Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(99,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1225.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.99 |
Dual form | 1225.2.b.f.99.1 |
$q$-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 \(\left(\mathbb{Z}/1225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.56155i | 1.81129i | 0.424035 | + | 0.905646i | \(0.360613\pi\) | ||||
−0.424035 | + | 0.905646i | \(0.639387\pi\) | |||||||
\(3\) | − 1.56155i | − 0.901563i | −0.892634 | − | 0.450781i | \(-0.851145\pi\) | ||||
0.892634 | − | 0.450781i | \(-0.148855\pi\) | |||||||
\(4\) | −4.56155 | −2.28078 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.00000 | 1.63299 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 6.56155i | − 2.31986i | ||||||||
\(9\) | 0.561553 | 0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.56155 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(12\) | 7.12311i | 2.05626i | ||||||||
\(13\) | − 0.438447i | − 0.121603i | −0.998150 | − | 0.0608017i | \(-0.980634\pi\) | ||||
0.998150 | − | 0.0608017i | \(-0.0193657\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.68466 | 1.92116 | ||||||||
\(17\) | − 0.438447i | − 0.106339i | −0.998586 | − | 0.0531695i | \(-0.983068\pi\) | ||||
0.998586 | − | 0.0531695i | \(-0.0169324\pi\) | |||||||
\(18\) | 1.43845i | 0.339045i | ||||||||
\(19\) | −7.12311 | −1.63415 | −0.817076 | − | 0.576530i | \(-0.804407\pi\) | ||||
−0.817076 | + | 0.576530i | \(0.804407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 4.00000i | − 0.852803i | ||||||||
\(23\) | 3.12311i | 0.651213i | 0.945505 | + | 0.325606i | \(0.105568\pi\) | ||||
−0.945505 | + | 0.325606i | \(0.894432\pi\) | |||||||
\(24\) | −10.2462 | −2.09150 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.12311 | 0.220259 | ||||||||
\(27\) | − 5.56155i | − 1.07032i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.68466 | −1.24131 | −0.620655 | − | 0.784084i | \(-0.713133\pi\) | ||||
−0.620655 | + | 0.784084i | \(0.713133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 6.56155i | 1.15993i | ||||||||
\(33\) | 2.43845i | 0.424479i | ||||||||
\(34\) | 1.12311 | 0.192611 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.56155 | −0.426925 | ||||||||
\(37\) | − 6.00000i | − 0.986394i | −0.869918 | − | 0.493197i | \(-0.835828\pi\) | ||||
0.869918 | − | 0.493197i | \(-0.164172\pi\) | |||||||
\(38\) | − 18.2462i | − 2.95993i | ||||||||
\(39\) | −0.684658 | −0.109633 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.12311 | −0.800095 | −0.400047 | − | 0.916494i | \(-0.631006\pi\) | ||||
−0.400047 | + | 0.916494i | \(0.631006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.876894i | 0.133725i | 0.997762 | + | 0.0668626i | \(0.0212989\pi\) | ||||
−0.997762 | + | 0.0668626i | \(0.978701\pi\) | |||||||
\(44\) | 7.12311 | 1.07385 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | − 8.68466i | − 1.26679i | −0.773830 | − | 0.633394i | \(-0.781661\pi\) | ||||
0.773830 | − | 0.633394i | \(-0.218339\pi\) | |||||||
\(48\) | − 12.0000i | − 1.73205i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.684658 | −0.0958714 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | − 5.12311i | − 0.703713i | −0.936054 | − | 0.351856i | \(-0.885551\pi\) | ||||
0.936054 | − | 0.351856i | \(-0.114449\pi\) | |||||||
\(54\) | 14.2462 | 1.93866 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.1231i | 1.47329i | ||||||||
\(58\) | − 17.1231i | − 2.24837i | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.3693 | −1.96784 | −0.983920 | − | 0.178611i | \(-0.942839\pi\) | ||||
−0.983920 | + | 0.178611i | \(0.942839\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.43845 | −0.179806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.24621 | −0.768855 | ||||||||
\(67\) | − 10.2462i | − 1.25177i | −0.779914 | − | 0.625887i | \(-0.784737\pi\) | ||||
0.779914 | − | 0.625887i | \(-0.215263\pi\) | |||||||
\(68\) | 2.00000i | 0.242536i | ||||||||
\(69\) | 4.87689 | 0.587109 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | − 3.68466i | − 0.434241i | ||||||||
\(73\) | 12.2462i | 1.43331i | 0.697428 | + | 0.716655i | \(0.254328\pi\) | ||||
−0.697428 | + | 0.716655i | \(0.745672\pi\) | |||||||
\(74\) | 15.3693 | 1.78665 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 32.4924 | 3.72714 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − 1.75379i | − 0.198577i | ||||||||
\(79\) | 2.43845 | 0.274347 | 0.137173 | − | 0.990547i | \(-0.456198\pi\) | ||||
0.137173 | + | 0.990547i | \(0.456198\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | − 13.1231i | − 1.44920i | ||||||||
\(83\) | − 4.00000i | − 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.24621 | −0.242215 | ||||||||
\(87\) | 10.4384i | 1.11912i | ||||||||
\(88\) | 10.2462i | 1.09225i | ||||||||
\(89\) | −1.12311 | −0.119049 | −0.0595245 | − | 0.998227i | \(-0.518958\pi\) | ||||
−0.0595245 | + | 0.998227i | \(0.518958\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 14.2462i | − 1.48527i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22.2462 | 2.29452 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 10.2462 | 1.04575 | ||||||||
\(97\) | 5.80776i | 0.589689i | 0.955545 | + | 0.294845i | \(0.0952679\pi\) | ||||
−0.955545 | + | 0.294845i | \(0.904732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.876894 | −0.0881312 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2462 | 1.61656 | 0.808279 | − | 0.588799i | \(-0.200399\pi\) | ||||
0.808279 | + | 0.588799i | \(0.200399\pi\) | |||||||
\(102\) | − 1.75379i | − 0.173651i | ||||||||
\(103\) | − 5.56155i | − 0.547996i | −0.961730 | − | 0.273998i | \(-0.911654\pi\) | ||||
0.961730 | − | 0.273998i | \(-0.0883462\pi\) | |||||||
\(104\) | −2.87689 | −0.282103 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.1231 | 1.27463 | ||||||||
\(107\) | − 13.3693i | − 1.29246i | −0.763142 | − | 0.646230i | \(-0.776345\pi\) | ||||
0.763142 | − | 0.646230i | \(-0.223655\pi\) | |||||||
\(108\) | 25.3693i | 2.44116i | ||||||||
\(109\) | −5.31534 | −0.509117 | −0.254559 | − | 0.967057i | \(-0.581930\pi\) | ||||
−0.254559 | + | 0.967057i | \(0.581930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.36932 | −0.889296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 14.0000i | − 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | −28.4924 | −2.66856 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 30.4924 | 2.83115 | ||||||||
\(117\) | − 0.246211i | − 0.0227622i | ||||||||
\(118\) | − 10.2462i | − 0.943240i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | − 39.3693i | − 3.56433i | ||||||||
