Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(113,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.0.20322144469993472.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.5 | ||
Root | \(-0.171092 + 1.72358i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.113 |
Dual form | 912.2.f.h.113.6 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.171092 | − | 1.72358i | 0.0987799 | − | 0.995109i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.81594i | 1.70654i | 0.521469 | + | 0.853270i | \(0.325384\pi\) | ||||
−0.521469 | + | 0.853270i | \(0.674616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.25057 | −0.850635 | −0.425318 | − | 0.905044i | \(-0.639838\pi\) | ||||
−0.425318 | + | 0.905044i | \(0.639838\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.94146 | − | 0.589781i | −0.980485 | − | 0.196594i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.65557i | − | 0.800683i | −0.916366 | − | 0.400342i | \(-0.868891\pi\) | ||
0.916366 | − | 0.400342i | \(-0.131109\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.28678i | − | 0.634240i | −0.948385 | − | 0.317120i | \(-0.897284\pi\) | ||
0.948385 | − | 0.317120i | \(-0.102716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.57708 | + | 0.652876i | 1.69819 | + | 0.168572i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.83491i | 0.687567i | 0.939049 | + | 0.343783i | \(0.111709\pi\) | ||||
−0.939049 | + | 0.343783i | \(0.888291\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.80672 | + | 3.33502i | −0.643905 | + | 0.765106i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.385054 | + | 3.87904i | −0.0840257 | + | 0.846475i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.55438i | 0.949654i | 0.880079 | + | 0.474827i | \(0.157489\pi\) | ||||
−0.880079 | + | 0.474827i | \(0.842511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.56140 | −1.91228 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.51979 | + | 4.96893i | −0.292484 | + | 0.956270i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.88291 | −1.09243 | −0.546215 | − | 0.837645i | \(-0.683932\pi\) | ||||
−0.546215 | + | 0.837645i | \(0.683932\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.46613i | − | 0.442930i | −0.975168 | − | 0.221465i | \(-0.928916\pi\) | ||
0.975168 | − | 0.221465i | \(-0.0710838\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.57708 | − | 0.454346i | −0.796767 | − | 0.0790914i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 8.58804i | − | 1.45164i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.73910i | 1.43670i | 0.695682 | + | 0.718350i | \(0.255102\pi\) | ||||
−0.695682 | + | 0.718350i | \(0.744898\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.94146 | − | 0.391250i | −0.631138 | − | 0.0626502i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.54073 | −0.865316 | −0.432658 | − | 0.901558i | \(-0.642424\pi\) | ||||
−0.432658 | + | 0.901558i | \(0.642424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2458 | −1.71496 | −0.857482 | − | 0.514514i | \(-0.827972\pi\) | ||||
−0.857482 | + | 0.514514i | \(0.827972\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.25057 | − | 11.2244i | 0.335495 | − | 1.67324i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.494972i | − | 0.0721991i | −0.999348 | − | 0.0360995i | \(-0.988507\pi\) | ||
0.999348 | − | 0.0360995i | \(-0.0114933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.93494 | −0.276420 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.88619 | + | 0.485030i | 0.684204 | + | 0.0679178i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.27125 | 0.998783 | 0.499391 | − | 0.866377i | \(-0.333557\pi\) | ||||
0.499391 | + | 0.866377i | \(0.333557\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1335 | 1.36640 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.26796 | + | 5.40819i | 0.697759 | + | 0.716333i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.5359 | −1.63204 | −0.816019 | − | 0.578024i | \(-0.803824\pi\) | ||||
−0.816019 | + | 0.578024i | \(0.803824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.44911 | 0.953761 | 0.476881 | − | 0.878968i | \(-0.341767\pi\) | ||||
0.476881 | + | 0.878968i | \(0.341767\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.61995 | + | 1.32734i | 0.834035 | + | 0.167230i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.72623 | 1.08236 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.50053i | − | 0.549827i | −0.961469 | − | 0.274914i | \(-0.911351\pi\) | ||
0.961469 | − | 0.274914i | \(-0.0886493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.84984 | + | 0.779218i | 0.945010 | + | 0.0938068i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.61166 | 0.309947 | 0.154974 | − | 0.987919i | \(-0.450471\pi\) | ||||
0.154974 | + | 0.987919i | \(0.450471\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.17963 | −1.07439 | −0.537197 | − | 0.843457i | \(-0.680517\pi\) | ||||
−0.537197 | + | 0.843457i | \(0.680517\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.63588 | + | 16.4798i | −0.188895 | + | 1.90293i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.97653i | 0.681089i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.69557i | 0.640802i | 0.947282 | + | 0.320401i | \(0.103818\pi\) | ||||
−0.947282 | + | 0.320401i | \(0.896182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.30432 | + | 3.46963i | 0.922702 | + | 0.385514i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2052i | 1.22993i | 0.788553 | + | 0.614967i | \(0.210831\pi\) | ||||
−0.788553 | + | 0.614967i | \(0.789169\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.8178 | −1.17336 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00652 | + | 10.1397i | −0.107910 | + | 1.08709i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.6553 | 1.65946 | 0.829729 | − | 0.558166i | \(-0.188495\pi\) | ||||
0.829729 | + | 0.558166i | \(0.188495\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.14657i | 0.539507i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.25057 | − | 0.421935i | −0.440764 | − | 0.0437526i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.7262 | − | 10.7103i | −1.30568 | − | 1.09885i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 18.9286i | − | 1.92191i | −0.276701 | − | 0.960956i | \(-0.589241\pi\) | ||
0.276701 | − | 0.960956i | \(-0.410759\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.56620 | + | 7.81123i | −0.157409 | + | 0.785058i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.35529i | 0.632375i | 0.948697 | + | 0.316187i | \(0.102403\pi\) | ||||
−0.948697 | + | 0.316187i | \(0.897597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.42351i | − | 0.928526i | −0.885697 | − | 0.464263i | \(-0.846319\pi\) | ||
0.885697 | − | 0.464263i | \(-0.153681\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.8022 | − | 1.46934i | −1.44454 | − | 0.143393i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6997 | 1.51775 | 0.758873 | − | 0.651239i | \(-0.225750\pi\) | ||||
0.758873 | + | 0.651239i | \(0.225750\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.91372i | 0.757997i | 0.925397 | + | 0.378999i | \(0.123731\pi\) | ||||
