Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5265,2,Mod(1,5265)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5265, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("5265.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5265 = 3^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5265.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: | \(42.0412366642\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 11x^{6} - 2x^{5} + 38x^{4} + 14x^{3} - 39x^{2} - 22x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.46324\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5265.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46324 | −1.03467 | −0.517333 | − | 0.855784i | \(-0.673075\pi\) | ||||
−0.517333 | + | 0.855784i | \(0.673075\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.141066 | 0.0705330 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.95241 | −1.87183 | −0.935917 | − | 0.352220i | \(-0.885427\pi\) | ||||
−0.935917 | + | 0.352220i | \(0.885427\pi\) | |||||||
\(8\) | 2.72006 | 0.961688 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.46324 | −0.462717 | ||||||||
\(11\) | 1.59098 | 0.479700 | 0.239850 | − | 0.970810i | \(-0.422902\pi\) | ||||
0.239850 | + | 0.970810i | \(0.422902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 7.24655 | 1.93672 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.26223 | −1.06556 | ||||||||
\(17\) | 5.55131 | 1.34639 | 0.673195 | − | 0.739465i | \(-0.264922\pi\) | ||||
0.673195 | + | 0.739465i | \(0.264922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.74454 | −1.08847 | −0.544236 | − | 0.838932i | \(-0.683181\pi\) | ||||
−0.544236 | + | 0.838932i | \(0.683181\pi\) | |||||||
\(20\) | 0.141066 | 0.0315433 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.32799 | −0.496329 | ||||||||
\(23\) | −0.0764816 | −0.0159475 | −0.00797376 | − | 0.999968i | \(-0.502538\pi\) | ||||
−0.00797376 | + | 0.999968i | \(0.502538\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.46324 | 0.286965 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.698616 | −0.132026 | ||||||||
\(29\) | −3.53848 | −0.657079 | −0.328539 | − | 0.944490i | \(-0.606556\pi\) | ||||
−0.328539 | + | 0.944490i | \(0.606556\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.59217 | 0.285962 | 0.142981 | − | 0.989725i | \(-0.454331\pi\) | ||||
0.142981 | + | 0.989725i | \(0.454331\pi\) | |||||||
\(32\) | 0.796535 | 0.140809 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.12288 | −1.39306 | ||||||||
\(35\) | −4.95241 | −0.837110 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.13079 | 0.679099 | 0.339549 | − | 0.940588i | \(-0.389725\pi\) | ||||
0.339549 | + | 0.940588i | \(0.389725\pi\) | |||||||
\(38\) | 6.94240 | 1.12621 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.72006 | 0.430080 | ||||||||
\(41\) | 4.90631 | 0.766237 | 0.383119 | − | 0.923699i | \(-0.374850\pi\) | ||||
0.383119 | + | 0.923699i | \(0.374850\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.71684 | 0.719311 | 0.359656 | − | 0.933085i | \(-0.382894\pi\) | ||||
0.359656 | + | 0.933085i | \(0.382894\pi\) | |||||||
\(44\) | 0.224434 | 0.0338347 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.111911 | 0.0165003 | ||||||||
\(47\) | −11.5366 | −1.68279 | −0.841395 | − | 0.540421i | \(-0.818265\pi\) | ||||
−0.841395 | + | 0.540421i | \(0.818265\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.5264 | 2.50377 | ||||||||
\(50\) | −1.46324 | −0.206933 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.141066 | −0.0195623 | ||||||||
\(53\) | 1.29315 | 0.177628 | 0.0888139 | − | 0.996048i | \(-0.471692\pi\) | ||||
0.0888139 | + | 0.996048i | \(0.471692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.59098 | 0.214528 | ||||||||
\(56\) | −13.4709 | −1.80012 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.17764 | 0.679857 | ||||||||
\(59\) | −4.66770 | −0.607683 | −0.303841 | − | 0.952723i | \(-0.598269\pi\) | ||||
−0.303841 | + | 0.952723i | \(0.598269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.6244 | −1.36032 | −0.680160 | − | 0.733063i | \(-0.738090\pi\) | ||||
−0.680160 | + | 0.733063i | \(0.738090\pi\) | |||||||
\(62\) | −2.32972 | −0.295875 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.35894 | 0.919868 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.55688 | −0.190203 | −0.0951014 | − | 0.995468i | \(-0.530318\pi\) | ||||
−0.0951014 | + | 0.995468i | \(0.530318\pi\) | |||||||
\(68\) | 0.783100 | 0.0949649 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.24655 | 0.866129 | ||||||||
\(71\) | 2.51438 | 0.298402 | 0.149201 | − | 0.988807i | \(-0.452330\pi\) | ||||
0.149201 | + | 0.988807i | \(0.452330\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.90174 | 0.339624 | 0.169812 | − | 0.985477i | \(-0.445684\pi\) | ||||
0.169812 | + | 0.985477i | \(0.445684\pi\) | |||||||
\(74\) | −6.04434 | −0.702640 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.669293 | −0.0767732 | ||||||||
\(77\) | −7.87921 | −0.897919 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.32589 | 0.374192 | 0.187096 | − | 0.982342i | \(-0.440092\pi\) | ||||
0.187096 | + | 0.982342i | \(0.440092\pi\) | |||||||
\(80\) | −4.26223 | −0.476532 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.17911 | −0.792800 | ||||||||
\(83\) | 5.35683 | 0.587988 | 0.293994 | − | 0.955807i | \(-0.405015\pi\) | ||||
0.293994 | + | 0.955807i | \(0.405015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.55131 | 0.602124 | ||||||||
\(86\) | −6.90186 | −0.744247 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.32758 | 0.461322 | ||||||||
\(89\) | 0.225989 | 0.0239548 | 0.0119774 | − | 0.999928i | \(-0.496187\pi\) | ||||
0.0119774 | + | 0.999928i | \(0.496187\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.95241 | 0.519154 | ||||||||
\(92\) | −0.0107889 | −0.00112483 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 16.8808 | 1.74112 | ||||||||
\(95\) | −4.74454 | −0.486780 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.8550 | 1.91444 | 0.957219 | − | 0.289363i | \(-0.0934435\pi\) | ||||
0.957219 | + | 0.289363i | \(0.0934435\pi\) | |||||||
\(98\) | −25.6452 | −2.59056 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.141066 | 0.0141066 | ||||||||
\(101\) | 10.3079 | 1.02567 | 0.512837 | − | 0.858486i | \(-0.328594\pi\) | ||||
0.512837 | + | 0.858486i | \(0.328594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.65848 | −0.261948 | −0.130974 | − | 0.991386i | \(-0.541810\pi\) | ||||
−0.130974 | + | 0.991386i | \(0.541810\pi\) | |||||||
\(104\) | −2.72006 | −0.266724 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.89219 | −0.183785 | ||||||||
