Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(337,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.c (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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.337 |
Dual form | 1183.2.c.c.337.4 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.61803i | − 1.85123i | −0.378467 | − | 0.925615i | \(-0.623549\pi\) | ||||
0.378467 | − | 0.925615i | \(-0.376451\pi\) | |||||||
\(3\) | −2.61803 | −1.51152 | −0.755761 | − | 0.654847i | \(-0.772733\pi\) | ||||
−0.755761 | + | 0.654847i | \(0.772733\pi\) | |||||||
\(4\) | −4.85410 | −2.42705 | ||||||||
\(5\) | − 2.61803i | − 1.17082i | −0.810737 | − | 0.585410i | \(-0.800933\pi\) | ||||
0.810737 | − | 0.585410i | \(-0.199067\pi\) | |||||||
\(6\) | 6.85410i | 2.79818i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 7.47214i | 2.64180i | ||||||||
\(9\) | 3.85410 | 1.28470 | ||||||||
\(10\) | −6.85410 | −2.16746 | ||||||||
\(11\) | 1.85410i | 0.559033i | 0.960141 | + | 0.279516i | \(0.0901741\pi\) | ||||
−0.960141 | + | 0.279516i | \(0.909826\pi\) | |||||||
\(12\) | 12.7082 | 3.66854 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.61803 | 0.699699 | ||||||||
\(15\) | 6.85410i | 1.76972i | ||||||||
\(16\) | 9.85410 | 2.46353 | ||||||||
\(17\) | 1.47214 | 0.357045 | 0.178523 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178523 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(18\) | − 10.0902i | − 2.37828i | ||||||||
\(19\) | 1.85410i | 0.425360i | 0.977122 | + | 0.212680i | \(0.0682192\pi\) | ||||
−0.977122 | + | 0.212680i | \(0.931781\pi\) | |||||||
\(20\) | 12.7082i | 2.84164i | ||||||||
\(21\) | − 2.61803i | − 0.571302i | ||||||||
\(22\) | 4.85410 | 1.03490 | ||||||||
\(23\) | 4.47214 | 0.932505 | 0.466252 | − | 0.884652i | \(-0.345604\pi\) | ||||
0.466252 | + | 0.884652i | \(0.345604\pi\) | |||||||
\(24\) | − 19.5623i | − 3.99314i | ||||||||
\(25\) | −1.85410 | −0.370820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | − 4.85410i | − 0.917339i | ||||||||
\(29\) | 7.09017 | 1.31661 | 0.658306 | − | 0.752751i | \(-0.271273\pi\) | ||||
0.658306 | + | 0.752751i | \(0.271273\pi\) | |||||||
\(30\) | 17.9443 | 3.27616 | ||||||||
\(31\) | 4.70820i | 0.845618i | 0.906219 | + | 0.422809i | \(0.138956\pi\) | ||||
−0.906219 | + | 0.422809i | \(0.861044\pi\) | |||||||
\(32\) | − 10.8541i | − 1.91875i | ||||||||
\(33\) | − 4.85410i | − 0.844991i | ||||||||
\(34\) | − 3.85410i | − 0.660973i | ||||||||
\(35\) | 2.61803 | 0.442529 | ||||||||
\(36\) | −18.7082 | −3.11803 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 4.85410 | 0.787439 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 19.5623 | 3.09307 | ||||||||
\(41\) | − 0.763932i | − 0.119306i | −0.998219 | − | 0.0596531i | \(-0.981001\pi\) | ||||
0.998219 | − | 0.0596531i | \(-0.0189994\pi\) | |||||||
\(42\) | −6.85410 | −1.05761 | ||||||||
\(43\) | −12.5623 | −1.91573 | −0.957867 | − | 0.287213i | \(-0.907271\pi\) | ||||
−0.957867 | + | 0.287213i | \(0.907271\pi\) | |||||||
\(44\) | − 9.00000i | − 1.35680i | ||||||||
\(45\) | − 10.0902i | − 1.50415i | ||||||||
\(46\) | − 11.7082i | − 1.72628i | ||||||||
\(47\) | − 2.23607i | − 0.326164i | −0.986613 | − | 0.163082i | \(-0.947856\pi\) | ||||
0.986613 | − | 0.163082i | \(-0.0521435\pi\) | |||||||
\(48\) | −25.7984 | −3.72367 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 4.85410i | 0.686474i | ||||||||
\(51\) | −3.85410 | −0.539682 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.76393 | 0.517016 | 0.258508 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258508 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(54\) | 5.85410i | 0.796642i | ||||||||
\(55\) | 4.85410 | 0.654527 | ||||||||
\(56\) | −7.47214 | −0.998506 | ||||||||
\(57\) | − 4.85410i | − 0.642942i | ||||||||
\(58\) | − 18.5623i | − 2.43735i | ||||||||
\(59\) | − 2.23607i | − 0.291111i | −0.989350 | − | 0.145556i | \(-0.953503\pi\) | ||||
0.989350 | − | 0.145556i | \(-0.0464970\pi\) | |||||||
\(60\) | − 33.2705i | − 4.29520i | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 12.3262 | 1.56543 | ||||||||
\(63\) | 3.85410i | 0.485571i | ||||||||
\(64\) | −8.70820 | −1.08853 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12.7082 | −1.56427 | ||||||||
\(67\) | 12.7082i | 1.55255i | 0.630392 | + | 0.776277i | \(0.282894\pi\) | ||||
−0.630392 | + | 0.776277i | \(0.717106\pi\) | |||||||
\(68\) | −7.14590 | −0.866567 | ||||||||
\(69\) | −11.7082 | −1.40950 | ||||||||
\(70\) | − 6.85410i | − 0.819222i | ||||||||
\(71\) | 14.1803i | 1.68290i | 0.540338 | + | 0.841448i | \(0.318297\pi\) | ||||
−0.540338 | + | 0.841448i | \(0.681703\pi\) | |||||||
\(72\) | 28.7984i | 3.39392i | ||||||||
\(73\) | − 2.00000i | − 0.234082i | −0.993127 | − | 0.117041i | \(-0.962659\pi\) | ||||
0.993127 | − | 0.117041i | \(-0.0373409\pi\) | |||||||
\(74\) | 10.4721 | 1.21736 | ||||||||
\(75\) | 4.85410 | 0.560503 | ||||||||
\(76\) | − 9.00000i | − 1.03237i | ||||||||
\(77\) | −1.85410 | −0.211295 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | − 25.7984i | − 2.88435i | ||||||||
\(81\) | −5.70820 | −0.634245 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | − 6.70820i | − 0.736321i | −0.929762 | − | 0.368161i | \(-0.879988\pi\) | ||||
0.929762 | − | 0.368161i | \(-0.120012\pi\) | |||||||
\(84\) | 12.7082i | 1.38658i | ||||||||
\(85\) | − 3.85410i | − 0.418036i | ||||||||
\(86\) | 32.8885i | 3.54646i | ||||||||
\(87\) | −18.5623 | −1.99009 | ||||||||
\(88\) | −13.8541 | −1.47685 | ||||||||
\(89\) | 4.90983i | 0.520441i | 0.965549 | + | 0.260220i | \(0.0837952\pi\) | ||||
−0.965549 | + | 0.260220i | \(0.916205\pi\) | |||||||
\(90\) | −26.4164 | −2.78453 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −21.7082 | −2.26324 | ||||||||
\(93\) | − 12.3262i | − 1.27817i | ||||||||
\(94\) | −5.85410 | −0.603805 | ||||||||
\(95\) | 4.85410 | 0.498020 | ||||||||
\(96\) | 28.4164i | 2.90024i | ||||||||
\(97\) | − 18.8541i | − 1.91434i | −0.289520 | − | 0.957172i | \(-0.593496\pi\) | ||||
0.289520 | − | 0.957172i | \(-0.406504\pi\) | |||||||
\(98\) | 2.61803i | 0.264461i | ||||||||
\(99\) | 7.14590i | 0.718190i | ||||||||
\(100\) | 9.00000 | 0.900000 | ||||||||
\(101\) | 11.5623 | 1.15049 | 0.575246 | − | 0.817980i | \(-0.304906\pi\) | ||||
0.575246 | + | 0.817980i | \(0.304906\pi\) | |||||||
\(102\) | 10.0902i | 0.999076i | ||||||||
\(103\) | 8.70820 | 0.858045 | 0.429022 | − | 0.903294i | \(-0.358858\pi\) | ||||
0.429022 | + | 0.903294i | \(0.358858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.85410 | −0.668892 | ||||||||
\(106\) | − 9.85410i | − 0.957115i | ||||||||
\(107\) | −3.38197 | −0.326947 | −0.163473 | − | 0.986548i | \(-0.552270\pi\) | ||||
−0.163473 | + | 0.986548i | \(0.552270\pi\) | |||||||
\(108\) | 10.8541 | 1.04444 | ||||||||
\(109\) | 2.70820i | 0.259399i | 0.991553 | + | 0.129699i | \(0.0414012\pi\) | ||||
−0.991553 | + | 0.129699i | \(0.958599\pi\) | |||||||
\(110\) | − 12.7082i | − 1.21168i | ||||||||
\(111\) | − 10.4721i | − 0.993971i | ||||||||
\(112\) | 9.85410i | 0.931125i | ||||||||
\(113\) | 1.47214 | 0.138487 | 0.0692435 | − | 0.997600i | \(-0.477941\pi\) | ||||
0.0692435 | + | 0.997600i | \(0.477941\pi\) | |||||||
\(114\) | −12.7082 | −1.19023 | ||||||||
\(115\) | − 11.7082i | − 1.09180i | ||||||||
\(116\) | −34.4164 | −3.19548 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.85410 | −0.538914 | ||||||||