−0.925397 | + | 0.378999i | \(0.876269\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.0625 | + | 1.49519i | 1.42967 | + | 0.141917i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3770 | 1.35247 | 0.676236 | − | 0.736685i | \(-0.263610\pi\) | ||||
0.676236 | + | 0.736685i | \(0.263610\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.3793 | −1.62062 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.34870 | + | 6.72647i | −0.124688 | + | 0.621863i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.38016i | − | 0.584868i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.94797 | 0.358907 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.947973 | + | 9.54988i | −0.0854759 | + | 0.861084i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 17.4060i | − | 1.55684i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 19.0356i | − | 1.68914i | −0.535445 | − | 0.844570i | \(-0.679856\pi\) | ||
0.535445 | − | 0.844570i | \(-0.320144\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.92406 | + | 19.3830i | −0.169404 | + | 1.70658i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.97632i | 0.434783i | 0.976085 | + | 0.217391i | \(0.0697548\pi\) | ||||
−0.976085 | + | 0.217391i | \(0.930245\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.31671 | − | 7.50569i | 0.547728 | − | 0.650826i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18.9611 | − | 5.79944i | −1.63191 | − | 0.499137i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18.9827i | − | 1.62180i | −0.585185 | − | 0.810900i | \(-0.698978\pi\) | ||
0.585185 | − | 0.810900i | \(-0.301022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00108 | −0.254548 | −0.127274 | − | 0.991868i | \(-0.540623\pi\) | ||||
−0.127274 | + | 0.991868i | \(0.540623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.853124 | − | 0.0846857i | −0.0718460 | − | 0.00713182i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.07270 | −0.507825 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 22.4488i | − | 1.86427i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.331052 | + | 3.33502i | −0.0273047 | + | 0.275068i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.61357i | 0.623728i | 0.950127 | + | 0.311864i | \(0.100953\pi\) | ||||
−0.950127 | + | 0.311864i | \(0.899047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.94125i | − | 0.320735i | −0.987057 | − | 0.160367i | \(-0.948732\pi\) | ||
0.987057 | − | 0.160367i | \(-0.0512679\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.67198 | − | 8.33876i | 0.135171 | − | 0.674149i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.41060 | 0.755878 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.86987 | 0.308850 | 0.154425 | − | 0.988005i | \(-0.450648\pi\) | ||||
0.154425 | + | 0.988005i | \(0.450648\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.24405 | − | 12.5326i | 0.0986597 | − | 0.993898i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 10.2500i | − | 0.807809i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.867596 | 0.0679554 | 0.0339777 | − | 0.999423i | \(-0.489182\pi\) | ||||
0.0339777 | + | 0.999423i | \(0.489182\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.73376 | − | 17.4659i | 0.134973 | − | 1.35972i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.30604 | 0.720123 | 0.360061 | − | 0.932929i | \(-0.382756\pi\) | ||||
0.360061 | + | 0.932929i | \(0.382756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.77062 | 0.597740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.2228 | − | 8.15446i | 0.781754 | − | 0.623587i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.0436 | −1.59992 | −0.799959 | − | 0.600055i | \(-0.795145\pi\) | ||||
−0.799959 | + | 0.600055i | \(0.795145\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.5186 | 1.62665 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.14480 | + | 21.6067i | −0.161213 | + | 1.62406i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.5117 | −1.23414 | −0.617070 | − | 0.786909i | \(-0.711680\pi\) | ||||
−0.617070 | + | 0.786909i | \(0.711680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.25684i | 0.242079i | 0.992648 | + | 0.121040i | \(0.0386228\pi\) | ||||
−0.992648 | + | 0.121040i | \(0.961377\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.27448 | − | 12.8391i | 0.0942125 | − | 0.949097i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.3479 | −2.45179 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.52829 | 0.550523 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.42040 | − | 11.1829i | 0.248798 | − | 0.813437i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.3069i | 0.818135i | 0.912504 | + | 0.409068i | \(0.134146\pi\) | ||||
−0.912504 | + | 0.409068i | \(0.865854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.09844i | 0.223031i | 0.993763 | + | 0.111515i | \(0.0355705\pi\) | ||||
−0.993763 | + | 0.111515i | \(0.964430\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.49299 | − | 15.0404i | 0.106915 | − | 1.07706i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.0935i | 1.14662i | 0.819339 | + | 0.573309i | \(0.194341\pi\) | ||||
−0.819339 | + | 0.573309i | \(0.805659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.6477 | −1.18012 | −0.590060 | − | 0.807359i | \(-0.700896\pi\) | ||||
−0.590060 | + | 0.807359i | \(0.700896\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.75702 | − | 0.770004i | −0.547138 | − | 0.0543119i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.2399 | 0.929259 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 21.1431i | − | 1.47670i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.68609 | − | 13.3965i | 0.186696 | − | 0.931122i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.85636 | + | 7.45342i | 0.612607 | + | 0.515564i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.08804i | − | 0.0749035i | −0.999298 | − | 0.0374517i | \(-0.988076\pi\) | ||
0.999298 | − | 0.0374517i | \(-0.0119240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.446834 | − | 4.50141i | 0.0306166 | − | 0.308432i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 42.9132i | − | 2.92666i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.55019i | 0.376772i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.57056 | + | 15.8218i | −0.106129 | + | 1.06914i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.48283 | 0.436082 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.72681i | − | 0.115636i | −0.998327 | − | 0.0578178i | \(-0.981586\pi\) | ||
0.998327 | − | 0.0578178i | \(-0.0184143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 28.1244 | + | 5.63913i | 1.87496 | + | 0.375942i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.56905 | 0.236886 | 0.118443 | − | 0.992961i | \(-0.462210\pi\) | ||||
0.118443 | + | 0.992961i | \(0.462210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.7138 | −0.972315 | −0.486157 | − | 0.873871i | \(-0.661602\pi\) | ||||
−0.486157 | + | 0.873871i | \(0.661602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.3010 | + | 1.02254i | 0.677758 | + | 0.0672780i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.1712i | 0.666339i | 0.942867 | + | 0.333170i | \(0.108118\pi\) | ||||