\(107\) | 17.5939 | 1.70087 | 0.850433 | − | 0.526084i | \(-0.176340\pi\) | ||||
0.850433 | + | 0.526084i | \(0.176340\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.2053 | −1.64797 | −0.823985 | − | 0.566612i | \(-0.808254\pi\) | ||||
−0.823985 | + | 0.566612i | \(0.808254\pi\) | |||||||
\(110\) | −2.32799 | −0.221965 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 21.1083 | 1.99455 | ||||||||
\(113\) | 16.3236 | 1.53560 | 0.767799 | − | 0.640690i | \(-0.221352\pi\) | ||||
0.767799 | + | 0.640690i | \(0.221352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0764816 | −0.00713195 | ||||||||
\(116\) | −0.499159 | −0.0463457 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.82996 | 0.628748 | ||||||||
\(119\) | −27.4923 | −2.52022 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.46877 | −0.769888 | ||||||||
\(122\) | 15.5461 | 1.40748 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.224601 | 0.0201698 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1380 | −0.988342 | −0.494171 | − | 0.869365i | \(-0.664528\pi\) | ||||
−0.494171 | + | 0.869365i | \(0.664528\pi\) | |||||||
\(128\) | −12.3610 | −1.09256 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.46324 | 0.128334 | ||||||||
\(131\) | −9.15691 | −0.800043 | −0.400022 | − | 0.916506i | \(-0.630997\pi\) | ||||
−0.400022 | + | 0.916506i | \(0.630997\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23.4969 | 2.03744 | ||||||||
\(134\) | 2.27808 | 0.196796 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0999 | 1.29481 | ||||||||
\(137\) | −14.3061 | −1.22225 | −0.611125 | − | 0.791534i | \(-0.709283\pi\) | ||||
−0.611125 | + | 0.791534i | \(0.709283\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.68341 | 0.227604 | 0.113802 | − | 0.993503i | \(-0.463697\pi\) | ||||
0.113802 | + | 0.993503i | \(0.463697\pi\) | |||||||
\(140\) | −0.698616 | −0.0590439 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.67913 | −0.308746 | ||||||||
\(143\) | −1.59098 | −0.133045 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.53848 | −0.293855 | ||||||||
\(146\) | −4.24594 | −0.351397 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.582715 | 0.0478988 | ||||||||
\(149\) | 8.10911 | 0.664324 | 0.332162 | − | 0.943222i | \(-0.392222\pi\) | ||||
0.332162 | + | 0.943222i | \(0.392222\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.49289 | −0.772520 | −0.386260 | − | 0.922390i | \(-0.626233\pi\) | ||||
−0.386260 | + | 0.922390i | \(0.626233\pi\) | |||||||
\(152\) | −12.9055 | −1.04677 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 11.5292 | 0.929046 | ||||||||
\(155\) | 1.59217 | 0.127886 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.37156 | −0.109463 | −0.0547314 | − | 0.998501i | \(-0.517430\pi\) | ||||
−0.0547314 | + | 0.998501i | \(0.517430\pi\) | |||||||
\(158\) | −4.86657 | −0.387164 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.796535 | 0.0629716 | ||||||||
\(161\) | 0.378768 | 0.0298511 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.03430 | −0.629295 | −0.314648 | − | 0.949209i | \(-0.601886\pi\) | ||||
−0.314648 | + | 0.949209i | \(0.601886\pi\) | |||||||
\(164\) | 0.692114 | 0.0540450 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.83832 | −0.608371 | ||||||||
\(167\) | −23.4981 | −1.81834 | −0.909171 | − | 0.416424i | \(-0.863283\pi\) | ||||
−0.909171 | + | 0.416424i | \(0.863283\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −8.12288 | −0.622997 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.665386 | 0.0507352 | ||||||||
\(173\) | −1.84099 | −0.139968 | −0.0699839 | − | 0.997548i | \(-0.522295\pi\) | ||||
−0.0699839 | + | 0.997548i | \(0.522295\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.95241 | −0.374367 | ||||||||
\(176\) | −6.78115 | −0.511148 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.330676 | −0.0247852 | ||||||||
\(179\) | 12.4946 | 0.933888 | 0.466944 | − | 0.884287i | \(-0.345355\pi\) | ||||
0.466944 | + | 0.884287i | \(0.345355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.3250 | −1.73374 | −0.866868 | − | 0.498538i | \(-0.833870\pi\) | ||||
−0.866868 | + | 0.498538i | \(0.833870\pi\) | |||||||
\(182\) | −7.24655 | −0.537150 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.208035 | −0.0153365 | ||||||||
\(185\) | 4.13079 | 0.303702 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.83204 | 0.645863 | ||||||||
\(188\) | −1.62742 | −0.118692 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.94240 | 0.503654 | ||||||||
\(191\) | −19.5264 | −1.41288 | −0.706439 | − | 0.707774i | \(-0.749700\pi\) | ||||
−0.706439 | + | 0.707774i | \(0.749700\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.3207 | 1.67866 | 0.839332 | − | 0.543620i | \(-0.182947\pi\) | ||||
0.839332 | + | 0.543620i | \(0.182947\pi\) | |||||||
\(194\) | −27.5894 | −1.98080 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.47237 | 0.176598 | ||||||||
\(197\) | −9.68456 | −0.689996 | −0.344998 | − | 0.938603i | \(-0.612120\pi\) | ||||
−0.344998 | + | 0.938603i | \(0.612120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.9358 | −0.916993 | −0.458497 | − | 0.888696i | \(-0.651612\pi\) | ||||
−0.458497 | + | 0.888696i | \(0.651612\pi\) | |||||||
\(200\) | 2.72006 | 0.192338 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.0829 | −1.06123 | ||||||||
\(203\) | 17.5240 | 1.22994 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.90631 | 0.342672 | ||||||||
\(206\) | 3.88999 | 0.271028 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.26223 | 0.295533 | ||||||||
\(209\) | −7.54850 | −0.522140 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0435 | 1.17332 | 0.586661 | − | 0.809833i | \(-0.300442\pi\) | ||||
0.586661 | + | 0.809833i | \(0.300442\pi\) | |||||||
\(212\) | 0.182419 | 0.0125286 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −25.7441 | −1.75983 | ||||||||
\(215\) | 4.71684 | 0.321686 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.88508 | −0.535274 | ||||||||
\(218\) | 25.1755 | 1.70510 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.224434 | 0.0151313 | ||||||||
\(221\) | −5.55131 | −0.373421 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2204 | 0.684407 | 0.342203 | − | 0.939626i | \(-0.388827\pi\) | ||||
0.342203 | + | 0.939626i | \(0.388827\pi\) | |||||||
\(224\) | −3.94476 | −0.263571 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.8854 | −1.58883 | ||||||||
\(227\) | −21.9465 | −1.45664 | −0.728319 | − | 0.685238i | \(-0.759698\pi\) | ||||
−0.728319 | + | 0.685238i | \(0.759698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.2117 | −1.53387 | −0.766937 | − | 0.641722i | \(-0.778220\pi\) | ||||
−0.766937 | + | 0.641722i | \(0.778220\pi\) | |||||||
