Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (of order \(3\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 263.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.263 |
Dual form | 637.2.g.f.373.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20711 | − | 2.09077i | 0.853553 | − | 1.47840i | −0.0244272 | − | 0.999702i | \(-0.507776\pi\) |
0.877981 | − | 0.478696i | \(-0.158890\pi\) | |||||||
\(3\) | −1.41421 | −0.816497 | −0.408248 | − | 0.912871i | \(-0.633860\pi\) | ||||
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(4\) | −1.91421 | − | 3.31552i | −0.957107 | − | 1.65776i | ||||
\(5\) | −1.91421 | − | 3.31552i | −0.856062 | − | 1.48274i | −0.875656 | − | 0.482935i | \(-0.839571\pi\) |
0.0195936 | − | 0.999808i | \(-0.493763\pi\) | |||||||
\(6\) | −1.70711 | + | 2.95680i | −0.696923 | + | 1.20711i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.41421 | −1.56066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −9.24264 | −2.92278 | ||||||||
\(11\) | 3.41421 | 1.02942 | 0.514712 | − | 0.857363i | \(-0.327899\pi\) | ||||
0.514712 | + | 0.857363i | \(0.327899\pi\) | |||||||
\(12\) | 2.70711 | + | 4.68885i | 0.781474 | + | 1.35355i | ||||
\(13\) | −3.50000 | + | 0.866025i | −0.970725 | + | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.70711 | + | 4.68885i | 0.698972 | + | 1.21065i | ||||
\(16\) | −1.50000 | + | 2.59808i | −0.375000 | + | 0.649519i | ||||
\(17\) | 0.0857864 | + | 0.148586i | 0.0208063 | + | 0.0360375i | 0.876241 | − | 0.481873i | \(-0.160043\pi\) |
−0.855435 | + | 0.517911i | \(0.826710\pi\) | |||||||
\(18\) | −1.20711 | + | 2.09077i | −0.284518 | + | 0.492799i | ||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | −7.32843 | + | 12.6932i | −1.63869 | + | 2.83829i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.12132 | − | 7.13834i | 0.878668 | − | 1.52190i | ||||
\(23\) | −0.707107 | + | 1.22474i | −0.147442 | + | 0.255377i | −0.930281 | − | 0.366847i | \(-0.880437\pi\) |
0.782839 | + | 0.622224i | \(0.213771\pi\) | |||||||
\(24\) | 6.24264 | 1.27427 | ||||||||
\(25\) | −4.82843 | + | 8.36308i | −0.965685 | + | 1.67262i | ||||
\(26\) | −2.41421 | + | 8.36308i | −0.473466 | + | 1.64014i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.91421 | − | 8.51167i | −0.912547 | − | 1.58058i | −0.810454 | − | 0.585802i | \(-0.800780\pi\) |
−0.102092 | − | 0.994775i | \(-0.532554\pi\) | |||||||
\(30\) | 13.0711 | 2.38644 | ||||||||
\(31\) | −2.70711 | + | 4.68885i | −0.486211 | + | 0.842142i | −0.999874 | − | 0.0158500i | \(-0.994955\pi\) |
0.513664 | + | 0.857992i | \(0.328288\pi\) | |||||||
\(32\) | −0.792893 | − | 1.37333i | −0.140165 | − | 0.242773i | ||||
\(33\) | −4.82843 | −0.840521 | ||||||||
\(34\) | 0.414214 | 0.0710370 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.91421 | + | 3.31552i | 0.319036 | + | 0.552586i | ||||
\(37\) | −3.74264 | + | 6.48244i | −0.615286 | + | 1.06571i | 0.375048 | + | 0.927005i | \(0.377626\pi\) |
−0.990334 | + | 0.138702i | \(0.955707\pi\) | |||||||
\(38\) | 7.24264 | − | 12.5446i | 1.17491 | − | 2.03501i | ||||
\(39\) | 4.94975 | − | 1.22474i | 0.792594 | − | 0.196116i | ||||
\(40\) | 8.44975 | + | 14.6354i | 1.33602 | + | 2.31406i | ||||
\(41\) | −2.91421 | − | 5.04757i | −0.455124 | − | 0.788297i | 0.543572 | − | 0.839363i | \(-0.317072\pi\) |
−0.998695 | + | 0.0510654i | \(0.983738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.292893 | + | 0.507306i | −0.0446658 | + | 0.0773634i | −0.887494 | − | 0.460819i | \(-0.847556\pi\) |
0.842828 | + | 0.538183i | \(0.180889\pi\) | |||||||
\(44\) | −6.53553 | − | 11.3199i | −0.985269 | − | 1.70654i | ||||
\(45\) | 1.91421 | + | 3.31552i | 0.285354 | + | 0.494248i | ||||
\(46\) | 1.70711 | + | 2.95680i | 0.251699 | + | 0.435956i | ||||
\(47\) | −3.82843 | − | 6.63103i | −0.558433 | − | 0.967235i | −0.997628 | − | 0.0688429i | \(-0.978069\pi\) |
0.439194 | − | 0.898392i | \(-0.355264\pi\) | |||||||
\(48\) | 2.12132 | − | 3.67423i | 0.306186 | − | 0.530330i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 11.6569 | + | 20.1903i | 1.64853 | + | 2.85533i | ||||
\(51\) | −0.121320 | − | 0.210133i | −0.0169882 | − | 0.0294245i | ||||
\(52\) | 9.57107 | + | 9.94655i | 1.32727 | + | 1.37934i | ||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | 6.82843 | − | 11.8272i | 0.929231 | − | 1.60948i | ||||
\(55\) | −6.53553 | − | 11.3199i | −0.881251 | − | 1.52637i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.48528 | −1.12390 | ||||||||
\(58\) | −23.7279 | −3.11563 | ||||||||
\(59\) | 0.878680 | + | 1.52192i | 0.114394 | + | 0.198137i | 0.917537 | − | 0.397649i | \(-0.130174\pi\) |
−0.803143 | + | 0.595786i | \(0.796841\pi\) | |||||||
\(60\) | 10.3640 | − | 17.9509i | 1.33798 | − | 2.31745i | ||||
\(61\) | 9.82843 | 1.25840 | 0.629201 | − | 0.777243i | \(-0.283382\pi\) | ||||
0.629201 | + | 0.777243i | \(0.283382\pi\) | |||||||
\(62\) | 6.53553 | + | 11.3199i | 0.830014 | + | 1.43763i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.82843 | −1.22855 | ||||||||
\(65\) | 9.57107 | + | 9.94655i | 1.18714 | + | 1.23372i | ||||
\(66\) | −5.82843 | + | 10.0951i | −0.717430 | + | 1.24262i | ||||
\(67\) | −4.24264 | −0.518321 | −0.259161 | − | 0.965834i | \(-0.583446\pi\) | ||||
−0.259161 | + | 0.965834i | \(0.583446\pi\) | |||||||
\(68\) | 0.328427 | − | 0.568852i | 0.0398276 | − | 0.0689835i | ||||
\(69\) | 1.00000 | − | 1.73205i | 0.120386 | − | 0.208514i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.171573 | − | 0.297173i | 0.0203620 | − | 0.0352679i | −0.855665 | − | 0.517530i | \(-0.826851\pi\) |
0.876027 | + | 0.482262i | \(0.160185\pi\) | |||||||
\(72\) | 4.41421 | 0.520220 | ||||||||
\(73\) | −0.328427 | + | 0.568852i | −0.0384395 | + | 0.0665791i | −0.884605 | − | 0.466341i | \(-0.845572\pi\) |
0.846166 | + | 0.532920i | \(0.178905\pi\) | |||||||
\(74\) | 9.03553 | + | 15.6500i | 1.05036 | + | 1.81928i | ||||
\(75\) | 6.82843 | − | 11.8272i | 0.788479 | − | 1.36569i | ||||
\(76\) | −11.4853 | − | 19.8931i | −1.31745 | − | 2.28189i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.41421 | − | 11.8272i | 0.386584 | − | 1.33916i | ||||
\(79\) | −5.12132 | − | 8.87039i | −0.576194 | − | 0.997997i | −0.995911 | − | 0.0903416i | \(-0.971204\pi\) |
0.419717 | − | 0.907655i | \(-0.362129\pi\) | |||||||
\(80\) | 11.4853 | 1.28409 | ||||||||
\(81\) | −5.00000 | −0.555556 | ||||||||
\(82\) | −14.0711 | −1.55389 | ||||||||
\(83\) | −13.0711 | −1.43474 | −0.717368 | − | 0.696694i | \(-0.754653\pi\) | ||||
−0.717368 | + | 0.696694i | \(0.754653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.328427 | − | 0.568852i | 0.0356229 | − | 0.0617007i | ||||
\(86\) | 0.707107 | + | 1.22474i | 0.0762493 | + | 0.132068i | ||||
\(87\) | 6.94975 | + | 12.0373i | 0.745091 | + | 1.29054i | ||||
\(88\) | −15.0711 | −1.60658 | ||||||||
\(89\) | 3.65685 | − | 6.33386i | 0.387626 | − | 0.671388i | −0.604504 | − | 0.796602i | \(-0.706629\pi\) |
0.992130 | + | 0.125215i | \(0.0399620\pi\) | |||||||
\(90\) | 9.24264 | 0.974260 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.41421 | 0.564471 | ||||||||
\(93\) | 3.82843 | − | 6.63103i | 0.396989 | − | 0.687606i | ||||
\(94\) | −18.4853 | −1.90661 | ||||||||
\(95\) | −11.4853 | − | 19.8931i | −1.17837 | − | 2.04099i | ||||
\(96\) | 1.12132 | + | 1.94218i | 0.114444 | + | 0.198223i | ||||
\(97\) | 2.58579 | − | 4.47871i | 0.262547 | − | 0.454744i | −0.704371 | − | 0.709832i | \(-0.748771\pi\) |
0.966918 | + | 0.255087i | \(0.0821042\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.41421 | −0.343141 | ||||||||
\(100\) | 36.9706 | 3.69706 | ||||||||
\(101\) | 3.34315 | 0.332655 | 0.166328 | − | 0.986071i | \(-0.446809\pi\) | ||||
0.166328 | + | 0.986071i | \(0.446809\pi\) | |||||||
\(102\) | −0.585786 | −0.0580015 | ||||||||
\(103\) | −7.00000 | − | 12.1244i | −0.689730 | − | 1.19465i | −0.971925 | − | 0.235291i | \(-0.924396\pi\) |
0.282194 | − | 0.959357i | \(-0.408938\pi\) | |||||||
\(104\) | 15.4497 | − | 3.82282i | 1.51497 | − | 0.374858i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.62132 | − | 6.27231i | −0.351734 | − | 0.609221i | ||||
\(107\) | 2.65685 | − | 4.60181i | 0.256848 | − | 0.444873i | −0.708548 | − | 0.705663i | \(-0.750649\pi\) |
0.965396 | + | 0.260789i | \(0.0839828\pi\) | |||||||
\(108\) | −10.8284 | − | 18.7554i | −1.04197 | − | 1.80474i | ||||
\(109\) | 1.17157 | − | 2.02922i | 0.112216 | − | 0.194364i | −0.804447 | − | 0.594024i | \(-0.797538\pi\) |
0.916664 | + | 0.399660i | \(0.130872\pi\) | |||||||
\(110\) | −31.5563 | −3.00878 | ||||||||
\(111\) | 5.29289 | − | 9.16756i | 0.502379 | − | 0.870146i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.15685 | − | 2.00373i | 0.108828 | − | 0.188495i | −0.806468 | − | 0.591278i | \(-0.798624\pi\) |
0.915296 | + | 0.402783i | \(0.131957\pi\) | |||||||
\(114\) | −10.2426 | + | 17.7408i | −0.959311 | + | 1.66158i | ||||
\(115\) | 5.41421 | 0.504878 | ||||||||
\(116\) | −18.8137 | + | 32.5863i | −1.74681 | + | 3.02556i | ||||
\(117\) | 3.50000 | − | 0.866025i | 0.323575 | − | 0.0800641i | ||||
