Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,2,Mod(26,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.p (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: | \(1.50917259820\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.6 | ||
Root | \(-0.617942 + 0.356769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 189.80 |
Dual form | 189.2.p.d.26.6 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.15715 | − | 1.24543i | 1.52534 | − | 0.880653i | 0.525787 | − | 0.850616i | \(-0.323771\pi\) |
0.999549 | − | 0.0300373i | \(-0.00956260\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.10220 | − | 3.64112i | 1.05110 | − | 1.82056i | ||||
\(5\) | 0.617942 | + | 1.07031i | 0.276352 | + | 0.478656i | 0.970475 | − | 0.241200i | \(-0.0775411\pi\) |
−0.694123 | + | 0.719856i | \(0.744208\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.53189 | + | 2.15715i | −0.579001 | + | 0.815327i | ||||
\(8\) | − | 5.49086i | − | 1.94131i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.66599 | + | 1.53921i | 0.843060 | + | 0.486741i | ||||
\(11\) | −4.75523 | − | 2.74543i | −1.43376 | − | 0.827779i | −0.436350 | − | 0.899777i | \(-0.643729\pi\) |
−0.997405 | + | 0.0719981i | \(0.977062\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.96793i | 0.823157i | 0.911374 | + | 0.411578i | \(0.135022\pi\) | ||||
−0.911374 | + | 0.411578i | \(0.864978\pi\) | |||||||
\(14\) | −0.617942 | + | 6.56117i | −0.165152 | + | 1.75355i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.63409 | − | 4.56239i | −0.658524 | − | 1.14060i | ||||
\(17\) | 2.15715 | − | 3.73630i | 0.523186 | − | 0.906185i | −0.476450 | − | 0.879202i | \(-0.658077\pi\) |
0.999636 | − | 0.0269831i | \(-0.00859003\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.80660 | + | 2.77509i | −1.10271 | + | 0.636650i | −0.936932 | − | 0.349513i | \(-0.886347\pi\) |
−0.165779 | + | 0.986163i | \(0.553014\pi\) | |||||||
\(20\) | 5.19615 | 1.16190 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −13.6770 | −2.91594 | ||||||||
\(23\) | 1.41290 | − | 0.815739i | 0.294610 | − | 0.170093i | −0.345409 | − | 0.938452i | \(-0.612260\pi\) |
0.640019 | + | 0.768359i | \(0.278926\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.73630 | − | 3.00735i | 0.347259 | − | 0.601470i | ||||
\(26\) | 3.69636 | + | 6.40228i | 0.724916 | + | 1.25559i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.63409 | + | 10.1126i | 0.875762 | + | 1.91110i | ||||
\(29\) | − | 0.509136i | − | 0.0945443i | −0.998882 | − | 0.0472721i | \(-0.984947\pi\) | ||
0.998882 | − | 0.0472721i | \(-0.0150528\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.04290 | + | 4.06622i | 1.26494 | + | 0.730314i | 0.974026 | − | 0.226434i | \(-0.0727069\pi\) |
0.290915 | + | 0.956749i | \(0.406040\pi\) | |||||||
\(32\) | −1.85383 | − | 1.07031i | −0.327713 | − | 0.189205i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 10.7463i | − | 1.84298i | ||||||
\(35\) | −3.25544 | − | 0.306602i | −0.550269 | − | 0.0518253i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.53189 | + | 2.65332i | 0.251842 | + | 0.436203i | 0.964033 | − | 0.265783i | \(-0.0856304\pi\) |
−0.712191 | + | 0.701986i | \(0.752297\pi\) | |||||||
\(38\) | −6.91238 | + | 11.9726i | −1.12134 | + | 1.94221i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.87691 | − | 3.39304i | 0.929221 | − | 0.536486i | ||||
\(41\) | −0.354034 | −0.0552908 | −0.0276454 | − | 0.999618i | \(-0.508801\pi\) | ||||
−0.0276454 | + | 0.999618i | \(0.508801\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0637877 | −0.00972754 | −0.00486377 | − | 0.999988i | \(-0.501548\pi\) | ||||
−0.00486377 | + | 0.999988i | \(0.501548\pi\) | |||||||
\(44\) | −19.9929 | + | 11.5429i | −3.01404 | + | 1.74016i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.03189 | − | 3.51934i | 0.299586 | − | 0.518899i | ||||
\(47\) | −4.93224 | − | 8.54290i | −0.719442 | − | 1.24611i | −0.961221 | − | 0.275778i | \(-0.911064\pi\) |
0.241779 | − | 0.970331i | \(-0.422269\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.30660 | − | 6.60905i | −0.329515 | − | 0.944150i | ||||
\(50\) | − | 8.64975i | − | 1.22326i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.8066 | + | 6.23919i | 1.49861 | + | 0.865221i | ||||
\(53\) | 3.57005 | + | 2.06117i | 0.490384 | + | 0.283124i | 0.724734 | − | 0.689029i | \(-0.241963\pi\) |
−0.234350 | + | 0.972152i | \(0.575296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.78607i | − | 0.915034i | ||||||
\(56\) | 11.8446 | + | 8.41142i | 1.58280 | + | 1.12402i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.634095 | − | 1.09828i | −0.0832607 | − | 0.144212i | ||||
\(59\) | −1.53921 | + | 2.66599i | −0.200388 | + | 0.347082i | −0.948653 | − | 0.316317i | \(-0.897554\pi\) |
0.748266 | + | 0.663399i | \(0.230887\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.97259 | + | 3.44828i | −0.764712 | + | 0.441507i | −0.830985 | − | 0.556295i | \(-0.812222\pi\) |
0.0662730 | + | 0.997802i | \(0.478889\pi\) | |||||||
\(62\) | 20.2568 | 2.57262 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.20440 | 0.650550 | ||||||||
\(65\) | −3.17660 | + | 1.83401i | −0.394009 | + | 0.227481i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.16599 | − | 10.6798i | 0.753295 | − | 1.30475i | −0.192922 | − | 0.981214i | \(-0.561796\pi\) |
0.946217 | − | 0.323532i | \(-0.104870\pi\) | |||||||
\(68\) | −9.06953 | − | 15.7089i | −1.09984 | − | 1.90498i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.40432 | + | 3.39304i | −0.884985 | + | 0.405545i | ||||
\(71\) | 4.63148i | 0.549655i | 0.961494 | + | 0.274828i | \(0.0886208\pi\) | ||||
−0.961494 | + | 0.274828i | \(0.911379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.09568 | − | 3.51934i | −0.713446 | − | 0.411908i | 0.0988899 | − | 0.995098i | \(-0.468471\pi\) |
−0.812336 | + | 0.583190i | \(0.801804\pi\) | |||||||
\(74\) | 6.60905 | + | 3.81574i | 0.768287 | + | 0.443571i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 23.3352i | 2.67673i | ||||||||
\(77\) | 13.2068 | − | 6.05203i | 1.50506 | − | 0.689693i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.165989 | + | 0.287501i | 0.0186752 | + | 0.0323463i | 0.875212 | − | 0.483740i | \(-0.160722\pi\) |
−0.856537 | + | 0.516086i | \(0.827388\pi\) | |||||||
\(80\) | 3.25544 | − | 5.63858i | 0.363969 | − | 0.630412i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.763705 | + | 0.440925i | −0.0843371 | + | 0.0486920i | ||||
\(83\) | −7.39272 | −0.811457 | −0.405728 | − | 0.913994i | \(-0.632982\pi\) | ||||
−0.405728 | + | 0.913994i | \(0.632982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.33198 | 0.578334 | ||||||||
\(86\) | −0.137600 | + | 0.0794433i | −0.0148378 | + | 0.00856659i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.0748 | + | 26.1103i | −1.60698 | + | 2.78337i | ||||
\(89\) | 1.71623 | + | 2.97259i | 0.181920 | + | 0.315094i | 0.942534 | − | 0.334110i | \(-0.108436\pi\) |
−0.760615 | + | 0.649204i | \(0.775102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.40228 | − | 4.54656i | −0.671142 | − | 0.476609i | ||||
\(92\) | − | 6.85939i | − | 0.715140i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21.2792 | − | 12.2855i | −2.19478 | − | 1.26716i | ||||
\(95\) | −5.94040 | − | 3.42969i | −0.609472 | − | 0.351879i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.45644i | − | 0.452482i | −0.974071 | − | 0.226241i | \(-0.927356\pi\) | ||
0.974071 | − | 0.226241i | \(-0.0726438\pi\) | |||||||
\(98\) | −13.2068 | − | 11.3840i | −1.33409 | − | 1.14996i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.30008 | − | 12.6441i | −0.730008 | − | 1.26441i | ||||
\(101\) | 4.57821 | − | 7.92969i | 0.455549 | − | 0.789034i | −0.543171 | − | 0.839622i | \(-0.682776\pi\) |
0.998720 | + | 0.0505884i | \(0.0161097\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.64061 | + | 2.10191i | −0.358720 | + | 0.207107i | −0.668519 | − | 0.743695i | \(-0.733072\pi\) |
0.309799 | + | 0.950802i | \(0.399738\pi\) | |||||||
\(104\) | 16.2965 | 1.59801 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.2682 | 0.997335 | ||||||||
\(107\) | −8.93193 | + | 5.15685i | −0.863482 | + | 0.498532i | −0.865177 | − | 0.501467i | \(-0.832794\pi\) |
0.00169460 | + | 0.999999i | \(0.499461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0637877 | + | 0.110484i | −0.00610976 | + | 0.0105824i | −0.869064 | − | 0.494699i | \(-0.835278\pi\) |
0.862954 | + | 0.505282i | \(0.168611\pi\) | |||||||
\(110\) | −8.45159 | − | 14.6386i | −0.805827 | − | 1.39573i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.8769 | + | 1.30695i | 1.31124 | + | 0.123495i | ||||
