Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(643,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("966.643");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.g (of order \(2\), degree \(1\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 326x^{12} + 27081x^{8} + 96196x^{4} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 643.14 | ||
Root | \(2.48351 + 2.48351i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.643 |
Dual form | 966.2.g.e.643.6 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.36314 | 0.609614 | 0.304807 | − | 0.952414i | \(-0.401408\pi\) | ||||
0.304807 | + | 0.952414i | \(0.401408\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.48351 | + | 0.912244i | 0.938678 | + | 0.344796i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.36314 | 0.431062 | ||||||||
\(11\) | 5.58196i | 1.68302i | 0.540238 | + | 0.841512i | \(0.318334\pi\) | ||||
−0.540238 | + | 0.841512i | \(0.681666\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − | 4.43338i | − | 1.22960i | −0.788684 | − | 0.614799i | \(-0.789237\pi\) | ||
0.788684 | − | 0.614799i | \(-0.210763\pi\) | |||||||
\(14\) | 2.48351 | + | 0.912244i | 0.663745 | + | 0.243807i | ||||
\(15\) | 1.36314i | 0.351961i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.96702 | 1.20468 | 0.602339 | − | 0.798240i | \(-0.294235\pi\) | ||||
0.602339 | + | 0.798240i | \(0.294235\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.68017 | −1.07370 | −0.536852 | − | 0.843676i | \(-0.680387\pi\) | ||||
−0.536852 | + | 0.843676i | \(0.680387\pi\) | |||||||
\(20\) | 1.36314 | 0.304807 | ||||||||
\(21\) | −0.912244 | + | 2.48351i | −0.199068 | + | 0.541946i | ||||
\(22\) | 5.58196i | 1.19008i | ||||||||
\(23\) | −4.53113 | − | 1.57126i | −0.944806 | − | 0.327631i | ||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −3.14185 | −0.628370 | ||||||||
\(26\) | − | 4.43338i | − | 0.869457i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.48351 | + | 0.912244i | 0.469339 | + | 0.172398i | ||||
\(29\) | 7.94635 | 1.47560 | 0.737800 | − | 0.675020i | \(-0.235865\pi\) | ||||
0.737800 | + | 0.675020i | \(0.235865\pi\) | |||||||
\(30\) | 1.36314i | 0.248874i | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.58196 | −0.971694 | ||||||||
\(34\) | 4.96702 | 0.851836 | ||||||||
\(35\) | 3.38537 | + | 1.24352i | 0.572231 | + | 0.210192i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.60388i | 0.592474i | 0.955115 | + | 0.296237i | \(0.0957318\pi\) | ||||
−0.955115 | + | 0.296237i | \(0.904268\pi\) | |||||||
\(38\) | −4.68017 | −0.759224 | ||||||||
\(39\) | 4.43338 | 0.709908 | ||||||||
\(40\) | 1.36314 | 0.215531 | ||||||||
\(41\) | − | 8.43338i | − | 1.31707i | −0.752549 | − | 0.658536i | \(-0.771176\pi\) | ||
0.752549 | − | 0.658536i | \(-0.228824\pi\) | |||||||
\(42\) | −0.912244 | + | 2.48351i | −0.140762 | + | 0.383214i | ||||
\(43\) | 5.42836i | 0.827818i | 0.910318 | + | 0.413909i | \(0.135837\pi\) | ||||
−0.910318 | + | 0.413909i | \(0.864163\pi\) | |||||||
\(44\) | 5.58196i | 0.841512i | ||||||||
\(45\) | −1.36314 | −0.203205 | ||||||||
\(46\) | −4.53113 | − | 1.57126i | −0.668079 | − | 0.231670i | ||||
\(47\) | 6.14185i | 0.895881i | 0.894063 | + | 0.447941i | \(0.147842\pi\) | ||||
−0.894063 | + | 0.447941i | \(0.852158\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 5.33562 | + | 4.53113i | 0.762232 | + | 0.647304i | ||||
\(50\) | −3.14185 | −0.444325 | ||||||||
\(51\) | 4.96702i | 0.695521i | ||||||||
\(52\) | − | 4.43338i | − | 0.614799i | ||||||
\(53\) | − | 5.25386i | − | 0.721674i | −0.932629 | − | 0.360837i | \(-0.882491\pi\) | ||
0.932629 | − | 0.360837i | \(-0.117509\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 7.60899i | 1.02600i | ||||||||
\(56\) | 2.48351 | + | 0.912244i | 0.331873 | + | 0.121904i | ||||
\(57\) | − | 4.68017i | − | 0.619904i | ||||||
\(58\) | 7.94635 | 1.04341 | ||||||||
\(59\) | − | 10.3797i | − | 1.35132i | −0.737211 | − | 0.675662i | \(-0.763858\pi\) | ||
0.737211 | − | 0.675662i | \(-0.236142\pi\) | |||||||
\(60\) | 1.36314i | 0.175981i | ||||||||
\(61\) | −0.286847 | −0.0367270 | −0.0183635 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183635 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.48351 | − | 0.912244i | −0.312893 | − | 0.114932i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | − | 6.04331i | − | 0.749580i | ||||||
\(66\) | −5.58196 | −0.687092 | ||||||||
\(67\) | − | 8.74539i | − | 1.06842i | −0.845352 | − | 0.534210i | \(-0.820609\pi\) | ||
0.845352 | − | 0.534210i | \(-0.179391\pi\) | |||||||
\(68\) | 4.96702 | 0.602339 | ||||||||
\(69\) | 1.57126 | − | 4.53113i | 0.189158 | − | 0.545484i | ||||
\(70\) | 3.38537 | + | 1.24352i | 0.404629 | + | 0.148628i | ||||
\(71\) | −14.3797 | −1.70656 | −0.853279 | − | 0.521454i | \(-0.825390\pi\) | ||||
−0.853279 | + | 0.521454i | \(0.825390\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 6.57523i | 0.769572i | 0.923006 | + | 0.384786i | \(0.125725\pi\) | ||||
−0.923006 | + | 0.384786i | \(0.874275\pi\) | |||||||
\(74\) | 3.60388i | 0.418942i | ||||||||
\(75\) | − | 3.14185i | − | 0.362790i | ||||||
\(76\) | −4.68017 | −0.536852 | ||||||||
\(77\) | −5.09211 | + | 13.8628i | −0.580300 | + | 1.57982i | ||||
\(78\) | 4.43338 | 0.501981 | ||||||||
\(79\) | 10.8358i | 1.21913i | 0.792738 | + | 0.609563i | \(0.208655\pi\) | ||||
−0.792738 | + | 0.609563i | \(0.791345\pi\) | |||||||
\(80\) | 1.36314 | 0.152404 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 8.43338i | − | 0.931311i | ||||||
\(83\) | 2.43943 | 0.267762 | 0.133881 | − | 0.990997i | \(-0.457256\pi\) | ||||
0.133881 | + | 0.990997i | \(0.457256\pi\) | |||||||
\(84\) | −0.912244 | + | 2.48351i | −0.0995339 | + | 0.270973i | ||||
\(85\) | 6.77073 | 0.734389 | ||||||||
\(86\) | 5.42836i | 0.585356i | ||||||||
\(87\) | 7.94635i | 0.851938i | ||||||||
\(88\) | 5.58196i | 0.595039i | ||||||||
\(89\) | 17.0536 | 1.80768 | 0.903841 | − | 0.427869i | \(-0.140736\pi\) | ||||
0.903841 | + | 0.427869i | \(0.140736\pi\) | |||||||
\(90\) | −1.36314 | −0.143687 | ||||||||
\(91\) | 4.04432 | − | 11.0103i | 0.423960 | − | 1.15420i | ||||
\(92\) | −4.53113 | − | 1.57126i | −0.472403 | − | 0.163816i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.14185i | 0.633484i | ||||||||
\(95\) | −6.37972 | −0.654546 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −4.19792 | −0.426234 | −0.213117 | − | 0.977027i | \(-0.568362\pi\) | ||||
−0.213117 | + | 0.977027i | \(0.568362\pi\) | |||||||
\(98\) | 5.33562 | + | 4.53113i | 0.538979 | + | 0.457713i | ||||
\(99\) | − | 5.58196i | − | 0.561008i | ||||||
\(100\) | −3.14185 | −0.314185 | ||||||||
\(101\) | − | 1.90398i | − | 0.189453i | −0.995503 | − | 0.0947266i | \(-0.969802\pi\) | ||
0.995503 | − | 0.0947266i | \(-0.0301977\pi\) | |||||||
\(102\) | 4.96702i | 0.491808i | ||||||||
\(103\) | −13.7366 | −1.35351 | −0.676754 | − | 0.736209i | \(-0.736614\pi\) | ||||
−0.676754 | + | 0.736209i | \(0.736614\pi\) | |||||||
\(104\) | − | 4.43338i | − | 0.434728i | ||||||
\(105\) | −1.24352 | + | 3.38537i | −0.121355 | + | 0.330378i | ||||
\(106\) | − | 5.25386i | − | 0.510300i | ||||||
\(107\) | 6.50466i | 0.628829i | 0.949286 | + | 0.314414i | \(0.101808\pi\) | ||||
−0.949286 | + | 0.314414i | \(0.898192\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 6.33015i | − | 0.606319i | −0.952940 | − | 0.303159i | \(-0.901959\pi\) | ||
0.952940 | − | 0.303159i | \(-0.0980415\pi\) | |||||||
\(110\) | 7.60899i | 0.725489i | ||||||||
\(111\) | −3.60388 | −0.342065 | ||||||||
\(112\) | 2.48351 | + | 0.912244i | 0.234669 | + | 0.0861989i | ||||
\(113\) | − | 4.37626i | − | 0.411684i | −0.978585 | − | 0.205842i | \(-0.934007\pi\) | ||
0.978585 | − | 0.205842i | \(-0.0659933\pi\) | |||||||
\(114\) | − | 4.68017i | − | 0.438338i | ||||||
\(115\) | −6.17656 | − | 2.14185i | −0.575967 | − | 0.199729i | ||||
\(116\) | 7.94635 | 0.737800 | ||||||||
\(117\) | 4.43338i | 0.409866i | ||||||||