\(118\) | 4.24264 | 0.390567 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −11.9497 | − | 20.6976i | −1.09086 | − | 1.88942i | ||||
\(121\) | 0.656854 | 0.0597140 | ||||||||
\(122\) | 11.8640 | − | 20.5490i | 1.07411 | − | 1.86042i | ||||
\(123\) | 4.12132 | + | 7.13834i | 0.371607 | + | 0.643642i | ||||
\(124\) | 20.7279 | 1.86142 | ||||||||
\(125\) | 17.8284 | 1.59462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.65685 | + | 8.06591i | 0.413229 | + | 0.715734i | 0.995241 | − | 0.0974468i | \(-0.0310676\pi\) |
−0.582012 | + | 0.813180i | \(0.697734\pi\) | |||||||
\(128\) | −10.2782 | + | 17.8023i | −0.908471 | + | 1.57352i | ||||
\(129\) | 0.414214 | − | 0.717439i | 0.0364695 | − | 0.0631670i | ||||
\(130\) | 32.3492 | − | 8.00436i | 2.83722 | − | 0.702029i | ||||
\(131\) | 0.656854 | + | 1.13770i | 0.0573896 | + | 0.0994017i | 0.893293 | − | 0.449475i | \(-0.148389\pi\) |
−0.835903 | + | 0.548877i | \(0.815056\pi\) | |||||||
\(132\) | 9.24264 | + | 16.0087i | 0.804469 | + | 1.39338i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −5.12132 | + | 8.87039i | −0.442415 | + | 0.766285i | ||||
\(135\) | −10.8284 | − | 18.7554i | −0.931963 | − | 1.61421i | ||||
\(136\) | −0.378680 | − | 0.655892i | −0.0324715 | − | 0.0562423i | ||||
\(137\) | 2.91421 | + | 5.04757i | 0.248978 | + | 0.431243i | 0.963243 | − | 0.268633i | \(-0.0865720\pi\) |
−0.714264 | + | 0.699876i | \(0.753239\pi\) | |||||||
\(138\) | −2.41421 | − | 4.18154i | −0.205512 | − | 0.355956i | ||||
\(139\) | −3.94975 | + | 6.84116i | −0.335013 | + | 0.580260i | −0.983487 | − | 0.180977i | \(-0.942074\pi\) |
0.648474 | + | 0.761237i | \(0.275407\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.41421 | + | 9.37769i | 0.455959 | + | 0.789744i | ||||
\(142\) | −0.414214 | − | 0.717439i | −0.0347600 | − | 0.0602061i | ||||
\(143\) | −11.9497 | + | 2.95680i | −0.999288 | + | 0.247260i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | −18.8137 | + | 32.5863i | −1.56239 | + | 2.70614i | ||||
\(146\) | 0.792893 | + | 1.37333i | 0.0656203 | + | 0.113658i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.6569 | 2.35558 | ||||||||
\(149\) | 3.00000 | 0.245770 | 0.122885 | − | 0.992421i | \(-0.460785\pi\) | ||||
0.122885 | + | 0.992421i | \(0.460785\pi\) | |||||||
\(150\) | −16.4853 | − | 28.5533i | −1.34602 | − | 2.33137i | ||||
\(151\) | 9.48528 | − | 16.4290i | 0.771901 | − | 1.33697i | −0.164618 | − | 0.986357i | \(-0.552639\pi\) |
0.936520 | − | 0.350615i | \(-0.114027\pi\) | |||||||
\(152\) | −26.4853 | −2.14824 | ||||||||
\(153\) | −0.0857864 | − | 0.148586i | −0.00693542 | − | 0.0120125i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.7279 | 1.66491 | ||||||||
\(156\) | −13.5355 | − | 14.0665i | −1.08371 | − | 1.12622i | ||||
\(157\) | 5.74264 | − | 9.94655i | 0.458313 | − | 0.793821i | −0.540559 | − | 0.841306i | \(-0.681787\pi\) |
0.998872 | + | 0.0474852i | \(0.0151207\pi\) | |||||||
\(158\) | −24.7279 | −1.96725 | ||||||||
\(159\) | −2.12132 | + | 3.67423i | −0.168232 | + | 0.291386i | ||||
\(160\) | −3.03553 | + | 5.25770i | −0.239980 | + | 0.415658i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.03553 | + | 10.4539i | −0.474196 | + | 0.821332i | ||||
\(163\) | 15.4142 | 1.20733 | 0.603667 | − | 0.797236i | \(-0.293706\pi\) | ||||
0.603667 | + | 0.797236i | \(0.293706\pi\) | |||||||
\(164\) | −11.1569 | + | 19.3242i | −0.871204 | + | 1.50897i | ||||
\(165\) | 9.24264 | + | 16.0087i | 0.719539 | + | 1.24628i | ||||
\(166\) | −15.7782 | + | 27.3286i | −1.22462 | + | 2.12111i | ||||
\(167\) | 9.36396 | + | 16.2189i | 0.724605 | + | 1.25505i | 0.959136 | + | 0.282944i | \(0.0913111\pi\) |
−0.234531 | + | 0.972109i | \(0.575356\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | −0.792893 | − | 1.37333i | −0.0608121 | − | 0.105330i | ||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | 2.24264 | 0.171000 | ||||||||
\(173\) | 18.1421 | 1.37932 | 0.689661 | − | 0.724133i | \(-0.257760\pi\) | ||||
0.689661 | + | 0.724133i | \(0.257760\pi\) | |||||||
\(174\) | 33.5563 | 2.54390 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.12132 | + | 8.87039i | −0.386034 | + | 0.668631i | ||||
\(177\) | −1.24264 | − | 2.15232i | −0.0934026 | − | 0.161778i | ||||
\(178\) | −8.82843 | − | 15.2913i | −0.661719 | − | 1.14613i | ||||
\(179\) | 5.65685 | 0.422813 | 0.211407 | − | 0.977398i | \(-0.432196\pi\) | ||||
0.211407 | + | 0.977398i | \(0.432196\pi\) | |||||||
\(180\) | 7.32843 | − | 12.6932i | 0.546229 | − | 0.946096i | ||||
\(181\) | −19.1421 | −1.42282 | −0.711412 | − | 0.702775i | \(-0.751944\pi\) | ||||
−0.711412 | + | 0.702775i | \(0.751944\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.8995 | −1.02748 | ||||||||
\(184\) | 3.12132 | − | 5.40629i | 0.230107 | − | 0.398557i | ||||
\(185\) | 28.6569 | 2.10689 | ||||||||
\(186\) | −9.24264 | − | 16.0087i | −0.677703 | − | 1.17382i | ||||
\(187\) | 0.292893 | + | 0.507306i | 0.0214185 | + | 0.0370979i | ||||
\(188\) | −14.6569 | + | 25.3864i | −1.06896 | + | 1.85149i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −55.4558 | −4.02319 | ||||||||
\(191\) | 7.75736 | 0.561303 | 0.280651 | − | 0.959810i | \(-0.409450\pi\) | ||||
0.280651 | + | 0.959810i | \(0.409450\pi\) | |||||||
\(192\) | 13.8995 | 1.00311 | ||||||||
\(193\) | −21.1421 | −1.52184 | −0.760922 | − | 0.648843i | \(-0.775253\pi\) | ||||
−0.760922 | + | 0.648843i | \(0.775253\pi\) | |||||||
\(194\) | −6.24264 | − | 10.8126i | −0.448195 | − | 0.776297i | ||||
\(195\) | −13.5355 | − | 14.0665i | −0.969300 | − | 1.00733i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.58579 | − | 7.94282i | −0.326724 | − | 0.565902i | 0.655136 | − | 0.755511i | \(-0.272611\pi\) |
−0.981860 | + | 0.189609i | \(0.939278\pi\) | |||||||
\(198\) | −4.12132 | + | 7.13834i | −0.292889 | + | 0.507299i | ||||
\(199\) | −9.48528 | − | 16.4290i | −0.672394 | − | 1.16462i | −0.977223 | − | 0.212213i | \(-0.931933\pi\) |
0.304830 | − | 0.952407i | \(-0.401400\pi\) | |||||||
\(200\) | 21.3137 | − | 36.9164i | 1.50711 | − | 2.61039i | ||||
\(201\) | 6.00000 | 0.423207 | ||||||||
\(202\) | 4.03553 | − | 6.98975i | 0.283939 | − | 0.491797i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.464466 | + | 0.804479i | −0.0325191 | + | 0.0563248i | ||||
\(205\) | −11.1569 | + | 19.3242i | −0.779229 | + | 1.34966i | ||||
\(206\) | −33.7990 | −2.35489 | ||||||||
\(207\) | 0.707107 | − | 1.22474i | 0.0491473 | − | 0.0851257i | ||||
\(208\) | 3.00000 | − | 10.3923i | 0.208013 | − | 0.720577i | ||||
\(209\) | 20.4853 | 1.41700 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.363961 | + | 0.630399i | 0.0250561 | + | 0.0433985i | 0.878282 | − | 0.478144i | \(-0.158690\pi\) |
−0.853225 | + | 0.521542i | \(0.825357\pi\) | |||||||
\(212\) | −11.4853 | −0.788812 | ||||||||
\(213\) | −0.242641 | + | 0.420266i | −0.0166255 | + | 0.0287962i | ||||
\(214\) | −6.41421 | − | 11.1097i | −0.438467 | − | 0.759446i | ||||
\(215\) | 2.24264 | 0.152947 | ||||||||
\(216\) | −24.9706 | −1.69903 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.82843 | − | 4.89898i | −0.191565 | − | 0.331801i | ||||
\(219\) | 0.464466 | − | 0.804479i | 0.0313857 | − | 0.0543616i | ||||
\(220\) | −25.0208 | + | 43.3373i | −1.68690 | + | 2.92180i | ||||
\(221\) | −0.428932 | − | 0.445759i | −0.0288531 | − | 0.0299850i | ||||
\(222\) | −12.7782 | − | 22.1324i | −0.857615 | − | 1.48543i | ||||
\(223\) | −1.00000 | − | 1.73205i | −0.0669650 | − | 0.115987i | 0.830599 | − | 0.556871i | \(-0.187998\pi\) |
−0.897564 | + | 0.440884i | \(0.854665\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.82843 | − | 8.36308i | 0.321895 | − | 0.557539i | ||||
\(226\) | −2.79289 | − | 4.83743i | −0.185780 | − | 0.321781i | ||||
\(227\) | 6.94975 | + | 12.0373i | 0.461271 | + | 0.798945i | 0.999025 | − | 0.0441573i | \(-0.0140603\pi\) |
−0.537754 | + | 0.843102i | \(0.680727\pi\) | |||||||
\(228\) | 16.2426 | + | 28.1331i | 1.07570 | + | 1.86316i | ||||
\(229\) | −2.24264 | − | 3.88437i | −0.148198 | − | 0.256686i | 0.782364 | − | 0.622822i | \(-0.214014\pi\) |
−0.930561 | + | 0.366136i | \(0.880681\pi\) | |||||||
\(230\) | 6.53553 | − | 11.3199i | 0.430940 | − | 0.746411i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 21.6924 | + | 37.5723i | 1.42418 | + | 2.46674i | ||||
\(233\) | 1.41421 | + | 2.44949i | 0.0926482 | + | 0.160471i | 0.908625 | − | 0.417614i | \(-0.137133\pi\) |
−0.815976 | + | 0.578085i | \(0.803800\pi\) | |||||||
\(234\) | 2.41421 | − | 8.36308i | 0.157822 | − | 0.546712i | ||||
\(235\) | −14.6569 | + | 25.3864i | −0.956108 | + | 1.65603i | ||||
\(236\) | 3.36396 | − | 5.82655i | 0.218975 | − | 0.379276i | ||||
\(237\) | 7.24264 | + | 12.5446i | 0.470460 | + | 0.814861i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.3848 | −0.801105 | −0.400552 | − | 0.916274i | \(-0.631182\pi\) | ||||
−0.400552 | + | 0.916274i | \(0.631182\pi\) | |||||||
\(240\) | −16.2426 | −1.04846 | ||||||||
\(241\) | 0.742641 | + | 1.28629i | 0.0478377 | + | 0.0828573i | 0.888953 | − | 0.457999i | \(-0.151434\pi\) |
−0.841115 | + | 0.540856i | \(0.818100\pi\) | |||||||
