Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, 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("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.302776 | −0.174808 | −0.0874038 | − | 0.996173i | \(-0.527857\pi\) | ||||
−0.0874038 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.302776 | 0.123608 | ||||||||
\(7\) | −3.30278 | −1.24833 | −0.624166 | − | 0.781292i | \(-0.714561\pi\) | ||||
−0.624166 | + | 0.781292i | \(0.714561\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.90833 | −0.969442 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.69722 | 0.511732 | 0.255866 | − | 0.966712i | \(-0.417639\pi\) | ||||
0.255866 | + | 0.966712i | \(0.417639\pi\) | |||||||
\(12\) | −0.302776 | −0.0874038 | ||||||||
\(13\) | 3.30278 | 0.916025 | 0.458013 | − | 0.888946i | \(-0.348561\pi\) | ||||
0.458013 | + | 0.888946i | \(0.348561\pi\) | |||||||
\(14\) | 3.30278 | 0.882704 | ||||||||
\(15\) | 0.302776 | 0.0781763 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.90833 | −1.67552 | −0.837758 | − | 0.546042i | \(-0.816134\pi\) | ||||
−0.837758 | + | 0.546042i | \(0.816134\pi\) | |||||||
\(18\) | 2.90833 | 0.685499 | ||||||||
\(19\) | −5.90833 | −1.35546 | −0.677732 | − | 0.735309i | \(-0.737037\pi\) | ||||
−0.677732 | + | 0.735309i | \(0.737037\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.69722 | −0.361849 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0.302776 | 0.0618038 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.30278 | −0.647728 | ||||||||
\(27\) | 1.78890 | 0.344273 | ||||||||
\(28\) | −3.30278 | −0.624166 | ||||||||
\(29\) | −2.60555 | −0.483839 | −0.241919 | − | 0.970296i | \(-0.577777\pi\) | ||||
−0.241919 | + | 0.970296i | \(0.577777\pi\) | |||||||
\(30\) | −0.302776 | −0.0552790 | ||||||||
\(31\) | −7.90833 | −1.42038 | −0.710189 | − | 0.704011i | \(-0.751390\pi\) | ||||
−0.710189 | + | 0.704011i | \(0.751390\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.513878 | −0.0894547 | ||||||||
\(34\) | 6.90833 | 1.18477 | ||||||||
\(35\) | 3.30278 | 0.558271 | ||||||||
\(36\) | −2.90833 | −0.484721 | ||||||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 5.90833 | 0.958457 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.908327 | 0.141857 | 0.0709284 | − | 0.997481i | \(-0.477404\pi\) | ||||
0.0709284 | + | 0.997481i | \(0.477404\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | 9.21110 | 1.40468 | 0.702340 | − | 0.711842i | \(-0.252139\pi\) | ||||
0.702340 | + | 0.711842i | \(0.252139\pi\) | |||||||
\(44\) | 1.69722 | 0.255866 | ||||||||
\(45\) | 2.90833 | 0.433548 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.60555 | −0.380059 | −0.190029 | − | 0.981778i | \(-0.560858\pi\) | ||||
−0.190029 | + | 0.981778i | \(0.560858\pi\) | |||||||
\(48\) | −0.302776 | −0.0437019 | ||||||||
\(49\) | 3.90833 | 0.558332 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 2.09167 | 0.292893 | ||||||||
\(52\) | 3.30278 | 0.458013 | ||||||||
\(53\) | 11.2111 | 1.53996 | 0.769982 | − | 0.638066i | \(-0.220265\pi\) | ||||
0.769982 | + | 0.638066i | \(0.220265\pi\) | |||||||
\(54\) | −1.78890 | −0.243438 | ||||||||
\(55\) | −1.69722 | −0.228854 | ||||||||
\(56\) | 3.30278 | 0.441352 | ||||||||
\(57\) | 1.78890 | 0.236945 | ||||||||
\(58\) | 2.60555 | 0.342126 | ||||||||
\(59\) | −3.39445 | −0.441920 | −0.220960 | − | 0.975283i | \(-0.570919\pi\) | ||||
−0.220960 | + | 0.975283i | \(0.570919\pi\) | |||||||
\(60\) | 0.302776 | 0.0390882 | ||||||||
\(61\) | −11.5139 | −1.47420 | −0.737101 | − | 0.675783i | \(-0.763806\pi\) | ||||
−0.737101 | + | 0.675783i | \(0.763806\pi\) | |||||||
\(62\) | 7.90833 | 1.00436 | ||||||||
\(63\) | 9.60555 | 1.21019 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.30278 | −0.409659 | ||||||||
\(66\) | 0.513878 | 0.0632540 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | −6.90833 | −0.837758 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.30278 | −0.394757 | ||||||||
\(71\) | −16.3028 | −1.93478 | −0.967392 | − | 0.253285i | \(-0.918489\pi\) | ||||
−0.967392 | + | 0.253285i | \(0.918489\pi\) | |||||||
\(72\) | 2.90833 | 0.342750 | ||||||||
\(73\) | −5.81665 | −0.680788 | −0.340394 | − | 0.940283i | \(-0.610560\pi\) | ||||
−0.340394 | + | 0.940283i | \(0.610560\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | −0.302776 | −0.0349615 | ||||||||
\(76\) | −5.90833 | −0.677732 | ||||||||
\(77\) | −5.60555 | −0.638812 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 14.4222 | 1.62262 | 0.811312 | − | 0.584613i | \(-0.198754\pi\) | ||||
0.811312 | + | 0.584613i | \(0.198754\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.18335 | 0.909261 | ||||||||
\(82\) | −0.908327 | −0.100308 | ||||||||
\(83\) | −11.2111 | −1.23058 | −0.615289 | − | 0.788301i | \(-0.710961\pi\) | ||||
−0.615289 | + | 0.788301i | \(0.710961\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 6.90833 | 0.749313 | ||||||||
\(86\) | −9.21110 | −0.993259 | ||||||||
\(87\) | 0.788897 | 0.0845787 | ||||||||
\(88\) | −1.69722 | −0.180925 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | −2.90833 | −0.306565 | ||||||||
\(91\) | −10.9083 | −1.14350 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.39445 | 0.248293 | ||||||||
\(94\) | 2.60555 | 0.268742 | ||||||||
\(95\) | 5.90833 | 0.606182 | ||||||||
\(96\) | 0.302776 | 0.0309019 | ||||||||
\(97\) | −6.30278 | −0.639950 | −0.319975 | − | 0.947426i | \(-0.603675\pi\) | ||||
−0.319975 | + | 0.947426i | \(0.603675\pi\) | |||||||
\(98\) | −3.90833 | −0.394801 | ||||||||
\(99\) | −4.93608 | −0.496095 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 2.60555 | 0.259262 | 0.129631 | − | 0.991562i | \(-0.458621\pi\) | ||||
0.129631 | + | 0.991562i | \(0.458621\pi\) | |||||||
\(102\) | −2.09167 | −0.207106 | ||||||||
\(103\) | −8.11943 | −0.800031 | −0.400016 | − | 0.916508i | \(-0.630995\pi\) | ||||
−0.400016 | + | 0.916508i | \(0.630995\pi\) | |||||||
\(104\) | −3.30278 | −0.323864 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | −11.2111 | −1.08892 | ||||||||
\(107\) | 2.60555 | 0.251888 | 0.125944 | − | 0.992037i | \(-0.459804\pi\) | ||||
0.125944 | + | 0.992037i | \(0.459804\pi\) | |||||||
\(108\) | 1.78890 | 0.172137 | ||||||||
\(109\) | −1.48612 | −0.142345 | −0.0711723 | − | 0.997464i | \(-0.522674\pi\) | ||||
−0.0711723 | + | 0.997464i | \(0.522674\pi\) | |||||||
\(110\) | 1.69722 | 0.161824 | ||||||||
\(111\) | 2.42221 | 0.229906 | ||||||||
\(112\) | −3.30278 | −0.312083 | ||||||||
\(113\) | 16.4222 | 1.54487 | 0.772436 | − | 0.635093i | \(-0.219038\pi\) | ||||
0.772436 | + | 0.635093i | \(0.219038\pi\) | |||||||
\(114\) | −1.78890 | −0.167546 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.60555 | −0.241919 | ||||||||
\(117\) | −9.60555 | −0.888034 | ||||||||
\(118\) | 3.39445 | 0.312484 | ||||||||
\(119\) | 22.8167 | 2.09160 | ||||||||
\(120\) | −0.302776 | −0.0276395 | ||||||||
\(121\) | −8.11943 | −0.738130 | ||||||||
\(122\) | 11.5139 | 1.04242 | ||||||||