\(119\) | 1.47214i | 0.134950i | ||||||||
\(120\) | −51.2148 | −4.67525 | ||||||||
\(121\) | 7.56231 | 0.687482 | ||||||||
\(122\) | 15.7082i | 1.42215i | ||||||||
\(123\) | 2.00000i | 0.180334i | ||||||||
\(124\) | − 22.8541i | − 2.05236i | ||||||||
\(125\) | − 8.23607i | − 0.736656i | ||||||||
\(126\) | 10.0902 | 0.898904 | ||||||||
\(127\) | 20.8541 | 1.85050 | 0.925251 | − | 0.379355i | \(-0.123854\pi\) | ||||
0.925251 | + | 0.379355i | \(0.123854\pi\) | |||||||
\(128\) | 1.09017i | 0.0963583i | ||||||||
\(129\) | 32.8885 | 2.89567 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3262 | −1.33906 | −0.669530 | − | 0.742785i | \(-0.733504\pi\) | ||||
−0.669530 | + | 0.742785i | \(0.733504\pi\) | |||||||
\(132\) | 23.5623i | 2.05084i | ||||||||
\(133\) | −1.85410 | −0.160771 | ||||||||
\(134\) | 33.2705 | 2.87413 | ||||||||
\(135\) | 5.85410i | 0.503841i | ||||||||
\(136\) | 11.0000i | 0.943242i | ||||||||
\(137\) | − 2.61803i | − 0.223674i | −0.993727 | − | 0.111837i | \(-0.964327\pi\) | ||||
0.993727 | − | 0.111837i | \(-0.0356734\pi\) | |||||||
\(138\) | 30.6525i | 2.60931i | ||||||||
\(139\) | 4.56231 | 0.386970 | 0.193485 | − | 0.981103i | \(-0.438021\pi\) | ||||
0.193485 | + | 0.981103i | \(0.438021\pi\) | |||||||
\(140\) | −12.7082 | −1.07404 | ||||||||
\(141\) | 5.85410i | 0.493004i | ||||||||
\(142\) | 37.1246 | 3.11543 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 37.9787 | 3.16489 | ||||||||
\(145\) | − 18.5623i | − 1.54152i | ||||||||
\(146\) | −5.23607 | −0.433340 | ||||||||
\(147\) | 2.61803 | 0.215932 | ||||||||
\(148\) | − 19.4164i | − 1.59602i | ||||||||
\(149\) | − 1.85410i | − 0.151894i | −0.997112 | − | 0.0759470i | \(-0.975802\pi\) | ||||
0.997112 | − | 0.0759470i | \(-0.0241980\pi\) | |||||||
\(150\) | − 12.7082i | − 1.03762i | ||||||||
\(151\) | − 1.29180i | − 0.105125i | −0.998618 | − | 0.0525624i | \(-0.983261\pi\) | ||||
0.998618 | − | 0.0525624i | \(-0.0167389\pi\) | |||||||
\(152\) | −13.8541 | −1.12372 | ||||||||
\(153\) | 5.67376 | 0.458696 | ||||||||
\(154\) | 4.85410i | 0.391155i | ||||||||
\(155\) | 12.3262 | 0.990067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8541 | 1.18549 | 0.592743 | − | 0.805392i | \(-0.298045\pi\) | ||||
0.592743 | + | 0.805392i | \(0.298045\pi\) | |||||||
\(158\) | − 10.4721i | − 0.833118i | ||||||||
\(159\) | −9.85410 | −0.781481 | ||||||||
\(160\) | −28.4164 | −2.24651 | ||||||||
\(161\) | 4.47214i | 0.352454i | ||||||||
\(162\) | 14.9443i | 1.17413i | ||||||||
\(163\) | − 3.70820i | − 0.290449i | −0.989399 | − | 0.145224i | \(-0.953610\pi\) | ||||
0.989399 | − | 0.145224i | \(-0.0463904\pi\) | |||||||
\(164\) | 3.70820i | 0.289562i | ||||||||
\(165\) | −12.7082 | −0.989332 | ||||||||
\(166\) | −17.5623 | −1.36310 | ||||||||
\(167\) | 14.2361i | 1.10162i | 0.834631 | + | 0.550810i | \(0.185681\pi\) | ||||
−0.834631 | + | 0.550810i | \(0.814319\pi\) | |||||||
\(168\) | 19.5623 | 1.50926 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −10.0902 | −0.773881 | ||||||||
\(171\) | 7.14590i | 0.546460i | ||||||||
\(172\) | 60.9787 | 4.64958 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | 48.5967i | 3.68411i | ||||||||
\(175\) | − 1.85410i | − 0.140157i | ||||||||
\(176\) | 18.2705i | 1.37719i | ||||||||
\(177\) | 5.85410i | 0.440021i | ||||||||
\(178\) | 12.8541 | 0.963456 | ||||||||
\(179\) | 9.00000 | 0.672692 | 0.336346 | − | 0.941739i | \(-0.390809\pi\) | ||||
0.336346 | + | 0.941739i | \(0.390809\pi\) | |||||||
\(180\) | 48.9787i | 3.65066i | ||||||||
\(181\) | −9.70820 | −0.721605 | −0.360803 | − | 0.932642i | \(-0.617497\pi\) | ||||
−0.360803 | + | 0.932642i | \(0.617497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7082 | 1.16118 | ||||||||
\(184\) | 33.4164i | 2.46349i | ||||||||
\(185\) | 10.4721 | 0.769927 | ||||||||
\(186\) | −32.2705 | −2.36619 | ||||||||
\(187\) | 2.72949i | 0.199600i | ||||||||
\(188\) | 10.8541i | 0.791617i | ||||||||
\(189\) | − 2.23607i | − 0.162650i | ||||||||
\(190\) | − 12.7082i | − 0.921950i | ||||||||
\(191\) | 21.3820 | 1.54714 | 0.773572 | − | 0.633708i | \(-0.218468\pi\) | ||||
0.773572 | + | 0.633708i | \(0.218468\pi\) | |||||||
\(192\) | 22.7984 | 1.64533 | ||||||||
\(193\) | − 6.00000i | − 0.431889i | −0.976406 | − | 0.215945i | \(-0.930717\pi\) | ||||
0.976406 | − | 0.215945i | \(-0.0692831\pi\) | |||||||
\(194\) | −49.3607 | −3.54389 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.85410 | 0.346722 | ||||||||
\(197\) | 16.7984i | 1.19683i | 0.801185 | + | 0.598417i | \(0.204203\pi\) | ||||
−0.801185 | + | 0.598417i | \(0.795797\pi\) | |||||||
\(198\) | 18.7082 | 1.32953 | ||||||||
\(199\) | 24.4164 | 1.73083 | 0.865417 | − | 0.501053i | \(-0.167054\pi\) | ||||
0.865417 | + | 0.501053i | \(0.167054\pi\) | |||||||
\(200\) | − 13.8541i | − 0.979633i | ||||||||
\(201\) | − 33.2705i | − 2.34672i | ||||||||
\(202\) | − 30.2705i | − 2.12983i | ||||||||
\(203\) | 7.09017i | 0.497632i | ||||||||
\(204\) | 18.7082 | 1.30984 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | − 22.7984i | − 1.58844i | ||||||||
\(207\) | 17.2361 | 1.19799 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.43769 | −0.237790 | ||||||||
\(210\) | 17.9443i | 1.23827i | ||||||||
\(211\) | 4.70820 | 0.324126 | 0.162063 | − | 0.986780i | \(-0.448185\pi\) | ||||
0.162063 | + | 0.986780i | \(0.448185\pi\) | |||||||
\(212\) | −18.2705 | −1.25482 | ||||||||
\(213\) | − 37.1246i | − 2.54374i | ||||||||
\(214\) | 8.85410i | 0.605254i | ||||||||
\(215\) | 32.8885i | 2.24298i | ||||||||
\(216\) | − 16.7082i | − 1.13685i | ||||||||
\(217\) | −4.70820 | −0.319614 | ||||||||
\(218\) | 7.09017 | 0.480207 | ||||||||
\(219\) | 5.23607i | 0.353821i | ||||||||
\(220\) | −23.5623 | −1.58857 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −27.4164 | −1.84007 | ||||||||
\(223\) | − 20.2705i | − 1.35741i | −0.734409 | − | 0.678707i | \(-0.762541\pi\) | ||||
0.734409 | − | 0.678707i | \(-0.237459\pi\) | |||||||
\(224\) | 10.8541 | 0.725220 | ||||||||
\(225\) | −7.14590 | −0.476393 | ||||||||
\(226\) | − 3.85410i | − 0.256371i | ||||||||
\(227\) | − 1.47214i | − 0.0977091i | −0.998806 | − | 0.0488545i | \(-0.984443\pi\) | ||||
0.998806 | − | 0.0488545i | \(-0.0155571\pi\) | |||||||
\(228\) | 23.5623i | 1.56045i | ||||||||
\(229\) | − 13.1246i | − 0.867299i | −0.901082 | − | 0.433649i | \(-0.857226\pi\) | ||||
0.901082 | − | 0.433649i | \(-0.142774\pi\) | |||||||
\(230\) | −30.6525 | −2.02116 | ||||||||
\(231\) | 4.85410 | 0.319376 | ||||||||
\(232\) | 52.9787i | 3.47822i | ||||||||
\(233\) | −2.61803 | −0.171513 | −0.0857566 | − | 0.996316i | \(-0.527331\pi\) | ||||
−0.0857566 | + | 0.996316i | \(0.527331\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.85410 | −0.381880 | ||||||||
\(236\) | 10.8541i | 0.706542i | ||||||||
\(237\) | −10.4721 | −0.680238 | ||||||||
\(238\) | 3.85410 | 0.249824 | ||||||||
\(239\) | 24.7082i | 1.59824i | 0.601171 | + | 0.799120i | \(0.294701\pi\) | ||||
−0.601171 | + | 0.799120i | \(0.705299\pi\) | |||||||
\(240\) | 67.5410i | 4.35975i | ||||||||
\(241\) | 24.5623i | 1.58220i | 0.611689 | + | 0.791099i | \(0.290491\pi\) | ||||
−0.611689 | + | 0.791099i | \(0.709509\pi\) | |||||||
\(242\) | − 19.7984i | − 1.27269i | ||||||||
\(243\) | 21.6525 | 1.38901 | ||||||||
\(244\) | 29.1246 | 1.86451 | ||||||||
\(245\) | 2.61803i | 0.167260i | ||||||||
