Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.48774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(-0.671462 - 1.24464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.31 |
Dual form | 128.3.f.b.95.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −0.146365 | − | 0.146365i | −0.0487885 | − | 0.0487885i | 0.682292 | − | 0.731080i | \(-0.260983\pi\) |
−0.731080 | + | 0.682292i | \(0.760983\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.68585 | − | 3.68585i | −0.737169 | − | 0.737169i | 0.234860 | − | 0.972029i | \(-0.424537\pi\) |
−0.972029 | + | 0.234860i | \(0.924537\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.66442 | −1.38063 | −0.690316 | − | 0.723508i | \(-0.742528\pi\) | ||||
−0.690316 | + | 0.723508i | \(0.742528\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 8.95715i | − | 0.995239i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.51806 | + | 5.51806i | −0.501642 | + | 0.501642i | −0.911948 | − | 0.410306i | \(-0.865422\pi\) |
0.410306 | + | 0.911948i | \(0.365422\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.27131 | − | 6.27131i | 0.482408 | − | 0.482408i | −0.423492 | − | 0.905900i | \(-0.639196\pi\) |
0.905900 | + | 0.423492i | \(0.139196\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.07896i | 0.0719308i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.78623 | −0.399190 | −0.199595 | − | 0.979878i | \(-0.563963\pi\) | ||||
−0.199595 | + | 0.979878i | \(0.563963\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.5181 | − | 13.5181i | −0.711477 | − | 0.711477i | 0.255367 | − | 0.966844i | \(-0.417804\pi\) |
−0.966844 | + | 0.255367i | \(0.917804\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41454 | + | 1.41454i | 0.0673590 | + | 0.0673590i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.0790 | 0.742564 | 0.371282 | − | 0.928520i | \(-0.378918\pi\) | ||||
0.371282 | + | 0.928520i | \(0.378918\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.17092i | 0.0868370i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.62831 | + | 2.62831i | −0.0973447 | + | 0.0973447i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.85677 | + | 4.85677i | −0.167475 | + | 0.167475i | −0.785868 | − | 0.618394i | \(-0.787784\pi\) |
0.618394 | + | 0.785868i | \(0.287784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.25662i | 0.169568i | 0.996399 | + | 0.0847841i | \(0.0270201\pi\) | ||||
−0.996399 | + | 0.0847841i | \(0.972980\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.61531 | 0.0489487 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.6216 | + | 35.6216i | 1.01776 | + | 1.01776i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.1856 | + | 18.1856i | 0.491503 | + | 0.491503i | 0.908780 | − | 0.417276i | \(-0.137015\pi\) |
−0.417276 | + | 0.908780i | \(0.637015\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.83581 | −0.0470720 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.2302i | 1.17635i | 0.808735 | + | 0.588173i | \(0.200152\pi\) | ||||
−0.808735 | + | 0.588173i | \(0.799848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 54.5113 | − | 54.5113i | 1.26771 | − | 1.26771i | 0.320435 | − | 0.947271i | \(-0.396171\pi\) |
0.947271 | − | 0.320435i | \(-0.103829\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −33.0147 | + | 33.0147i | −0.733660 | + | 0.733660i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 40.4015i | − | 0.859607i | −0.902922 | − | 0.429804i | \(-0.858583\pi\) | ||
0.902922 | − | 0.429804i | \(-0.141417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.4011 | 0.906144 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.993270 | + | 0.993270i | 0.0194759 | + | 0.0194759i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8996 | − | 10.8996i | −0.205653 | − | 0.205653i | 0.596764 | − | 0.802417i | \(-0.296453\pi\) |
−0.802417 | + | 0.596764i | \(0.796453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40.6774 | 0.739590 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.95715i | 0.0694238i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −50.8898 | + | 50.8898i | −0.862538 | + | 0.862538i | −0.991632 | − | 0.129094i | \(-0.958793\pi\) |
0.129094 | + | 0.991632i | \(0.458793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17.0147 | − | 17.0147i | 0.278929 | − | 0.278929i | −0.553752 | − | 0.832682i | \(-0.686804\pi\) |
0.832682 | + | 0.553752i | \(0.186804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 86.5657i | 1.37406i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −46.2302 | −0.711233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −22.9191 | − | 22.9191i | −0.342077 | − | 0.342077i | 0.515071 | − | 0.857148i | \(-0.327766\pi\) |
−0.857148 | + | 0.515071i | \(0.827766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.49977 | − | 2.49977i | −0.0362286 | − | 0.0362286i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −51.6047 | −0.726827 | −0.363414 | − | 0.931628i | \(-0.618389\pi\) | ||||
−0.363414 | + | 0.931628i | \(0.618389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 78.5032i | − | 1.07539i | −0.843141 | − | 0.537693i | \(-0.819296\pi\) | ||
0.843141 | − | 0.537693i | \(-0.180704\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.317748 | − | 0.317748i | 0.00423664 | − | 0.00423664i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 53.3288 | − | 53.3288i | 0.692582 | − | 0.692582i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 108.512i | − | 1.37357i | −0.726859 | − | 0.686787i | \(-0.759021\pi\) | ||
0.726859 | − | 0.686787i | \(-0.240979\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.8450 | −0.985741 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −57.3173 | − | 57.3173i | −0.690570 | − | 0.690570i | 0.271788 | − | 0.962357i | \(-0.412385\pi\) |
−0.962357 | + | 0.271788i | \(0.912385\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 25.0130 | + | 25.0130i | 0.294271 | + | 0.294271i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.42173 | 0.0163417 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 44.1276i | − | 0.495816i | −0.968784 | − | 0.247908i | \(-0.920257\pi\) | ||
0.968784 | − | 0.247908i | \(-0.0797431\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −60.6086 | + | 60.6086i | −0.666028 | + | 0.666028i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.769387 | − | 0.769387i | 0.00827298 | − | 0.00827298i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 99.6510i | 1.04896i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 112.700 | 1.16185 | 0.580926 | − | 0.813956i | \(-0.302691\pi\) | ||||
0.580926 | + | 0.813956i | \(0.302691\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 49.4261 | + | 49.4261i | 0.499253 | + | 0.499253i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −97.3859 | − | 97.3859i | −0.964217 | − | 0.964217i | 0.0351644 | − | 0.999382i | \(-0.488805\pi\) |
−0.999382 | + | 0.0351644i | \(0.988805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −138.698 | −1.34658 | −0.673290 | − | 0.739379i | \(-0.735119\pi\) | ||||
−0.673290 | + | 0.739379i | \(0.735119\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 10.4275i | − | 0.0993099i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 31.7386 | − | 31.7386i | 0.296622 | − | 0.296622i | −0.543067 | − | 0.839689i | \(-0.682737\pi\) |
0.839689 | + | 0.543067i | \(0.182737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.712308 | + | 0.712308i | −0.00653493 | + | 0.00653493i | −0.710367 | − | 0.703832i | \(-0.751471\pi\) |
0.703832 | + | 0.710367i | \(0.251471\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 5.32349i | − | 0.0479594i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.8888 | 0.131759 | 0.0658795 | − | 0.997828i | \(-0.479015\pi\) | ||||