\(123\) | 8.00000i | 0.721336i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.24621i | 0.554262i | 0.960832 | + | 0.277131i | \(0.0893835\pi\) | ||||
−0.960832 | + | 0.277131i | \(0.910616\pi\) | |||||||
\(128\) | 9.43845i | 0.834249i | ||||||||
\(129\) | 1.36932 | 0.120562 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.876894 | 0.0766146 | 0.0383073 | − | 0.999266i | \(-0.487803\pi\) | ||||
0.0383073 | + | 0.999266i | \(0.487803\pi\) | |||||||
\(132\) | − 11.1231i | − 0.968142i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 26.2462 | 2.26733 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.87689 | −0.246692 | ||||||||
\(137\) | 17.1231i | 1.46293i | 0.681881 | + | 0.731463i | \(0.261162\pi\) | ||||
−0.681881 | + | 0.731463i | \(0.738838\pi\) | |||||||
\(138\) | 12.4924i | 1.06343i | ||||||||
\(139\) | −15.1231 | −1.28273 | −0.641363 | − | 0.767238i | \(-0.721631\pi\) | ||||
−0.641363 | + | 0.767238i | \(0.721631\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.5616 | −1.14209 | ||||||||
\(142\) | 20.4924i | 1.71969i | ||||||||
\(143\) | 0.684658i | 0.0572540i | ||||||||
\(144\) | 4.31534 | 0.359612 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −31.3693 | −2.59614 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 27.3693i | 2.24974i | ||||||||
\(149\) | −12.2462 | −1.00325 | −0.501624 | − | 0.865086i | \(-0.667264\pi\) | ||||
−0.501624 | + | 0.865086i | \(0.667264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.93087 | −0.564026 | −0.282013 | − | 0.959411i | \(-0.591002\pi\) | ||||
−0.282013 | + | 0.959411i | \(0.591002\pi\) | |||||||
\(152\) | 46.7386i | 3.79100i | ||||||||
\(153\) | − 0.246211i | − 0.0199050i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.12311 | 0.250049 | ||||||||
\(157\) | 20.2462i | 1.61582i | 0.589303 | + | 0.807912i | \(0.299402\pi\) | ||||
−0.589303 | + | 0.807912i | \(0.700598\pi\) | |||||||
\(158\) | 6.24621i | 0.496922i | ||||||||
\(159\) | −8.00000 | −0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − 17.9309i | − 1.40878i | ||||||||
\(163\) | − 7.12311i | − 0.557925i | −0.960302 | − | 0.278962i | \(-0.910010\pi\) | ||||
0.960302 | − | 0.278962i | \(-0.0899905\pi\) | |||||||
\(164\) | 23.3693 | 1.82484 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.2462 | 0.795260 | ||||||||
\(167\) | − 6.93087i | − 0.536327i | −0.963373 | − | 0.268163i | \(-0.913583\pi\) | ||||
0.963373 | − | 0.268163i | \(-0.0864167\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8078 | 0.985213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | − 4.00000i | − 0.304997i | ||||||||
\(173\) | 4.43845i | 0.337449i | 0.985663 | + | 0.168724i | \(0.0539648\pi\) | ||||
−0.985663 | + | 0.168724i | \(0.946035\pi\) | |||||||
\(174\) | −26.7386 | −2.02705 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0000 | −0.904534 | ||||||||
\(177\) | 6.24621i | 0.469494i | ||||||||
\(178\) | − 2.87689i | − 0.215632i | ||||||||
\(179\) | −20.0000 | −1.49487 | −0.747435 | − | 0.664335i | \(-0.768715\pi\) | ||||
−0.747435 | + | 0.664335i | \(0.768715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6155 | 1.30935 | 0.654676 | − | 0.755910i | \(-0.272805\pi\) | ||||
0.654676 | + | 0.755910i | \(0.272805\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.0000i | 1.77413i | ||||||||
\(184\) | 20.4924 | 1.51072 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.684658i | 0.0500672i | ||||||||
\(188\) | 39.6155i | 2.88926i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5616 | −0.981280 | −0.490640 | − | 0.871363i | \(-0.663237\pi\) | ||||
−0.490640 | + | 0.871363i | \(0.663237\pi\) | |||||||
\(192\) | 2.24621i | 0.162106i | ||||||||
\(193\) | 19.3693i | 1.39423i | 0.716957 | + | 0.697117i | \(0.245534\pi\) | ||||
−0.716957 | + | 0.697117i | \(0.754466\pi\) | |||||||
\(194\) | −14.8769 | −1.06810 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.12311i | − 0.0800180i | −0.999199 | − | 0.0400090i | \(-0.987261\pi\) | ||||
0.999199 | − | 0.0400090i | \(-0.0127387\pi\) | |||||||
\(198\) | − 2.24621i | − 0.159631i | ||||||||
\(199\) | −1.75379 | −0.124323 | −0.0621614 | − | 0.998066i | \(-0.519799\pi\) | ||||
−0.0621614 | + | 0.998066i | \(0.519799\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0000 | −1.12855 | ||||||||
\(202\) | 41.6155i | 2.92806i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.12311 | 0.218661 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 14.2462 | 0.992581 | ||||||||
\(207\) | 1.75379i | 0.121897i | ||||||||
\(208\) | − 3.36932i | − 0.233620i | ||||||||
\(209\) | 11.1231 | 0.769401 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0540 | 0.967516 | 0.483758 | − | 0.875202i | \(-0.339272\pi\) | ||||
0.483758 | + | 0.875202i | \(0.339272\pi\) | |||||||
\(212\) | 23.3693i | 1.60501i | ||||||||
\(213\) | − 12.4924i | − 0.855967i | ||||||||
\(214\) | 34.2462 | 2.34102 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −36.4924 | −2.48299 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 13.6155i | − 0.922160i | ||||||||
\(219\) | 19.1231 | 1.29222 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.192236 | −0.0129312 | ||||||||
\(222\) | − 24.0000i | − 1.61077i | ||||||||
\(223\) | 2.43845i | 0.163291i | 0.996661 | + | 0.0816453i | \(0.0260175\pi\) | ||||
−0.996661 | + | 0.0816453i | \(0.973983\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 35.8617 | 2.38549 | ||||||||
\(227\) | 11.3153i | 0.751026i | 0.926817 | + | 0.375513i | \(0.122533\pi\) | ||||
−0.926817 | + | 0.375513i | \(0.877467\pi\) | |||||||
\(228\) | − 50.7386i | − 3.36025i | ||||||||
\(229\) | 10.8769 | 0.718765 | 0.359383 | − | 0.933190i | \(-0.382987\pi\) | ||||
0.359383 | + | 0.933190i | \(0.382987\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 43.8617i | 2.87966i | ||||||||
\(233\) | 5.12311i | 0.335626i | 0.985819 | + | 0.167813i | \(0.0536704\pi\) | ||||
−0.985819 | + | 0.167813i | \(0.946330\pi\) | |||||||
\(234\) | 0.630683 | 0.0412290 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.2462 | 1.18773 | ||||||||
\(237\) | − 3.80776i | − 0.247341i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.8078 | −1.28126 | −0.640629 | − | 0.767851i | \(-0.721326\pi\) | ||||
−0.640629 | + | 0.767851i | \(0.721326\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.24621 | 0.273523 | 0.136761 | − | 0.990604i | \(-0.456331\pi\) | ||||
0.136761 | + | 0.990604i | \(0.456331\pi\) | |||||||
\(242\) | − 21.9309i | − 1.40977i | ||||||||
\(243\) | − 5.75379i | − 0.369106i | ||||||||
\(244\) | 70.1080 | 4.48820 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.4924 | −1.30655 | ||||||||
