Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.8 | ||
Root | \(1.11836 - 1.32260i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.c.881.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.64990 | + | 0.527098i | 0.952570 | + | 0.304320i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.527098 | − | 1.64990i | 0.215187 | − | 0.673569i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.44434 | + | 1.73932i | 0.814779 | + | 0.579772i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | 0.183234i | 0.0552471i | 0.999618 | + | 0.0276235i | \(0.00879396\pi\) | ||||
−0.999618 | + | 0.0276235i | \(0.991206\pi\) | |||||||
\(12\) | −1.64990 | − | 0.527098i | −0.476285 | − | 0.152160i | ||||
\(13\) | − | 2.22106i | − | 0.616011i | −0.951385 | − | 0.308006i | \(-0.900338\pi\) | ||
0.951385 | − | 0.308006i | \(-0.0996615\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.64990 | − | 0.527098i | −0.426002 | − | 0.136096i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.92858 | 1.43789 | 0.718946 | − | 0.695066i | \(-0.244625\pi\) | ||||
0.718946 | + | 0.695066i | \(0.244625\pi\) | |||||||
\(18\) | 1.73932 | − | 2.44434i | 0.409961 | − | 0.576135i | ||||
\(19\) | 2.74533i | 0.629823i | 0.949121 | + | 0.314911i | \(0.101975\pi\) | ||||
−0.949121 | + | 0.314911i | \(0.898025\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.183234 | 0.0390656 | ||||||||
\(23\) | 1.86609i | 0.389106i | 0.980892 | + | 0.194553i | \(0.0623257\pi\) | ||||
−0.980892 | + | 0.194553i | \(0.937674\pi\) | |||||||
\(24\) | −0.527098 | + | 1.64990i | −0.107593 | + | 0.336784i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.22106 | −0.435586 | ||||||||
\(27\) | 3.11612 | + | 4.15810i | 0.599697 | + | 0.800227i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 10.0295i | − | 1.86243i | −0.364473 | − | 0.931214i | \(-0.618751\pi\) | ||
0.364473 | − | 0.931214i | \(-0.381249\pi\) | |||||||
\(30\) | −0.527098 | + | 1.64990i | −0.0962344 | + | 0.301229i | ||||
\(31\) | 8.13368i | 1.46085i | 0.682992 | + | 0.730426i | \(0.260678\pi\) | ||||
−0.682992 | + | 0.730426i | \(0.739322\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −0.0965821 | + | 0.302317i | −0.0168128 | + | 0.0526267i | ||||
\(34\) | − | 5.92858i | − | 1.01674i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.44434 | − | 1.73932i | −0.407389 | − | 0.289886i | ||||
\(37\) | 8.64068 | 1.42052 | 0.710260 | − | 0.703940i | \(-0.248577\pi\) | ||||
0.710260 | + | 0.703940i | \(0.248577\pi\) | |||||||
\(38\) | 2.74533 | 0.445352 | ||||||||
\(39\) | 1.17072 | − | 3.66453i | 0.187465 | − | 0.586794i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 5.35770 | 0.836732 | 0.418366 | − | 0.908278i | \(-0.362603\pi\) | ||||
0.418366 | + | 0.908278i | \(0.362603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.74103 | −0.418004 | −0.209002 | − | 0.977915i | \(-0.567021\pi\) | ||||
−0.209002 | + | 0.977915i | \(0.567021\pi\) | |||||||
\(44\) | − | 0.183234i | − | 0.0276235i | ||||||
\(45\) | −2.44434 | − | 1.73932i | −0.364380 | − | 0.259282i | ||||
\(46\) | 1.86609 | 0.275140 | ||||||||
\(47\) | 3.00263 | 0.437979 | 0.218989 | − | 0.975727i | \(-0.429724\pi\) | ||||
0.218989 | + | 0.975727i | \(0.429724\pi\) | |||||||
\(48\) | 1.64990 | + | 0.527098i | 0.238142 | + | 0.0760800i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 9.78156 | + | 3.12494i | 1.36969 | + | 0.437579i | ||||
\(52\) | 2.22106i | 0.308006i | ||||||||
\(53\) | 1.72832i | 0.237403i | 0.992930 | + | 0.118701i | \(0.0378731\pi\) | ||||
−0.992930 | + | 0.118701i | \(0.962127\pi\) | |||||||
\(54\) | 4.15810 | − | 3.11612i | 0.565846 | − | 0.424050i | ||||
\(55\) | − | 0.183234i | − | 0.0247072i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.44706 | + | 4.52952i | −0.191668 | + | 0.599950i | ||||
\(58\) | −10.0295 | −1.31694 | ||||||||
\(59\) | 11.8401 | 1.54146 | 0.770728 | − | 0.637165i | \(-0.219893\pi\) | ||||
0.770728 | + | 0.637165i | \(0.219893\pi\) | |||||||
\(60\) | 1.64990 | + | 0.527098i | 0.213001 | + | 0.0680480i | ||||
\(61\) | 5.73054i | 0.733720i | 0.930276 | + | 0.366860i | \(0.119567\pi\) | ||||
−0.930276 | + | 0.366860i | \(0.880433\pi\) | |||||||
\(62\) | 8.13368 | 1.03298 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.22106i | 0.275489i | ||||||||
\(66\) | 0.302317 | + | 0.0965821i | 0.0372127 | + | 0.0118884i | ||||
\(67\) | −3.79196 | −0.463262 | −0.231631 | − | 0.972804i | \(-0.574406\pi\) | ||||
−0.231631 | + | 0.972804i | \(0.574406\pi\) | |||||||
\(68\) | −5.92858 | −0.718946 | ||||||||
\(69\) | −0.983611 | + | 3.07886i | −0.118413 | + | 0.370651i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.3992i | − | 1.35283i | −0.736519 | − | 0.676417i | \(-0.763532\pi\) | ||
0.736519 | − | 0.676417i | \(-0.236468\pi\) | |||||||
\(72\) | −1.73932 | + | 2.44434i | −0.204980 | + | 0.288068i | ||||
\(73\) | − | 8.37048i | − | 0.979690i | −0.871809 | − | 0.489845i | \(-0.837053\pi\) | ||
0.871809 | − | 0.489845i | \(-0.162947\pi\) | |||||||
\(74\) | − | 8.64068i | − | 1.00446i | ||||||
\(75\) | 1.64990 | + | 0.527098i | 0.190514 | + | 0.0608640i | ||||
\(76\) | − | 2.74533i | − | 0.314911i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.66453 | − | 1.17072i | −0.414926 | − | 0.132557i | ||||
\(79\) | −8.97002 | −1.00921 | −0.504603 | − | 0.863351i | \(-0.668361\pi\) | ||||
−0.504603 | + | 0.863351i | \(0.668361\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 2.94956 | + | 8.50295i | 0.327728 | + | 0.944772i | ||||
\(82\) | − | 5.35770i | − | 0.591659i | ||||||
\(83\) | 9.25852 | 1.01625 | 0.508127 | − | 0.861282i | \(-0.330338\pi\) | ||||
0.508127 | + | 0.861282i | \(0.330338\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.92858 | −0.643045 | ||||||||
\(86\) | 2.74103i | 0.295573i | ||||||||
\(87\) | 5.28652 | − | 16.5476i | 0.566774 | − | 1.77409i | ||||
\(88\) | −0.183234 | −0.0195328 | ||||||||
\(89\) | 12.1711 | 1.29013 | 0.645066 | − | 0.764127i | \(-0.276830\pi\) | ||||
0.645066 | + | 0.764127i | \(0.276830\pi\) | |||||||
\(90\) | −1.73932 | + | 2.44434i | −0.183340 | + | 0.257656i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1.86609i | − | 0.194553i | ||||||
\(93\) | −4.28724 | + | 13.4198i | −0.444567 | + | 1.39156i | ||||
\(94\) | − | 3.00263i | − | 0.309698i | ||||||
\(95\) | − | 2.74533i | − | 0.281665i | ||||||
\(96\) | 0.527098 | − | 1.64990i | 0.0537967 | − | 0.168392i | ||||
\(97\) | − | 7.23005i | − | 0.734100i | −0.930201 | − | 0.367050i | \(-0.880368\pi\) | ||
0.930201 | − | 0.367050i | \(-0.119632\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.318701 | + | 0.447885i | −0.0320307 | + | 0.0450141i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −7.98749 | −0.794785 | −0.397393 | − | 0.917649i | \(-0.630085\pi\) | ||||
−0.397393 | + | 0.917649i | \(0.630085\pi\) | |||||||
\(102\) | 3.12494 | − | 9.78156i | 0.309415 | − | 0.968518i | ||||
\(103\) | 15.2633i | 1.50393i | 0.659200 | + | 0.751967i | \(0.270895\pi\) | ||||
−0.659200 | + | 0.751967i | \(0.729105\pi\) | |||||||
\(104\) | 2.22106 | 0.217793 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.72832 | 0.167869 | ||||||||
\(107\) | − | 6.18268i | − | 0.597702i | −0.954300 | − | 0.298851i | \(-0.903397\pi\) | ||
0.954300 | − | 0.298851i | \(-0.0966034\pi\) | |||||||
\(108\) | −3.11612 | − | 4.15810i | −0.299849 | − | 0.400113i | ||||
\(109\) | −18.5699 | −1.77868 | −0.889338 | − | 0.457251i | \(-0.848834\pi\) | ||||
−0.889338 | + | 0.457251i | \(0.848834\pi\) | |||||||
\(110\) | −0.183234 | −0.0174707 | ||||||||
\(111\) | 14.2563 | + | 4.55448i | 1.35314 | + | 0.432293i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.96035i | 0.842919i | 0.906847 | + | 0.421459i | \(0.138482\pi\) | ||||
−0.906847 | + | 0.421459i | \(0.861518\pi\) | |||||||
\(114\) | 4.52952 | + | 1.44706i | 0.424229 | + | 0.135530i | ||||
\(115\) | − | 1.86609i | − | 0.174014i | ||||||
\(116\) | 10.0295i | 0.931214i | ||||||||
\(117\) | 3.86313 | − | 5.42902i | 0.357146 | − | 0.501913i | ||||
\(118\) | − | 11.8401i | − | 1.08997i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.527098 | − | 1.64990i | 0.0481172 | − | 0.150615i | ||||
