Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(299,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.h (of order \(2\), degree \(1\), not 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: | \(2.39551206064\) |
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: | \( x^{16} - 2 x^{15} + 2 x^{14} + 10 x^{13} - 42 x^{11} + 134 x^{10} + 110 x^{9} + 92 x^{8} + 142 x^{7} + \cdots + 100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 299.8 | ||
Root | \(-1.77516 - 0.994127i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.299 |
Dual form | 300.2.h.c.299.6 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.569745 | + | 1.29437i | −0.402871 | + | 0.915257i | ||||
\(3\) | 1.47492 | − | 0.908080i | 0.851546 | − | 0.524280i | ||||
\(4\) | −1.35078 | − | 1.47492i | −0.675391 | − | 0.737460i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.335062 | + | 2.42647i | 0.136788 | + | 0.990600i | ||||
\(7\) | 2.50967 | 0.948566 | 0.474283 | − | 0.880373i | \(-0.342707\pi\) | ||||
0.474283 | + | 0.880373i | \(0.342707\pi\) | |||||||
\(8\) | 2.67869 | − | 0.908080i | 0.947061 | − | 0.321055i | ||||
\(9\) | 1.35078 | − | 2.67869i | 0.450260 | − | 0.892897i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.36131 | −1.01347 | −0.506737 | − | 0.862101i | \(-0.669149\pi\) | ||||
−0.506737 | + | 0.862101i | \(0.669149\pi\) | |||||||
\(12\) | −3.33164 | − | 0.948773i | −0.961762 | − | 0.273887i | ||||
\(13\) | − | 3.70156i | − | 1.02663i | −0.858201 | − | 0.513314i | \(-0.828418\pi\) | ||
0.858201 | − | 0.513314i | \(-0.171582\pi\) | |||||||
\(14\) | −1.42987 | + | 3.24844i | −0.382149 | + | 0.868181i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.350781 | + | 3.98459i | −0.0876953 | + | 0.996147i | ||||
\(17\) | 7.63636 | 1.85209 | 0.926045 | − | 0.377413i | \(-0.123186\pi\) | ||||
0.926045 | + | 0.377413i | \(0.123186\pi\) | |||||||
\(18\) | 2.69761 | + | 3.27458i | 0.635834 | + | 0.771826i | ||||
\(19\) | 0.440172i | 0.100982i | 0.998725 | + | 0.0504912i | \(0.0160787\pi\) | ||||
−0.998725 | + | 0.0504912i | \(0.983921\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.70156 | − | 2.27898i | 0.807747 | − | 0.497314i | ||||
\(22\) | 1.91509 | − | 4.35078i | 0.408299 | − | 0.927590i | ||||
\(23\) | 5.17748i | 1.07958i | 0.841800 | + | 0.539789i | \(0.181496\pi\) | ||||
−0.841800 | + | 0.539789i | \(0.818504\pi\) | |||||||
\(24\) | 3.12625 | − | 3.77181i | 0.638143 | − | 0.769918i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.79119 | + | 2.10895i | 0.939629 | + | 0.413599i | ||||
\(27\) | −0.440172 | − | 5.17748i | −0.0847112 | − | 0.996406i | ||||
\(28\) | −3.39001 | − | 3.70156i | −0.640652 | − | 0.699529i | ||||
\(29\) | − | 2.27898i | − | 0.423196i | −0.977357 | − | 0.211598i | \(-0.932133\pi\) | ||
0.977357 | − | 0.211598i | \(-0.0678668\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.39001i | 0.608864i | 0.952534 | + | 0.304432i | \(0.0984667\pi\) | ||||
−0.952534 | + | 0.304432i | \(0.901533\pi\) | |||||||
\(32\) | −4.95767 | − | 2.72424i | −0.876401 | − | 0.481582i | ||||
\(33\) | −4.95767 | + | 3.05234i | −0.863020 | + | 0.531345i | ||||
\(34\) | −4.35078 | + | 9.88427i | −0.746153 | + | 1.69514i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.77547 | + | 1.62603i | −0.962578 | + | 0.271005i | ||||
\(37\) | 7.40312i | 1.21707i | 0.793529 | + | 0.608533i | \(0.208242\pi\) | ||||
−0.793529 | + | 0.608533i | \(0.791758\pi\) | |||||||
\(38\) | −0.569745 | − | 0.250786i | −0.0924249 | − | 0.0406828i | ||||
\(39\) | −3.36131 | − | 5.45951i | −0.538241 | − | 0.874221i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.07840i | − | 0.480766i | −0.970678 | − | 0.240383i | \(-0.922727\pi\) | ||
0.970678 | − | 0.240383i | \(-0.0772730\pi\) | |||||||
\(42\) | 0.840894 | + | 6.08962i | 0.129753 | + | 0.939649i | ||||
\(43\) | −8.40935 | −1.28241 | −0.641207 | − | 0.767368i | \(-0.721566\pi\) | ||||
−0.641207 | + | 0.767368i | \(0.721566\pi\) | |||||||
\(44\) | 4.54040 | + | 4.95767i | 0.684491 | + | 0.747397i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.70156 | − | 2.94984i | −0.988091 | − | 0.434930i | ||||
\(47\) | 3.63232i | 0.529828i | 0.964272 | + | 0.264914i | \(0.0853436\pi\) | ||||
−0.964272 | + | 0.264914i | \(0.914656\pi\) | |||||||
\(48\) | 3.10095 | + | 6.19549i | 0.447584 | + | 0.894242i | ||||
\(49\) | −0.701562 | −0.100223 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.2630 | − | 6.93443i | 1.57714 | − | 0.971014i | ||||
\(52\) | −5.45951 | + | 5.00000i | −0.757098 | + | 0.693375i | ||||
\(53\) | 2.27898 | 0.313042 | 0.156521 | − | 0.987675i | \(-0.449972\pi\) | ||||
0.156521 | + | 0.987675i | \(0.449972\pi\) | |||||||
\(54\) | 6.95235 | + | 2.38010i | 0.946095 | + | 0.323890i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.72263 | − | 2.27898i | 0.898349 | − | 0.304542i | ||||
\(57\) | 0.399712 | + | 0.649219i | 0.0529431 | + | 0.0859911i | ||||
\(58\) | 2.94984 | + | 1.29844i | 0.387333 | + | 0.170493i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.70156 | −0.730010 | −0.365005 | − | 0.931006i | \(-0.618933\pi\) | ||||
−0.365005 | + | 0.931006i | \(0.618933\pi\) | |||||||
\(62\) | −4.38793 | − | 1.93144i | −0.557267 | − | 0.245294i | ||||
\(63\) | 3.39001 | − | 6.72263i | 0.427102 | − | 0.846972i | ||||
\(64\) | 6.35078 | − | 4.86493i | 0.793848 | − | 0.608117i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.12625 | − | 8.15611i | −0.138632 | − | 1.00395i | ||||
\(67\) | −5.45951 | −0.666985 | −0.333493 | − | 0.942753i | \(-0.608227\pi\) | ||||
−0.333493 | + | 0.942753i | \(0.608227\pi\) | |||||||
\(68\) | −10.3151 | − | 11.2630i | −1.25088 | − | 1.36584i | ||||
\(69\) | 4.70156 | + | 7.63636i | 0.566002 | + | 0.919310i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4421 | −1.47661 | −0.738304 | − | 0.674468i | \(-0.764373\pi\) | ||||
−0.738304 | + | 0.674468i | \(0.764373\pi\) | |||||||
\(72\) | 1.18586 | − | 8.40201i | 0.139755 | − | 0.990186i | ||||
\(73\) | 1.29844i | 0.151971i | 0.997109 | + | 0.0759853i | \(0.0242102\pi\) | ||||
−0.997109 | + | 0.0759853i | \(0.975790\pi\) | |||||||
\(74\) | −9.58237 | − | 4.21789i | −1.11393 | − | 0.490320i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.649219 | − | 0.594576i | 0.0744705 | − | 0.0682026i | ||||
\(77\) | −8.43579 | −0.961347 | ||||||||
\(78\) | 8.98171 | − | 1.24025i | 1.01698 | − | 0.140431i | ||||
\(79\) | 5.01934i | 0.564720i | 0.959309 | + | 0.282360i | \(0.0911172\pi\) | ||||
−0.959309 | + | 0.282360i | \(0.908883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.35078 | − | 7.23665i | −0.594531 | − | 0.804073i | ||||
\(82\) | 3.98459 | + | 1.75391i | 0.440024 | + | 0.193686i | ||||
\(83\) | − | 1.81616i | − | 0.199349i | −0.995020 | − | 0.0996747i | \(-0.968220\pi\) | ||
0.995020 | − | 0.0996747i | \(-0.0317802\pi\) | |||||||
\(84\) | −8.36131 | − | 2.38111i | −0.912294 | − | 0.259800i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.79119 | − | 10.8848i | 0.516647 | − | 1.17374i | ||||
\(87\) | −2.06950 | − | 3.36131i | −0.221873 | − | 0.360371i | ||||
\(88\) | −9.00393 | + | 3.05234i | −0.959822 | + | 0.325381i | ||||
\(89\) | − | 5.35738i | − | 0.567882i | −0.958842 | − | 0.283941i | \(-0.908358\pi\) | ||
0.958842 | − | 0.283941i | \(-0.0916419\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.28970i | − | 0.973825i | ||||||
\(92\) | 7.63636 | − | 6.99364i | 0.796146 | − | 0.729137i | ||||
\(93\) | 3.07840 | + | 5.00000i | 0.319216 | + | 0.518476i | ||||
\(94\) | −4.70156 | − | 2.06950i | −0.484929 | − | 0.213452i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.78600 | + | 0.483926i | −0.998780 | + | 0.0493905i | ||||
\(97\) | − | 11.1047i | − | 1.12751i | −0.825942 | − | 0.563755i | \(-0.809356\pi\) | ||
0.825942 | − | 0.563755i | \(-0.190644\pi\) | |||||||
\(98\) | 0.399712 | − | 0.908080i | 0.0403770 | − | 0.0917299i | ||||
\(99\) | −4.54040 | + | 9.00393i | −0.456327 | + | 0.904929i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.5517i | 1.74646i | 0.487308 | + | 0.873230i | \(0.337979\pi\) | ||||
−0.487308 | + | 0.873230i | \(0.662021\pi\) | |||||||
\(102\) | 2.55865 | + | 18.5294i | 0.253344 | + | 1.83468i | ||||
\(103\) | 10.9190 | 1.07588 | 0.537941 | − | 0.842982i | \(-0.319202\pi\) | ||||
0.537941 | + | 0.842982i | \(0.319202\pi\) | |||||||
\(104\) | −3.36131 | − | 9.91534i | −0.329604 | − | 0.972280i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.29844 | + | 2.94984i | −0.126115 | + | 0.286514i | ||||
\(107\) | 6.45162i | 0.623702i | 0.950131 | + | 0.311851i | \(0.100949\pi\) | ||||
−0.950131 | + | 0.311851i | \(0.899051\pi\) | |||||||
\(108\) | −7.04179 | + | 7.64285i | −0.677596 | + | 0.735434i | ||||
\(109\) | −2.29844 | −0.220150 | −0.110075 | − | 0.993923i | \(-0.535109\pi\) | ||||
−0.110075 | + | 0.993923i | \(0.535109\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.72263 | + | 10.9190i | 0.638084 | + | 1.03639i | ||||
