Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3900,2,Mod(1849,3900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3900.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3900.by (of order \(6\), degree \(2\), 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: | \(31.1416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} + 192x^{8} - 952x^{6} + 3520x^{4} - 2304x^{2} + 1296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 780) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(-0.708892 + 0.409279i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3900.1849 |
Dual form | 3900.2.by.j.3649.1 |
$q$-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 \(\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1951\) | \(3277\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.04097 | − | 1.75570i | −1.14938 | − | 0.663593i | −0.200642 | − | 0.979665i | \(-0.564303\pi\) |
−0.948735 | + | 0.316072i | \(0.897636\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.818558 | − | 1.41778i | −0.246805 | − | 0.427478i | 0.715833 | − | 0.698272i | \(-0.246047\pi\) |
−0.962637 | + | 0.270794i | \(0.912714\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.157133 | − | 3.60213i | 0.0435809 | − | 0.999050i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.32478 | − | 3.07426i | −1.29145 | − | 0.745618i | −0.312537 | − | 0.949906i | \(-0.601179\pi\) |
−0.978911 | + | 0.204288i | \(0.934512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.84642 | − | 4.93015i | 0.653014 | − | 1.13105i | −0.329373 | − | 0.944200i | \(-0.606837\pi\) |
0.982388 | − | 0.186854i | \(-0.0598292\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.51140 | 0.766251 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.409279 | − | 0.708892i | −0.0760012 | − | 0.131638i | 0.825520 | − | 0.564373i | \(-0.190882\pi\) |
−0.901521 | + | 0.432735i | \(0.857549\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.329963 | −0.0592631 | −0.0296315 | − | 0.999561i | \(-0.509433\pi\) | ||||
−0.0296315 | + | 0.999561i | \(0.509433\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.41778 | + | 0.818558i | 0.246805 | + | 0.142493i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.66415 | + | 2.69285i | −0.766781 | + | 0.442701i | −0.831725 | − | 0.555188i | \(-0.812646\pi\) |
0.0649441 | + | 0.997889i | \(0.479313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.66498 | + | 3.19810i | 0.266610 | + | 0.512106i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.92068 | + | 3.32672i | 0.299960 | + | 0.519547i | 0.976127 | − | 0.217203i | \(-0.0696932\pi\) |
−0.676166 | + | 0.736749i | \(0.736360\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.65685 | + | 4.42068i | 1.16766 | + | 0.674148i | 0.953127 | − | 0.302569i | \(-0.0978443\pi\) |
0.214531 | + | 0.976717i | \(0.431178\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.87429i | 0.419258i | 0.977781 | + | 0.209629i | \(0.0672256\pi\) | ||||
−0.977781 | + | 0.209629i | \(0.932774\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.66498 | + | 4.61588i | 0.380712 | + | 0.659412i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.14852 | 0.860965 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.02281i | − | 1.23938i | −0.784847 | − | 0.619689i | \(-0.787259\pi\) | ||
0.784847 | − | 0.619689i | \(-0.212741\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.69285i | 0.754036i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.73924 | + | 9.94066i | −0.747186 | + | 1.29416i | 0.201981 | + | 0.979389i | \(0.435262\pi\) |
−0.949167 | + | 0.314774i | \(0.898071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.835019 | − | 1.44629i | 0.106913 | − | 0.185179i | −0.807605 | − | 0.589724i | \(-0.799237\pi\) |
0.914518 | + | 0.404545i | \(0.132570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.04097 | + | 1.75570i | −0.383126 | + | 0.221198i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.55333 | + | 3.78357i | −0.800617 | + | 0.462236i | −0.843687 | − | 0.536836i | \(-0.819619\pi\) |
0.0430700 | + | 0.999072i | \(0.486286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.40928 | + | 5.90504i | −0.404607 | + | 0.700800i | −0.994276 | − | 0.106845i | \(-0.965925\pi\) |
0.589669 | + | 0.807645i | \(0.299258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.87429i | − | 0.219369i | −0.993966 | − | 0.109684i | \(-0.965016\pi\) | ||
0.993966 | − | 0.109684i | \(-0.0349840\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.74858i | 0.655111i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.7157 | 1.54313 | 0.771566 | − | 0.636149i | \(-0.219474\pi\) | ||||
0.771566 | + | 0.636149i | \(0.219474\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 9.27423i | − | 1.01798i | −0.860773 | − | 0.508990i | \(-0.830019\pi\) | ||
0.860773 | − | 0.508990i | \(-0.169981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.708892 | + | 0.409279i | 0.0760012 | + | 0.0438793i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.28357 | + | 5.68731i | 0.348057 | + | 0.602853i | 0.985904 | − | 0.167310i | \(-0.0535081\pi\) |
−0.637847 | + | 0.770163i | \(0.720175\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.80210 | + | 10.6781i | −0.713054 | + | 1.11936i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.285756 | − | 0.164981i | 0.0296315 | − | 0.0171078i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0530 | − | 8.11353i | −1.42687 | − | 0.823804i | −0.429998 | − | 0.902830i | \(-0.641486\pi\) |
−0.996873 | + | 0.0790256i | \(0.974819\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.63712 | −0.164536 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.69285 | − | 6.39620i | −0.367452 | − | 0.636445i | 0.621714 | − | 0.783244i | \(-0.286436\pi\) |
−0.989166 | + | 0.146799i | \(0.953103\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5899i | 1.63466i | 0.576173 | + | 0.817328i | \(0.304546\pi\) | ||||
−0.576173 | + | 0.817328i | \(0.695454\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.74256 | + | 3.89282i | −0.651828 | + | 0.376333i | −0.789156 | − | 0.614193i | \(-0.789482\pi\) |
0.137328 | + | 0.990526i | \(0.456148\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.38569 | 0.228508 | 0.114254 | − | 0.993452i | \(-0.463552\pi\) | ||||