\(247\) | 3.12311i | 0.198718i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.24621 | −0.395838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.87689 | 0.560305 | 0.280152 | − | 0.959956i | \(-0.409615\pi\) | ||||
0.280152 | + | 0.959956i | \(0.409615\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 4.87689i | − 0.306608i | ||||||||
\(254\) | −16.0000 | −1.00393 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27.0540 | −1.69087 | ||||||||
\(257\) | − 10.4924i | − 0.654499i | −0.944938 | − | 0.327250i | \(-0.893878\pi\) | ||||
0.944938 | − | 0.327250i | \(-0.106122\pi\) | |||||||
\(258\) | 3.50758i | 0.218372i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.75379 | −0.232354 | ||||||||
\(262\) | 2.24621i | 0.138771i | ||||||||
\(263\) | − 12.8769i | − 0.794023i | −0.917814 | − | 0.397012i | \(-0.870047\pi\) | ||||
0.917814 | − | 0.397012i | \(-0.129953\pi\) | |||||||
\(264\) | 16.0000 | 0.984732 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.75379i | 0.107330i | ||||||||
\(268\) | 46.7386i | 2.85502i | ||||||||
\(269\) | −20.7386 | −1.26446 | −0.632228 | − | 0.774782i | \(-0.717860\pi\) | ||||
−0.632228 | + | 0.774782i | \(0.717860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | − 3.36932i | − 0.204295i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −43.8617 | −2.64978 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −22.2462 | −1.33906 | ||||||||
\(277\) | 0.246211i | 0.0147934i | 0.999973 | + | 0.00739670i | \(0.00235446\pi\) | ||||
−0.999973 | + | 0.00739670i | \(0.997646\pi\) | |||||||
\(278\) | − 38.7386i | − 2.32339i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.4384 | 0.742016 | 0.371008 | − | 0.928630i | \(-0.379012\pi\) | ||||
0.371008 | + | 0.928630i | \(0.379012\pi\) | |||||||
\(282\) | − 34.7386i | − 2.06866i | ||||||||
\(283\) | 11.3153i | 0.672627i | 0.941750 | + | 0.336314i | \(0.109180\pi\) | ||||
−0.941750 | + | 0.336314i | \(0.890820\pi\) | |||||||
\(284\) | −36.4924 | −2.16543 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.75379 | −0.103704 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.68466i | 0.217121i | ||||||||
\(289\) | 16.8078 | 0.988692 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.06913 | 0.531642 | ||||||||
\(292\) | − 55.8617i | − 3.26906i | ||||||||
\(293\) | 2.68466i | 0.156839i | 0.996920 | + | 0.0784197i | \(0.0249874\pi\) | ||||
−0.996920 | + | 0.0784197i | \(0.975013\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −39.3693 | −2.28830 | ||||||||
\(297\) | 8.68466i | 0.503935i | ||||||||
\(298\) | − 31.3693i | − 1.81718i | ||||||||
\(299\) | 1.36932 | 0.0791896 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 17.7538i | − 1.02162i | ||||||||
\(303\) | − 25.3693i | − 1.45743i | ||||||||
\(304\) | −54.7386 | −3.13948 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.630683 | 0.0360538 | ||||||||
\(307\) | − 19.3153i | − 1.10238i | −0.834378 | − | 0.551192i | \(-0.814173\pi\) | ||||
0.834378 | − | 0.551192i | \(-0.185827\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.68466 | −0.494053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.6155 | −1.79275 | −0.896376 | − | 0.443294i | \(-0.853810\pi\) | ||||
−0.896376 | + | 0.443294i | \(0.853810\pi\) | |||||||
\(312\) | 4.49242i | 0.254333i | ||||||||
\(313\) | 22.3002i | 1.26048i | 0.776400 | + | 0.630241i | \(0.217044\pi\) | ||||
−0.776400 | + | 0.630241i | \(0.782956\pi\) | |||||||
\(314\) | −51.8617 | −2.92673 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.1231 | −0.625724 | ||||||||
\(317\) | − 10.4924i | − 0.589313i | −0.955603 | − | 0.294657i | \(-0.904795\pi\) | ||||
0.955603 | − | 0.294657i | \(-0.0952053\pi\) | |||||||
\(318\) | − 20.4924i | − 1.14916i | ||||||||
\(319\) | 10.4384 | 0.584441 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.8769 | −1.16523 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.12311i | 0.173774i | ||||||||
\(324\) | 31.9309 | 1.77394 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 18.2462 | 1.01056 | ||||||||
\(327\) | 8.30019i | 0.459001i | ||||||||
\(328\) | 33.6155i | 1.85611i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000 | 0.659580 | 0.329790 | − | 0.944054i | \(-0.393022\pi\) | ||||
0.329790 | + | 0.944054i | \(0.393022\pi\) | |||||||
\(332\) | 18.2462i | 1.00139i | ||||||||
\(333\) | − 3.36932i | − 0.184637i | ||||||||
\(334\) | 17.7538 | 0.971444 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.50758i | 0.0821230i | 0.999157 | + | 0.0410615i | \(0.0130740\pi\) | ||||
−0.999157 | + | 0.0410615i | \(0.986926\pi\) | |||||||
\(338\) | 32.8078i | 1.78451i | ||||||||
\(339\) | −21.8617 | −1.18737 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − 10.2462i | − 0.554052i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.75379 | 0.310223 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.3693 | −0.611218 | ||||||||
\(347\) | − 7.12311i | − 0.382388i | −0.981552 | − | 0.191194i | \(-0.938764\pi\) | ||||
0.981552 | − | 0.191194i | \(-0.0612360\pi\) | |||||||
\(348\) | − 47.6155i | − 2.55246i | ||||||||
\(349\) | 10.4924 | 0.561646 | 0.280823 | − | 0.959760i | \(-0.409393\pi\) | ||||
0.280823 | + | 0.959760i | \(0.409393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.43845 | −0.130155 | ||||||||
\(352\) | − 10.2462i | − 0.546125i | ||||||||
\(353\) | − 5.80776i | − 0.309116i | −0.987984 | − | 0.154558i | \(-0.950605\pi\) | ||||
0.987984 | − | 0.154558i | \(-0.0493954\pi\) | |||||||
\(354\) | −16.0000 | −0.850390 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.12311 | 0.271524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 51.2311i | − 2.70765i | ||||||||
\(359\) | −8.00000 | −0.422224 | −0.211112 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211112 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.7386 | 1.67045 | ||||||||
\(362\) | 45.1231i | 2.37162i | ||||||||
\(363\) | 13.3693i | 0.701707i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −61.4773 | −3.21347 | ||||||||
\(367\) | − 8.68466i | − 0.453335i | −0.973972 | − | 0.226668i | \(-0.927217\pi\) | ||||
0.973972 | − | 0.226668i | \(-0.0727831\pi\) | |||||||
\(368\) | 24.0000i | 1.25109i | ||||||||
\(369\) | −2.87689 | −0.149765 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.63068i | 0.239768i | 0.992788 | + | 0.119884i | \(0.0382522\pi\) | ||||
−0.992788 | + | 0.119884i | \(0.961748\pi\) | |||||||
\(374\) | −1.75379 | −0.0906863 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −56.9848 | −2.93877 | ||||||||
\(377\) | 2.93087i | 0.150947i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.4924 | 0.847159 | 0.423579 | − | 0.905859i | \(-0.360773\pi\) | ||||