\(113\) | 2.29950i | 0.216319i | 0.994134 | + | 0.108159i | \(0.0344957\pi\) | ||||
−0.994134 | + | 0.108159i | \(0.965504\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.74618 | + | 1.00816i | 0.162832 | + | 0.0940113i | ||||
\(116\) | −1.85383 | − | 1.07031i | −0.172123 | − | 0.0993755i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.66792i | 0.705889i | ||||||||
\(119\) | 4.75523 | + | 10.3769i | 0.435911 | + | 0.951250i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.57479 | + | 16.5840i | 0.870436 | + | 1.50764i | ||||
\(122\) | −8.58919 | + | 14.8769i | −0.777629 | + | 1.34689i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 29.6112 | − | 17.0960i | 2.65916 | − | 1.53527i | ||||
\(125\) | 10.4711 | 0.936567 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.386795 | −0.0343225 | −0.0171613 | − | 0.999853i | \(-0.505463\pi\) | ||||
−0.0171613 | + | 0.999853i | \(0.505463\pi\) | |||||||
\(128\) | 14.9343 | − | 8.62234i | 1.32002 | − | 0.762114i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.56827 | + | 7.91248i | −0.400664 | + | 0.693970i | ||||
\(131\) | 10.4317 | + | 18.0683i | 0.911424 | + | 1.57863i | 0.812054 | + | 0.583582i | \(0.198349\pi\) |
0.0993693 | + | 0.995051i | \(0.468317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37691 | − | 14.6197i | 0.119393 | − | 1.26769i | ||||
\(134\) | − | 30.7173i | − | 2.65357i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.5155 | − | 11.8446i | −1.75919 | − | 1.01567i | ||||
\(137\) | 0.606650 | + | 0.350250i | 0.0518296 | + | 0.0299239i | 0.525691 | − | 0.850676i | \(-0.323807\pi\) |
−0.473861 | + | 0.880600i | \(0.657140\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.5965i | − | 0.983606i | −0.870707 | − | 0.491803i | \(-0.836338\pi\) | ||
0.870707 | − | 0.491803i | \(-0.163662\pi\) | |||||||
\(140\) | −7.95995 | + | 11.2089i | −0.672739 | + | 0.947324i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.76819 | + | 9.99080i | 0.484056 | + | 0.838409i | ||||
\(143\) | 8.14826 | − | 14.1132i | 0.681392 | − | 1.18021i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.544932 | − | 0.314617i | 0.0452542 | − | 0.0261275i | ||||
\(146\) | −17.5324 | −1.45099 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.8814 | 1.05884 | ||||||||
\(149\) | 0.303325 | − | 0.175125i | 0.0248494 | − | 0.0143468i | −0.487524 | − | 0.873110i | \(-0.662100\pi\) |
0.512373 | + | 0.858763i | \(0.328766\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.32749 | + | 4.03133i | −0.189409 | + | 0.328065i | −0.945053 | − | 0.326916i | \(-0.893990\pi\) |
0.755645 | + | 0.654982i | \(0.227324\pi\) | |||||||
\(152\) | 15.2377 | + | 26.3924i | 1.23594 | + | 2.14071i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.9517 | − | 29.5033i | 1.68834 | − | 2.37745i | ||||
\(155\) | 10.0507i | 0.807296i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.07031 | − | 0.617942i | −0.0854198 | − | 0.0493171i | 0.456682 | − | 0.889630i | \(-0.349038\pi\) |
−0.542101 | + | 0.840313i | \(0.682371\pi\) | |||||||
\(158\) | 0.716125 | + | 0.413455i | 0.0569718 | + | 0.0328927i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.64555i | − | 0.209149i | ||||||
\(161\) | −0.404743 | + | 4.29747i | −0.0318982 | + | 0.338688i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.80660 | + | 16.9855i | 0.768112 | + | 1.33041i | 0.938585 | + | 0.345047i | \(0.112137\pi\) |
−0.170473 | + | 0.985362i | \(0.554530\pi\) | |||||||
\(164\) | −0.744250 | + | 1.28908i | −0.0581162 | + | 0.100660i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.9472 | + | 9.20713i | −1.23774 | + | 0.714612i | ||||
\(167\) | −23.6892 | −1.83313 | −0.916564 | − | 0.399887i | \(-0.869049\pi\) | ||||
−0.916564 | + | 0.399887i | \(0.869049\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.19136 | 0.322413 | ||||||||
\(170\) | 11.5019 | − | 6.64061i | 0.882154 | − | 0.509312i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.134095 | + | 0.232259i | −0.0102246 | + | 0.0177096i | ||||
\(173\) | 5.99111 | + | 10.3769i | 0.455496 | + | 0.788942i | 0.998717 | − | 0.0506481i | \(-0.0161287\pi\) |
−0.543221 | + | 0.839590i | \(0.682795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.82749 | + | 8.35240i | 0.289331 | + | 0.631382i | ||||
\(176\) | 28.9269i | 2.18045i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.40432 | + | 4.27489i | 0.554977 | + | 0.320416i | ||||
\(179\) | −19.3862 | − | 11.1926i | −1.44900 | − | 0.836578i | −0.450574 | − | 0.892739i | \(-0.648780\pi\) |
−0.998422 | + | 0.0561615i | \(0.982114\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.90380i | 0.661815i | 0.943663 | + | 0.330907i | \(0.107355\pi\) | ||||
−0.943663 | + | 0.330907i | \(0.892645\pi\) | |||||||
\(182\) | −19.4731 | − | 1.83401i | −1.44344 | − | 0.135946i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.47911 | − | 7.75805i | −0.330204 | − | 0.571931i | ||||
\(185\) | −1.89324 | + | 3.27919i | −0.139194 | + | 0.241091i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.5155 | + | 11.8446i | −1.50024 | + | 0.866165i | ||||
\(188\) | −41.4743 | −3.02482 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.0858 | −1.23953 | ||||||||
\(191\) | 9.95138 | − | 5.74543i | 0.720057 | − | 0.415725i | −0.0947169 | − | 0.995504i | \(-0.530195\pi\) |
0.814774 | + | 0.579779i | \(0.196861\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.51100 | + | 9.54534i | −0.396691 | + | 0.687089i | −0.993315 | − | 0.115432i | \(-0.963175\pi\) |
0.596625 | + | 0.802520i | \(0.296508\pi\) | |||||||
\(194\) | −5.55019 | − | 9.61320i | −0.398480 | − | 0.690188i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28.9133 | − | 5.49494i | −2.06523 | − | 0.392496i | ||||
\(197\) | 19.8228i | 1.41232i | 0.708053 | + | 0.706159i | \(0.249574\pi\) | ||||
−0.708053 | + | 0.706159i | \(0.750426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.50000 | − | 4.33013i | −0.531661 | − | 0.306955i | 0.210032 | − | 0.977695i | \(-0.432643\pi\) |
−0.741693 | + | 0.670740i | \(0.765977\pi\) | |||||||
\(200\) | −16.5130 | − | 9.53376i | −1.16764 | − | 0.674139i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 22.8074i | − | 1.60472i | ||||||
\(203\) | 1.09828 | + | 0.779943i | 0.0770844 | + | 0.0547413i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.218772 | − | 0.378925i | −0.0152797 | − | 0.0264653i | ||||
\(206\) | −5.23557 | + | 9.06827i | −0.364779 | + | 0.631816i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.5409 | − | 7.81782i | 0.938890 | − | 0.542068i | ||||
\(209\) | 30.4753 | 2.10802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1626 | 1.52574 | 0.762869 | − | 0.646553i | \(-0.223790\pi\) | ||||
0.762869 | + | 0.646553i | \(0.223790\pi\) | |||||||
\(212\) | 15.0099 | − | 8.66599i | 1.03089 | − | 0.595183i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.8450 | + | 22.2482i | −0.878067 | + | 1.52086i | ||||
\(215\) | −0.0394171 | − | 0.0682725i | −0.00268823 | − | 0.00465614i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.5604 | + | 8.96358i | −1.32785 | + | 0.608487i | ||||
\(218\) | 0.317773i | 0.0215223i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −24.7089 | − | 14.2657i | −1.66587 | − | 0.961792i | ||||
\(221\) | 11.0891 | + | 6.40228i | 0.745932 | + | 0.430664i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7457i | 1.25531i | 0.778493 | + | 0.627653i | \(0.215984\pi\) | ||||
−0.778493 | + | 0.627653i | \(0.784016\pi\) | |||||||
\(224\) | 5.14868 | − | 2.35939i | 0.344011 | − | 0.157643i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.86387 | + | 4.96037i | 0.190502 | + | 0.329959i | ||||
\(227\) | −7.08940 | + | 12.2792i | −0.470540 | + | 0.814999i | −0.999432 | − | 0.0336901i | \(-0.989274\pi\) |
0.528893 | + | 0.848689i | \(0.322607\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.52537 | + | 2.03538i | −0.232963 | + | 0.134501i | −0.611938 | − | 0.790905i | \(-0.709610\pi\) |
0.378975 | + | 0.925407i | \(0.376277\pi\) | |||||||
\(230\) | 5.02237 | 0.331165 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.79560 | −0.183540 | ||||||||
\(233\) | 6.03053 | − | 3.48173i | 0.395073 | − | 0.228096i | −0.289283 | − | 0.957244i | \(-0.593417\pi\) |
0.684356 | + | 0.729148i | \(0.260083\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.09568 | − | 10.5580i | 0.397638 | − | 0.688730i | ||||
\(236\) | 6.47145 | + | 11.2089i | 0.421256 | + | 0.729636i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.1815 | + | 16.4623i | 1.50263 | + | 1.06709i | ||||
