Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.59105344.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 21x^{4} + 116x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.3 | ||
Root | \(-3.29707i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.j.3649.4 |
$q$-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 \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.786802i | − 0.454260i | −0.973864 | − | 0.227130i | \(-0.927066\pi\) | ||||
0.973864 | − | 0.227130i | \(-0.0729343\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.08387i | − 0.787630i | −0.919190 | − | 0.393815i | \(-0.871155\pi\) | ||||
0.919190 | − | 0.393815i | \(-0.128845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.38094 | 0.793648 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.29707 | 0.391081 | 0.195541 | − | 0.980696i | \(-0.437354\pi\) | ||||
0.195541 | + | 0.980696i | \(0.437354\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.21320i | − 0.336481i | −0.985746 | − | 0.168240i | \(-0.946192\pi\) | ||||
0.985746 | − | 0.168240i | \(-0.0538085\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.08387i | 0.990485i | 0.868755 | + | 0.495242i | \(0.164921\pi\) | ||||
−0.868755 | + | 0.495242i | \(0.835079\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.63959 | −0.357789 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.95455i | 1.86715i | 0.358379 | + | 0.933576i | \(0.383329\pi\) | ||||
−0.358379 | + | 0.933576i | \(0.616671\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 4.23374i | − 0.814783i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.38094 | 1.74200 | 0.870999 | − | 0.491285i | \(-0.163473\pi\) | ||||
0.870999 | + | 0.491285i | \(0.163473\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 1.02054i | − 0.177653i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.00000i | − 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.954547 | −0.152850 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.57360 | 0.558103 | 0.279052 | − | 0.960276i | \(-0.409980\pi\) | ||||
0.279052 | + | 0.960276i | \(0.409980\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.72347i | − 1.17782i | −0.808199 | − | 0.588909i | \(-0.799558\pi\) | ||||
0.808199 | − | 0.588909i | \(-0.200442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.46482i | 1.38059i | 0.723530 | + | 0.690293i | \(0.242518\pi\) | ||||
−0.723530 | + | 0.690293i | \(0.757482\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.65748 | 0.379639 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.21320 | 0.449938 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.9751i | 1.64490i | 0.568834 | + | 0.822452i | \(0.307395\pi\) | ||||
−0.568834 | + | 0.822452i | \(0.692605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 0.786802i | − 0.104214i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.21320 | 0.939078 | 0.469539 | − | 0.882912i | \(-0.344420\pi\) | ||||
0.469539 | + | 0.882912i | \(0.344420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.87067 | 0.623626 | 0.311813 | − | 0.950144i | \(-0.399064\pi\) | ||||
0.311813 | + | 0.950144i | \(0.399064\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.96158i | − 0.625100i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3809i | 1.39040i | 0.718815 | + | 0.695202i | \(0.244685\pi\) | ||||
−0.718815 | + | 0.695202i | \(0.755315\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.04545 | 0.848173 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.02054 | −1.07054 | −0.535270 | − | 0.844681i | \(-0.679790\pi\) | ||||
−0.535270 | + | 0.844681i | \(0.679790\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.65748i | − 0.662157i | −0.943603 | − | 0.331079i | \(-0.892587\pi\) | ||||
0.943603 | − | 0.331079i | \(-0.107413\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.70293i | − 0.308027i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.57360 | −1.07711 | −0.538557 | − | 0.842589i | \(-0.681030\pi\) | ||||
−0.538557 | + | 0.842589i | \(0.681030\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.81172 | 0.423524 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 10.7619i | − 1.18127i | −0.806939 | − | 0.590635i | \(-0.798877\pi\) | ||||
0.806939 | − | 0.590635i | \(-0.201123\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 7.38094i | − 0.791320i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0205 | −1.16817 | −0.584087 | − | 0.811691i | \(-0.698547\pi\) | ||||
−0.584087 | + | 0.811691i | \(0.698547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.52815 | −0.265022 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 8.59414i | − 0.872603i | −0.899801 | − | 0.436301i | \(-0.856288\pi\) | ||||
0.899801 | − | 0.436301i | \(-0.143712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.08825 | 0.310381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.14721 | 0.910181 | 0.455091 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455091 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 17.3560i | − 1.71014i | −0.518512 | − | 0.855070i | \(-0.673514\pi\) | ||||
0.518512 | − | 0.855070i | \(-0.326486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 0.786802i | − 0.0760630i | −0.999277 | − | 0.0380315i | \(-0.987891\pi\) | ||||
0.999277 | − | 0.0380315i | \(-0.0121087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5487 | 1.29773 | 0.648864 | − | 0.760904i | \(-0.275244\pi\) | ||||
