Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(31,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.31");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Character | \(\chi\) | \(=\) | 1216.31 |
Dual form | 1216.2.s.i.863.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −2.52536 | + | 1.45802i | −1.45802 | + | 0.841788i | −0.998914 | − | 0.0465944i | \(-0.985163\pi\) |
−0.459105 | + | 0.888382i | \(0.651830\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.80656 | − | 1.04302i | 0.807917 | − | 0.466451i | −0.0383149 | − | 0.999266i | \(-0.512199\pi\) |
0.846232 | + | 0.532815i | \(0.178866\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.63975i | 1.37570i | 0.725855 | + | 0.687848i | \(0.241444\pi\) | ||||
−0.725855 | + | 0.687848i | \(0.758556\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.75164 | − | 4.76598i | 0.917213 | − | 1.58866i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.65398 | −1.10171 | −0.550857 | − | 0.834599i | \(-0.685699\pi\) | ||||
−0.550857 | + | 0.834599i | \(0.685699\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.883346 | + | 1.53000i | −0.244996 | + | 0.424346i | −0.962131 | − | 0.272589i | \(-0.912120\pi\) |
0.717134 | + | 0.696935i | \(0.245453\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.04148 | + | 5.26799i | −0.785306 | + | 1.36019i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.68776 | + | 4.65534i | 0.651878 | + | 1.12909i | 0.982667 | + | 0.185381i | \(0.0593518\pi\) |
−0.330789 | + | 0.943705i | \(0.607315\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.96933 | − | 3.88867i | 0.451795 | − | 0.892122i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.30682 | − | 9.19168i | −1.15804 | − | 2.00579i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.04148 | − | 1.75600i | −0.634192 | − | 0.366151i | 0.148182 | − | 0.988960i | \(-0.452658\pi\) |
−0.782374 | + | 0.622809i | \(0.785991\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.324233 | + | 0.561588i | −0.0648466 | + | 0.112318i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.29965i | 1.40482i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.87617 | + | 4.98168i | −0.534092 | + | 0.925074i | 0.465115 | + | 0.885250i | \(0.346013\pi\) |
−0.999207 | + | 0.0398238i | \(0.987320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.30423 | 1.13227 | 0.566136 | − | 0.824312i | \(-0.308438\pi\) | ||||
0.566136 | + | 0.824312i | \(0.308438\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9.22761 | − | 5.32756i | 1.60632 | − | 0.927410i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.79632 | + | 6.57542i | 0.641695 | + | 1.11145i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.58389 | −0.753587 | −0.376794 | − | 0.926297i | \(-0.622973\pi\) | ||||
−0.376794 | + | 0.926297i | \(0.622973\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.15174i | − | 0.824939i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.75491 | + | 3.89995i | −1.05494 | + | 0.609070i | −0.924028 | − | 0.382324i | \(-0.875124\pi\) |
−0.130912 | + | 0.991394i | \(0.541791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.53000 | + | 2.65004i | 0.233323 | + | 0.404127i | 0.958784 | − | 0.284136i | \(-0.0917068\pi\) |
−0.725461 | + | 0.688263i | \(0.758373\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 11.4800i | − | 1.71134i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.26920 | + | 3.61952i | 0.914457 | + | 0.527962i | 0.881862 | − | 0.471507i | \(-0.156290\pi\) |
0.0325945 | + | 0.999469i | \(0.489623\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.24777 | −0.892538 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.5751 | − | 7.83761i | −1.90090 | − | 1.09749i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.03269 | − | 3.52073i | 0.279212 | − | 0.483609i | −0.691977 | − | 0.721919i | \(-0.743260\pi\) |
0.971189 | + | 0.238310i | \(0.0765936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.60112 | + | 3.81116i | −0.890094 | + | 0.513896i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.696478 | + | 12.6916i | 0.0922508 | + | 1.68105i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.00169 | + | 5.19713i | −1.17192 | + | 0.676608i | −0.954132 | − | 0.299388i | \(-0.903218\pi\) |
−0.217788 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.65731 | − | 5.57565i | −1.23649 | − | 0.713889i | −0.268117 | − | 0.963386i | \(-0.586401\pi\) |
−0.968375 | + | 0.249498i | \(0.919735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17.3470 | + | 10.0153i | 2.18551 | + | 1.26181i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.68538i | 0.457115i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.01096 | − | 4.04778i | −0.856525 | − | 0.494515i | 0.00632174 | − | 0.999980i | \(-0.497988\pi\) |
−0.862847 | + | 0.505465i | \(0.831321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.2411 | 1.23288 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.92564 | − | 13.7276i | −0.940601 | − | 1.62917i | −0.764329 | − | 0.644826i | \(-0.776930\pi\) |
−0.176271 | − | 0.984342i | \(-0.556404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.76363 | − | 13.4470i | −0.908664 | − | 1.57385i | −0.815921 | − | 0.578163i | \(-0.803770\pi\) |
−0.0927429 | − | 0.995690i | \(-0.529563\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.89095i | − | 0.218348i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13.2995i | − | 1.51562i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.68926 | − | 13.3182i | −0.865110 | − | 1.49841i | −0.866938 | − | 0.498416i | \(-0.833915\pi\) |
0.00182823 | − | 0.999998i | \(-0.499418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.38811 | − | 4.13633i | −0.265346 | − | 0.459592i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.97484 | 0.546060 | 0.273030 | − | 0.962006i | \(-0.411974\pi\) | ||||
0.273030 | + | 0.962006i | \(0.411974\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.71119 | + | 5.60676i | 1.05333 | + | 0.608138i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 16.7741i | − | 1.79837i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.44655 | + | 3.14456i | 0.577333 | + | 0.333323i | 0.760073 | − | 0.649838i | \(-0.225163\pi\) |
−0.182740 | + | 0.983161i | \(0.558497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.56882 | − | 3.21516i | −0.583771 | − | 0.337040i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.9205 | + | 9.19168i | −1.65088 | + | 0.953133i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.498237 | − | 9.07915i | −0.0511180 | − | 0.931501i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.4192 | + | 7.17025i | −1.26098 | + | 0.728029i | −0.973265 | − | 0.229686i | \(-0.926230\pi\) |
−0.287718 | + | 0.957715i | \(0.592897\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.0544 | + | 17.4148i | −1.01051 | + | 1.75025i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.80656 | − | 1.04302i | −0.179759 | − | 0.103784i | 0.407420 | − | 0.913241i | \(-0.366428\pi\) |
−0.587180 | + | 0.809457i | \(0.699762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.92820 | −0.682656 | −0.341328 | − | 0.939944i | \(-0.610877\pi\) | ||||
−0.341328 | + | 0.939944i | \(0.610877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19.1742 | − | 11.0702i | −1.87121 | − | 1.08034i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.5917i | 1.60398i | 0.597338 | + | 0.801990i | \(0.296225\pi\) | ||||
−0.597338 | + | 0.801990i | \(0.703775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.72977 | − | 4.72810i | −0.261464 | − | 0.452870i | 0.705167 | − | 0.709041i | \(-0.250872\pi\) |