0.423579 | + | 0.905859i | \(0.360773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.75379 | 0.499702 | ||||||||
\(382\) | − 34.7386i | − 1.77738i | ||||||||
\(383\) | − 6.24621i | − 0.319166i | −0.987184 | − | 0.159583i | \(-0.948985\pi\) | ||||
0.987184 | − | 0.159583i | \(-0.0510150\pi\) | |||||||
\(384\) | 14.7386 | 0.752128 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −49.6155 | −2.52536 | ||||||||
\(387\) | 0.492423i | 0.0250312i | ||||||||
\(388\) | − 26.4924i | − 1.34495i | ||||||||
\(389\) | 24.9309 | 1.26405 | 0.632023 | − | 0.774950i | \(-0.282225\pi\) | ||||
0.632023 | + | 0.774950i | \(0.282225\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.36932 | 0.0692493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.36932i | − 0.0690729i | ||||||||
\(394\) | 2.87689 | 0.144936 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.00000 | 0.201008 | ||||||||
\(397\) | 27.5616i | 1.38327i | 0.722245 | + | 0.691637i | \(0.243110\pi\) | ||||
−0.722245 | + | 0.691637i | \(0.756890\pi\) | |||||||
\(398\) | − 4.49242i | − 0.225185i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.5616 | 1.57611 | 0.788054 | − | 0.615606i | \(-0.211089\pi\) | ||||
0.788054 | + | 0.615606i | \(0.211089\pi\) | |||||||
\(402\) | − 40.9848i | − 2.04414i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −74.1080 | −3.68701 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.36932i | 0.464420i | ||||||||
\(408\) | 4.49242i | 0.222408i | ||||||||
\(409\) | 6.49242 | 0.321030 | 0.160515 | − | 0.987033i | \(-0.448685\pi\) | ||||
0.160515 | + | 0.987033i | \(0.448685\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 26.7386 | 1.31892 | ||||||||
\(412\) | 25.3693i | 1.24986i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.49242 | −0.220791 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.87689 | 0.141051 | ||||||||
\(417\) | 23.6155i | 1.15646i | ||||||||
\(418\) | 28.4924i | 1.39361i | ||||||||
\(419\) | 26.2462 | 1.28221 | 0.641106 | − | 0.767453i | \(-0.278476\pi\) | ||||
0.641106 | + | 0.767453i | \(0.278476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.68466 | −0.130842 | −0.0654211 | − | 0.997858i | \(-0.520839\pi\) | ||||
−0.0654211 | + | 0.997858i | \(0.520839\pi\) | |||||||
\(422\) | 36.0000i | 1.75245i | ||||||||
\(423\) | − 4.87689i | − 0.237123i | ||||||||
\(424\) | −33.6155 | −1.63251 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 32.0000 | 1.55041 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 60.9848i | 2.94781i | ||||||||
\(429\) | 1.06913 | 0.0516181 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.8078 | −0.954106 | −0.477053 | − | 0.878874i | \(-0.658295\pi\) | ||||
−0.477053 | + | 0.878874i | \(0.658295\pi\) | |||||||
\(432\) | − 42.7386i | − 2.05626i | ||||||||
\(433\) | − 8.24621i | − 0.396288i | −0.980173 | − | 0.198144i | \(-0.936509\pi\) | ||||
0.980173 | − | 0.198144i | \(-0.0634913\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.2462 | 1.16118 | ||||||||
\(437\) | − 22.2462i | − 1.06418i | ||||||||
\(438\) | 48.9848i | 2.34059i | ||||||||
\(439\) | 9.36932 | 0.447173 | 0.223587 | − | 0.974684i | \(-0.428223\pi\) | ||||
0.223587 | + | 0.974684i | \(0.428223\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 0.492423i | − 0.0234221i | ||||||||
\(443\) | − 2.63068i | − 0.124988i | −0.998045 | − | 0.0624938i | \(-0.980095\pi\) | ||||
0.998045 | − | 0.0624938i | \(-0.0199054\pi\) | |||||||
\(444\) | 42.7386 | 2.02829 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.24621 | −0.295767 | ||||||||
\(447\) | 19.1231i | 0.904492i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.80776 | 0.0853137 | 0.0426568 | − | 0.999090i | \(-0.486418\pi\) | ||||
0.0426568 | + | 0.999090i | \(0.486418\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 63.8617i | 3.00380i | ||||||||
\(453\) | 10.8229i | 0.508505i | ||||||||
\(454\) | −28.9848 | −1.36033 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 72.9848 | 3.41783 | ||||||||
\(457\) | 17.1231i | 0.800985i | 0.916300 | + | 0.400493i | \(0.131161\pi\) | ||||
−0.916300 | + | 0.400493i | \(0.868839\pi\) | |||||||
\(458\) | 27.8617i | 1.30189i | ||||||||
\(459\) | −2.43845 | −0.113817 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.1231 | 0.611204 | 0.305602 | − | 0.952159i | \(-0.401142\pi\) | ||||
0.305602 | + | 0.952159i | \(0.401142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4924i | 0.580572i | 0.956940 | + | 0.290286i | \(0.0937505\pi\) | ||||
−0.956940 | + | 0.290286i | \(0.906250\pi\) | |||||||
\(464\) | −51.3693 | −2.38476 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.1231 | −0.607916 | ||||||||
\(467\) | 22.4384i | 1.03833i | 0.854675 | + | 0.519164i | \(0.173757\pi\) | ||||
−0.854675 | + | 0.519164i | \(0.826243\pi\) | |||||||
\(468\) | 1.12311i | 0.0519156i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.6155 | 1.45677 | ||||||||
\(472\) | 26.2462i | 1.20808i | ||||||||
\(473\) | − 1.36932i | − 0.0629613i | ||||||||
\(474\) | 9.75379 | 0.448006 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.87689i | − 0.131724i | ||||||||
\(478\) | − 50.7386i | − 2.32073i | ||||||||
\(479\) | 4.87689 | 0.222831 | 0.111415 | − | 0.993774i | \(-0.464462\pi\) | ||||
0.111415 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.63068 | −0.119949 | ||||||||
\(482\) | 10.8769i | 0.495429i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.0540 | 1.77518 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.7386 | 0.668558 | ||||||||
\(487\) | 3.12311i | 0.141521i | 0.997493 | + | 0.0707607i | \(0.0225427\pi\) | ||||
−0.997493 | + | 0.0707607i | \(0.977457\pi\) | |||||||
\(488\) | 100.847i | 4.56511i | ||||||||
\(489\) | −11.1231 | −0.503004 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.1771 | −1.85830 | −0.929148 | − | 0.369708i | \(-0.879458\pi\) | ||||
−0.929148 | + | 0.369708i | \(0.879458\pi\) | |||||||
\(492\) | − 36.4924i | − 1.64521i | ||||||||
\(493\) | 2.93087i | 0.132000i | ||||||||
\(494\) | −8.00000 | −0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − 16.0000i | − 0.716977i | ||||||||
\(499\) | −41.1771 | −1.84334 | −0.921670 | − | 0.387976i | \(-0.873174\pi\) | ||||
−0.921670 | + | 0.387976i | \(0.873174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.8229 | −0.483532 | ||||||||
\(502\) | 22.7386i | 1.01487i | ||||||||
\(503\) | − 38.9309i | − 1.73584i | −0.496703 | − | 0.867921i | \(-0.665456\pi\) | ||||
0.496703 | − | 0.867921i | \(-0.334544\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.4924 | 0.555356 | ||||||||
\(507\) | − 20.0000i | − 0.888231i | ||||||||
\(508\) | − 28.4924i | − 1.26415i | ||||||||
\(509\) | −11.7538 | −0.520978 | −0.260489 | − | 0.965477i | \(-0.583884\pi\) | ||||