−0.942867 | + | 0.333170i | \(0.891882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.88878 | 0.123211 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.81677 | + | 0.974466i | 0.637668 | + | 0.0632984i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.2902i | 1.89462i | 0.320311 | + | 0.947312i | \(0.396212\pi\) | ||||
−0.320311 | + | 0.947312i | \(0.603788\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.87075i | 0.184922i | 0.995716 | + | 0.0924608i | \(0.0294733\pi\) | ||||
−0.995716 | + | 0.0924608i | \(0.970527\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.40098 | − | 13.7195i | 0.474773 | − | 0.880108i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 7.38361i | − | 0.471721i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.62647 | + | 6.41835i | 0.485260 | + | 0.408390i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.3131 | + | 1.91712i | 1.22392 | + | 0.121493i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2.16863i | − | 0.136883i | −0.997655 | − | 0.0684413i | \(-0.978197\pi\) | ||
0.997655 | − | 0.0684413i | \(-0.0218026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0945 | 0.760372 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.85085 | + | 18.6454i | −0.115904 | + | 1.16762i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.8626 | −1.67564 | −0.837820 | − | 0.545946i | \(-0.816170\pi\) | ||||
−0.837820 | + | 0.545946i | \(0.816170\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 19.6680i | − | 1.22211i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.3043 | + | 3.46963i | 1.07111 | + | 0.214765i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.20316i | 0.382503i | 0.981541 | + | 0.191252i | \(0.0612547\pi\) | ||||
−0.981541 | + | 0.191252i | \(0.938745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.7466i | 1.70446i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.67849 | − | 26.9832i | 0.163921 | − | 1.65134i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0218 | 0.732979 | 0.366490 | − | 0.930422i | \(-0.380560\pi\) | ||||
0.366490 | + | 0.930422i | \(0.380560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.1381 | 1.46629 | 0.733143 | − | 0.680074i | \(-0.238052\pi\) | ||||
0.733143 | + | 0.680074i | \(0.238052\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.87052 | + | 0.880536i | 0.536868 | + | 0.0532924i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.3909i | 1.53113i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.68544 | −0.101268 | −0.0506342 | − | 0.998717i | \(-0.516124\pi\) | ||||
−0.0506342 | + | 0.998717i | \(0.516124\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.45448 | + | 7.25401i | −0.0870772 | + | 0.434286i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.07094 | 0.302507 | 0.151253 | − | 0.988495i | \(-0.451669\pi\) | ||||
0.151253 | + | 0.988495i | \(0.451669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.63234 | −0.0970326 | −0.0485163 | − | 0.998822i | \(-0.515449\pi\) | ||||
−0.0485163 | + | 0.998822i | \(0.515449\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −20.6373 | + | 20.1022i | −1.22245 | + | 1.19075i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.4698 | 0.736068 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.96329 | 0.527252 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.6250 | − | 3.23854i | −1.91251 | − | 0.189846i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.0567 | −1.34699 | −0.673493 | − | 0.739194i | \(-0.735207\pi\) | ||||
−0.673493 | + | 0.739194i | \(0.735207\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 47.8364i | − | 2.78514i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.1953 | + | 4.03591i | 0.765669 | + | 0.234187i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.4149 | 0.602309 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 25.3094 | 1.45881 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.9538 | + | 1.08734i | 0.629282 | + | 0.0624659i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 28.4254i | 1.62763i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.7799i | 1.41426i | 0.707083 | + | 0.707131i | \(0.250011\pi\) | ||||
−0.707083 | + | 0.707131i | \(0.749989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −16.2422 | − | 1.61229i | −0.923985 | − | 0.0917198i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9484i | 0.904348i | 0.891930 | + | 0.452174i | \(0.149351\pi\) | ||||
−0.891930 | + | 0.452174i | \(0.850649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3639 | −0.698851 | −0.349426 | − | 0.936964i | \(-0.613623\pi\) | ||||
−0.349426 | + | 0.936964i | \(0.613623\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.06506 | + | 25.2613i | −0.285384 | + | 1.42331i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.32435 | −0.299045 | −0.149523 | − | 0.988758i | \(-0.547774\pi\) | ||||
−0.149523 | + | 0.988758i | \(0.547774\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.6225i | 0.874689i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.68609 | − | 27.0597i | 0.149923 | − | 1.51032i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.45448 | − | 7.95678i | −0.526061 | − | 0.442727i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.8649i | 1.21284i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.6399 | + | 1.35397i | 0.754290 | + | 0.0748749i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.11397i | 0.0614151i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.7284i | 1.57905i | 0.613716 | + | 0.789527i | \(0.289674\pi\) | ||||
−0.613716 | + | 0.789527i | \(0.710326\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.15416 | − | 25.7057i | 0.282446 | − | 1.40866i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.1738 | 0.938303 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.6377i | − | 0.742893i | −0.928454 | − | 0.371446i | \(-0.878862\pi\) | ||
0.928454 | − | 0.371446i | \(-0.121138\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.45978 | − | 24.7799i | 0.133597 | − | 1.34586i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.54897 | −0.354646 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1087 | 1.08577 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.97345 | + | 29.9545i | −0.160085 | + | 1.61270i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 12.6100i | − | 0.676938i | −0.940978 | − | 0.338469i | \(-0.890091\pi\) | ||
0.940978 | − | 0.338469i | \(-0.109909\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.8201 | −1.16800 | −0.584002 | − | 0.811752i | \(-0.698514\pi\) | ||||
−0.584002 | + | 0.811752i | \(0.698514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.3629 | + | 3.47544i | 0.606505 | + | 0.185505i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 35.9018i | − | 1.91086i | −0.295219 | − | 0.955430i | \(-0.595393\pi\) | ||
0.295219 | − | 0.955430i | \(-0.404607\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.96595i | 0.528938i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.9967 | − | 1.09159i | −0.582008 | − | 0.0577733i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.5408i | 0.767434i | 0.923451 | + | 0.383717i | \(0.125356\pi\) | ||||
