Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(257,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.r (of order \(4\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.6040479020157644046336.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.6 | ||
Root | \(1.73122 + 0.0537601i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.257 |
Dual form | 600.2.r.f.593.6 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.912166 | + | 1.47240i | 0.526639 | + | 0.850089i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.78498 | − | 1.78498i | −0.674658 | − | 0.674658i | 0.284129 | − | 0.958786i | \(-0.408296\pi\) |
−0.958786 | + | 0.284129i | \(0.908296\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.33591 | + | 2.68614i | −0.445302 | + | 0.895380i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.25639i | 1.28335i | 0.766977 | + | 0.641675i | \(0.221760\pi\) | ||||
−0.766977 | + | 0.641675i | \(0.778240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.90544 | + | 2.90544i | −0.805824 | + | 0.805824i | −0.983999 | − | 0.178175i | \(-0.942981\pi\) |
0.178175 | + | 0.983999i | \(0.442981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.443864 | − | 0.443864i | 0.107653 | − | 0.107653i | −0.651229 | − | 0.758882i | \(-0.725746\pi\) |
0.758882 | + | 0.651229i | \(0.225746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.74456i | 1.77672i | 0.459143 | + | 0.888362i | \(0.348156\pi\) | ||||
−0.459143 | + | 0.888362i | \(0.651844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 4.25639i | 0.218218 | − | 0.928820i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94070 | + | 1.94070i | 0.404664 | + | 0.404664i | 0.879873 | − | 0.475209i | \(-0.157628\pi\) |
−0.475209 | + | 0.879873i | \(0.657628\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.17364 | + | 0.483219i | −0.995667 | + | 0.0929956i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.0974 | 1.87503 | 0.937516 | − | 0.347943i | \(-0.113120\pi\) | ||||
0.937516 | + | 0.347943i | \(0.113120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.372281 | 0.0668637 | 0.0334318 | − | 0.999441i | \(-0.489356\pi\) | ||||
0.0334318 | + | 0.999441i | \(0.489356\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.26709 | + | 3.88253i | −1.09096 | + | 0.675862i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.12046 | − | 1.12046i | −0.184203 | − | 0.184203i | 0.608981 | − | 0.793184i | \(-0.291578\pi\) |
−0.793184 | + | 0.608981i | \(0.791578\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.92820 | − | 1.62772i | −1.10940 | − | 0.260644i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.42554i | − | 1.15967i | −0.814733 | − | 0.579837i | \(-0.803116\pi\) | ||
0.814733 | − | 0.579837i | \(-0.196884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.68396 | + | 6.68396i | −1.01929 | + | 1.01929i | −0.0194835 | + | 0.999810i | \(0.506202\pi\) |
−0.999810 | + | 0.0194835i | \(0.993798\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65685 | − | 5.65685i | 0.825137 | − | 0.825137i | −0.161703 | − | 0.986840i | \(-0.551699\pi\) |
0.986840 | + | 0.161703i | \(0.0516985\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 0.627719i | − | 0.0896741i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.05842 | + | 0.248667i | 0.148209 | + | 0.0348203i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.59755 | − | 7.59755i | −1.04360 | − | 1.04360i | −0.999005 | − | 0.0445992i | \(-0.985799\pi\) |
−0.0445992 | − | 0.999005i | \(-0.514201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.4031 | + | 7.06432i | −1.51037 | + | 0.935693i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.34363 | 0.695681 | 0.347841 | − | 0.937554i | \(-0.386915\pi\) | ||||
0.347841 | + | 0.937554i | \(0.386915\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.37228 | −0.559813 | −0.279907 | − | 0.960027i | \(-0.590304\pi\) | ||||
−0.279907 | + | 0.960027i | \(0.590304\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.17926 | − | 2.41013i | 0.904502 | − | 0.303648i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.22474 | − | 1.22474i | −0.149626 | − | 0.149626i | 0.628325 | − | 0.777951i | \(-0.283741\pi\) |
−0.777951 | + | 0.628325i | \(0.783741\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.08724 | + | 4.62772i | −0.130888 | + | 0.557112i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0974i | 1.19834i | 0.800624 | + | 0.599168i | \(0.204502\pi\) | ||||
−0.800624 | + | 0.599168i | \(0.795498\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.90870 | − | 7.90870i | 0.925643 | − | 0.925643i | −0.0717773 | − | 0.997421i | \(-0.522867\pi\) |
0.997421 | + | 0.0717773i | \(0.0228671\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.59755 | − | 7.59755i | 0.865822 | − | 0.865822i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.74456i | − | 0.308787i | −0.988009 | − | 0.154394i | \(-0.950658\pi\) | ||
0.988009 | − | 0.154394i | \(-0.0493424\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.43070 | − | 7.17687i | −0.603411 | − | 0.797430i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.04142 | + | 8.04142i | 0.882660 | + | 0.882660i | 0.993804 | − | 0.111144i | \(-0.0354515\pi\) |
−0.111144 | + | 0.993804i | \(0.535452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.21046 | + | 14.8673i | 0.987465 | + | 1.59394i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.497333 | −0.0527172 | −0.0263586 | − | 0.999653i | \(-0.508391\pi\) | ||||
−0.0263586 | + | 0.999653i | \(0.508391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3723 | 1.08731 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.339582 | + | 0.548146i | 0.0352130 | + | 0.0568401i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.47539 | + | 6.47539i | 0.657476 | + | 0.657476i | 0.954782 | − | 0.297306i | \(-0.0960881\pi\) |
−0.297306 | + | 0.954782i | \(0.596088\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.4333 | − | 5.68614i | −1.14909 | − | 0.571479i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.4410i | 1.53643i | 0.640189 | + | 0.768217i | \(0.278856\pi\) | ||||
−0.640189 | + | 0.768217i | \(0.721144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.81088 | − | 5.81088i | 0.572563 | − | 0.572563i | −0.360281 | − | 0.932844i | \(-0.617319\pi\) |
0.932844 | + | 0.360281i | \(0.117319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.21299 | − | 5.21299i | 0.503959 | − | 0.503959i | −0.408707 | − | 0.912666i | \(-0.634020\pi\) |
0.912666 | + | 0.408707i | \(0.134020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.8614i | − | 1.71081i | −0.517958 | − | 0.855406i | \(-0.673308\pi\) | ||
