(744\) | −27369.1 | −0.0494441 | ||||||||
\(745\) | −592890. | −1.06822 | ||||||||
\(746\) | −18849.3 | −0.0338701 | ||||||||
\(747\) | 262042. | 0.469602 | ||||||||
\(748\) | 370158. | 0.661583 | ||||||||
\(749\) | 563741.i | 1.00488i | ||||||||
\(750\) | − | 29444.0i | − | 0.0523449i | ||||||
\(751\) | − | 478034.i | − | 0.847576i | −0.905761 | − | 0.423788i | \(-0.860700\pi\) | ||
0.905761 | − | 0.423788i | \(-0.139300\pi\) | |||||||
\(752\) | 256138. | 0.452938 | ||||||||
\(753\) | − | 57428.5i | − | 0.101283i | ||||||
\(754\) | 27623.1 | 0.0485881 | ||||||||
\(755\) | 96130.6 | 0.168643 | ||||||||
\(756\) | 1.19100e6 | 2.08386 | ||||||||
\(757\) | − | 1.05095e6i | − | 1.83395i | −0.398939 | − | 0.916977i | \(-0.630622\pi\) | ||
0.398939 | − | 0.916977i | \(-0.369378\pi\) | |||||||
\(758\) | 29856.6i | 0.0519640i | ||||||||
\(759\) | 1.20020e6i | 2.08338i | ||||||||
\(760\) | 33885.5i | 0.0586661i | ||||||||
\(761\) | 38638.8i | 0.0667197i | 0.999443 | + | 0.0333599i | \(0.0106207\pi\) | ||||
−0.999443 | + | 0.0333599i | \(0.989379\pi\) | |||||||
\(762\) | −51412.5 | −0.0885440 | ||||||||
\(763\) | 1.37908e6i | 2.36886i | ||||||||
\(764\) | − | 396075.i | − | 0.678565i | ||||||
\(765\) | 819903.i | 1.40100i | ||||||||
\(766\) | −7940.38 | −0.0135327 | ||||||||
\(767\) | −244972. | −0.416414 | ||||||||
\(768\) | − | 959592.i | − | 1.62691i | ||||||
\(769\) | −582597. | −0.985181 | −0.492590 | − | 0.870261i | \(-0.663950\pi\) | ||||
−0.492590 | + | 0.870261i | \(0.663950\pi\) | |||||||
\(770\) | 31055.9i | 0.0523796i | ||||||||
\(771\) | −492612. | −0.828698 | ||||||||
\(772\) | −468947. | −0.786846 | ||||||||
\(773\) | − | 247652.i | − | 0.414461i | −0.978292 | − | 0.207230i | \(-0.933555\pi\) | ||
0.978292 | − | 0.207230i | \(-0.0664450\pi\) | |||||||
\(774\) | −34021.4 | − | 2541.78i | −0.0567898 | − | 0.00424283i | ||||
\(775\) | −22813.2 | −0.0379825 | ||||||||
\(776\) | − | 46548.8i | − | 0.0773010i | ||||||
\(777\) | 403634.i | 0.668568i | ||||||||
\(778\) | 36534.9 | 0.0603599 | ||||||||
\(779\) | 408342.i | 0.672898i | ||||||||
\(780\) | 1.17582e6 | 1.93264 | ||||||||
\(781\) | 432878.i | 0.709682i | ||||||||
\(782\) | 24246.4i | 0.0396491i | ||||||||
\(783\) | −919028. | −1.49901 | ||||||||
\(784\) | −1.35979e6 | −2.21228 | ||||||||
\(785\) | −396532. | −0.643486 | ||||||||
\(786\) | 542.606i | 0.000878294i | ||||||||
\(787\) | 840560. | 1.35712 | 0.678561 | − | 0.734544i | \(-0.262604\pi\) | ||||
0.678561 | + | 0.734544i | \(0.262604\pi\) | |||||||
\(788\) | −635427. | −1.02332 | ||||||||