−0.923451 | + | 0.383717i | \(0.874644\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.24470 | − | 18.7209i | −0.170773 | − | 0.985310i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.675466 | − | 6.80465i | 0.0354528 | − | 0.357151i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 35.0289i | − | 1.83350i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.8603 | −1.24550 | −0.622748 | − | 0.782422i | \(-0.713984\pi\) | ||||
−0.622748 | + | 0.782422i | \(0.713984\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.2978 | + | 3.26782i | 0.848430 | + | 0.170116i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.3644 | −0.849600 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.5769i | − | 0.806543i | −0.915080 | − | 0.403271i | \(-0.867873\pi\) | ||
0.915080 | − | 0.403271i | \(-0.132127\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −30.0007 | − | 2.97803i | −1.54923 | − | 0.153785i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.4529i | 0.692862i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.11160i | 0.262565i | 0.991345 | + | 0.131283i | \(0.0419095\pi\) | ||||
−0.991345 | + | 0.131283i | \(0.958090\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.8095 | − | 3.25684i | −1.68088 | − | 0.166853i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.56084 | −0.488536 | −0.244268 | − | 0.969708i | \(-0.578548\pi\) | ||||
−0.244268 | + | 0.969708i | \(0.578548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.8061 | −1.16231 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.0789 | + | 6.63254i | 1.68150 | + | 0.337151i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 28.6239i | − | 1.45129i | −0.688070 | − | 0.725645i | \(-0.741542\pi\) | ||
0.688070 | − | 0.725645i | \(-0.258458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.9113 | −0.652951 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.57708 | + | 0.851407i | 0.432656 | + | 0.0429478i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.7340 | −1.09355 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.1771 | 1.56473 | 0.782367 | − | 0.622817i | \(-0.214012\pi\) | ||||
0.782367 | + | 0.622817i | \(0.214012\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.8559 | − | 12.1715i | −0.593538 | − | 0.609338i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.8686 | 1.19194 | 0.595972 | − | 0.803006i | \(-0.296767\pi\) | ||||
0.595972 | + | 0.803006i | \(0.296767\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.63950 | −0.280924 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.2399 | + | 31.6888i | −0.657896 | + | 1.57463i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.2073 | 1.15034 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.6493i | − | 0.773806i | −0.922120 | − | 0.386903i | \(-0.873545\pi\) | ||
0.922120 | − | 0.386903i | \(-0.126455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32.7182 | − | 3.24778i | −1.61387 | − | 0.160201i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.2130 | 1.38827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.7585 | −2.09893 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.513460 | + | 5.17259i | −0.0251442 | + | 0.253303i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.8833i | 0.775952i | 0.921669 | + | 0.387976i | \(0.126826\pi\) | ||||
−0.921669 | + | 0.387976i | \(0.873174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.2495i | 0.548266i | 0.961692 | + | 0.274133i | \(0.0883908\pi\) | ||||
−0.961692 | + | 0.274133i | \(0.911609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.291925 | + | 1.45594i | −0.0141939 | + | 0.0707901i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 27.1057i | − | 1.31482i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.7647 | −0.811303 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.03899 | + | 10.4668i | −0.0501629 | + | 0.505341i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0654 | −0.822011 | −0.411005 | − | 0.911633i | \(-0.634822\pi\) | ||||
−0.411005 | + | 0.911633i | \(0.634822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.09844i | 0.148902i | 0.997225 | + | 0.0744509i | \(0.0237204\pi\) | ||||
−0.997225 | + | 0.0744509i | \(0.976280\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38.6924 | − | 3.84081i | −1.85516 | − | 0.184153i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.1889 | − | 12.7829i | −0.726586 | − | 0.611487i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0460i | 1.19538i | 0.801728 | + | 0.597689i | \(0.203914\pi\) | ||||
−0.801728 | + | 0.597689i | \(0.796086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.69153 | + | 1.14119i | 0.271025 | + | 0.0543423i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 14.1750i | − | 0.673473i | −0.941599 | − | 0.336736i | \(-0.890677\pi\) | ||
0.941599 | − | 0.336736i | \(-0.109323\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 59.7397i | 2.83193i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.1226 | + | 1.30262i | 0.620678 | + | 0.0616118i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.2647 | −1.38109 | −0.690543 | − | 0.723291i | \(-0.742628\pi\) | ||||
−0.690543 | + | 0.723291i | \(0.742628\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.7138i | 0.692844i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.79306 | − | 0.674316i | −0.319166 | − | 0.0316821i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.6390 | −0.920690 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0600 | −1.07870 | −0.539351 | − | 0.842081i | \(-0.681330\pi\) | ||||
−0.539351 | + | 0.842081i | \(0.681330\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.0865 | − | 4.30848i | −0.657499 | − | 0.201103i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.5397i | 1.56210i | 0.624468 | + | 0.781050i | \(0.285316\pi\) | ||||
−0.624468 | + | 0.781050i | \(0.714684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.0911044 | 0.00423398 | 0.00211699 | − | 0.999998i | \(-0.499326\pi\) | ||||
0.00211699 | + | 0.999998i | \(0.499326\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.61008 | − | 16.2199i | 0.0746655 | − | 0.752181i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 15.5968i | − | 0.721735i | −0.932617 | − | 0.360867i | \(-0.882481\pi\) | ||
0.932617 | − | 0.360867i | \(-0.117519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1288i | 0.467703i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.662104 | − | 6.67004i | 0.0305081 | − | 0.307339i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 29.8639i | 1.37314i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.8361 | − | 31.8875i | 1.23133 | − | 1.46310i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.3880 | − | 4.28844i | −0.979291 | − | 0.196354i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.6287i | 1.12531i | 0.826690 | + | 0.562657i | \(0.190221\pi\) | ||||
−0.826690 | + | 0.562657i | \(0.809779\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.9844 | 0.911212 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.6666 | − | 1.75368i | −0.803859 | − | 0.0797954i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 72.2306 | 3.27982 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.30362i | − | 0.104387i | −0.998637 | − | 0.0521936i | \(-0.983379\pi\) | ||
0.998637 | − | 0.0521936i | \(-0.0166213\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.148439 | − | 1.49537i | 0.00671263 | − | 0.0676230i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.9715i | − | 0.585394i | −0.956205 | − | 0.292697i | \(-0.905447\pi\) | ||
