Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(109,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.o (of order \(10\), degree \(4\), 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: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 109.6 | ||
Character | \(\chi\) | \(=\) | 300.109 |
Dual form | 300.2.o.a.289.6 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | ||||||||
\(3\) | 0.951057 | − | 0.309017i | 0.549093 | − | 0.178411i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23394 | − | 0.0974182i | 0.999051 | − | 0.0435667i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.31873i | − | 0.498431i | −0.968448 | − | 0.249216i | \(-0.919827\pi\) | ||
0.968448 | − | 0.249216i | \(-0.0801728\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.25737 | − | 0.913532i | −0.379111 | − | 0.275440i | 0.381868 | − | 0.924217i | \(-0.375281\pi\) |
−0.760979 | + | 0.648777i | \(0.775281\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.42727 | + | 1.96447i | 0.395854 | + | 0.544846i | 0.959697 | − | 0.281036i | \(-0.0906780\pi\) |
−0.563844 | + | 0.825882i | \(0.690678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.09450 | − | 0.782977i | 0.540799 | − | 0.202164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.25004 | − | 0.406161i | −0.303178 | − | 0.0985085i | 0.153477 | − | 0.988152i | \(-0.450953\pi\) |
−0.456655 | + | 0.889644i | \(0.650953\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.315522 | − | 0.971077i | 0.0723857 | − | 0.222780i | −0.908318 | − | 0.418280i | \(-0.862633\pi\) |
0.980704 | + | 0.195500i | \(0.0626330\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.407508 | − | 1.25418i | −0.0889256 | − | 0.273685i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.94350 | + | 4.05137i | −0.613761 | + | 0.844770i | −0.996880 | − | 0.0789291i | \(-0.974850\pi\) |
0.383119 | + | 0.923699i | \(0.374850\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.98102 | − | 0.435254i | 0.996204 | − | 0.0870507i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.587785 | − | 0.809017i | 0.113119 | − | 0.155695i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.82443 | + | 5.61503i | 0.338789 | + | 1.04268i | 0.964825 | + | 0.262891i | \(0.0846760\pi\) |
−0.626037 | + | 0.779794i | \(0.715324\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.73547 | − | 8.41891i | 0.491305 | − | 1.51208i | −0.331332 | − | 0.943514i | \(-0.607498\pi\) |
0.822637 | − | 0.568567i | \(-0.192502\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.47813 | − | 0.480272i | −0.257309 | − | 0.0836047i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.128468 | − | 2.94596i | −0.0217150 | − | 0.497958i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.95370 | − | 4.06542i | −0.485586 | − | 0.668352i | 0.493981 | − | 0.869473i | \(-0.335541\pi\) |
−0.979566 | + | 0.201121i | \(0.935541\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.96447 | + | 1.42727i | 0.314567 | + | 0.228546i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.43499 | + | 4.67529i | −1.00498 | + | 0.730158i | −0.963150 | − | 0.268967i | \(-0.913318\pi\) |
−0.0418271 | + | 0.999125i | \(0.513318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.84831i | 1.04436i | 0.852836 | + | 0.522179i | \(0.174881\pi\) | ||||
−0.852836 | + | 0.522179i | \(0.825119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.75004 | − | 1.39189i | 0.260880 | − | 0.207491i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.37336 | + | 2.39575i | −1.07552 | + | 0.349456i | −0.792633 | − | 0.609698i | \(-0.791291\pi\) |
−0.282882 | + | 0.959155i | \(0.591291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.26096 | 0.751566 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.31436 | −0.184048 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.75685 | + | 1.22067i | −0.516043 | + | 0.167673i | −0.555449 | − | 0.831551i | \(-0.687454\pi\) |
0.0394057 | + | 0.999223i | \(0.487454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.89789 | − | 1.91829i | −0.390751 | − | 0.258662i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.02105i | − | 0.135241i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.35355 | + | 4.61613i | −0.827162 | + | 0.600969i | −0.918755 | − | 0.394828i | \(-0.870804\pi\) |
0.0915928 | + | 0.995797i | \(0.470804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.83287 | + | 2.05820i | 0.362711 | + | 0.263525i | 0.754182 | − | 0.656665i | \(-0.228034\pi\) |
−0.391471 | + | 0.920191i | \(0.628034\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.775127 | − | 1.06687i | −0.0976568 | − | 0.134413i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.37982 | + | 4.24947i | 0.419215 | + | 0.527082i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.92426 | − | 2.57475i | −0.968102 | − | 0.314555i | −0.218052 | − | 0.975937i | \(-0.569970\pi\) |
−0.750050 | + | 0.661382i | \(0.769970\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.54749 | + | 4.76268i | −0.186296 | + | 0.573359i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00454 | − | 12.3247i | −0.475252 | − | 1.46267i | −0.845618 | − | 0.533788i | \(-0.820768\pi\) |
0.370366 | − | 0.928886i | \(-0.379232\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.47339 | + | 10.2862i | −0.874694 | + | 1.20391i | 0.103168 | + | 0.994664i | \(0.467102\pi\) |
−0.977862 | + | 0.209249i | \(0.932898\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.60273 | − | 1.95317i | 0.531477 | − | 0.225533i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.20470 | + | 1.65812i | −0.137288 | + | 0.188961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.386585 | + | 1.18979i | 0.0434942 | + | 0.133861i | 0.970446 | − | 0.241320i | \(-0.0775804\pi\) |
−0.926951 | + | 0.375182i | \(0.877580\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.80521 | − | 2.53607i | −0.856734 | − | 0.278370i | −0.152470 | − | 0.988308i | \(-0.548723\pi\) |
−0.704264 | + | 0.709939i | \(0.748723\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.83208 | − | 0.785565i | −0.307182 | − | 0.0852065i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.47028 | + | 4.77643i | 0.372053 | + | 0.512087i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.74667 | + | 5.62829i | 0.821146 | + | 0.596597i | 0.917040 | − | 0.398794i | \(-0.130571\pi\) |
−0.0958948 | + | 0.995391i | \(0.530571\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.59059 | − | 1.88218i | 0.271568 | − | 0.197306i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.85217i | − | 0.917927i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.610258 | − | 2.20007i | 0.0626112 | − | 0.225722i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.4769 | + | 5.02874i | −1.57144 | + | 0.510591i | −0.959833 | − | 0.280573i | \(-0.909476\pi\) |
−0.611604 | + | 0.791164i | \(0.709476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.55419 | −0.156202 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.63722 | 0.560925 | 0.280462 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280462 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00179 | − | 2.59994i | 0.788439 | − | 0.256179i | 0.113000 | − | 0.993595i | \(-0.463954\pi\) |
0.675439 | + | 0.737415i | \(0.263954\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.03253 | − | 2.76208i | −0.100765 | − | 0.269551i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.06196i | − | 0.199337i | −0.995021 | − | 0.0996687i | \(-0.968222\pi\) | ||
0.995021 | − | 0.0996687i | \(-0.0317783\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3052 | − | 8.21372i | 1.08284 | − | 0.786731i | 0.104666 | − | 0.994507i | \(-0.466623\pi\) |
0.978176 | + | 0.207776i | \(0.0666226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.06542 | − | 2.95370i | −0.385873 | − | 0.280353i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.50093 | + | 4.81862i | 0.329340 | + | 0.453297i | 0.941290 | − | 0.337599i | \(-0.109615\pi\) |
