Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.a (trivial) |
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: | yes |
Analytic conductor: | \(44.9158511370\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.5444000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} - 4x^{4} - 30x^{3} + 7x^{2} + 12x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.35083\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35083 | 1.66229 | 0.831144 | − | 0.556058i | \(-0.187687\pi\) | ||||
0.831144 | + | 0.556058i | \(0.187687\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.52640 | 1.76320 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.48189 | −1.31603 | −0.658015 | − | 0.753005i | \(-0.728604\pi\) | ||||
−0.658015 | + | 0.753005i | \(0.728604\pi\) | |||||||
\(8\) | 3.58831 | 1.26866 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.93111 | −0.883762 | −0.441881 | − | 0.897074i | \(-0.645689\pi\) | ||||
−0.441881 | + | 0.897074i | \(0.645689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.87575 | 0.520239 | 0.260119 | − | 0.965576i | \(-0.416238\pi\) | ||||
0.260119 | + | 0.965576i | \(0.416238\pi\) | |||||||
\(14\) | −8.18532 | −2.18762 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.38270 | 0.345674 | ||||||||
\(17\) | 6.78566 | 1.64576 | 0.822882 | − | 0.568212i | \(-0.192365\pi\) | ||||
0.822882 | + | 0.568212i | \(0.192365\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.94950 | −0.676662 | −0.338331 | − | 0.941027i | \(-0.609862\pi\) | ||||
−0.338331 | + | 0.941027i | \(0.609862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.89053 | −1.46907 | ||||||||
\(23\) | −5.49019 | −1.14478 | −0.572392 | − | 0.819980i | \(-0.693985\pi\) | ||||
−0.572392 | + | 0.819980i | \(0.693985\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.40956 | 0.864786 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12.2785 | −2.32042 | ||||||||
\(29\) | −2.55593 | −0.474625 | −0.237313 | − | 0.971433i | \(-0.576267\pi\) | ||||
−0.237313 | + | 0.971433i | \(0.576267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.418084 | 0.0750901 | 0.0375451 | − | 0.999295i | \(-0.488046\pi\) | ||||
0.0375451 | + | 0.999295i | \(0.488046\pi\) | |||||||
\(32\) | −3.92613 | −0.694048 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15.9519 | 2.73573 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.23959 | −0.861383 | −0.430691 | − | 0.902499i | \(-0.641730\pi\) | ||||
−0.430691 | + | 0.902499i | \(0.641730\pi\) | |||||||
\(38\) | −6.93377 | −1.12481 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.67869 | −0.262167 | −0.131084 | − | 0.991371i | \(-0.541846\pi\) | ||||
−0.131084 | + | 0.991371i | \(0.541846\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.9233 | −1.66578 | −0.832892 | − | 0.553436i | \(-0.813316\pi\) | ||||
−0.832892 | + | 0.553436i | \(0.813316\pi\) | |||||||
\(44\) | −10.3363 | −1.55825 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.9065 | −1.90296 | ||||||||
\(47\) | −7.49178 | −1.09279 | −0.546394 | − | 0.837528i | \(-0.684000\pi\) | ||||
−0.546394 | + | 0.837528i | \(0.684000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.12353 | 0.731933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.61463 | 0.917285 | ||||||||
\(53\) | 3.70953 | 0.509543 | 0.254771 | − | 0.967001i | \(-0.418000\pi\) | ||||
0.254771 | + | 0.967001i | \(0.418000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.4941 | −1.66959 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00857 | −0.788964 | ||||||||
\(59\) | 7.10854 | 0.925453 | 0.462727 | − | 0.886501i | \(-0.346871\pi\) | ||||
0.462727 | + | 0.886501i | \(0.346871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.43710 | −0.824186 | −0.412093 | − | 0.911142i | \(-0.635202\pi\) | ||||
−0.412093 | + | 0.911142i | \(0.635202\pi\) | |||||||
\(62\) | 0.982844 | 0.124821 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.9951 | −1.49938 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0415 | −1.22677 | −0.613383 | − | 0.789786i | \(-0.710192\pi\) | ||||
−0.613383 | + | 0.789786i | \(0.710192\pi\) | |||||||
\(68\) | 23.9290 | 2.90181 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.728602 | −0.0864691 | −0.0432346 | − | 0.999065i | \(-0.513766\pi\) | ||||
−0.0432346 | + | 0.999065i | \(0.513766\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.59269 | 0.420492 | 0.210246 | − | 0.977648i | \(-0.432573\pi\) | ||||
0.210246 | + | 0.977648i | \(0.432573\pi\) | |||||||
\(74\) | −12.3174 | −1.43187 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.4011 | −1.19309 | ||||||||
\(77\) | 10.2058 | 1.16306 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.07265 | 0.345700 | 0.172850 | − | 0.984948i | \(-0.444702\pi\) | ||||
0.172850 | + | 0.984948i | \(0.444702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.94632 | −0.435798 | ||||||||
\(83\) | 10.1152 | 1.11029 | 0.555146 | − | 0.831753i | \(-0.312662\pi\) | ||||
0.555146 | + | 0.831753i | \(0.312662\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −25.6788 | −2.76901 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.5177 | −1.12119 | ||||||||
\(89\) | −0.287512 | −0.0304762 | −0.0152381 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152381 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.53114 | −0.684649 | ||||||||
\(92\) | −19.3606 | −2.01848 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.6119 | −1.81653 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4090 | 1.05688 | 0.528439 | − | 0.848971i | \(-0.322778\pi\) | ||||
0.528439 | + | 0.848971i | \(0.322778\pi\) | |||||||
\(98\) | 12.0446 | 1.21668 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.65744 | −0.761943 | −0.380972 | − | 0.924587i | \(-0.624410\pi\) | ||||
−0.380972 | + | 0.924587i | \(0.624410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.98602 | 0.294221 | 0.147111 | − | 0.989120i | \(-0.453003\pi\) | ||||
0.147111 | + | 0.989120i | \(0.453003\pi\) | |||||||
\(104\) | 6.73076 | 0.660005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.72047 | 0.847007 | ||||||||
\(107\) | −7.07213 | −0.683689 | −0.341844 | − | 0.939757i | \(-0.611052\pi\) | ||||