\(121\) | 10.9664 | 0.996948 | ||||||||
\(122\) | 5.73054 | 0.518818 | ||||||||
\(123\) | 8.83967 | + | 2.82403i | 0.797046 | + | 0.254634i | ||||
\(124\) | − | 8.13368i | − | 0.730426i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.46529 | 0.839908 | 0.419954 | − | 0.907545i | \(-0.362046\pi\) | ||||
0.419954 | + | 0.907545i | \(0.362046\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.52243 | − | 1.44479i | −0.398178 | − | 0.127207i | ||||
\(130\) | 2.22106 | 0.194800 | ||||||||
\(131\) | −18.0259 | −1.57493 | −0.787467 | − | 0.616357i | \(-0.788608\pi\) | ||||
−0.787467 | + | 0.616357i | \(0.788608\pi\) | |||||||
\(132\) | 0.0965821 | − | 0.302317i | 0.00840639 | − | 0.0263133i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.79196i | 0.327576i | ||||||||
\(135\) | −3.11612 | − | 4.15810i | −0.268193 | − | 0.357872i | ||||
\(136\) | 5.92858i | 0.508371i | ||||||||
\(137\) | − | 1.58312i | − | 0.135255i | −0.997711 | − | 0.0676275i | \(-0.978457\pi\) | ||
0.997711 | − | 0.0676275i | \(-0.0215429\pi\) | |||||||
\(138\) | 3.07886 | + | 0.983611i | 0.262090 | + | 0.0837305i | ||||
\(139\) | 8.23768i | 0.698711i | 0.936990 | + | 0.349356i | \(0.113599\pi\) | ||||
−0.936990 | + | 0.349356i | \(0.886401\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.95404 | + | 1.58268i | 0.417205 | + | 0.133286i | ||||
\(142\) | −11.3992 | −0.956598 | ||||||||
\(143\) | 0.406973 | 0.0340328 | ||||||||
\(144\) | 2.44434 | + | 1.73932i | 0.203695 | + | 0.144943i | ||||
\(145\) | 10.0295i | 0.832903i | ||||||||
\(146\) | −8.37048 | −0.692746 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.64068 | −0.710260 | ||||||||
\(149\) | 9.35407i | 0.766315i | 0.923683 | + | 0.383158i | \(0.125163\pi\) | ||||
−0.923683 | + | 0.383158i | \(0.874837\pi\) | |||||||
\(150\) | 0.527098 | − | 1.64990i | 0.0430374 | − | 0.134714i | ||||
\(151\) | −14.2685 | −1.16115 | −0.580575 | − | 0.814207i | \(-0.697172\pi\) | ||||
−0.580575 | + | 0.814207i | \(0.697172\pi\) | |||||||
\(152\) | −2.74533 | −0.222676 | ||||||||
\(153\) | 14.4914 | + | 10.3117i | 1.17156 | + | 0.833649i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 8.13368i | − | 0.653313i | ||||||
\(156\) | −1.17072 | + | 3.66453i | −0.0937323 | + | 0.293397i | ||||
\(157\) | 5.01925i | 0.400580i | 0.979737 | + | 0.200290i | \(0.0641884\pi\) | ||||
−0.979737 | + | 0.200290i | \(0.935812\pi\) | |||||||
\(158\) | 8.97002i | 0.713616i | ||||||||
\(159\) | −0.910992 | + | 2.85155i | −0.0722464 | + | 0.226143i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.50295 | − | 2.94956i | 0.668055 | − | 0.231739i | ||||
\(163\) | −23.9391 | −1.87505 | −0.937526 | − | 0.347916i | \(-0.886889\pi\) | ||||
−0.937526 | + | 0.347916i | \(0.886889\pi\) | |||||||
\(164\) | −5.35770 | −0.418366 | ||||||||
\(165\) | 0.0965821 | − | 0.302317i | 0.00751891 | − | 0.0235354i | ||||
\(166\) | − | 9.25852i | − | 0.718601i | ||||||
\(167\) | −12.2295 | −0.946349 | −0.473174 | − | 0.880969i | \(-0.656892\pi\) | ||||
−0.473174 | + | 0.880969i | \(0.656892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.06689 | 0.620530 | ||||||||
\(170\) | 5.92858i | 0.454701i | ||||||||
\(171\) | −4.77500 | + | 6.71052i | −0.365154 | + | 0.513166i | ||||
\(172\) | 2.74103 | 0.209002 | ||||||||
\(173\) | −2.75498 | −0.209457 | −0.104729 | − | 0.994501i | \(-0.533397\pi\) | ||||
−0.104729 | + | 0.994501i | \(0.533397\pi\) | |||||||
\(174\) | −16.5476 | − | 5.28652i | −1.25447 | − | 0.400770i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.183234i | 0.0138118i | ||||||||
\(177\) | 19.5350 | + | 6.24091i | 1.46834 | + | 0.469096i | ||||
\(178\) | − | 12.1711i | − | 0.912261i | ||||||
\(179\) | − | 5.15274i | − | 0.385134i | −0.981284 | − | 0.192567i | \(-0.938319\pi\) | ||
0.981284 | − | 0.192567i | \(-0.0616812\pi\) | |||||||
\(180\) | 2.44434 | + | 1.73932i | 0.182190 | + | 0.129641i | ||||
\(181\) | − | 18.1045i | − | 1.34569i | −0.739781 | − | 0.672847i | \(-0.765071\pi\) | ||
0.739781 | − | 0.672847i | \(-0.234929\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.02055 | + | 9.45481i | −0.223286 | + | 0.698919i | ||||
\(184\) | −1.86609 | −0.137570 | ||||||||
\(185\) | −8.64068 | −0.635276 | ||||||||
\(186\) | 13.4198 | + | 4.28724i | 0.983984 | + | 0.314356i | ||||
\(187\) | 1.08632i | 0.0794393i | ||||||||
\(188\) | −3.00263 | −0.218989 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.74533 | −0.199167 | ||||||||
\(191\) | − | 15.0739i | − | 1.09071i | −0.838206 | − | 0.545353i | \(-0.816396\pi\) | ||
0.838206 | − | 0.545353i | \(-0.183604\pi\) | |||||||
\(192\) | −1.64990 | − | 0.527098i | −0.119071 | − | 0.0380400i | ||||
\(193\) | −24.3119 | −1.75001 | −0.875004 | − | 0.484115i | \(-0.839142\pi\) | ||||
−0.875004 | + | 0.484115i | \(0.839142\pi\) | |||||||
\(194\) | −7.23005 | −0.519087 | ||||||||
\(195\) | −1.17072 | + | 3.66453i | −0.0838367 | + | 0.262422i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.763219i | − | 0.0543771i | −0.999630 | − | 0.0271885i | \(-0.991345\pi\) | ||
0.999630 | − | 0.0271885i | \(-0.00865545\pi\) | |||||||
\(198\) | 0.447885 | + | 0.318701i | 0.0318298 | + | 0.0226491i | ||||
\(199\) | 7.53057i | 0.533828i | 0.963720 | + | 0.266914i | \(0.0860040\pi\) | ||||
−0.963720 | + | 0.266914i | \(0.913996\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −6.25636 | − | 1.99874i | −0.441289 | − | 0.140980i | ||||
\(202\) | 7.98749i | 0.561998i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9.78156 | − | 3.12494i | −0.684846 | − | 0.218790i | ||||
\(205\) | −5.35770 | −0.374198 | ||||||||
\(206\) | 15.2633 | 1.06344 | ||||||||
\(207\) | −3.24572 | + | 4.56135i | −0.225593 | + | 0.317036i | ||||
\(208\) | − | 2.22106i | − | 0.154003i | ||||||
\(209\) | −0.503038 | −0.0347959 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.9076 | 0.957438 | 0.478719 | − | 0.877968i | \(-0.341101\pi\) | ||||
0.478719 | + | 0.877968i | \(0.341101\pi\) | |||||||
\(212\) | − | 1.72832i | − | 0.118701i | ||||||
\(213\) | 6.00848 | − | 18.8075i | 0.411694 | − | 1.28867i | ||||
\(214\) | −6.18268 | −0.422639 | ||||||||
\(215\) | 2.74103 | 0.186937 | ||||||||
\(216\) | −4.15810 | + | 3.11612i | −0.282923 | + | 0.212025i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 18.5699i | 1.25771i | ||||||||
\(219\) | 4.41206 | − | 13.8104i | 0.298139 | − | 0.933223i | ||||
\(220\) | 0.183234i | 0.0123536i | ||||||||
\(221\) | − | 13.1677i | − | 0.885757i | ||||||
\(222\) | 4.55448 | − | 14.2563i | 0.305677 | − | 0.956817i | ||||
\(223\) | 18.8741i | 1.26390i | 0.775009 | + | 0.631951i | \(0.217745\pi\) | ||||
−0.775009 | + | 0.631951i | \(0.782255\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.44434 | + | 1.73932i | 0.162956 | + | 0.115954i | ||||
\(226\) | 8.96035 | 0.596034 | ||||||||
\(227\) | −3.61611 | −0.240009 | −0.120005 | − | 0.992773i | \(-0.538291\pi\) | ||||
−0.120005 | + | 0.992773i | \(0.538291\pi\) | |||||||
\(228\) | 1.44706 | − | 4.52952i | 0.0958338 | − | 0.299975i | ||||
\(229\) | − | 20.4388i | − | 1.35063i | −0.737528 | − | 0.675317i | \(-0.764007\pi\) | ||
0.737528 | − | 0.675317i | \(-0.235993\pi\) | |||||||
\(230\) | −1.86609 | −0.123046 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0295 | 0.658468 | ||||||||
\(233\) | − | 13.8804i | − | 0.909333i | −0.890662 | − | 0.454667i | \(-0.849758\pi\) | ||
0.890662 | − | 0.454667i | \(-0.150242\pi\) | |||||||
\(234\) | −5.42902 | − | 3.86313i | −0.354906 | − | 0.252540i | ||||
\(235\) | −3.00263 | −0.195870 | ||||||||
\(236\) | −11.8401 | −0.770728 | ||||||||
\(237\) | −14.7996 | − | 4.72808i | −0.961339 | − | 0.307122i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 25.8786i | − | 1.67395i | −0.547243 | − | 0.836974i | \(-0.684323\pi\) | ||
0.547243 | − | 0.836974i | \(-0.315677\pi\) | |||||||
\(240\) | −1.64990 | − | 0.527098i | −0.106501 | − | 0.0340240i | ||||
\(241\) | 26.2005i | 1.68772i | 0.536561 | + | 0.843862i | \(0.319723\pi\) | ||||
−0.536561 | + | 0.843862i | \(0.680277\pi\) | |||||||