0.0658795 | + | 0.997828i | \(0.479015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −62.9504 | − | 62.9504i | −0.547395 | − | 0.547395i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −56.1731 | − | 56.1731i | −0.480112 | − | 0.480112i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 65.5850 | 0.551134 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 60.1021i | 0.496711i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.05923 | − | 7.05923i | 0.0573921 | − | 0.0573921i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −84.1445 | + | 84.1445i | −0.673156 | + | 0.673156i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 106.861i | − | 0.841425i | −0.907194 | − | 0.420712i | \(-0.861780\pi\) | ||
0.907194 | − | 0.420712i | \(-0.138220\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.9572 | −0.123699 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 153.198 | + | 153.198i | 1.16945 | + | 1.16945i | 0.982338 | + | 0.187116i | \(0.0599139\pi\) |
0.187116 | + | 0.982338i | \(0.440086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 130.644 | + | 130.644i | 0.982287 | + | 0.982287i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.3751 | 0.143519 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 75.1700i | 0.548686i | 0.961632 | + | 0.274343i | \(0.0884604\pi\) | ||||
−0.961632 | + | 0.274343i | \(0.911540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 107.425 | − | 107.425i | 0.772843 | − | 0.772843i | −0.205760 | − | 0.978603i | \(-0.565966\pi\) |
0.978603 | + | 0.205760i | \(0.0659665\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.91339 | + | 5.91339i | −0.0419389 | + | 0.0419389i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 69.2109i | 0.483992i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 35.8026 | 0.246915 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.49879 | − | 6.49879i | −0.0442094 | − | 0.0442094i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 146.031 | + | 146.031i | 0.980074 | + | 0.980074i | 0.999805 | − | 0.0197310i | \(-0.00628097\pi\) |
−0.0197310 | + | 0.999805i | \(0.506281\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 220.513 | 1.46035 | 0.730175 | − | 0.683260i | \(-0.239439\pi\) | ||||
0.730175 | + | 0.683260i | \(0.239439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 60.7853i | 0.397290i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.3751 | − | 19.3751i | 0.125000 | − | 0.125000i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 109.561 | − | 109.561i | 0.697839 | − | 0.697839i | −0.266105 | − | 0.963944i | \(-0.585737\pi\) |
0.963944 | + | 0.266105i | \(0.0857369\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.19066i | 0.0200670i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −165.058 | −1.02521 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −56.7781 | − | 56.7781i | −0.348332 | − | 0.348332i | 0.511156 | − | 0.859488i | \(-0.329217\pi\) |
−0.859488 | + | 0.511156i | \(0.829217\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.95377 | − | 5.95377i | −0.0360835 | − | 0.0360835i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 106.677 | 0.638781 | 0.319391 | − | 0.947623i | \(-0.396522\pi\) | ||||
0.319391 | + | 0.947623i | \(0.396522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 90.3414i | 0.534564i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −121.083 | + | 121.083i | −0.708090 | + | 0.708090i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −178.360 | + | 178.360i | −1.03098 | + | 1.03098i | −0.0314805 | + | 0.999504i | \(0.510022\pi\) |
−0.999504 | + | 0.0314805i | \(0.989978\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 20.9807i | − | 0.119890i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.8970 | 0.0841639 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −60.4622 | − | 60.4622i | −0.337778 | − | 0.337778i | 0.517753 | − | 0.855530i | \(-0.326769\pi\) |
−0.855530 | + | 0.517753i | \(0.826769\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −147.113 | − | 147.113i | −0.812779 | − | 0.812779i | 0.172271 | − | 0.985050i | \(-0.444890\pi\) |
−0.985050 | + | 0.172271i | \(0.944890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.98073 | −0.0272171 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 134.059i | − | 0.724642i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 37.4468 | − | 37.4468i | 0.200250 | − | 0.200250i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 25.4011 | − | 25.4011i | 0.134397 | − | 0.134397i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 106.861i | 0.559481i | 0.960076 | + | 0.279741i | \(0.0902485\pi\) | ||||
−0.960076 | + | 0.279741i | \(0.909752\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 68.1873 | 0.353302 | 0.176651 | − | 0.984274i | \(-0.443474\pi\) | ||||
0.176651 | + | 0.984274i | \(0.443474\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.76650 | + | 6.76650i | 0.0347000 | + | 0.0347000i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 61.8529 | + | 61.8529i | 0.313974 | + | 0.313974i | 0.846447 | − | 0.532473i | \(-0.178737\pi\) |
−0.532473 | + | 0.846447i | \(0.678737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −158.466 | −0.796310 | −0.398155 | − | 0.917318i | \(-0.630349\pi\) | ||||
−0.398155 | + | 0.917318i | \(0.630349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.70914i | 0.0333788i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 46.9379 | − | 46.9379i | 0.231221 | − | 0.231221i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 177.769 | − | 177.769i | 0.867166 | − | 0.867166i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 152.979i | − | 0.739028i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 149.187 | 0.713813 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 197.031 | + | 197.031i | 0.933798 | + | 0.933798i | 0.997941 | − | 0.0641430i | \(-0.0204314\pi\) |
−0.0641430 | + | 0.997941i | \(0.520431\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.55315 | + | 7.55315i | 0.0354608 | + | 0.0354608i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −401.841 | −1.86903 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 50.8022i | − | 0.234111i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.4902 | + | 11.4902i | −0.0524664 | + | 0.0524664i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −42.5585 | + | 42.5585i | −0.192573 | + | 0.192573i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.7698i | − | 0.0707168i | −0.999375 | − | 0.0353584i | \(-0.988743\pi\) | ||
0.999375 | − | 0.0353584i | \(-0.0112573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.4453 | 0.0864236 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −199.289 | − | 199.289i | −0.877927 | − | 0.877927i | 0.115393 | − | 0.993320i | \(-0.463187\pi\) |
−0.993320 | + | 0.115393i | \(0.963187\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −230.522 | − | 230.522i | −1.00664 | − | 1.00664i | −0.999978 | − | 0.00666715i | \(-0.997878\pi\) |
−0.00666715 | − | 0.999978i | \(-0.502122\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.6110 | −0.0675801 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 344.791i | − | 1.47979i | −0.672722 | − | 0.739895i | \(-0.734875\pi\) | ||
0.672722 | − | 0.739895i | \(-0.265125\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −148.914 | + | 148.914i | −0.633676 | + | 0.633676i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.8825 | + | 15.8825i | −0.0670146 | + | 0.0670146i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 77.1978i | 0.323004i | 0.986872 | + | 0.161502i | \(0.0516337\pi\) | ||||
−0.986872 | + | 0.161502i | \(0.948366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −293.483 | −1.21777 | −0.608885 | − | 0.793259i | \(-0.708383\pi\) | ||||