0.648864 | + | 0.760904i | \(0.275244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.57360 | −0.149360 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.14721i | 0.107920i | 0.998543 | + | 0.0539601i | \(0.0171844\pi\) | ||||
−0.998543 | + | 0.0539601i | \(0.982816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.88856i | − 0.267047i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.51027 | 0.780135 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.31761 | −0.847055 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.81172i | − 0.253524i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.02054i | − 0.0905581i | −0.998974 | − | 0.0452790i | \(-0.985582\pi\) | ||||
0.998974 | − | 0.0452790i | \(-0.0144177\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.07684 | −0.535036 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.72347 | −0.674802 | −0.337401 | − | 0.941361i | \(-0.609548\pi\) | ||||
−0.337401 | + | 0.941361i | \(0.609548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.08387i | − 0.180695i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.2311i | 1.30128i | 0.759387 | + | 0.650639i | \(0.225499\pi\) | ||||
−0.759387 | + | 0.650639i | \(0.774501\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0590 | −1.36210 | −0.681051 | − | 0.732236i | \(-0.738477\pi\) | ||||
−0.681051 | + | 0.732236i | \(0.738477\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.44693 | 0.627145 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.57360i | − 0.131591i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.09091i | − 0.172455i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.10879 | 0.172759 | 0.0863793 | − | 0.996262i | \(-0.472470\pi\) | ||||
0.0863793 | + | 0.996262i | \(0.472470\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3560 | 1.41241 | 0.706207 | − | 0.708006i | \(-0.250405\pi\) | ||||
0.706207 | + | 0.708006i | \(0.250405\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.72347i | 0.786096i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000i | 1.11732i | 0.829396 | + | 0.558661i | \(0.188685\pi\) | ||||
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.42202 | 0.747215 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.6601 | 1.47062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.852793i | 0.0667959i | 0.999442 | + | 0.0333979i | \(0.0106329\pi\) | ||||
−0.999442 | + | 0.0333979i | \(0.989367\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 18.5941i | − 1.43886i | −0.694566 | − | 0.719429i | \(-0.744404\pi\) | ||||
0.694566 | − | 0.719429i | \(-0.255596\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5282 | 0.886781 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.38094 | 0.182075 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2.85279i | − 0.216894i | −0.994102 | − | 0.108447i | \(-0.965412\pi\) | ||||
0.994102 | − | 0.108447i | \(-0.0345877\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 5.67536i | − 0.426586i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.0768 | 1.94907 | 0.974537 | − | 0.224226i | \(-0.0719854\pi\) | ||||
0.974537 | + | 0.224226i | \(0.0719854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.18828 | 0.236983 | 0.118492 | − | 0.992955i | \(-0.462194\pi\) | ||||
0.118492 | + | 0.992955i | \(0.462194\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 3.83226i | − 0.283288i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.29707i | 0.387360i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.82256 | −0.641747 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.95720 | 0.575763 | 0.287881 | − | 0.957666i | \(-0.407049\pi\) | ||||
0.287881 | + | 0.957666i | \(0.407049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 20.9296i | − 1.50655i | −0.657707 | − | 0.753274i | \(-0.728473\pi\) | ||||
0.657707 | − | 0.753274i | \(-0.271527\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 3.57360i | − 0.254609i | −0.991864 | − | 0.127304i | \(-0.959368\pi\) | ||||
0.991864 | − | 0.127304i | \(-0.0406325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.4194 | 1.87282 | 0.936409 | − | 0.350909i | \(-0.114127\pi\) | ||||
0.936409 | + | 0.350909i | \(0.114127\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.95455 | 0.631605 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 19.5487i | − 1.37205i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.3203i | 1.48186i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.29707 | 0.0897202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.5487 | −1.62116 | −0.810579 | − | 0.585629i | \(-0.800848\pi\) | ||||
−0.810579 | + | 0.585629i | \(0.800848\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.09738i | 0.486304i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.45131 | −0.300792 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.95455 | 0.333279 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.02054i | − 0.0683402i | −0.999416 | − | 0.0341701i | \(-0.989121\pi\) | ||||
0.999416 | − | 0.0341701i | \(-0.0108788\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.04545i | 0.202134i | 0.994880 | + | 0.101067i | \(0.0322256\pi\) | ||||
−0.994880 | + | 0.101067i | \(0.967774\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.01788 | 0.265509 | 0.132755 | − | 0.991149i | \(-0.457618\pi\) | ||||
0.132755 | + | 0.991149i | \(0.457618\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.12667 | −0.139925 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 25.2062i | − 1.65131i | −0.564175 | − | 0.825655i | \(-0.690806\pi\) | ||||