0.517958 | − | 0.855406i | \(-0.326692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.627719 | − | 2.67181i | 0.0595804 | − | 0.253597i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.38456 | − | 2.38456i | −0.224321 | − | 0.224321i | 0.585994 | − | 0.810315i | \(-0.300704\pi\) |
−0.810315 | + | 0.585994i | \(0.800704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.92302 | − | 11.6858i | −0.362683 | − | 1.08035i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.58457 | −0.145258 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.11684 | −0.646986 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.9333 | − | 6.77332i | 0.985826 | − | 0.610730i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.208564 | − | 0.208564i | −0.0185070 | − | 0.0185070i | 0.697793 | − | 0.716300i | \(-0.254166\pi\) |
−0.716300 | + | 0.697793i | \(0.754166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.9383 | − | 3.74456i | −1.40329 | − | 0.329690i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.58457i | 0.138445i | 0.997601 | + | 0.0692224i | \(0.0220518\pi\) | ||||
−0.997601 | + | 0.0692224i | \(0.977948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.8239 | − | 13.8239i | 1.19868 | − | 1.19868i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.15369 | + | 7.15369i | −0.611181 | + | 0.611181i | −0.943254 | − | 0.332073i | \(-0.892252\pi\) |
0.332073 | + | 0.943254i | \(0.392252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.11684i | − | 0.179548i | −0.995962 | − | 0.0897742i | \(-0.971385\pi\) | ||
0.995962 | − | 0.0897742i | \(-0.0286145\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.4891 | + | 3.16915i | 1.13599 | + | 0.266890i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.3667 | − | 12.3667i | −1.03415 | − | 1.03415i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.924251 | − | 0.572583i | 0.0762310 | − | 0.0472259i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.0256 | 1.39479 | 0.697394 | − | 0.716688i | \(-0.254343\pi\) | ||||
0.697394 | + | 0.716688i | \(0.254343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.37228 | −0.681327 | −0.340663 | − | 0.940185i | \(-0.610652\pi\) | ||||
−0.340663 | + | 0.940185i | \(0.610652\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.599320 | + | 1.78524i | 0.0484522 | + | 0.144328i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.5829 | + | 11.5829i | 0.924419 | + | 0.924419i | 0.997338 | − | 0.0729190i | \(-0.0232315\pi\) |
−0.0729190 | + | 0.997338i | \(0.523231\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.25639 | − | 18.1168i | 0.337554 | − | 1.43676i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.92820i | − | 0.546019i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.88280 | + | 3.88280i | −0.304124 | + | 0.304124i | −0.842625 | − | 0.538501i | \(-0.818991\pi\) |
0.538501 | + | 0.842625i | \(0.318991\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.82843 | + | 2.82843i | −0.218870 | + | 0.218870i | −0.808022 | − | 0.589152i | \(-0.799462\pi\) |
0.589152 | + | 0.808022i | \(0.299462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.88316i | − | 0.298704i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.8030 | − | 10.3460i | −1.59084 | − | 0.791180i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.48528 | + | 8.48528i | 0.645124 | + | 0.645124i | 0.951811 | − | 0.306687i | \(-0.0992203\pi\) |
−0.306687 | + | 0.951811i | \(0.599220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.87428 | + | 7.86794i | 0.366373 | + | 0.591391i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.67181 | 0.199701 | 0.0998504 | − | 0.995002i | \(-0.468164\pi\) | ||||
0.0998504 | + | 0.995002i | \(0.468164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.88316 | −0.214303 | −0.107152 | − | 0.994243i | \(-0.534173\pi\) | ||||
−0.107152 | + | 0.994243i | \(0.534173\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.98825 | − | 6.43773i | −0.294820 | − | 0.475891i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.88926 | + | 1.88926i | 0.138156 | + | 0.138156i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.0974 | + | 8.37228i | 0.734474 | + | 0.608994i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 7.92287i | − | 0.573279i | −0.958039 | − | 0.286639i | \(-0.907462\pi\) | ||
0.958039 | − | 0.286639i | \(-0.0925381\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.01618 | − | 1.01618i | 0.0731463 | − | 0.0731463i | −0.669587 | − | 0.742733i | \(-0.733529\pi\) |
0.742733 | + | 0.669587i | \(0.233529\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.3074 | − | 14.3074i | 1.01936 | − | 1.01936i | 0.0195496 | − | 0.999809i | \(-0.493777\pi\) |
0.999809 | − | 0.0195496i | \(-0.00622322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3723i | 0.735272i | 0.929970 | + | 0.367636i | \(0.119833\pi\) | ||||
−0.929970 | + | 0.367636i | \(0.880167\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.686141 | − | 2.92048i | 0.0483966 | − | 0.205995i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.0235 | − | 18.0235i | −1.26500 | − | 1.26500i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.80558 | + | 2.62040i | −0.542526 | + | 0.182130i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −32.9639 | −2.28016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.74456 | −0.120101 | −0.0600503 | − | 0.998195i | \(-0.519126\pi\) | ||||
−0.0600503 | + | 0.998195i | \(0.519126\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.8673 | + | 9.21046i | −1.01869 | + | 0.631090i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.664513 | − | 0.664513i | −0.0451101 | − | 0.0451101i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.8588 | + | 4.43070i | 1.27436 | + | 0.299399i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.57924i | 0.173499i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.71632 | + | 8.71632i | −0.583688 | + | 0.583688i | −0.935915 | − | 0.352227i | \(-0.885425\pi\) |
0.352227 | + | 0.935915i | \(0.385425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.82843 | + | 2.82843i | −0.187729 | + | 0.187729i | −0.794714 | − | 0.606984i | \(-0.792379\pi\) |
0.606984 | + | 0.794714i | \(0.292379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.3723i | − | 0.685420i | −0.939441 | − | 0.342710i | \(-0.888655\pi\) | ||
0.939441 | − | 0.342710i | \(-0.111345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.1168 | + | 4.25639i | 1.19200 | + | 0.280050i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.4790 | + | 11.4790i | 0.752011 | + | 0.752011i | 0.974854 | − | 0.222843i | \(-0.0715338\pi\) |