\(246\) | 5.23607 | 0.333840 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −35.1803 | −2.23395 | ||||||||
\(249\) | 17.5623i | 1.11297i | ||||||||
\(250\) | −21.5623 | −1.36372 | ||||||||
\(251\) | −0.763932 | −0.0482190 | −0.0241095 | − | 0.999709i | \(-0.507675\pi\) | ||||
−0.0241095 | + | 0.999709i | \(0.507675\pi\) | |||||||
\(252\) | − 18.7082i | − 1.17851i | ||||||||
\(253\) | 8.29180i | 0.521301i | ||||||||
\(254\) | − 54.5967i | − 3.42570i | ||||||||
\(255\) | 10.0902i | 0.631871i | ||||||||
\(256\) | −14.5623 | −0.910144 | ||||||||
\(257\) | −16.7426 | −1.04438 | −0.522189 | − | 0.852830i | \(-0.674884\pi\) | ||||
−0.522189 | + | 0.852830i | \(0.674884\pi\) | |||||||
\(258\) | − 86.1033i | − 5.36056i | ||||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.3262 | 1.69145 | ||||||||
\(262\) | 40.1246i | 2.47891i | ||||||||
\(263\) | 9.00000 | 0.554964 | 0.277482 | − | 0.960731i | \(-0.410500\pi\) | ||||
0.277482 | + | 0.960731i | \(0.410500\pi\) | |||||||
\(264\) | 36.2705 | 2.23230 | ||||||||
\(265\) | − 9.85410i | − 0.605333i | ||||||||
\(266\) | 4.85410i | 0.297624i | ||||||||
\(267\) | − 12.8541i | − 0.786658i | ||||||||
\(268\) | − 61.6869i | − 3.76813i | ||||||||
\(269\) | −28.7426 | −1.75247 | −0.876235 | − | 0.481884i | \(-0.839953\pi\) | ||||
−0.876235 | + | 0.481884i | \(0.839953\pi\) | |||||||
\(270\) | 15.3262 | 0.932725 | ||||||||
\(271\) | − 8.41641i | − 0.511260i | −0.966775 | − | 0.255630i | \(-0.917717\pi\) | ||||
0.966775 | − | 0.255630i | \(-0.0822829\pi\) | |||||||
\(272\) | 14.5066 | 0.879590 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.85410 | −0.414071 | ||||||||
\(275\) | − 3.43769i | − 0.207301i | ||||||||
\(276\) | 56.8328 | 3.42093 | ||||||||
\(277\) | 5.00000 | 0.300421 | 0.150210 | − | 0.988654i | \(-0.452005\pi\) | ||||
0.150210 | + | 0.988654i | \(0.452005\pi\) | |||||||
\(278\) | − 11.9443i | − 0.716370i | ||||||||
\(279\) | 18.1459i | 1.08637i | ||||||||
\(280\) | 19.5623i | 1.16907i | ||||||||
\(281\) | 20.1803i | 1.20386i | 0.798550 | + | 0.601929i | \(0.205601\pi\) | ||||
−0.798550 | + | 0.601929i | \(0.794399\pi\) | |||||||
\(282\) | 15.3262 | 0.912664 | ||||||||
\(283\) | −13.4164 | −0.797523 | −0.398761 | − | 0.917055i | \(-0.630560\pi\) | ||||
−0.398761 | + | 0.917055i | \(0.630560\pi\) | |||||||
\(284\) | − 68.8328i | − 4.08448i | ||||||||
\(285\) | −12.7082 | −0.752769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.763932 | 0.0450935 | ||||||||
\(288\) | − 41.8328i | − 2.46502i | ||||||||
\(289\) | −14.8328 | −0.872519 | ||||||||
\(290\) | −48.5967 | −2.85370 | ||||||||
\(291\) | 49.3607i | 2.89357i | ||||||||
\(292\) | 9.70820i | 0.568130i | ||||||||
\(293\) | − 6.76393i | − 0.395153i | −0.980287 | − | 0.197577i | \(-0.936693\pi\) | ||||
0.980287 | − | 0.197577i | \(-0.0633071\pi\) | |||||||
\(294\) | − 6.85410i | − 0.399739i | ||||||||
\(295\) | −5.85410 | −0.340839 | ||||||||
\(296\) | −29.8885 | −1.73724 | ||||||||
\(297\) | − 4.14590i | − 0.240569i | ||||||||
\(298\) | −4.85410 | −0.281191 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −23.5623 | −1.36037 | ||||||||
\(301\) | − 12.5623i | − 0.724079i | ||||||||
\(302\) | −3.38197 | −0.194610 | ||||||||
\(303\) | −30.2705 | −1.73900 | ||||||||
\(304\) | 18.2705i | 1.04789i | ||||||||
\(305\) | 15.7082i | 0.899449i | ||||||||
\(306\) | − 14.8541i | − 0.849152i | ||||||||
\(307\) | − 4.85410i | − 0.277038i | −0.990360 | − | 0.138519i | \(-0.955766\pi\) | ||||
0.990360 | − | 0.138519i | \(-0.0442342\pi\) | |||||||
\(308\) | 9.00000 | 0.512823 | ||||||||
\(309\) | −22.7984 | −1.29695 | ||||||||
\(310\) | − 32.2705i | − 1.83284i | ||||||||
\(311\) | −3.32624 | −0.188614 | −0.0943068 | − | 0.995543i | \(-0.530063\pi\) | ||||
−0.0943068 | + | 0.995543i | \(0.530063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1246 | 1.42013 | 0.710064 | − | 0.704138i | \(-0.248666\pi\) | ||||
0.710064 | + | 0.704138i | \(0.248666\pi\) | |||||||
\(314\) | − 38.8885i | − 2.19461i | ||||||||
\(315\) | 10.0902 | 0.568517 | ||||||||
\(316\) | −19.4164 | −1.09226 | ||||||||
\(317\) | − 26.2361i | − 1.47356i | −0.676130 | − | 0.736782i | \(-0.736344\pi\) | ||||
0.676130 | − | 0.736782i | \(-0.263656\pi\) | |||||||
\(318\) | 25.7984i | 1.44670i | ||||||||
\(319\) | 13.1459i | 0.736029i | ||||||||
\(320\) | 22.7984i | 1.27447i | ||||||||
\(321\) | 8.85410 | 0.494188 | ||||||||
\(322\) | 11.7082 | 0.652473 | ||||||||
\(323\) | 2.72949i | 0.151873i | ||||||||
\(324\) | 27.7082 | 1.53934 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.70820 | −0.537688 | ||||||||
\(327\) | − 7.09017i | − 0.392087i | ||||||||
\(328\) | 5.70820 | 0.315183 | ||||||||
\(329\) | 2.23607 | 0.123278 | ||||||||
\(330\) | 33.2705i | 1.83148i | ||||||||
\(331\) | 10.1459i | 0.557669i | 0.960339 | + | 0.278834i | \(0.0899481\pi\) | ||||
−0.960339 | + | 0.278834i | \(0.910052\pi\) | |||||||
\(332\) | 32.5623i | 1.78709i | ||||||||
\(333\) | 15.4164i | 0.844814i | ||||||||
\(334\) | 37.2705 | 2.03935 | ||||||||
\(335\) | 33.2705 | 1.81776 | ||||||||
\(336\) | − 25.7984i | − 1.40742i | ||||||||
\(337\) | 11.5623 | 0.629839 | 0.314919 | − | 0.949118i | \(-0.398022\pi\) | ||||
0.314919 | + | 0.949118i | \(0.398022\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.85410 | −0.209326 | ||||||||
\(340\) | 18.7082i | 1.01459i | ||||||||
\(341\) | −8.72949 | −0.472728 | ||||||||
\(342\) | 18.7082 | 1.01162 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | − 93.8673i | − 5.06098i | ||||||||
\(345\) | 30.6525i | 1.65027i | ||||||||
\(346\) | − 23.5623i | − 1.26672i | ||||||||
\(347\) | 30.7639 | 1.65149 | 0.825747 | − | 0.564040i | \(-0.190754\pi\) | ||||
0.825747 | + | 0.564040i | \(0.190754\pi\) | |||||||
\(348\) | 90.1033 | 4.83005 | ||||||||
\(349\) | 20.7082i | 1.10848i | 0.832355 | + | 0.554242i | \(0.186992\pi\) | ||||
−0.832355 | + | 0.554242i | \(0.813008\pi\) | |||||||
\(350\) | −4.85410 | −0.259463 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.1246 | 1.07265 | ||||||||
\(353\) | − 22.1459i | − 1.17871i | −0.807875 | − | 0.589354i | \(-0.799382\pi\) | ||||
0.807875 | − | 0.589354i | \(-0.200618\pi\) | |||||||
\(354\) | 15.3262 | 0.814580 | ||||||||
\(355\) | 37.1246 | 1.97037 | ||||||||
\(356\) | − 23.8328i | − 1.26314i | ||||||||
\(357\) | − 3.85410i | − 0.203981i | ||||||||
\(358\) | − 23.5623i | − 1.24531i | ||||||||
\(359\) | − 22.0902i | − 1.16587i | −0.812517 | − | 0.582937i | \(-0.801903\pi\) | ||||
0.812517 | − | 0.582937i | \(-0.198097\pi\) | |||||||
\(360\) | 75.3951 | 3.97367 | ||||||||
\(361\) | 15.5623 | 0.819069 | ||||||||
\(362\) | 25.4164i | 1.33586i | ||||||||
\(363\) | −19.7984 | −1.03915 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.23607 | −0.274068 | ||||||||
\(366\) | − 41.1246i | − 2.14962i | ||||||||
\(367\) | −1.41641 | −0.0739359 | −0.0369679 | − | 0.999316i | \(-0.511770\pi\) | ||||
−0.0369679 | + | 0.999316i | \(0.511770\pi\) | |||||||
\(368\) | 44.0689 | 2.29725 | ||||||||
\(369\) | − 2.94427i | − 0.153273i | ||||||||
\(370\) | − 27.4164i | − 1.42531i | ||||||||
\(371\) | 3.76393i | 0.195414i | ||||||||
\(372\) | 59.8328i | 3.10219i | ||||||||
\(373\) | −20.5623 | −1.06468 | −0.532338 | − | 0.846532i | \(-0.678686\pi\) | ||||
−0.532338 | + | 0.846532i | \(0.678686\pi\) | |||||||
\(374\) | 7.14590 | 0.369506 | ||||||||
\(375\) | 21.5623i | 1.11347i | ||||||||
\(376\) | 16.7082 | 0.861660 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.85410 | −0.301103 | ||||||||