\(789\) | −597719. | −0.960158 | ||||||||
\(790\) | −790.036 | −0.00126588 | ||||||||
\(791\) | −1.30117e6 | −2.07960 | ||||||||
\(792\) | − | 59989.2i | − | 0.0956363i | ||||||
\(793\) | − | 434770.i | − | 0.691374i | ||||||
\(794\) | − | 25183.0i | − | 0.0399454i | ||||||
\(795\) | −1.40638e6 | −2.22520 | ||||||||
\(796\) | − | 47805.4i | − | 0.0754485i | ||||||
\(797\) | 1.23636e6 | 1.94638 | 0.973188 | − | 0.230013i | \(-0.0738768\pi\) | ||||
0.973188 | + | 0.230013i | \(0.0738768\pi\) | |||||||
\(798\) | −52985.5 | −0.0832054 | ||||||||
\(799\) | −228717. | −0.358265 | ||||||||
\(800\) | 5392.43i | 0.00842567i | ||||||||
\(801\) | − | 1.49388e6i | − | 2.32837i | ||||||
\(802\) | 3733.95i | 0.00580524i | ||||||||
\(803\) | − | 337638.i | − | 0.523625i | ||||||
\(804\) | 1.12487e6i | 1.74017i | ||||||||
\(805\) | 1.82502e6 | 2.81628 | ||||||||
\(806\) | − | 11031.1i | − | 0.0169805i | ||||||
\(807\) | − | 1.37642e6i | − | 2.11351i | ||||||
\(808\) | − | 40264.7i | − | 0.0616739i | ||||||
\(809\) | 825010. | 1.26056 | 0.630278 | − | 0.776370i | \(-0.282941\pi\) | ||||
0.630278 | + | 0.776370i | \(0.282941\pi\) | |||||||
\(810\) | 4698.08 | 0.00716061 | ||||||||
\(811\) | 980675.i | 1.49102i | 0.666495 | + | 0.745510i | \(0.267794\pi\) | ||||
−0.666495 | + | 0.745510i | \(0.732206\pi\) | |||||||
\(812\) | 1.52369e6 | 2.31092 | ||||||||
\(813\) | 915255.i | 1.38472i | ||||||||
\(814\) | 4206.78 | 0.00634894 | ||||||||
\(815\) | 184024. | 0.277050 | ||||||||
\(816\) | 860715.i | 1.29264i | ||||||||
\(817\) | −562256. | − | 42006.8i | −0.842346 | − | 0.0629326i | ||||
\(818\) | −2979.36 | −0.00445263 | ||||||||
\(819\) | 2.31991e6i | 3.45862i | ||||||||
\(820\) | 557144.i | 0.828591i | ||||||||
\(821\) | 886552. | 1.31528 | 0.657639 | − | 0.753333i | \(-0.271555\pi\) | ||||
0.657639 | + | 0.753333i | \(0.271555\pi\) | |||||||
\(822\) | 52624.0i | 0.0778826i | ||||||||
\(823\) | 26373.5 | 0.0389376 | 0.0194688 | − | 0.999810i | \(-0.493803\pi\) | ||||
0.0194688 | + | 0.999810i | \(0.493803\pi\) | |||||||
\(824\) | 60449.0i | 0.0890296i | ||||||||
\(825\) | − | 79302.0i | − | 0.116513i | ||||||
\(826\) | 15061.8 | 0.0220758 | ||||||||
\(827\) | 778115. | 1.13771 | 0.568857 | − | 0.822437i | \(-0.307386\pi\) | ||||
0.568857 | + | 0.822437i | \(0.307386\pi\) | |||||||
\(828\) | −1.76167e6 | −2.56959 | ||||||||
\(829\) | − | 263982.i | − | 0.384119i | −0.981383 | − | 0.192059i | \(-0.938483\pi\) | ||
0.981383 | − | 0.192059i | \(-0.0615166\pi\) | |||||||
\(830\) | −6586.17 | −0.00956042 | ||||||||