−0.222843 | + | 0.974854i | \(0.571534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.04109 | − | 2.50350i | 0.262497 | − | 0.162620i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.2665 | 0.858138 | 0.429069 | − | 0.903272i | \(-0.358842\pi\) | ||||
0.429069 | + | 0.903272i | \(0.358842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.2337 | 1.36778 | 0.683891 | − | 0.729584i | \(-0.260286\pi\) | ||||
0.683891 | + | 0.729584i | \(0.260286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.61350 | − | 14.5426i | 0.360106 | − | 0.932911i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.5014 | − | 22.5014i | −1.43173 | − | 1.43173i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.50506 | + | 19.1753i | −0.285496 | + | 1.21518i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.0357i | − | 1.64336i | −0.569952 | − | 0.821678i | \(-0.693038\pi\) | ||
0.569952 | − | 0.821678i | \(-0.306962\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.26037 | + | 8.26037i | −0.519325 | + | 0.519325i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.3074 | + | 14.3074i | −0.892470 | + | 0.892470i | −0.994755 | − | 0.102285i | \(-0.967385\pi\) |
0.102285 | + | 0.994755i | \(0.467385\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000i | 0.248548i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.4891 | + | 27.1229i | −0.834956 | + | 1.67887i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.9113 | + | 18.9113i | 1.16612 | + | 1.16612i | 0.983112 | + | 0.183007i | \(0.0585830\pi\) |
0.183007 | + | 0.983112i | \(0.441417\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.453650 | − | 0.732272i | −0.0277630 | − | 0.0448143i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.589907 | −0.0359673 | −0.0179836 | − | 0.999838i | \(-0.505725\pi\) | ||||
−0.0179836 | + | 0.999838i | \(0.505725\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2337 | −0.986126 | −0.493063 | − | 0.869994i | \(-0.664123\pi\) | ||||
−0.493063 | + | 0.869994i | \(0.664123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.46124 | + | 15.2721i | 0.572620 | + | 0.924311i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.8562 | − | 15.8562i | −0.952708 | − | 0.952708i | 0.0462230 | − | 0.998931i | \(-0.485282\pi\) |
−0.998931 | + | 0.0462230i | \(0.985282\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.497333 | + | 1.00000i | −0.0297746 | + | 0.0598684i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.7846i | 1.23991i | 0.784639 | + | 0.619953i | \(0.212848\pi\) | ||||
−0.784639 | + | 0.619953i | \(0.787152\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3970 | + | 10.3970i | −0.618038 | + | 0.618038i | −0.945028 | − | 0.326990i | \(-0.893966\pi\) |
0.326990 | + | 0.945028i | \(0.393966\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.2544 | + | 13.2544i | −0.782383 | + | 0.782383i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6060i | 0.976822i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.62772 | + | 15.4410i | −0.212661 | + | 0.905166i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.99367 | + | 2.99367i | 0.174892 | + | 0.174892i | 0.789125 | − | 0.614233i | \(-0.210534\pi\) |
−0.614233 | + | 0.789125i | \(0.710534\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.05677 | − | 22.0210i | −0.119346 | − | 1.27779i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.2772 | −0.652175 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.8614 | 1.37535 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.7353 | + | 14.0847i | −1.30611 | + | 0.809147i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8012 | + | 14.8012i | 0.844750 | + | 0.844750i | 0.989472 | − | 0.144722i | \(-0.0462288\pi\) |
−0.144722 | + | 0.989472i | \(0.546229\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.8564 | + | 3.25544i | 0.788263 | + | 0.185195i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19.2000i | − | 1.08873i | −0.838847 | − | 0.544367i | \(-0.816770\pi\) | ||
0.838847 | − | 0.544367i | \(-0.183230\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.99354 | − | 1.99354i | 0.112682 | − | 0.112682i | −0.648518 | − | 0.761199i | \(-0.724611\pi\) |
0.761199 | + | 0.648518i | \(0.224611\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.53825 | − | 9.53825i | 0.535722 | − | 0.535722i | −0.386548 | − | 0.922269i | \(-0.626333\pi\) |
0.922269 | + | 0.386548i | \(0.126333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.9783i | 2.40632i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.4307 | + | 2.92048i | 0.693814 | + | 0.163005i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.43753 | + | 3.43753i | 0.191269 | + | 0.191269i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.2991 | − | 16.2926i | 1.45434 | − | 0.900981i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.1947 | −1.11337 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.6277 | 1.13380 | 0.566901 | − | 0.823786i | \(-0.308142\pi\) | ||||
0.566901 | + | 0.823786i | \(0.308142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.50656 | − | 1.51289i | 0.246958 | − | 0.0829057i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.67423 | + | 3.67423i | 0.200148 | + | 0.200148i | 0.800064 | − | 0.599915i | \(-0.204799\pi\) |
−0.599915 | + | 0.800064i | \(0.704799\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.33591 | − | 5.68614i | 0.0725565 | − | 0.308829i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.58457i | 0.0858095i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.6153 | + | 13.6153i | −0.735157 | + | 0.735157i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.9228 | + | 11.9228i | −0.640050 | + | 0.640050i | −0.950568 | − | 0.310517i | \(-0.899498\pi\) |
0.310517 | + | 0.950568i | \(0.399498\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.4891i | 1.47146i | 0.677275 | + | 0.735730i | \(0.263161\pi\) | ||||
−0.677275 | + | 0.735730i | \(0.736839\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.6277 | − | 16.4356i | 0.727394 | − | 0.877270i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.2544 | + | 13.2544i | 0.705461 | + | 0.705461i | 0.965577 | − | 0.260116i | \(-0.0837609\pi\) |
−0.260116 | + | 0.965577i | \(0.583761\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.44539 | − | 2.33312i | −0.0764984 | − | 0.123482i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.58457 | −0.0836306 | −0.0418153 | − | 0.999125i | \(-0.513314\pi\) | ||||
−0.0418153 | + | 0.999125i | \(0.513314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −40.9783 | −2.15675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.49174 | − | 10.4788i | −0.340728 | − | 0.549995i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.99354 | − | 1.99354i | −0.104062 | − | 0.104062i | 0.653159 | − | 0.757221i | \(-0.273443\pi\) |