\(118\) | − | 10.3797i | − | 0.955531i | ||||||
\(119\) | 12.3356 | + | 4.53113i | 1.13080 | + | 0.415368i | ||||
\(120\) | 1.36314i | 0.124437i | ||||||||
\(121\) | −20.1583 | −1.83257 | ||||||||
\(122\) | −0.286847 | −0.0259699 | ||||||||
\(123\) | 8.43338 | 0.760412 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0985 | −0.992678 | ||||||||
\(126\) | −2.48351 | − | 0.912244i | −0.221248 | − | 0.0812691i | ||||
\(127\) | 9.49563 | 0.842601 | 0.421301 | − | 0.906921i | \(-0.361574\pi\) | ||||
0.421301 | + | 0.906921i | \(0.361574\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −5.42836 | −0.477941 | ||||||||
\(130\) | − | 6.04331i | − | 0.530033i | ||||||
\(131\) | − | 15.8927i | − | 1.38855i | −0.719709 | − | 0.694275i | \(-0.755725\pi\) | ||
0.719709 | − | 0.694275i | \(-0.244275\pi\) | |||||||
\(132\) | −5.58196 | −0.485847 | ||||||||
\(133\) | −11.6232 | − | 4.26945i | −1.00786 | − | 0.370209i | ||||
\(134\) | − | 8.74539i | − | 0.755487i | ||||||
\(135\) | − | 1.36314i | − | 0.117320i | ||||||
\(136\) | 4.96702 | 0.425918 | ||||||||
\(137\) | − | 16.4629i | − | 1.40652i | −0.710933 | − | 0.703259i | \(-0.751727\pi\) | ||
0.710933 | − | 0.703259i | \(-0.248273\pi\) | |||||||
\(138\) | 1.57126 | − | 4.53113i | 0.133755 | − | 0.385715i | ||||
\(139\) | − | 18.8131i | − | 1.59571i | −0.602852 | − | 0.797853i | \(-0.705969\pi\) | ||
0.602852 | − | 0.797853i | \(-0.294031\pi\) | |||||||
\(140\) | 3.38537 | + | 1.24352i | 0.286116 | + | 0.105096i | ||||
\(141\) | −6.14185 | −0.517237 | ||||||||
\(142\) | −14.3797 | −1.20672 | ||||||||
\(143\) | 24.7469 | 2.06944 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 10.8320 | 0.899547 | ||||||||
\(146\) | 6.57523i | 0.544170i | ||||||||
\(147\) | −4.53113 | + | 5.33562i | −0.373721 | + | 0.440075i | ||||
\(148\) | 3.60388i | 0.296237i | ||||||||
\(149\) | − | 10.1327i | − | 0.830105i | −0.909797 | − | 0.415053i | \(-0.863763\pi\) | ||
0.909797 | − | 0.415053i | \(-0.136237\pi\) | |||||||
\(150\) | − | 3.14185i | − | 0.256531i | ||||||
\(151\) | 12.5216 | 1.01899 | 0.509496 | − | 0.860473i | \(-0.329832\pi\) | ||||
0.509496 | + | 0.860473i | \(0.329832\pi\) | |||||||
\(152\) | −4.68017 | −0.379612 | ||||||||
\(153\) | −4.96702 | −0.401559 | ||||||||
\(154\) | −5.09211 | + | 13.8628i | −0.410334 | + | 1.11710i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.43338 | 0.354954 | ||||||||
\(157\) | −5.73940 | −0.458054 | −0.229027 | − | 0.973420i | \(-0.573554\pi\) | ||||
−0.229027 | + | 0.973420i | \(0.573554\pi\) | |||||||
\(158\) | 10.8358i | 0.862052i | ||||||||
\(159\) | 5.25386 | 0.416658 | ||||||||
\(160\) | 1.36314 | 0.107766 | ||||||||
\(161\) | −9.81972 | − | 8.03574i | −0.773902 | − | 0.633305i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −5.25776 | −0.411820 | −0.205910 | − | 0.978571i | \(-0.566015\pi\) | ||||
−0.205910 | + | 0.978571i | \(0.566015\pi\) | |||||||
\(164\) | − | 8.43338i | − | 0.658536i | ||||||
\(165\) | −7.60899 | −0.592359 | ||||||||
\(166\) | 2.43943 | 0.189337 | ||||||||
\(167\) | − | 11.5493i | − | 0.893711i | −0.894606 | − | 0.446855i | \(-0.852544\pi\) | ||
0.894606 | − | 0.446855i | \(-0.147456\pi\) | |||||||
\(168\) | −0.912244 | + | 2.48351i | −0.0703811 | + | 0.191607i | ||||
\(169\) | −6.65482 | −0.511909 | ||||||||
\(170\) | 6.77073 | 0.519292 | ||||||||
\(171\) | 4.68017 | 0.357901 | ||||||||
\(172\) | 5.42836i | 0.413909i | ||||||||
\(173\) | 4.67125i | 0.355148i | 0.984107 | + | 0.177574i | \(0.0568249\pi\) | ||||
−0.984107 | + | 0.177574i | \(0.943175\pi\) | |||||||
\(174\) | 7.94635i | 0.602411i | ||||||||
\(175\) | −7.80281 | − | 2.86613i | −0.589837 | − | 0.216659i | ||||
\(176\) | 5.58196i | 0.420756i | ||||||||
\(177\) | 10.3797 | 0.780188 | ||||||||
\(178\) | 17.0536 | 1.27822 | ||||||||
\(179\) | −4.62888 | −0.345979 | −0.172989 | − | 0.984924i | \(-0.555343\pi\) | ||||
−0.172989 | + | 0.984924i | \(0.555343\pi\) | |||||||
\(180\) | −1.36314 | −0.101602 | ||||||||
\(181\) | −15.0095 | −1.11565 | −0.557825 | − | 0.829958i | \(-0.688364\pi\) | ||||
−0.557825 | + | 0.829958i | \(0.688364\pi\) | |||||||
\(182\) | 4.04432 | − | 11.0103i | 0.299785 | − | 0.816140i | ||||
\(183\) | − | 0.286847i | − | 0.0212043i | ||||||
\(184\) | −4.53113 | − | 1.57126i | −0.334039 | − | 0.115835i | ||||
\(185\) | 4.91259i | 0.361180i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 27.7257i | 2.02750i | ||||||||
\(188\) | 6.14185i | 0.447941i | ||||||||
\(189\) | 0.912244 | − | 2.48351i | 0.0663560 | − | 0.180649i | ||||
\(190\) | −6.37972 | −0.462834 | ||||||||
\(191\) | − | 17.9554i | − | 1.29921i | −0.760272 | − | 0.649604i | \(-0.774935\pi\) | ||
0.760272 | − | 0.649604i | \(-0.225065\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | −14.4334 | −1.03894 | −0.519469 | − | 0.854490i | \(-0.673870\pi\) | ||||
−0.519469 | + | 0.854490i | \(0.673870\pi\) | |||||||
\(194\) | −4.19792 | −0.301393 | ||||||||
\(195\) | 6.04331 | 0.432770 | ||||||||
\(196\) | 5.33562 | + | 4.53113i | 0.381116 | + | 0.323652i | ||||
\(197\) | −20.3624 | −1.45076 | −0.725380 | − | 0.688349i | \(-0.758336\pi\) | ||||
−0.725380 | + | 0.688349i | \(0.758336\pi\) | |||||||
\(198\) | − | 5.58196i | − | 0.396693i | ||||||
\(199\) | −18.5253 | −1.31322 | −0.656611 | − | 0.754230i | \(-0.728011\pi\) | ||||
−0.656611 | + | 0.754230i | \(0.728011\pi\) | |||||||
\(200\) | −3.14185 | −0.222162 | ||||||||
\(201\) | 8.74539 | 0.616853 | ||||||||
\(202\) | − | 1.90398i | − | 0.133964i | ||||||
\(203\) | 19.7348 | + | 7.24900i | 1.38511 | + | 0.508780i | ||||
\(204\) | 4.96702i | 0.347761i | ||||||||
\(205\) | − | 11.4959i | − | 0.802906i | ||||||
\(206\) | −13.7366 | −0.957074 | ||||||||
\(207\) | 4.53113 | + | 1.57126i | 0.314935 | + | 0.109210i | ||||
\(208\) | − | 4.43338i | − | 0.307399i | ||||||
\(209\) | − | 26.1245i | − | 1.80707i | ||||||
\(210\) | −1.24352 | + | 3.38537i | −0.0858107 | + | 0.233613i | ||||
\(211\) | 28.3087 | 1.94885 | 0.974427 | − | 0.224706i | \(-0.0721420\pi\) | ||||
0.974427 | + | 0.224706i | \(0.0721420\pi\) | |||||||
\(212\) | − | 5.25386i | − | 0.360837i | ||||||
\(213\) | − | 14.3797i | − | 0.985282i | ||||||
\(214\) | 6.50466i | 0.444649i | ||||||||
\(215\) | 7.39962i | 0.504650i | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 6.33015i | − | 0.428732i | ||||||
\(219\) | −6.57523 | −0.444313 | ||||||||
\(220\) | 7.60899i | 0.512998i | ||||||||
\(221\) | − | 22.0206i | − | 1.48127i | ||||||
\(222\) | −3.60388 | −0.241876 | ||||||||
\(223\) | 3.02594i | 0.202632i | 0.994854 | + | 0.101316i | \(0.0323053\pi\) | ||||
−0.994854 | + | 0.101316i | \(0.967695\pi\) | |||||||
\(224\) | 2.48351 | + | 0.912244i | 0.165936 | + | 0.0609518i | ||||
\(225\) | 3.14185 | 0.209457 | ||||||||
\(226\) | − | 4.37626i | − | 0.291105i | ||||||
\(227\) | −1.18479 | −0.0786373 | −0.0393186 | − | 0.999227i | \(-0.512519\pi\) | ||||
−0.0393186 | + | 0.999227i | \(0.512519\pi\) | |||||||
\(228\) | − | 4.68017i | − | 0.309952i | ||||||
\(229\) | 2.34924 | 0.155242 | 0.0776209 | − | 0.996983i | \(-0.475268\pi\) | ||||
0.0776209 | + | 0.996983i | \(0.475268\pi\) | |||||||
\(230\) | −6.17656 | − | 2.14185i | −0.407270 | − | 0.141230i | ||||
\(231\) | −13.8628 | − | 5.09211i | −0.912108 | − | 0.335036i | ||||
\(232\) | 7.94635 | 0.521703 | ||||||||
\(233\) | 6.39101 | 0.418689 | 0.209345 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209345 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(234\) | 4.43338i | 0.289819i | ||||||||
\(235\) | 8.37220i | 0.546142i | ||||||||
\(236\) | − | 10.3797i | − | 0.675662i | ||||||
\(237\) | −10.8358 | −0.703862 | ||||||||
\(238\) | 12.3356 | + | 4.53113i | 0.799600 | + | 0.293709i | ||||
\(239\) | 12.0882 | 0.781920 | 0.390960 | − | 0.920408i | \(-0.372143\pi\) | ||||
0.390960 | + | 0.920408i | \(0.372143\pi\) | |||||||
\(240\) | 1.36314i | 0.0879903i | ||||||||
\(241\) | 4.19792 | 0.270411 | 0.135206 | − | 0.990818i | \(-0.456830\pi\) | ||||