\(123\) | −0.275019 | −0.0247977 | ||||||||
\(124\) | −7.90833 | −0.710189 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −9.60555 | −0.855731 | ||||||||
\(127\) | 9.81665 | 0.871087 | 0.435544 | − | 0.900168i | \(-0.356556\pi\) | ||||
0.435544 | + | 0.900168i | \(0.356556\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −2.78890 | −0.245549 | ||||||||
\(130\) | 3.30278 | 0.289673 | ||||||||
\(131\) | −11.2111 | −0.979519 | −0.489759 | − | 0.871858i | \(-0.662915\pi\) | ||||
−0.489759 | + | 0.871858i | \(0.662915\pi\) | |||||||
\(132\) | −0.513878 | −0.0447274 | ||||||||
\(133\) | 19.5139 | 1.69207 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −1.78890 | −0.153964 | ||||||||
\(136\) | 6.90833 | 0.592384 | ||||||||
\(137\) | −3.90833 | −0.333911 | −0.166955 | − | 0.985964i | \(-0.553394\pi\) | ||||
−0.166955 | + | 0.985964i | \(0.553394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.6056 | −1.06919 | −0.534594 | − | 0.845109i | \(-0.679536\pi\) | ||||
−0.534594 | + | 0.845109i | \(0.679536\pi\) | |||||||
\(140\) | 3.30278 | 0.279135 | ||||||||
\(141\) | 0.788897 | 0.0664372 | ||||||||
\(142\) | 16.3028 | 1.36810 | ||||||||
\(143\) | 5.60555 | 0.468760 | ||||||||
\(144\) | −2.90833 | −0.242361 | ||||||||
\(145\) | 2.60555 | 0.216379 | ||||||||
\(146\) | 5.81665 | 0.481390 | ||||||||
\(147\) | −1.18335 | −0.0976007 | ||||||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | −13.3028 | −1.08981 | −0.544903 | − | 0.838499i | \(-0.683433\pi\) | ||||
−0.544903 | + | 0.838499i | \(0.683433\pi\) | |||||||
\(150\) | 0.302776 | 0.0247215 | ||||||||
\(151\) | 8.90833 | 0.724949 | 0.362475 | − | 0.931994i | \(-0.381932\pi\) | ||||
0.362475 | + | 0.931994i | \(0.381932\pi\) | |||||||
\(152\) | 5.90833 | 0.479229 | ||||||||
\(153\) | 20.0917 | 1.62432 | ||||||||
\(154\) | 5.60555 | 0.451708 | ||||||||
\(155\) | 7.90833 | 0.635212 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 18.6056 | 1.48488 | 0.742442 | − | 0.669910i | \(-0.233667\pi\) | ||||
0.742442 | + | 0.669910i | \(0.233667\pi\) | |||||||
\(158\) | −14.4222 | −1.14737 | ||||||||
\(159\) | −3.39445 | −0.269197 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −8.18335 | −0.642944 | ||||||||
\(163\) | 9.30278 | 0.728650 | 0.364325 | − | 0.931272i | \(-0.381300\pi\) | ||||
0.364325 | + | 0.931272i | \(0.381300\pi\) | |||||||
\(164\) | 0.908327 | 0.0709284 | ||||||||
\(165\) | 0.513878 | 0.0400054 | ||||||||
\(166\) | 11.2111 | 0.870150 | ||||||||
\(167\) | 6.78890 | 0.525341 | 0.262670 | − | 0.964886i | \(-0.415397\pi\) | ||||
0.262670 | + | 0.964886i | \(0.415397\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −2.09167 | −0.160898 | ||||||||
\(170\) | −6.90833 | −0.529844 | ||||||||
\(171\) | 17.1833 | 1.31404 | ||||||||
\(172\) | 9.21110 | 0.702340 | ||||||||
\(173\) | 19.6972 | 1.49755 | 0.748776 | − | 0.662823i | \(-0.230642\pi\) | ||||
0.748776 | + | 0.662823i | \(0.230642\pi\) | |||||||
\(174\) | −0.788897 | −0.0598062 | ||||||||
\(175\) | −3.30278 | −0.249666 | ||||||||
\(176\) | 1.69722 | 0.127933 | ||||||||
\(177\) | 1.02776 | 0.0772509 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.39445 | 0.702174 | 0.351087 | − | 0.936343i | \(-0.385812\pi\) | ||||
0.351087 | + | 0.936343i | \(0.385812\pi\) | |||||||
\(180\) | 2.90833 | 0.216774 | ||||||||
\(181\) | −17.1194 | −1.27248 | −0.636239 | − | 0.771492i | \(-0.719511\pi\) | ||||
−0.636239 | + | 0.771492i | \(0.719511\pi\) | |||||||
\(182\) | 10.9083 | 0.808579 | ||||||||
\(183\) | 3.48612 | 0.257702 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.00000 | 0.588172 | ||||||||
\(186\) | −2.39445 | −0.175569 | ||||||||
\(187\) | −11.7250 | −0.857416 | ||||||||
\(188\) | −2.60555 | −0.190029 | ||||||||
\(189\) | −5.90833 | −0.429768 | ||||||||
\(190\) | −5.90833 | −0.428635 | ||||||||
\(191\) | 8.60555 | 0.622676 | 0.311338 | − | 0.950299i | \(-0.399223\pi\) | ||||
0.311338 | + | 0.950299i | \(0.399223\pi\) | |||||||
\(192\) | −0.302776 | −0.0218509 | ||||||||
\(193\) | −17.8167 | −1.28247 | −0.641235 | − | 0.767344i | \(-0.721578\pi\) | ||||
−0.641235 | + | 0.767344i | \(0.721578\pi\) | |||||||
\(194\) | 6.30278 | 0.452513 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 3.90833 | 0.279166 | ||||||||
\(197\) | 4.30278 | 0.306560 | 0.153280 | − | 0.988183i | \(-0.451016\pi\) | ||||
0.153280 | + | 0.988183i | \(0.451016\pi\) | |||||||
\(198\) | 4.93608 | 0.350792 | ||||||||
\(199\) | 20.4222 | 1.44769 | 0.723846 | − | 0.689962i | \(-0.242373\pi\) | ||||
0.723846 | + | 0.689962i | \(0.242373\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −1.21110 | −0.0854246 | ||||||||
\(202\) | −2.60555 | −0.183326 | ||||||||
\(203\) | 8.60555 | 0.603991 | ||||||||
\(204\) | 2.09167 | 0.146446 | ||||||||
\(205\) | −0.908327 | −0.0634403 | ||||||||
\(206\) | 8.11943 | 0.565707 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.30278 | 0.229006 | ||||||||
\(209\) | −10.0278 | −0.693634 | ||||||||
\(210\) | 1.00000 | 0.0690066 | ||||||||
\(211\) | 7.21110 | 0.496433 | 0.248216 | − | 0.968705i | \(-0.420156\pi\) | ||||
0.248216 | + | 0.968705i | \(0.420156\pi\) | |||||||
\(212\) | 11.2111 | 0.769982 | ||||||||
\(213\) | 4.93608 | 0.338215 | ||||||||
\(214\) | −2.60555 | −0.178112 | ||||||||
\(215\) | −9.21110 | −0.628192 | ||||||||
\(216\) | −1.78890 | −0.121719 | ||||||||
\(217\) | 26.1194 | 1.77310 | ||||||||
\(218\) | 1.48612 | 0.100653 | ||||||||
\(219\) | 1.76114 | 0.119007 | ||||||||
\(220\) | −1.69722 | −0.114427 | ||||||||
\(221\) | −22.8167 | −1.53481 | ||||||||
\(222\) | −2.42221 | −0.162568 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 3.30278 | 0.220676 | ||||||||
\(225\) | −2.90833 | −0.193888 | ||||||||
\(226\) | −16.4222 | −1.09239 | ||||||||
\(227\) | 14.6056 | 0.969404 | 0.484702 | − | 0.874679i | \(-0.338928\pi\) | ||||
0.484702 | + | 0.874679i | \(0.338928\pi\) | |||||||
\(228\) | 1.78890 | 0.118473 | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.69722 | 0.111669 | ||||||||
\(232\) | 2.60555 | 0.171063 | ||||||||
\(233\) | 25.8167 | 1.69131 | 0.845653 | − | 0.533734i | \(-0.179212\pi\) | ||||
0.845653 | + | 0.533734i | \(0.179212\pi\) | |||||||
\(234\) | 9.60555 | 0.627935 | ||||||||
\(235\) | 2.60555 | 0.169967 | ||||||||
\(236\) | −3.39445 | −0.220960 | ||||||||
\(237\) | −4.36669 | −0.283647 | ||||||||
\(238\) | −22.8167 | −1.47898 | ||||||||
\(239\) | 5.21110 | 0.337078 | 0.168539 | − | 0.985695i | \(-0.446095\pi\) | ||||
0.168539 | + | 0.985695i | \(0.446095\pi\) | |||||||
\(240\) | 0.302776 | 0.0195441 | ||||||||
\(241\) | 14.4222 | 0.929016 | 0.464508 | − | 0.885569i | \(-0.346231\pi\) | ||||
0.464508 | + | 0.885569i | \(0.346231\pi\) | |||||||
\(242\) | 8.11943 | 0.521937 | ||||||||
\(243\) | −7.84441 | −0.503219 | ||||||||
\(244\) | −11.5139 | −0.737101 | ||||||||
\(245\) | −3.90833 | −0.249694 | ||||||||
\(246\) | 0.275019 | 0.0175346 | ||||||||
\(247\) | −19.5139 | −1.24164 | ||||||||
\(248\) | 7.90833 | 0.502179 | ||||||||