−0.611950 | + | 0.790896i | \(0.709615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.18093 | + | 9.33730i | −0.576375 | + | 0.870707i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.30937 | + | 0.750360i | 0.213502 | + | 0.0693708i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.535615 | + | 1.64845i | −0.0490997 | + | 0.151113i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.65275 | − | 8.16433i | −0.241159 | − | 0.742211i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.67529 | + | 6.43499i | −0.421557 | + | 0.580224i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0849 | − | 1.45757i | 0.991465 | − | 0.130369i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.42406 | + | 1.96004i | −0.126364 | + | 0.173926i | −0.867512 | − | 0.497417i | \(-0.834282\pi\) |
0.741147 | + | 0.671342i | \(0.234282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.11624 | + | 6.51313i | 0.186325 | + | 0.573449i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.37948 | − | 10.4010i | 0.295267 | − | 0.908737i | −0.687865 | − | 0.725839i | \(-0.741452\pi\) |
0.983132 | − | 0.182899i | \(-0.0585481\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.28058 | − | 0.416087i | −0.111041 | − | 0.0360793i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.23427 | − | 1.86456i | 0.106229 | − | 0.160476i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.19602 | + | 3.02256i | 0.187618 | + | 0.258235i | 0.892456 | − | 0.451134i | \(-0.148980\pi\) |
−0.704838 | + | 0.709368i | \(0.748980\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.73765 | − | 1.26247i | −0.147385 | − | 0.107082i | 0.511649 | − | 0.859194i | \(-0.329035\pi\) |
−0.659034 | + | 0.752113i | \(0.729035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.27216 | + | 4.55699i | −0.528211 | + | 0.383768i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.77392i | − | 0.315591i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.62269 | + | 12.3659i | 0.383894 | + | 1.02693i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.00347 | − | 1.62573i | 0.412680 | − | 0.134088i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.85344 | 0.643379 | 0.321690 | − | 0.946845i | \(-0.395749\pi\) | ||||
0.321690 | + | 0.946845i | \(0.395749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5124 | 1.83203 | 0.916016 | − | 0.401141i | \(-0.131386\pi\) | ||||
0.916016 | + | 0.401141i | \(0.131386\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.25004 | + | 0.406161i | −0.101059 | + | 0.0328362i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.29073 | − | 19.0739i | 0.424962 | − | 1.53205i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.4083i | − | 1.54895i | −0.632602 | − | 0.774477i | \(-0.718013\pi\) | ||
0.632602 | − | 0.774477i | \(-0.281987\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.19577 | + | 2.32186i | −0.253441 | + | 0.184136i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.34265 | + | 3.88166i | 0.421060 | + | 0.305918i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.89817 | + | 12.2473i | 0.696959 | + | 0.959281i | 0.999980 | + | 0.00629741i | \(0.00200454\pi\) |
−0.303022 | + | 0.952984i | \(0.597995\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.34884 | − | 0.928906i | −0.260707 | − | 0.0723152i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.9807 | + | 5.84227i | 1.39139 | + | 0.452089i | 0.906395 | − | 0.422431i | \(-0.138823\pi\) |
0.484990 | + | 0.874519i | \(0.338823\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.19518 | − | 6.75608i | 0.168860 | − | 0.519698i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.315522 | − | 0.971077i | −0.0241286 | − | 0.0742601i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1479 | − | 19.4729i | 1.07564 | − | 1.48050i | 0.211415 | − | 0.977396i | \(-0.432193\pi\) |
0.864228 | − | 0.503100i | \(-0.167807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.573980 | − | 6.56860i | −0.0433888 | − | 0.496539i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.61613 | + | 6.35355i | −0.346969 | + | 0.477562i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.461162 | − | 1.41931i | −0.0344689 | − | 0.106084i | 0.932342 | − | 0.361578i | \(-0.117762\pi\) |
−0.966811 | + | 0.255494i | \(0.917762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.809018 | + | 2.48990i | −0.0601338 | + | 0.185073i | −0.976611 | − | 0.215014i | \(-0.931020\pi\) |
0.916477 | + | 0.400087i | \(0.131020\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.33023 | + | 1.08206i | 0.246178 | + | 0.0799881i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.99446 | − | 8.79419i | −0.514243 | − | 0.646562i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.20071 | + | 1.65264i | 0.0878050 | + | 0.120853i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.06687 | − | 0.775127i | −0.0776035 | − | 0.0563822i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6599 | + | 12.1041i | −1.20547 | + | 0.875824i | −0.994811 | − | 0.101736i | \(-0.967560\pi\) |
−0.210657 | + | 0.977560i | \(0.567560\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.15953i | − | 0.371391i | −0.982607 | − | 0.185696i | \(-0.940546\pi\) | ||
0.982607 | − | 0.185696i | \(-0.0594539\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.52756 | + | 2.99707i | 0.324225 | + | 0.214625i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.99630 | − | 3.24799i | 0.712207 | − | 0.231410i | 0.0695657 | − | 0.997577i | \(-0.477839\pi\) |
0.642641 | + | 0.766167i | \(0.277839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.65216 | −0.258895 | −0.129447 | − | 0.991586i | \(-0.541320\pi\) | ||||
−0.129447 | + | 0.991586i | \(0.541320\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.33206 | −0.587698 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.40468 | − | 2.40593i | 0.519707 | − | 0.168863i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.9200 | + | 11.0712i | −0.972212 | + | 0.773249i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.00777i | 0.348064i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.28384 | + | 0.932763i | −0.0888049 | + | 0.0645206i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3259 | + | 15.4941i | 1.46813 | + | 1.06666i | 0.981150 | + | 0.193249i | \(0.0619026\pi\) |
0.486983 | + | 0.873411i | \(0.338097\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.61709 | − | 10.4840i | −0.521914 | − | 0.718354i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.667150 | + | 15.2988i | 0.0454993 | + | 1.04337i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.1022 | − | 3.60733i | −0.753669 | − | 0.244882i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.92899 | + | 12.0922i | −0.265497 | + | 0.817115i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.986247 | − | 3.03536i | −0.0663422 | − | 0.204180i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8706 | + | 14.9621i | −0.727950 | + | 1.00194i | 0.271272 | + | 0.962503i | \(0.412556\pi\) |
−0.999222 | + | 0.0394348i | \(0.987444\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.77389 | − | 3.27990i | 0.251593 | − | 0.218660i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.9690 | − | 15.0976i | 0.728039 | − | 1.00206i | −0.271179 | − | 0.962529i | \(-0.587414\pi\) |
0.999218 | − | 0.0395311i | \(-0.0125864\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.63423 | − | 26.5734i | −0.570566 | − | 1.75602i | −0.650803 | − | 0.759247i | \(-0.725568\pi\) |
0.0802368 | − | 0.996776i | \(-0.474432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.633347 | + | 1.94924i | −0.0416712 | + | 0.128251i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.5456 | − | 7.65043i | −1.54252 | − | 0.501196i | −0.590452 | − | 0.807073i | \(-0.701050\pi\) |
−0.952071 | + | 0.305877i | \(0.901050\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.2383 | + | 6.07028i | −1.05927 | + | 0.395981i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.735329 | + | 1.01209i | 0.0477647 | + | 0.0657425i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.47102 | − | 6.88110i | −0.612629 | − | 0.445101i | 0.237710 | − | 0.971336i | \(-0.423603\pi\) |