0.135206 | + | 0.990818i | \(0.456830\pi\) | |||||||
\(242\) | −20.1583 | −1.29582 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.286847 | −0.0183635 | ||||||||
\(245\) | 7.27320 | + | 6.17656i | 0.464667 | + | 0.394606i | ||||
\(246\) | 8.43338 | 0.537692 | ||||||||
\(247\) | 20.7489i | 1.32022i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.43943i | 0.154593i | ||||||||
\(250\) | −11.0985 | −0.701929 | ||||||||
\(251\) | 3.60388 | 0.227475 | 0.113737 | − | 0.993511i | \(-0.463718\pi\) | ||||
0.113737 | + | 0.993511i | \(0.463718\pi\) | |||||||
\(252\) | −2.48351 | − | 0.912244i | −0.156446 | − | 0.0574660i | ||||
\(253\) | 8.77073 | − | 25.2926i | 0.551411 | − | 1.59013i | ||||
\(254\) | 9.49563 | 0.595809 | ||||||||
\(255\) | 6.77073i | 0.424000i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 3.22145i | − | 0.200948i | −0.994940 | − | 0.100474i | \(-0.967964\pi\) | ||
0.994940 | − | 0.100474i | \(-0.0320360\pi\) | |||||||
\(258\) | −5.42836 | −0.337955 | ||||||||
\(259\) | −3.28761 | + | 8.95026i | −0.204282 | + | 0.556142i | ||||
\(260\) | − | 6.04331i | − | 0.374790i | ||||||
\(261\) | −7.94635 | −0.491866 | ||||||||
\(262\) | − | 15.8927i | − | 0.981854i | ||||||
\(263\) | 23.6915i | 1.46088i | 0.682975 | + | 0.730441i | \(0.260686\pi\) | ||||
−0.682975 | + | 0.730441i | \(0.739314\pi\) | |||||||
\(264\) | −5.58196 | −0.343546 | ||||||||
\(265\) | − | 7.16175i | − | 0.439943i | ||||||
\(266\) | −11.6232 | − | 4.26945i | −0.712666 | − | 0.261777i | ||||
\(267\) | 17.0536i | 1.04367i | ||||||||
\(268\) | − | 8.74539i | − | 0.534210i | ||||||
\(269\) | 23.3538i | 1.42391i | 0.702228 | + | 0.711953i | \(0.252189\pi\) | ||||
−0.702228 | + | 0.711953i | \(0.747811\pi\) | |||||||
\(270\) | − | 1.36314i | − | 0.0829580i | ||||||
\(271\) | 16.8668i | 1.02458i | 0.858812 | + | 0.512291i | \(0.171203\pi\) | ||||
−0.858812 | + | 0.512291i | \(0.828797\pi\) | |||||||
\(272\) | 4.96702 | 0.301170 | ||||||||
\(273\) | 11.0103 | + | 4.04432i | 0.666375 | + | 0.244773i | ||||
\(274\) | − | 16.4629i | − | 0.994559i | ||||||
\(275\) | − | 17.5377i | − | 1.05756i | ||||||
\(276\) | 1.57126 | − | 4.53113i | 0.0945790 | − | 0.272742i | ||||
\(277\) | −1.02594 | −0.0616427 | −0.0308214 | − | 0.999525i | \(-0.509812\pi\) | ||||
−0.0308214 | + | 0.999525i | \(0.509812\pi\) | |||||||
\(278\) | − | 18.8131i | − | 1.12833i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.38537 | + | 1.24352i | 0.202314 | + | 0.0743142i | ||||
\(281\) | 26.3067i | 1.56933i | 0.619922 | + | 0.784664i | \(0.287164\pi\) | ||||
−0.619922 | + | 0.784664i | \(0.712836\pi\) | |||||||
\(282\) | −6.14185 | −0.365742 | ||||||||
\(283\) | −31.5797 | −1.87722 | −0.938609 | − | 0.344984i | \(-0.887884\pi\) | ||||
−0.938609 | + | 0.344984i | \(0.887884\pi\) | |||||||
\(284\) | −14.3797 | −0.853279 | ||||||||
\(285\) | − | 6.37972i | − | 0.377902i | ||||||
\(286\) | 24.7469 | 1.46332 | ||||||||
\(287\) | 7.69329 | − | 20.9444i | 0.454121 | − | 1.23631i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 7.67125 | 0.451250 | ||||||||
\(290\) | 10.8320 | 0.636075 | ||||||||
\(291\) | − | 4.19792i | − | 0.246086i | ||||||
\(292\) | 6.57523i | 0.384786i | ||||||||
\(293\) | 4.77037 | 0.278688 | 0.139344 | − | 0.990244i | \(-0.455501\pi\) | ||||
0.139344 | + | 0.990244i | \(0.455501\pi\) | |||||||
\(294\) | −4.53113 | + | 5.33562i | −0.264261 | + | 0.311180i | ||||
\(295\) | − | 14.1490i | − | 0.823787i | ||||||
\(296\) | 3.60388i | 0.209471i | ||||||||
\(297\) | 5.58196 | 0.323898 | ||||||||
\(298\) | − | 10.1327i | − | 0.586973i | ||||||
\(299\) | −6.96600 | + | 20.0882i | −0.402854 | + | 1.16173i | ||||
\(300\) | − | 3.14185i | − | 0.181395i | ||||||
\(301\) | −4.95199 | + | 13.4814i | −0.285428 | + | 0.777054i | ||||
\(302\) | 12.5216 | 0.720536 | ||||||||
\(303\) | 1.90398 | 0.109381 | ||||||||
\(304\) | −4.68017 | −0.268426 | ||||||||
\(305\) | −0.391012 | −0.0223893 | ||||||||
\(306\) | −4.96702 | −0.283945 | ||||||||
\(307\) | − | 28.9376i | − | 1.65156i | −0.563995 | − | 0.825778i | \(-0.690736\pi\) | ||
0.563995 | − | 0.825778i | \(-0.309264\pi\) | |||||||
\(308\) | −5.09211 | + | 13.8628i | −0.290150 | + | 0.789909i | ||||
\(309\) | − | 13.7366i | − | 0.781448i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0882i | 0.685459i | 0.939434 | + | 0.342729i | \(0.111351\pi\) | ||||
−0.939434 | + | 0.342729i | \(0.888649\pi\) | |||||||
\(312\) | 4.43338 | 0.250990 | ||||||||
\(313\) | −19.2944 | −1.09058 | −0.545291 | − | 0.838247i | \(-0.683581\pi\) | ||||
−0.545291 | + | 0.838247i | \(0.683581\pi\) | |||||||
\(314\) | −5.73940 | −0.323893 | ||||||||
\(315\) | −3.38537 | − | 1.24352i | −0.190744 | − | 0.0700641i | ||||
\(316\) | 10.8358i | 0.609563i | ||||||||
\(317\) | 30.6539 | 1.72170 | 0.860848 | − | 0.508863i | \(-0.169934\pi\) | ||||
0.860848 | + | 0.508863i | \(0.169934\pi\) | |||||||
\(318\) | 5.25386 | 0.294622 | ||||||||
\(319\) | 44.3562i | 2.48347i | ||||||||
\(320\) | 1.36314 | 0.0762018 | ||||||||
\(321\) | −6.50466 | −0.363055 | ||||||||
\(322\) | −9.81972 | − | 8.03574i | −0.547232 | − | 0.447814i | ||||
\(323\) | −23.2465 | −1.29347 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 13.9290i | 0.772642i | ||||||||
\(326\) | −5.25776 | −0.291201 | ||||||||
\(327\) | 6.33015 | 0.350058 | ||||||||
\(328\) | − | 8.43338i | − | 0.465655i | ||||||
\(329\) | −5.60287 | + | 15.2533i | −0.308896 | + | 0.840944i | ||||
\(330\) | −7.60899 | −0.418861 | ||||||||
\(331\) | −2.96624 | −0.163039 | −0.0815196 | − | 0.996672i | \(-0.525977\pi\) | ||||
−0.0815196 | + | 0.996672i | \(0.525977\pi\) | |||||||
\(332\) | 2.43943 | 0.133881 | ||||||||
\(333\) | − | 3.60388i | − | 0.197491i | ||||||
\(334\) | − | 11.5493i | − | 0.631949i | ||||||
\(335\) | − | 11.9212i | − | 0.651324i | ||||||
\(336\) | −0.912244 | + | 2.48351i | −0.0497670 | + | 0.135486i | ||||
\(337\) | 5.14536i | 0.280286i | 0.990131 | + | 0.140143i | \(0.0447562\pi\) | ||||
−0.990131 | + | 0.140143i | \(0.955244\pi\) | |||||||
\(338\) | −6.65482 | −0.361975 | ||||||||
\(339\) | 4.37626 | 0.237686 | ||||||||
\(340\) | 6.77073 | 0.367195 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.68017 | 0.253075 | ||||||||
\(343\) | 9.11757 | + | 16.1205i | 0.492302 | + | 0.870424i | ||||
\(344\) | 5.42836i | 0.292678i | ||||||||
\(345\) | 2.14185 | − | 6.17656i | 0.115313 | − | 0.332535i | ||||
\(346\) | 4.67125i | 0.251128i | ||||||||
\(347\) | 19.9385 | 1.07036 | 0.535178 | − | 0.844739i | \(-0.320245\pi\) | ||||
0.535178 | + | 0.844739i | \(0.320245\pi\) | |||||||
\(348\) | 7.94635i | 0.425969i | ||||||||
\(349\) | − | 6.32002i | − | 0.338303i | −0.985590 | − | 0.169151i | \(-0.945897\pi\) | ||
0.985590 | − | 0.169151i | \(-0.0541027\pi\) | |||||||
\(350\) | −7.80281 | − | 2.86613i | −0.417078 | − | 0.153201i | ||||
\(351\) | −4.43338 | −0.236636 | ||||||||
\(352\) | 5.58196i | 0.297519i | ||||||||
\(353\) | − | 3.45932i | − | 0.184121i | −0.995753 | − | 0.0920604i | \(-0.970655\pi\) | ||
0.995753 | − | 0.0920604i | \(-0.0293453\pi\) | |||||||
\(354\) | 10.3797 | 0.551676 | ||||||||
\(355\) | −19.6016 | −1.04034 | ||||||||
\(356\) | 17.0536 | 0.903841 | ||||||||
\(357\) | −4.53113 | + | 12.3356i | −0.239813 | + | 0.652870i | ||||
\(358\) | −4.62888 | −0.244644 | ||||||||
\(359\) | 33.3591i | 1.76062i | 0.474395 | + | 0.880312i | \(0.342667\pi\) | ||||
−0.474395 | + | 0.880312i | \(0.657333\pi\) | |||||||
\(360\) | −1.36314 | −0.0718437 | ||||||||
\(361\) | 2.90398 | 0.152841 | ||||||||
\(362\) | −15.0095 | −0.788884 | ||||||||
\(363\) | − | 20.1583i | − | 1.05804i | ||||||
\(364\) | 4.04432 | − | 11.0103i | 0.211980 | − | 0.577098i | ||||
\(365\) | 8.96295i | 0.469142i | ||||||||
\(366\) | − | 0.286847i | − | 0.0149937i | ||||||
\(367\) | −1.16649 | −0.0608902 | −0.0304451 | − | 0.999536i | \(-0.509692\pi\) | ||||
−0.0304451 | + | 0.999536i | \(0.509692\pi\) | |||||||
\(368\) | −4.53113 | − | 1.57126i | −0.236201 | − | 0.0819078i | ||||