0.564175 | − | 0.825655i | \(-0.309194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.53253i | 0.489290i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.93667 | 0.448696 | 0.224348 | − | 0.974509i | \(-0.427975\pi\) | ||||
0.224348 | + | 0.974509i | \(0.427975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.761886 | 0.0490774 | 0.0245387 | − | 0.999699i | \(-0.492188\pi\) | ||||
0.0245387 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.7003i | − 1.00717i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.21320i | − 0.0771940i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.46747 | −0.536604 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.14986 | −0.388176 | −0.194088 | − | 0.980984i | \(-0.562175\pi\) | ||||
−0.194088 | + | 0.980984i | \(0.562175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.6147i | 0.730209i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 23.3560i | − 1.45691i | −0.685094 | − | 0.728454i | \(-0.740239\pi\) | ||||
0.685094 | − | 0.728454i | \(-0.259761\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.16774 | −0.258971 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.3355 | 1.38253 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 12.2765i | − 0.757003i | −0.925601 | − | 0.378502i | \(-0.876439\pi\) | ||||
0.925601 | − | 0.378502i | \(-0.123561\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.67098i | 0.530655i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.74135 | 0.471998 | 0.235999 | − | 0.971753i | \(-0.424164\pi\) | ||||
0.235999 | + | 0.971753i | \(0.424164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.954547 | −0.0579846 | −0.0289923 | − | 0.999580i | \(-0.509230\pi\) | ||||
−0.0289923 | + | 0.999580i | \(0.509230\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.98915i | 0.120389i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.0384i | 1.02374i | 0.859063 | + | 0.511870i | \(0.171047\pi\) | ||||
−0.859063 | + | 0.511870i | \(0.828953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.0974 | −0.781324 | −0.390662 | − | 0.920534i | \(-0.627754\pi\) | ||||
−0.390662 | + | 0.920534i | \(0.627754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.29707i | − 0.0771028i | −0.999257 | − | 0.0385514i | \(-0.987726\pi\) | ||||
0.999257 | − | 0.0385514i | \(-0.0122743\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 7.44693i | − 0.439579i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.321987 | 0.0189404 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.76189 | −0.396389 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.5487i | 1.25889i | 0.777046 | + | 0.629444i | \(0.216717\pi\) | ||||
−0.777046 | + | 0.629444i | \(0.783283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 5.49145i | − 0.318646i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.8636 | 0.628260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.0947 | −0.927684 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 7.19704i | − 0.413459i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.18828i | − 0.524403i | −0.965013 | − | 0.262201i | \(-0.915551\pi\) | ||||
0.965013 | − | 0.262201i | \(-0.0844485\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.6558 | −0.776849 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.48973 | −0.424704 | −0.212352 | − | 0.977193i | \(-0.568112\pi\) | ||||
−0.212352 | + | 0.977193i | \(0.568112\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.76626i | 0.552022i | 0.961154 | + | 0.276011i | \(0.0890126\pi\) | ||||
−0.961154 | + | 0.276011i | \(0.910987\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.7164i | 0.770392i | 0.922835 | + | 0.385196i | \(0.125866\pi\) | ||||
−0.922835 | + | 0.385196i | \(0.874134\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1677 | 0.681263 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.619057 | −0.0345524 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.08387i | 0.227233i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 10.6601i | − 0.589507i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.7235 | 1.08739 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.5282 | −0.798539 | −0.399270 | − | 0.916834i | \(-0.630736\pi\) | ||||
−0.399270 | + | 0.916834i | \(0.630736\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 4.76189i | − 0.260950i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.31495i | 0.507418i | 0.967281 | + | 0.253709i | \(0.0816505\pi\) | ||||
−0.967281 | + | 0.253709i | \(0.918349\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.902625 | 0.0490238 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 20.1249i | − 1.08665i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 9.29707i | − 0.499093i | −0.968363 | − | 0.249546i | \(-0.919718\pi\) | ||||
0.968363 | − | 0.249546i | \(-0.0802815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0590 | 0.752559 | 0.376279 | − | 0.926506i | \(-0.377203\pi\) | ||||
0.376279 | + | 0.926506i | \(0.377203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.13636 | −0.274159 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.4783i | 1.08995i | 0.838452 | + | 0.544975i | \(0.183461\pi\) | ||||
−0.838452 | + | 0.544975i | \(0.816539\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 6.69589i | − 0.354384i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.9724 | −1.00133 | −0.500663 | − | 0.865642i | \(-0.666910\pi\) | ||||
−0.500663 | + | 0.865642i | \(0.666910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.33111i | 0.384784i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.85279i | − 0.253314i | −0.991947 | − | 0.126657i | \(-0.959575\pi\) | ||||