\(242\) | − | 10.9664i | − | 0.704949i | ||||||
\(243\) | 0.384586 | + | 15.5837i | 0.0246712 | + | 0.999696i | ||||
\(244\) | − | 5.73054i | − | 0.366860i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.82403 | − | 8.83967i | 0.180054 | − | 0.563597i | ||||
\(247\) | 6.09755 | 0.387978 | ||||||||
\(248\) | −8.13368 | −0.516489 | ||||||||
\(249\) | 15.2756 | + | 4.88015i | 0.968053 | + | 0.309267i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −17.1154 | −1.08031 | −0.540156 | − | 0.841565i | \(-0.681635\pi\) | ||||
−0.540156 | + | 0.841565i | \(0.681635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.341930 | −0.0214970 | ||||||||
\(254\) | − | 9.46529i | − | 0.593905i | ||||||
\(255\) | −9.78156 | − | 3.12494i | −0.612545 | − | 0.195691i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.1541 | 1.00766 | 0.503832 | − | 0.863802i | \(-0.331923\pi\) | ||||
0.503832 | + | 0.863802i | \(0.331923\pi\) | |||||||
\(258\) | −1.44479 | + | 4.52243i | −0.0899488 | + | 0.281554i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 2.22106i | − | 0.137744i | ||||||
\(261\) | 17.4444 | − | 24.5154i | 1.07978 | − | 1.51747i | ||||
\(262\) | 18.0259i | 1.11365i | ||||||||
\(263\) | 3.79029i | 0.233719i | 0.993148 | + | 0.116860i | \(0.0372828\pi\) | ||||
−0.993148 | + | 0.116860i | \(0.962717\pi\) | |||||||
\(264\) | −0.302317 | − | 0.0965821i | −0.0186063 | − | 0.00594422i | ||||
\(265\) | − | 1.72832i | − | 0.106170i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.0811 | + | 6.41535i | 1.22894 | + | 0.392613i | ||||
\(268\) | 3.79196 | 0.231631 | ||||||||
\(269\) | −1.67131 | −0.101901 | −0.0509507 | − | 0.998701i | \(-0.516225\pi\) | ||||
−0.0509507 | + | 0.998701i | \(0.516225\pi\) | |||||||
\(270\) | −4.15810 | + | 3.11612i | −0.253054 | + | 0.189641i | ||||
\(271\) | − | 27.8686i | − | 1.69290i | −0.532469 | − | 0.846449i | \(-0.678736\pi\) | ||
0.532469 | − | 0.846449i | \(-0.321264\pi\) | |||||||
\(272\) | 5.92858 | 0.359473 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.58312 | −0.0956397 | ||||||||
\(275\) | 0.183234i | 0.0110494i | ||||||||
\(276\) | 0.983611 | − | 3.07886i | 0.0592064 | − | 0.185326i | ||||
\(277\) | −2.08837 | −0.125478 | −0.0627389 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627389 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(278\) | 8.23768 | 0.494063 | ||||||||
\(279\) | −14.1470 | + | 19.8814i | −0.846961 | + | 1.19027i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.4447i | 1.15997i | 0.814625 | + | 0.579987i | \(0.196943\pi\) | ||||
−0.814625 | + | 0.579987i | \(0.803057\pi\) | |||||||
\(282\) | 1.58268 | − | 4.95404i | 0.0942472 | − | 0.295009i | ||||
\(283\) | − | 1.11859i | − | 0.0664931i | −0.999447 | − | 0.0332465i | \(-0.989415\pi\) | ||
0.999447 | − | 0.0332465i | \(-0.0105847\pi\) | |||||||
\(284\) | 11.3992i | 0.676417i | ||||||||
\(285\) | 1.44706 | − | 4.52952i | 0.0857164 | − | 0.268306i | ||||
\(286\) | − | 0.406973i | − | 0.0240648i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.73932 | − | 2.44434i | 0.102490 | − | 0.144034i | ||||
\(289\) | 18.1480 | 1.06753 | ||||||||
\(290\) | 10.0295 | 0.588951 | ||||||||
\(291\) | 3.81094 | − | 11.9289i | 0.223401 | − | 0.699282i | ||||
\(292\) | 8.37048i | 0.489845i | ||||||||
\(293\) | −25.9736 | −1.51739 | −0.758697 | − | 0.651444i | \(-0.774164\pi\) | ||||
−0.758697 | + | 0.651444i | \(0.774164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.8401 | −0.689360 | ||||||||
\(296\) | 8.64068i | 0.502229i | ||||||||
\(297\) | −0.761904 | + | 0.570978i | −0.0442102 | + | 0.0331315i | ||||
\(298\) | 9.35407 | 0.541867 | ||||||||
\(299\) | 4.14469 | 0.239694 | ||||||||
\(300\) | −1.64990 | − | 0.527098i | −0.0952570 | − | 0.0304320i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14.2685i | 0.821057i | ||||||||
\(303\) | −13.1786 | − | 4.21019i | −0.757089 | − | 0.241869i | ||||
\(304\) | 2.74533i | 0.157456i | ||||||||
\(305\) | − | 5.73054i | − | 0.328130i | ||||||
\(306\) | 10.3117 | − | 14.4914i | 0.589479 | − | 0.828420i | ||||
\(307\) | − | 14.8678i | − | 0.848548i | −0.905534 | − | 0.424274i | \(-0.860529\pi\) | ||
0.905534 | − | 0.424274i | \(-0.139471\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.04524 | + | 25.1829i | −0.457677 | + | 1.43260i | ||||
\(310\) | −8.13368 | −0.461962 | ||||||||
\(311\) | −10.1085 | −0.573201 | −0.286600 | − | 0.958050i | \(-0.592525\pi\) | ||||
−0.286600 | + | 0.958050i | \(0.592525\pi\) | |||||||
\(312\) | 3.66453 | + | 1.17072i | 0.207463 | + | 0.0662787i | ||||
\(313\) | 30.7635i | 1.73886i | 0.494058 | + | 0.869429i | \(0.335513\pi\) | ||||
−0.494058 | + | 0.869429i | \(0.664487\pi\) | |||||||
\(314\) | 5.01925 | 0.283253 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.97002 | 0.504603 | ||||||||
\(317\) | − | 15.3849i | − | 0.864102i | −0.901849 | − | 0.432051i | \(-0.857790\pi\) | ||
0.901849 | − | 0.432051i | \(-0.142210\pi\) | |||||||
\(318\) | 2.85155 | + | 0.910992i | 0.159907 | + | 0.0510859i | ||||
\(319\) | 1.83774 | 0.102894 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 3.25888 | − | 10.2008i | 0.181893 | − | 0.569353i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.2759i | 0.905617i | ||||||||
\(324\) | −2.94956 | − | 8.50295i | −0.163864 | − | 0.472386i | ||||
\(325\) | − | 2.22106i | − | 0.123202i | ||||||
\(326\) | 23.9391i | 1.32586i | ||||||||
\(327\) | −30.6385 | − | 9.78816i | −1.69431 | − | 0.541287i | ||||
\(328\) | 5.35770i | 0.295830i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.302317 | − | 0.0965821i | −0.0166420 | − | 0.00531667i | ||||
\(331\) | −11.3036 | −0.621300 | −0.310650 | − | 0.950524i | \(-0.600547\pi\) | ||||
−0.310650 | + | 0.950524i | \(0.600547\pi\) | |||||||
\(332\) | −9.25852 | −0.508127 | ||||||||
\(333\) | 21.1207 | + | 15.0289i | 1.15741 | + | 0.823578i | ||||
\(334\) | 12.2295i | 0.669170i | ||||||||
\(335\) | 3.79196 | 0.207177 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.2334 | −1.91929 | −0.959643 | − | 0.281221i | \(-0.909261\pi\) | ||||
−0.959643 | + | 0.281221i | \(0.909261\pi\) | |||||||
\(338\) | − | 8.06689i | − | 0.438781i | ||||||
\(339\) | −4.72298 | + | 14.7837i | −0.256517 | + | 0.802939i | ||||
\(340\) | 5.92858 | 0.321522 | ||||||||
\(341\) | −1.49036 | −0.0807078 | ||||||||
\(342\) | 6.71052 | + | 4.77500i | 0.362863 | + | 0.258203i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 2.74103i | − | 0.147787i | ||||||
\(345\) | 0.983611 | − | 3.07886i | 0.0529558 | − | 0.165760i | ||||
\(346\) | 2.75498i | 0.148109i | ||||||||
\(347\) | 36.4627i | 1.95742i | 0.205243 | + | 0.978711i | \(0.434201\pi\) | ||||
−0.205243 | + | 0.978711i | \(0.565799\pi\) | |||||||
\(348\) | −5.28652 | + | 16.5476i | −0.283387 | + | 0.887046i | ||||
\(349\) | − | 5.80210i | − | 0.310580i | −0.987869 | − | 0.155290i | \(-0.950369\pi\) | ||
0.987869 | − | 0.155290i | \(-0.0496311\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.23539 | − | 6.92109i | 0.492949 | − | 0.369420i | ||||
\(352\) | 0.183234 | 0.00976639 | ||||||||
\(353\) | −36.8540 | −1.96154 | −0.980770 | − | 0.195167i | \(-0.937475\pi\) | ||||
−0.980770 | + | 0.195167i | \(0.937475\pi\) | |||||||
\(354\) | 6.24091 | − | 19.5350i | 0.331701 | − | 1.03828i | ||||
\(355\) | 11.3992i | 0.605006i | ||||||||
\(356\) | −12.1711 | −0.645066 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.15274 | −0.272331 | ||||||||
\(359\) | 14.6764i | 0.774589i | 0.921956 | + | 0.387294i | \(0.126590\pi\) | ||||
−0.921956 | + | 0.387294i | \(0.873410\pi\) | |||||||
\(360\) | 1.73932 | − | 2.44434i | 0.0916700 | − | 0.128828i | ||||
\(361\) | 11.4631 | 0.603323 | ||||||||
\(362\) | −18.1045 | −0.951550 | ||||||||
\(363\) | 18.0935 | + | 5.78038i | 0.949662 | + | 0.303391i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.37048i | 0.438131i | ||||||||
\(366\) | 9.45481 | + | 3.02055i | 0.494211 | + | 0.157887i | ||||
\(367\) | 28.9944i | 1.51350i | 0.653707 | + | 0.756748i | \(0.273213\pi\) | ||||
−0.653707 | + | 0.756748i | \(0.726787\pi\) | |||||||
\(368\) | 1.86609i | 0.0972766i | ||||||||