0.114254 | + | 0.993452i | \(0.463552\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.69285 | − | 4.66415i | 0.255594 | − | 0.442701i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1746 | − | 5.87429i | −0.957143 | − | 0.552607i | −0.0618502 | − | 0.998085i | \(-0.519700\pi\) |
−0.895292 | + | 0.445479i | \(0.853033\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.04097 | − | 1.93714i | −0.281137 | − | 0.179089i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.7950 | + | 18.6974i | 0.989573 | + | 1.71399i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.15993 | − | 7.20520i | 0.378175 | − | 0.655018i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.32672 | − | 1.92068i | −0.299960 | − | 0.173182i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.93745 | + | 1.11859i | −0.171921 | + | 0.0992585i | −0.583491 | − | 0.812119i | \(-0.698314\pi\) |
0.411570 | + | 0.911378i | \(0.364980\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.84137 | −0.778439 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.5013 | −1.79121 | −0.895603 | − | 0.444854i | \(-0.853256\pi\) | ||||
−0.895603 | + | 0.444854i | \(0.853256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.3118 | + | 9.99494i | −1.50112 | + | 0.866672i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.7527 | + | 11.4042i | 1.68759 | + | 0.974329i | 0.956359 | + | 0.292195i | \(0.0943857\pi\) |
0.731228 | + | 0.682133i | \(0.238948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.64852 | + | 11.5156i | −0.563920 | + | 0.976738i | 0.433229 | + | 0.901284i | \(0.357374\pi\) |
−0.997149 | + | 0.0754545i | \(0.975959\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.43714 | − | 2.48921i | −0.121029 | − | 0.209629i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.23566 | + | 2.72577i | −0.437828 | + | 0.227940i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.61588 | − | 2.66498i | −0.380712 | − | 0.219804i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.48860 | − | 7.77448i | 0.367720 | − | 0.636910i | −0.621489 | − | 0.783423i | \(-0.713472\pi\) |
0.989209 | + | 0.146513i | \(0.0468051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2413 | 0.996184 | 0.498092 | − | 0.867124i | \(-0.334034\pi\) | ||||
0.498092 | + | 0.867124i | \(0.334034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.32478 | + | 3.07426i | −0.430483 | + | 0.248539i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.84137i | − | 0.386383i | −0.981161 | − | 0.193192i | \(-0.938116\pi\) | ||
0.981161 | − | 0.193192i | \(-0.0618839\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.51140 | + | 7.81398i | 0.357778 | + | 0.619689i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.205397 | + | 0.118586i | 0.0160880 | + | 0.00928839i | 0.508022 | − | 0.861344i | \(-0.330377\pi\) |
−0.491934 | + | 0.870632i | \(0.663710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.16054 | − | 0.670037i | 0.0898052 | − | 0.0518490i | −0.454425 | − | 0.890785i | \(-0.650155\pi\) |
0.544230 | + | 0.838936i | \(0.316822\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9506 | − | 1.13203i | −0.996201 | − | 0.0870791i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.84642 | − | 4.93015i | −0.217671 | − | 0.377018i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.128623 | − | 0.0742604i | −0.00977901 | − | 0.00564591i | 0.495103 | − | 0.868835i | \(-0.335130\pi\) |
−0.504882 | + | 0.863189i | \(0.668464\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 11.4785i | − | 0.862776i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.97641 | + | 12.0835i | 0.521442 | + | 0.903163i | 0.999689 | + | 0.0249383i | \(0.00793892\pi\) |
−0.478247 | + | 0.878225i | \(0.658728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.05573 | −0.450119 | −0.225059 | − | 0.974345i | \(-0.572258\pi\) | ||||
−0.225059 | + | 0.974345i | \(0.572258\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.67004i | 0.123453i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0658i | 0.736087i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.75570 | − | 3.04097i | 0.127709 | − | 0.221198i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.04640 | − | 8.74061i | 0.365144 | − | 0.632449i | −0.623655 | − | 0.781700i | \(-0.714353\pi\) |
0.988799 | + | 0.149251i | \(0.0476863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.82632 | − | 4.51853i | 0.563351 | − | 0.325251i | −0.191138 | − | 0.981563i | \(-0.561218\pi\) |
0.754489 | + | 0.656312i | \(0.227885\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.61783 | + | 1.51140i | −0.186513 | + | 0.107683i | −0.590349 | − | 0.807148i | \(-0.701010\pi\) |
0.403836 | + | 0.914831i | \(0.367677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.52281 | + | 6.10168i | −0.249725 | + | 0.432537i | −0.963450 | − | 0.267890i | \(-0.913674\pi\) |
0.713724 | + | 0.700427i | \(0.247007\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.78357 | − | 6.55333i | 0.266872 | − | 0.462236i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.87429i | 0.201736i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.31985 | −0.644668 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.98860 | − | 6.90845i | −0.274586 | − | 0.475597i | 0.695444 | − | 0.718580i | \(-0.255208\pi\) |
−0.970031 | + | 0.242983i | \(0.921874\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.81856i | − | 0.467200i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00341 | + | 0.579316i | 0.0681156 | + | 0.0393266i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.937144 | + | 1.62318i | 0.0633263 | + | 0.109684i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.9106 | + | 18.6974i | −0.801192 | + | 1.25773i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.8134 | + | 13.1713i | −1.52770 | + | 0.882018i | −0.528241 | + | 0.849094i | \(0.677148\pi\) |
−0.999458 | + | 0.0329232i | \(0.989518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.5032 | + | 6.64140i | 0.763496 | + | 0.440805i | 0.830550 | − | 0.556944i | \(-0.188026\pi\) |
−0.0670532 | + | 0.997749i | \(0.521360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.35277 | 0.419803 | 0.209901 | − | 0.977723i | \(-0.432686\pi\) | ||||
0.209901 | + | 0.977723i | \(0.432686\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.87429 | − | 4.97841i | −0.189114 | − | 0.327556i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.25142i | 0.409544i | 0.978810 | + | 0.204772i | \(0.0656453\pi\) | ||||