−0.608885 | + | 0.793259i | \(0.708383\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 35.3413 | + | 35.3413i | 0.145438 | + | 0.145438i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −163.656 | − | 163.656i | −0.667982 | − | 0.667982i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −169.552 | −0.686445 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.7785i | 0.0673837i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −79.6322 | + | 79.6322i | −0.317260 | + | 0.317260i | −0.847714 | − | 0.530454i | \(-0.822021\pi\) |
0.530454 | + | 0.847714i | \(0.322021\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −94.2427 | + | 94.2427i | −0.372501 | + | 0.372501i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 7.32208i | − | 0.0287140i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 221.860 | 0.863270 | 0.431635 | − | 0.902048i | \(-0.357937\pi\) | ||||
0.431635 | + | 0.902048i | \(0.357937\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −175.753 | − | 175.753i | −0.678585 | − | 0.678585i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 43.5028 | + | 43.5028i | 0.166678 | + | 0.166678i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 374.223 | 1.42290 | 0.711451 | − | 0.702736i | \(-0.248039\pi\) | ||||
0.711451 | + | 0.702736i | \(0.248039\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 80.3486i | 0.303202i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.45876 | + | 6.45876i | −0.0241901 | + | 0.0241901i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 357.970 | − | 357.970i | 1.33075 | − | 1.33075i | 0.426042 | − | 0.904704i | \(-0.359908\pi\) |
0.904704 | − | 0.426042i | \(-0.140092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 359.030i | 1.32484i | 0.749135 | + | 0.662418i | \(0.230470\pi\) | ||||
−0.749135 | + | 0.662418i | \(0.769530\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.7420 | 0.0649890 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.9793 | − | 11.9793i | −0.0435610 | − | 0.0435610i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 351.765 | + | 351.765i | 1.26991 | + | 1.26991i | 0.946134 | + | 0.323775i | \(0.104952\pi\) |
0.323775 | + | 0.946134i | \(0.395048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 47.0843 | 0.168761 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 191.390i | 0.681103i | 0.940226 | + | 0.340552i | \(0.110614\pi\) | ||||
−0.940226 | + | 0.340552i | \(0.889386\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.3119 | − | 31.3119i | 0.110643 | − | 0.110643i | −0.649618 | − | 0.760261i | \(-0.725071\pi\) |
0.760261 | + | 0.649618i | \(0.225071\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.5855 | − | 14.5855i | 0.0511771 | − | 0.0511771i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 466.117i | − | 1.62410i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −242.947 | −0.840647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4953 | − | 16.4953i | −0.0566850 | − | 0.0566850i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 92.0889 | + | 92.0889i | 0.314297 | + | 0.314297i | 0.846572 | − | 0.532275i | \(-0.178663\pi\) |
−0.532275 | + | 0.846572i | \(0.678663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 375.144 | 1.27167 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 29.0063i | − | 0.0976643i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 107.107 | − | 107.107i | 0.358219 | − | 0.358219i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −526.821 | + | 526.821i | −1.75023 | + | 1.75023i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.5079i | 0.0940854i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −125.427 | −0.411236 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 257.566 | + | 257.566i | 0.838978 | + | 0.838978i | 0.988724 | − | 0.149746i | \(-0.0478457\pi\) |
−0.149746 | + | 0.988724i | \(0.547846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.3005 | + | 20.3005i | 0.0656976 | + | 0.0656976i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −130.914 | −0.420946 | −0.210473 | − | 0.977600i | \(-0.567500\pi\) | ||||
−0.210473 | + | 0.977600i | \(0.567500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 51.8354i | 0.165608i | 0.996566 | + | 0.0828041i | \(0.0263876\pi\) | ||||
−0.996566 | + | 0.0828041i | \(0.973612\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 319.068 | − | 319.068i | 1.01291 | − | 1.01291i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 109.636 | − | 109.636i | 0.345856 | − | 0.345856i | −0.512707 | − | 0.858563i | \(-0.671357\pi\) |
0.858563 | + | 0.512707i | \(0.171357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 53.5999i | − | 0.168025i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.29086 | −0.0289435 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 91.7367 | + | 91.7367i | 0.284014 | + | 0.284014i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.6145 | + | 13.6145i | 0.0418909 | + | 0.0418909i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.208514 | 0.000637659 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 390.458i | 1.18680i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −323.226 | + | 323.226i | −0.976515 | + | 0.976515i | −0.999730 | − | 0.0232157i | \(-0.992610\pi\) |
0.0232157 | + | 0.999730i | \(0.492610\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 162.891 | − | 162.891i | 0.489163 | − | 0.489163i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 168.953i | 0.504337i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 315.159 | 0.935191 | 0.467596 | − | 0.883943i | \(-0.345120\pi\) | ||||
0.467596 | + | 0.883943i | \(0.345120\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.17920 | − | 2.17920i | −0.00642832 | − | 0.00642832i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −29.0063 | − | 29.0063i | −0.0850625 | − | 0.0850625i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.4459 | 0.129580 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.4275i | 0.0534132i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 307.568 | − | 307.568i | 0.886363 | − | 0.886363i | −0.107809 | − | 0.994172i | \(-0.534384\pi\) |
0.994172 | + | 0.107809i | \(0.0343835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −170.461 | + | 170.461i | −0.488427 | + | 0.488427i | −0.907810 | − | 0.419382i | \(-0.862247\pi\) |
0.419382 | + | 0.907810i | \(0.362247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.9659i | 0.0939198i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 238.136 | 0.674606 | 0.337303 | − | 0.941396i | \(-0.390485\pi\) | ||||
0.337303 | + | 0.941396i | \(0.390485\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 190.207 | + | 190.207i | 0.535795 | + | 0.535795i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.59938 | − | 9.59938i | −0.0268890 | − | 0.0268890i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.6470 | 0.0937241 | 0.0468620 | − | 0.998901i | \(-0.485078\pi\) | ||||
0.0468620 | + | 0.998901i | \(0.485078\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.47577i | 0.0123983i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.79687 | − | 8.79687i | 0.0242338 | − | 0.0242338i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −289.351 | + | 289.351i | −0.792741 | + | 0.792741i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 240.758i | 0.656016i | 0.944675 | + | 0.328008i | \(0.106377\pi\) | ||||
−0.944675 | + | 0.328008i | \(0.893623\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 432.005 | 1.17075 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 105.339 | + | 105.339i | 0.283931 | + | 0.283931i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −432.504 | − | 432.504i | −1.15953 | − | 1.15953i | −0.984577 | − | 0.174951i | \(-0.944023\pi\) |
