Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(647,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + 16903 x^{8} - 23292 x^{7} + 26994 x^{6} - 25716 x^{5} + 19962 x^{4} + \cdots + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 647.4 | ||
Root | \(0.500000 + 1.97090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.647 |
Dual form | 1134.2.k.d.971.4 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 2.08560 | + | 3.61236i | 0.932707 | + | 1.61550i | 0.778673 | + | 0.627429i | \(0.215893\pi\) |
0.154033 | + | 0.988066i | \(0.450774\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.94402 | − | 1.79465i | 0.734771 | − | 0.678315i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.61236 | − | 2.08560i | −1.14233 | − | 0.659523i | ||||
\(11\) | 0.0814333 | + | 0.0470156i | 0.0245531 | + | 0.0141757i | 0.512226 | − | 0.858851i | \(-0.328821\pi\) |
−0.487673 | + | 0.873026i | \(0.662154\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.79497i | − | 1.05253i | −0.850319 | − | 0.526267i | \(-0.823591\pi\) | ||
0.850319 | − | 0.526267i | \(-0.176409\pi\) | |||||||
\(14\) | −0.786244 | + | 2.52623i | −0.210133 | + | 0.675162i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.82627 | − | 6.62729i | 0.928006 | − | 1.60735i | 0.141353 | − | 0.989959i | \(-0.454855\pi\) |
0.786654 | − | 0.617395i | \(-0.211812\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.77624 | − | 3.91226i | 1.55458 | − | 0.897534i | 0.556815 | − | 0.830636i | \(-0.312023\pi\) |
0.997760 | − | 0.0668980i | \(-0.0213102\pi\) | |||||||
\(20\) | 4.17119 | 0.932707 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0940311 | −0.0200475 | ||||||||
\(23\) | 3.31685 | − | 1.91499i | 0.691612 | − | 0.399302i | −0.112604 | − | 0.993640i | \(-0.535919\pi\) |
0.804216 | + | 0.594338i | \(0.202586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.19941 | + | 10.7377i | −1.23988 | + | 2.14754i | ||||
\(26\) | 1.89748 | + | 3.28654i | 0.372127 | + | 0.644543i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.582206 | − | 2.58090i | −0.110027 | − | 0.487744i | ||||
\(29\) | − | 2.03174i | − | 0.377285i | −0.982046 | − | 0.188642i | \(-0.939591\pi\) | ||
0.982046 | − | 0.188642i | \(-0.0604087\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.45596 | − | 0.840596i | −0.261497 | − | 0.150976i | 0.363520 | − | 0.931586i | \(-0.381575\pi\) |
−0.625017 | + | 0.780611i | \(0.714908\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.65254i | 1.31240i | ||||||||
\(35\) | 10.5374 | + | 3.27958i | 1.78114 | + | 0.554349i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.18343 | − | 3.78182i | −0.358954 | − | 0.621727i | 0.628832 | − | 0.777541i | \(-0.283533\pi\) |
−0.987786 | + | 0.155814i | \(0.950200\pi\) | |||||||
\(38\) | −3.91226 | + | 6.77624i | −0.634653 | + | 1.09925i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.61236 | + | 2.08560i | −0.571164 | + | 0.329762i | ||||
\(41\) | −3.07145 | −0.479680 | −0.239840 | − | 0.970812i | \(-0.577095\pi\) | ||||
−0.239840 | + | 0.970812i | \(0.577095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.12790 | −0.781997 | −0.390999 | − | 0.920391i | \(-0.627870\pi\) | ||||
−0.390999 | + | 0.920391i | \(0.627870\pi\) | |||||||
\(44\) | 0.0814333 | − | 0.0470156i | 0.0122765 | − | 0.00708786i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.91499 | + | 3.31685i | −0.282349 | + | 0.489044i | ||||
\(47\) | 2.54960 | + | 4.41603i | 0.371897 | + | 0.644145i | 0.989857 | − | 0.142065i | \(-0.0453741\pi\) |
−0.617960 | + | 0.786209i | \(0.712041\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.558434 | − | 6.97769i | 0.0797763 | − | 0.996813i | ||||
\(50\) | − | 12.3988i | − | 1.75346i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.28654 | − | 1.89748i | −0.455761 | − | 0.263134i | ||||
\(53\) | −6.05506 | − | 3.49589i | −0.831726 | − | 0.480197i | 0.0227173 | − | 0.999742i | \(-0.492768\pi\) |
−0.854443 | + | 0.519545i | \(0.826102\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.392222i | 0.0528872i | ||||||||
\(56\) | 1.79465 | + | 1.94402i | 0.239821 | + | 0.259781i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.01587 | + | 1.75954i | 0.133390 | + | 0.231039i | ||||
\(59\) | −5.21303 | + | 9.02922i | −0.678678 | + | 1.17550i | 0.296701 | + | 0.954970i | \(0.404114\pi\) |
−0.975379 | + | 0.220535i | \(0.929220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.69902 | − | 1.55828i | 0.345574 | − | 0.199517i | −0.317160 | − | 0.948372i | \(-0.602729\pi\) |
0.662734 | + | 0.748855i | \(0.269396\pi\) | |||||||
\(62\) | 1.68119 | 0.213512 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 13.7088 | − | 7.91477i | 1.70036 | − | 0.981706i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.76669 | + | 6.52409i | −0.460174 | + | 0.797045i | −0.998969 | − | 0.0453920i | \(-0.985546\pi\) |
0.538795 | + | 0.842437i | \(0.318880\pi\) | |||||||
\(68\) | −3.82627 | − | 6.62729i | −0.464003 | − | 0.803677i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.7654 | + | 2.42849i | −1.28671 | + | 0.290260i | ||||
\(71\) | 8.61322i | 1.02220i | 0.859521 | + | 0.511100i | \(0.170762\pi\) | ||||
−0.859521 | + | 0.511100i | \(0.829238\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.129966 | − | 0.0750360i | −0.0152114 | − | 0.00878230i | 0.492375 | − | 0.870383i | \(-0.336129\pi\) |
−0.507586 | + | 0.861601i | \(0.669462\pi\) | |||||||
\(74\) | 3.78182 | + | 2.18343i | 0.439628 | + | 0.253819i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.82452i | − | 0.897534i | ||||||
\(77\) | 0.242685 | − | 0.0547454i | 0.0276565 | − | 0.00623882i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.48425 | + | 11.2311i | 0.729535 | + | 1.26359i | 0.957080 | + | 0.289825i | \(0.0935970\pi\) |
−0.227544 | + | 0.973768i | \(0.573070\pi\) | |||||||
\(80\) | 2.08560 | − | 3.61236i | 0.233177 | − | 0.403874i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.65995 | − | 1.53573i | 0.293743 | − | 0.169592i | ||||
\(83\) | −2.58840 | −0.284114 | −0.142057 | − | 0.989858i | \(-0.545372\pi\) | ||||
−0.142057 | + | 0.989858i | \(0.545372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31.9202 | 3.46223 | ||||||||
\(86\) | 4.44089 | − | 2.56395i | 0.478873 | − | 0.276478i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0470156 | + | 0.0814333i | −0.00501188 | + | 0.00868082i | ||||
\(89\) | 1.37123 | + | 2.37504i | 0.145350 | + | 0.251754i | 0.929504 | − | 0.368813i | \(-0.120236\pi\) |
−0.784153 | + | 0.620567i | \(0.786902\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.81065 | − | 7.37750i | −0.713950 | − | 0.773372i | ||||
\(92\) | − | 3.82997i | − | 0.399302i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.41603 | − | 2.54960i | −0.455479 | − | 0.262971i | ||||
\(95\) | 28.2650 | + | 16.3188i | 2.89992 | + | 1.67427i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.06398i | 0.412634i | 0.978485 | + | 0.206317i | \(0.0661479\pi\) | ||||
−0.978485 | + | 0.206317i | \(0.933852\pi\) | |||||||
\(98\) | 3.00523 | + | 6.32207i | 0.303574 | + | 0.638626i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.19941 | + | 10.7377i | 0.619941 | + | 1.07377i | ||||
\(101\) | −6.16567 | + | 10.6793i | −0.613507 | + | 1.06263i | 0.377137 | + | 0.926157i | \(0.376908\pi\) |
−0.990644 | + | 0.136468i | \(0.956425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.57103 | + | 0.907035i | −0.154798 | + | 0.0893728i | −0.575398 | − | 0.817873i | \(-0.695153\pi\) |
0.420600 | + | 0.907246i | \(0.361820\pi\) | |||||||
\(104\) | 3.79497 | 0.372127 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.99178 | 0.679101 | ||||||||
\(107\) | 2.70445 | − | 1.56142i | 0.261449 | − | 0.150948i | −0.363546 | − | 0.931576i | \(-0.618434\pi\) |
0.624996 | + | 0.780628i | \(0.285101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.12213 | − | 1.94358i | 0.107480 | − | 0.186161i | −0.807269 | − | 0.590184i | \(-0.799055\pi\) |
0.914749 | + | 0.404023i | \(0.132388\pi\) | |||||||
\(110\) | −0.196111 | − | 0.339674i | −0.0186984 | − | 0.0323866i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.52623 | − | 0.786244i | −0.238706 | − | 0.0742931i | ||||
\(113\) | 3.58148i | 0.336917i | 0.985709 | + | 0.168458i | \(0.0538789\pi\) | ||||
−0.985709 | + | 0.168458i | \(0.946121\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8352 | + | 7.98778i | 1.29014 | + | 0.744864i | ||||
\(116\) | −1.75954 | − | 1.01587i | −0.163369 | − | 0.0943212i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 10.4261i | − | 0.959796i | ||||||