\(242\) | 0.792893 | − | 1.37333i | 0.0509691 | − | 0.0882811i | ||||
\(243\) | −9.89949 | −0.635053 | ||||||||
\(244\) | −18.8137 | − | 32.5863i | −1.20442 | − | 2.08612i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 19.8995 | 1.26875 | ||||||||
\(247\) | −21.0000 | + | 5.19615i | −1.33620 | + | 0.330623i | ||||
\(248\) | 11.9497 | − | 20.6976i | 0.758810 | − | 1.31430i | ||||
\(249\) | 18.4853 | 1.17146 | ||||||||
\(250\) | 21.5208 | − | 37.2751i | 1.36110 | − | 2.35749i | ||||
\(251\) | 5.48528 | − | 9.50079i | 0.346228 | − | 0.599684i | −0.639348 | − | 0.768917i | \(-0.720796\pi\) |
0.985576 | + | 0.169233i | \(0.0541291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.41421 | + | 4.18154i | −0.151780 | + | 0.262891i | ||||
\(254\) | 22.4853 | 1.41085 | ||||||||
\(255\) | −0.464466 | + | 0.804479i | −0.0290860 | + | 0.0503784i | ||||
\(256\) | 14.9853 | + | 25.9553i | 0.936580 | + | 1.62220i | ||||
\(257\) | −7.50000 | + | 12.9904i | −0.467837 | + | 0.810318i | −0.999325 | − | 0.0367485i | \(-0.988300\pi\) |
0.531487 | + | 0.847066i | \(0.321633\pi\) | |||||||
\(258\) | −1.00000 | − | 1.73205i | −0.0622573 | − | 0.107833i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.6569 | − | 50.7728i | 0.908980 | − | 3.14880i | ||||
\(261\) | 4.91421 | + | 8.51167i | 0.304182 | + | 0.526859i | ||||
\(262\) | 3.17157 | 0.195940 | ||||||||
\(263\) | 18.7279 | 1.15481 | 0.577407 | − | 0.816457i | \(-0.304065\pi\) | ||||
0.577407 | + | 0.816457i | \(0.304065\pi\) | |||||||
\(264\) | 21.3137 | 1.31177 | ||||||||
\(265\) | −11.4853 | −0.705535 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.17157 | + | 8.95743i | −0.316495 | + | 0.548186i | ||||
\(268\) | 8.12132 | + | 14.0665i | 0.496089 | + | 0.859251i | ||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | −52.2843 | −3.18192 | ||||||||
\(271\) | 3.46447 | − | 6.00063i | 0.210451 | − | 0.364512i | −0.741405 | − | 0.671058i | \(-0.765840\pi\) |
0.951856 | + | 0.306546i | \(0.0991733\pi\) | |||||||
\(272\) | −0.514719 | −0.0312094 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0711 | 0.850064 | ||||||||
\(275\) | −16.4853 | + | 28.5533i | −0.994100 | + | 1.72183i | ||||
\(276\) | −7.65685 | −0.460888 | ||||||||
\(277\) | 15.9853 | + | 27.6873i | 0.960462 | + | 1.66357i | 0.721341 | + | 0.692580i | \(0.243526\pi\) |
0.239122 | + | 0.970990i | \(0.423141\pi\) | |||||||
\(278\) | 9.53553 | + | 16.5160i | 0.571903 | + | 0.990566i | ||||
\(279\) | 2.70711 | − | 4.68885i | 0.162070 | − | 0.280714i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.514719 | −0.0307055 | −0.0153528 | − | 0.999882i | \(-0.504887\pi\) | ||||
−0.0153528 | + | 0.999882i | \(0.504887\pi\) | |||||||
\(282\) | 26.1421 | 1.55674 | ||||||||
\(283\) | −0.100505 | −0.00597441 | −0.00298720 | − | 0.999996i | \(-0.500951\pi\) | ||||
−0.00298720 | + | 0.999996i | \(0.500951\pi\) | |||||||
\(284\) | −1.31371 | −0.0779543 | ||||||||
\(285\) | 16.2426 | + | 28.1331i | 0.962131 | + | 1.66646i | ||||
\(286\) | −8.24264 | + | 28.5533i | −0.487398 | + | 1.68839i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.792893 | + | 1.37333i | 0.0467217 | + | 0.0809243i | ||||
\(289\) | 8.48528 | − | 14.6969i | 0.499134 | − | 0.864526i | ||||
\(290\) | 45.4203 | + | 78.6703i | 2.66717 | + | 4.61968i | ||||
\(291\) | −3.65685 | + | 6.33386i | −0.214369 | + | 0.371297i | ||||
\(292\) | 2.51472 | 0.147163 | ||||||||
\(293\) | 11.2279 | − | 19.4473i | 0.655942 | − | 1.13613i | −0.325714 | − | 0.945468i | \(-0.605605\pi\) |
0.981657 | − | 0.190657i | \(-0.0610618\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.36396 | − | 5.82655i | 0.195857 | − | 0.339235i | ||||
\(296\) | 16.5208 | − | 28.6149i | 0.960253 | − | 1.66321i | ||||
\(297\) | 19.3137 | 1.12070 | ||||||||
\(298\) | 3.62132 | − | 6.27231i | 0.209777 | − | 0.363345i | ||||
\(299\) | 1.41421 | − | 4.89898i | 0.0817861 | − | 0.283315i | ||||
\(300\) | −52.2843 | −3.01863 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22.8995 | − | 39.6631i | −1.31772 | − | 2.28235i | ||||
\(303\) | −4.72792 | −0.271612 | ||||||||
\(304\) | −9.00000 | + | 15.5885i | −0.516185 | + | 0.894059i | ||||
\(305\) | −18.8137 | − | 32.5863i | −1.07727 | − | 1.86589i | ||||
\(306\) | −0.414214 | −0.0236790 | ||||||||
\(307\) | −7.27208 | −0.415039 | −0.207520 | − | 0.978231i | \(-0.566539\pi\) | ||||
−0.207520 | + | 0.978231i | \(0.566539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.89949 | + | 17.1464i | 0.563163 | + | 0.975426i | ||||
\(310\) | 25.0208 | − | 43.3373i | 1.42109 | − | 2.46139i | ||||
\(311\) | 13.5355 | − | 23.4442i | 0.767530 | − | 1.32940i | −0.171369 | − | 0.985207i | \(-0.554819\pi\) |
0.938899 | − | 0.344194i | \(-0.111848\pi\) | |||||||
\(312\) | −21.8492 | + | 5.40629i | −1.23697 | + | 0.306071i | ||||
\(313\) | 7.00000 | + | 12.1244i | 0.395663 | + | 0.685309i | 0.993186 | − | 0.116543i | \(-0.0371814\pi\) |
−0.597522 | + | 0.801852i | \(0.703848\pi\) | |||||||
\(314\) | −13.8640 | − | 24.0131i | −0.782389 | − | 1.35514i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6066 | + | 33.9596i | −1.10296 | + | 1.91038i | ||||
\(317\) | −10.6716 | − | 18.4837i | −0.599375 | − | 1.03815i | −0.992913 | − | 0.118840i | \(-0.962082\pi\) |
0.393538 | − | 0.919308i | \(-0.371251\pi\) | |||||||
\(318\) | 5.12132 | + | 8.87039i | 0.287189 | + | 0.497427i | ||||
\(319\) | −16.7782 | − | 29.0607i | −0.939397 | − | 1.62708i | ||||
\(320\) | 18.8137 | + | 32.5863i | 1.05172 | + | 1.82163i | ||||
\(321\) | −3.75736 | + | 6.50794i | −0.209715 | + | 0.363238i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.514719 | + | 0.891519i | 0.0286397 | + | 0.0496054i | ||||
\(324\) | 9.57107 | + | 16.5776i | 0.531726 | + | 0.920976i | ||||
\(325\) | 9.65685 | − | 33.4523i | 0.535666 | − | 1.85560i | ||||
\(326\) | 18.6066 | − | 32.2276i | 1.03052 | − | 1.78492i | ||||
\(327\) | −1.65685 | + | 2.86976i | −0.0916242 | + | 0.158698i | ||||
\(328\) | 12.8640 | + | 22.2810i | 0.710293 | + | 1.23026i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 44.6274 | 2.45666 | ||||||||
\(331\) | 28.8701 | 1.58684 | 0.793421 | − | 0.608673i | \(-0.208298\pi\) | ||||
0.793421 | + | 0.608673i | \(0.208298\pi\) | |||||||
\(332\) | 25.0208 | + | 43.3373i | 1.37320 | + | 2.37844i | ||||
\(333\) | 3.74264 | − | 6.48244i | 0.205095 | − | 0.355236i | ||||
\(334\) | 45.2132 | 2.47396 | ||||||||
\(335\) | 8.12132 | + | 14.0665i | 0.443715 | + | 0.768537i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4853 | 0.734590 | 0.367295 | − | 0.930104i | \(-0.380284\pi\) | ||||
0.367295 | + | 0.930104i | \(0.380284\pi\) | |||||||
\(338\) | 1.20711 | − | 31.3616i | 0.0656580 | − | 1.70584i | ||||
\(339\) | −1.63604 | + | 2.83370i | −0.0888574 | + | 0.153906i | ||||
\(340\) | −2.51472 | −0.136380 | ||||||||
\(341\) | −9.24264 | + | 16.0087i | −0.500517 | + | 0.866921i | ||||
\(342\) | −7.24264 | + | 12.5446i | −0.391637 | + | 0.678335i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.29289 | − | 2.23936i | 0.0697081 | − | 0.120738i | ||||
\(345\) | −7.65685 | −0.412231 | ||||||||
\(346\) | 21.8995 | − | 37.9310i | 1.17732 | − | 2.03919i | ||||
\(347\) | 12.9497 | + | 22.4296i | 0.695179 | + | 1.20409i | 0.970120 | + | 0.242624i | \(0.0780082\pi\) |
−0.274941 | + | 0.961461i | \(0.588658\pi\) | |||||||
\(348\) | 26.6066 | − | 46.0840i | 1.42626 | − | 2.47036i | ||||
\(349\) | 6.65685 | + | 11.5300i | 0.356333 | + | 0.617187i | 0.987345 | − | 0.158586i | \(-0.0506935\pi\) |
−0.631012 | + | 0.775773i | \(0.717360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.7990 | + | 4.89898i | −1.05679 | + | 0.261488i | ||||
\(352\) | −2.70711 | − | 4.68885i | −0.144289 | − | 0.249916i | ||||
\(353\) | 0.171573 | 0.00913190 | 0.00456595 | − | 0.999990i | \(-0.498547\pi\) | ||||
0.00456595 | + | 0.999990i | \(0.498547\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | −1.31371 | −0.0697244 | ||||||||
\(356\) | −28.0000 | −1.48400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.82843 | − | 11.8272i | 0.360894 | − | 0.625086i | ||||
\(359\) | −8.48528 | − | 14.6969i | −0.447836 | − | 0.775675i | 0.550409 | − | 0.834895i | \(-0.314472\pi\) |
−0.998245 | + | 0.0592205i | \(0.981138\pi\) | |||||||
\(360\) | −8.44975 | − | 14.6354i | −0.445341 | − | 0.771353i | ||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −23.1066 | + | 40.0218i | −1.21446 | + | 2.10350i | ||||
\(363\) | −0.928932 | −0.0487563 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.51472 | 0.131626 | ||||||||
\(366\) | −16.7782 | + | 29.0607i | −0.877009 | + | 1.51902i | ||||
\(367\) | −3.27208 | −0.170801 | −0.0854005 | − | 0.996347i | \(-0.527217\pi\) | ||||
−0.0854005 | + | 0.996347i | \(0.527217\pi\) | |||||||
\(368\) | −2.12132 | − | 3.67423i | −0.110581 | − | 0.191533i | ||||
\(369\) | 2.91421 | + | 5.04757i | 0.151708 | + | 0.262766i | ||||
\(370\) | 34.5919 | − | 59.9149i | 1.79835 | − | 3.11483i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −29.3137 | −1.51984 | ||||||||
\(373\) | −24.4558 | −1.26628 | −0.633138 | − | 0.774039i | \(-0.718233\pi\) | ||||