\(369\) | 8.43338i | 0.439024i | ||||||||
\(370\) | 4.91259i | 0.255393i | ||||||||
\(371\) | 4.79280 | − | 13.0480i | 0.248830 | − | 0.677419i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.55855i | − | 0.0806985i | −0.999186 | − | 0.0403492i | \(-0.987153\pi\) | ||
0.999186 | − | 0.0403492i | \(-0.0128470\pi\) | |||||||
\(374\) | 27.7257i | 1.43366i | ||||||||
\(375\) | − | 11.0985i | − | 0.573123i | ||||||
\(376\) | 6.14185i | 0.316742i | ||||||||
\(377\) | − | 35.2291i | − | 1.81439i | ||||||
\(378\) | 0.912244 | − | 2.48351i | 0.0469208 | − | 0.127738i | ||||
\(379\) | 38.7031i | 1.98805i | 0.109170 | + | 0.994023i | \(0.465181\pi\) | ||||
−0.109170 | + | 0.994023i | \(0.534819\pi\) | |||||||
\(380\) | −6.37972 | −0.327273 | ||||||||
\(381\) | 9.49563i | 0.486476i | ||||||||
\(382\) | − | 17.9554i | − | 0.918679i | ||||||
\(383\) | 20.8391 | 1.06483 | 0.532415 | − | 0.846483i | \(-0.321284\pi\) | ||||
0.532415 | + | 0.846483i | \(0.321284\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −6.94125 | + | 18.8970i | −0.353759 | + | 0.963079i | ||||
\(386\) | −14.4334 | −0.734639 | ||||||||
\(387\) | − | 5.42836i | − | 0.275939i | ||||||
\(388\) | −4.19792 | −0.213117 | ||||||||
\(389\) | 3.49867i | 0.177389i | 0.996059 | + | 0.0886947i | \(0.0282695\pi\) | ||||
−0.996059 | + | 0.0886947i | \(0.971730\pi\) | |||||||
\(390\) | 6.04331 | 0.306015 | ||||||||
\(391\) | −22.5062 | − | 7.80449i | −1.13819 | − | 0.394690i | ||||
\(392\) | 5.33562 | + | 4.53113i | 0.269490 | + | 0.228857i | ||||
\(393\) | 15.8927 | 0.801680 | ||||||||
\(394\) | −20.3624 | −1.02584 | ||||||||
\(395\) | 14.7707i | 0.743196i | ||||||||
\(396\) | − | 5.58196i | − | 0.280504i | ||||||
\(397\) | − | 1.31746i | − | 0.0661216i | −0.999453 | − | 0.0330608i | \(-0.989475\pi\) | ||
0.999453 | − | 0.0330608i | \(-0.0105255\pi\) | |||||||
\(398\) | −18.5253 | −0.928588 | ||||||||
\(399\) | 4.26945 | − | 11.6232i | 0.213740 | − | 0.581890i | ||||
\(400\) | −3.14185 | −0.157093 | ||||||||
\(401\) | − | 12.3918i | − | 0.618815i | −0.950930 | − | 0.309408i | \(-0.899869\pi\) | ||
0.950930 | − | 0.309408i | \(-0.100131\pi\) | |||||||
\(402\) | 8.74539 | 0.436181 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | − | 1.90398i | − | 0.0947266i | ||||||
\(405\) | 1.36314 | 0.0677349 | ||||||||
\(406\) | 19.7348 | + | 7.24900i | 0.979422 | + | 0.359762i | ||||
\(407\) | −20.1167 | −0.997148 | ||||||||
\(408\) | 4.96702i | 0.245904i | ||||||||
\(409\) | 29.7370i | 1.47040i | 0.677851 | + | 0.735199i | \(0.262911\pi\) | ||||
−0.677851 | + | 0.735199i | \(0.737089\pi\) | |||||||
\(410\) | − | 11.4959i | − | 0.567740i | ||||||
\(411\) | 16.4629 | 0.812054 | ||||||||
\(412\) | −13.7366 | −0.676754 | ||||||||
\(413\) | 9.46884 | − | 25.7781i | 0.465931 | − | 1.26846i | ||||
\(414\) | 4.53113 | + | 1.57126i | 0.222693 | + | 0.0772234i | ||||
\(415\) | 3.32528 | 0.163232 | ||||||||
\(416\) | − | 4.43338i | − | 0.217364i | ||||||
\(417\) | 18.8131 | 0.921281 | ||||||||
\(418\) | − | 26.1245i | − | 1.27779i | ||||||
\(419\) | 5.43221 | 0.265381 | 0.132690 | − | 0.991158i | \(-0.457638\pi\) | ||||
0.132690 | + | 0.991158i | \(0.457638\pi\) | |||||||
\(420\) | −1.24352 | + | 3.38537i | −0.0606773 | + | 0.165189i | ||||
\(421\) | − | 28.0436i | − | 1.36676i | −0.730062 | − | 0.683381i | \(-0.760509\pi\) | ||
0.730062 | − | 0.683381i | \(-0.239491\pi\) | |||||||
\(422\) | 28.3087 | 1.37805 | ||||||||
\(423\) | − | 6.14185i | − | 0.298627i | ||||||
\(424\) | − | 5.25386i | − | 0.255150i | ||||||
\(425\) | −15.6056 | −0.756984 | ||||||||
\(426\) | − | 14.3797i | − | 0.696700i | ||||||
\(427\) | −0.712386 | − | 0.261674i | −0.0344748 | − | 0.0126633i | ||||
\(428\) | 6.50466i | 0.314414i | ||||||||
\(429\) | 24.7469i | 1.19479i | ||||||||
\(430\) | 7.39962i | 0.356841i | ||||||||
\(431\) | 25.4049i | 1.22371i | 0.790969 | + | 0.611856i | \(0.209577\pi\) | ||||
−0.790969 | + | 0.611856i | \(0.790423\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 1.56183 | 0.0750569 | 0.0375285 | − | 0.999296i | \(-0.488052\pi\) | ||||
0.0375285 | + | 0.999296i | \(0.488052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.8320i | 0.519353i | ||||||||
\(436\) | − | 6.33015i | − | 0.303159i | ||||||
\(437\) | 21.2064 | + | 7.35378i | 1.01444 | + | 0.351779i | ||||
\(438\) | −6.57523 | −0.314177 | ||||||||
\(439\) | − | 25.0431i | − | 1.19524i | −0.801778 | − | 0.597622i | \(-0.796112\pi\) | ||
0.801778 | − | 0.597622i | \(-0.203888\pi\) | |||||||
\(440\) | 7.60899i | 0.362744i | ||||||||
\(441\) | −5.33562 | − | 4.53113i | −0.254077 | − | 0.215768i | ||||
\(442\) | − | 22.0206i | − | 1.04742i | ||||||
\(443\) | 6.72490 | 0.319510 | 0.159755 | − | 0.987157i | \(-0.448930\pi\) | ||||
0.159755 | + | 0.987157i | \(0.448930\pi\) | |||||||
\(444\) | −3.60388 | −0.171032 | ||||||||
\(445\) | 23.2465 | 1.10199 | ||||||||
\(446\) | 3.02594i | 0.143282i | ||||||||
\(447\) | 10.1327 | 0.479261 | ||||||||
\(448\) | 2.48351 | + | 0.912244i | 0.117335 | + | 0.0430995i | ||||
\(449\) | 14.4757 | 0.683152 | 0.341576 | − | 0.939854i | \(-0.389039\pi\) | ||||
0.341576 | + | 0.939854i | \(0.389039\pi\) | |||||||
\(450\) | 3.14185 | 0.148108 | ||||||||
\(451\) | 47.0748 | 2.21666 | ||||||||
\(452\) | − | 4.37626i | − | 0.205842i | ||||||
\(453\) | 12.5216i | 0.588315i | ||||||||
\(454\) | −1.18479 | −0.0556049 | ||||||||
\(455\) | 5.51297 | − | 15.0086i | 0.258452 | − | 0.703614i | ||||
\(456\) | − | 4.68017i | − | 0.219169i | ||||||
\(457\) | − | 0.880885i | − | 0.0412061i | −0.999788 | − | 0.0206030i | \(-0.993441\pi\) | ||
0.999788 | − | 0.0206030i | \(-0.00655861\pi\) | |||||||
\(458\) | 2.34924 | 0.109773 | ||||||||
\(459\) | − | 4.96702i | − | 0.231840i | ||||||
\(460\) | −6.17656 | − | 2.14185i | −0.287984 | − | 0.0998644i | ||||
\(461\) | 22.2724i | 1.03733i | 0.854978 | + | 0.518665i | \(0.173571\pi\) | ||||
−0.854978 | + | 0.518665i | \(0.826429\pi\) | |||||||
\(462\) | −13.8628 | − | 5.09211i | −0.644958 | − | 0.236906i | ||||
\(463\) | 6.46969 | 0.300672 | 0.150336 | − | 0.988635i | \(-0.451964\pi\) | ||||
0.150336 | + | 0.988635i | \(0.451964\pi\) | |||||||
\(464\) | 7.94635 | 0.368900 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.39101 | 0.296058 | ||||||||
\(467\) | 24.0863 | 1.11458 | 0.557291 | − | 0.830317i | \(-0.311841\pi\) | ||||
0.557291 | + | 0.830317i | \(0.311841\pi\) | |||||||
\(468\) | 4.43338i | 0.204933i | ||||||||
\(469\) | 7.97793 | − | 21.7193i | 0.368387 | − | 1.00290i | ||||
\(470\) | 8.37220i | 0.386181i | ||||||||
\(471\) | − | 5.73940i | − | 0.264458i | ||||||
\(472\) | − | 10.3797i | − | 0.477765i | ||||||
\(473\) | −30.3009 | −1.39324 | ||||||||
\(474\) | −10.8358 | −0.497706 | ||||||||
\(475\) | 14.7044 | 0.674684 | ||||||||
\(476\) | 12.3356 | + | 4.53113i | 0.565402 | + | 0.207684i | ||||
\(477\) | 5.25386i | 0.240558i | ||||||||
\(478\) | 12.0882 | 0.552901 | ||||||||
\(479\) | −10.9392 | −0.499826 | −0.249913 | − | 0.968268i | \(-0.580402\pi\) | ||||
−0.249913 | + | 0.968268i | \(0.580402\pi\) | |||||||
\(480\) | 1.36314i | 0.0622185i | ||||||||
\(481\) | 15.9773 | 0.728504 | ||||||||
\(482\) | 4.19792 | 0.191210 | ||||||||
\(483\) | 8.03574 | − | 9.81972i | 0.365639 | − | 0.446813i | ||||
\(484\) | −20.1583 | −0.916285 | ||||||||
\(485\) | −5.72234 | −0.259838 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 0.237870 | 0.0107789 | 0.00538946 | − | 0.999985i | \(-0.498284\pi\) | ||||
0.00538946 | + | 0.999985i | \(0.498284\pi\) | |||||||
\(488\) | −0.286847 | −0.0129849 | ||||||||
\(489\) | − | 5.25776i | − | 0.237764i | ||||||
\(490\) | 7.27320 | + | 6.17656i | 0.328570 | + | 0.279028i | ||||
\(491\) | 10.0519 | 0.453635 | 0.226817 | − | 0.973937i | \(-0.427168\pi\) | ||||
0.226817 | + | 0.973937i | \(0.427168\pi\) | |||||||
\(492\) | 8.43338 | 0.380206 | ||||||||
\(493\) | 39.4696 | 1.77762 | ||||||||
\(494\) | 20.7489i | 0.933539i | ||||||||