0.991947 | − | 0.126657i | \(-0.0404247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.50855 | 0.442937 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.9545 | 1.29558 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1071i | 0.626880i | 0.949608 | + | 0.313440i | \(0.101481\pi\) | ||||
−0.949608 | + | 0.313440i | \(0.898519\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 11.3809i | − 0.586148i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.02492 | 0.104013 | 0.0520065 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520065 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.802961 | −0.0411369 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.23811i | 0.0632647i | 0.999500 | + | 0.0316323i | \(0.0100706\pi\) | ||||
−0.999500 | + | 0.0316323i | \(0.989929\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 18.3891i | − 0.934772i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.8707 | −0.652569 | −0.326285 | − | 0.945272i | \(-0.605797\pi\) | ||||
−0.326285 | + | 0.945272i | \(0.605797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.5692 | −1.84939 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.07684i | 0.306536i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.3739i | 0.871971i | 0.899954 | + | 0.435986i | \(0.143600\pi\) | ||||
−0.899954 | + | 0.435986i | \(0.856400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.63959 | −0.0820824 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.0205 | 0.949840 | 0.474920 | − | 0.880029i | \(-0.342477\pi\) | ||||
0.474920 | + | 0.880029i | \(0.342477\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.59414i | − 0.128587i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.4622 | −1.01179 | −0.505894 | − | 0.862595i | \(-0.668837\pi\) | ||||
−0.505894 | + | 0.862595i | \(0.668837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.9838 | 0.591119 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 15.0314i | − 0.739646i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.6352i | 0.618749i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.14721 | 0.349164 | 0.174582 | − | 0.984643i | \(-0.444143\pi\) | ||||
0.174582 | + | 0.984643i | \(0.444143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3604 | 0.602409 | 0.301205 | − | 0.953560i | \(-0.402611\pi\) | ||||
0.301205 | + | 0.953560i | \(0.402611\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.5352i | 1.09570i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 10.1499i | − 0.491186i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.23811 | −0.0597767 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.90909 | −0.0919578 | −0.0459789 | − | 0.998942i | \(-0.514641\pi\) | ||||
−0.0459789 | + | 0.998942i | \(0.514641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 4.04107i | − 0.194202i | −0.995275 | − | 0.0971008i | \(-0.969043\pi\) | ||||
0.995275 | − | 0.0971008i | \(-0.0309569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.95455i | 0.428354i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0768 | −0.671851 | −0.335925 | − | 0.941889i | \(-0.609049\pi\) | ||||
−0.335925 | + | 0.941889i | \(0.609049\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.32730 | 0.301300 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6736i | 0.934723i | 0.884066 | + | 0.467361i | \(0.154795\pi\) | ||||
−0.884066 | + | 0.467361i | \(0.845205\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.65920i | − 0.0784774i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5531 | −0.498030 | −0.249015 | − | 0.968500i | \(-0.580107\pi\) | ||||
−0.249015 | + | 0.968500i | \(0.580107\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.63522 | 0.218264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 13.6558i | − 0.641603i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.72785i | 0.127603i | 0.997963 | + | 0.0638016i | \(0.0203225\pi\) | ||||
−0.997963 | + | 0.0638016i | \(0.979678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.2900 | 0.807030 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.1153 | −1.63548 | −0.817740 | − | 0.575587i | \(-0.804773\pi\) | ||||
−0.817740 | + | 0.575587i | \(0.804773\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 17.1293i | − 0.796067i | −0.917371 | − | 0.398034i | \(-0.869693\pi\) | ||||
0.917371 | − | 0.398034i | \(-0.130307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7029i | 0.680370i | 0.940358 | + | 0.340185i | \(0.110490\pi\) | ||||
−0.940358 | + | 0.340185i | \(0.889510\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.7164 | 1.09512 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0152 | 0.507555 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 10.0179i | − 0.460623i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.5120i | 1.30547i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0411 | −0.458788 | −0.229394 | − | 0.973334i | \(-0.573674\pi\) | ||||
−0.229394 | + | 0.973334i | \(0.573674\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.42640 | −0.110634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 14.6818i | − 0.668046i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.6504i | − 1.07170i | −0.844312 | − | 0.535852i | \(-0.819991\pi\) | ||||
0.844312 | − | 0.535852i | \(-0.180009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.670979 | 0.0303427 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.3766 | −1.73191 | −0.865955 | − | 0.500122i | \(-0.833289\pi\) | ||||