\(119\) | −4.45535 | − | 19.7504i | −0.408421 | − | 1.81052i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.49558 | − | 9.51862i | −0.499598 | − | 0.865329i | ||||
\(122\) | −1.55828 | + | 2.69902i | −0.141080 | + | 0.244358i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.45596 | + | 0.840596i | −0.130749 | + | 0.0754878i | ||||
\(125\) | −30.8619 | −2.76037 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.49968 | 0.842960 | 0.421480 | − | 0.906838i | \(-0.361511\pi\) | ||||
0.421480 | + | 0.906838i | \(0.361511\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.91477 | + | 13.7088i | −0.694171 | + | 1.20234i | ||||
\(131\) | 1.51601 | + | 2.62581i | 0.132455 | + | 0.229418i | 0.924622 | − | 0.380886i | \(-0.124381\pi\) |
−0.792168 | + | 0.610304i | \(0.791047\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.15199 | − | 19.7665i | 0.533445 | − | 1.71397i | ||||
\(134\) | − | 7.53337i | − | 0.650784i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.62729 | + | 3.82627i | 0.568285 | + | 0.328100i | ||||
\(137\) | −3.82389 | − | 2.20773i | −0.326697 | − | 0.188619i | 0.327677 | − | 0.944790i | \(-0.393734\pi\) |
−0.654374 | + | 0.756171i | \(0.727068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.32729i | − | 0.112579i | −0.998414 | − | 0.0562896i | \(-0.982073\pi\) | ||
0.998414 | − | 0.0562896i | \(-0.0179270\pi\) | |||||||
\(140\) | 8.10888 | − | 7.48584i | 0.685326 | − | 0.632669i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.30661 | − | 7.45926i | −0.361403 | − | 0.625968i | ||||
\(143\) | 0.178423 | − | 0.309037i | 0.0149204 | − | 0.0258430i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.33937 | − | 4.23739i | 0.609502 | − | 0.351896i | ||||
\(146\) | 0.150072 | 0.0124200 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.36687 | −0.358954 | ||||||||
\(149\) | −9.16722 | + | 5.29269i | −0.751008 | + | 0.433594i | −0.826058 | − | 0.563585i | \(-0.809422\pi\) |
0.0750503 | + | 0.997180i | \(0.476088\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.86400 | − | 6.69264i | 0.314448 | − | 0.544639i | −0.664872 | − | 0.746957i | \(-0.731514\pi\) |
0.979320 | + | 0.202318i | \(0.0648474\pi\) | |||||||
\(152\) | 3.91226 | + | 6.77624i | 0.317326 | + | 0.549625i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.182798 | + | 0.168753i | −0.0147303 | + | 0.0135985i | ||||
\(155\) | − | 7.01257i | − | 0.563264i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.37019 | − | 1.94578i | −0.268970 | − | 0.155290i | 0.359449 | − | 0.933165i | \(-0.382965\pi\) |
−0.628419 | + | 0.777875i | \(0.716298\pi\) | |||||||
\(158\) | −11.2311 | − | 6.48425i | −0.893495 | − | 0.515859i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.17119i | 0.329762i | ||||||||
\(161\) | 3.01130 | − | 9.67538i | 0.237323 | − | 0.762527i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.82699 | + | 15.2888i | 0.691383 | + | 1.19751i | 0.971385 | + | 0.237511i | \(0.0763317\pi\) |
−0.280002 | + | 0.960000i | \(0.590335\pi\) | |||||||
\(164\) | −1.53573 | + | 2.65995i | −0.119920 | + | 0.207708i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.24162 | − | 1.29420i | 0.173984 | − | 0.100450i | ||||
\(167\) | −16.3967 | −1.26881 | −0.634407 | − | 0.772999i | \(-0.718756\pi\) | ||||
−0.634407 | + | 0.772999i | \(0.718756\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.40178 | −0.107829 | ||||||||
\(170\) | −27.6437 | + | 15.9601i | −2.12017 | + | 1.22408i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.56395 | + | 4.44089i | −0.195499 | + | 0.338615i | ||||
\(173\) | 3.92819 | + | 6.80383i | 0.298655 | + | 0.517286i | 0.975829 | − | 0.218538i | \(-0.0701287\pi\) |
−0.677173 | + | 0.735823i | \(0.736795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.21867 | + | 32.0001i | 0.545680 | + | 2.41898i | ||||
\(176\) | − | 0.0940311i | − | 0.00708786i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.37504 | − | 1.37123i | −0.178017 | − | 0.102778i | ||||
\(179\) | 15.7884 | + | 9.11541i | 1.18008 | + | 0.681318i | 0.956032 | − | 0.293261i | \(-0.0947406\pi\) |
0.224044 | + | 0.974579i | \(0.428074\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.2290i | 1.05763i | 0.848736 | + | 0.528817i | \(0.177364\pi\) | ||||
−0.848736 | + | 0.528817i | \(0.822636\pi\) | |||||||
\(182\) | 9.58695 | + | 2.98377i | 0.710632 | + | 0.221172i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.91499 | + | 3.31685i | 0.141175 | + | 0.244522i | ||||
\(185\) | 9.10752 | − | 15.7747i | 0.669598 | − | 1.15978i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.623171 | − | 0.359788i | 0.0455708 | − | 0.0263103i | ||||
\(188\) | 5.09920 | 0.371897 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −32.6376 | −2.36778 | ||||||||
\(191\) | −16.6452 | + | 9.61013i | −1.20441 | + | 0.695365i | −0.961532 | − | 0.274693i | \(-0.911424\pi\) |
−0.242875 | + | 0.970058i | \(0.578091\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.77817 | + | 6.54399i | −0.271959 | + | 0.471046i | −0.969363 | − | 0.245631i | \(-0.921005\pi\) |
0.697405 | + | 0.716678i | \(0.254338\pi\) | |||||||
\(194\) | −2.03199 | − | 3.51951i | −0.145888 | − | 0.252686i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.76364 | − | 3.97246i | −0.411689 | − | 0.283747i | ||||
\(197\) | − | 2.10437i | − | 0.149930i | −0.997186 | − | 0.0749651i | \(-0.976115\pi\) | ||
0.997186 | − | 0.0749651i | \(-0.0238845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.24340 | + | 0.717876i | 0.0881421 | + | 0.0508889i | 0.543423 | − | 0.839459i | \(-0.317128\pi\) |
−0.455281 | + | 0.890348i | \(0.650461\pi\) | |||||||
\(200\) | −10.7377 | − | 6.19941i | −0.759270 | − | 0.438365i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 12.3313i | − | 0.867630i | ||||||
\(203\) | −3.64627 | − | 3.94975i | −0.255918 | − | 0.277218i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.40580 | − | 11.0952i | −0.447401 | − | 0.774921i | ||||
\(206\) | 0.907035 | − | 1.57103i | 0.0631961 | − | 0.109459i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.28654 | + | 1.89748i | −0.227880 | + | 0.131567i | ||||
\(209\) | 0.735749 | 0.0508928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.36800 | −0.300706 | −0.150353 | − | 0.988632i | \(-0.548041\pi\) | ||||
−0.150353 | + | 0.988632i | \(0.548041\pi\) | |||||||
\(212\) | −6.05506 | + | 3.49589i | −0.415863 | + | 0.240099i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.56142 | + | 2.70445i | −0.106736 | + | 0.184873i | ||||
\(215\) | −10.6947 | − | 18.5238i | −0.729374 | − | 1.26331i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.33899 | + | 0.978800i | −0.294550 | + | 0.0664452i | ||||
\(218\) | 2.24425i | 0.152000i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.339674 | + | 0.196111i | 0.0229008 | + | 0.0132218i | ||||
\(221\) | −25.1503 | − | 14.5206i | −1.69180 | − | 0.976759i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 17.2931i | − | 1.15803i | −0.815315 | − | 0.579017i | \(-0.803436\pi\) | ||
0.815315 | − | 0.579017i | \(-0.196564\pi\) | |||||||
\(224\) | 2.58090 | − | 0.582206i | 0.172444 | − | 0.0389002i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.79074 | − | 3.10165i | −0.119118 | − | 0.206319i | ||||
\(227\) | −4.25063 | + | 7.36231i | −0.282124 | + | 0.488653i | −0.971908 | − | 0.235362i | \(-0.924372\pi\) |
0.689784 | + | 0.724016i | \(0.257706\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.0383 | + | 12.1465i | −1.39025 | + | 0.802662i | −0.993343 | − | 0.115196i | \(-0.963250\pi\) |
−0.396909 | + | 0.917858i | \(0.629917\pi\) | |||||||
\(230\) | −15.9756 | −1.05340 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.03174 | 0.133390 | ||||||||
\(233\) | 14.2442 | − | 8.22389i | 0.933168 | − | 0.538765i | 0.0453562 | − | 0.998971i | \(-0.485558\pi\) |
0.887812 | + | 0.460206i | \(0.152224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.6349 | + | 18.4201i | −0.693742 | + | 1.20160i | ||||
\(236\) | 5.21303 | + | 9.02922i | 0.339339 | + | 0.587752i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.7337 | + | 14.8767i | 0.890220 | + | 0.964312i | ||||
\(239\) | − | 17.8574i | − | 1.15510i | −0.816356 | − | 0.577549i | \(-0.804009\pi\) | ||
0.816356 | − | 0.577549i | \(-0.195991\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.27380 | + | 4.19953i | 0.468546 | + | 0.270515i | 0.715631 | − | 0.698479i | \(-0.246139\pi\) |
−0.247085 | + | 0.968994i | \(0.579473\pi\) | |||||||
