Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1189,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1189");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1189.10 | ||
Root | \(2.48777 + 1.43632i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1189 |
Dual form | 3420.2.bj.c.2629.10 |
$q$-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 \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.21230 | + | 0.325180i | 0.989369 | + | 0.145425i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.54568i | 1.34014i | 0.742298 | + | 0.670070i | \(0.233736\pi\) | ||||
−0.742298 | + | 0.670070i | \(0.766264\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.81575 | 0.547470 | 0.273735 | − | 0.961805i | \(-0.411741\pi\) | ||||
0.273735 | + | 0.961805i | \(0.411741\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.78308 | + | 1.60681i | −0.771887 | + | 0.445649i | −0.833547 | − | 0.552448i | \(-0.813694\pi\) |
0.0616606 | + | 0.998097i | \(0.480360\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.92193 | − | 3.99638i | −1.67881 | − | 0.969264i | −0.962419 | − | 0.271570i | \(-0.912457\pi\) |
−0.716396 | − | 0.697694i | \(-0.754210\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.863760 | − | 4.27246i | 0.198160 | − | 0.980170i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.30026 | + | 4.21480i | −1.52221 | + | 0.878848i | −0.522553 | + | 0.852607i | \(0.675020\pi\) |
−0.999656 | + | 0.0262406i | \(0.991646\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.78852 | + | 1.43879i | 0.957703 | + | 0.287758i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.29124 | + | 7.43265i | 0.796863 | + | 1.38021i | 0.921649 | + | 0.388024i | \(0.126842\pi\) |
−0.124786 | + | 0.992184i | \(0.539824\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.70874 | −0.306899 | −0.153450 | − | 0.988156i | \(-0.549038\pi\) | ||||
−0.153450 | + | 0.988156i | \(0.549038\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.15298 | + | 7.84409i | −0.194890 | + | 1.32589i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.50608i | 0.905193i | 0.891715 | + | 0.452597i | \(0.149502\pi\) | ||||
−0.891715 | + | 0.452597i | \(0.850498\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.05694 | + | 7.02683i | −0.633588 | + | 1.09741i | 0.353224 | + | 0.935539i | \(0.385085\pi\) |
−0.986812 | + | 0.161868i | \(0.948248\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.35373 | − | 2.51363i | −0.663938 | − | 0.383325i | 0.129838 | − | 0.991535i | \(-0.458554\pi\) |
−0.793776 | + | 0.608211i | \(0.791888\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.16834 | − | 0.674543i | 0.170420 | − | 0.0983922i | −0.412364 | − | 0.911019i | \(-0.635297\pi\) |
0.582784 | + | 0.812627i | \(0.301963\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.57183 | −0.795976 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.92201 | + | 1.10967i | −0.264009 | + | 0.152426i | −0.626162 | − | 0.779693i | \(-0.715375\pi\) |
0.362153 | + | 0.932119i | \(0.382042\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.01698 | + | 0.590447i | 0.541650 | + | 0.0796158i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.960774 | + | 1.66411i | −0.125082 | + | 0.216649i | −0.921765 | − | 0.387749i | \(-0.873253\pi\) |
0.796683 | + | 0.604398i | \(0.206586\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.83047 | + | 4.90251i | 0.362404 | + | 0.627702i | 0.988356 | − | 0.152159i | \(-0.0486227\pi\) |
−0.625952 | + | 0.779862i | \(0.715289\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.67950 | + | 2.64974i | −0.828489 | + | 0.328660i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.04360 | + | 4.64397i | −0.982682 | + | 0.567352i | −0.903079 | − | 0.429475i | \(-0.858699\pi\) |
−0.0796032 | + | 0.996827i | \(0.525365\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.94365 | − | 5.09854i | 0.349346 | − | 0.605086i | −0.636787 | − | 0.771040i | \(-0.719737\pi\) |
0.986134 | + | 0.165954i | \(0.0530703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.82716 | + | 1.63226i | 0.330894 | + | 0.191042i | 0.656238 | − | 0.754554i | \(-0.272147\pi\) |
−0.325344 | + | 0.945596i | \(0.605480\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.43807i | 0.733687i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.08739 | − | 3.61546i | 0.234850 | − | 0.406771i | −0.724379 | − | 0.689402i | \(-0.757874\pi\) |
0.959229 | + | 0.282630i | \(0.0912069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.30268i | 0.691809i | 0.938270 | + | 0.345905i | \(0.112428\pi\) | ||||
−0.938270 | + | 0.345905i | \(0.887572\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.0138 | − | 11.0920i | −1.52001 | − | 1.20310i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.73646 | − | 4.73968i | −0.290064 | − | 0.502405i | 0.683761 | − | 0.729706i | \(-0.260343\pi\) |
−0.973825 | + | 0.227301i | \(0.927010\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.69723 | − | 9.86789i | −0.597232 | − | 1.03444i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.30021 | − | 9.17107i | 0.338595 | − | 0.940932i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.91255 | − | 3.99096i | −0.701863 | − | 0.405221i | 0.106178 | − | 0.994347i | \(-0.466139\pi\) |
−0.808041 | + | 0.589126i | \(0.799472\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.46731 | − | 4.27351i | −0.245507 | − | 0.425230i | 0.716767 | − | 0.697313i | \(-0.245621\pi\) |
−0.962274 | + | 0.272082i | \(0.912288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.56291i | − | 0.548130i | −0.961711 | − | 0.274065i | \(-0.911632\pi\) | ||
0.961711 | − | 0.274065i | \(-0.0883684\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.12251i | − | 0.881907i | −0.897530 | − | 0.440953i | \(-0.854640\pi\) | ||
0.897530 | − | 0.440953i | \(-0.145360\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.57225 | − | 13.1155i | 0.725290 | − | 1.25624i | −0.233565 | − | 0.972341i | \(-0.575039\pi\) |