−0.865955 | + | 0.500122i | \(0.833289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.3106i | 1.72542i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.7976i | 0.843190i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.3176 | −0.461880 | −0.230940 | − | 0.972968i | \(-0.574180\pi\) | ||||
−0.230940 | + | 0.972968i | \(0.574180\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.6299 | −0.653616 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.4372i | 0.911252i | 0.890171 | + | 0.455626i | \(0.150584\pi\) | ||||
−0.890171 | + | 0.455626i | \(0.849416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.07037i | − 0.402829i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.4059 | 0.682853 | 0.341426 | − | 0.939909i | \(-0.389090\pi\) | ||||
0.341426 | + | 0.939909i | \(0.389090\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.7895 | −0.521535 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.23374i | − 0.186924i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.2765i | 0.539921i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.24458 | −0.0985262 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0270 | 1.57837 | 0.789186 | − | 0.614154i | \(-0.210503\pi\) | ||||
0.789186 | + | 0.614154i | \(0.210503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 44.7370i | − 1.95621i | −0.208109 | − | 0.978106i | \(-0.566731\pi\) | ||||
0.208109 | − | 0.978106i | \(-0.433269\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −57.1839 | −2.48626 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.1742 | 0.745297 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.33549i | − 0.187791i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 20.5173i | − 0.885387i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.44693 | 0.148470 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.5059 | −1.61250 | −0.806252 | − | 0.591572i | \(-0.798507\pi\) | ||||
−0.806252 | + | 0.591572i | \(0.798507\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 2.50855i | − 0.107652i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.5968 | 0.494939 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.38094 | 0.399642 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.9502i | 0.848367i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 33.3381i | − 1.41258i | −0.707921 | − | 0.706291i | \(-0.750367\pi\) | ||||
0.707921 | − | 0.706291i | \(-0.249633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.37010 | −0.396313 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.16774 | 0.175962 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 3.44693i | − 0.145271i | −0.997359 | − | 0.0726355i | \(-0.976859\pi\) | ||||
0.997359 | − | 0.0726355i | \(-0.0231410\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 7.94313i | − 0.333580i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.0205 | −1.13276 | −0.566380 | − | 0.824144i | \(-0.691657\pi\) | ||||
−0.566380 | + | 0.824144i | \(0.691657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.70559 | −0.238771 | −0.119386 | − | 0.992848i | \(-0.538092\pi\) | ||||
−0.119386 | + | 0.992848i | \(0.538092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 6.26074i | − 0.261546i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.34252i | 0.264043i | 0.991247 | + | 0.132021i | \(0.0421467\pi\) | ||||
−0.991247 | + | 0.132021i | \(0.957853\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.4675 | −0.684365 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.4264 | −0.930404 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5325i | 0.643292i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 37.5827i | − 1.55121i | −0.631222 | − | 0.775603i | \(-0.717446\pi\) | ||||
0.631222 | − | 0.775603i | \(-0.282554\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.81172 | −0.115659 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.48270i | 0.389408i | 0.980862 | + | 0.194704i | \(0.0623746\pi\) | ||||
−0.980862 | + | 0.194704i | \(0.937625\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 20.7868i | − 0.850747i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.6710 | −1.00803 | −0.504014 | − | 0.863695i | \(-0.668144\pi\) | ||||
−0.504014 | + | 0.863695i | \(0.668144\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.4329 | 1.69008 | 0.845041 | − | 0.534702i | \(-0.179576\pi\) | ||||
0.845041 | + | 0.534702i | \(0.179576\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.0974i | 1.10349i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.32026i | 0.215943i | 0.994154 | + | 0.107971i | \(0.0344355\pi\) | ||||
−0.994154 | + | 0.107971i | \(0.965564\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.3809 | −0.623267 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.4827 | 0.464540 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.2472i | 1.10051i | 0.834998 | + | 0.550253i | \(0.185469\pi\) | ||||
−0.834998 | + | 0.550253i | \(0.814531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 30.9117i | − 1.24446i | −0.782834 | − | 0.622230i | \(-0.786227\pi\) | ||||
0.782834 | − | 0.622230i | \(-0.213773\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.2857 | 0.976123 | 0.488061 | − | 0.872809i | \(-0.337704\pi\) | ||||