\(112\) | −0.880344 | + | 10.0000i | −0.0831847 | + | 0.944911i | ||||
\(113\) | −0.799423 | −0.0752034 | −0.0376017 | − | 0.999293i | \(-0.511972\pi\) | ||||
−0.0376017 | + | 0.999293i | \(0.511972\pi\) | |||||||
\(114\) | −1.06806 | + | 0.147485i | −0.100033 | + | 0.0138132i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.36131 | + | 3.07840i | −0.312090 | + | 0.285823i | ||||
\(117\) | −9.91534 | − | 5.00000i | −0.916674 | − | 0.462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.1647 | 1.75683 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.298438 | 0.0271307 | ||||||||
\(122\) | 3.24844 | − | 7.37992i | 0.294100 | − | 0.668147i | ||||
\(123\) | −2.79544 | − | 4.54040i | −0.252056 | − | 0.409394i | ||||
\(124\) | 5.00000 | − | 4.57917i | 0.449013 | − | 0.411221i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.77012 | + | 8.21811i | 0.603130 | + | 0.732128i | ||||
\(127\) | 12.6797 | 1.12514 | 0.562571 | − | 0.826749i | \(-0.309812\pi\) | ||||
0.562571 | + | 0.826749i | \(0.309812\pi\) | |||||||
\(128\) | 2.67869 | + | 10.9920i | 0.236765 | + | 0.971567i | ||||
\(129\) | −12.4031 | + | 7.63636i | −1.09203 | + | 0.672344i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.71949 | 0.499714 | 0.249857 | − | 0.968283i | \(-0.419616\pi\) | ||||
0.249857 | + | 0.968283i | \(0.419616\pi\) | |||||||
\(132\) | 11.1987 | + | 3.18913i | 0.974721 | + | 0.277578i | ||||
\(133\) | 1.10469i | 0.0957885i | ||||||||
\(134\) | 3.11053 | − | 7.06662i | 0.268709 | − | 0.610463i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.4555 | − | 6.93443i | 1.75404 | − | 0.594623i | ||||
\(137\) | −9.91534 | −0.847125 | −0.423563 | − | 0.905867i | \(-0.639221\pi\) | ||||
−0.423563 | + | 0.905867i | \(0.639221\pi\) | |||||||
\(138\) | −12.5630 | + | 1.73477i | −1.06943 | + | 0.147674i | ||||
\(139\) | − | 2.94984i | − | 0.250202i | −0.992144 | − | 0.125101i | \(-0.960074\pi\) | ||
0.992144 | − | 0.125101i | \(-0.0399255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.29844 | + | 5.35738i | 0.277779 | + | 0.451173i | ||||
\(142\) | 7.08883 | − | 16.1047i | 0.594882 | − | 1.35148i | ||||
\(143\) | 12.4421i | 1.04046i | ||||||||
\(144\) | 10.1997 | + | 6.32194i | 0.849972 | + | 0.526829i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.68066 | − | 0.739779i | −0.139092 | − | 0.0612245i | ||||
\(147\) | −1.03475 | + | 0.637075i | −0.0853446 | + | 0.0525450i | ||||
\(148\) | 10.9190 | − | 10.0000i | 0.897538 | − | 0.821995i | ||||
\(149\) | 15.2727i | 1.25119i | 0.780148 | + | 0.625595i | \(0.215144\pi\) | ||||
−0.780148 | + | 0.625595i | \(0.784856\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.3284i | 1.57292i | 0.617641 | + | 0.786460i | \(0.288089\pi\) | ||||
−0.617641 | + | 0.786460i | \(0.711911\pi\) | |||||||
\(152\) | 0.399712 | + | 1.17909i | 0.0324209 | + | 0.0956365i | ||||
\(153\) | 10.3151 | − | 20.4555i | 0.833923 | − | 1.65373i | ||||
\(154\) | 4.80625 | − | 10.9190i | 0.387299 | − | 0.879880i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.51194 | + | 12.3323i | −0.281180 | + | 0.987372i | ||||
\(157\) | − | 11.1047i | − | 0.886250i | −0.896460 | − | 0.443125i | \(-0.853870\pi\) | ||
0.896460 | − | 0.443125i | \(-0.146130\pi\) | |||||||
\(158\) | −6.49687 | − | 2.85974i | −0.516864 | − | 0.227509i | ||||
\(159\) | 3.36131 | − | 2.06950i | 0.266570 | − | 0.164122i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9937i | 1.02405i | ||||||||
\(162\) | 12.4155 | − | 2.80284i | 0.975452 | − | 0.220212i | ||||
\(163\) | −0.440172 | −0.0344769 | −0.0172385 | − | 0.999851i | \(-0.505487\pi\) | ||||
−0.0172385 | + | 0.999851i | \(0.505487\pi\) | |||||||
\(164\) | −4.54040 | + | 4.15825i | −0.354546 | + | 0.324705i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.35078 | + | 1.03475i | 0.182456 | + | 0.0803120i | ||||
\(167\) | 15.5324i | 1.20194i | 0.799273 | + | 0.600968i | \(0.205218\pi\) | ||||
−0.799273 | + | 0.600968i | \(0.794782\pi\) | |||||||
\(168\) | 7.84585 | − | 9.46600i | 0.605320 | − | 0.730318i | ||||
\(169\) | −0.701562 | −0.0539663 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.17909 | + | 0.594576i | 0.0901669 | + | 0.0454684i | ||||
\(172\) | 11.3592 | + | 12.4031i | 0.866130 | + | 0.945729i | ||||
\(173\) | 8.43579 | 0.641361 | 0.320681 | − | 0.947187i | \(-0.396088\pi\) | ||||
0.320681 | + | 0.947187i | \(0.396088\pi\) | |||||||
\(174\) | 5.52987 | − | 0.763599i | 0.419218 | − | 0.0578883i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.17909 | − | 13.3935i | 0.0888769 | − | 1.00957i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.93443 | + | 3.05234i | 0.519758 | + | 0.228783i | ||||
\(179\) | −9.08080 | −0.678731 | −0.339365 | − | 0.940655i | \(-0.610212\pi\) | ||||
−0.339365 | + | 0.940655i | \(0.610212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5078 | 0.781039 | 0.390520 | − | 0.920595i | \(-0.372295\pi\) | ||||
0.390520 | + | 0.920595i | \(0.372295\pi\) | |||||||
\(182\) | 12.0243 | + | 5.29276i | 0.891300 | + | 0.392325i | ||||
\(183\) | −8.40935 | + | 5.17748i | −0.621637 | + | 0.382730i | ||||
\(184\) | 4.70156 | + | 13.8689i | 0.346604 | + | 1.02243i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −8.22575 | + | 1.13586i | −0.603141 | + | 0.0832856i | ||||
\(187\) | −25.6682 | −1.87705 | ||||||||
\(188\) | 5.35738 | − | 4.90647i | 0.390727 | − | 0.357841i | ||||
\(189\) | −1.10469 | − | 12.9937i | −0.0803541 | − | 0.945156i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4421 | −0.900280 | −0.450140 | − | 0.892958i | \(-0.648626\pi\) | ||||
−0.450140 | + | 0.892958i | \(0.648626\pi\) | |||||||
\(192\) | 4.94915 | − | 12.9424i | 0.357174 | − | 0.934038i | ||||
\(193\) | 19.8062i | 1.42568i | 0.701324 | + | 0.712842i | \(0.252593\pi\) | ||||
−0.701324 | + | 0.712842i | \(0.747407\pi\) | |||||||
\(194\) | 14.3736 | + | 6.32684i | 1.03196 | + | 0.454241i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.947657 | + | 1.03475i | 0.0676898 | + | 0.0739106i | ||||
\(197\) | 10.7148 | 0.763396 | 0.381698 | − | 0.924287i | \(-0.375340\pi\) | ||||
0.381698 | + | 0.924287i | \(0.375340\pi\) | |||||||
\(198\) | −9.06753 | − | 11.0069i | −0.644401 | − | 0.782226i | ||||
\(199\) | − | 21.0891i | − | 1.49496i | −0.664282 | − | 0.747482i | \(-0.731263\pi\) | ||
0.664282 | − | 0.747482i | \(-0.268737\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.05234 | + | 4.95767i | −0.567968 | + | 0.349687i | ||||
\(202\) | −22.7184 | − | 10.0000i | −1.59846 | − | 0.703598i | ||||
\(203\) | − | 5.71949i | − | 0.401429i | ||||||
\(204\) | −25.4416 | − | 7.24518i | −1.78127 | − | 0.507264i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.22106 | + | 14.1332i | −0.433442 | + | 0.984709i | ||||
\(207\) | 13.8689 | + | 6.99364i | 0.963952 | + | 0.486091i | ||||
\(208\) | 14.7492 | + | 1.29844i | 1.02267 | + | 0.0900305i | ||||
\(209\) | − | 1.47956i | − | 0.102343i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 18.1392i | − | 1.24876i | −0.781123 | − | 0.624378i | \(-0.785353\pi\) | ||
0.781123 | − | 0.624378i | \(-0.214647\pi\) | |||||||
\(212\) | −3.07840 | − | 3.36131i | −0.211426 | − | 0.230856i | ||||
\(213\) | −18.3511 | + | 11.2984i | −1.25740 | + | 0.774156i | ||||
\(214\) | −8.35078 | − | 3.67578i | −0.570848 | − | 0.251271i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.88065 | − | 13.4691i | −0.400127 | − | 0.916460i | ||||
\(217\) | 8.50781i | 0.577548i | ||||||||
\(218\) | 1.30952 | − | 2.97503i | 0.0886921 | − | 0.201494i | ||||
\(219\) | 1.17909 | + | 1.91509i | 0.0796752 | + | 0.129410i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 28.2665i | − | 1.90141i | ||||||
\(222\) | −17.9634 | + | 2.48050i | −1.20563 | + | 0.166481i | ||||
\(223\) | 21.0891 | 1.41223 | 0.706114 | − | 0.708098i | \(-0.250447\pi\) | ||||
0.706114 | + | 0.708098i | \(0.250447\pi\) | |||||||
\(224\) | −12.4421 | − | 6.83694i | −0.831324 | − | 0.456812i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.455467 | − | 1.03475i | 0.0302972 | − | 0.0688304i | ||||
\(227\) | − | 22.2551i | − | 1.47712i | −0.674188 | − | 0.738560i | \(-0.735506\pi\) | ||
0.674188 | − | 0.738560i | \(-0.264494\pi\) | |||||||
\(228\) | 0.417624 | − | 1.46650i | 0.0276578 | − | 0.0971210i | ||||
\(229\) | −2.29844 | −0.151885 | −0.0759425 | − | 0.997112i | \(-0.524197\pi\) | ||||
−0.0759425 | + | 0.997112i | \(0.524197\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.4421 | + | 7.66037i | −0.818631 | + | 0.504015i | ||||
\(232\) | −2.06950 | − | 6.10469i | −0.135869 | − | 0.400792i | ||||
\(233\) | 8.43579 | 0.552647 | 0.276323 | − | 0.961065i | \(-0.410884\pi\) | ||||
0.276323 | + | 0.961065i | \(0.410884\pi\) | |||||||
\(234\) | 12.1211 | − | 9.98539i | 0.792379 | − | 0.652765i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.55796 | + | 7.40312i | 0.296071 | + | 0.480885i | ||||
\(238\) | −10.9190 | + | 24.8062i | −0.707775 | + | 1.60795i | ||||