\(239\) | − | 26.5401i | − | 1.71674i | −0.513033 | − | 0.858369i | \(-0.671478\pi\) | ||
0.513033 | − | 0.858369i | \(-0.328522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7812 | + | 6.80189i | 0.758896 | + | 0.438149i | 0.828899 | − | 0.559398i | \(-0.188968\pi\) |
−0.0700035 | + | 0.997547i | \(0.522301\pi\) | |||||||
\(242\) | 41.3085 | + | 23.8495i | 2.65541 | + | 1.53310i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.9959i | 1.85627i | ||||||||
\(245\) | 5.64837 | − | 6.55278i | 0.360861 | − | 0.418642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.23630 | − | 14.2657i | −0.524063 | − | 0.907704i | ||||
\(248\) | 22.3271 | − | 38.6716i | 1.41777 | − | 2.45565i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 22.5878 | − | 13.0411i | 1.42858 | − | 0.824791i | ||||
\(251\) | 2.55060 | 0.160993 | 0.0804963 | − | 0.996755i | \(-0.474349\pi\) | ||||
0.0804963 | + | 0.996755i | \(0.474349\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.95822 | −0.563198 | ||||||||
\(254\) | −0.834376 | + | 0.481727i | −0.0523534 | + | 0.0302263i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.2727 | − | 28.1851i | 1.01704 | − | 1.76157i | ||||
\(257\) | −9.03011 | − | 15.6406i | −0.563283 | − | 0.975635i | −0.997207 | − | 0.0746853i | \(-0.976205\pi\) |
0.433924 | − | 0.900949i | \(-0.357129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.07031 | − | 0.760075i | −0.501464 | − | 0.0472288i | ||||
\(260\) | 15.4218i | 0.956422i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 45.0056 | + | 25.9840i | 2.78046 | + | 1.60530i | ||||
\(263\) | −6.98798 | − | 4.03451i | −0.430897 | − | 0.248779i | 0.268832 | − | 0.963187i | \(-0.413362\pi\) |
−0.699729 | + | 0.714409i | \(0.746696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.09474i | 0.312967i | ||||||||
\(266\) | −15.2377 | − | 33.2518i | −0.934281 | − | 2.03880i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.9243 | − | 44.9022i | −1.58358 | − | 2.74284i | ||||
\(269\) | 1.04758 | − | 1.81445i | 0.0638718 | − | 0.110629i | −0.832321 | − | 0.554294i | \(-0.812988\pi\) |
0.896193 | + | 0.443664i | \(0.146322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3066 | − | 12.3014i | 1.29428 | − | 0.747255i | 0.314873 | − | 0.949134i | \(-0.398038\pi\) |
0.979411 | + | 0.201879i | \(0.0647046\pi\) | |||||||
\(272\) | −22.7286 | −1.37812 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.74485 | 0.105410 | ||||||||
\(275\) | −16.5130 | + | 9.53376i | −0.995769 | + | 0.574907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.8495 | − | 18.7919i | 0.651883 | − | 1.12909i | −0.330782 | − | 0.943707i | \(-0.607313\pi\) |
0.982665 | − | 0.185388i | \(-0.0593541\pi\) | |||||||
\(278\) | −14.4427 | − | 25.0155i | −0.866216 | − | 1.50033i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.68351 | + | 17.8752i | −0.100609 | + | 1.06824i | ||||
\(281\) | 22.6315i | 1.35008i | 0.737781 | + | 0.675040i | \(0.235874\pi\) | ||||
−0.737781 | + | 0.675040i | \(0.764126\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.26370 | − | 4.77105i | −0.491226 | − | 0.283610i | 0.233857 | − | 0.972271i | \(-0.424865\pi\) |
−0.725083 | + | 0.688661i | \(0.758199\pi\) | |||||||
\(284\) | 16.8638 | + | 9.73630i | 1.00068 | + | 0.577743i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 40.5924i | − | 2.40028i | ||||||
\(287\) | 0.542342 | − | 0.763705i | 0.0320135 | − | 0.0450801i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.806602 | − | 1.39708i | −0.0474472 | − | 0.0821810i | ||||
\(290\) | 0.783667 | − | 1.35735i | 0.0460185 | − | 0.0797064i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −25.6287 | + | 14.7967i | −1.49981 | + | 0.865913i | ||||
\(293\) | −26.3348 | −1.53850 | −0.769248 | − | 0.638951i | \(-0.779369\pi\) | ||||
−0.769248 | + | 0.638951i | \(0.779369\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.80457 | −0.221511 | ||||||||
\(296\) | 14.5690 | − | 8.41142i | 0.846806 | − | 0.488904i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.436212 | − | 0.755542i | 0.0252691 | − | 0.0437674i | ||||
\(299\) | 2.42106 | + | 4.19340i | 0.140013 | + | 0.242510i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0977161 | − | 0.137600i | 0.00563226 | − | 0.00793112i | ||||
\(302\) | 11.5949i | 0.667213i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 25.3221 | + | 14.6197i | 1.45232 | + | 0.838498i | ||||
\(305\) | −7.38143 | − | 4.26167i | −0.422659 | − | 0.244023i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.81772i | − | 0.389108i | −0.980892 | − | 0.194554i | \(-0.937674\pi\) | ||
0.980892 | − | 0.194554i | \(-0.0623259\pi\) | |||||||
\(308\) | 5.72720 | − | 60.8102i | 0.326338 | − | 3.46498i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.5175 | + | 21.6810i | 0.710948 | + | 1.23140i | ||||
\(311\) | 13.4707 | − | 23.3320i | 0.763855 | − | 1.32304i | −0.176995 | − | 0.984212i | \(-0.556638\pi\) |
0.940850 | − | 0.338823i | \(-0.110029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0584 | − | 11.5807i | 1.13377 | − | 0.654581i | 0.188887 | − | 0.981999i | \(-0.439512\pi\) |
0.944880 | + | 0.327418i | \(0.106179\pi\) | |||||||
\(314\) | −3.07842 | −0.173725 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.39576 | 0.0785179 | ||||||||
\(317\) | −21.7091 | + | 12.5338i | −1.21931 | + | 0.703966i | −0.964769 | − | 0.263097i | \(-0.915256\pi\) |
−0.254536 | + | 0.967063i | \(0.581923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.39780 | + | 2.42106i | −0.0782617 | + | 0.135553i | ||||
\(320\) | 3.21602 | + | 5.57031i | 0.179781 | + | 0.311390i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.47911 | + | 9.77436i | 0.249611 | + | 0.544704i | ||||
\(323\) | 23.9452i | 1.33235i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.92562 | + | 5.15321i | 0.495105 | + | 0.285849i | ||||
\(326\) | 42.3086 | + | 24.4269i | 2.34326 | + | 1.35288i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.94395i | 0.107337i | ||||||||
\(329\) | 25.9840 | + | 2.44722i | 1.43254 | + | 0.134919i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.19788 | + | 7.27095i | 0.230736 | + | 0.399647i | 0.958025 | − | 0.286684i | \(-0.0925531\pi\) |
−0.727289 | + | 0.686332i | \(0.759220\pi\) | |||||||
\(332\) | −15.5410 | + | 26.9178i | −0.852922 | + | 1.47730i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −51.1013 | + | 29.5033i | −2.79614 | + | 1.61435i | ||||
\(335\) | 15.2409 | 0.832699 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.2902 | −1.54107 | −0.770533 | − | 0.637401i | \(-0.780010\pi\) | ||||
−0.770533 | + | 0.637401i | \(0.780010\pi\) | |||||||
\(338\) | 9.04140 | − | 5.22006i | 0.491788 | − | 0.283934i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 11.2089 | − | 19.4144i | 0.607887 | − | 1.05289i | ||||
\(341\) | −22.3271 | − | 38.6716i | −1.20908 | − | 2.09418i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7902 | + | 5.14868i | 0.960580 | + | 0.278003i | ||||
\(344\) | 0.350250i | 0.0188842i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.8475 | + | 14.9230i | 1.38957 | + | 0.802268i | ||||
\(347\) | −8.62860 | − | 4.98173i | −0.463208 | − | 0.267433i | 0.250184 | − | 0.968198i | \(-0.419509\pi\) |
−0.713392 | + | 0.700765i | \(0.752842\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22.4624i | − | 1.20239i | −0.799104 | − | 0.601193i | \(-0.794692\pi\) | ||
0.799104 | − | 0.601193i | \(-0.205308\pi\) | |||||||
\(350\) | 18.6588 | + | 13.2505i | 0.997356 | + | 0.708269i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.87691 | + | 10.1791i | 0.313240 | + | 0.542548i | ||||
\(353\) | 16.0326 | − | 27.7693i | 0.853330 | − | 1.47801i | −0.0248555 | − | 0.999691i | \(-0.507913\pi\) |
0.878186 | − | 0.478320i | \(-0.158754\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.95710 | + | 2.86198i | −0.263096 | + | 0.151898i | ||||
\(356\) | 14.4314 | 0.764863 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −55.7587 | −2.94694 | ||||||||
\(359\) | 10.2828 | − | 5.93680i | 0.542707 | − | 0.313332i | −0.203468 | − | 0.979082i | \(-0.565221\pi\) |
0.746175 | + | 0.665749i | \(0.231888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.90228 | − | 10.2231i | 0.310647 | − | 0.538056i | ||||
\(362\) | 11.0891 | + | 19.2069i | 0.582829 | + | 1.00949i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −30.0135 | + | 13.7537i | −1.57313 | + | 0.720889i | ||||
\(365\) | − | 8.69900i | − | 0.455326i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.7538 | − | 6.78607i | −0.613544 | − | 0.354230i | 0.160807 | − | 0.986986i | \(-0.448590\pi\) |
−0.774351 | + | 0.632756i | \(0.781924\pi\) | |||||||