−0.757221 | + | 0.653159i | \(0.773443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.9460 | + | 9.91983i | 1.03835 | + | 0.516406i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.1229i | 1.40815i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.78498 | + | 1.78498i | −0.0924226 | + | 0.0924226i | −0.751806 | − | 0.659384i | \(-0.770817\pi\) |
0.659384 | + | 0.751806i | \(0.270817\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.3372 | + | 29.3372i | −1.51094 | + | 1.51094i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.4891i | − | 1.36065i | −0.732908 | − | 0.680327i | \(-0.761838\pi\) | ||
0.732908 | − | 0.680327i | \(-0.238162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.116844 | − | 0.497333i | 0.00598610 | − | 0.0254792i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.3074 | − | 14.3074i | −0.731073 | − | 0.731073i | 0.239759 | − | 0.970832i | \(-0.422931\pi\) |
−0.970832 | + | 0.239759i | \(0.922931\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.02490 | − | 26.8832i | −0.458761 | − | 1.36655i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.10268 | −0.461524 | −0.230762 | − | 0.973010i | \(-0.574122\pi\) | ||||
−0.230762 | + | 0.973010i | \(0.574122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.72281 | 0.0871264 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.33312 | + | 1.44539i | −0.117690 | + | 0.0729105i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.7034 | − | 12.7034i | −0.637565 | − | 0.637565i | 0.312389 | − | 0.949954i | \(-0.398871\pi\) |
−0.949954 | + | 0.312389i | \(0.898871\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 32.9639 | + | 7.74456i | 1.65026 | + | 0.387713i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 26.6256i | − | 1.32962i | −0.747014 | − | 0.664809i | \(-0.768513\pi\) | ||
0.747014 | − | 0.664809i | \(-0.231487\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.08164 | + | 1.08164i | −0.0538804 | + | 0.0538804i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.76913 | − | 4.76913i | 0.236397 | − | 0.236397i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.4891i | − | 1.01312i | −0.862204 | − | 0.506561i | \(-0.830916\pi\) | ||
0.862204 | − | 0.506561i | \(-0.169084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.0584 | − | 4.00772i | −0.841430 | − | 0.197686i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.53825 | − | 9.53825i | −0.469347 | − | 0.469347i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.11684 | − | 1.93091i | 0.152632 | − | 0.0945572i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.7692 | −0.623815 | −0.311907 | − | 0.950113i | \(-0.600968\pi\) | ||||
−0.311907 | + | 0.950113i | \(0.600968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.7446 | −0.816080 | −0.408040 | − | 0.912964i | \(-0.633788\pi\) | ||||
−0.408040 | + | 0.912964i | \(0.633788\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.63807 | + | 22.7521i | 0.371376 | + | 1.10625i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.80442 | + | 7.80442i | 0.377682 | + | 0.377682i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.92820 | − | 29.4891i | 0.334497 | − | 1.42375i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 29.2974i | − | 1.41121i | −0.708608 | − | 0.705603i | \(-0.750676\pi\) | ||
0.708608 | − | 0.705603i | \(-0.249324\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.12372 | + | 6.12372i | −0.294287 | + | 0.294287i | −0.838771 | − | 0.544484i | \(-0.816726\pi\) |
0.544484 | + | 0.838771i | \(0.316726\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.0299 | + | 15.0299i | −0.718976 | + | 0.718976i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.3723i | − | 0.685952i | −0.939344 | − | 0.342976i | \(-0.888565\pi\) | ||
0.939344 | − | 0.342976i | \(-0.111435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.68614 | + | 0.838574i | 0.0802924 | + | 0.0399321i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.37823 | − | 5.37823i | −0.255528 | − | 0.255528i | 0.567705 | − | 0.823232i | \(-0.307832\pi\) |
−0.823232 | + | 0.567705i | \(0.807832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 15.5301 | + | 25.0684i | 0.734550 | + | 1.18569i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3537 | 0.677395 | 0.338697 | − | 0.940895i | \(-0.390014\pi\) | ||||
0.338697 | + | 0.940895i | \(0.390014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.6060 | 1.48827 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.63691 | − | 12.3273i | −0.358813 | − | 0.579188i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.351668 | + | 0.351668i | 0.0164503 | + | 0.0164503i | 0.715284 | − | 0.698834i | \(-0.246297\pi\) |
−0.698834 | + | 0.715284i | \(0.746297\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.08191 | + | 2.51087i | −0.0971751 | + | 0.117198i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.75906i | 0.175077i | 0.996161 | + | 0.0875383i | \(0.0279000\pi\) | ||||
−0.996161 | + | 0.0875383i | \(0.972100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5078 | − | 20.5078i | 0.953079 | − | 0.953079i | −0.0458684 | − | 0.998947i | \(-0.514605\pi\) |
0.998947 | + | 0.0458684i | \(0.0146055\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.82843 | + | 2.82843i | −0.130884 | + | 0.130884i | −0.769514 | − | 0.638630i | \(-0.779501\pi\) |
0.638630 | + | 0.769514i | \(0.279501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.37228i | 0.201893i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.48913 | + | 27.6202i | −0.299003 | + | 1.27267i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.4495 | − | 28.4495i | −1.30811 | − | 1.30811i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.5577 | − | 10.2585i | 1.39914 | − | 0.469703i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.7075 | −1.31168 | −0.655839 | − | 0.754901i | \(-0.727685\pi\) | ||||
−0.655839 | + | 0.754901i | \(0.727685\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.51087 | 0.296870 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.2011 | − | 6.31967i | 0.464165 | − | 0.287555i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.1658 | − | 11.1658i | −0.505971 | − | 0.505971i | 0.407316 | − | 0.913287i | \(-0.366465\pi\) |
−0.913287 | + | 0.407316i | \(0.866465\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.25878 | − | 2.17527i | −0.418696 | − | 0.0983689i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 28.7075i | − | 1.29555i | −0.761832 | − | 0.647775i | \(-0.775700\pi\) | ||