\(239\) | −25.8874 | −1.67452 | −0.837258 | − | 0.546809i | \(-0.815842\pi\) | ||||
−0.837258 | + | 0.546809i | \(0.815842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | −0.170034 | + | 0.386289i | −0.0109302 | + | 0.0248316i | ||||
\(243\) | −14.4634 | − | 5.81455i | −0.927830 | − | 0.373004i | ||||
\(244\) | 7.70156 | + | 8.40935i | 0.493042 | + | 0.538354i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.46964 | − | 1.03146i | 0.476247 | − | 0.0657632i | ||||
\(247\) | 1.62932 | 0.103671 | ||||||||
\(248\) | 3.07840 | + | 9.08080i | 0.195479 | + | 0.576631i | ||||
\(249\) | −1.64922 | − | 2.67869i | −0.104515 | − | 0.169755i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.5261 | 1.42183 | 0.710916 | − | 0.703277i | \(-0.248281\pi\) | ||||
0.710916 | + | 0.703277i | \(0.248281\pi\) | |||||||
\(252\) | −14.4945 | + | 4.08080i | −0.913068 | + | 0.257066i | ||||
\(253\) | − | 17.4031i | − | 1.09413i | ||||||
\(254\) | −7.22420 | + | 16.4122i | −0.453287 | + | 1.02979i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.7539 | − | 2.79544i | −0.984619 | − | 0.174715i | ||||
\(257\) | 4.55796 | 0.284318 | 0.142159 | − | 0.989844i | \(-0.454596\pi\) | ||||
0.142159 | + | 0.989844i | \(0.454596\pi\) | |||||||
\(258\) | −2.81765 | − | 20.4050i | −0.175419 | − | 1.27036i | ||||
\(259\) | 18.5794i | 1.15447i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.10469 | − | 3.07840i | −0.377871 | − | 0.190548i | ||||
\(262\) | −3.25865 | + | 7.40312i | −0.201320 | + | 0.457367i | ||||
\(263\) | − | 18.6227i | − | 1.14833i | −0.818741 | − | 0.574164i | \(-0.805327\pi\) | ||
0.818741 | − | 0.574164i | \(-0.194673\pi\) | |||||||
\(264\) | −10.5083 | + | 12.6783i | −0.646741 | + | 0.780292i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.42987 | − | 0.629390i | −0.0876710 | − | 0.0385904i | ||||
\(267\) | −4.86493 | − | 7.90172i | −0.297729 | − | 0.483577i | ||||
\(268\) | 7.37460 | + | 8.05234i | 0.450476 | + | 0.491875i | ||||
\(269\) | − | 8.43579i | − | 0.514339i | −0.966366 | − | 0.257170i | \(-0.917210\pi\) | ||
0.966366 | − | 0.257170i | \(-0.0827899\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 9.15833i | − | 0.556329i | −0.960533 | − | 0.278165i | \(-0.910274\pi\) | ||
0.960533 | − | 0.278165i | \(-0.0897260\pi\) | |||||||
\(272\) | −2.67869 | + | 30.4278i | −0.162420 | + | 1.84495i | ||||
\(273\) | −8.43579 | − | 13.7016i | −0.510557 | − | 0.829256i | ||||
\(274\) | 5.64922 | − | 12.8341i | 0.341282 | − | 0.775337i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.91225 | − | 17.2495i | 0.295683 | − | 1.03830i | ||||
\(277\) | 8.89531i | 0.534468i | 0.963632 | + | 0.267234i | \(0.0861096\pi\) | ||||
−0.963632 | + | 0.267234i | \(0.913890\pi\) | |||||||
\(278\) | 3.81818 | + | 1.68066i | 0.228999 | + | 0.100799i | ||||
\(279\) | 9.08080 | + | 4.57917i | 0.543653 | + | 0.274147i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.5517i | − | 1.04705i | −0.852011 | − | 0.523524i | \(-0.824617\pi\) | ||
0.852011 | − | 0.523524i | \(-0.175383\pi\) | |||||||
\(282\) | −8.81370 | + | 1.21705i | −0.524848 | + | 0.0724744i | ||||
\(283\) | −16.3785 | −0.973603 | −0.486801 | − | 0.873513i | \(-0.661836\pi\) | ||||
−0.486801 | + | 0.873513i | \(0.661836\pi\) | |||||||
\(284\) | 16.8066 | + | 18.3511i | 0.997287 | + | 1.08894i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.1047 | − | 7.08883i | −0.952290 | − | 0.419172i | ||||
\(287\) | − | 7.72577i | − | 0.456038i | ||||||
\(288\) | −13.9941 | + | 9.60022i | −0.824612 | + | 0.565699i | ||||
\(289\) | 41.3141 | 2.43024 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.0839 | − | 16.3785i | −0.591131 | − | 0.960126i | ||||
\(292\) | 1.91509 | − | 1.75391i | 0.112072 | − | 0.102640i | ||||
\(293\) | −21.4295 | −1.25193 | −0.625963 | − | 0.779852i | \(-0.715294\pi\) | ||||
−0.625963 | + | 0.779852i | \(0.715294\pi\) | |||||||
\(294\) | −0.235067 | − | 1.70232i | −0.0137094 | − | 0.0992811i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.72263 | + | 19.8307i | 0.390745 | + | 1.15264i | ||||
\(297\) | 1.47956 | + | 17.4031i | 0.0858526 | + | 1.00983i | ||||
\(298\) | −19.7685 | − | 8.70156i | −1.14516 | − | 0.504068i | ||||
\(299\) | 19.1647 | 1.10833 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.1047 | −1.21645 | ||||||||
\(302\) | −25.0180 | − | 11.0122i | −1.43963 | − | 0.633683i | ||||
\(303\) | 15.9384 | + | 25.8874i | 0.915635 | + | 1.48719i | ||||
\(304\) | −1.75391 | − | 0.154404i | −0.100593 | − | 0.00885568i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 20.6000 | + | 25.0059i | 1.17762 | + | 1.42949i | ||||
\(307\) | 26.4172 | 1.50771 | 0.753855 | − | 0.657041i | \(-0.228192\pi\) | ||||
0.753855 | + | 0.657041i | \(0.228192\pi\) | |||||||
\(308\) | 11.3949 | + | 12.4421i | 0.649285 | + | 0.708955i | ||||
\(309\) | 16.1047 | − | 9.91534i | 0.916164 | − | 0.564064i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.4453 | 0.762411 | 0.381205 | − | 0.924490i | \(-0.375509\pi\) | ||||
0.381205 | + | 0.924490i | \(0.375509\pi\) | |||||||
\(312\) | −13.9616 | − | 11.5720i | −0.790420 | − | 0.655136i | ||||
\(313\) | 16.2984i | 0.921242i | 0.887597 | + | 0.460621i | \(0.152373\pi\) | ||||
−0.887597 | + | 0.460621i | \(0.847627\pi\) | |||||||
\(314\) | 14.3736 | + | 6.32684i | 0.811147 | + | 0.357044i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.40312 | − | 6.78003i | 0.416458 | − | 0.381406i | ||||
\(317\) | 16.8716 | 0.947602 | 0.473801 | − | 0.880632i | \(-0.342882\pi\) | ||||
0.473801 | + | 0.880632i | \(0.342882\pi\) | |||||||
\(318\) | 0.763599 | + | 5.52987i | 0.0428205 | + | 0.310100i | ||||
\(319\) | 7.66037i | 0.428898i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.85859 | + | 9.51563i | 0.326995 | + | 0.531111i | ||||
\(322\) | −16.8187 | − | 7.40312i | −0.937270 | − | 0.412560i | ||||
\(323\) | 3.36131i | 0.187029i | ||||||||
\(324\) | −3.44575 | + | 17.6671i | −0.191431 | + | 0.981506i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.250786 | − | 0.569745i | 0.0138897 | − | 0.0315553i | ||||
\(327\) | −3.39001 | + | 2.08717i | −0.187468 | + | 0.115421i | ||||
\(328\) | −2.79544 | − | 8.24609i | −0.154352 | − | 0.455314i | ||||
\(329\) | 9.11592i | 0.502577i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.1275i | − | 0.941413i | −0.882290 | − | 0.470707i | \(-0.843999\pi\) | ||
0.882290 | − | 0.470707i | \(-0.156001\pi\) | |||||||
\(332\) | −2.67869 | + | 2.45323i | −0.147012 | + | 0.134639i | ||||
\(333\) | 19.8307 | + | 10.0000i | 1.08672 | + | 0.547997i | ||||
\(334\) | −20.1047 | − | 8.84952i | −1.10008 | − | 0.484224i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.78236 | + | 15.5486i | 0.424563 | + | 0.848247i | ||||
\(337\) | 12.4031i | 0.675641i | 0.941211 | + | 0.337821i | \(0.109690\pi\) | ||||
−0.941211 | + | 0.337821i | \(0.890310\pi\) | |||||||
\(338\) | 0.399712 | − | 0.908080i | 0.0217414 | − | 0.0493930i | ||||
\(339\) | −1.17909 | + | 0.725940i | −0.0640391 | + | 0.0394277i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.3949i | − | 0.617069i | ||||||
\(342\) | −1.44138 | + | 1.18741i | −0.0779409 | + | 0.0642080i | ||||
\(343\) | −19.3284 | −1.04363 | ||||||||
\(344\) | −22.5261 | + | 7.63636i | −1.21452 | + | 0.411725i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.80625 | + | 10.9190i | −0.258386 | + | 0.587010i | ||||
\(347\) | − | 19.4358i | − | 1.04337i | −0.853139 | − | 0.521683i | \(-0.825304\pi\) | ||
0.853139 | − | 0.521683i | \(-0.174696\pi\) | |||||||
\(348\) | −2.16224 | + | 7.59274i | −0.115908 | + | 0.407014i | ||||
\(349\) | −26.2094 | −1.40296 | −0.701478 | − | 0.712691i | \(-0.747476\pi\) | ||||
−0.701478 | + | 0.712691i | \(0.747476\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.1647 | + | 1.62932i | −1.02294 | + | 0.0869669i | ||||
\(352\) | 16.6643 | + | 9.15703i | 0.888210 | + | 0.488071i | ||||
\(353\) | −26.6676 | −1.41937 | −0.709687 | − | 0.704517i | \(-0.751164\pi\) | ||||
−0.709687 | + | 0.704517i | \(0.751164\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.90172 | + | 7.23665i | −0.418790 | + | 0.383542i | ||||
\(357\) | 28.2665 | − | 17.4031i | 1.49602 | − | 0.921071i | ||||
\(358\) | 5.17374 | − | 11.7539i | 0.273441 | − | 0.621213i | ||||
\(359\) | −7.72577 | −0.407751 | −0.203875 | − | 0.978997i | \(-0.565354\pi\) | ||||
−0.203875 | + | 0.978997i | \(0.565354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.8062 | 0.989803 | ||||||||
\(362\) | −5.98677 | + | 13.6010i | −0.314658 | + | 0.714852i | ||||
\(363\) | 0.440172 | − | 0.271006i | 0.0231030 | − | 0.0142241i | ||||
\(364\) | −13.7016 | + | 12.5483i | −0.718157 | + | 0.657712i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.91038 | − | 13.8346i | −0.0998569 | − | 0.723148i | ||||
\(367\) | 2.50967 | 0.131004 | 0.0655018 | − | 0.997852i | \(-0.479135\pi\) | ||||
0.0655018 | + | 0.997852i | \(0.479135\pi\) | |||||||