0.958855 | − | 0.283898i | \(-0.0916276\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.46091i | 0.419647i | 0.977739 | + | 0.209823i | \(0.0672889\pi\) | ||||
−0.977739 | + | 0.209823i | \(0.932711\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.5209 | + | 6.95050i | −1.63383 | + | 0.648138i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.1699 | − | 24.5429i | 1.29895 | − | 2.24985i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.70304 | −0.700277 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1258 | + | 4.74016i | 0.905675 | + | 0.423973i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.180177 | + | 0.104025i | −0.0159881 | + | 0.00923073i | −0.507973 | − | 0.861373i | \(-0.669605\pi\) |
0.491985 | + | 0.870604i | \(0.336272\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.55409 | + | 13.0841i | −0.660004 | + | 1.14316i | 0.320610 | + | 0.947211i | \(0.396112\pi\) |
−0.980614 | + | 0.195950i | \(0.937221\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.1488 | + | 3.06261i | 1.31356 | + | 0.265562i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.56291 | + | 2.63439i | −0.389835 | + | 0.225072i | −0.682089 | − | 0.731269i | \(-0.738928\pi\) |
0.292253 | + | 0.956341i | \(0.405595\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.38336 | + | 5.86016i | 0.286973 | + | 0.497052i | 0.973086 | − | 0.230443i | \(-0.0740176\pi\) |
−0.686113 | + | 0.727495i | \(0.740684\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.05338 | + | 2.91757i | −0.422585 | + | 0.243979i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.07655 | + | 17.8386i | 0.587675 | + | 1.48142i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.83003 | + | 8.36586i | −0.395692 | + | 0.685358i | −0.993189 | − | 0.116513i | \(-0.962828\pi\) |
0.597498 | + | 0.801871i | \(0.296162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0256 | −0.978631 | −0.489316 | − | 0.872107i | \(-0.662753\pi\) | ||||
−0.489316 | + | 0.872107i | \(0.662753\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.78025 | − | 0.555649i | −0.303637 | − | 0.0446308i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.36610 | + | 0.788721i | 0.109027 | + | 0.0629468i | 0.553522 | − | 0.832835i | \(-0.313284\pi\) |
−0.444495 | + | 0.895781i | \(0.646617\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.9443 | − | 25.8844i | −1.17778 | − | 2.03997i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0641i | 1.25823i | 0.777310 | + | 0.629117i | \(0.216584\pi\) | ||||
−0.777310 | + | 0.629117i | \(0.783416\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.16826 | − | 3.56125i | 0.477314 | − | 0.275578i | −0.241982 | − | 0.970281i | \(-0.577798\pi\) |
0.719297 | + | 0.694703i | \(0.244464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.33632 | + | 2.31458i | −0.102794 | + | 0.178044i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8757 | + | 8.58850i | 1.13098 | + | 0.652972i | 0.944181 | − | 0.329427i | \(-0.106855\pi\) |
0.186799 | + | 0.982398i | \(0.440189\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.10149 | + | 16.9785i | −0.385636 | + | 1.28346i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.38519 | −0.253021 | −0.126510 | − | 0.991965i | \(-0.540378\pi\) | ||||
−0.126510 | + | 0.991965i | \(0.540378\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4226 | + | 18.0524i | 0.774704 | + | 1.34183i | 0.934961 | + | 0.354751i | \(0.115434\pi\) |
−0.160257 | + | 0.987075i | \(0.551232\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.79047 | + | 12.1811i | −0.131638 | + | 0.895571i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.5685 | − | 7.25643i | −0.919101 | − | 0.530643i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.58794 | −0.331972 | −0.165986 | − | 0.986128i | \(-0.553081\pi\) | ||||
−0.165986 | + | 0.986128i | \(0.553081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.4238 | + | 10.0596i | 1.25419 | + | 0.724108i | 0.971939 | − | 0.235232i | \(-0.0755851\pi\) |
0.282252 | + | 0.959340i | \(0.408918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.983439i | 0.0700671i | 0.999386 | + | 0.0350336i | \(0.0111538\pi\) | ||||
−0.999386 | + | 0.0350336i | \(0.988846\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.84473 | − | 10.1234i | −0.414322 | − | 0.717626i | 0.581035 | − | 0.813878i | \(-0.302648\pi\) |
−0.995357 | + | 0.0962520i | \(0.969315\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.3538 | + | 15.2154i | −1.84967 | + | 1.06791i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.2602 | + | 14.2262i | −0.786443 | + | 0.993601i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.56837 | − | 7.75773i | 0.108487 | − | 0.536613i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.35987 | + | 9.28357i | −0.368989 | + | 0.639107i | −0.989408 | − | 0.145163i | \(-0.953629\pi\) |
0.620419 | + | 0.784270i | \(0.286963\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.81436 | − | 6.97664i | −0.601135 | − | 0.475803i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.05865i | − | 0.411288i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.6857 | 1.72781 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8291 | − | 10.2936i | −1.19393 | − | 0.689313i | −0.234731 | − | 0.972060i | \(-0.575421\pi\) |
−0.959195 | + | 0.282747i | \(0.908754\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 7.47441i | − | 0.496094i | −0.968748 | − | 0.248047i | \(-0.920211\pi\) | ||
0.968748 | − | 0.248047i | \(-0.0797887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0863 | 0.732604 | 0.366302 | − | 0.930496i | \(-0.380624\pi\) | ||||
0.366302 | + | 0.930496i | \(0.380624\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.8785 | + | 9.16743i | 1.04023 | + | 0.600578i | 0.919899 | − | 0.392155i | \(-0.128270\pi\) |