−0.633138 | + | 0.774039i | \(0.718233\pi\) | |||||||
\(374\) | 1.41421 | 0.0731272 | ||||||||
\(375\) | −25.2132 | −1.30200 | ||||||||
\(376\) | 16.8995 | + | 29.2708i | 0.871525 | + | 1.50953i | ||||
\(377\) | 24.5711 | + | 25.5350i | 1.26547 | + | 1.31512i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.12132 | − | 7.13834i | −0.211698 | − | 0.366672i | 0.740548 | − | 0.672003i | \(-0.234566\pi\) |
−0.952246 | + | 0.305332i | \(0.901233\pi\) | |||||||
\(380\) | −43.9706 | + | 76.1592i | −2.25564 | + | 3.90689i | ||||
\(381\) | −6.58579 | − | 11.4069i | −0.337400 | − | 0.584394i | ||||
\(382\) | 9.36396 | − | 16.2189i | 0.479102 | − | 0.829829i | ||||
\(383\) | 14.0416 | 0.717494 | 0.358747 | − | 0.933435i | \(-0.383204\pi\) | ||||
0.358747 | + | 0.933435i | \(0.383204\pi\) | |||||||
\(384\) | 14.5355 | − | 25.1763i | 0.741763 | − | 1.28477i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.5208 | + | 44.2033i | −1.29898 | + | 2.24989i | ||||
\(387\) | 0.292893 | − | 0.507306i | 0.0148886 | − | 0.0257878i | ||||
\(388\) | −19.7990 | −1.00514 | ||||||||
\(389\) | 0.571068 | − | 0.989118i | 0.0289543 | − | 0.0501503i | −0.851185 | − | 0.524866i | \(-0.824116\pi\) |
0.880139 | + | 0.474715i | \(0.157449\pi\) | |||||||
\(390\) | −45.7487 | + | 11.3199i | −2.31658 | + | 0.573204i | ||||
\(391\) | −0.242641 | −0.0122709 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.928932 | − | 1.60896i | −0.0468584 | − | 0.0811612i | ||||
\(394\) | −22.1421 | −1.11550 | ||||||||
\(395\) | −19.6066 | + | 33.9596i | −0.986515 | + | 1.70869i | ||||
\(396\) | 6.53553 | + | 11.3199i | 0.328423 | + | 0.568845i | ||||
\(397\) | −38.6274 | −1.93865 | −0.969327 | − | 0.245774i | \(-0.920958\pi\) | ||||
−0.969327 | + | 0.245774i | \(0.920958\pi\) | |||||||
\(398\) | −45.7990 | −2.29570 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.4853 | − | 25.0892i | −0.724264 | − | 1.25446i | ||||
\(401\) | 15.3995 | − | 26.6727i | 0.769014 | − | 1.33197i | −0.169084 | − | 0.985602i | \(-0.554081\pi\) |
0.938098 | − | 0.346370i | \(-0.112586\pi\) | |||||||
\(402\) | 7.24264 | − | 12.5446i | 0.361230 | − | 0.625669i | ||||
\(403\) | 5.41421 | − | 18.7554i | 0.269701 | − | 0.934272i | ||||
\(404\) | −6.39949 | − | 11.0843i | −0.318387 | − | 0.551462i | ||||
\(405\) | 9.57107 | + | 16.5776i | 0.475590 | + | 0.823746i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7782 | + | 22.1324i | −0.633391 | + | 1.09706i | ||||
\(408\) | 0.535534 | + | 0.927572i | 0.0265129 | + | 0.0459217i | ||||
\(409\) | −5.98528 | − | 10.3668i | −0.295953 | − | 0.512606i | 0.679253 | − | 0.733904i | \(-0.262304\pi\) |
−0.975206 | + | 0.221298i | \(0.928971\pi\) | |||||||
\(410\) | 26.9350 | + | 46.6528i | 1.33023 | + | 2.30402i | ||||
\(411\) | −4.12132 | − | 7.13834i | −0.203290 | − | 0.352108i | ||||
\(412\) | −26.7990 | + | 46.4172i | −1.32029 | + | 2.28681i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.70711 | − | 2.95680i | −0.0838997 | − | 0.145319i | ||||
\(415\) | 25.0208 | + | 43.3373i | 1.22822 | + | 2.12735i | ||||
\(416\) | 3.96447 | + | 4.11999i | 0.194374 | + | 0.201999i | ||||
\(417\) | 5.58579 | − | 9.67487i | 0.273537 | − | 0.473780i | ||||
\(418\) | 24.7279 | − | 42.8300i | 1.20948 | − | 2.09488i | ||||
\(419\) | −9.77817 | − | 16.9363i | −0.477695 | − | 0.827392i | 0.521978 | − | 0.852959i | \(-0.325194\pi\) |
−0.999673 | + | 0.0255668i | \(0.991861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.51472 | 0.220034 | 0.110017 | − | 0.993930i | \(-0.464909\pi\) | ||||
0.110017 | + | 0.993930i | \(0.464909\pi\) | |||||||
\(422\) | 1.75736 | 0.0855469 | ||||||||
\(423\) | 3.82843 | + | 6.63103i | 0.186144 | + | 0.322412i | ||||
\(424\) | −6.62132 | + | 11.4685i | −0.321560 | + | 0.556958i | ||||
\(425\) | −1.65685 | −0.0803692 | ||||||||
\(426\) | 0.585786 | + | 1.01461i | 0.0283814 | + | 0.0491581i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −20.3431 | −0.983323 | ||||||||
\(429\) | 16.8995 | − | 4.18154i | 0.815915 | − | 0.201887i | ||||
\(430\) | 2.70711 | − | 4.68885i | 0.130548 | − | 0.226116i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | −8.48528 | + | 14.6969i | −0.408248 | + | 0.707107i | ||||
\(433\) | −0.257359 | + | 0.445759i | −0.0123679 | + | 0.0214218i | −0.872143 | − | 0.489251i | \(-0.837270\pi\) |
0.859775 | + | 0.510673i | \(0.170604\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 26.6066 | − | 46.0840i | 1.27569 | − | 2.20956i | ||||
\(436\) | −8.97056 | −0.429612 | ||||||||
\(437\) | −4.24264 | + | 7.34847i | −0.202953 | + | 0.351525i | ||||
\(438\) | −1.12132 | − | 1.94218i | −0.0535788 | − | 0.0928011i | ||||
\(439\) | 13.3640 | − | 23.1471i | 0.637827 | − | 1.10475i | −0.348082 | − | 0.937464i | \(-0.613167\pi\) |
0.985909 | − | 0.167285i | \(-0.0534999\pi\) | |||||||
\(440\) | 28.8492 | + | 49.9684i | 1.37533 | + | 2.38215i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.44975 | + | 0.358719i | −0.0689575 | + | 0.0170625i | ||||
\(443\) | −7.17157 | − | 12.4215i | −0.340732 | − | 0.590165i | 0.643837 | − | 0.765163i | \(-0.277341\pi\) |
−0.984569 | + | 0.174998i | \(0.944008\pi\) | |||||||
\(444\) | −40.5269 | −1.92332 | ||||||||
\(445\) | −28.0000 | −1.32733 | ||||||||
\(446\) | −4.82843 | −0.228633 | ||||||||
\(447\) | −4.24264 | −0.200670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.75736 | + | 13.4361i | −0.366092 | + | 0.634091i | −0.988951 | − | 0.148244i | \(-0.952638\pi\) |
0.622858 | + | 0.782335i | \(0.285971\pi\) | |||||||
\(450\) | −11.6569 | − | 20.1903i | −0.549509 | − | 0.951778i | ||||
\(451\) | −9.94975 | − | 17.2335i | −0.468515 | − | 0.811492i | ||||
\(452\) | −8.85786 | −0.416639 | ||||||||
\(453\) | −13.4142 | + | 23.2341i | −0.630255 | + | 1.09163i | ||||
\(454\) | 33.5563 | 1.57488 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 37.4558 | 1.75403 | ||||||||
\(457\) | 12.5000 | − | 21.6506i | 0.584725 | − | 1.01277i | −0.410184 | − | 0.912003i | \(-0.634536\pi\) |
0.994910 | − | 0.100771i | \(-0.0321310\pi\) | |||||||
\(458\) | −10.8284 | −0.505979 | ||||||||
\(459\) | 0.485281 | + | 0.840532i | 0.0226510 | + | 0.0392327i | ||||
\(460\) | −10.3640 | − | 17.9509i | −0.483222 | − | 0.836965i | ||||
\(461\) | −6.32843 | + | 10.9612i | −0.294744 | + | 0.510512i | −0.974925 | − | 0.222532i | \(-0.928568\pi\) |
0.680181 | + | 0.733044i | \(0.261901\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.7279 | −0.870360 | −0.435180 | − | 0.900343i | \(-0.643315\pi\) | ||||
−0.435180 | + | 0.900343i | \(0.643315\pi\) | |||||||
\(464\) | 29.4853 | 1.36882 | ||||||||
\(465\) | −29.3137 | −1.35939 | ||||||||
\(466\) | 6.82843 | 0.316321 | ||||||||
\(467\) | −4.29289 | − | 7.43551i | −0.198651 | − | 0.344074i | 0.749440 | − | 0.662072i | \(-0.230323\pi\) |
−0.948091 | + | 0.317998i | \(0.896989\pi\) | |||||||
\(468\) | −9.57107 | − | 9.94655i | −0.442423 | − | 0.459779i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 35.3848 | + | 61.2882i | 1.63218 | + | 2.82702i | ||||
\(471\) | −8.12132 | + | 14.0665i | −0.374211 | + | 0.648152i | ||||
\(472\) | −3.87868 | − | 6.71807i | −0.178531 | − | 0.309224i | ||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | 34.9706 | 1.60625 | ||||||||
\(475\) | −28.9706 | + | 50.1785i | −1.32926 | + | 2.30235i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.50000 | + | 2.59808i | −0.0686803 | + | 0.118958i | ||||
\(478\) | −14.9497 | + | 25.8937i | −0.683786 | + | 1.18435i | ||||
\(479\) | −38.3848 | −1.75385 | −0.876923 | − | 0.480632i | \(-0.840407\pi\) | ||||
−0.876923 | + | 0.480632i | \(0.840407\pi\) | |||||||
\(480\) | 4.29289 | − | 7.43551i | 0.195943 | − | 0.339383i | ||||
\(481\) | 7.48528 | − | 25.9298i | 0.341299 | − | 1.18230i | ||||
\(482\) | 3.58579 | 0.163328 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.25736 | − | 2.17781i | −0.0571527 | − | 0.0989914i | ||||
\(485\) | −19.7990 | −0.899026 | ||||||||
\(486\) | −11.9497 | + | 20.6976i | −0.542052 | + | 0.938861i | ||||
\(487\) | −10.4853 | − | 18.1610i | −0.475133 | − | 0.822955i | 0.524461 | − | 0.851435i | \(-0.324267\pi\) |
−0.999594 | + | 0.0284792i | \(0.990934\pi\) | |||||||
\(488\) | −43.3848 | −1.96394 | ||||||||
\(489\) | −21.7990 | −0.985784 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.6569 | − | 30.5826i | −0.796843 | − | 1.38017i | −0.921662 | − | 0.387993i | \(-0.873169\pi\) |
0.124820 | − | 0.992179i | \(-0.460165\pi\) | |||||||
\(492\) | 15.7782 | − | 27.3286i | 0.711335 | − | 1.23207i | ||||
\(493\) | 0.843146 | − | 1.46037i | 0.0379734 | − | 0.0657718i | ||||
\(494\) | −14.4853 | + | 50.1785i | −0.651724 | + | 2.25764i | ||||
\(495\) | 6.53553 | + | 11.3199i | 0.293750 | + | 0.508791i | ||||
\(496\) | −8.12132 | − | 14.0665i | −0.364658 | − | 0.631606i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 22.3137 | − | 38.6485i | 0.999901 | − | 1.73188i | ||||
\(499\) | 14.0208 | + | 24.2848i | 0.627658 | + | 1.08714i | 0.988020 | + | 0.154323i | \(0.0493196\pi\) |
−0.360363 | + | 0.932812i | \(0.617347\pi\) | |||||||
\(500\) | −34.1274 | − | 59.1104i | −1.52622 | − | 2.64350i | ||||