−0.978810 | + | 0.204772i | \(0.934355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.8781 | + | 6.85783i | −0.771566 | + | 0.445464i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.4085 | −1.44949 | −0.724743 | − | 0.689020i | \(-0.758041\pi\) | ||||
−0.724743 | + | 0.689020i | \(0.758041\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.23212 | − | 9.06229i | 0.337030 | − | 0.583754i | −0.646842 | − | 0.762624i | \(-0.723911\pi\) |
0.983873 | + | 0.178870i | \(0.0572442\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.3118 | − | 11.0279i | −1.10152 | − | 0.701686i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.63712 | + | 8.03172i | 0.293865 | + | 0.508990i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.05573 | + | 8.75678i | −0.319115 | + | 0.552723i | −0.980304 | − | 0.197496i | \(-0.936719\pi\) |
0.661189 | + | 0.750220i | \(0.270052\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.7311 | + | 14.2785i | −1.54268 | + | 0.890669i | −0.544016 | + | 0.839075i | \(0.683097\pi\) |
−0.998668 | + | 0.0515942i | \(0.983570\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.9113 | 1.17509 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.818558 | −0.0506675 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.6994 | + | 9.64140i | −1.02973 | + | 0.594514i | −0.916907 | − | 0.399101i | \(-0.869322\pi\) |
−0.112821 | + | 0.993615i | \(0.535989\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.68731 | − | 3.28357i | −0.348057 | − | 0.200951i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.77216 | + | 8.26563i | −0.290964 | + | 0.503964i | −0.974038 | − | 0.226385i | \(-0.927309\pi\) |
0.683074 | + | 0.730349i | \(0.260643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.3971 | + | 21.4724i | 0.753070 | + | 1.30436i | 0.946328 | + | 0.323208i | \(0.104761\pi\) |
−0.193258 | + | 0.981148i | \(0.561905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.551759 | − | 12.6485i | 0.0333940 | − | 0.765523i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.5167 | − | 13.0000i | −1.35290 | − | 0.781094i | −0.364241 | − | 0.931305i | \(-0.618672\pi\) |
−0.988654 | + | 0.150210i | \(0.952005\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.164981 | + | 0.285756i | −0.00987718 | + | 0.0171078i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.58994 | −0.214158 | −0.107079 | − | 0.994251i | \(-0.534150\pi\) | ||||
−0.107079 | + | 0.994251i | \(0.534150\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2365 | − | 13.4156i | 1.38127 | − | 0.797476i | 0.388960 | − | 0.921255i | \(-0.372835\pi\) |
0.992310 | + | 0.123779i | \(0.0395012\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 13.4886i | − | 0.796207i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4022 | + | 18.0171i | 0.611891 | + | 1.05983i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.2271 | 0.951247 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.6062 | + | 15.9384i | 1.61277 | + | 0.931133i | 0.988725 | + | 0.149746i | \(0.0478455\pi\) |
0.624046 | + | 0.781388i | \(0.285488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.41778 | − | 0.818558i | 0.0822682 | − | 0.0474976i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.5228 | − | 26.8863i | −0.894720 | − | 1.54970i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.39620 | + | 3.69285i | 0.367452 | + | 0.212148i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.90721i | 0.394215i | 0.980382 | + | 0.197108i | \(0.0631548\pi\) | ||||
−0.980382 | + | 0.197108i | \(0.936845\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.29497 | − | 14.3673i | −0.471884 | − | 0.817328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.4557 | 1.50016 | 0.750082 | − | 0.661345i | \(-0.230014\pi\) | ||||
0.750082 | + | 0.661345i | \(0.230014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 33.1840i | − | 1.87567i | −0.347079 | − | 0.937836i | \(-0.612826\pi\) | ||
0.347079 | − | 0.937836i | \(-0.387174\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.0228i | 1.51775i | 0.651235 | + | 0.758876i | \(0.274251\pi\) | ||||
−0.651235 | + | 0.758876i | \(0.725749\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.670037 | + | 1.16054i | −0.0375149 | + | 0.0649777i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.89282 | − | 6.74256i | 0.217276 | − | 0.376333i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −30.3131 | + | 17.5013i | −1.68667 | + | 0.973798i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.06607 | + | 1.19285i | −0.114254 | + | 0.0659646i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.04640 | − | 8.74061i | 0.278217 | − | 0.481886i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.37429 | − | 16.2367i | 0.515257 | − | 0.892452i | −0.484586 | − | 0.874744i | \(-0.661030\pi\) |
0.999843 | − | 0.0177084i | \(-0.00563705\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.38569i | 0.295134i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.1156i | − | 1.42261i | −0.702885 | − | 0.711304i | \(-0.748105\pi\) | ||
0.702885 | − | 0.711304i | \(-0.251895\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.7486 | 0.638095 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.270094 | + | 0.467816i | 0.0146264 | + | 0.0253337i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.86418i | 0.316636i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.81398 | − | 4.51140i | −0.419477 | − | 0.242185i | 0.275377 | − | 0.961336i | \(-0.411197\pi\) |
−0.694853 | + | 0.719151i | \(0.744531\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.89075 | − | 5.00692i | −0.154738 | − | 0.268015i | 0.778225 | − | 0.627985i | \(-0.216120\pi\) |
−0.932964 | + | 0.359970i | \(0.882787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.60213 | + | 0.157133i | 0.192267 | + | 0.00838716i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.3668 | + | 11.1814i | −1.03079 | + | 0.595128i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
−0.113581 | + | 0.993529i | \(0.536232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.6974 | − | 10.7950i | −0.989573 | − | 0.571331i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.1814 | −0.906802 | −0.453401 | − | 0.891307i | \(-0.649789\pi\) | ||||
−0.453401 | + | 0.891307i | \(0.649789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.70425 | − | 11.6121i | −0.352855 | − | 0.611163i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.31985i | 0.436679i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.42841 | + | 5.44349i | −0.492159 | + | 0.284148i | −0.725470 | − | 0.688254i | \(-0.758377\pi\) |