\(230\) | 0.111911 | 0.00737918 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.62488 | −0.631905 | ||||||||
\(233\) | 14.7926 | 0.969096 | 0.484548 | − | 0.874765i | \(-0.338984\pi\) | ||||
0.484548 | + | 0.874765i | \(0.338984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.5366 | −0.752566 | ||||||||
\(236\) | −0.658453 | −0.0428617 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 40.2278 | 2.60758 | ||||||||
\(239\) | 2.62092 | 0.169533 | 0.0847666 | − | 0.996401i | \(-0.472986\pi\) | ||||
0.0847666 | + | 0.996401i | \(0.472986\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.32645 | −0.278691 | −0.139346 | − | 0.990244i | \(-0.544500\pi\) | ||||
−0.139346 | + | 0.990244i | \(0.544500\pi\) | |||||||
\(242\) | 12.3918 | 0.796577 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.49875 | −0.0959475 | ||||||||
\(245\) | 17.5264 | 1.11972 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.74454 | 0.301888 | ||||||||
\(248\) | 4.33081 | 0.275006 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.46324 | −0.0925433 | ||||||||
\(251\) | −10.8607 | −0.685520 | −0.342760 | − | 0.939423i | \(-0.611362\pi\) | ||||
−0.342760 | + | 0.939423i | \(0.611362\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.121681 | −0.00765002 | ||||||||
\(254\) | 16.2976 | 1.02260 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.36914 | 0.210571 | ||||||||
\(257\) | −7.01308 | −0.437464 | −0.218732 | − | 0.975785i | \(-0.570192\pi\) | ||||
−0.218732 | + | 0.975785i | \(0.570192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.4574 | −1.27116 | ||||||||
\(260\) | −0.141066 | −0.00874854 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.3987 | 0.827777 | ||||||||
\(263\) | 8.84407 | 0.545349 | 0.272674 | − | 0.962106i | \(-0.412092\pi\) | ||||
0.272674 | + | 0.962106i | \(0.412092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.29315 | 0.0794375 | ||||||||
\(266\) | −34.3816 | −2.10807 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.219622 | −0.0134156 | ||||||||
\(269\) | −25.3530 | −1.54580 | −0.772899 | − | 0.634529i | \(-0.781194\pi\) | ||||
−0.772899 | + | 0.634529i | \(0.781194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7057 | 1.25778 | 0.628892 | − | 0.777493i | \(-0.283509\pi\) | ||||
0.628892 | + | 0.777493i | \(0.283509\pi\) | |||||||
\(272\) | −23.6610 | −1.43466 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.9332 | 1.26462 | ||||||||
\(275\) | 1.59098 | 0.0959400 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1257 | 1.20924 | 0.604620 | − | 0.796514i | \(-0.293325\pi\) | ||||
0.604620 | + | 0.796514i | \(0.293325\pi\) | |||||||
\(278\) | −3.92647 | −0.235494 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.4709 | −0.805038 | ||||||||
\(281\) | −14.2406 | −0.849523 | −0.424762 | − | 0.905305i | \(-0.639642\pi\) | ||||
−0.424762 | + | 0.905305i | \(0.639642\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.4221 | 1.57063 | 0.785315 | − | 0.619096i | \(-0.212501\pi\) | ||||
0.785315 | + | 0.619096i | \(0.212501\pi\) | |||||||
\(284\) | 0.354693 | 0.0210472 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.32799 | 0.137657 | ||||||||
\(287\) | −24.2981 | −1.43427 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.8170 | 0.812765 | ||||||||
\(290\) | 5.17764 | 0.304041 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.409337 | 0.0239547 | ||||||||
\(293\) | 17.0177 | 0.994183 | 0.497091 | − | 0.867698i | \(-0.334401\pi\) | ||||
0.497091 | + | 0.867698i | \(0.334401\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.66770 | −0.271764 | ||||||||
\(296\) | 11.2360 | 0.653081 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.8656 | −0.687354 | ||||||||
\(299\) | 0.0764816 | 0.00442304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.3597 | −1.34643 | ||||||||
\(302\) | 13.8904 | 0.799300 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.2223 | 1.15983 | ||||||||
\(305\) | −10.6244 | −0.608354 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3829 | 0.992095 | 0.496048 | − | 0.868295i | \(-0.334784\pi\) | ||||
0.496048 | + | 0.868295i | \(0.334784\pi\) | |||||||
\(308\) | −1.11149 | −0.0633329 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.32972 | −0.132319 | ||||||||
\(311\) | −13.6360 | −0.773225 | −0.386612 | − | 0.922242i | \(-0.626355\pi\) | ||||
−0.386612 | + | 0.922242i | \(0.626355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.12157 | 0.459058 | 0.229529 | − | 0.973302i | \(-0.426281\pi\) | ||||
0.229529 | + | 0.973302i | \(0.426281\pi\) | |||||||
\(314\) | 2.00693 | 0.113257 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.469170 | 0.0263929 | ||||||||
\(317\) | −18.6219 | −1.04591 | −0.522955 | − | 0.852361i | \(-0.675170\pi\) | ||||
−0.522955 | + | 0.852361i | \(0.675170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.62967 | −0.315201 | ||||||||
\(320\) | 7.35894 | 0.411378 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.554228 | −0.0308859 | ||||||||
\(323\) | −26.3384 | −1.46551 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 11.7561 | 0.651110 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.3455 | 0.736881 | ||||||||
\(329\) | 57.1341 | 3.14990 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.7903 | −1.58246 | −0.791229 | − | 0.611519i | \(-0.790559\pi\) | ||||
−0.791229 | + | 0.611519i | \(0.790559\pi\) | |||||||
\(332\) | 0.755666 | 0.0414726 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 34.3834 | 1.88138 | ||||||||
\(335\) | −1.55688 | −0.0850613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8343 | −0.644658 | −0.322329 | − | 0.946628i | \(-0.604466\pi\) | ||||
−0.322329 | + | 0.946628i | \(0.604466\pi\) | |||||||
\(338\) | −1.46324 | −0.0795897 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.783100 | 0.0424696 | ||||||||
\(341\) | 2.53312 | 0.137176 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −52.1308 | −2.81480 | ||||||||
\(344\) | 12.8301 | 0.691753 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.69380 | 0.144820 | ||||||||
\(347\) | −31.9068 | −1.71285 | −0.856423 | − | 0.516275i | \(-0.827318\pi\) | ||||
−0.856423 | + | 0.516275i | \(0.827318\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.2577 | 1.67319 | 0.836594 | − | 0.547824i | \(-0.184544\pi\) | ||||
0.836594 | + | 0.547824i | \(0.184544\pi\) | |||||||
\(350\) | 7.24655 | 0.387345 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.26727 | 0.0675459 | ||||||||
\(353\) | −10.2084 | −0.543336 | −0.271668 | − | 0.962391i | \(-0.587575\pi\) | ||||
−0.271668 | + | 0.962391i | \(0.587575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.51438 | 0.133449 | ||||||||