−0.966631 | + | 0.256172i | \(0.917539\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.5760 | − | 6.68340i | 1.09874 | − | 0.634360i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.51077i | 0.142122i | 0.997472 | + | 0.0710608i | \(0.0226384\pi\) | ||||
−0.997472 | + | 0.0710608i | \(0.977362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.32614 | −0.683166 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.86130 | + | 8.42002i | 0.449427 | + | 0.778431i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.9443 | + | 9.78277i | −1.55328 | + | 0.896785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.35153 | 0.213776 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.3724 | − | 19.6976i | 1.02542 | − | 1.77607i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7829i | 1.05389i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.95721 | + | 10.3182i | −0.528617 | + | 0.915592i | 0.470826 | + | 0.882226i | \(0.343956\pi\) |
−0.999443 | + | 0.0333658i | \(0.989377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.72761 | − | 4.46154i | −0.680378 | − | 0.392817i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.14403 | + | 15.8379i | 0.798918 | + | 1.38377i | 0.920322 | + | 0.391163i | \(0.127927\pi\) |
−0.121404 | + | 0.992603i | \(0.538740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.1538 | + | 7.16787i | 1.22729 | + | 0.621533i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.61365 | + | 13.1872i | 0.655279 | + | 1.13498i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.01199 | − | 3.48488i | 0.171896 | − | 0.297733i | −0.767187 | − | 0.641424i | \(-0.778344\pi\) |
0.939083 | + | 0.343691i | \(0.111677\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.815078 | − | 1.41176i | 0.0691340 | − | 0.119744i | −0.829386 | − | 0.558676i | \(-0.811310\pi\) |
0.898520 | + | 0.438932i | \(0.144643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.1093 | −1.77773 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.22773 | − | 5.59058i | 0.269916 | − | 0.467508i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.9996i | 0.996511i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.7779 | − | 9.10936i | 1.30134 | − | 0.751328i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.13543 | + | 4.69699i | −0.666480 | + | 0.384793i | −0.794742 | − | 0.606948i | \(-0.792394\pi\) |
0.128261 | + | 0.991740i | \(0.459060\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.76833 | −0.794935 | −0.397468 | − | 0.917616i | \(-0.630111\pi\) | ||||
−0.397468 | + | 0.917616i | \(0.630111\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.5830 | 2.39164 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.3890 | − | 6.57542i | 0.914783 | − | 0.528150i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0113 | − | 8.66676i | 1.19803 | − | 0.691683i | 0.237914 | − | 0.971286i | \(-0.423536\pi\) |
0.960116 | + | 0.279604i | \(0.0902030\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.8548i | 0.940148i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.39139 | − | 11.0702i | 0.503712 | − | 0.872454i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.8569 | 1.86861 | 0.934307 | − | 0.356468i | \(-0.116019\pi\) | ||||
0.934307 | + | 0.356468i | \(0.116019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.1135 | − | 19.2491i | 0.865183 | − | 1.49854i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.72949 | − | 4.72761i | 0.211214 | − | 0.365834i | −0.740881 | − | 0.671637i | \(-0.765592\pi\) |
0.952095 | + | 0.305803i | \(0.0989249\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.93940 | + | 8.55529i | 0.379954 | + | 0.658099i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.1144 | − | 20.0860i | −1.00288 | − | 1.53601i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.963077 | − | 1.66810i | −0.0732214 | − | 0.126823i | 0.827090 | − | 0.562069i | \(-0.189995\pi\) |
−0.900311 | + | 0.435246i | \(0.856661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.04404 | − | 1.18013i | −0.154515 | − | 0.0892091i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.1550 | − | 26.2493i | 1.13912 | − | 1.97302i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.44804i | 0.257718i | 0.991663 | + | 0.128859i | \(0.0411315\pi\) | ||||
−0.991663 | + | 0.128859i | \(0.958868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.65774 | − | 13.2636i | 0.569195 | − | 0.985875i | −0.427450 | − | 0.904039i | \(-0.640588\pi\) |
0.996646 | − | 0.0818365i | \(-0.0260785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.5176 | 2.40377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.28107 | + | 4.78108i | −0.608836 | + | 0.351512i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.82101 | − | 17.0105i | −0.718183 | − | 1.24393i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −26.5689 | −1.93260 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.0240i | 1.37653i | 0.725461 | + | 0.688264i | \(0.241627\pi\) | ||||
−0.725461 | + | 0.688264i | \(0.758373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.553454 | − | 0.319537i | 0.0398385 | − | 0.0230008i | −0.479948 | − | 0.877297i | \(-0.659345\pi\) |
0.519787 | + | 0.854296i | \(0.326011\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.37335 | − | 9.30692i | −0.384794 | − | 0.666482i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.09130i | 0.576481i | 0.957558 | + | 0.288241i | \(0.0930703\pi\) | ||||
−0.957558 | + | 0.288241i | \(0.906930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.42132 | − | 5.43940i | −0.667859 | − | 0.385589i | 0.127406 | − | 0.991851i | \(-0.459335\pi\) |
−0.795265 | + | 0.606262i | \(0.792668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.6070 | 1.66511 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.1320 | − | 10.4685i | −1.27262 | − | 0.734748i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.13543 | + | 14.0910i | −0.568203 | + | 0.984156i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.7381 | + | 9.66374i | −1.16338 | + | 0.671676i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.19588 | + | 14.2091i | −0.497750 | + | 0.982864i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.15513 | + | 2.97631i | −0.354894 | + | 0.204898i | −0.666838 | − | 0.745202i | \(-0.732353\pi\) |
0.311945 | + | 0.950100i | \(0.399020\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40.0302 | + | 23.1115i | 2.74283 | + | 1.58357i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.52807 | + | 3.19163i | 0.377011 | + | 0.217667i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.9458i | 1.55766i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.2120 | + | 22.6390i | 2.64970 | + | 1.52980i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.49689 | −0.638830 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.80510 | + | 4.85857i | 0.187843 | + | 0.325354i | 0.944531 | − | 0.328422i | \(-0.106517\pi\) |
−0.756688 | + | 0.653777i | \(0.773184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.78434 | + | 3.09057i | 0.118956 | + | 0.206038i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8135i | 0.850462i | 0.905085 | + | 0.425231i | \(0.139807\pi\) | ||||
−0.905085 | + | 0.425231i | \(0.860193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.0150i | − | 1.25654i | −0.777994 | − | 0.628272i | \(-0.783763\pi\) | ||
0.777994 | − | 0.628272i | \(-0.216237\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.3910 | + | 33.5862i | 1.27583 | + | 2.20981i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.51586 | − | 9.55376i | −0.361356 | − | 0.625887i | 0.626828 | − | 0.779158i | \(-0.284353\pi\) |
−0.988184 | + | 0.153270i | \(0.951020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.1009 | 0.985074 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 38.8364 | + | 22.4222i | 2.52269 | + | 1.45648i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.56988i | − | 0.360285i | −0.983640 | − | 0.180143i | \(-0.942344\pi\) | ||