0.488061 | + | 0.872809i | \(0.337704\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.9112 | 1.52132 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.9654i | 0.920089i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 1.02054i | − 0.0407563i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.16774 | 0.325669 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.9117 | 0.991721 | 0.495861 | − | 0.868402i | \(-0.334853\pi\) | ||||
0.495861 | + | 0.868402i | \(0.334853\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.5282i | 0.736428i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.22405i | − 0.127741i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.4774 | −0.849632 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.25865 | 0.168207 | 0.0841033 | − | 0.996457i | \(-0.473197\pi\) | ||||
0.0841033 | + | 0.996457i | \(0.473197\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.9323i | 0.549436i | 0.961525 | + | 0.274718i | \(0.0885845\pi\) | ||||
−0.961525 | + | 0.274718i | \(0.911416\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.58064i | 0.219398i | 0.993965 | + | 0.109699i | \(0.0349886\pi\) | ||||
−0.993965 | + | 0.109699i | \(0.965011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.35603 | 0.367256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.77330i | 0.0693945i | 0.999398 | + | 0.0346973i | \(0.0110467\pi\) | ||||
−0.999398 | + | 0.0346973i | \(0.988953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 13.4701i | − 0.525520i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.12229 | 0.0437183 | 0.0218591 | − | 0.999761i | \(-0.493041\pi\) | ||||
0.0218591 | + | 0.999761i | \(0.493041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.9340 | 0.853134 | 0.426567 | − | 0.904456i | \(-0.359723\pi\) | ||||
0.426567 | + | 0.904456i | \(0.359723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.89825i | − 0.151395i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 84.0021i | 3.25257i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.802961 | −0.0310443 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.31761 | 0.243889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.24458i | 0.317805i | 0.987294 | + | 0.158903i | \(0.0507956\pi\) | ||||
−0.987294 | + | 0.158903i | \(0.949204\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.76626i | − 0.221616i | −0.993842 | − | 0.110808i | \(-0.964656\pi\) | ||||
0.993842 | − | 0.110808i | \(-0.0353438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.9091 | −0.687288 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.39617 | 0.0918214 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 3.16128i | − 0.120610i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.5282 | 0.553478 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.0384 | 0.876423 | 0.438211 | − | 0.898872i | \(-0.355612\pi\) | ||||
0.438211 | + | 0.898872i | \(0.355612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 6.43552i | − 0.244465i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.5941i | 0.552793i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.8323 | −0.750125 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.90909 | −0.147644 | −0.0738222 | − | 0.997271i | \(-0.523520\pi\) | ||||
−0.0738222 | + | 0.997271i | \(0.523520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 2.00000i | − 0.0754314i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 19.0616i | − 0.716886i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.0411 | 0.452212 | 0.226106 | − | 0.974103i | \(-0.427400\pi\) | ||||
0.226106 | + | 0.974103i | \(0.427400\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.7942 | −0.854849 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 5.45778i | − 0.203825i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.2927 | −1.20431 | −0.602157 | − | 0.798378i | \(-0.705692\pi\) | ||||
−0.602157 | + | 0.798378i | \(0.705692\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.1677 | −1.34696 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 0.599453i | − 0.0222939i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1812i | 1.52733i | 0.645614 | + | 0.763664i | \(0.276602\pi\) | ||||
−0.645614 | + | 0.763664i | \(0.723398\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.917850 | −0.0339945 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.5417 | 1.16661 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.27919i | − 0.0472479i | −0.999721 | − | 0.0236240i | \(-0.992480\pi\) | ||||
0.999721 | − | 0.0236240i | \(-0.00752044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.7619i | 0.543761i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.3534 | −1.11657 | −0.558283 | − | 0.829650i | \(-0.688540\pi\) | ||||
−0.558283 | + | 0.829650i | \(0.688540\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.954547 | −0.0350661 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.4827i | 0.714751i | 0.933961 | + | 0.357375i | \(0.116328\pi\) | ||||
−0.933961 | + | 0.357375i | \(0.883672\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 25.6234i | − 0.937512i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.63959 | −0.0599095 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.6710 | −1.77603 | −0.888015 | − | 0.459815i | \(-0.847916\pi\) | ||||
−0.888015 | + | 0.459815i | \(0.847916\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.83872i | 0.176333i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.7235i | 1.51647i | 0.651984 | + | 0.758233i | \(0.273937\pi\) | ||||
−0.651984 | + | 0.758233i | \(0.726063\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.13845 | 0.331705 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.10441 | −0.330035 | −0.165017 | − | 0.986291i | \(-0.552768\pi\) | ||||