\(368\) | −7.44343 | − | 4.29747i | −0.388016 | − | 0.224021i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.43162i | 0.490327i | ||||||||
\(371\) | −9.91520 | + | 4.54365i | −0.514771 | + | 0.235894i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.0858 | − | 26.1294i | −0.781113 | − | 1.35293i | −0.931294 | − | 0.364269i | \(-0.881319\pi\) |
0.150181 | − | 0.988659i | \(-0.452014\pi\) | |||||||
\(374\) | −29.5033 | + | 51.1013i | −1.52558 | + | 2.64238i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −46.9079 | + | 27.0823i | −2.41909 | + | 1.39666i | ||||
\(377\) | 1.51108 | 0.0778248 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.6770 | −0.651173 | −0.325587 | − | 0.945512i | \(-0.605562\pi\) | ||||
−0.325587 | + | 0.945512i | \(0.605562\pi\) | |||||||
\(380\) | −24.9758 | + | 14.4198i | −1.28123 | + | 0.739720i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.3111 | − | 24.7875i | 0.732219 | − | 1.26824i | ||||
\(383\) | 15.9932 | + | 27.7010i | 0.817214 | + | 1.41546i | 0.907727 | + | 0.419561i | \(0.137816\pi\) |
−0.0905126 | + | 0.995895i | \(0.528851\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.6386 | + | 10.3955i | 0.746051 | + | 0.529806i | ||||
\(386\) | 27.4543i | 1.39739i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.2264 | − | 9.36832i | −0.823771 | − | 0.475604i | ||||
\(389\) | −6.56158 | − | 3.78833i | −0.332685 | − | 0.192076i | 0.324347 | − | 0.945938i | \(-0.394855\pi\) |
−0.657033 | + | 0.753862i | \(0.728189\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.03869i | − | 0.355962i | ||||||
\(392\) | −36.2894 | + | 12.6652i | −1.83289 | + | 0.639691i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.6880 | + | 42.7609i | 1.24376 | + | 2.15426i | ||||
\(395\) | −0.205143 | + | 0.355317i | −0.0103218 | + | 0.0178780i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.824125 | + | 0.475809i | −0.0413617 | + | 0.0238802i | −0.520538 | − | 0.853838i | \(-0.674269\pi\) |
0.479177 | + | 0.877719i | \(0.340935\pi\) | |||||||
\(398\) | −21.5715 | −1.08128 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.2943 | −0.914713 | ||||||||
\(401\) | −18.2147 | + | 10.5162i | −0.909597 | + | 0.525156i | −0.880301 | − | 0.474415i | \(-0.842660\pi\) |
−0.0292953 | + | 0.999571i | \(0.509326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.0683 | + | 20.9029i | −0.601163 | + | 1.04125i | ||||
\(404\) | −19.2486 | − | 33.3396i | −0.957655 | − | 1.65871i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.34053 | + | 0.314617i | 0.165788 | + | 0.0156142i | ||||
\(407\) | − | 16.8228i | − | 0.833877i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.4472 | + | 10.0732i | 0.862709 | + | 0.498085i | 0.864919 | − | 0.501912i | \(-0.167370\pi\) |
−0.00220932 | + | 0.999998i | \(0.500703\pi\) | |||||||
\(410\) | −0.943850 | − | 0.544932i | −0.0466134 | − | 0.0269123i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.6745i | 0.870762i | ||||||||
\(413\) | −3.39304 | − | 7.40432i | −0.166960 | − | 0.364343i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.56827 | − | 7.91248i | −0.224248 | − | 0.388408i | ||||
\(416\) | 3.17660 | − | 5.50203i | 0.155746 | − | 0.269759i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 65.7399 | − | 37.9549i | 3.21544 | − | 1.85644i | ||||
\(419\) | −9.58929 | −0.468467 | −0.234234 | − | 0.972180i | \(-0.575258\pi\) | ||||
−0.234234 | + | 0.972180i | \(0.575258\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.61320 | 0.419782 | 0.209891 | − | 0.977725i | \(-0.432689\pi\) | ||||
0.209891 | + | 0.977725i | \(0.432689\pi\) | |||||||
\(422\) | 47.8081 | − | 27.6020i | 2.32726 | − | 1.34365i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.3176 | − | 19.6027i | 0.549632 | − | 0.951990i | ||||
\(425\) | −7.49090 | − | 12.9746i | −0.363362 | − | 0.629362i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.71092 | − | 18.1662i | 0.0827973 | − | 0.879123i | ||||
\(428\) | 43.3630i | 2.09603i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.170057 | − | 0.0981827i | −0.00820090 | − | 0.00473479i | ||||
\(431\) | −9.99885 | − | 5.77284i | −0.481628 | − | 0.278068i | 0.239467 | − | 0.970905i | \(-0.423027\pi\) |
−0.721095 | + | 0.692837i | \(0.756361\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 22.8707i | − | 1.09910i | −0.835462 | − | 0.549548i | \(-0.814800\pi\) | ||
0.835462 | − | 0.549548i | \(-0.185200\pi\) | |||||||
\(434\) | −31.0313 | + | 43.6970i | −1.48955 | + | 2.09752i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.268189 | + | 0.464517i | 0.0128439 | + | 0.0222464i | ||||
\(437\) | −4.52750 | + | 7.84186i | −0.216580 | + | 0.375127i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.218772 | − | 0.126308i | 0.0104414 | − | 0.00602837i | −0.494770 | − | 0.869024i | \(-0.664748\pi\) |
0.505212 | + | 0.862995i | \(0.331414\pi\) | |||||||
\(440\) | −37.2614 | −1.77637 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.8944 | 1.51706 | ||||||||
\(443\) | 18.8552 | − | 10.8860i | 0.895837 | − | 0.517212i | 0.0199896 | − | 0.999800i | \(-0.493637\pi\) |
0.875847 | + | 0.482589i | \(0.160303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.12106 | + | 3.67378i | −0.100548 | + | 0.174154i | ||||
\(446\) | 23.3465 | + | 40.4373i | 1.10549 | + | 1.91476i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.97259 | + | 11.2267i | −0.376670 | + | 0.530411i | ||||
\(449\) | − | 10.7904i | − | 0.509229i | −0.967043 | − | 0.254614i | \(-0.918051\pi\) | ||
0.967043 | − | 0.254614i | \(-0.0819485\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.68351 | + | 0.971976i | 0.0792735 | + | 0.0457686i | ||||
\(452\) | 8.37275 | + | 4.83401i | 0.393821 | + | 0.227373i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 35.3174i | 1.65753i | ||||||||
\(455\) | 0.909976 | − | 9.66192i | 0.0426603 | − | 0.452958i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.5110 | − | 30.3299i | −0.819130 | − | 1.41878i | −0.906324 | − | 0.422584i | \(-0.861123\pi\) |
0.0871937 | − | 0.996191i | \(-0.472210\pi\) | |||||||
\(458\) | −5.06984 | + | 8.78123i | −0.236898 | + | 0.410320i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.34165 | − | 4.23870i | 0.342306 | − | 0.197631i | ||||
\(461\) | −32.9471 | −1.53450 | −0.767249 | − | 0.641349i | \(-0.778375\pi\) | ||||
−0.767249 | + | 0.641349i | \(0.778375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.22641 | −0.242892 | −0.121446 | − | 0.992598i | \(-0.538753\pi\) | ||||
−0.121446 | + | 0.992598i | \(0.538753\pi\) | |||||||
\(464\) | −2.32288 | + | 1.34111i | −0.107837 | + | 0.0622596i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.67251 | − | 15.0212i | 0.401746 | − | 0.695845i | ||||
\(467\) | 10.8332 | + | 18.7637i | 0.501302 | + | 0.868281i | 0.999999 | + | 0.00150418i | \(0.000478796\pi\) |
−0.498697 | + | 0.866777i | \(0.666188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5923 | + | 29.6613i | 0.627635 | + | 1.36963i | ||||
\(470\) | − | 30.3670i | − | 1.40073i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.6386 | + | 8.45159i | 0.673795 | + | 0.389016i | ||||
\(473\) | 0.303325 | + | 0.175125i | 0.0139469 | + | 0.00805225i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.2735i | 0.884330i | ||||||||
\(476\) | 47.7800 | + | 4.50000i | 2.18999 | + | 0.206257i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −33.0539 | − | 57.2510i | −1.51185 | − | 2.61860i | ||||
\(479\) | 11.2154 | − | 19.4256i | 0.512444 | − | 0.887579i | −0.487452 | − | 0.873150i | \(-0.662073\pi\) |
0.999896 | − | 0.0144295i | \(-0.00459320\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.87487 | + | 4.54656i | −0.359063 | + | 0.207305i | ||||
\(482\) | 33.8852 | 1.54343 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 80.5125 | 3.65966 | ||||||||
\(485\) | 4.76975 | − | 2.75382i | 0.216583 | − | 0.125044i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0813 | + | 19.1934i | −0.502142 | + | 0.869736i | 0.497855 | + | 0.867260i | \(0.334121\pi\) |
−0.999997 | + | 0.00247528i | \(0.999212\pi\) | |||||||
\(488\) | 18.9340 | + | 32.7947i | 0.857103 | + | 1.48455i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.02334 | − | 21.1700i | 0.181756 | − | 0.956363i | ||||
\(491\) | − | 15.4543i | − | 0.697444i | −0.937226 | − | 0.348722i | \(-0.886616\pi\) | ||
0.937226 | − | 0.348722i | \(-0.113384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.90228 | − | 1.09828i | −0.0856746 | − | 0.0494642i | ||||
\(494\) | −35.5339 | − | 20.5155i | −1.59874 | − | 0.923035i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 42.8432i | − | 1.92372i | ||||||