0.983640 | − | 0.180143i | \(-0.0576559\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2909 | + | 6.51880i | 0.727310 | + | 0.419913i | 0.817437 | − | 0.576017i | \(-0.195394\pi\) |
−0.0901270 | + | 0.995930i | \(0.528727\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.90335 | − | 3.98565i | −0.442850 | − | 0.255680i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.2870 | + | 6.51652i | −0.721097 | + | 0.416325i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.21006 | + | 6.44812i | 0.267880 | + | 0.410284i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.5633 | + | 7.25341i | −0.796166 | + | 0.459666i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.63743 | + | 6.30021i | −0.229592 | + | 0.397666i | −0.957687 | − | 0.287811i | \(-0.907073\pi\) |
0.728095 | + | 0.685476i | \(0.240406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1135 | + | 6.41637i | 0.698698 | + | 0.403394i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −32.6990 | −2.04769 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.16433 | + | 0.672226i | 0.0726289 | + | 0.0419323i | 0.535875 | − | 0.844298i | \(-0.319982\pi\) |
−0.463246 | + | 0.886230i | \(0.653315\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 16.6842i | − | 1.03671i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.8284 | + | 27.4155i | 0.979752 | + | 1.69698i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.12310 | − | 2.38048i | 0.254241 | − | 0.146786i | −0.367463 | − | 0.930038i | \(-0.619774\pi\) |
0.621705 | + | 0.783252i | \(0.286440\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.48052i | − | 0.520954i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.3393 | −1.12235 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.67883 | − | 6.37192i | −0.224302 | − | 0.388503i | 0.731808 | − | 0.681511i | \(-0.238677\pi\) |
−0.956110 | + | 0.293008i | \(0.905344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.7696 | − | 10.2593i | 1.07943 | − | 0.623206i | 0.148684 | − | 0.988885i | \(-0.452496\pi\) |
0.930741 | + | 0.365678i | \(0.119163\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 18.7510 | 1.13486 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.18474 | − | 2.05203i | 0.0714424 | − | 0.123742i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8661i | 0.953299i | 0.879093 | + | 0.476650i | \(0.158149\pi\) | ||||
−0.879093 | + | 0.476650i | \(0.841851\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.3470 | − | 30.0458i | 1.03854 | − | 1.79880i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.7003 | + | 11.9513i | 1.23488 | + | 0.712957i | 0.968043 | − | 0.250786i | \(-0.0806890\pi\) |
0.266834 | + | 0.963742i | \(0.414022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.8342 | + | 23.9615i | 0.822357 | + | 1.42436i | 0.903922 | + | 0.427696i | \(0.140675\pi\) |
−0.0815654 | + | 0.996668i | \(0.525992\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.4958 | + | 22.2017i | 0.858657 | + | 1.31512i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.1948 | − | 24.5862i | −0.837895 | − | 1.45128i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.94812 | + | 10.3024i | −0.349889 | + | 0.606026i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.9087 | − | 36.2150i | 1.22569 | − | 2.12296i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.7017 | −1.73519 | −0.867596 | − | 0.497270i | \(-0.834336\pi\) | ||||
−0.867596 | + | 0.497270i | \(0.834336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.8414 | + | 18.7778i | −0.631209 | + | 1.09329i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 26.6727i | − | 1.54771i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.37335 | − | 3.10231i | 0.310749 | − | 0.179411i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.64547 | + | 5.56882i | −0.555956 | + | 0.320981i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.08295 | 0.349456 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.2620 | −1.33198 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.85832 | + | 1.65025i | −0.163133 | + | 0.0941849i | −0.579344 | − | 0.815083i | \(-0.696691\pi\) |
0.416211 | + | 0.909268i | \(0.363358\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.4962 | − | 10.1015i | 0.995326 | − | 0.574651i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.9432i | 1.01747i | 0.860924 | + | 0.508734i | \(0.169886\pi\) | ||||
−0.860924 | + | 0.508734i | \(0.830114\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47542 | + | 4.28755i | −0.139919 | + | 0.242347i | −0.927466 | − | 0.373908i | \(-0.878018\pi\) |
0.787547 | + | 0.616255i | \(0.211351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 41.7844 | 2.35428 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.58042 | + | 2.73737i | −0.0887654 | + | 0.153746i | −0.906990 | − | 0.421153i | \(-0.861625\pi\) |
0.818224 | + | 0.574899i | \(0.194959\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.5095 | − | 18.2029i | 0.588417 | − | 1.01917i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.1910 | − | 41.9000i | −1.35021 | − | 2.33863i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.3962 | − | 1.28391i | 1.30180 | − | 0.0714387i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.572820 | − | 0.992153i | −0.0317743 | − | 0.0550347i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.7873 | + | 7.96011i | 0.762440 | + | 0.440195i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.1742 | + | 22.8183i | −0.726315 | + | 1.25801i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.14294i | − | 0.117786i | −0.998264 | − | 0.0588932i | \(-0.981243\pi\) | ||
0.998264 | − | 0.0588932i | \(-0.0187571\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.6132 | + | 21.8467i | −0.691200 | + | 1.19719i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.8876 | −0.922669 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.58076 | + | 1.49000i | −0.140583 | + | 0.0811655i | −0.568642 | − | 0.822585i | \(-0.692531\pi\) |
0.428059 | + | 0.903751i | \(0.359198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.20274 | − | 3.81525i | −0.119636 | − | 0.207216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.0355 | −1.24744 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.73794i | 0.147835i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.5011 | − | 10.6816i | 0.996068 | − | 0.575080i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.76301 | − | 4.78568i | −0.148326 | − | 0.256909i | 0.782283 | − | 0.622924i | \(-0.214055\pi\) |
−0.930609 | + | 0.366015i | \(0.880722\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.2867i | 1.35357i | 0.736182 | + | 0.676784i | \(0.236627\pi\) | ||||
−0.736182 | + | 0.676784i | \(0.763373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.1685 | − | 6.44812i | −0.596129 | − | 0.344175i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.95314 | −0.476528 | −0.238264 | − | 0.971200i | \(-0.576578\pi\) | ||||
−0.238264 | + | 0.971200i | \(0.576578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.6363 | − | 16.5331i | −1.51985 | − | 0.877488i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.5269 | − | 49.4101i | 1.50981 | − | 2.61506i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.186249 | − | 0.107531i | 0.00982987 | − | 0.00567528i | −0.495077 | − | 0.868849i | \(-0.664860\pi\) |
0.504907 | + | 0.863174i | \(0.331527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.2435 | − | 15.3161i | −0.591762 | − | 0.806113i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.93848 | + | 3.42858i | −0.311689 | + | 0.179954i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.0509 | − | 16.1952i | −1.46825 | − | 0.847695i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.4512 | − | 16.4263i | −1.48514 | − | 0.857445i | −0.485281 | − | 0.874358i | \(-0.661283\pi\) |