0.761832 | − | 0.647775i | \(-0.224300\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.48185 | − | 4.48185i | 0.201852 | − | 0.201852i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.0235 | − | 18.0235i | 0.808466 | − | 0.808466i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 17.6277i | − | 0.789125i | −0.918869 | − | 0.394563i | \(-0.870896\pi\) | ||
0.918869 | − | 0.394563i | \(-0.129104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.74456 | − | 1.58457i | −0.301325 | − | 0.0707935i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.2481 | + | 16.2481i | 0.724466 | + | 0.724466i | 0.969512 | − | 0.245046i | \(-0.0788029\pi\) |
−0.245046 | + | 0.969512i | \(0.578803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.71755 | − | 3.54208i | 0.253925 | − | 0.157309i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.17448 | 0.0963822 | 0.0481911 | − | 0.998838i | \(-0.484654\pi\) | ||||
0.0481911 | + | 0.998838i | \(0.484654\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.2337 | −1.24898 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.74232 | − | 40.0675i | −0.165228 | − | 1.76903i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0778 | + | 24.0778i | 1.05894 | + | 1.05894i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.75372 | + | 20.2337i | −0.208665 | + | 0.888160i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 26.6256i | − | 1.16649i | −0.812297 | − | 0.583244i | \(-0.801783\pi\) | ||
0.812297 | − | 0.583244i | \(-0.198217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.2960 | − | 15.2960i | 0.668847 | − | 0.668847i | −0.288602 | − | 0.957449i | \(-0.593190\pi\) |
0.957449 | + | 0.288602i | \(0.0931905\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.165242 | − | 0.165242i | 0.00719807 | − | 0.00719807i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 15.4674i | − | 0.672495i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.13859 | + | 14.3537i | −0.309789 | + | 0.622899i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.5744 | + | 21.5744i | 0.934493 | + | 0.934493i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.43714 | + | 3.93397i | 0.105170 | + | 0.169763i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.67181 | 0.115083 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.1168 | 0.993871 | 0.496935 | − | 0.867788i | \(-0.334459\pi\) | ||||
0.496935 | + | 0.867788i | \(0.334459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.62992 | − | 4.24515i | −0.112861 | − | 0.182177i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.6380 | + | 24.6380i | 1.05344 | + | 1.05344i | 0.998489 | + | 0.0549561i | \(0.0175019\pi\) |
0.0549561 | + | 0.998489i | \(0.482498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.84096 | − | 11.7446i | 0.249286 | − | 0.501246i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 78.1996i | 3.33141i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.89898 | + | 4.89898i | −0.208326 | + | 0.208326i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.76280 | + | 7.76280i | −0.328920 | + | 0.328920i | −0.852176 | − | 0.523256i | \(-0.824717\pi\) |
0.523256 | + | 0.852176i | \(0.324717\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 38.8397i | − | 1.64274i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.05842 | + | 4.50506i | −0.0446866 | + | 0.190204i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.7863 | + | 25.7863i | 1.08676 | + | 1.08676i | 0.995860 | + | 0.0909046i | \(0.0289758\pi\) |
0.0909046 | + | 0.995860i | \(0.471024\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.11687 | + | 22.5042i | −0.130896 | + | 0.945088i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.7745 | −0.493613 | −0.246806 | − | 0.969065i | \(-0.579381\pi\) | ||||
−0.246806 | + | 0.969065i | \(0.579381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.8397 | −1.79278 | −0.896392 | − | 0.443262i | \(-0.853821\pi\) | ||||
−0.896392 | + | 0.443262i | \(0.853821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.6656 | − | 7.22697i | 0.487338 | − | 0.301911i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.61850 | + | 6.61850i | 0.275532 | + | 0.275532i | 0.831322 | − | 0.555791i | \(-0.187584\pi\) |
−0.555791 | + | 0.831322i | \(0.687584\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.42315 | + | 0.569297i | 0.100703 | + | 0.0236592i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 28.7075i | − | 1.19099i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 32.3381 | − | 32.3381i | 1.33931 | − | 1.33931i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.43753 | − | 3.43753i | 0.141882 | − | 0.141882i | −0.632598 | − | 0.774480i | \(-0.718011\pi\) |
0.774480 | + | 0.632598i | \(0.218011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.88316i | 0.118798i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.1168 | + | 8.01544i | 1.40338 | + | 0.329711i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.33159 | + | 1.33159i | 0.0546819 | + | 0.0546819i | 0.733919 | − | 0.679237i | \(-0.237689\pi\) |
−0.679237 | + | 0.733919i | \(0.737689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.2721 | + | 9.46124i | −0.625046 | + | 0.387223i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.0202 | −0.736286 | −0.368143 | − | 0.929769i | \(-0.620006\pi\) | ||||
−0.368143 | + | 0.929769i | \(0.620006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.74456 | 0.315907 | 0.157954 | − | 0.987447i | \(-0.449510\pi\) | ||||
0.157954 | + | 0.987447i | \(0.449510\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.92598 | − | 1.65369i | 0.200602 | − | 0.0673435i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1659 | − | 23.1659i | −0.940274 | − | 0.940274i | 0.0580405 | − | 0.998314i | \(-0.481515\pi\) |
−0.998314 | + | 0.0580405i | \(0.981515\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.0974 | − | 42.9783i | 0.409165 | − | 1.74157i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.8713i | 1.32983i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9573 | − | 22.9573i | 0.927237 | − | 0.927237i | −0.0702897 | − | 0.997527i | \(-0.522392\pi\) |
0.997527 | + | 0.0702897i | \(0.0223924\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.6741 | − | 26.6741i | 1.07386 | − | 1.07386i | 0.0768115 | − | 0.997046i | \(-0.475526\pi\) |
0.997046 | − | 0.0768115i | \(-0.0244740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.8614i | 0.637524i | 0.947835 | + | 0.318762i | \(0.103267\pi\) | ||||
−0.947835 | + | 0.318762i | \(0.896733\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.9783 | − | 9.10268i | −0.440542 | − | 0.365278i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.887728 | + | 0.887728i | 0.0355661 | + | 0.0355661i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −30.0685 | − | 48.5359i | −1.20082 | − | 1.93834i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.994667 | −0.0396600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.6060 | 0.581454 | 0.290727 | − | 0.956806i | \(-0.406103\pi\) | ||||