\(369\) | 13.0960 | + | 9.31874i | 0.681752 | + | 0.485114i | ||||
\(370\) | 8.64068i | 0.449208i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.28724 | − | 13.4198i | 0.222283 | − | 0.695782i | ||||
\(373\) | −27.5619 | −1.42710 | −0.713552 | − | 0.700603i | \(-0.752915\pi\) | ||||
−0.713552 | + | 0.700603i | \(0.752915\pi\) | |||||||
\(374\) | 1.08632 | 0.0561720 | ||||||||
\(375\) | −1.64990 | − | 0.527098i | −0.0852004 | − | 0.0272192i | ||||
\(376\) | 3.00263i | 0.154849i | ||||||||
\(377\) | −22.2761 | −1.14728 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.9475 | 1.33283 | 0.666417 | − | 0.745580i | \(-0.267827\pi\) | ||||
0.666417 | + | 0.745580i | \(0.267827\pi\) | |||||||
\(380\) | 2.74533i | 0.140833i | ||||||||
\(381\) | 15.6168 | + | 4.98913i | 0.800071 | + | 0.255601i | ||||
\(382\) | −15.0739 | −0.771246 | ||||||||
\(383\) | 36.5542 | 1.86783 | 0.933917 | − | 0.357491i | \(-0.116368\pi\) | ||||
0.933917 | + | 0.357491i | \(0.116368\pi\) | |||||||
\(384\) | −0.527098 | + | 1.64990i | −0.0268983 | + | 0.0841961i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.3119i | 1.23744i | ||||||||
\(387\) | −6.70001 | − | 4.76752i | −0.340580 | − | 0.242347i | ||||
\(388\) | 7.23005i | 0.367050i | ||||||||
\(389\) | − | 19.5029i | − | 0.988839i | −0.869224 | − | 0.494419i | \(-0.835381\pi\) | ||
0.869224 | − | 0.494419i | \(-0.164619\pi\) | |||||||
\(390\) | 3.66453 | + | 1.17072i | 0.185560 | + | 0.0592815i | ||||
\(391\) | 11.0633i | 0.559493i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −29.7410 | − | 9.50143i | −1.50023 | − | 0.479284i | ||||
\(394\) | −0.763219 | −0.0384504 | ||||||||
\(395\) | 8.97002 | 0.451331 | ||||||||
\(396\) | 0.318701 | − | 0.447885i | 0.0160154 | − | 0.0225071i | ||||
\(397\) | 8.12748i | 0.407907i | 0.978981 | + | 0.203953i | \(0.0653791\pi\) | ||||
−0.978981 | + | 0.203953i | \(0.934621\pi\) | |||||||
\(398\) | 7.53057 | 0.377473 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − | 19.8417i | − | 0.990845i | −0.868652 | − | 0.495422i | \(-0.835013\pi\) | ||
0.868652 | − | 0.495422i | \(-0.164987\pi\) | |||||||
\(402\) | −1.99874 | + | 6.25636i | −0.0996878 | + | 0.312039i | ||||
\(403\) | 18.0654 | 0.899901 | ||||||||
\(404\) | 7.98749 | 0.397393 | ||||||||
\(405\) | −2.94956 | − | 8.50295i | −0.146565 | − | 0.422515i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.58326i | 0.0784795i | ||||||||
\(408\) | −3.12494 | + | 9.78156i | −0.154708 | + | 0.484259i | ||||
\(409\) | − | 3.20599i | − | 0.158526i | −0.996854 | − | 0.0792629i | \(-0.974743\pi\) | ||
0.996854 | − | 0.0792629i | \(-0.0252567\pi\) | |||||||
\(410\) | 5.35770i | 0.264598i | ||||||||
\(411\) | 0.834458 | − | 2.61199i | 0.0411608 | − | 0.128840i | ||||
\(412\) | − | 15.2633i | − | 0.751967i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.56135 | + | 3.24572i | 0.224178 | + | 0.159518i | ||||
\(415\) | −9.25852 | −0.454483 | ||||||||
\(416\) | −2.22106 | −0.108896 | ||||||||
\(417\) | −4.34206 | + | 13.5913i | −0.212632 | + | 0.665571i | ||||
\(418\) | 0.503038i | 0.0246044i | ||||||||
\(419\) | 6.99137 | 0.341551 | 0.170775 | − | 0.985310i | \(-0.445373\pi\) | ||||
0.170775 | + | 0.985310i | \(0.445373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.7534 | 0.865246 | 0.432623 | − | 0.901575i | \(-0.357588\pi\) | ||||
0.432623 | + | 0.901575i | \(0.357588\pi\) | |||||||
\(422\) | − | 13.9076i | − | 0.677011i | ||||||
\(423\) | 7.33944 | + | 5.22253i | 0.356856 | + | 0.253928i | ||||
\(424\) | −1.72832 | −0.0839345 | ||||||||
\(425\) | 5.92858 | 0.287578 | ||||||||
\(426\) | −18.8075 | − | 6.00848i | −0.911226 | − | 0.291112i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.18268i | 0.298851i | ||||||||
\(429\) | 0.671465 | + | 0.214515i | 0.0324186 | + | 0.0103569i | ||||
\(430\) | − | 2.74103i | − | 0.132184i | ||||||
\(431\) | − | 21.5466i | − | 1.03786i | −0.854816 | − | 0.518931i | \(-0.826330\pi\) | ||
0.854816 | − | 0.518931i | \(-0.173670\pi\) | |||||||
\(432\) | 3.11612 | + | 4.15810i | 0.149924 | + | 0.200057i | ||||
\(433\) | − | 2.22339i | − | 0.106850i | −0.998572 | − | 0.0534248i | \(-0.982986\pi\) | ||
0.998572 | − | 0.0534248i | \(-0.0170137\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.28652 | + | 16.5476i | −0.253469 | + | 0.793398i | ||||
\(436\) | 18.5699 | 0.889338 | ||||||||
\(437\) | −5.12304 | −0.245068 | ||||||||
\(438\) | −13.8104 | − | 4.41206i | −0.659889 | − | 0.210816i | ||||
\(439\) | − | 1.07643i | − | 0.0513751i | −0.999670 | − | 0.0256876i | \(-0.991822\pi\) | ||
0.999670 | − | 0.0256876i | \(-0.00817750\pi\) | |||||||
\(440\) | 0.183234 | 0.00873533 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.1677 | −0.626325 | ||||||||
\(443\) | 22.1450i | 1.05214i | 0.850442 | + | 0.526070i | \(0.176335\pi\) | ||||
−0.850442 | + | 0.526070i | \(0.823665\pi\) | |||||||
\(444\) | −14.2563 | − | 4.55448i | −0.676572 | − | 0.216146i | ||||
\(445\) | −12.1711 | −0.576964 | ||||||||
\(446\) | 18.8741 | 0.893713 | ||||||||
\(447\) | −4.93051 | + | 15.4333i | −0.233205 | + | 0.729969i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.54766i | − | 0.120231i | −0.998191 | − | 0.0601157i | \(-0.980853\pi\) | ||
0.998191 | − | 0.0601157i | \(-0.0191470\pi\) | |||||||
\(450\) | 1.73932 | − | 2.44434i | 0.0819922 | − | 0.115227i | ||||
\(451\) | 0.981712i | 0.0462270i | ||||||||
\(452\) | − | 8.96035i | − | 0.421459i | ||||||
\(453\) | −23.5415 | − | 7.52087i | −1.10608 | − | 0.353361i | ||||
\(454\) | 3.61611i | 0.169712i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.52952 | − | 1.44706i | −0.212114 | − | 0.0677648i | ||||
\(457\) | 4.69058 | 0.219416 | 0.109708 | − | 0.993964i | \(-0.465008\pi\) | ||||
0.109708 | + | 0.993964i | \(0.465008\pi\) | |||||||
\(458\) | −20.4388 | −0.955042 | ||||||||
\(459\) | 18.4742 | + | 24.6516i | 0.862300 | + | 1.15064i | ||||
\(460\) | 1.86609i | 0.0870068i | ||||||||
\(461\) | 5.10979 | 0.237986 | 0.118993 | − | 0.992895i | \(-0.462033\pi\) | ||||
0.118993 | + | 0.992895i | \(0.462033\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6740 | −0.960804 | −0.480402 | − | 0.877048i | \(-0.659509\pi\) | ||||
−0.480402 | + | 0.877048i | \(0.659509\pi\) | |||||||
\(464\) | − | 10.0295i | − | 0.465607i | ||||||
\(465\) | 4.28724 | − | 13.4198i | 0.198816 | − | 0.622326i | ||||
\(466\) | −13.8804 | −0.642996 | ||||||||
\(467\) | 2.10185 | 0.0972621 | 0.0486310 | − | 0.998817i | \(-0.484514\pi\) | ||||
0.0486310 | + | 0.998817i | \(0.484514\pi\) | |||||||
\(468\) | −3.86313 | + | 5.42902i | −0.178573 | + | 0.250956i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.00263i | 0.138501i | ||||||||
\(471\) | −2.64564 | + | 8.28126i | −0.121904 | + | 0.381580i | ||||
\(472\) | 11.8401i | 0.544987i | ||||||||
\(473\) | − | 0.502250i | − | 0.0230935i | ||||||
\(474\) | −4.72808 | + | 14.7996i | −0.217168 | + | 0.679769i | ||||
\(475\) | 2.74533i | 0.125965i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00609 | + | 4.22459i | −0.137639 | + | 0.193431i | ||||
\(478\) | −25.8786 | −1.18366 | ||||||||
\(479\) | 10.7574 | 0.491517 | 0.245759 | − | 0.969331i | \(-0.420963\pi\) | ||||
0.245759 | + | 0.969331i | \(0.420963\pi\) | |||||||
\(480\) | −0.527098 | + | 1.64990i | −0.0240586 | + | 0.0753073i | ||||
\(481\) | − | 19.1915i | − | 0.875056i | ||||||
\(482\) | 26.2005 | 1.19340 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9664 | −0.498474 | ||||||||
\(485\) | 7.23005i | 0.328300i | ||||||||
\(486\) | 15.5837 | − | 0.384586i | 0.706892 | − | 0.0174452i | ||||
\(487\) | 27.2491 | 1.23477 | 0.617386 | − | 0.786660i | \(-0.288192\pi\) | ||||
0.617386 | + | 0.786660i | \(0.288192\pi\) | |||||||
\(488\) | −5.73054 | −0.259409 | ||||||||
\(489\) | −39.4970 | − | 12.6182i | −1.78612 | − | 0.570616i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.39148i | 0.423831i | 0.977288 | + | 0.211916i | \(0.0679702\pi\) | ||||
−0.977288 | + | 0.211916i | \(0.932030\pi\) | |||||||
\(492\) | −8.83967 | − | 2.82403i | −0.398523 | − | 0.127317i | ||||
\(493\) | − | 59.4605i | − | 2.67797i | ||||||