\(831\) | 1.77522e6 | 2.57069 | ||||||||
\(832\) | 776571. | 1.12185 | ||||||||
\(833\) | 1.21421e6 | 1.74987 | ||||||||
\(834\) | 6344.94 | 0.00912211 | ||||||||
\(835\) | − | 873668.i | − | 1.25307i | ||||||
\(836\) | − | 495431.i | − | 0.708876i | ||||||
\(837\) | 367009.i | 0.523873i | ||||||||
\(838\) | −21370.4 | −0.0304316 | ||||||||
\(839\) | 521605.i | 0.741000i | 0.928833 | + | 0.370500i | \(0.120814\pi\) | ||||
−0.928833 | + | 0.370500i | \(0.879186\pi\) | |||||||
\(840\) | −144668. | −0.205028 | ||||||||
\(841\) | −468467. | −0.662349 | ||||||||
\(842\) | −38658.7 | −0.0545285 | ||||||||
\(843\) | − | 356010.i | − | 0.500965i | ||||||
\(844\) | 457758.i | 0.642615i | ||||||||
\(845\) | 204848.i | 0.286892i | ||||||||
\(846\) | 18523.0i | 0.0258804i | ||||||||
\(847\) | 378658.i | 0.527813i | ||||||||
\(848\) | −930926. | −1.29456 | ||||||||
\(849\) | − | 1.65913e6i | − | 2.30179i | ||||||
\(850\) | − | 1602.06i | − | 0.00221738i | ||||||
\(851\) | − | 247214.i | − | 0.341361i | ||||||
\(852\) | −1.00768e6 | −1.38817 | ||||||||
\(853\) | 259667. | 0.356876 | 0.178438 | − | 0.983951i | \(-0.442896\pi\) | ||||
0.178438 | + | 0.983951i | \(0.442896\pi\) | |||||||
\(854\) | 26731.3i | 0.0366525i | ||||||||
\(855\) | 1.09738e6 | 1.50116 | ||||||||
\(856\) | 27369.7i | 0.0373528i | ||||||||
\(857\) | −265487. | −0.361478 | −0.180739 | − | 0.983531i | \(-0.557849\pi\) | ||||
−0.180739 | + | 0.983531i | \(0.557849\pi\) | |||||||
\(858\) | 38345.8 | 0.0520886 | ||||||||
\(859\) | − | 579588.i | − | 0.785476i | −0.919650 | − | 0.392738i | \(-0.871528\pi\) | ||
0.919650 | − | 0.392738i | \(-0.128472\pi\) | |||||||
\(860\) | −767146. | − | 57314.3i | −1.03724 | − | 0.0774937i | ||||
\(861\) | −1.74334e6 | −2.35167 | ||||||||
\(862\) | 933.767i | 0.00125668i | ||||||||
\(863\) | 255334.i | 0.342836i | 0.985198 | + | 0.171418i | \(0.0548349\pi\) | ||||
−0.985198 | + | 0.171418i | \(0.945165\pi\) | |||||||
\(864\) | 86750.9 | 0.116211 | ||||||||
\(865\) | 631641.i | 0.844185i | ||||||||
\(866\) | 25468.5 | 0.0339599 | ||||||||
\(867\) | 468111.i | 0.622746i | ||||||||
\(868\) | − | 608477.i | − | 0.807616i | ||||||
\(869\) | 23114.7 | 0.0306089 | ||||||||
\(870\) | 55785.1 | 0.0737021 | ||||||||
\(871\) | −907267. | −1.19591 | ||||||||
\(872\) | 66954.4i | 0.0880534i | ||||||||
\(873\) | −1.50748e6 | −1.97799 | ||||||||
\(874\) | 32452.1 | 0.0424835 | ||||||||
\(875\) | 1.30994e6 | 1.71095 | ||||||||
\(876\) | 785975. | 1.02424 | ||||||||
\(877\) | −914351. | −1.18881 | −0.594407 | − | 0.804164i | \(-0.702613\pi\) | ||||