0.956205 | − | 0.292697i | \(-0.0945528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.6775i | − | 0.751118i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.8072 | − | 5.97653i | −1.33973 | − | 0.268625i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.87773 | −0.263652 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.6523 | −0.566396 | −0.283198 | − | 0.959061i | \(-0.591395\pi\) | ||||
−0.283198 | + | 0.959061i | \(0.591395\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.59219 | − | 16.0397i | 0.0711337 | − | 0.716601i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.6642i | 1.01055i | 0.862959 | + | 0.505274i | \(0.168608\pi\) | ||||
−0.862959 | + | 0.505274i | \(0.831392\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.2514 | −1.07917 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.32949 | − | 13.3933i | 0.0590447 | − | 0.594816i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.4307 | 1.12720 | 0.563598 | − | 0.826049i | \(-0.309417\pi\) | ||||
0.563598 | + | 0.826049i | \(0.309417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.6594 | 0.913918 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.3058 | − | 19.0149i | −0.543316 | − | 0.839528i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.9596 | 1.58457 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.31443 | −0.0578086 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.60039 | + | 36.2704i | −0.158040 | + | 1.59209i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.871132 | 0.0381650 | 0.0190825 | − | 0.999818i | \(-0.493925\pi\) | ||||
0.0190825 | + | 0.999818i | \(0.493925\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.22847i | 0.359806i | 0.983684 | + | 0.179903i | \(0.0575784\pi\) | ||||
−0.983684 | + | 0.179903i | \(0.942422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.68166 | − | 37.0890i | 0.160681 | − | 1.61870i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.99125 | 0.304544 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.25761 | 0.0981568 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.8739 | + | 7.39345i | 1.60019 | + | 0.320849i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.6704i | 0.548818i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.9091i | 2.59009i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.82501 | + | 28.4592i | −0.121908 | + | 1.22810i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.13835i | 0.221324i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0921 | −0.605868 | −0.302934 | − | 0.953012i | \(-0.597966\pi\) | ||||
−0.302934 | + | 0.953012i | \(0.597966\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.61343 | + | 0.557220i | 0.240895 | + | 0.0239126i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30.1983 | −1.29355 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.2685i | − | 0.695590i | −0.937571 | − | 0.347795i | \(-0.886930\pi\) | ||
0.937571 | − | 0.347795i | \(-0.113070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.9112 | − | 4.39335i | −0.935148 | − | 0.187503i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.5117 | − | 19.6196i | 0.703420 | − | 0.835824i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 12.8183i | − | 0.545089i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.70556 | + | 57.4778i | −0.242187 | + | 2.43980i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.902307i | 0.0382320i | 0.999817 | + | 0.0191160i | \(0.00608518\pi\) | ||||
−0.999817 | + | 0.0191160i | \(0.993915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.7167i | 1.08770i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.28803 | − | 12.9756i | 0.0543806 | − | 0.547830i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.2095 | −0.514571 | −0.257285 | − | 0.966335i | \(-0.582828\pi\) | ||||
−0.257285 | + | 0.966335i | \(0.582828\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 54.8617i | 2.30805i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.6894 | − | 7.80864i | −0.784883 | − | 0.327932i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.4024 | 1.02300 | 0.511500 | − | 0.859283i | \(-0.329090\pi\) | ||||
0.511500 | + | 0.859283i | \(0.329090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.61343 | 0.234915 | 0.117457 | − | 0.993078i | \(-0.462526\pi\) | ||||
0.117457 | + | 0.993078i | \(0.462526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.4883 | + | 1.93451i | 0.814134 | + | 0.0808153i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 43.5463i | − | 1.81601i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.55433 | −0.356121 | −0.178061 | − | 0.984020i | \(-0.556982\pi\) | ||||
−0.178061 | + | 0.984020i | \(0.556982\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.34042 | + | 0.530119i | 0.221940 | + | 0.0220310i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 25.2182i | − | 1.04623i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 19.3093i | − | 0.799708i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.6678 | − | 5.14657i | −1.06123 | − | 0.212784i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.8038i | 0.858663i | 0.903147 | + | 0.429332i | \(0.141251\pi\) | ||||
−0.903147 | + | 0.429332i | \(0.858749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.22458 | + | 6.92172i | 0.338888 | + | 0.285205i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.7385 | + | 2.75348i | 1.14101 | + | 0.113263i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.86257i | 0.199682i | 0.995003 | + | 0.0998408i | \(0.0318334\pi\) | ||||
−0.995003 | + | 0.0998408i | \(0.968167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.3463 | 0.998102 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.84828 | + | 28.6936i | −0.116572 | + | 1.17435i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.185633 | 0.00758475 | 0.00379238 | − | 0.999993i | \(-0.498793\pi\) | ||||
0.00379238 | + | 0.999993i | \(0.498793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6772i | 0.680278i | 0.940375 | + | 0.340139i | \(0.110474\pi\) | ||||
−0.940375 | + | 0.340139i | \(0.889526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.65433 | + | 13.2381i | −0.108093 | + | 0.539098i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.0652i | 0.612489i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.42863i | 0.260930i | 0.991453 | + | 0.130465i | \(0.0416470\pi\) | ||||
−0.991453 | + | 0.130465i | \(0.958353\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.26524 | − | 22.8200i | 0.0917921 | − | 0.924714i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.13189 | −0.0457915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.4017 | 0.702848 | 0.351424 | − | 0.936216i | \(-0.385698\pi\) | ||||
0.351424 | + | 0.936216i | \(0.385698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.4418 | − | 3.61741i | −1.46947 | − | 0.145868i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.5793i | 1.02978i | 0.857255 | + | 0.514892i | \(0.172168\pi\) | ||||
−0.857255 | + | 0.514892i | \(0.827832\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0223 | 0.965536 | 0.482768 | − | 0.875748i | \(-0.339631\pi\) | ||||