−0.165017 | + | 0.986291i | \(0.552768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 28.2337i | − 1.02213i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.75104i | − 0.315982i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.14548 | −0.257673 | −0.128836 | − | 0.991666i | \(-0.541124\pi\) | ||||
−0.128836 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.3766 | −0.661816 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.9956i | 1.04290i | 0.853282 | + | 0.521450i | \(0.174609\pi\) | ||||
−0.853282 | + | 0.521450i | \(0.825391\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.27919i | 0.117640i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.57360 | 0.128038 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.7003 | −0.418669 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 39.7164i | − 1.41935i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 23.3311i | − 0.831664i | −0.909441 | − | 0.415832i | \(-0.863490\pi\) | ||||
0.909441 | − | 0.415832i | \(-0.136510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.65920 | −0.343877 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.39063 | 0.0850011 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 5.90909i | − 0.209838i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.2543i | 0.682021i | 0.940059 | + | 0.341011i | \(0.110769\pi\) | ||||
−0.940059 | + | 0.341011i | \(0.889231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38.6531 | −1.36745 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.2393 | −0.927119 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.33815i | − 0.258958i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 6.09091i | − 0.214410i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.9983 | −0.984367 | −0.492184 | − | 0.870491i | \(-0.663801\pi\) | ||||
−0.492184 | + | 0.870491i | \(0.663801\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.4631 | −1.66665 | −0.833327 | − | 0.552780i | \(-0.813567\pi\) | ||||
−0.833327 | + | 0.552780i | \(0.813567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.751039i | 0.0263401i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 7.72347i | − 0.270210i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.01938 | −0.210334 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.14455 | 0.0748454 | 0.0374227 | − | 0.999300i | \(-0.488085\pi\) | ||||
0.0374227 | + | 0.999300i | \(0.488085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.8458i | 1.14493i | 0.819929 | + | 0.572466i | \(0.194013\pi\) | ||||
−0.819929 | + | 0.572466i | \(0.805987\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.6103i | 0.925331i | 0.886533 | + | 0.462665i | \(0.153107\pi\) | ||||
−0.886533 | + | 0.462665i | \(0.846893\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.6871 | −1.76044 | −0.880219 | − | 0.474569i | \(-0.842604\pi\) | ||||
−0.880219 | + | 0.474569i | \(0.842604\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.4059 | 0.465044 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.8528i | 0.376027i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.2651 | 1.76987 | 0.884934 | − | 0.465716i | \(-0.154203\pi\) | ||||
0.884934 | + | 0.465716i | \(0.154203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0021 | 2.03455 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.3050i | 0.354924i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.4167i | 0.667166i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.02054 | −0.0350248 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.9091 | 0.613916 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.95893i | 0.272508i | 0.990674 | + | 0.136254i | \(0.0435064\pi\) | ||||
−0.990674 | + | 0.136254i | \(0.956494\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 4.09091i | − 0.139743i | −0.997556 | − | 0.0698714i | \(-0.977741\pi\) | ||||
0.997556 | − | 0.0698714i | \(-0.0222589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3328 | 0.454910 | 0.227455 | − | 0.973789i | \(-0.426959\pi\) | ||||
0.227455 | + | 0.973789i | \(0.426959\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.85926 | −0.199683 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.1677i | 0.686518i | 0.939241 | + | 0.343259i | \(0.111531\pi\) | ||||
−0.939241 | + | 0.343259i | \(0.888469\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 0.253340i | − 0.00860386i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.4176 | −0.421240 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.8073 | 0.467844 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 20.4622i | − 0.692539i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.8572i | 0.805599i | 0.915288 | + | 0.402800i | \(0.131963\pi\) | ||||
−0.915288 | + | 0.402800i | \(0.868037\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.9545 | 0.571863 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.9182 | −1.61441 | −0.807203 | − | 0.590274i | \(-0.799020\pi\) | ||||
−0.807203 | + | 0.590274i | \(0.799020\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.5622i | 0.961194i | 0.876942 | + | 0.480597i | \(0.159580\pi\) | ||||
−0.876942 | + | 0.480597i | \(0.840420\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.3150i | 1.58868i | 0.607473 | + | 0.794340i | \(0.292183\pi\) | ||||