−0.999857 | + | 0.0169129i | \(0.994616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 42.9250i | 2.23459i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.8146 | + | 7.39849i | 0.665298 | + | 0.384110i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.12436 | 0.472441 | 0.236221 | − | 0.971699i | \(-0.424091\pi\) | ||||
0.236221 | + | 0.971699i | \(0.424091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.1797 | − | 29.7561i | −0.887154 | − | 1.53660i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.08131 | − | 8.80109i | −0.261701 | − | 0.453279i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7418i | 0.962702i | 0.876528 | + | 0.481351i | \(0.159854\pi\) | ||||
−0.876528 | + | 0.481351i | \(0.840146\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 34.7429i | − | 1.77993i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.23763 | + | 14.2680i | 0.420923 | + | 0.729060i | 0.996030 | − | 0.0890180i | \(-0.0283729\pi\) |
−0.575107 | + | 0.818078i | \(0.695040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.8717 | − | 24.0264i | −0.706965 | − | 1.22450i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.8400 | 0.856027 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.5367 | + | 12.4342i | 1.09195 | + | 0.630440i | 0.934096 | − | 0.357021i | \(-0.116208\pi\) |
0.157859 | + | 0.987462i | \(0.449541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 18.8788i | − | 0.954742i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.1840 | − | 26.6643i | −2.32967 | − | 1.34504i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.7822 | − | 16.0401i | −1.39787 | − | 0.807063i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.3186 | − | 15.7724i | 1.37108 | − | 0.791595i | 0.380018 | − | 0.924979i | \(-0.375918\pi\) |
0.991064 | + | 0.133385i | \(0.0425846\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −46.1943 | + | 2.53501i | −2.31261 | + | 0.126909i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.03598 | − | 3.48488i | 0.301423 | − | 0.174026i | −0.341659 | − | 0.939824i | \(-0.610989\pi\) |
0.643082 | + | 0.765798i | \(0.277656\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.56882 | + | 9.64547i | −0.277403 | + | 0.480475i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.62852 | − | 4.98168i | −0.428754 | − | 0.247542i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.7494 | 0.830238 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.3455 | + | 7.12768i | 0.610446 | + | 0.352441i | 0.773140 | − | 0.634236i | \(-0.218685\pi\) |
−0.162694 | + | 0.986677i | \(0.552018\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.7341i | 0.578800i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.9162 | − | 32.7639i | −0.930807 | − | 1.61220i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.98734 | − | 5.18884i | 0.441171 | − | 0.254710i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.75360i | 0.232785i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.6856 | −0.863998 | −0.431999 | − | 0.901874i | \(-0.642192\pi\) | ||||
−0.431999 | + | 0.901874i | \(0.642192\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9345 | + | 27.5993i | 0.776599 | + | 1.34511i | 0.933891 | + | 0.357557i | \(0.116390\pi\) |
−0.157292 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.5011 | − | 19.9192i | 1.67750 | − | 0.968507i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.48584 | −0.169088 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.2940 | − | 35.1502i | 0.982094 | − | 1.70104i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.8243i | 0.908848i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.3179 | − | 31.7276i | 0.882344 | − | 1.52827i | 0.0336170 | − | 0.999435i | \(-0.489297\pi\) |
0.848727 | − | 0.528831i | \(-0.177369\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.47270 | + | 3.15966i | 0.263001 | + | 0.151844i | 0.625703 | − | 0.780062i | \(-0.284812\pi\) |
−0.362702 | + | 0.931905i | \(0.618146\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −17.4956 | − | 30.3033i | −0.838851 | − | 1.45293i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.8182 | + | 8.36915i | −0.613176 | + | 0.400351i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.0501271 | − | 0.0868226i | −0.00239243 | − | 0.00414382i | 0.864827 | − | 0.502070i | \(-0.167428\pi\) |
−0.867219 | + | 0.497927i | \(0.834095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.1916 | + | 29.7767i | −0.818647 | + | 1.41794i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.29140 | + | 12.6291i | −0.346425 | + | 0.600026i | −0.985612 | − | 0.169026i | \(-0.945938\pi\) |
0.639187 | + | 0.769052i | \(0.279271\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1193 | 0.621916 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.6966 | − | 23.7232i | 0.647827 | − | 1.12207i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.42562i | 0.0672791i | 0.999434 | + | 0.0336395i | \(0.0107098\pi\) | ||||
−0.999434 | + | 0.0336395i | \(0.989290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.6823 | − | 14.2503i | 1.16224 | − | 0.671022i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.6686 | − | 14.2424i | 1.15903 | − | 0.669167i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.4139 | −0.628851 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.9105 | 1.58627 | 0.793134 | − | 0.609047i | \(-0.208448\pi\) | ||||
0.793134 | + | 0.609047i | \(0.208448\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.9823 | + | 19.6197i | −1.58616 | + | 0.915770i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.7141 | + | 14.2687i | −1.15105 | + | 0.664558i | −0.949143 | − | 0.314847i | \(-0.898047\pi\) |
−0.201906 | + | 0.979405i | \(0.564714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.75537i | 0.221001i | 0.993876 | + | 0.110500i | \(0.0352454\pi\) | ||||
−0.993876 | + | 0.110500i | \(0.964755\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.1742 | + | 33.2106i | −0.889180 | + | 1.54011i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.65398 | −0.169086 | −0.0845429 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845429 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.7329 | − | 25.5181i | 0.680302 | − | 1.17832i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.2726 | + | 43.7734i | −1.16450 | + | 2.01697i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.59058 | − | 9.68318i | −0.257055 | − | 0.445233i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.54531 | + | 2.36679i | 0.0709035 | + | 0.108596i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.1865 | − | 19.3755i | −0.512193 | − | 0.887144i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.7756 | − | 10.8401i | −0.857879 | − | 0.495297i | 0.00542242 | − | 0.999985i | \(-0.498274\pi\) |
−0.863301 | + | 0.504689i | \(0.831607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.04916 | − | 7.01336i | 0.184626 | − | 0.319782i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.2750i | 1.69607i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.9574 | + | 25.9070i | −0.679180 | + | 1.17637i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0163 | 0.499195 | 0.249598 | − | 0.968350i | \(-0.419702\pi\) | ||||
0.249598 | + | 0.968350i | \(0.419702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −60.2473 | + | 34.7838i | −2.72448 | + | 1.57298i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1742 | + | 31.4787i | 0.820192 | + | 1.42061i | 0.905539 | + | 0.424263i | \(0.139467\pi\) |