\(497\) | −9.99080 | − | 7.09493i | −0.448148 | − | 0.318251i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.672508 | + | 1.16482i | 0.0301056 | + | 0.0521444i | 0.880686 | − | 0.473701i | \(-0.157082\pi\) |
−0.850580 | + | 0.525846i | \(0.823749\pi\) | |||||||
\(500\) | 22.0124 | − | 38.1267i | 0.984426 | − | 1.70508i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.50203 | − | 3.17660i | 0.245568 | − | 0.141779i | ||||
\(503\) | 18.1391 | 0.808781 | 0.404390 | − | 0.914586i | \(-0.367484\pi\) | ||||
0.404390 | + | 0.914586i | \(0.367484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.3163 | 0.503568 | ||||||||
\(506\) | −19.3242 | + | 11.1569i | −0.859067 | + | 0.495983i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.813121 | + | 1.40837i | −0.0360764 | + | 0.0624862i | ||||
\(509\) | 14.0919 | + | 24.4079i | 0.624612 | + | 1.08186i | 0.988616 | + | 0.150463i | \(0.0480764\pi\) |
−0.364003 | + | 0.931398i | \(0.618590\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.9297 | − | 7.75805i | 0.748926 | − | 0.343196i | ||||
\(512\) | − | 46.5767i | − | 2.05842i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −38.9586 | − | 22.4928i | −1.71839 | − | 0.992114i | ||||
\(515\) | −4.49938 | − | 2.59772i | −0.198266 | − | 0.114469i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 54.1646i | 2.38215i | ||||||||
\(518\) | −18.3555 | + | 8.41142i | −0.806494 | + | 0.369577i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.0703 | + | 17.4423i | 0.441612 | + | 0.764895i | ||||
\(521\) | −17.0915 | + | 29.6033i | −0.748792 | + | 1.29694i | 0.199611 | + | 0.979875i | \(0.436032\pi\) |
−0.948402 | + | 0.317070i | \(0.897301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.9157 | − | 18.4266i | 1.39558 | − | 0.805737i | 0.401652 | − | 0.915792i | \(-0.368436\pi\) |
0.993925 | + | 0.110055i | \(0.0351027\pi\) | |||||||
\(524\) | 87.7183 | 3.83199 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.0988 | −0.876351 | ||||||||
\(527\) | 30.3852 | − | 17.5429i | 1.32360 | − | 0.764181i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.1691 | + | 17.6135i | −0.442137 | + | 0.765803i | ||||
\(530\) | 6.34515 | + | 10.9901i | 0.275615 | + | 0.477380i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −50.3376 | − | 35.7471i | −2.18241 | − | 1.54983i | ||||
\(533\) | − | 1.05075i | − | 0.0455130i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.0388 | − | 6.37327i | −0.477250 | − | 0.275541i | ||||
\(536\) | −58.6414 | − | 33.8566i | −2.53292 | − | 1.46238i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 5.21874i | − | 0.224996i | ||||||
\(539\) | −7.17629 | + | 37.7602i | −0.309105 | + | 1.62645i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.2089 | + | 33.2708i | 0.825855 | + | 1.43042i | 0.901264 | + | 0.433269i | \(0.142640\pi\) |
−0.0754099 | + | 0.997153i | \(0.524027\pi\) | |||||||
\(542\) | 30.6410 | − | 53.0718i | 1.31615 | − | 2.27963i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.99797 | + | 4.61763i | −0.342910 | + | 0.197979i | ||||
\(545\) | −0.157669 | −0.00675378 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.9959 | 0.512909 | 0.256454 | − | 0.966556i | \(-0.417446\pi\) | ||||
0.256454 | + | 0.966556i | \(0.417446\pi\) | |||||||
\(548\) | 2.55060 | − | 1.47259i | 0.108956 | − | 0.0629060i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.7473 | + | 41.1315i | −1.01259 | + | 1.75385i | ||||
\(551\) | 1.41290 | + | 2.44722i | 0.0601916 | + | 0.104255i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.874459 | − | 0.0823580i | −0.0371858 | − | 0.00350222i | ||||
\(554\) | − | 54.0492i | − | 2.29633i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −42.2244 | − | 24.3783i | −1.79071 | − | 1.03387i | ||||
\(557\) | 7.53838 | + | 4.35228i | 0.319411 | + | 0.184412i | 0.651130 | − | 0.758966i | \(-0.274295\pi\) |
−0.331719 | + | 0.943378i | \(0.607629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.189318i | − | 0.00800729i | ||||||
\(560\) | 7.17629 | + | 15.6602i | 0.303253 | + | 0.661763i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.1860 | + | 48.8195i | 1.18895 | + | 2.05933i | ||||
\(563\) | −11.7183 | + | 20.2967i | −0.493868 | + | 0.855405i | −0.999975 | − | 0.00706612i | \(-0.997751\pi\) |
0.506107 | + | 0.862471i | \(0.331084\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.46117 | + | 1.42096i | −0.103542 | + | 0.0597801i | ||||
\(566\) | −23.7681 | −0.999047 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.4308 | 1.06705 | ||||||||
\(569\) | −29.7165 | + | 17.1569i | −1.24578 | + | 0.719253i | −0.970265 | − | 0.242044i | \(-0.922182\pi\) |
−0.275517 | + | 0.961296i | \(0.588849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7363 | + | 18.5958i | −0.449300 | + | 0.778210i | −0.998341 | − | 0.0575853i | \(-0.981660\pi\) |
0.549041 | + | 0.835796i | \(0.314993\pi\) | |||||||
\(572\) | −34.2586 | − | 59.3376i | −1.43242 | − | 2.48103i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.218772 | − | 2.32288i | 0.00913138 | − | 0.0969550i | ||||
\(575\) | − | 5.66545i | − | 0.236266i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7850 | − | 14.3096i | −1.03181 | − | 0.595718i | −0.114310 | − | 0.993445i | \(-0.536466\pi\) |
−0.917504 | + | 0.397727i | \(0.869799\pi\) | |||||||
\(578\) | −3.47993 | − | 2.00914i | −0.144746 | − | 0.0835691i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.64555i | − | 0.109850i | ||||||
\(581\) | 11.3249 | − | 15.9472i | 0.469835 | − | 0.661602i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3176 | − | 19.6027i | −0.468727 | − | 0.811860i | ||||
\(584\) | −19.3242 | + | 33.4706i | −0.799643 | + | 1.38502i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −56.8081 | + | 32.7982i | −2.34672 | + | 1.35488i | ||||
\(587\) | −18.5157 | −0.764224 | −0.382112 | − | 0.924116i | \(-0.624803\pi\) | ||||
−0.382112 | + | 0.924116i | \(0.624803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −45.1365 | −1.85982 | ||||||||
\(590\) | −8.20703 | + | 4.73833i | −0.337878 | + | 0.195074i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.07031 | − | 13.9782i | 0.331688 | − | 0.574500i | ||||
\(593\) | −9.37285 | − | 16.2343i | −0.384897 | − | 0.666661i | 0.606858 | − | 0.794810i | \(-0.292430\pi\) |
−0.991755 | + | 0.128149i | \(0.959096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.16802 | + | 11.5019i | −0.334856 | + | 0.471531i | ||||
\(596\) | − | 1.47259i | − | 0.0603197i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.4452 | + | 6.03053i | 0.427135 | + | 0.246607i | ||||
\(599\) | 22.4059 | + | 12.9360i | 0.915480 | + | 0.528552i | 0.882190 | − | 0.470893i | \(-0.156068\pi\) |
0.0332896 | + | 0.999446i | \(0.489402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.5735i | 0.594467i | 0.954805 | + | 0.297234i | \(0.0960640\pi\) | ||||
−0.954805 | + | 0.297234i | \(0.903936\pi\) | |||||||
\(602\) | 0.0394171 | − | 0.418522i | 0.00160652 | − | 0.0170577i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.78571 | + | 16.9494i | 0.398175 | + | 0.689659i | ||||
\(605\) | −11.8333 | + | 20.4959i | −0.481093 | + | 0.833278i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.2947 | − | 11.1398i | 0.783147 | − | 0.452150i | −0.0543974 | − | 0.998519i | \(-0.517324\pi\) |
0.837544 | + | 0.546369i | \(0.183990\pi\) | |||||||
\(608\) | 11.8808 | 0.481830 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.2305 | −0.859597 | ||||||||
\(611\) | 25.3548 | − | 14.6386i | 1.02574 | − | 0.592214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.6112 | + | 21.8432i | −0.509360 | + | 0.882238i | 0.490581 | + | 0.871396i | \(0.336785\pi\) |
−0.999941 | + | 0.0108424i | \(0.996549\pi\) | |||||||
\(614\) | −8.49100 | − | 14.7069i | −0.342669 | − | 0.593520i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −33.2309 | − | 72.5168i | −1.33891 | − | 2.92179i | ||||
\(617\) | − | 2.03655i | − | 0.0819882i | −0.999159 | − | 0.0409941i | \(-0.986948\pi\) | ||
0.999159 | − | 0.0409941i | \(-0.0130525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9099 | + | 19.0006i | 1.32276 | + | 0.763697i | 0.984168 | − | 0.177236i | \(-0.0567157\pi\) |
0.338593 | + | 0.940933i | \(0.390049\pi\) | |||||||
\(620\) | 36.5960 | + | 21.1287i | 1.46973 | + | 0.848549i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 67.1075i | − | 2.69076i | ||||||
\(623\) | −9.04140 | − | 0.851535i | −0.362236 | − | 0.0341160i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.21092 | − | 3.82943i | −0.0884368 | − | 0.153177i | ||||