\(494\) | − | 6.09755i | − | 0.274342i | ||||||
\(495\) | 0.318701 | − | 0.447885i | 0.0143246 | − | 0.0201309i | ||||
\(496\) | 8.13368i | 0.365213i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.88015 | − | 15.2756i | 0.218685 | − | 0.684517i | ||||
\(499\) | −23.4355 | −1.04912 | −0.524558 | − | 0.851374i | \(-0.675770\pi\) | ||||
−0.524558 | + | 0.851374i | \(0.675770\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −20.1775 | − | 6.44615i | −0.901463 | − | 0.287993i | ||||
\(502\) | 17.1154i | 0.763896i | ||||||||
\(503\) | −33.0002 | −1.47140 | −0.735702 | − | 0.677305i | \(-0.763148\pi\) | ||||
−0.735702 | + | 0.677305i | \(0.763148\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.98749 | 0.355439 | ||||||||
\(506\) | 0.341930i | 0.0152007i | ||||||||
\(507\) | 13.3096 | + | 4.25204i | 0.591098 | + | 0.188840i | ||||
\(508\) | −9.46529 | −0.419954 | ||||||||
\(509\) | −6.56393 | −0.290941 | −0.145471 | − | 0.989363i | \(-0.546470\pi\) | ||||
−0.145471 | + | 0.989363i | \(0.546470\pi\) | |||||||
\(510\) | −3.12494 | + | 9.78156i | −0.138375 | + | 0.433135i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −11.4154 | + | 8.55478i | −0.504001 | + | 0.377703i | ||||
\(514\) | − | 16.1541i | − | 0.712526i | ||||||
\(515\) | − | 15.2633i | − | 0.672580i | ||||||
\(516\) | 4.52243 | + | 1.44479i | 0.199089 | + | 0.0636034i | ||||
\(517\) | 0.550183i | 0.0241970i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.54544 | − | 1.45214i | −0.199523 | − | 0.0637421i | ||||
\(520\) | −2.22106 | −0.0973999 | ||||||||
\(521\) | 4.70072 | 0.205942 | 0.102971 | − | 0.994684i | \(-0.467165\pi\) | ||||
0.102971 | + | 0.994684i | \(0.467165\pi\) | |||||||
\(522\) | −24.5154 | − | 17.4444i | −1.07301 | − | 0.763522i | ||||
\(523\) | 3.39241i | 0.148340i | 0.997246 | + | 0.0741700i | \(0.0236307\pi\) | ||||
−0.997246 | + | 0.0741700i | \(0.976369\pi\) | |||||||
\(524\) | 18.0259 | 0.787467 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.79029 | 0.165265 | ||||||||
\(527\) | 48.2212i | 2.10055i | ||||||||
\(528\) | −0.0965821 | + | 0.302317i | −0.00420320 | + | 0.0131567i | ||||
\(529\) | 19.5177 | 0.848596 | ||||||||
\(530\) | −1.72832 | −0.0750733 | ||||||||
\(531\) | 28.9413 | + | 20.5938i | 1.25594 | + | 0.893693i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.8998i | − | 0.515436i | ||||||
\(534\) | 6.41535 | − | 20.0811i | 0.277619 | − | 0.868992i | ||||
\(535\) | 6.18268i | 0.267301i | ||||||||
\(536\) | − | 3.79196i | − | 0.163788i | ||||||
\(537\) | 2.71600 | − | 8.50150i | 0.117204 | − | 0.366867i | ||||
\(538\) | 1.67131i | 0.0720552i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.11612 | + | 4.15810i | 0.134096 | + | 0.178936i | ||||
\(541\) | 25.7143 | 1.10555 | 0.552773 | − | 0.833332i | \(-0.313570\pi\) | ||||
0.552773 | + | 0.833332i | \(0.313570\pi\) | |||||||
\(542\) | −27.8686 | −1.19706 | ||||||||
\(543\) | 9.54282 | − | 29.8705i | 0.409522 | − | 1.28187i | ||||
\(544\) | − | 5.92858i | − | 0.254186i | ||||||
\(545\) | 18.5699 | 0.795448 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.86827 | 0.122638 | 0.0613192 | − | 0.998118i | \(-0.480469\pi\) | ||||
0.0613192 | + | 0.998118i | \(0.480469\pi\) | |||||||
\(548\) | 1.58312i | 0.0676275i | ||||||||
\(549\) | −9.96722 | + | 14.0074i | −0.425390 | + | 0.597819i | ||||
\(550\) | 0.183234 | 0.00781311 | ||||||||
\(551\) | 27.5343 | 1.17300 | ||||||||
\(552\) | −3.07886 | − | 0.983611i | −0.131045 | − | 0.0418653i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.08837i | 0.0887262i | ||||||||
\(555\) | −14.2563 | − | 4.55448i | −0.605144 | − | 0.193327i | ||||
\(556\) | − | 8.23768i | − | 0.349356i | ||||||
\(557\) | 23.1881i | 0.982511i | 0.871015 | + | 0.491256i | \(0.163462\pi\) | ||||
−0.871015 | + | 0.491256i | \(0.836538\pi\) | |||||||
\(558\) | 19.8814 | + | 14.1470i | 0.841649 | + | 0.598892i | ||||
\(559\) | 6.08800i | 0.257495i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.572595 | + | 1.79231i | −0.0241750 | + | 0.0756714i | ||||
\(562\) | 19.4447 | 0.820226 | ||||||||
\(563\) | 5.87313 | 0.247523 | 0.123761 | − | 0.992312i | \(-0.460504\pi\) | ||||
0.123761 | + | 0.992312i | \(0.460504\pi\) | |||||||
\(564\) | −4.95404 | − | 1.58268i | −0.208603 | − | 0.0666429i | ||||
\(565\) | − | 8.96035i | − | 0.376965i | ||||||
\(566\) | −1.11859 | −0.0470177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.3992 | 0.478299 | ||||||||
\(569\) | 31.9287i | 1.33852i | 0.743028 | + | 0.669261i | \(0.233389\pi\) | ||||
−0.743028 | + | 0.669261i | \(0.766611\pi\) | |||||||
\(570\) | −4.52952 | − | 1.44706i | −0.189721 | − | 0.0606106i | ||||
\(571\) | −18.5344 | −0.775640 | −0.387820 | − | 0.921735i | \(-0.626772\pi\) | ||||
−0.387820 | + | 0.921735i | \(0.626772\pi\) | |||||||
\(572\) | −0.406973 | −0.0170164 | ||||||||
\(573\) | 7.94540 | − | 24.8704i | 0.331924 | − | 1.03897i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.86609i | 0.0778213i | ||||||||
\(576\) | −2.44434 | − | 1.73932i | −0.101847 | − | 0.0724715i | ||||
\(577\) | 15.3847i | 0.640474i | 0.947337 | + | 0.320237i | \(0.103763\pi\) | ||||
−0.947337 | + | 0.320237i | \(0.896237\pi\) | |||||||
\(578\) | − | 18.1480i | − | 0.754859i | ||||||
\(579\) | −40.1122 | − | 12.8147i | −1.66701 | − | 0.532563i | ||||
\(580\) | − | 10.0295i | − | 0.416451i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.9289 | − | 3.81094i | −0.494467 | − | 0.157969i | ||||
\(583\) | −0.316686 | −0.0131158 | ||||||||
\(584\) | 8.37048 | 0.346373 | ||||||||
\(585\) | −3.86313 | + | 5.42902i | −0.159721 | + | 0.224462i | ||||
\(586\) | 25.9736i | 1.07296i | ||||||||
\(587\) | −3.04776 | −0.125795 | −0.0628973 | − | 0.998020i | \(-0.520034\pi\) | ||||
−0.0628973 | + | 0.998020i | \(0.520034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.3297 | −0.920078 | ||||||||
\(590\) | 11.8401i | 0.487451i | ||||||||
\(591\) | 0.402291 | − | 1.25923i | 0.0165480 | − | 0.0517980i | ||||
\(592\) | 8.64068 | 0.355130 | ||||||||
\(593\) | −7.74576 | −0.318080 | −0.159040 | − | 0.987272i | \(-0.550840\pi\) | ||||
−0.159040 | + | 0.987272i | \(0.550840\pi\) | |||||||
\(594\) | 0.570978 | + | 0.761904i | 0.0234275 | + | 0.0312613i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 9.35407i | − | 0.383158i | ||||||
\(597\) | −3.96935 | + | 12.4247i | −0.162455 | + | 0.508508i | ||||
\(598\) | − | 4.14469i | − | 0.169489i | ||||||
\(599\) | 33.6603i | 1.37532i | 0.726032 | + | 0.687661i | \(0.241362\pi\) | ||||
−0.726032 | + | 0.687661i | \(0.758638\pi\) | |||||||
\(600\) | −0.527098 | + | 1.64990i | −0.0215187 | + | 0.0673569i | ||||
\(601\) | − | 38.9597i | − | 1.58920i | −0.607134 | − | 0.794600i | \(-0.707681\pi\) | ||
0.607134 | − | 0.794600i | \(-0.292319\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.26883 | − | 6.59542i | −0.377456 | − | 0.268586i | ||||
\(604\) | 14.2685 | 0.580575 | ||||||||
\(605\) | −10.9664 | −0.445849 | ||||||||
\(606\) | −4.21019 | + | 13.1786i | −0.171027 | + | 0.535342i | ||||
\(607\) | − | 23.5510i | − | 0.955906i | −0.878386 | − | 0.477953i | \(-0.841379\pi\) | ||
0.878386 | − | 0.477953i | \(-0.158621\pi\) | |||||||
\(608\) | 2.74533 | 0.111338 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.73054 | −0.232023 | ||||||||
\(611\) | − | 6.66902i | − | 0.269800i | ||||||
\(612\) | −14.4914 | − | 10.3117i | −0.585782 | − | 0.416825i | ||||
\(613\) | 4.95160 | 0.199993 | 0.0999966 | − | 0.994988i | \(-0.468117\pi\) | ||||
0.0999966 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(614\) | −14.8678 | −0.600014 | ||||||||
\(615\) | −8.83967 | − | 2.82403i | −0.356450 | − | 0.113876i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 32.5086i | − | 1.30875i | −0.756172 | − | 0.654373i | \(-0.772933\pi\) | ||
0.756172 | − | 0.654373i | \(-0.227067\pi\) | |||||||
\(618\) | 25.1829 | + | 8.04524i | 1.01300 | + | 0.323627i | ||||
\(619\) | − | 28.1229i | − | 1.13035i | −0.824970 | − | 0.565177i | \(-0.808808\pi\) | ||
0.824970 | − | 0.565177i | \(-0.191192\pi\) | |||||||
\(620\) | 8.13368i | 0.326656i | ||||||||