0.120333 | + | 0.992734i | \(0.461604\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.80407 | − | 1.11237i | 0.182917 | − | 0.0725628i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8518 | 0.766630 | 0.383315 | − | 0.923618i | \(-0.374782\pi\) | ||||
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.34317 | − | 4.05850i | −0.150937 | − | 0.261431i | 0.780635 | − | 0.624987i | \(-0.214896\pi\) |
−0.931572 | + | 0.363556i | \(0.881562\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.3265 | − | 1.81185i | −0.787514 | − | 0.115755i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.46112 | + | 13.2785i | 0.283854 | + | 0.844890i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.0510129 | − | 0.0883569i | −0.00321990 | − | 0.00557704i | 0.864411 | − | 0.502786i | \(-0.167692\pi\) |
−0.867631 | + | 0.497209i | \(0.834358\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.2555 | + | 7.65304i | −0.833363 | + | 0.481143i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.3268 | − | 7.69424i | 0.831303 | − | 0.479953i | −0.0229953 | − | 0.999736i | \(-0.507320\pi\) |
0.854299 | + | 0.519782i | \(0.173987\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −19.5228 | −1.21309 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.9467 | + | 9.78416i | 1.04498 | + | 0.603317i | 0.921239 | − | 0.388998i | \(-0.127179\pi\) |
0.123737 | + | 0.992315i | \(0.460512\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.61291 | + | 1.82993i | −0.283369 | + | 0.112412i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.585331 | + | 1.01382i | −0.0356883 | + | 0.0618139i | −0.883318 | − | 0.468775i | \(-0.844696\pi\) |
0.847630 | + | 0.530588i | \(0.178029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.40442 | − | 11.0928i | 0.389041 | − | 0.673838i | −0.603280 | − | 0.797529i | \(-0.706140\pi\) |
0.992321 | + | 0.123691i | \(0.0394732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.69476 | + | 2.61249i | 0.524314 | + | 0.157539i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0122i | 0.661656i | 0.943691 | + | 0.330828i | \(0.107328\pi\) | ||||
−0.943691 | + | 0.330828i | \(0.892672\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.93481 | + | 3.35119i | 0.115421 | + | 0.199915i | 0.917948 | − | 0.396701i | \(-0.129845\pi\) |
−0.802527 | + | 0.596616i | \(0.796512\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.5893 | − | 11.3099i | −1.16446 | − | 0.672303i | −0.212093 | − | 0.977249i | \(-0.568028\pi\) |
−0.952369 | + | 0.304947i | \(0.901361\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −24.9149 | − | 14.3846i | −1.47068 | − | 0.849097i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 23.4421 | + | 40.6029i | 1.37895 | + | 2.38840i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 28.4482i | − | 1.66196i | −0.556303 | − | 0.830980i | \(-0.687781\pi\) | ||
0.556303 | − | 0.830980i | \(-0.312219\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.66665 | + | 3.36908i | −0.155259 | + | 0.196155i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.5448 | − | 23.4603i | 0.783315 | − | 1.35674i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.91251 | − | 15.4369i | 0.513709 | − | 0.889770i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.66763 | + | 11.7662i | 0.267268 | + | 0.673732i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.2248 | − | 7.05802i | −0.697709 | − | 0.402822i | 0.108785 | − | 0.994065i | \(-0.465304\pi\) |
−0.806494 | + | 0.591243i | \(0.798637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.4672 | −0.933768 | −0.466884 | − | 0.884319i | \(-0.654623\pi\) | ||||
−0.466884 | + | 0.884319i | \(0.654623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.6363 | − | 12.4917i | 1.22295 | − | 0.706073i | 0.257408 | − | 0.966303i | \(-0.417132\pi\) |
0.965547 | + | 0.260229i | \(0.0837982\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.91012 | + | 1.10281i | −0.107283 | + | 0.0619399i | −0.552681 | − | 0.833393i | \(-0.686395\pi\) |
0.445398 | + | 0.895332i | \(0.353062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.79183 | + | 13.4958i | 0.436259 | + | 0.755622i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.0533 | + | 26.1218i | −1.28272 | + | 1.45345i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.6387 | + | 3.68997i | −0.867477 | + | 0.204683i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.39171 | + | 4.14257i | 0.131859 | + | 0.228387i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.5415 | −1.51382 | −0.756910 | − | 0.653519i | \(-0.773292\pi\) | ||||
−0.756910 | + | 0.653519i | \(0.773292\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.3050 | + | 7.65823i | −1.05474 | + | 0.418414i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9464 | + | 9.20668i | 0.868658 | + | 0.501520i | 0.866902 | − | 0.498479i | \(-0.166108\pi\) |
0.00175582 | + | 0.999998i | \(0.499441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.10265 | −0.168018 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.06383i | 0.273421i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.8072 | + | 13.1677i | 1.22435 | + | 0.706881i | 0.965843 | − | 0.259128i | \(-0.0834351\pi\) |
0.258510 | + | 0.966009i | \(0.416768\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.40515 | 0.396388 | 0.198194 | − | 0.980163i | \(-0.436492\pi\) | ||||
0.198194 | + | 0.980163i | \(0.436492\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.42201i | − | 0.128910i | −0.997921 | − | 0.0644552i | \(-0.979469\pi\) | ||
0.997921 | − | 0.0644552i | \(-0.0205309\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.17016 | − | 10.3223i | 0.433627 | − | 0.547850i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.28083 | + | 3.95051i | −0.120377 | + | 0.208500i | −0.919917 | − | 0.392114i | \(-0.871744\pi\) |
0.799539 | + | 0.600614i | \(0.205077\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5078 | − | 7.38076i | −0.921465 | − | 0.388461i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.72373 | + | 4.53038i | 0.299594 | + | 0.237131i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.11478 | + | 5.26242i | −0.475788 | + | 0.274696i | −0.718659 | − | 0.695362i | \(-0.755244\pi\) |