\(379\) | 6.14590i | 0.315694i | 0.987464 | + | 0.157847i | \(0.0504552\pi\) | ||||
−0.987464 | + | 0.157847i | \(0.949545\pi\) | |||||||
\(380\) | −23.5623 | −1.20872 | ||||||||
\(381\) | −54.5967 | −2.79708 | ||||||||
\(382\) | − 55.9787i | − 2.86412i | ||||||||
\(383\) | 21.9787i | 1.12306i | 0.827456 | + | 0.561530i | \(0.189787\pi\) | ||||
−0.827456 | + | 0.561530i | \(0.810213\pi\) | |||||||
\(384\) | − 2.85410i | − 0.145648i | ||||||||
\(385\) | 4.85410i | 0.247388i | ||||||||
\(386\) | −15.7082 | −0.799527 | ||||||||
\(387\) | −48.4164 | −2.46114 | ||||||||
\(388\) | 91.5197i | 4.64621i | ||||||||
\(389\) | 11.8885 | 0.602773 | 0.301387 | − | 0.953502i | \(-0.402551\pi\) | ||||
0.301387 | + | 0.953502i | \(0.402551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.58359 | 0.332947 | ||||||||
\(392\) | − 7.47214i | − 0.377400i | ||||||||
\(393\) | 40.1246 | 2.02402 | ||||||||
\(394\) | 43.9787 | 2.21562 | ||||||||
\(395\) | − 10.4721i | − 0.526910i | ||||||||
\(396\) | − 34.6869i | − 1.74308i | ||||||||
\(397\) | 1.41641i | 0.0710875i | 0.999368 | + | 0.0355437i | \(0.0113163\pi\) | ||||
−0.999368 | + | 0.0355437i | \(0.988684\pi\) | |||||||
\(398\) | − 63.9230i | − 3.20417i | ||||||||
\(399\) | 4.85410 | 0.243009 | ||||||||
\(400\) | −18.2705 | −0.913525 | ||||||||
\(401\) | 35.4508i | 1.77033i | 0.465276 | + | 0.885165i | \(0.345955\pi\) | ||||
−0.465276 | + | 0.885165i | \(0.654045\pi\) | |||||||
\(402\) | −87.1033 | −4.34432 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −56.1246 | −2.79230 | ||||||||
\(405\) | 14.9443i | 0.742587i | ||||||||
\(406\) | 18.5623 | 0.921232 | ||||||||
\(407\) | −7.41641 | −0.367618 | ||||||||
\(408\) | − 28.7984i | − 1.42573i | ||||||||
\(409\) | − 14.4377i | − 0.713898i | −0.934124 | − | 0.356949i | \(-0.883817\pi\) | ||||
0.934124 | − | 0.356949i | \(-0.116183\pi\) | |||||||
\(410\) | 5.23607i | 0.258591i | ||||||||
\(411\) | 6.85410i | 0.338088i | ||||||||
\(412\) | −42.2705 | −2.08252 | ||||||||
\(413\) | 2.23607 | 0.110030 | ||||||||
\(414\) | − 45.1246i | − 2.21775i | ||||||||
\(415\) | −17.5623 | −0.862100 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.9443 | −0.584914 | ||||||||
\(418\) | 9.00000i | 0.440204i | ||||||||
\(419\) | −11.9443 | −0.583516 | −0.291758 | − | 0.956492i | \(-0.594240\pi\) | ||||
−0.291758 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(420\) | 33.2705 | 1.62343 | ||||||||
\(421\) | − 1.41641i | − 0.0690315i | −0.999404 | − | 0.0345157i | \(-0.989011\pi\) | ||||
0.999404 | − | 0.0345157i | \(-0.0109889\pi\) | |||||||
\(422\) | − 12.3262i | − 0.600032i | ||||||||
\(423\) | − 8.61803i | − 0.419023i | ||||||||
\(424\) | 28.1246i | 1.36585i | ||||||||
\(425\) | −2.72949 | −0.132400 | ||||||||
\(426\) | −97.1935 | −4.70904 | ||||||||
\(427\) | − 6.00000i | − 0.290360i | ||||||||
\(428\) | 16.4164 | 0.793517 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 86.1033 | 4.15227 | ||||||||
\(431\) | − 7.79837i | − 0.375634i | −0.982204 | − | 0.187817i | \(-0.939859\pi\) | ||||
0.982204 | − | 0.187817i | \(-0.0601413\pi\) | |||||||
\(432\) | −22.0344 | −1.06013 | ||||||||
\(433\) | −1.00000 | −0.0480569 | −0.0240285 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240285 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(434\) | 12.3262i | 0.591678i | ||||||||
\(435\) | 48.5967i | 2.33004i | ||||||||
\(436\) | − 13.1459i | − 0.629574i | ||||||||
\(437\) | 8.29180i | 0.396650i | ||||||||
\(438\) | 13.7082 | 0.655003 | ||||||||
\(439\) | −14.8541 | −0.708948 | −0.354474 | − | 0.935066i | \(-0.615340\pi\) | ||||
−0.354474 | + | 0.935066i | \(0.615340\pi\) | |||||||
\(440\) | 36.2705i | 1.72913i | ||||||||
\(441\) | −3.85410 | −0.183529 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.23607 | −0.248773 | −0.124387 | − | 0.992234i | \(-0.539696\pi\) | ||||
−0.124387 | + | 0.992234i | \(0.539696\pi\) | |||||||
\(444\) | 50.8328i | 2.41242i | ||||||||
\(445\) | 12.8541 | 0.609343 | ||||||||
\(446\) | −53.0689 | −2.51288 | ||||||||
\(447\) | 4.85410i | 0.229591i | ||||||||
\(448\) | − 8.70820i | − 0.411424i | ||||||||
\(449\) | 19.5279i | 0.921577i | 0.887510 | + | 0.460788i | \(0.152433\pi\) | ||||
−0.887510 | + | 0.460788i | \(0.847567\pi\) | |||||||
\(450\) | 18.7082i | 0.881913i | ||||||||
\(451\) | 1.41641 | 0.0666960 | ||||||||
\(452\) | −7.14590 | −0.336115 | ||||||||
\(453\) | 3.38197i | 0.158899i | ||||||||
\(454\) | −3.85410 | −0.180882 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 36.2705 | 1.69852 | ||||||||
\(457\) | − 15.4164i | − 0.721149i | −0.932730 | − | 0.360575i | \(-0.882581\pi\) | ||||
0.932730 | − | 0.360575i | \(-0.117419\pi\) | |||||||
\(458\) | −34.3607 | −1.60557 | ||||||||
\(459\) | −3.29180 | −0.153648 | ||||||||
\(460\) | 56.8328i | 2.64984i | ||||||||
\(461\) | 12.2148i | 0.568899i | 0.958691 | + | 0.284450i | \(0.0918108\pi\) | ||||
−0.958691 | + | 0.284450i | \(0.908189\pi\) | |||||||
\(462\) | − 12.7082i | − 0.591239i | ||||||||
\(463\) | 6.70820i | 0.311757i | 0.987776 | + | 0.155878i | \(0.0498208\pi\) | ||||
−0.987776 | + | 0.155878i | \(0.950179\pi\) | |||||||
\(464\) | 69.8673 | 3.24351 | ||||||||
\(465\) | −32.2705 | −1.49651 | ||||||||
\(466\) | 6.85410i | 0.317510i | ||||||||
\(467\) | −2.34752 | −0.108630 | −0.0543152 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543152 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7082 | −0.586810 | ||||||||
\(470\) | 15.3262i | 0.706947i | ||||||||
\(471\) | −38.8885 | −1.79189 | ||||||||
\(472\) | 16.7082 | 0.769057 | ||||||||
\(473\) | − 23.2918i | − 1.07096i | ||||||||
\(474\) | 27.4164i | 1.25928i | ||||||||
\(475\) | − 3.43769i | − 0.157732i | ||||||||
\(476\) | − 7.14590i | − 0.327532i | ||||||||
\(477\) | 14.5066 | 0.664211 | ||||||||
\(478\) | 64.6869 | 2.95871 | ||||||||
\(479\) | 24.9787i | 1.14131i | 0.821191 | + | 0.570653i | \(0.193310\pi\) | ||||
−0.821191 | + | 0.570653i | \(0.806690\pi\) | |||||||
\(480\) | 74.3951 | 3.39566 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 64.3050 | 2.92901 | ||||||||
\(483\) | − 11.7082i | − 0.532742i | ||||||||
\(484\) | −36.7082 | −1.66855 | ||||||||
\(485\) | −49.3607 | −2.24135 | ||||||||
\(486\) | − 56.6869i | − 2.57137i | ||||||||
\(487\) | − 29.9787i | − 1.35847i | −0.733923 | − | 0.679233i | \(-0.762313\pi\) | ||||
0.733923 | − | 0.679233i | \(-0.237687\pi\) | |||||||
\(488\) | − 44.8328i | − 2.02949i | ||||||||
\(489\) | 9.70820i | 0.439020i | ||||||||
\(490\) | 6.85410 | 0.309637 | ||||||||
\(491\) | −12.3820 | −0.558790 | −0.279395 | − | 0.960176i | \(-0.590134\pi\) | ||||
−0.279395 | + | 0.960176i | \(0.590134\pi\) | |||||||
\(492\) | − 9.70820i | − 0.437680i | ||||||||
\(493\) | 10.4377 | 0.470090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.7082 | 0.840871 | ||||||||
\(496\) | 46.3951i | 2.08320i | ||||||||
\(497\) | −14.1803 | −0.636075 | ||||||||
\(498\) | 45.9787 | 2.06036 | ||||||||
\(499\) | − 14.8541i | − 0.664961i | −0.943110 | − | 0.332480i | \(-0.892114\pi\) | ||||
0.943110 | − | 0.332480i | \(-0.107886\pi\) | |||||||
\(500\) | 39.9787i | 1.78790i | ||||||||
\(501\) | − 37.2705i | − 1.66512i | ||||||||
\(502\) | 2.00000i | 0.0892644i | ||||||||
\(503\) | 26.6180 | 1.18684 | 0.593420 | − | 0.804893i | \(-0.297777\pi\) | ||||
0.593420 | + | 0.804893i | \(0.297777\pi\) | |||||||
\(504\) | −28.7984 | −1.28278 | ||||||||
