Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.6 | ||
Root | \(0.917374i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.i.337.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.917374i | 0.324341i | 0.986763 | + | 0.162170i | \(0.0518494\pi\) | ||||
−0.986763 | + | 0.162170i | \(0.948151\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 7.15843 | 0.894803 | ||||||||
\(5\) | − 15.4704i | − 1.38372i | −0.722034 | − | 0.691858i | \(-0.756792\pi\) | ||||
0.722034 | − | 0.691858i | \(-0.243208\pi\) | |||||||
\(6\) | 2.75212i | 0.187258i | ||||||||
\(7\) | 20.5833i | 1.11140i | 0.831384 | + | 0.555698i | \(0.187549\pi\) | ||||
−0.831384 | + | 0.555698i | \(0.812451\pi\) | |||||||
\(8\) | 13.9059i | 0.614562i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 14.1922 | 0.448795 | ||||||||
\(11\) | 65.8420i | 1.80474i | 0.430964 | + | 0.902369i | \(0.358173\pi\) | ||||
−0.430964 | + | 0.902369i | \(0.641827\pi\) | |||||||
\(12\) | 21.4753 | 0.516615 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −18.8826 | −0.360471 | ||||||||
\(15\) | − 46.4112i | − 0.798889i | ||||||||
\(16\) | 44.5105 | 0.695476 | ||||||||
\(17\) | −44.2956 | −0.631957 | −0.315979 | − | 0.948766i | \(-0.602333\pi\) | ||||
−0.315979 | + | 0.948766i | \(0.602333\pi\) | |||||||
\(18\) | 8.25636i | 0.108114i | ||||||||
\(19\) | 147.053i | 1.77560i | 0.460234 | + | 0.887798i | \(0.347766\pi\) | ||||
−0.460234 | + | 0.887798i | \(0.652234\pi\) | |||||||
\(20\) | − 110.744i | − 1.23815i | ||||||||
\(21\) | 61.7500i | 0.641665i | ||||||||
\(22\) | −60.4017 | −0.585350 | ||||||||
\(23\) | −53.1586 | −0.481928 | −0.240964 | − | 0.970534i | \(-0.577464\pi\) | ||||
−0.240964 | + | 0.970534i | \(0.577464\pi\) | |||||||
\(24\) | 41.7178i | 0.354817i | ||||||||
\(25\) | −114.334 | −0.914669 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 147.344i | 0.994480i | ||||||||
\(29\) | −38.6257 | −0.247331 | −0.123666 | − | 0.992324i | \(-0.539465\pi\) | ||||
−0.123666 | + | 0.992324i | \(0.539465\pi\) | |||||||
\(30\) | 42.5765 | 0.259112 | ||||||||
\(31\) | 88.3894i | 0.512104i | 0.966663 | + | 0.256052i | \(0.0824218\pi\) | ||||
−0.966663 | + | 0.256052i | \(0.917578\pi\) | |||||||
\(32\) | 152.080i | 0.840133i | ||||||||
\(33\) | 197.526i | 1.04197i | ||||||||
\(34\) | − 40.6357i | − 0.204969i | ||||||||
\(35\) | 318.433 | 1.53786 | ||||||||
\(36\) | 64.4258 | 0.298268 | ||||||||
\(37\) | − 78.9587i | − 0.350831i | −0.984495 | − | 0.175415i | \(-0.943873\pi\) | ||||
0.984495 | − | 0.175415i | \(-0.0561268\pi\) | |||||||
\(38\) | −134.903 | −0.575898 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 215.131 | 0.850379 | ||||||||
\(41\) | − 354.966i | − 1.35211i | −0.736852 | − | 0.676054i | \(-0.763689\pi\) | ||||
0.736852 | − | 0.676054i | \(-0.236311\pi\) | |||||||
\(42\) | −56.6478 | −0.208118 | ||||||||
\(43\) | 407.846 | 1.44642 | 0.723208 | − | 0.690630i | \(-0.242667\pi\) | ||||
0.723208 | + | 0.690630i | \(0.242667\pi\) | |||||||
\(44\) | 471.325i | 1.61489i | ||||||||
\(45\) | − 139.234i | − 0.461239i | ||||||||
\(46\) | − 48.7663i | − 0.156309i | ||||||||
\(47\) | 67.9674i | 0.210938i | 0.994423 | + | 0.105469i | \(0.0336343\pi\) | ||||
−0.994423 | + | 0.105469i | \(0.966366\pi\) | |||||||
\(48\) | 133.531 | 0.401533 | ||||||||
\(49\) | −80.6738 | −0.235201 | ||||||||
\(50\) | − 104.887i | − 0.296664i | ||||||||
\(51\) | −132.887 | −0.364861 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 226.572 | 0.587209 | 0.293604 | − | 0.955927i | \(-0.405145\pi\) | ||||
0.293604 | + | 0.955927i | \(0.405145\pi\) | |||||||
\(54\) | 24.7691i | 0.0624194i | ||||||||
\(55\) | 1018.60 | 2.49724 | ||||||||
\(56\) | −286.231 | −0.683021 | ||||||||
\(57\) | 441.160i | 1.02514i | ||||||||
\(58\) | − 35.4342i | − 0.0802196i | ||||||||
\(59\) | − 142.031i | − 0.313404i | −0.987646 | − | 0.156702i | \(-0.949914\pi\) | ||||
0.987646 | − | 0.156702i | \(-0.0500862\pi\) | |||||||
\(60\) | − 332.231i | − 0.714848i | ||||||||
\(61\) | 266.831 | 0.560069 | 0.280035 | − | 0.959990i | \(-0.409654\pi\) | ||||
0.280035 | + | 0.959990i | \(0.409654\pi\) | |||||||
\(62\) | −81.0862 | −0.166096 | ||||||||
\(63\) | 185.250i | 0.370465i | ||||||||
\(64\) | 216.569 | 0.422987 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −181.205 | −0.337952 | ||||||||
\(67\) | − 411.187i | − 0.749768i | −0.927072 | − | 0.374884i | \(-0.877683\pi\) | ||||
0.927072 | − | 0.374884i | \(-0.122317\pi\) | |||||||
\(68\) | −317.087 | −0.565477 | ||||||||
\(69\) | −159.476 | −0.278241 | ||||||||
\(70\) | 292.122i | 0.498789i | ||||||||
\(71\) | − 91.5052i | − 0.152953i | −0.997071 | − | 0.0764765i | \(-0.975633\pi\) | ||||
0.997071 | − | 0.0764765i | \(-0.0243670\pi\) | |||||||
\(72\) | 125.153i | 0.204854i | ||||||||
\(73\) | − 63.1328i | − 0.101221i | −0.998718 | − | 0.0506105i | \(-0.983883\pi\) | ||||
0.998718 | − | 0.0506105i | \(-0.0161167\pi\) | |||||||
\(74\) | 72.4347 | 0.113789 | ||||||||
\(75\) | −343.001 | −0.528084 | ||||||||
\(76\) | 1052.67i | 1.58881i | ||||||||
\(77\) | −1355.25 | −2.00578 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −287.115 | −0.408899 | −0.204449 | − | 0.978877i | \(-0.565540\pi\) | ||||
−0.204449 | + | 0.978877i | \(0.565540\pi\) | |||||||
\(80\) | − 688.595i | − 0.962341i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 325.637 | 0.438543 | ||||||||
\(83\) | − 373.812i | − 0.494352i | −0.968971 | − | 0.247176i | \(-0.920497\pi\) | ||||
0.968971 | − | 0.247176i | \(-0.0795026\pi\) | |||||||
\(84\) | 442.033i | 0.574164i | ||||||||
\(85\) | 685.272i | 0.874449i | ||||||||
\(86\) | 374.147i | 0.469132i | ||||||||
\(87\) | −115.877 | −0.142797 | ||||||||
\(88\) | −915.595 | −1.10912 | ||||||||
\(89\) | − 119.403i | − 0.142209i | −0.997469 | − | 0.0711047i | \(-0.977348\pi\) | ||||
0.997469 | − | 0.0711047i | \(-0.0226525\pi\) | |||||||
\(90\) | 127.729 | 0.149598 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −380.532 | −0.431231 | ||||||||
\(93\) | 265.168i | 0.295663i | ||||||||
\(94\) | −62.3515 | −0.0684157 | ||||||||
\(95\) | 2274.97 | 2.45692 | ||||||||
\(96\) | 456.241i | 0.485051i | ||||||||
\(97\) | 554.650i | 0.580579i | 0.956939 | + | 0.290290i | \(0.0937516\pi\) | ||||
−0.956939 | + | 0.290290i | \(0.906248\pi\) | |||||||
\(98\) | − 74.0080i | − 0.0762851i | ||||||||
\(99\) | 592.578i | 0.601579i | ||||||||
\(100\) | −818.449 | −0.818449 | ||||||||
\(101\) | 462.565 | 0.455712 | 0.227856 | − | 0.973695i | \(-0.426828\pi\) | ||||
0.227856 | + | 0.973695i | \(0.426828\pi\) | |||||||
\(102\) | − 121.907i | − 0.118339i | ||||||||
\(103\) | −1122.07 | −1.07341 | −0.536704 | − | 0.843771i | \(-0.680331\pi\) | ||||
−0.536704 | + | 0.843771i | \(0.680331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 955.298 | 0.887881 | ||||||||
\(106\) | 207.851i | 0.190456i | ||||||||
\(107\) | 602.756 | 0.544585 | 0.272293 | − | 0.962214i | \(-0.412218\pi\) | ||||
0.272293 | + | 0.962214i | \(0.412218\pi\) | |||||||
\(108\) | 193.277 | 0.172205 | ||||||||
\(109\) | 1421.89i | 1.24947i | 0.780837 | + | 0.624735i | \(0.214793\pi\) | ||||
−0.780837 | + | 0.624735i | \(0.785207\pi\) | |||||||
\(110\) | 934.440i | 0.809958i | ||||||||
\(111\) | − 236.876i | − 0.202552i | ||||||||
\(112\) | 916.174i | 0.772949i | ||||||||
\(113\) | −396.719 | −0.330267 | −0.165134 | − | 0.986271i | \(-0.552806\pi\) | ||||