−0.341844 | + | 0.939757i | \(0.611052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.3022 | −1.27412 | −0.637058 | − | 0.770816i | \(-0.719849\pi\) | ||||
−0.637058 | + | 0.770816i | \(0.719849\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.81440 | −0.454918 | ||||||||
\(113\) | 10.0233 | 0.942911 | 0.471456 | − | 0.881890i | \(-0.343729\pi\) | ||||
0.471456 | + | 0.881890i | \(0.343729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.01325 | −0.836859 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.7110 | 1.53837 | ||||||||
\(119\) | −23.6269 | −2.16587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.40861 | −0.218965 | ||||||||
\(122\) | −15.1325 | −1.37003 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.47433 | 0.132399 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5730 | −0.938205 | −0.469103 | − | 0.883144i | \(-0.655423\pi\) | ||||
−0.469103 | + | 0.883144i | \(0.655423\pi\) | |||||||
\(128\) | −20.3461 | −1.79836 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.02608 | 0.788612 | 0.394306 | − | 0.918979i | \(-0.370985\pi\) | ||||
0.394306 | + | 0.918979i | \(0.370985\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.2698 | 0.890507 | ||||||||
\(134\) | −23.6059 | −2.03924 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 24.3490 | 2.08791 | ||||||||
\(137\) | −19.6646 | −1.68006 | −0.840029 | − | 0.542541i | \(-0.817462\pi\) | ||||
−0.840029 | + | 0.542541i | \(0.817462\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6520 | −0.988310 | −0.494155 | − | 0.869374i | \(-0.664522\pi\) | ||||
−0.494155 | + | 0.869374i | \(0.664522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.71282 | −0.143737 | ||||||||
\(143\) | −5.49801 | −0.459767 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.44580 | 0.698979 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −18.4769 | −1.51879 | ||||||||
\(149\) | 7.33020 | 0.600513 | 0.300257 | − | 0.953858i | \(-0.402928\pi\) | ||||
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7358 | −1.36194 | −0.680968 | − | 0.732313i | \(-0.738441\pi\) | ||||
−0.680968 | + | 0.732313i | \(0.738441\pi\) | |||||||
\(152\) | −10.5837 | −0.858453 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23.9921 | 1.93333 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.88635 | −0.629399 | −0.314700 | − | 0.949191i | \(-0.601904\pi\) | ||||
−0.314700 | + | 0.949191i | \(0.601904\pi\) | |||||||
\(158\) | 7.22328 | 0.574653 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.1162 | 1.50657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.93992 | 0.778555 | 0.389277 | − | 0.921121i | \(-0.372725\pi\) | ||||
0.389277 | + | 0.921121i | \(0.372725\pi\) | |||||||
\(164\) | −5.91973 | −0.462254 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.7792 | 1.84563 | ||||||||
\(167\) | 5.57767 | 0.431613 | 0.215806 | − | 0.976436i | \(-0.430762\pi\) | ||||
0.215806 | + | 0.976436i | \(0.430762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.48157 | −0.729352 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −38.5198 | −2.93711 | ||||||||
\(173\) | 16.5682 | 1.25966 | 0.629828 | − | 0.776734i | \(-0.283125\pi\) | ||||
0.629828 | + | 0.776734i | \(0.283125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.05284 | −0.305494 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.675892 | −0.0506602 | ||||||||
\(179\) | 5.36021 | 0.400641 | 0.200321 | − | 0.979730i | \(-0.435802\pi\) | ||||
0.200321 | + | 0.979730i | \(0.435802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.327745 | −0.0243611 | −0.0121805 | − | 0.999926i | \(-0.503877\pi\) | ||||
−0.0121805 | + | 0.999926i | \(0.503877\pi\) | |||||||
\(182\) | −15.3536 | −1.13808 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.7005 | −1.45234 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.8895 | −1.45446 | ||||||||
\(188\) | −26.4190 | −1.92680 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.46992 | 0.251074 | 0.125537 | − | 0.992089i | \(-0.459935\pi\) | ||||
0.125537 | + | 0.992089i | \(0.459935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.3134 | 1.75012 | 0.875058 | − | 0.484018i | \(-0.160823\pi\) | ||||
0.875058 | + | 0.484018i | \(0.160823\pi\) | |||||||
\(194\) | 24.4699 | 1.75684 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.0676 | 1.29055 | ||||||||
\(197\) | 14.9561 | 1.06558 | 0.532789 | − | 0.846248i | \(-0.321144\pi\) | ||||
0.532789 | + | 0.846248i | \(0.321144\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3251 | −0.802817 | −0.401408 | − | 0.915899i | \(-0.631479\pi\) | ||||
−0.401408 | + | 0.915899i | \(0.631479\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.0013 | −1.26657 | ||||||||
\(203\) | 8.89948 | 0.624621 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.01963 | 0.489081 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.59359 | 0.179833 | ||||||||
\(209\) | 8.64530 | 0.598008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.54283 | 0.519270 | 0.259635 | − | 0.965707i | \(-0.416398\pi\) | ||||
0.259635 | + | 0.965707i | \(0.416398\pi\) | |||||||
\(212\) | 13.0813 | 0.898426 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.6254 | −1.13649 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.45572 | −0.0988208 | ||||||||
\(218\) | −31.2711 | −2.11795 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.7282 | 0.856190 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.79539 | 0.522018 | 0.261009 | − | 0.965336i | \(-0.415945\pi\) | ||||
0.261009 | + | 0.965336i | \(0.415945\pi\) | |||||||
\(224\) | 13.6703 | 0.913387 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.5630 | 1.56739 | ||||||||
\(227\) | −12.8319 | −0.851686 | −0.425843 | − | 0.904797i | \(-0.640022\pi\) | ||||
−0.425843 | + | 0.904797i | \(0.640022\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.5033 | −0.958405 | −0.479203 | − | 0.877704i | \(-0.659074\pi\) | ||||
−0.479203 | + | 0.877704i | \(0.659074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.17148 | −0.602137 | ||||||||
\(233\) | 11.3970 | 0.746646 | 0.373323 | − | 0.927702i | \(-0.378218\pi\) | ||||