\(242\) | 9.51862 | + | 5.49558i | 0.611880 | + | 0.353269i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.11656i | − | 0.199517i | ||||||
\(245\) | 26.3706 | − | 12.5354i | 1.68475 | − | 0.800856i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.8469 | − | 25.7156i | −0.944686 | − | 1.63624i | ||||
\(248\) | 0.840596 | − | 1.45596i | 0.0533779 | − | 0.0924533i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 26.7272 | − | 15.4310i | 1.69038 | − | 0.975940i | ||||
\(251\) | −12.3552 | −0.779850 | −0.389925 | − | 0.920847i | \(-0.627499\pi\) | ||||
−0.389925 | + | 0.920847i | \(0.627499\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.360137 | 0.0226416 | ||||||||
\(254\) | −8.22696 | + | 4.74984i | −0.516206 | + | 0.298031i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.94605 | + | 12.0309i | 0.433283 | + | 0.750468i | 0.997154 | − | 0.0753950i | \(-0.0240218\pi\) |
−0.563871 | + | 0.825863i | \(0.690688\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0317 | − | 3.43343i | −0.685476 | − | 0.213343i | ||||
\(260\) | − | 15.8295i | − | 0.981706i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.62581 | − | 1.51601i | −0.162223 | − | 0.0936595i | ||||
\(263\) | −9.51479 | − | 5.49337i | −0.586707 | − | 0.338736i | 0.177087 | − | 0.984195i | \(-0.443333\pi\) |
−0.763794 | + | 0.645460i | \(0.776666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 29.1640i | − | 1.79153i | ||||||
\(266\) | 4.55548 | + | 20.1943i | 0.279314 | + | 1.23819i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.76669 | + | 6.52409i | 0.230087 | + | 0.398522i | ||||
\(269\) | −10.0800 | + | 17.4590i | −0.614585 | + | 1.06449i | 0.375872 | + | 0.926672i | \(0.377343\pi\) |
−0.990457 | + | 0.137821i | \(0.955990\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.1106 | + | 6.99205i | −0.735666 | + | 0.424737i | −0.820491 | − | 0.571659i | \(-0.806300\pi\) |
0.0848253 | + | 0.996396i | \(0.472967\pi\) | |||||||
\(272\) | −7.65254 | −0.464003 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.41545 | 0.266747 | ||||||||
\(275\) | −1.00968 | + | 0.582938i | −0.0608859 | + | 0.0351525i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.47254 | − | 16.4069i | 0.569150 | − | 0.985796i | −0.427501 | − | 0.904015i | \(-0.640606\pi\) |
0.996650 | − | 0.0817810i | \(-0.0260608\pi\) | |||||||
\(278\) | 0.663644 | + | 1.14947i | 0.0398028 | + | 0.0689404i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.27958 | + | 10.5374i | −0.195992 | + | 0.629728i | ||||
\(281\) | − | 6.12155i | − | 0.365181i | −0.983189 | − | 0.182591i | \(-0.941552\pi\) | ||
0.983189 | − | 0.182591i | \(-0.0584483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6497 | + | 13.6542i | 1.40583 | + | 0.811657i | 0.994983 | − | 0.100047i | \(-0.0318993\pi\) |
0.410848 | + | 0.911704i | \(0.365233\pi\) | |||||||
\(284\) | 7.45926 | + | 4.30661i | 0.442626 | + | 0.255550i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.356845i | 0.0211007i | ||||||||
\(287\) | −5.97096 | + | 5.51219i | −0.352455 | + | 0.325374i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.7806 | − | 35.9931i | −1.22239 | − | 2.11724i | ||||
\(290\) | −4.23739 | + | 7.33937i | −0.248828 | + | 0.430983i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.129966 | + | 0.0750360i | −0.00760569 | + | 0.00439115i | ||||
\(293\) | −15.2713 | −0.892158 | −0.446079 | − | 0.894994i | \(-0.647180\pi\) | ||||
−0.446079 | + | 0.894994i | \(0.647180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −43.4890 | −2.53203 | ||||||||
\(296\) | 3.78182 | − | 2.18343i | 0.219814 | − | 0.126910i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.29269 | − | 9.16722i | 0.306598 | − | 0.531043i | ||||
\(299\) | −7.26731 | − | 12.5874i | −0.420280 | − | 0.727946i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.96874 | + | 9.20280i | −0.574589 | + | 0.530441i | ||||
\(302\) | 7.72799i | 0.444696i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.77624 | − | 3.91226i | −0.388644 | − | 0.224384i | ||||
\(305\) | 11.2581 | + | 6.49988i | 0.644638 | + | 0.372182i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.9407i | 1.65173i | 0.563866 | + | 0.825866i | \(0.309313\pi\) | ||||
−0.563866 | + | 0.825866i | \(0.690687\pi\) | |||||||
\(308\) | 0.0739314 | − | 0.237544i | 0.00421263 | − | 0.0135353i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.50629 | + | 6.07307i | 0.199144 | + | 0.344927i | ||||
\(311\) | −3.22911 | + | 5.59299i | −0.183106 | + | 0.317149i | −0.942937 | − | 0.332972i | \(-0.891949\pi\) |
0.759830 | + | 0.650121i | \(0.225282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.7283 | − | 13.6995i | 1.34120 | − | 0.774344i | 0.354220 | − | 0.935162i | \(-0.384747\pi\) |
0.986984 | + | 0.160818i | \(0.0514132\pi\) | |||||||
\(314\) | 3.89155 | 0.219613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.9685 | 0.729535 | ||||||||
\(317\) | −16.8167 | + | 9.70915i | −0.944522 | + | 0.545320i | −0.891375 | − | 0.453267i | \(-0.850258\pi\) |
−0.0531469 | + | 0.998587i | \(0.516925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0955235 | − | 0.165451i | 0.00534829 | − | 0.00926350i | ||||
\(320\) | −2.08560 | − | 3.61236i | −0.116588 | − | 0.201937i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.22983 | + | 9.88477i | 0.124264 | + | 0.550857i | ||||
\(323\) | − | 59.8774i | − | 3.33167i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40.7492 | + | 23.5266i | 2.26036 | + | 1.30502i | ||||
\(326\) | −15.2888 | − | 8.82699i | −0.846768 | − | 0.488882i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 3.07145i | − | 0.169592i | ||||||
\(329\) | 12.8817 | + | 4.00922i | 0.710193 | + | 0.221035i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.55931 | − | 11.3611i | −0.360532 | − | 0.624460i | 0.627516 | − | 0.778603i | \(-0.284072\pi\) |
−0.988048 | + | 0.154143i | \(0.950738\pi\) | |||||||
\(332\) | −1.29420 | + | 2.24162i | −0.0710286 | + | 0.123025i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.2000 | − | 8.19835i | 0.776987 | − | 0.448594i | ||||
\(335\) | −31.4231 | −1.71683 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7311 | 1.29272 | 0.646359 | − | 0.763034i | \(-0.276291\pi\) | ||||
0.646359 | + | 0.763034i | \(0.276291\pi\) | |||||||
\(338\) | 1.21398 | − | 0.700889i | 0.0660315 | − | 0.0381233i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.9601 | − | 27.6437i | 0.865557 | − | 1.49919i | ||||
\(341\) | −0.0790422 | − | 0.136905i | −0.00428038 | − | 0.00741383i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4369 | − | 14.5670i | −0.617536 | − | 0.786542i | ||||
\(344\) | − | 5.12790i | − | 0.276478i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.80383 | − | 3.92819i | −0.365776 | − | 0.211181i | ||||
\(347\) | −7.21858 | − | 4.16765i | −0.387514 | − | 0.223731i | 0.293568 | − | 0.955938i | \(-0.405157\pi\) |
−0.681082 | + | 0.732207i | \(0.738490\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 18.7486i | − | 1.00359i | −0.864987 | − | 0.501794i | \(-0.832674\pi\) | ||
0.864987 | − | 0.501794i | \(-0.167326\pi\) | |||||||
\(350\) | −22.2516 | − | 24.1036i | −1.18940 | − | 1.28839i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0470156 | + | 0.0814333i | 0.00250594 | + | 0.00434041i | ||||
\(353\) | 9.76869 | − | 16.9199i | 0.519935 | − | 0.900554i | −0.479797 | − | 0.877380i | \(-0.659290\pi\) |
0.999731 | − | 0.0231739i | \(-0.00737714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.1140 | + | 17.9637i | −1.65136 | + | 0.953413i | ||||
\(356\) | 2.74246 | 0.145350 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.2308 | −0.963529 | ||||||||
\(359\) | 14.3290 | − | 8.27288i | 0.756258 | − | 0.436626i | −0.0716925 | − | 0.997427i | \(-0.522840\pi\) |
0.827951 | + | 0.560801i | \(0.189507\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.1116 | − | 36.5663i | 1.11114 | − | 1.92454i | ||||
\(362\) | −7.11450 | − | 12.3227i | −0.373930 | − | 0.647665i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.79443 | + | 2.20945i | −0.513367 | + | 0.115807i | ||||
\(365\) | − | 0.625979i | − | 0.0327652i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.8308 | + | 16.0681i | 1.45276 | + | 0.838749i | 0.998637 | − | 0.0521924i | \(-0.0166209\pi\) |
0.454119 | + | 0.890941i | \(0.349954\pi\) | |||||||
\(368\) | −3.31685 | − | 1.91499i | −0.172903 | − | 0.0998256i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.2150i | 0.946955i | ||||||||