\(505\) | − 30.2705i | − 1.34702i | ||||||||
\(506\) | 21.7082 | 0.965047 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −101.228 | −4.49126 | ||||||||
\(509\) | 18.5967i | 0.824286i | 0.911119 | + | 0.412143i | \(0.135220\pi\) | ||||
−0.911119 | + | 0.412143i | \(0.864780\pi\) | |||||||
\(510\) | 26.4164 | 1.16974 | ||||||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | 40.3050i | 1.78124i | ||||||||
\(513\) | − 4.14590i | − 0.183046i | ||||||||
\(514\) | 43.8328i | 1.93338i | ||||||||
\(515\) | − 22.7984i | − 1.00462i | ||||||||
\(516\) | −159.644 | −7.02795 | ||||||||
\(517\) | 4.14590 | 0.182336 | ||||||||
\(518\) | 10.4721i | 0.460119i | ||||||||
\(519\) | −23.5623 | −1.03427 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.6525 | 0.817180 | 0.408590 | − | 0.912718i | \(-0.366021\pi\) | ||||
0.408590 | + | 0.912718i | \(0.366021\pi\) | |||||||
\(522\) | − 71.5410i | − 3.13127i | ||||||||
\(523\) | 1.12461 | 0.0491758 | 0.0245879 | − | 0.999698i | \(-0.492173\pi\) | ||||
0.0245879 | + | 0.999698i | \(0.492173\pi\) | |||||||
\(524\) | 74.3951 | 3.24997 | ||||||||
\(525\) | 4.85410i | 0.211850i | ||||||||
\(526\) | − 23.5623i | − 1.02737i | ||||||||
\(527\) | 6.93112i | 0.301924i | ||||||||
\(528\) | − 47.8328i | − 2.08166i | ||||||||
\(529\) | −3.00000 | −0.130435 | ||||||||
\(530\) | −25.7984 | −1.12061 | ||||||||
\(531\) | − 8.61803i | − 0.373991i | ||||||||
\(532\) | 9.00000 | 0.390199 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −33.6525 | −1.45629 | ||||||||
\(535\) | 8.85410i | 0.382796i | ||||||||
\(536\) | −94.9574 | −4.10154 | ||||||||
\(537\) | −23.5623 | −1.01679 | ||||||||
\(538\) | 75.2492i | 3.24422i | ||||||||
\(539\) | − 1.85410i | − 0.0798618i | ||||||||
\(540\) | − 28.4164i | − 1.22285i | ||||||||
\(541\) | 35.2705i | 1.51640i | 0.652023 | + | 0.758199i | \(0.273920\pi\) | ||||
−0.652023 | + | 0.758199i | \(0.726080\pi\) | |||||||
\(542\) | −22.0344 | −0.946460 | ||||||||
\(543\) | 25.4164 | 1.09072 | ||||||||
\(544\) | − 15.9787i | − 0.685082i | ||||||||
\(545\) | 7.09017 | 0.303710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.00000 | −0.128271 | −0.0641354 | − | 0.997941i | \(-0.520429\pi\) | ||||
−0.0641354 | + | 0.997941i | \(0.520429\pi\) | |||||||
\(548\) | 12.7082i | 0.542868i | ||||||||
\(549\) | −23.1246 | −0.986934 | ||||||||
\(550\) | −9.00000 | −0.383761 | ||||||||
\(551\) | 13.1459i | 0.560034i | ||||||||
\(552\) | − 87.4853i | − 3.72362i | ||||||||
\(553\) | 4.00000i | 0.170097i | ||||||||
\(554\) | − 13.0902i | − 0.556148i | ||||||||
\(555\) | −27.4164 | −1.16376 | ||||||||
\(556\) | −22.1459 | −0.939195 | ||||||||
\(557\) | − 27.9787i | − 1.18550i | −0.805388 | − | 0.592748i | \(-0.798043\pi\) | ||||
0.805388 | − | 0.592748i | \(-0.201957\pi\) | |||||||
\(558\) | 47.5066 | 2.01111 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 25.7984 | 1.09018 | ||||||||
\(561\) | − 7.14590i | − 0.301700i | ||||||||
\(562\) | 52.8328 | 2.22862 | ||||||||
\(563\) | 21.0557 | 0.887393 | 0.443697 | − | 0.896177i | \(-0.353667\pi\) | ||||
0.443697 | + | 0.896177i | \(0.353667\pi\) | |||||||
\(564\) | − 28.4164i | − 1.19655i | ||||||||
\(565\) | − 3.85410i | − 0.162143i | ||||||||
\(566\) | 35.1246i | 1.47640i | ||||||||
\(567\) | − 5.70820i | − 0.239722i | ||||||||
\(568\) | −105.957 | −4.44587 | ||||||||
\(569\) | −14.9443 | −0.626496 | −0.313248 | − | 0.949671i | \(-0.601417\pi\) | ||||
−0.313248 | + | 0.949671i | \(0.601417\pi\) | |||||||
\(570\) | 33.2705i | 1.39355i | ||||||||
\(571\) | −24.6869 | −1.03312 | −0.516558 | − | 0.856252i | \(-0.672787\pi\) | ||||
−0.516558 | + | 0.856252i | \(0.672787\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −55.9787 | −2.33854 | ||||||||
\(574\) | − 2.00000i | − 0.0834784i | ||||||||
\(575\) | −8.29180 | −0.345792 | ||||||||
\(576\) | −33.5623 | −1.39843 | ||||||||
\(577\) | 43.8328i | 1.82478i | 0.409318 | + | 0.912392i | \(0.365767\pi\) | ||||
−0.409318 | + | 0.912392i | \(0.634233\pi\) | |||||||
\(578\) | 38.8328i | 1.61523i | ||||||||
\(579\) | 15.7082i | 0.652811i | ||||||||
\(580\) | 90.1033i | 3.74134i | ||||||||
\(581\) | 6.70820 | 0.278303 | ||||||||
\(582\) | 129.228 | 5.35667 | ||||||||
\(583\) | 6.97871i | 0.289029i | ||||||||
\(584\) | 14.9443 | 0.618398 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.7082 | −0.731519 | ||||||||
\(587\) | 19.9098i | 0.821767i | 0.911688 | + | 0.410883i | \(0.134780\pi\) | ||||
−0.911688 | + | 0.410883i | \(0.865220\pi\) | |||||||
\(588\) | −12.7082 | −0.524077 | ||||||||
\(589\) | −8.72949 | −0.359692 | ||||||||
\(590\) | 15.3262i | 0.630971i | ||||||||
\(591\) | − 43.9787i | − 1.80904i | ||||||||
\(592\) | 39.4164i | 1.62000i | ||||||||
\(593\) | 43.7984i | 1.79858i | 0.437349 | + | 0.899292i | \(0.355917\pi\) | ||||
−0.437349 | + | 0.899292i | \(0.644083\pi\) | |||||||
\(594\) | −10.8541 | −0.445349 | ||||||||
\(595\) | 3.85410 | 0.158003 | ||||||||
\(596\) | 9.00000i | 0.368654i | ||||||||
\(597\) | −63.9230 | −2.61619 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5066 | 1.20561 | 0.602803 | − | 0.797890i | \(-0.294050\pi\) | ||||
0.602803 | + | 0.797890i | \(0.294050\pi\) | |||||||
\(600\) | 36.2705i | 1.48074i | ||||||||
\(601\) | 40.3951 | 1.64775 | 0.823876 | − | 0.566771i | \(-0.191807\pi\) | ||||
0.823876 | + | 0.566771i | \(0.191807\pi\) | |||||||
\(602\) | −32.8885 | −1.34044 | ||||||||
\(603\) | 48.9787i | 1.99457i | ||||||||
\(604\) | 6.27051i | 0.255143i | ||||||||
\(605\) | − 19.7984i | − 0.804918i | ||||||||
\(606\) | 79.2492i | 3.21928i | ||||||||
\(607\) | −23.0000 | −0.933541 | −0.466771 | − | 0.884378i | \(-0.654583\pi\) | ||||
−0.466771 | + | 0.884378i | \(0.654583\pi\) | |||||||
\(608\) | 20.1246 | 0.816161 | ||||||||
\(609\) | − 18.5623i | − 0.752183i | ||||||||
\(610\) | 41.1246 | 1.66509 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −27.5410 | −1.11328 | ||||||||
\(613\) | − 34.5623i | − 1.39596i | −0.716118 | − | 0.697979i | \(-0.754083\pi\) | ||||
0.716118 | − | 0.697979i | \(-0.245917\pi\) | |||||||
\(614\) | −12.7082 | −0.512861 | ||||||||
\(615\) | 5.23607 | 0.211139 | ||||||||
\(616\) | − 13.8541i | − 0.558198i | ||||||||
\(617\) | − 0.0557281i | − 0.00224353i | −0.999999 | − | 0.00112176i | \(-0.999643\pi\) | ||||
0.999999 | − | 0.00112176i | \(-0.000357069\pi\) | |||||||
\(618\) | 59.6869i | 2.40096i | ||||||||
\(619\) | 9.41641i | 0.378477i | 0.981931 | + | 0.189239i | \(0.0606020\pi\) | ||||
−0.981931 | + | 0.189239i | \(0.939398\pi\) | |||||||
\(620\) | −59.8328 | −2.40294 | ||||||||
\(621\) | −10.0000 | −0.401286 | ||||||||
\(622\) | 8.70820i | 0.349167i | ||||||||
\(623\) | −4.90983 | −0.196708 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8328 | −1.23331 | ||||||||
\(626\) | − 65.7771i | − 2.62898i | ||||||||
\(627\) | 9.00000 | 0.359425 | ||||||||
\(628\) | −72.1033 | −2.87724 | ||||||||
\(629\) | 5.88854i | 0.234792i | ||||||||
\(630\) | − 26.4164i | − 1.05245i | ||||||||
\(631\) | 34.3951i | 1.36925i | 0.728896 | + | 0.684624i | \(0.240034\pi\) | ||||
−0.728896 | + | 0.684624i | \(0.759966\pi\) | |||||||
\(632\) | 29.8885i | 1.18890i | ||||||||
\(633\) | −12.3262 | −0.489924 | ||||||||
\(634\) | −68.6869 | −2.72791 | ||||||||
\(635\) | − 54.5967i | − 2.16661i | ||||||||
\(636\) | 47.8328 | 1.89669 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.4164 | 1.36256 | ||||||||
\(639\) | 54.6525i | 2.16202i | ||||||||