−0.174951 | − | 0.984577i | \(-0.555977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.6317 | 0.0656845 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 60.9166i | 0.161583i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 174.716 | − | 174.716i | 0.460993 | − | 0.460993i | −0.437988 | − | 0.898981i | \(-0.644309\pi\) |
0.898981 | + | 0.437988i | \(0.144309\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.6408 | + | 15.6408i | −0.0410518 | + | 0.0410518i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 673.381i | − | 1.75817i | −0.476661 | − | 0.879087i | \(-0.658153\pi\) | ||
0.476661 | − | 0.879087i | \(-0.341847\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −393.124 | −1.02110 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −488.266 | − | 488.266i | −1.26167 | − | 1.26167i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 274.646 | + | 274.646i | 0.706031 | + | 0.706031i | 0.965698 | − | 0.259667i | \(-0.0836129\pi\) |
−0.259667 | + | 0.965698i | \(0.583613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −115.902 | −0.296424 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 44.8459i | − | 0.114112i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −399.960 | + | 399.960i | −1.01256 | + | 1.01256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 271.254 | − | 271.254i | 0.683259 | − | 0.683259i | −0.277474 | − | 0.960733i | \(-0.589497\pi\) |
0.960733 | + | 0.277474i | \(0.0894972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 38.2436i | − | 0.0958487i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −415.193 | −1.03539 | −0.517697 | − | 0.855564i | \(-0.673210\pi\) | ||||
−0.517697 | + | 0.855564i | \(0.673210\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.9659 | + | 32.9659i | 0.0818011 | + | 0.0818011i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 294.296 | + | 294.296i | 0.726658 | + | 0.726658i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −200.699 | −0.493117 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 634.686i | − | 1.55180i | −0.630856 | − | 0.775900i | \(-0.717296\pi\) | ||
0.630856 | − | 0.775900i | \(-0.282704\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.0023 | − | 11.0023i | 0.0267696 | − | 0.0267696i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 491.820 | − | 491.820i | 1.19085 | − | 1.19085i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 422.525i | 1.01813i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −31.4467 | −0.0754117 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.2687 | − | 19.2687i | −0.0459873 | − | 0.0459873i | 0.683739 | − | 0.729726i | \(-0.260353\pi\) |
−0.729726 | + | 0.683739i | \(0.760353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −244.505 | − | 244.505i | −0.580773 | − | 0.580773i | 0.354343 | − | 0.935116i | \(-0.384705\pi\) |
−0.935116 | + | 0.354343i | \(0.884705\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −361.883 | −0.855515 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 14.7324i | − | 0.0346644i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −164.437 | + | 164.437i | −0.385099 | + | 0.385099i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.1301 | − | 10.1301i | 0.0236133 | − | 0.0236133i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 337.331i | 0.782670i | 0.920248 | + | 0.391335i | \(0.127987\pi\) | ||||
−0.920248 | + | 0.391335i | \(0.872013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −424.560 | −0.980508 | −0.490254 | − | 0.871580i | \(-0.663096\pi\) | ||||
−0.490254 | + | 0.871580i | \(0.663096\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.24027 | − | 5.24027i | −0.0120466 | − | 0.0120466i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −230.874 | − | 230.874i | −0.528317 | − | 0.528317i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −162.004 | −0.369029 | −0.184514 | − | 0.982830i | \(-0.559071\pi\) | ||||
−0.184514 | + | 0.982830i | \(0.559071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 397.707i | − | 0.901831i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −492.189 | + | 492.189i | −1.11104 | + | 1.11104i | −0.118026 | + | 0.993010i | \(0.537657\pi\) |
−0.993010 | + | 0.118026i | \(0.962343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −162.648 | + | 162.648i | −0.365500 | + | 0.365500i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 42.7478i | − | 0.0956327i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 195.434 | 0.435266 | 0.217633 | − | 0.976031i | \(-0.430166\pi\) | ||||
0.217633 | + | 0.976031i | \(0.430166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −266.137 | − | 266.137i | −0.590104 | − | 0.590104i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.2755 | − | 32.2755i | −0.0712483 | − | 0.0712483i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 446.788 | 0.981951 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 386.874i | − | 0.846552i | −0.906001 | − | 0.423276i | \(-0.860880\pi\) | ||
0.906001 | − | 0.423276i | \(-0.139120\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.8363 | − | 17.8363i | 0.0388590 | − | 0.0388590i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 174.401 | − | 174.401i | 0.378310 | − | 0.378310i | −0.492182 | − | 0.870492i | \(-0.663801\pi\) |
0.870492 | + | 0.492182i | \(0.163801\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 60.5295i | − | 0.130733i | −0.997861 | − | 0.0653666i | \(-0.979178\pi\) | ||
0.997861 | − | 0.0653666i | \(-0.0208217\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.67168 | −0.0121972 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −306.482 | − | 306.482i | −0.656279 | − | 0.656279i | 0.298219 | − | 0.954497i | \(-0.403607\pi\) |
−0.954497 | + | 0.298219i | \(0.903607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 221.500 | + | 221.500i | 0.472282 | + | 0.472282i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.0718 | −0.0680930 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 601.593i | 1.27187i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.3467 | − | 29.3467i | 0.0617825 | − | 0.0617825i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −97.6295 | + | 97.6295i | −0.204674 | + | 0.204674i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 376.452i | − | 0.785912i | −0.919557 | − | 0.392956i | \(-0.871453\pi\) | ||
0.919557 | − | 0.392956i | \(-0.128547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 228.095 | 0.474210 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.1588 | + | 24.1588i | 0.0500183 | + | 0.0500183i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −415.393 | − | 415.393i | −0.856481 | − | 0.856481i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 77.2033 | 0.158528 | 0.0792641 | − | 0.996854i | \(-0.474743\pi\) | ||||
0.0792641 | + | 0.996854i | \(0.474743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.6207i | 0.0339892i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 581.438 | − | 581.438i | 1.18419 | − | 1.18419i | 0.205543 | − | 0.978648i | \(-0.434104\pi\) |
0.978648 | − | 0.205543i | \(-0.0658960\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.9592 | − | 32.9592i | 0.0668543 | − | 0.0668543i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 364.354i | − | 0.736069i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 498.730 | 1.00348 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 174.006 | + | 174.006i | 0.348709 | + | 0.348709i | 0.859629 | − | 0.510920i | \(-0.170695\pi\) |
−0.510920 | + | 0.859629i | \(0.670695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.6138 | − | 15.6138i | −0.0311652 | − | 0.0311652i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −355.262 | −0.706286 | −0.353143 | − | 0.935569i | \(-0.614887\pi\) | ||||