−0.260489 | + | 0.965477i | \(0.583884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 50.4233i | − 2.22842i | ||||||||
\(513\) | 39.6155i | 1.74907i | ||||||||
\(514\) | 26.8769 | 1.18549 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.24621 | −0.274974 | ||||||||
\(517\) | 13.5616i | 0.596436i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.93087 | 0.304231 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | − 9.61553i | − 0.420860i | ||||||||
\(523\) | − 40.4924i | − 1.77061i | −0.465011 | − | 0.885305i | \(-0.653950\pi\) | ||||
0.465011 | − | 0.885305i | \(-0.346050\pi\) | |||||||
\(524\) | −4.00000 | −0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.9848 | 1.43821 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 18.7386i | 0.815494i | ||||||||
\(529\) | 13.2462 | 0.575922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.24621 | −0.0974773 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.24621i | 0.0972942i | ||||||||
\(534\) | −4.49242 | −0.194406 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −67.2311 | −2.90394 | ||||||||
\(537\) | 31.2311i | 1.34772i | ||||||||
\(538\) | − 53.1231i | − 2.29030i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.8078 | −1.62548 | −0.812741 | − | 0.582625i | \(-0.802026\pi\) | ||||
−0.812741 | + | 0.582625i | \(0.802026\pi\) | |||||||
\(542\) | 40.9848i | 1.76045i | ||||||||
\(543\) | − 27.5076i | − 1.18046i | ||||||||
\(544\) | 2.87689 | 0.123346 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.24621i | 0.0960411i | 0.998846 | + | 0.0480205i | \(0.0152913\pi\) | ||||
−0.998846 | + | 0.0480205i | \(0.984709\pi\) | |||||||
\(548\) | − 78.1080i | − 3.33661i | ||||||||
\(549\) | −8.63068 | −0.368349 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.6155 | 2.02849 | ||||||||
\(552\) | − 32.0000i | − 1.36201i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −0.630683 | −0.0267952 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 68.9848 | 2.92561 | ||||||||
\(557\) | 13.1231i | 0.556044i | 0.960575 | + | 0.278022i | \(0.0896788\pi\) | ||||
−0.960575 | + | 0.278022i | \(0.910321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.384472 | 0.0162614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.06913 | 0.0451387 | ||||||||
\(562\) | 31.8617i | 1.34401i | ||||||||
\(563\) | 28.0000i | 1.18006i | 0.807382 | + | 0.590030i | \(0.200884\pi\) | ||||
−0.807382 | + | 0.590030i | \(0.799116\pi\) | |||||||
\(564\) | 61.8617 | 2.60485 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −28.9848 | −1.21832 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 52.4924i | − 2.20253i | ||||||||
\(569\) | 30.9848 | 1.29895 | 0.649476 | − | 0.760382i | \(-0.274988\pi\) | ||||
0.649476 | + | 0.760382i | \(0.274988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.4924 | 1.69456 | 0.847278 | − | 0.531150i | \(-0.178240\pi\) | ||||
0.847278 | + | 0.531150i | \(0.178240\pi\) | |||||||
\(572\) | − 3.12311i | − 0.130584i | ||||||||
\(573\) | 21.1771i | 0.884685i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.807764 | −0.0336568 | ||||||||
\(577\) | − 24.0540i | − 1.00138i | −0.865627 | − | 0.500690i | \(-0.833080\pi\) | ||||
0.865627 | − | 0.500690i | \(-0.166920\pi\) | |||||||
\(578\) | 43.0540i | 1.79081i | ||||||||
\(579\) | 30.2462 | 1.25699 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 23.2311i | 0.962958i | ||||||||
\(583\) | 8.00000i | 0.331326i | ||||||||
\(584\) | 80.3542 | 3.32508 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.87689 | −0.284082 | ||||||||
\(587\) | − 26.2462i | − 1.08330i | −0.840605 | − | 0.541649i | \(-0.817800\pi\) | ||||
0.840605 | − | 0.541649i | \(-0.182200\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.75379 | −0.0721412 | ||||||||
\(592\) | − 46.1080i | − 1.89503i | ||||||||
\(593\) | 27.5616i | 1.13182i | 0.824468 | + | 0.565909i | \(0.191475\pi\) | ||||
−0.824468 | + | 0.565909i | \(0.808525\pi\) | |||||||
\(594\) | −22.2462 | −0.912773 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 55.8617 | 2.28819 | ||||||||
\(597\) | 2.73863i | 0.112085i | ||||||||
\(598\) | 3.50758i | 0.143436i | ||||||||
\(599\) | 11.8078 | 0.482452 | 0.241226 | − | 0.970469i | \(-0.422450\pi\) | ||||
0.241226 | + | 0.970469i | \(0.422450\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.49242 | −0.264831 | −0.132416 | − | 0.991194i | \(-0.542273\pi\) | ||||
−0.132416 | + | 0.991194i | \(0.542273\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.75379i | − 0.234312i | ||||||||
\(604\) | 31.6155 | 1.28642 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 64.9848 | 2.63983 | ||||||||
\(607\) | − 42.0540i | − 1.70692i | −0.521160 | − | 0.853459i | \(-0.674500\pi\) | ||||
0.521160 | − | 0.853459i | \(-0.325500\pi\) | |||||||
\(608\) | − 46.7386i | − 1.89550i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.80776 | −0.154046 | ||||||||
\(612\) | 1.12311i | 0.0453989i | ||||||||
\(613\) | 40.7386i | 1.64542i | 0.568463 | + | 0.822709i | \(0.307538\pi\) | ||||
−0.568463 | + | 0.822709i | \(0.692462\pi\) | |||||||
\(614\) | 49.4773 | 1.99674 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 32.2462i | − 1.29818i | −0.760710 | − | 0.649092i | \(-0.775149\pi\) | ||||
0.760710 | − | 0.649092i | \(-0.224851\pi\) | |||||||
\(618\) | − 22.2462i | − 0.894874i | ||||||||
\(619\) | 32.1080 | 1.29053 | 0.645264 | − | 0.763960i | \(-0.276747\pi\) | ||||
0.645264 | + | 0.763960i | \(0.276747\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.3693 | 0.697007 | ||||||||
\(622\) | − 80.9848i | − 3.24720i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.26137 | −0.210623 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −57.1231 | −2.28310 | ||||||||
\(627\) | − 17.3693i | − 0.693664i | ||||||||
\(628\) | − 92.3542i | − 3.68533i | ||||||||
\(629\) | −2.63068 | −0.104892 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8078 | −0.470060 | −0.235030 | − | 0.971988i | \(-0.575519\pi\) | ||||
−0.235030 | + | 0.971988i | \(0.575519\pi\) | |||||||
\(632\) | − 16.0000i | − 0.636446i | ||||||||
\(633\) | − 21.9460i | − 0.872276i | ||||||||
\(634\) | 26.8769 | 1.06742 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 36.4924 | 1.44702 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.7386i | 1.05859i | ||||||||
\(639\) | 4.49242 | 0.177717 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | − 53.4773i | − 2.11058i | ||||||||
\(643\) | − 1.56155i | − 0.0615816i | −0.999526 | − | 0.0307908i | \(-0.990197\pi\) | ||||
0.999526 | − | 0.0307908i | \(-0.00980257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | −0.314756 | ||||||||