\(626\) | 28.8460 | − | 49.9627i | 1.15292 | − | 1.99691i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.50000 | + | 2.59808i | −0.179570 | + | 0.103675i | ||||
\(629\) | 13.2181 | 0.527040 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.80457 | 0.111648 | 0.0558240 | − | 0.998441i | \(-0.482221\pi\) | ||||
0.0558240 | + | 0.998441i | \(0.482221\pi\) | |||||||
\(632\) | 1.57863 | − | 0.911420i | 0.0627944 | − | 0.0362544i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −31.2199 | + | 54.0744i | −1.23990 | + | 2.14757i | ||||
\(635\) | −0.239017 | − | 0.413990i | −0.00948510 | − | 0.0164287i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.6152 | − | 6.84585i | 0.777184 | − | 0.271242i | ||||
\(638\) | 6.96345i | 0.275686i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.4571 | + | 10.6562i | 0.729581 | + | 0.421224i | ||||
\(641\) | −1.62610 | − | 0.938829i | −0.0642271 | − | 0.0370815i | 0.467543 | − | 0.883971i | \(-0.345139\pi\) |
−0.531770 | + | 0.846889i | \(0.678473\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.5735i | − | 0.574724i | −0.957822 | − | 0.287362i | \(-0.907222\pi\) | ||
0.957822 | − | 0.287362i | \(-0.0927783\pi\) | |||||||
\(644\) | 14.7967 | + | 10.5079i | 0.583073 | + | 0.414067i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.8221 | + | 51.6534i | 1.17333 | + | 2.03227i | ||||
\(647\) | 18.2292 | − | 31.5739i | 0.716663 | − | 1.24130i | −0.245651 | − | 0.969358i | \(-0.579002\pi\) |
0.962315 | − | 0.271939i | \(-0.0876648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.6386 | − | 8.45159i | 0.574615 | − | 0.331754i | ||||
\(650\) | 25.6719 | 1.00693 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 82.4618 | 3.22945 | ||||||||
\(653\) | −13.0524 | + | 7.53580i | −0.510779 | + | 0.294898i | −0.733154 | − | 0.680063i | \(-0.761952\pi\) |
0.222375 | + | 0.974961i | \(0.428619\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.8924 | + | 22.3303i | −0.503748 | + | 0.872517i | ||||
\(656\) | 0.932559 | + | 1.61524i | 0.0364103 | + | 0.0630645i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 59.0992 | − | 27.0823i | 2.30393 | − | 1.05578i | ||||
\(659\) | 31.4670i | 1.22578i | 0.790168 | + | 0.612891i | \(0.209993\pi\) | ||||
−0.790168 | + | 0.612891i | \(0.790007\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.9099 | − | 6.87620i | −0.463242 | − | 0.267453i | 0.250164 | − | 0.968203i | \(-0.419515\pi\) |
−0.713407 | + | 0.700750i | \(0.752849\pi\) | |||||||
\(662\) | 18.1109 | + | 10.4564i | 0.703901 | + | 0.406398i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 40.5924i | 1.57529i | ||||||||
\(665\) | 16.4984 | − | 7.56042i | 0.639782 | − | 0.293181i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.415322 | − | 0.719359i | −0.0160813 | − | 0.0278537i | ||||
\(668\) | −49.7996 | + | 86.2554i | −1.92680 | + | 3.33732i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32.8769 | − | 18.9815i | 1.27015 | − | 0.733319i | ||||
\(671\) | 37.8680 | 1.46188 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.7448 | 0.452731 | 0.226365 | − | 0.974042i | \(-0.427316\pi\) | ||||
0.226365 | + | 0.974042i | \(0.427316\pi\) | |||||||
\(674\) | −61.0262 | + | 35.2335i | −2.35064 | + | 1.35714i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.81109 | − | 15.2613i | 0.338888 | − | 0.586971i | ||||
\(677\) | −10.8726 | − | 18.8320i | −0.417870 | − | 0.723772i | 0.577855 | − | 0.816139i | \(-0.303890\pi\) |
−0.995725 | + | 0.0923676i | \(0.970557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.61320 | + | 6.82679i | 0.368921 | + | 0.261988i | ||||
\(680\) | − | 29.2772i | − | 1.12273i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −96.3257 | − | 55.6136i | −3.68850 | − | 2.12956i | ||||
\(683\) | 11.1647 | + | 6.44593i | 0.427205 | + | 0.246647i | 0.698155 | − | 0.715947i | \(-0.254005\pi\) |
−0.270950 | + | 0.962593i | \(0.587338\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.865736i | 0.0330781i | ||||||||
\(686\) | 44.7885 | − | 11.0500i | 1.71003 | − | 0.421891i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.168023 | + | 0.291024i | 0.00640582 | + | 0.0110952i | ||||
\(689\) | −6.11742 | + | 10.5957i | −0.233055 | + | 0.403663i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.95303 | + | 5.16904i | −0.340589 | + | 0.196639i | −0.660533 | − | 0.750797i | \(-0.729669\pi\) |
0.319943 | + | 0.947437i | \(0.396336\pi\) | |||||||
\(692\) | 50.3781 | 1.91509 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.8176 | −0.942063 | ||||||||
\(695\) | 12.4119 | − | 7.16599i | 0.470809 | − | 0.271821i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.763705 | + | 1.32278i | −0.0289274 | + | 0.0501037i | ||||
\(698\) | −27.9754 | − | 48.4549i | −1.05889 | − | 1.83404i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 38.4582 | + | 3.62206i | 1.45358 | + | 0.136901i | ||||
\(701\) | 41.2056i | 1.55631i | 0.628071 | + | 0.778156i | \(0.283845\pi\) | ||||
−0.628071 | + | 0.778156i | \(0.716155\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.7264 | − | 8.50230i | −0.555417 | − | 0.320670i | ||||
\(704\) | −24.7481 | − | 14.2883i | −0.932730 | − | 0.538512i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 79.8701i | − | 3.00595i | ||||||
\(707\) | 10.0922 | + | 22.0233i | 0.379557 | + | 0.828273i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.3001 | − | 24.7685i | −0.537051 | − | 0.930199i | −0.999061 | − | 0.0433248i | \(-0.986205\pi\) |
0.462010 | − | 0.886875i | \(-0.347128\pi\) | |||||||
\(710\) | −7.12881 | + | 12.3475i | −0.267540 | + | 0.463392i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.3221 | − | 9.42356i | 0.611696 | − | 0.353163i | ||||
\(713\) | 13.2679 | 0.496886 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.1406 | 0.753216 | ||||||||
\(716\) | −81.5075 | + | 47.0584i | −3.04608 | + | 1.75865i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.7877 | − | 25.6131i | 0.551874 | − | 0.955873i | ||||
\(719\) | −0.881850 | − | 1.52741i | −0.0328875 | − | 0.0569627i | 0.849113 | − | 0.528211i | \(-0.177137\pi\) |
−0.882001 | + | 0.471248i | \(0.843804\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.04290 | − | 11.0733i | 0.0388395 | − | 0.412390i | ||||
\(722\) | − | 29.4036i | − | 1.09429i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 32.4198 | + | 18.7176i | 1.20487 | + | 0.695634i | ||||
\(725\) | −1.53115 | − | 0.884011i | −0.0568656 | − | 0.0328314i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0358i | 0.743088i | 0.928415 | + | 0.371544i | \(0.121171\pi\) | ||||
−0.928415 | + | 0.371544i | \(0.878829\pi\) | |||||||
\(728\) | −24.9645 | + | 35.1541i | −0.925248 | + | 1.30290i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.8340 | − | 18.7651i | −0.400985 | − | 0.694526i | ||||
\(731\) | −0.137600 | + | 0.238330i | −0.00508931 | + | 0.00881495i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.3574 | − | 7.71187i | 0.493365 | − | 0.284844i | −0.232604 | − | 0.972571i | \(-0.574725\pi\) |
0.725969 | + | 0.687727i | \(0.241391\pi\) | |||||||
\(734\) | −33.8064 | −1.24782 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.49236 | −0.128730 | ||||||||
\(737\) | −58.6414 | + | 33.8566i | −2.16008 | + | 1.24712i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.2284 | − | 28.1085i | 0.596973 | − | 1.03399i | −0.396292 | − | 0.918124i | \(-0.629703\pi\) |
0.993265 | − | 0.115863i | \(-0.0369634\pi\) | |||||||
\(740\) | 7.95995 | + | 13.7870i | 0.292614 | + | 0.506822i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15.7298 | + | 22.1500i | −0.577458 | + | 0.813153i | ||||
\(743\) | 7.52184i | 0.275950i | 0.990436 | + | 0.137975i | \(0.0440593\pi\) | ||||
−0.990436 | + | 0.137975i | \(0.955941\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.374875 | + | 0.216434i | 0.0137343 | + | 0.00792953i | ||||
\(746\) | −65.0847 | − | 37.5767i | −2.38292 | − | 1.37578i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 99.5991i | 3.64170i | ||||||||
\(749\) | 2.55866 | − | 27.1673i | 0.0934914 | − | 0.992671i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9232 | − | 22.3836i | −0.471573 | − | 0.816789i | 0.527898 | − | 0.849308i | \(-0.322980\pi\) |
−0.999471 | + | 0.0325190i | \(0.989647\pi\) | |||||||
\(752\) | −25.9840 | + | 45.0056i | −0.947539 | + | 1.64119i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.25964 | − | 1.88195i | 0.118709 | − | 0.0685366i | ||||
\(755\) | −5.75302 | −0.209374 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.5103 | 1.21795 | 0.608976 | − | 0.793188i | \(-0.291580\pi\) | ||||
0.608976 | + | 0.793188i | \(0.291580\pi\) | |||||||