0.373323 | + | 0.927702i | \(0.378218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 25.0676 | 1.63176 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −55.5428 | −3.60031 | ||||||||
\(239\) | −6.90072 | −0.446371 | −0.223185 | − | 0.974776i | \(-0.571646\pi\) | ||||
−0.223185 | + | 0.974776i | \(0.571646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4467 | −1.83242 | −0.916208 | − | 0.400704i | \(-0.868766\pi\) | ||||
−0.916208 | + | 0.400704i | \(0.868766\pi\) | |||||||
\(242\) | −5.66224 | −0.363982 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −22.6998 | −1.45320 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.53252 | −0.352026 | ||||||||
\(248\) | 1.50021 | 0.0952637 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.3258 | 0.777999 | 0.389000 | − | 0.921238i | \(-0.372821\pi\) | ||||
0.389000 | + | 0.921238i | \(0.372821\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0923 | 1.01172 | ||||||||
\(254\) | −24.8554 | −1.55957 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −23.8400 | −1.49000 | ||||||||
\(257\) | 20.8274 | 1.29918 | 0.649590 | − | 0.760285i | \(-0.274941\pi\) | ||||
0.649590 | + | 0.760285i | \(0.274941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.2437 | 1.13361 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.2188 | 1.31090 | ||||||||
\(263\) | 2.23517 | 0.137826 | 0.0689131 | − | 0.997623i | \(-0.478047\pi\) | ||||
0.0689131 | + | 0.997623i | \(0.478047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 24.1426 | 1.48028 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −35.4104 | −2.16303 | ||||||||
\(269\) | 19.3036 | 1.17696 | 0.588482 | − | 0.808511i | \(-0.299726\pi\) | ||||
0.588482 | + | 0.808511i | \(0.299726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.9411 | −0.725372 | −0.362686 | − | 0.931911i | \(-0.618140\pi\) | ||||
−0.362686 | + | 0.931911i | \(0.618140\pi\) | |||||||
\(272\) | 9.38252 | 0.568899 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −46.2281 | −2.79274 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.1466 | −1.57100 | −0.785499 | − | 0.618863i | \(-0.787594\pi\) | ||||
−0.785499 | + | 0.618863i | \(0.787594\pi\) | |||||||
\(278\) | −27.3919 | −1.64285 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.1219 | −0.603820 | −0.301910 | − | 0.953336i | \(-0.597624\pi\) | ||||
−0.301910 | + | 0.953336i | \(0.597624\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.8638 | 1.89410 | 0.947052 | − | 0.321081i | \(-0.104046\pi\) | ||||
0.947052 | + | 0.321081i | \(0.104046\pi\) | |||||||
\(284\) | −2.56934 | −0.152462 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.9249 | −0.764265 | ||||||||
\(287\) | 5.84501 | 0.345020 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.0452 | 1.70854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.6693 | 0.741412 | ||||||||
\(293\) | 16.6235 | 0.971153 | 0.485576 | − | 0.874194i | \(-0.338610\pi\) | ||||
0.485576 | + | 0.874194i | \(0.338610\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −18.8012 | −1.09280 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.2320 | 0.998225 | ||||||||
\(299\) | −10.2982 | −0.595561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.0336 | 2.19222 | ||||||||
\(302\) | −39.3429 | −2.26393 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.07827 | −0.233905 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1643 | 0.808402 | 0.404201 | − | 0.914670i | \(-0.367550\pi\) | ||||
0.404201 | + | 0.914670i | \(0.367550\pi\) | |||||||
\(308\) | 35.9897 | 2.05070 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.0500 | −0.853406 | −0.426703 | − | 0.904392i | \(-0.640325\pi\) | ||||
−0.426703 | + | 0.904392i | \(0.640325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.57476 | 0.202057 | 0.101029 | − | 0.994884i | \(-0.467787\pi\) | ||||
0.101029 | + | 0.994884i | \(0.467787\pi\) | |||||||
\(314\) | −18.5395 | −1.04624 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.8354 | 0.609539 | ||||||||
\(317\) | 12.7820 | 0.717907 | 0.358954 | − | 0.933355i | \(-0.383134\pi\) | ||||
0.358954 | + | 0.933355i | \(0.383134\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.49172 | 0.419456 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 44.9390 | 2.50435 | ||||||||
\(323\) | −20.0143 | −1.11363 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.3671 | 1.29418 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.02366 | −0.332601 | ||||||||
\(329\) | 26.0855 | 1.43814 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.70504 | 0.258612 | 0.129306 | − | 0.991605i | \(-0.458725\pi\) | ||||
0.129306 | + | 0.991605i | \(0.458725\pi\) | |||||||
\(332\) | 35.6704 | 1.95767 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.1121 | 0.717465 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4048 | 0.948098 | 0.474049 | − | 0.880499i | \(-0.342792\pi\) | ||||
0.474049 | + | 0.880499i | \(0.342792\pi\) | |||||||
\(338\) | −22.2896 | −1.21239 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.22545 | −0.0663618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.53364 | 0.352783 | ||||||||
\(344\) | −39.1961 | −2.11331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.9490 | 2.09391 | ||||||||
\(347\) | 14.0106 | 0.752130 | 0.376065 | − | 0.926593i | \(-0.377277\pi\) | ||||
0.376065 | + | 0.926593i | \(0.377277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.9459 | 1.92414 | 0.962069 | − | 0.272806i | \(-0.0879518\pi\) | ||||
0.962069 | + | 0.272806i | \(0.0879518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.5079 | 0.613373 | ||||||||
\(353\) | 8.80198 | 0.468482 | 0.234241 | − | 0.972179i | \(-0.424740\pi\) | ||||
0.234241 | + | 0.972179i | \(0.424740\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.01388 | −0.0537357 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.6009 | 0.665981 | ||||||||
\(359\) | −6.02962 | −0.318231 | −0.159116 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159116 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3004 | −0.542129 | ||||||||