\(356\) | 0.0318794 | 0.00168960 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.2825 | −0.966261 | ||||||||
\(359\) | −8.03454 | −0.424047 | −0.212023 | − | 0.977265i | \(-0.568005\pi\) | ||||
−0.212023 | + | 0.977265i | \(0.568005\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51068 | 0.184773 | ||||||||
\(362\) | 34.1301 | 1.79384 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.698616 | 0.0366174 | ||||||||
\(365\) | 2.90174 | 0.151884 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5639 | −1.23002 | −0.615012 | − | 0.788518i | \(-0.710849\pi\) | ||||
−0.615012 | + | 0.788518i | \(0.710849\pi\) | |||||||
\(368\) | 0.325982 | 0.0169930 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.04434 | −0.314230 | ||||||||
\(371\) | −6.40420 | −0.332490 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.3593 | −0.639942 | −0.319971 | − | 0.947427i | \(-0.603673\pi\) | ||||
−0.319971 | + | 0.947427i | \(0.603673\pi\) | |||||||
\(374\) | −12.9234 | −0.668252 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.3803 | −1.61832 | ||||||||
\(377\) | 3.53848 | 0.182241 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.6886 | −1.57637 | −0.788183 | − | 0.615442i | \(-0.788978\pi\) | ||||
−0.788183 | + | 0.615442i | \(0.788978\pi\) | |||||||
\(380\) | −0.669293 | −0.0343340 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.5717 | 1.46186 | ||||||||
\(383\) | −23.2200 | −1.18649 | −0.593244 | − | 0.805023i | \(-0.702153\pi\) | ||||
−0.593244 | + | 0.805023i | \(0.702153\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.87921 | −0.401562 | ||||||||
\(386\) | −34.1238 | −1.73686 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.65980 | 0.135031 | ||||||||
\(389\) | 23.0785 | 1.17013 | 0.585064 | − | 0.810987i | \(-0.301069\pi\) | ||||
0.585064 | + | 0.810987i | \(0.301069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.424573 | −0.0214716 | ||||||||
\(392\) | 47.6728 | 2.40784 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.1708 | 0.713916 | ||||||||
\(395\) | 3.32589 | 0.167344 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.3847 | 0.822325 | 0.411163 | − | 0.911562i | \(-0.365123\pi\) | ||||
0.411163 | + | 0.911562i | \(0.365123\pi\) | |||||||
\(398\) | 18.9281 | 0.948781 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.26223 | −0.213112 | ||||||||
\(401\) | −19.8915 | −0.993335 | −0.496668 | − | 0.867941i | \(-0.665443\pi\) | ||||
−0.496668 | + | 0.867941i | \(0.665443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.59217 | −0.0793117 | ||||||||
\(404\) | 1.45409 | 0.0723439 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.6418 | −1.27258 | ||||||||
\(407\) | 6.57203 | 0.325764 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.2385 | −1.64354 | −0.821769 | − | 0.569820i | \(-0.807013\pi\) | ||||
−0.821769 | + | 0.569820i | \(0.807013\pi\) | |||||||
\(410\) | −7.17911 | −0.354551 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.375021 | −0.0184759 | ||||||||
\(413\) | 23.1164 | 1.13748 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.35683 | 0.262956 | ||||||||
\(416\) | −0.796535 | −0.0390533 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.0452 | 0.540241 | ||||||||
\(419\) | 7.92162 | 0.386996 | 0.193498 | − | 0.981101i | \(-0.438017\pi\) | ||||
0.193498 | + | 0.981101i | \(0.438017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.23413 | 0.0601477 | 0.0300738 | − | 0.999548i | \(-0.490426\pi\) | ||||
0.0300738 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(422\) | −24.9387 | −1.21400 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.51745 | 0.170822 | ||||||||
\(425\) | 5.55131 | 0.269278 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.6166 | 2.54630 | ||||||||
\(428\) | 2.48190 | 0.119967 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.90186 | −0.332837 | ||||||||
\(431\) | 5.34263 | 0.257345 | 0.128673 | − | 0.991687i | \(-0.458928\pi\) | ||||
0.128673 | + | 0.991687i | \(0.458928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.4233 | −1.02954 | −0.514770 | − | 0.857328i | \(-0.672123\pi\) | ||||
−0.514770 | + | 0.857328i | \(0.672123\pi\) | |||||||
\(434\) | 11.5378 | 0.553830 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.42708 | −0.116236 | ||||||||
\(437\) | 0.362870 | 0.0173584 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.8049 | −0.897510 | −0.448755 | − | 0.893655i | \(-0.648132\pi\) | ||||
−0.448755 | + | 0.893655i | \(0.648132\pi\) | |||||||
\(440\) | 4.32758 | 0.206309 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.12288 | 0.386366 | ||||||||
\(443\) | 15.0986 | 0.717355 | 0.358678 | − | 0.933461i | \(-0.383228\pi\) | ||||
0.358678 | + | 0.933461i | \(0.383228\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.225989 | 0.0107129 | ||||||||
\(446\) | −14.9548 | −0.708132 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −36.4445 | −1.72184 | ||||||||
\(449\) | 6.11019 | 0.288358 | 0.144179 | − | 0.989552i | \(-0.453946\pi\) | ||||
0.144179 | + | 0.989552i | \(0.453946\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.80587 | 0.367564 | ||||||||
\(452\) | 2.30271 | 0.108310 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 32.1129 | 1.50713 | ||||||||
\(455\) | 4.95241 | 0.232173 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.2218 | −1.69438 | −0.847192 | − | 0.531287i | \(-0.821709\pi\) | ||||
−0.847192 | + | 0.531287i | \(0.821709\pi\) | |||||||
\(458\) | 33.9643 | 1.58705 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0107889 | −0.000503037 0 | ||||||||
\(461\) | 15.2538 | 0.710441 | 0.355220 | − | 0.934783i | \(-0.384406\pi\) | ||||
0.355220 | + | 0.934783i | \(0.384406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.34655 | 0.341423 | 0.170712 | − | 0.985321i | \(-0.445393\pi\) | ||||
0.170712 | + | 0.985321i | \(0.445393\pi\) | |||||||
\(464\) | 15.0818 | 0.700156 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.6451 | −1.00269 | ||||||||
\(467\) | 2.11495 | 0.0978682 | 0.0489341 | − | 0.998802i | \(-0.484418\pi\) | ||||
0.0489341 | + | 0.998802i | \(0.484418\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.71029 | 0.356028 | ||||||||
\(470\) | 16.8808 | 0.778655 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.6964 | −0.584401 | ||||||||
\(473\) | 7.50442 | 0.345054 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.74454 | −0.217695 | ||||||||
\(476\) | −3.87823 | −0.177759 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.83503 | −0.175410 | ||||||||
\(479\) | −19.6744 | −0.898944 | −0.449472 | − | 0.893294i | \(-0.648388\pi\) | ||||
−0.449472 | + | 0.893294i | \(0.648388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.13079 | −0.188348 | ||||||||