\(495\) | − | 7.60899i | − | 0.341999i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.7122 | − | 13.1178i | −1.60191 | − | 0.588414i | ||||
\(498\) | 2.43943i | 0.109314i | ||||||||
\(499\) | −32.7594 | −1.46651 | −0.733257 | − | 0.679952i | \(-0.762001\pi\) | ||||
−0.733257 | + | 0.679952i | \(0.762001\pi\) | |||||||
\(500\) | −11.0985 | −0.496339 | ||||||||
\(501\) | 11.5493 | 0.515984 | ||||||||
\(502\) | 3.60388 | 0.160849 | ||||||||
\(503\) | −22.2376 | −0.991527 | −0.495764 | − | 0.868457i | \(-0.665112\pi\) | ||||
−0.495764 | + | 0.868457i | \(0.665112\pi\) | |||||||
\(504\) | −2.48351 | − | 0.912244i | −0.110624 | − | 0.0406346i | ||||
\(505\) | − | 2.59539i | − | 0.115493i | ||||||
\(506\) | 8.77073 | − | 25.2926i | 0.389907 | − | 1.12439i | ||||
\(507\) | − | 6.65482i | − | 0.295551i | ||||||
\(508\) | 9.49563 | 0.421301 | ||||||||
\(509\) | 2.93774i | 0.130213i | 0.997878 | + | 0.0651066i | \(0.0207387\pi\) | ||||
−0.997878 | + | 0.0651066i | \(0.979261\pi\) | |||||||
\(510\) | 6.77073i | 0.299813i | ||||||||
\(511\) | −5.99821 | + | 16.3296i | −0.265345 | + | 0.722380i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.68017i | 0.206635i | ||||||||
\(514\) | − | 3.22145i | − | 0.142092i | ||||||
\(515\) | −18.7249 | −0.825118 | ||||||||
\(516\) | −5.42836 | −0.238970 | ||||||||
\(517\) | −34.2836 | −1.50779 | ||||||||
\(518\) | −3.28761 | + | 8.95026i | −0.144449 | + | 0.393252i | ||||
\(519\) | −4.67125 | −0.205045 | ||||||||
\(520\) | − | 6.04331i | − | 0.265017i | ||||||
\(521\) | −15.5154 | −0.679743 | −0.339872 | − | 0.940472i | \(-0.610384\pi\) | ||||
−0.339872 | + | 0.940472i | \(0.610384\pi\) | |||||||
\(522\) | −7.94635 | −0.347802 | ||||||||
\(523\) | 29.6936 | 1.29841 | 0.649205 | − | 0.760613i | \(-0.275102\pi\) | ||||
0.649205 | + | 0.760613i | \(0.275102\pi\) | |||||||
\(524\) | − | 15.8927i | − | 0.694275i | ||||||
\(525\) | 2.86613 | − | 7.80281i | 0.125088 | − | 0.340543i | ||||
\(526\) | 23.6915i | 1.03300i | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −5.58196 | −0.242924 | ||||||||
\(529\) | 18.0623 | + | 14.2392i | 0.785316 | + | 0.619096i | ||||
\(530\) | − | 7.16175i | − | 0.311086i | ||||||
\(531\) | 10.3797i | 0.450442i | ||||||||
\(532\) | −11.6232 | − | 4.26945i | −0.503931 | − | 0.185104i | ||||
\(533\) | −37.3883 | −1.61947 | ||||||||
\(534\) | 17.0536i | 0.737983i | ||||||||
\(535\) | 8.86675i | 0.383343i | ||||||||
\(536\) | − | 8.74539i | − | 0.377743i | ||||||
\(537\) | − | 4.62888i | − | 0.199751i | ||||||
\(538\) | 23.3538i | 1.00685i | ||||||||
\(539\) | −25.2926 | + | 29.7832i | −1.08943 | + | 1.28285i | ||||
\(540\) | − | 1.36314i | − | 0.0586602i | ||||||
\(541\) | −26.6963 | −1.14776 | −0.573881 | − | 0.818939i | \(-0.694563\pi\) | ||||
−0.573881 | + | 0.818939i | \(0.694563\pi\) | |||||||
\(542\) | 16.8668i | 0.724489i | ||||||||
\(543\) | − | 15.0095i | − | 0.644121i | ||||||
\(544\) | 4.96702 | 0.212959 | ||||||||
\(545\) | − | 8.62888i | − | 0.369621i | ||||||
\(546\) | 11.0103 | + | 4.04432i | 0.471198 | + | 0.173081i | ||||
\(547\) | −11.4420 | −0.489224 | −0.244612 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244612 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(548\) | − | 16.4629i | − | 0.703259i | ||||||
\(549\) | 0.286847 | 0.0122423 | ||||||||
\(550\) | − | 17.5377i | − | 0.747810i | ||||||
\(551\) | −37.1902 | −1.58436 | ||||||||
\(552\) | 1.57126 | − | 4.53113i | 0.0668774 | − | 0.192858i | ||||
\(553\) | −9.88491 | + | 26.9109i | −0.420349 | + | 1.14437i | ||||
\(554\) | −1.02594 | −0.0435880 | ||||||||
\(555\) | −4.91259 | −0.208528 | ||||||||
\(556\) | − | 18.8131i | − | 0.797853i | ||||||
\(557\) | 14.5240i | 0.615402i | 0.951483 | + | 0.307701i | \(0.0995596\pi\) | ||||
−0.951483 | + | 0.307701i | \(0.900440\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0660 | 1.01788 | ||||||||
\(560\) | 3.38537 | + | 1.24352i | 0.143058 | + | 0.0525481i | ||||
\(561\) | −27.7257 | −1.17058 | ||||||||
\(562\) | 26.3067i | 1.10968i | ||||||||
\(563\) | 38.0183 | 1.60228 | 0.801141 | − | 0.598476i | \(-0.204227\pi\) | ||||
0.801141 | + | 0.598476i | \(0.204227\pi\) | |||||||
\(564\) | −6.14185 | −0.258619 | ||||||||
\(565\) | − | 5.96546i | − | 0.250969i | ||||||
\(566\) | −31.5797 | −1.32739 | ||||||||
\(567\) | 2.48351 | + | 0.912244i | 0.104298 | + | 0.0383106i | ||||
\(568\) | −14.3797 | −0.603360 | ||||||||
\(569\) | 31.5423i | 1.32232i | 0.750244 | + | 0.661161i | \(0.229936\pi\) | ||||
−0.750244 | + | 0.661161i | \(0.770064\pi\) | |||||||
\(570\) | − | 6.37972i | − | 0.267217i | ||||||
\(571\) | 3.69023i | 0.154431i | 0.997014 | + | 0.0772156i | \(0.0246030\pi\) | ||||
−0.997014 | + | 0.0772156i | \(0.975397\pi\) | |||||||
\(572\) | 24.7469 | 1.03472 | ||||||||
\(573\) | 17.9554 | 0.750099 | ||||||||
\(574\) | 7.69329 | − | 20.9444i | 0.321112 | − | 0.874201i | ||||
\(575\) | 14.2361 | + | 4.93668i | 0.593688 | + | 0.205874i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 19.3538i | 0.805708i | 0.915264 | + | 0.402854i | \(0.131982\pi\) | ||||
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(578\) | 7.67125 | 0.319082 | ||||||||
\(579\) | − | 14.4334i | − | 0.599831i | ||||||
\(580\) | 10.8320 | 0.449773 | ||||||||
\(581\) | 6.05835 | + | 2.22536i | 0.251343 | + | 0.0923233i | ||||
\(582\) | − | 4.19792i | − | 0.174009i | ||||||
\(583\) | 29.3268 | 1.21459 | ||||||||
\(584\) | 6.57523i | 0.272085i | ||||||||
\(585\) | 6.04331i | 0.249860i | ||||||||
\(586\) | 4.77037 | 0.197062 | ||||||||
\(587\) | − | 12.4757i | − | 0.514929i | −0.966288 | − | 0.257464i | \(-0.917113\pi\) | ||
0.966288 | − | 0.257464i | \(-0.0828870\pi\) | |||||||
\(588\) | −4.53113 | + | 5.33562i | −0.186861 | + | 0.220037i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − | 14.1490i | − | 0.582505i | ||||||
\(591\) | − | 20.3624i | − | 0.837597i | ||||||
\(592\) | 3.60388i | 0.148118i | ||||||||
\(593\) | − | 16.5181i | − | 0.678317i | −0.940729 | − | 0.339159i | \(-0.889858\pi\) | ||
0.940729 | − | 0.339159i | \(-0.110142\pi\) | |||||||
\(594\) | 5.58196 | 0.229031 | ||||||||
\(595\) | 16.8152 | + | 6.17656i | 0.689355 | + | 0.253214i | ||||
\(596\) | − | 10.1327i | − | 0.415053i | ||||||
\(597\) | − | 18.5253i | − | 0.758189i | ||||||
\(598\) | −6.96600 | + | 20.0882i | −0.284861 | + | 0.821467i | ||||
\(599\) | 28.9549 | 1.18307 | 0.591534 | − | 0.806280i | \(-0.298523\pi\) | ||||
0.591534 | + | 0.806280i | \(0.298523\pi\) | |||||||
\(600\) | − | 3.14185i | − | 0.128266i | ||||||
\(601\) | − | 21.0873i | − | 0.860168i | −0.902789 | − | 0.430084i | \(-0.858484\pi\) | ||
0.902789 | − | 0.430084i | \(-0.141516\pi\) | |||||||
\(602\) | −4.95199 | + | 13.4814i | −0.201828 | + | 0.549460i | ||||
\(603\) | 8.74539i | 0.356140i | ||||||||
\(604\) | 12.5216 | 0.509496 | ||||||||
\(605\) | −27.4785 | −1.11716 | ||||||||
\(606\) | 1.90398 | 0.0773440 | ||||||||
\(607\) | 29.8408i | 1.21120i | 0.795769 | + | 0.605601i | \(0.207067\pi\) | ||||
−0.795769 | + | 0.605601i | \(0.792933\pi\) | |||||||
\(608\) | −4.68017 | −0.189806 | ||||||||
\(609\) | −7.24900 | + | 19.7348i | −0.293744 | + | 0.799695i | ||||
\(610\) | −0.391012 | −0.0158316 | ||||||||
\(611\) | 27.2291 | 1.10157 | ||||||||
\(612\) | −4.96702 | −0.200780 | ||||||||
\(613\) | 15.0266i | 0.606919i | 0.952844 | + | 0.303459i | \(0.0981417\pi\) | ||||
−0.952844 | + | 0.303459i | \(0.901858\pi\) | |||||||
\(614\) | − | 28.9376i | − | 1.16783i | ||||||
\(615\) | 11.4959 | 0.463558 | ||||||||
\(616\) | −5.09211 | + | 13.8628i | −0.205167 | + | 0.558550i | ||||
\(617\) | 22.7232i | 0.914801i | 0.889261 | + | 0.457400i | \(0.151219\pi\) | ||||
−0.889261 | + | 0.457400i | \(0.848781\pi\) | |||||||
\(618\) | − | 13.7366i | − | 0.552567i | ||||||
\(619\) | −15.6194 | −0.627797 | −0.313898 | − | 0.949457i | \(-0.601635\pi\) | ||||
−0.313898 | + | 0.949457i | \(0.601635\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.57126 | + | 4.53113i | −0.0630527 | + | 0.181828i | ||||