−0.850339 | + | 0.526235i | \(0.823603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.1221 | + | 17.5257i | −1.55384 | + | 1.12893i | −0.612998 | + | 0.790084i | \(0.710037\pi\) |
−0.940842 | + | 0.338846i | \(0.889963\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.7527 | − | 0.512514i | 0.750853 | − | 0.0327433i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.35799 | − | 0.766156i | 0.150035 | − | 0.0487493i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.20689 | −0.520090 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.87297 | −0.181340 | −0.0906700 | − | 0.995881i | \(-0.528901\pi\) | ||||
−0.0906700 | + | 0.995881i | \(0.528901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.40212 | − | 2.40510i | 0.465367 | − | 0.151207i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.93622 | + | 0.128043i | −0.183873 | + | 0.00801837i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.11716i | 0.506334i | 0.967423 | + | 0.253167i | \(0.0814723\pi\) | ||||
−0.967423 | + | 0.253167i | \(0.918528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.36118 | + | 3.89512i | −0.333127 | + | 0.242031i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.77643 | + | 3.47028i | 0.295654 | + | 0.214805i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.1117 | + | 18.0467i | 0.808501 | + | 1.11281i | 0.991553 | + | 0.129703i | \(0.0414025\pi\) |
−0.183051 | + | 0.983103i | \(0.558597\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.27368 | + | 3.09291i | −0.508248 | + | 0.189996i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.10676 | + | 2.95897i | 0.557325 | + | 0.181086i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.53369 | − | 7.79789i | 0.154482 | − | 0.475446i | −0.843626 | − | 0.536931i | \(-0.819584\pi\) |
0.998108 | + | 0.0614851i | \(0.0195837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.93158 | − | 9.02246i | −0.178081 | − | 0.548075i | 0.821680 | − | 0.569949i | \(-0.193037\pi\) |
−0.999761 | + | 0.0218733i | \(0.993037\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.88218 | − | 2.59059i | 0.113915 | − | 0.156790i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.66060 | − | 4.00305i | −0.401649 | − | 0.241393i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.270190 | − | 0.371885i | 0.0162341 | − | 0.0223444i | −0.800823 | − | 0.598901i | \(-0.795604\pi\) |
0.817057 | + | 0.576557i | \(0.195604\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.73547 | − | 8.41891i | −0.163768 | − | 0.504027i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.71493 | + | 14.5111i | −0.281269 | + | 0.865658i | 0.706223 | + | 0.707990i | \(0.250398\pi\) |
−0.987492 | + | 0.157668i | \(0.949602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1502 | + | 3.29800i | 0.603366 | + | 0.196046i | 0.594741 | − | 0.803917i | \(-0.297255\pi\) |
0.00862506 | + | 0.999963i | \(0.497255\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0994689 | − | 2.28097i | −0.00589203 | − | 0.135113i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.16543 | + | 8.48598i | 0.363934 | + | 0.500912i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3557 | − | 8.97692i | −0.726804 | − | 0.528054i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.1654 | + | 9.56522i | −0.771770 | + | 0.560723i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.8334i | − | 1.80130i | −0.434541 | − | 0.900652i | \(-0.643089\pi\) | ||
0.434541 | − | 0.900652i | \(-0.356911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.7438 | + | 10.9311i | −0.800195 | + | 0.636435i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.47813 | + | 0.480272i | −0.0857696 | + | 0.0278682i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.1600 | −0.703229 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.03104 | 0.520541 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.36132 | − | 1.74200i | 0.308000 | − | 0.100075i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.52897 | + | 4.32193i | 0.373848 | + | 0.247473i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.8634i | 1.01952i | 0.860318 | + | 0.509758i | \(0.170265\pi\) | ||||
−0.860318 | + | 0.509758i | \(0.829735\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.80673 | − | 4.94538i | 0.387221 | − | 0.281333i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.75942 | + | 7.09063i | 0.553406 | + | 0.402073i | 0.829040 | − | 0.559190i | \(-0.188888\pi\) |
−0.275634 | + | 0.961263i | \(0.588888\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0264 | + | 15.1766i | 0.623250 | + | 0.857830i | 0.997584 | − | 0.0694641i | \(-0.0221289\pi\) |
−0.374335 | + | 0.927294i | \(0.622129\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.83552 | − | 2.30782i | −0.103420 | − | 0.130031i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.1912 | − | 3.31133i | −0.572395 | − | 0.185983i | 0.00849553 | − | 0.999964i | \(-0.497296\pi\) |
−0.580891 | + | 0.813981i | \(0.697296\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.83552 | − | 8.72685i | 0.158759 | − | 0.488610i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.637181 | − | 1.96104i | −0.0355640 | − | 0.109455i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.788827 | + | 1.08573i | −0.0438915 | + | 0.0604115i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.96430 | + | 9.16383i | 0.441780 | + | 0.508318i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.21372 | − | 11.3052i | 0.454219 | − | 0.625179i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.15934 | + | 9.72344i | 0.174180 | + | 0.536071i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.671547 | − | 2.06681i | 0.0369116 | − | 0.113602i | −0.930903 | − | 0.365266i | \(-0.880978\pi\) |
0.967815 | + | 0.251664i | \(0.0809779\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.77919 | − | 1.55285i | −0.261898 | − | 0.0850959i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.9532 | − | 4.97988i | −0.980887 | − | 0.272080i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.91844 | − | 8.14603i | −0.322398 | − | 0.443743i | 0.616800 | − | 0.787120i | \(-0.288429\pi\) |
−0.939197 | + | 0.343378i | \(0.888429\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.81862 | + | 3.50093i | 0.261711 | + | 0.190144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.1304 | + | 8.08674i | −0.602747 | + | 0.437922i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.1688i | − | 0.873035i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.99303 | + | 10.7903i | −0.161139 | + | 0.580931i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.9570 | − | 4.53489i | 0.749249 | − | 0.243446i | 0.0905912 | − | 0.995888i | \(-0.471124\pi\) |
0.658658 | + | 0.752442i | \(0.271124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.5685 | −0.993949 | −0.496974 | − | 0.867765i | \(-0.665556\pi\) | ||||
−0.496974 | + | 0.867765i | \(0.665556\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.42822 | 0.129609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5663 | − | 5.70763i | 0.934959 | − | 0.303787i | 0.198370 | − | 0.980127i | \(-0.436435\pi\) |
0.736589 | + | 0.676340i | \(0.236435\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1466 | − | 27.1426i | −0.538524 | − | 1.44058i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.73329i | 0.0917352i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.9550 | + | 14.4981i | −1.05318 | + | 0.765182i | −0.972815 | − | 0.231583i | \(-0.925609\pi\) |
−0.0803676 | + | 0.996765i | \(0.525609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5279 | + | 10.5551i | 0.764626 | + | 0.555533i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.04583 | − | 6.94499i | −0.264837 | − | 0.364517i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.6931 | + | 23.7069i | −0.821413 | + | 1.24088i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4469 | + | 4.04423i | 0.649721 | + | 0.211107i | 0.615291 | − | 0.788300i | \(-0.289038\pi\) |