−0.607473 | + | 0.794340i | \(0.707817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.12667 | −0.0713262 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.94407 | 0.165632 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.46482i | 0.316728i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 8.54753i | − 0.285394i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.9047 | −1.62925 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.6634i | 0.421410i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 15.8982i | − 0.527893i | −0.964537 | − | 0.263946i | \(-0.914976\pi\) | ||||
0.964537 | − | 0.263946i | \(-0.0850242\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 21.7790 | 0.722363 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.2997 | −0.672560 | −0.336280 | − | 0.941762i | \(-0.609169\pi\) | ||||
−0.336280 | + | 0.941762i | \(0.609169\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 13.9589i | − 0.461973i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0947i | 0.531494i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.6191 | −1.07600 | −0.538002 | − | 0.842944i | \(-0.680821\pi\) | ||||
−0.538002 | + | 0.842944i | \(0.680821\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.22936 | −0.238215 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.9437i | 0.360216i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 41.3237i | − 1.35725i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.4631 | −1.75407 | −0.877034 | − | 0.480429i | \(-0.840481\pi\) | ||||
−0.877034 | + | 0.480429i | \(0.840481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.65748 | 0.0870953 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.89293i | 0.192926i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 43.0135i | − 1.40519i | −0.711590 | − | 0.702595i | \(-0.752025\pi\) | ||||
0.711590 | − | 0.702595i | \(-0.247975\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.68411 | 0.250762 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.3311 | 0.825771 | 0.412885 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412885 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000i | 1.04206i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.6710i | 0.411751i | 0.978578 | + | 0.205876i | \(0.0660043\pi\) | ||||
−0.978578 | + | 0.205876i | \(0.933996\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.86364 | −0.222803 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.7921 | 0.349958 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.2240i | 1.01145i | 0.862696 | + | 0.505723i | \(0.168774\pi\) | ||||
−0.862696 | + | 0.505723i | \(0.831226\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.57360i | − 0.309471i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.7396 | 1.02493 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.87333i | − 0.0603672i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.29441i | 0.202415i | 0.994865 | + | 0.101207i | \(0.0322706\pi\) | ||||
−0.994865 | + | 0.101207i | \(0.967729\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.21320 | 0.103223 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.0000 | 0.641831 | 0.320915 | − | 0.947108i | \(-0.396010\pi\) | ||||
0.320915 | + | 0.947108i | \(0.396010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.4648i | 1.07283i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 34.1677i | − 1.09312i | −0.837419 | − | 0.546561i | \(-0.815936\pi\) | ||||
0.837419 | − | 0.546561i | \(-0.184064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.2944 | −0.456851 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32.2587 | 1.02994 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 30.4264i | − 0.970451i | −0.874389 | − | 0.485226i | \(-0.838737\pi\) | ||||
0.874389 | − | 0.485226i | \(-0.161263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 15.5185i | − 0.493958i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 69.1601 | 2.19916 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.1179 | −0.766131 | −0.383065 | − | 0.923721i | \(-0.625132\pi\) | ||||
−0.383065 | + | 0.923721i | \(0.625132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.4308i | 0.362745i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.9323i | 0.504581i | 0.967652 | + | 0.252290i | \(0.0811838\pi\) | ||||
−0.967652 | + | 0.252290i | \(0.918816\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.46747 | −0.267899 |
(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 | 3800.2.d.j.3649.3 | 6 | ||
5.2 | odd | 4 | 3800.2.a.r.1.2 | 3 | |||
5.3 | odd | 4 | 152.2.a.c.1.2 | ✓ | 3 | ||
5.4 | even | 2 | inner | 3800.2.d.j.3649.4 | 6 | ||
15.8 | even | 4 | 1368.2.a.n.1.1 | 3 | |||
20.3 | even | 4 | 304.2.a.g.1.2 | 3 | |||
20.7 | even | 4 | 7600.2.a.bv.1.2 | 3 | |||
35.13 | even | 4 | 7448.2.a.bf.1.2 | 3 | |||
40.3 | even | 4 | 1216.2.a.v.1.2 | 3 | |||
40.13 | odd | 4 | 1216.2.a.u.1.2 | 3 | |||
60.23 | odd | 4 | 2736.2.a.bd.1.1 | 3 | |||
95.18 | even | 4 | 2888.2.a.o.1.2 | 3 | |||
380.303 | odd | 4 | 5776.2.a.bp.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.a.c.1.2 | ✓ | 3 | 5.3 | odd | 4 | ||
304.2.a.g.1.2 | 3 | 20.3 | even | 4 | |||
1216.2.a.u.1.2 | 3 | 40.13 | odd | 4 | |||
1216.2.a.v.1.2 | 3 | 40.3 | even | 4 | |||
1368.2.a.n.1.1 | 3 | 15.8 | even | 4 | |||
2736.2.a.bd.1.1 | 3 | 60.23 | odd | 4 | |||
2888.2.a.o.1.2 | 3 | 95.18 | even | 4 | |||
3800.2.a.r.1.2 | 3 | 5.2 | odd | 4 | |||
3800.2.d.j.3649.3 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.d.j.3649.4 | 6 | 5.4 | even | 2 | inner | ||
5776.2.a.bp.1.2 | 3 | 380.303 | odd | 4 | |||
7448.2.a.bf.1.2 | 3 | 35.13 | even | 4 | |||
7600.2.a.bv.1.2 | 3 | 20.7 | even | 4 |