\(249\) | 3.39445 | 0.215114 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −12.5139 | −0.789869 | −0.394934 | − | 0.918709i | \(-0.629233\pi\) | ||||
−0.394934 | + | 0.918709i | \(0.629233\pi\) | |||||||
\(252\) | 9.60555 | 0.605093 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.81665 | −0.615952 | ||||||||
\(255\) | −2.09167 | −0.130986 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.81665 | −0.113320 | −0.0566599 | − | 0.998394i | \(-0.518045\pi\) | ||||
−0.0566599 | + | 0.998394i | \(0.518045\pi\) | |||||||
\(258\) | 2.78890 | 0.173629 | ||||||||
\(259\) | 26.4222 | 1.64180 | ||||||||
\(260\) | −3.30278 | −0.204829 | ||||||||
\(261\) | 7.57779 | 0.469054 | ||||||||
\(262\) | 11.2111 | 0.692624 | ||||||||
\(263\) | −3.51388 | −0.216675 | −0.108338 | − | 0.994114i | \(-0.534553\pi\) | ||||
−0.108338 | + | 0.994114i | \(0.534553\pi\) | |||||||
\(264\) | 0.513878 | 0.0316270 | ||||||||
\(265\) | −11.2111 | −0.688693 | ||||||||
\(266\) | −19.5139 | −1.19647 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 4.18335 | 0.255063 | 0.127532 | − | 0.991835i | \(-0.459295\pi\) | ||||
0.127532 | + | 0.991835i | \(0.459295\pi\) | |||||||
\(270\) | 1.78890 | 0.108869 | ||||||||
\(271\) | −2.69722 | −0.163845 | −0.0819224 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819224 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(272\) | −6.90833 | −0.418879 | ||||||||
\(273\) | 3.30278 | 0.199893 | ||||||||
\(274\) | 3.90833 | 0.236111 | ||||||||
\(275\) | 1.69722 | 0.102346 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.2111 | −1.63496 | −0.817478 | − | 0.575959i | \(-0.804629\pi\) | ||||
−0.817478 | + | 0.575959i | \(0.804629\pi\) | |||||||
\(278\) | 12.6056 | 0.756031 | ||||||||
\(279\) | 23.0000 | 1.37697 | ||||||||
\(280\) | −3.30278 | −0.197379 | ||||||||
\(281\) | 26.6056 | 1.58715 | 0.793577 | − | 0.608470i | \(-0.208216\pi\) | ||||
0.793577 | + | 0.608470i | \(0.208216\pi\) | |||||||
\(282\) | −0.788897 | −0.0469782 | ||||||||
\(283\) | −2.00000 | −0.118888 | −0.0594438 | − | 0.998232i | \(-0.518933\pi\) | ||||
−0.0594438 | + | 0.998232i | \(0.518933\pi\) | |||||||
\(284\) | −16.3028 | −0.967392 | ||||||||
\(285\) | −1.78890 | −0.105965 | ||||||||
\(286\) | −5.60555 | −0.331463 | ||||||||
\(287\) | −3.00000 | −0.177084 | ||||||||
\(288\) | 2.90833 | 0.171375 | ||||||||
\(289\) | 30.7250 | 1.80735 | ||||||||
\(290\) | −2.60555 | −0.153003 | ||||||||
\(291\) | 1.90833 | 0.111868 | ||||||||
\(292\) | −5.81665 | −0.340394 | ||||||||
\(293\) | −23.2111 | −1.35601 | −0.678004 | − | 0.735059i | \(-0.737155\pi\) | ||||
−0.678004 | + | 0.735059i | \(0.737155\pi\) | |||||||
\(294\) | 1.18335 | 0.0690142 | ||||||||
\(295\) | 3.39445 | 0.197632 | ||||||||
\(296\) | 8.00000 | 0.464991 | ||||||||
\(297\) | 3.03616 | 0.176176 | ||||||||
\(298\) | 13.3028 | 0.770609 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.302776 | −0.0174808 | ||||||||
\(301\) | −30.4222 | −1.75351 | ||||||||
\(302\) | −8.90833 | −0.512617 | ||||||||
\(303\) | −0.788897 | −0.0453210 | ||||||||
\(304\) | −5.90833 | −0.338866 | ||||||||
\(305\) | 11.5139 | 0.659283 | ||||||||
\(306\) | −20.0917 | −1.14856 | ||||||||
\(307\) | −11.6972 | −0.667596 | −0.333798 | − | 0.942645i | \(-0.608330\pi\) | ||||
−0.333798 | + | 0.942645i | \(0.608330\pi\) | |||||||
\(308\) | −5.60555 | −0.319406 | ||||||||
\(309\) | 2.45837 | 0.139852 | ||||||||
\(310\) | −7.90833 | −0.449163 | ||||||||
\(311\) | 22.4222 | 1.27145 | 0.635723 | − | 0.771917i | \(-0.280702\pi\) | ||||
0.635723 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −19.7250 | −1.11492 | −0.557461 | − | 0.830203i | \(-0.688224\pi\) | ||||
−0.557461 | + | 0.830203i | \(0.688224\pi\) | |||||||
\(314\) | −18.6056 | −1.04997 | ||||||||
\(315\) | −9.60555 | −0.541212 | ||||||||
\(316\) | 14.4222 | 0.811312 | ||||||||
\(317\) | 17.7250 | 0.995534 | 0.497767 | − | 0.867311i | \(-0.334153\pi\) | ||||
0.497767 | + | 0.867311i | \(0.334153\pi\) | |||||||
\(318\) | 3.39445 | 0.190351 | ||||||||
\(319\) | −4.42221 | −0.247596 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −0.788897 | −0.0440320 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.8167 | 2.27110 | ||||||||
\(324\) | 8.18335 | 0.454630 | ||||||||
\(325\) | 3.30278 | 0.183205 | ||||||||
\(326\) | −9.30278 | −0.515233 | ||||||||
\(327\) | 0.449961 | 0.0248829 | ||||||||
\(328\) | −0.908327 | −0.0501540 | ||||||||
\(329\) | 8.60555 | 0.474439 | ||||||||
\(330\) | −0.513878 | −0.0282881 | ||||||||
\(331\) | 16.6056 | 0.912724 | 0.456362 | − | 0.889794i | \(-0.349152\pi\) | ||||
0.456362 | + | 0.889794i | \(0.349152\pi\) | |||||||
\(332\) | −11.2111 | −0.615289 | ||||||||
\(333\) | 23.2666 | 1.27500 | ||||||||
\(334\) | −6.78890 | −0.371472 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 22.5139 | 1.22641 | 0.613205 | − | 0.789924i | \(-0.289880\pi\) | ||||
0.613205 | + | 0.789924i | \(0.289880\pi\) | |||||||
\(338\) | 2.09167 | 0.113772 | ||||||||
\(339\) | −4.97224 | −0.270055 | ||||||||
\(340\) | 6.90833 | 0.374657 | ||||||||
\(341\) | −13.4222 | −0.726853 | ||||||||
\(342\) | −17.1833 | −0.929169 | ||||||||
\(343\) | 10.2111 | 0.551348 | ||||||||
\(344\) | −9.21110 | −0.496629 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.6972 | −1.05893 | ||||||||
\(347\) | 28.5416 | 1.53220 | 0.766098 | − | 0.642724i | \(-0.222196\pi\) | ||||
0.766098 | + | 0.642724i | \(0.222196\pi\) | |||||||
\(348\) | 0.788897 | 0.0422893 | ||||||||
\(349\) | −27.2111 | −1.45658 | −0.728288 | − | 0.685271i | \(-0.759684\pi\) | ||||
−0.728288 | + | 0.685271i | \(0.759684\pi\) | |||||||
\(350\) | 3.30278 | 0.176541 | ||||||||
\(351\) | 5.90833 | 0.315363 | ||||||||
\(352\) | −1.69722 | −0.0904624 | ||||||||
\(353\) | −10.4222 | −0.554718 | −0.277359 | − | 0.960766i | \(-0.589459\pi\) | ||||
−0.277359 | + | 0.960766i | \(0.589459\pi\) | |||||||
\(354\) | −1.02776 | −0.0546246 | ||||||||
\(355\) | 16.3028 | 0.865261 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.90833 | −0.365627 | ||||||||
\(358\) | −9.39445 | −0.496512 | ||||||||
\(359\) | −11.2111 | −0.591699 | −0.295850 | − | 0.955235i | \(-0.595603\pi\) | ||||
−0.295850 | + | 0.955235i | \(0.595603\pi\) | |||||||
\(360\) | −2.90833 | −0.153282 | ||||||||
\(361\) | 15.9083 | 0.837280 | ||||||||
\(362\) | 17.1194 | 0.899777 | ||||||||
\(363\) | 2.45837 | 0.129031 | ||||||||
\(364\) | −10.9083 | −0.571752 | ||||||||
\(365\) | 5.81665 | 0.304458 | ||||||||
\(366\) | −3.48612 | −0.182223 | ||||||||
\(367\) | −14.7889 | −0.771974 | −0.385987 | − | 0.922504i | \(-0.626139\pi\) | ||||
−0.385987 | + | 0.922504i | \(0.626139\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.64171 | −0.137522 | ||||||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | −37.0278 | −1.92239 | ||||||||
\(372\) | 2.39445 | 0.124146 | ||||||||
\(373\) | −4.60555 | −0.238466 | −0.119233 | − | 0.992866i | \(-0.538044\pi\) | ||||
−0.119233 | + | 0.992866i | \(0.538044\pi\) | |||||||