0.242872 | + | 0.970058i | \(0.421911\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.93455 | − | 6.81484i | −0.204272 | − | 0.353809i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 21.8633i | − | 1.13204i | −0.824392 | − | 0.566019i | \(-0.808483\pi\) | ||
0.824392 | − | 0.566019i | \(-0.191517\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.8857 | − | 13.7904i | −1.23018 | − | 0.710243i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.33617 | −0.479567 | −0.239783 | − | 0.970826i | \(-0.577076\pi\) | ||||
−0.239783 | + | 0.970826i | \(0.577076\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.77320 | − | 2.75581i | −0.243899 | − | 0.140815i | 0.373068 | − | 0.927804i | \(-0.378306\pi\) |
−0.616968 | + | 0.786989i | \(0.711639\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.09353 | + | 14.2429i | −0.106696 | + | 0.725887i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.50605 | − | 14.7329i | −0.431274 | − | 0.746988i | 0.565709 | − | 0.824605i | \(-0.308602\pi\) |
−0.996983 | + | 0.0776163i | \(0.975269\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 67.3758 | 3.40734 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.79360 | − | 7.31970i | 0.291508 | − | 0.368294i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.2122 | + | 15.7110i | 1.36574 | + | 0.788512i | 0.990381 | − | 0.138366i | \(-0.0441851\pi\) |
0.375362 | + | 0.926878i | \(0.377518\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4762 | + | 23.3415i | −0.672971 | + | 1.16562i | 0.304087 | + | 0.952644i | \(0.401649\pi\) |
−0.977058 | + | 0.212976i | \(0.931685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.75556 | − | 2.74563i | 0.236891 | − | 0.136769i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.99767i | 0.495566i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.0791 | − | 29.5819i | −0.844509 | − | 1.46273i | −0.886047 | − | 0.463596i | \(-0.846559\pi\) |
0.0415373 | − | 0.999137i | \(-0.486774\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.90040 | − | 3.40660i | −0.290340 | − | 0.167628i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.04951 | + | 13.9434i | −0.100606 | + | 0.684455i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.5998 | 1.78802 | 0.894009 | − | 0.448049i | \(-0.147881\pi\) | ||||
0.894009 | + | 0.448049i | \(0.147881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.85007 | + | 8.40057i | −0.236378 | + | 0.409419i | −0.959672 | − | 0.281121i | \(-0.909294\pi\) |
0.723294 | + | 0.690540i | \(0.242627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −27.3958 | − | 29.0959i | −1.32889 | − | 1.41136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.3827 | + | 10.0359i | −0.841209 | + | 0.485672i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.4779 | + | 25.0764i | 0.697375 | + | 1.20789i | 0.969373 | + | 0.245591i | \(0.0789821\pi\) |
−0.271999 | + | 0.962298i | \(0.587685\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.44994 | + | 3.72388i | −0.309965 | + | 0.178958i | −0.646911 | − | 0.762566i | \(-0.723939\pi\) |
0.336946 | + | 0.941524i | \(0.390606\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7019 | + | 34.8306i | 0.559779 | + | 1.66618i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.70008 | − | 9.87283i | 0.272050 | − | 0.471204i | −0.697337 | − | 0.716744i | \(-0.745632\pi\) |
0.969387 | + | 0.245539i | \(0.0789650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.66042 | − | 3.84540i | 0.316446 | − | 0.182700i | −0.333361 | − | 0.942799i | \(-0.608183\pi\) |
0.649807 | + | 0.760099i | \(0.274850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.51260 | − | 11.3754i | −0.213918 | − | 0.539247i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.0590 | 1.74892 | 0.874460 | − | 0.485097i | \(-0.161216\pi\) | ||||
0.874460 | + | 0.485097i | \(0.161216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.36641 | + | 12.7590i | −0.346871 | + | 0.600797i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.39512 | − | 23.6833i | −0.440450 | − | 1.11029i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.1647i | 1.03682i | 0.855131 | + | 0.518411i | \(0.173476\pi\) | ||||
−0.855131 | + | 0.518411i | \(0.826524\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0779 | + | 36.5080i | −0.981697 | + | 1.70035i | −0.325914 | + | 0.945400i | \(0.605672\pi\) |
−0.655783 | + | 0.754949i | \(0.727661\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.16758i | 0.240158i | 0.992764 | + | 0.120079i | \(0.0383148\pi\) | ||||
−0.992764 | + | 0.120079i | \(0.961685\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.7096i | 0.588129i | 0.955786 | + | 0.294064i | \(0.0950080\pi\) | ||||
−0.955786 | + | 0.294064i | \(0.904992\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4660 | − | 28.5200i | −0.760331 | − | 1.31693i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.90530 | − | 4.56413i | −0.363486 | − | 0.209859i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2833 | − | 19.2160i | 0.471830 | − | 0.881689i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.0555 | + | 19.1487i | 0.505140 | + | 0.874928i | 0.999982 | + | 0.00594539i | \(0.00189249\pi\) |
−0.494842 | + | 0.868983i | \(0.664774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.84722 | − | 15.3238i | −0.403399 | − | 0.698707i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.9948 | − | 11.0770i | −0.635473 | − | 0.502981i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 28.3389i | − | 1.28416i | −0.766639 | − | 0.642078i | \(-0.778072\pi\) | ||
0.766639 | − | 0.642078i | \(-0.221928\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.33288 | − | 7.50477i | 0.195540 | − | 0.338686i | −0.751537 | − | 0.659691i | \(-0.770687\pi\) |