\(758\) | −27.3462 | + | 15.7883i | −0.993258 | + | 0.573458i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.8320 | + | 32.6179i | −0.683108 | + | 1.18318i | ||||
\(761\) | −4.36501 | − | 7.56042i | −0.158232 | − | 0.274065i | 0.775999 | − | 0.630734i | \(-0.217246\pi\) |
−0.934231 | + | 0.356668i | \(0.883913\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.140614 | − | 0.306849i | −0.00509056 | − | 0.0111087i | ||||
\(764\) | − | 48.3122i | − | 1.74787i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 68.9995 | + | 39.8369i | 2.49305 | + | 1.43936i | ||||
\(767\) | −7.91248 | − | 4.56827i | −0.285703 | − | 0.164951i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.04495i | − | 0.181926i | −0.995854 | − | 0.0909628i | \(-0.971006\pi\) | ||
0.995854 | − | 0.0909628i | \(-0.0289944\pi\) | |||||||
\(770\) | 44.5246 | + | 4.19340i | 1.60455 | + | 0.151120i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.1705 | + | 40.1324i | 0.833924 | + | 1.44440i | ||||
\(773\) | 2.90140 | − | 5.02537i | 0.104356 | − | 0.180750i | −0.809119 | − | 0.587645i | \(-0.800055\pi\) |
0.913475 | + | 0.406895i | \(0.133388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.4571 | − | 14.1203i | 0.878525 | − | 0.507217i | ||||
\(776\) | −24.4697 | −0.878410 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.8724 | −0.676609 | ||||||||
\(779\) | 1.70170 | − | 0.982477i | 0.0609697 | − | 0.0352009i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.7154 | − | 22.0237i | 0.454993 | − | 0.788071i | ||||
\(782\) | −8.76620 | − | 15.1835i | −0.313479 | − | 0.542961i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −24.0772 | + | 27.9325i | −0.859901 | + | 0.997589i | ||||
\(785\) | − | 1.52741i | − | 0.0545156i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.3944 | − | 12.3521i | −0.762629 | − | 0.440304i | 0.0676098 | − | 0.997712i | \(-0.478463\pi\) |
−0.830239 | + | 0.557408i | \(0.811796\pi\) | |||||||
\(788\) | 72.1773 | + | 41.6716i | 2.57121 | + | 1.48449i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.02196i | 0.0363599i | ||||||||
\(791\) | −4.96037 | − | 3.52259i | −0.176370 | − | 0.125249i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2343 | − | 17.7263i | −0.363429 | − | 0.629478i | ||||
\(794\) | −1.18518 | + | 2.05278i | −0.0420603 | + | 0.0728506i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.5330 | + | 18.2056i | −1.11766 | + | 0.645280i | ||||
\(797\) | −4.39314 | −0.155613 | −0.0778064 | − | 0.996968i | \(-0.524792\pi\) | ||||
−0.0778064 | + | 0.996968i | \(0.524792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.5584 | −1.50561 | ||||||||
\(800\) | −6.43758 | + | 3.71674i | −0.227603 | + | 0.131407i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.1945 | + | 45.3702i | −0.924960 | + | 1.60208i | ||||
\(803\) | 19.3242 | + | 33.4706i | 0.681937 | + | 1.18115i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.84971 | + | 2.22239i | −0.170930 | + | 0.0783288i | ||||
\(806\) | 60.1208i | 2.11767i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −43.5409 | − | 25.1383i | −1.53176 | − | 0.884363i | ||||
\(809\) | 43.9347 | + | 25.3657i | 1.54466 | + | 0.891812i | 0.998535 | + | 0.0541105i | \(0.0172323\pi\) |
0.546129 | + | 0.837701i | \(0.316101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.8126i | 1.11709i | 0.829474 | + | 0.558546i | \(0.188641\pi\) | ||||
−0.829474 | + | 0.558546i | \(0.811359\pi\) | |||||||
\(812\) | 5.14868 | − | 2.35939i | 0.180683 | − | 0.0827982i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.9517 | − | 36.2894i | −0.734357 | − | 1.27194i | ||||
\(815\) | −12.1198 | + | 20.9921i | −0.424539 | + | 0.735323i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.306602 | − | 0.177017i | 0.0107267 | − | 0.00619304i | ||||
\(818\) | 50.1817 | 1.75456 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.83961 | −0.0642421 | ||||||||
\(821\) | 22.4679 | − | 12.9718i | 0.784135 | − | 0.452720i | −0.0537589 | − | 0.998554i | \(-0.517120\pi\) |
0.837894 | + | 0.545834i | \(0.183787\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0703069 | − | 0.121775i | 0.00245074 | − | 0.00424481i | −0.864797 | − | 0.502121i | \(-0.832553\pi\) |
0.867248 | + | 0.497876i | \(0.165887\pi\) | |||||||
\(824\) | 11.5413 | + | 19.9901i | 0.402060 | + | 0.696389i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.5409 | − | 11.7464i | −0.575530 | − | 0.408711i | ||||
\(827\) | − | 16.1772i | − | 0.562535i | −0.959629 | − | 0.281267i | \(-0.909245\pi\) | ||
0.959629 | − | 0.281267i | \(-0.0907548\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.8592 | − | 16.6619i | −1.00232 | − | 0.578690i | −0.0933864 | − | 0.995630i | \(-0.529769\pi\) |
−0.908934 | + | 0.416940i | \(0.863103\pi\) | |||||||
\(830\) | −19.7089 | − | 11.3789i | −0.684106 | − | 0.394969i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.4463i | 0.535505i | ||||||||
\(833\) | −29.6691 | − | 5.63858i | −1.02797 | − | 0.195365i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6386 | − | 25.3548i | −0.506589 | − | 0.877438i | ||||
\(836\) | 64.0652 | − | 110.964i | 2.21574 | − | 3.83778i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.6855 | + | 11.9428i | −0.714570 | + | 0.412557i | ||||
\(839\) | 21.4701 | 0.741230 | 0.370615 | − | 0.928787i | \(-0.379147\pi\) | ||||
0.370615 | + | 0.928787i | \(0.379147\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7408 | 0.991061 | ||||||||
\(842\) | 18.5800 | − | 10.7272i | 0.640309 | − | 0.369682i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 46.5903 | − | 80.6967i | 1.60370 | − | 2.77770i | ||||
\(845\) | 2.59002 | + | 4.48605i | 0.0890994 | + | 0.154325i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.4418 | − | 4.75069i | −1.73320 | − | 0.163236i | ||||
\(848\) | − | 21.7173i | − | 0.745774i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −32.3180 | − | 18.6588i | −1.10850 | − | 0.639992i | ||||
\(851\) | 4.32883 | + | 2.49925i | 0.148390 | + | 0.0856732i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.1842i | − | 0.862291i | −0.902282 | − | 0.431146i | \(-0.858110\pi\) | ||
0.902282 | − | 0.431146i | \(-0.141890\pi\) | |||||||
\(854\) | −18.9340 | − | 41.3180i | −0.647909 | − | 1.41387i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 28.3156 | + | 49.0440i | 0.967806 | + | 1.67629i | ||||
\(857\) | −14.5183 | + | 25.1464i | −0.495936 | + | 0.858986i | −0.999989 | − | 0.00468678i | \(-0.998508\pi\) |
0.504053 | + | 0.863673i | \(0.331841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.6386 | + | 11.9157i | −0.704179 | + | 0.406558i | −0.808902 | − | 0.587943i | \(-0.799938\pi\) |
0.104723 | + | 0.994501i | \(0.466604\pi\) | |||||||
\(860\) | −0.331451 | −0.0113024 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28.7587 | −0.979526 | ||||||||
\(863\) | 27.6069 | − | 15.9388i | 0.939749 | − | 0.542564i | 0.0498671 | − | 0.998756i | \(-0.484120\pi\) |
0.889881 | + | 0.456192i | \(0.150787\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.40432 | + | 12.8247i | −0.251754 | + | 0.436051i | ||||
\(866\) | −28.4839 | − | 49.3355i | −0.967922 | − | 1.67649i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.48248 | + | 90.0651i | −0.287914 | + | 3.05701i | ||||
\(869\) | − | 1.82284i | − | 0.0618356i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6970 | + | 18.3003i | 1.07401 | + | 0.620080i | ||||
\(872\) | 0.606650 | + | 0.350250i | 0.0205438 | + | 0.0118610i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 22.5548i | 0.762927i | ||||||||
\(875\) | −16.0407 | + | 22.5878i | −0.542274 | + | 0.763608i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.14061 | + | 1.97560i | 0.0385158 | + | 0.0667113i | 0.884641 | − | 0.466273i | \(-0.154404\pi\) |
−0.846125 | + | 0.532985i | \(0.821070\pi\) | |||||||
\(878\) | 0.314617 | − | 0.544932i | 0.0106178 | − | 0.0183906i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30.9607 | + | 17.8752i | −1.04368 | + | 0.602571i | ||||
\(881\) | −11.8808 | −0.400275 | −0.200137 | − | 0.979768i | \(-0.564139\pi\) | ||||
−0.200137 | + | 0.979768i | \(0.564139\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.7120 | −1.67294 | −0.836472 | − | 0.548010i | \(-0.815385\pi\) | ||||
−0.836472 | + | 0.548010i | \(0.815385\pi\) | |||||||
\(884\) | 46.6229 | − | 26.9178i | 1.56810 | − | 0.905343i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 27.1157 | − | 46.9657i | 0.910968 | − | 1.57784i | ||||
\(887\) | 6.17942 | + | 10.7031i | 0.207485 | + | 0.359374i | 0.950922 | − | 0.309432i | \(-0.100139\pi\) |