0.0344301 | + | 0.999407i | \(0.489038\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.45795 | + | 7.56478i | −0.127956 | + | 0.393807i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.60973 | + | 4.95425i | 0.0835733 | + | 0.257212i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.174079 | + | 0.239599i | −0.00901348 | + | 0.0124060i | −0.813500 | − | 0.581565i | \(-0.802441\pi\) |
0.804486 | + | 0.593971i | \(0.202441\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0920 | − | 4.81166i | 0.521147 | − | 0.248473i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.42659 | + | 11.5982i | −0.433992 | + | 0.597338i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.41901 | − | 7.44495i | −0.124256 | − | 0.382421i | 0.869509 | − | 0.493918i | \(-0.164436\pi\) |
−0.993765 | + | 0.111496i | \(0.964436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.748670 | + | 2.30417i | −0.0383555 | + | 0.118046i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.8293 | − | 6.44294i | −1.01323 | − | 0.329219i | −0.245090 | − | 0.969500i | \(-0.578818\pi\) |
−0.768140 | + | 0.640282i | \(0.778818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.52970 | + | 3.82152i | −0.128925 | + | 0.194763i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.02534 | + | 5.54040i | 0.204619 | + | 0.281634i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.6010 | − | 16.4206i | −1.14592 | − | 0.832558i | −0.157985 | − | 0.987441i | \(-0.550500\pi\) |
−0.987933 | + | 0.154883i | \(0.950500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.32498 | − | 3.86883i | 0.269296 | − | 0.195655i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.9362i | − | 0.551660i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.979517 | + | 2.62026i | 0.0492848 | + | 0.131839i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.6358 | − | 9.95418i | 1.53757 | − | 0.499586i | 0.586863 | − | 0.809686i | \(-0.300363\pi\) |
0.950704 | + | 0.310100i | \(0.100363\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.34649 | −0.0674086 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3441 | −0.516562 | −0.258281 | − | 0.966070i | \(-0.583156\pi\) | ||||
−0.258281 | + | 0.966070i | \(0.583156\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.4429 | − | 6.64232i | 1.01834 | − | 0.330877i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.597677 | − | 2.15471i | 0.0296988 | − | 0.107068i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.81004i | 0.387129i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.7399 | − | 21.6073i | 1.47054 | − | 1.06841i | 0.490087 | − | 0.871673i | \(-0.336965\pi\) |
0.980456 | − | 0.196739i | \(-0.0630351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.02256 | + | 2.19602i | 0.149092 | + | 0.108322i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.08740 | + | 8.37859i | 0.299542 | + | 0.412284i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.6835 | − | 4.90507i | −0.868048 | − | 0.240780i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.04272 | − | 0.663721i | −0.100033 | − | 0.0325026i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.74262 | − | 26.9070i | 0.427105 | − | 1.31449i | −0.473859 | − | 0.880601i | \(-0.657139\pi\) |
0.900964 | − | 0.433894i | \(-0.142861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.392142 | + | 1.20689i | 0.0191118 | + | 0.0588202i | 0.960158 | − | 0.279459i | \(-0.0901551\pi\) |
−0.941046 | + | 0.338279i | \(0.890155\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.55699 | + | 6.27216i | −0.221568 | + | 0.304963i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.40323 | − | 1.47901i | −0.310602 | − | 0.0717427i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.71420 | − | 3.73577i | 0.131349 | − | 0.180787i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.16621 | − | 3.58921i | −0.0563049 | − | 0.173289i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.24011 | − | 6.89434i | 0.107902 | − | 0.332089i | −0.882498 | − | 0.470315i | \(-0.844140\pi\) |
0.990401 | + | 0.138226i | \(0.0441402\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.64988 | + | 1.18592i | 0.175402 | + | 0.0569916i | 0.395401 | − | 0.918508i | \(-0.370606\pi\) |
−0.219999 | + | 0.975500i | \(0.570606\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.21772 | + | 10.3322i | 0.394010 | + | 0.495392i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00546 | + | 4.13666i | 0.143771 | + | 0.197883i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.5358 | + | 18.5528i | 1.21876 | + | 0.885479i | 0.995996 | − | 0.0893940i | \(-0.0284930\pi\) |
0.222761 | + | 0.974873i | \(0.428493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.25621 | − | 3.09232i | 0.202677 | − | 0.147253i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.65284i | 0.126040i | 0.998012 | + | 0.0630200i | \(0.0200732\pi\) | ||||
−0.998012 | + | 0.0630200i | \(0.979927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.8539 | + | 11.8186i | 0.846358 | + | 0.560256i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.46907 | − | 2.42685i | 0.353275 | − | 0.114786i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.3646 | 1.29142 | 0.645709 | − | 0.763584i | \(-0.276562\pi\) | ||||
0.645709 | + | 0.763584i | \(0.276562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.3622 | 0.582113 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.4106 | − | 6.95671i | 1.00596 | − | 0.326855i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.60389 | − | 4.45705i | 0.262714 | − | 0.208950i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.66698i | − | 0.0779781i | −0.999240 | − | 0.0389891i | \(-0.987586\pi\) | ||
0.999240 | − | 0.0389891i | \(-0.0124138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.06334 | + | 0.772564i | −0.0496326 | + | 0.0360602i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.8272 | + | 20.2176i | 1.29604 | + | 0.941630i | 0.999909 | − | 0.0135170i | \(-0.00430273\pi\) |
0.296133 | + | 0.955147i | \(0.404303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.7939 | − | 28.6204i | −0.966377 | − | 1.33010i | −0.943856 | − | 0.330357i | \(-0.892831\pi\) |
−0.0225205 | − | 0.999746i | \(-0.507169\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.862362 | − | 19.7753i | −0.0399911 | − | 0.917055i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.9613 | + | 7.46057i | 1.06252 | + | 0.345234i | 0.787571 | − | 0.616224i | \(-0.211338\pi\) |
0.274951 | + | 0.961458i | \(0.411338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.39538 | + | 10.4499i | −0.156784 | + | 0.482532i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.99751 | − | 18.4584i | −0.276351 | − | 0.850520i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.25615 | − | 8.61086i | 0.287658 | − | 0.395928i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.14896 | − | 4.97428i | 0.0527177 | − | 0.228236i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.32186 | + | 3.19577i | −0.106311 | + | 0.146324i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.03656 | + | 21.6563i | 0.321509 | + | 0.989502i | 0.972992 | + | 0.230839i | \(0.0741470\pi\) |
−0.651483 | + | 0.758663i | \(0.725853\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.77067 | − | 11.6049i | 0.171928 | − | 0.529139i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.28066 | + | 2.04071i | 0.285780 | + | 0.0928555i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.0846 | + | 12.7416i | −1.54770 | + | 0.578568i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.49973 | − | 7.56973i | −0.249217 | − | 0.343017i | 0.666020 | − | 0.745934i | \(-0.267996\pi\) |
−0.915237 | + | 0.402917i | \(0.867996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.2473 | + | 8.89817i | 0.553841 | + | 0.402389i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7363 | + | 10.7066i | −0.665042 | + | 0.483181i | −0.868362 | − | 0.495931i | \(-0.834827\pi\) |
0.203320 | + | 0.979112i | \(0.434827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.76000i | − | 0.349493i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.47198 | + | 0.151407i | −0.156054 | + | 0.00680523i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.2529 | + | 5.28089i | −0.729043 | + | 0.236880i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.14936 | −0.275283 | −0.137642 | − | 0.990482i | \(-0.543952\pi\) | ||||