\(368\) | −20.6301 | − | 1.81616i | −1.07542 | − | 0.0946739i | ||||
\(369\) | −8.24609 | − | 4.15825i | −0.429275 | − | 0.216470i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.71949 | 0.296941 | ||||||||
\(372\) | 3.21635 | − | 11.2943i | 0.166760 | − | 0.585582i | ||||
\(373\) | − | 23.7016i | − | 1.22722i | −0.789609 | − | 0.613610i | \(-0.789717\pi\) | ||
0.789609 | − | 0.613610i | \(-0.210283\pi\) | |||||||
\(374\) | 14.6243 | − | 33.2241i | 0.756207 | − | 1.71798i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.29844 | + | 9.72987i | 0.170104 | + | 0.501780i | ||||
\(377\) | −8.43579 | −0.434465 | ||||||||
\(378\) | 17.4481 | + | 5.97325i | 0.897433 | + | 0.307231i | ||||
\(379\) | − | 13.1199i | − | 0.673923i | −0.941518 | − | 0.336961i | \(-0.890601\pi\) | ||
0.941518 | − | 0.336961i | \(-0.109399\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.7016 | − | 11.5142i | 0.958110 | − | 0.589890i | ||||
\(382\) | 7.08883 | − | 16.1047i | 0.362696 | − | 0.823987i | ||||
\(383\) | 7.26464i | 0.371206i | 0.982625 | + | 0.185603i | \(0.0594238\pi\) | ||||
−0.982625 | + | 0.185603i | \(0.940576\pi\) | |||||||
\(384\) | 13.9325 | + | 13.7799i | 0.710990 | + | 0.703202i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.6366 | − | 11.2845i | −1.30487 | − | 0.574367i | ||||
\(387\) | −11.3592 | + | 22.5261i | −0.577420 | + | 1.14506i | ||||
\(388\) | −16.3785 | + | 15.0000i | −0.831494 | + | 0.761510i | ||||
\(389\) | − | 37.3824i | − | 1.89536i | −0.319218 | − | 0.947681i | \(-0.603420\pi\) | ||
0.319218 | − | 0.947681i | \(-0.396580\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 39.5371i | 1.99948i | ||||||||
\(392\) | −1.87927 | + | 0.637075i | −0.0949174 | + | 0.0321771i | ||||
\(393\) | 8.43579 | − | 5.19375i | 0.425529 | − | 0.261990i | ||||
\(394\) | −6.10469 | + | 13.8689i | −0.307550 | + | 0.698703i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 19.4132 | − | 5.46560i | 0.975548 | − | 0.274657i | ||||
\(397\) | 15.9109i | 0.798547i | 0.916832 | + | 0.399273i | \(0.130738\pi\) | ||||
−0.916832 | + | 0.399273i | \(0.869262\pi\) | |||||||
\(398\) | 27.2970 | + | 12.0154i | 1.36828 | + | 0.602277i | ||||
\(399\) | 1.00314 | + | 1.62932i | 0.0502200 | + | 0.0815683i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.23521i | 0.461184i | 0.973050 | + | 0.230592i | \(0.0740663\pi\) | ||||
−0.973050 | + | 0.230592i | \(0.925934\pi\) | |||||||
\(402\) | −1.82927 | − | 13.2473i | −0.0912359 | − | 0.660716i | ||||
\(403\) | 12.5483 | 0.625078 | ||||||||
\(404\) | 25.8874 | − | 23.7085i | 1.28795 | − | 1.17954i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.40312 | + | 3.25865i | 0.367411 | + | 0.161724i | ||||
\(407\) | − | 24.8842i | − | 1.23347i | ||||||
\(408\) | 23.8732 | − | 28.8029i | 1.18190 | − | 1.42596i | ||||
\(409\) | −11.2094 | −0.554268 | −0.277134 | − | 0.960831i | \(-0.589385\pi\) | ||||
−0.277134 | + | 0.960831i | \(0.589385\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.6243 | + | 9.00393i | −0.721366 | + | 0.444131i | ||||
\(412\) | −14.7492 | − | 16.1047i | −0.726641 | − | 0.793421i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −16.9541 | + | 13.9668i | −0.833247 | + | 0.686432i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −10.0839 | + | 18.3511i | −0.494406 | + | 0.899738i | ||||
\(417\) | −2.67869 | − | 4.35078i | −0.131176 | − | 0.213059i | ||||
\(418\) | 1.91509 | + | 0.842970i | 0.0936702 | + | 0.0412310i | ||||
\(419\) | −34.9682 | −1.70831 | −0.854154 | − | 0.520021i | \(-0.825924\pi\) | ||||
−0.854154 | + | 0.520021i | \(0.825924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.2094 | −0.692522 | −0.346261 | − | 0.938138i | \(-0.612549\pi\) | ||||
−0.346261 | + | 0.938138i | \(0.612549\pi\) | |||||||
\(422\) | 23.4788 | + | 10.3347i | 1.14293 | + | 0.503087i | ||||
\(423\) | 9.72987 | + | 4.90647i | 0.473082 | + | 0.238561i | ||||
\(424\) | 6.10469 | − | 2.06950i | 0.296470 | − | 0.100504i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.16888 | − | 30.1904i | −0.201983 | − | 1.46273i | ||||
\(427\) | −14.3090 | −0.692463 | ||||||||
\(428\) | 9.51563 | − | 8.71473i | 0.459955 | − | 0.421242i | ||||
\(429\) | 11.2984 | + | 18.3511i | 0.545494 | + | 0.886001i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.71949 | 0.275498 | 0.137749 | − | 0.990467i | \(-0.456013\pi\) | ||||
0.137749 | + | 0.990467i | \(0.456013\pi\) | |||||||
\(432\) | 20.7845 | + | 0.0622549i | 0.999996 | + | 0.00299524i | ||||
\(433\) | − | 7.20937i | − | 0.346460i | −0.984881 | − | 0.173230i | \(-0.944580\pi\) | ||
0.984881 | − | 0.173230i | \(-0.0554205\pi\) | |||||||
\(434\) | −11.0122 | − | 4.84728i | −0.528605 | − | 0.232677i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.10469 | + | 3.39001i | 0.148688 | + | 0.162352i | ||||
\(437\) | −2.27898 | −0.109018 | ||||||||
\(438\) | −3.15061 | + | 0.435057i | −0.150542 | + | 0.0207878i | ||||
\(439\) | − | 23.4674i | − | 1.12004i | −0.828480 | − | 0.560018i | \(-0.810794\pi\) | ||
0.828480 | − | 0.560018i | \(-0.189206\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.947657 | + | 1.87927i | −0.0451265 | + | 0.0894890i | ||||
\(442\) | 36.5872 | + | 16.1047i | 1.74028 | + | 0.766022i | ||||
\(443\) | − | 29.7907i | − | 1.41540i | −0.706514 | − | 0.707699i | \(-0.749733\pi\) | ||
0.706514 | − | 0.707699i | \(-0.250267\pi\) | |||||||
\(444\) | 7.02389 | − | 24.6645i | 0.333339 | − | 1.17053i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.0154 | + | 27.2970i | −0.568945 | + | 1.29255i | ||||
\(447\) | 13.8689 | + | 22.5261i | 0.655975 | + | 1.06545i | ||||
\(448\) | 15.9384 | − | 12.2094i | 0.753017 | − | 0.576839i | ||||
\(449\) | 29.7460i | 1.40380i | 0.712274 | + | 0.701901i | \(0.247665\pi\) | ||||
−0.712274 | + | 0.701901i | \(0.752335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3475i | 0.487244i | ||||||||
\(452\) | 1.07985 | + | 1.17909i | 0.0507917 | + | 0.0554595i | ||||
\(453\) | 17.5517 | + | 28.5078i | 0.824651 | + | 1.33941i | ||||
\(454\) | 28.8062 | + | 12.6797i | 1.35194 | + | 0.595088i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.66025 | + | 1.37609i | 0.0777482 | + | 0.0644412i | ||||
\(457\) | − | 36.1047i | − | 1.68891i | −0.535630 | − | 0.844453i | \(-0.679926\pi\) | ||
0.535630 | − | 0.844453i | \(-0.320074\pi\) | |||||||
\(458\) | 1.30952 | − | 2.97503i | 0.0611900 | − | 0.139014i | ||||
\(459\) | −3.36131 | − | 39.5371i | −0.156893 | − | 1.84543i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.5517i | 0.817465i | 0.912654 | + | 0.408732i | \(0.134029\pi\) | ||||
−0.912654 | + | 0.408732i | \(0.865971\pi\) | |||||||
\(462\) | −2.82651 | − | 20.4691i | −0.131501 | − | 0.952311i | ||||
\(463\) | −5.01934 | −0.233268 | −0.116634 | − | 0.993175i | \(-0.537211\pi\) | ||||
−0.116634 | + | 0.993175i | \(0.537211\pi\) | |||||||
\(464\) | 9.08080 | + | 0.799423i | 0.421566 | + | 0.0371123i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.80625 | + | 10.9190i | −0.222645 | + | 0.505814i | ||||
\(467\) | 29.5197i | 1.36601i | 0.730414 | + | 0.683004i | \(0.239327\pi\) | ||||
−0.730414 | + | 0.683004i | \(0.760673\pi\) | |||||||
\(468\) | 6.01886 | + | 21.3783i | 0.278222 | + | 0.988210i | ||||
\(469\) | −13.7016 | −0.632679 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.0839 | − | 16.3785i | −0.464644 | − | 0.754683i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.2665 | 1.29969 | ||||||||
\(474\) | −12.1792 | + | 1.68179i | −0.559411 | + | 0.0772471i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −25.8874 | − | 28.2665i | −1.18655 | − | 1.29559i | ||||
\(477\) | 3.07840 | − | 6.10469i | 0.140950 | − | 0.279514i | ||||
\(478\) | 14.7492 | − | 33.5078i | 0.674613 | − | 1.53261i | ||||
\(479\) | 33.6131 | 1.53582 | 0.767912 | − | 0.640555i | \(-0.221296\pi\) | ||||
0.767912 | + | 0.640555i | \(0.221296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.4031 | 1.24947 | ||||||||
\(482\) | −3.98822 | + | 9.06058i | −0.181658 | + | 0.412698i | ||||
\(483\) | 11.7994 | + | 19.1647i | 0.536890 | + | 0.872026i | ||||
\(484\) | −0.403124 | − | 0.440172i | −0.0183238 | − | 0.0200078i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.7666 | − | 15.4082i | 0.715189 | − | 0.698931i | ||||
\(487\) | 0.131364 | 0.00595267 | 0.00297634 | − | 0.999996i | \(-0.499053\pi\) | ||||
0.00297634 | + | 0.999996i | \(0.499053\pi\) | |||||||
\(488\) | −15.2727 | + | 5.17748i | −0.691364 | + | 0.234373i | ||||
\(489\) | −0.649219 | + | 0.399712i | −0.0293587 | + | 0.0180756i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4453 | 0.606776 | 0.303388 | − | 0.952867i | \(-0.401882\pi\) | ||||
0.303388 | + | 0.952867i | \(0.401882\pi\) | |||||||
\(492\) | −2.92071 | + | 10.2561i | −0.131676 | + | 0.462382i | ||||
\(493\) | − | 17.4031i | − | 0.783797i | ||||||
\(494\) | −0.928300 | + | 2.10895i | −0.0417662 | + | 0.0948860i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.5078 | − | 1.18915i | −0.606519 | − | 0.0533945i | ||||