\(482\) | 6.33063 | 0.288352 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.19465 | −0.0543025 | ||||||||
\(485\) | 18.8550 | 0.856163 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.4574 | 0.881698 | 0.440849 | − | 0.897581i | \(-0.354677\pi\) | ||||
0.440849 | + | 0.897581i | \(0.354677\pi\) | |||||||
\(488\) | −28.8992 | −1.30820 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −25.6452 | −1.15853 | ||||||||
\(491\) | 14.0281 | 0.633077 | 0.316539 | − | 0.948580i | \(-0.397479\pi\) | ||||
0.316539 | + | 0.948580i | \(0.397479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.6432 | −0.884684 | ||||||||
\(494\) | −6.94240 | −0.312353 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.78620 | −0.304709 | ||||||||
\(497\) | −12.4522 | −0.558559 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.41203 | −0.287042 | −0.143521 | − | 0.989647i | \(-0.545842\pi\) | ||||
−0.143521 | + | 0.989647i | \(0.545842\pi\) | |||||||
\(500\) | 0.141066 | 0.00630866 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 15.8918 | 0.709284 | ||||||||
\(503\) | −1.58905 | −0.0708521 | −0.0354260 | − | 0.999372i | \(-0.511279\pi\) | ||||
−0.0354260 | + | 0.999372i | \(0.511279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3079 | 0.458696 | ||||||||
\(506\) | 0.178048 | 0.00791522 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.57120 | −0.0697107 | ||||||||
\(509\) | −40.4369 | −1.79233 | −0.896167 | − | 0.443717i | \(-0.853659\pi\) | ||||
−0.896167 | + | 0.443717i | \(0.853659\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.3706 | −0.635719 | ||||||||
\(512\) | 19.7921 | 0.874694 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.2618 | 0.452629 | ||||||||
\(515\) | −2.65848 | −0.117147 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.3546 | −0.807234 | ||||||||
\(518\) | 29.9340 | 1.31523 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.72006 | −0.119283 | ||||||||
\(521\) | −20.3148 | −0.890007 | −0.445003 | − | 0.895529i | \(-0.646797\pi\) | ||||
−0.445003 | + | 0.895529i | \(0.646797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.84446 | −0.430468 | −0.215234 | − | 0.976563i | \(-0.569051\pi\) | ||||
−0.215234 | + | 0.976563i | \(0.569051\pi\) | |||||||
\(524\) | −1.29173 | −0.0564294 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.9410 | −0.564254 | ||||||||
\(527\) | 8.83863 | 0.385017 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9942 | −0.999746 | ||||||||
\(530\) | −1.89219 | −0.0821913 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.31461 | 0.143707 | ||||||||
\(533\) | −4.90631 | −0.212516 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.5939 | 0.760650 | ||||||||
\(536\) | −4.23480 | −0.182916 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 37.0974 | 1.59938 | ||||||||
\(539\) | 27.8842 | 1.20106 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.7146 | −0.847596 | −0.423798 | − | 0.905757i | \(-0.639303\pi\) | ||||
−0.423798 | + | 0.905757i | \(0.639303\pi\) | |||||||
\(542\) | −30.2974 | −1.30139 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.42181 | 0.189583 | ||||||||
\(545\) | −17.2053 | −0.736994 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7344 | 0.672756 | 0.336378 | − | 0.941727i | \(-0.390798\pi\) | ||||
0.336378 | + | 0.941727i | \(0.390798\pi\) | |||||||
\(548\) | −2.01810 | −0.0862090 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.32799 | −0.0992658 | ||||||||
\(551\) | 16.7885 | 0.715212 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.4712 | −0.700426 | ||||||||
\(554\) | −29.4488 | −1.25116 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.378538 | 0.0160536 | ||||||||
\(557\) | −8.29587 | −0.351507 | −0.175754 | − | 0.984434i | \(-0.556236\pi\) | ||||
−0.175754 | + | 0.984434i | \(0.556236\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.71684 | −0.199501 | ||||||||
\(560\) | 21.1083 | 0.891989 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.8374 | 0.878973 | ||||||||
\(563\) | −42.1827 | −1.77779 | −0.888893 | − | 0.458114i | \(-0.848525\pi\) | ||||
−0.888893 | + | 0.458114i | \(0.848525\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.3236 | 0.686741 | ||||||||
\(566\) | −38.6618 | −1.62508 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.83927 | 0.286969 | ||||||||
\(569\) | 7.79477 | 0.326774 | 0.163387 | − | 0.986562i | \(-0.447758\pi\) | ||||
0.163387 | + | 0.986562i | \(0.447758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.3684 | −1.22903 | −0.614516 | − | 0.788905i | \(-0.710649\pi\) | ||||
−0.614516 | + | 0.788905i | \(0.710649\pi\) | |||||||
\(572\) | −0.224434 | −0.00938405 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 35.5539 | 1.48399 | ||||||||
\(575\) | −0.0764816 | −0.00318950 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.7191 | −1.69516 | −0.847580 | − | 0.530668i | \(-0.821941\pi\) | ||||
−0.847580 | + | 0.530668i | \(0.821941\pi\) | |||||||
\(578\) | −20.2176 | −0.840940 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.499159 | −0.0207264 | ||||||||
\(581\) | −26.5292 | −1.10062 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.05738 | 0.0852080 | ||||||||
\(584\) | 7.89293 | 0.326612 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.9009 | −1.02865 | ||||||||
\(587\) | −25.7170 | −1.06145 | −0.530726 | − | 0.847543i | \(-0.678081\pi\) | ||||
−0.530726 | + | 0.847543i | \(0.678081\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.55412 | −0.311262 | ||||||||
\(590\) | 6.82996 | 0.281185 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.6064 | −0.723619 | ||||||||
\(593\) | 10.7998 | 0.443497 | 0.221748 | − | 0.975104i | \(-0.428824\pi\) | ||||
0.221748 | + | 0.975104i | \(0.428824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.4923 | −1.12708 | ||||||||
\(596\) | 1.14392 | 0.0468568 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.111911 | −0.00457637 | ||||||||
\(599\) | −14.7325 | −0.601954 | −0.300977 | − | 0.953631i | \(-0.597313\pi\) | ||||
−0.300977 | + | 0.953631i | \(0.597313\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.1542 | −0.699734 | −0.349867 | − | 0.936799i | \(-0.613773\pi\) | ||||
−0.349867 | + | 0.936799i | \(0.613773\pi\) | |||||||
\(602\) | 34.1808 | 1.39311 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.33912 | −0.0544882 | ||||||||
\(605\) | −8.46877 | −0.344304 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.2003 | −1.30697 | −0.653486 | − | 0.756939i | \(-0.726694\pi\) | ||||
−0.653486 | + | 0.756939i | \(0.726694\pi\) | |||||||
\(608\) | −3.77919 | −0.153266 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.5461 | 0.629443 | ||||||||