−0.0853474 | + | 0.996351i | \(0.527200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.9219 | −1.39265 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 41.9477i | 1.88541i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 49.9651 | − | 28.8473i | 2.24124 | − | 1.29398i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.93139 | + | 3.34526i | 0.0864608 | + | 0.149755i | 0.906013 | − | 0.423250i | \(-0.139111\pi\) |
−0.819552 | + | 0.573005i | \(0.805778\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.9186i | 0.711190i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.0173 | − | 10.4023i | −0.803352 | − | 0.463816i | 0.0412899 | − | 0.999147i | \(-0.486853\pi\) |
−0.844642 | + | 0.535332i | \(0.820187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.35153 | −0.193641 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.9475 | − | 14.4035i | −1.10796 | − | 0.639681i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.17192 | + | 7.22598i | −0.184917 | + | 0.320286i | −0.943549 | − | 0.331234i | \(-0.892535\pi\) |
0.758631 | + | 0.651520i | \(0.225868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.9437 | − | 28.2577i | 2.16514 | − | 1.25005i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.3859 | + | 14.3754i | 1.25327 | + | 0.634690i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.5162 | + | 7.22623i | −0.551530 | + | 0.318426i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.9075 | − | 13.2257i | −1.00747 | − | 0.581664i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.86424 | + | 2.80837i | 0.213516 | + | 0.123274i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 19.2965i | − | 0.845397i | −0.906270 | − | 0.422698i | \(-0.861083\pi\) | ||
0.906270 | − | 0.422698i | \(-0.138917\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.3479 | − | 18.6761i | −1.41448 | − | 0.816648i | −0.418670 | − | 0.908138i | \(-0.637504\pi\) |
−0.995806 | + | 0.0914902i | \(0.970837\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.88258 | 0.300381 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9443 | + | 29.3483i | 0.738104 | + | 1.27843i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.33295 | − | 9.23694i | −0.231867 | − | 0.401606i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 57.2024i | 2.48237i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13.7800i | − | 0.596879i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.3054 | + | 29.9738i | 0.748178 | + | 1.29588i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.02730 | − | 8.70754i | −0.216944 | − | 0.375758i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.8292 | 0.983323 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.9488 | + | 8.05336i | 0.599707 | + | 0.346241i | 0.768926 | − | 0.639337i | \(-0.220791\pi\) |
−0.169219 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 44.6605i | 1.91657i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.86297 | − | 5.69439i | −0.422483 | − | 0.243921i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.05336 | − | 4.64961i | −0.344337 | − | 0.198803i | 0.317851 | − | 0.948141i | \(-0.397039\pi\) |
−0.662188 | + | 0.749338i | \(0.730372\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −53.1468 | + | 30.6843i | −2.26825 | + | 1.30958i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.7080 | + | 20.9950i | 0.583978 | + | 0.894419i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 48.4749 | − | 27.9870i | 2.06136 | − | 1.19013i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.9418 | − | 24.1479i | 0.591796 | − | 1.02502i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.6532 | + | 11.3468i | 0.832732 | + | 0.480778i | 0.854787 | − | 0.518979i | \(-0.173688\pi\) |
−0.0220553 | + | 0.999757i | \(0.507021\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.40608 | −0.228653 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 49.6032 | + | 28.6384i | 2.09425 | + | 1.20912i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.7497i | 1.25380i | 0.779100 | + | 0.626900i | \(0.215677\pi\) | ||||
−0.779100 | + | 0.626900i | \(0.784323\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.57576 | + | 2.72930i | 0.0662928 | + | 0.114822i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.0552 | − | 8.69212i | 0.632259 | − | 0.365035i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.2216i | 1.47657i | 0.674490 | + | 0.738284i | \(0.264363\pi\) | ||||
−0.674490 | + | 0.738284i | \(0.735637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.45311 | 0.353752 | 0.176876 | − | 0.984233i | \(-0.443401\pi\) | ||||
0.176876 | + | 0.984233i | \(0.443401\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.7373 | − | 48.0425i | −1.15874 | − | 2.00700i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.97229 | − | 1.13870i | 0.0822503 | − | 0.0474872i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.3569 | −0.431163 | −0.215582 | − | 0.976486i | \(-0.569165\pi\) | ||||
−0.215582 | + | 0.976486i | \(0.569165\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.931781 | + | 1.61389i | −0.0387235 | + | 0.0670711i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.1072i | 0.751212i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.42740 | + | 12.8646i | −0.307612 | + | 0.532799i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.5644 | + | 10.1408i | 0.726200 | + | 0.419272i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.87469 | + | 8.44321i | 0.201200 | + | 0.348488i | 0.948915 | − | 0.315531i | \(-0.102183\pi\) |
−0.747715 | + | 0.664019i | \(0.768849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4151 | − | 24.5151i | 0.511556 | − | 1.01013i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.7973 | − | 20.4335i | −0.485275 | − | 0.840521i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.3226 | − | 28.2716i | 0.670290 | − | 1.16098i | −0.307532 | − | 0.951538i | \(-0.599503\pi\) |
0.977822 | − | 0.209438i | \(-0.0671636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.4072 | + | 35.3463i | −0.836613 | + | 1.44906i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 31.7230 | 1.29834 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0691 | + | 24.3684i | −0.574848 | + | 0.995666i | 0.421210 | + | 0.906963i | \(0.361605\pi\) |
−0.996058 | + | 0.0887029i | \(0.971728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.8077i | 0.644808i | 0.946602 | + | 0.322404i | \(0.104491\pi\) | ||||
−0.946602 | + | 0.322404i | \(0.895509\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −38.5833 | + | 22.2761i | −1.57123 | + | 0.907151i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.24818 | − | 2.45269i | 0.172713 | − | 0.0997160i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.52198 | 0.305308 | 0.152654 | − | 0.988280i | \(-0.451218\pi\) | ||||
0.152654 | + | 0.988280i | \(0.451218\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 61.0533 | 2.47401 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.0757 | + | 6.39459i | −0.448077 | + | 0.258697i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.55967 | − | 3.78723i | 0.264942 | − | 0.152965i | −0.361645 | − | 0.932316i | \(-0.617785\pi\) |
0.626587 | + | 0.779351i | \(0.284451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 47.4464i | − | 1.91322i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.85153 | − | 4.93900i | 0.114798 | − | 0.198837i | −0.802901 | − | 0.596113i | \(-0.796711\pi\) |
0.917699 | + | 0.397276i | \(0.130044\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5470 | −1.14740 | −0.573701 | − | 0.819065i | \(-0.694493\pi\) | ||||