\(621\) | −7.75939 | + | 5.81495i | −0.311373 | + | 0.233346i | ||||
\(622\) | 10.1085i | 0.405314i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.17072 | − | 3.66453i | 0.0468661 | − | 0.146698i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 30.7635 | 1.22956 | ||||||||
\(627\) | −0.829962 | − | 0.265150i | −0.0331455 | − | 0.0105891i | ||||
\(628\) | − | 5.01925i | − | 0.200290i | ||||||
\(629\) | 51.2270 | 2.04255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5082 | 0.896038 | 0.448019 | − | 0.894024i | \(-0.352130\pi\) | ||||
0.448019 | + | 0.894024i | \(0.352130\pi\) | |||||||
\(632\) | − | 8.97002i | − | 0.356808i | ||||||
\(633\) | 22.9461 | + | 7.33066i | 0.912026 | + | 0.291367i | ||||
\(634\) | −15.3849 | −0.611012 | ||||||||
\(635\) | −9.46529 | −0.375618 | ||||||||
\(636\) | 0.910992 | − | 2.85155i | 0.0361232 | − | 0.113071i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 1.83774i | − | 0.0727568i | ||||||
\(639\) | 19.8268 | − | 27.8634i | 0.784335 | − | 1.10226i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | − | 48.5107i | − | 1.91606i | −0.286670 | − | 0.958029i | \(-0.592548\pi\) | ||
0.286670 | − | 0.958029i | \(-0.407452\pi\) | |||||||
\(642\) | −10.2008 | − | 3.25888i | −0.402593 | − | 0.128618i | ||||
\(643\) | 18.4380i | 0.727123i | 0.931570 | + | 0.363561i | \(0.118439\pi\) | ||||
−0.931570 | + | 0.363561i | \(0.881561\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.52243 | + | 1.44479i | 0.178070 | + | 0.0568886i | ||||
\(646\) | 16.2759 | 0.640368 | ||||||||
\(647\) | 16.2081 | 0.637208 | 0.318604 | − | 0.947888i | \(-0.396786\pi\) | ||||
0.318604 | + | 0.947888i | \(0.396786\pi\) | |||||||
\(648\) | −8.50295 | + | 2.94956i | −0.334027 | + | 0.115870i | ||||
\(649\) | 2.16951i | 0.0851609i | ||||||||
\(650\) | −2.22106 | −0.0871171 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.9391 | 0.937526 | ||||||||
\(653\) | − | 10.1843i | − | 0.398544i | −0.979944 | − | 0.199272i | \(-0.936142\pi\) | ||
0.979944 | − | 0.199272i | \(-0.0638578\pi\) | |||||||
\(654\) | −9.78816 | + | 30.6385i | −0.382747 | + | 1.19806i | ||||
\(655\) | 18.0259 | 0.704332 | ||||||||
\(656\) | 5.35770 | 0.209183 | ||||||||
\(657\) | 14.5589 | − | 20.4603i | 0.567997 | − | 0.798231i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11.7903i | − | 0.459287i | −0.973275 | − | 0.229643i | \(-0.926244\pi\) | ||
0.973275 | − | 0.229643i | \(-0.0737560\pi\) | |||||||
\(660\) | −0.0965821 | + | 0.302317i | −0.00375945 | + | 0.0117677i | ||||
\(661\) | − | 26.8096i | − | 1.04277i | −0.853320 | − | 0.521387i | \(-0.825415\pi\) | ||
0.853320 | − | 0.521387i | \(-0.174585\pi\) | |||||||
\(662\) | 11.3036i | 0.439326i | ||||||||
\(663\) | 6.94068 | − | 21.7254i | 0.269554 | − | 0.843746i | ||||
\(664\) | 9.25852i | 0.359300i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15.0289 | − | 21.1207i | 0.582357 | − | 0.818412i | ||||
\(667\) | 18.7159 | 0.724682 | ||||||||
\(668\) | 12.2295 | 0.473174 | ||||||||
\(669\) | −9.94848 | + | 31.1403i | −0.384630 | + | 1.20395i | ||||
\(670\) | − | 3.79196i | − | 0.146496i | ||||||
\(671\) | −1.05003 | −0.0405359 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.41415 | −0.208700 | −0.104350 | − | 0.994541i | \(-0.533276\pi\) | ||||
−0.104350 | + | 0.994541i | \(0.533276\pi\) | |||||||
\(674\) | 35.2334i | 1.35714i | ||||||||
\(675\) | 3.11612 | + | 4.15810i | 0.119939 | + | 0.160045i | ||||
\(676\) | −8.06689 | −0.310265 | ||||||||
\(677\) | −27.7636 | −1.06704 | −0.533521 | − | 0.845787i | \(-0.679131\pi\) | ||||
−0.533521 | + | 0.845787i | \(0.679131\pi\) | |||||||
\(678\) | 14.7837 | + | 4.72298i | 0.567764 | + | 0.181385i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 5.92858i | − | 0.227351i | ||||||
\(681\) | −5.96621 | − | 1.90604i | −0.228626 | − | 0.0730397i | ||||
\(682\) | 1.49036i | 0.0570690i | ||||||||
\(683\) | − | 0.877923i | − | 0.0335928i | −0.999859 | − | 0.0167964i | \(-0.994653\pi\) | ||
0.999859 | − | 0.0167964i | \(-0.00534671\pi\) | |||||||
\(684\) | 4.77500 | − | 6.71052i | 0.182577 | − | 0.256583i | ||||
\(685\) | 1.58312i | 0.0604879i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7732 | − | 33.7220i | 0.411025 | − | 1.28657i | ||||
\(688\) | −2.74103 | −0.104501 | ||||||||
\(689\) | 3.83870 | 0.146243 | ||||||||
\(690\) | −3.07886 | − | 0.983611i | −0.117210 | − | 0.0374454i | ||||
\(691\) | − | 34.2334i | − | 1.30230i | −0.758949 | − | 0.651151i | \(-0.774287\pi\) | ||
0.758949 | − | 0.651151i | \(-0.225713\pi\) | |||||||
\(692\) | 2.75498 | 0.104729 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.4627 | 1.38411 | ||||||||
\(695\) | − | 8.23768i | − | 0.312473i | ||||||
\(696\) | 16.5476 | + | 5.28652i | 0.627236 | + | 0.200385i | ||||
\(697\) | 31.7635 | 1.20313 | ||||||||
\(698\) | −5.80210 | −0.219613 | ||||||||
\(699\) | 7.31631 | − | 22.9012i | 0.276728 | − | 0.866203i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 16.9235i | − | 0.639191i | −0.947554 | − | 0.319596i | \(-0.896453\pi\) | ||
0.947554 | − | 0.319596i | \(-0.103547\pi\) | |||||||
\(702\) | −6.92109 | − | 9.23539i | −0.261220 | − | 0.348567i | ||||
\(703\) | 23.7216i | 0.894675i | ||||||||
\(704\) | − | 0.183234i | − | 0.00690588i | ||||||
\(705\) | −4.95404 | − | 1.58268i | −0.186580 | − | 0.0596072i | ||||
\(706\) | 36.8540i | 1.38702i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −19.5350 | − | 6.24091i | −0.734172 | − | 0.234548i | ||||
\(709\) | 6.85139 | 0.257310 | 0.128655 | − | 0.991689i | \(-0.458934\pi\) | ||||
0.128655 | + | 0.991689i | \(0.458934\pi\) | |||||||
\(710\) | 11.3992 | 0.427804 | ||||||||
\(711\) | −21.9257 | − | 15.6017i | −0.822280 | − | 0.585110i | ||||
\(712\) | 12.1711i | 0.456130i | ||||||||
\(713\) | −15.1782 | −0.568427 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.406973 | −0.0152199 | ||||||||
\(716\) | 5.15274i | 0.192567i | ||||||||
\(717\) | 13.6406 | − | 42.6971i | 0.509416 | − | 1.59455i | ||||
\(718\) | 14.6764 | 0.547717 | ||||||||
\(719\) | −22.2069 | −0.828179 | −0.414089 | − | 0.910236i | \(-0.635900\pi\) | ||||
−0.414089 | + | 0.910236i | \(0.635900\pi\) | |||||||
\(720\) | −2.44434 | − | 1.73932i | −0.0910950 | − | 0.0648205i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 11.4631i | − | 0.426614i | ||||||
\(723\) | −13.8102 | + | 43.2282i | −0.513608 | + | 1.60767i | ||||
\(724\) | 18.1045i | 0.672847i | ||||||||
\(725\) | − | 10.0295i | − | 0.372486i | ||||||
\(726\) | 5.78038 | − | 18.0935i | 0.214530 | − | 0.671513i | ||||
\(727\) | 7.00749i | 0.259894i | 0.991521 | + | 0.129947i | \(0.0414806\pi\) | ||||
−0.991521 | + | 0.129947i | \(0.958519\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.57961 | + | 25.9143i | −0.280726 | + | 0.959788i | ||||
\(730\) | 8.37048 | 0.309805 | ||||||||
\(731\) | −16.2504 | −0.601044 | ||||||||
\(732\) | 3.02055 | − | 9.45481i | 0.111643 | − | 0.349460i | ||||
\(733\) | − | 36.7024i | − | 1.35563i | −0.735231 | − | 0.677816i | \(-0.762926\pi\) | ||
0.735231 | − | 0.677816i | \(-0.237074\pi\) | |||||||
\(734\) | 28.9944 | 1.07020 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.86609 | 0.0687849 | ||||||||
\(737\) | − | 0.694816i | − | 0.0255939i | ||||||
\(738\) | 9.31874 | − | 13.0960i | 0.343027 | − | 0.482071i | ||||
\(739\) | 20.6386 | 0.759203 | 0.379602 | − | 0.925150i | \(-0.376061\pi\) | ||||
0.379602 | + | 0.925150i | \(0.376061\pi\) | |||||||
\(740\) | 8.64068 | 0.317638 | ||||||||
\(741\) | 10.0603 | + | 3.21401i | 0.369576 | + | 0.118069i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.62699i | 0.316494i | 0.987400 | + | 0.158247i | \(0.0505842\pi\) | ||||
−0.987400 | + | 0.158247i | \(0.949416\pi\) | |||||||
\(744\) | −13.4198 | − | 4.28724i | −0.491992 | − | 0.157178i | ||||
\(745\) | − | 9.35407i | − | 0.342707i | ||||||
\(746\) | 27.5619i | 1.00911i | ||||||||
\(747\) | 22.6309 | + | 16.1035i | 0.828023 | + | 0.589196i | ||||
\(748\) | − | 1.08632i | − | 0.0397196i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.527098 | + | 1.64990i | −0.0192469 | + | 0.0602458i | ||||