0.233311 | + | 0.972402i | \(0.425044\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.84137 | 0.199974 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.8414 | + | 27.4381i | −0.822443 | + | 1.42451i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2225 | − | 8.21138i | −0.736414 | − | 0.425169i | 0.0843499 | − | 0.996436i | \(-0.473119\pi\) |
−0.820764 | + | 0.571267i | \(0.806452\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.61783 | + | 1.36288i | −0.134825 | + | 0.0701921i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.9506 | − | 18.9670i | −0.562495 | − | 0.974271i | −0.997278 | − | 0.0737352i | \(-0.976508\pi\) |
0.434782 | − | 0.900536i | \(-0.356825\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.11859 | − | 1.93745i | 0.0573069 | − | 0.0992585i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.4993 | + | 8.94855i | 0.791979 | + | 0.457249i | 0.840659 | − | 0.541565i | \(-0.182168\pi\) |
−0.0486796 | + | 0.998814i | \(0.515501\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.65685 | − | 4.42068i | 0.389219 | − | 0.224716i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.4972 | 0.887141 | 0.443570 | − | 0.896239i | \(-0.353712\pi\) | ||||
0.443570 | + | 0.896239i | \(0.353712\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7546 | − | 10.2506i | 0.895603 | − | 0.517077i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.9989 | + | 11.5464i | 1.00372 | + | 0.579497i | 0.909346 | − | 0.416040i | \(-0.136582\pi\) |
0.0943719 | + | 0.995537i | \(0.469916\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.99494 | − | 17.3118i | 0.500373 | − | 0.866672i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.20425 | + | 14.2102i | 0.409701 | + | 0.709623i | 0.994856 | − | 0.101299i | \(-0.0322998\pi\) |
−0.585155 | + | 0.810921i | \(0.698966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0518481 | + | 1.18857i | −0.00258274 | + | 0.0592067i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.63575 | + | 4.40850i | 0.378490 | + | 0.218521i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.85783 | + | 11.8781i | −0.339098 | + | 0.587335i | −0.984263 | − | 0.176708i | \(-0.943455\pi\) |
0.645165 | + | 0.764043i | \(0.276788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.8084 | −1.12506 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.9057 | − | 20.1528i | 1.71760 | − | 0.991654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 13.2970i | − | 0.651159i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.8178 | − | 18.7369i | −0.528483 | − | 0.915360i | −0.999448 | − | 0.0332080i | \(-0.989428\pi\) |
0.470965 | − | 0.882152i | \(-0.343906\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.26412 | 0.305295 | 0.152647 | − | 0.988281i | \(-0.451220\pi\) | ||||
0.152647 | + | 0.988281i | \(0.451220\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.48921 | + | 1.43714i | 0.121029 | + | 0.0698763i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.07853 | + | 2.93209i | −0.245767 | + | 0.141894i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.17133 | − | 4.97841i | 0.153113 | − | 0.240360i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.795749 | − | 1.37828i | −0.0383299 | − | 0.0663893i | 0.846224 | − | 0.532827i | \(-0.178870\pi\) |
−0.884554 | + | 0.466438i | \(0.845537\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.7183 | + | 14.8485i | 1.23594 | + | 0.713573i | 0.968263 | − | 0.249934i | \(-0.0804090\pi\) |
0.267682 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5507 | − | 28.6666i | −0.789921 | − | 1.36818i | −0.926015 | − | 0.377487i | \(-0.876788\pi\) |
0.136094 | − | 0.990696i | \(-0.456545\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.32996 | 0.253808 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.1713i | 1.86109i | 0.366183 | + | 0.930543i | \(0.380665\pi\) | ||||
−0.366183 | + | 0.930543i | \(0.619335\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.97719i | 0.424607i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.2271 | + | 35.0343i | −0.954574 | + | 1.65337i | −0.219234 | + | 0.975672i | \(0.570356\pi\) |
−0.735340 | + | 0.677698i | \(0.762978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.14438 | − | 5.44623i | 0.148063 | − | 0.256453i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.6013 | + | 6.12066i | −0.498092 | + | 0.287573i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.66074 | − | 2.11353i | 0.171242 | − | 0.0988668i | −0.411929 | − | 0.911216i | \(-0.635145\pi\) |
0.583171 | + | 0.812349i | \(0.301812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.07426 | − | 5.32478i | 0.143494 | − | 0.248539i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.1807 | + | 26.2937i | −0.707034 | + | 1.22462i | 0.258918 | + | 0.965899i | \(0.416634\pi\) |
−0.965952 | + | 0.258720i | \(0.916699\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.9300i | − | 1.01917i | −0.860419 | − | 0.509587i | \(-0.829798\pi\) | ||
0.860419 | − | 0.509587i | \(-0.170202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.4684i | 1.82638i | 0.407536 | + | 0.913189i | \(0.366388\pi\) | ||||
−0.407536 | + | 0.913189i | \(0.633612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.5713 | 1.22695 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.42068 | + | 4.19275i | 0.111539 | + | 0.193192i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 14.4743i | − | 0.665531i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.81398 | − | 4.51140i | −0.357778 | − | 0.206563i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.9435 | − | 24.1508i | −0.637094 | − | 1.10348i | −0.986067 | − | 0.166347i | \(-0.946803\pi\) |
0.348973 | − | 0.937133i | \(-0.386531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.96708 | + | 17.2240i | 0.408864 | + | 0.785346i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.9574 | + | 18.4506i | 1.44813 | + | 0.836077i | 0.998370 | − | 0.0570729i | \(-0.0181768\pi\) |
0.449758 | + | 0.893150i | \(0.351510\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.237172 | −0.0107253 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.66926 | + | 8.08740i | 0.210721 | + | 0.364979i | 0.951940 | − | 0.306284i | \(-0.0990856\pi\) |