\(497\) | −31.2256 | −1.40066 | ||||||||
\(498\) | 4.40685 | − | 0.608526i | 0.197476 | − | 0.0272687i | ||||
\(499\) | 40.2861i | 1.80345i | 0.432308 | + | 0.901726i | \(0.357699\pi\) | ||||
−0.432308 | + | 0.901726i | \(0.642301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.1047 | + | 22.9091i | 0.630151 | + | 1.02350i | ||||
\(502\) | −12.8341 | + | 29.1570i | −0.572814 | + | 1.30134i | ||||
\(503\) | − | 12.9841i | − | 0.578934i | −0.957188 | − | 0.289467i | \(-0.906522\pi\) | ||
0.957188 | − | 0.289467i | \(-0.0934780\pi\) | |||||||
\(504\) | 2.97611 | − | 21.0863i | 0.132567 | − | 0.939257i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.5261 | + | 9.91534i | 1.00141 | + | 0.440791i | ||||
\(507\) | −1.03475 | + | 0.637075i | −0.0459548 | + | 0.0282935i | ||||
\(508\) | −17.1275 | − | 18.7016i | −0.759910 | − | 0.829748i | ||||
\(509\) | 2.95911i | 0.131160i | 0.997847 | + | 0.0655802i | \(0.0208898\pi\) | ||||
−0.997847 | + | 0.0655802i | \(0.979110\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.25865i | 0.144154i | ||||||||
\(512\) | 12.5940 | − | 18.7987i | 0.556583 | − | 0.830792i | ||||
\(513\) | 2.27898 | − | 0.193752i | 0.100619 | − | 0.00855434i | ||||
\(514\) | −2.59688 | + | 5.89968i | −0.114543 | + | 0.260224i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 28.0169 | + | 7.97857i | 1.23338 | + | 0.351237i | ||||
\(517\) | − | 12.2094i | − | 0.536968i | ||||||
\(518\) | −24.0486 | − | 10.5855i | −1.05663 | − | 0.465101i | ||||
\(519\) | 12.4421 | − | 7.66037i | 0.546148 | − | 0.336253i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.07840i | 0.134867i | 0.997724 | + | 0.0674337i | \(0.0214811\pi\) | ||||
−0.997724 | + | 0.0674337i | \(0.978519\pi\) | |||||||
\(522\) | 7.46270 | − | 6.14781i | 0.326634 | − | 0.269082i | ||||
\(523\) | −14.0002 | −0.612187 | −0.306094 | − | 0.952001i | \(-0.599022\pi\) | ||||
−0.306094 | + | 0.952001i | \(0.599022\pi\) | |||||||
\(524\) | −7.72577 | − | 8.43579i | −0.337502 | − | 0.368519i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.1047 | + | 10.6102i | 1.05101 | + | 0.462627i | ||||
\(527\) | 25.8874i | 1.12767i | ||||||||
\(528\) | −10.4233 | − | 20.8250i | −0.453615 | − | 0.906291i | ||||
\(529\) | −3.80625 | −0.165489 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.62932 | − | 1.49219i | 0.0706402 | − | 0.0646946i | ||||
\(533\) | −11.3949 | −0.493568 | ||||||||
\(534\) | 12.9995 | − | 1.79505i | 0.562544 | − | 0.0776796i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.6243 | + | 4.95767i | −0.631676 | + | 0.214139i | ||||
\(537\) | −13.3935 | + | 8.24609i | −0.577970 | + | 0.355845i | ||||
\(538\) | 10.9190 | + | 4.80625i | 0.470752 | + | 0.207212i | ||||
\(539\) | 2.35817 | 0.101574 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.7016 | −1.10500 | −0.552498 | − | 0.833514i | \(-0.686325\pi\) | ||||
−0.552498 | + | 0.833514i | \(0.686325\pi\) | |||||||
\(542\) | 11.8543 | + | 5.21791i | 0.509184 | + | 0.224129i | ||||
\(543\) | 15.4982 | − | 9.54193i | 0.665091 | − | 0.409484i | ||||
\(544\) | −37.8586 | − | 20.8033i | −1.62317 | − | 0.891934i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 22.5411 | − | 3.11262i | 0.964671 | − | 0.133208i | ||||
\(547\) | 4.71053 | 0.201408 | 0.100704 | − | 0.994916i | \(-0.467891\pi\) | ||||
0.100704 | + | 0.994916i | \(0.467891\pi\) | |||||||
\(548\) | 13.3935 | + | 14.6243i | 0.572140 | + | 0.624721i | ||||
\(549\) | −7.70156 | + | 15.2727i | −0.328695 | + | 0.651824i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.00314 | 0.0427354 | ||||||||
\(552\) | 19.5285 | + | 16.1861i | 0.831187 | + | 0.688925i | ||||
\(553\) | 12.5969i | 0.535674i | ||||||||
\(554\) | −11.5138 | − | 5.06806i | −0.489175 | − | 0.215321i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.35078 | + | 3.98459i | −0.184514 | + | 0.168984i | ||||
\(557\) | −36.7023 | −1.55512 | −0.777562 | − | 0.628806i | \(-0.783544\pi\) | ||||
−0.777562 | + | 0.628806i | \(0.783544\pi\) | |||||||
\(558\) | −11.1009 | + | 9.14495i | −0.469937 | + | 0.387137i | ||||
\(559\) | 31.1277i | 1.31656i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −37.8586 | + | 23.3088i | −1.59839 | + | 0.984098i | ||||
\(562\) | 22.7184 | + | 10.0000i | 0.958317 | + | 0.421825i | ||||
\(563\) | 23.3391i | 0.983625i | 0.870701 | + | 0.491812i | \(0.163665\pi\) | ||||
−0.870701 | + | 0.491812i | \(0.836335\pi\) | |||||||
\(564\) | 3.44625 | − | 12.1016i | 0.145113 | − | 0.509569i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.33159 | − | 21.1999i | 0.392236 | − | 0.891096i | ||||
\(567\) | −13.4287 | − | 18.1616i | −0.563952 | − | 0.762716i | ||||
\(568\) | −33.3286 | + | 11.2984i | −1.39844 | + | 0.474072i | ||||
\(569\) | − | 10.5955i | − | 0.444186i | −0.975026 | − | 0.222093i | \(-0.928711\pi\) | ||
0.975026 | − | 0.222093i | \(-0.0712888\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.9501i | 0.709338i | 0.934992 | + | 0.354669i | \(0.115406\pi\) | ||||
−0.934992 | + | 0.354669i | \(0.884594\pi\) | |||||||
\(572\) | 18.3511 | − | 16.8066i | 0.767299 | − | 0.702718i | ||||
\(573\) | −18.3511 | + | 11.2984i | −0.766630 | + | 0.471999i | ||||
\(574\) | 10.0000 | + | 4.40172i | 0.417392 | + | 0.183724i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.45314 | − | 23.5832i | −0.185548 | − | 0.982635i | ||||
\(577\) | 12.4031i | 0.516349i | 0.966098 | + | 0.258174i | \(0.0831209\pi\) | ||||
−0.966098 | + | 0.258174i | \(0.916879\pi\) | |||||||
\(578\) | −23.5385 | + | 53.4756i | −0.979072 | + | 2.22429i | ||||
\(579\) | 17.9857 | + | 29.2126i | 0.747459 | + | 1.21404i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 4.55796i | − | 0.189096i | ||||||
\(582\) | 26.9451 | − | 3.72076i | 1.11691 | − | 0.154230i | ||||
\(583\) | −7.66037 | −0.317260 | ||||||||
\(584\) | 1.17909 | + | 3.47812i | 0.0487909 | + | 0.143925i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.2094 | − | 27.7377i | 0.504365 | − | 1.14583i | ||||
\(587\) | − | 31.3359i | − | 1.29337i | −0.762758 | − | 0.646685i | \(-0.776155\pi\) | ||
0.762758 | − | 0.646685i | \(-0.223845\pi\) | |||||||
\(588\) | 2.33735 | + | 0.665623i | 0.0963908 | + | 0.0274498i | ||||
\(589\) | −1.49219 | −0.0614846 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.8034 | − | 9.72987i | 0.650066 | − | 0.400233i | ||||
\(592\) | −29.4984 | − | 2.59688i | −1.21238 | − | 0.106731i | ||||
\(593\) | 10.5955 | 0.435104 | 0.217552 | − | 0.976049i | \(-0.430193\pi\) | ||||
0.217552 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(594\) | −23.3690 | − | 8.00025i | −0.958843 | − | 0.328254i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.5261 | − | 20.6301i | 0.922703 | − | 0.845042i | ||||
\(597\) | −19.1506 | − | 31.1047i | −0.783780 | − | 1.27303i | ||||
\(598\) | −10.9190 | + | 24.8062i | −0.446512 | + | 1.01440i | ||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.0156 | −1.63227 | −0.816136 | − | 0.577860i | \(-0.803888\pi\) | ||||
−0.816136 | + | 0.577860i | \(0.803888\pi\) | |||||||
\(602\) | 12.0243 | − | 27.3172i | 0.490074 | − | 1.11337i | ||||
\(603\) | −7.37460 | + | 14.6243i | −0.300317 | + | 0.595549i | ||||
\(604\) | 28.5078 | − | 26.1084i | 1.15997 | − | 1.06234i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −42.5886 | + | 5.88091i | −1.73004 | + | 0.238896i | ||||
\(607\) | −3.25865 | −0.132264 | −0.0661322 | − | 0.997811i | \(-0.521066\pi\) | ||||
−0.0661322 | + | 0.997811i | \(0.521066\pi\) | |||||||
\(608\) | 1.19913 | − | 2.18223i | 0.0486313 | − | 0.0885011i | ||||
\(609\) | −5.19375 | − | 8.43579i | −0.210461 | − | 0.341835i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4453 | 0.543937 | ||||||||
\(612\) | −44.1036 | + | 12.4170i | −1.78278 | + | 0.501926i | ||||
\(613\) | 4.80625i | 0.194123i | 0.995278 | + | 0.0970613i | \(0.0309443\pi\) | ||||
−0.995278 | + | 0.0970613i | \(0.969056\pi\) | |||||||
\(614\) | −15.0511 | + | 34.1936i | −0.607412 | + | 1.37994i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.5969 | + | 7.66037i | −0.910454 | + | 0.308645i | ||||
\(617\) | 22.1097 | 0.890102 | 0.445051 | − | 0.895505i | \(-0.353186\pi\) | ||||
0.445051 | + | 0.895505i | \(0.353186\pi\) | |||||||
\(618\) | 3.65855 | + | 26.4946i | 0.147168 | + | 1.06577i | ||||
\(619\) | − | 5.15070i | − | 0.207024i | −0.994628 | − | 0.103512i | \(-0.966992\pi\) | ||
0.994628 | − | 0.103512i | \(-0.0330080\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.8062 | − | 2.27898i | 1.07570 | − | 0.0914523i | ||||
\(622\) | −7.66037 | + | 17.4031i | −0.307153 | + | 0.697802i | ||||
\(623\) | − | 13.4453i | − | 0.538673i | ||||||
\(624\) | 22.9330 | − | 11.4784i | 0.918054 | − | 0.459502i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −21.0962 | − | 9.28595i | −0.843173 | − | 0.371141i | ||||
\(627\) | −1.34356 | − | 2.18223i | −0.0536565 | − | 0.0871498i | ||||