\(640\) | 2.85410 | 0.112818 | ||||||||
\(641\) | 47.5066 | 1.87640 | 0.938199 | − | 0.346098i | \(-0.112493\pi\) | ||||
0.938199 | + | 0.346098i | \(0.112493\pi\) | |||||||
\(642\) | − 23.1803i | − 0.914855i | ||||||||
\(643\) | 7.00000i | 0.276053i | 0.990429 | + | 0.138027i | \(0.0440759\pi\) | ||||
−0.990429 | + | 0.138027i | \(0.955924\pi\) | |||||||
\(644\) | − 21.7082i | − 0.855423i | ||||||||
\(645\) | − 86.1033i | − 3.39032i | ||||||||
\(646\) | 7.14590 | 0.281152 | ||||||||
\(647\) | −24.7639 | −0.973571 | −0.486785 | − | 0.873522i | \(-0.661831\pi\) | ||||
−0.486785 | + | 0.873522i | \(0.661831\pi\) | |||||||
\(648\) | − 42.6525i | − 1.67555i | ||||||||
\(649\) | 4.14590 | 0.162741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.3262 | 0.483103 | ||||||||
\(652\) | 18.0000i | 0.704934i | ||||||||
\(653\) | −0.381966 | −0.0149475 | −0.00747374 | − | 0.999972i | \(-0.502379\pi\) | ||||
−0.00747374 | + | 0.999972i | \(0.502379\pi\) | |||||||
\(654\) | −18.5623 | −0.725844 | ||||||||
\(655\) | 40.1246i | 1.56780i | ||||||||
\(656\) | − 7.52786i | − 0.293914i | ||||||||
\(657\) | − 7.70820i | − 0.300726i | ||||||||
\(658\) | − 5.85410i | − 0.228217i | ||||||||
\(659\) | −23.8885 | −0.930566 | −0.465283 | − | 0.885162i | \(-0.654047\pi\) | ||||
−0.465283 | + | 0.885162i | \(0.654047\pi\) | |||||||
\(660\) | 61.6869 | 2.40116 | ||||||||
\(661\) | − 48.5410i | − 1.88803i | −0.329907 | − | 0.944013i | \(-0.607017\pi\) | ||||
0.329907 | − | 0.944013i | \(-0.392983\pi\) | |||||||
\(662\) | 26.5623 | 1.03237 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 50.1246 | 1.94521 | ||||||||
\(665\) | 4.85410i | 0.188234i | ||||||||
\(666\) | 40.3607 | 1.56394 | ||||||||
\(667\) | 31.7082 | 1.22775 | ||||||||
\(668\) | − 69.1033i | − 2.67369i | ||||||||
\(669\) | 53.0689i | 2.05176i | ||||||||
\(670\) | − 87.1033i | − 3.36510i | ||||||||
\(671\) | − 11.1246i | − 0.429461i | ||||||||
\(672\) | −28.4164 | −1.09619 | ||||||||
\(673\) | 39.2492 | 1.51295 | 0.756473 | − | 0.654025i | \(-0.226921\pi\) | ||||
0.756473 | + | 0.654025i | \(0.226921\pi\) | |||||||
\(674\) | − 30.2705i | − 1.16598i | ||||||||
\(675\) | 4.14590 | 0.159576 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.7426 | 1.68117 | 0.840583 | − | 0.541682i | \(-0.182212\pi\) | ||||
0.840583 | + | 0.541682i | \(0.182212\pi\) | |||||||
\(678\) | 10.0902i | 0.387511i | ||||||||
\(679\) | 18.8541 | 0.723554 | ||||||||
\(680\) | 28.7984 | 1.10437 | ||||||||
\(681\) | 3.85410i | 0.147690i | ||||||||
\(682\) | 22.8541i | 0.875129i | ||||||||
\(683\) | 1.47214i | 0.0563297i | 0.999603 | + | 0.0281649i | \(0.00896634\pi\) | ||||
−0.999603 | + | 0.0281649i | \(0.991034\pi\) | |||||||
\(684\) | − 34.6869i | − 1.32629i | ||||||||
\(685\) | −6.85410 | −0.261882 | ||||||||
\(686\) | −2.61803 | −0.0999570 | ||||||||
\(687\) | 34.3607i | 1.31094i | ||||||||
\(688\) | −123.790 | −4.71946 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 80.2492 | 3.05504 | ||||||||
\(691\) | 5.85410i | 0.222701i | 0.993781 | + | 0.111350i | \(0.0355175\pi\) | ||||
−0.993781 | + | 0.111350i | \(0.964482\pi\) | |||||||
\(692\) | −43.6869 | −1.66073 | ||||||||
\(693\) | −7.14590 | −0.271450 | ||||||||
\(694\) | − 80.5410i | − 3.05730i | ||||||||
\(695\) | − 11.9443i | − 0.453072i | ||||||||
\(696\) | − 138.700i | − 5.25741i | ||||||||
\(697\) | − 1.12461i | − 0.0425977i | ||||||||
\(698\) | 54.2148 | 2.05206 | ||||||||
\(699\) | 6.85410 | 0.259246 | ||||||||
\(700\) | 9.00000i | 0.340168i | ||||||||
\(701\) | −11.2361 | −0.424380 | −0.212190 | − | 0.977228i | \(-0.568060\pi\) | ||||
−0.212190 | + | 0.977228i | \(0.568060\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.41641 | −0.279715 | ||||||||
\(704\) | − 16.1459i | − 0.608521i | ||||||||
\(705\) | 15.3262 | 0.577220 | ||||||||
\(706\) | −57.9787 | −2.18206 | ||||||||
\(707\) | 11.5623i | 0.434845i | ||||||||
\(708\) | − 28.4164i | − 1.06795i | ||||||||
\(709\) | 23.5623i | 0.884901i | 0.896793 | + | 0.442450i | \(0.145891\pi\) | ||||
−0.896793 | + | 0.442450i | \(0.854109\pi\) | |||||||
\(710\) | − 97.1935i | − 3.64761i | ||||||||
\(711\) | 15.4164 | 0.578160 | ||||||||
\(712\) | −36.6869 | −1.37490 | ||||||||
\(713\) | 21.0557i | 0.788543i | ||||||||
\(714\) | −10.0902 | −0.377615 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −43.6869 | −1.63266 | ||||||||
\(717\) | − 64.6869i | − 2.41578i | ||||||||
\(718\) | −57.8328 | −2.15830 | ||||||||
\(719\) | −8.12461 | −0.302997 | −0.151498 | − | 0.988457i | \(-0.548410\pi\) | ||||
−0.151498 | + | 0.988457i | \(0.548410\pi\) | |||||||
\(720\) | − 99.4296i | − 3.70552i | ||||||||
\(721\) | 8.70820i | 0.324310i | ||||||||
\(722\) | − 40.7426i | − 1.51628i | ||||||||
\(723\) | − 64.3050i | − 2.39153i | ||||||||
\(724\) | 47.1246 | 1.75137 | ||||||||
\(725\) | −13.1459 | −0.488226 | ||||||||
\(726\) | 51.8328i | 1.92370i | ||||||||
\(727\) | 30.7082 | 1.13890 | 0.569452 | − | 0.822025i | \(-0.307155\pi\) | ||||
0.569452 | + | 0.822025i | \(0.307155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.5623 | −1.46527 | ||||||||
\(730\) | 13.7082i | 0.507363i | ||||||||
\(731\) | −18.4934 | −0.684004 | ||||||||
\(732\) | −76.2492 | −2.81825 | ||||||||
\(733\) | 32.2705i | 1.19194i | 0.803007 | + | 0.595969i | \(0.203232\pi\) | ||||
−0.803007 | + | 0.595969i | \(0.796768\pi\) | |||||||
\(734\) | 3.70820i | 0.136872i | ||||||||
\(735\) | − 6.85410i | − 0.252817i | ||||||||
\(736\) | − 48.5410i | − 1.78925i | ||||||||
\(737\) | −23.5623 | −0.867929 | ||||||||
\(738\) | −7.70820 | −0.283743 | ||||||||
\(739\) | − 6.87539i | − 0.252915i | −0.991972 | − | 0.126458i | \(-0.959639\pi\) | ||||
0.991972 | − | 0.126458i | \(-0.0403608\pi\) | |||||||
\(740\) | −50.8328 | −1.86865 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.85410 | 0.361755 | ||||||||
\(743\) | − 39.3262i | − 1.44274i | −0.692550 | − | 0.721370i | \(-0.743513\pi\) | ||||
0.692550 | − | 0.721370i | \(-0.256487\pi\) | |||||||
\(744\) | 92.1033 | 3.37667 | ||||||||
\(745\) | −4.85410 | −0.177841 | ||||||||
\(746\) | 53.8328i | 1.97096i | ||||||||
\(747\) | − 25.8541i | − 0.945952i | ||||||||
\(748\) | − 13.2492i | − 0.484440i | ||||||||
\(749\) | − 3.38197i | − 0.123574i | ||||||||
\(750\) | 56.4508 | 2.06129 | ||||||||
\(751\) | −22.7082 | −0.828634 | −0.414317 | − | 0.910133i | \(-0.635980\pi\) | ||||
−0.414317 | + | 0.910133i | \(0.635980\pi\) | |||||||
\(752\) | − 22.0344i | − 0.803513i | ||||||||
\(753\) | 2.00000 | 0.0728841 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.38197 | −0.123082 | ||||||||
\(756\) | 10.8541i | 0.394760i | ||||||||
\(757\) | 28.0000 | 1.01768 | 0.508839 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508839 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(758\) | 16.0902 | 0.584421 | ||||||||
\(759\) | − 21.7082i | − 0.787958i | ||||||||
\(760\) | 36.2705i | 1.31567i | ||||||||
\(761\) | − 28.8541i | − 1.04596i | −0.852345 | − | 0.522980i | \(-0.824820\pi\) | ||||
0.852345 | − | 0.522980i | \(-0.175180\pi\) | |||||||
\(762\) | 142.936i | 5.17803i | ||||||||
\(763\) | −2.70820 | −0.0980436 | ||||||||
\(764\) | −103.790 | −3.75500 | ||||||||
\(765\) | − 14.8541i | − 0.537051i | ||||||||
\(766\) | 57.5410 | 2.07904 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 38.1246 | 1.37570 | ||||||||
\(769\) | 18.4164i | 0.664113i | 0.943260 | + | 0.332056i | \(0.107742\pi\) | ||||