0.947077 | + | 0.321005i | \(0.104021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 68.5977i | − | 3.08948i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.0778 | + | 10.4372i | 0.810900 | + | 0.468173i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.07784 | + | 13.9912i | −0.361614 | + | 0.626334i | −0.988227 | − | 0.152997i | \(-0.951107\pi\) |
0.626613 | + | 0.779331i | \(0.284441\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.3262 | + | 12.8900i | −0.995474 | + | 0.574737i | −0.906906 | − | 0.421333i | \(-0.861562\pi\) |
−0.0885682 | + | 0.996070i | \(0.528229\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.06877 | − | 10.2566i | −0.181058 | − | 0.456413i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.15335 | + | 10.6579i | 0.272743 | + | 0.472404i | 0.969563 | − | 0.244842i | \(-0.0787359\pi\) |
−0.696821 | + | 0.717246i | \(0.745403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.78747 | + | 10.0242i | −0.256023 | + | 0.443444i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.80895 | − | 12.3068i | 0.0797118 | − | 0.542303i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.12142 | − | 1.22480i | 0.0933000 | − | 0.0538668i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0934 | −0.748875 | −0.374438 | − | 0.927252i | \(-0.622164\pi\) | ||||
−0.374438 | + | 0.927252i | \(0.622164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.29269 | + | 1.32368i | −0.100252 | + | 0.0578806i | −0.549288 | − | 0.835633i | \(-0.685101\pi\) |
0.449036 | + | 0.893514i | \(0.351768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.8278 | + | 6.82878i | 0.515227 | + | 0.297466i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.0292 | − | 41.6197i | 1.04475 | − | 1.80955i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 26.0750i | − | 1.12943i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.96646 | − | 20.1817i | 0.128251 | − | 0.872531i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.1171 | −0.435773 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.06701 | − | 8.77631i | −0.217848 | − | 0.377323i | 0.736302 | − | 0.676653i | \(-0.236570\pi\) |
−0.954150 | + | 0.299330i | \(0.903237\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21.0170 | − | 26.5531i | 0.900268 | − | 1.13741i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4639 | − | 11.2375i | 0.832217 | − | 0.480480i | −0.0223944 | − | 0.999749i | \(-0.507129\pi\) |
0.854611 | + | 0.519269i | \(0.173796\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.4623 | − | 11.9141i | 1.51074 | − | 0.507559i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.8193 | + | 7.40121i | 0.545131 | + | 0.314731i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.86157 | − | 2.22948i | 0.163620 | − | 0.0944659i | −0.415954 | − | 0.909386i | \(-0.636552\pi\) |
0.579574 | + | 0.814920i | \(0.303219\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.1557 | 0.683313 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 10.0514i | − | 0.423616i | −0.977311 | − | 0.211808i | \(-0.932065\pi\) | ||
0.977311 | − | 0.211808i | \(-0.0679352\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.45060 | + | 9.86885i | −0.0610271 | + | 0.415186i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.41442 | −0.226984 | −0.113492 | − | 0.993539i | \(-0.536204\pi\) | ||||
−0.113492 | + | 0.993539i | \(0.536204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0418 | −1.00612 | −0.503059 | − | 0.864252i | \(-0.667792\pi\) | ||||
−0.503059 | + | 0.864252i | \(0.667792\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −41.0216 | + | 9.67912i | −1.71072 | + | 0.403647i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.40727i | − | 0.0585855i | −0.999571 | − | 0.0292928i | \(-0.990674\pi\) | ||
0.999571 | − | 0.0292928i | \(-0.00932551\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.3473 | −0.927121 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.48990 | + | 2.01489i | −0.144537 | + | 0.0834484i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.224303 | − | 0.129501i | −0.00925798 | − | 0.00534510i | 0.495364 | − | 0.868686i | \(-0.335035\pi\) |
−0.504622 | + | 0.863340i | \(0.668368\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.47594 | + | 7.30054i | −0.0608152 | + | 0.300813i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.57044 | − | 1.48405i | 0.105555 | − | 0.0609425i | −0.446293 | − | 0.894887i | \(-0.647256\pi\) |
0.551848 | + | 0.833944i | \(0.313923\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.3288 | − | 49.6885i | 1.61232 | − | 2.03703i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.7083 | − | 41.0640i | −0.968696 | − | 1.67783i | −0.699338 | − | 0.714791i | \(-0.746522\pi\) |
−0.269359 | − | 0.963040i | \(-0.586812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2047 | −0.905747 | −0.452874 | − | 0.891575i | \(-0.649601\pi\) | ||||
−0.452874 | + | 0.891575i | \(0.649601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.0414 | − | 2.50488i | −0.692832 | − | 0.101838i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.6580i | 1.52849i | 0.644925 | + | 0.764246i | \(0.276888\pi\) | ||||
−0.644925 | + | 0.764246i | \(0.723112\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.16772 | + | 3.75461i | −0.0876968 | + | 0.151895i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.3694 | + | 22.1526i | 1.54973 | + | 0.894734i | 0.998162 | + | 0.0606013i | \(0.0193018\pi\) |
0.551563 | + | 0.834133i | \(0.314031\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.1247 | − | 11.6190i | 0.810190 | − | 0.467764i | −0.0368317 | − | 0.999321i | \(-0.511727\pi\) |
0.847022 | + | 0.531558i | \(0.178393\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.8420 | 1.15926 | 0.579630 | − | 0.814880i | \(-0.303197\pi\) | ||||