0.290727 | + | 0.956806i | \(0.406103\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.59133 | − | 2.56869i | −0.0632497 | − | 0.102096i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.82380 | + | 1.82380i | 0.0722615 | + | 0.0722615i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.1229 | − | 13.4891i | −1.07297 | − | 0.533622i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.6873i | 0.422121i | 0.977473 | + | 0.211061i | \(0.0676918\pi\) | ||||
−0.977473 | + | 0.211061i | \(0.932308\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.4884 | − | 14.4884i | 0.571366 | − | 0.571366i | −0.361144 | − | 0.932510i | \(-0.617614\pi\) |
0.932510 | + | 0.361144i | \(0.117614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.7446i | 0.892802i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.372281 | − | 1.58457i | 0.0145909 | − | 0.0621044i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.2779 | − | 31.2779i | −1.22400 | − | 1.22400i | −0.966198 | − | 0.257803i | \(-0.917001\pi\) |
−0.257803 | − | 0.966198i | \(-0.582999\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.6786 | + | 31.8092i | 0.416612 | + | 1.24099i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.9585 | −1.32284 | −0.661418 | − | 0.750017i | \(-0.730045\pi\) | ||||
−0.661418 | + | 0.750017i | \(0.730045\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.76631 | 0.224284 | 0.112142 | − | 0.993692i | \(-0.464229\pi\) | ||||
0.112142 | + | 0.993692i | \(0.464229\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.79767 | + | 2.35269i | −0.147489 | + | 0.0913711i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.5959 | + | 19.5959i | 0.758757 | + | 0.758757i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.7846 | − | 4.88316i | −0.803579 | − | 0.188794i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18.6101i | − | 0.718436i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.3187 | + | 26.3187i | −1.01451 | + | 1.01451i | −0.0146180 | + | 0.999893i | \(0.504653\pi\) |
−0.999893 | + | 0.0146180i | \(0.995347\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.2481 | + | 16.2481i | −0.624464 | + | 0.624464i | −0.946670 | − | 0.322205i | \(-0.895576\pi\) |
0.322205 | + | 0.946670i | \(0.395576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 23.1168i | − | 0.887143i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.74456 | − | 1.58457i | −0.258452 | − | 0.0607210i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.0351 | − | 11.0351i | −0.422246 | − | 0.422246i | 0.463730 | − | 0.885976i | \(-0.346511\pi\) |
−0.885976 | + | 0.463730i | \(0.846511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.2721 | − | 9.46124i | 0.582668 | − | 0.360969i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.1485 | 1.68192 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3505 | 1.15459 | 0.577294 | − | 0.816536i | \(-0.304109\pi\) | ||||
0.577294 | + | 0.816536i | \(0.304109\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.2585 | + | 30.5577i | 0.389687 | + | 1.16079i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.29593 | − | 3.29593i | −0.124842 | − | 0.124842i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.43087 | + | 27.3723i | −0.243238 | + | 1.03531i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.2665i | − | 0.501069i | −0.968108 | − | 0.250534i | \(-0.919394\pi\) | ||
0.968108 | − | 0.250534i | \(-0.0806063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.67750 | − | 8.67750i | 0.327278 | − | 0.327278i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.5618 | − | 27.5618i | 1.03657 | − | 1.03657i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 27.8614i | − | 1.04636i | −0.852223 | − | 0.523179i | \(-0.824746\pi\) | ||
0.852223 | − | 0.523179i | \(-0.175254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.37228 | + | 3.66648i | 0.276482 | + | 0.137504i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.722486 | + | 0.722486i | 0.0270573 | + | 0.0270573i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.1012 | + | 19.5336i | 0.451929 | + | 0.729494i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.1431 | 1.68355 | 0.841777 | − | 0.539825i | \(-0.181510\pi\) | ||||
0.841777 | + | 0.539825i | \(0.181510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.7446 | −0.772568 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.3686 | + | 31.2644i | 0.720328 | + | 1.16274i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.6024 | + | 17.6024i | 0.652836 | + | 0.652836i | 0.953675 | − | 0.300839i | \(-0.0972667\pi\) |
−0.300839 | + | 0.953675i | \(0.597267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.5330 | − | 5.00000i | 0.982704 | − | 0.185185i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.93354i | 0.219460i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.2929 | + | 34.2929i | −1.26664 | + | 1.26664i | −0.318820 | + | 0.947815i | \(0.603287\pi\) |
−0.947815 | + | 0.318820i | \(0.896713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.21299 | − | 5.21299i | 0.192023 | − | 0.192023i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.4674i | 0.900047i | 0.893017 | + | 0.450023i | \(0.148584\pi\) | ||||
−0.893017 | + | 0.450023i | \(0.851416\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.6060 | − | 53.6559i | 0.463092 | − | 1.97110i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.32004 | − | 8.32004i | −0.305233 | − | 0.305233i | 0.537824 | − | 0.843057i | \(-0.319246\pi\) |
−0.843057 | + | 0.537824i | \(0.819246\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −32.3430 | + | 10.8578i | −1.18337 | + | 0.397266i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.6101 | −0.679999 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.0000 | −1.60558 | −0.802791 | − | 0.596260i | \(-0.796653\pi\) | ||||
−0.802791 | + | 0.596260i | \(0.796653\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.3348 | − | 23.7488i | 1.39700 | − | 0.865456i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.5895 | − | 21.5895i | −0.784682 | − | 0.784682i | 0.195935 | − | 0.980617i | \(-0.437226\pi\) |
−0.980617 | + | 0.195935i | \(0.937226\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −19.6974 | − | 4.62772i | −0.714969 | − | 0.167976i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.01011i | 0.326616i | 0.986575 | + | 0.163308i | \(0.0522165\pi\) | ||||