−0.573701 | + | 0.819065i | \(0.694493\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.8182 | − | 22.2017i | 0.514375 | − | 0.890924i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.4454 | + | 19.8241i | −0.458551 | + | 0.794234i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.6686 | + | 18.4785i | 0.426743 | + | 0.739141i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.54491 | − | 46.3749i | −0.101634 | − | 1.85203i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.3204 | − | 21.3396i | −0.491247 | − | 0.850864i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.32283 | + | 0.763739i | 0.0526612 | + | 0.0304040i | 0.526099 | − | 0.850423i | \(-0.323654\pi\) |
−0.473438 | + | 0.880827i | \(0.656987\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.67904 | − | 15.0325i | 0.344961 | − | 0.597490i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.8539i | 0.986297i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.51894 | − | 9.55909i | 0.218668 | − | 0.378745i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −87.2340 | −3.45092 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.4668 | + | 14.1259i | −0.966382 | + | 0.557941i | −0.898131 | − | 0.439727i | \(-0.855075\pi\) |
−0.0682507 | + | 0.997668i | \(0.521742\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5235 | − | 25.1554i | −0.572750 | − | 0.992032i | −0.996282 | − | 0.0861507i | \(-0.972543\pi\) |
0.423532 | − | 0.905881i | \(-0.360790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.6138 | −0.732919 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 33.4084i | 1.31342i | 0.754144 | + | 0.656709i | \(0.228052\pi\) | ||||
−0.754144 | + | 0.656709i | \(0.771948\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.8919 | − | 18.9902i | 1.29112 | − | 0.745429i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −33.4554 | − | 57.9465i | −1.31122 | − | 2.27110i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 33.9732i | − | 1.32948i | −0.747077 | − | 0.664738i | \(-0.768543\pi\) | ||
0.747077 | − | 0.664738i | \(-0.231457\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.0384 | + | 19.0748i | 1.29092 | + | 0.745312i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −85.4508 | −3.33375 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.84953 | + | 5.68663i | 0.383683 | + | 0.221520i | 0.679420 | − | 0.733750i | \(-0.262232\pi\) |
−0.295736 | + | 0.955270i | \(0.595565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0983 | − | 38.2753i | 0.859523 | − | 1.48874i | −0.0128614 | − | 0.999917i | \(-0.504094\pi\) |
0.872384 | − | 0.488820i | \(-0.162573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.9831 | − | 13.8466i | 0.931426 | − | 0.537759i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.0458 | − | 1.81346i | 1.28146 | − | 0.0703228i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.4956 | − | 10.1011i | 0.677433 | − | 0.391116i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.1678 | − | 8.17978i | −0.547758 | − | 0.316248i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.2876 | + | 20.3733i | 1.36226 | + | 0.786502i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 0.883049i | − | 0.0340390i | −0.999855 | − | 0.0170195i | \(-0.994582\pi\) | ||
0.999855 | − | 0.0170195i | \(-0.00541774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.09939 | − | 2.36679i | −0.157786 | − | 0.0910976i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.99154 | −0.230273 | −0.115137 | − | 0.993350i | \(-0.536731\pi\) | ||||
−0.115137 | + | 0.993350i | \(0.536731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.0979 | − | 45.2029i | −1.00155 | − | 1.73473i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.6823 | − | 32.3587i | −0.715908 | − | 1.23999i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.2700i | 0.392970i | 0.980507 | + | 0.196485i | \(0.0629528\pi\) | ||||
−0.980507 | + | 0.196485i | \(0.937047\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.39417i | − | 0.320725i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.7242 | + | 48.0197i | 1.05774 | + | 1.83206i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.59114 | + | 6.22004i | 0.136812 | + | 0.236965i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −63.3853 | − | 36.5955i | −2.40781 | − | 1.39015i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.40056i | − | 0.128991i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −36.3112 | − | 20.9643i | −1.37538 | − | 0.794079i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.8591 | + | 16.0845i | 1.05373 | + | 0.608371i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2289 | − | 12.2565i | 0.801806 | − | 0.462923i | −0.0422963 | − | 0.999105i | \(-0.513467\pi\) |
0.844102 | + | 0.536182i | \(0.180134\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.02720 | + | 17.8252i | −0.340467 | + | 0.672292i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.1352 | + | 22.0174i | −1.43626 | + | 0.829223i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.79632 | − | 6.57542i | 0.142775 | − | 0.247294i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −45.3505 | − | 26.1832i | −1.70318 | − | 0.983329i | −0.942506 | − | 0.334190i | \(-0.891537\pi\) |
−0.760670 | − | 0.649139i | \(-0.775129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −84.6323 | −3.17396 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.1742 | − | 11.0702i | −0.718078 | − | 0.414582i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 13.4663i | − | 0.503610i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.12098 | + | 14.0660i | 0.303284 | + | 0.525303i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0020 | − | 9.81611i | 0.634068 | − | 0.366079i | −0.148258 | − | 0.988949i | \(-0.547367\pi\) |
0.782326 | + | 0.622870i | \(0.214033\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 25.2169i | − | 0.939127i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −38.0181 | −1.41391 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.86510 | − | 3.23045i | −0.0692680 | − | 0.119976i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.6121 | − | 17.0966i | 1.09825 | − | 0.634077i | 0.162492 | − | 0.986710i | \(-0.448047\pi\) |
0.935762 | + | 0.352633i | \(0.114713\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 37.5733 | 1.39160 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.22455 | + | 14.2453i | −0.304196 | + | 0.526883i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.0010i | 1.51441i | 0.653179 | + | 0.757204i | \(0.273435\pi\) | ||||
−0.653179 | + | 0.757204i | \(0.726565\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.0024 | − | 32.9132i | 0.700915 | − | 1.21402i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.6179 | + | 14.7905i | 0.943647 | + | 0.544815i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.3449 | + | 23.1141i | 0.490902 | + | 0.850267i | 0.999945 | − | 0.0104741i | \(-0.00333406\pi\) |
−0.509043 | + | 0.860741i | \(0.670001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.0334 | − | 10.1455i | −0.735946 | − | 0.372704i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.75843 | + | 8.24184i | 0.174570 | + | 0.302364i | 0.940012 | − | 0.341141i | \(-0.110813\pi\) |
−0.765443 | + | 0.643504i | \(0.777480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.79808 | + | 16.9708i | −0.358974 | + | 0.621761i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.6890 | − | 23.7100i | 0.500853 | − | 0.867503i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −60.3896 | −2.20659 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.40013 | + | 2.42510i | −0.0510916 | + | 0.0884933i | −0.890440 | − | 0.455100i | \(-0.849603\pi\) |