\(371\) | −18.0451 | + | 4.07065i | −0.936853 | + | 0.211338i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.8677 | + | 22.2875i | 0.666264 | + | 1.15400i | 0.978941 | + | 0.204144i | \(0.0654410\pi\) |
−0.312677 | + | 0.949860i | \(0.601226\pi\) | |||||||
\(374\) | −0.359788 | + | 0.623171i | −0.0186042 | + | 0.0322234i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.41603 | + | 2.54960i | −0.227740 | + | 0.131485i | ||||
\(377\) | −7.71039 | −0.397105 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.3772 | −1.86857 | −0.934285 | − | 0.356527i | \(-0.883961\pi\) | ||||
−0.934285 | + | 0.356527i | \(0.883961\pi\) | |||||||
\(380\) | 28.2650 | − | 16.3188i | 1.44996 | − | 0.837136i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.61013 | − | 16.6452i | 0.491697 | − | 0.851645i | ||||
\(383\) | 12.5773 | + | 21.7845i | 0.642670 | + | 1.11314i | 0.984834 | + | 0.173497i | \(0.0555066\pi\) |
−0.342165 | + | 0.939640i | \(0.611160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.703902 | + | 0.762487i | 0.0358742 | + | 0.0388599i | ||||
\(386\) | − | 7.55634i | − | 0.384608i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.51951 | + | 2.03199i | 0.178676 | + | 0.103159i | ||||
\(389\) | 8.39614 | + | 4.84752i | 0.425701 | + | 0.245779i | 0.697514 | − | 0.716571i | \(-0.254290\pi\) |
−0.271812 | + | 0.962350i | \(0.587623\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 29.3090i | − | 1.48222i | ||||||
\(392\) | 6.97769 | + | 0.558434i | 0.352427 | + | 0.0282052i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.05219 | + | 1.82244i | 0.0530083 | + | 0.0918131i | ||||
\(395\) | −27.0471 | + | 46.8469i | −1.36088 | + | 2.35712i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.1844 | + | 6.45731i | −0.561329 | + | 0.324083i | −0.753679 | − | 0.657243i | \(-0.771722\pi\) |
0.192350 | + | 0.981326i | \(0.438389\pi\) | |||||||
\(398\) | −1.43575 | −0.0719677 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.3988 | 0.619941 | ||||||||
\(401\) | −24.9194 | + | 14.3872i | −1.24442 | + | 0.718464i | −0.969990 | − | 0.243144i | \(-0.921821\pi\) |
−0.274427 | + | 0.961608i | \(0.588488\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.19004 | + | 5.52530i | −0.158907 | + | 0.275235i | ||||
\(404\) | 6.16567 | + | 10.6793i | 0.306754 | + | 0.531313i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.13264 | + | 1.59745i | 0.254729 | + | 0.0792799i | ||||
\(407\) | − | 0.410622i | − | 0.0203538i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.7809 | − | 16.6167i | −1.42312 | − | 0.821641i | −0.426559 | − | 0.904460i | \(-0.640274\pi\) |
−0.996565 | + | 0.0828189i | \(0.973608\pi\) | |||||||
\(410\) | 11.0952 | + | 6.40580i | 0.547952 | + | 0.316360i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.81407i | 0.0893728i | ||||||||
\(413\) | 6.07010 | + | 26.9086i | 0.298690 | + | 1.32408i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.39836 | − | 9.35024i | −0.264995 | − | 0.458985i | ||||
\(416\) | 1.89748 | − | 3.28654i | 0.0930318 | − | 0.161136i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.637177 | + | 0.367874i | −0.0311653 | + | 0.0179933i | ||||
\(419\) | 2.16604 | 0.105818 | 0.0529090 | − | 0.998599i | \(-0.483151\pi\) | ||||
0.0529090 | + | 0.998599i | \(0.483151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3865 | 0.603682 | 0.301841 | − | 0.953358i | \(-0.402399\pi\) | ||||
0.301841 | + | 0.953358i | \(0.402399\pi\) | |||||||
\(422\) | 3.78280 | − | 2.18400i | 0.184144 | − | 0.106316i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.49589 | − | 6.05506i | 0.169775 | − | 0.294060i | ||||
\(425\) | 47.4412 | + | 82.1706i | 2.30124 | + | 3.98586i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.45038 | − | 7.87313i | 0.118582 | − | 0.381008i | ||||
\(428\) | − | 3.12283i | − | 0.150948i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.5238 | + | 10.6947i | 0.893297 | + | 0.515745i | ||||
\(431\) | 20.2513 | + | 11.6921i | 0.975468 | + | 0.563187i | 0.900899 | − | 0.434029i | \(-0.142908\pi\) |
0.0745695 | + | 0.997216i | \(0.476242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 30.6220i | − | 1.47160i | −0.677199 | − | 0.735800i | \(-0.736806\pi\) | ||
0.677199 | − | 0.735800i | \(-0.263194\pi\) | |||||||
\(434\) | 3.26827 | − | 3.01716i | 0.156882 | − | 0.144828i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.12213 | − | 1.94358i | −0.0537401 | − | 0.0930807i | ||||
\(437\) | 14.9839 | − | 25.9528i | 0.716775 | − | 1.24149i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.8443 | + | 15.4986i | −1.28121 | + | 0.739707i | −0.977070 | − | 0.212920i | \(-0.931703\pi\) |
−0.304141 | + | 0.952627i | \(0.598369\pi\) | |||||||
\(440\) | −0.392222 | −0.0186984 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 29.0411 | 1.38135 | ||||||||
\(443\) | 8.70257 | − | 5.02443i | 0.413472 | − | 0.238718i | −0.278809 | − | 0.960347i | \(-0.589940\pi\) |
0.692280 | + | 0.721629i | \(0.256606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.71967 | + | 9.90676i | −0.271138 | + | 0.469626i | ||||
\(446\) | 8.64657 | + | 14.9763i | 0.409427 | + | 0.709148i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.94402 | + | 1.79465i | −0.0918464 | + | 0.0847894i | ||||
\(449\) | − | 3.58784i | − | 0.169320i | −0.996410 | − | 0.0846602i | \(-0.973020\pi\) | ||
0.996410 | − | 0.0846602i | \(-0.0269805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.250118 | − | 0.144406i | −0.0117776 | − | 0.00679981i | ||||
\(452\) | 3.10165 | + | 1.79074i | 0.145889 | + | 0.0842292i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 8.50126i | − | 0.398984i | ||||||
\(455\) | 12.4459 | − | 39.9890i | 0.583472 | − | 1.87471i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.28677 | − | 2.22875i | −0.0601926 | − | 0.104257i | 0.834359 | − | 0.551222i | \(-0.185838\pi\) |
−0.894551 | + | 0.446965i | \(0.852505\pi\) | |||||||
\(458\) | 12.1465 | − | 21.0383i | 0.567568 | − | 0.983056i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.8352 | − | 7.98778i | 0.645071 | − | 0.372432i | ||||
\(461\) | 17.4108 | 0.810902 | 0.405451 | − | 0.914117i | \(-0.367114\pi\) | ||||
0.405451 | + | 0.914117i | \(0.367114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8825 | 0.738121 | 0.369061 | − | 0.929405i | \(-0.379679\pi\) | ||||
0.369061 | + | 0.929405i | \(0.379679\pi\) | |||||||
\(464\) | −1.75954 | + | 1.01587i | −0.0816846 | + | 0.0471606i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.22389 | + | 14.2442i | −0.380964 | + | 0.659850i | ||||
\(467\) | 16.3177 | + | 28.2631i | 0.755093 | + | 1.30786i | 0.945328 | + | 0.326121i | \(0.105742\pi\) |
−0.190235 | + | 0.981739i | \(0.560925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.38597 | + | 19.4429i | 0.202525 | + | 0.897788i | ||||
\(470\) | − | 21.2697i | − | 0.981099i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.02922 | − | 5.21303i | −0.415604 | − | 0.239949i | ||||
\(473\) | −0.417582 | − | 0.241091i | −0.0192004 | − | 0.0110854i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 97.0149i | 4.45135i | ||||||||
\(476\) | −19.3320 | − | 6.01676i | −0.886082 | − | 0.275778i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.92870 | + | 15.4650i | 0.408389 | + | 0.707351i | ||||
\(479\) | −5.58651 | + | 9.67613i | −0.255254 | + | 0.442113i | −0.964965 | − | 0.262380i | \(-0.915493\pi\) |
0.709710 | + | 0.704494i | \(0.248826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3519 | + | 8.28606i | −0.654389 | + | 0.377812i | ||||
\(482\) | −8.39906 | −0.382566 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9912 | −0.499598 | ||||||||
\(485\) | −14.6805 | + | 8.47581i | −0.666609 | + | 0.384867i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.1951 | + | 28.0507i | −0.733868 | + | 1.27110i | 0.221350 | + | 0.975194i | \(0.428954\pi\) |
−0.955218 | + | 0.295902i | \(0.904380\pi\) | |||||||
\(488\) | 1.55828 | + | 2.69902i | 0.0705400 | + | 0.122179i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.5699 | + | 24.0412i | −0.748552 | + | 1.08607i | ||||
\(491\) | − | 33.1341i | − | 1.49532i | −0.664081 | − | 0.747661i | \(-0.731177\pi\) | ||
0.664081 | − | 0.747661i | \(-0.268823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.4649 | − | 7.77399i | −0.606430 | − | 0.350123i | ||||
\(494\) | 25.7156 | + | 14.8469i | 1.15700 | + | 0.667994i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.68119i | 0.0754878i | ||||||||