\(374\) | 11.7250 | 0.606284 | ||||||||
\(375\) | 0.302776 | 0.0156353 | ||||||||
\(376\) | 2.60555 | 0.134371 | ||||||||
\(377\) | −8.60555 | −0.443208 | ||||||||
\(378\) | 5.90833 | 0.303892 | ||||||||
\(379\) | −14.9083 | −0.765789 | −0.382895 | − | 0.923792i | \(-0.625073\pi\) | ||||
−0.382895 | + | 0.923792i | \(0.625073\pi\) | |||||||
\(380\) | 5.90833 | 0.303091 | ||||||||
\(381\) | −2.97224 | −0.152273 | ||||||||
\(382\) | −8.60555 | −0.440298 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0.302776 | 0.0154510 | ||||||||
\(385\) | 5.60555 | 0.285685 | ||||||||
\(386\) | 17.8167 | 0.906844 | ||||||||
\(387\) | −26.7889 | −1.36176 | ||||||||
\(388\) | −6.30278 | −0.319975 | ||||||||
\(389\) | 25.9361 | 1.31501 | 0.657506 | − | 0.753449i | \(-0.271612\pi\) | ||||
0.657506 | + | 0.753449i | \(0.271612\pi\) | |||||||
\(390\) | −1.00000 | −0.0506370 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.90833 | −0.197400 | ||||||||
\(393\) | 3.39445 | 0.171227 | ||||||||
\(394\) | −4.30278 | −0.216771 | ||||||||
\(395\) | −14.4222 | −0.725660 | ||||||||
\(396\) | −4.93608 | −0.248048 | ||||||||
\(397\) | 10.7250 | 0.538271 | 0.269136 | − | 0.963102i | \(-0.413262\pi\) | ||||
0.269136 | + | 0.963102i | \(0.413262\pi\) | |||||||
\(398\) | −20.4222 | −1.02367 | ||||||||
\(399\) | −5.90833 | −0.295786 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 8.60555 | 0.429741 | 0.214870 | − | 0.976643i | \(-0.431067\pi\) | ||||
0.214870 | + | 0.976643i | \(0.431067\pi\) | |||||||
\(402\) | 1.21110 | 0.0604043 | ||||||||
\(403\) | −26.1194 | −1.30110 | ||||||||
\(404\) | 2.60555 | 0.129631 | ||||||||
\(405\) | −8.18335 | −0.406634 | ||||||||
\(406\) | −8.60555 | −0.427086 | ||||||||
\(407\) | −13.5778 | −0.673026 | ||||||||
\(408\) | −2.09167 | −0.103553 | ||||||||
\(409\) | −25.9083 | −1.28108 | −0.640542 | − | 0.767923i | \(-0.721290\pi\) | ||||
−0.640542 | + | 0.767923i | \(0.721290\pi\) | |||||||
\(410\) | 0.908327 | 0.0448591 | ||||||||
\(411\) | 1.18335 | 0.0583702 | ||||||||
\(412\) | −8.11943 | −0.400016 | ||||||||
\(413\) | 11.2111 | 0.551662 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.2111 | 0.550331 | ||||||||
\(416\) | −3.30278 | −0.161932 | ||||||||
\(417\) | 3.81665 | 0.186902 | ||||||||
\(418\) | 10.0278 | 0.490474 | ||||||||
\(419\) | −3.63331 | −0.177499 | −0.0887493 | − | 0.996054i | \(-0.528287\pi\) | ||||
−0.0887493 | + | 0.996054i | \(0.528287\pi\) | |||||||
\(420\) | −1.00000 | −0.0487950 | ||||||||
\(421\) | −30.6972 | −1.49609 | −0.748046 | − | 0.663647i | \(-0.769008\pi\) | ||||
−0.748046 | + | 0.663647i | \(0.769008\pi\) | |||||||
\(422\) | −7.21110 | −0.351031 | ||||||||
\(423\) | 7.57779 | 0.368445 | ||||||||
\(424\) | −11.2111 | −0.544459 | ||||||||
\(425\) | −6.90833 | −0.335103 | ||||||||
\(426\) | −4.93608 | −0.239154 | ||||||||
\(427\) | 38.0278 | 1.84029 | ||||||||
\(428\) | 2.60555 | 0.125944 | ||||||||
\(429\) | −1.69722 | −0.0819428 | ||||||||
\(430\) | 9.21110 | 0.444199 | ||||||||
\(431\) | 30.2389 | 1.45655 | 0.728277 | − | 0.685283i | \(-0.240321\pi\) | ||||
0.728277 | + | 0.685283i | \(0.240321\pi\) | |||||||
\(432\) | 1.78890 | 0.0860684 | ||||||||
\(433\) | 24.0917 | 1.15777 | 0.578886 | − | 0.815409i | \(-0.303488\pi\) | ||||
0.578886 | + | 0.815409i | \(0.303488\pi\) | |||||||
\(434\) | −26.1194 | −1.25377 | ||||||||
\(435\) | −0.788897 | −0.0378247 | ||||||||
\(436\) | −1.48612 | −0.0711723 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1.76114 | −0.0841506 | ||||||||
\(439\) | −14.6972 | −0.701460 | −0.350730 | − | 0.936477i | \(-0.614067\pi\) | ||||
−0.350730 | + | 0.936477i | \(0.614067\pi\) | |||||||
\(440\) | 1.69722 | 0.0809120 | ||||||||
\(441\) | −11.3667 | −0.541271 | ||||||||
\(442\) | 22.8167 | 1.08528 | ||||||||
\(443\) | 17.4861 | 0.830791 | 0.415395 | − | 0.909641i | \(-0.363643\pi\) | ||||
0.415395 | + | 0.909641i | \(0.363643\pi\) | |||||||
\(444\) | 2.42221 | 0.114953 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | 4.02776 | 0.190506 | ||||||||
\(448\) | −3.30278 | −0.156041 | ||||||||
\(449\) | −2.09167 | −0.0987122 | −0.0493561 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493561 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(450\) | 2.90833 | 0.137100 | ||||||||
\(451\) | 1.54163 | 0.0725927 | ||||||||
\(452\) | 16.4222 | 0.772436 | ||||||||
\(453\) | −2.69722 | −0.126727 | ||||||||
\(454\) | −14.6056 | −0.685472 | ||||||||
\(455\) | 10.9083 | 0.511390 | ||||||||
\(456\) | −1.78890 | −0.0837728 | ||||||||
\(457\) | 32.4222 | 1.51665 | 0.758323 | − | 0.651879i | \(-0.226019\pi\) | ||||
0.758323 | + | 0.651879i | \(0.226019\pi\) | |||||||
\(458\) | 2.00000 | 0.0934539 | ||||||||
\(459\) | −12.3583 | −0.576836 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1833 | 0.474286 | 0.237143 | − | 0.971475i | \(-0.423789\pi\) | ||||
0.237143 | + | 0.971475i | \(0.423789\pi\) | |||||||
\(462\) | −1.69722 | −0.0789620 | ||||||||
\(463\) | 17.6333 | 0.819489 | 0.409745 | − | 0.912200i | \(-0.365618\pi\) | ||||
0.409745 | + | 0.912200i | \(0.365618\pi\) | |||||||
\(464\) | −2.60555 | −0.120960 | ||||||||
\(465\) | −2.39445 | −0.111040 | ||||||||
\(466\) | −25.8167 | −1.19593 | ||||||||
\(467\) | 1.81665 | 0.0840647 | 0.0420324 | − | 0.999116i | \(-0.486617\pi\) | ||||
0.0420324 | + | 0.999116i | \(0.486617\pi\) | |||||||
\(468\) | −9.60555 | −0.444017 | ||||||||
\(469\) | −13.2111 | −0.610032 | ||||||||
\(470\) | −2.60555 | −0.120185 | ||||||||
\(471\) | −5.63331 | −0.259569 | ||||||||
\(472\) | 3.39445 | 0.156242 | ||||||||
\(473\) | 15.6333 | 0.718820 | ||||||||
\(474\) | 4.36669 | 0.200569 | ||||||||
\(475\) | −5.90833 | −0.271093 | ||||||||
\(476\) | 22.8167 | 1.04580 | ||||||||
\(477\) | −32.6056 | −1.49291 | ||||||||
\(478\) | −5.21110 | −0.238350 | ||||||||
\(479\) | 30.0000 | 1.37073 | 0.685367 | − | 0.728197i | \(-0.259642\pi\) | ||||
0.685367 | + | 0.728197i | \(0.259642\pi\) | |||||||
\(480\) | −0.302776 | −0.0138198 | ||||||||
\(481\) | −26.4222 | −1.20475 | ||||||||
\(482\) | −14.4222 | −0.656913 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.11943 | −0.369065 | ||||||||
\(485\) | 6.30278 | 0.286194 | ||||||||
\(486\) | 7.84441 | 0.355830 | ||||||||
\(487\) | 9.81665 | 0.444835 | 0.222418 | − | 0.974952i | \(-0.428605\pi\) | ||||
0.222418 | + | 0.974952i | \(0.428605\pi\) | |||||||
\(488\) | 11.5139 | 0.521209 | ||||||||
\(489\) | −2.81665 | −0.127373 | ||||||||
\(490\) | 3.90833 | 0.176560 | ||||||||
\(491\) | −4.18335 | −0.188792 | −0.0943959 | − | 0.995535i | \(-0.530092\pi\) | ||||
−0.0943959 | + | 0.995535i | \(0.530092\pi\) | |||||||
\(492\) | −0.275019 | −0.0123988 | ||||||||
\(493\) | 18.0000 | 0.810679 | ||||||||
\(494\) | 19.5139 | 0.877971 | ||||||||
\(495\) | 4.93608 | 0.221860 | ||||||||
\(496\) | −7.90833 | −0.355094 | ||||||||
\(497\) | 53.8444 | 2.41525 | ||||||||
\(498\) | −3.39445 | −0.152109 | ||||||||
\(499\) | −31.6333 | −1.41610 | −0.708051 | − | 0.706162i | \(-0.750425\pi\) | ||||