0.839349 | + | 0.543594i | \(0.182937\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 21.2138i | − | 0.773072i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.6471 | + | 10.1885i | −0.642242 | + | 0.370799i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.41111 | − | 2.54676i | 0.160325 | − | 0.0925635i | −0.417691 | − | 0.908589i | \(-0.637161\pi\) |
0.578016 | + | 0.816026i | \(0.303827\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −37.4207 | −1.35829 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.4509 | −0.958844 | −0.479422 | − | 0.877584i | \(-0.659154\pi\) | ||||
−0.479422 | + | 0.877584i | \(0.659154\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.2091 | − | 9.93567i | 0.623011 | − | 0.359695i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 53.4434 | − | 30.8555i | 1.93225 | − | 1.11558i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 18.3634i | − | 0.663066i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.1355 | + | 27.9474i | −0.581860 | + | 1.00781i | 0.413399 | + | 0.910550i | \(0.364341\pi\) |
−0.995259 | + | 0.0972605i | \(0.968992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.92048 | −0.141192 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.08657 | − | 3.61405i | 0.0750487 | − | 0.129988i | −0.826059 | − | 0.563584i | \(-0.809422\pi\) |
0.901107 | + | 0.433596i | \(0.142755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.04404 | + | 3.54038i | −0.0734240 | + | 0.127174i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.3259 | + | 42.1337i | 0.872687 | + | 1.51154i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.86296 | + | 33.9479i | 0.0667475 | + | 1.21631i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.9601 | + | 50.1604i | 1.03627 | + | 1.79488i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −36.3645 | − | 20.9950i | −1.29956 | − | 0.750302i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.0791 | − | 31.3140i | 0.645272 | − | 1.11764i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.0039i | − | 0.641770i | −0.947118 | − | 0.320885i | \(-0.896020\pi\) | ||
0.947118 | − | 0.320885i | \(-0.103980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.94156 | + | 12.0231i | −0.247126 | + | 0.428035i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.49883 | −0.195516 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.0615 | − | 9.85046i | 0.605872 | − | 0.349800i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.3648 | + | 21.4164i | 0.438533 | + | 0.759561i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.2555 | 1.74472 | 0.872360 | − | 0.488864i | \(-0.162589\pi\) | ||||
0.872360 | + | 0.488864i | \(0.162589\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.9137i | 1.37667i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.9738 | − | 17.3054i | 1.05907 | − | 0.611457i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.3681 | + | 49.1350i | 1.00109 | + | 1.73394i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 26.6653i | − | 0.939828i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.5808 | + | 10.7276i | 0.654074 | + | 0.377630i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.1309 | −0.391341 | −0.195671 | − | 0.980670i | \(-0.562688\pi\) | ||||
−0.195671 | + | 0.980670i | \(0.562688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.34237 | + | 5.39382i | 0.328055 | + | 0.189403i | 0.654977 | − | 0.755649i | \(-0.272678\pi\) |
−0.326922 | + | 0.945051i | \(0.606012\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.9164 | + | 51.8168i | −1.04921 | + | 1.81729i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.0988 | − | 24.8831i | 1.50969 | − | 0.871618i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.3182 | − | 0.730863i | 0.465945 | − | 0.0255697i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −30.6467 | + | 17.6939i | −1.07088 | + | 0.618275i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.11190 | − | 2.95135i | −0.178406 | − | 0.103003i | 0.408137 | − | 0.912921i | \(-0.366178\pi\) |
−0.586544 | + | 0.809918i | \(0.699512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.97231 | + | 3.44812i | 0.208182 | + | 0.120194i | 0.600466 | − | 0.799650i | \(-0.294982\pi\) |
−0.392284 | + | 0.919844i | \(0.628315\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.90949i | 0.240557i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8328 | + | 8.56370i | 0.515786 | + | 0.297789i | 0.735209 | − | 0.677841i | \(-0.237084\pi\) |
−0.219423 | + | 0.975630i | \(0.570417\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.7083 | −1.48332 | −0.741660 | − | 0.670776i | \(-0.765961\pi\) | ||||
−0.741660 | + | 0.670776i | \(0.765961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.1330 | − | 40.0676i | −0.802476 | − | 1.38993i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.7925 | − | 29.0855i | −0.581826 | − | 1.00775i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 11.3876i | − | 0.394084i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 46.0187i | 1.59064i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.1003 | − | 41.7429i | −0.832033 | − | 1.44112i | −0.896423 | − | 0.443199i | \(-0.853843\pi\) |
0.0643898 | − | 0.997925i | \(-0.479490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04474 | − | 3.54159i | −0.0705082 | − | 0.122124i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −69.7011 | −2.40063 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.8466 | + | 10.3037i | 0.613942 | + | 0.354460i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.55899i | 0.294090i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −69.8727 | − | 40.3410i | −2.39802 | − | 1.38450i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.9418 | + | 8.04930i | 0.477919 | + | 0.275926i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.2023 | + | 15.1279i | −0.897150 | + | 0.517970i | −0.876274 | − | 0.481813i | \(-0.839979\pi\) |
−0.0208753 | + | 0.999782i | \(0.506645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −44.6420 | − | 22.6079i | −1.52672 | − | 0.773175i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.6812 | + | 9.05353i | −0.535658 | + | 0.309263i | −0.743318 | − | 0.668939i | \(-0.766749\pi\) |
0.207659 | + | 0.978201i | \(0.433416\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.99360 | − | 3.45302i | 0.0680209 | − | 0.117816i | −0.830009 | − | 0.557750i | \(-0.811665\pi\) |
0.898030 | + | 0.439934i | \(0.144998\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 71.6943 | + | 41.3927i | 2.44333 | + | 1.41066i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.83148 | 0.198506 | 0.0992529 | − | 0.995062i | \(-0.468355\pi\) | ||||
0.0992529 | + | 0.995062i | \(0.468355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.47971 | − | 2.00901i | −0.118314 | − | 0.0683084i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 34.6899i | − | 1.17813i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.0964 | + | 48.6644i | 0.953104 | + | 1.65083i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.3862 | − | 7.15119i | 0.419691 | − | 0.242309i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 78.9198i | 2.67103i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −42.8867 | −1.44984 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.5211 | + | 26.8834i | 0.524111 | + | 0.907787i | 0.999606 | + | 0.0280684i | \(0.00893564\pi\) |
−0.475495 | + | 0.879718i | \(0.657731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 75.0076 | − | 43.3056i | 2.52994 | − | 1.46066i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.4870 | −0.690223 | −0.345112 | − | 0.938562i | \(-0.612159\pi\) | ||||
−0.345112 | + | 0.938562i | \(0.612159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0901 | − | 39.9932i | 0.777043 | − | 1.34588i | −0.156596 | − | 0.987663i | \(-0.550052\pi\) |