\(497\) | 15.4577 | + | 16.7443i | 0.693375 | + | 0.751083i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0418 | + | 20.8569i | 0.539063 | + | 0.933685i | 0.998955 | + | 0.0457097i | \(0.0145549\pi\) |
−0.459892 | + | 0.887975i | \(0.652112\pi\) | |||||||
\(500\) | −15.4310 | + | 26.7272i | −0.690094 | + | 1.19528i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.6999 | − | 6.17758i | 0.477559 | − | 0.275719i | ||||
\(503\) | 30.1146 | 1.34274 | 0.671372 | − | 0.741121i | \(-0.265705\pi\) | ||||
0.671372 | + | 0.741121i | \(0.265705\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −51.4364 | −2.28889 | ||||||||
\(506\) | −0.311888 | + | 0.180068i | −0.0138651 | + | 0.00800502i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.74984 | − | 8.22696i | 0.210740 | − | 0.365013i | ||||
\(509\) | −4.94736 | − | 8.56907i | −0.219288 | − | 0.379817i | 0.735303 | − | 0.677739i | \(-0.237040\pi\) |
−0.954590 | + | 0.297921i | \(0.903707\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.387320 | + | 0.0873727i | −0.0171340 | + | 0.00386514i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.0309 | − | 6.94605i | −0.530661 | − | 0.306377i | ||||
\(515\) | −6.55307 | − | 3.78341i | −0.288763 | − | 0.166717i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.479483i | 0.0210876i | ||||||||
\(518\) | 11.2704 | − | 2.54242i | 0.495195 | − | 0.111707i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.91477 | + | 13.7088i | 0.347085 | + | 0.601170i | ||||
\(521\) | 0.0257283 | − | 0.0445628i | 0.00112718 | − | 0.00195233i | −0.865461 | − | 0.500976i | \(-0.832975\pi\) |
0.866588 | + | 0.499024i | \(0.166308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.58537 | + | 2.07001i | −0.156777 | + | 0.0905154i | −0.576336 | − | 0.817213i | \(-0.695518\pi\) |
0.419559 | + | 0.907728i | \(0.362185\pi\) | |||||||
\(524\) | 3.03202 | 0.132455 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9867 | 0.479045 | ||||||||
\(527\) | −11.1418 | + | 6.43269i | −0.485342 | + | 0.280212i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.16565 | + | 7.21512i | −0.181115 | + | 0.313701i | ||||
\(530\) | 14.5820 | + | 25.2568i | 0.633402 | + | 1.09708i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −14.0423 | − | 15.2110i | −0.608811 | − | 0.659482i | ||||
\(533\) | 11.6561i | 0.504880i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.2808 | + | 6.51296i | 0.487711 | + | 0.281580i | ||||
\(536\) | −6.52409 | − | 3.76669i | −0.281798 | − | 0.162696i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 20.1599i | − | 0.869155i | ||||||
\(539\) | 0.373535 | − | 0.541961i | 0.0160893 | − | 0.0233439i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.98675 | + | 17.2976i | 0.429364 | + | 0.743680i | 0.996817 | − | 0.0797258i | \(-0.0254045\pi\) |
−0.567453 | + | 0.823406i | \(0.692071\pi\) | |||||||
\(542\) | 6.99205 | − | 12.1106i | 0.300334 | − | 0.520194i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.62729 | − | 3.82627i | 0.284143 | − | 0.164050i | ||||
\(545\) | 9.36121 | 0.400990 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.91405 | −0.338381 | −0.169190 | − | 0.985583i | \(-0.554115\pi\) | ||||
−0.169190 | + | 0.985583i | \(0.554115\pi\) | |||||||
\(548\) | −3.82389 | + | 2.20773i | −0.163349 | + | 0.0943094i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.582938 | − | 1.00968i | 0.0248566 | − | 0.0430528i | ||||
\(551\) | −7.94870 | − | 13.7676i | −0.338626 | − | 0.586518i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 32.7614 | + | 10.1964i | 1.39316 | + | 0.433596i | ||||
\(554\) | 18.9451i | 0.804899i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.14947 | − | 0.663644i | −0.0487482 | − | 0.0281448i | ||||
\(557\) | −30.5833 | − | 17.6573i | −1.29586 | − | 0.748163i | −0.316171 | − | 0.948702i | \(-0.602397\pi\) |
−0.979686 | + | 0.200539i | \(0.935731\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.4602i | 0.823079i | ||||||||
\(560\) | −2.42849 | − | 10.7654i | −0.102622 | − | 0.454922i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.06078 | + | 5.30142i | 0.129111 | + | 0.223627i | ||||
\(563\) | 18.0983 | − | 31.3471i | 0.762751 | − | 1.32112i | −0.178677 | − | 0.983908i | \(-0.557182\pi\) |
0.941428 | − | 0.337215i | \(-0.109485\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.9376 | + | 7.46951i | −0.544288 | + | 0.314245i | ||||
\(566\) | −27.3084 | −1.14786 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.61322 | −0.361403 | ||||||||
\(569\) | −19.1602 | + | 11.0622i | −0.803239 | + | 0.463750i | −0.844602 | − | 0.535394i | \(-0.820163\pi\) |
0.0413637 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0521 | − | 20.8748i | 0.504363 | − | 0.873582i | −0.495624 | − | 0.868537i | \(-0.665061\pi\) |
0.999987 | − | 0.00504524i | \(-0.00160596\pi\) | |||||||
\(572\) | −0.178423 | − | 0.309037i | −0.00746022 | − | 0.0129215i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.41491 | − | 7.75918i | 0.100796 | − | 0.323862i | ||||
\(575\) | 47.4872i | 1.98035i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.03494 | + | 5.21633i | 0.376129 | + | 0.217158i | 0.676133 | − | 0.736780i | \(-0.263654\pi\) |
−0.300003 | + | 0.953938i | \(0.596988\pi\) | |||||||
\(578\) | 35.9931 | + | 20.7806i | 1.49712 | + | 0.864361i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 8.47478i | − | 0.351896i | ||||||
\(581\) | −5.03191 | + | 4.64529i | −0.208759 | + | 0.192719i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.328722 | − | 0.569364i | −0.0136143 | − | 0.0235806i | ||||
\(584\) | 0.0750360 | − | 0.129966i | 0.00310501 | − | 0.00537804i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.2253 | − | 7.63564i | 0.546333 | − | 0.315425i | ||||
\(587\) | 20.1447 | 0.831460 | 0.415730 | − | 0.909488i | \(-0.363526\pi\) | ||||
0.415730 | + | 0.909488i | \(0.363526\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.1545 | −0.542023 | ||||||||
\(590\) | 37.6626 | − | 21.7445i | 1.55055 | − | 0.895208i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.18343 | + | 3.78182i | −0.0897386 | + | 0.155432i | ||||
\(593\) | −9.16661 | − | 15.8770i | −0.376428 | − | 0.651992i | 0.614112 | − | 0.789219i | \(-0.289514\pi\) |
−0.990540 | + | 0.137227i | \(0.956181\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 62.0535 | − | 57.2857i | 2.54395 | − | 2.34848i | ||||
\(596\) | 10.5854i | 0.433594i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.5874 | + | 7.26731i | 0.514735 | + | 0.297183i | ||||
\(599\) | 13.7613 | + | 7.94509i | 0.562272 | + | 0.324628i | 0.754057 | − | 0.656809i | \(-0.228094\pi\) |
−0.191785 | + | 0.981437i | \(0.561428\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.2556i | 1.64206i | 0.570884 | + | 0.821030i | \(0.306600\pi\) | ||||
−0.570884 | + | 0.821030i | \(0.693400\pi\) | |||||||
\(602\) | 4.03178 | − | 12.9542i | 0.164323 | − | 0.527975i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.86400 | − | 6.69264i | −0.157224 | − | 0.272320i | ||||
\(605\) | 22.9231 | − | 39.7040i | 0.931957 | − | 1.61420i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.94932 | + | 4.01219i | −0.282064 | + | 0.162850i | −0.634358 | − | 0.773040i | \(-0.718735\pi\) |
0.352293 | + | 0.935890i | \(0.385402\pi\) | |||||||
\(608\) | 7.82452 | 0.317326 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.9998 | −0.526345 | ||||||||
\(611\) | 16.7587 | − | 9.67564i | 0.677985 | − | 0.391435i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.4658 | − | 35.4478i | 0.826606 | − | 1.43172i | −0.0740802 | − | 0.997252i | \(-0.523602\pi\) |
0.900686 | − | 0.434471i | \(-0.143065\pi\) | |||||||
\(614\) | −14.4703 | − | 25.0634i | −0.583975 | − | 1.01148i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0547454 | + | 0.242685i | 0.00220576 | + | 0.00977805i | ||||
\(617\) | − | 5.98876i | − | 0.241098i | −0.992707 | − | 0.120549i | \(-0.961534\pi\) | ||
0.992707 | − | 0.120549i | \(-0.0384655\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5700 | − | 9.56672i | −0.666006 | − | 0.384519i | 0.128556 | − | 0.991702i | \(-0.458966\pi\) |
−0.794562 | + | 0.607183i | \(0.792299\pi\) | |||||||
\(620\) | −6.07307 | − | 3.50629i | −0.243900 | − | 0.140816i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.45823i | − | 0.258951i | ||||||
\(623\) | 6.92809 | + | 2.15625i | 0.277568 | + | 0.0863882i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −33.3684 | − | 57.7958i | −1.33474 | − | 2.31183i | ||||