\(647\) | 36.4924i | 1.43467i | 0.696731 | + | 0.717333i | \(0.254637\pi\) | ||||
−0.696731 | + | 0.717333i | \(0.745363\pi\) | |||||||
\(648\) | 45.9309i | 1.80433i | ||||||||
\(649\) | 6.24621 | 0.245185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.4924i | 1.27250i | ||||||||
\(653\) | − 33.2311i | − 1.30043i | −0.759750 | − | 0.650216i | \(-0.774678\pi\) | ||||
0.759750 | − | 0.650216i | \(-0.225322\pi\) | |||||||
\(654\) | −21.2614 | −0.831385 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −39.3693 | −1.53711 | ||||||||
\(657\) | 6.87689i | 0.268293i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.17708 | −0.357488 | −0.178744 | − | 0.983896i | \(-0.557203\pi\) | ||||
−0.178744 | + | 0.983896i | \(0.557203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.12311 | 0.199266 | 0.0996329 | − | 0.995024i | \(-0.468233\pi\) | ||||
0.0996329 | + | 0.995024i | \(0.468233\pi\) | |||||||
\(662\) | 30.7386i | 1.19469i | ||||||||
\(663\) | 0.300187i | 0.0116583i | ||||||||
\(664\) | −26.2462 | −1.01855 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.63068 | 0.334432 | ||||||||
\(667\) | − 20.8769i | − 0.808357i | ||||||||
\(668\) | 31.6155i | 1.22324i | ||||||||
\(669\) | 3.80776 | 0.147217 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.8617i | 1.22818i | 0.789236 | + | 0.614090i | \(0.210477\pi\) | ||||
−0.789236 | + | 0.614090i | \(0.789523\pi\) | |||||||
\(674\) | −3.86174 | −0.148749 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −58.4233 | −2.24705 | ||||||||
\(677\) | 4.93087i | 0.189509i | 0.995501 | + | 0.0947544i | \(0.0302066\pi\) | ||||
−0.995501 | + | 0.0947544i | \(0.969793\pi\) | |||||||
\(678\) | − 56.0000i | − 2.15067i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6695 | 0.677097 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 6.73863i | − 0.257847i | −0.991655 | − | 0.128923i | \(-0.958848\pi\) | ||||
0.991655 | − | 0.128923i | \(-0.0411521\pi\) | |||||||
\(684\) | 18.2462 | 0.697661 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 16.9848i | − 0.648012i | ||||||||
\(688\) | 6.73863i | 0.256908i | ||||||||
\(689\) | −2.24621 | −0.0855738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.4924 | 0.931736 | 0.465868 | − | 0.884854i | \(-0.345742\pi\) | ||||
0.465868 | + | 0.884854i | \(0.345742\pi\) | |||||||
\(692\) | − 20.2462i | − 0.769645i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.2462 | 0.692617 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 68.4924 | 2.59620 | ||||||||
\(697\) | 2.24621i | 0.0850813i | ||||||||
\(698\) | 26.8769i | 1.01731i | ||||||||
\(699\) | 8.00000 | 0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.9309 | 1.09270 | 0.546352 | − | 0.837556i | \(-0.316016\pi\) | ||||
0.546352 | + | 0.837556i | \(0.316016\pi\) | |||||||
\(702\) | − 6.24621i | − 0.235748i | ||||||||
\(703\) | 42.7386i | 1.61192i | ||||||||
\(704\) | 2.24621 | 0.0846573 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.8769 | 0.559899 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − 28.4924i | − 1.07081i | ||||||||
\(709\) | −27.1771 | −1.02066 | −0.510328 | − | 0.859980i | \(-0.670476\pi\) | ||||
−0.510328 | + | 0.859980i | \(0.670476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.36932 | 0.0513534 | ||||||||
\(712\) | 7.36932i | 0.276177i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 91.2311 | 3.40946 | ||||||||
\(717\) | 30.9309i | 1.15513i | ||||||||
\(718\) | − 20.4924i | − 0.764770i | ||||||||
\(719\) | 8.38447 | 0.312688 | 0.156344 | − | 0.987703i | \(-0.450029\pi\) | ||||
0.156344 | + | 0.987703i | \(0.450029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 81.3002i | 3.02568i | ||||||||
\(723\) | − 6.63068i | − 0.246598i | ||||||||
\(724\) | −80.3542 | −2.98634 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −34.2462 | −1.27100 | ||||||||
\(727\) | 52.4924i | 1.94684i | 0.229035 | + | 0.973418i | \(0.426443\pi\) | ||||
−0.229035 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9848 | −1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.384472 | 0.0142202 | ||||||||
\(732\) | − 109.477i | − 4.04640i | ||||||||
\(733\) | − 6.68466i | − 0.246903i | −0.992351 | − | 0.123452i | \(-0.960604\pi\) | ||||
0.992351 | − | 0.123452i | \(-0.0393964\pi\) | |||||||
\(734\) | 22.2462 | 0.821123 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.4924 | −0.755361 | ||||||||
\(737\) | 16.0000i | 0.589368i | ||||||||
\(738\) | − 7.36932i | − 0.271268i | ||||||||
\(739\) | −34.9309 | −1.28495 | −0.642476 | − | 0.766305i | \(-0.722093\pi\) | ||||
−0.642476 | + | 0.766305i | \(0.722093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.87689 | 0.179157 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 32.9848i | − 1.21010i | −0.796189 | − | 0.605048i | \(-0.793154\pi\) | ||||
0.796189 | − | 0.605048i | \(-0.206846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11.8617 | −0.434289 | ||||||||
\(747\) | − 2.24621i | − 0.0821846i | ||||||||
\(748\) | − 3.12311i | − 0.114192i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.0691 | 0.622861 | 0.311431 | − | 0.950269i | \(-0.399192\pi\) | ||||
0.311431 | + | 0.950269i | \(0.399192\pi\) | |||||||
\(752\) | − 66.7386i | − 2.43371i | ||||||||
\(753\) | − 13.8617i | − 0.505150i | ||||||||
\(754\) | −7.50758 | −0.273410 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 39.3693i | − 1.43090i | −0.698663 | − | 0.715451i | \(-0.746221\pi\) | ||||
0.698663 | − | 0.715451i | \(-0.253779\pi\) | |||||||
\(758\) | 42.2462i | 1.53445i | ||||||||
\(759\) | −7.61553 | −0.276426 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.2462 | −1.74892 | −0.874462 | − | 0.485094i | \(-0.838785\pi\) | ||||
−0.874462 | + | 0.485094i | \(0.838785\pi\) | |||||||
\(762\) | 24.9848i | 0.905105i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 61.8617 | 2.23808 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.0000 | 0.578103 | ||||||||
\(767\) | 1.75379i | 0.0633256i | ||||||||
\(768\) | 42.2462i | 1.52443i | ||||||||
\(769\) | −42.4924 | −1.53232 | −0.766158 | − | 0.642652i | \(-0.777834\pi\) | ||||
−0.766158 | + | 0.642652i | \(0.777834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.3845 | −0.590072 | ||||||||
\(772\) | − 88.3542i | − 3.17994i | ||||||||
\(773\) | − 36.9309i | − 1.32831i | −0.747594 | − | 0.664156i | \(-0.768791\pi\) | ||||
0.747594 | − | 0.664156i | \(-0.231209\pi\) | |||||||
\(774\) | −1.26137 | −0.0453389 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 38.1080 | 1.36800 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 63.8617i | 2.28955i | ||||||||
\(779\) | 36.4924 | 1.30748 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4924 | −0.447014 | ||||||||