0.482768 | + | 0.875748i | \(0.339631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.6304 | − | 6.92172i | −0.908126 | − | 0.277759i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.2333 | −1.41159 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.6134 | 0.744537 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.3618 | − | 13.9894i | 0.573555 | − | 0.558684i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.7746 | −0.987827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.6250 | 0.661832 | 0.330916 | − | 0.943660i | \(-0.392642\pi\) | ||||
0.330916 | + | 0.943660i | \(0.392642\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.87532 | − | 0.186154i | −0.0745371 | − | 0.00739896i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 72.6389 | 2.88259 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.42478i | 0.175316i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.68209 | − | 1.54031i | −0.303899 | − | 0.0609337i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.3470 | −0.685165 | −0.342582 | − | 0.939488i | \(-0.611302\pi\) | ||||
−0.342582 | + | 0.939488i | \(0.611302\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.7478 | 1.33088 | 0.665442 | − | 0.746449i | \(-0.268243\pi\) | ||||
0.665442 | + | 0.746449i | \(0.268243\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −73.9643 | − | 7.34210i | −2.91234 | − | 0.289095i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.6469i | − | 0.968971i | −0.874799 | − | 0.484485i | \(-0.839007\pi\) | ||
0.874799 | − | 0.484485i | \(-0.160993\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.2900i | 1.30675i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.56620 | + | 0.949593i | 0.374929 | + | 0.0372175i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 16.5941i | − | 0.649377i | −0.945821 | − | 0.324688i | \(-0.894741\pi\) | ||
0.945821 | − | 0.324688i | \(-0.105259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.9893 | −0.741974 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 27.0015 | + | 5.41397i | 1.05343 | + | 0.211219i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.1807 | −0.864038 | −0.432019 | − | 0.901865i | \(-0.642199\pi\) | ||||
−0.432019 | + | 0.901865i | \(0.642199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.15429i | 0.356061i | 0.984025 | + | 0.178030i | \(0.0569725\pi\) | ||||
−0.984025 | + | 0.178030i | \(0.943027\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.10916 | − | 11.1737i | 0.0430762 | − | 0.433949i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.6413 | + | 24.1042i | 1.11066 | + | 0.934720i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 26.7930i | − | 1.03743i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.97629 | − | 0.295443i | −0.115070 | − | 0.0114225i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 19.7816i | − | 0.763660i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.9193i | − | 1.11476i | −0.830259 | − | 0.557378i | \(-0.811807\pi\) | ||
0.830259 | − | 0.557378i | \(-0.188193\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.5314 | − | 47.5099i | 0.559312 | − | 1.82866i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.2974 | −1.70249 | −0.851244 | − | 0.524770i | \(-0.824151\pi\) | ||||
−0.851244 | + | 0.524770i | \(0.824151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.6002i | 1.63485i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.610635 | − | 6.15154i | 0.0233996 | − | 0.235727i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.8231 | −1.56205 | −0.781026 | − | 0.624498i | \(-0.785303\pi\) | ||||
−0.781026 | + | 0.624498i | \(0.785303\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 72.4368 | 2.76767 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.51741 | + | 25.3604i | −0.0960452 | + | 0.967560i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 16.6278i | − | 0.633468i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.00931 | 0.0764379 | 0.0382190 | − | 0.999269i | \(-0.487832\pi\) | ||||
0.0382190 | + | 0.999269i | \(0.487832\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.52485 | − | 17.5797i | 0.133898 | − | 0.667798i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 11.4519i | − | 0.434396i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 15.7075i | − | 0.594962i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.5309 | + | 1.74021i | 0.663081 | + | 0.0658210i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.7737i | 1.61554i | 0.589498 | + | 0.807770i | \(0.299326\pi\) | ||||
−0.589498 | + | 0.807770i | \(0.700674\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.1451 | − | 24.5282i | −1.09923 | − | 0.925098i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.323156 | − | 3.25547i | 0.0121707 | − | 0.122608i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 14.3030i | − | 0.537920i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.35699 | −0.276297 | −0.138149 | − | 0.990411i | \(-0.544115\pi\) | ||||
−0.138149 | + | 0.990411i | \(0.544115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.35914 | − | 16.7533i | 0.125978 | − | 0.628297i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.2317 | 0.420630 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 23.1731i | − | 0.866624i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 50.4840 | + | 5.01131i | 1.88536 | + | 0.187151i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 28.5523i | − | 1.06482i | −0.846487 | − | 0.532410i | \(-0.821287\pi\) | ||
0.846487 | − | 0.532410i | \(-0.178713\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21.2083i | 0.789837i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.94797 | + | 0.491163i | 0.184017 | + | 0.0182665i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 56.2489 | 2.08903 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.2105 | −0.638301 | −0.319151 | − | 0.947704i | \(-0.603398\pi\) | ||||
−0.319151 | + | 0.947704i | \(0.603398\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.3805 | − | 15.1035i | −0.828906 | − | 0.559388i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 31.8807i | − | 1.17915i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.4961 | 1.71737 | 0.858686 | − | 0.512502i | \(-0.171281\pi\) | ||||
0.858686 | + | 0.512502i | \(0.171281\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.7262 | − | 1.26327i | −0.469414 | − | 0.0465966i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.9515 | −0.440237 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.9538 | 1.17544 | 0.587720 | − | 0.809065i | \(-0.300026\pi\) | ||||
0.587720 | + | 0.809065i | \(0.300026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.3674 | − | 12.0467i | 0.454327 | − | 0.442546i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.76126 | 0.211360 | 0.105680 | − | 0.994400i | \(-0.466298\pi\) | ||||
0.105680 | + | 0.994400i | \(0.466298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.0529 | −1.06442 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.60863 | − | 32.9597i | 0.241797 | − | 1.20593i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.3332 | −1.29105 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.9383i | 0.910010i | 0.890489 | + | 0.455005i | \(0.150363\pi\) | ||||