−0.741220 | + | 0.671263i | \(0.765752\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.03292i | 0.226671i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.7350 | − | 11.9714i | 0.930092 | − | 0.536989i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.6498 | −1.28254 | −0.641271 | − | 0.767315i | \(-0.721593\pi\) | ||||
−0.641271 | + | 0.767315i | \(0.721593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.670037 | + | 1.16054i | −0.0299351 | + | 0.0518490i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.4279 | − | 8.32996i | −0.643309 | − | 0.371415i | 0.142579 | − | 0.989783i | \(-0.454461\pi\) |
−0.785888 | + | 0.618369i | \(0.787794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.7816 | − | 5.49494i | 0.523238 | − | 0.244039i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.39994 | + | 11.0850i | 0.283673 | + | 0.491335i | 0.972286 | − | 0.233793i | \(-0.0751138\pi\) |
−0.688614 | + | 0.725128i | \(0.741780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.29069 | + | 5.69965i | −0.145572 | + | 0.252138i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.93015 | + | 2.84642i | 0.217671 | + | 0.125673i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.07512 | − | 2.35277i | 0.179224 | − | 0.103475i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.148521 | 0.00651934 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.2727 | −1.54532 | −0.772662 | − | 0.634818i | \(-0.781075\pi\) | ||||
−0.772662 | + | 0.634818i | \(0.781075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5176 | − | 7.22706i | 0.547358 | − | 0.316017i | −0.200698 | − | 0.979653i | \(-0.564321\pi\) |
0.748056 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.75698 | + | 1.01439i | 0.0765351 | + | 0.0441876i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.5000 | + | 19.9186i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.73924 | + | 9.94066i | 0.249062 | + | 0.431388i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.2851 | − | 6.39581i | 0.532126 | − | 0.277033i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0835 | − | 6.97641i | −0.521442 | − | 0.301054i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.36288 | − | 7.55674i | 0.187923 | − | 0.325492i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.748577 | −0.0321838 | −0.0160919 | − | 0.999871i | \(-0.505122\pi\) | ||||
−0.0160919 | + | 0.999871i | \(0.505122\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.24442 | − | 3.02787i | 0.225059 | − | 0.129938i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.50129i | 0.0641906i | 0.999485 | + | 0.0320953i | \(0.0102180\pi\) | ||||
−0.999485 | + | 0.0320953i | \(0.989782\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.835019 | − | 1.44629i | −0.0356377 | − | 0.0617264i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.65993 | −0.198519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.7088 | − | 24.0806i | −1.77364 | − | 1.02401i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.3554 | − | 21.5671i | 1.58280 | − | 0.913829i | 0.588349 | − | 0.808607i | \(-0.299778\pi\) |
0.994449 | − | 0.105222i | \(-0.0335553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.1270 | − | 26.8863i | 0.724395 | − | 1.13717i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.03292 | − | 8.71728i | −0.212490 | − | 0.368044i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.4240 | − | 10.6371i | −0.776480 | − | 0.448301i | 0.0587013 | − | 0.998276i | \(-0.481304\pi\) |
−0.835181 | + | 0.549975i | \(0.814637\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.51140i | 0.147465i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.45490 | + | 16.3764i | 0.396370 | + | 0.686533i | 0.993275 | − | 0.115779i | \(-0.0369364\pi\) |
−0.596905 | + | 0.802312i | \(0.703603\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.9842 | 1.71514 | 0.857568 | − | 0.514371i | \(-0.171975\pi\) | ||||
0.857568 | + | 0.514371i | \(0.171975\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.0928i | 0.421632i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.8911i | 1.61906i | 0.587079 | + | 0.809529i | \(0.300278\pi\) | ||||
−0.587079 | + | 0.809529i | \(0.699722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.51853 | + | 7.82632i | −0.187784 | + | 0.325251i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.2828 | + | 28.2026i | −0.675524 | + | 1.17004i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.7924 | + | 7.38569i | −0.529807 | + | 0.305884i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.346361 | + | 0.199972i | −0.0142959 | + | 0.00825372i | −0.507131 | − | 0.861869i | \(-0.669294\pi\) |
0.492835 | + | 0.870123i | \(0.335961\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.939214 | + | 1.62677i | −0.0386996 | + | 0.0670297i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.51140 | − | 2.61783i | 0.0621709 | − | 0.107683i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 37.7740i | − | 1.55119i | −0.631230 | − | 0.775596i | \(-0.717450\pi\) | ||
0.631230 | − | 0.775596i | \(-0.282550\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.04562i | − | 0.288358i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.04717 | 0.165363 | 0.0826815 | − | 0.996576i | \(-0.473652\pi\) | ||||
0.0826815 | + | 0.996576i | \(0.473652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9250 | − | 29.3149i | −0.690384 | − | 1.19578i | −0.971712 | − | 0.236168i | \(-0.924108\pi\) |
0.281329 | − | 0.959611i | \(-0.409225\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.56714i | 0.308158i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.7974 | − | 9.12066i | −0.641198 | − | 0.370196i | 0.143878 | − | 0.989595i | \(-0.454043\pi\) |
−0.785076 | + | 0.619399i | \(0.787376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.43714 | − | 2.48921i | −0.0582360 | − | 0.100868i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3535 | + | 0.451647i | 0.418860 | + | 0.0182717i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.44610 | − | 4.87636i | 0.341135 | − | 0.196954i | −0.319639 | − | 0.947539i | \(-0.603562\pi\) |
0.660774 | + | 0.750585i | \(0.270228\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2102 | + | 8.20425i | 0.572080 | + | 0.330291i | 0.757980 | − | 0.652278i | \(-0.226187\pi\) |
−0.185899 | + | 0.982569i | \(0.559520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.4541 | −1.82696 | −0.913478 | − | 0.406889i | \(-0.866614\pi\) | ||||