−0.353143 | + | 0.935569i | \(0.614887\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 717.899i | 1.42158i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.2229 | − | 13.2229i | 0.0260806 | − | 0.0260806i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −279.667 | + | 279.667i | −0.549444 | + | 0.549444i | −0.926280 | − | 0.376836i | \(-0.877012\pi\) |
0.376836 | + | 0.926280i | \(0.377012\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 758.688i | 1.48471i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 71.0592 | 0.138517 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 511.218 | + | 511.218i | 0.992657 | + | 0.992657i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 222.938 | + | 222.938i | 0.431215 | + | 0.431215i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 52.2116 | 0.100600 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 705.745i | − | 1.35460i | −0.735708 | − | 0.677299i | \(-0.763151\pi\) | ||
0.735708 | − | 0.677299i | \(-0.236849\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 186.762 | − | 186.762i | 0.357098 | − | 0.357098i | −0.505644 | − | 0.862742i | \(-0.668745\pi\) |
0.862742 | + | 0.505644i | \(0.168745\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.07085 | + | 3.07085i | −0.00584925 | + | 0.00584925i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 35.6726i | − | 0.0676899i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −237.309 | −0.448599 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 455.827 | + | 455.827i | 0.858432 | + | 0.858432i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 302.466 | + | 302.466i | 0.567479 | + | 0.567479i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −233.967 | −0.437321 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.6992i | 0.0329593i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −245.008 | + | 245.008i | −0.454560 | + | 0.454560i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −119.274 | + | 119.274i | −0.220470 | + | 0.220470i | −0.808696 | − | 0.588226i | \(-0.799826\pi\) |
0.588226 | + | 0.808696i | \(0.299826\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 43.0645i | 0.0793085i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.25091 | 0.00963470 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 141.472 | + | 141.472i | 0.258632 | + | 0.258632i | 0.824498 | − | 0.565865i | \(-0.191458\pi\) |
−0.565865 | + | 0.824498i | \(0.691458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −152.403 | − | 152.403i | −0.277602 | − | 0.277602i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 131.308 | 0.238309 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1048.71i | 1.89640i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.6216 | + | 19.6216i | −0.0353542 | + | 0.0353542i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −375.881 | + | 375.881i | −0.674831 | + | 0.674831i | −0.958826 | − | 0.283995i | \(-0.908340\pi\) |
0.283995 | + | 0.958826i | \(0.408340\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 683.715i | − | 1.22310i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.9618 | −0.0195398 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −305.349 | − | 305.349i | −0.542360 | − | 0.542360i | 0.381860 | − | 0.924220i | \(-0.375284\pi\) |
−0.924220 | + | 0.381860i | \(0.875284\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −54.8777 | − | 54.8777i | −0.0971287 | − | 0.0971287i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 771.656 | 1.36095 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 296.778i | − | 0.521578i | −0.965396 | − | 0.260789i | \(-0.916017\pi\) | ||
0.965396 | − | 0.260789i | \(-0.0839827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 347.717 | − | 347.717i | 0.608961 | − | 0.608961i | −0.333714 | − | 0.942674i | \(-0.608302\pi\) |
0.942674 | + | 0.333714i | \(0.108302\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.6408 | − | 15.6408i | 0.0272963 | − | 0.0272963i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.0771i | 0.0644820i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −189.382 | −0.328218 | −0.164109 | − | 0.986442i | \(-0.552475\pi\) | ||||
−0.164109 | + | 0.986442i | \(0.552475\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.98027 | − | 9.98027i | −0.0172371 | − | 0.0172371i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 553.939 | + | 553.939i | 0.953423 | + | 0.953423i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 120.289 | 0.206328 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 414.091i | 0.707847i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 641.187 | − | 641.187i | 1.09231 | − | 1.09231i | 0.0970301 | − | 0.995281i | \(-0.469066\pi\) |
0.995281 | − | 0.0970301i | \(-0.0309343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 71.0592 | − | 71.0592i | 0.120644 | − | 0.120644i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 18.1063i | − | 0.0306367i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −127.909 | −0.215697 | −0.107849 | − | 0.994167i | \(-0.534396\pi\) | ||||
−0.107849 | + | 0.994167i | \(0.534396\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −241.736 | − | 241.736i | −0.406279 | − | 0.406279i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.1939 | + | 23.1939i | 0.0388508 | + | 0.0388508i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 794.804 | 1.32688 | 0.663442 | − | 0.748227i | \(-0.269095\pi\) | ||||
0.663442 | + | 0.748227i | \(0.269095\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 89.2746i | 0.148543i | 0.997238 | + | 0.0742717i | \(0.0236632\pi\) | ||||
−0.997238 | + | 0.0742717i | \(0.976337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −205.290 | + | 205.290i | −0.340448 | + | 0.340448i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 221.527 | − | 221.527i | 0.366160 | − | 0.366160i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 316.002i | 0.520596i | 0.965528 | + | 0.260298i | \(0.0838208\pi\) | ||||
−0.965528 | + | 0.260298i | \(0.916179\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.7402 | −0.0225619 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −253.370 | − | 253.370i | −0.414682 | − | 0.414682i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 192.003 | + | 192.003i | 0.313219 | + | 0.313219i | 0.846155 | − | 0.532936i | \(-0.178911\pi\) |
−0.532936 | + | 0.846155i | \(0.678911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −52.0385 | −0.0846154 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 105.762i | 0.171413i | 0.996320 | + | 0.0857066i | \(0.0273148\pi\) | ||||
−0.996320 | + | 0.0857066i | \(0.972685\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −553.819 | + | 553.819i | −0.894699 | + | 0.894699i | −0.994961 | − | 0.100262i | \(-0.968032\pi\) |
0.100262 | + | 0.994961i | \(0.468032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −44.8888 | + | 44.8888i | −0.0722846 | + | 0.0722846i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 426.468i | 0.684539i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 674.560 | 1.07930 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −21.8358 | − | 21.8358i | −0.0348258 | − | 0.0348258i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −123.412 | − | 123.412i | −0.196203 | − | 0.196203i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 762.907 | 1.20904 | 0.604522 | − | 0.796589i | \(-0.293364\pi\) | ||||
0.604522 | + | 0.796589i | \(0.293364\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 57.6772i | − | 0.0911172i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −393.873 | + | 393.873i | −0.620272 | + | 0.620272i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 278.453 | − | 278.453i | 0.437132 | − | 0.437132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 462.232i | 0.723367i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −412.834 | −0.644046 | −0.322023 | − | 0.946732i | \(-0.604363\pi\) | ||||