−0.137642 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.9060 | 0.844657 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.0653 | + | 4.89502i | −0.671730 | + | 0.218258i | −0.624971 | − | 0.780648i | \(-0.714889\pi\) |
−0.0467590 | + | 0.998906i | \(0.514889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.5932 | − | 0.549168i | 0.560392 | − | 0.0244377i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.10376i | − | 0.315489i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.09898 | + | 2.97808i | −0.181684 | + | 0.132001i | −0.674910 | − | 0.737900i | \(-0.735818\pi\) |
0.493226 | + | 0.869901i | \(0.335818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.5647 | + | 9.85535i | 0.600068 | + | 0.435975i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.600159 | − | 0.826047i | −0.0264976 | − | 0.0364709i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.6223 | − | 6.58764i | 0.776530 | − | 0.290286i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.4596 | + | 3.72346i | 0.503994 | + | 0.163758i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.43798 | − | 22.8918i | 0.326491 | − | 1.00484i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2578 | − | 34.6481i | −0.493215 | − | 1.51796i | −0.819720 | − | 0.572764i | \(-0.805871\pi\) |
0.326505 | − | 0.945195i | \(-0.394129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.80572 | + | 9.36727i | −0.297593 | + | 0.409602i | −0.931462 | − | 0.363839i | \(-0.881466\pi\) |
0.633869 | + | 0.773441i | \(0.281466\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.57570 | − | 6.06974i | −0.112413 | − | 0.264905i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.83887 | + | 9.41289i | −0.297906 | + | 0.410032i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.642075 | − | 1.97610i | −0.0279163 | − | 0.0859175i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.42684 | + | 7.46905i | −0.105316 | + | 0.324129i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.3689 | − | 5.96843i | −0.795647 | − | 0.258521i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.200873 | − | 4.60631i | −0.00868448 | − | 0.199148i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.877183 | − | 1.20734i | −0.0378532 | − | 0.0521005i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.61498 | − | 4.80606i | −0.284927 | − | 0.207012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2715 | + | 12.5485i | −0.742559 | + | 0.539500i | −0.893511 | − | 0.449041i | \(-0.851766\pi\) |
0.150953 | + | 0.988541i | \(0.451766\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.61804i | 0.112351i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.4550 | − | 19.4503i | 1.04754 | − | 0.833160i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.1049 | + | 7.83217i | −1.03065 | + | 0.334879i | −0.775048 | − | 0.631902i | \(-0.782274\pi\) |
−0.255604 | + | 0.966781i | \(0.582274\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.50161 | 0.149445 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.02827 | 0.256813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.56900 | − | 0.509800i | 0.0667207 | − | 0.0216789i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.36968 | − | 6.20236i | −0.397721 | − | 0.263276i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.953134i | 0.0403856i | 0.999796 | + | 0.0201928i | \(0.00642800\pi\) | ||||
−0.999796 | + | 0.0201928i | \(0.993572\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4533 | + | 9.77439i | −0.569014 | + | 0.413413i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.65264 | + | 1.20071i | 0.0697746 | + | 0.0506942i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.9315 | + | 24.6806i | 0.755723 | + | 1.04016i | 0.997558 | + | 0.0698461i | \(0.0222508\pi\) |
−0.241835 | + | 0.970317i | \(0.577749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.29030 | + | 10.4235i | 0.348776 | + | 0.438519i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.25418 | − | 0.407508i | −0.0526707 | − | 0.0171137i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.81510 | + | 30.2078i | −0.411471 | + | 1.26638i | 0.503899 | + | 0.863762i | \(0.331898\pi\) |
−0.915370 | + | 0.402614i | \(0.868102\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.65796 | − | 26.6465i | −0.362324 | − | 1.11512i | −0.951640 | − | 0.307217i | \(-0.900602\pi\) |
0.589315 | − | 0.807903i | \(-0.299398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.1041 | + | 16.6599i | −0.505657 | + | 0.695977i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.8982 | + | 21.4611i | −0.537893 | + | 0.894991i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.33187 | + | 4.58593i | −0.138708 | + | 0.190915i | −0.872719 | − | 0.488222i | \(-0.837646\pi\) |
0.734012 | + | 0.679137i | \(0.237646\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.59438 | − | 4.90701i | −0.0662603 | − | 0.203928i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.34438 | + | 10.2929i | −0.138748 | + | 0.427023i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.83888 | + | 1.89717i | 0.241822 | + | 0.0785726i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.23211 | + | 1.45129i | 0.216321 | + | 0.0600034i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.9949 | − | 27.5206i | −0.825278 | − | 1.13590i | −0.988784 | − | 0.149355i | \(-0.952280\pi\) |
0.163506 | − | 0.986542i | \(-0.447720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.31231 | − | 5.31270i | −0.301298 | − | 0.218906i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.50336 | − | 6.17805i | 0.349781 | − | 0.254131i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.9225i | 0.941313i | 0.882316 | + | 0.470657i | \(0.155983\pi\) | ||||
−0.882316 | + | 0.470657i | \(0.844017\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.03594 | + | 3.73473i | −0.0424696 | + | 0.153109i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.47341 | + | 1.12858i | −0.142157 | + | 0.0461896i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.7017 | 0.723270 | 0.361635 | − | 0.932320i | \(-0.382219\pi\) | ||||
0.361635 | + | 0.932320i | \(0.382219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.8773 | −1.17793 | −0.588964 | − | 0.808159i | \(-0.700464\pi\) | ||||
−0.588964 | + | 0.808159i | \(0.700464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.92426 | + | 2.57475i | −0.322701 | + | 0.104852i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.72145 | − | 17.9802i | −0.273266 | − | 0.731000i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.5926i | 0.470528i | 0.971932 | + | 0.235264i | \(0.0755954\pi\) | ||||
−0.971932 | + | 0.235264i | \(0.924405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.29880 | − | 4.57634i | 0.255240 | − | 0.185443i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.2302 | − | 11.0654i | −0.616146 | − | 0.447657i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.48123 | − | 10.2970i | −0.302164 | − | 0.415893i | 0.630754 | − | 0.775983i | \(-0.282746\pi\) |
−0.932917 | + | 0.360090i | \(0.882746\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.81746 | + | 14.8309i | −0.395878 | + | 0.598038i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.7643 | − | 13.2451i | −1.64111 | − | 0.533229i | −0.664323 | − | 0.747446i | \(-0.731280\pi\) |
−0.976786 | + | 0.214217i | \(0.931280\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.30448 | + | 13.2478i | −0.173012 | + | 0.532475i | −0.999537 | − | 0.0304242i | \(-0.990314\pi\) |
0.826525 | + | 0.562899i | \(0.190314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.54749 | + | 4.76268i | 0.0620985 | + | 0.191120i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.42216 | − | 10.2157i | 0.297363 | − | 0.409285i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.6211 | − | 4.33601i | 0.984844 | − | 0.173441i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.932763 | + | 1.28384i | −0.0372510 | + | 0.0512715i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.04102 | + | 6.28160i | 0.0813806 | + | 0.250464i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.66089 | + | 8.18939i | −0.105928 | + | 0.326014i | −0.989947 | − | 0.141437i | \(-0.954828\pi\) |