\(626\) | −13.6995 | + | 23.7283i | −0.547544 | + | 0.948374i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.37019 | + | 1.94578i | −0.134485 | + | 0.0776450i | ||||
\(629\) | −33.4176 | −1.33245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 44.6986 | 1.77942 | 0.889712 | − | 0.456522i | \(-0.150905\pi\) | ||||
0.889712 | + | 0.456522i | \(0.150905\pi\) | |||||||
\(632\) | −11.2311 | + | 6.48425i | −0.446747 | + | 0.257930i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.70915 | − | 16.8167i | 0.385599 | − | 0.667878i | ||||
\(635\) | 19.8125 | + | 34.3162i | 0.786235 | + | 1.36180i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.4801 | − | 2.11924i | −1.04918 | − | 0.0839673i | ||||
\(638\) | 0.191047i | 0.00756362i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.61236 | + | 2.08560i | 0.142791 | + | 0.0824404i | ||||
\(641\) | 23.6804 | + | 13.6719i | 0.935321 | + | 0.540008i | 0.888490 | − | 0.458895i | \(-0.151755\pi\) |
0.0468305 | + | 0.998903i | \(0.485088\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 0.714773i | − | 0.0281879i | −0.999901 | − | 0.0140939i | \(-0.995514\pi\) | ||
0.999901 | − | 0.0140939i | \(-0.00448639\pi\) | |||||||
\(644\) | −6.87348 | − | 7.44555i | −0.270853 | − | 0.293396i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.9387 | + | 51.8554i | 1.17792 | + | 2.04022i | ||||
\(647\) | 6.33080 | − | 10.9653i | 0.248889 | − | 0.431089i | −0.714329 | − | 0.699810i | \(-0.753268\pi\) |
0.963218 | + | 0.268722i | \(0.0866011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.849028 | + | 0.490187i | −0.0333273 | + | 0.0192415i | ||||
\(650\) | −47.0531 | −1.84558 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.6540 | 0.691383 | ||||||||
\(653\) | 32.8218 | − | 18.9497i | 1.28442 | − | 0.741558i | 0.306764 | − | 0.951786i | \(-0.400754\pi\) |
0.977652 | + | 0.210228i | \(0.0674206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.32357 | + | 10.9528i | −0.247083 | + | 0.427959i | ||||
\(656\) | 1.53573 | + | 2.65995i | 0.0599600 | + | 0.103854i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.1605 | + | 2.96878i | −0.513050 | + | 0.115735i | ||||
\(659\) | − | 47.1979i | − | 1.83857i | −0.393595 | − | 0.919284i | \(-0.628769\pi\) | ||
0.393595 | − | 0.919284i | \(-0.371231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.0106 | − | 12.7078i | −0.856112 | − | 0.494276i | 0.00659651 | − | 0.999978i | \(-0.497900\pi\) |
−0.862708 | + | 0.505702i | \(0.831234\pi\) | |||||||
\(662\) | 11.3611 | + | 6.55931i | 0.441560 | + | 0.254935i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.58840i | − | 0.100450i | ||||||
\(665\) | 84.2343 | − | 19.0018i | 3.26646 | − | 0.736857i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.89076 | − | 6.73899i | −0.150651 | − | 0.260935i | ||||
\(668\) | −8.19835 | + | 14.2000i | −0.317204 | + | 0.549413i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.2132 | − | 15.7116i | 1.05134 | − | 0.606991i | ||||
\(671\) | 0.293054 | 0.0113132 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.57996 | 0.137997 | 0.0689987 | − | 0.997617i | \(-0.478020\pi\) | ||||
0.0689987 | + | 0.997617i | \(0.478020\pi\) | |||||||
\(674\) | −20.5518 | + | 11.8656i | −0.791624 | + | 0.457045i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.700889 | + | 1.21398i | −0.0269573 | + | 0.0466914i | ||||
\(677\) | −12.0629 | − | 20.8936i | −0.463617 | − | 0.803008i | 0.535521 | − | 0.844522i | \(-0.320115\pi\) |
−0.999138 | + | 0.0415142i | \(0.986782\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.29343 | + | 7.90046i | 0.279896 | + | 0.303192i | ||||
\(680\) | 31.9202i | 1.22408i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.136905 | + | 0.0790422i | 0.00524237 | + | 0.00302668i | ||||
\(683\) | −12.8920 | − | 7.44319i | −0.493298 | − | 0.284806i | 0.232644 | − | 0.972562i | \(-0.425262\pi\) |
−0.725942 | + | 0.687756i | \(0.758596\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18.4177i | − | 0.703704i | ||||||
\(686\) | 17.1882 | + | 6.89690i | 0.656247 | + | 0.263325i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.56395 | + | 4.44089i | 0.0977496 | + | 0.169307i | ||||
\(689\) | −13.2668 | + | 22.9787i | −0.505424 | + | 0.875420i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.3291 | − | 18.0879i | 1.19182 | − | 0.688095i | 0.233097 | − | 0.972453i | \(-0.425114\pi\) |
0.958718 | + | 0.284359i | \(0.0917807\pi\) | |||||||
\(692\) | 7.85639 | 0.298655 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.33530 | 0.316404 | ||||||||
\(695\) | 4.79464 | − | 2.76819i | 0.181871 | − | 0.105003i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.7522 | + | 20.3554i | −0.445146 | + | 0.771015i | ||||
\(698\) | 9.37428 | + | 16.2367i | 0.354822 | + | 0.614569i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 31.3222 | + | 9.74851i | 1.18387 | + | 0.368459i | ||||
\(701\) | 23.4537i | 0.885834i | 0.896563 | + | 0.442917i | \(0.146056\pi\) | ||||
−0.896563 | + | 0.442917i | \(0.853944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.5909 | − | 17.0843i | −1.11604 | − | 0.644348i | ||||
\(704\) | −0.0814333 | − | 0.0470156i | −0.00306913 | − | 0.00177197i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19.5374i | 0.735299i | ||||||||
\(707\) | 7.17937 | + | 31.8259i | 0.270008 | + | 1.19694i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.06708 | + | 15.7046i | 0.340521 | + | 0.589800i | 0.984530 | − | 0.175218i | \(-0.0560631\pi\) |
−0.644008 | + | 0.765018i | \(0.722730\pi\) | |||||||
\(710\) | 17.9637 | − | 31.1140i | 0.674165 | − | 1.16769i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.37504 | + | 1.37123i | −0.0890085 | + | 0.0513891i | ||||
\(713\) | −6.43892 | −0.241140 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.48847 | 0.0556656 | ||||||||
\(716\) | 15.7884 | − | 9.11541i | 0.590038 | − | 0.340659i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.27288 | + | 14.3290i | −0.308741 | + | 0.534755i | ||||
\(719\) | −16.4312 | − | 28.4597i | −0.612781 | − | 1.06137i | −0.990769 | − | 0.135558i | \(-0.956717\pi\) |
0.377988 | − | 0.925810i | \(-0.376616\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.42630 | + | 4.58275i | −0.0531183 | + | 0.170671i | ||||
\(722\) | 42.2232i | 1.57138i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.3227 | + | 7.11450i | 0.457969 | + | 0.264408i | ||||
\(725\) | 21.8162 | + | 12.5956i | 0.810234 | + | 0.467789i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.24873i | − | 0.268840i | −0.990924 | − | 0.134420i | \(-0.957083\pi\) | ||
0.990924 | − | 0.134420i | \(-0.0429172\pi\) | |||||||
\(728\) | 7.37750 | − | 6.81065i | 0.273428 | − | 0.252420i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.312989 | + | 0.542113i | 0.0115843 | + | 0.0200645i | ||||
\(731\) | −19.6207 | + | 33.9841i | −0.725698 | + | 1.25695i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.5250 | − | 17.0463i | 1.09053 | − | 0.629619i | 0.156814 | − | 0.987628i | \(-0.449878\pi\) |
0.933718 | + | 0.358010i | \(0.116544\pi\) | |||||||
\(734\) | −32.1362 | −1.18617 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.82997 | 0.141175 | ||||||||
\(737\) | −0.613468 | + | 0.354186i | −0.0225974 | + | 0.0130466i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.4439 | + | 30.2137i | −0.641683 | + | 1.11143i | 0.343373 | + | 0.939199i | \(0.388430\pi\) |
−0.985057 | + | 0.172229i | \(0.944903\pi\) | |||||||
\(740\) | −9.10752 | − | 15.7747i | −0.334799 | − | 0.579889i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.5922 | − | 12.5478i | 0.498984 | − | 0.460645i | ||||
\(743\) | − | 45.8060i | − | 1.68046i | −0.542230 | − | 0.840230i | \(-0.682420\pi\) | ||
0.542230 | − | 0.840230i | \(-0.317580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.2382 | − | 22.0768i | −1.40094 | − | 0.808833i | ||||
\(746\) | −22.2875 | − | 12.8677i | −0.816004 | − | 0.471120i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 0.719576i | − | 0.0263103i | ||||||
\(749\) | 2.45531 | − | 7.88898i | 0.0897151 | − | 0.288257i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.7630 | − | 27.3024i | −0.575201 | − | 0.996277i | −0.996020 | − | 0.0891324i | \(-0.971591\pi\) |
0.420819 | − | 0.907145i | \(-0.361743\pi\) | |||||||
\(752\) | 2.54960 | − | 4.41603i | 0.0929743 | − | 0.161036i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.67740 | − | 3.85520i | 0.243176 | − | 0.140398i | ||||