0.579630 | + | 0.814880i | \(0.303197\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.8054 | − | 9.70259i | 0.673294 | − | 0.388726i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8598 | + | 13.7793i | 0.834391 | + | 0.551174i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.0044 | − | 38.1127i | 0.877371 | − | 1.51965i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.79323 | + | 11.7662i | 0.270434 | + | 0.468406i | 0.968973 | − | 0.247166i | \(-0.0794994\pi\) |
−0.698539 | + | 0.715572i | \(0.746166\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.432431 | + | 0.171544i | −0.0171605 | + | 0.00680753i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5068 | − | 8.95287i | 0.614403 | − | 0.354726i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.15731 | + | 5.46863i | −0.124706 | + | 0.215998i | −0.921618 | − | 0.388098i | \(-0.873132\pi\) |
0.796912 | + | 0.604096i | \(0.206466\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.8657 | + | 6.85067i | 0.467938 | + | 0.270164i | 0.715376 | − | 0.698740i | \(-0.246255\pi\) |
−0.247438 | + | 0.968904i | \(0.579589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.50227i | 0.334259i | 0.985935 | + | 0.167129i | \(0.0534497\pi\) | ||||
−0.985935 | + | 0.167129i | \(0.946550\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.74453 | + | 3.02161i | −0.0684787 | + | 0.118609i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.89369i | 0.269771i | 0.990861 | + | 0.134885i | \(0.0430667\pi\) | ||||
−0.990861 | + | 0.134885i | \(0.956933\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.9666 | + | 26.4894i | −0.819232 | + | 1.03503i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.9585 | + | 18.9807i | 0.426884 | + | 0.739384i | 0.996594 | − | 0.0824611i | \(-0.0262780\pi\) |
−0.569711 | + | 0.821845i | \(0.692945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.5768 | + | 26.9797i | 0.605866 | + | 1.04939i | 0.991914 | + | 0.126912i | \(0.0405065\pi\) |
−0.386048 | + | 0.922479i | \(0.626160\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.5177 | + | 11.7015i | 1.26098 | + | 0.453764i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −62.6543 | − | 36.1735i | −2.42598 | − | 1.40064i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.13943 | + | 8.90175i | 0.198405 | + | 0.343648i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 24.5193i | − | 0.945150i | −0.881290 | − | 0.472575i | \(-0.843325\pi\) | ||
0.881290 | − | 0.472575i | \(-0.156675\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.89395i | 0.303389i | 0.988427 | + | 0.151695i | \(0.0484730\pi\) | ||||
−0.988427 | + | 0.151695i | \(0.951527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.1507 | − | 24.5097i | 0.543053 | − | 0.940595i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 44.3352i | − | 1.69644i | −0.529644 | − | 0.848220i | \(-0.677675\pi\) | ||
0.529644 | − | 0.848220i | \(-0.322325\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9512 | + | 4.34430i | −0.418422 | + | 0.165987i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.56607 | − | 6.17662i | 0.135857 | − | 0.235311i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.2501 | 1.68335 | 0.841676 | − | 0.539982i | \(-0.181569\pi\) | ||||
0.841676 | + | 0.539982i | \(0.181569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.57940 | + | 14.0646i | 0.211639 | + | 0.533501i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56.1638 | − | 32.4262i | 2.12735 | − | 1.22823i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.27840 | − | 16.0707i | 0.350440 | − | 0.606980i | −0.635886 | − | 0.771783i | \(-0.719365\pi\) |
0.986327 | + | 0.164802i | \(0.0526987\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23.5245 | + | 4.75593i | 0.887243 | + | 0.179373i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.1525 | − | 8.74830i | 0.569868 | − | 0.329014i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.4349 | + | 37.1263i | 0.805003 | + | 1.39431i | 0.916289 | + | 0.400518i | \(0.131170\pi\) |
−0.111285 | + | 0.993788i | \(0.535497\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.4743 | − | 7.20202i | 0.467165 | − | 0.269718i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.1283 | + | 4.81127i | −0.453573 | + | 0.179931i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.5024 | − | 30.3150i | 0.652728 | − | 1.13056i | −0.329730 | − | 0.944075i | \(-0.606958\pi\) |
0.982458 | − | 0.186483i | \(-0.0597088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.7243 | 0.734571 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.85465 | + | 41.7655i | 0.365993 | + | 1.55113i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.436587 | − | 0.252064i | −0.0161921 | − | 0.00934852i | 0.491882 | − | 0.870662i | \(-0.336309\pi\) |
−0.508074 | + | 0.861313i | \(0.669642\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0908 | + | 34.7983i | 0.743086 | + | 1.28706i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.5745i | − | 0.981553i | −0.871285 | − | 0.490777i | \(-0.836713\pi\) | ||
0.871285 | − | 0.490777i | \(-0.163287\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.6052 | + | 8.43231i | −0.537989 | + | 0.310608i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.8643 | − | 22.2817i | 0.473222 | − | 0.819645i | −0.526308 | − | 0.850294i | \(-0.676424\pi\) |
0.999530 | + | 0.0306492i | \(0.00975746\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.70400 | + | 2.13851i | 0.135887 | + | 0.0784542i | 0.566402 | − | 0.824129i | \(-0.308335\pi\) |
−0.430516 | + | 0.902583i | \(0.641668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.4059 | + | 16.9371i | −0.491153 | + | 0.620529i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.3455 | 1.18188 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.26869 | − | 12.5897i | −0.265238 | − | 0.459406i | 0.702388 | − | 0.711795i | \(-0.252117\pi\) |
−0.967626 | + | 0.252388i | \(0.918784\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.6042 | − | 3.91049i | −0.968228 | − | 0.142317i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.1482 | + | 8.16844i | 0.514224 | + | 0.296887i | 0.734568 | − | 0.678535i | \(-0.237385\pi\) |