−0.708051 | + | 0.706162i | \(0.750425\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −2.05551 | −0.0918335 | ||||||||
\(502\) | 12.5139 | 0.558522 | ||||||||
\(503\) | −29.7250 | −1.32537 | −0.662686 | − | 0.748898i | \(-0.730583\pi\) | ||||
−0.662686 | + | 0.748898i | \(0.730583\pi\) | |||||||
\(504\) | −9.60555 | −0.427865 | ||||||||
\(505\) | −2.60555 | −0.115946 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.633308 | 0.0281262 | ||||||||
\(508\) | 9.81665 | 0.435544 | ||||||||
\(509\) | −35.4500 | −1.57129 | −0.785646 | − | 0.618676i | \(-0.787669\pi\) | ||||
−0.785646 | + | 0.618676i | \(0.787669\pi\) | |||||||
\(510\) | 2.09167 | 0.0926208 | ||||||||
\(511\) | 19.2111 | 0.849849 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −10.5694 | −0.466650 | ||||||||
\(514\) | 1.81665 | 0.0801292 | ||||||||
\(515\) | 8.11943 | 0.357785 | ||||||||
\(516\) | −2.78890 | −0.122774 | ||||||||
\(517\) | −4.42221 | −0.194488 | ||||||||
\(518\) | −26.4222 | −1.16093 | ||||||||
\(519\) | −5.96384 | −0.261784 | ||||||||
\(520\) | 3.30278 | 0.144836 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | −7.57779 | −0.331671 | ||||||||
\(523\) | 20.4222 | 0.893001 | 0.446500 | − | 0.894783i | \(-0.352670\pi\) | ||||
0.446500 | + | 0.894783i | \(0.352670\pi\) | |||||||
\(524\) | −11.2111 | −0.489759 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 3.51388 | 0.153212 | ||||||||
\(527\) | 54.6333 | 2.37986 | ||||||||
\(528\) | −0.513878 | −0.0223637 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 11.2111 | 0.486979 | ||||||||
\(531\) | 9.87217 | 0.428416 | ||||||||
\(532\) | 19.5139 | 0.846034 | ||||||||
\(533\) | 3.00000 | 0.129944 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.60555 | −0.112648 | ||||||||
\(536\) | −4.00000 | −0.172774 | ||||||||
\(537\) | −2.84441 | −0.122745 | ||||||||
\(538\) | −4.18335 | −0.180357 | ||||||||
\(539\) | 6.63331 | 0.285717 | ||||||||
\(540\) | −1.78890 | −0.0769819 | ||||||||
\(541\) | 28.8444 | 1.24012 | 0.620059 | − | 0.784555i | \(-0.287109\pi\) | ||||
0.620059 | + | 0.784555i | \(0.287109\pi\) | |||||||
\(542\) | 2.69722 | 0.115856 | ||||||||
\(543\) | 5.18335 | 0.222439 | ||||||||
\(544\) | 6.90833 | 0.296192 | ||||||||
\(545\) | 1.48612 | 0.0636585 | ||||||||
\(546\) | −3.30278 | −0.141346 | ||||||||
\(547\) | −10.5139 | −0.449541 | −0.224770 | − | 0.974412i | \(-0.572163\pi\) | ||||
−0.224770 | + | 0.974412i | \(0.572163\pi\) | |||||||
\(548\) | −3.90833 | −0.166955 | ||||||||
\(549\) | 33.4861 | 1.42915 | ||||||||
\(550\) | −1.69722 | −0.0723699 | ||||||||
\(551\) | 15.3944 | 0.655826 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −47.6333 | −2.02557 | ||||||||
\(554\) | 27.2111 | 1.15609 | ||||||||
\(555\) | −2.42221 | −0.102817 | ||||||||
\(556\) | −12.6056 | −0.534594 | ||||||||
\(557\) | −22.4222 | −0.950059 | −0.475030 | − | 0.879970i | \(-0.657563\pi\) | ||||
−0.475030 | + | 0.879970i | \(0.657563\pi\) | |||||||
\(558\) | −23.0000 | −0.973668 | ||||||||
\(559\) | 30.4222 | 1.28672 | ||||||||
\(560\) | 3.30278 | 0.139568 | ||||||||
\(561\) | 3.55004 | 0.149883 | ||||||||
\(562\) | −26.6056 | −1.12229 | ||||||||
\(563\) | 3.63331 | 0.153126 | 0.0765628 | − | 0.997065i | \(-0.475605\pi\) | ||||
0.0765628 | + | 0.997065i | \(0.475605\pi\) | |||||||
\(564\) | 0.788897 | 0.0332186 | ||||||||
\(565\) | −16.4222 | −0.690887 | ||||||||
\(566\) | 2.00000 | 0.0840663 | ||||||||
\(567\) | −27.0278 | −1.13506 | ||||||||
\(568\) | 16.3028 | 0.684049 | ||||||||
\(569\) | −28.4222 | −1.19152 | −0.595760 | − | 0.803162i | \(-0.703149\pi\) | ||||
−0.595760 | + | 0.803162i | \(0.703149\pi\) | |||||||
\(570\) | 1.78890 | 0.0749287 | ||||||||
\(571\) | 16.1194 | 0.674577 | 0.337289 | − | 0.941401i | \(-0.390490\pi\) | ||||
0.337289 | + | 0.941401i | \(0.390490\pi\) | |||||||
\(572\) | 5.60555 | 0.234380 | ||||||||
\(573\) | −2.60555 | −0.108848 | ||||||||
\(574\) | 3.00000 | 0.125218 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.90833 | −0.121180 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | −30.7250 | −1.27799 | ||||||||
\(579\) | 5.39445 | 0.224186 | ||||||||
\(580\) | 2.60555 | 0.108190 | ||||||||
\(581\) | 37.0278 | 1.53617 | ||||||||
\(582\) | −1.90833 | −0.0791027 | ||||||||
\(583\) | 19.0278 | 0.788049 | ||||||||
\(584\) | 5.81665 | 0.240695 | ||||||||
\(585\) | 9.60555 | 0.397141 | ||||||||
\(586\) | 23.2111 | 0.958842 | ||||||||
\(587\) | 16.5416 | 0.682746 | 0.341373 | − | 0.939928i | \(-0.389108\pi\) | ||||
0.341373 | + | 0.939928i | \(0.389108\pi\) | |||||||
\(588\) | −1.18335 | −0.0488004 | ||||||||
\(589\) | 46.7250 | 1.92527 | ||||||||
\(590\) | −3.39445 | −0.139747 | ||||||||
\(591\) | −1.30278 | −0.0535890 | ||||||||
\(592\) | −8.00000 | −0.328798 | ||||||||
\(593\) | −1.81665 | −0.0746010 | −0.0373005 | − | 0.999304i | \(-0.511876\pi\) | ||||
−0.0373005 | + | 0.999304i | \(0.511876\pi\) | |||||||
\(594\) | −3.03616 | −0.124575 | ||||||||
\(595\) | −22.8167 | −0.935392 | ||||||||
\(596\) | −13.3028 | −0.544903 | ||||||||
\(597\) | −6.18335 | −0.253068 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.3305 | −1.44357 | −0.721783 | − | 0.692119i | \(-0.756677\pi\) | ||||
−0.721783 | + | 0.692119i | \(0.756677\pi\) | |||||||
\(600\) | 0.302776 | 0.0123608 | ||||||||
\(601\) | 42.9361 | 1.75140 | 0.875700 | − | 0.482856i | \(-0.160401\pi\) | ||||
0.875700 | + | 0.482856i | \(0.160401\pi\) | |||||||
\(602\) | 30.4222 | 1.23992 | ||||||||
\(603\) | −11.6333 | −0.473745 | ||||||||
\(604\) | 8.90833 | 0.362475 | ||||||||
\(605\) | 8.11943 | 0.330102 | ||||||||
\(606\) | 0.788897 | 0.0320468 | ||||||||
\(607\) | 46.0555 | 1.86934 | 0.934668 | − | 0.355522i | \(-0.115697\pi\) | ||||
0.934668 | + | 0.355522i | \(0.115697\pi\) | |||||||
\(608\) | 5.90833 | 0.239614 | ||||||||
\(609\) | −2.60555 | −0.105582 | ||||||||
\(610\) | −11.5139 | −0.466183 | ||||||||
\(611\) | −8.60555 | −0.348143 | ||||||||
\(612\) | 20.0917 | 0.812158 | ||||||||
\(613\) | −3.57779 | −0.144506 | −0.0722529 | − | 0.997386i | \(-0.523019\pi\) | ||||
−0.0722529 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(614\) | 11.6972 | 0.472062 | ||||||||
\(615\) | 0.275019 | 0.0110898 | ||||||||
\(616\) | 5.60555 | 0.225854 | ||||||||
\(617\) | −18.9083 | −0.761221 | −0.380610 | − | 0.924736i | \(-0.624286\pi\) | ||||
−0.380610 | + | 0.924736i | \(0.624286\pi\) | |||||||
\(618\) | −2.45837 | −0.0988900 | ||||||||
\(619\) | 12.3305 | 0.495606 | 0.247803 | − | 0.968810i | \(-0.420291\pi\) | ||||
0.247803 | + | 0.968810i | \(0.420291\pi\) | |||||||
\(620\) | 7.90833 | 0.317606 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.4222 | −0.899049 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 19.7250 | 0.788369 | ||||||||
\(627\) | 3.03616 | 0.121253 | ||||||||
\(628\) | 18.6056 | 0.742442 | ||||||||
\(629\) | 55.2666 | 2.20362 | ||||||||
\(630\) | 9.60555 | 0.382694 | ||||||||
\(631\) | −23.3944 | −0.931318 | −0.465659 | − | 0.884964i | \(-0.654183\pi\) | ||||