0.884019 | + | 0.467451i | \(0.154828\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.0701 | + | 8.14575i | 0.996445 | + | 0.323765i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.99032 | + | 4.51736i | −0.118667 | + | 0.179266i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.50882 | + | 10.3350i | 0.297510 | + | 0.409488i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.4840 | − | 7.61709i | −0.414742 | − | 0.301327i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0591 | − | 12.3942i | 0.673794 | − | 0.489540i | −0.197499 | − | 0.980303i | \(-0.563282\pi\) |
0.871293 | + | 0.490763i | \(0.163282\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.2412i | − | 0.482747i | −0.970432 | − | 0.241374i | \(-0.922402\pi\) | ||
0.970432 | − | 0.241374i | \(-0.0775979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.36207 | + | 14.3438i | 0.211131 | + | 0.564787i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.7461 | − | 3.49162i | 0.422472 | − | 0.137270i | −0.0900623 | − | 0.995936i | \(-0.528707\pi\) |
0.512535 | + | 0.858667i | \(0.328707\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.2057 | 0.479117 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.6736 | −0.457524 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.2319 | + | 6.57373i | −0.791734 | + | 0.257250i | −0.676842 | − | 0.736128i | \(-0.736652\pi\) |
−0.114892 | + | 0.993378i | \(0.536652\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.53633 | − | 23.5644i | 0.255396 | − | 0.920738i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.7145i | 0.496039i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.9986 | + | 10.8971i | −0.584263 | + | 0.424492i | −0.840258 | − | 0.542186i | \(-0.817597\pi\) |
0.255995 | + | 0.966678i | \(0.417597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0800 | − | 11.6828i | −0.625441 | − | 0.454409i | 0.229377 | − | 0.973338i | \(-0.426331\pi\) |
−0.854818 | + | 0.518928i | \(0.826331\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.87595 | − | 2.58203i | −0.0728560 | − | 0.100278i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.90129 | − | 0.804763i | −0.112507 | − | 0.0312074i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.1188 | − | 9.13635i | −1.08876 | − | 0.353761i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.71502 | + | 17.5890i | −0.220955 | + | 0.680031i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.68173 | − | 5.17583i | −0.0649224 | − | 0.199811i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.6055 | + | 35.2430i | −0.987021 | + | 1.35852i | −0.0540603 | + | 0.998538i | \(0.517216\pi\) |
−0.932960 | + | 0.359980i | \(0.882784\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.57564 | − | 4.28557i | 0.0991365 | − | 0.164951i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.73904 | + | 3.76996i | −0.105270 | + | 0.144891i | −0.858402 | − | 0.512978i | \(-0.828542\pi\) |
0.753132 | + | 0.657870i | \(0.228542\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.63152 | + | 20.4097i | 0.254494 | + | 0.783253i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.76675 | − | 17.7482i | 0.220982 | − | 0.680114i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.0242 | − | 12.0299i | −1.41669 | − | 0.460311i | −0.502141 | − | 0.864786i | \(-0.667454\pi\) |
−0.914549 | + | 0.404475i | \(0.867454\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.20024 | + | 6.53830i | 0.198691 | + | 0.249816i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.4233 | − | 22.6047i | −0.626588 | − | 0.862424i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.76002 | − | 5.63798i | −0.295633 | − | 0.214790i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.81060 | − | 5.67473i | 0.297129 | − | 0.215877i | −0.429225 | − | 0.903198i | \(-0.641213\pi\) |
0.726354 | + | 0.687321i | \(0.241213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.04956i | 0.0778562i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.00479 | − | 2.65102i | −0.151910 | − | 0.100559i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.94289 | − | 3.23064i | 0.376614 | − | 0.122369i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.7573 | −0.936407 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.6430 | 0.704135 | 0.352068 | − | 0.935975i | \(-0.385479\pi\) | ||||
0.352068 | + | 0.935975i | \(0.385479\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.87980 | + | 1.58554i | −0.184045 | + | 0.0597999i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.5677 | + | 10.7911i | −0.510990 | + | 0.406416i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 7.43395i | − | 0.279582i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.85935 | + | 7.16324i | −0.370276 | + | 0.269021i | −0.757325 | − | 0.653038i | \(-0.773494\pi\) |
0.387050 | + | 0.922059i | \(0.373494\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.01209 | + | 0.735329i | 0.0379565 | + | 0.0275770i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26.0563 | + | 35.8634i | 0.975817 | + | 1.34310i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.367649 | − | 8.43073i | −0.0137493 | − | 0.315291i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.1338 | − | 3.61761i | −0.415801 | − | 0.135102i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.2311 | − | 40.7210i | 0.493435 | − | 1.51864i | −0.325947 | − | 0.945388i | \(-0.605683\pi\) |
0.819382 | − | 0.573248i | \(-0.194317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.42860 | − | 10.5522i | −0.127688 | − | 0.392983i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.5257 | + | 24.1221i | −0.651788 | + | 0.897110i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.5315 | + | 27.1745i | 0.428269 | + | 1.00923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.631037 | − | 0.868548i | 0.0234039 | − | 0.0322126i | −0.797155 | − | 0.603775i | \(-0.793663\pi\) |
0.820559 | + | 0.571562i | \(0.193663\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.78152 | − | 8.56063i | 0.102878 | − | 0.316626i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.773538 | + | 0.251338i | 0.0285713 | + | 0.00928337i | 0.323268 | − | 0.946308i | \(-0.395219\pi\) |
−0.294696 | + | 0.955591i | \(0.595219\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.0191 | − | 4.11921i | 0.406446 | − | 0.151940i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.61160 | + | 10.4765i | 0.280377 | + | 0.385906i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.6000 | + | 22.2322i | 1.12564 | + | 0.817824i | 0.985054 | − | 0.172244i | \(-0.0551018\pi\) |
0.140585 | + | 0.990069i | \(0.455102\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00582 | − | 1.45732i | 0.0736857 | − | 0.0535358i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 45.7517i | 1.67847i | 0.543772 | + | 0.839233i | \(0.316996\pi\) | ||||
−0.543772 | + | 0.839233i | \(0.683004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.5442 | − | 0.765068i | 0.642768 | − | 0.0280299i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.80521 | + | 2.53607i | −0.285578 | + | 0.0927899i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.71916 | −0.0993560 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.1925 | −1.43016 | −0.715078 | − | 0.699045i | \(-0.753609\pi\) | ||||
−0.715078 | + | 0.699045i | \(0.753609\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.73235 | + | 0.887796i | −0.0995725 | + | 0.0323531i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 50.2915 | − | 2.19312i | 1.83029 | − | 0.0798157i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.48615i | − | 0.163052i | −0.996671 | − | 0.0815259i | \(-0.974021\pi\) | ||