−0.890489 | + | 0.455005i | \(0.849637\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.73780 | − | 0.371034i | −0.136213 | − | 0.0135212i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.0396 | 0.547347 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.0990 | −1.67550 | −0.837748 | − | 0.546056i | \(-0.816128\pi\) | ||||
−0.837748 | + | 0.546056i | \(0.816128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.06926 | − | 20.8458i | 0.0751095 | − | 0.756653i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.9040i | 0.504019i | 0.967725 | + | 0.252009i | \(0.0810914\pi\) | ||||
−0.967725 | + | 0.252009i | \(0.918909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 17.8104i | − | 0.644779i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.8202 | + | 6.38016i | 1.15046 | + | 0.230675i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.6670i | 1.03510i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.8204 | −0.390192 | −0.195096 | − | 0.980784i | \(-0.562502\pi\) | ||||
−0.195096 | + | 0.980784i | \(0.562502\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.59597 | + | 46.2998i | −0.165520 | + | 1.66745i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.2320 | −0.979469 | −0.489734 | − | 0.871872i | \(-0.662906\pi\) | ||||
−0.489734 | + | 0.871872i | \(0.662906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.5797i | 0.847006i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.8993 | − | 3.36503i | −1.21613 | − | 0.120720i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.5512 | − | 18.4784i | 0.557181 | − | 0.662058i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.93544i | − | 0.248170i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.94081 | − | 29.2317i | 0.319518 | − | 1.04466i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.7672i | 0.527064i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.8222i | 0.635292i | 0.948209 | + | 0.317646i | \(0.102892\pi\) | ||||
−0.948209 | + | 0.317646i | \(0.897108\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.6916 | + | 1.06131i | 0.380633 | + | 0.0377837i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.3564 | −1.15046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 17.0345i | − | 0.604913i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 47.8236 | + | 4.74723i | 1.69613 | + | 0.168367i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.42768 | −0.333946 | −0.166973 | − | 0.985961i | \(-0.553399\pi\) | ||||
−0.166973 | + | 0.985961i | \(0.553399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.40320 | 0.0496417 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −46.0494 | − | 9.23320i | −1.62707 | − | 0.326239i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.3771i | 0.860250i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39.1132 | 1.37856 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.05682 | − | 20.7205i | 0.0724036 | − | 0.729394i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 17.3813i | − | 0.611094i | −0.952177 | − | 0.305547i | \(-0.901161\pi\) | ||
0.952177 | − | 0.305547i | \(-0.0988393\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 16.7489i | − | 0.588132i | −0.955785 | − | 0.294066i | \(-0.904991\pi\) | ||
0.955785 | − | 0.294066i | \(-0.0950086\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.12984 | − | 41.6040i | 0.144840 | − | 1.45912i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.31070i | 0.115969i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.5637 | − | 37.5049i | 1.10427 | − | 1.31213i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.03535 | − | 15.1384i | 0.106064 | − | 0.528978i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.825562i | 0.0288123i | 0.999896 | + | 0.0144061i | \(0.00458578\pi\) | ||||
−0.999896 | + | 0.0144061i | \(0.995414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.5102 | 1.44696 | 0.723478 | − | 0.690348i | \(-0.242543\pi\) | ||||
0.723478 | + | 0.690348i | \(0.242543\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 43.7633 | + | 4.34418i | 1.52364 | + | 0.151245i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.7955 | −0.514490 | −0.257245 | − | 0.966346i | \(-0.582815\pi\) | ||||
−0.257245 | + | 0.966346i | \(0.582815\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 24.0746i | − | 0.836146i | −0.908413 | − | 0.418073i | \(-0.862706\pi\) | ||
0.908413 | − | 0.418073i | \(-0.137294\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.288366 | + | 2.90500i | −0.0100033 | + | 0.100773i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.48537i | − | 0.190057i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 35.5113i | 1.22892i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2540 | + | 3.74801i | 0.423561 | + | 0.129550i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.4785 | −1.01771 | −0.508856 | − | 0.860852i | \(-0.669931\pi\) | ||||
−0.508856 | + | 0.860852i | \(0.669931\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.60863 | 0.193401 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.867596 | − | 8.74016i | 0.0298816 | − | 0.301027i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29.6522i | 1.02007i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.88519 | −0.305299 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.279280 | + | 2.81347i | −0.00958487 | + | 0.0965580i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.8012 | −1.36437 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.1274 | −0.860345 | −0.430172 | − | 0.902747i | \(-0.641547\pi\) | ||||
−0.430172 | + | 0.902747i | \(0.641547\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.1169 | + | 39.0094i | 1.06418 | + | 1.33409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.6045 | 0.498879 | 0.249440 | − | 0.968390i | \(-0.419754\pi\) | ||||
0.249440 | + | 0.968390i | \(0.419754\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.8175 | −1.49503 | −0.747517 | − | 0.664243i | \(-0.768754\pi\) | ||||
−0.747517 | + | 0.664243i | \(0.768754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.13348 | − | 21.4927i | 0.0727088 | − | 0.732469i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.32564 | −0.181287 | −0.0906434 | − | 0.995883i | \(-0.528892\pi\) | ||||
−0.0906434 | + | 0.995883i | \(0.528892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 80.3013i | − | 2.73032i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.53355 | − | 15.4489i | 0.0520819 | − | 0.524674i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.1250 | 0.513079 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.2917 | −0.348722 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.1638 | + | 55.6777i | −0.377836 | + | 1.88441i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 39.1735i | 1.32431i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.4136i | 0.959460i | 0.877416 | + | 0.479730i | \(0.159265\pi\) | ||||
−0.877416 | + | 0.479730i | \(0.840735\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.94481 | + | 39.7400i | −0.133055 | + | 1.34040i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.8937i | 1.41143i | 0.708494 | + | 0.705717i | \(0.249375\pi\) | ||||