−0.594407 | + | 0.804164i | \(0.702613\pi\) | |||||||
\(878\) | − | 38022.5i | − | 0.0493233i | ||||||
\(879\) | − | 286037.i | − | 0.370207i | ||||||
\(880\) | − | 675215.i | − | 0.871920i | ||||||
\(881\) | −284724. | −0.366837 | −0.183418 | − | 0.983035i | \(-0.558716\pi\) | ||||
−0.183418 | + | 0.983035i | \(0.558716\pi\) | |||||||
\(882\) | − | 98335.3i | − | 0.126407i | ||||||
\(883\) | 10870.8 | 0.0139425 | 0.00697126 | − | 0.999976i | \(-0.497781\pi\) | ||||
0.00697126 | + | 0.999976i | \(0.497781\pi\) | |||||||
\(884\) | −694986. | −0.889347 | ||||||||
\(885\) | −494723. | −0.631648 | ||||||||
\(886\) | − | 37174.4i | − | 0.0473561i | ||||||
\(887\) | 1.28800e6i | 1.63708i | 0.574451 | + | 0.818539i | \(0.305216\pi\) | ||||
−0.574451 | + | 0.818539i | \(0.694784\pi\) | |||||||
\(888\) | 19596.5i | 0.0248515i | ||||||||
\(889\) | − | 2.28731e6i | − | 2.89415i | ||||||
\(890\) | 37547.3i | 0.0474022i | ||||||||
\(891\) | −137455. | −0.173143 | ||||||||
\(892\) | 565399.i | 0.710601i | ||||||||
\(893\) | 306121.i | 0.383876i | ||||||||
\(894\) | − | 45009.9i | − | 0.0563161i | ||||||
\(895\) | 1.03161e6 | 1.28786 | ||||||||
\(896\) | −191734. | −0.238827 | ||||||||
\(897\) | − | 2.25341e6i | − | 2.80063i | ||||||
\(898\) | 1933.32 | 0.00239745 | ||||||||
\(899\) | 469529.i | 0.580955i | ||||||||
\(900\) | 116401. | 0.143705 | ||||||||
\(901\) | 831263. | 1.02397 | ||||||||
\(902\) | 18169.6i | 0.0223322i | ||||||||
\(903\) | 179340. | − | 2.40045e6i | 0.219939 | − | 2.94386i | ||||
\(904\) | −63172.0 | −0.0773015 | ||||||||
\(905\) | 864604.i | 1.05565i | ||||||||
\(906\) | 7297.86i | 0.00889076i | ||||||||
\(907\) | −52749.5 | −0.0641215 | −0.0320607 | − | 0.999486i | \(-0.510207\pi\) | ||||
−0.0320607 | + | 0.999486i | \(0.510207\pi\) | |||||||
\(908\) | 948178.i | 1.15005i | ||||||||
\(909\) | −1.30397e6 | −1.57812 | ||||||||
\(910\) | − | 58308.6i | − | 0.0704125i | ||||||
\(911\) | 618900.i | 0.745733i | 0.927885 | + | 0.372867i | \(0.121625\pi\) | ||||
−0.927885 | + | 0.372867i | \(0.878375\pi\) | |||||||
\(912\) | 1.15201e6 | 1.38505 | ||||||||
\(913\) | 192697. | 0.231170 | ||||||||
\(914\) | −47100.5 | −0.0563810 | ||||||||
\(915\) | − | 878021.i | − | 1.04873i | ||||||
\(916\) | −214373. | −0.255494 | ||||||||
\(917\) | −24140.2 | −0.0287079 | ||||||||
\(918\) | −25773.2 | −0.0305832 | ||||||||
\(919\) | −973558. | −1.15274 | −0.576370 | − | 0.817189i | \(-0.695531\pi\) | ||||
−0.576370 | + | 0.817189i | \(0.695531\pi\) | |||||||
\(920\) | 88605.1 | 0.104685 | ||||||||
\(921\) | − | 654939.i | − | 0.772114i | ||||||