\(782\) | 3.50758i | 0.125431i | ||||||||
\(783\) | 37.1771i | 1.32860i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.50758 | 0.125111 | ||||||||
\(787\) | − 49.1771i | − 1.75297i | −0.481426 | − | 0.876487i | \(-0.659881\pi\) | ||||
0.481426 | − | 0.876487i | \(-0.340119\pi\) | |||||||
\(788\) | 5.12311i | 0.182503i | ||||||||
\(789\) | −20.1080 | −0.715862 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.75379i | 0.204452i | ||||||||
\(793\) | 6.73863i | 0.239296i | ||||||||
\(794\) | −70.6004 | −2.50551 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00000 | 0.283552 | ||||||||
\(797\) | 24.0540i | 0.852036i | 0.904715 | + | 0.426018i | \(0.140084\pi\) | ||||
−0.904715 | + | 0.426018i | \(0.859916\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.80776 | −0.134709 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.630683 | −0.0222841 | ||||||||
\(802\) | 80.8466i | 2.85479i | ||||||||
\(803\) | − 19.1231i | − 0.674840i | ||||||||
\(804\) | 72.9848 | 2.57398 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.3845i | 1.13999i | ||||||||
\(808\) | − 106.600i | − 3.75019i | ||||||||
\(809\) | −16.5464 | −0.581740 | −0.290870 | − | 0.956763i | \(-0.593945\pi\) | ||||
−0.290870 | + | 0.956763i | \(0.593945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.6155 | −0.688794 | −0.344397 | − | 0.938824i | \(-0.611917\pi\) | ||||
−0.344397 | + | 0.938824i | \(0.611917\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 24.9848i | − 0.876257i | ||||||||
\(814\) | −24.0000 | −0.841200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.26137 | −0.184185 | ||||||||
\(817\) | − 6.24621i | − 0.218527i | ||||||||
\(818\) | 16.6307i | 0.581478i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4233 | −0.747678 | −0.373839 | − | 0.927494i | \(-0.621959\pi\) | ||||
−0.373839 | + | 0.927494i | \(0.621959\pi\) | |||||||
\(822\) | 68.4924i | 2.38895i | ||||||||
\(823\) | − 36.4924i | − 1.27205i | −0.771670 | − | 0.636023i | \(-0.780578\pi\) | ||||
0.771670 | − | 0.636023i | \(-0.219422\pi\) | |||||||
\(824\) | −36.4924 | −1.27127 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.36932i | 0.186709i | 0.995633 | + | 0.0933547i | \(0.0297591\pi\) | ||||
−0.995633 | + | 0.0933547i | \(0.970241\pi\) | |||||||
\(828\) | − 8.00000i | − 0.278019i | ||||||||
\(829\) | 34.8769 | 1.21132 | 0.605662 | − | 0.795722i | \(-0.292908\pi\) | ||||
0.605662 | + | 0.795722i | \(0.292908\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.384472 | 0.0133372 | ||||||||
\(832\) | 0.630683i | 0.0218650i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −60.4924 | −2.09468 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −50.7386 | −1.75483 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 67.2311i | 2.32246i | ||||||||
\(839\) | −28.8769 | −0.996941 | −0.498471 | − | 0.866907i | \(-0.666105\pi\) | ||||
−0.498471 | + | 0.866907i | \(0.666105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6847 | 0.540850 | ||||||||
\(842\) | − 6.87689i | − 0.236993i | ||||||||
\(843\) | − 19.4233i | − 0.668974i | ||||||||
\(844\) | −64.1080 | −2.20669 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.4924 | 0.429498 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 39.3693i | − 1.35195i | ||||||||
\(849\) | 17.6695 | 0.606416 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.7386 | 0.642352 | ||||||||
\(852\) | 56.9848i | 1.95227i | ||||||||
\(853\) | 7.26137i | 0.248624i | 0.992243 | + | 0.124312i | \(0.0396724\pi\) | ||||
−0.992243 | + | 0.124312i | \(0.960328\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −87.7235 | −2.99833 | ||||||||
\(857\) | − 15.7538i | − 0.538139i | −0.963121 | − | 0.269070i | \(-0.913284\pi\) | ||||
0.963121 | − | 0.269070i | \(-0.0867162\pi\) | |||||||
\(858\) | 2.73863i | 0.0934954i | ||||||||
\(859\) | −16.4924 | −0.562714 | −0.281357 | − | 0.959603i | \(-0.590785\pi\) | ||||
−0.281357 | + | 0.959603i | \(0.590785\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 50.7386i | − 1.72816i | ||||||||
\(863\) | − 25.7538i | − 0.876669i | −0.898812 | − | 0.438335i | \(-0.855569\pi\) | ||||
0.898812 | − | 0.438335i | \(-0.144431\pi\) | |||||||
\(864\) | 36.4924 | 1.24150 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 21.1231 | 0.717792 | ||||||||
\(867\) | − 26.2462i | − 0.891368i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.80776 | −0.129170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.49242 | −0.152220 | ||||||||
\(872\) | 34.8769i | 1.18108i | ||||||||
\(873\) | 3.26137i | 0.110381i | ||||||||
\(874\) | 56.9848 | 1.92754 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −87.2311 | −2.94726 | ||||||||
\(877\) | 40.2462i | 1.35902i | 0.733667 | + | 0.679509i | \(0.237807\pi\) | ||||
−0.733667 | + | 0.679509i | \(0.762193\pi\) | |||||||
\(878\) | 24.0000i | 0.809961i | ||||||||
\(879\) | 4.19224 | 0.141401 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.8617 | 0.399632 | 0.199816 | − | 0.979833i | \(-0.435966\pi\) | ||||
0.199816 | + | 0.979833i | \(0.435966\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 8.49242i | − 0.285793i | −0.989738 | − | 0.142896i | \(-0.954358\pi\) | ||||
0.989738 | − | 0.142896i | \(-0.0456416\pi\) | |||||||
\(884\) | 0.876894 | 0.0294931 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.73863 | 0.226389 | ||||||||
\(887\) | 20.4924i | 0.688068i | 0.938957 | + | 0.344034i | \(0.111794\pi\) | ||||
−0.938957 | + | 0.344034i | \(0.888206\pi\) | |||||||
\(888\) | 61.4773i | 2.06304i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9309 | 0.366198 | ||||||||
\(892\) | − 11.1231i | − 0.372429i | ||||||||
\(893\) | 61.8617i | 2.07012i | ||||||||
\(894\) | −48.9848 | −1.63830 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 2.13826i | − 0.0713944i | ||||||||
\(898\) | 4.63068i | 0.154528i | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.24621 | −0.0748321 | ||||||||
\(902\) | 20.4924i | 0.682323i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −91.8617 | −3.05528 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −27.7235 | −0.921051 | ||||||||
\(907\) | 24.1080i | 0.800491i | 0.916408 | + | 0.400246i | \(0.131075\pi\) | ||||
−0.916408 | + | 0.400246i | \(0.868925\pi\) | |||||||
\(908\) | − 51.6155i | − 1.71292i | ||||||||
\(909\) | 9.12311 | 0.302594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.4924 | −0.943996 | −0.471998 | − | 0.881600i | \(-0.656467\pi\) | ||||
−0.471998 | + | 0.881600i | \(0.656467\pi\) | |||||||
\(912\) | 85.4773i | 2.83044i | ||||||||
\(913\) | 6.24621i | 0.206719i | ||||||||