0.996671 | − | 0.0815259i | \(-0.0259793\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.29662 | − | 4.57476i | 0.228553 | − | 0.166053i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.2776 | − | 12.5529i | −0.626312 | − | 0.455043i | 0.228808 | − | 0.973471i | \(-0.426517\pi\) |
−0.855121 | + | 0.518429i | \(0.826517\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8316 | − | 14.9085i | −0.392131 | − | 0.539723i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.75294 | + | 1.02912i | −0.0995328 | + | 0.0372078i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.1365 | − | 5.89290i | −0.654870 | − | 0.212780i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.94179 | + | 24.4423i | −0.286388 | + | 0.881413i | 0.699591 | + | 0.714544i | \(0.253366\pi\) |
−0.985979 | + | 0.166869i | \(0.946634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.50834 | + | 7.71988i | 0.0903357 | + | 0.278025i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.4223 | − | 23.9797i | 0.626636 | − | 0.862490i | −0.371179 | − | 0.928561i | \(-0.621046\pi\) |
0.997815 | + | 0.0660712i | \(0.0210465\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.96107 | − | 43.1254i | 0.357812 | − | 1.54911i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.89512 | + | 5.36118i | −0.139737 | + | 0.192331i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.50969 | + | 7.72403i | 0.0899189 | + | 0.276742i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.22383 | + | 19.1550i | −0.222706 | + | 0.685420i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.61503 | + | 1.82443i | 0.200665 | + | 0.0651999i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.89073 | − | 43.3572i | −0.0674829 | − | 1.54748i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.72360 | − | 6.50148i | −0.168378 | − | 0.231753i | 0.716486 | − | 0.697601i | \(-0.245749\pi\) |
−0.884865 | + | 0.465848i | \(0.845749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.0467 | + | 13.1117i | 0.642479 | + | 0.466789i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.35443 | − | 4.61676i | 0.225938 | − | 0.164153i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.50268i | 0.301939i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.91298 | + | 5.49824i | −0.245178 | + | 0.195002i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.6232 | − | 5.07628i | 0.553401 | − | 0.179811i | −0.0189486 | − | 0.999820i | \(-0.506032\pi\) |
0.572350 | + | 0.820009i | \(0.306032\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.1900 | 0.360497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.57541 | 0.338331 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.7936 | − | 6.10642i | 0.663213 | − | 0.215491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.3133 | + | 8.15095i | 0.433988 | + | 0.287283i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.19918i | − | 0.288625i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39.2743 | − | 28.5344i | 1.38081 | − | 1.00322i | 0.384006 | − | 0.923330i | \(-0.374544\pi\) |
0.996804 | − | 0.0798870i | \(-0.0254560\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2584 | − | 12.5390i | −0.606024 | − | 0.440302i | 0.241988 | − | 0.970279i | \(-0.422201\pi\) |
−0.848012 | + | 0.529977i | \(0.822201\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.57619 | − | 7.67496i | −0.195565 | − | 0.269173i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.0711 | + | 26.4929i | 0.738090 | + | 0.928006i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.65024 | + | 2.16079i | 0.232662 | + | 0.0755966i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.989519 | − | 3.04543i | 0.0345766 | − | 0.106416i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.922371 | + | 2.83877i | 0.0321910 | + | 0.0990736i | 0.965861 | − | 0.259061i | \(-0.0834130\pi\) |
−0.933670 | + | 0.358134i | \(0.883413\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.01233 | + | 2.76974i | −0.0701455 | + | 0.0965469i | −0.842648 | − | 0.538464i | \(-0.819005\pi\) |
0.772503 | + | 0.635011i | \(0.219005\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.57162 | − | 1.74889i | −0.263610 | − | 0.0608884i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.58186 | − | 6.30639i | 0.159327 | − | 0.219295i | −0.721889 | − | 0.692009i | \(-0.756726\pi\) |
0.881216 | + | 0.472715i | \(0.156726\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.65047 | + | 20.4680i | 0.230980 | + | 0.710884i | 0.997629 | + | 0.0688179i | \(0.0219227\pi\) |
−0.766649 | + | 0.642067i | \(0.778077\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.142047 | − | 0.437177i | 0.00492757 | − | 0.0151655i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.57639 | − | 2.13680i | −0.227858 | − | 0.0740357i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 40.7370 | + | 11.2997i | 1.40976 | + | 0.391041i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.20317 | − | 7.16155i | −0.179848 | − | 0.247540i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.31004 | + | 2.40488i | 0.114275 | + | 0.0830258i | 0.643455 | − | 0.765484i | \(-0.277500\pi\) |
−0.529180 | + | 0.848510i | \(0.677500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.73850 | + | 3.44272i | −0.163397 | + | 0.118715i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.2578i | 0.525508i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.24575 | − | 15.3066i | 0.146058 | − | 0.526562i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.7665 | + | 3.49825i | −0.369941 | + | 0.120201i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.6725 | 0.366281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.1648 | 0.862637 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.8815 | + | 7.75958i | −0.817688 | + | 0.265683i | −0.687850 | − | 0.725852i | \(-0.741446\pi\) |
−0.129837 | + | 0.991535i | \(0.541446\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.799459 | − | 2.13859i | −0.0273409 | − | 0.0731384i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 35.8315i | − | 1.22398i | −0.790865 | − | 0.611991i | \(-0.790369\pi\) | ||
0.790865 | − | 0.611991i | \(-0.209631\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.2363 | + | 16.8821i | −0.792811 | + | 0.576011i | −0.908796 | − | 0.417240i | \(-0.862997\pi\) |
0.115985 | + | 0.993251i | \(0.462997\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.48598 | + | 6.16543i | 0.289202 | + | 0.210117i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.3598 | + | 17.0119i | 0.420734 | + | 0.579090i | 0.965795 | − | 0.259306i | \(-0.0834937\pi\) |
−0.545062 | + | 0.838396i | \(0.683494\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.7086 | − | 44.8796i | 1.01012 | − | 1.52595i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.5250 | − | 4.71945i | −0.493293 | − | 0.160281i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.600828 | − | 1.84916i | 0.0203817 | − | 0.0627284i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.25204 | − | 19.2418i | −0.211842 | − | 0.651984i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.56522 | + | 13.1654i | −0.323734 | + | 0.445581i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.92214 | − | 14.6180i | −0.0649802 | − | 0.494177i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.13682 | − | 5.69384i | 0.139690 | − | 0.192267i | −0.733440 | − | 0.679754i | \(-0.762086\pi\) |
0.873130 | + | 0.487487i | \(0.162086\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.52803 | − | 29.3243i | −0.321373 | − | 0.989083i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.1220 | − | 46.5406i | 0.509472 | − | 1.56799i | −0.283649 | − | 0.958928i | \(-0.591545\pi\) |
0.793121 | − | 0.609064i | \(-0.208455\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.09007 | − | 2.62862i | −0.272252 | − | 0.0884602i | 0.169709 | − | 0.985494i | \(-0.445717\pi\) |
−0.441961 | + | 0.897034i | \(0.645717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.69322 | + | 14.6432i | −0.325834 | + | 0.492225i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.7983 | − | 27.2500i | −0.664761 | − | 0.914966i | 0.334866 | − | 0.942266i | \(-0.391309\pi\) |