−0.322023 | + | 0.946732i | \(0.604363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 372.515 | + | 372.515i | 0.579339 | + | 0.579339i | 0.934721 | − | 0.355382i | \(-0.115649\pi\) |
−0.355382 | + | 0.934721i | \(0.615649\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 58.8156 | + | 58.8156i | 0.0911870 | + | 0.0911870i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1170.94 | −1.80980 | −0.904899 | − | 0.425627i | \(-0.860054\pi\) | ||||
−0.904899 | + | 0.425627i | \(0.860054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 561.625i | − | 0.865370i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.43568 | + | 7.43568i | −0.0114219 | + | 0.0114219i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.7523 | + | 13.7523i | −0.0210602 | + | 0.0210602i | −0.717558 | − | 0.696498i | \(-0.754740\pi\) |
0.696498 | + | 0.717558i | \(0.254740\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1129.33i | − | 1.72417i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −703.165 | −1.07027 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −283.149 | − | 283.149i | −0.429664 | − | 0.429664i | 0.458850 | − | 0.888514i | \(-0.348262\pi\) |
−0.888514 | + | 0.458850i | \(0.848262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −287.535 | − | 287.535i | −0.435000 | − | 0.435000i | 0.455325 | − | 0.890325i | \(-0.349523\pi\) |
−0.890325 | + | 0.455325i | \(0.849523\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.4582 | 0.0187907 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 963.069i | − | 1.44822i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −82.9486 | + | 82.9486i | −0.124361 | + | 0.124361i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.30816 | + | 2.30816i | −0.00345017 | + | 0.00345017i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 187.776i | 0.279845i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.5265 | −0.0676471 | −0.0338236 | − | 0.999428i | \(-0.510768\pi\) | ||||
−0.0338236 | + | 0.999428i | \(0.510768\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.70586 | − | 5.70586i | −0.00845312 | − | 0.00845312i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −208.341 | − | 208.341i | −0.307742 | − | 0.307742i | 0.536291 | − | 0.844033i | \(-0.319825\pi\) |
−0.844033 | + | 0.536291i | \(0.819825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1089.18 | −1.60409 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 58.3382i | 0.0856655i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 219.645 | − | 219.645i | 0.321589 | − | 0.321589i | −0.527787 | − | 0.849377i | \(-0.676978\pi\) |
0.849377 | + | 0.527787i | \(0.176978\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 277.065 | − | 277.065i | 0.404475 | − | 0.404475i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 67.4808i | 0.0982254i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −136.710 | −0.198418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −692.991 | − | 692.991i | −1.00288 | − | 1.00288i | −0.999996 | − | 0.00288571i | \(-0.999081\pi\) |
−0.00288571 | − | 0.999996i | \(-0.500919\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −477.675 | − | 477.675i | −0.689285 | − | 0.689285i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −791.905 | −1.13943 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 327.301i | − | 0.469585i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −50.4655 | + | 50.4655i | −0.0721967 | + | 0.0721967i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −195.377 | + | 195.377i | −0.278712 | + | 0.278712i | −0.832595 | − | 0.553883i | \(-0.813146\pi\) |
0.553883 | + | 0.832595i | \(0.313146\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 491.668i | − | 0.699386i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 43.5917 | 0.0618322 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 941.179 | + | 941.179i | 1.33123 | + | 1.33123i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −318.083 | − | 318.083i | −0.448636 | − | 0.448636i | 0.446265 | − | 0.894901i | \(-0.352754\pi\) |
−0.894901 | + | 0.446265i | \(0.852754\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −971.962 | −1.36703 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 89.7775i | 0.125915i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 255.101 | − | 255.101i | 0.356784 | − | 0.356784i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.2991 | − | 11.2991i | 0.0157589 | − | 0.0157589i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1122.38i | 1.56103i | 0.625139 | + | 0.780514i | \(0.285042\pi\) | ||||
−0.625139 | + | 0.780514i | \(0.714958\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1340.43 | 1.85913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 42.9557 | + | 42.9557i | 0.0594132 | + | 0.0594132i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.5437 | − | 10.5437i | −0.0145430 | − | 0.0145430i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 529.192 | 0.727911 | 0.363956 | − | 0.931416i | \(-0.381426\pi\) | ||||
0.363956 | + | 0.931416i | \(0.381426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 708.260i | 0.971549i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −369.926 | + | 369.926i | −0.506055 | + | 0.506055i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 263.121 | − | 263.121i | 0.358965 | − | 0.358965i | −0.504466 | − | 0.863431i | \(-0.668311\pi\) |
0.863431 | + | 0.504466i | \(0.168311\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 47.9070i | 0.0651797i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 252.938 | 0.343200 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.5459 | + | 44.5459i | 0.0602787 | + | 0.0602787i | 0.736603 | − | 0.676325i | \(-0.236428\pi\) |
−0.676325 | + | 0.736603i | \(0.736428\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.8165 | + | 24.8165i | 0.0334906 | + | 0.0334906i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 762.894 | 1.02678 | 0.513388 | − | 0.858157i | \(-0.328390\pi\) | ||||
0.513388 | + | 0.858157i | \(0.328390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1076.50i | − | 1.44496i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −513.400 | + | 513.400i | −0.687282 | + | 0.687282i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −306.735 | + | 306.735i | −0.409526 | + | 0.409526i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1342.93i | − | 1.78819i | −0.447876 | − | 0.894095i | \(-0.647820\pi\) | ||
0.447876 | − | 0.894095i | \(-0.352180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.3108 | 0.0309573 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −812.776 | − | 812.776i | −1.07652 | − | 1.07652i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 394.830 | + | 394.830i | 0.521573 | + | 0.521573i | 0.918046 | − | 0.396474i | \(-0.129766\pi\) |
−0.396474 | + | 0.918046i | \(0.629766\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.5878 | 0.0363475 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 480.213i | 0.631029i | 0.948921 | + | 0.315514i | \(0.102177\pi\) | ||||
−0.948921 | + | 0.315514i | \(0.897823\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.88404 | − | 6.88404i | 0.00902233 | − | 0.00902233i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 224.045 | − | 224.045i | 0.292870 | − | 0.292870i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 638.291i | 0.832191i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 472.763 | 0.614777 | 0.307388 | − | 0.951584i | \(-0.400545\pi\) | ||||
0.307388 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.4727 | − | 32.4727i | −0.0421177 | − | 0.0421177i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −857.735 | − | 857.735i | −1.10962 | − | 1.10962i | −0.993200 | − | 0.116418i | \(-0.962859\pi\) |