−0.743437 | + | 0.668806i | \(0.766806\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.592529 | − | 0.834376i | 0.0198728 | − | 0.0279841i | ||||
\(890\) | 10.5665i | 0.354191i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 68.2554 | + | 39.4072i | 2.28536 | + | 1.31945i | ||||
\(893\) | 47.4147 | + | 27.3749i | 1.58667 | + | 0.916065i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 27.6656i | − | 0.924760i | ||||||
\(896\) | −4.27812 | + | 45.4241i | −0.142922 | + | 1.51751i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.4387 | − | 23.2764i | −0.448454 | − | 0.776745i | ||||
\(899\) | 2.07026 | − | 3.58580i | 0.0690470 | − | 0.119593i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4023 | − | 8.89251i | 0.513124 | − | 0.296253i | ||||
\(902\) | 4.84212 | 0.161225 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.6262 | 0.419943 | ||||||||
\(905\) | −9.52980 | + | 5.50203i | −0.316781 | + | 0.182894i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8814 | − | 30.9715i | 0.593742 | − | 1.02839i | −0.399981 | − | 0.916523i | \(-0.630983\pi\) |
0.993723 | − | 0.111868i | \(-0.0356833\pi\) | |||||||
\(908\) | 29.8067 | + | 51.6267i | 0.989169 | + | 1.71329i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.0703 | − | 21.9755i | −0.333827 | − | 0.728482i | ||||
\(911\) | − | 47.9228i | − | 1.58775i | −0.608078 | − | 0.793877i | \(-0.708059\pi\) | ||
0.608078 | − | 0.793877i | \(-0.291941\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35.1541 | + | 20.2962i | 1.16343 | + | 0.671707i | ||||
\(914\) | −75.5478 | − | 43.6175i | −2.49890 | − | 1.44274i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.1151i | 0.565498i | ||||||||
\(917\) | −54.9563 | − | 5.17587i | −1.81482 | − | 0.170922i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.2408 | + | 29.8619i | 0.568721 | + | 0.985053i | 0.996693 | + | 0.0812614i | \(0.0258949\pi\) |
−0.427972 | + | 0.903792i | \(0.640772\pi\) | |||||||
\(920\) | 5.53566 | − | 9.58804i | 0.182505 | − | 0.316108i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −71.0718 | + | 41.0333i | −2.34063 | + | 1.35136i | ||||
\(923\) | −13.7459 | −0.452453 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6393 | 0.349817 | ||||||||
\(926\) | −11.2742 | + | 6.50914i | −0.370492 | + | 0.213903i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.544932 | + | 0.943850i | −0.0178883 | + | 0.0309834i | ||||
\(929\) | −29.1774 | − | 50.5368i | −0.957280 | − | 1.65806i | −0.729061 | − | 0.684449i | \(-0.760043\pi\) |
−0.228219 | − | 0.973610i | \(-0.573290\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.4277 | + | 25.3661i | 0.964453 | + | 0.831339i | ||||
\(932\) | − | 29.2772i | − | 0.959005i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 46.7378 | + | 26.9841i | 1.52931 | + | 0.882947i | ||||
\(935\) | −25.3548 | − | 14.6386i | −0.829189 | − | 0.478733i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29.8596i | − | 0.975471i | −0.872992 | − | 0.487735i | \(-0.837823\pi\) | ||
0.872992 | − | 0.487735i | \(-0.162177\pi\) | |||||||
\(938\) | 66.2618 | + | 47.0556i | 2.16352 | + | 1.53642i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −25.6287 | − | 44.3902i | −0.835916 | − | 1.44785i | ||||
\(941\) | 8.10885 | − | 14.0449i | 0.264341 | − | 0.457852i | −0.703050 | − | 0.711141i | \(-0.748179\pi\) |
0.967391 | + | 0.253289i | \(0.0815123\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.500215 | + | 0.288799i | −0.0162892 | + | 0.00940459i | ||||
\(944\) | 16.2177 | 0.527841 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.872425 | 0.0283650 | ||||||||
\(947\) | 24.4167 | − | 14.0970i | 0.793435 | − | 0.458090i | −0.0477355 | − | 0.998860i | \(-0.515200\pi\) |
0.841170 | + | 0.540770i | \(0.181867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4452 | − | 18.0916i | 0.339065 | − | 0.587278i | ||||
\(950\) | 24.0039 | + | 41.5759i | 0.778788 | + | 1.34890i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 56.9782 | − | 26.1103i | 1.84667 | − | 0.846240i | ||||
\(953\) | − | 56.3488i | − | 1.82532i | −0.408725 | − | 0.912658i | \(-0.634027\pi\) | ||
0.408725 | − | 0.912658i | \(-0.365973\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.2988 | + | 7.10069i | 0.397978 | + | 0.229773i | ||||
\(956\) | −96.6357 | − | 55.7926i | −3.12542 | − | 1.80446i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 55.8720i | − | 1.80514i | ||||||
\(959\) | −1.68487 | + | 0.772091i | −0.0544072 | + | 0.0249321i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.5683 | + | 30.4291i | 0.566718 | + | 0.981585i | ||||
\(962\) | −11.3249 | + | 19.6152i | −0.365128 | + | 0.632421i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 49.5330 | − | 28.5979i | 1.59535 | − | 0.921076i | ||||
\(965\) | −13.6219 | −0.438505 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0310 | 1.09436 | 0.547181 | − | 0.837014i | \(-0.315701\pi\) | ||||
0.547181 | + | 0.837014i | \(0.315701\pi\) | |||||||
\(968\) | 91.0606 | − | 52.5739i | 2.92680 | − | 1.68979i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.85939 | − | 11.8808i | 0.220242 | − | 0.381470i | ||||
\(971\) | 16.3472 | + | 28.3142i | 0.524608 | + | 0.908647i | 0.999589 | + | 0.0286515i | \(0.00912132\pi\) |
−0.474982 | + | 0.879996i | \(0.657545\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25.0155 | + | 17.7647i | 0.801960 | + | 0.569509i | ||||
\(974\) | 55.2041i | 1.76885i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 31.4647 | + | 18.1662i | 1.00716 | + | 0.581485i | ||||
\(977\) | −21.3583 | − | 12.3312i | −0.683313 | − | 0.394511i | 0.117789 | − | 0.993039i | \(-0.462419\pi\) |
−0.801102 | + | 0.598528i | \(0.795753\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 18.8471i | − | 0.602357i | ||||||
\(980\) | −11.9855 | − | 34.3416i | −0.382861 | − | 1.09700i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.2473 | − | 33.3373i | −0.614206 | − | 1.06384i | ||||
\(983\) | −8.89575 | + | 15.4079i | −0.283730 | + | 0.491435i | −0.972300 | − | 0.233734i | \(-0.924905\pi\) |
0.688570 | + | 0.725170i | \(0.258239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.2165 | + | 12.2494i | −0.676015 | + | 0.390297i | ||||
\(986\) | −5.47135 | −0.174243 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −69.2574 | −2.20337 | ||||||||
\(989\) | −0.0901258 | + | 0.0520341i | −0.00286583 | + | 0.00165459i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.9517 | − | 27.6292i | 0.506722 | − | 0.877669i | −0.493247 | − | 0.869889i | \(-0.664190\pi\) |
0.999970 | − | 0.00777992i | \(-0.00247645\pi\) | |||||||
\(992\) | −8.70420 | − | 15.0761i | −0.276359 | − | 0.478667i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −30.3879 | − | 2.86198i | −0.963846 | − | 0.0907766i | ||||
\(995\) | − | 10.7031i | − | 0.339310i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.7363 | − | 19.4777i | −1.06844 | − | 0.616864i | −0.140685 | − | 0.990054i | \(-0.544930\pi\) |
−0.927755 | + | 0.373191i | \(0.878264\pi\) | |||||||
\(998\) | 2.90140 | + | 1.67512i | 0.0918423 | + | 0.0530252i | ||||
\(999\) | 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 | 189.2.p.d.80.6 | yes | 12 | |
3.2 | odd | 2 | inner | 189.2.p.d.80.1 | yes | 12 | |
7.3 | odd | 6 | 1323.2.c.d.1322.12 | 12 | |||
7.4 | even | 3 | 1323.2.c.d.1322.11 | 12 | |||
7.5 | odd | 6 | inner | 189.2.p.d.26.1 | ✓ | 12 | |
9.2 | odd | 6 | 567.2.s.f.458.6 | 12 | |||
9.4 | even | 3 | 567.2.i.f.269.6 | 12 | |||
9.5 | odd | 6 | 567.2.i.f.269.1 | 12 | |||
9.7 | even | 3 | 567.2.s.f.458.1 | 12 | |||
21.5 | even | 6 | inner | 189.2.p.d.26.6 | yes | 12 | |
21.11 | odd | 6 | 1323.2.c.d.1322.2 | 12 | |||
21.17 | even | 6 | 1323.2.c.d.1322.1 | 12 | |||
63.5 | even | 6 | 567.2.s.f.26.1 | 12 | |||
63.40 | odd | 6 | 567.2.s.f.26.6 | 12 | |||
63.47 | even | 6 | 567.2.i.f.215.1 | 12 | |||
63.61 | odd | 6 | 567.2.i.f.215.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.p.d.26.1 | ✓ | 12 | 7.5 | odd | 6 | inner | |
189.2.p.d.26.6 | yes | 12 | 21.5 | even | 6 | inner | |
189.2.p.d.80.1 | yes | 12 | 3.2 | odd | 2 | inner | |
189.2.p.d.80.6 | yes | 12 | 1.1 | even | 1 | trivial | |
567.2.i.f.215.1 | 12 | 63.47 | even | 6 | |||
567.2.i.f.215.6 | 12 | 63.61 | odd | 6 | |||
567.2.i.f.269.1 | 12 | 9.5 | odd | 6 | |||
567.2.i.f.269.6 | 12 | 9.4 | even | 3 | |||
567.2.s.f.26.1 | 12 | 63.5 | even | 6 | |||
567.2.s.f.26.6 | 12 | 63.40 | odd | 6 | |||
567.2.s.f.458.1 | 12 | 9.7 | even | 3 | |||
567.2.s.f.458.6 | 12 | 9.2 | odd | 6 | |||
1323.2.c.d.1322.1 | 12 | 21.17 | even | 6 | |||
1323.2.c.d.1322.2 | 12 | 21.11 | odd | 6 | |||
1323.2.c.d.1322.11 | 12 | 7.4 | even | 3 | |||
1323.2.c.d.1322.12 | 12 | 7.3 | odd | 6 |