\(501\) | −13.2426 | − | 22.9369i | −0.591638 | − | 1.02475i | ||||
\(502\) | −13.2426 | − | 22.9369i | −0.591048 | − | 1.02373i | ||||
\(503\) | 16.7782 | − | 29.0607i | 0.748102 | − | 1.29575i | −0.200630 | − | 0.979667i | \(-0.564299\pi\) |
0.948731 | − | 0.316083i | \(-0.102368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.39949 | − | 11.0843i | −0.284774 | − | 0.493243i | ||||
\(506\) | 5.82843 | + | 10.0951i | 0.259105 | + | 0.448783i | ||||
\(507\) | −16.2635 | + | 8.57321i | −0.722285 | + | 0.380750i | ||||
\(508\) | 17.8284 | − | 30.8797i | 0.791009 | − | 1.37007i | ||||
\(509\) | 3.32843 | − | 5.76500i | 0.147530 | − | 0.255529i | −0.782784 | − | 0.622293i | \(-0.786201\pi\) |
0.930314 | + | 0.366764i | \(0.119534\pi\) | |||||||
\(510\) | 1.12132 | + | 1.94218i | 0.0496529 | + | 0.0860013i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426 | 1.38074 | ||||||||
\(513\) | 33.9411 | 1.49854 | ||||||||
\(514\) | 18.1066 | + | 31.3616i | 0.798648 | + | 1.38330i | ||||
\(515\) | −26.7990 | + | 46.4172i | −1.18090 | + | 2.04539i | ||||
\(516\) | −3.17157 | −0.139621 | ||||||||
\(517\) | −13.0711 | − | 22.6398i | −0.574865 | − | 0.995695i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.6569 | −1.12621 | ||||||||
\(520\) | −42.2487 | − | 43.9062i | −1.85273 | − | 1.92541i | ||||
\(521\) | 6.67157 | − | 11.5555i | 0.292287 | − | 0.506256i | −0.682063 | − | 0.731293i | \(-0.738917\pi\) |
0.974350 | + | 0.225037i | \(0.0722504\pi\) | |||||||
\(522\) | 23.7279 | 1.03854 | ||||||||
\(523\) | −8.48528 | + | 14.6969i | −0.371035 | + | 0.642652i | −0.989725 | − | 0.142983i | \(-0.954331\pi\) |
0.618690 | + | 0.785635i | \(0.287664\pi\) | |||||||
\(524\) | 2.51472 | − | 4.35562i | 0.109856 | − | 0.190276i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.6066 | − | 39.1558i | 0.985695 | − | 1.70727i | ||||
\(527\) | −0.928932 | −0.0404649 | ||||||||
\(528\) | 7.24264 | − | 12.5446i | 0.315195 | − | 0.545935i | ||||
\(529\) | 10.5000 | + | 18.1865i | 0.456522 | + | 0.790719i | ||||
\(530\) | −13.8640 | + | 24.0131i | −0.602212 | + | 1.04306i | ||||
\(531\) | −0.878680 | − | 1.52192i | −0.0381314 | − | 0.0660456i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.5711 | + | 15.1427i | 0.631143 | + | 0.655903i | ||||
\(534\) | 12.4853 | + | 21.6251i | 0.540291 | + | 0.935811i | ||||
\(535\) | −20.3431 | −0.879511 | ||||||||
\(536\) | 18.7279 | 0.808923 | ||||||||
\(537\) | −8.00000 | −0.345225 | ||||||||
\(538\) | 43.4558 | 1.87351 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −41.4558 | + | 71.8036i | −1.78398 | + | 3.08994i | ||||
\(541\) | −2.74264 | − | 4.75039i | −0.117915 | − | 0.204235i | 0.801026 | − | 0.598630i | \(-0.204288\pi\) |
−0.918941 | + | 0.394394i | \(0.870954\pi\) | |||||||
\(542\) | −8.36396 | − | 14.4868i | −0.359263 | − | 0.622262i | ||||
\(543\) | 27.0711 | 1.16173 | ||||||||
\(544\) | 0.136039 | − | 0.235626i | 0.00583262 | − | 0.0101024i | ||||
\(545\) | −8.97056 | −0.384257 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0711 | 0.644392 | 0.322196 | − | 0.946673i | \(-0.395579\pi\) | ||||
0.322196 | + | 0.946673i | \(0.395579\pi\) | |||||||
\(548\) | 11.1569 | − | 19.3242i | 0.476597 | − | 0.825491i | ||||
\(549\) | −9.82843 | −0.419467 | ||||||||
\(550\) | 39.7990 | + | 68.9339i | 1.69703 | + | 2.93935i | ||||
\(551\) | −29.4853 | − | 51.0700i | −1.25612 | − | 2.17566i | ||||
\(552\) | −4.41421 | + | 7.64564i | −0.187881 | + | 0.325420i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 77.1838 | 3.27922 | ||||||||
\(555\) | −40.5269 | −1.72027 | ||||||||
\(556\) | 30.2426 | 1.28257 | ||||||||
\(557\) | −10.3137 | −0.437006 | −0.218503 | − | 0.975836i | \(-0.570117\pi\) | ||||
−0.218503 | + | 0.975836i | \(0.570117\pi\) | |||||||
\(558\) | −6.53553 | − | 11.3199i | −0.276671 | − | 0.479209i | ||||
\(559\) | 0.585786 | − | 2.02922i | 0.0247761 | − | 0.0858270i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.414214 | − | 0.717439i | −0.0174881 | − | 0.0302903i | ||||
\(562\) | −0.621320 | + | 1.07616i | −0.0262088 | + | 0.0453950i | ||||
\(563\) | −9.94975 | − | 17.2335i | −0.419332 | − | 0.726304i | 0.576541 | − | 0.817069i | \(-0.304402\pi\) |
−0.995872 | + | 0.0907645i | \(0.971069\pi\) | |||||||
\(564\) | 20.7279 | − | 35.9018i | 0.872803 | − | 1.51174i | ||||
\(565\) | −8.85786 | −0.372653 | ||||||||
\(566\) | −0.121320 | + | 0.210133i | −0.00509947 | + | 0.00883255i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.757359 | + | 1.31178i | −0.0317781 | + | 0.0550413i | ||||
\(569\) | −6.58579 | + | 11.4069i | −0.276091 | + | 0.478203i | −0.970410 | − | 0.241464i | \(-0.922372\pi\) |
0.694319 | + | 0.719667i | \(0.255706\pi\) | |||||||
\(570\) | 78.4264 | 3.28492 | ||||||||
\(571\) | 2.48528 | − | 4.30463i | 0.104006 | − | 0.180143i | −0.809326 | − | 0.587360i | \(-0.800167\pi\) |
0.913332 | + | 0.407217i | \(0.133501\pi\) | |||||||
\(572\) | 32.6777 | + | 33.9596i | 1.36632 | + | 1.41992i | ||||
\(573\) | −10.9706 | −0.458302 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.82843 | − | 11.8272i | −0.284765 | − | 0.493228i | ||||
\(576\) | 9.82843 | 0.409518 | ||||||||
\(577\) | 18.1569 | − | 31.4486i | 0.755880 | − | 1.30922i | −0.189056 | − | 0.981966i | \(-0.560543\pi\) |
0.944936 | − | 0.327256i | \(-0.106124\pi\) | |||||||
\(578\) | −20.4853 | − | 35.4815i | −0.852075 | − | 1.47584i | ||||
\(579\) | 29.8995 | 1.24258 | ||||||||
\(580\) | 144.054 | 5.98151 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 8.82843 | + | 15.2913i | 0.365950 | + | 0.633844i | ||||
\(583\) | 5.12132 | − | 8.87039i | 0.212103 | − | 0.367374i | ||||
\(584\) | 1.44975 | − | 2.51104i | 0.0599910 | − | 0.103907i | ||||
\(585\) | −9.57107 | − | 9.94655i | −0.395715 | − | 0.411239i | ||||
\(586\) | −27.1066 | − | 46.9500i | −1.11976 | − | 1.93949i | ||||
\(587\) | 9.17157 | + | 15.8856i | 0.378551 | + | 0.655670i | 0.990852 | − | 0.134955i | \(-0.0430890\pi\) |
−0.612300 | + | 0.790625i | \(0.709756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.2426 | + | 28.1331i | −0.669266 | + | 1.15920i | ||||
\(590\) | −8.12132 | − | 14.0665i | −0.334349 | − | 0.579110i | ||||
\(591\) | 6.48528 | + | 11.2328i | 0.266769 | + | 0.462057i | ||||
\(592\) | −11.2279 | − | 19.4473i | −0.461465 | − | 0.799280i | ||||
\(593\) | 15.6421 | + | 27.0930i | 0.642346 | + | 1.11258i | 0.984908 | + | 0.173080i | \(0.0553719\pi\) |
−0.342562 | + | 0.939495i | \(0.611295\pi\) | |||||||
\(594\) | 23.3137 | − | 40.3805i | 0.956573 | − | 1.65683i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.74264 | − | 9.94655i | −0.235228 | − | 0.407426i | ||||
\(597\) | 13.4142 | + | 23.2341i | 0.549007 | + | 0.950908i | ||||
\(598\) | −8.53553 | − | 8.87039i | −0.349044 | − | 0.362737i | ||||
\(599\) | −19.8284 | + | 34.3438i | −0.810168 | + | 1.40325i | 0.102579 | + | 0.994725i | \(0.467291\pi\) |
−0.912746 | + | 0.408527i | \(0.866043\pi\) | |||||||
\(600\) | −30.1421 | + | 52.2077i | −1.23055 | + | 2.13137i | ||||
\(601\) | 18.4706 | + | 31.9920i | 0.753430 | + | 1.30498i | 0.946151 | + | 0.323725i | \(0.104935\pi\) |
−0.192721 | + | 0.981254i | \(0.561731\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.24264 | 0.172774 | ||||||||
\(604\) | −72.6274 | −2.95517 | ||||||||
\(605\) | −1.25736 | − | 2.17781i | −0.0511189 | − | 0.0885406i | ||||
\(606\) | −5.70711 | + | 9.88500i | −0.231835 | + | 0.401551i | ||||
\(607\) | −43.6569 | −1.77198 | −0.885989 | − | 0.463707i | \(-0.846519\pi\) | ||||
−0.885989 | + | 0.463707i | \(0.846519\pi\) | |||||||
\(608\) | −4.75736 | − | 8.23999i | −0.192936 | − | 0.334176i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −90.8406 | −3.67803 | ||||||||
\(611\) | 19.1421 | + | 19.8931i | 0.774408 | + | 0.804788i | ||||
\(612\) | −0.328427 | + | 0.568852i | −0.0132759 | + | 0.0229945i | ||||
\(613\) | 24.7990 | 1.00162 | 0.500811 | − | 0.865557i | \(-0.333035\pi\) | ||||
0.500811 | + | 0.865557i | \(0.333035\pi\) | |||||||
\(614\) | −8.77817 | + | 15.2042i | −0.354258 | + | 0.613593i | ||||
\(615\) | 15.7782 | − | 27.3286i | 0.636237 | − | 1.10200i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.42893 | − | 2.47498i | 0.0575266 | − | 0.0996391i | −0.835828 | − | 0.548992i | \(-0.815012\pi\) |
0.893355 | + | 0.449352i | \(0.148345\pi\) | |||||||
\(618\) | 47.7990 | 1.92276 | ||||||||
\(619\) | −5.22183 | + | 9.04447i | −0.209883 | + | 0.363528i | −0.951677 | − | 0.307099i | \(-0.900642\pi\) |
0.741795 | + | 0.670627i | \(0.233975\pi\) | |||||||
\(620\) | −39.6777 | − | 68.7237i | −1.59349 | − | 2.76001i | ||||
\(621\) | −4.00000 | + | 6.92820i | −0.160514 | + | 0.278019i | ||||
\(622\) | −32.6777 | − | 56.5994i | −1.31026 | − | 2.26943i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.24264 | + | 14.6969i | −0.169842 | + | 0.588348i | ||||
\(625\) | −9.98528 | − | 17.2950i | −0.399411 | − | 0.691801i | ||||
\(626\) | 33.7990 | 1.35088 | ||||||||
\(627\) | −28.9706 | −1.15697 | ||||||||
\(628\) | −43.9706 | −1.75462 | ||||||||