−0.913478 | + | 0.406889i | \(0.866614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 23.0599i | − | 0.923874i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.07123 | − | 4.65993i | 0.322334 | − | 0.186099i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.1140 | 1.32034 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.39204 | − | 14.5354i | 0.334082 | − | 0.578647i | −0.649226 | − | 0.760595i | \(-0.724907\pi\) |
0.983308 | + | 0.181949i | \(0.0582404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.90845 | + | 3.98860i | 0.274586 | + | 0.158532i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.0457 | − | 8.87429i | 0.675377 | − | 0.351612i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.40928 | + | 5.90504i | 0.134869 | + | 0.233600i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.6371 | + | 34.0125i | −0.775619 | + | 1.34341i | 0.158826 | + | 0.987307i | \(0.449229\pi\) |
−0.934446 | + | 0.356106i | \(0.884104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.5477 | + | 6.66705i | 0.455396 | + | 0.262923i | 0.710106 | − | 0.704095i | \(-0.248647\pi\) |
−0.254711 | + | 0.967017i | \(0.581980\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.0993 | − | 15.0684i | 1.02607 | − | 0.592401i | 0.110213 | − | 0.993908i | \(-0.464847\pi\) |
0.915856 | + | 0.401507i | \(0.131513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.7916 | 0.737635 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.15863 | −0.0454104 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.9273 | − | 17.2785i | 1.17114 | − | 0.676160i | 0.217195 | − | 0.976128i | \(-0.430309\pi\) |
0.953949 | + | 0.299968i | \(0.0969760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.62318 | − | 0.937144i | −0.0633263 | − | 0.0365615i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.20425 | + | 3.81788i | −0.0858654 | + | 0.148723i | −0.905760 | − | 0.423792i | \(-0.860699\pi\) |
0.819894 | + | 0.572515i | \(0.194032\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.885693 | − | 1.53407i | −0.0344495 | − | 0.0596682i | 0.848287 | − | 0.529537i | \(-0.177634\pi\) |
−0.882736 | + | 0.469869i | \(0.844301\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.966138 | − | 22.1477i | 0.0375217 | − | 0.860147i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.1713 | − | 22.8134i | 0.509233 | − | 0.882018i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.73404 | −0.105547 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.54829 | + | 2.04861i | −0.136776 | + | 0.0789679i | −0.566827 | − | 0.823837i | \(-0.691829\pi\) |
0.430050 | + | 0.902805i | \(0.358496\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.8828i | − | 1.41752i | −0.705448 | − | 0.708761i | \(-0.749254\pi\) | ||
0.705448 | − | 0.708761i | \(-0.250746\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.4899 | + | 49.3459i | 1.09334 | + | 1.89372i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.2828 | −0.508998 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.10314 | + | 5.25570i | 0.348322 | + | 0.201104i | 0.663946 | − | 0.747781i | \(-0.268880\pi\) |
−0.315624 | + | 0.948884i | \(0.602214\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.50166 | + | 3.17639i | −0.209901 | + | 0.121187i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −32.5013 | − | 1.41778i | −1.23820 | − | 0.0540133i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.8806 | + | 22.3099i | 0.490003 | + | 0.848709i | 0.999934 | − | 0.0115059i | \(-0.00366251\pi\) |
−0.509931 | + | 0.860215i | \(0.670329\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.97841 | + | 2.87429i | 0.189114 | + | 0.109185i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 23.6187i | − | 0.894623i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.12571 | − | 5.41389i | −0.118225 | − | 0.204772i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9772 | 0.565681 | 0.282840 | − | 0.959167i | \(-0.408723\pi\) | ||||
0.282840 | + | 0.959167i | \(0.408723\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.6599i | 1.15636i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.9342i | 0.975354i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.2055 | − | 33.2650i | 0.721279 | − | 1.24929i | −0.239208 | − | 0.970968i | \(-0.576888\pi\) |
0.960487 | − | 0.278324i | \(-0.0897789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.85783 | − | 11.8781i | 0.257189 | − | 0.445464i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.4063 | − | 11.2043i | 0.724743 | − | 0.418430i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.4777 | − | 26.8082i | 0.577221 | − | 0.999776i | −0.418575 | − | 0.908182i | \(-0.637470\pi\) |
0.995796 | − | 0.0915941i | \(-0.0291962\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.1270 | − | 50.4495i | 1.08475 | − | 1.87884i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.4642i | 0.389169i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.2043i | − | 1.23148i | −0.787950 | − | 0.615739i | \(-0.788858\pi\) | ||
0.787950 | − | 0.615739i | \(-0.211142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.1807 | − | 47.0783i | −1.00531 | − | 1.74125i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.3012i | 0.823713i | 0.911249 | + | 0.411856i | \(0.135119\pi\) | ||||
−0.911249 | + | 0.411856i | \(0.864881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.7286 | + | 6.19414i | 0.395192 | + | 0.228164i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.9199 | + | 22.3779i | 0.475266 | + | 0.823186i | 0.999599 | − | 0.0283281i | \(-0.00901833\pi\) |
−0.524332 | + | 0.851514i | \(0.675685\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.5063 | + | 0.894536i | 0.753320 | + | 0.0328616i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4954 | + | 11.2557i | −0.715219 | + | 0.412932i | −0.812990 | − | 0.582277i | \(-0.802162\pi\) |
0.0977717 | + | 0.995209i | \(0.468829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.03172 | − | 4.63712i | −0.293865 | − | 0.169663i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.3385 | 0.998928 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3021 | − | 19.5758i | −0.412419 | − | 0.714331i | 0.582734 | − | 0.812663i | \(-0.301983\pi\) |
−0.995154 | + | 0.0983314i | \(0.968649\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 10.1115i | − | 0.368482i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.6078 | − | 19.4034i | 1.22149 | − | 0.705230i | 0.256258 | − | 0.966608i | \(-0.417510\pi\) |