−0.943260 | + | 0.332056i | \(0.892258\pi\) | |||||||
\(770\) | 12.7082 | 0.457972 | ||||||||
\(771\) | 43.8328 | 1.57860 | ||||||||
\(772\) | 29.1246i | 1.04822i | ||||||||
\(773\) | − 25.3607i | − 0.912160i | −0.889939 | − | 0.456080i | \(-0.849253\pi\) | ||||
0.889939 | − | 0.456080i | \(-0.150747\pi\) | |||||||
\(774\) | 126.756i | 4.55614i | ||||||||
\(775\) | − 8.72949i | − 0.313573i | ||||||||
\(776\) | 140.880 | 5.05731 | ||||||||
\(777\) | 10.4721 | 0.375686 | ||||||||
\(778\) | − 31.1246i | − 1.11587i | ||||||||
\(779\) | 1.41641 | 0.0507481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.2918 | −0.940794 | ||||||||
\(782\) | − 17.2361i | − 0.616361i | ||||||||
\(783\) | −15.8541 | −0.566579 | ||||||||
\(784\) | −9.85410 | −0.351932 | ||||||||
\(785\) | − 38.8885i | − 1.38799i | ||||||||
\(786\) | − 105.048i | − 3.74692i | ||||||||
\(787\) | 2.58359i | 0.0920951i | 0.998939 | + | 0.0460476i | \(0.0146626\pi\) | ||||
−0.998939 | + | 0.0460476i | \(0.985337\pi\) | |||||||
\(788\) | − 81.5410i | − 2.90478i | ||||||||
\(789\) | −23.5623 | −0.838840 | ||||||||
\(790\) | −27.4164 | −0.975432 | ||||||||
\(791\) | 1.47214i | 0.0523431i | ||||||||
\(792\) | −53.3951 | −1.89731 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 3.70820 | 0.131599 | ||||||||
\(795\) | 25.7984i | 0.914974i | ||||||||
\(796\) | −118.520 | −4.20082 | ||||||||
\(797\) | 8.18034 | 0.289763 | 0.144881 | − | 0.989449i | \(-0.453720\pi\) | ||||
0.144881 | + | 0.989449i | \(0.453720\pi\) | |||||||
\(798\) | − 12.7082i | − 0.449866i | ||||||||
\(799\) | − 3.29180i | − 0.116455i | ||||||||
\(800\) | 20.1246i | 0.711512i | ||||||||
\(801\) | 18.9230i | 0.668611i | ||||||||
\(802\) | 92.8115 | 3.27729 | ||||||||
\(803\) | 3.70820 | 0.130860 | ||||||||
\(804\) | 161.498i | 5.69561i | ||||||||
\(805\) | 11.7082 | 0.412660 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 75.2492 | 2.64890 | ||||||||
\(808\) | 86.3951i | 3.03937i | ||||||||
\(809\) | −4.41641 | −0.155273 | −0.0776363 | − | 0.996982i | \(-0.524737\pi\) | ||||
−0.0776363 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(810\) | 39.1246 | 1.37470 | ||||||||
\(811\) | − 39.2705i | − 1.37897i | −0.724298 | − | 0.689487i | \(-0.757836\pi\) | ||||
0.724298 | − | 0.689487i | \(-0.242164\pi\) | |||||||
\(812\) | − 34.4164i | − 1.20778i | ||||||||
\(813\) | 22.0344i | 0.772782i | ||||||||
\(814\) | 19.4164i | 0.680545i | ||||||||
\(815\) | −9.70820 | −0.340064 | ||||||||
\(816\) | −37.9787 | −1.32952 | ||||||||
\(817\) | − 23.2918i | − 0.814877i | ||||||||
\(818\) | −37.7984 | −1.32159 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.70820 | 0.339025 | ||||||||
\(821\) | 7.36068i | 0.256889i | 0.991717 | + | 0.128445i | \(0.0409985\pi\) | ||||
−0.991717 | + | 0.128445i | \(0.959002\pi\) | |||||||
\(822\) | 17.9443 | 0.625878 | ||||||||
\(823\) | 38.4164 | 1.33911 | 0.669556 | − | 0.742762i | \(-0.266484\pi\) | ||||
0.669556 | + | 0.742762i | \(0.266484\pi\) | |||||||
\(824\) | 65.0689i | 2.26678i | ||||||||
\(825\) | 9.00000i | 0.313340i | ||||||||
\(826\) | − 5.85410i | − 0.203690i | ||||||||
\(827\) | 15.9787i | 0.555634i | 0.960634 | + | 0.277817i | \(0.0896109\pi\) | ||||
−0.960634 | + | 0.277817i | \(0.910389\pi\) | |||||||
\(828\) | −83.6656 | −2.90758 | ||||||||
\(829\) | −7.56231 | −0.262650 | −0.131325 | − | 0.991339i | \(-0.541923\pi\) | ||||
−0.131325 | + | 0.991339i | \(0.541923\pi\) | |||||||
\(830\) | 45.9787i | 1.59594i | ||||||||
\(831\) | −13.0902 | −0.454093 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.47214 | −0.0510065 | ||||||||
\(834\) | 31.2705i | 1.08281i | ||||||||
\(835\) | 37.2705 | 1.28980 | ||||||||
\(836\) | 16.6869 | 0.577129 | ||||||||
\(837\) | − 10.5279i | − 0.363896i | ||||||||
\(838\) | 31.2705i | 1.08022i | ||||||||
\(839\) | 13.7426i | 0.474449i | 0.971455 | + | 0.237224i | \(0.0762377\pi\) | ||||
−0.971455 | + | 0.237224i | \(0.923762\pi\) | |||||||
\(840\) | − 51.2148i | − 1.76708i | ||||||||
\(841\) | 21.2705 | 0.733466 | ||||||||
\(842\) | −3.70820 | −0.127793 | ||||||||
\(843\) | − 52.8328i | − 1.81966i | ||||||||
\(844\) | −22.8541 | −0.786671 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −22.5623 | −0.775708 | ||||||||
\(847\) | 7.56231i | 0.259844i | ||||||||
\(848\) | 37.0902 | 1.27368 | ||||||||
\(849\) | 35.1246 | 1.20547 | ||||||||
\(850\) | 7.14590i | 0.245102i | ||||||||
\(851\) | 17.8885i | 0.613211i | ||||||||
\(852\) | 180.207i | 6.17378i | ||||||||
\(853\) | 14.1246i | 0.483617i | 0.970324 | + | 0.241809i | \(0.0777407\pi\) | ||||
−0.970324 | + | 0.241809i | \(0.922259\pi\) | |||||||
\(854\) | −15.7082 | −0.537524 | ||||||||
\(855\) | 18.7082 | 0.639807 | ||||||||
\(856\) | − 25.2705i | − 0.863728i | ||||||||
\(857\) | 26.4508 | 0.903544 | 0.451772 | − | 0.892133i | \(-0.350792\pi\) | ||||
0.451772 | + | 0.892133i | \(0.350792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.2492 | −1.50976 | −0.754882 | − | 0.655861i | \(-0.772306\pi\) | ||||
−0.754882 | + | 0.655861i | \(0.772306\pi\) | |||||||
\(860\) | − 159.644i | − 5.44383i | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | −20.4164 | −0.695386 | ||||||||
\(863\) | − 11.8885i | − 0.404691i | −0.979314 | − | 0.202345i | \(-0.935144\pi\) | ||||
0.979314 | − | 0.202345i | \(-0.0648564\pi\) | |||||||
\(864\) | 24.2705i | 0.825700i | ||||||||
\(865\) | − 23.5623i | − 0.801142i | ||||||||
\(866\) | 2.61803i | 0.0889644i | ||||||||
\(867\) | 38.8328 | 1.31883 | ||||||||
\(868\) | 22.8541 | 0.775719 | ||||||||
\(869\) | 7.41641i | 0.251584i | ||||||||
\(870\) | 127.228 | 4.31343 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.2361 | −0.685280 | ||||||||
\(873\) | − 72.6656i | − 2.45936i | ||||||||
\(874\) | 21.7082 | 0.734291 | ||||||||
\(875\) | 8.23607 | 0.278430 | ||||||||
\(876\) | − 25.4164i | − 0.858741i | ||||||||
\(877\) | − 0.708204i | − 0.0239143i | −0.999929 | − | 0.0119572i | \(-0.996194\pi\) | ||||
0.999929 | − | 0.0119572i | \(-0.00380618\pi\) | |||||||
\(878\) | 38.8885i | 1.31242i | ||||||||
\(879\) | 17.7082i | 0.597283i | ||||||||
\(880\) | 47.8328 | 1.61244 | ||||||||
\(881\) | 36.5967 | 1.23298 | 0.616488 | − | 0.787364i | \(-0.288555\pi\) | ||||
0.616488 | + | 0.787364i | \(0.288555\pi\) | |||||||
\(882\) | 10.0902i | 0.339754i | ||||||||
\(883\) | −29.0000 | −0.975928 | −0.487964 | − | 0.872864i | \(-0.662260\pi\) | ||||
−0.487964 | + | 0.872864i | \(0.662260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.3262 | 0.515186 | ||||||||
\(886\) | 13.7082i | 0.460536i | ||||||||
\(887\) | 54.6525 | 1.83505 | 0.917525 | − | 0.397677i | \(-0.130184\pi\) | ||||
0.917525 | + | 0.397677i | \(0.130184\pi\) | |||||||
\(888\) | 78.2492 | 2.62587 | ||||||||
\(889\) | 20.8541i | 0.699424i | ||||||||
\(890\) | − 33.6525i | − 1.12803i | ||||||||
\(891\) | − 10.5836i | − 0.354564i | ||||||||
\(892\) | 98.3951i | 3.29451i | ||||||||
\(893\) | 4.14590 | 0.138737 | ||||||||
\(894\) | 12.7082 | 0.425026 | ||||||||
\(895\) | − 23.5623i | − 0.787601i | ||||||||
\(896\) | −1.09017 | −0.0364200 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 51.1246 | 1.70605 | ||||||||
\(899\) | 33.3820i | 1.11335i | ||||||||
\(900\) | 34.6869 | 1.15623 | ||||||||
\(901\) | 5.54102 | 0.184598 | ||||||||
\(902\) | − 3.70820i | − 0.123470i | ||||||||
\(903\) | 32.8885i | 1.09446i | ||||||||
\(904\) | 11.0000i | 0.365855i | ||||||||