−0.220345 | + | 0.975422i | \(0.570718\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.9812 | 0.796819 | 0.398409 | − | 0.917208i | \(-0.369562\pi\) | ||||
0.398409 | + | 0.917208i | \(0.369562\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.5034 | + | 26.8488i | 1.68354 | + | 0.971990i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.17513i | − | 0.222971i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.1977 | + | 40.1796i | 0.836530 | + | 1.44891i | 0.892778 | + | 0.450496i | \(0.148753\pi\) |
−0.0562477 | + | 0.998417i | \(0.517914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.6426 | + | 12.4954i | −0.778431 | + | 0.449428i | −0.835874 | − | 0.548921i | \(-0.815039\pi\) |
0.0574426 | + | 0.998349i | \(0.481705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.18234 | − | 2.45852i | −0.293918 | − | 0.0883127i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.5176 | + | 23.4026i | 0.950093 | + | 0.838486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.34493 | − | 9.25769i | 0.191257 | − | 0.331266i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.76575 | + | 2.18911i | 0.0987139 | + | 0.0781328i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.4986i | − | 1.30103i | −0.759492 | − | 0.650517i | \(-0.774552\pi\) | ||
0.759492 | − | 0.650517i | \(-0.225448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.8169 | −0.562385 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.7548 | − | 9.09604i | −0.559470 | − | 0.323010i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.9753i | 0.424188i | 0.977249 | + | 0.212094i | \(0.0680283\pi\) | ||||
−0.977249 | + | 0.212094i | \(0.931972\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.7829 | −0.381472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.13342 | + | 2.96378i | 0.181154 | + | 0.104590i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.6442 | − | 62.1235i | −0.868595 | − | 2.18956i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.4153 | 1.03419 | 0.517093 | − | 0.855929i | \(-0.327014\pi\) | ||||
0.517093 | + | 0.855929i | \(0.327014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.4062 | − | 47.4690i | −0.962363 | − | 1.66686i | −0.716538 | − | 0.697548i | \(-0.754274\pi\) |
−0.245825 | − | 0.969314i | \(-0.579059\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.22372 | + | 35.5385i | −0.182979 | + | 1.24486i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5000 | + | 16.4300i | −0.507289 | + | 0.574812i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.32200 | − | 7.48592i | −0.150839 | − | 0.261260i | 0.780697 | − | 0.624909i | \(-0.214864\pi\) |
−0.931536 | + | 0.363649i | \(0.881531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.1614 | + | 20.3004i | −1.22565 | + | 0.707628i | −0.966117 | − | 0.258106i | \(-0.916902\pi\) |
−0.259532 | + | 0.965735i | \(0.583568\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.64002 | − | 0.946864i | 0.0570290 | − | 0.0329257i | −0.471214 | − | 0.882019i | \(-0.656184\pi\) |
0.528243 | + | 0.849093i | \(0.322851\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 54.2488 | 1.88414 | 0.942070 | − | 0.335416i | \(-0.108877\pi\) | ||||
0.942070 | + | 0.335416i | \(0.108877\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.5678 | + | 22.2671i | 1.33630 | + | 0.771511i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.8041 | − | 5.87274i | 0.512316 | − | 0.203235i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.4931 | + | 33.7630i | −0.672976 | + | 1.16563i | 0.304080 | + | 0.952647i | \(0.401651\pi\) |
−0.977056 | + | 0.212982i | \(0.931682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.3295 | + | 38.6758i | −0.769982 | + | 1.33365i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.70899 | + | 4.68599i | −0.127593 | + | 0.161203i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 27.3125i | − | 0.938469i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.2070 | − | 40.1958i | −0.795527 | − | 1.37789i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.5103 | − | 15.3058i | −0.907697 | − | 0.524059i | −0.0280076 | − | 0.999608i | \(-0.508916\pi\) |
−0.879689 | + | 0.475549i | \(0.842250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.6725 | − | 6.73913i | −0.398726 | − | 0.230204i | 0.287208 | − | 0.957868i | \(-0.407273\pi\) |
−0.685934 | + | 0.727664i | \(0.740606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.96411 | − | 8.59809i | −0.169373 | − | 0.293363i | 0.768826 | − | 0.639458i | \(-0.220841\pi\) |
−0.938200 | + | 0.346094i | \(0.887508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 36.8000i | − | 1.25269i | −0.779547 | − | 0.626344i | \(-0.784551\pi\) | ||
0.779547 | − | 0.626344i | \(-0.215449\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.1167 | + | 23.8376i | 1.02400 | + | 0.810503i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.79018 | − | 6.56479i | 0.128573 | − | 0.222695i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.9240 | − | 25.8491i | 0.505679 | − | 0.875862i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.8071 | + | 35.9027i | −0.568183 | + | 1.21373i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.96267 | − | 2.86520i | −0.167577 | − | 0.0967509i | 0.413866 | − | 0.910338i | \(-0.364178\pi\) |
−0.581443 | + | 0.813587i | \(0.697512\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.5926 | −0.727474 | −0.363737 | − | 0.931502i | \(-0.618499\pi\) | ||||
−0.363737 | + | 0.931502i | \(0.618499\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0904 | + | 20.8368i | −1.21454 | + | 0.701214i | −0.963745 | − | 0.266826i | \(-0.914025\pi\) |
−0.250794 | + | 0.968040i | \(0.580692\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.9856 | − | 25.3951i | 1.47689 | − | 0.852685i | 0.477234 | − | 0.878776i | \(-0.341639\pi\) |