−0.165134 | + | 0.986271i | \(0.552806\pi\) | |||||||
\(114\) | −404.708 | −0.332495 | ||||||||
\(115\) | 822.386i | 0.666851i | ||||||||
\(116\) | −276.499 | −0.221313 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 130.295 | 0.101650 | ||||||||
\(119\) | − 911.752i | − 0.702354i | ||||||||
\(120\) | 645.392 | 0.490966 | ||||||||
\(121\) | −3004.17 | −2.25708 | ||||||||
\(122\) | 244.784i | 0.181653i | ||||||||
\(123\) | − 1064.90i | − 0.780639i | ||||||||
\(124\) | 632.729i | 0.458232i | ||||||||
\(125\) | − 165.013i | − 0.118074i | ||||||||
\(126\) | −169.944 | −0.120157 | ||||||||
\(127\) | −437.868 | −0.305941 | −0.152970 | − | 0.988231i | \(-0.548884\pi\) | ||||
−0.152970 | + | 0.988231i | \(0.548884\pi\) | |||||||
\(128\) | 1415.32i | 0.977324i | ||||||||
\(129\) | 1223.54 | 0.835089 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1657.44 | 1.10543 | 0.552715 | − | 0.833370i | \(-0.313592\pi\) | ||||
0.552715 | + | 0.833370i | \(0.313592\pi\) | |||||||
\(132\) | 1413.98i | 0.932354i | ||||||||
\(133\) | −3026.85 | −1.97339 | ||||||||
\(134\) | 377.212 | 0.243180 | ||||||||
\(135\) | − 417.701i | − 0.266296i | ||||||||
\(136\) | − 615.973i | − 0.388377i | ||||||||
\(137\) | − 1967.42i | − 1.22692i | −0.789725 | − | 0.613460i | \(-0.789777\pi\) | ||||
0.789725 | − | 0.613460i | \(-0.210223\pi\) | |||||||
\(138\) | − 146.299i | − 0.0902449i | ||||||||
\(139\) | 2825.13 | 1.72392 | 0.861960 | − | 0.506977i | \(-0.169237\pi\) | ||||
0.861960 | + | 0.506977i | \(0.169237\pi\) | |||||||
\(140\) | 2279.48 | 1.37608 | ||||||||
\(141\) | 203.902i | 0.121785i | ||||||||
\(142\) | 83.9445 | 0.0496089 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 400.594 | 0.231825 | ||||||||
\(145\) | 597.555i | 0.342236i | ||||||||
\(146\) | 57.9164 | 0.0328301 | ||||||||
\(147\) | −242.021 | −0.135793 | ||||||||
\(148\) | − 565.220i | − 0.313924i | ||||||||
\(149\) | 797.658i | 0.438569i | 0.975661 | + | 0.219284i | \(0.0703722\pi\) | ||||
−0.975661 | + | 0.219284i | \(0.929628\pi\) | |||||||
\(150\) | − 314.660i | − 0.171279i | ||||||||
\(151\) | 161.987i | 0.0873003i | 0.999047 | + | 0.0436501i | \(0.0138987\pi\) | ||||
−0.999047 | + | 0.0436501i | \(0.986101\pi\) | |||||||
\(152\) | −2044.91 | −1.09121 | ||||||||
\(153\) | −398.661 | −0.210652 | ||||||||
\(154\) | − 1243.27i | − 0.650555i | ||||||||
\(155\) | 1367.42 | 0.708606 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −342.000 | −0.173851 | −0.0869255 | − | 0.996215i | \(-0.527704\pi\) | ||||
−0.0869255 | + | 0.996215i | \(0.527704\pi\) | |||||||
\(158\) | − 263.392i | − 0.132622i | ||||||||
\(159\) | 679.716 | 0.339025 | ||||||||
\(160\) | 2352.74 | 1.16250 | ||||||||
\(161\) | − 1094.18i | − 0.535613i | ||||||||
\(162\) | 74.3073i | 0.0360378i | ||||||||
\(163\) | 556.597i | 0.267460i | 0.991018 | + | 0.133730i | \(0.0426956\pi\) | ||||
−0.991018 | + | 0.133730i | \(0.957304\pi\) | |||||||
\(164\) | − 2541.00i | − 1.20987i | ||||||||
\(165\) | 3055.81 | 1.44178 | ||||||||
\(166\) | 342.926 | 0.160339 | ||||||||
\(167\) | − 3136.42i | − 1.45332i | −0.686999 | − | 0.726658i | \(-0.741072\pi\) | ||||
0.686999 | − | 0.726658i | \(-0.258928\pi\) | |||||||
\(168\) | −858.692 | −0.394342 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −628.650 | −0.283619 | ||||||||
\(171\) | 1323.48i | 0.591865i | ||||||||
\(172\) | 2919.53 | 1.29426 | ||||||||
\(173\) | −3324.19 | −1.46089 | −0.730444 | − | 0.682972i | \(-0.760687\pi\) | ||||
−0.730444 | + | 0.682972i | \(0.760687\pi\) | |||||||
\(174\) | − 106.303i | − 0.0463148i | ||||||||
\(175\) | − 2353.37i | − 1.01656i | ||||||||
\(176\) | 2930.66i | 1.25515i | ||||||||
\(177\) | − 426.092i | − 0.180944i | ||||||||
\(178\) | 109.537 | 0.0461243 | ||||||||
\(179\) | 3313.25 | 1.38349 | 0.691743 | − | 0.722144i | \(-0.256843\pi\) | ||||
0.691743 | + | 0.722144i | \(0.256843\pi\) | |||||||
\(180\) | − 996.694i | − 0.412718i | ||||||||
\(181\) | −76.0118 | −0.0312150 | −0.0156075 | − | 0.999878i | \(-0.504968\pi\) | ||||
−0.0156075 | + | 0.999878i | \(0.504968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 800.494 | 0.323356 | ||||||||
\(184\) | − 739.221i | − 0.296174i | ||||||||
\(185\) | −1221.52 | −0.485450 | ||||||||
\(186\) | −243.258 | −0.0958956 | ||||||||
\(187\) | − 2916.51i | − 1.14052i | ||||||||
\(188\) | 486.540i | 0.188748i | ||||||||
\(189\) | 555.750i | 0.213888i | ||||||||
\(190\) | 2087.00i | 0.796879i | ||||||||
\(191\) | −4073.39 | −1.54314 | −0.771572 | − | 0.636142i | \(-0.780529\pi\) | ||||
−0.771572 | + | 0.636142i | \(0.780529\pi\) | |||||||
\(192\) | 649.708 | 0.244211 | ||||||||
\(193\) | − 867.581i | − 0.323574i | −0.986826 | − | 0.161787i | \(-0.948274\pi\) | ||||
0.986826 | − | 0.161787i | \(-0.0517258\pi\) | |||||||
\(194\) | −508.821 | −0.188305 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −577.497 | −0.210458 | ||||||||
\(197\) | − 1887.69i | − 0.682703i | −0.939936 | − | 0.341352i | \(-0.889115\pi\) | ||||
0.939936 | − | 0.341352i | \(-0.110885\pi\) | |||||||
\(198\) | −543.616 | −0.195117 | ||||||||
\(199\) | −2786.22 | −0.992511 | −0.496256 | − | 0.868176i | \(-0.665292\pi\) | ||||
−0.496256 | + | 0.868176i | \(0.665292\pi\) | |||||||
\(200\) | − 1589.92i | − 0.562120i | ||||||||
\(201\) | − 1233.56i | − 0.432879i | ||||||||
\(202\) | 424.345i | 0.147806i | ||||||||
\(203\) | − 795.045i | − 0.274883i | ||||||||
\(204\) | −951.261 | −0.326478 | ||||||||
\(205\) | −5491.47 | −1.87093 | ||||||||
\(206\) | − 1029.36i | − 0.348150i | ||||||||
\(207\) | −478.428 | −0.160643 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9682.28 | −3.20448 | ||||||||
\(210\) | 876.365i | 0.287976i | ||||||||
\(211\) | 708.789 | 0.231256 | 0.115628 | − | 0.993293i | \(-0.463112\pi\) | ||||
0.115628 | + | 0.993293i | \(0.463112\pi\) | |||||||
\(212\) | 1621.90 | 0.525436 | ||||||||
\(213\) | − 274.516i | − 0.0883075i | ||||||||
\(214\) | 552.953i | 0.176631i | ||||||||
\(215\) | − 6309.54i | − 2.00143i | ||||||||
\(216\) | 375.460i | 0.118272i | ||||||||
\(217\) | −1819.35 | −0.569150 | ||||||||
\(218\) | −1304.40 | −0.405254 | ||||||||
\(219\) | − 189.398i | − 0.0584400i | ||||||||
\(220\) | 7291.59 | 2.23454 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 217.304 | 0.0656959 | ||||||||
\(223\) | 5396.64i | 1.62056i | 0.586041 | + | 0.810281i | \(0.300686\pi\) | ||||
−0.586041 | + | 0.810281i | \(0.699314\pi\) | |||||||
\(224\) | −3130.32 | −0.933720 | ||||||||
\(225\) | −1029.00 | −0.304890 | ||||||||
\(226\) | − 363.940i | − 0.107119i | ||||||||
\(227\) | 3181.79i | 0.930321i | 0.885226 | + | 0.465160i | \(0.154003\pi\) | ||||
−0.885226 | + | 0.465160i | \(0.845997\pi\) | |||||||
\(228\) | 3158.01i | 0.917299i | ||||||||
\(229\) | − 2034.00i | − 0.586945i | −0.955967 | − | 0.293473i | \(-0.905189\pi\) | ||||
0.955967 | − | 0.293473i | \(-0.0948110\pi\) | |||||||
\(230\) | −754.435 | −0.216287 | ||||||||
\(231\) | −4065.75 | −1.15804 | ||||||||
\(232\) | − 537.126i | − 0.152000i | ||||||||
\(233\) | 2794.22 | 0.785645 | 0.392823 | − | 0.919614i | \(-0.371499\pi\) | ||||
0.392823 | + | 0.919614i | \(0.371499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1051.48 | 0.291878 | ||||||||
\(236\) | − 1016.72i | − 0.280435i | ||||||||
\(237\) | −861.346 | −0.236078 | ||||||||
\(238\) | 836.417 | 0.227802 | ||||||||
\(239\) | − 5493.81i | − 1.48688i | −0.668800 | − | 0.743442i | \(-0.733192\pi\) | ||||