\(611\) | 11.5366 | 0.466722 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3120 | 0.578058 | 0.289029 | − | 0.957320i | \(-0.406668\pi\) | ||||
0.289029 | + | 0.957320i | \(0.406668\pi\) | |||||||
\(614\) | −25.4353 | −1.02649 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.4319 | −0.863518 | ||||||||
\(617\) | −44.8862 | −1.80705 | −0.903525 | − | 0.428536i | \(-0.859030\pi\) | ||||
−0.903525 | + | 0.428536i | \(0.859030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.99365 | 0.0801317 | 0.0400659 | − | 0.999197i | \(-0.487243\pi\) | ||||
0.0400659 | + | 0.999197i | \(0.487243\pi\) | |||||||
\(620\) | 0.224601 | 0.00902020 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.9527 | 0.800029 | ||||||||
\(623\) | −1.11919 | −0.0448394 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −11.8838 | −0.474972 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.193481 | −0.00772073 | ||||||||
\(629\) | 22.9313 | 0.914331 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.9679 | 1.35224 | 0.676121 | − | 0.736791i | \(-0.263660\pi\) | ||||
0.676121 | + | 0.736791i | \(0.263660\pi\) | |||||||
\(632\) | 9.04664 | 0.359856 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.2482 | 1.08217 | ||||||||
\(635\) | −11.1380 | −0.442000 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.5264 | −0.694420 | ||||||||
\(638\) | 8.23754 | 0.326127 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.3610 | −0.488610 | ||||||||
\(641\) | 46.5675 | 1.83931 | 0.919653 | − | 0.392732i | \(-0.128470\pi\) | ||||
0.919653 | + | 0.392732i | \(0.128470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.04675 | 0.0412799 | 0.0206400 | − | 0.999787i | \(-0.493430\pi\) | ||||
0.0206400 | + | 0.999787i | \(0.493430\pi\) | |||||||
\(644\) | 0.0534313 | 0.00210549 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.5394 | 1.51631 | ||||||||
\(647\) | −38.3293 | −1.50688 | −0.753440 | − | 0.657517i | \(-0.771607\pi\) | ||||
−0.753440 | + | 0.657517i | \(0.771607\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.42624 | −0.291505 | ||||||||
\(650\) | 1.46324 | 0.0573929 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.13337 | −0.0443861 | ||||||||
\(653\) | −13.8726 | −0.542878 | −0.271439 | − | 0.962456i | \(-0.587500\pi\) | ||||
−0.271439 | + | 0.962456i | \(0.587500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.15691 | −0.357790 | ||||||||
\(656\) | −20.9118 | −0.816471 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −83.6008 | −3.25910 | ||||||||
\(659\) | −4.74266 | −0.184748 | −0.0923740 | − | 0.995724i | \(-0.529446\pi\) | ||||
−0.0923740 | + | 0.995724i | \(0.529446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.74129 | −0.262206 | −0.131103 | − | 0.991369i | \(-0.541852\pi\) | ||||
−0.131103 | + | 0.991369i | \(0.541852\pi\) | |||||||
\(662\) | 42.1271 | 1.63732 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.5709 | 0.565461 | ||||||||
\(665\) | 23.4969 | 0.911171 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.270628 | 0.0104788 | ||||||||
\(668\) | −3.31479 | −0.128253 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.27808 | 0.0880100 | ||||||||
\(671\) | −16.9033 | −0.652546 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.58340 | −0.0995828 | −0.0497914 | − | 0.998760i | \(-0.515856\pi\) | ||||
−0.0497914 | + | 0.998760i | \(0.515856\pi\) | |||||||
\(674\) | 17.3165 | 0.667005 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.141066 | 0.00542561 | ||||||||
\(677\) | 42.7696 | 1.64377 | 0.821884 | − | 0.569654i | \(-0.192923\pi\) | ||||
0.821884 | + | 0.569654i | \(0.192923\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −93.3779 | −3.58351 | ||||||||
\(680\) | 15.0999 | 0.579055 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.70656 | −0.141931 | ||||||||
\(683\) | −14.8065 | −0.566553 | −0.283277 | − | 0.959038i | \(-0.591421\pi\) | ||||
−0.283277 | + | 0.959038i | \(0.591421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.3061 | −0.546607 | ||||||||
\(686\) | 76.2798 | 2.91238 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.1043 | −0.766468 | ||||||||
\(689\) | −1.29315 | −0.0492651 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.7360 | 0.598624 | 0.299312 | − | 0.954155i | \(-0.403243\pi\) | ||||
0.299312 | + | 0.954155i | \(0.403243\pi\) | |||||||
\(692\) | −0.259701 | −0.00987234 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.6872 | 1.77222 | ||||||||
\(695\) | 2.68341 | 0.101788 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.2364 | 1.03165 | ||||||||
\(698\) | −45.7375 | −1.73119 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.698616 | −0.0264052 | ||||||||
\(701\) | −31.5607 | −1.19203 | −0.596015 | − | 0.802973i | \(-0.703250\pi\) | ||||
−0.596015 | + | 0.802973i | \(0.703250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.5987 | −0.739180 | ||||||||
\(704\) | 11.7080 | 0.441261 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.9373 | 0.562172 | ||||||||
\(707\) | −51.0490 | −1.91989 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.4938 | 1.52078 | 0.760388 | − | 0.649469i | \(-0.225009\pi\) | ||||
0.760388 | + | 0.649469i | \(0.225009\pi\) | |||||||
\(710\) | −3.67913 | −0.138075 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.614705 | 0.0230370 | ||||||||
\(713\) | −0.121772 | −0.00456039 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.59098 | −0.0594995 | ||||||||
\(716\) | 1.76256 | 0.0658699 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.7564 | 0.438747 | ||||||||
\(719\) | −34.6714 | −1.29302 | −0.646512 | − | 0.762904i | \(-0.723773\pi\) | ||||
−0.646512 | + | 0.762904i | \(0.723773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.1659 | 0.490323 | ||||||||
\(722\) | −5.13697 | −0.191178 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.29037 | −0.122286 | ||||||||
\(725\) | −3.53848 | −0.131416 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.1748 | 1.34165 | 0.670824 | − | 0.741616i | \(-0.265940\pi\) | ||||
0.670824 | + | 0.741616i | \(0.265940\pi\) | |||||||
\(728\) | 13.4709 | 0.499264 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.24594 | −0.157149 | ||||||||
\(731\) | 26.1846 | 0.968473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.2468 | −1.74510 | −0.872549 | − | 0.488526i | \(-0.837535\pi\) | ||||
−0.872549 | + | 0.488526i | \(0.837535\pi\) | |||||||
\(734\) | 34.4796 | 1.27266 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0609202 | −0.00224555 | ||||||||
\(737\) | −2.47697 | −0.0912403 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.4117 | 0.861215 | 0.430607 | − | 0.902539i | \(-0.358299\pi\) | ||||
0.430607 | + | 0.902539i | \(0.358299\pi\) | |||||||