−0.708494 | + | 0.705717i | \(0.750625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.5054 | 1.16120 | 0.580600 | − | 0.814189i | \(-0.302818\pi\) | ||||
0.580600 | + | 0.814189i | \(0.302818\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −82.4498 | − | 8.18441i | −2.77152 | − | 0.275116i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.4766 | 1.05688 | 0.528441 | − | 0.848970i | \(-0.322777\pi\) | ||||
0.528441 | + | 0.848970i | \(0.322777\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.8410i | 1.43684i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.21383 | − | 22.0527i | 0.308675 | − | 0.738792i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.65074 | + | 1.38925i | 0.0552399 | + | 0.0464893i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 63.0075i | − | 2.10611i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.78190 | − | 17.9509i | 0.0594960 | − | 0.599363i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.5080i | 0.483869i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.6133i | 0.686730i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.33023 | − | 43.6228i | 0.144101 | − | 1.45167i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.4279 | −0.413118 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 27.2812i | − | 0.905859i | −0.891546 | − | 0.452929i | \(-0.850379\pi\) | ||
0.891546 | − | 0.452929i | \(-0.149621\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.74823 | − | 18.6938i | 0.124321 | − | 0.620034i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.78855 | −0.324309 | −0.162155 | − | 0.986765i | \(-0.551844\pi\) | ||||
−0.162155 | + | 0.986765i | \(0.551844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.7562 | 0.984787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48.9934 | + | 4.86335i | 1.61967 | + | 0.160777i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 11.1995i | − | 0.369842i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0317 | −0.726758 | −0.363379 | − | 0.931641i | \(-0.618377\pi\) | ||||
−0.363379 | + | 0.931641i | \(0.618377\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 42.7101 | + | 4.23963i | 1.40734 | + | 0.139701i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5.97231i | − | 0.196581i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 83.5581i | − | 2.74737i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.55781 | + | 27.7188i | −0.182542 | + | 0.910406i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 33.7271i | − | 1.10655i | −0.832999 | − | 0.553275i | \(-0.813378\pi\) | ||
0.832999 | − | 0.553275i | \(-0.186622\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.43082 | − | 6.45305i | 0.177988 | − | 0.211490i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.4883 | + | 2.72863i | 0.899925 | + | 0.0893315i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.7275i | 0.939490i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.78483 | −0.123645 | −0.0618224 | − | 0.998087i | \(-0.519691\pi\) | ||||
−0.0618224 | + | 0.998087i | \(0.519691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.11537 | + | 21.3102i | −0.0690325 | + | 0.695433i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.8637 | 1.49511 | 0.747557 | − | 0.664197i | \(-0.231227\pi\) | ||||
0.747557 | + | 0.664197i | \(0.231227\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 25.2346i | − | 0.821751i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 42.6733 | + | 13.0520i | 1.38816 | + | 0.424583i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 59.6666i | 1.93890i | 0.245282 | + | 0.969452i | \(0.421119\pi\) | ||||
−0.245282 | + | 0.969452i | \(0.578881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.9918i | 0.681424i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.910953 | + | 9.17694i | −0.0295397 | + | 0.297583i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.1016 | −0.489188 | −0.244594 | − | 0.969626i | \(-0.578655\pi\) | ||||
−0.244594 | + | 0.969626i | \(0.578655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.1463 | −1.39618 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 26.9265 | + | 2.67287i | 0.870412 | + | 0.0864018i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 42.7218i | 1.37956i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.9182 | 0.803813 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −46.1799 | − | 9.25937i | −1.48813 | − | 0.298379i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.8235 | −0.380611 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.4893 | 1.20557 | 0.602787 | − | 0.797902i | \(-0.294057\pi\) | ||||
0.602787 | + | 0.797902i | \(0.294057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.3317 | + | 14.9342i | −0.492526 | + | 0.479756i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.2468 | −0.585569 | −0.292785 | − | 0.956178i | \(-0.594582\pi\) | ||||
−0.292785 | + | 0.956178i | \(0.594582\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.75413 | 0.216527 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 37.6858 | + | 3.74090i | 1.20691 | + | 0.119805i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.75446 | 0.280080 | 0.140040 | − | 0.990146i | \(-0.455277\pi\) | ||||
0.140040 | + | 0.990146i | \(0.455277\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 41.5737i | − | 1.32870i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.66736 | − | 23.2779i | 0.149017 | − | 0.743205i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.3083 | 1.60459 | 0.802293 | − | 0.596930i | \(-0.203613\pi\) | ||||
0.802293 | + | 0.596930i | \(0.203613\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −61.4120 | −1.95675 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.92001 | + | 0.190591i | 0.0611147 | + | 0.00606658i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 51.2175i | − | 1.62862i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 41.2656i | − | 1.31085i | −0.755262 | − | 0.655423i | \(-0.772491\pi\) | ||
0.755262 | − | 0.655423i | \(-0.227509\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 49.5157 | + | 4.91519i | 1.57133 | + | 0.155979i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 63.5265i | − | 2.01392i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.380791 | −0.0120598 | −0.00602988 | − | 0.999982i | \(-0.501919\pi\) | ||||
−0.00602988 | + | 0.999982i | \(0.501919\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −43.4240 | − | 13.2816i | −1.37387 | − | 0.420212i |
(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 | 912.2.f.h.113.5 | 10 | ||
3.2 | odd | 2 | 912.2.f.i.113.5 | 10 | |||
4.3 | odd | 2 | 456.2.f.b.113.6 | yes | 10 | ||
12.11 | even | 2 | 456.2.f.a.113.6 | yes | 10 | ||
19.18 | odd | 2 | 912.2.f.i.113.6 | 10 | |||
57.56 | even | 2 | inner | 912.2.f.h.113.6 | 10 | ||
76.75 | even | 2 | 456.2.f.a.113.5 | ✓ | 10 | ||
228.227 | odd | 2 | 456.2.f.b.113.5 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.f.a.113.5 | ✓ | 10 | 76.75 | even | 2 | ||
456.2.f.a.113.6 | yes | 10 | 12.11 | even | 2 | ||
456.2.f.b.113.5 | yes | 10 | 228.227 | odd | 2 | ||
456.2.f.b.113.6 | yes | 10 | 4.3 | odd | 2 | ||
912.2.f.h.113.5 | 10 | 1.1 | even | 1 | trivial | ||
912.2.f.h.113.6 | 10 | 57.56 | even | 2 | inner | ||
912.2.f.i.113.5 | 10 | 3.2 | odd | 2 | |||
912.2.f.i.113.6 | 10 | 19.18 | odd | 2 |