0.668800 | − | 0.743442i | \(-0.266808\pi\) | |||||||
\(240\) | − 2065.79i | − 0.555608i | ||||||||
\(241\) | − 4061.27i | − 1.08552i | −0.839889 | − | 0.542758i | \(-0.817380\pi\) | ||||
0.839889 | − | 0.542758i | \(-0.182620\pi\) | |||||||
\(242\) | − 2755.95i | − 0.732062i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1910.09 | 0.501152 | ||||||||
\(245\) | 1248.06i | 0.325451i | ||||||||
\(246\) | 976.910 | 0.253193 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1229.14 | −0.314719 | ||||||||
\(249\) | − 1121.44i | − 0.285414i | ||||||||
\(250\) | 151.379 | 0.0382961 | ||||||||
\(251\) | 3570.88 | 0.897977 | 0.448988 | − | 0.893538i | \(-0.351784\pi\) | ||||
0.448988 | + | 0.893538i | \(0.351784\pi\) | |||||||
\(252\) | 1326.10i | 0.331493i | ||||||||
\(253\) | − 3500.07i | − 0.869753i | ||||||||
\(254\) | − 401.688i | − 0.0992290i | ||||||||
\(255\) | 2055.82i | 0.504863i | ||||||||
\(256\) | 434.179 | 0.106001 | ||||||||
\(257\) | 7518.26 | 1.82481 | 0.912405 | − | 0.409288i | \(-0.134223\pi\) | ||||
0.912405 | + | 0.409288i | \(0.134223\pi\) | |||||||
\(258\) | 1122.44i | 0.270853i | ||||||||
\(259\) | 1625.23 | 0.389912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −347.631 | −0.0824437 | ||||||||
\(262\) | 1520.49i | 0.358536i | ||||||||
\(263\) | −4660.18 | −1.09262 | −0.546310 | − | 0.837583i | \(-0.683968\pi\) | ||||
−0.546310 | + | 0.837583i | \(0.683968\pi\) | |||||||
\(264\) | −2746.79 | −0.640352 | ||||||||
\(265\) | − 3505.16i | − 0.812530i | ||||||||
\(266\) | − 2776.75i | − 0.640050i | ||||||||
\(267\) | − 358.208i | − 0.0821047i | ||||||||
\(268\) | − 2943.45i | − 0.670895i | ||||||||
\(269\) | 5347.44 | 1.21204 | 0.606021 | − | 0.795449i | \(-0.292765\pi\) | ||||
0.606021 | + | 0.795449i | \(0.292765\pi\) | |||||||
\(270\) | 383.188 | 0.0863707 | ||||||||
\(271\) | − 2973.08i | − 0.666427i | −0.942851 | − | 0.333214i | \(-0.891867\pi\) | ||||
0.942851 | − | 0.333214i | \(-0.108133\pi\) | |||||||
\(272\) | −1971.62 | −0.439511 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1804.86 | 0.397940 | ||||||||
\(275\) | − 7527.96i | − 1.65074i | ||||||||
\(276\) | −1141.60 | −0.248971 | ||||||||
\(277\) | 764.153 | 0.165753 | 0.0828764 | − | 0.996560i | \(-0.473589\pi\) | ||||
0.0828764 | + | 0.996560i | \(0.473589\pi\) | |||||||
\(278\) | 2591.70i | 0.559137i | ||||||||
\(279\) | 795.505i | 0.170701i | ||||||||
\(280\) | 4428.11i | 0.945107i | ||||||||
\(281\) | 7040.34i | 1.49463i | 0.664469 | + | 0.747316i | \(0.268658\pi\) | ||||
−0.664469 | + | 0.747316i | \(0.731342\pi\) | |||||||
\(282\) | −187.055 | −0.0394998 | ||||||||
\(283\) | 9035.17 | 1.89783 | 0.948913 | − | 0.315537i | \(-0.102185\pi\) | ||||
0.948913 | + | 0.315537i | \(0.102185\pi\) | |||||||
\(284\) | − 655.033i | − 0.136863i | ||||||||
\(285\) | 6824.92 | 1.41850 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7306.39 | 1.50273 | ||||||||
\(288\) | 1368.72i | 0.280044i | ||||||||
\(289\) | −2950.90 | −0.600630 | ||||||||
\(290\) | −548.181 | −0.111001 | ||||||||
\(291\) | 1663.95i | 0.335197i | ||||||||
\(292\) | − 451.931i | − 0.0905729i | ||||||||
\(293\) | − 1785.23i | − 0.355954i | −0.984035 | − | 0.177977i | \(-0.943045\pi\) | ||||
0.984035 | − | 0.177977i | \(-0.0569553\pi\) | |||||||
\(294\) | − 222.024i | − 0.0440432i | ||||||||
\(295\) | −2197.27 | −0.433662 | ||||||||
\(296\) | 1098.00 | 0.215607 | ||||||||
\(297\) | 1777.73i | 0.347322i | ||||||||
\(298\) | −731.751 | −0.142246 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2455.35 | −0.472532 | ||||||||
\(301\) | 8394.83i | 1.60754i | ||||||||
\(302\) | −148.603 | −0.0283150 | ||||||||
\(303\) | 1387.69 | 0.263105 | ||||||||
\(304\) | 6545.40i | 1.23488i | ||||||||
\(305\) | − 4127.99i | − 0.774977i | ||||||||
\(306\) | − 365.721i | − 0.0683231i | ||||||||
\(307\) | − 5323.13i | − 0.989600i | −0.869007 | − | 0.494800i | \(-0.835241\pi\) | ||||
0.869007 | − | 0.494800i | \(-0.164759\pi\) | |||||||
\(308\) | −9701.45 | −1.79478 | ||||||||
\(309\) | −3366.22 | −0.619733 | ||||||||
\(310\) | 1254.44i | 0.229830i | ||||||||
\(311\) | −6265.64 | −1.14242 | −0.571209 | − | 0.820805i | \(-0.693525\pi\) | ||||
−0.571209 | + | 0.820805i | \(0.693525\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7193.77 | 1.29909 | 0.649547 | − | 0.760322i | \(-0.274959\pi\) | ||||
0.649547 | + | 0.760322i | \(0.274959\pi\) | |||||||
\(314\) | − 313.742i | − 0.0563869i | ||||||||
\(315\) | 2865.89 | 0.512619 | ||||||||
\(316\) | −2055.29 | −0.365884 | ||||||||
\(317\) | − 9576.87i | − 1.69682i | −0.529343 | − | 0.848408i | \(-0.677561\pi\) | ||||
0.529343 | − | 0.848408i | \(-0.322439\pi\) | |||||||
\(318\) | 623.554i | 0.109960i | ||||||||
\(319\) | − 2543.19i | − 0.446368i | ||||||||
\(320\) | − 3350.41i | − 0.585293i | ||||||||
\(321\) | 1808.27 | 0.314417 | ||||||||
\(322\) | 1003.77 | 0.173721 | ||||||||
\(323\) | − 6513.81i | − 1.12210i | ||||||||
\(324\) | 579.832 | 0.0994226 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −510.608 | −0.0867483 | ||||||||
\(327\) | 4265.67i | 0.721382i | ||||||||
\(328\) | 4936.14 | 0.830953 | ||||||||
\(329\) | −1399.00 | −0.234435 | ||||||||
\(330\) | 2803.32i | 0.467629i | ||||||||
\(331\) | 5773.13i | 0.958670i | 0.877632 | + | 0.479335i | \(0.159122\pi\) | ||||
−0.877632 | + | 0.479335i | \(0.840878\pi\) | |||||||
\(332\) | − 2675.91i | − 0.442348i | ||||||||
\(333\) | − 710.629i | − 0.116944i | ||||||||
\(334\) | 2877.27 | 0.471370 | ||||||||
\(335\) | −6361.23 | −1.03747 | ||||||||
\(336\) | 2748.52i | 0.446262i | ||||||||
\(337\) | −1238.09 | −0.200127 | −0.100063 | − | 0.994981i | \(-0.531905\pi\) | ||||
−0.100063 | + | 0.994981i | \(0.531905\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1190.16 | −0.190680 | ||||||||
\(340\) | 4905.47i | 0.782460i | ||||||||
\(341\) | −5819.74 | −0.924213 | ||||||||
\(342\) | −1214.12 | −0.191966 | ||||||||
\(343\) | 5399.55i | 0.849995i | ||||||||
\(344\) | 5671.48i | 0.888912i | ||||||||
\(345\) | 2467.16i | 0.385007i | ||||||||
\(346\) | − 3049.53i | − 0.473826i | ||||||||
\(347\) | 5449.97 | 0.843140 | 0.421570 | − | 0.906796i | \(-0.361479\pi\) | ||||
0.421570 | + | 0.906796i | \(0.361479\pi\) | |||||||
\(348\) | −829.497 | −0.127775 | ||||||||
\(349\) | 1374.03i | 0.210746i | 0.994433 | + | 0.105373i | \(0.0336036\pi\) | ||||
−0.994433 | + | 0.105373i | \(0.966396\pi\) | |||||||
\(350\) | 2158.92 | 0.329711 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10013.3 | −1.51622 | ||||||||
\(353\) | − 5970.44i | − 0.900211i | −0.892975 | − | 0.450106i | \(-0.851386\pi\) | ||||
0.892975 | − | 0.450106i | \(-0.148614\pi\) | |||||||
\(354\) | 390.886 | 0.0586874 | ||||||||
\(355\) | −1415.62 | −0.211644 | ||||||||
\(356\) | − 854.734i | − 0.127249i | ||||||||
\(357\) | − 2735.26i | − 0.405504i | ||||||||
\(358\) | 3039.49i | 0.448720i | ||||||||
\(359\) | 7813.71i | 1.14872i | 0.818602 | + | 0.574362i | \(0.194750\pi\) | ||||
−0.818602 | + | 0.574362i | \(0.805250\pi\) | |||||||
\(360\) | 1936.18 | 0.283460 | ||||||||
\(361\) | −14765.6 | −2.15274 | ||||||||
\(362\) | − 69.7313i | − 0.0101243i | ||||||||
\(363\) | −9012.52 | −1.30312 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −976.690 | −0.140061 | ||||||||
\(366\) | 734.352i | 0.104878i | ||||||||
\(367\) | 1688.39 | 0.240145 | 0.120073 | − | 0.992765i | \(-0.461687\pi\) | ||||