−0.116418 | − | 0.993200i | \(-0.537141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.4117 | −0.0147248 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 51.4485i | 0.0662143i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 651.978 | − | 651.978i | 0.836942 | − | 0.836942i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 284.758 | − | 284.758i | 0.364607 | − | 0.364607i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 25.5302i | − | 0.0326056i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −807.648 | −1.02885 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −170.355 | − | 170.355i | −0.216462 | − | 0.216462i | 0.590544 | − | 0.807006i | \(-0.298913\pi\) |
−0.807006 | + | 0.590544i | \(0.798913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −54.7733 | − | 54.7733i | −0.0694212 | − | 0.0694212i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −143.891 | −0.181911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 213.409i | − | 0.269116i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.7603 | − | 11.7603i | 0.0147928 | − | 0.0147928i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −835.571 | + | 835.571i | −1.04840 | + | 1.04840i | −0.0496277 | + | 0.998768i | \(0.515803\pi\) |
−0.998768 | + | 0.0496277i | \(0.984197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 274.174i | 0.343147i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −395.258 | −0.493456 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 433.185 | + | 433.185i | 0.539458 | + | 0.539458i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 608.380 | + | 608.380i | 0.755751 | + | 0.755751i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −104.789 | −0.129850 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 371.926i | 0.459735i | 0.973222 | + | 0.229868i | \(0.0738293\pi\) | ||||
−0.973222 | + | 0.229868i | \(0.926171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 275.629 | − | 275.629i | 0.339863 | − | 0.339863i | −0.516453 | − | 0.856316i | \(-0.672748\pi\) |
0.856316 | + | 0.516453i | \(0.172748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 52.5497 | − | 52.5497i | 0.0646367 | − | 0.0646367i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 418.550i | 0.513559i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1473.77 | −1.80389 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 542.880 | + | 542.880i | 0.662858 | + | 0.662858i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 904.923 | + | 904.923i | 1.10222 | + | 1.10222i | 0.994142 | + | 0.108079i | \(0.0344699\pi\) |
0.108079 | + | 0.994142i | \(0.465530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 523.237 | 0.635768 | 0.317884 | − | 0.948130i | \(-0.397028\pi\) | ||||
0.317884 | + | 0.948130i | \(0.397028\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.50671i | 0.00425055i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −722.805 | + | 722.805i | −0.874008 | + | 0.874008i | −0.992906 | − | 0.118898i | \(-0.962064\pi\) |
0.118898 | + | 0.992906i | \(0.462064\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 286.380 | − | 286.380i | 0.345453 | − | 0.345453i | −0.512960 | − | 0.858413i | \(-0.671451\pi\) |
0.858413 | + | 0.512960i | \(0.171451\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 102.972i | − | 0.123914i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −301.316 | −0.361724 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −393.193 | − | 393.193i | −0.470890 | − | 0.470890i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.8160 | − | 13.8160i | −0.0165066 | − | 0.0165066i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1353.58 | 1.61333 | 0.806666 | − | 0.591008i | \(-0.201270\pi\) | ||||
0.806666 | + | 0.591008i | \(0.201270\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 793.824i | 0.943904i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.0129 | − | 28.0129i | 0.0332300 | − | 0.0332300i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 332.984 | − | 332.984i | 0.394064 | − | 0.394064i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 580.852i | − | 0.685776i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.16597 | −0.0107962 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 310.591 | + | 310.591i | 0.364972 | + | 0.364972i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 668.253 | + | 668.253i | 0.783415 | + | 0.783415i | 0.980405 | − | 0.196990i | \(-0.0631167\pi\) |
−0.196990 | + | 0.980405i | \(0.563117\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 892.589 | 1.04396 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 488.688i | 0.570230i | 0.958493 | + | 0.285115i | \(0.0920319\pi\) | ||||
−0.958493 | + | 0.285115i | \(0.907968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 268.818 | − | 268.818i | 0.312943 | − | 0.312943i | −0.533106 | − | 0.846048i | \(-0.678975\pi\) |
0.846048 | + | 0.533106i | \(0.178975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −68.2234 | + | 68.2234i | −0.0792374 | + | 0.0792374i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 152.667i | − | 0.176903i | −0.996080 | − | 0.0884514i | \(-0.971808\pi\) | ||
0.996080 | − | 0.0884514i | \(-0.0281918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1314.82 | 1.52002 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 35.5591 | + | 35.5591i | 0.0410139 | + | 0.0410139i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 598.777 | + | 598.777i | 0.689042 | + | 0.689042i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −287.466 | −0.330041 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1009.47i | − | 1.15632i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 813.208 | − | 813.208i | 0.929380 | − | 0.929380i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −162.637 | + | 162.637i | −0.185447 | + | 0.185447i | −0.793725 | − | 0.608277i | \(-0.791861\pi\) |
0.608277 | + | 0.793725i | \(0.291861\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 26.9573i | − | 0.0306681i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 873.243 | 0.991196 | 0.495598 | − | 0.868552i | \(-0.334949\pi\) | ||||
0.495598 | + | 0.868552i | \(0.334949\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 230.025 | + | 230.025i | 0.260504 | + | 0.260504i | 0.825259 | − | 0.564755i | \(-0.191029\pi\) |
−0.564755 | + | 0.825259i | \(0.691029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −54.9081 | − | 54.9081i | −0.0620430 | − | 0.0620430i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 430.685 | 0.485552 | 0.242776 | − | 0.970082i | \(-0.421942\pi\) | ||||
0.242776 | + | 0.970082i | \(0.421942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1032.75i | 1.16170i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 440.589 | − | 440.589i | 0.494489 | − | 0.494489i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −546.150 | + | 546.150i | −0.611590 | + | 0.611590i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 445.709i | 0.497999i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31.3537 | −0.0349539 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.5302 | − | 25.5302i | −0.0283984 | − | 0.0283984i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73.9673 | + | 73.9673i | 0.0820947 | + | 0.0820947i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 154.217 | 0.170783 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1084.47i | 1.19831i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.2262 | + | 22.2262i | −0.0245052 | + | 0.0245052i | −0.719253 | − | 0.694748i | \(-0.755516\pi\) |
0.694748 | + | 0.719253i | \(0.255516\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −872.301 | + | 872.301i | −0.959627 | + | 0.959627i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1399.85i | − | 1.53661i | −0.640083 | − | 0.768306i | \(-0.721100\pi\) | ||