\(905\) | 25.4164i | 0.844870i | ||||||||
\(906\) | 8.85410 | 0.294158 | ||||||||
\(907\) | 24.0000 | 0.796907 | 0.398453 | − | 0.917189i | \(-0.369547\pi\) | ||||
0.398453 | + | 0.917189i | \(0.369547\pi\) | |||||||
\(908\) | 7.14590i | 0.237145i | ||||||||
\(909\) | 44.5623 | 1.47804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.6869 | −0.751651 | −0.375826 | − | 0.926690i | \(-0.622641\pi\) | ||||
−0.375826 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(912\) | − 47.8328i | − 1.58390i | ||||||||
\(913\) | 12.4377 | 0.411628 | ||||||||
\(914\) | −40.3607 | −1.33501 | ||||||||
\(915\) | − 41.1246i | − 1.35954i | ||||||||
\(916\) | 63.7082i | 2.10498i | ||||||||
\(917\) | − 15.3262i | − 0.506117i | ||||||||
\(918\) | 8.61803i | 0.284438i | ||||||||
\(919\) | −30.0000 | −0.989609 | −0.494804 | − | 0.869004i | \(-0.664760\pi\) | ||||
−0.494804 | + | 0.869004i | \(0.664760\pi\) | |||||||
\(920\) | 87.4853 | 2.88430 | ||||||||
\(921\) | 12.7082i | 0.418750i | ||||||||
\(922\) | 31.9787 | 1.05316 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −23.5623 | −0.775143 | ||||||||
\(925\) | − 7.41641i | − 0.243850i | ||||||||
\(926\) | 17.5623 | 0.577133 | ||||||||
\(927\) | 33.5623 | 1.10233 | ||||||||
\(928\) | − 76.9574i | − 2.52625i | ||||||||
\(929\) | − 11.0689i | − 0.363158i | −0.983376 | − | 0.181579i | \(-0.941879\pi\) | ||||
0.983376 | − | 0.181579i | \(-0.0581209\pi\) | |||||||
\(930\) | 84.4853i | 2.77038i | ||||||||
\(931\) | − 1.85410i | − 0.0607657i | ||||||||
\(932\) | 12.7082 | 0.416271 | ||||||||
\(933\) | 8.70820 | 0.285094 | ||||||||
\(934\) | 6.14590i | 0.201100i | ||||||||
\(935\) | 7.14590 | 0.233696 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8754 | −0.518626 | −0.259313 | − | 0.965793i | \(-0.583496\pi\) | ||||
−0.259313 | + | 0.965793i | \(0.583496\pi\) | |||||||
\(938\) | 33.2705i | 1.08632i | ||||||||
\(939\) | −65.7771 | −2.14655 | ||||||||
\(940\) | 28.4164 | 0.926841 | ||||||||
\(941\) | − 20.3475i | − 0.663310i | −0.943401 | − | 0.331655i | \(-0.892393\pi\) | ||||
0.943401 | − | 0.331655i | \(-0.107607\pi\) | |||||||
\(942\) | 101.812i | 3.31720i | ||||||||
\(943\) | − 3.41641i | − 0.111254i | ||||||||
\(944\) | − 22.0344i | − 0.717160i | ||||||||
\(945\) | −5.85410 | −0.190434 | ||||||||
\(946\) | −60.9787 | −1.98259 | ||||||||
\(947\) | − 36.8673i | − 1.19802i | −0.800740 | − | 0.599012i | \(-0.795560\pi\) | ||||
0.800740 | − | 0.599012i | \(-0.204440\pi\) | |||||||
\(948\) | 50.8328 | 1.65097 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −9.00000 | −0.291999 | ||||||||
\(951\) | 68.6869i | 2.22733i | ||||||||
\(952\) | −11.0000 | −0.356512 | ||||||||
\(953\) | −26.7771 | −0.867395 | −0.433697 | − | 0.901059i | \(-0.642791\pi\) | ||||
−0.433697 | + | 0.901059i | \(0.642791\pi\) | |||||||
\(954\) | − 37.9787i | − 1.22961i | ||||||||
\(955\) | − 55.9787i | − 1.81143i | ||||||||
\(956\) | − 119.936i | − 3.87901i | ||||||||
\(957\) | − 34.4164i | − 1.11252i | ||||||||
\(958\) | 65.3951 | 2.11282 | ||||||||
\(959\) | 2.61803 | 0.0845407 | ||||||||
\(960\) | − 59.6869i | − 1.92639i | ||||||||
\(961\) | 8.83282 | 0.284930 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.0344 | −0.420029 | ||||||||
\(964\) | − 119.228i | − 3.84007i | ||||||||
\(965\) | −15.7082 | −0.505665 | ||||||||
\(966\) | −30.6525 | −0.986227 | ||||||||
\(967\) | 39.0000i | 1.25416i | 0.778957 | + | 0.627078i | \(0.215749\pi\) | ||||
−0.778957 | + | 0.627078i | \(0.784251\pi\) | |||||||
\(968\) | 56.5066i | 1.81619i | ||||||||
\(969\) | − 7.14590i | − 0.229559i | ||||||||
\(970\) | 129.228i | 4.14926i | ||||||||
\(971\) | 31.5836 | 1.01357 | 0.506783 | − | 0.862074i | \(-0.330835\pi\) | ||||
0.506783 | + | 0.862074i | \(0.330835\pi\) | |||||||
\(972\) | −105.103 | −3.37119 | ||||||||
\(973\) | 4.56231i | 0.146261i | ||||||||
\(974\) | −78.4853 | −2.51483 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −59.1246 | −1.89253 | ||||||||
\(977\) | 22.5279i | 0.720730i | 0.932811 | + | 0.360365i | \(0.117348\pi\) | ||||
−0.932811 | + | 0.360365i | \(0.882652\pi\) | |||||||
\(978\) | 25.4164 | 0.812727 | ||||||||
\(979\) | −9.10333 | −0.290944 | ||||||||
\(980\) | − 12.7082i | − 0.405949i | ||||||||
\(981\) | 10.4377i | 0.333250i | ||||||||
\(982\) | 32.4164i | 1.03445i | ||||||||
\(983\) | 18.3820i | 0.586294i | 0.956067 | + | 0.293147i | \(0.0947025\pi\) | ||||
−0.956067 | + | 0.293147i | \(0.905298\pi\) | |||||||
\(984\) | −14.9443 | −0.476406 | ||||||||
\(985\) | 43.9787 | 1.40128 | ||||||||
\(986\) | − 27.3262i | − 0.870245i | ||||||||
\(987\) | −5.85410 | −0.186338 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.1803 | −1.78643 | ||||||||
\(990\) | − 48.9787i | − 1.55665i | ||||||||
\(991\) | −16.1459 | −0.512891 | −0.256446 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256446 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(992\) | 51.1033 | 1.62253 | ||||||||
\(993\) | − 26.5623i | − 0.842929i | ||||||||
\(994\) | 37.1246i | 1.17752i | ||||||||
\(995\) | − 63.9230i | − 2.02649i | ||||||||
\(996\) | − 85.2492i | − 2.70123i | ||||||||
\(997\) | 49.0000 | 1.55185 | 0.775923 | − | 0.630828i | \(-0.217285\pi\) | ||||
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(998\) | −38.8885 | −1.23100 | ||||||||
\(999\) | − 8.94427i | − 0.282984i |
(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 | 1183.2.c.c.337.1 | 4 | ||
13.5 | odd | 4 | 1183.2.a.c.1.1 | 2 | |||
13.7 | odd | 12 | 91.2.f.a.29.1 | yes | 4 | ||
13.8 | odd | 4 | 1183.2.a.g.1.2 | 2 | |||
13.11 | odd | 12 | 91.2.f.a.22.1 | ✓ | 4 | ||
13.12 | even | 2 | inner | 1183.2.c.c.337.4 | 4 | ||
39.11 | even | 12 | 819.2.o.c.568.2 | 4 | |||
39.20 | even | 12 | 819.2.o.c.757.2 | 4 | |||
52.7 | even | 12 | 1456.2.s.h.1121.1 | 4 | |||
52.11 | even | 12 | 1456.2.s.h.113.1 | 4 | |||
91.11 | odd | 12 | 637.2.g.b.373.1 | 4 | |||
91.20 | even | 12 | 637.2.f.c.393.1 | 4 | |||
91.24 | even | 12 | 637.2.g.c.373.1 | 4 | |||
91.33 | even | 12 | 637.2.g.c.263.1 | 4 | |||
91.34 | even | 4 | 8281.2.a.bb.1.2 | 2 | |||
91.37 | odd | 12 | 637.2.h.g.165.2 | 4 | |||
91.46 | odd | 12 | 637.2.h.g.471.2 | 4 | |||
91.59 | even | 12 | 637.2.h.f.471.2 | 4 | |||
91.72 | odd | 12 | 637.2.g.b.263.1 | 4 | |||
91.76 | even | 12 | 637.2.f.c.295.1 | 4 | |||
91.83 | even | 4 | 8281.2.a.n.1.1 | 2 | |||
91.89 | even | 12 | 637.2.h.f.165.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.a.22.1 | ✓ | 4 | 13.11 | odd | 12 | ||
91.2.f.a.29.1 | yes | 4 | 13.7 | odd | 12 | ||
637.2.f.c.295.1 | 4 | 91.76 | even | 12 | |||
637.2.f.c.393.1 | 4 | 91.20 | even | 12 | |||
637.2.g.b.263.1 | 4 | 91.72 | odd | 12 | |||
637.2.g.b.373.1 | 4 | 91.11 | odd | 12 | |||
637.2.g.c.263.1 | 4 | 91.33 | even | 12 | |||
637.2.g.c.373.1 | 4 | 91.24 | even | 12 | |||
637.2.h.f.165.2 | 4 | 91.89 | even | 12 | |||
637.2.h.f.471.2 | 4 | 91.59 | even | 12 | |||
637.2.h.g.165.2 | 4 | 91.37 | odd | 12 | |||
637.2.h.g.471.2 | 4 | 91.46 | odd | 12 | |||
819.2.o.c.568.2 | 4 | 39.11 | even | 12 | |||
819.2.o.c.757.2 | 4 | 39.20 | even | 12 | |||
1183.2.a.c.1.1 | 2 | 13.5 | odd | 4 | |||
1183.2.a.g.1.2 | 2 | 13.8 | odd | 4 | |||
1183.2.c.c.337.1 | 4 | 1.1 | even | 1 | trivial | ||
1183.2.c.c.337.4 | 4 | 13.12 | even | 2 | inner | ||
1456.2.s.h.113.1 | 4 | 52.11 | even | 12 | |||
1456.2.s.h.1121.1 | 4 | 52.7 | even | 12 | |||
8281.2.a.n.1.1 | 2 | 91.83 | even | 4 | |||
8281.2.a.bb.1.2 | 2 | 91.34 | even | 4 |