\(629\) | −1.28427 | −0.0512072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.1421 | − | 27.9590i | 0.642608 | − | 1.11303i | −0.342240 | − | 0.939613i | \(-0.611186\pi\) |
0.984848 | − | 0.173418i | \(-0.0554810\pi\) | |||||||
\(632\) | 22.6066 | + | 39.1558i | 0.899242 | + | 1.55753i | ||||
\(633\) | −0.514719 | − | 0.891519i | −0.0204582 | − | 0.0354347i | ||||
\(634\) | −51.5269 | −2.04640 | ||||||||
\(635\) | 17.8284 | − | 30.8797i | 0.707500 | − | 1.22543i | ||||
\(636\) | 16.2426 | 0.644063 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −81.0122 | −3.20730 | ||||||||
\(639\) | −0.171573 | + | 0.297173i | −0.00678732 | + | 0.0117560i | ||||
\(640\) | 78.6985 | 3.11083 | ||||||||
\(641\) | −12.3995 | − | 21.4766i | −0.489751 | − | 0.848273i | 0.510180 | − | 0.860068i | \(-0.329579\pi\) |
−0.999930 | + | 0.0117948i | \(0.996246\pi\) | |||||||
\(642\) | 9.07107 | + | 15.7116i | 0.358006 | + | 0.620085i | ||||
\(643\) | −24.4853 | + | 42.4098i | −0.965605 | + | 1.67248i | −0.257625 | + | 0.966245i | \(0.582940\pi\) |
−0.707980 | + | 0.706232i | \(0.750393\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.17157 | −0.124881 | ||||||||
\(646\) | 2.48528 | 0.0977821 | ||||||||
\(647\) | 5.31371 | 0.208903 | 0.104452 | − | 0.994530i | \(-0.466691\pi\) | ||||
0.104452 | + | 0.994530i | \(0.466691\pi\) | |||||||
\(648\) | 22.0711 | 0.867033 | ||||||||
\(649\) | 3.00000 | + | 5.19615i | 0.117760 | + | 0.203967i | ||||
\(650\) | −58.2843 | − | 60.5708i | −2.28610 | − | 2.37578i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.5061 | − | 51.1061i | −1.15555 | − | 2.00147i | ||||
\(653\) | 1.07107 | − | 1.85514i | 0.0419141 | − | 0.0725974i | −0.844307 | − | 0.535859i | \(-0.819988\pi\) |
0.886221 | + | 0.463262i | \(0.153321\pi\) | |||||||
\(654\) | 4.00000 | + | 6.92820i | 0.156412 | + | 0.270914i | ||||
\(655\) | 2.51472 | − | 4.35562i | 0.0982582 | − | 0.170188i | ||||
\(656\) | 17.4853 | 0.682686 | ||||||||
\(657\) | 0.328427 | − | 0.568852i | 0.0128132 | − | 0.0221930i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.65685 | + | 6.33386i | −0.142451 | + | 0.246732i | −0.928419 | − | 0.371535i | \(-0.878832\pi\) |
0.785968 | + | 0.618267i | \(0.212165\pi\) | |||||||
\(660\) | 35.3848 | − | 61.2882i | 1.37735 | − | 2.38564i | ||||
\(661\) | −4.85786 | −0.188949 | −0.0944745 | − | 0.995527i | \(-0.530117\pi\) | ||||
−0.0944745 | + | 0.995527i | \(0.530117\pi\) | |||||||
\(662\) | 34.8492 | − | 60.3607i | 1.35445 | − | 2.34598i | ||||
\(663\) | 0.606602 | + | 0.630399i | 0.0235585 | + | 0.0244827i | ||||
\(664\) | 57.6985 | 2.23914 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.03553 | − | 15.6500i | −0.350120 | − | 0.606425i | ||||
\(667\) | 13.8995 | 0.538191 | ||||||||
\(668\) | 35.8492 | − | 62.0927i | 1.38705 | − | 2.40244i | ||||
\(669\) | 1.41421 | + | 2.44949i | 0.0546767 | + | 0.0947027i | ||||
\(670\) | 39.2132 | 1.51494 | ||||||||
\(671\) | 33.5563 | 1.29543 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.7426 | − | 27.2671i | −0.606834 | − | 1.05107i | −0.991759 | − | 0.128120i | \(-0.959106\pi\) |
0.384925 | − | 0.922948i | \(-0.374227\pi\) | |||||||
\(674\) | 16.2782 | − | 28.1946i | 0.627012 | − | 1.08602i | ||||
\(675\) | −27.3137 | + | 47.3087i | −1.05131 | + | 1.82091i | ||||
\(676\) | −42.1127 | − | 26.5241i | −1.61972 | − | 1.02016i | ||||
\(677\) | 3.17157 | + | 5.49333i | 0.121893 | + | 0.211126i | 0.920514 | − | 0.390709i | \(-0.127770\pi\) |
−0.798621 | + | 0.601834i | \(0.794437\pi\) | |||||||
\(678\) | 3.94975 | + | 6.84116i | 0.151689 | + | 0.262733i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.44975 | + | 2.51104i | −0.0555953 | + | 0.0962938i | ||||
\(681\) | −9.82843 | − | 17.0233i | −0.376626 | − | 0.652336i | ||||
\(682\) | 22.3137 | + | 38.6485i | 0.854436 | + | 1.47993i | ||||
\(683\) | 8.65685 | + | 14.9941i | 0.331245 | + | 0.573734i | 0.982756 | − | 0.184905i | \(-0.0591979\pi\) |
−0.651511 | + | 0.758639i | \(0.725865\pi\) | |||||||
\(684\) | 11.4853 | + | 19.8931i | 0.439151 | + | 0.760631i | ||||
\(685\) | 11.1569 | − | 19.3242i | 0.426281 | − | 0.738341i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.17157 | + | 5.49333i | 0.121003 | + | 0.209583i | ||||
\(688\) | −0.878680 | − | 1.52192i | −0.0334993 | − | 0.0580226i | ||||
\(689\) | −3.00000 | + | 10.3923i | −0.114291 | + | 0.395915i | ||||
\(690\) | −9.24264 | + | 16.0087i | −0.351861 | + | 0.609442i | ||||
\(691\) | 18.9706 | − | 32.8580i | 0.721674 | − | 1.24998i | −0.238654 | − | 0.971105i | \(-0.576706\pi\) |
0.960328 | − | 0.278872i | \(-0.0899604\pi\) | |||||||
\(692\) | −34.7279 | − | 60.1505i | −1.32016 | − | 2.28658i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 62.5269 | 2.37349 | ||||||||
\(695\) | 30.2426 | 1.14717 | ||||||||
\(696\) | −30.6777 | − | 53.1353i | −1.16283 | − | 2.01409i | ||||
\(697\) | 0.500000 | − | 0.866025i | 0.0189389 | − | 0.0328031i | ||||
\(698\) | 32.1421 | 1.21660 | ||||||||
\(699\) | −2.00000 | − | 3.46410i | −0.0756469 | − | 0.131024i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.1421 | 1.59169 | 0.795843 | − | 0.605503i | \(-0.207028\pi\) | ||||
0.795843 | + | 0.605503i | \(0.207028\pi\) | |||||||
\(702\) | −13.6569 | + | 47.3087i | −0.515445 | + | 1.78555i | ||||
\(703\) | −22.4558 | + | 38.8947i | −0.846938 | + | 1.46694i | ||||
\(704\) | −33.5563 | −1.26470 | ||||||||
\(705\) | 20.7279 | − | 35.9018i | 0.780659 | − | 1.35214i | ||||
\(706\) | 0.207107 | − | 0.358719i | 0.00779457 | − | 0.0135006i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.75736 | + | 8.23999i | −0.178793 | + | 0.309678i | ||||
\(709\) | −27.6274 | −1.03757 | −0.518785 | − | 0.854905i | \(-0.673615\pi\) | ||||
−0.518785 | + | 0.854905i | \(0.673615\pi\) | |||||||
\(710\) | −1.58579 | + | 2.74666i | −0.0595135 | + | 0.103080i | ||||
\(711\) | 5.12132 | + | 8.87039i | 0.192065 | + | 0.332666i | ||||
\(712\) | −16.1421 | + | 27.9590i | −0.604952 | + | 1.04781i | ||||
\(713\) | −3.82843 | − | 6.63103i | −0.143376 | − | 0.248334i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.6777 | + | 33.9596i | 1.22208 | + | 1.27002i | ||||
\(716\) | −10.8284 | − | 18.7554i | −0.404677 | − | 0.700922i | ||||
\(717\) | 17.5147 | 0.654099 | ||||||||
\(718\) | −40.9706 | −1.52901 | ||||||||
\(719\) | −36.3848 | −1.35692 | −0.678462 | − | 0.734636i | \(-0.737353\pi\) | ||||
−0.678462 | + | 0.734636i | \(0.737353\pi\) | |||||||
\(720\) | −11.4853 | −0.428031 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.5208 | − | 35.5431i | 0.763706 | − | 1.32278i | ||||
\(723\) | −1.05025 | − | 1.81909i | −0.0390593 | − | 0.0676527i | ||||
\(724\) | 36.6421 | + | 63.4660i | 1.36179 | + | 2.35870i | ||||
\(725\) | 94.9117 | 3.52493 | ||||||||
\(726\) | −1.12132 | + | 1.94218i | −0.0416161 | + | 0.0720812i | ||||
\(727\) | −8.97056 | −0.332700 | −0.166350 | − | 0.986067i | \(-0.553198\pi\) | ||||
−0.166350 | + | 0.986067i | \(0.553198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 3.03553 | − | 5.25770i | 0.112350 | − | 0.194596i | ||||
\(731\) | −0.100505 | −0.00371731 | ||||||||
\(732\) | 26.6066 | + | 46.0840i | 0.983408 | + | 1.70331i | ||||
\(733\) | 10.5000 | + | 18.1865i | 0.387826 | + | 0.671735i | 0.992157 | − | 0.124999i | \(-0.0398927\pi\) |
−0.604331 | + | 0.796734i | \(0.706559\pi\) | |||||||
\(734\) | −3.94975 | + | 6.84116i | −0.145788 | + | 0.252512i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.24264 | 0.0826648 | ||||||||
\(737\) | −14.4853 | −0.533572 | ||||||||
\(738\) | 14.0711 | 0.517963 | ||||||||
\(739\) | 36.2843 | 1.33474 | 0.667369 | − | 0.744727i | \(-0.267420\pi\) | ||||
0.667369 | + | 0.744727i | \(0.267420\pi\) | |||||||
\(740\) | −54.8553 | − | 95.0122i | −2.01652 | − | 3.49272i | ||||
\(741\) | 29.6985 | − | 7.34847i | 1.09100 | − | 0.269953i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7990 | + | 41.2211i | 0.873100 | + | 1.51225i | 0.858773 | + | 0.512357i | \(0.171227\pi\) |
0.0143275 | + | 0.999897i | \(0.495439\pi\) | |||||||
\(744\) | −16.8995 | + | 29.2708i | −0.619566 | + | 1.07312i | ||||
\(745\) | −5.74264 | − | 9.94655i | −0.210394 | − | 0.364413i | ||||
\(746\) | −29.5208 | + | 51.1316i | −1.08083 | + | 1.87206i | ||||
\(747\) | 13.0711 | 0.478245 | ||||||||
\(748\) | 1.12132 | − | 1.94218i | 0.0409995 | − | 0.0710133i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −30.4350 | + | 52.7150i | −1.11133 | + | 1.92488i | ||||
\(751\) | −6.77817 | + | 11.7401i | −0.247339 | + | 0.428404i | −0.962787 | − | 0.270263i | \(-0.912889\pi\) |
0.715448 | + | 0.698666i | \(0.246223\pi\) | |||||||
\(752\) | 22.9706 | 0.837650 | ||||||||
\(753\) | −7.75736 | + | 13.4361i | −0.282694 | + | 0.489640i | ||||
\(754\) | 83.0477 | − | 20.5490i | 3.02442 | − | 0.748350i | ||||
\(755\) | −72.6274 | −2.64318 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7279 | + | 18.5813i | 0.389913 | + | 0.675349i | 0.992437 | − | 0.122751i | \(-0.0391718\pi\) |
−0.602525 | + | 0.798100i | \(0.705838\pi\) | |||||||
\(758\) | −19.8995 | −0.722782 | ||||||||
\(759\) | 3.41421 | − | 5.91359i | 0.123928 | − | 0.214650i | ||||
\(760\) | 50.6985 | + | 87.8124i | 1.83903 | + | 3.18529i | ||||