\(755\) | 32.2349 | 1.17315 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.176603 | −0.00641874 | −0.00320937 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00320937 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(758\) | 31.5036 | − | 18.1886i | 1.14426 | − | 0.660639i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.3188 | + | 28.2650i | −0.591945 | + | 1.02528i | ||||
\(761\) | −19.0504 | − | 32.9963i | −0.690576 | − | 1.19611i | −0.971649 | − | 0.236427i | \(-0.924024\pi\) |
0.281073 | − | 0.959686i | \(-0.409310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.30662 | − | 5.79219i | −0.0473027 | − | 0.209691i | ||||
\(764\) | 19.2203i | 0.695365i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.7845 | − | 12.5773i | −0.787107 | − | 0.454436i | ||||
\(767\) | 34.2656 | + | 19.7833i | 1.23726 | + | 0.714332i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.6927i | − | 0.638016i | −0.947752 | − | 0.319008i | \(-0.896650\pi\) | ||
0.947752 | − | 0.319008i | \(-0.103350\pi\) | |||||||
\(770\) | −0.990841 | − | 0.308382i | −0.0357074 | − | 0.0111133i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.77817 | + | 6.54399i | 0.135979 | + | 0.235523i | ||||
\(773\) | −5.67628 | + | 9.83160i | −0.204162 | + | 0.353618i | −0.949865 | − | 0.312659i | \(-0.898780\pi\) |
0.745704 | + | 0.666278i | \(0.232113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0521 | − | 10.4224i | 0.648452 | − | 0.374384i | ||||
\(776\) | −4.06398 | −0.145888 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.69503 | −0.347584 | ||||||||
\(779\) | −20.8129 | + | 12.0163i | −0.745699 | + | 0.430529i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.404955 | + | 0.701403i | −0.0144904 | + | 0.0250982i | ||||
\(782\) | 14.6545 | + | 25.3823i | 0.524044 | + | 0.907671i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.32207 | + | 3.00523i | −0.225788 | + | 0.107330i | ||||
\(785\) | − | 16.2324i | − | 0.579360i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.5394 | − | 14.1678i | −0.874735 | − | 0.505028i | −0.00581596 | − | 0.999983i | \(-0.501851\pi\) |
−0.868919 | + | 0.494955i | \(0.835185\pi\) | |||||||
\(788\) | −1.82244 | − | 1.05219i | −0.0649217 | − | 0.0374825i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 54.0941i | − | 1.92458i | ||||||
\(791\) | 6.42751 | + | 6.96246i | 0.228536 | + | 0.247557i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.91362 | − | 10.2427i | −0.209999 | − | 0.363729i | ||||
\(794\) | 6.45731 | − | 11.1844i | 0.229161 | − | 0.396919i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.24340 | − | 0.717876i | 0.0440710 | − | 0.0254444i | ||||
\(797\) | 47.9417 | 1.69818 | 0.849091 | − | 0.528246i | \(-0.177150\pi\) | ||||
0.849091 | + | 0.528246i | \(0.177150\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 39.0218 | 1.38049 | ||||||||
\(800\) | −10.7377 | + | 6.19941i | −0.379635 | + | 0.219182i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.3872 | − | 24.9194i | 0.508031 | − | 0.879936i | ||||
\(803\) | −0.00705572 | − | 0.0122209i | −0.000248991 | − | 0.000431265i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 41.2313 | − | 9.30105i | 1.45321 | − | 0.327819i | ||||
\(806\) | − | 6.38007i | − | 0.224728i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.6793 | − | 6.16567i | −0.375695 | − | 0.216908i | ||||
\(809\) | −29.3232 | − | 16.9297i | −1.03095 | − | 0.595218i | −0.113692 | − | 0.993516i | \(-0.536268\pi\) |
−0.917256 | + | 0.398298i | \(0.869601\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.8364i | 1.15304i | 0.817082 | + | 0.576521i | \(0.195590\pi\) | ||||
−0.817082 | + | 0.576521i | \(0.804410\pi\) | |||||||
\(812\) | −5.24372 | + | 1.18289i | −0.184018 | + | 0.0415113i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.205311 | + | 0.355609i | 0.00719614 | + | 0.0124641i | ||||
\(815\) | −36.8191 | + | 63.7725i | −1.28972 | + | 2.23385i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.7478 | + | 20.0617i | −1.21567 | + | 0.701869i | ||||
\(818\) | 33.2333 | 1.16198 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.8116 | −0.447401 | ||||||||
\(821\) | −30.0927 | + | 17.3740i | −1.05024 | + | 0.606357i | −0.922717 | − | 0.385479i | \(-0.874036\pi\) |
−0.127524 | + | 0.991835i | \(0.540703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.1948 | + | 38.4426i | −0.773663 | + | 1.34002i | 0.161880 | + | 0.986810i | \(0.448244\pi\) |
−0.935543 | + | 0.353213i | \(0.885089\pi\) | |||||||
\(824\) | −0.907035 | − | 1.57103i | −0.0315981 | − | 0.0547294i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.7112 | − | 20.2685i | −0.651044 | − | 0.705230i | ||||
\(827\) | 13.2991i | 0.462456i | 0.972900 | + | 0.231228i | \(0.0742743\pi\) | ||||
−0.972900 | + | 0.231228i | \(0.925726\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.16441 | + | 0.672270i | 0.0404415 | + | 0.0233489i | 0.520084 | − | 0.854115i | \(-0.325900\pi\) |
−0.479643 | + | 0.877464i | \(0.659234\pi\) | |||||||
\(830\) | 9.35024 | + | 5.39836i | 0.324552 | + | 0.187380i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.79497i | 0.131567i | ||||||||
\(833\) | −44.1065 | − | 30.3994i | −1.52820 | − | 1.05328i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.1969 | − | 59.2307i | −1.18343 | − | 2.04976i | ||||
\(836\) | 0.367874 | − | 0.637177i | 0.0127232 | − | 0.0220372i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.87584 | + | 1.08302i | −0.0648000 | + | 0.0374123i | ||||
\(839\) | 3.10045 | 0.107039 | 0.0535196 | − | 0.998567i | \(-0.482956\pi\) | ||||
0.0535196 | + | 0.998567i | \(0.482956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.8720 | 0.857656 | ||||||||
\(842\) | −10.7270 | + | 6.19326i | −0.369678 | + | 0.213434i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.18400 | + | 3.78280i | −0.0751764 | + | 0.130209i | ||||
\(845\) | −2.92354 | − | 5.06372i | −0.100573 | − | 0.174197i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.7662 | − | 8.64174i | −0.954056 | − | 0.296934i | ||||
\(848\) | 6.99178i | 0.240099i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −82.1706 | − | 47.4412i | −2.81843 | − | 1.62722i | ||||
\(851\) | −14.4843 | − | 8.36250i | −0.496514 | − | 0.286663i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.1021i | 0.996439i | 0.867051 | + | 0.498219i | \(0.166013\pi\) | ||||
−0.867051 | + | 0.498219i | \(0.833987\pi\) | |||||||
\(854\) | 1.81448 | + | 8.04352i | 0.0620902 | + | 0.275244i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.56142 | + | 2.70445i | 0.0533681 | + | 0.0924363i | ||||
\(857\) | 2.37441 | − | 4.11260i | 0.0811084 | − | 0.140484i | −0.822618 | − | 0.568595i | \(-0.807487\pi\) |
0.903726 | + | 0.428111i | \(0.140821\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.2496 | + | 18.0419i | −1.06622 | + | 0.615583i | −0.927147 | − | 0.374699i | \(-0.877746\pi\) |
−0.139075 | + | 0.990282i | \(0.544413\pi\) | |||||||
\(860\) | −21.3894 | −0.729374 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.3841 | −0.796467 | ||||||||
\(863\) | 10.3650 | − | 5.98423i | 0.352829 | − | 0.203706i | −0.313102 | − | 0.949720i | \(-0.601368\pi\) |
0.665930 | + | 0.746014i | \(0.268035\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.3852 | + | 28.3801i | −0.557115 | + | 0.964952i | ||||
\(866\) | 15.3110 | + | 26.5194i | 0.520289 | + | 0.901167i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.32183 | + | 4.24707i | −0.0448658 | + | 0.144155i | ||||
\(869\) | 1.21944i | 0.0413668i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.7587 | + | 14.2945i | 0.838917 | + | 0.484349i | ||||
\(872\) | 1.94358 | + | 1.12213i | 0.0658180 | + | 0.0380000i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.9677i | 1.01367i | ||||||||
\(875\) | −59.9962 | + | 55.3865i | −2.02824 | + | 1.87240i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0096 | + | 20.8013i | 0.405537 | + | 0.702410i | 0.994384 | − | 0.105834i | \(-0.0337514\pi\) |
−0.588847 | + | 0.808244i | \(0.700418\pi\) | |||||||
\(878\) | 15.4986 | − | 26.8443i | 0.523052 | − | 0.905953i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.339674 | − | 0.196111i | 0.0114504 | − | 0.00661089i | ||||
\(881\) | 13.4264 | 0.452348 | 0.226174 | − | 0.974087i | \(-0.427378\pi\) | ||||
0.226174 | + | 0.974087i | \(0.427378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.1649 | 0.914172 | 0.457086 | − | 0.889423i | \(-0.348893\pi\) | ||||
0.457086 | + | 0.889423i | \(0.348893\pi\) | |||||||
\(884\) | −25.1503 | + | 14.5206i | −0.845898 | + | 0.488379i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.02443 | + | 8.70257i | −0.168799 | + | 0.292369i | ||||