\(922\) | 24539.9i | 0.0288677i | ||||||||
\(923\) | − | 812745.i | − | 0.954005i | ||||||
\(924\) | 2.11515e6 | 2.47741 | ||||||||
\(925\) | 16334.5i | 0.0190907i | ||||||||
\(926\) | 4441.41 | 0.00517963 | ||||||||
\(927\) | 1.95764e6 | 2.27810 | ||||||||
\(928\) | 110984. | 0.128873 | ||||||||
\(929\) | 585104.i | 0.677956i | 0.940794 | + | 0.338978i | \(0.110081\pi\) | ||||
−0.940794 | + | 0.338978i | \(0.889919\pi\) | |||||||
\(930\) | − | 22277.5i | − | 0.0257573i | ||||||
\(931\) | − | 1.62514e6i | − | 1.87496i | ||||||
\(932\) | 631741.i | 0.727290i | ||||||||
\(933\) | − | 910186.i | − | 1.04560i | ||||||
\(934\) | 2188.94 | 0.00250922 | ||||||||
\(935\) | 602927.i | 0.689670i | ||||||||
\(936\) | 112632.i | 0.128561i | ||||||||
\(937\) | − | 152458.i | − | 0.173649i | −0.996224 | − | 0.0868243i | \(-0.972328\pi\) | ||
0.996224 | − | 0.0868243i | \(-0.0276719\pi\) | |||||||
\(938\) | 55782.1 | 0.0634000 | ||||||||
\(939\) | −747919. | −0.848249 | ||||||||
\(940\) | 417674.i | 0.472695i | ||||||||
\(941\) | −765397. | −0.864386 | −0.432193 | − | 0.901781i | \(-0.642260\pi\) | ||||
−0.432193 | + | 0.901781i | \(0.642260\pi\) | |||||||
\(942\) | − | 30103.1i | − | 0.0339242i | ||||||
\(943\) | 1.06775e6 | 1.20073 | ||||||||
\(944\) | −327472. | −0.367477 | ||||||||
\(945\) | 1.93994e6i | 2.17233i | ||||||||
\(946\) | −25018.1 | − | 1869.13i | −0.0279559 | − | 0.00208861i | ||||
\(947\) | 703600. | 0.784559 | 0.392279 | − | 0.919846i | \(-0.371687\pi\) | ||||
0.392279 | + | 0.919846i | \(0.371687\pi\) | |||||||
\(948\) | 53807.7i | 0.0598726i | ||||||||
\(949\) | 633929.i | 0.703895i | ||||||||
\(950\) | −2144.25 | −0.00237589 | ||||||||
\(951\) | 424430.i | 0.469294i | ||||||||
\(952\) | 85508.3 | 0.0943483 | ||||||||
\(953\) | 1.52841e6i | 1.68288i | 0.540349 | + | 0.841441i | \(0.318292\pi\) | ||||
−0.540349 | + | 0.841441i | \(0.681708\pi\) | |||||||
\(954\) | − | 67321.3i | − | 0.0739700i | ||||||
\(955\) | 645142. | 0.707374 | ||||||||
\(956\) | −392745. | −0.429729 | ||||||||
\(957\) | −1.63215e6 | −1.78211 | ||||||||
\(958\) | 53390.0i | 0.0581740i | ||||||||
\(959\) | −2.34121e6 | −2.54567 | ||||||||
\(960\) | 1.56829e6 | 1.70170 | ||||||||
\(961\) | −736017. | −0.796969 | ||||||||
\(962\) | −7898.39 | −0.00853470 | ||||||||
\(963\) | 886369. | 0.955789 | ||||||||
\(964\) | 340229.i | 0.366114i | ||||||||
\(965\) | − | 763839.i | − | 0.820252i | ||||||
\(966\) | 138548.i | 0.148473i | ||||||||
\(967\) | 443128. | 0.473888 | 0.236944 | − | 0.971523i | \(-0.423854\pi\) | ||||