0.120073 | + | 0.992765i | \(0.461687\pi\) | |||||||
\(368\) | −2366.11 | −0.335169 | ||||||||
\(369\) | − 3194.69i | − 0.450702i | ||||||||
\(370\) | − 1120.59i | − 0.157451i | ||||||||
\(371\) | 4663.61i | 0.652622i | ||||||||
\(372\) | 1898.19i | 0.264560i | ||||||||
\(373\) | 1870.61 | 0.259670 | 0.129835 | − | 0.991536i | \(-0.458555\pi\) | ||||
0.129835 | + | 0.991536i | \(0.458555\pi\) | |||||||
\(374\) | 2675.53 | 0.369916 | ||||||||
\(375\) | − 495.039i | − 0.0681699i | ||||||||
\(376\) | −945.151 | −0.129634 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −509.831 | −0.0693726 | ||||||||
\(379\) | − 11667.0i | − 1.58125i | −0.612298 | − | 0.790627i | \(-0.709755\pi\) | ||||
0.612298 | − | 0.790627i | \(-0.290245\pi\) | |||||||
\(380\) | 16285.2 | 2.19846 | ||||||||
\(381\) | −1313.60 | −0.176635 | ||||||||
\(382\) | − 3736.82i | − 0.500504i | ||||||||
\(383\) | 6676.60i | 0.890753i | 0.895343 | + | 0.445376i | \(0.146930\pi\) | ||||
−0.895343 | + | 0.445376i | \(0.853070\pi\) | |||||||
\(384\) | 4245.95i | 0.564259i | ||||||||
\(385\) | 20966.3i | 2.77543i | ||||||||
\(386\) | 795.896 | 0.104948 | ||||||||
\(387\) | 3670.61 | 0.482139 | ||||||||
\(388\) | 3970.42i | 0.519504i | ||||||||
\(389\) | −14285.3 | −1.86194 | −0.930969 | − | 0.365099i | \(-0.881035\pi\) | ||||
−0.930969 | + | 0.365099i | \(0.881035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2354.69 | 0.304558 | ||||||||
\(392\) | − 1121.85i | − 0.144545i | ||||||||
\(393\) | 4972.32 | 0.638220 | ||||||||
\(394\) | 1731.72 | 0.221428 | ||||||||
\(395\) | 4441.79i | 0.565800i | ||||||||
\(396\) | 4241.93i | 0.538295i | ||||||||
\(397\) | 3569.28i | 0.451227i | 0.974217 | + | 0.225614i | \(0.0724387\pi\) | ||||
−0.974217 | + | 0.225614i | \(0.927561\pi\) | |||||||
\(398\) | − 2556.00i | − 0.321912i | ||||||||
\(399\) | −9080.54 | −1.13934 | ||||||||
\(400\) | −5089.04 | −0.636130 | ||||||||
\(401\) | 499.348i | 0.0621852i | 0.999517 | + | 0.0310926i | \(0.00989868\pi\) | ||||
−0.999517 | + | 0.0310926i | \(0.990101\pi\) | |||||||
\(402\) | 1131.64 | 0.140400 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3311.23 | 0.407772 | ||||||||
\(405\) | − 1253.10i | − 0.153746i | ||||||||
\(406\) | 729.354 | 0.0891557 | ||||||||
\(407\) | 5198.80 | 0.633158 | ||||||||
\(408\) | − 1847.92i | − 0.224229i | ||||||||
\(409\) | − 10457.5i | − 1.26428i | −0.774855 | − | 0.632140i | \(-0.782177\pi\) | ||||
0.774855 | − | 0.632140i | \(-0.217823\pi\) | |||||||
\(410\) | − 5037.73i | − 0.606819i | ||||||||
\(411\) | − 5902.26i | − 0.708363i | ||||||||
\(412\) | −8032.27 | −0.960489 | ||||||||
\(413\) | 2923.47 | 0.348316 | ||||||||
\(414\) | − 438.897i | − 0.0521029i | ||||||||
\(415\) | −5783.03 | −0.684043 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8475.40 | 0.995305 | ||||||||
\(418\) | − 8882.27i | − 1.03934i | ||||||||
\(419\) | −1705.42 | −0.198843 | −0.0994215 | − | 0.995045i | \(-0.531699\pi\) | ||||
−0.0994215 | + | 0.995045i | \(0.531699\pi\) | |||||||
\(420\) | 6838.43 | 0.794479 | ||||||||
\(421\) | 8765.57i | 1.01475i | 0.861727 | + | 0.507373i | \(0.169383\pi\) | ||||
−0.861727 | + | 0.507373i | \(0.830617\pi\) | |||||||
\(422\) | 650.225i | 0.0750058i | ||||||||
\(423\) | 611.707i | 0.0703126i | ||||||||
\(424\) | 3150.70i | 0.360876i | ||||||||
\(425\) | 5064.48 | 0.578032 | ||||||||
\(426\) | 251.833 | 0.0286417 | ||||||||
\(427\) | 5492.28i | 0.622459i | ||||||||
\(428\) | 4314.79 | 0.487297 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5788.21 | 0.649145 | ||||||||
\(431\) | 8080.37i | 0.903057i | 0.892257 | + | 0.451529i | \(0.149121\pi\) | ||||
−0.892257 | + | 0.451529i | \(0.850879\pi\) | |||||||
\(432\) | 1201.78 | 0.133844 | ||||||||
\(433\) | 4124.48 | 0.457760 | 0.228880 | − | 0.973455i | \(-0.426494\pi\) | ||||
0.228880 | + | 0.973455i | \(0.426494\pi\) | |||||||
\(434\) | − 1669.02i | − 0.184598i | ||||||||
\(435\) | 1792.66i | 0.197590i | ||||||||
\(436\) | 10178.5i | 1.11803i | ||||||||
\(437\) | − 7817.14i | − 0.855709i | ||||||||
\(438\) | 173.749 | 0.0189545 | ||||||||
\(439\) | 6115.52 | 0.664870 | 0.332435 | − | 0.943126i | \(-0.392130\pi\) | ||||
0.332435 | + | 0.943126i | \(0.392130\pi\) | |||||||
\(440\) | 14164.6i | 1.53471i | ||||||||
\(441\) | −726.064 | −0.0784002 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11058.8 | −1.18605 | −0.593025 | − | 0.805184i | \(-0.702067\pi\) | ||||
−0.593025 | + | 0.805184i | \(0.702067\pi\) | |||||||
\(444\) | − 1695.66i | − 0.181244i | ||||||||
\(445\) | −1847.21 | −0.196777 | ||||||||
\(446\) | −4950.73 | −0.525614 | ||||||||
\(447\) | 2392.97i | 0.253208i | ||||||||
\(448\) | 4457.72i | 0.470106i | ||||||||
\(449\) | 242.012i | 0.0254371i | 0.999919 | + | 0.0127185i | \(0.00404854\pi\) | ||||
−0.999919 | + | 0.0127185i | \(0.995951\pi\) | |||||||
\(450\) | − 943.980i | − 0.0988881i | ||||||||
\(451\) | 23371.7 | 2.44020 | ||||||||
\(452\) | −2839.88 | −0.295524 | ||||||||
\(453\) | 485.962i | 0.0504028i | ||||||||
\(454\) | −2918.89 | −0.301741 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6134.74 | −0.630012 | ||||||||
\(457\) | − 11052.2i | − 1.13129i | −0.824650 | − | 0.565644i | \(-0.808628\pi\) | ||||
0.824650 | − | 0.565644i | \(-0.191372\pi\) | |||||||
\(458\) | 1865.94 | 0.190370 | ||||||||
\(459\) | −1195.98 | −0.121620 | ||||||||
\(460\) | 5886.99i | 0.596700i | ||||||||
\(461\) | 273.763i | 0.0276582i | 0.999904 | + | 0.0138291i | \(0.00440208\pi\) | ||||
−0.999904 | + | 0.0138291i | \(0.995598\pi\) | |||||||
\(462\) | − 3729.81i | − 0.375598i | ||||||||
\(463\) | − 11579.2i | − 1.16227i | −0.813808 | − | 0.581134i | \(-0.802609\pi\) | ||||
0.813808 | − | 0.581134i | \(-0.197391\pi\) | |||||||
\(464\) | −1719.25 | −0.172013 | ||||||||
\(465\) | 4102.26 | 0.409114 | ||||||||
\(466\) | 2563.34i | 0.254817i | ||||||||
\(467\) | −902.915 | −0.0894688 | −0.0447344 | − | 0.998999i | \(-0.514244\pi\) | ||||
−0.0447344 | + | 0.998999i | \(0.514244\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8463.59 | 0.833289 | ||||||||
\(470\) | 964.604i | 0.0946678i | ||||||||
\(471\) | −1026.00 | −0.100373 | ||||||||
\(472\) | 1975.07 | 0.192606 | ||||||||
\(473\) | 26853.4i | 2.61040i | ||||||||
\(474\) | − 790.176i | − 0.0765696i | ||||||||
\(475\) | − 16813.1i | − 1.62408i | ||||||||
\(476\) | − 6526.71i | − 0.628469i | ||||||||
\(477\) | 2039.15 | 0.195736 | ||||||||
\(478\) | 5039.88 | 0.482257 | ||||||||
\(479\) | 12068.8i | 1.15122i | 0.817723 | + | 0.575611i | \(0.195236\pi\) | ||||
−0.817723 | + | 0.575611i | \(0.804764\pi\) | |||||||
\(480\) | 7058.23 | 0.671172 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3725.70 | 0.352077 | ||||||||
\(483\) | − 3282.55i | − 0.309236i | ||||||||
\(484\) | −21505.1 | −2.01964 | ||||||||
\(485\) | 8580.66 | 0.803356 | ||||||||
\(486\) | 222.922i | 0.0208065i | ||||||||
\(487\) | 11492.5i | 1.06936i | 0.845056 | + | 0.534678i | \(0.179567\pi\) | ||||
−0.845056 | + | 0.534678i | \(0.820433\pi\) | |||||||
\(488\) | 3710.54i | 0.344197i | ||||||||
\(489\) | 1669.79i | 0.154418i | ||||||||
\(490\) | −1144.93 | −0.105557 | ||||||||
\(491\) | −15704.2 | −1.44342 | −0.721710 | − | 0.692196i | \(-0.756643\pi\) | ||||
−0.721710 | + | 0.692196i | \(0.756643\pi\) | |||||||
\(492\) | − 7622.99i | − 0.698519i | ||||||||