\(914\) | −43.8617 | −1.45082 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −49.6155 | −1.63934 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − 6.24621i | − 0.206156i | ||||||||
\(919\) | −40.3002 | −1.32938 | −0.664690 | − | 0.747119i | \(-0.731436\pi\) | ||||
−0.664690 | + | 0.747119i | \(0.731436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.1619 | −0.993869 | ||||||||
\(922\) | 33.6155i | 1.10707i | ||||||||
\(923\) | − 3.50758i | − 0.115453i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −32.0000 | −1.05159 | ||||||||
\(927\) | − 3.12311i | − 0.102576i | ||||||||
\(928\) | − 43.8617i | − 1.43983i | ||||||||
\(929\) | 22.1080 | 0.725338 | 0.362669 | − | 0.931918i | \(-0.381866\pi\) | ||||
0.362669 | + | 0.931918i | \(0.381866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 23.3693i | − 0.765487i | ||||||||
\(933\) | 49.3693i | 1.61628i | ||||||||
\(934\) | −57.4773 | −1.88071 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.61553 | −0.0528052 | ||||||||
\(937\) | − 55.6695i | − 1.81864i | −0.416094 | − | 0.909322i | \(-0.636601\pi\) | ||||
0.416094 | − | 0.909322i | \(-0.363399\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.8229 | 1.13640 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.8617 | −1.42985 | −0.714926 | − | 0.699200i | \(-0.753540\pi\) | ||||
−0.714926 | + | 0.699200i | \(0.753540\pi\) | |||||||
\(942\) | 80.9848i | 2.63863i | ||||||||
\(943\) | − 16.0000i | − 0.521032i | ||||||||
\(944\) | −30.7386 | −1.00046 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.50758 | 0.114041 | ||||||||
\(947\) | − 4.00000i | − 0.129983i | −0.997886 | − | 0.0649913i | \(-0.979298\pi\) | ||||
0.997886 | − | 0.0649913i | \(-0.0207020\pi\) | |||||||
\(948\) | 17.3693i | 0.564129i | ||||||||
\(949\) | 5.36932 | 0.174295 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.3845 | −0.531303 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 33.1231i | − 1.07296i | −0.843912 | − | 0.536481i | \(-0.819753\pi\) | ||||
0.843912 | − | 0.536481i | \(-0.180247\pi\) | |||||||
\(954\) | 7.36932 | 0.238590 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 90.3542 | 2.92226 | ||||||||
\(957\) | − 16.3002i | − 0.526910i | ||||||||
\(958\) | 12.4924i | 0.403612i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | − 6.73863i | − 0.217262i | ||||||||
\(963\) | − 7.50758i | − 0.241928i | ||||||||
\(964\) | −19.3693 | −0.623844 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.1231i | 1.12948i | 0.825268 | + | 0.564741i | \(0.191024\pi\) | ||||
−0.825268 | + | 0.564741i | \(0.808976\pi\) | |||||||
\(968\) | 56.1771i | 1.80560i | ||||||||
\(969\) | 4.87689 | 0.156668 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.4773 | −1.58780 | −0.793901 | − | 0.608048i | \(-0.791953\pi\) | ||||
−0.793901 | + | 0.608048i | \(0.791953\pi\) | |||||||
\(972\) | 26.2462i | 0.841848i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −118.108 | −3.78054 | ||||||||
\(977\) | − 33.2311i | − 1.06316i | −0.847009 | − | 0.531578i | \(-0.821599\pi\) | ||||
0.847009 | − | 0.531578i | \(-0.178401\pi\) | |||||||
\(978\) | − 28.4924i | − 0.911087i | ||||||||
\(979\) | 1.75379 | 0.0560513 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.98485 | −0.0952988 | ||||||||
\(982\) | − 105.477i | − 3.36591i | ||||||||
\(983\) | − 51.4233i | − 1.64015i | −0.572257 | − | 0.820074i | \(-0.693932\pi\) | ||||
0.572257 | − | 0.820074i | \(-0.306068\pi\) | |||||||
\(984\) | 52.4924 | 1.67340 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.50758 | −0.239090 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 14.2462i | − 0.453232i | ||||||||
\(989\) | −2.73863 | −0.0870835 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4924 | 0.396835 | 0.198417 | − | 0.980118i | \(-0.436420\pi\) | ||||
0.198417 | + | 0.980118i | \(0.436420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 18.7386i | − 0.594653i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 28.4924 | 0.902817 | ||||||||
\(997\) | − 2.68466i | − 0.0850240i | −0.999096 | − | 0.0425120i | \(-0.986464\pi\) | ||||
0.999096 | − | 0.0425120i | \(-0.0135361\pi\) | |||||||
\(998\) | − 105.477i | − 3.33882i | ||||||||
\(999\) | −33.3693 | −1.05576 |
(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 | 1225.2.b.f.99.4 | 4 | ||
5.2 | odd | 4 | 245.2.a.d.1.1 | 2 | |||
5.3 | odd | 4 | 1225.2.a.s.1.2 | 2 | |||
5.4 | even | 2 | inner | 1225.2.b.f.99.1 | 4 | ||
7.6 | odd | 2 | 175.2.b.b.99.4 | 4 | |||
15.2 | even | 4 | 2205.2.a.x.1.2 | 2 | |||
20.7 | even | 4 | 3920.2.a.bs.1.2 | 2 | |||
21.20 | even | 2 | 1575.2.d.e.1324.1 | 4 | |||
28.27 | even | 2 | 2800.2.g.t.449.2 | 4 | |||
35.2 | odd | 12 | 245.2.e.h.116.2 | 4 | |||
35.12 | even | 12 | 245.2.e.i.116.2 | 4 | |||
35.13 | even | 4 | 175.2.a.f.1.2 | 2 | |||
35.17 | even | 12 | 245.2.e.i.226.2 | 4 | |||
35.27 | even | 4 | 35.2.a.b.1.1 | ✓ | 2 | ||
35.32 | odd | 12 | 245.2.e.h.226.2 | 4 | |||
35.34 | odd | 2 | 175.2.b.b.99.1 | 4 | |||
105.62 | odd | 4 | 315.2.a.e.1.2 | 2 | |||
105.83 | odd | 4 | 1575.2.a.p.1.1 | 2 | |||
105.104 | even | 2 | 1575.2.d.e.1324.4 | 4 | |||
140.27 | odd | 4 | 560.2.a.i.1.1 | 2 | |||
140.83 | odd | 4 | 2800.2.a.bi.1.2 | 2 | |||
140.139 | even | 2 | 2800.2.g.t.449.3 | 4 | |||
280.27 | odd | 4 | 2240.2.a.bd.1.2 | 2 | |||
280.237 | even | 4 | 2240.2.a.bh.1.1 | 2 | |||
385.307 | odd | 4 | 4235.2.a.m.1.2 | 2 | |||
420.167 | even | 4 | 5040.2.a.bt.1.1 | 2 | |||
455.272 | even | 4 | 5915.2.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.a.b.1.1 | ✓ | 2 | 35.27 | even | 4 | ||
175.2.a.f.1.2 | 2 | 35.13 | even | 4 | |||
175.2.b.b.99.1 | 4 | 35.34 | odd | 2 | |||
175.2.b.b.99.4 | 4 | 7.6 | odd | 2 | |||
245.2.a.d.1.1 | 2 | 5.2 | odd | 4 | |||
245.2.e.h.116.2 | 4 | 35.2 | odd | 12 | |||
245.2.e.h.226.2 | 4 | 35.32 | odd | 12 | |||
245.2.e.i.116.2 | 4 | 35.12 | even | 12 | |||
245.2.e.i.226.2 | 4 | 35.17 | even | 12 | |||
315.2.a.e.1.2 | 2 | 105.62 | odd | 4 | |||
560.2.a.i.1.1 | 2 | 140.27 | odd | 4 | |||
1225.2.a.s.1.2 | 2 | 5.3 | odd | 4 | |||
1225.2.b.f.99.1 | 4 | 5.4 | even | 2 | inner | ||
1225.2.b.f.99.4 | 4 | 1.1 | even | 1 | trivial | ||
1575.2.a.p.1.1 | 2 | 105.83 | odd | 4 | |||
1575.2.d.e.1324.1 | 4 | 21.20 | even | 2 | |||
1575.2.d.e.1324.4 | 4 | 105.104 | even | 2 | |||
2205.2.a.x.1.2 | 2 | 15.2 | even | 4 | |||
2240.2.a.bd.1.2 | 2 | 280.27 | odd | 4 | |||
2240.2.a.bh.1.1 | 2 | 280.237 | even | 4 | |||
2800.2.a.bi.1.2 | 2 | 140.83 | odd | 4 | |||
2800.2.g.t.449.2 | 4 | 28.27 | even | 2 | |||
2800.2.g.t.449.3 | 4 | 140.139 | even | 2 | |||
3920.2.a.bs.1.2 | 2 | 20.7 | even | 4 | |||
4235.2.a.m.1.2 | 2 | 385.307 | odd | 4 | |||
5040.2.a.bt.1.1 | 2 | 420.167 | even | 4 | |||
5915.2.a.l.1.2 | 2 | 455.272 | even | 4 |