\(362\) | −0.770472 | −0.0404951 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −23.0314 | −1.20717 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.7662 | −1.50158 | −0.750792 | − | 0.660539i | \(-0.770328\pi\) | ||||
−0.750792 | + | 0.660539i | \(0.770328\pi\) | |||||||
\(368\) | −7.59128 | −0.395723 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.9162 | −0.670574 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.6000 | −1.73974 | −0.869872 | − | 0.493278i | \(-0.835799\pi\) | ||||
−0.869872 | + | 0.493278i | \(0.835799\pi\) | |||||||
\(374\) | −46.7568 | −2.41774 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.8828 | −1.38637 | ||||||||
\(377\) | −4.79429 | −0.246918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.63403 | 0.238034 | 0.119017 | − | 0.992892i | \(-0.462026\pi\) | ||||
0.119017 | + | 0.992892i | \(0.462026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.15718 | 0.417358 | ||||||||
\(383\) | −12.9058 | −0.659453 | −0.329727 | − | 0.944076i | \(-0.606957\pi\) | ||||
−0.329727 | + | 0.944076i | \(0.606957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 57.1567 | 2.90920 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 36.7064 | 1.86349 | ||||||||
\(389\) | 17.5246 | 0.888532 | 0.444266 | − | 0.895895i | \(-0.353465\pi\) | ||||
0.444266 | + | 0.895895i | \(0.353465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.2546 | −1.88405 | ||||||||
\(392\) | 18.3848 | 0.928573 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.1593 | 1.77130 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.0176 | 1.35597 | 0.677987 | − | 0.735074i | \(-0.262853\pi\) | ||||
0.677987 | + | 0.735074i | \(0.262853\pi\) | |||||||
\(398\) | −26.6234 | −1.33451 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.9792 | 0.797965 | 0.398983 | − | 0.916958i | \(-0.369363\pi\) | ||||
0.398983 | + | 0.916958i | \(0.369363\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.784220 | 0.0390648 | ||||||||
\(404\) | −27.0032 | −1.34346 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.9212 | 1.03830 | ||||||||
\(407\) | 15.3578 | 0.761258 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.9962 | −1.53266 | −0.766331 | − | 0.642446i | \(-0.777920\pi\) | ||||
−0.766331 | + | 0.642446i | \(0.777920\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.5299 | 0.518771 | ||||||||
\(413\) | −24.7511 | −1.21792 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.36442 | −0.361070 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.3236 | 0.994061 | ||||||||
\(419\) | −25.9153 | −1.26605 | −0.633024 | − | 0.774132i | \(-0.718186\pi\) | ||||
−0.633024 | + | 0.774132i | \(0.718186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.92646 | 0.191364 | 0.0956821 | − | 0.995412i | \(-0.469497\pi\) | ||||
0.0956821 | + | 0.995412i | \(0.469497\pi\) | |||||||
\(422\) | 17.7319 | 0.863176 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.3109 | 0.646436 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.4132 | 1.08465 | ||||||||
\(428\) | −24.9392 | −1.20548 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.4632 | 1.70820 | 0.854101 | − | 0.520108i | \(-0.174108\pi\) | ||||
0.854101 | + | 0.520108i | \(0.174108\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0959 | −0.485178 | −0.242589 | − | 0.970129i | \(-0.577997\pi\) | ||||
−0.242589 | + | 0.970129i | \(0.577997\pi\) | |||||||
\(434\) | −3.42215 | −0.164269 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −46.9088 | −2.24652 | ||||||||
\(437\) | 16.1933 | 0.774632 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.10560 | 0.339132 | 0.169566 | − | 0.985519i | \(-0.445763\pi\) | ||||
0.169566 | + | 0.985519i | \(0.445763\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 29.9218 | 1.42323 | ||||||||
\(443\) | 20.6841 | 0.982733 | 0.491366 | − | 0.870953i | \(-0.336498\pi\) | ||||
0.491366 | + | 0.870953i | \(0.336498\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 18.3256 | 0.867744 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 41.7654 | 1.97323 | ||||||||
\(449\) | −19.4940 | −0.919980 | −0.459990 | − | 0.887924i | \(-0.652147\pi\) | ||||
−0.459990 | + | 0.887924i | \(0.652147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92042 | 0.231694 | ||||||||
\(452\) | 35.3461 | 1.66254 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.1657 | −1.41575 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.34194 | 0.203107 | 0.101554 | − | 0.994830i | \(-0.467619\pi\) | ||||
0.101554 | + | 0.994830i | \(0.467619\pi\) | |||||||
\(458\) | −34.0948 | −1.59315 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.7897 | −0.549102 | −0.274551 | − | 0.961573i | \(-0.588529\pi\) | ||||
−0.274551 | + | 0.961573i | \(0.588529\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.07870 | 0.421923 | 0.210962 | − | 0.977494i | \(-0.432341\pi\) | ||||
0.210962 | + | 0.977494i | \(0.432341\pi\) | |||||||
\(464\) | −3.53409 | −0.164066 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.7925 | 1.24114 | ||||||||
\(467\) | −34.9181 | −1.61582 | −0.807910 | − | 0.589307i | \(-0.799401\pi\) | ||||
−0.807910 | + | 0.589307i | \(0.799401\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.9634 | 1.61446 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25.5076 | 1.17408 | ||||||||
\(473\) | 32.0173 | 1.47216 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −83.3179 | −3.81887 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.2224 | −0.741996 | ||||||||
\(479\) | 8.64649 | 0.395068 | 0.197534 | − | 0.980296i | \(-0.436707\pi\) | ||||
0.197534 | + | 0.980296i | \(0.436707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.82814 | −0.448125 | ||||||||
\(482\) | −66.8734 | −3.04600 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.49373 | −0.386079 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.84462 | −0.128902 | −0.0644510 | − | 0.997921i | \(-0.520530\pi\) | ||||
−0.0644510 | + | 0.997921i | \(0.520530\pi\) | |||||||
\(488\) | −23.0983 | −1.04561 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.8041 | −1.66095 | −0.830473 | − | 0.557059i | \(-0.811930\pi\) | ||||
−0.830473 | + | 0.557059i | \(0.811930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.3437 | −0.781121 | ||||||||