0.999660 | + | 0.0260915i | \(0.00830612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.368839 | − | 0.638849i | −0.0123705 | − | 0.0214263i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.87279 | − | 5.57434i | −0.0626705 | − | 0.186538i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.48905 | − | 1.10080i | −0.250331 | − | 0.0367956i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.33263 | − | 12.7005i | −0.244557 | − | 0.423585i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.7387 | 0.590962 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.1875 | + | 43.3265i | 0.571333 | + | 1.44022i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.4646 | + | 10.0832i | 0.579902 | + | 0.334806i | 0.761094 | − | 0.648641i | \(-0.224662\pi\) |
−0.181193 | + | 0.983448i | \(0.557996\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.2962 | −1.56699 | −0.783496 | − | 0.621397i | \(-0.786566\pi\) | ||||
−0.783496 | + | 0.621397i | \(0.786566\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.4441i | 0.378745i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46.3919 | − | 26.7844i | −1.53200 | − | 0.884498i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.8678 | 1.11719 | 0.558597 | − | 0.829439i | \(-0.311340\pi\) | ||||
0.558597 | + | 0.829439i | \(0.311340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.9195i | 0.622744i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.92209 | + | 26.3659i | −0.260477 | + | 0.866907i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.457146 | − | 0.791800i | 0.0149985 | − | 0.0259781i | −0.858429 | − | 0.512933i | \(-0.828559\pi\) |
0.873427 | + | 0.486955i | \(0.161892\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.81272 | + | 23.8054i | −0.157731 | + | 0.780191i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.4456 | − | 20.1404i | −0.832161 | − | 0.658662i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.0186 | − | 25.9915i | 1.47069 | − | 0.849106i | 0.471236 | − | 0.882007i | \(-0.343808\pi\) |
0.999459 | + | 0.0329014i | \(0.0104747\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.4228 | − | 21.5169i | −0.404972 | − | 0.701432i | 0.589346 | − | 0.807880i | \(-0.299385\pi\) |
−0.994318 | + | 0.106449i | \(0.966052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 68.3969i | − | 2.22731i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24.0042 | − | 13.8588i | −0.780032 | − | 0.450352i | 0.0564097 | − | 0.998408i | \(-0.482035\pi\) |
−0.836442 | + | 0.548056i | \(0.815368\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4909 | −0.340550 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.3605 | − | 8.29103i | −0.465182 | − | 0.268573i | 0.249039 | − | 0.968494i | \(-0.419885\pi\) |
−0.714221 | + | 0.699921i | \(0.753219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.1499 | − | 1.49191i | −0.328443 | − | 0.0482770i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.34072 | − | 16.1786i | −0.301627 | − | 0.522434i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0802 | −0.905813 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35.2754 | + | 27.9208i | 1.13556 | + | 0.898801i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5612 | + | 9.56159i | 0.532571 | + | 0.307480i | 0.742063 | − | 0.670330i | \(-0.233848\pi\) |
−0.209492 | + | 0.977810i | \(0.567181\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.56801 | + | 13.1082i | −0.242869 | + | 0.420661i | −0.961530 | − | 0.274699i | \(-0.911422\pi\) |
0.718661 | + | 0.695360i | \(0.244755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.7782 | + | 11.9963i | −0.666120 | + | 0.384584i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.83858i | − | 0.186793i | −0.995629 | − | 0.0933964i | \(-0.970228\pi\) | ||
0.995629 | − | 0.0933964i | \(-0.0297724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.96873 | − | 8.60609i | −0.158801 | − | 0.275052i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.9231 | + | 10.3479i | 0.571657 | + | 0.330047i | 0.757811 | − | 0.652474i | \(-0.226269\pi\) |
−0.186154 | + | 0.982521i | \(0.559602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.319795 | + | 2.17566i | −0.0101895 | + | 0.0693223i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.3778 | 1.34754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9776 | + | 39.7984i | −0.729907 | + | 1.26424i | 0.227014 | + | 0.973891i | \(0.427104\pi\) |
−0.956922 | + | 0.290345i | \(0.906230\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.63836 | − | 24.2965i | −0.305556 | − | 0.770250i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.31974 | − | 3.64870i | 0.200148 | − | 0.115556i | −0.396576 | − | 0.918002i | \(-0.629802\pi\) |
0.596725 | + | 0.802446i | \(0.296468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3420.2.bj.c.1189.10 | 20 | ||
3.2 | odd | 2 | 380.2.r.a.49.10 | yes | 20 | ||
5.4 | even | 2 | inner | 3420.2.bj.c.1189.4 | 20 | ||
15.2 | even | 4 | 1900.2.i.g.201.10 | 20 | |||
15.8 | even | 4 | 1900.2.i.g.201.1 | 20 | |||
15.14 | odd | 2 | 380.2.r.a.49.1 | ✓ | 20 | ||
19.7 | even | 3 | inner | 3420.2.bj.c.2629.4 | 20 | ||
57.26 | odd | 6 | 380.2.r.a.349.1 | yes | 20 | ||
95.64 | even | 6 | inner | 3420.2.bj.c.2629.10 | 20 | ||
285.83 | even | 12 | 1900.2.i.g.501.1 | 20 | |||
285.197 | even | 12 | 1900.2.i.g.501.10 | 20 | |||
285.254 | odd | 6 | 380.2.r.a.349.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.r.a.49.1 | ✓ | 20 | 15.14 | odd | 2 | ||
380.2.r.a.49.10 | yes | 20 | 3.2 | odd | 2 | ||
380.2.r.a.349.1 | yes | 20 | 57.26 | odd | 6 | ||
380.2.r.a.349.10 | yes | 20 | 285.254 | odd | 6 | ||
1900.2.i.g.201.1 | 20 | 15.8 | even | 4 | |||
1900.2.i.g.201.10 | 20 | 15.2 | even | 4 | |||
1900.2.i.g.501.1 | 20 | 285.83 | even | 12 | |||
1900.2.i.g.501.10 | 20 | 285.197 | even | 12 | |||
3420.2.bj.c.1189.4 | 20 | 5.4 | even | 2 | inner | ||
3420.2.bj.c.1189.10 | 20 | 1.1 | even | 1 | trivial | ||
3420.2.bj.c.2629.4 | 20 | 19.7 | even | 3 | inner | ||
3420.2.bj.c.2629.10 | 20 | 95.64 | even | 6 | inner |