−0.999627 | + | 0.0273002i | \(0.991309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.58476 | + | 1.87794i | 0.0866901 | + | 0.0629840i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.25737 | + | 0.913532i | −0.0421235 | + | 0.0306045i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.91602i | 0.264899i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.16848 | − | 3.12574i | −0.0390579 | − | 0.104482i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.5648 | + | 3.75764i | −0.386138 | + | 0.125464i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 52.2631 | 1.74307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.19199 | 0.172970 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.58903 | − | 2.79075i | 0.285825 | − | 0.0928702i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.56474 | + | 5.64112i | −0.0520137 | + | 0.187517i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.2382i | 1.40250i | 0.712918 | + | 0.701248i | \(0.247373\pi\) | ||||
−0.712918 | + | 0.701248i | \(0.752627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.56061 | − | 3.31348i | 0.151266 | − | 0.109901i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4371 | + | 22.1138i | 1.00843 | + | 0.732664i | 0.963878 | − | 0.266343i | \(-0.0858153\pi\) |
0.0445478 | + | 0.999007i | \(0.485815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.49726 | + | 10.3191i | 0.248123 | + | 0.341512i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.54497 | + | 2.09283i | 0.249429 | + | 0.0691869i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.7160 | − | 4.45661i | −0.452943 | − | 0.147170i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.7537 | + | 36.1742i | −0.387719 | + | 1.19328i | 0.546769 | + | 0.837283i | \(0.315857\pi\) |
−0.934488 | + | 0.355993i | \(0.884143\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.52009 | + | 16.9891i | 0.181893 | + | 0.559809i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.4960 | − | 25.4575i | 0.608802 | − | 0.837944i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4819 | − | 18.9643i | −0.541923 | − | 0.623544i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.94538 | − | 6.80673i | 0.162427 | − | 0.223562i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.91592 | + | 24.3627i | 0.259713 | + | 0.799314i | 0.992864 | + | 0.119249i | \(0.0380486\pi\) |
−0.733152 | + | 0.680065i | \(0.761951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65995 | − | 5.10880i | 0.0544027 | − | 0.167434i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.4729 | + | 3.72777i | 0.375605 | + | 0.122042i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.84333 | + | 3.57494i | 0.0929868 | + | 0.116913i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.3315 | + | 30.7367i | 0.729538 | + | 1.00412i | 0.999153 | + | 0.0411552i | \(0.0131038\pi\) |
−0.269614 | + | 0.962968i | \(0.586896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.1766 | + | 11.0264i | 0.495268 | + | 0.359833i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.3522 | − | 22.0522i | 0.989454 | − | 0.718881i | 0.0296528 | − | 0.999560i | \(-0.490560\pi\) |
0.959802 | + | 0.280680i | \(0.0905598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 39.8323i | − | 1.29712i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.45884 | − | 1.62766i | −0.0799862 | − | 0.0529477i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.4391 | + | 10.8650i | −1.08663 | + | 0.353066i | −0.796942 | − | 0.604056i | \(-0.793550\pi\) |
−0.289684 | + | 0.957122i | \(0.593550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.8735 | −1.00220 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.7157 | −0.347480 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49.5641 | + | 16.1044i | −1.60554 | + | 0.521671i | −0.968469 | − | 0.249134i | \(-0.919854\pi\) |
−0.637071 | + | 0.770805i | \(0.719854\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.0381 | + | 28.6629i | −1.16617 | + | 0.927511i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 9.17595i | − | 0.296616i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.98593 | − | 2.89594i | 0.128712 | − | 0.0935149i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38.3157 | − | 27.8380i | −1.23599 | − | 0.898001i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.21199 | − | 1.66816i | −0.0390559 | − | 0.0537558i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.502632 | − | 11.5261i | −0.0161803 | − | 0.371039i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.7277 | + | 12.9083i | 1.27756 | + | 0.415103i | 0.867719 | − | 0.497055i | \(-0.165585\pi\) |
0.409838 | + | 0.912158i | \(0.365585\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.414711 | + | 1.27635i | −0.0133224 | + | 0.0410022i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.141561 | + | 0.435679i | 0.00454289 | + | 0.0139816i | 0.953302 | − | 0.302018i | \(-0.0976602\pi\) |
−0.948759 | + | 0.315999i | \(0.897660\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.66486 | + | 2.29148i | −0.0533728 | + | 0.0734614i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.4063 | + | 6.25422i | 0.333268 | + | 0.200295i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.29079 | + | 3.15300i | −0.0732888 | + | 0.100873i | −0.844088 | − | 0.536205i | \(-0.819857\pi\) |
0.770799 | + | 0.637079i | \(0.219857\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.59881 | − | 14.1537i | −0.146979 | − | 0.452353i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.31821 | − | 13.2901i | 0.137870 | − | 0.424319i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53.5388 | + | 17.3958i | 1.70762 | + | 0.554841i | 0.989935 | − | 0.141523i | \(-0.0452000\pi\) |
0.717689 | + | 0.696364i | \(0.245200\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.0148 | − | 8.22966i | 0.701449 | − | 0.262219i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00942 | + | 8.27125i | 0.191282 | + | 0.263277i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.7451 | − | 20.1580i | −0.882242 | − | 0.640986i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.5804 | + | 12.7729i | −0.558460 | + | 0.405745i | −0.830895 | − | 0.556429i | \(-0.812171\pi\) |
0.272435 | + | 0.962174i | \(0.412171\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.17317i | − | 0.0689636i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.15872 | + | 0.355786i | −0.258649 | + | 0.0112792i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.6447 | − | 11.9066i | 1.16055 | − | 0.377085i | 0.335441 | − | 0.942061i | \(-0.391115\pi\) |
0.825107 | + | 0.564976i | \(0.191115\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.02514 | −0.158988 |
(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 | 300.2.o.a.109.6 | ✓ | 24 | |
3.2 | odd | 2 | 900.2.w.c.109.1 | 24 | |||
5.2 | odd | 4 | 1500.2.m.d.1201.5 | 24 | |||
5.3 | odd | 4 | 1500.2.m.c.1201.2 | 24 | |||
5.4 | even | 2 | 1500.2.o.c.49.2 | 24 | |||
25.2 | odd | 20 | 1500.2.m.d.301.5 | 24 | |||
25.6 | even | 5 | 7500.2.d.g.1249.4 | 24 | |||
25.8 | odd | 20 | 7500.2.a.n.1.4 | 12 | |||
25.11 | even | 5 | 1500.2.o.c.949.2 | 24 | |||
25.14 | even | 10 | inner | 300.2.o.a.289.6 | yes | 24 | |
25.17 | odd | 20 | 7500.2.a.m.1.9 | 12 | |||
25.19 | even | 10 | 7500.2.d.g.1249.21 | 24 | |||
25.23 | odd | 20 | 1500.2.m.c.301.2 | 24 | |||
75.14 | odd | 10 | 900.2.w.c.289.1 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.6 | ✓ | 24 | 1.1 | even | 1 | trivial | |
300.2.o.a.289.6 | yes | 24 | 25.14 | even | 10 | inner | |
900.2.w.c.109.1 | 24 | 3.2 | odd | 2 | |||
900.2.w.c.289.1 | 24 | 75.14 | odd | 10 | |||
1500.2.m.c.301.2 | 24 | 25.23 | odd | 20 | |||
1500.2.m.c.1201.2 | 24 | 5.3 | odd | 4 | |||
1500.2.m.d.301.5 | 24 | 25.2 | odd | 20 | |||
1500.2.m.d.1201.5 | 24 | 5.2 | odd | 4 | |||
1500.2.o.c.49.2 | 24 | 5.4 | even | 2 | |||
1500.2.o.c.949.2 | 24 | 25.11 | even | 5 | |||
7500.2.a.m.1.9 | 12 | 25.17 | odd | 20 | |||
7500.2.a.n.1.4 | 12 | 25.8 | odd | 20 | |||
7500.2.d.g.1249.4 | 24 | 25.6 | even | 5 | |||
7500.2.d.g.1249.21 | 24 | 25.19 | even | 10 |