−0.465659 | + | 0.884964i | \(0.654183\pi\) | |||||||
\(632\) | −14.4222 | −0.573685 | ||||||||
\(633\) | −2.18335 | −0.0867802 | ||||||||
\(634\) | −17.7250 | −0.703949 | ||||||||
\(635\) | −9.81665 | −0.389562 | ||||||||
\(636\) | −3.39445 | −0.134599 | ||||||||
\(637\) | 12.9083 | 0.511447 | ||||||||
\(638\) | 4.42221 | 0.175077 | ||||||||
\(639\) | 47.4138 | 1.87566 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 36.0000 | 1.42191 | 0.710957 | − | 0.703235i | \(-0.248262\pi\) | ||||
0.710957 | + | 0.703235i | \(0.248262\pi\) | |||||||
\(642\) | 0.788897 | 0.0311353 | ||||||||
\(643\) | 34.2389 | 1.35025 | 0.675124 | − | 0.737704i | \(-0.264090\pi\) | ||||
0.675124 | + | 0.737704i | \(0.264090\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.78890 | 0.109813 | ||||||||
\(646\) | −40.8167 | −1.60591 | ||||||||
\(647\) | 26.8444 | 1.05536 | 0.527681 | − | 0.849442i | \(-0.323062\pi\) | ||||
0.527681 | + | 0.849442i | \(0.323062\pi\) | |||||||
\(648\) | −8.18335 | −0.321472 | ||||||||
\(649\) | −5.76114 | −0.226145 | ||||||||
\(650\) | −3.30278 | −0.129546 | ||||||||
\(651\) | −7.90833 | −0.309952 | ||||||||
\(652\) | 9.30278 | 0.364325 | ||||||||
\(653\) | 41.7250 | 1.63282 | 0.816412 | − | 0.577469i | \(-0.195960\pi\) | ||||
0.816412 | + | 0.577469i | \(0.195960\pi\) | |||||||
\(654\) | −0.449961 | −0.0175949 | ||||||||
\(655\) | 11.2111 | 0.438054 | ||||||||
\(656\) | 0.908327 | 0.0354642 | ||||||||
\(657\) | 16.9167 | 0.659985 | ||||||||
\(658\) | −8.60555 | −0.335479 | ||||||||
\(659\) | −15.6333 | −0.608987 | −0.304494 | − | 0.952514i | \(-0.598487\pi\) | ||||
−0.304494 | + | 0.952514i | \(0.598487\pi\) | |||||||
\(660\) | 0.513878 | 0.0200027 | ||||||||
\(661\) | 34.9083 | 1.35778 | 0.678888 | − | 0.734242i | \(-0.262462\pi\) | ||||
0.678888 | + | 0.734242i | \(0.262462\pi\) | |||||||
\(662\) | −16.6056 | −0.645393 | ||||||||
\(663\) | 6.90833 | 0.268297 | ||||||||
\(664\) | 11.2111 | 0.435075 | ||||||||
\(665\) | −19.5139 | −0.756716 | ||||||||
\(666\) | −23.2666 | −0.901563 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.78890 | 0.262670 | ||||||||
\(669\) | 1.21110 | 0.0468239 | ||||||||
\(670\) | 4.00000 | 0.154533 | ||||||||
\(671\) | −19.5416 | −0.754396 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −37.6333 | −1.45066 | −0.725329 | − | 0.688403i | \(-0.758312\pi\) | ||||
−0.725329 | + | 0.688403i | \(0.758312\pi\) | |||||||
\(674\) | −22.5139 | −0.867202 | ||||||||
\(675\) | 1.78890 | 0.0688547 | ||||||||
\(676\) | −2.09167 | −0.0804490 | ||||||||
\(677\) | −16.4222 | −0.631157 | −0.315578 | − | 0.948900i | \(-0.602198\pi\) | ||||
−0.315578 | + | 0.948900i | \(0.602198\pi\) | |||||||
\(678\) | 4.97224 | 0.190958 | ||||||||
\(679\) | 20.8167 | 0.798870 | ||||||||
\(680\) | −6.90833 | −0.264922 | ||||||||
\(681\) | −4.42221 | −0.169459 | ||||||||
\(682\) | 13.4222 | 0.513963 | ||||||||
\(683\) | −0.275019 | −0.0105233 | −0.00526166 | − | 0.999986i | \(-0.501675\pi\) | ||||
−0.00526166 | + | 0.999986i | \(0.501675\pi\) | |||||||
\(684\) | 17.1833 | 0.657022 | ||||||||
\(685\) | 3.90833 | 0.149329 | ||||||||
\(686\) | −10.2111 | −0.389862 | ||||||||
\(687\) | 0.605551 | 0.0231032 | ||||||||
\(688\) | 9.21110 | 0.351170 | ||||||||
\(689\) | 37.0278 | 1.41065 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.8167 | 1.97120 | 0.985599 | − | 0.169098i | \(-0.0540855\pi\) | ||||
0.985599 | + | 0.169098i | \(0.0540855\pi\) | |||||||
\(692\) | 19.6972 | 0.748776 | ||||||||
\(693\) | 16.3028 | 0.619291 | ||||||||
\(694\) | −28.5416 | −1.08343 | ||||||||
\(695\) | 12.6056 | 0.478156 | ||||||||
\(696\) | −0.788897 | −0.0299031 | ||||||||
\(697\) | −6.27502 | −0.237683 | ||||||||
\(698\) | 27.2111 | 1.02996 | ||||||||
\(699\) | −7.81665 | −0.295653 | ||||||||
\(700\) | −3.30278 | −0.124833 | ||||||||
\(701\) | −32.0917 | −1.21209 | −0.606043 | − | 0.795432i | \(-0.707244\pi\) | ||||
−0.606043 | + | 0.795432i | \(0.707244\pi\) | |||||||
\(702\) | −5.90833 | −0.222995 | ||||||||
\(703\) | 47.2666 | 1.78269 | ||||||||
\(704\) | 1.69722 | 0.0639665 | ||||||||
\(705\) | −0.788897 | −0.0297116 | ||||||||
\(706\) | 10.4222 | 0.392245 | ||||||||
\(707\) | −8.60555 | −0.323645 | ||||||||
\(708\) | 1.02776 | 0.0386254 | ||||||||
\(709\) | 15.8806 | 0.596407 | 0.298204 | − | 0.954502i | \(-0.403613\pi\) | ||||
0.298204 | + | 0.954502i | \(0.403613\pi\) | |||||||
\(710\) | −16.3028 | −0.611832 | ||||||||
\(711\) | −41.9445 | −1.57304 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 6.90833 | 0.258538 | ||||||||
\(715\) | −5.60555 | −0.209636 | ||||||||
\(716\) | 9.39445 | 0.351087 | ||||||||
\(717\) | −1.57779 | −0.0589238 | ||||||||
\(718\) | 11.2111 | 0.418395 | ||||||||
\(719\) | 10.6972 | 0.398939 | 0.199470 | − | 0.979904i | \(-0.436078\pi\) | ||||
0.199470 | + | 0.979904i | \(0.436078\pi\) | |||||||
\(720\) | 2.90833 | 0.108387 | ||||||||
\(721\) | 26.8167 | 0.998704 | ||||||||
\(722\) | −15.9083 | −0.592047 | ||||||||
\(723\) | −4.36669 | −0.162399 | ||||||||
\(724\) | −17.1194 | −0.636239 | ||||||||
\(725\) | −2.60555 | −0.0967677 | ||||||||
\(726\) | −2.45837 | −0.0912385 | ||||||||
\(727\) | −2.90833 | −0.107864 | −0.0539319 | − | 0.998545i | \(-0.517175\pi\) | ||||
−0.0539319 | + | 0.998545i | \(0.517175\pi\) | |||||||
\(728\) | 10.9083 | 0.404289 | ||||||||
\(729\) | −22.1749 | −0.821294 | ||||||||
\(730\) | −5.81665 | −0.215284 | ||||||||
\(731\) | −63.6333 | −2.35356 | ||||||||
\(732\) | 3.48612 | 0.128851 | ||||||||
\(733\) | −29.6333 | −1.09453 | −0.547266 | − | 0.836959i | \(-0.684331\pi\) | ||||
−0.547266 | + | 0.836959i | \(0.684331\pi\) | |||||||
\(734\) | 14.7889 | 0.545868 | ||||||||
\(735\) | 1.18335 | 0.0436484 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.78890 | 0.250072 | ||||||||
\(738\) | 2.64171 | 0.0972427 | ||||||||
\(739\) | 35.6333 | 1.31079 | 0.655396 | − | 0.755285i | \(-0.272502\pi\) | ||||
0.655396 | + | 0.755285i | \(0.272502\pi\) | |||||||
\(740\) | 8.00000 | 0.294086 | ||||||||
\(741\) | 5.90833 | 0.217048 | ||||||||
\(742\) | 37.0278 | 1.35933 | ||||||||
\(743\) | 32.3305 | 1.18609 | 0.593046 | − | 0.805169i | \(-0.297925\pi\) | ||||
0.593046 | + | 0.805169i | \(0.297925\pi\) | |||||||
\(744\) | −2.39445 | −0.0877847 | ||||||||
\(745\) | 13.3028 | 0.487376 | ||||||||
\(746\) | 4.60555 | 0.168621 | ||||||||
\(747\) | 32.6056 | 1.19297 | ||||||||
\(748\) | −11.7250 | −0.428708 | ||||||||
\(749\) | −8.60555 | −0.314440 | ||||||||
\(750\) | −0.302776 | −0.0110558 | ||||||||
\(751\) | −21.8167 | −0.796101 | −0.398051 | − | 0.917364i | \(-0.630313\pi\) | ||||
−0.398051 | + | 0.917364i | \(0.630313\pi\) | |||||||
\(752\) | −2.60555 | −0.0950147 | ||||||||
\(753\) | 3.78890 | 0.138075 | ||||||||
\(754\) | 8.60555 | 0.313396 | ||||||||
\(755\) | −8.90833 | −0.324207 | ||||||||
\(756\) | −5.90833 | −0.214884 | ||||||||
\(757\) | −13.2111 | −0.480166 | −0.240083 | − | 0.970752i | \(-0.577175\pi\) | ||||
−0.240083 | + | 0.970752i | \(0.577175\pi\) | |||||||