0.965236 | + | 0.261378i | \(0.0841769\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.6457 | + | 25.3671i | −0.530905 | + | 0.919555i | 0.468444 | + | 0.883493i | \(0.344815\pi\) |
−0.999350 | + | 0.0360619i | \(0.988519\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.25481 | − | 4.18857i | −0.262642 | − | 0.151636i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.9057 | + | 22.2355i | 1.26037 | + | 0.802877i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.7435 | − | 37.6609i | −0.784091 | − | 1.35809i | −0.929540 | − | 0.368720i | \(-0.879796\pi\) |
0.145449 | − | 0.989366i | \(-0.453537\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.2785 | − | 24.7311i | 0.514228 | − | 0.890669i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.6064 | + | 11.8971i | 0.741160 | + | 0.427909i | 0.822491 | − | 0.568778i | \(-0.192584\pi\) |
−0.0813310 | + | 0.996687i | \(0.525917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.3777 | + | 9.45567i | −0.587547 | + | 0.339220i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21.8683 | 0.783514 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.1628 | 0.399435 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.708892 | − | 0.409279i | 0.0253337 | − | 0.0146264i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5654 | + | 10.1414i | 0.626139 | + | 0.361502i | 0.779255 | − | 0.626707i | \(-0.215598\pi\) |
−0.153116 | + | 0.988208i | \(0.548931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.64140 | − | 16.6994i | 0.343243 | − | 0.594514i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.6270 | + | 35.7270i | 0.733412 | + | 1.27031i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.07853 | − | 3.23510i | −0.180344 | − | 0.114882i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.03192 | − | 0.595777i | −0.0365523 | − | 0.0211035i | 0.481612 | − | 0.876384i | \(-0.340051\pi\) |
−0.518165 | + | 0.855281i | \(0.673385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.83631 | − | 15.3049i | 0.312606 | − | 0.541450i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.56714 | 0.232038 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.65734 | + | 1.53421i | −0.0937754 | + | 0.0541412i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.54433i | − | 0.335976i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.4785 | − | 19.8813i | −0.403562 | − | 0.698990i | 0.590591 | − | 0.806971i | \(-0.298895\pi\) |
−0.994153 | + | 0.107981i | \(0.965561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.7055 | 0.551496 | 0.275748 | − | 0.961230i | \(-0.411074\pi\) | ||||
0.275748 | + | 0.961230i | \(0.411074\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.4724 | − | 12.3971i | −0.753070 | − | 0.434785i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43.5893 | − | 25.1663i | 1.52500 | − | 0.880456i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.84642 | + | 11.2298i | 0.204291 | + | 0.392402i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6270 | − | 46.1193i | −0.929289 | − | 1.60958i | −0.784514 | − | 0.620111i | \(-0.787088\pi\) |
−0.144775 | − | 0.989465i | \(-0.546246\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.8850 | + | 9.74858i | 0.588575 | + | 0.339814i | 0.764534 | − | 0.644584i | \(-0.222969\pi\) |
−0.175959 | + | 0.984398i | \(0.556303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.4912i | 0.643001i | 0.946909 | + | 0.321501i | \(0.104187\pi\) | ||||
−0.946909 | + | 0.321501i | \(0.895813\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.01646 | − | 15.6170i | −0.313155 | − | 0.542400i | 0.665889 | − | 0.746051i | \(-0.268052\pi\) |
−0.979044 | + | 0.203651i | \(0.934719\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.0000 | 0.901930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 32.7714i | − | 1.13546i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 0.329963i | − | 0.0114052i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.0785 | + | 19.1886i | −0.382474 | + | 0.662464i | −0.991415 | − | 0.130751i | \(-0.958261\pi\) |
0.608942 | + | 0.793215i | \(0.291594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.1650 | − | 24.5345i | 0.488448 | − | 0.846016i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.10898 | − | 1.79497i | 0.107079 | − | 0.0618221i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.3004 | + | 14.6072i | −0.869331 | + | 0.501909i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.4156 | + | 23.2365i | −0.460423 | + | 0.797476i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5798i | 0.499204i | 0.968349 | + | 0.249602i | \(0.0802998\pi\) | ||||
−0.968349 | + | 0.249602i | \(0.919700\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 30.9857i | − | 1.05845i | −0.848481 | − | 0.529227i | \(-0.822482\pi\) | ||
0.848481 | − | 0.529227i | \(-0.177518\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.67004 | −0.193459 | −0.0967296 | − | 0.995311i | \(-0.530838\pi\) | ||||
−0.0967296 | + | 0.995311i | \(0.530838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.74430 | + | 11.6815i | 0.229845 | + | 0.398103i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.63712i | − | 0.259970i | −0.991516 | − | 0.129985i | \(-0.958507\pi\) | ||
0.991516 | − | 0.129985i | \(-0.0414930\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.0171 | − | 10.4022i | −0.611891 | − | 0.353276i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.2271 | − | 19.4458i | −0.380852 | − | 0.659655i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5991 | + | 24.2004i | 0.426906 | + | 0.820001i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.0530 | + | 8.11353i | −0.475624 | + | 0.274601i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.42477 | − | 1.39994i | −0.0818788 | − | 0.0472727i | 0.458502 | − | 0.888694i | \(-0.348386\pi\) |
−0.540380 | + | 0.841421i | \(0.681720\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.8769 | −1.07518 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.8084 | − | 49.8977i | −0.970581 | − | 1.68110i | −0.693807 | − | 0.720161i | \(-0.744068\pi\) |
−0.276774 | − | 0.960935i | \(-0.589265\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.7983i | − | 0.464351i | −0.972674 | − | 0.232175i | \(-0.925416\pi\) | ||