\(493\) | 1710.95 | 0.156303 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9167.43 | 0.832415 | ||||||||
\(496\) | 3934.25i | 0.356156i | ||||||||
\(497\) | 1883.48 | 0.169991 | ||||||||
\(498\) | 1028.78 | 0.0925715 | ||||||||
\(499\) | 9019.80i | 0.809181i | 0.914498 | + | 0.404591i | \(0.132586\pi\) | ||||
−0.914498 | + | 0.404591i | \(0.867414\pi\) | |||||||
\(500\) | − 1181.23i | − 0.105653i | ||||||||
\(501\) | − 9409.27i | − 0.839073i | ||||||||
\(502\) | 3275.83i | 0.291250i | ||||||||
\(503\) | −6033.84 | −0.534862 | −0.267431 | − | 0.963577i | \(-0.586175\pi\) | ||||
−0.267431 | + | 0.963577i | \(0.586175\pi\) | |||||||
\(504\) | −2576.08 | −0.227674 | ||||||||
\(505\) | − 7156.06i | − 0.630576i | ||||||||
\(506\) | 3210.87 | 0.282096 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3134.44 | −0.273757 | ||||||||
\(509\) | 22451.5i | 1.95510i | 0.210699 | + | 0.977551i | \(0.432426\pi\) | ||||
−0.210699 | + | 0.977551i | \(0.567574\pi\) | |||||||
\(510\) | −1885.95 | −0.163748 | ||||||||
\(511\) | 1299.48 | 0.112497 | ||||||||
\(512\) | 11720.8i | 1.01170i | ||||||||
\(513\) | 3970.44i | 0.341714i | ||||||||
\(514\) | 6897.06i | 0.591860i | ||||||||
\(515\) | 17358.9i | 1.48529i | ||||||||
\(516\) | 8758.60 | 0.747240 | ||||||||
\(517\) | −4475.11 | −0.380687 | ||||||||
\(518\) | 1490.95i | 0.126464i | ||||||||
\(519\) | −9972.58 | −0.843445 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15674.7 | 1.31808 | 0.659040 | − | 0.752108i | \(-0.270963\pi\) | ||||
0.659040 | + | 0.752108i | \(0.270963\pi\) | |||||||
\(522\) | − 318.908i | − 0.0267399i | ||||||||
\(523\) | 13510.8 | 1.12961 | 0.564804 | − | 0.825225i | \(-0.308952\pi\) | ||||
0.564804 | + | 0.825225i | \(0.308952\pi\) | |||||||
\(524\) | 11864.7 | 0.989142 | ||||||||
\(525\) | − 7060.10i | − 0.586911i | ||||||||
\(526\) | − 4275.13i | − 0.354381i | ||||||||
\(527\) | − 3915.27i | − 0.323627i | ||||||||
\(528\) | 8791.97i | 0.724662i | ||||||||
\(529\) | −9341.16 | −0.767746 | ||||||||
\(530\) | 3215.55 | 0.263537 | ||||||||
\(531\) | − 1278.28i | − 0.104468i | ||||||||
\(532\) | −21667.4 | −1.76580 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 328.610 | 0.0266299 | ||||||||
\(535\) | − 9324.89i | − 0.753551i | ||||||||
\(536\) | 5717.94 | 0.460778 | ||||||||
\(537\) | 9939.75 | 0.798756 | ||||||||
\(538\) | 4905.60i | 0.393114i | ||||||||
\(539\) | − 5311.73i | − 0.424475i | ||||||||
\(540\) | − 2990.08i | − 0.238283i | ||||||||
\(541\) | − 12103.6i | − 0.961875i | −0.876755 | − | 0.480937i | \(-0.840296\pi\) | ||||
0.876755 | − | 0.480937i | \(-0.159704\pi\) | |||||||
\(542\) | 2727.43 | 0.216149 | ||||||||
\(543\) | −228.036 | −0.0180220 | ||||||||
\(544\) | − 6736.49i | − 0.530928i | ||||||||
\(545\) | 21997.2 | 1.72891 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15228.6 | −1.19036 | −0.595181 | − | 0.803592i | \(-0.702920\pi\) | ||||
−0.595181 | + | 0.803592i | \(0.702920\pi\) | |||||||
\(548\) | − 14083.6i | − 1.09785i | ||||||||
\(549\) | 2401.48 | 0.186690 | ||||||||
\(550\) | 6905.95 | 0.535401 | ||||||||
\(551\) | − 5680.03i | − 0.439160i | ||||||||
\(552\) | − 2217.66i | − 0.170996i | ||||||||
\(553\) | − 5909.79i | − 0.454448i | ||||||||
\(554\) | 701.014i | 0.0537603i | ||||||||
\(555\) | −3664.57 | −0.280275 | ||||||||
\(556\) | 20223.5 | 1.54257 | ||||||||
\(557\) | − 23596.9i | − 1.79503i | −0.440982 | − | 0.897516i | \(-0.645370\pi\) | ||||
0.440982 | − | 0.897516i | \(-0.354630\pi\) | |||||||
\(558\) | −729.775 | −0.0553653 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14173.6 | 1.06954 | ||||||||
\(561\) | − 8749.54i | − 0.658478i | ||||||||
\(562\) | −6458.63 | −0.484770 | ||||||||
\(563\) | −7941.62 | −0.594493 | −0.297246 | − | 0.954801i | \(-0.596068\pi\) | ||||
−0.297246 | + | 0.954801i | \(0.596068\pi\) | |||||||
\(564\) | 1459.62i | 0.108974i | ||||||||
\(565\) | 6137.40i | 0.456996i | ||||||||
\(566\) | 8288.63i | 0.615542i | ||||||||
\(567\) | 1667.25i | 0.123488i | ||||||||
\(568\) | 1272.47 | 0.0939991 | ||||||||
\(569\) | −2274.65 | −0.167590 | −0.0837948 | − | 0.996483i | \(-0.526704\pi\) | ||||
−0.0837948 | + | 0.996483i | \(0.526704\pi\) | |||||||
\(570\) | 6261.00i | 0.460078i | ||||||||
\(571\) | 4499.84 | 0.329794 | 0.164897 | − | 0.986311i | \(-0.447271\pi\) | ||||
0.164897 | + | 0.986311i | \(0.447271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12220.2 | −0.890934 | ||||||||
\(574\) | 6702.69i | 0.487395i | ||||||||
\(575\) | 6077.82 | 0.440804 | ||||||||
\(576\) | 1949.12 | 0.140996 | ||||||||
\(577\) | − 25253.3i | − 1.82202i | −0.412381 | − | 0.911011i | \(-0.635303\pi\) | ||||
0.412381 | − | 0.911011i | \(-0.364697\pi\) | |||||||
\(578\) | − 2707.08i | − 0.194809i | ||||||||
\(579\) | − 2602.74i | − 0.186816i | ||||||||
\(580\) | 4277.55i | 0.306234i | ||||||||
\(581\) | 7694.31 | 0.549421 | ||||||||
\(582\) | −1526.46 | −0.108718 | ||||||||
\(583\) | 14918.0i | 1.05976i | ||||||||
\(584\) | 877.921 | 0.0622066 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1637.73 | 0.115450 | ||||||||
\(587\) | − 11285.2i | − 0.793508i | −0.917925 | − | 0.396754i | \(-0.870137\pi\) | ||||
0.917925 | − | 0.396754i | \(-0.129863\pi\) | |||||||
\(588\) | −1732.49 | −0.121508 | ||||||||
\(589\) | −12997.9 | −0.909289 | ||||||||
\(590\) | − 2015.72i | − 0.140654i | ||||||||
\(591\) | − 5663.08i | − 0.394159i | ||||||||
\(592\) | − 3514.49i | − 0.243994i | ||||||||
\(593\) | − 12824.5i | − 0.888090i | −0.896005 | − | 0.444045i | \(-0.853543\pi\) | ||||
0.896005 | − | 0.444045i | \(-0.146457\pi\) | |||||||
\(594\) | −1630.85 | −0.112651 | ||||||||
\(595\) | −14105.2 | −0.971859 | ||||||||
\(596\) | 5709.98i | 0.392433i | ||||||||
\(597\) | −8358.65 | −0.573027 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26180.3 | −1.78581 | −0.892905 | − | 0.450245i | \(-0.851336\pi\) | ||||
−0.892905 | + | 0.450245i | \(0.851336\pi\) | |||||||
\(600\) | − 4769.75i | − 0.324540i | ||||||||
\(601\) | 16012.6 | 1.08680 | 0.543399 | − | 0.839474i | \(-0.317137\pi\) | ||||
0.543399 | + | 0.839474i | \(0.317137\pi\) | |||||||
\(602\) | −7701.20 | −0.521391 | ||||||||
\(603\) | − 3700.68i | − 0.249923i | ||||||||
\(604\) | 1159.57i | 0.0781166i | ||||||||
\(605\) | 46475.8i | 3.12316i | ||||||||
\(606\) | 1273.03i | 0.0853357i | ||||||||
\(607\) | −9531.48 | −0.637349 | −0.318674 | − | 0.947864i | \(-0.603238\pi\) | ||||
−0.318674 | + | 0.947864i | \(0.603238\pi\) | |||||||
\(608\) | −22363.9 | −1.49174 | ||||||||
\(609\) | − 2385.14i | − 0.158704i | ||||||||
\(610\) | 3786.91 | 0.251356 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2853.78 | −0.188492 | ||||||||
\(613\) | 10187.1i | 0.671211i | 0.942003 | + | 0.335605i | \(0.108941\pi\) | ||||
−0.942003 | + | 0.335605i | \(0.891059\pi\) | |||||||
\(614\) | 4883.30 | 0.320967 | ||||||||
\(615\) | −16474.4 | −1.08018 | ||||||||
\(616\) | − 18846.0i | − 1.23267i | ||||||||
\(617\) | 8012.62i | 0.522813i | 0.965229 | + | 0.261407i | \(0.0841864\pi\) | ||||
−0.965229 | + | 0.261407i | \(0.915814\pi\) | |||||||
\(618\) | − 3088.08i | − 0.201004i | ||||||||
\(619\) | − 1886.59i | − 0.122501i | −0.998122 | − | 0.0612506i | \(-0.980491\pi\) | ||||
0.998122 | − | 0.0612506i | \(-0.0195089\pi\) | |||||||
\(620\) | 9788.58 | 0.634063 | ||||||||
\(621\) | −1435.28 | −0.0927470 | ||||||||
\(622\) | − 5747.94i | − 0.370533i | ||||||||