\(758\) | 14.9083 | 0.541495 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.90833 | −0.214318 | ||||||||
\(761\) | −49.5416 | −1.79588 | −0.897941 | − | 0.440115i | \(-0.854938\pi\) | ||||
−0.897941 | + | 0.440115i | \(0.854938\pi\) | |||||||
\(762\) | 2.97224 | 0.107673 | ||||||||
\(763\) | 4.90833 | 0.177693 | ||||||||
\(764\) | 8.60555 | 0.311338 | ||||||||
\(765\) | −20.0917 | −0.726416 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.2111 | −0.404809 | ||||||||
\(768\) | −0.302776 | −0.0109255 | ||||||||
\(769\) | −45.2666 | −1.63236 | −0.816178 | − | 0.577801i | \(-0.803911\pi\) | ||||
−0.816178 | + | 0.577801i | \(0.803911\pi\) | |||||||
\(770\) | −5.60555 | −0.202010 | ||||||||
\(771\) | 0.550039 | 0.0198092 | ||||||||
\(772\) | −17.8167 | −0.641235 | ||||||||
\(773\) | −12.0000 | −0.431610 | −0.215805 | − | 0.976436i | \(-0.569238\pi\) | ||||
−0.215805 | + | 0.976436i | \(0.569238\pi\) | |||||||
\(774\) | 26.7889 | 0.962907 | ||||||||
\(775\) | −7.90833 | −0.284075 | ||||||||
\(776\) | 6.30278 | 0.226256 | ||||||||
\(777\) | −8.00000 | −0.286998 | ||||||||
\(778\) | −25.9361 | −0.929854 | ||||||||
\(779\) | −5.36669 | −0.192282 | ||||||||
\(780\) | 1.00000 | 0.0358057 | ||||||||
\(781\) | −27.6695 | −0.990091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.66106 | −0.166573 | ||||||||
\(784\) | 3.90833 | 0.139583 | ||||||||
\(785\) | −18.6056 | −0.664061 | ||||||||
\(786\) | −3.39445 | −0.121076 | ||||||||
\(787\) | −37.4500 | −1.33495 | −0.667473 | − | 0.744634i | \(-0.732624\pi\) | ||||
−0.667473 | + | 0.744634i | \(0.732624\pi\) | |||||||
\(788\) | 4.30278 | 0.153280 | ||||||||
\(789\) | 1.06392 | 0.0378764 | ||||||||
\(790\) | 14.4222 | 0.513119 | ||||||||
\(791\) | −54.2389 | −1.92851 | ||||||||
\(792\) | 4.93608 | 0.175396 | ||||||||
\(793\) | −38.0278 | −1.35041 | ||||||||
\(794\) | −10.7250 | −0.380615 | ||||||||
\(795\) | 3.39445 | 0.120389 | ||||||||
\(796\) | 20.4222 | 0.723846 | ||||||||
\(797\) | −1.81665 | −0.0643492 | −0.0321746 | − | 0.999482i | \(-0.510243\pi\) | ||||
−0.0321746 | + | 0.999482i | \(0.510243\pi\) | |||||||
\(798\) | 5.90833 | 0.209153 | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.60555 | −0.303873 | ||||||||
\(803\) | −9.87217 | −0.348381 | ||||||||
\(804\) | −1.21110 | −0.0427123 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.1194 | 0.920018 | ||||||||
\(807\) | −1.26662 | −0.0445870 | ||||||||
\(808\) | −2.60555 | −0.0916630 | ||||||||
\(809\) | 50.7250 | 1.78340 | 0.891698 | − | 0.452631i | \(-0.149515\pi\) | ||||
0.891698 | + | 0.452631i | \(0.149515\pi\) | |||||||
\(810\) | 8.18335 | 0.287533 | ||||||||
\(811\) | −41.0278 | −1.44068 | −0.720340 | − | 0.693621i | \(-0.756014\pi\) | ||||
−0.720340 | + | 0.693621i | \(0.756014\pi\) | |||||||
\(812\) | 8.60555 | 0.301996 | ||||||||
\(813\) | 0.816654 | 0.0286413 | ||||||||
\(814\) | 13.5778 | 0.475901 | ||||||||
\(815\) | −9.30278 | −0.325862 | ||||||||
\(816\) | 2.09167 | 0.0732232 | ||||||||
\(817\) | −54.4222 | −1.90399 | ||||||||
\(818\) | 25.9083 | 0.905863 | ||||||||
\(819\) | 31.7250 | 1.10856 | ||||||||
\(820\) | −0.908327 | −0.0317202 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | −1.18335 | −0.0412739 | ||||||||
\(823\) | −15.2111 | −0.530226 | −0.265113 | − | 0.964217i | \(-0.585409\pi\) | ||||
−0.265113 | + | 0.964217i | \(0.585409\pi\) | |||||||
\(824\) | 8.11943 | 0.282854 | ||||||||
\(825\) | −0.513878 | −0.0178909 | ||||||||
\(826\) | −11.2111 | −0.390084 | ||||||||
\(827\) | 29.4500 | 1.02408 | 0.512038 | − | 0.858963i | \(-0.328891\pi\) | ||||
0.512038 | + | 0.858963i | \(0.328891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.2111 | 1.08401 | 0.542003 | − | 0.840376i | \(-0.317666\pi\) | ||||
0.542003 | + | 0.840376i | \(0.317666\pi\) | |||||||
\(830\) | −11.2111 | −0.389143 | ||||||||
\(831\) | 8.23886 | 0.285803 | ||||||||
\(832\) | 3.30278 | 0.114503 | ||||||||
\(833\) | −27.0000 | −0.935495 | ||||||||
\(834\) | −3.81665 | −0.132160 | ||||||||
\(835\) | −6.78890 | −0.234939 | ||||||||
\(836\) | −10.0278 | −0.346817 | ||||||||
\(837\) | −14.1472 | −0.488998 | ||||||||
\(838\) | 3.63331 | 0.125511 | ||||||||
\(839\) | 43.8167 | 1.51272 | 0.756359 | − | 0.654156i | \(-0.226976\pi\) | ||||
0.756359 | + | 0.654156i | \(0.226976\pi\) | |||||||
\(840\) | 1.00000 | 0.0345033 | ||||||||
\(841\) | −22.2111 | −0.765900 | ||||||||
\(842\) | 30.6972 | 1.05790 | ||||||||
\(843\) | −8.05551 | −0.277447 | ||||||||
\(844\) | 7.21110 | 0.248216 | ||||||||
\(845\) | 2.09167 | 0.0719557 | ||||||||
\(846\) | −7.57779 | −0.260530 | ||||||||
\(847\) | 26.8167 | 0.921431 | ||||||||
\(848\) | 11.2111 | 0.384991 | ||||||||
\(849\) | 0.605551 | 0.0207825 | ||||||||
\(850\) | 6.90833 | 0.236954 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 4.93608 | 0.169107 | ||||||||
\(853\) | −21.7250 | −0.743849 | −0.371925 | − | 0.928263i | \(-0.621302\pi\) | ||||
−0.371925 | + | 0.928263i | \(0.621302\pi\) | |||||||
\(854\) | −38.0278 | −1.30128 | ||||||||
\(855\) | −17.1833 | −0.587658 | ||||||||
\(856\) | −2.60555 | −0.0890559 | ||||||||
\(857\) | 9.63331 | 0.329068 | 0.164534 | − | 0.986371i | \(-0.447388\pi\) | ||||
0.164534 | + | 0.986371i | \(0.447388\pi\) | |||||||
\(858\) | 1.69722 | 0.0579423 | ||||||||
\(859\) | −35.8167 | −1.22205 | −0.611024 | − | 0.791612i | \(-0.709242\pi\) | ||||
−0.611024 | + | 0.791612i | \(0.709242\pi\) | |||||||
\(860\) | −9.21110 | −0.314096 | ||||||||
\(861\) | 0.908327 | 0.0309557 | ||||||||
\(862\) | −30.2389 | −1.02994 | ||||||||
\(863\) | −41.4500 | −1.41097 | −0.705487 | − | 0.708723i | \(-0.749271\pi\) | ||||
−0.705487 | + | 0.708723i | \(0.749271\pi\) | |||||||
\(864\) | −1.78890 | −0.0608595 | ||||||||
\(865\) | −19.6972 | −0.669726 | ||||||||
\(866\) | −24.0917 | −0.818668 | ||||||||
\(867\) | −9.30278 | −0.315939 | ||||||||
\(868\) | 26.1194 | 0.886551 | ||||||||
\(869\) | 24.4777 | 0.830350 | ||||||||
\(870\) | 0.788897 | 0.0267461 | ||||||||
\(871\) | 13.2111 | 0.447641 | ||||||||
\(872\) | 1.48612 | 0.0503264 | ||||||||
\(873\) | 18.3305 | 0.620395 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.30278 | 0.111654 | ||||||||
\(876\) | 1.76114 | 0.0595034 | ||||||||
\(877\) | −48.1749 | −1.62675 | −0.813376 | − | 0.581738i | \(-0.802373\pi\) | ||||
−0.813376 | + | 0.581738i | \(0.802373\pi\) | |||||||
\(878\) | 14.6972 | 0.496007 | ||||||||
\(879\) | 7.02776 | 0.237040 | ||||||||
\(880\) | −1.69722 | −0.0572134 | ||||||||
\(881\) | −55.2666 | −1.86198 | −0.930990 | − | 0.365045i | \(-0.881054\pi\) | ||||
−0.930990 | + | 0.365045i | \(0.881054\pi\) | |||||||
\(882\) | 11.3667 | 0.382736 | ||||||||
\(883\) | 8.27502 | 0.278477 | 0.139238 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139238 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(884\) | −22.8167 | −0.767407 | ||||||||
\(885\) | −1.02776 | −0.0345477 | ||||||||
\(886\) | −17.4861 | −0.587458 | ||||||||
\(887\) | 27.6333 | 0.927836 | 0.463918 | − | 0.885878i | \(-0.346443\pi\) | ||||