\(622\) | 12.0882i | 0.484693i | ||||||||
\(623\) | 42.3528 | + | 15.5571i | 1.69683 | + | 0.623281i | ||||
\(624\) | 4.43338 | 0.177477 | ||||||||
\(625\) | 0.580491 | 0.0232196 | ||||||||
\(626\) | −19.2944 | −0.771158 | ||||||||
\(627\) | 26.1245 | 1.04331 | ||||||||
\(628\) | −5.73940 | −0.229027 | ||||||||
\(629\) | 17.9005i | 0.713740i | ||||||||
\(630\) | −3.38537 | − | 1.24352i | −0.134876 | − | 0.0495428i | ||||
\(631\) | − | 28.1162i | − | 1.11929i | −0.828733 | − | 0.559644i | \(-0.810938\pi\) | ||
0.828733 | − | 0.559644i | \(-0.189062\pi\) | |||||||
\(632\) | 10.8358i | 0.431026i | ||||||||
\(633\) | 28.3087i | 1.12517i | ||||||||
\(634\) | 30.6539 | 1.21742 | ||||||||
\(635\) | 12.9439 | 0.513662 | ||||||||
\(636\) | 5.25386 | 0.208329 | ||||||||
\(637\) | 20.0882 | − | 23.6548i | 0.795923 | − | 0.937238i | ||||
\(638\) | 44.3562i | 1.75608i | ||||||||
\(639\) | 14.3797 | 0.568853 | ||||||||
\(640\) | 1.36314 | 0.0538828 | ||||||||
\(641\) | 30.5778i | 1.20775i | 0.797079 | + | 0.603875i | \(0.206377\pi\) | ||||
−0.797079 | + | 0.603875i | \(0.793623\pi\) | |||||||
\(642\) | −6.50466 | −0.256718 | ||||||||
\(643\) | −33.9988 | −1.34078 | −0.670390 | − | 0.742009i | \(-0.733873\pi\) | ||||
−0.670390 | + | 0.742009i | \(0.733873\pi\) | |||||||
\(644\) | −9.81972 | − | 8.03574i | −0.386951 | − | 0.316653i | ||||
\(645\) | −7.39962 | −0.291360 | ||||||||
\(646\) | −23.2465 | −0.914620 | ||||||||
\(647\) | − | 20.0882i | − | 0.789749i | −0.918735 | − | 0.394874i | \(-0.870788\pi\) | ||
0.918735 | − | 0.394874i | \(-0.129212\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 57.9392 | 2.27431 | ||||||||
\(650\) | 13.9290i | 0.546341i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.25776 | −0.205910 | ||||||||
\(653\) | 37.5128 | 1.46799 | 0.733995 | − | 0.679154i | \(-0.237653\pi\) | ||||
0.733995 | + | 0.679154i | \(0.237653\pi\) | |||||||
\(654\) | 6.33015 | 0.247529 | ||||||||
\(655\) | − | 21.6639i | − | 0.846481i | ||||||
\(656\) | − | 8.43338i | − | 0.329268i | ||||||
\(657\) | − | 6.57523i | − | 0.256524i | ||||||
\(658\) | −5.60287 | + | 15.2533i | −0.218422 | + | 0.594637i | ||||
\(659\) | 38.7324i | 1.50880i | 0.656415 | + | 0.754400i | \(0.272072\pi\) | ||||
−0.656415 | + | 0.754400i | \(0.727928\pi\) | |||||||
\(660\) | −7.60899 | −0.296179 | ||||||||
\(661\) | 43.8446 | 1.70536 | 0.852680 | − | 0.522434i | \(-0.174976\pi\) | ||||
0.852680 | + | 0.522434i | \(0.174976\pi\) | |||||||
\(662\) | −2.96624 | −0.115286 | ||||||||
\(663\) | 22.0206 | 0.855211 | ||||||||
\(664\) | 2.43943 | 0.0946683 | ||||||||
\(665\) | −15.8441 | − | 5.81986i | −0.614407 | − | 0.225685i | ||||
\(666\) | − | 3.60388i | − | 0.139647i | ||||||
\(667\) | −36.0059 | − | 12.4858i | −1.39415 | − | 0.483452i | ||||
\(668\) | − | 11.5493i | − | 0.446855i | ||||||
\(669\) | −3.02594 | −0.116990 | ||||||||
\(670\) | − | 11.9212i | − | 0.460556i | ||||||
\(671\) | − | 1.60117i | − | 0.0618124i | ||||||
\(672\) | −0.912244 | + | 2.48351i | −0.0351906 | + | 0.0958034i | ||||
\(673\) | 16.7249 | 0.644698 | 0.322349 | − | 0.946621i | \(-0.395528\pi\) | ||||
0.322349 | + | 0.946621i | \(0.395528\pi\) | |||||||
\(674\) | 5.14536i | 0.198192i | ||||||||
\(675\) | 3.14185i | 0.120930i | ||||||||
\(676\) | −6.65482 | −0.255955 | ||||||||
\(677\) | −38.1796 | −1.46736 | −0.733681 | − | 0.679494i | \(-0.762199\pi\) | ||||
−0.733681 | + | 0.679494i | \(0.762199\pi\) | |||||||
\(678\) | 4.37626 | 0.168069 | ||||||||
\(679\) | −10.4256 | − | 3.82952i | −0.400096 | − | 0.146964i | ||||
\(680\) | 6.77073 | 0.259646 | ||||||||
\(681\) | − | 1.18479i | − | 0.0454013i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −37.7620 | −1.44492 | −0.722461 | − | 0.691411i | \(-0.756989\pi\) | ||||
−0.722461 | + | 0.691411i | \(0.756989\pi\) | |||||||
\(684\) | 4.68017 | 0.178951 | ||||||||
\(685\) | − | 22.4412i | − | 0.857434i | ||||||
\(686\) | 9.11757 | + | 16.1205i | 0.348110 | + | 0.615483i | ||||
\(687\) | 2.34924i | 0.0896289i | ||||||||
\(688\) | 5.42836i | 0.206954i | ||||||||
\(689\) | −23.2923 | −0.887368 | ||||||||
\(690\) | 2.14185 | − | 6.17656i | 0.0815389 | − | 0.235138i | ||||
\(691\) | 12.2379i | 0.465551i | 0.972531 | + | 0.232775i | \(0.0747807\pi\) | ||||
−0.972531 | + | 0.232775i | \(0.925219\pi\) | |||||||
\(692\) | 4.67125i | 0.177574i | ||||||||
\(693\) | 5.09211 | − | 13.8628i | 0.193433 | − | 0.526606i | ||||
\(694\) | 19.9385 | 0.756856 | ||||||||
\(695\) | − | 25.6449i | − | 0.972765i | ||||||
\(696\) | 7.94635i | 0.301205i | ||||||||
\(697\) | − | 41.8887i | − | 1.58665i | ||||||
\(698\) | − | 6.32002i | − | 0.239216i | ||||||
\(699\) | 6.39101i | 0.241730i | ||||||||
\(700\) | −7.80281 | − | 2.86613i | −0.294919 | − | 0.108330i | ||||
\(701\) | − | 8.67815i | − | 0.327769i | −0.986480 | − | 0.163885i | \(-0.947598\pi\) | ||
0.986480 | − | 0.163885i | \(-0.0524025\pi\) | |||||||
\(702\) | −4.43338 | −0.167327 | ||||||||
\(703\) | − | 16.8668i | − | 0.636142i | ||||||
\(704\) | 5.58196i | 0.210378i | ||||||||
\(705\) | −8.37220 | −0.315315 | ||||||||
\(706\) | − | 3.45932i | − | 0.130193i | ||||||
\(707\) | 1.73690 | − | 4.72855i | 0.0653227 | − | 0.177836i | ||||
\(708\) | 10.3797 | 0.390094 | ||||||||
\(709\) | 20.5523i | 0.771858i | 0.922529 | + | 0.385929i | \(0.126119\pi\) | ||||
−0.922529 | + | 0.385929i | \(0.873881\pi\) | |||||||
\(710\) | −19.6016 | −0.735633 | ||||||||
\(711\) | − | 10.8358i | − | 0.406375i | ||||||
\(712\) | 17.0536 | 0.639112 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −4.53113 | + | 12.3356i | −0.169573 | + | 0.461649i | ||||
\(715\) | 33.7335 | 1.26156 | ||||||||
\(716\) | −4.62888 | −0.172989 | ||||||||
\(717\) | 12.0882i | 0.451442i | ||||||||
\(718\) | 33.3591i | 1.24495i | ||||||||
\(719\) | 27.9351i | 1.04180i | 0.853617 | + | 0.520901i | \(0.174404\pi\) | ||||
−0.853617 | + | 0.520901i | \(0.825596\pi\) | |||||||
\(720\) | −1.36314 | −0.0508012 | ||||||||
\(721\) | −34.1150 | − | 12.5311i | −1.27051 | − | 0.466684i | ||||
\(722\) | 2.90398 | 0.108075 | ||||||||
\(723\) | 4.19792i | 0.156122i | ||||||||
\(724\) | −15.0095 | −0.557825 | ||||||||
\(725\) | −24.9662 | −0.927223 | ||||||||
\(726\) | − | 20.1583i | − | 0.748144i | ||||||
\(727\) | 2.54793 | 0.0944975 | 0.0472487 | − | 0.998883i | \(-0.484955\pi\) | ||||
0.0472487 | + | 0.998883i | \(0.484955\pi\) | |||||||
\(728\) | 4.04432 | − | 11.0103i | 0.149892 | − | 0.408070i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 8.96295i | 0.331734i | ||||||||
\(731\) | 26.9628i | 0.997254i | ||||||||
\(732\) | − | 0.286847i | − | 0.0106022i | ||||||
\(733\) | −22.3075 | −0.823946 | −0.411973 | − | 0.911196i | \(-0.635160\pi\) | ||||
−0.411973 | + | 0.911196i | \(0.635160\pi\) | |||||||
\(734\) | −1.16649 | −0.0430559 | ||||||||
\(735\) | −6.17656 | + | 7.27320i | −0.227826 | + | 0.268276i | ||||
\(736\) | −4.53113 | − | 1.57126i | −0.167020 | − | 0.0579176i | ||||
\(737\) | 48.8164 | 1.79818 | ||||||||
\(738\) | 8.43338i | 0.310437i | ||||||||
\(739\) | 8.84172 | 0.325248 | 0.162624 | − | 0.986688i | \(-0.448004\pi\) | ||||
0.162624 | + | 0.986688i | \(0.448004\pi\) | |||||||
\(740\) | 4.91259i | 0.180590i | ||||||||
\(741\) | −20.7489 | −0.762232 | ||||||||
\(742\) | 4.79280 | − | 13.0480i | 0.175949 | − | 0.479007i | ||||
\(743\) | − | 32.1121i | − | 1.17808i | −0.808104 | − | 0.589040i | \(-0.799506\pi\) | ||
0.808104 | − | 0.589040i | \(-0.200494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.8123i | − | 0.506044i | ||||||
\(746\) | − | 1.55855i | − | 0.0570624i | ||||||
\(747\) | −2.43943 | −0.0892541 | ||||||||
\(748\) | 27.7257i | 1.01375i | ||||||||
\(749\) | −5.93383 | + | 16.1544i | −0.216817 | + | 0.590268i | ||||
\(750\) | − | 11.0985i | − | 0.405259i | ||||||
\(751\) | 50.5719i | 1.84540i | 0.385523 | + | 0.922698i | \(0.374021\pi\) | ||||
−0.385523 | + | 0.922698i | \(0.625979\pi\) | |||||||
\(752\) | 6.14185i | 0.223970i | ||||||||