\(494\) | −13.0060 | −0.585168 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.578084 | 0.0259567 | ||||||||
\(497\) | 2.53691 | 0.113796 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.85775 | 0.262229 | 0.131114 | − | 0.991367i | \(-0.458144\pi\) | ||||
0.131114 | + | 0.991367i | \(0.458144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.9759 | 1.29326 | ||||||||
\(503\) | −30.2874 | −1.35045 | −0.675223 | − | 0.737613i | \(-0.735953\pi\) | ||||
−0.675223 | + | 0.737613i | \(0.735953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 37.8304 | 1.68177 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −37.2848 | −1.65424 | ||||||||
\(509\) | −15.1430 | −0.671201 | −0.335601 | − | 0.942004i | \(-0.608939\pi\) | ||||
−0.335601 | + | 0.942004i | \(0.608939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5093 | −0.553380 | ||||||||
\(512\) | −15.3517 | −0.678457 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 48.9618 | 2.15961 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.9592 | 0.965765 | ||||||||
\(518\) | 42.8877 | 1.88438 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.0832 | −1.71227 | −0.856134 | − | 0.516754i | \(-0.827140\pi\) | ||||
−0.856134 | + | 0.516754i | \(0.827140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.7976 | 1.69650 | 0.848251 | − | 0.529594i | \(-0.177656\pi\) | ||||
0.848251 | + | 0.529594i | \(0.177656\pi\) | |||||||
\(524\) | 31.8296 | 1.39048 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.25449 | 0.229107 | ||||||||
\(527\) | 2.83698 | 0.123581 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.14224 | 0.310532 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 36.2155 | 1.57014 | ||||||||
\(533\) | −3.14880 | −0.136390 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −36.0320 | −1.55635 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 45.3796 | 1.95645 | ||||||||
\(539\) | −15.0176 | −0.646855 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2280 | 0.611710 | 0.305855 | − | 0.952078i | \(-0.401058\pi\) | ||||
0.305855 | + | 0.952078i | \(0.401058\pi\) | |||||||
\(542\) | −28.0716 | −1.20578 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −26.6414 | −1.14224 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.3229 | −1.68133 | −0.840663 | − | 0.541559i | \(-0.817834\pi\) | ||||
−0.840663 | + | 0.541559i | \(0.817834\pi\) | |||||||
\(548\) | −69.3452 | −2.96228 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.53873 | 0.321161 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.6986 | −0.454952 | ||||||||
\(554\) | −61.4662 | −2.61145 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −41.0896 | −1.74259 | ||||||||
\(557\) | 35.3849 | 1.49931 | 0.749654 | − | 0.661830i | \(-0.230220\pi\) | ||||
0.749654 | + | 0.661830i | \(0.230220\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.4893 | −0.866605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.7948 | −1.00372 | ||||||||
\(563\) | 15.0386 | 0.633800 | 0.316900 | − | 0.948459i | \(-0.397358\pi\) | ||||
0.316900 | + | 0.948459i | \(0.397358\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 74.9063 | 3.14855 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.61445 | −0.109700 | ||||||||
\(569\) | 2.72409 | 0.114200 | 0.0570998 | − | 0.998368i | \(-0.481815\pi\) | ||||
0.0570998 | + | 0.998368i | \(0.481815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6236 | 0.528282 | 0.264141 | − | 0.964484i | \(-0.414912\pi\) | ||||
0.264141 | + | 0.964484i | \(0.414912\pi\) | |||||||
\(572\) | −19.3882 | −0.810661 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.7406 | 0.573522 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5844 | 0.981831 | 0.490915 | − | 0.871207i | \(-0.336662\pi\) | ||||
0.490915 | + | 0.871207i | \(0.336662\pi\) | |||||||
\(578\) | 68.2803 | 2.84009 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −35.2201 | −1.46118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.8730 | −0.450315 | ||||||||
\(584\) | 12.8917 | 0.533461 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 39.0789 | 1.61434 | ||||||||
\(587\) | −22.6772 | −0.935988 | −0.467994 | − | 0.883732i | \(-0.655023\pi\) | ||||
−0.467994 | + | 0.883732i | \(0.655023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.23314 | −0.0508106 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.24477 | −0.297758 | ||||||||
\(593\) | −8.74287 | −0.359027 | −0.179513 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179513 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 25.8492 | 1.05882 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.2094 | −0.989994 | ||||||||
\(599\) | −16.3209 | −0.666854 | −0.333427 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333427 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2713 | 1.47954 | 0.739768 | − | 0.672862i | \(-0.234935\pi\) | ||||
0.739768 | + | 0.672862i | \(0.234935\pi\) | |||||||
\(602\) | 89.4105 | 3.64410 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −59.0170 | −2.40137 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.6820 | 0.677102 | 0.338551 | − | 0.940948i | \(-0.390063\pi\) | ||||
0.338551 | + | 0.940948i | \(0.390063\pi\) | |||||||
\(608\) | 11.5801 | 0.469636 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.0527 | −0.568511 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.7967 | −1.00153 | −0.500765 | − | 0.865583i | \(-0.666948\pi\) | ||||
−0.500765 | + | 0.865583i | \(0.666948\pi\) | |||||||
\(614\) | 33.2980 | 1.34380 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.6215 | 1.47552 | ||||||||
\(617\) | 27.9669 | 1.12591 | 0.562953 | − | 0.826489i | \(-0.309665\pi\) | ||||
0.562953 | + | 0.826489i | \(0.309665\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.2686 | 1.09602 | 0.548009 | − | 0.836473i | \(-0.315386\pi\) | ||||
0.548009 | + | 0.836473i | \(0.315386\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −35.3799 | −1.41861 | ||||||||
\(623\) | 1.00108 | 0.0401076 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.40365 | 0.335878 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −27.8104 | −1.10976 | ||||||||