−0.986575 | + | 0.163308i | \(0.947784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31.8822 | + | 31.8822i | −1.15421 | + | 1.15421i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.5256 | + | 15.5256i | −0.560597 | + | 0.560597i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.4891i | 1.09947i | 0.835340 | + | 0.549733i | \(0.185271\pi\) | ||||
−0.835340 | + | 0.549733i | \(0.814729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.1168 | − | 8.01544i | −1.22869 | − | 0.288669i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36.7696 | − | 36.7696i | −1.32251 | − | 1.32251i | −0.911739 | − | 0.410770i | \(-0.865260\pi\) |
−0.410770 | − | 0.911739i | \(-0.634740\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.88959 | + | 3.64866i | −0.211288 | + | 0.130895i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 57.5075 | 2.06042 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.9783 | −1.53788 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −52.2400 | + | 4.87923i | −1.86691 | + | 0.174370i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.78498 | + | 1.78498i | 0.0636275 | + | 0.0636275i | 0.738205 | − | 0.674577i | \(-0.235674\pi\) |
−0.674577 | + | 0.738205i | \(0.735674\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.5947 | + | 45.0951i | −0.377181 | + | 1.60543i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.51278i | 0.302680i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7034 | − | 12.7034i | 0.451111 | − | 0.451111i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.3074 | + | 14.3074i | −0.506793 | + | 0.506793i | −0.913541 | − | 0.406747i | \(-0.866663\pi\) |
0.406747 | + | 0.913541i | \(0.366663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.02175i | − | 0.177657i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.664391 | − | 1.33591i | 0.0234751 | − | 0.0472020i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.6625 | + | 33.6625i | 1.18792 | + | 1.18792i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.538093 | − | 0.868578i | −0.0189418 | − | 0.0305754i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 47.3176 | 1.66360 | 0.831799 | − | 0.555077i | \(-0.187311\pi\) | ||||
0.831799 | + | 0.555077i | \(0.187311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.3723 | 1.34743 | 0.673717 | − | 0.738990i | \(-0.264697\pi\) | ||||
0.673717 | + | 0.738990i | \(0.264697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.8078 | − | 23.9024i | −0.519333 | − | 0.838295i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −51.7643 | − | 51.7643i | −1.81100 | − | 1.81100i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.8564 | + | 27.8614i | −0.484182 | + | 0.973556i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2000i | 0.670086i | 0.942203 | + | 0.335043i | \(0.108751\pi\) | ||||
−0.942203 | + | 0.335043i | \(0.891249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.5143 | − | 18.5143i | 0.645367 | − | 0.645367i | −0.306503 | − | 0.951870i | \(-0.599159\pi\) |
0.951870 | + | 0.306503i | \(0.0991588\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.09439 | + | 9.09439i | −0.316243 | + | 0.316243i | −0.847322 | − | 0.531079i | \(-0.821787\pi\) |
0.531079 | + | 0.847322i | \(0.321787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.7446i | 0.859414i | 0.902968 | + | 0.429707i | \(0.141383\pi\) | ||||
−0.902968 | + | 0.429707i | \(0.858617\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.88316 | − | 37.8102i | 0.308153 | − | 1.31162i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.278622 | − | 0.278622i | −0.00965367 | − | 0.00965367i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.92605 | + | 0.179893i | −0.0665739 | + | 0.00621803i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.4463 | −0.498742 | −0.249371 | − | 0.968408i | \(-0.580224\pi\) | ||||
−0.249371 | + | 0.968408i | \(0.580224\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 72.9565 | 2.51574 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30.6032 | + | 18.9590i | −1.05403 | + | 0.652983i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.7034 | + | 12.7034i | 0.436494 | + | 0.436494i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.7923 | − | 5.82473i | −0.850871 | − | 0.199904i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.34896i | − | 0.149081i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.3575 | + | 26.3575i | −0.902464 | + | 0.902464i | −0.995649 | − | 0.0931846i | \(-0.970295\pi\) |
0.0931846 | + | 0.995649i | \(0.470295\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.5502 | − | 34.5502i | 1.18021 | − | 1.18021i | 0.200525 | − | 0.979689i | \(-0.435735\pi\) |
0.979689 | − | 0.200525i | \(-0.0642647\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 16.8614i | − | 0.575304i | −0.957735 | − | 0.287652i | \(-0.907125\pi\) | ||
0.957735 | − | 0.287652i | \(-0.0928746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.6060 | − | 7.42554i | −1.07713 | − | 0.253062i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.65685 | − | 5.65685i | −0.192562 | − | 0.192562i | 0.604240 | − | 0.796802i | \(-0.293477\pi\) |
−0.796802 | + | 0.604240i | \(0.793477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.4506 | + | 15.1474i | −0.830385 | + | 0.514433i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6819 | 0.396282 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.11684 | 0.241145 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.0443 | + | 8.74329i | −0.881467 | + | 0.295916i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.80442 | − | 7.80442i | −0.263536 | − | 0.263536i | 0.562953 | − | 0.826489i | \(-0.309665\pi\) |
−0.826489 | + | 0.562953i | \(0.809665\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.67715 | + | 7.13859i | −0.0565688 | + | 0.240779i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.8820i | 1.04044i | 0.854032 | + | 0.520220i | \(0.174150\pi\) | ||||
−0.854032 | + | 0.520220i | \(0.825850\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.2339 | + | 32.2339i | −1.08476 | + | 1.08476i | −0.0886970 | + | 0.996059i | \(0.528270\pi\) |
−0.996059 | + | 0.0886970i | \(0.971730\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.6274 | − | 22.6274i | 0.759754 | − | 0.759754i | −0.216523 | − | 0.976277i | \(-0.569472\pi\) |
0.976277 | + | 0.216523i | \(0.0694717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.744563i | 0.0249718i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 30.5475 | − | 23.1152i | 1.02338 | − | 0.774388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43.8099 | + | 43.8099i | 1.46604 | + | 1.46604i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.2866 | − | 16.6045i | −0.343461 | − | 0.554407i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.75906 | 0.125372 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.74456 | −0.224694 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.7656 | + | 35.1335i | 0.724312 | + | 1.16917i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.7940 | − | 20.7940i | −0.690454 | − | 0.690454i | 0.271878 | − | 0.962332i | \(-0.412355\pi\) |