0.463918 | + | 0.885878i | \(0.346443\pi\) | |||||||
\(888\) | −2.42221 | −0.0812839 | ||||||||
\(889\) | −32.4222 | −1.08741 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.8890 | 0.465298 | ||||||||
\(892\) | −4.00000 | −0.133930 | ||||||||
\(893\) | 15.3944 | 0.515156 | ||||||||
\(894\) | −4.02776 | −0.134708 | ||||||||
\(895\) | −9.39445 | −0.314022 | ||||||||
\(896\) | 3.30278 | 0.110338 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.09167 | 0.0698000 | ||||||||
\(899\) | 20.6056 | 0.687234 | ||||||||
\(900\) | −2.90833 | −0.0969442 | ||||||||
\(901\) | −77.4500 | −2.58023 | ||||||||
\(902\) | −1.54163 | −0.0513308 | ||||||||
\(903\) | 9.21110 | 0.306526 | ||||||||
\(904\) | −16.4222 | −0.546194 | ||||||||
\(905\) | 17.1194 | 0.569069 | ||||||||
\(906\) | 2.69722 | 0.0896093 | ||||||||
\(907\) | −48.6611 | −1.61576 | −0.807882 | − | 0.589344i | \(-0.799386\pi\) | ||||
−0.807882 | + | 0.589344i | \(0.799386\pi\) | |||||||
\(908\) | 14.6056 | 0.484702 | ||||||||
\(909\) | −7.57779 | −0.251340 | ||||||||
\(910\) | −10.9083 | −0.361608 | ||||||||
\(911\) | 4.18335 | 0.138600 | 0.0693002 | − | 0.997596i | \(-0.477923\pi\) | ||||
0.0693002 | + | 0.997596i | \(0.477923\pi\) | |||||||
\(912\) | 1.78890 | 0.0592363 | ||||||||
\(913\) | −19.0278 | −0.629727 | ||||||||
\(914\) | −32.4222 | −1.07243 | ||||||||
\(915\) | −3.48612 | −0.115248 | ||||||||
\(916\) | −2.00000 | −0.0660819 | ||||||||
\(917\) | 37.0278 | 1.22276 | ||||||||
\(918\) | 12.3583 | 0.407884 | ||||||||
\(919\) | −44.0000 | −1.45143 | −0.725713 | − | 0.687998i | \(-0.758490\pi\) | ||||
−0.725713 | + | 0.687998i | \(0.758490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.54163 | 0.116701 | ||||||||
\(922\) | −10.1833 | −0.335371 | ||||||||
\(923\) | −53.8444 | −1.77231 | ||||||||
\(924\) | 1.69722 | 0.0558346 | ||||||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | −17.6333 | −0.579466 | ||||||||
\(927\) | 23.6140 | 0.775584 | ||||||||
\(928\) | 2.60555 | 0.0855314 | ||||||||
\(929\) | −14.3667 | −0.471356 | −0.235678 | − | 0.971831i | \(-0.575731\pi\) | ||||
−0.235678 | + | 0.971831i | \(0.575731\pi\) | |||||||
\(930\) | 2.39445 | 0.0785171 | ||||||||
\(931\) | −23.0917 | −0.756799 | ||||||||
\(932\) | 25.8167 | 0.845653 | ||||||||
\(933\) | −6.78890 | −0.222259 | ||||||||
\(934\) | −1.81665 | −0.0594427 | ||||||||
\(935\) | 11.7250 | 0.383448 | ||||||||
\(936\) | 9.60555 | 0.313967 | ||||||||
\(937\) | −37.9638 | −1.24022 | −0.620112 | − | 0.784513i | \(-0.712913\pi\) | ||||
−0.620112 | + | 0.784513i | \(0.712913\pi\) | |||||||
\(938\) | 13.2111 | 0.431358 | ||||||||
\(939\) | 5.97224 | 0.194897 | ||||||||
\(940\) | 2.60555 | 0.0849837 | ||||||||
\(941\) | −25.9361 | −0.845492 | −0.422746 | − | 0.906248i | \(-0.638934\pi\) | ||||
−0.422746 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(942\) | 5.63331 | 0.183543 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.39445 | −0.110480 | ||||||||
\(945\) | 5.90833 | 0.192198 | ||||||||
\(946\) | −15.6333 | −0.508283 | ||||||||
\(947\) | −4.93608 | −0.160401 | −0.0802006 | − | 0.996779i | \(-0.525556\pi\) | ||||
−0.0802006 | + | 0.996779i | \(0.525556\pi\) | |||||||
\(948\) | −4.36669 | −0.141824 | ||||||||
\(949\) | −19.2111 | −0.623619 | ||||||||
\(950\) | 5.90833 | 0.191691 | ||||||||
\(951\) | −5.36669 | −0.174027 | ||||||||
\(952\) | −22.8167 | −0.739492 | ||||||||
\(953\) | 41.3305 | 1.33883 | 0.669414 | − | 0.742890i | \(-0.266545\pi\) | ||||
0.669414 | + | 0.742890i | \(0.266545\pi\) | |||||||
\(954\) | 32.6056 | 1.05564 | ||||||||
\(955\) | −8.60555 | −0.278469 | ||||||||
\(956\) | 5.21110 | 0.168539 | ||||||||
\(957\) | 1.33894 | 0.0432817 | ||||||||
\(958\) | −30.0000 | −0.969256 | ||||||||
\(959\) | 12.9083 | 0.416832 | ||||||||
\(960\) | 0.302776 | 0.00977204 | ||||||||
\(961\) | 31.5416 | 1.01747 | ||||||||
\(962\) | 26.4222 | 0.851886 | ||||||||
\(963\) | −7.57779 | −0.244191 | ||||||||
\(964\) | 14.4222 | 0.464508 | ||||||||
\(965\) | 17.8167 | 0.573538 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6056 | −0.405367 | −0.202684 | − | 0.979244i | \(-0.564966\pi\) | ||||
−0.202684 | + | 0.979244i | \(0.564966\pi\) | |||||||
\(968\) | 8.11943 | 0.260968 | ||||||||
\(969\) | −12.3583 | −0.397005 | ||||||||
\(970\) | −6.30278 | −0.202370 | ||||||||
\(971\) | 17.0917 | 0.548498 | 0.274249 | − | 0.961659i | \(-0.411571\pi\) | ||||
0.274249 | + | 0.961659i | \(0.411571\pi\) | |||||||
\(972\) | −7.84441 | −0.251610 | ||||||||
\(973\) | 41.6333 | 1.33470 | ||||||||
\(974\) | −9.81665 | −0.314546 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | −11.5139 | −0.368550 | ||||||||
\(977\) | −6.51388 | −0.208397 | −0.104199 | − | 0.994556i | \(-0.533228\pi\) | ||||
−0.104199 | + | 0.994556i | \(0.533228\pi\) | |||||||
\(978\) | 2.81665 | 0.0900667 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.90833 | −0.124847 | ||||||||
\(981\) | 4.32213 | 0.137995 | ||||||||
\(982\) | 4.18335 | 0.133496 | ||||||||
\(983\) | −34.5416 | −1.10171 | −0.550854 | − | 0.834602i | \(-0.685698\pi\) | ||||
−0.550854 | + | 0.834602i | \(0.685698\pi\) | |||||||
\(984\) | 0.275019 | 0.00876729 | ||||||||
\(985\) | −4.30278 | −0.137098 | ||||||||
\(986\) | −18.0000 | −0.573237 | ||||||||
\(987\) | −2.60555 | −0.0829356 | ||||||||
\(988\) | −19.5139 | −0.620819 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −4.93608 | −0.156879 | ||||||||
\(991\) | −15.3305 | −0.486990 | −0.243495 | − | 0.969902i | \(-0.578294\pi\) | ||||
−0.243495 | + | 0.969902i | \(0.578294\pi\) | |||||||
\(992\) | 7.90833 | 0.251090 | ||||||||
\(993\) | −5.02776 | −0.159551 | ||||||||
\(994\) | −53.8444 | −1.70784 | ||||||||
\(995\) | −20.4222 | −0.647427 | ||||||||
\(996\) | 3.39445 | 0.107557 | ||||||||
\(997\) | −16.7889 | −0.531710 | −0.265855 | − | 0.964013i | \(-0.585654\pi\) | ||||
−0.265855 | + | 0.964013i | \(0.585654\pi\) | |||||||
\(998\) | 31.6333 | 1.00133 | ||||||||
\(999\) | −14.3112 | −0.452786 |
(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 | 5290.2.a.j.1.1 | 2 | ||
23.22 | odd | 2 | 230.2.a.b.1.1 | ✓ | 2 | ||
69.68 | even | 2 | 2070.2.a.w.1.2 | 2 | |||
92.91 | even | 2 | 1840.2.a.j.1.2 | 2 | |||
115.22 | even | 4 | 1150.2.b.f.599.2 | 4 | |||
115.68 | even | 4 | 1150.2.b.f.599.3 | 4 | |||
115.114 | odd | 2 | 1150.2.a.m.1.2 | 2 | |||
184.45 | odd | 2 | 7360.2.a.bc.1.2 | 2 | |||
184.91 | even | 2 | 7360.2.a.bu.1.1 | 2 | |||
460.459 | even | 2 | 9200.2.a.ca.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.b.1.1 | ✓ | 2 | 23.22 | odd | 2 | ||
1150.2.a.m.1.2 | 2 | 115.114 | odd | 2 | |||
1150.2.b.f.599.2 | 4 | 115.22 | even | 4 | |||
1150.2.b.f.599.3 | 4 | 115.68 | even | 4 | |||
1840.2.a.j.1.2 | 2 | 92.91 | even | 2 | |||
2070.2.a.w.1.2 | 2 | 69.68 | even | 2 | |||
5290.2.a.j.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7360.2.a.bc.1.2 | 2 | 184.45 | odd | 2 | |||
7360.2.a.bu.1.1 | 2 | 184.91 | even | 2 | |||
9200.2.a.ca.1.1 | 2 | 460.459 | even | 2 |