0.972674 | − | 0.232175i | \(-0.0745844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.5844 | − | 15.3485i | 0.892616 | − | 0.515352i | 0.0178186 | − | 0.999841i | \(-0.494328\pi\) |
0.874797 | + | 0.484489i | \(0.160995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.85562 | 0.263469 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.818558 | + | 1.41778i | −0.0274227 | + | 0.0474976i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.1707 | + | 8.18144i | 0.474203 | + | 0.273782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.135047 | + | 0.233908i | 0.00450406 | + | 0.00780127i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.7385 | + | 48.0444i | −0.924102 | + | 1.60059i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 26.8863 | + | 15.5228i | 0.894720 | + | 0.516567i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.3968 | + | 16.3949i | −0.942900 | + | 0.544383i | −0.890868 | − | 0.454262i | \(-0.849903\pi\) |
−0.0520315 | + | 0.998645i | \(0.516570\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.38569 | −0.244968 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.7284 | 0.852418 | 0.426209 | − | 0.904625i | \(-0.359849\pi\) | ||||
0.426209 | + | 0.904625i | \(0.359849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.1489 | + | 7.59150i | −0.435164 | + | 0.251242i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 62.3437 | + | 35.9942i | 2.05877 | + | 1.18863i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.53927 | − | 11.3263i | 0.215711 | − | 0.373622i | −0.737782 | − | 0.675040i | \(-0.764127\pi\) |
0.953492 | + | 0.301418i | \(0.0974599\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.45360 | − | 5.98182i | −0.113800 | − | 0.197108i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.7350 | + | 13.2085i | 0.682501 | + | 0.434764i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.3673 | + | 8.29497i | 0.471884 | + | 0.272443i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.44142 | + | 5.96072i | −0.112909 | + | 0.195565i | −0.916942 | − | 0.399020i | \(-0.869350\pi\) |
0.804033 | + | 0.594585i | \(0.202684\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.3427 | 0.994441 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.9113 | + | 13.2278i | −0.750082 | + | 0.433060i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 10.0912i | − | 0.329666i | −0.986321 | − | 0.164833i | \(-0.947291\pi\) | ||
0.986321 | − | 0.164833i | \(-0.0527086\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.5920 | + | 28.7382i | 0.541460 | + | 0.937836i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −52.6869 | −1.71754 | −0.858771 | − | 0.512359i | \(-0.828772\pi\) | ||||
−0.858771 | + | 0.512359i | \(0.828772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.8841 | − | 23.0271i | 1.29606 | − | 0.748280i | 0.316338 | − | 0.948647i | \(-0.397547\pi\) |
0.979721 | + | 0.200367i | \(0.0642134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.75142 | − | 0.294513i | −0.219160 | − | 0.00956030i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.5114 | − | 23.4024i | −0.438137 | − | 0.758876i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.1631 | − | 16.2600i | −0.912293 | − | 0.526712i | −0.0311246 | − | 0.999516i | \(-0.509909\pi\) |
−0.881168 | + | 0.472803i | \(0.843242\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.34007i | − | 0.0433185i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.0448 | − | 69.3597i | −1.29312 | − | 2.23974i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8911 | −0.996488 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.78564i | 0.250889i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.93157i | 0.158589i | 0.996851 | + | 0.0792943i | \(0.0252667\pi\) | ||||
−0.996851 | + | 0.0792943i | \(0.974733\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.5013 | − | 30.3131i | 0.562223 | − | 0.973798i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9899 | + | 22.4991i | −0.416865 | + | 0.722032i | −0.995622 | − | 0.0934681i | \(-0.970205\pi\) |
0.578757 | + | 0.815500i | \(0.303538\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.4358 | − | 23.3456i | 1.29631 | − | 0.748427i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.41000 | + | 5.43286i | −0.301053 | + | 0.173813i | −0.642916 | − | 0.765937i | \(-0.722275\pi\) |
0.341863 | + | 0.939750i | \(0.388942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.37558 | − | 9.31078i | 0.171804 | − | 0.297574i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.19285 | − | 2.06607i | 0.0380847 | − | 0.0659646i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.04303i | 0.0332676i | 0.999862 | + | 0.0166338i | \(0.00529495\pi\) | ||||
−0.999862 | + | 0.0166338i | \(0.994705\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.0928i | 0.321257i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.52916 | + | 4.38063i | 0.0803414 | + | 0.139155i | 0.903397 | − | 0.428806i | \(-0.141066\pi\) |
−0.823055 | + | 0.567961i | \(0.807732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7486i | 0.594968i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.2009 | + | 11.0857i | 0.608100 | + | 0.351087i | 0.772221 | − | 0.635354i | \(-0.219146\pi\) |
−0.164122 | + | 0.986440i | \(0.552479\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.69285 | − | 4.66415i | −0.0851979 | − | 0.147567i |
(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 | 3900.2.by.j.1849.1 | 12 | ||
5.2 | odd | 4 | 3900.2.q.n.601.3 | 6 | |||
5.3 | odd | 4 | 780.2.q.e.601.1 | yes | 6 | ||
5.4 | even | 2 | inner | 3900.2.by.j.1849.6 | 12 | ||
13.9 | even | 3 | inner | 3900.2.by.j.3649.6 | 12 | ||
15.8 | even | 4 | 2340.2.q.h.2161.1 | 6 | |||
65.9 | even | 6 | inner | 3900.2.by.j.3649.1 | 12 | ||
65.22 | odd | 12 | 3900.2.q.n.2401.3 | 6 | |||
65.48 | odd | 12 | 780.2.q.e.61.1 | ✓ | 6 | ||
195.113 | even | 12 | 2340.2.q.h.1621.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
780.2.q.e.61.1 | ✓ | 6 | 65.48 | odd | 12 | ||
780.2.q.e.601.1 | yes | 6 | 5.3 | odd | 4 | ||
2340.2.q.h.1621.1 | 6 | 195.113 | even | 12 | |||
2340.2.q.h.2161.1 | 6 | 15.8 | even | 4 | |||
3900.2.q.n.601.3 | 6 | 5.2 | odd | 4 | |||
3900.2.q.n.2401.3 | 6 | 65.22 | odd | 12 | |||
3900.2.by.j.1849.1 | 12 | 1.1 | even | 1 | trivial | ||
3900.2.by.j.1849.6 | 12 | 5.4 | even | 2 | inner | ||
3900.2.by.j.3649.1 | 12 | 65.9 | even | 6 | inner | ||
3900.2.by.j.3649.6 | 12 | 13.9 | even | 3 | inner |