0.640083 | − | 0.768306i | \(-0.278900\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 632.560 | 0.692837 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 18.3582 | + | 18.3582i | 0.0200636 | + | 0.0200636i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1480.57 | − | 1480.57i | −1.61458 | − | 1.61458i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −806.944 | −0.878068 | −0.439034 | − | 0.898470i | \(-0.644679\pi\) | ||||
−0.439034 | + | 0.898470i | \(0.644679\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 75.3976i | − | 0.0818650i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −323.629 | + | 323.629i | −0.350628 | + | 0.350628i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.4796 | + | 39.4796i | −0.0426806 | + | 0.0426806i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1242.34i | 1.34017i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1620.69 | −1.74455 | −0.872276 | − | 0.489013i | \(-0.837357\pi\) | ||||
−0.872276 | + | 0.489013i | \(0.837357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −600.216 | − | 600.216i | −0.644701 | − | 0.644701i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 19.1613 | + | 19.1613i | 0.0205373 | + | 0.0205373i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −276.046 | −0.295237 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 598.181i | 0.638400i | 0.947687 | + | 0.319200i | \(0.103414\pi\) | ||||
−0.947687 | + | 0.319200i | \(0.896586\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.58691 | − | 7.58691i | 0.00807978 | − | 0.00807978i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 977.842 | − | 977.842i | 1.03915 | − | 1.03915i | 0.0399498 | − | 0.999202i | \(-0.487280\pi\) |
0.999202 | − | 0.0399498i | \(-0.0127198\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 823.721i | 0.873511i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −187.249 | −0.198147 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 827.881 | + | 827.881i | 0.874215 | + | 0.874215i | 0.992929 | − | 0.118714i | \(-0.0378771\pi\) |
−0.118714 | + | 0.992929i | \(0.537877\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −492.317 | − | 492.317i | −0.518775 | − | 0.518775i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.0939 | −0.0337476 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1846.78i | − | 1.93786i | −0.247333 | − | 0.968930i | \(-0.579554\pi\) | ||
0.247333 | − | 0.968930i | \(-0.420446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 393.873 | − | 393.873i | 0.412432 | − | 0.412432i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.84517 | + | 7.84517i | −0.00819767 | + | 0.00819767i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 726.475i | − | 0.757534i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 933.368 | 0.971247 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −284.287 | − | 284.287i | −0.295210 | − | 0.295210i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −251.328 | − | 251.328i | −0.260443 | − | 0.260443i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −363.922 | −0.376341 | −0.188170 | − | 0.982136i | \(-0.560256\pi\) | ||||
−0.188170 | + | 0.982136i | \(0.560256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 26.8542i | − | 0.0277133i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1161.30 | + | 1161.30i | −1.19598 | + | 1.19598i | −0.220619 | + | 0.975360i | \(0.570808\pi\) |
−0.975360 | + | 0.220619i | \(0.929192\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1038.20 | + | 1038.20i | −1.06701 | + | 1.06701i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 3.98540i | − | 0.00408759i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1159.63 | 1.18693 | 0.593467 | − | 0.804858i | \(-0.297759\pi\) | ||||
0.593467 | + | 0.804858i | \(0.297759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 243.499 | + | 243.499i | 0.248722 | + | 0.248722i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.38025 | + | 6.38025i | 0.00650382 | + | 0.00650382i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1780.51 | −1.81131 | −0.905653 | − | 0.424020i | \(-0.860618\pi\) | ||||
−0.905653 | + | 0.424020i | \(0.860618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 455.961i | − | 0.462904i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 57.1495 | − | 57.1495i | 0.0579022 | − | 0.0579022i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 930.997 | − | 930.997i | 0.941352 | − | 0.941352i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 675.783i | − | 0.681920i | −0.940078 | − | 0.340960i | \(-0.889248\pi\) | ||
0.940078 | − | 0.340960i | \(-0.110752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 94.6184 | 0.0952854 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 584.080 | + | 584.080i | 0.587015 | + | 0.587015i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.44963 | − | 9.44963i | −0.00947806 | − | 0.00947806i | 0.702352 | − | 0.711830i | \(-0.252133\pi\) |
−0.711830 | + | 0.702352i | \(0.752133\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −95.5948 | −0.0956905 |
(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 | 128.3.f.b.31.2 | 6 | ||
3.2 | odd | 2 | 1152.3.m.a.415.3 | 6 | |||
4.3 | odd | 2 | 128.3.f.a.31.2 | 6 | |||
8.3 | odd | 2 | 64.3.f.a.15.2 | 6 | |||
8.5 | even | 2 | 16.3.f.a.11.2 | yes | 6 | ||
12.11 | even | 2 | 1152.3.m.b.415.3 | 6 | |||
16.3 | odd | 4 | inner | 128.3.f.b.95.2 | 6 | ||
16.5 | even | 4 | 64.3.f.a.47.2 | 6 | |||
16.11 | odd | 4 | 16.3.f.a.3.2 | ✓ | 6 | ||
16.13 | even | 4 | 128.3.f.a.95.2 | 6 | |||
24.5 | odd | 2 | 144.3.m.a.91.2 | 6 | |||
24.11 | even | 2 | 576.3.m.a.271.1 | 6 | |||
32.3 | odd | 8 | 1024.3.c.j.1023.8 | 12 | |||
32.5 | even | 8 | 1024.3.d.k.511.7 | 12 | |||
32.11 | odd | 8 | 1024.3.d.k.511.8 | 12 | |||
32.13 | even | 8 | 1024.3.c.j.1023.7 | 12 | |||
32.19 | odd | 8 | 1024.3.c.j.1023.5 | 12 | |||
32.21 | even | 8 | 1024.3.d.k.511.6 | 12 | |||
32.27 | odd | 8 | 1024.3.d.k.511.5 | 12 | |||
32.29 | even | 8 | 1024.3.c.j.1023.6 | 12 | |||
40.13 | odd | 4 | 400.3.k.d.299.1 | 6 | |||
40.29 | even | 2 | 400.3.r.c.251.2 | 6 | |||
40.37 | odd | 4 | 400.3.k.c.299.3 | 6 | |||
48.5 | odd | 4 | 576.3.m.a.559.1 | 6 | |||
48.11 | even | 4 | 144.3.m.a.19.2 | 6 | |||
48.29 | odd | 4 | 1152.3.m.b.991.3 | 6 | |||
48.35 | even | 4 | 1152.3.m.a.991.3 | 6 | |||
80.27 | even | 4 | 400.3.k.d.99.1 | 6 | |||
80.43 | even | 4 | 400.3.k.c.99.3 | 6 | |||
80.59 | odd | 4 | 400.3.r.c.51.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.3.f.a.3.2 | ✓ | 6 | 16.11 | odd | 4 | ||
16.3.f.a.11.2 | yes | 6 | 8.5 | even | 2 | ||
64.3.f.a.15.2 | 6 | 8.3 | odd | 2 | |||
64.3.f.a.47.2 | 6 | 16.5 | even | 4 | |||
128.3.f.a.31.2 | 6 | 4.3 | odd | 2 | |||
128.3.f.a.95.2 | 6 | 16.13 | even | 4 | |||
128.3.f.b.31.2 | 6 | 1.1 | even | 1 | trivial | ||
128.3.f.b.95.2 | 6 | 16.3 | odd | 4 | inner | ||
144.3.m.a.19.2 | 6 | 48.11 | even | 4 | |||
144.3.m.a.91.2 | 6 | 24.5 | odd | 2 | |||
400.3.k.c.99.3 | 6 | 80.43 | even | 4 | |||
400.3.k.c.299.3 | 6 | 40.37 | odd | 4 | |||
400.3.k.d.99.1 | 6 | 80.27 | even | 4 | |||
400.3.k.d.299.1 | 6 | 40.13 | odd | 4 | |||
400.3.r.c.51.2 | 6 | 80.59 | odd | 4 | |||
400.3.r.c.251.2 | 6 | 40.29 | even | 2 | |||
576.3.m.a.271.1 | 6 | 24.11 | even | 2 | |||
576.3.m.a.559.1 | 6 | 48.5 | odd | 4 | |||
1024.3.c.j.1023.5 | 12 | 32.19 | odd | 8 | |||
1024.3.c.j.1023.6 | 12 | 32.29 | even | 8 | |||
1024.3.c.j.1023.7 | 12 | 32.13 | even | 8 | |||
1024.3.c.j.1023.8 | 12 | 32.3 | odd | 8 | |||
1024.3.d.k.511.5 | 12 | 32.27 | odd | 8 | |||
1024.3.d.k.511.6 | 12 | 32.21 | even | 8 | |||
1024.3.d.k.511.7 | 12 | 32.5 | even | 8 | |||
1024.3.d.k.511.8 | 12 | 32.11 | odd | 8 | |||
1152.3.m.a.415.3 | 6 | 3.2 | odd | 2 | |||
1152.3.m.a.991.3 | 6 | 48.35 | even | 4 | |||
1152.3.m.b.415.3 | 6 | 12.11 | even | 2 | |||
1152.3.m.b.991.3 | 6 | 48.29 | odd | 4 |