\(751\) | −4.16116 | −0.151843 | −0.0759214 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759214 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(752\) | 3.00263 | 0.109495 | ||||||||
\(753\) | −28.2386 | − | 9.02147i | −1.02907 | − | 0.328761i | ||||
\(754\) | 22.2761i | 0.811247i | ||||||||
\(755\) | 14.2685 | 0.519282 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.4589 | 0.707244 | 0.353622 | − | 0.935388i | \(-0.384950\pi\) | ||||
0.353622 | + | 0.935388i | \(0.384950\pi\) | |||||||
\(758\) | − | 25.9475i | − | 0.942455i | ||||||
\(759\) | −0.564151 | − | 0.180231i | −0.0204774 | − | 0.00654196i | ||||
\(760\) | 2.74533 | 0.0995837 | ||||||||
\(761\) | −2.91036 | −0.105500 | −0.0527502 | − | 0.998608i | \(-0.516799\pi\) | ||||
−0.0527502 | + | 0.998608i | \(0.516799\pi\) | |||||||
\(762\) | 4.98913 | − | 15.6168i | 0.180737 | − | 0.565736i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.0739i | 0.545353i | ||||||||
\(765\) | −14.4914 | − | 10.3117i | −0.523939 | − | 0.372819i | ||||
\(766\) | − | 36.5542i | − | 1.32076i | ||||||
\(767\) | − | 26.2977i | − | 0.949554i | ||||||
\(768\) | 1.64990 | + | 0.527098i | 0.0595356 | + | 0.0190200i | ||||
\(769\) | − | 13.9115i | − | 0.501661i | −0.968031 | − | 0.250830i | \(-0.919296\pi\) | ||
0.968031 | − | 0.250830i | \(-0.0807036\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.6526 | + | 8.51478i | 0.959870 | + | 0.306652i | ||||
\(772\) | 24.3119 | 0.875004 | ||||||||
\(773\) | −8.15536 | −0.293328 | −0.146664 | − | 0.989186i | \(-0.546854\pi\) | ||||
−0.146664 | + | 0.989186i | \(0.546854\pi\) | |||||||
\(774\) | −4.76752 | + | 6.70001i | −0.171365 | + | 0.240827i | ||||
\(775\) | 8.13368i | 0.292170i | ||||||||
\(776\) | 7.23005 | 0.259544 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.5029 | −0.699214 | ||||||||
\(779\) | 14.7087i | 0.526993i | ||||||||
\(780\) | 1.17072 | − | 3.66453i | 0.0419183 | − | 0.131211i | ||||
\(781\) | 2.08871 | 0.0747401 | ||||||||
\(782\) | 11.0633 | 0.395621 | ||||||||
\(783\) | 41.7036 | − | 31.2530i | 1.49036 | − | 1.11689i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.01925i | − | 0.179145i | ||||||
\(786\) | −9.50143 | + | 29.7410i | −0.338905 | + | 1.06083i | ||||
\(787\) | − | 1.35697i | − | 0.0483707i | −0.999707 | − | 0.0241854i | \(-0.992301\pi\) | ||
0.999707 | − | 0.0241854i | \(-0.00769919\pi\) | |||||||
\(788\) | 0.763219i | 0.0271885i | ||||||||
\(789\) | −1.99785 | + | 6.25360i | −0.0711255 | + | 0.222634i | ||||
\(790\) | − | 8.97002i | − | 0.319139i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.447885 | − | 0.318701i | −0.0159149 | − | 0.0113246i | ||||
\(793\) | 12.7279 | 0.451980 | ||||||||
\(794\) | 8.12748 | 0.288434 | ||||||||
\(795\) | 0.910992 | − | 2.85155i | 0.0323096 | − | 0.101134i | ||||
\(796\) | − | 7.53057i | − | 0.266914i | ||||||
\(797\) | −11.4530 | −0.405688 | −0.202844 | − | 0.979211i | \(-0.565018\pi\) | ||||
−0.202844 | + | 0.979211i | \(0.565018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.8013 | 0.629766 | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 29.7502 | + | 21.1694i | 1.05117 | + | 0.747983i | ||||
\(802\) | −19.8417 | −0.700633 | ||||||||
\(803\) | 1.53375 | 0.0541250 | ||||||||
\(804\) | 6.25636 | + | 1.99874i | 0.220645 | + | 0.0704899i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 18.0654i | − | 0.636326i | ||||||
\(807\) | −2.75749 | − | 0.880942i | −0.0970682 | − | 0.0310106i | ||||
\(808\) | − | 7.98749i | − | 0.280999i | ||||||
\(809\) | 6.10324i | 0.214579i | 0.994228 | + | 0.107289i | \(0.0342171\pi\) | ||||
−0.994228 | + | 0.107289i | \(0.965783\pi\) | |||||||
\(810\) | −8.50295 | + | 2.94956i | −0.298763 | + | 0.103637i | ||||
\(811\) | − | 32.4705i | − | 1.14019i | −0.821578 | − | 0.570097i | \(-0.806906\pi\) | ||
0.821578 | − | 0.570097i | \(-0.193094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.6895 | − | 45.9804i | 0.515183 | − | 1.61260i | ||||
\(814\) | 1.58326 | 0.0554934 | ||||||||
\(815\) | 23.9391 | 0.838548 | ||||||||
\(816\) | 9.78156 | + | 3.12494i | 0.342423 | + | 0.109395i | ||||
\(817\) | − | 7.52505i | − | 0.263268i | ||||||
\(818\) | −3.20599 | −0.112095 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.35770 | 0.187099 | ||||||||
\(821\) | − | 36.7165i | − | 1.28142i | −0.767785 | − | 0.640708i | \(-0.778641\pi\) | ||
0.767785 | − | 0.640708i | \(-0.221359\pi\) | |||||||
\(822\) | −2.61199 | − | 0.834458i | −0.0911035 | − | 0.0291051i | ||||
\(823\) | −10.6302 | −0.370545 | −0.185273 | − | 0.982687i | \(-0.559317\pi\) | ||||
−0.185273 | + | 0.982687i | \(0.559317\pi\) | |||||||
\(824\) | −15.2633 | −0.531721 | ||||||||
\(825\) | −0.0965821 | + | 0.302317i | −0.00336256 | + | 0.0105253i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.9955i | − | 0.660537i | −0.943887 | − | 0.330269i | \(-0.892861\pi\) | ||
0.943887 | − | 0.330269i | \(-0.107139\pi\) | |||||||
\(828\) | 3.24572 | − | 4.56135i | 0.112797 | − | 0.158518i | ||||
\(829\) | − | 29.1165i | − | 1.01126i | −0.862751 | − | 0.505628i | \(-0.831261\pi\) | ||
0.862751 | − | 0.505628i | \(-0.168739\pi\) | |||||||
\(830\) | 9.25852i | 0.321368i | ||||||||
\(831\) | −3.44560 | − | 1.10077i | −0.119526 | − | 0.0381854i | ||||
\(832\) | 2.22106i | 0.0770014i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 13.5913 | + | 4.34206i | 0.470630 | + | 0.150353i | ||||
\(835\) | 12.2295 | 0.423220 | ||||||||
\(836\) | 0.503038 | 0.0173979 | ||||||||
\(837\) | −33.8207 | + | 25.3455i | −1.16901 | + | 0.876069i | ||||
\(838\) | − | 6.99137i | − | 0.241513i | ||||||
\(839\) | 37.0577 | 1.27937 | 0.639687 | − | 0.768636i | \(-0.279064\pi\) | ||||
0.639687 | + | 0.768636i | \(0.279064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −71.5905 | −2.46864 | ||||||||
\(842\) | − | 17.7534i | − | 0.611822i | ||||||
\(843\) | −10.2493 | + | 32.0818i | −0.353004 | + | 1.10496i | ||||
\(844\) | −13.9076 | −0.478719 | ||||||||
\(845\) | −8.06689 | −0.277510 | ||||||||
\(846\) | 5.22253 | − | 7.33944i | 0.179554 | − | 0.252335i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.72832i | 0.0593506i | ||||||||
\(849\) | 0.589605 | − | 1.84556i | 0.0202352 | − | 0.0633393i | ||||
\(850\) | − | 5.92858i | − | 0.203349i | ||||||
\(851\) | 16.1243i | 0.552733i | ||||||||
\(852\) | −6.00848 | + | 18.8075i | −0.205847 | + | 0.644334i | ||||
\(853\) | − | 0.176745i | − | 0.00605163i | −0.999995 | − | 0.00302581i | \(-0.999037\pi\) | ||
0.999995 | − | 0.00302581i | \(-0.000963148\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.77500 | − | 6.71052i | 0.163302 | − | 0.229495i | ||||
\(856\) | 6.18268 | 0.211320 | ||||||||
\(857\) | 14.9114 | 0.509365 | 0.254682 | − | 0.967025i | \(-0.418029\pi\) | ||||
0.254682 | + | 0.967025i | \(0.418029\pi\) | |||||||
\(858\) | 0.214515 | − | 0.671465i | 0.00732341 | − | 0.0229234i | ||||
\(859\) | − | 22.9969i | − | 0.784646i | −0.919828 | − | 0.392323i | \(-0.871672\pi\) | ||
0.919828 | − | 0.392323i | \(-0.128328\pi\) | |||||||
\(860\) | −2.74103 | −0.0934684 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.5466 | −0.733879 | ||||||||
\(863\) | 23.1453i | 0.787877i | 0.919137 | + | 0.393938i | \(0.128888\pi\) | ||||
−0.919137 | + | 0.393938i | \(0.871112\pi\) | |||||||
\(864\) | 4.15810 | − | 3.11612i | 0.141461 | − | 0.106013i | ||||
\(865\) | 2.75498 | 0.0936722 | ||||||||
\(866\) | −2.22339 | −0.0755540 | ||||||||
\(867\) | 29.9424 | + | 9.56579i | 1.01690 | + | 0.324871i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.64361i | − | 0.0557557i | ||||||
\(870\) | 16.5476 | + | 5.28652i | 0.561017 | + | 0.179230i | ||||
\(871\) | 8.42218i | 0.285375i | ||||||||
\(872\) | − | 18.5699i | − | 0.628857i | ||||||
\(873\) | 12.5753 | − | 17.6727i | 0.425611 | − | 0.598129i | ||||
\(874\) | 5.12304i | 0.173289i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.41206 | + | 13.8104i | −0.149070 | + | 0.466612i | ||||
\(877\) | 7.97467 | 0.269286 | 0.134643 | − | 0.990894i | \(-0.457011\pi\) | ||||
0.134643 | + | 0.990894i | \(0.457011\pi\) | |||||||