\(629\) | −35.5541 | −1.41763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.2603 | 1.68235 | 0.841177 | − | 0.540759i | \(-0.181863\pi\) | ||||
0.841177 | + | 0.540759i | \(0.181863\pi\) | |||||||
\(632\) | 11.0256 | 0.438575 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.0482 | 1.19337 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.61045 | 0.380780 | ||||||||
\(638\) | 17.6118 | 0.697256 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −45.8456 | −1.81079 | −0.905396 | − | 0.424569i | \(-0.860426\pi\) | ||||
−0.905396 | + | 0.424569i | \(0.860426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.6710 | 1.84052 | 0.920261 | − | 0.391304i | \(-0.127976\pi\) | ||||
0.920261 | + | 0.391304i | \(0.127976\pi\) | |||||||
\(644\) | 67.4115 | 2.65639 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −47.0502 | −1.85117 | ||||||||
\(647\) | −12.1264 | −0.476740 | −0.238370 | − | 0.971174i | \(-0.576613\pi\) | ||||
−0.238370 | + | 0.971174i | \(0.576613\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.8359 | −0.817880 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 35.0521 | 1.37275 | ||||||||
\(653\) | −1.72017 | −0.0673154 | −0.0336577 | − | 0.999433i | \(-0.510716\pi\) | ||||
−0.0336577 | + | 0.999433i | \(0.510716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.32112 | −0.0906246 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 61.3226 | 2.39060 | ||||||||
\(659\) | −5.47947 | −0.213450 | −0.106725 | − | 0.994289i | \(-0.534036\pi\) | ||||
−0.106725 | + | 0.994289i | \(0.534036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.797448 | 0.0310171 | 0.0155086 | − | 0.999880i | \(-0.495063\pi\) | ||||
0.0155086 | + | 0.999880i | \(0.495063\pi\) | |||||||
\(662\) | 11.0607 | 0.429888 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 36.2966 | 1.40858 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0326 | 0.543344 | ||||||||
\(668\) | 19.6691 | 0.761020 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.8678 | 0.728384 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.3280 | 1.97855 | 0.989274 | − | 0.146074i | \(-0.0466639\pi\) | ||||
0.989274 | + | 0.146074i | \(0.0466639\pi\) | |||||||
\(674\) | 40.9156 | 1.57601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33.4358 | −1.28599 | ||||||||
\(677\) | 15.0929 | 0.580069 | 0.290034 | − | 0.957016i | \(-0.406333\pi\) | ||||
0.290034 | + | 0.957016i | \(0.406333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.2431 | −1.39088 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.88082 | −0.110312 | ||||||||
\(683\) | −10.8602 | −0.415555 | −0.207777 | − | 0.978176i | \(-0.566623\pi\) | ||||
−0.207777 | + | 0.978176i | \(0.566623\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.3595 | 0.586428 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.1036 | −0.575819 | ||||||||
\(689\) | 6.95814 | 0.265084 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.44552 | 0.321283 | 0.160641 | − | 0.987013i | \(-0.448644\pi\) | ||||
0.160641 | + | 0.987013i | \(0.448644\pi\) | |||||||
\(692\) | 58.4261 | 2.22103 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.9366 | 1.25026 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.3910 | −0.431466 | ||||||||
\(698\) | 84.5026 | 3.19847 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.9399 | −1.84843 | −0.924216 | − | 0.381869i | \(-0.875281\pi\) | ||||
−0.924216 | + | 0.381869i | \(0.875281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.4542 | 0.582865 | ||||||||
\(704\) | 35.1588 | 1.32510 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.6920 | 0.778752 | ||||||||
\(707\) | 26.6623 | 1.00274 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.7834 | 0.930762 | 0.465381 | − | 0.885111i | \(-0.345917\pi\) | ||||
0.465381 | + | 0.885111i | \(0.345917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.03168 | −0.0386639 | ||||||||
\(713\) | −2.29536 | −0.0859620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.9023 | 0.706410 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14.1746 | −0.528992 | ||||||||
\(719\) | 18.2171 | 0.679382 | 0.339691 | − | 0.940537i | \(-0.389678\pi\) | ||||
0.339691 | + | 0.940537i | \(0.389678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3970 | −0.387204 | ||||||||
\(722\) | −24.2146 | −0.901174 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.15576 | −0.0429534 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.6699 | −0.618253 | −0.309127 | − | 0.951021i | \(-0.600037\pi\) | ||||
−0.309127 | + | 0.951021i | \(0.600037\pi\) | |||||||
\(728\) | −23.4357 | −0.868586 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −74.1216 | −2.74149 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.0644 | −0.741094 | −0.370547 | − | 0.928814i | \(-0.620830\pi\) | ||||
−0.370547 | + | 0.928814i | \(0.620830\pi\) | |||||||
\(734\) | −67.6245 | −2.49606 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.5552 | 0.794535 | ||||||||
\(737\) | 29.4328 | 1.08417 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.0571 | −1.25281 | −0.626406 | − | 0.779497i | \(-0.715475\pi\) | ||||
−0.626406 | + | 0.779497i | \(0.715475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −30.3637 | −1.11469 | ||||||||
\(743\) | −38.5355 | −1.41373 | −0.706865 | − | 0.707348i | \(-0.749891\pi\) | ||||
−0.706865 | + | 0.707348i | \(0.749891\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −78.9880 | −2.89195 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −70.1383 | −2.56451 | ||||||||
\(749\) | 24.6244 | 0.899754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0351 | −1.31494 | −0.657470 | − | 0.753481i | \(-0.728373\pi\) | ||||
−0.657470 | + | 0.753481i | \(0.728373\pi\) | |||||||
\(752\) | −10.3589 | −0.377749 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.2706 | −0.410449 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.0131 | −1.27257 | −0.636287 | − | 0.771453i | \(-0.719530\pi\) | ||||
−0.636287 | + | 0.771453i | \(0.719530\pi\) | |||||||
\(758\) | 10.8938 | 0.395681 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3577 | −1.13672 | −0.568358 | − | 0.822781i | \(-0.692421\pi\) | ||||