0.933639 | − | 0.358215i | \(-0.116615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 63.2277i | − | 2.12538i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.75932 | − | 13.4395i | 0.260532 | − | 0.451255i | −0.705851 | − | 0.708360i | \(-0.749435\pi\) |
0.966384 | + | 0.257105i | \(0.0827686\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.5556 | − | 21.6828i | −1.25958 | − | 0.727216i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.72610 | + | 15.1140i | 0.292335 | + | 0.506339i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.4213 | − | 17.2508i | 0.884154 | − | 0.577276i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.59636 | + | 6.22908i | 0.120213 | + | 0.208215i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.04644 | + | 15.6689i | −0.302052 | + | 0.523169i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.1320 | + | 31.4056i | −0.604738 | + | 1.04744i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.8536 | 0.728047 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.2389 | − | 28.1266i | 0.540396 | − | 0.935993i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 31.9486i | − | 1.06201i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.72331 | + | 2.14966i | −0.123631 | + | 0.0713782i | −0.560540 | − | 0.828127i | \(-0.689406\pi\) |
0.436909 | + | 0.899506i | \(0.356073\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.94199 | + | 5.74001i | −0.329755 | + | 0.190384i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.6153 | 1.67696 | 0.838479 | − | 0.544934i | \(-0.183445\pi\) | ||||
0.838479 | + | 0.544934i | \(0.183445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.1780 | −0.601602 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 58.7450 | − | 33.9164i | 1.94205 | − | 1.12124i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −57.6461 | + | 33.2820i | −1.90364 | + | 1.09907i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.9736i | 0.823804i | 0.911228 | + | 0.411902i | \(0.135135\pi\) | ||||
−0.911228 | + | 0.411902i | \(0.864865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.81220 | − | 8.33498i | 0.158567 | − | 0.274647i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.0043 | 0.921774 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.48625 | − | 2.57426i | 0.0488676 | − | 0.0846411i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.0639 | + | 33.0197i | −0.626141 | + | 1.08451i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.52399 | + | 9.56783i | 0.181236 | + | 0.313910i | 0.942302 | − | 0.334765i | \(-0.108657\pi\) |
−0.761066 | + | 0.648675i | \(0.775324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.3039 | + | 24.2955i | −0.403245 | + | 0.796253i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.1616 | − | 45.3132i | −0.856491 | − | 1.48349i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −35.4844 | − | 20.4870i | −1.16047 | − | 0.669995i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.9219 | + | 29.3096i | −0.552815 | + | 0.957504i | 0.445255 | + | 0.895404i | \(0.353113\pi\) |
−0.998070 | + | 0.0621001i | \(0.980220\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 14.4368i | − | 0.471128i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2116 | − | 41.9358i | 0.789277 | − | 1.36707i | −0.137133 | − | 0.990553i | \(-0.543789\pi\) |
0.926410 | − | 0.376516i | \(-0.122878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.3932 | 0.892046 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −47.9982 | + | 27.7118i | −1.56138 | + | 0.901464i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.7669 | − | 44.6295i | −0.837311 | − | 1.45026i | −0.892135 | − | 0.451769i | \(-0.850793\pi\) |
0.0548242 | − | 0.998496i | \(-0.482540\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.4319 | 0.890477 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 9.21715i | − | 0.298887i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.728762 | + | 0.420751i | −0.0236069 | + | 0.0136295i | −0.511757 | − | 0.859130i | \(-0.671005\pi\) |
0.488150 | + | 0.872760i | \(0.337672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.8423 | + | 34.3679i | 0.642083 | + | 1.11212i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 61.2920i | 1.98129i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.6841 | + | 7.32315i | 0.409590 | + | 0.236477i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.74330 | 0.282042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 79.0756 | + | 45.6543i | 2.54818 | + | 1.47119i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.666564 | − | 1.15452i | 0.0214575 | − | 0.0371654i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.3932 | + | 21.5890i | −1.20248 | + | 0.694255i | −0.961107 | − | 0.276177i | \(-0.910933\pi\) |
−0.241377 | + | 0.970431i | \(0.577599\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −57.2118 | + | 37.3544i | −1.83791 | + | 1.20000i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.5296 | − | 8.96600i | 0.498367 | − | 0.287733i | −0.229672 | − | 0.973268i | \(-0.573765\pi\) |
0.728039 | + | 0.685536i | \(0.240432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.13844 | + | 2.96668i | 0.164731 | + | 0.0951074i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.89316 | + | 1.67036i | 0.0926551 | + | 0.0534945i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.5841i | 1.29840i | 0.760618 | + | 0.649200i | \(0.224896\pi\) | ||||
−0.760618 | + | 0.649200i | \(0.775104\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.9015 | − | 11.4902i | −0.636056 | − | 0.367227i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.0453 | −0.959274 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.93699 | + | 13.7473i | 0.253151 | + | 0.438470i | 0.964392 | − | 0.264479i | \(-0.0851998\pi\) |
−0.711241 | + | 0.702948i | \(0.751866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.43936 | + | 14.6174i | 0.268900 | + | 0.465749i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 76.8327i | − | 2.44561i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 10.7467i | − | 0.341725i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.06529 | − | 12.2374i | −0.224436 | − | 0.388735i | 0.731714 | − | 0.681612i | \(-0.238721\pi\) |
−0.956150 | + | 0.292877i | \(0.905387\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.12444 | + | 5.41169i | 0.0991511 | + | 0.171735i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.6935 | −0.719433 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.24947 | + | 2.45344i | 0.134582 | + | 0.0777011i | 0.565779 | − | 0.824557i | \(-0.308575\pi\) |
−0.431197 | + | 0.902258i | \(0.641909\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 33.4608i | − | 1.05865i |
(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 | 1216.2.s.i.31.1 | ✓ | 32 | |
4.3 | odd | 2 | inner | 1216.2.s.i.31.15 | yes | 32 | |
8.3 | odd | 2 | inner | 1216.2.s.i.31.2 | yes | 32 | |
8.5 | even | 2 | inner | 1216.2.s.i.31.16 | yes | 32 | |
19.8 | odd | 6 | inner | 1216.2.s.i.863.2 | yes | 32 | |
76.27 | even | 6 | inner | 1216.2.s.i.863.16 | yes | 32 | |
152.27 | even | 6 | inner | 1216.2.s.i.863.1 | yes | 32 | |
152.141 | odd | 6 | inner | 1216.2.s.i.863.15 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.s.i.31.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1216.2.s.i.31.2 | yes | 32 | 8.3 | odd | 2 | inner | |
1216.2.s.i.31.15 | yes | 32 | 4.3 | odd | 2 | inner | |
1216.2.s.i.31.16 | yes | 32 | 8.5 | even | 2 | inner | |
1216.2.s.i.863.1 | yes | 32 | 152.27 | even | 6 | inner | |
1216.2.s.i.863.2 | yes | 32 | 19.8 | odd | 6 | inner | |
1216.2.s.i.863.15 | yes | 32 | 152.141 | odd | 6 | inner | |
1216.2.s.i.863.16 | yes | 32 | 76.27 | even | 6 | inner |