\(761\) | 46.1421 | 1.67265 | 0.836326 | − | 0.548233i | \(-0.184699\pi\) | ||||
0.836326 | + | 0.548233i | \(0.184699\pi\) | |||||||
\(762\) | −31.7990 | −1.15196 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −14.8492 | − | 25.7196i | −0.537227 | − | 0.930504i | ||||
\(765\) | −0.328427 | + | 0.568852i | −0.0118743 | + | 0.0205669i | ||||
\(766\) | 16.9497 | − | 29.3578i | 0.612419 | − | 1.06074i | ||||
\(767\) | −4.39340 | − | 4.56575i | −0.158636 | − | 0.164860i | ||||
\(768\) | −21.1924 | − | 36.7063i | −0.764714 | − | 1.32452i | ||||
\(769\) | −0.727922 | − | 1.26080i | −0.0262495 | − | 0.0454655i | 0.852602 | − | 0.522560i | \(-0.175023\pi\) |
−0.878852 | + | 0.477095i | \(0.841690\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6066 | − | 18.3712i | 0.381987 | − | 0.661622i | ||||
\(772\) | 40.4706 | + | 70.0971i | 1.45657 | + | 2.52285i | ||||
\(773\) | −8.82843 | − | 15.2913i | −0.317536 | − | 0.549989i | 0.662437 | − | 0.749118i | \(-0.269522\pi\) |
−0.979973 | + | 0.199128i | \(0.936189\pi\) | |||||||
\(774\) | −0.707107 | − | 1.22474i | −0.0254164 | − | 0.0440225i | ||||
\(775\) | −26.1421 | − | 45.2795i | −0.939053 | − | 1.62649i | ||||
\(776\) | −11.4142 | + | 19.7700i | −0.409746 | + | 0.709702i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.37868 | − | 2.38794i | −0.0494281 | − | 0.0856119i | ||||
\(779\) | −17.4853 | − | 30.2854i | −0.626475 | − | 1.08509i | ||||
\(780\) | −20.7279 | + | 71.8036i | −0.742179 | + | 2.57098i | ||||
\(781\) | 0.585786 | − | 1.01461i | 0.0209611 | − | 0.0363057i | ||||
\(782\) | −0.292893 | + | 0.507306i | −0.0104738 | + | 0.0181412i | ||||
\(783\) | −27.7990 | − | 48.1493i | −0.993455 | − | 1.72071i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43.9706 | −1.56938 | ||||||||
\(786\) | −4.48528 | −0.159985 | ||||||||
\(787\) | −2.94975 | − | 5.10911i | −0.105147 | − | 0.182120i | 0.808651 | − | 0.588288i | \(-0.200198\pi\) |
−0.913798 | + | 0.406168i | \(0.866865\pi\) | |||||||
\(788\) | −17.5563 | + | 30.4085i | −0.625419 | + | 1.08326i | ||||
\(789\) | −26.4853 | −0.942901 | ||||||||
\(790\) | 47.3345 | + | 81.9858i | 1.68409 | + | 2.91692i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 15.0711 | 0.535527 | ||||||||
\(793\) | −34.3995 | + | 8.51167i | −1.22156 | + | 0.302258i | ||||
\(794\) | −46.6274 | + | 80.7611i | −1.65475 | + | 2.86610i | ||||
\(795\) | 16.2426 | 0.576067 | ||||||||
\(796\) | −36.3137 | + | 62.8972i | −1.28711 | + | 2.22933i | ||||
\(797\) | −5.07107 | + | 8.78335i | −0.179626 | + | 0.311122i | −0.941753 | − | 0.336306i | \(-0.890822\pi\) |
0.762126 | + | 0.647429i | \(0.224156\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.656854 | − | 1.13770i | 0.0232378 | − | 0.0402491i | ||||
\(800\) | 15.3137 | 0.541421 | ||||||||
\(801\) | −3.65685 | + | 6.33386i | −0.129209 | + | 0.223796i | ||||
\(802\) | −37.1777 | − | 64.3936i | −1.31279 | − | 2.27382i | ||||
\(803\) | −1.12132 | + | 1.94218i | −0.0395705 | + | 0.0685382i | ||||
\(804\) | −11.4853 | − | 19.8931i | −0.405055 | − | 0.701575i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.6777 | − | 33.9596i | −1.15102 | − | 1.19618i | ||||
\(807\) | −12.7279 | − | 22.0454i | −0.448044 | − | 0.776035i | ||||
\(808\) | −14.7574 | −0.519162 | ||||||||
\(809\) | 6.85786 | 0.241110 | 0.120555 | − | 0.992707i | \(-0.461533\pi\) | ||||
0.120555 | + | 0.992707i | \(0.461533\pi\) | |||||||
\(810\) | 46.2132 | 1.62377 | ||||||||
\(811\) | 34.1838 | 1.20035 | 0.600177 | − | 0.799867i | \(-0.295097\pi\) | ||||
0.600177 | + | 0.799867i | \(0.295097\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.89949 | + | 8.48617i | −0.171833 | + | 0.297623i | ||||
\(814\) | 30.8492 | + | 53.4325i | 1.08127 | + | 1.87281i | ||||
\(815\) | −29.5061 | − | 51.1061i | −1.03355 | − | 1.79017i | ||||
\(816\) | 0.727922 | 0.0254824 | ||||||||
\(817\) | −1.75736 | + | 3.04384i | −0.0614822 | + | 0.106490i | ||||
\(818\) | −28.8995 | −1.01045 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 85.4264 | 2.98322 | ||||||||
\(821\) | −13.9706 | + | 24.1977i | −0.487576 | + | 0.844506i | −0.999898 | − | 0.0142871i | \(-0.995452\pi\) |
0.512322 | + | 0.858793i | \(0.328785\pi\) | |||||||
\(822\) | −19.8995 | −0.694075 | ||||||||
\(823\) | 1.65685 | + | 2.86976i | 0.0577543 | + | 0.100033i | 0.893457 | − | 0.449149i | \(-0.148273\pi\) |
−0.835703 | + | 0.549182i | \(0.814939\pi\) | |||||||
\(824\) | 30.8995 | + | 53.5195i | 1.07643 | + | 1.86444i | ||||
\(825\) | 23.3137 | − | 40.3805i | 0.811679 | − | 1.40587i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.6690 | 1.41420 | 0.707101 | − | 0.707113i | \(-0.250003\pi\) | ||||
0.707101 | + | 0.707113i | \(0.250003\pi\) | |||||||
\(828\) | −5.41421 | −0.188157 | ||||||||
\(829\) | 23.6863 | 0.822659 | 0.411329 | − | 0.911487i | \(-0.365065\pi\) | ||||
0.411329 | + | 0.911487i | \(0.365065\pi\) | |||||||
\(830\) | 120.811 | 4.19342 | ||||||||
\(831\) | −22.6066 | − | 39.1558i | −0.784214 | − | 1.35830i | ||||
\(832\) | 34.3995 | − | 8.51167i | 1.19259 | − | 0.295089i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −13.4853 | − | 23.3572i | −0.466957 | − | 0.808793i | ||||
\(835\) | 35.8492 | − | 62.0927i | 1.24061 | − | 2.14881i | ||||
\(836\) | −39.2132 | − | 67.9193i | −1.35622 | − | 2.34904i | ||||
\(837\) | −15.3137 | + | 26.5241i | −0.529319 | + | 0.916808i | ||||
\(838\) | −47.2132 | −1.63095 | ||||||||
\(839\) | −18.7990 | + | 32.5608i | −0.649013 | + | 1.12412i | 0.334346 | + | 0.942450i | \(0.391485\pi\) |
−0.983359 | + | 0.181673i | \(0.941849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −33.7990 | + | 58.5416i | −1.16548 | + | 2.01867i | ||||
\(842\) | 5.44975 | − | 9.43924i | 0.187811 | − | 0.325298i | ||||
\(843\) | 0.727922 | 0.0250710 | ||||||||
\(844\) | 1.39340 | − | 2.41344i | 0.0479627 | − | 0.0830739i | ||||
\(845\) | −42.1127 | − | 26.5241i | −1.44872 | − | 0.912458i | ||||
\(846\) | 18.4853 | 0.635537 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.50000 | + | 7.79423i | 0.154531 | + | 0.267655i | ||||
\(849\) | 0.142136 | 0.00487808 | ||||||||
\(850\) | −2.00000 | + | 3.46410i | −0.0685994 | + | 0.118818i | ||||
\(851\) | −5.29289 | − | 9.16756i | −0.181438 | − | 0.314260i | ||||
\(852\) | 1.85786 | 0.0636494 | ||||||||
\(853\) | −35.0000 | −1.19838 | −0.599189 | − | 0.800608i | \(-0.704510\pi\) | ||||
−0.599189 | + | 0.800608i | \(0.704510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.4853 | + | 19.8931i | 0.392788 | + | 0.680329i | ||||
\(856\) | −11.7279 | + | 20.3134i | −0.400852 | + | 0.694296i | ||||
\(857\) | −20.3995 | + | 35.3330i | −0.696833 | + | 1.20695i | 0.272725 | + | 0.962092i | \(0.412075\pi\) |
−0.969559 | + | 0.244859i | \(0.921258\pi\) | |||||||
\(858\) | 11.6569 | − | 40.3805i | 0.397958 | − | 1.37857i | ||||
\(859\) | 13.5355 | + | 23.4442i | 0.461826 | + | 0.799907i | 0.999052 | − | 0.0435317i | \(-0.0138610\pi\) |
−0.537226 | + | 0.843439i | \(0.680528\pi\) | |||||||
\(860\) | −4.29289 | − | 7.43551i | −0.146386 | − | 0.253549i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.4853 | − | 25.0892i | 0.493371 | − | 0.854543i | ||||
\(863\) | −28.0919 | − | 48.6566i | −0.956259 | − | 1.65629i | −0.731461 | − | 0.681883i | \(-0.761161\pi\) |
−0.224798 | − | 0.974405i | \(-0.572172\pi\) | |||||||
\(864\) | −4.48528 | − | 7.76874i | −0.152592 | − | 0.264298i | ||||
\(865\) | −34.7279 | − | 60.1505i | −1.18078 | − | 2.04518i | ||||
\(866\) | 0.621320 | + | 1.07616i | 0.0211133 | + | 0.0365694i | ||||
\(867\) | −12.0000 | + | 20.7846i | −0.407541 | + | 0.705882i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.4853 | − | 30.2854i | −0.593148 | − | 1.02736i | ||||
\(870\) | −64.2340 | − | 111.257i | −2.17774 | − | 3.77195i | ||||
\(871\) | 14.8492 | − | 3.67423i | 0.503147 | − | 0.124497i | ||||
\(872\) | −5.17157 | + | 8.95743i | −0.175132 | + | 0.303337i | ||||
\(873\) | −2.58579 | + | 4.47871i | −0.0875156 | + | 0.151581i | ||||
\(874\) | 10.2426 | + | 17.7408i | 0.346462 | + | 0.600091i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.55635 | −0.120158 | ||||||||
\(877\) | 17.0000 | 0.574049 | 0.287025 | − | 0.957923i | \(-0.407334\pi\) | ||||
0.287025 | + | 0.957923i | \(0.407334\pi\) | |||||||
\(878\) | −32.2635 | − | 55.8819i | −1.08884 | − | 1.88592i | ||||
\(879\) | −15.8787 | + | 27.5027i | −0.535575 | + | 0.927642i | ||||
\(880\) | 39.2132 | 1.32188 | ||||||||
\(881\) | 23.2279 | + | 40.2319i | 0.782569 | + | 1.35545i | 0.930441 | + | 0.366442i | \(0.119424\pi\) |
−0.147872 | + | 0.989006i | \(0.547242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.95837 | 0.267820 | 0.133910 | − | 0.990993i | \(-0.457247\pi\) | ||||
0.133910 | + | 0.990993i | \(0.457247\pi\) | |||||||
\(884\) | −0.656854 | + | 2.27541i | −0.0220924 | + | 0.0765303i | ||||
\(885\) | −4.75736 | + | 8.23999i | −0.159917 | + | 0.276984i | ||||
\(886\) | −34.6274 | −1.16333 | ||||||||
\(887\) | −5.31371 | + | 9.20361i | −0.178417 | + | 0.309027i | −0.941338 | − | 0.337464i | \(-0.890431\pi\) |
0.762922 | + | 0.646491i | \(0.223764\pi\) | |||||||