\(623\) | 2457.70 | 0.158051 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16844.5 | −1.07805 | ||||||||
\(626\) | 6599.38i | 0.421349i | ||||||||
\(627\) | −29046.8 | −1.85011 | ||||||||
\(628\) | −2448.18 | −0.155562 | ||||||||
\(629\) | 3497.53i | 0.221710i | ||||||||
\(630\) | 2629.10i | 0.166263i | ||||||||
\(631\) | − 14956.1i | − 0.943569i | −0.881714 | − | 0.471784i | \(-0.843610\pi\) | ||||
0.881714 | − | 0.471784i | \(-0.156390\pi\) | |||||||
\(632\) | − 3992.61i | − 0.251293i | ||||||||
\(633\) | 2126.37 | 0.133516 | ||||||||
\(634\) | 8785.57 | 0.550346 | ||||||||
\(635\) | 6773.99i | 0.423335i | ||||||||
\(636\) | 4865.70 | 0.303361 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2333.06 | 0.144775 | ||||||||
\(639\) | − 823.547i | − 0.0509844i | ||||||||
\(640\) | 21895.5 | 1.35234 | ||||||||
\(641\) | −23691.7 | −1.45985 | −0.729927 | − | 0.683525i | \(-0.760446\pi\) | ||||
−0.729927 | + | 0.683525i | \(0.760446\pi\) | |||||||
\(642\) | 1658.86i | 0.101978i | ||||||||
\(643\) | 13651.3i | 0.837254i | 0.908158 | + | 0.418627i | \(0.137489\pi\) | ||||
−0.908158 | + | 0.418627i | \(0.862511\pi\) | |||||||
\(644\) | − 7832.62i | − 0.479268i | ||||||||
\(645\) | − 18928.6i | − 1.15553i | ||||||||
\(646\) | 5975.60 | 0.363943 | ||||||||
\(647\) | 18132.3 | 1.10178 | 0.550892 | − | 0.834577i | \(-0.314288\pi\) | ||||
0.550892 | + | 0.834577i | \(0.314288\pi\) | |||||||
\(648\) | 1126.38i | 0.0682846i | ||||||||
\(649\) | 9351.59 | 0.565612 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5458.05 | −0.328599 | ||||||||
\(652\) | 3984.36i | 0.239324i | ||||||||
\(653\) | 6363.47 | 0.381351 | 0.190675 | − | 0.981653i | \(-0.438932\pi\) | ||||
0.190675 | + | 0.981653i | \(0.438932\pi\) | |||||||
\(654\) | −3913.21 | −0.233973 | ||||||||
\(655\) | − 25641.3i | − 1.52960i | ||||||||
\(656\) | − 15799.7i | − 0.940358i | ||||||||
\(657\) | − 568.195i | − 0.0337403i | ||||||||
\(658\) | − 1283.40i | − 0.0760369i | ||||||||
\(659\) | −1051.43 | −0.0621518 | −0.0310759 | − | 0.999517i | \(-0.509893\pi\) | ||||
−0.0310759 | + | 0.999517i | \(0.509893\pi\) | |||||||
\(660\) | 21874.8 | 1.29011 | ||||||||
\(661\) | − 8119.75i | − 0.477794i | −0.971045 | − | 0.238897i | \(-0.923214\pi\) | ||||
0.971045 | − | 0.238897i | \(-0.0767858\pi\) | |||||||
\(662\) | −5296.12 | −0.310936 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5198.21 | 0.303810 | ||||||||
\(665\) | 46826.5i | 2.73061i | ||||||||
\(666\) | 651.912 | 0.0379296 | ||||||||
\(667\) | 2053.29 | 0.119196 | ||||||||
\(668\) | − 22451.9i | − 1.30043i | ||||||||
\(669\) | 16189.9i | 0.935632i | ||||||||
\(670\) | − 5835.62i | − 0.336492i | ||||||||
\(671\) | 17568.7i | 1.01078i | ||||||||
\(672\) | −9390.96 | −0.539083 | ||||||||
\(673\) | 190.264 | 0.0108977 | 0.00544885 | − | 0.999985i | \(-0.498266\pi\) | ||||
0.00544885 | + | 0.999985i | \(0.498266\pi\) | |||||||
\(674\) | − 1135.79i | − 0.0649093i | ||||||||
\(675\) | −3087.01 | −0.176028 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4861.93 | 0.276010 | 0.138005 | − | 0.990431i | \(-0.455931\pi\) | ||||
0.138005 | + | 0.990431i | \(0.455931\pi\) | |||||||
\(678\) | − 1091.82i | − 0.0618452i | ||||||||
\(679\) | −11416.5 | −0.645253 | ||||||||
\(680\) | −9529.35 | −0.537403 | ||||||||
\(681\) | 9545.37i | 0.537121i | ||||||||
\(682\) | − 5338.88i | − 0.299760i | ||||||||
\(683\) | 14539.6i | 0.814556i | 0.913304 | + | 0.407278i | \(0.133522\pi\) | ||||
−0.913304 | + | 0.407278i | \(0.866478\pi\) | |||||||
\(684\) | 9474.02i | 0.529603i | ||||||||
\(685\) | −30436.8 | −1.69771 | ||||||||
\(686\) | −4953.40 | −0.275688 | ||||||||
\(687\) | − 6102.00i | − 0.338873i | ||||||||
\(688\) | 18153.4 | 1.00595 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2263.31 | −0.124873 | ||||||||
\(691\) | − 22106.5i | − 1.21703i | −0.793541 | − | 0.608517i | \(-0.791765\pi\) | ||||
0.793541 | − | 0.608517i | \(-0.208235\pi\) | |||||||
\(692\) | −23796.0 | −1.30721 | ||||||||
\(693\) | −12197.2 | −0.668593 | ||||||||
\(694\) | 4999.66i | 0.273465i | ||||||||
\(695\) | − 43706.0i | − 2.38541i | ||||||||
\(696\) | − 1611.38i | − 0.0877574i | ||||||||
\(697\) | 15723.4i | 0.854474i | ||||||||
\(698\) | −1260.50 | −0.0683534 | ||||||||
\(699\) | 8382.66 | 0.453593 | ||||||||
\(700\) | − 16846.4i | − 0.909620i | ||||||||
\(701\) | −229.971 | −0.0123907 | −0.00619535 | − | 0.999981i | \(-0.501972\pi\) | ||||
−0.00619535 | + | 0.999981i | \(0.501972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11611.1 | 0.622934 | ||||||||
\(704\) | 14259.4i | 0.763380i | ||||||||
\(705\) | 3154.45 | 0.168516 | ||||||||
\(706\) | 5477.13 | 0.291975 | ||||||||
\(707\) | 9521.12i | 0.506476i | ||||||||
\(708\) | − 3050.15i | − 0.161909i | ||||||||
\(709\) | 4802.22i | 0.254374i | 0.991879 | + | 0.127187i | \(0.0405948\pi\) | ||||
−0.991879 | + | 0.127187i | \(0.959405\pi\) | |||||||
\(710\) | − 1298.66i | − 0.0686446i | ||||||||
\(711\) | −2584.04 | −0.136300 | ||||||||
\(712\) | 1660.40 | 0.0873965 | ||||||||
\(713\) | − 4698.66i | − 0.246797i | ||||||||
\(714\) | 2509.25 | 0.131522 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23717.6 | 1.23795 | ||||||||
\(717\) | − 16481.4i | − 0.858453i | ||||||||
\(718\) | −7168.09 | −0.372578 | ||||||||
\(719\) | 11016.9 | 0.571435 | 0.285718 | − | 0.958314i | \(-0.407768\pi\) | ||||
0.285718 | + | 0.958314i | \(0.407768\pi\) | |||||||
\(720\) | − 6197.36i | − 0.320780i | ||||||||
\(721\) | − 23096.0i | − 1.19298i | ||||||||
\(722\) | − 13545.6i | − 0.698221i | ||||||||
\(723\) | − 12183.8i | − 0.626723i | ||||||||
\(724\) | −544.125 | −0.0279313 | ||||||||
\(725\) | 4416.21 | 0.226226 | ||||||||
\(726\) | − 8267.85i | − 0.422656i | ||||||||
\(727\) | 13498.2 | 0.688612 | 0.344306 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344306 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 895.990i | − 0.0454275i | ||||||||
\(731\) | −18065.8 | −0.914073 | ||||||||
\(732\) | 5730.27 | 0.289340 | ||||||||
\(733\) | − 17014.7i | − 0.857368i | −0.903455 | − | 0.428684i | \(-0.858977\pi\) | ||||
0.903455 | − | 0.428684i | \(-0.141023\pi\) | |||||||
\(734\) | 1548.88i | 0.0778888i | ||||||||
\(735\) | 3744.17i | 0.187899i | ||||||||
\(736\) | − 8084.38i | − 0.404883i | ||||||||
\(737\) | 27073.4 | 1.35313 | ||||||||
\(738\) | 2930.73 | 0.146181 | ||||||||
\(739\) | − 13392.6i | − 0.666651i | −0.942812 | − | 0.333326i | \(-0.891829\pi\) | ||||
0.942812 | − | 0.333326i | \(-0.108171\pi\) | |||||||
\(740\) | −8744.19 | −0.434382 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4278.27 | −0.211672 | ||||||||
\(743\) | 11796.5i | 0.582467i | 0.956652 | + | 0.291233i | \(0.0940656\pi\) | ||||
−0.956652 | + | 0.291233i | \(0.905934\pi\) | |||||||
\(744\) | −3687.42 | −0.181703 | ||||||||
\(745\) | 12340.1 | 0.606854 | ||||||||
\(746\) | 1716.05i | 0.0842214i | ||||||||
\(747\) | − 3364.31i | − 0.164784i | ||||||||
\(748\) | − 20877.6i | − 1.02054i | ||||||||
\(749\) | 12406.7i | 0.605250i | ||||||||
\(750\) | 454.136 | 0.0221103 | ||||||||
\(751\) | 12450.5 | 0.604961 | 0.302480 | − | 0.953156i | \(-0.402185\pi\) | ||||
0.302480 | + | 0.953156i | \(0.402185\pi\) | |||||||
\(752\) | 3025.26i | 0.146702i | ||||||||
\(753\) | 10712.6 | 0.518447 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2506.01 | 0.120799 | ||||||||
\(756\) | 3978.30i | 0.191388i | ||||||||