\(887\) | −4.12273 | − | 7.14078i | −0.138428 | − | 0.239764i | 0.788474 | − | 0.615068i | \(-0.210872\pi\) |
−0.926902 | + | 0.375304i | \(0.877538\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.4676 | − | 17.0486i | 0.619383 | − | 0.571793i | ||||
\(890\) | − | 11.4393i | − | 0.383448i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.9763 | − | 8.64657i | −0.501444 | − | 0.289509i | ||||
\(893\) | 34.5534 | + | 19.9494i | 1.15628 | + | 0.667581i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 76.0442i | 2.54188i | ||||||||
\(896\) | 0.786244 | − | 2.52623i | 0.0262666 | − | 0.0843953i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.79392 | + | 3.10716i | 0.0598638 | + | 0.103687i | ||||
\(899\) | −1.70787 | + | 2.95813i | −0.0569608 | + | 0.0986590i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.3365 | + | 26.7524i | −1.54369 | + | 0.891252i | ||||
\(902\) | 0.288812 | 0.00961638 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.58148 | −0.119118 | ||||||||
\(905\) | −51.4002 | + | 29.6759i | −1.70860 | + | 0.986461i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.6275 | − | 32.2638i | 0.618517 | − | 1.07130i | −0.371239 | − | 0.928537i | \(-0.621067\pi\) |
0.989756 | − | 0.142766i | \(-0.0455997\pi\) | |||||||
\(908\) | 4.25063 | + | 7.36231i | 0.141062 | + | 0.244327i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9.21604 | + | 40.8544i | 0.305509 | + | 1.35431i | ||||
\(911\) | − | 15.3829i | − | 0.509657i | −0.966986 | − | 0.254829i | \(-0.917981\pi\) | ||
0.966986 | − | 0.254829i | \(-0.0820190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.210782 | − | 0.121695i | −0.00697588 | − | 0.00402753i | ||||
\(914\) | 2.22875 | + | 1.28677i | 0.0737206 | + | 0.0425626i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.2930i | 0.802662i | ||||||||
\(917\) | 7.65958 | + | 2.38391i | 0.252942 | + | 0.0787237i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.3211 | + | 43.8575i | 0.835267 | + | 1.44673i | 0.893812 | + | 0.448441i | \(0.148021\pi\) |
−0.0585450 | + | 0.998285i | \(0.518646\pi\) | |||||||
\(920\) | −7.98778 | + | 13.8352i | −0.263349 | + | 0.456134i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.0782 | + | 8.70540i | −0.496574 | + | 0.286697i | ||||
\(923\) | 32.6869 | 1.07590 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54.1441 | 1.78025 | ||||||||
\(926\) | −13.7546 | + | 7.94124i | −0.452005 | + | 0.260965i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.01587 | − | 1.75954i | 0.0333476 | − | 0.0577597i | ||||
\(929\) | −15.1981 | − | 26.3239i | −0.498634 | − | 0.863659i | 0.501365 | − | 0.865236i | \(-0.332831\pi\) |
−0.999999 | + | 0.00157664i | \(0.999498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.5145 | − | 49.4672i | −0.770655 | − | 1.62122i | ||||
\(932\) | − | 16.4478i | − | 0.538765i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.2631 | − | 16.3177i | −0.924796 | − | 0.533931i | ||||
\(935\) | 2.59937 | + | 1.50075i | 0.0850084 | + | 0.0490796i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13.7262i | − | 0.448416i | −0.974541 | − | 0.224208i | \(-0.928020\pi\) | ||
0.974541 | − | 0.224208i | \(-0.0719796\pi\) | |||||||
\(938\) | −13.5198 | − | 14.6450i | −0.441437 | − | 0.478177i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.6349 | + | 18.4201i | 0.346871 | + | 0.600798i | ||||
\(941\) | −15.7219 | + | 27.2311i | −0.512520 | + | 0.887710i | 0.487375 | + | 0.873193i | \(0.337954\pi\) |
−0.999895 | + | 0.0145172i | \(0.995379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.1876 | + | 5.88179i | −0.331752 | + | 0.191537i | ||||
\(944\) | 10.4261 | 0.339339 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.482182 | 0.0156771 | ||||||||
\(947\) | −0.726997 | + | 0.419732i | −0.0236242 | + | 0.0136395i | −0.511766 | − | 0.859125i | \(-0.671008\pi\) |
0.488141 | + | 0.872765i | \(0.337675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.284759 | + | 0.493217i | −0.00924367 | + | 0.0160105i | ||||
\(950\) | −48.5075 | − | 84.0174i | −1.57379 | − | 2.72588i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 19.7504 | − | 4.45535i | 0.640115 | − | 0.144399i | ||||
\(953\) | − | 41.8952i | − | 1.35712i | −0.734545 | − | 0.678560i | \(-0.762604\pi\) | ||
0.734545 | − | 0.678560i | \(-0.237396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −69.4305 | − | 40.0857i | −2.24672 | − | 1.29714i | ||||
\(956\) | −15.4650 | − | 8.92870i | −0.500172 | − | 0.288775i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 11.1730i | − | 0.360984i | ||||||
\(959\) | −11.3958 | + | 2.57070i | −0.367991 | + | 0.0830122i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0868 | − | 24.3990i | −0.454413 | − | 0.787066i | ||||
\(962\) | 8.28606 | − | 14.3519i | 0.267153 | − | 0.462723i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.27380 | − | 4.19953i | 0.234273 | − | 0.135258i | ||||
\(965\) | −31.5190 | −1.01463 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.6870 | −1.50135 | −0.750676 | − | 0.660671i | \(-0.770272\pi\) | ||||
−0.750676 | + | 0.660671i | \(0.770272\pi\) | |||||||
\(968\) | 9.51862 | − | 5.49558i | 0.305940 | − | 0.176635i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.47581 | − | 14.6805i | 0.272142 | − | 0.471364i | ||||
\(971\) | 11.6725 | + | 20.2173i | 0.374587 | + | 0.648804i | 0.990265 | − | 0.139194i | \(-0.0444512\pi\) |
−0.615678 | + | 0.787998i | \(0.711118\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.38202 | − | 2.58028i | −0.0763642 | − | 0.0827199i | ||||
\(974\) | − | 32.3901i | − | 1.03785i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.69902 | − | 1.55828i | −0.0863935 | − | 0.0498793i | ||||
\(977\) | −27.0245 | − | 15.6026i | −0.864589 | − | 0.499171i | 0.000957477 | − | 1.00000i | \(-0.499695\pi\) |
−0.865546 | + | 0.500829i | \(0.833029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.257877i | 0.00824179i | ||||||||
\(980\) | 2.32933 | − | 29.1053i | 0.0744079 | − | 0.929734i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.5671 | + | 28.6950i | 0.528676 | + | 0.915693i | ||||
\(983\) | 1.41367 | − | 2.44856i | 0.0450892 | − | 0.0780968i | −0.842600 | − | 0.538540i | \(-0.818976\pi\) |
0.887689 | + | 0.460443i | \(0.152309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.60174 | − | 4.38887i | 0.242211 | − | 0.139841i | ||||
\(986\) | 15.5480 | 0.495148 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.6938 | −0.944686 | ||||||||
\(989\) | −17.0085 | + | 9.81986i | −0.540839 | + | 0.312253i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4402 | − | 25.0111i | 0.458708 | − | 0.794505i | −0.540185 | − | 0.841546i | \(-0.681646\pi\) |
0.998893 | + | 0.0470409i | \(0.0149791\pi\) | |||||||
\(992\) | −0.840596 | − | 1.45596i | −0.0266890 | − | 0.0462266i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −21.7589 | − | 6.77209i | −0.690152 | − | 0.214798i | ||||
\(995\) | 5.98879i | 0.189857i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.6911 | + | 17.1421i | 0.940326 | + | 0.542897i | 0.890062 | − | 0.455839i | \(-0.150661\pi\) |
0.0502633 | + | 0.998736i | \(0.483994\pi\) | |||||||
\(998\) | −20.8569 | − | 12.0418i | −0.660215 | − | 0.381175i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.k.d.647.4 | yes | 16 | |
3.2 | odd | 2 | 1134.2.k.c.647.5 | ✓ | 16 | ||
7.5 | odd | 6 | 1134.2.k.c.971.5 | yes | 16 | ||
9.2 | odd | 6 | 1134.2.t.h.1025.4 | 16 | |||
9.4 | even | 3 | 1134.2.l.g.269.4 | 16 | |||
9.5 | odd | 6 | 1134.2.l.h.269.5 | 16 | |||
9.7 | even | 3 | 1134.2.t.g.1025.5 | 16 | |||
21.5 | even | 6 | inner | 1134.2.k.d.971.4 | yes | 16 | |
63.5 | even | 6 | 1134.2.t.g.593.5 | 16 | |||
63.40 | odd | 6 | 1134.2.t.h.593.4 | 16 | |||
63.47 | even | 6 | 1134.2.l.g.215.8 | 16 | |||
63.61 | odd | 6 | 1134.2.l.h.215.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.k.c.647.5 | ✓ | 16 | 3.2 | odd | 2 | ||
1134.2.k.c.971.5 | yes | 16 | 7.5 | odd | 6 | ||
1134.2.k.d.647.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1134.2.k.d.971.4 | yes | 16 | 21.5 | even | 6 | inner | |
1134.2.l.g.215.8 | 16 | 63.47 | even | 6 | |||
1134.2.l.g.269.4 | 16 | 9.4 | even | 3 | |||
1134.2.l.h.215.1 | 16 | 63.61 | odd | 6 | |||
1134.2.l.h.269.5 | 16 | 9.5 | odd | 6 | |||
1134.2.t.g.593.5 | 16 | 63.5 | even | 6 | |||
1134.2.t.g.1025.5 | 16 | 9.7 | even | 3 | |||
1134.2.t.h.593.4 | 16 | 63.40 | odd | 6 | |||
1134.2.t.h.1025.4 | 16 | 9.2 | odd | 6 |