\(888\) | −23.3640 | + | 40.4676i | −0.784043 | + | 1.35800i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −33.7990 | + | 58.5416i | −1.13294 | + | 1.96232i | ||||
\(891\) | −17.0711 | −0.571902 | ||||||||
\(892\) | −3.82843 | + | 6.63103i | −0.128185 | + | 0.222023i | ||||
\(893\) | −22.9706 | − | 39.7862i | −0.768681 | − | 1.33139i | ||||
\(894\) | −5.12132 | + | 8.87039i | −0.171283 | + | 0.296670i | ||||
\(895\) | −10.8284 | − | 18.7554i | −0.361954 | − | 0.626923i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | + | 6.92820i | −0.0667781 | + | 0.231326i | ||||
\(898\) | 18.7279 | + | 32.4377i | 0.624959 | + | 1.08246i | ||||
\(899\) | 53.2132 | 1.77476 | ||||||||
\(900\) | −36.9706 | −1.23235 | ||||||||
\(901\) | 0.514719 | 0.0171478 | ||||||||
\(902\) | −48.0416 | −1.59961 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.10660 | + | 8.84489i | −0.169843 | + | 0.294177i | ||||
\(905\) | 36.6421 | + | 63.4660i | 1.21803 | + | 2.10968i | ||||
\(906\) | 32.3848 | + | 56.0921i | 1.07591 | + | 1.86353i | ||||
\(907\) | 18.7279 | 0.621850 | 0.310925 | − | 0.950434i | \(-0.399361\pi\) | ||||
0.310925 | + | 0.950434i | \(0.399361\pi\) | |||||||
\(908\) | 26.6066 | − | 46.0840i | 0.882971 | − | 1.52935i | ||||
\(909\) | −3.34315 | −0.110885 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.3431 | −0.607736 | −0.303868 | − | 0.952714i | \(-0.598278\pi\) | ||||
−0.303868 | + | 0.952714i | \(0.598278\pi\) | |||||||
\(912\) | 12.7279 | − | 22.0454i | 0.421464 | − | 0.729996i | ||||
\(913\) | −44.6274 | −1.47695 | ||||||||
\(914\) | −30.1777 | − | 52.2693i | −0.998189 | − | 1.72891i | ||||
\(915\) | 26.6066 | + | 46.0840i | 0.879587 | + | 1.52349i | ||||
\(916\) | −8.58579 | + | 14.8710i | −0.283682 | + | 0.491352i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.34315 | 0.0773353 | ||||||||
\(919\) | 25.3137 | 0.835022 | 0.417511 | − | 0.908672i | \(-0.362902\pi\) | ||||
0.417511 | + | 0.908672i | \(0.362902\pi\) | |||||||
\(920\) | −23.8995 | −0.787943 | ||||||||
\(921\) | 10.2843 | 0.338878 | ||||||||
\(922\) | 15.2782 | + | 26.4626i | 0.503160 | + | 0.871498i | ||||
\(923\) | −0.343146 | + | 1.18869i | −0.0112948 | + | 0.0391263i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.1421 | − | 62.6000i | −1.18835 | − | 2.05828i | ||||
\(926\) | −22.6066 | + | 39.1558i | −0.742899 | + | 1.28674i | ||||
\(927\) | 7.00000 | + | 12.1244i | 0.229910 | + | 0.398216i | ||||
\(928\) | −7.79289 | + | 13.4977i | −0.255814 | + | 0.443083i | ||||
\(929\) | −18.9411 | −0.621438 | −0.310719 | − | 0.950502i | \(-0.600570\pi\) | ||||
−0.310719 | + | 0.950502i | \(0.600570\pi\) | |||||||
\(930\) | −35.3848 | + | 61.2882i | −1.16031 | + | 2.00972i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 5.41421 | − | 9.37769i | 0.177348 | − | 0.307177i | ||||
\(933\) | −19.1421 | + | 33.1552i | −0.626685 | + | 1.08545i | ||||
\(934\) | −20.7279 | −0.678238 | ||||||||
\(935\) | 1.12132 | − | 1.94218i | 0.0366711 | − | 0.0635162i | ||||
\(936\) | −15.4497 | + | 3.82282i | −0.504991 | + | 0.124953i | ||||
\(937\) | −8.85786 | −0.289374 | −0.144687 | − | 0.989477i | \(-0.546217\pi\) | ||||
−0.144687 | + | 0.989477i | \(0.546217\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.89949 | − | 17.1464i | −0.323058 | − | 0.559553i | ||||
\(940\) | 112.225 | 3.66039 | ||||||||
\(941\) | −9.51472 | + | 16.4800i | −0.310171 | + | 0.537232i | −0.978399 | − | 0.206724i | \(-0.933720\pi\) |
0.668228 | + | 0.743956i | \(0.267053\pi\) | |||||||
\(942\) | 19.6066 | + | 33.9596i | 0.638818 | + | 1.10646i | ||||
\(943\) | 8.24264 | 0.268417 | ||||||||
\(944\) | −5.27208 | −0.171592 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.41421 | + | 4.18154i | 0.0784929 | + | 0.135954i | ||||
\(947\) | −9.29289 | + | 16.0958i | −0.301978 | + | 0.523042i | −0.976584 | − | 0.215136i | \(-0.930980\pi\) |
0.674606 | + | 0.738178i | \(0.264314\pi\) | |||||||
\(948\) | 27.7279 | − | 48.0262i | 0.900561 | − | 1.55982i | ||||
\(949\) | 0.656854 | − | 2.27541i | 0.0213224 | − | 0.0738629i | ||||
\(950\) | 69.9411 | + | 121.142i | 2.26919 | + | 3.93035i | ||||
\(951\) | 15.0919 | + | 26.1399i | 0.489388 | + | 0.847645i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.3137 | − | 33.4523i | 0.625632 | − | 1.08363i | −0.362786 | − | 0.931873i | \(-0.618174\pi\) |
0.988418 | − | 0.151755i | \(-0.0484923\pi\) | |||||||
\(954\) | 3.62132 | + | 6.27231i | 0.117245 | + | 0.203074i | ||||
\(955\) | −14.8492 | − | 25.7196i | −0.480510 | − | 0.832268i | ||||
\(956\) | 23.7071 | + | 41.0619i | 0.766743 | + | 1.32804i | ||||
\(957\) | 23.7279 | + | 41.0980i | 0.767015 | + | 1.32851i | ||||
\(958\) | −46.3345 | + | 80.2537i | −1.49700 | + | 2.59288i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −26.6066 | − | 46.0840i | −0.858724 | − | 1.48735i | ||||
\(961\) | 0.843146 | + | 1.46037i | 0.0271983 | + | 0.0471088i | ||||
\(962\) | −45.1777 | − | 46.9500i | −1.45659 | − | 1.51373i | ||||
\(963\) | −2.65685 | + | 4.60181i | −0.0856159 | + | 0.148291i | ||||
\(964\) | 2.84315 | − | 4.92447i | 0.0915716 | − | 0.158607i | ||||
\(965\) | 40.4706 | + | 70.0971i | 1.30279 | + | 2.25650i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.2426 | −0.908222 | −0.454111 | − | 0.890945i | \(-0.650043\pi\) | ||||
−0.454111 | + | 0.890945i | \(0.650043\pi\) | |||||||
\(968\) | −2.89949 | −0.0931933 | ||||||||
\(969\) | −0.727922 | − | 1.26080i | −0.0233842 | − | 0.0405027i | ||||
\(970\) | −23.8995 | + | 41.3951i | −0.767367 | + | 1.32912i | ||||
\(971\) | 40.3431 | 1.29467 | 0.647337 | − | 0.762204i | \(-0.275883\pi\) | ||||
0.647337 | + | 0.762204i | \(0.275883\pi\) | |||||||
\(972\) | 18.9497 | + | 32.8219i | 0.607813 | + | 1.05276i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −50.6274 | −1.62221 | ||||||||
\(975\) | −13.6569 | + | 47.3087i | −0.437369 | + | 1.51509i | ||||
\(976\) | −14.7426 | + | 25.5350i | −0.471900 | + | 0.817356i | ||||
\(977\) | −48.5980 | −1.55479 | −0.777394 | − | 0.629015i | \(-0.783459\pi\) | ||||
−0.777394 | + | 0.629015i | \(0.783459\pi\) | |||||||
\(978\) | −26.3137 | + | 45.5767i | −0.841420 | + | 1.45738i | ||||
\(979\) | 12.4853 | − | 21.6251i | 0.399031 | − | 0.691143i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.17157 | + | 2.02922i | −0.0374054 | + | 0.0647881i | ||||
\(982\) | −85.2548 | −2.72059 | ||||||||
\(983\) | 21.0000 | − | 36.3731i | 0.669796 | − | 1.16012i | −0.308165 | − | 0.951333i | \(-0.599715\pi\) |
0.977961 | − | 0.208788i | \(-0.0669518\pi\) | |||||||
\(984\) | −18.1924 | − | 31.5101i | −0.579952 | − | 1.00451i | ||||
\(985\) | −17.5563 | + | 30.4085i | −0.559392 | + | 0.968895i | ||||
\(986\) | −2.03553 | − | 3.52565i | −0.0648246 | − | 0.112280i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 57.4264 | + | 59.6793i | 1.82698 | + | 1.89865i | ||||
\(989\) | −0.414214 | − | 0.717439i | −0.0131712 | − | 0.0228132i | ||||
\(990\) | 31.5563 | 1.00293 | ||||||||
\(991\) | 28.2426 | 0.897157 | 0.448579 | − | 0.893743i | \(-0.351930\pi\) | ||||
0.448579 | + | 0.893743i | \(0.351930\pi\) | |||||||
\(992\) | 8.58579 | 0.272599 | ||||||||
\(993\) | −40.8284 | −1.29565 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −36.3137 | + | 62.8972i | −1.15122 | + | 1.99397i | ||||
\(996\) | −35.3848 | − | 61.2882i | −1.12121 | − | 1.94199i | ||||
\(997\) | 9.98528 | + | 17.2950i | 0.316237 | + | 0.547739i | 0.979700 | − | 0.200471i | \(-0.0642472\pi\) |
−0.663463 | + | 0.748209i | \(0.730914\pi\) | |||||||
\(998\) | 67.6985 | 2.14296 | ||||||||
\(999\) | −21.1716 | + | 36.6702i | −0.669839 | + | 1.16020i |
(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 | 637.2.g.f.263.2 | 4 | ||
7.2 | even | 3 | 637.2.h.b.471.1 | 4 | |||
7.3 | odd | 6 | 637.2.f.e.393.2 | yes | 4 | ||
7.4 | even | 3 | 637.2.f.f.393.2 | yes | 4 | ||
7.5 | odd | 6 | 637.2.h.c.471.1 | 4 | |||
7.6 | odd | 2 | 637.2.g.g.263.2 | 4 | |||
13.9 | even | 3 | 637.2.h.b.165.1 | 4 | |||
91.3 | odd | 6 | 8281.2.a.o.1.1 | 2 | |||
91.9 | even | 3 | inner | 637.2.g.f.373.2 | 4 | ||
91.10 | odd | 6 | 8281.2.a.y.1.2 | 2 | |||
91.48 | odd | 6 | 637.2.h.c.165.1 | 4 | |||
91.61 | odd | 6 | 637.2.g.g.373.2 | 4 | |||
91.74 | even | 3 | 637.2.f.f.295.2 | yes | 4 | ||
91.81 | even | 3 | 8281.2.a.p.1.1 | 2 | |||
91.87 | odd | 6 | 637.2.f.e.295.2 | ✓ | 4 | ||
91.88 | even | 6 | 8281.2.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.e.295.2 | ✓ | 4 | 91.87 | odd | 6 | ||
637.2.f.e.393.2 | yes | 4 | 7.3 | odd | 6 | ||
637.2.f.f.295.2 | yes | 4 | 91.74 | even | 3 | ||
637.2.f.f.393.2 | yes | 4 | 7.4 | even | 3 | ||
637.2.g.f.263.2 | 4 | 1.1 | even | 1 | trivial | ||
637.2.g.f.373.2 | 4 | 91.9 | even | 3 | inner | ||
637.2.g.g.263.2 | 4 | 7.6 | odd | 2 | |||
637.2.g.g.373.2 | 4 | 91.61 | odd | 6 | |||
637.2.h.b.165.1 | 4 | 13.9 | even | 3 | |||
637.2.h.b.471.1 | 4 | 7.2 | even | 3 | |||
637.2.h.c.165.1 | 4 | 91.48 | odd | 6 | |||
637.2.h.c.471.1 | 4 | 7.5 | odd | 6 | |||
8281.2.a.o.1.1 | 2 | 91.3 | odd | 6 | |||
8281.2.a.p.1.1 | 2 | 91.81 | even | 3 | |||
8281.2.a.x.1.2 | 2 | 91.88 | even | 6 | |||
8281.2.a.y.1.2 | 2 | 91.10 | odd | 6 |