\(628\) | −16.3785 | + | 15.0000i | −0.653574 | + | 0.598565i | ||||
\(629\) | 56.5330i | 2.25412i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 42.0468i | − | 1.67385i | −0.547314 | − | 0.836927i | \(-0.684350\pi\) | ||
0.547314 | − | 0.836927i | \(-0.315650\pi\) | |||||||
\(632\) | 4.55796 | + | 13.4453i | 0.181306 | + | 0.534824i | ||||
\(633\) | −16.4719 | − | 26.7539i | −0.654698 | − | 1.06337i | ||||
\(634\) | −9.61250 | + | 21.8380i | −0.381761 | + | 0.867299i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.59274 | − | 2.16224i | −0.301072 | − | 0.0857382i | ||||
\(637\) | 2.59688i | 0.102892i | ||||||||
\(638\) | −9.91534 | − | 4.36446i | −0.392552 | − | 0.172791i | ||||
\(639\) | −16.8066 | + | 33.3286i | −0.664858 | + | 1.31846i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.3136i | − | 0.486359i | −0.969981 | − | 0.243179i | \(-0.921810\pi\) | ||
0.969981 | − | 0.243179i | \(-0.0781903\pi\) | |||||||
\(642\) | −15.6546 | + | 2.16169i | −0.617839 | + | 0.0853152i | ||||
\(643\) | 24.4791 | 0.965360 | 0.482680 | − | 0.875797i | \(-0.339663\pi\) | ||||
0.482680 | + | 0.875797i | \(0.339663\pi\) | |||||||
\(644\) | 19.1647 | − | 17.5517i | 0.755197 | − | 0.691634i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.35078 | − | 1.91509i | −0.171179 | − | 0.0753483i | ||||
\(647\) | − | 10.3550i | − | 0.407095i | −0.979065 | − | 0.203548i | \(-0.934753\pi\) | ||
0.979065 | − | 0.203548i | \(-0.0652472\pi\) | |||||||
\(648\) | −20.9046 | − | 14.5258i | −0.821208 | − | 0.570628i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.72577 | + | 12.5483i | 0.302797 | + | 0.491808i | ||||
\(652\) | 0.594576 | + | 0.649219i | 0.0232854 | + | 0.0254254i | ||||
\(653\) | 25.9875 | 1.01697 | 0.508485 | − | 0.861071i | \(-0.330206\pi\) | ||||
0.508485 | + | 0.861071i | \(0.330206\pi\) | |||||||
\(654\) | −0.770119 | − | 5.57708i | −0.0301140 | − | 0.218081i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.2662 | + | 1.07985i | 0.478914 | + | 0.0421609i | ||||
\(657\) | 3.47812 | + | 1.75391i | 0.135694 | + | 0.0684264i | ||||
\(658\) | −11.7994 | − | 5.19375i | −0.459987 | − | 0.202474i | ||||
\(659\) | 16.8066 | 0.654691 | 0.327346 | − | 0.944905i | \(-0.393846\pi\) | ||||
0.327346 | + | 0.944905i | \(0.393846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | 22.1693 | + | 9.75831i | 0.861635 | + | 0.379268i | ||||
\(663\) | −25.6682 | − | 41.6908i | −0.996871 | − | 1.61914i | ||||
\(664\) | −1.64922 | − | 4.86493i | −0.0640021 | − | 0.188796i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −24.2421 | + | 19.9708i | −0.939363 | + | 0.773852i | ||||
\(667\) | 11.7994 | 0.456873 | ||||||||
\(668\) | 22.9091 | − | 20.9809i | 0.886379 | − | 0.811776i | ||||
\(669\) | 31.1047 | − | 19.1506i | 1.20258 | − | 0.740403i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.1647 | 0.739847 | ||||||||
\(672\) | −24.5596 | + | 1.21449i | −0.947408 | + | 0.0468501i | ||||
\(673\) | 24.8062i | 0.956211i | 0.878303 | + | 0.478105i | \(0.158676\pi\) | ||||
−0.878303 | + | 0.478105i | \(0.841324\pi\) | |||||||
\(674\) | −16.0542 | − | 7.06662i | −0.618385 | − | 0.272196i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.947657 | + | 1.03475i | 0.0364483 | + | 0.0397980i | ||||
\(677\) | −12.9937 | −0.499390 | −0.249695 | − | 0.968324i | \(-0.580330\pi\) | ||||
−0.249695 | + | 0.968324i | \(0.580330\pi\) | |||||||
\(678\) | −0.267856 | − | 1.93977i | −0.0102870 | − | 0.0744965i | ||||
\(679\) | − | 27.8691i | − | 1.06952i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.2094 | − | 32.8244i | −0.774425 | − | 1.25784i | ||||
\(682\) | 14.7492 | + | 6.49219i | 0.564776 | + | 0.248599i | ||||
\(683\) | − | 11.6291i | − | 0.444975i | −0.974936 | − | 0.222488i | \(-0.928582\pi\) | ||
0.974936 | − | 0.222488i | \(-0.0714177\pi\) | |||||||
\(684\) | −0.715734 | − | 2.54220i | −0.0273668 | − | 0.0972034i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.0122 | − | 25.0180i | 0.420449 | − | 0.955193i | ||||
\(687\) | −3.39001 | + | 2.08717i | −0.129337 | + | 0.0796303i | ||||
\(688\) | 2.94984 | − | 33.5078i | 0.112462 | − | 1.27747i | ||||
\(689\) | − | 8.43579i | − | 0.321378i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.18915i | − | 0.0452375i | −0.999744 | − | 0.0226187i | \(-0.992800\pi\) | ||
0.999744 | − | 0.0226187i | \(-0.00720038\pi\) | |||||||
\(692\) | −11.3949 | − | 12.4421i | −0.433169 | − | 0.472978i | ||||
\(693\) | −11.3949 | + | 22.5969i | −0.432857 | + | 0.858384i | ||||
\(694\) | 25.1570 | + | 11.0734i | 0.954948 | + | 0.420341i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.59589 | − | 7.12466i | −0.325826 | − | 0.270059i | ||||
\(697\) | − | 23.5078i | − | 0.890422i | ||||||
\(698\) | 14.9327 | − | 33.9246i | 0.565210 | − | 1.28406i | ||||
\(699\) | 12.4421 | − | 7.66037i | 0.470604 | − | 0.289742i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.3949i | 0.430380i | 0.976572 | + | 0.215190i | \(0.0690370\pi\) | ||||
−0.976572 | + | 0.215190i | \(0.930963\pi\) | |||||||
\(702\) | 8.81007 | − | 25.7345i | 0.332515 | − | 0.971288i | ||||
\(703\) | −3.25865 | −0.122902 | ||||||||
\(704\) | −21.3470 | + | 16.3526i | −0.804544 | + | 0.616311i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.1938 | − | 34.5177i | 0.571824 | − | 1.29909i | ||||
\(707\) | 44.0490i | 1.65663i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7016 | 0.664796 | 0.332398 | − | 0.943139i | \(-0.392142\pi\) | ||||
0.332398 | + | 0.943139i | \(0.392142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.4453 | + | 6.78003i | 0.504237 | + | 0.254271i | ||||
\(712\) | −4.86493 | − | 14.3508i | −0.182321 | − | 0.537818i | ||||
\(713\) | −17.5517 | −0.657317 | ||||||||
\(714\) | 6.42137 | + | 46.5026i | 0.240314 | + | 1.74032i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.2662 | + | 13.3935i | 0.458408 | + | 0.500537i | ||||
\(717\) | −38.1818 | + | 23.5078i | −1.42593 | + | 0.877915i | ||||
\(718\) | 4.40172 | − | 10.0000i | 0.164271 | − | 0.373197i | ||||
\(719\) | −44.0490 | −1.64275 | −0.821375 | − | 0.570389i | \(-0.806793\pi\) | ||||
−0.821375 | + | 0.570389i | \(0.806793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4031 | 1.02055 | ||||||||
\(722\) | −10.7148 | + | 24.3422i | −0.398762 | + | 0.905924i | ||||
\(723\) | 10.3244 | − | 6.35656i | 0.383970 | − | 0.236403i | ||||
\(724\) | −14.1938 | − | 15.4982i | −0.527507 | − | 0.575986i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0999951 | + | 0.724149i | 0.00371117 | + | 0.0268757i | ||||
\(727\) | −40.5488 | −1.50387 | −0.751936 | − | 0.659236i | \(-0.770880\pi\) | ||||
−0.751936 | + | 0.659236i | \(0.770880\pi\) | |||||||
\(728\) | −8.43579 | − | 24.8842i | −0.312651 | − | 0.922271i | ||||
\(729\) | −26.6125 | + | 4.55796i | −0.985648 | + | 0.168813i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −64.2169 | −2.37515 | ||||||||
\(732\) | 18.9956 | + | 5.40949i | 0.702096 | + | 0.199940i | ||||
\(733\) | 4.80625i | 0.177523i | 0.996053 | + | 0.0887614i | \(0.0282909\pi\) | ||||
−0.996053 | + | 0.0887614i | \(0.971709\pi\) | |||||||
\(734\) | −1.42987 | + | 3.24844i | −0.0527775 | + | 0.119902i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.1047 | − | 25.6682i | 0.519906 | − | 0.946143i | ||||
\(737\) | 18.3511 | 0.675973 | ||||||||
\(738\) | 10.0805 | − | 8.30435i | 0.371068 | − | 0.305687i | ||||
\(739\) | − | 29.2357i | − | 1.07545i | −0.843120 | − | 0.537726i | \(-0.819283\pi\) | ||
0.843120 | − | 0.537726i | \(-0.180717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.40312 | − | 1.47956i | 0.0882810 | − | 0.0543529i | ||||
\(742\) | −3.25865 | + | 7.40312i | −0.119629 | + | 0.271777i | ||||
\(743\) | 40.8778i | 1.49966i | 0.661630 | + | 0.749830i | \(0.269865\pi\) | ||||
−0.661630 | + | 0.749830i | \(0.730135\pi\) | |||||||
\(744\) | 12.7865 | + | 10.5980i | 0.468776 | + | 0.388542i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 30.6786 | + | 13.5038i | 1.12322 | + | 0.494411i | ||||
\(747\) | −4.86493 | − | 2.45323i | −0.177999 | − | 0.0897592i | ||||
\(748\) | 34.6722 | + | 37.8586i | 1.26774 | + | 1.38425i | ||||
\(749\) | 16.1914i | 0.591622i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36.2784i | − | 1.32382i | −0.749584 | − | 0.661909i | \(-0.769746\pi\) | ||
0.749584 | − | 0.661909i | \(-0.230254\pi\) | |||||||
\(752\) | −14.4733 | − | 1.27415i | −0.527787 | − | 0.0464634i | ||||
\(753\) | 33.2241 | − | 20.4555i | 1.21076 | − | 0.745439i | ||||
\(754\) | 4.80625 | − | 10.9190i | 0.175033 | − | 0.397647i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −17.6726 | + | 19.1810i | −0.642745 | + | 0.697607i | ||||
\(757\) | 35.9109i | 1.30521i | 0.757700 | + | 0.652603i | \(0.226323\pi\) | ||||
−0.757700 | + | 0.652603i | \(0.773677\pi\) | |||||||
\(758\) | 16.9820 | + | 7.47499i | 0.616813 | + | 0.271504i | ||||