−0.568358 | + | 0.822781i | \(0.692421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.3166 | 1.67678 | ||||||||
\(764\) | 12.2363 | 0.442694 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.3392 | −1.09620 | ||||||||
\(767\) | 13.3338 | 0.481456 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.39815 | 0.0864793 | 0.0432397 | − | 0.999065i | \(-0.486232\pi\) | ||||
0.0432397 | + | 0.999065i | \(0.486232\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 85.7388 | 3.08581 | ||||||||
\(773\) | −10.9226 | −0.392858 | −0.196429 | − | 0.980518i | \(-0.562935\pi\) | ||||
−0.196429 | + | 0.980518i | \(0.562935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 37.3508 | 1.34082 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.1973 | 1.47700 | ||||||||
\(779\) | 4.95130 | 0.177399 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.13561 | 0.0764181 | ||||||||
\(782\) | −87.5792 | −3.13183 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.08430 | 0.253011 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.5724 | −0.412511 | −0.206256 | − | 0.978498i | \(-0.566128\pi\) | ||||
−0.206256 | + | 0.978498i | \(0.566128\pi\) | |||||||
\(788\) | 52.7412 | 1.87883 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.8999 | −1.24090 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0744 | −0.428773 | ||||||||
\(794\) | 63.5137 | 2.25402 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.9369 | −1.41553 | ||||||||
\(797\) | 21.8923 | 0.775467 | 0.387733 | − | 0.921772i | \(-0.373258\pi\) | ||||
0.387733 | + | 0.921772i | \(0.373258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −50.8367 | −1.79847 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 37.5645 | 1.32645 | ||||||||
\(803\) | −10.5306 | −0.371615 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.84357 | 0.0649369 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −27.4772 | −0.966646 | ||||||||
\(809\) | 21.5498 | 0.757652 | 0.378826 | − | 0.925468i | \(-0.376328\pi\) | ||||
0.378826 | + | 0.925468i | \(0.376328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.9615 | −1.54370 | −0.771848 | − | 0.635807i | \(-0.780667\pi\) | ||||
−0.771848 | + | 0.635807i | \(0.780667\pi\) | |||||||
\(812\) | 31.3831 | 1.10133 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 36.1036 | 1.26543 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 32.2182 | 1.12717 | ||||||||
\(818\) | −72.8667 | −2.54772 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −33.5061 | −1.16937 | −0.584686 | − | 0.811260i | \(-0.698782\pi\) | ||||
−0.584686 | + | 0.811260i | \(0.698782\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.9860 | −1.95155 | −0.975774 | − | 0.218781i | \(-0.929792\pi\) | ||||
−0.975774 | + | 0.218781i | \(0.929792\pi\) | |||||||
\(824\) | 10.7148 | 0.373266 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.1857 | −2.02454 | ||||||||
\(827\) | −40.8100 | −1.41910 | −0.709552 | − | 0.704653i | \(-0.751103\pi\) | ||||
−0.709552 | + | 0.704653i | \(0.751103\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.122914 | 0.00426896 | 0.00213448 | − | 0.999998i | \(-0.499321\pi\) | ||||
0.00213448 | + | 0.999998i | \(0.499321\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.4997 | −0.780036 | ||||||||
\(833\) | 34.7666 | 1.20459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 30.4868 | 1.05441 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −60.9226 | −2.10454 | ||||||||
\(839\) | −14.8083 | −0.511241 | −0.255620 | − | 0.966777i | \(-0.582280\pi\) | ||||
−0.255620 | + | 0.966777i | \(0.582280\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4672 | −0.774731 | ||||||||
\(842\) | 9.23045 | 0.318102 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26.5990 | 0.915577 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.38651 | 0.288164 | ||||||||
\(848\) | 5.12916 | 0.176136 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.7664 | 0.986098 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.26474 | −0.248740 | −0.124370 | − | 0.992236i | \(-0.539691\pi\) | ||||
−0.124370 | + | 0.992236i | \(0.539691\pi\) | |||||||
\(854\) | 52.6897 | 1.80301 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.3770 | −0.867367 | ||||||||
\(857\) | −26.8175 | −0.916068 | −0.458034 | − | 0.888935i | \(-0.651446\pi\) | ||||
−0.458034 | + | 0.888935i | \(0.651446\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.6038 | −0.702991 | −0.351496 | − | 0.936190i | \(-0.614327\pi\) | ||||
−0.351496 | + | 0.936190i | \(0.614327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 83.3679 | 2.83952 | ||||||||
\(863\) | 13.7488 | 0.468015 | 0.234008 | − | 0.972235i | \(-0.424816\pi\) | ||||
0.234008 | + | 0.972235i | \(0.424816\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.7338 | −0.806506 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.13346 | −0.174241 | ||||||||
\(869\) | −9.00627 | −0.305517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.8353 | −0.638211 | ||||||||
\(872\) | −47.7323 | −1.61642 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.0678 | 1.28766 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.0430 | −0.744339 | −0.372170 | − | 0.928165i | \(-0.621386\pi\) | ||||
−0.372170 | + | 0.928165i | \(0.621386\pi\) | |||||||
\(878\) | 16.7041 | 0.563735 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.03929 | 0.304541 | 0.152271 | − | 0.988339i | \(-0.451341\pi\) | ||||
0.152271 | + | 0.988339i | \(0.451341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.60120 | 0.0538848 | 0.0269424 | − | 0.999637i | \(-0.491423\pi\) | ||||
0.0269424 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(884\) | 44.8847 | 1.50963 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48.6249 | 1.63358 | ||||||||
\(887\) | 17.4253 | 0.585083 | 0.292541 | − | 0.956253i | \(-0.405499\pi\) | ||||
0.292541 | + | 0.956253i | \(0.405499\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.8141 | 1.23471 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.4897 | 0.920423 | ||||||||
\(893\) | 22.0970 | 0.739448 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 70.8427 | 2.36669 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −45.8272 | −1.52927 | ||||||||