\(753\) | 3.60388i | 0.131333i | ||||||||
\(754\) | − | 35.2291i | − | 1.28297i | ||||||
\(755\) | 17.0686 | 0.621192 | ||||||||
\(756\) | 0.912244 | − | 2.48351i | 0.0331780 | − | 0.0903243i | ||||
\(757\) | − | 19.2806i | − | 0.700765i | −0.936607 | − | 0.350383i | \(-0.886052\pi\) | ||
0.936607 | − | 0.350383i | \(-0.113948\pi\) | |||||||
\(758\) | 38.7031i | 1.40576i | ||||||||
\(759\) | 25.2926 | + | 8.77073i | 0.918062 | + | 0.318357i | ||||
\(760\) | −6.37972 | −0.231417 | ||||||||
\(761\) | 49.3234i | 1.78797i | 0.448096 | + | 0.893986i | \(0.352102\pi\) | ||||
−0.448096 | + | 0.893986i | \(0.647898\pi\) | |||||||
\(762\) | 9.49563i | 0.343991i | ||||||||
\(763\) | 5.77464 | − | 15.7210i | 0.209056 | − | 0.569138i | ||||
\(764\) | − | 17.9554i | − | 0.649604i | ||||||
\(765\) | −6.77073 | −0.244796 | ||||||||
\(766\) | 20.8391 | 0.752949 | ||||||||
\(767\) | −46.0172 | −1.66159 | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 30.3928 | 1.09599 | 0.547997 | − | 0.836480i | \(-0.315391\pi\) | ||||
0.547997 | + | 0.836480i | \(0.315391\pi\) | |||||||
\(770\) | −6.94125 | + | 18.8970i | −0.250145 | + | 0.681000i | ||||
\(771\) | 3.22145 | 0.116018 | ||||||||
\(772\) | −14.4334 | −0.519469 | ||||||||
\(773\) | 3.99922 | 0.143842 | 0.0719210 | − | 0.997410i | \(-0.477087\pi\) | ||||
0.0719210 | + | 0.997410i | \(0.477087\pi\) | |||||||
\(774\) | − | 5.42836i | − | 0.195119i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.19792 | −0.150696 | ||||||||
\(777\) | −8.95026 | − | 3.28761i | −0.321089 | − | 0.117942i | ||||
\(778\) | 3.49867i | 0.125433i | ||||||||
\(779\) | 39.4696i | 1.41415i | ||||||||
\(780\) | 6.04331 | 0.216385 | ||||||||
\(781\) | − | 80.2670i | − | 2.87218i | ||||||
\(782\) | −22.5062 | − | 7.80449i | −0.804820 | − | 0.279088i | ||||
\(783\) | − | 7.94635i | − | 0.283979i | ||||||
\(784\) | 5.33562 | + | 4.53113i | 0.190558 | + | 0.161826i | ||||
\(785\) | −7.82361 | −0.279236 | ||||||||
\(786\) | 15.8927 | 0.566874 | ||||||||
\(787\) | 36.0612 | 1.28544 | 0.642721 | − | 0.766101i | \(-0.277806\pi\) | ||||
0.642721 | + | 0.766101i | \(0.277806\pi\) | |||||||
\(788\) | −20.3624 | −0.725380 | ||||||||
\(789\) | −23.6915 | −0.843441 | ||||||||
\(790\) | 14.7707i | 0.525519i | ||||||||
\(791\) | 3.99222 | − | 10.8685i | 0.141947 | − | 0.386439i | ||||
\(792\) | − | 5.58196i | − | 0.198346i | ||||||
\(793\) | 1.27170i | 0.0451594i | ||||||||
\(794\) | − | 1.31746i | − | 0.0467550i | ||||||
\(795\) | 7.16175 | 0.254001 | ||||||||
\(796\) | −18.5253 | −0.656611 | ||||||||
\(797\) | −46.7688 | −1.65664 | −0.828318 | − | 0.560258i | \(-0.810702\pi\) | ||||
−0.828318 | + | 0.560258i | \(0.810702\pi\) | |||||||
\(798\) | 4.26945 | − | 11.6232i | 0.151137 | − | 0.411458i | ||||
\(799\) | 30.5067i | 1.07925i | ||||||||
\(800\) | −3.14185 | −0.111081 | ||||||||
\(801\) | −17.0536 | −0.602560 | ||||||||
\(802\) | − | 12.3918i | − | 0.437568i | ||||||
\(803\) | −36.7027 | −1.29521 | ||||||||
\(804\) | 8.74539 | 0.308426 | ||||||||
\(805\) | −13.3856 | − | 10.9538i | −0.471782 | − | 0.386072i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.3538 | −0.822092 | ||||||||
\(808\) | − | 1.90398i | − | 0.0669818i | ||||||
\(809\) | −25.3823 | −0.892393 | −0.446197 | − | 0.894935i | \(-0.647222\pi\) | ||||
−0.446197 | + | 0.894935i | \(0.647222\pi\) | |||||||
\(810\) | 1.36314 | 0.0478958 | ||||||||
\(811\) | 24.4869i | 0.859851i | 0.902864 | + | 0.429926i | \(0.141460\pi\) | ||||
−0.902864 | + | 0.429926i | \(0.858540\pi\) | |||||||
\(812\) | 19.7348 | + | 7.24900i | 0.692556 | + | 0.254390i | ||||
\(813\) | −16.8668 | −0.591543 | ||||||||
\(814\) | −20.1167 | −0.705090 | ||||||||
\(815\) | −7.16706 | −0.251051 | ||||||||
\(816\) | 4.96702i | 0.173880i | ||||||||
\(817\) | − | 25.4057i | − | 0.888832i | ||||||
\(818\) | 29.7370i | 1.03973i | ||||||||
\(819\) | −4.04432 | + | 11.0103i | −0.141320 | + | 0.384732i | ||||
\(820\) | − | 11.4959i | − | 0.401453i | ||||||
\(821\) | 19.9099 | 0.694860 | 0.347430 | − | 0.937706i | \(-0.387054\pi\) | ||||
0.347430 | + | 0.937706i | \(0.387054\pi\) | |||||||
\(822\) | 16.4629 | 0.574209 | ||||||||
\(823\) | −53.3883 | −1.86100 | −0.930500 | − | 0.366292i | \(-0.880627\pi\) | ||||
−0.930500 | + | 0.366292i | \(0.880627\pi\) | |||||||
\(824\) | −13.7366 | −0.478537 | ||||||||
\(825\) | 17.5377 | 0.610584 | ||||||||
\(826\) | 9.46884 | − | 25.7781i | 0.329463 | − | 0.896936i | ||||
\(827\) | − | 57.0480i | − | 1.98375i | −0.127203 | − | 0.991877i | \(-0.540600\pi\) | ||
0.127203 | − | 0.991877i | \(-0.459400\pi\) | |||||||
\(828\) | 4.53113 | + | 1.57126i | 0.157468 | + | 0.0546052i | ||||
\(829\) | − | 6.83043i | − | 0.237231i | −0.992940 | − | 0.118615i | \(-0.962154\pi\) | ||
0.992940 | − | 0.118615i | \(-0.0378456\pi\) | |||||||
\(830\) | 3.32528 | 0.115422 | ||||||||
\(831\) | − | 1.02594i | − | 0.0355895i | ||||||
\(832\) | − | 4.43338i | − | 0.153700i | ||||||
\(833\) | 26.5021 | + | 22.5062i | 0.918244 | + | 0.779793i | ||||
\(834\) | 18.8131 | 0.651444 | ||||||||
\(835\) | − | 15.7433i | − | 0.544819i | ||||||
\(836\) | − | 26.1245i | − | 0.903535i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.43221 | 0.187653 | ||||||||
\(839\) | 23.1680 | 0.799849 | 0.399925 | − | 0.916548i | \(-0.369036\pi\) | ||||
0.399925 | + | 0.916548i | \(0.369036\pi\) | |||||||
\(840\) | −1.24352 | + | 3.38537i | −0.0429053 | + | 0.116806i | ||||
\(841\) | 34.1444 | 1.17739 | ||||||||
\(842\) | − | 28.0436i | − | 0.966447i | ||||||
\(843\) | −26.3067 | −0.906051 | ||||||||
\(844\) | 28.3087 | 0.974427 | ||||||||
\(845\) | −9.07145 | −0.312067 | ||||||||
\(846\) | − | 6.14185i | − | 0.211161i | ||||||
\(847\) | −50.0632 | − | 18.3893i | −1.72019 | − | 0.631862i | ||||
\(848\) | − | 5.25386i | − | 0.180418i | ||||||
\(849\) | − | 31.5797i | − | 1.08381i | ||||||
\(850\) | −15.6056 | −0.535269 | ||||||||
\(851\) | 5.66264 | − | 16.3296i | 0.194113 | − | 0.559772i | ||||
\(852\) | − | 14.3797i | − | 0.492641i | ||||||
\(853\) | − | 50.5138i | − | 1.72956i | −0.502153 | − | 0.864779i | \(-0.667458\pi\) | ||
0.502153 | − | 0.864779i | \(-0.332542\pi\) | |||||||
\(854\) | −0.712386 | − | 0.261674i | −0.0243774 | − | 0.00895431i | ||||
\(855\) | 6.37972 | 0.218182 | ||||||||
\(856\) | 6.50466i | 0.222325i | ||||||||
\(857\) | 9.99048i | 0.341268i | 0.985334 | + | 0.170634i | \(0.0545816\pi\) | ||||
−0.985334 | + | 0.170634i | \(0.945418\pi\) | |||||||
\(858\) | 24.7469i | 0.844846i | ||||||||
\(859\) | − | 43.0371i | − | 1.46841i | −0.678930 | − | 0.734203i | \(-0.737556\pi\) | ||
0.678930 | − | 0.734203i | \(-0.262444\pi\) | |||||||
\(860\) | 7.39962i | 0.252325i | ||||||||
\(861\) | 20.9444 | + | 7.69329i | 0.713782 | + | 0.262187i | ||||
\(862\) | 25.4049i | 0.865295i | ||||||||
\(863\) | 33.2578 | 1.13211 | 0.566054 | − | 0.824368i | \(-0.308469\pi\) | ||||
0.566054 | + | 0.824368i | \(0.308469\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 6.36756i | 0.216503i | ||||||||
\(866\) | 1.56183 | 0.0530733 | ||||||||
\(867\) | 7.67125i | 0.260529i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −60.4851 | −2.05182 | ||||||||
\(870\) | 10.8320i | 0.367238i | ||||||||
\(871\) | −38.7716 | −1.31373 | ||||||||
\(872\) | − | 6.33015i | − | 0.214366i | ||||||
\(873\) | 4.19792 | 0.142078 | ||||||||
\(874\) | 21.2064 | + | 7.35378i | 0.717319 | + | 0.248745i | ||||
\(875\) | −27.5632 | − | 10.1245i | −0.931805 | − | 0.342271i | ||||
\(876\) | −6.57523 | −0.222156 | ||||||||
\(877\) | −36.7076 | −1.23953 | −0.619763 | − | 0.784789i | \(-0.712771\pi\) | ||||
−0.619763 | + | 0.784789i | \(0.712771\pi\) | |||||||
\(878\) | − | 25.0431i | − | 0.845165i | ||||||
\(879\) | 4.77037i | 0.160900i | ||||||||
\(880\) | 7.60899i | 0.256499i | ||||||||
\(881\) | −13.8032 | −0.465041 | −0.232520 | − | 0.972592i | \(-0.574697\pi\) | ||||
−0.232520 | + | 0.972592i | \(0.574697\pi\) | |||||||
\(882\) | −5.33562 | − | 4.53113i | −0.179660 | − | 0.152571i | ||||