\(757\) | −7029.84 | −0.337522 | −0.168761 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168761 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(758\) | 10703.0 | 0.512865 | ||||||||
\(759\) | − 10500.2i | − 0.502152i | ||||||||
\(760\) | 31635.6i | 1.50993i | ||||||||
\(761\) | − 17740.6i | − 0.845067i | −0.906347 | − | 0.422533i | \(-0.861141\pi\) | ||||
0.906347 | − | 0.422533i | \(-0.138859\pi\) | |||||||
\(762\) | − 1205.06i | − 0.0572899i | ||||||||
\(763\) | −29267.2 | −1.38866 | ||||||||
\(764\) | −29159.1 | −1.38081 | ||||||||
\(765\) | 6167.45i | 0.291483i | ||||||||
\(766\) | −6124.94 | −0.288907 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1302.54 | 0.0611995 | ||||||||
\(769\) | 31976.5i | 1.49948i | 0.661732 | + | 0.749741i | \(0.269822\pi\) | ||||
−0.661732 | + | 0.749741i | \(0.730178\pi\) | |||||||
\(770\) | −19233.9 | −0.900184 | ||||||||
\(771\) | 22554.8 | 1.05355 | ||||||||
\(772\) | − 6210.51i | − 0.289535i | ||||||||
\(773\) | − 2135.11i | − 0.0993463i | −0.998766 | − | 0.0496732i | \(-0.984182\pi\) | ||||
0.998766 | − | 0.0496732i | \(-0.0158180\pi\) | |||||||
\(774\) | 3367.32i | 0.156377i | ||||||||
\(775\) | − 10105.9i | − 0.468405i | ||||||||
\(776\) | −7712.93 | −0.356802 | ||||||||
\(777\) | 4875.70 | 0.225116 | ||||||||
\(778\) | − 13105.0i | − 0.603902i | ||||||||
\(779\) | 52198.9 | 2.40080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6024.89 | 0.276040 | ||||||||
\(782\) | 2160.14i | 0.0987804i | ||||||||
\(783\) | −1042.89 | −0.0475989 | ||||||||
\(784\) | −3590.83 | −0.163576 | ||||||||
\(785\) | 5290.89i | 0.240560i | ||||||||
\(786\) | 4561.48i | 0.207001i | ||||||||
\(787\) | 11704.4i | 0.530134i | 0.964230 | + | 0.265067i | \(0.0853940\pi\) | ||||
−0.964230 | + | 0.265067i | \(0.914606\pi\) | |||||||
\(788\) | − 13512.9i | − 0.610885i | ||||||||
\(789\) | −13980.6 | −0.630825 | ||||||||
\(790\) | −4074.78 | −0.183512 | ||||||||
\(791\) | − 8165.80i | − 0.367057i | ||||||||
\(792\) | −8240.36 | −0.369708 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3274.37 | −0.146351 | ||||||||
\(795\) | − 10515.5i | − 0.469115i | ||||||||
\(796\) | −19944.9 | −0.888102 | ||||||||
\(797\) | 149.733 | 0.00665474 | 0.00332737 | − | 0.999994i | \(-0.498941\pi\) | ||||
0.00332737 | + | 0.999994i | \(0.498941\pi\) | |||||||
\(798\) | − 8330.25i | − 0.369533i | ||||||||
\(799\) | − 3010.66i | − 0.133304i | ||||||||
\(800\) | − 17387.9i | − 0.768443i | ||||||||
\(801\) | − 1074.62i | − 0.0474032i | ||||||||
\(802\) | −458.089 | −0.0201692 | ||||||||
\(803\) | 4156.79 | 0.182677 | ||||||||
\(804\) | − 8830.35i | − 0.387341i | ||||||||
\(805\) | −16927.4 | −0.741135 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16042.3 | 0.699772 | ||||||||
\(808\) | 6432.40i | 0.280063i | ||||||||
\(809\) | 23520.8 | 1.02219 | 0.511093 | − | 0.859526i | \(-0.329241\pi\) | ||||
0.511093 | + | 0.859526i | \(0.329241\pi\) | |||||||
\(810\) | 1149.56 | 0.0498661 | ||||||||
\(811\) | 29604.8i | 1.28183i | 0.767612 | + | 0.640915i | \(0.221445\pi\) | ||||
−0.767612 | + | 0.640915i | \(0.778555\pi\) | |||||||
\(812\) | − 5691.27i | − 0.245966i | ||||||||
\(813\) | − 8919.24i | − 0.384762i | ||||||||
\(814\) | 4769.25i | 0.205359i | ||||||||
\(815\) | 8610.79 | 0.370089 | ||||||||
\(816\) | −5914.86 | −0.253752 | ||||||||
\(817\) | 59975.0i | 2.56825i | ||||||||
\(818\) | 9593.44 | 0.410057 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39310.3 | −1.67412 | ||||||||
\(821\) | 43034.7i | 1.82938i | 0.404154 | + | 0.914691i | \(0.367566\pi\) | ||||
−0.404154 | + | 0.914691i | \(0.632434\pi\) | |||||||
\(822\) | 5414.58 | 0.229751 | ||||||||
\(823\) | −5584.95 | −0.236548 | −0.118274 | − | 0.992981i | \(-0.537736\pi\) | ||||
−0.118274 | + | 0.992981i | \(0.537736\pi\) | |||||||
\(824\) | − 15603.5i | − 0.659675i | ||||||||
\(825\) | − 22583.9i | − 0.953054i | ||||||||
\(826\) | 2681.91i | 0.112973i | ||||||||
\(827\) | 4788.13i | 0.201330i | 0.994920 | + | 0.100665i | \(0.0320970\pi\) | ||||
−0.994920 | + | 0.100665i | \(0.967903\pi\) | |||||||
\(828\) | −3424.79 | −0.143744 | ||||||||
\(829\) | 32392.2 | 1.35709 | 0.678546 | − | 0.734558i | \(-0.262610\pi\) | ||||
0.678546 | + | 0.734558i | \(0.262610\pi\) | |||||||
\(830\) | − 5305.20i | − 0.221863i | ||||||||
\(831\) | 2292.46 | 0.0956974 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3573.50 | 0.148637 | ||||||||
\(834\) | 7775.11i | 0.322818i | ||||||||
\(835\) | −48521.8 | −2.01098 | ||||||||
\(836\) | −69309.9 | −2.86738 | ||||||||
\(837\) | 2386.51i | 0.0985544i | ||||||||
\(838\) | − 1564.51i | − 0.0644929i | ||||||||
\(839\) | − 13598.9i | − 0.559577i | −0.960062 | − | 0.279788i | \(-0.909736\pi\) | ||||
0.960062 | − | 0.279788i | \(-0.0902643\pi\) | |||||||
\(840\) | 13284.3i | 0.545658i | ||||||||
\(841\) | −22897.1 | −0.938827 | ||||||||
\(842\) | −8041.31 | −0.329123 | ||||||||
\(843\) | 21121.0i | 0.862926i | ||||||||
\(844\) | 5073.82 | 0.206929 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −561.164 | −0.0228052 | ||||||||
\(847\) | − 61835.9i | − 2.50851i | ||||||||
\(848\) | 10084.8 | 0.408390 | ||||||||
\(849\) | 27105.5 | 1.09571 | ||||||||
\(850\) | 4646.02i | 0.187479i | ||||||||
\(851\) | 4197.34i | 0.169075i | ||||||||
\(852\) | − 1965.10i | − 0.0790178i | ||||||||
\(853\) | − 41037.0i | − 1.64722i | −0.567155 | − | 0.823611i | \(-0.691956\pi\) | ||||
0.567155 | − | 0.823611i | \(-0.308044\pi\) | |||||||
\(854\) | −5038.47 | −0.201889 | ||||||||
\(855\) | 20474.8 | 0.818973 | ||||||||
\(856\) | 8381.89i | 0.334681i | ||||||||
\(857\) | 39959.3 | 1.59275 | 0.796374 | − | 0.604804i | \(-0.206749\pi\) | ||||
0.796374 | + | 0.604804i | \(0.206749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32570.5 | −1.29371 | −0.646853 | − | 0.762615i | \(-0.723915\pi\) | ||||
−0.646853 | + | 0.762615i | \(0.723915\pi\) | |||||||
\(860\) | − 45166.4i | − 1.79088i | ||||||||
\(861\) | 21919.2 | 0.867599 | ||||||||
\(862\) | −7412.72 | −0.292898 | ||||||||
\(863\) | − 16951.8i | − 0.668652i | −0.942457 | − | 0.334326i | \(-0.891491\pi\) | ||||
0.942457 | − | 0.334326i | \(-0.108509\pi\) | |||||||
\(864\) | 4106.17i | 0.161684i | ||||||||
\(865\) | 51426.6i | 2.02145i | ||||||||
\(866\) | 3783.69i | 0.148470i | ||||||||
\(867\) | −8852.69 | −0.346774 | ||||||||
\(868\) | −13023.7 | −0.509277 | ||||||||
\(869\) | − 18904.3i | − 0.737955i | ||||||||
\(870\) | −1644.54 | −0.0640865 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −19772.7 | −0.767876 | ||||||||
\(873\) | 4991.85i | 0.193526i | ||||||||
\(874\) | 7171.24 | 0.277541 | ||||||||
\(875\) | 3396.52 | 0.131227 | ||||||||
\(876\) | − 1355.79i | − 0.0522923i | ||||||||
\(877\) | − 45939.2i | − 1.76882i | −0.466709 | − | 0.884411i | \(-0.654561\pi\) | ||||
0.466709 | − | 0.884411i | \(-0.345439\pi\) | |||||||
\(878\) | 5610.22i | 0.215644i | ||||||||
\(879\) | − 5355.70i | − 0.205510i | ||||||||
\(880\) | 45338.5 | 1.73677 | ||||||||
\(881\) | −37960.5 | −1.45167 | −0.725836 | − | 0.687868i | \(-0.758547\pi\) | ||||
−0.725836 | + | 0.687868i | \(0.758547\pi\) | |||||||
\(882\) | − 666.072i | − 0.0254284i | ||||||||
\(883\) | −43172.9 | −1.64539 | −0.822697 | − | 0.568480i | \(-0.807532\pi\) | ||||
−0.822697 | + | 0.568480i | \(0.807532\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6591.82 | −0.250375 | ||||||||
\(886\) | − 10145.1i | − 0.384684i | ||||||||