−0.962332 | + | 0.271878i | \(0.912355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.4766 | − | 20.6277i | −1.37569 | − | 0.684178i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.17981i | 0.0390890i | 0.999809 | + | 0.0195445i | \(0.00622160\pi\) | ||||
−0.999809 | + | 0.0195445i | \(0.993778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.2274 | + | 34.2274i | −1.13276 | + | 1.13276i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.82843 | − | 2.82843i | 0.0934029 | − | 0.0934029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.8397i | 1.34718i | 0.739107 | + | 0.673588i | \(0.235248\pi\) | ||||
−0.739107 | + | 0.673588i | \(0.764752\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.29211 | + | 35.2944i | −0.273234 | + | 1.16299i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.3372 | − | 29.3372i | −0.965647 | − | 0.965647i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.84604 | + | 23.3716i | 0.257698 | + | 0.767625i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.0974 | 0.331283 | 0.165642 | − | 0.986186i | \(-0.447030\pi\) | ||||
0.165642 | + | 0.986186i | \(0.447030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.86141 | 0.159326 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 28.2701 | − | 17.5136i | 0.925521 | − | 0.573370i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.67423 | − | 3.67423i | −0.120032 | − | 0.120032i | 0.644539 | − | 0.764571i | \(-0.277049\pi\) |
−0.764571 | + | 0.644539i | \(0.777049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.75372 | + | 1.11684i | 0.155132 | + | 0.0364468i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 9.50744i | − | 0.309934i | −0.987920 | − | 0.154967i | \(-0.950473\pi\) | ||
0.987920 | − | 0.154967i | \(-0.0495271\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.4107 | − | 14.4107i | 0.469278 | − | 0.469278i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.60388 | − | 4.60388i | 0.149606 | − | 0.149606i | −0.628336 | − | 0.777942i | \(-0.716264\pi\) |
0.777942 | + | 0.628336i | \(0.216264\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.9565i | 1.49181i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.7446 | + | 5.34363i | 0.737543 | + | 0.173279i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.0351 | + | 11.0351i | 0.357462 | + | 0.357462i | 0.862876 | − | 0.505415i | \(-0.168661\pi\) |
−0.505415 | + | 0.862876i | \(0.668661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −63.2811 | + | 39.2033i | −2.04559 | + | 1.26726i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.5383 | 0.824676 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8614 | −0.995529 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.03875 | + | 20.9669i | 0.226821 | + | 0.675649i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.30319 | − | 9.30319i | −0.299170 | − | 0.299170i | 0.541519 | − | 0.840689i | \(-0.317850\pi\) |
−0.840689 | + | 0.541519i | \(0.817850\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.92581 | + | 8.19702i | −0.0618661 | + | 0.263326i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 20.6920i | − | 0.664039i | −0.943273 | − | 0.332020i | \(-0.892270\pi\) | ||
0.943273 | − | 0.332020i | \(-0.107730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.77852 | + | 3.77852i | −0.121134 | + | 0.121134i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.27229 | + | 3.27229i | −0.104690 | + | 0.104690i | −0.757512 | − | 0.652822i | \(-0.773585\pi\) |
0.652822 | + | 0.757512i | \(0.273585\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.11684i | − | 0.0676546i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.9783 | + | 23.8612i | 1.53183 | + | 0.761829i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0828 | + | 16.0828i | 0.512963 | + | 0.512963i | 0.915433 | − | 0.402470i | \(-0.131848\pi\) |
−0.402470 | + | 0.915433i | \(0.631848\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −18.4209 | − | 29.7346i | −0.586344 | − | 0.946464i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.9431 | −0.824942 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.8397 | −0.534929 | −0.267465 | − | 0.963568i | \(-0.586186\pi\) | ||||
−0.267465 | + | 0.963568i | \(0.586186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.8159 | + | 30.3722i | 0.597104 | + | 0.963833i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33.4586 | + | 33.4586i | 1.05964 | + | 1.05964i | 0.998105 | + | 0.0615399i | \(0.0196011\pi\) |
0.0615399 | + | 0.998105i | \(0.480399\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.33830 | + | 5.25544i | 0.200535 | + | 0.166275i |
(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 | 600.2.r.f.257.6 | yes | 16 | |
3.2 | odd | 2 | inner | 600.2.r.f.257.2 | ✓ | 16 | |
4.3 | odd | 2 | 1200.2.v.m.257.3 | 16 | |||
5.2 | odd | 4 | inner | 600.2.r.f.593.7 | yes | 16 | |
5.3 | odd | 4 | inner | 600.2.r.f.593.2 | yes | 16 | |
5.4 | even | 2 | inner | 600.2.r.f.257.3 | yes | 16 | |
12.11 | even | 2 | 1200.2.v.m.257.7 | 16 | |||
15.2 | even | 4 | inner | 600.2.r.f.593.3 | yes | 16 | |
15.8 | even | 4 | inner | 600.2.r.f.593.6 | yes | 16 | |
15.14 | odd | 2 | inner | 600.2.r.f.257.7 | yes | 16 | |
20.3 | even | 4 | 1200.2.v.m.593.7 | 16 | |||
20.7 | even | 4 | 1200.2.v.m.593.2 | 16 | |||
20.19 | odd | 2 | 1200.2.v.m.257.6 | 16 | |||
60.23 | odd | 4 | 1200.2.v.m.593.3 | 16 | |||
60.47 | odd | 4 | 1200.2.v.m.593.6 | 16 | |||
60.59 | even | 2 | 1200.2.v.m.257.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.r.f.257.2 | ✓ | 16 | 3.2 | odd | 2 | inner | |
600.2.r.f.257.3 | yes | 16 | 5.4 | even | 2 | inner | |
600.2.r.f.257.6 | yes | 16 | 1.1 | even | 1 | trivial | |
600.2.r.f.257.7 | yes | 16 | 15.14 | odd | 2 | inner | |
600.2.r.f.593.2 | yes | 16 | 5.3 | odd | 4 | inner | |
600.2.r.f.593.3 | yes | 16 | 15.2 | even | 4 | inner | |
600.2.r.f.593.6 | yes | 16 | 15.8 | even | 4 | inner | |
600.2.r.f.593.7 | yes | 16 | 5.2 | odd | 4 | inner | |
1200.2.v.m.257.2 | 16 | 60.59 | even | 2 | |||
1200.2.v.m.257.3 | 16 | 4.3 | odd | 2 | |||
1200.2.v.m.257.6 | 16 | 20.19 | odd | 2 | |||
1200.2.v.m.257.7 | 16 | 12.11 | even | 2 | |||
1200.2.v.m.593.2 | 16 | 20.7 | even | 4 | |||
1200.2.v.m.593.3 | 16 | 60.23 | odd | 4 | |||
1200.2.v.m.593.6 | 16 | 60.47 | odd | 4 | |||
1200.2.v.m.593.7 | 16 | 20.3 | even | 4 |