0.236944 | + | 0.971523i | \(0.423854\pi\) | |||||||
\(968\) | 18383.9i | 0.0196195i | ||||||||
\(969\) | −1.02867e6 | −1.09555 | ||||||||
\(970\) | 37889.1 | 0.0402690 | ||||||||
\(971\) | 78265.6 | 0.0830104 | 0.0415052 | − | 0.999138i | \(-0.486785\pi\) | ||||
0.0415052 | + | 0.999138i | \(0.486785\pi\) | |||||||
\(972\) | 777242.i | 0.822666i | ||||||||
\(973\) | 282282.i | 0.298166i | ||||||||
\(974\) | − | 22167.9i | − | 0.0233672i | ||||||
\(975\) | 148892.i | 0.156626i | ||||||||
\(976\) | − | 581189.i | − | 0.610124i | ||||||
\(977\) | 900889. | 0.943805 | 0.471902 | − | 0.881651i | \(-0.343568\pi\) | ||||
0.471902 | + | 0.881651i | \(0.343568\pi\) | |||||||
\(978\) | 13970.3i | 0.0146059i | ||||||||
\(979\) | − | 1.09855e6i | − | 1.14618i | ||||||
\(980\) | − | 2.21735e6i | − | 2.30878i | ||||||
\(981\) | 2.16832e6 | 2.25312 | ||||||||
\(982\) | 42822.7 | 0.0444070 | ||||||||
\(983\) | − | 773395.i | − | 0.800376i | −0.916433 | − | 0.400188i | \(-0.868945\pi\) | ||
0.916433 | − | 0.400188i | \(-0.131055\pi\) | |||||||
\(984\) | −84639.6 | −0.0874145 | ||||||||
\(985\) | − | 1.03501e6i | − | 1.06677i | ||||||
\(986\) | −32972.6 | −0.0339156 | ||||||||
\(987\) | −1.30693e6 | −1.34158 | ||||||||
\(988\) | 930190.i | 0.952923i | ||||||||
\(989\) | −109841. | + | 1.47021e6i | −0.112298 | + | 1.50309i | ||||
\(990\) | 48829.1 | 0.0498205 | ||||||||
\(991\) | − | 1.19955e6i | − | 1.22144i | −0.791847 | − | 0.610719i | \(-0.790880\pi\) | ||
0.791847 | − | 0.610719i | \(-0.209120\pi\) | |||||||
\(992\) | − | 44320.8i | − | 0.0450385i | ||||||
\(993\) | −1.93123e6 | −1.95855 | ||||||||
\(994\) | 49970.6i | 0.0505757i | ||||||||
\(995\) | 77867.2 | 0.0786517 | ||||||||
\(996\) | 448571.i | 0.452181i | ||||||||
\(997\) | 1.04036e6i | 1.04663i | 0.852138 | + | 0.523317i | \(0.175306\pi\) | ||||
−0.852138 | + | 0.523317i | \(0.824694\pi\) | |||||||
\(998\) | −7571.82 | −0.00760220 | ||||||||
\(999\) | 262781. | 0.263308 |
(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 | 43.5.b.b.42.6 | ✓ | 12 | |
3.2 | odd | 2 | 387.5.b.c.343.7 | 12 | |||
4.3 | odd | 2 | 688.5.b.d.257.12 | 12 | |||
43.42 | odd | 2 | inner | 43.5.b.b.42.7 | yes | 12 | |
129.128 | even | 2 | 387.5.b.c.343.6 | 12 | |||
172.171 | even | 2 | 688.5.b.d.257.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
43.5.b.b.42.7 | yes | 12 | 43.42 | odd | 2 | inner | |
387.5.b.c.343.6 | 12 | 129.128 | even | 2 | |||
387.5.b.c.343.7 | 12 | 3.2 | odd | 2 | |||
688.5.b.d.257.1 | 12 | 172.171 | even | 2 | |||
688.5.b.d.257.12 | 12 | 4.3 | odd | 2 |