\(740\) | 0.582715 | 0.0214210 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.37088 | 0.344016 | ||||||||
\(743\) | −53.8155 | −1.97430 | −0.987150 | − | 0.159797i | \(-0.948916\pi\) | ||||
−0.987150 | + | 0.159797i | \(0.948916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.10911 | 0.297095 | ||||||||
\(746\) | 18.0847 | 0.662126 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.24590 | 0.0455546 | ||||||||
\(749\) | −87.1321 | −3.18374 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.6661 | 1.30148 | 0.650738 | − | 0.759302i | \(-0.274460\pi\) | ||||
0.650738 | + | 0.759302i | \(0.274460\pi\) | |||||||
\(752\) | 49.1718 | 1.79311 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.17764 | −0.188558 | ||||||||
\(755\) | −9.49289 | −0.345482 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.6061 | 1.69393 | 0.846963 | − | 0.531651i | \(-0.178428\pi\) | ||||
0.846963 | + | 0.531651i | \(0.178428\pi\) | |||||||
\(758\) | 44.9047 | 1.63101 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.9055 | −0.468130 | ||||||||
\(761\) | −18.2267 | −0.660716 | −0.330358 | − | 0.943856i | \(-0.607169\pi\) | ||||
−0.330358 | + | 0.943856i | \(0.607169\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 85.2077 | 3.08473 | ||||||||
\(764\) | −2.75451 | −0.0996545 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33.9764 | 1.22762 | ||||||||
\(767\) | 4.66770 | 0.168541 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.2917 | 0.371128 | 0.185564 | − | 0.982632i | \(-0.440589\pi\) | ||||
0.185564 | + | 0.982632i | \(0.440589\pi\) | |||||||
\(770\) | 11.5292 | 0.415482 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.28976 | 0.118401 | ||||||||
\(773\) | 33.1268 | 1.19149 | 0.595745 | − | 0.803174i | \(-0.296857\pi\) | ||||
0.595745 | + | 0.803174i | \(0.296857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.59217 | 0.0571925 | ||||||||
\(776\) | 51.2869 | 1.84109 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −33.7694 | −1.21069 | ||||||||
\(779\) | −23.2782 | −0.834029 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00034 | 0.143143 | ||||||||
\(782\) | 0.621251 | 0.0222159 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −74.7014 | −2.66791 | ||||||||
\(785\) | −1.37156 | −0.0489532 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.11339 | 0.146626 | 0.0733132 | − | 0.997309i | \(-0.476643\pi\) | ||||
0.0733132 | + | 0.997309i | \(0.476643\pi\) | |||||||
\(788\) | −1.36616 | −0.0486675 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.86657 | −0.173145 | ||||||||
\(791\) | −80.8413 | −2.87439 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.6244 | 0.377285 | ||||||||
\(794\) | −23.9747 | −0.850832 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.82480 | −0.0646783 | ||||||||
\(797\) | 31.2433 | 1.10670 | 0.553348 | − | 0.832950i | \(-0.313350\pi\) | ||||
0.553348 | + | 0.832950i | \(0.313350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −64.0433 | −2.26569 | ||||||||
\(800\) | 0.796535 | 0.0281617 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.1060 | 1.02777 | ||||||||
\(803\) | 4.61663 | 0.162917 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.378768 | 0.0133498 | ||||||||
\(806\) | 2.32972 | 0.0820611 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28.0382 | 0.986379 | ||||||||
\(809\) | −24.4812 | −0.860712 | −0.430356 | − | 0.902659i | \(-0.641612\pi\) | ||||
−0.430356 | + | 0.902659i | \(0.641612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.5036 | 0.965782 | 0.482891 | − | 0.875681i | \(-0.339587\pi\) | ||||
0.482891 | + | 0.875681i | \(0.339587\pi\) | |||||||
\(812\) | 2.47204 | 0.0867516 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.61645 | −0.337056 | ||||||||
\(815\) | −8.03430 | −0.281429 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.3793 | −0.782951 | ||||||||
\(818\) | 48.6359 | 1.70051 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.692114 | 0.0241697 | ||||||||
\(821\) | −19.2162 | −0.670649 | −0.335325 | − | 0.942103i | \(-0.608846\pi\) | ||||
−0.335325 | + | 0.942103i | \(0.608846\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −50.8253 | −1.77166 | −0.885829 | − | 0.464012i | \(-0.846409\pi\) | ||||
−0.885829 | + | 0.464012i | \(0.846409\pi\) | |||||||
\(824\) | −7.23123 | −0.251912 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33.8247 | −1.17691 | ||||||||
\(827\) | 56.5580 | 1.96671 | 0.983357 | − | 0.181684i | \(-0.0581547\pi\) | ||||
0.983357 | + | 0.181684i | \(0.0581547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.9253 | 0.900424 | 0.450212 | − | 0.892922i | \(-0.351348\pi\) | ||||
0.450212 | + | 0.892922i | \(0.351348\pi\) | |||||||
\(830\) | −7.83832 | −0.272072 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.35894 | −0.255126 | ||||||||
\(833\) | 97.2942 | 3.37104 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.4981 | −0.813187 | ||||||||
\(836\) | −1.06484 | −0.0368281 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.5912 | −0.400412 | ||||||||
\(839\) | 2.90284 | 0.100217 | 0.0501086 | − | 0.998744i | \(-0.484043\pi\) | ||||
0.0501086 | + | 0.998744i | \(0.484043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.4792 | −0.568247 | ||||||||
\(842\) | −1.80582 | −0.0622327 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.40425 | 0.0827578 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.9408 | 1.44110 | ||||||||
\(848\) | −5.51170 | −0.189273 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.12288 | −0.278613 | ||||||||
\(851\) | −0.315930 | −0.0108299 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.4101 | 1.14394 | 0.571971 | − | 0.820274i | \(-0.306179\pi\) | ||||
0.571971 | + | 0.820274i | \(0.306179\pi\) | |||||||
\(854\) | −76.9906 | −2.63456 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 47.8565 | 1.63570 | ||||||||
\(857\) | −17.5740 | −0.600316 | −0.300158 | − | 0.953890i | \(-0.597039\pi\) | ||||
−0.300158 | + | 0.953890i | \(0.597039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.25578 | −0.0428466 | −0.0214233 | − | 0.999770i | \(-0.506820\pi\) | ||||
−0.0214233 | + | 0.999770i | \(0.506820\pi\) | |||||||
\(860\) | 0.665386 | 0.0226895 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.81754 | −0.266266 | ||||||||
\(863\) | 16.8692 | 0.574235 | 0.287118 | − | 0.957895i | \(-0.407303\pi\) | ||||
0.287118 | + | 0.957895i | \(0.407303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.84099 | −0.0625955 | ||||||||
\(866\) | 31.3474 | 1.06523 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.11232 | −0.0377545 | ||||||||
\(869\) | 5.29145 | 0.179500 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.55688 | 0.0527528 | ||||||||