\(759\) | −15.8034 | − | 25.6682i | −0.573628 | − | 0.931698i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.6301i | 0.747841i | 0.927461 | + | 0.373920i | \(0.121987\pi\) | ||||
−0.927461 | + | 0.373920i | \(0.878013\pi\) | |||||||
\(762\) | 4.24849 | + | 30.7669i | 0.153906 | + | 1.11457i | ||||
\(763\) | −5.76832 | −0.208827 | ||||||||
\(764\) | 16.8066 | + | 18.3511i | 0.608041 | + | 0.663921i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.40312 | − | 4.13899i | −0.339749 | − | 0.149548i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −25.7742 | + | 10.1828i | −0.930048 | + | 0.367439i | ||||
\(769\) | 14.1938 | 0.511840 | 0.255920 | − | 0.966698i | \(-0.417622\pi\) | ||||
0.255920 | + | 0.966698i | \(0.417622\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.72263 | − | 4.13899i | 0.242110 | − | 0.149062i | ||||
\(772\) | 29.2126 | − | 26.7539i | 1.05139 | − | 0.962894i | ||||
\(773\) | 2.27898 | 0.0819692 | 0.0409846 | − | 0.999160i | \(-0.486951\pi\) | ||||
0.0409846 | + | 0.999160i | \(0.486951\pi\) | |||||||
\(774\) | −22.6852 | − | 27.5371i | −0.815402 | − | 0.989800i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.0839 | − | 29.7460i | −0.361993 | − | 1.06782i | ||||
\(777\) | 16.8716 | + | 27.4031i | 0.605264 | + | 0.983082i | ||||
\(778\) | 48.3866 | + | 21.2984i | 1.73474 | + | 0.763586i | ||||
\(779\) | 1.35503 | 0.0485489 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.8219 | 1.49650 | ||||||||
\(782\) | −51.1756 | − | 22.5261i | −1.83003 | − | 0.805530i | ||||
\(783\) | −11.7994 | + | 1.00314i | −0.421675 | + | 0.0358494i | ||||
\(784\) | 0.246095 | − | 2.79544i | 0.00878910 | − | 0.0998370i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.91638 | + | 13.8781i | 0.0683551 | + | 0.495017i | ||||
\(787\) | 18.4480 | 0.657601 | 0.328801 | − | 0.944399i | \(-0.393356\pi\) | ||||
0.328801 | + | 0.944399i | \(0.393356\pi\) | |||||||
\(788\) | −14.4733 | − | 15.8034i | −0.515590 | − | 0.562974i | ||||
\(789\) | −16.9109 | − | 27.4671i | −0.602045 | − | 0.977853i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.00629 | −0.0713354 | ||||||||
\(792\) | −3.98605 | + | 28.2418i | −0.141638 | + | 1.00353i | ||||
\(793\) | 21.1047i | 0.749449i | ||||||||
\(794\) | −20.5946 | − | 9.06518i | −0.730876 | − | 0.321711i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.1047 | + | 28.4867i | −1.10248 | + | 1.00968i | ||||
\(797\) | 45.8182 | 1.62296 | 0.811482 | − | 0.584378i | \(-0.198661\pi\) | ||||
0.811482 | + | 0.584378i | \(0.198661\pi\) | |||||||
\(798\) | −2.68048 | + | 0.370138i | −0.0948881 | + | 0.0131028i | ||||
\(799\) | 27.7377i | 0.981290i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.3508 | − | 7.23665i | −0.507060 | − | 0.255695i | ||||
\(802\) | −11.9538 | − | 5.26172i | −0.422102 | − | 0.185798i | ||||
\(803\) | − | 4.36446i | − | 0.154018i | ||||||
\(804\) | 18.1891 | + | 5.17984i | 0.641481 | + | 0.182679i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.14936 | + | 16.2422i | −0.251825 | + | 0.572107i | ||||
\(807\) | −7.66037 | − | 12.4421i | −0.269658 | − | 0.437983i | ||||
\(808\) | 15.9384 | + | 47.0156i | 0.560709 | + | 1.65400i | ||||
\(809\) | − | 43.5392i | − | 1.53076i | −0.643580 | − | 0.765378i | \(-0.722552\pi\) | ||
0.643580 | − | 0.765378i | \(-0.277448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.2667i | 1.23838i | 0.785240 | + | 0.619191i | \(0.212539\pi\) | ||||
−0.785240 | + | 0.619191i | \(0.787461\pi\) | |||||||
\(812\) | −8.43579 | + | 7.72577i | −0.296038 | + | 0.271121i | ||||
\(813\) | −8.31650 | − | 13.5078i | −0.291672 | − | 0.473740i | ||||
\(814\) | 32.2094 | + | 14.1777i | 1.12894 | + | 0.496927i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 23.6800 | + | 47.3110i | 0.828966 | + | 1.65622i | ||||
\(817\) | − | 3.70156i | − | 0.129501i | ||||||
\(818\) | 6.38649 | − | 14.5091i | 0.223298 | − | 0.507297i | ||||
\(819\) | −24.8842 | − | 12.5483i | −0.869525 | − | 0.438475i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 6.15681i | − | 0.214874i | −0.994212 | − | 0.107437i | \(-0.965736\pi\) | ||
0.994212 | − | 0.107437i | \(-0.0342644\pi\) | |||||||
\(822\) | −3.32225 | − | 24.0592i | −0.115877 | − | 0.839162i | ||||
\(823\) | −6.03105 | −0.210229 | −0.105115 | − | 0.994460i | \(-0.533521\pi\) | ||||
−0.105115 | + | 0.994460i | \(0.533521\pi\) | |||||||
\(824\) | 29.2487 | − | 9.91534i | 1.01893 | − | 0.345417i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.4389i | 0.710730i | 0.934728 | + | 0.355365i | \(0.115643\pi\) | ||||
−0.934728 | + | 0.355365i | \(0.884357\pi\) | |||||||
\(828\) | −8.41874 | − | 29.9023i | −0.292571 | − | 1.03918i | ||||
\(829\) | −19.1938 | −0.666627 | −0.333313 | − | 0.942816i | \(-0.608167\pi\) | ||||
−0.333313 | + | 0.942816i | \(0.608167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.07766 | + | 13.1199i | 0.280211 | + | 0.455124i | ||||
\(832\) | −18.0079 | − | 23.5078i | −0.624310 | − | 0.814987i | ||||
\(833\) | −5.35738 | −0.185622 | ||||||||
\(834\) | 7.15769 | − | 0.988379i | 0.247850 | − | 0.0342248i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.18223 | + | 1.99856i | −0.0754740 | + | 0.0691216i | ||||
\(837\) | 17.5517 | − | 1.49219i | 0.606676 | − | 0.0515776i | ||||
\(838\) | 19.9229 | − | 45.2617i | 0.688227 | − | 1.56354i | ||||
\(839\) | 44.0490 | 1.52074 | 0.760370 | − | 0.649490i | \(-0.225018\pi\) | ||||
0.760370 | + | 0.649490i | \(0.225018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.8062 | 0.820905 | ||||||||
\(842\) | 8.09572 | − | 18.3922i | 0.278997 | − | 0.633836i | ||||
\(843\) | −15.9384 | − | 25.8874i | −0.548946 | − | 0.891609i | ||||
\(844\) | −26.7539 | + | 24.5021i | −0.920907 | + | 0.843397i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11.8943 | + | 9.79860i | −0.408935 | + | 0.336883i | ||||
\(847\) | 0.748980 | 0.0257353 | ||||||||
\(848\) | −0.799423 | + | 9.08080i | −0.0274523 | + | 0.311836i | ||||
\(849\) | −24.1570 | + | 14.8730i | −0.829067 | + | 0.510441i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −38.3295 | −1.31392 | ||||||||
\(852\) | 41.4527 | + | 11.8047i | 1.42014 | + | 0.404424i | ||||
\(853\) | − | 43.7016i | − | 1.49631i | −0.663522 | − | 0.748156i | \(-0.730939\pi\) | ||
0.663522 | − | 0.748156i | \(-0.269061\pi\) | |||||||
\(854\) | 8.15250 | − | 18.5212i | 0.278973 | − | 0.633781i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.85859 | + | 17.2819i | 0.200243 | + | 0.590684i | ||||
\(857\) | 31.3449 | 1.07072 | 0.535360 | − | 0.844624i | \(-0.320176\pi\) | ||||
0.535360 | + | 0.844624i | \(0.320176\pi\) | |||||||
\(858\) | −30.1904 | + | 4.16888i | −1.03068 | + | 0.142323i | ||||
\(859\) | − | 50.7649i | − | 1.73208i | −0.499978 | − | 0.866038i | \(-0.666658\pi\) | ||
0.499978 | − | 0.866038i | \(-0.333342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.01562 | − | 11.3949i | −0.239092 | − | 0.388337i | ||||
\(862\) | −3.25865 | + | 7.40312i | −0.110990 | + | 0.252151i | ||||
\(863\) | 40.8778i | 1.39150i | 0.718286 | + | 0.695748i | \(0.244927\pi\) | ||||
−0.718286 | + | 0.695748i | \(0.755073\pi\) | |||||||
\(864\) | −11.9225 | + | 26.8674i | −0.405610 | + | 0.914046i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.33159 | + | 4.10750i | 0.317100 | + | 0.139579i | ||||
\(867\) | 60.9350 | − | 37.5165i | 2.06946 | − | 1.27413i | ||||
\(868\) | 12.5483 | − | 11.4922i | 0.425919 | − | 0.390070i | ||||
\(869\) | − | 16.8716i | − | 0.572329i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.2087i | 0.684746i | ||||||||
\(872\) | −6.15681 | + | 2.08717i | −0.208496 | + | 0.0706803i | ||||
\(873\) | −29.7460 | − | 15.0000i | −1.00675 | − | 0.507673i | ||||
\(874\) | 1.29844 | − | 2.94984i | 0.0439203 | − | 0.0997799i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.23192 | − | 4.32593i | 0.0416228 | − | 0.146160i | ||||
\(877\) | − | 4.08907i | − | 0.138078i | −0.997614 | − | 0.0690390i | \(-0.978007\pi\) | ||
0.997614 | − | 0.0690390i | \(-0.0219933\pi\) | |||||||
\(878\) | 30.3754 | + | 13.3704i | 1.02512 | + | 0.451230i | ||||
\(879\) | −31.6069 | + | 19.4597i | −1.06607 | + | 0.656361i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 47.4170i | − | 1.59752i | −0.601650 | − | 0.798760i | \(-0.705490\pi\) | ||
0.601650 | − | 0.798760i | \(-0.294510\pi\) | |||||||
\(882\) | −1.89254 | − | 2.29732i | −0.0637253 | − | 0.0773548i | ||||
\(883\) | 58.5566 | 1.97059 | 0.985294 | − | 0.170867i | \(-0.0546569\pi\) | ||||
0.985294 | + | 0.170867i | \(0.0546569\pi\) | |||||||
\(884\) | −41.6908 | + | 38.1818i | −1.40221 | + | 1.28419i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.5602 | + | 16.9731i | 1.29545 | + | 0.570223i | ||||
\(887\) | − | 14.5293i | − | 0.487846i | −0.969795 | − | 0.243923i | \(-0.921566\pi\) | ||
0.969795 | − | 0.243923i | \(-0.0784343\pi\) | |||||||
\(888\) | 27.9232 | + | 23.1440i | 0.937041 | + | 0.776662i | ||||
\(889\) | 31.8219 | 1.06727 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.9857 | + | 24.3247i | 0.602542 | + | 0.814907i | ||||