\(899\) | −1.06860 | −0.0356397 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1716 | 0.838588 | ||||||||
\(902\) | 11.5671 | 0.385141 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 35.9666 | 1.19623 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8690 | 0.692942 | 0.346471 | − | 0.938061i | \(-0.387380\pi\) | ||||
0.346471 | + | 0.938061i | \(0.387380\pi\) | |||||||
\(908\) | −45.2506 | −1.50169 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49.1748 | −1.62923 | −0.814617 | − | 0.580000i | \(-0.803053\pi\) | ||||
−0.814617 | + | 0.580000i | \(0.803053\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.6489 | −0.981234 | ||||||||
\(914\) | 10.2072 | 0.337623 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.1445 | −1.68986 | ||||||||
\(917\) | −31.4278 | −1.03784 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1959 | −0.369318 | −0.184659 | − | 0.982803i | \(-0.559118\pi\) | ||||
−0.184659 | + | 0.982803i | \(0.559118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −27.7156 | −0.912765 | ||||||||
\(923\) | −1.36667 | −0.0449846 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 21.3425 | 0.701357 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.0349 | 0.329413 | ||||||||
\(929\) | −48.2290 | −1.58234 | −0.791171 | − | 0.611596i | \(-0.790528\pi\) | ||||
−0.791171 | + | 0.611596i | \(0.790528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.1119 | −0.495271 | ||||||||
\(932\) | 40.1906 | 1.31649 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −82.0866 | −2.68596 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.5397 | −1.65106 | −0.825529 | − | 0.564359i | \(-0.809123\pi\) | ||||
−0.825529 | + | 0.564359i | \(0.809123\pi\) | |||||||
\(938\) | 82.1930 | 2.68370 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.1644 | 1.24412 | 0.622061 | − | 0.782969i | \(-0.286295\pi\) | ||||
0.622061 | + | 0.782969i | \(0.286295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.21634 | 0.300125 | ||||||||
\(944\) | 9.82896 | 0.319906 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 75.2672 | 2.44715 | ||||||||
\(947\) | 24.5190 | 0.796759 | 0.398380 | − | 0.917221i | \(-0.369573\pi\) | ||||
0.398380 | + | 0.917221i | \(0.369573\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.73897 | 0.218756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −84.7806 | −2.74775 | ||||||||
\(953\) | 13.0019 | 0.421173 | 0.210586 | − | 0.977575i | \(-0.432463\pi\) | ||||
0.210586 | + | 0.977575i | \(0.432463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −24.3347 | −0.787041 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.3264 | 0.656717 | ||||||||
\(959\) | 68.4698 | 2.21101 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8252 | −0.994361 | ||||||||
\(962\) | −23.1043 | −0.744912 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −100.315 | −3.23091 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.3212 | 1.39312 | 0.696559 | − | 0.717500i | \(-0.254714\pi\) | ||||
0.696559 | + | 0.717500i | \(0.254714\pi\) | |||||||
\(968\) | −8.64284 | −0.277791 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.5324 | 0.947741 | 0.473870 | − | 0.880595i | \(-0.342857\pi\) | ||||
0.473870 | + | 0.880595i | \(0.342857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.5709 | 1.30064 | ||||||||
\(974\) | −6.68721 | −0.214272 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.90056 | −0.284900 | ||||||||
\(977\) | −60.6153 | −1.93926 | −0.969628 | − | 0.244583i | \(-0.921349\pi\) | ||||
−0.969628 | + | 0.244583i | \(0.921349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.842729 | 0.0269337 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −86.5202 | −2.76097 | ||||||||
\(983\) | −40.2796 | −1.28472 | −0.642359 | − | 0.766404i | \(-0.722044\pi\) | ||||
−0.642359 | + | 0.766404i | \(0.722044\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −40.7721 | −1.29845 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.5099 | −0.620692 | ||||||||
\(989\) | 59.9709 | 1.90696 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.1495 | 1.21186 | 0.605930 | − | 0.795518i | \(-0.292801\pi\) | ||||
0.605930 | + | 0.795518i | \(0.292801\pi\) | |||||||
\(992\) | −1.64145 | −0.0521161 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.96384 | 0.189162 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.5777 | −0.841724 | −0.420862 | − | 0.907125i | \(-0.638272\pi\) | ||||
−0.420862 | + | 0.907125i | \(0.638272\pi\) | |||||||
\(998\) | 13.7706 | 0.435900 | ||||||||
\(999\) | 0 | 0 |
(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 | 5625.2.a.bd.1.7 | 8 | ||
3.2 | odd | 2 | 1875.2.a.m.1.2 | 8 | |||
5.4 | even | 2 | 5625.2.a.t.1.2 | 8 | |||
15.2 | even | 4 | 1875.2.b.h.1249.2 | 16 | |||
15.8 | even | 4 | 1875.2.b.h.1249.15 | 16 | |||
15.14 | odd | 2 | 1875.2.a.p.1.7 | 8 | |||
25.2 | odd | 20 | 225.2.m.b.154.4 | 16 | |||
25.13 | odd | 20 | 225.2.m.b.19.4 | 16 | |||
75.2 | even | 20 | 75.2.i.a.4.1 | ✓ | 16 | ||
75.11 | odd | 10 | 375.2.g.e.226.1 | 16 | |||
75.14 | odd | 10 | 375.2.g.d.226.4 | 16 | |||
75.23 | even | 20 | 375.2.i.c.274.4 | 16 | |||
75.38 | even | 20 | 75.2.i.a.19.1 | yes | 16 | ||
75.41 | odd | 10 | 375.2.g.e.151.1 | 16 | |||
75.59 | odd | 10 | 375.2.g.d.151.4 | 16 | |||
75.62 | even | 20 | 375.2.i.c.349.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.1 | ✓ | 16 | 75.2 | even | 20 | ||
75.2.i.a.19.1 | yes | 16 | 75.38 | even | 20 | ||
225.2.m.b.19.4 | 16 | 25.13 | odd | 20 | |||
225.2.m.b.154.4 | 16 | 25.2 | odd | 20 | |||
375.2.g.d.151.4 | 16 | 75.59 | odd | 10 | |||
375.2.g.d.226.4 | 16 | 75.14 | odd | 10 | |||
375.2.g.e.151.1 | 16 | 75.41 | odd | 10 | |||
375.2.g.e.226.1 | 16 | 75.11 | odd | 10 | |||
375.2.i.c.274.4 | 16 | 75.23 | even | 20 | |||
375.2.i.c.349.4 | 16 | 75.62 | even | 20 | |||
1875.2.a.m.1.2 | 8 | 3.2 | odd | 2 | |||
1875.2.a.p.1.7 | 8 | 15.14 | odd | 2 | |||
1875.2.b.h.1249.2 | 16 | 15.2 | even | 4 | |||
1875.2.b.h.1249.15 | 16 | 15.8 | even | 4 | |||
5625.2.a.t.1.2 | 8 | 5.4 | even | 2 | |||
5625.2.a.bd.1.7 | 8 | 1.1 | even | 1 | trivial |