\(872\) | −46.7995 | −1.58483 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.530965 | −0.0179602 | ||||||||
\(875\) | −4.95241 | −0.167422 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.9517 | −0.606186 | −0.303093 | − | 0.952961i | \(-0.598019\pi\) | ||||
−0.303093 | + | 0.952961i | \(0.598019\pi\) | |||||||
\(878\) | 27.5161 | 0.928623 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.78115 | −0.228592 | ||||||||
\(881\) | −33.1498 | −1.11685 | −0.558423 | − | 0.829556i | \(-0.688593\pi\) | ||||
−0.558423 | + | 0.829556i | \(0.688593\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.9328 | −0.839055 | −0.419528 | − | 0.907743i | \(-0.637804\pi\) | ||||
−0.419528 | + | 0.907743i | \(0.637804\pi\) | |||||||
\(884\) | −0.783100 | −0.0263385 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.0928 | −0.742223 | ||||||||
\(887\) | 54.6710 | 1.83567 | 0.917835 | − | 0.396961i | \(-0.129935\pi\) | ||||
0.917835 | + | 0.396961i | \(0.129935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.1602 | 1.85001 | ||||||||
\(890\) | −0.330676 | −0.0110843 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.44175 | 0.0482732 | ||||||||
\(893\) | 54.7360 | 1.83167 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.4946 | 0.417647 | ||||||||
\(896\) | 61.2165 | 2.04510 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.94067 | −0.298354 | ||||||||
\(899\) | −5.63386 | −0.187900 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.17867 | 0.239156 | ||||||||
\(902\) | −11.4218 | −0.380306 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 44.4013 | 1.47677 | ||||||||
\(905\) | −23.3250 | −0.775350 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 50.8770 | 1.68934 | 0.844671 | − | 0.535286i | \(-0.179796\pi\) | ||||
0.844671 | + | 0.535286i | \(0.179796\pi\) | |||||||
\(908\) | −3.09590 | −0.102741 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.24655 | −0.240221 | ||||||||
\(911\) | 37.0508 | 1.22755 | 0.613773 | − | 0.789482i | \(-0.289651\pi\) | ||||
0.613773 | + | 0.789482i | \(0.289651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.52263 | 0.282058 | ||||||||
\(914\) | 53.0011 | 1.75312 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.27439 | −0.108189 | ||||||||
\(917\) | 45.3488 | 1.49755 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.88820 | 0.128260 | 0.0641300 | − | 0.997942i | \(-0.479573\pi\) | ||||
0.0641300 | + | 0.997942i | \(0.479573\pi\) | |||||||
\(920\) | −0.208035 | −0.00685870 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.3200 | −0.735069 | ||||||||
\(923\) | −2.51438 | −0.0827618 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.13079 | 0.135820 | ||||||||
\(926\) | −10.7498 | −0.353259 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.81852 | −0.0925225 | ||||||||
\(929\) | 10.2003 | 0.334661 | 0.167330 | − | 0.985901i | \(-0.446485\pi\) | ||||
0.167330 | + | 0.985901i | \(0.446485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −83.1545 | −2.72528 | ||||||||
\(932\) | 2.08673 | 0.0683532 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.09467 | −0.101261 | ||||||||
\(935\) | 8.83204 | 0.288839 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.7823 | 1.59365 | 0.796825 | − | 0.604211i | \(-0.206511\pi\) | ||||
0.796825 | + | 0.604211i | \(0.206511\pi\) | |||||||
\(938\) | −11.2820 | −0.368370 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.62742 | −0.0530807 | ||||||||
\(941\) | −45.7324 | −1.49083 | −0.745416 | − | 0.666599i | \(-0.767749\pi\) | ||||
−0.745416 | + | 0.666599i | \(0.767749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.375243 | −0.0122196 | ||||||||
\(944\) | 19.8948 | 0.647521 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.9808 | −0.357015 | ||||||||
\(947\) | −14.7312 | −0.478699 | −0.239350 | − | 0.970933i | \(-0.576934\pi\) | ||||
−0.239350 | + | 0.970933i | \(0.576934\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.90174 | −0.0941946 | ||||||||
\(950\) | 6.94240 | 0.225241 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −74.7809 | −2.42366 | ||||||||
\(953\) | 57.2024 | 1.85297 | 0.926484 | − | 0.376334i | \(-0.122816\pi\) | ||||
0.926484 | + | 0.376334i | \(0.122816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5264 | −0.631858 | ||||||||
\(956\) | 0.369722 | 0.0119577 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 28.7883 | 0.930107 | ||||||||
\(959\) | 70.8495 | 2.28785 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4650 | −0.918226 | ||||||||
\(962\) | 6.04434 | 0.194877 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.610315 | −0.0196569 | ||||||||
\(965\) | 23.3207 | 0.750721 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2741 | 0.330391 | 0.165196 | − | 0.986261i | \(-0.447174\pi\) | ||||
0.165196 | + | 0.986261i | \(0.447174\pi\) | |||||||
\(968\) | −23.0356 | −0.740392 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.5894 | −0.885843 | ||||||||
\(971\) | −1.15531 | −0.0370757 | −0.0185378 | − | 0.999828i | \(-0.505901\pi\) | ||||
−0.0185378 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.2893 | −0.426037 | ||||||||
\(974\) | −28.4708 | −0.912263 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 45.2839 | 1.44950 | ||||||||
\(977\) | −20.7840 | −0.664940 | −0.332470 | − | 0.943114i | \(-0.607882\pi\) | ||||
−0.332470 | + | 0.943114i | \(0.607882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.359545 | 0.0114911 | ||||||||
\(980\) | 2.47237 | 0.0789770 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.5264 | −0.655023 | ||||||||
\(983\) | −44.1555 | −1.40834 | −0.704171 | − | 0.710030i | \(-0.748681\pi\) | ||||
−0.704171 | + | 0.710030i | \(0.748681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.68456 | −0.308576 | ||||||||
\(986\) | 28.7426 | 0.915352 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.669293 | 0.0212931 | ||||||||
\(989\) | −0.360752 | −0.0114712 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.86612 | −0.122811 | −0.0614056 | − | 0.998113i | \(-0.519558\pi\) | ||||
−0.0614056 | + | 0.998113i | \(0.519558\pi\) | |||||||
\(992\) | 1.26822 | 0.0402660 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.2206 | 0.577922 | ||||||||
\(995\) | −12.9358 | −0.410092 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.3098 | 1.59333 | 0.796663 | − | 0.604424i | \(-0.206597\pi\) | ||||
0.796663 | + | 0.604424i | \(0.206597\pi\) | |||||||
\(998\) | 9.38233 | 0.296993 | ||||||||
\(999\) | 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 | 5265.2.a.bd.1.3 | yes | 8 | |
3.2 | odd | 2 | 5265.2.a.bc.1.6 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5265.2.a.bc.1.6 | ✓ | 8 | 3.2 | odd | 2 | ||
5265.2.a.bd.1.3 | yes | 8 | 1.1 | even | 1 | trivial |