\(878\) | −1.07643 | −0.0363277 | ||||||||
\(879\) | −42.8538 | − | 13.6906i | −1.44542 | − | 0.461773i | ||||
\(880\) | − | 0.183234i | − | 0.00617681i | ||||||
\(881\) | 2.54981 | 0.0859054 | 0.0429527 | − | 0.999077i | \(-0.486324\pi\) | ||||
0.0429527 | + | 0.999077i | \(0.486324\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.8728 | 0.803384 | 0.401692 | − | 0.915775i | \(-0.368422\pi\) | ||||
0.401692 | + | 0.915775i | \(0.368422\pi\) | |||||||
\(884\) | 13.1677i | 0.442879i | ||||||||
\(885\) | −19.5350 | − | 6.24091i | −0.656663 | − | 0.209786i | ||||
\(886\) | 22.1450 | 0.743975 | ||||||||
\(887\) | 37.5185 | 1.25975 | 0.629874 | − | 0.776697i | \(-0.283106\pi\) | ||||
0.629874 | + | 0.776697i | \(0.283106\pi\) | |||||||
\(888\) | −4.55448 | + | 14.2563i | −0.152838 | + | 0.478409i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.1711i | 0.407976i | ||||||||
\(891\) | −1.55803 | + | 0.540458i | −0.0521959 | + | 0.0181060i | ||||
\(892\) | − | 18.8741i | − | 0.631951i | ||||||
\(893\) | 8.24323i | 0.275849i | ||||||||
\(894\) | 15.4333 | + | 4.93051i | 0.516166 | + | 0.164901i | ||||
\(895\) | 5.15274i | 0.172237i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.83833 | + | 2.18466i | 0.228325 | + | 0.0729437i | ||||
\(898\) | −2.54766 | −0.0850164 | ||||||||
\(899\) | 81.5766 | 2.72073 | ||||||||
\(900\) | −2.44434 | − | 1.73932i | −0.0814779 | − | 0.0579772i | ||||
\(901\) | 10.2465i | 0.341359i | ||||||||
\(902\) | 0.981712 | 0.0326874 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.96035 | −0.298017 | ||||||||
\(905\) | 18.1045i | 0.601813i | ||||||||
\(906\) | −7.52087 | + | 23.5415i | −0.249864 | + | 0.782114i | ||||
\(907\) | 29.2619 | 0.971625 | 0.485813 | − | 0.874063i | \(-0.338524\pi\) | ||||
0.485813 | + | 0.874063i | \(0.338524\pi\) | |||||||
\(908\) | 3.61611 | 0.120005 | ||||||||
\(909\) | −19.5241 | − | 13.8928i | −0.647574 | − | 0.460794i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22.2195i | − | 0.736164i | −0.929793 | − | 0.368082i | \(-0.880015\pi\) | ||
0.929793 | − | 0.368082i | \(-0.119985\pi\) | |||||||
\(912\) | −1.44706 | + | 4.52952i | −0.0479169 | + | 0.149988i | ||||
\(913\) | 1.69647i | 0.0561451i | ||||||||
\(914\) | − | 4.69058i | − | 0.155150i | ||||||
\(915\) | 3.02055 | − | 9.45481i | 0.0998564 | − | 0.312566i | ||||
\(916\) | 20.4388i | 0.675317i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 24.6516 | − | 18.4742i | 0.813625 | − | 0.609738i | ||||
\(919\) | −16.3855 | −0.540508 | −0.270254 | − | 0.962789i | \(-0.587108\pi\) | ||||
−0.270254 | + | 0.962789i | \(0.587108\pi\) | |||||||
\(920\) | 1.86609 | 0.0615231 | ||||||||
\(921\) | 7.83677 | − | 24.5303i | 0.258230 | − | 0.808302i | ||||
\(922\) | − | 5.10979i | − | 0.168282i | ||||||
\(923\) | −25.3183 | −0.833361 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.64068 | 0.284104 | ||||||||
\(926\) | 20.6740i | 0.679391i | ||||||||
\(927\) | −26.5477 | + | 37.3086i | −0.871939 | + | 1.22537i | ||||
\(928\) | −10.0295 | −0.329234 | ||||||||
\(929\) | −3.74333 | −0.122815 | −0.0614073 | − | 0.998113i | \(-0.519559\pi\) | ||||
−0.0614073 | + | 0.998113i | \(0.519559\pi\) | |||||||
\(930\) | −13.4198 | − | 4.28724i | −0.440051 | − | 0.140584i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 13.8804i | 0.454667i | ||||||||
\(933\) | −16.6780 | − | 5.32817i | −0.546014 | − | 0.174436i | ||||
\(934\) | − | 2.10185i | − | 0.0687747i | ||||||
\(935\) | − | 1.08632i | − | 0.0355263i | ||||||
\(936\) | 5.42902 | + | 3.86313i | 0.177453 | + | 0.126270i | ||||
\(937\) | 6.53832i | 0.213598i | 0.994281 | + | 0.106799i | \(0.0340601\pi\) | ||||
−0.994281 | + | 0.106799i | \(0.965940\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.2154 | + | 50.7567i | −0.529169 | + | 1.65638i | ||||
\(940\) | 3.00263 | 0.0979350 | ||||||||
\(941\) | −15.2301 | −0.496487 | −0.248244 | − | 0.968698i | \(-0.579853\pi\) | ||||
−0.248244 | + | 0.968698i | \(0.579853\pi\) | |||||||
\(942\) | 8.28126 | + | 2.64564i | 0.269818 | + | 0.0861995i | ||||
\(943\) | 9.99794i | 0.325578i | ||||||||
\(944\) | 11.8401 | 0.385364 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.502250 | −0.0163295 | ||||||||
\(947\) | 42.7603i | 1.38952i | 0.719241 | + | 0.694761i | \(0.244490\pi\) | ||||
−0.719241 | + | 0.694761i | \(0.755510\pi\) | |||||||
\(948\) | 14.7996 | + | 4.72808i | 0.480670 | + | 0.153561i | ||||
\(949\) | −18.5913 | −0.603500 | ||||||||
\(950\) | 2.74533 | 0.0890704 | ||||||||
\(951\) | 8.10934 | − | 25.3835i | 0.262963 | − | 0.823117i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25.9458i | − | 0.840466i | −0.907416 | − | 0.420233i | \(-0.861948\pi\) | ||
0.907416 | − | 0.420233i | \(-0.138052\pi\) | |||||||
\(954\) | 4.22459 | + | 3.00609i | 0.136776 | + | 0.0973258i | ||||
\(955\) | 15.0739i | 0.487779i | ||||||||
\(956\) | 25.8786i | 0.836974i | ||||||||
\(957\) | 3.03208 | + | 0.968668i | 0.0980134 | + | 0.0313126i | ||||
\(958\) | − | 10.7574i | − | 0.347555i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.64990 | + | 0.527098i | 0.0532503 | + | 0.0170120i | ||||
\(961\) | −35.1568 | −1.13409 | ||||||||
\(962\) | −19.1915 | −0.618758 | ||||||||
\(963\) | 10.7536 | − | 15.1125i | 0.346531 | − | 0.486995i | ||||
\(964\) | − | 26.2005i | − | 0.843862i | ||||||
\(965\) | 24.3119 | 0.782628 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.1260 | −1.32252 | −0.661262 | − | 0.750155i | \(-0.729979\pi\) | ||||
−0.661262 | + | 0.750155i | \(0.729979\pi\) | |||||||
\(968\) | 10.9664i | 0.352474i | ||||||||
\(969\) | −8.57900 | + | 26.8536i | −0.275597 | + | 0.862663i | ||||
\(970\) | 7.23005 | 0.232143 | ||||||||
\(971\) | −13.8976 | −0.445996 | −0.222998 | − | 0.974819i | \(-0.571584\pi\) | ||||
−0.222998 | + | 0.974819i | \(0.571584\pi\) | |||||||
\(972\) | −0.384586 | − | 15.5837i | −0.0123356 | − | 0.499848i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 27.2491i | − | 0.873116i | ||||||
\(975\) | 1.17072 | − | 3.66453i | 0.0374929 | − | 0.117359i | ||||
\(976\) | 5.73054i | 0.183430i | ||||||||
\(977\) | − | 47.6237i | − | 1.52362i | −0.647801 | − | 0.761809i | \(-0.724311\pi\) | ||
0.647801 | − | 0.761809i | \(-0.275689\pi\) | |||||||
\(978\) | −12.6182 | + | 39.4970i | −0.403486 | + | 1.26298i | ||||
\(979\) | 2.23015i | 0.0712760i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.3911 | − | 32.2990i | −1.44923 | − | 1.03123i | ||||
\(982\) | 9.39148 | 0.299694 | ||||||||
\(983\) | −39.7344 | −1.26733 | −0.633665 | − | 0.773607i | \(-0.718450\pi\) | ||||
−0.633665 | + | 0.773607i | \(0.718450\pi\) | |||||||
\(984\) | −2.82403 | + | 8.83967i | −0.0900268 | + | 0.281798i | ||||
\(985\) | 0.763219i | 0.0243182i | ||||||||
\(986\) | −59.4605 | −1.89361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.09755 | −0.193989 | ||||||||
\(989\) | − | 5.11501i | − | 0.162648i | ||||||
\(990\) | −0.447885 | − | 0.318701i | −0.0142347 | − | 0.0101290i | ||||
\(991\) | 35.1681 | 1.11715 | 0.558576 | − | 0.829454i | \(-0.311348\pi\) | ||||
0.558576 | + | 0.829454i | \(0.311348\pi\) | |||||||
\(992\) | 8.13368 | 0.258245 | ||||||||
\(993\) | −18.6498 | − | 5.95809i | −0.591832 | − | 0.189074i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 7.53057i | − | 0.238735i | ||||||
\(996\) | −15.2756 | − | 4.88015i | −0.484027 | − | 0.154633i | ||||
\(997\) | − | 20.2745i | − | 0.642101i | −0.947062 | − | 0.321050i | \(-0.895964\pi\) | ||
0.947062 | − | 0.321050i | \(-0.104036\pi\) | |||||||
\(998\) | 23.4355i | 0.741838i | ||||||||
\(999\) | 26.9254 | + | 35.9288i | 0.851882 | + | 1.13674i |
(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 | 1470.2.b.c.881.8 | ✓ | 16 | |
3.2 | odd | 2 | 1470.2.b.d.881.9 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.b.d.881.1 | yes | 16 | ||
21.20 | even | 2 | inner | 1470.2.b.c.881.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.b.c.881.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1470.2.b.c.881.16 | yes | 16 | 21.20 | even | 2 | inner | |
1470.2.b.d.881.1 | yes | 16 | 7.6 | odd | 2 | ||
1470.2.b.d.881.9 | yes | 16 | 3.2 | odd | 2 |