\(887\) | 28706.3 | 1.08665 | 0.543327 | − | 0.839521i | \(-0.317164\pi\) | ||||
0.543327 | + | 0.839521i | \(0.317164\pi\) | |||||||
\(888\) | 3293.99 | 0.124481 | ||||||||
\(889\) | − 9012.78i | − 0.340021i | ||||||||
\(890\) | − 1694.58i | − 0.0638229i | ||||||||
\(891\) | 5333.20i | 0.200526i | ||||||||
\(892\) | 38631.4i | 1.45008i | ||||||||
\(893\) | −9994.83 | −0.374540 | ||||||||
\(894\) | −2195.25 | −0.0821255 | ||||||||
\(895\) | − 51257.3i | − 1.91435i | ||||||||
\(896\) | −29131.9 | −1.08619 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −222.015 | −0.00825027 | ||||||||
\(899\) | − 3414.10i | − 0.126659i | ||||||||
\(900\) | −7366.04 | −0.272816 | ||||||||
\(901\) | −10036.2 | −0.371091 | ||||||||
\(902\) | 21440.6i | 0.791456i | ||||||||
\(903\) | 25184.5i | 0.928114i | ||||||||
\(904\) | − 5516.75i | − 0.202969i | ||||||||
\(905\) | 1175.93i | 0.0431927i | ||||||||
\(906\) | −445.809 | −0.0163477 | ||||||||
\(907\) | 22356.1 | 0.818435 | 0.409218 | − | 0.912437i | \(-0.365802\pi\) | ||||
0.409218 | + | 0.912437i | \(0.365802\pi\) | |||||||
\(908\) | 22776.6i | 0.832454i | ||||||||
\(909\) | 4163.08 | 0.151904 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6953.80 | 0.252897 | 0.126449 | − | 0.991973i | \(-0.459642\pi\) | ||||
0.126449 | + | 0.991973i | \(0.459642\pi\) | |||||||
\(912\) | 19636.2i | 0.712960i | ||||||||
\(913\) | 24612.6 | 0.892176 | ||||||||
\(914\) | 10139.0 | 0.366923 | ||||||||
\(915\) | − 12384.0i | − 0.447433i | ||||||||
\(916\) | − 14560.2i | − 0.525200i | ||||||||
\(917\) | 34115.7i | 1.22857i | ||||||||
\(918\) | − 1097.16i | − 0.0394464i | ||||||||
\(919\) | 40625.2 | 1.45822 | 0.729108 | − | 0.684399i | \(-0.239935\pi\) | ||||
0.729108 | + | 0.684399i | \(0.239935\pi\) | |||||||
\(920\) | −11436.0 | −0.409821 | ||||||||
\(921\) | − 15969.4i | − 0.571346i | ||||||||
\(922\) | −251.143 | −0.00897068 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −29104.3 | −1.03621 | ||||||||
\(925\) | 9027.64i | 0.320894i | ||||||||
\(926\) | 10622.4 | 0.376971 | ||||||||
\(927\) | −10098.6 | −0.357803 | ||||||||
\(928\) | − 5874.20i | − 0.207791i | ||||||||
\(929\) | 42813.8i | 1.51203i | 0.654555 | + | 0.756014i | \(0.272856\pi\) | ||||
−0.654555 | + | 0.756014i | \(0.727144\pi\) | |||||||
\(930\) | 3763.31i | 0.132692i | ||||||||
\(931\) | − 11863.3i | − 0.417621i | ||||||||
\(932\) | 20002.2 | 0.702998 | ||||||||
\(933\) | −18796.9 | −0.659575 | ||||||||
\(934\) | − 828.311i | − 0.0290184i | ||||||||
\(935\) | −45119.7 | −1.57815 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43484.1 | 1.51608 | 0.758038 | − | 0.652210i | \(-0.226158\pi\) | ||||
0.758038 | + | 0.652210i | \(0.226158\pi\) | |||||||
\(938\) | 7764.28i | 0.270269i | ||||||||
\(939\) | 21581.3 | 0.750032 | ||||||||
\(940\) | 7526.97 | 0.261173 | ||||||||
\(941\) | − 7108.58i | − 0.246263i | −0.992390 | − | 0.123131i | \(-0.960706\pi\) | ||||
0.992390 | − | 0.123131i | \(-0.0392936\pi\) | |||||||
\(942\) | − 941.227i | − 0.0325550i | ||||||||
\(943\) | 18869.5i | 0.651618i | ||||||||
\(944\) | − 6321.85i | − 0.217965i | ||||||||
\(945\) | 8597.68 | 0.295960 | ||||||||
\(946\) | −24634.6 | −0.846660 | ||||||||
\(947\) | − 1938.99i | − 0.0665351i | −0.999446 | − | 0.0332676i | \(-0.989409\pi\) | ||||
0.999446 | − | 0.0332676i | \(-0.0105913\pi\) | |||||||
\(948\) | −6165.88 | −0.211243 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 15423.9 | 0.526756 | ||||||||
\(951\) | − 28730.6i | − 0.979657i | ||||||||
\(952\) | 12678.8 | 0.431640 | ||||||||
\(953\) | 47806.7 | 1.62498 | 0.812492 | − | 0.582972i | \(-0.198110\pi\) | ||||
0.812492 | + | 0.582972i | \(0.198110\pi\) | |||||||
\(954\) | 1870.66i | 0.0634852i | ||||||||
\(955\) | 63017.1i | 2.13527i | ||||||||
\(956\) | − 39327.1i | − 1.33047i | ||||||||
\(957\) | − 7629.58i | − 0.257711i | ||||||||
\(958\) | −11071.6 | −0.373388 | ||||||||
\(959\) | 40496.1 | 1.36359 | ||||||||
\(960\) | − 10051.2i | − 0.337919i | ||||||||
\(961\) | 21978.3 | 0.737750 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5424.81 | 0.181528 | ||||||||
\(964\) | − 29072.3i | − 0.971323i | ||||||||
\(965\) | −13421.8 | −0.447735 | ||||||||
\(966\) | 3011.32 | 0.100298 | ||||||||
\(967\) | − 2832.71i | − 0.0942025i | −0.998890 | − | 0.0471013i | \(-0.985002\pi\) | ||||
0.998890 | − | 0.0471013i | \(-0.0149983\pi\) | |||||||
\(968\) | − 41775.8i | − 1.38711i | ||||||||
\(969\) | − 19541.4i | − 0.647845i | ||||||||
\(970\) | 7871.68i | 0.260561i | ||||||||
\(971\) | −41276.3 | −1.36418 | −0.682090 | − | 0.731268i | \(-0.738929\pi\) | ||||
−0.682090 | + | 0.731268i | \(0.738929\pi\) | |||||||
\(972\) | 1739.50 | 0.0574016 | ||||||||
\(973\) | 58150.7i | 1.91596i | ||||||||
\(974\) | −10542.9 | −0.346835 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11876.8 | 0.389515 | ||||||||
\(977\) | 4278.89i | 0.140117i | 0.997543 | + | 0.0700583i | \(0.0223185\pi\) | ||||
−0.997543 | + | 0.0700583i | \(0.977681\pi\) | |||||||
\(978\) | −1531.82 | −0.0500842 | ||||||||
\(979\) | 7861.70 | 0.256651 | ||||||||
\(980\) | 8934.12i | 0.291214i | ||||||||
\(981\) | 12797.0i | 0.416490i | ||||||||
\(982\) | − 14406.6i | − 0.468159i | ||||||||
\(983\) | − 22652.9i | − 0.735011i | −0.930021 | − | 0.367505i | \(-0.880212\pi\) | ||||
0.930021 | − | 0.367505i | \(-0.119788\pi\) | |||||||
\(984\) | 14808.4 | 0.479751 | ||||||||
\(985\) | −29203.4 | −0.944667 | ||||||||
\(986\) | 1569.58i | 0.0506953i | ||||||||
\(987\) | −4196.99 | −0.135351 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21680.5 | −0.697068 | ||||||||
\(990\) | 8409.96i | 0.269986i | ||||||||
\(991\) | 22060.2 | 0.707131 | 0.353565 | − | 0.935410i | \(-0.384969\pi\) | ||||
0.353565 | + | 0.935410i | \(0.384969\pi\) | |||||||
\(992\) | −13442.3 | −0.430235 | ||||||||
\(993\) | 17319.4i | 0.553488i | ||||||||
\(994\) | 1727.86i | 0.0551351i | ||||||||
\(995\) | 43103.9i | 1.37335i | ||||||||
\(996\) | − 8027.72i | − 0.255390i | ||||||||
\(997\) | 35635.5 | 1.13198 | 0.565992 | − | 0.824411i | \(-0.308493\pi\) | ||||
0.565992 | + | 0.824411i | \(0.308493\pi\) | |||||||
\(998\) | −8274.52 | −0.262450 | ||||||||
\(999\) | − 2131.89i | − 0.0675174i |
(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 | 507.4.b.i.337.6 | 10 | ||
13.3 | even | 3 | 39.4.j.c.4.3 | ✓ | 10 | ||
13.4 | even | 6 | 39.4.j.c.10.3 | yes | 10 | ||
13.5 | odd | 4 | 507.4.a.r.1.6 | 10 | |||
13.8 | odd | 4 | 507.4.a.r.1.5 | 10 | |||
13.12 | even | 2 | inner | 507.4.b.i.337.5 | 10 | ||
39.5 | even | 4 | 1521.4.a.bk.1.5 | 10 | |||
39.8 | even | 4 | 1521.4.a.bk.1.6 | 10 | |||
39.17 | odd | 6 | 117.4.q.e.10.3 | 10 | |||
39.29 | odd | 6 | 117.4.q.e.82.3 | 10 | |||
52.3 | odd | 6 | 624.4.bv.h.433.2 | 10 | |||
52.43 | odd | 6 | 624.4.bv.h.49.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.3 | ✓ | 10 | 13.3 | even | 3 | ||
39.4.j.c.10.3 | yes | 10 | 13.4 | even | 6 | ||
117.4.q.e.10.3 | 10 | 39.17 | odd | 6 | |||
117.4.q.e.82.3 | 10 | 39.29 | odd | 6 | |||
507.4.a.r.1.5 | 10 | 13.8 | odd | 4 | |||
507.4.a.r.1.6 | 10 | 13.5 | odd | 4 | |||
507.4.b.i.337.5 | 10 | 13.12 | even | 2 | inner | ||
507.4.b.i.337.6 | 10 | 1.1 | even | 1 | trivial | ||
624.4.bv.h.49.4 | 10 | 52.43 | odd | 6 | |||
624.4.bv.h.433.2 | 10 | 52.3 | odd | 6 | |||
1521.4.a.bk.1.5 | 10 | 39.5 | even | 4 | |||
1521.4.a.bk.1.6 | 10 | 39.8 | even | 4 |