\(892\) | −28.4867 | − | 31.1047i | −0.953805 | − | 1.04146i | ||||
\(893\) | −1.59885 | −0.0535034 | ||||||||
\(894\) | −37.0587 | + | 5.11731i | −1.23943 | + | 0.171148i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.72263 | + | 27.5863i | 0.224587 | + | 0.921595i | ||||
\(897\) | 28.2665 | − | 17.4031i | 0.943790 | − | 0.581073i | ||||
\(898\) | −38.5023 | − | 16.9477i | −1.28484 | − | 0.565551i | ||||
\(899\) | 7.72577 | 0.257669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.4031 | 0.579782 | ||||||||
\(902\) | −13.3935 | − | 5.89543i | −0.445953 | − | 0.196296i | ||||
\(903\) | −31.1277 | + | 19.1647i | −1.03587 | + | 0.637763i | ||||
\(904\) | −2.14141 | + | 0.725940i | −0.0712222 | + | 0.0241444i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −46.8996 | + | 6.47620i | −1.55814 | + | 0.215157i | ||||
\(907\) | −0.880344 | −0.0292314 | −0.0146157 | − | 0.999893i | \(-0.504652\pi\) | ||||
−0.0146157 | + | 0.999893i | \(0.504652\pi\) | |||||||
\(908\) | −32.8244 | + | 30.0617i | −1.08932 | + | 0.997633i | ||||
\(909\) | 47.0156 | + | 23.7085i | 1.55941 | + | 0.786362i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.00629 | −0.0664713 | −0.0332356 | − | 0.999448i | \(-0.510581\pi\) | ||||
−0.0332356 | + | 0.999448i | \(0.510581\pi\) | |||||||
\(912\) | −2.72708 | + | 1.36495i | −0.0903027 | + | 0.0451981i | ||||
\(913\) | 6.10469i | 0.202036i | ||||||||
\(914\) | 46.7328 | + | 20.5705i | 1.54578 | + | 0.680411i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.10469 | + | 3.39001i | 0.102582 | + | 0.112009i | ||||
\(917\) | 14.3540 | 0.474011 | ||||||||
\(918\) | 53.0907 | + | 18.1753i | 1.75225 | + | 0.599874i | ||||
\(919\) | 8.40935i | 0.277399i | 0.990335 | + | 0.138699i | \(0.0442922\pi\) | ||||
−0.990335 | + | 0.138699i | \(0.955708\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 38.9633 | − | 23.9889i | 1.28388 | − | 0.790462i | ||||
\(922\) | −22.7184 | − | 10.0000i | −0.748190 | − | 0.329332i | ||||
\(923\) | 46.0553i | 1.51593i | ||||||||
\(924\) | 28.1050 | + | 8.00365i | 0.924587 | + | 0.263301i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.85974 | − | 6.49687i | 0.0939770 | − | 0.213501i | ||||
\(927\) | 14.7492 | − | 29.2487i | 0.484427 | − | 0.960653i | ||||
\(928\) | −6.20849 | + | 11.2984i | −0.203804 | + | 0.370889i | ||||
\(929\) | − | 43.5392i | − | 1.42847i | −0.699903 | − | 0.714237i | \(-0.746774\pi\) | ||
0.699903 | − | 0.714237i | \(-0.253226\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.308808i | − | 0.0101208i | ||||||
\(932\) | −11.3949 | − | 12.4421i | −0.373252 | − | 0.407555i | ||||
\(933\) | 19.8307 | − | 12.2094i | 0.649228 | − | 0.399717i | ||||
\(934\) | −38.2094 | − | 16.8187i | −1.25025 | − | 0.550325i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −31.1006 | − | 4.38953i | −1.01655 | − | 0.143476i | ||||
\(937\) | − | 34.6125i | − | 1.13074i | −0.824837 | − | 0.565370i | \(-0.808733\pi\) | ||
0.824837 | − | 0.565370i | \(-0.191267\pi\) | |||||||
\(938\) | 7.80640 | − | 17.7349i | 0.254888 | − | 0.579064i | ||||
\(939\) | 14.8003 | + | 24.0389i | 0.482989 | + | 0.784480i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 53.5738i | 1.74646i | 0.487311 | + | 0.873229i | \(0.337978\pi\) | ||||
−0.487311 | + | 0.873229i | \(0.662022\pi\) | |||||||
\(942\) | 26.9451 | − | 3.72076i | 0.877920 | − | 0.121229i | ||||
\(943\) | 15.9384 | 0.519024 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.1047 | + | 36.5872i | −0.523609 | + | 1.18955i | ||||
\(947\) | − | 18.0807i | − | 0.587545i | −0.955875 | − | 0.293772i | \(-0.905089\pi\) | ||
0.955875 | − | 0.293772i | \(-0.0949107\pi\) | |||||||
\(948\) | 4.76221 | − | 16.7226i | 0.154669 | − | 0.543126i | ||||
\(949\) | 4.80625 | 0.156017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.8842 | − | 15.3207i | 0.806927 | − | 0.496809i | ||||
\(952\) | 51.3364 | − | 17.4031i | 1.66382 | − | 0.564038i | ||||
\(953\) | −42.0596 | −1.36245 | −0.681223 | − | 0.732076i | \(-0.738552\pi\) | ||||
−0.681223 | + | 0.732076i | \(0.738552\pi\) | |||||||
\(954\) | 6.14781 | + | 7.46270i | 0.199043 | + | 0.241614i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 34.9682 | + | 38.1818i | 1.13095 | + | 1.23489i | ||||
\(957\) | 6.95623 | + | 11.2984i | 0.224863 | + | 0.365227i | ||||
\(958\) | −19.1509 | + | 43.5078i | −0.618738 | + | 1.40567i | ||||
\(959\) | −24.8842 | −0.803554 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.5078 | 0.629284 | ||||||||
\(962\) | −15.6128 | + | 35.4697i | −0.503377 | + | 1.14359i | ||||
\(963\) | 17.2819 | + | 8.71473i | 0.556902 | + | 0.280828i | ||||
\(964\) | −9.45547 | − | 10.3244i | −0.304540 | − | 0.332528i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −31.5289 | + | 4.35371i | −1.01443 | + | 0.140078i | ||||
\(967\) | 1.49796 | 0.0481712 | 0.0240856 | − | 0.999710i | \(-0.492333\pi\) | ||||
0.0240856 | + | 0.999710i | \(0.492333\pi\) | |||||||
\(968\) | 0.799423 | − | 0.271006i | 0.0256944 | − | 0.00871045i | ||||
\(969\) | 3.05234 | + | 4.95767i | 0.0980554 | + | 0.159263i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.4103 | −1.52147 | −0.760734 | − | 0.649063i | \(-0.775161\pi\) | ||||
−0.760734 | + | 0.649063i | \(0.775161\pi\) | |||||||
\(972\) | 10.9609 | + | 29.1866i | 0.351572 | + | 0.936161i | ||||
\(973\) | − | 7.40312i | − | 0.237333i | ||||||
\(974\) | −0.0748440 | + | 0.170034i | −0.00239816 | + | 0.00544823i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | − | 22.7184i | 0.0640184 | − | 0.727198i | ||||
\(977\) | 19.0313 | 0.608864 | 0.304432 | − | 0.952534i | \(-0.401533\pi\) | ||||
0.304432 | + | 0.952534i | \(0.401533\pi\) | |||||||
\(978\) | −0.147485 | − | 1.06806i | −0.00471605 | − | 0.0341529i | ||||
\(979\) | 18.0079i | 0.575534i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.10469 | + | 6.15681i | −0.0991250 | + | 0.196572i | ||||
\(982\) | −7.66037 | + | 17.4031i | −0.244452 | + | 0.555356i | ||||
\(983\) | − | 57.0331i | − | 1.81907i | −0.415623 | − | 0.909537i | \(-0.636437\pi\) | ||
0.415623 | − | 0.909537i | \(-0.363563\pi\) | |||||||
\(984\) | −11.6112 | − | 9.62385i | −0.370150 | − | 0.306797i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 22.5261 | + | 9.91534i | 0.717376 | + | 0.315769i | ||||
\(987\) | 8.27799 | + | 13.4453i | 0.263491 | + | 0.427967i | ||||
\(988\) | −2.20086 | − | 2.40312i | −0.0700187 | − | 0.0764536i | ||||
\(989\) | − | 43.5392i | − | 1.38447i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 44.4251i | − | 1.41121i | −0.708606 | − | 0.705604i | \(-0.750676\pi\) | ||
0.708606 | − | 0.705604i | \(-0.249324\pi\) | |||||||
\(992\) | 9.23521 | − | 16.8066i | 0.293218 | − | 0.533609i | ||||
\(993\) | −15.5532 | − | 25.2617i | −0.493564 | − | 0.801656i | ||||
\(994\) | 17.7906 | − | 40.4174i | 0.564284 | − | 1.28196i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.72312 | + | 6.05079i | −0.0545993 | + | 0.191727i | ||||
\(997\) | 47.4031i | 1.50127i | 0.660716 | + | 0.750636i | \(0.270253\pi\) | ||||
−0.660716 | + | 0.750636i | \(0.729747\pi\) | |||||||
\(998\) | −52.1450 | − | 22.9528i | −1.65062 | − | 0.726558i | ||||
\(999\) | 38.3295 | − | 3.25865i | 1.21269 | − | 0.103099i |
(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 | 300.2.h.c.299.8 | 16 | ||
3.2 | odd | 2 | inner | 300.2.h.c.299.10 | 16 | ||
4.3 | odd | 2 | inner | 300.2.h.c.299.5 | 16 | ||
5.2 | odd | 4 | 300.2.e.e.251.1 | yes | 8 | ||
5.3 | odd | 4 | 300.2.e.d.251.8 | yes | 8 | ||
5.4 | even | 2 | inner | 300.2.h.c.299.9 | 16 | ||
12.11 | even | 2 | inner | 300.2.h.c.299.11 | 16 | ||
15.2 | even | 4 | 300.2.e.e.251.8 | yes | 8 | ||
15.8 | even | 4 | 300.2.e.d.251.1 | ✓ | 8 | ||
15.14 | odd | 2 | inner | 300.2.h.c.299.7 | 16 | ||
20.3 | even | 4 | 300.2.e.d.251.2 | yes | 8 | ||
20.7 | even | 4 | 300.2.e.e.251.7 | yes | 8 | ||
20.19 | odd | 2 | inner | 300.2.h.c.299.12 | 16 | ||
60.23 | odd | 4 | 300.2.e.d.251.7 | yes | 8 | ||
60.47 | odd | 4 | 300.2.e.e.251.2 | yes | 8 | ||
60.59 | even | 2 | inner | 300.2.h.c.299.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.e.d.251.1 | ✓ | 8 | 15.8 | even | 4 | ||
300.2.e.d.251.2 | yes | 8 | 20.3 | even | 4 | ||
300.2.e.d.251.7 | yes | 8 | 60.23 | odd | 4 | ||
300.2.e.d.251.8 | yes | 8 | 5.3 | odd | 4 | ||
300.2.e.e.251.1 | yes | 8 | 5.2 | odd | 4 | ||
300.2.e.e.251.2 | yes | 8 | 60.47 | odd | 4 | ||
300.2.e.e.251.7 | yes | 8 | 20.7 | even | 4 | ||
300.2.e.e.251.8 | yes | 8 | 15.2 | even | 4 | ||
300.2.h.c.299.5 | 16 | 4.3 | odd | 2 | inner | ||
300.2.h.c.299.6 | 16 | 60.59 | even | 2 | inner | ||
300.2.h.c.299.7 | 16 | 15.14 | odd | 2 | inner | ||
300.2.h.c.299.8 | 16 | 1.1 | even | 1 | trivial | ||
300.2.h.c.299.9 | 16 | 5.4 | even | 2 | inner | ||
300.2.h.c.299.10 | 16 | 3.2 | odd | 2 | inner | ||
300.2.h.c.299.11 | 16 | 12.11 | even | 2 | inner | ||
300.2.h.c.299.12 | 16 | 20.19 | odd | 2 | inner |