\(883\) | 28.2240 | 0.949813 | 0.474907 | − | 0.880036i | \(-0.342482\pi\) | ||||
0.474907 | + | 0.880036i | \(0.342482\pi\) | |||||||
\(884\) | − | 22.0206i | − | 0.740635i | ||||||
\(885\) | 14.1490 | 0.475614 | ||||||||
\(886\) | 6.72490 | 0.225927 | ||||||||
\(887\) | − | 11.3885i | − | 0.382387i | −0.981552 | − | 0.191193i | \(-0.938764\pi\) | ||
0.981552 | − | 0.191193i | \(-0.0612358\pi\) | |||||||
\(888\) | −3.60388 | −0.120938 | ||||||||
\(889\) | 23.5825 | + | 8.66233i | 0.790931 | + | 0.290525i | ||||
\(890\) | 23.2465 | 0.779224 | ||||||||
\(891\) | 5.58196i | 0.187003i | ||||||||
\(892\) | 3.02594i | 0.101316i | ||||||||
\(893\) | − | 28.7449i | − | 0.961912i | ||||||
\(894\) | 10.1327 | 0.338889 | ||||||||
\(895\) | −6.30981 | −0.210914 | ||||||||
\(896\) | 2.48351 | + | 0.912244i | 0.0829682 | + | 0.0304759i | ||||
\(897\) | −20.0882 | − | 6.96600i | −0.670725 | − | 0.232588i | ||||
\(898\) | 14.4757 | 0.483062 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 3.14185 | 0.104728 | ||||||||
\(901\) | − | 26.0960i | − | 0.869384i | ||||||
\(902\) | 47.0748 | 1.56742 | ||||||||
\(903\) | −13.4814 | − | 4.95199i | −0.448632 | − | 0.164792i | ||||
\(904\) | − | 4.37626i | − | 0.145552i | ||||||
\(905\) | −20.4601 | −0.680117 | ||||||||
\(906\) | 12.5216i | 0.416001i | ||||||||
\(907\) | − | 14.8305i | − | 0.492439i | −0.969214 | − | 0.246220i | \(-0.920812\pi\) | ||
0.969214 | − | 0.246220i | \(-0.0791884\pi\) | |||||||
\(908\) | −1.18479 | −0.0393186 | ||||||||
\(909\) | 1.90398i | 0.0631511i | ||||||||
\(910\) | 5.51297 | − | 15.0086i | 0.182753 | − | 0.497530i | ||||
\(911\) | − | 40.6152i | − | 1.34564i | −0.739805 | − | 0.672821i | \(-0.765082\pi\) | ||
0.739805 | − | 0.672821i | \(-0.234918\pi\) | |||||||
\(912\) | − | 4.68017i | − | 0.154976i | ||||||
\(913\) | 13.6168i | 0.450651i | ||||||||
\(914\) | − | 0.880885i | − | 0.0291371i | ||||||
\(915\) | − | 0.391012i | − | 0.0129265i | ||||||
\(916\) | 2.34924 | 0.0776209 | ||||||||
\(917\) | 14.4980 | − | 39.4696i | 0.478766 | − | 1.30340i | ||||
\(918\) | − | 4.96702i | − | 0.163936i | ||||||
\(919\) | − | 40.4132i | − | 1.33311i | −0.745456 | − | 0.666555i | \(-0.767768\pi\) | ||
0.745456 | − | 0.666555i | \(-0.232232\pi\) | |||||||
\(920\) | −6.17656 | − | 2.14185i | −0.203635 | − | 0.0706148i | ||||
\(921\) | 28.9376 | 0.953527 | ||||||||
\(922\) | 22.2724i | 0.733503i | ||||||||
\(923\) | 63.7507i | 2.09838i | ||||||||
\(924\) | −13.8628 | − | 5.09211i | −0.456054 | − | 0.167518i | ||||
\(925\) | − | 11.3228i | − | 0.372293i | ||||||
\(926\) | 6.46969 | 0.212607 | ||||||||
\(927\) | 13.7366 | 0.451169 | ||||||||
\(928\) | 7.94635 | 0.260852 | ||||||||
\(929\) | 18.9836i | 0.622831i | 0.950274 | + | 0.311415i | \(0.100803\pi\) | ||||
−0.950274 | + | 0.311415i | \(0.899197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.9716 | − | 21.2064i | −0.818412 | − | 0.695013i | ||||
\(932\) | 6.39101 | 0.209345 | ||||||||
\(933\) | −12.0882 | −0.395750 | ||||||||
\(934\) | 24.0863 | 0.788129 | ||||||||
\(935\) | 37.7940i | 1.23599i | ||||||||
\(936\) | 4.43338i | 0.144909i | ||||||||
\(937\) | 46.8748 | 1.53133 | 0.765667 | − | 0.643237i | \(-0.222409\pi\) | ||||
0.765667 | + | 0.643237i | \(0.222409\pi\) | |||||||
\(938\) | 7.97793 | − | 21.7193i | 0.260489 | − | 0.709159i | ||||
\(939\) | − | 19.2944i | − | 0.629648i | ||||||
\(940\) | 8.37220i | 0.273071i | ||||||||
\(941\) | −32.6198 | −1.06338 | −0.531688 | − | 0.846940i | \(-0.678442\pi\) | ||||
−0.531688 | + | 0.846940i | \(0.678442\pi\) | |||||||
\(942\) | − | 5.73940i | − | 0.187000i | ||||||
\(943\) | −13.2511 | + | 38.2127i | −0.431514 | + | 1.24438i | ||||
\(944\) | − | 10.3797i | − | 0.337831i | ||||||
\(945\) | 1.24352 | − | 3.38537i | 0.0404515 | − | 0.110126i | ||||
\(946\) | −30.3009 | −0.985168 | ||||||||
\(947\) | −41.4731 | −1.34769 | −0.673847 | − | 0.738871i | \(-0.735359\pi\) | ||||
−0.673847 | + | 0.738871i | \(0.735359\pi\) | |||||||
\(948\) | −10.8358 | −0.351931 | ||||||||
\(949\) | 29.1505 | 0.946264 | ||||||||
\(950\) | 14.7044 | 0.477074 | ||||||||
\(951\) | 30.6539i | 0.994021i | ||||||||
\(952\) | 12.3356 | + | 4.53113i | 0.399800 | + | 0.146855i | ||||
\(953\) | − | 21.2345i | − | 0.687853i | −0.938997 | − | 0.343926i | \(-0.888243\pi\) | ||
0.938997 | − | 0.343926i | \(-0.111757\pi\) | |||||||
\(954\) | 5.25386i | 0.170100i | ||||||||
\(955\) | − | 24.4757i | − | 0.792016i | ||||||
\(956\) | 12.0882 | 0.390960 | ||||||||
\(957\) | −44.3562 | −1.43383 | ||||||||
\(958\) | −10.9392 | −0.353430 | ||||||||
\(959\) | 15.0182 | − | 40.8857i | 0.484962 | − | 1.32027i | ||||
\(960\) | 1.36314i | 0.0439951i | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 15.9773 | 0.515130 | ||||||||
\(963\) | − | 6.50466i | − | 0.209610i | ||||||
\(964\) | 4.19792 | 0.135206 | ||||||||
\(965\) | −19.6747 | −0.633351 | ||||||||
\(966\) | 8.03574 | − | 9.81972i | 0.258546 | − | 0.315944i | ||||
\(967\) | 18.3009 | 0.588518 | 0.294259 | − | 0.955726i | \(-0.404927\pi\) | ||||
0.294259 | + | 0.955726i | \(0.404927\pi\) | |||||||
\(968\) | −20.1583 | −0.647912 | ||||||||
\(969\) | − | 23.2465i | − | 0.746784i | ||||||
\(970\) | −5.72234 | −0.183733 | ||||||||
\(971\) | −34.0033 | −1.09122 | −0.545609 | − | 0.838040i | \(-0.683702\pi\) | ||||
−0.545609 | + | 0.838040i | \(0.683702\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 17.1621 | − | 46.7225i | 0.550193 | − | 1.49785i | ||||
\(974\) | 0.237870 | 0.00762184 | ||||||||
\(975\) | −13.9290 | −0.446085 | ||||||||
\(976\) | −0.286847 | −0.00918174 | ||||||||
\(977\) | 11.2273i | 0.359194i | 0.983740 | + | 0.179597i | \(0.0574793\pi\) | ||||
−0.983740 | + | 0.179597i | \(0.942521\pi\) | |||||||
\(978\) | − | 5.25776i | − | 0.168125i | ||||||
\(979\) | 95.1927i | 3.04237i | ||||||||
\(980\) | 7.27320 | + | 6.17656i | 0.232334 | + | 0.197303i | ||||
\(981\) | 6.33015i | 0.202106i | ||||||||
\(982\) | 10.0519 | 0.320768 | ||||||||
\(983\) | −26.5087 | −0.845496 | −0.422748 | − | 0.906247i | \(-0.638934\pi\) | ||||
−0.422748 | + | 0.906247i | \(0.638934\pi\) | |||||||
\(984\) | 8.43338 | 0.268846 | ||||||||
\(985\) | −27.7568 | −0.884404 | ||||||||
\(986\) | 39.4696 | 1.25697 | ||||||||
\(987\) | −15.2533 | − | 5.60287i | −0.485519 | − | 0.178341i | ||||
\(988\) | 20.7489i | 0.660112i | ||||||||
\(989\) | 8.52939 | − | 24.5966i | 0.271219 | − | 0.782127i | ||||
\(990\) | − | 7.60899i | − | 0.241830i | ||||||
\(991\) | −52.0344 | −1.65293 | −0.826464 | − | 0.562990i | \(-0.809651\pi\) | ||||
−0.826464 | + | 0.562990i | \(0.809651\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.96624i | − | 0.0941308i | ||||||
\(994\) | −35.7122 | − | 13.1178i | −1.13272 | − | 0.416072i | ||||
\(995\) | −25.2525 | −0.800559 | ||||||||
\(996\) | 2.43943i | 0.0772963i | ||||||||
\(997\) | 47.4479i | 1.50269i | 0.659910 | + | 0.751345i | \(0.270595\pi\) | ||||
−0.659910 | + | 0.751345i | \(0.729405\pi\) | |||||||
\(998\) | −32.7594 | −1.03698 | ||||||||
\(999\) | 3.60388 | 0.114022 |
(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 | 966.2.g.e.643.14 | yes | 16 | |
3.2 | odd | 2 | 2898.2.g.j.2575.6 | 16 | |||
7.6 | odd | 2 | inner | 966.2.g.e.643.3 | ✓ | 16 | |
21.20 | even | 2 | 2898.2.g.j.2575.12 | 16 | |||
23.22 | odd | 2 | inner | 966.2.g.e.643.11 | yes | 16 | |
69.68 | even | 2 | 2898.2.g.j.2575.11 | 16 | |||
161.160 | even | 2 | inner | 966.2.g.e.643.6 | yes | 16 | |
483.482 | odd | 2 | 2898.2.g.j.2575.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.g.e.643.3 | ✓ | 16 | 7.6 | odd | 2 | inner | |
966.2.g.e.643.6 | yes | 16 | 161.160 | even | 2 | inner | |
966.2.g.e.643.11 | yes | 16 | 23.22 | odd | 2 | inner | |
966.2.g.e.643.14 | yes | 16 | 1.1 | even | 1 | trivial | |
2898.2.g.j.2575.5 | 16 | 483.482 | odd | 2 | |||
2898.2.g.j.2575.6 | 16 | 3.2 | odd | 2 | |||
2898.2.g.j.2575.11 | 16 | 69.68 | even | 2 | |||
2898.2.g.j.2575.12 | 16 | 21.20 | even | 2 |