Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(109,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.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: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1767277521.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(-1.54162 - 1.88572i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.109 |
Dual form | 567.2.g.j.541.1 |
$q$-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 \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10400 | + | 1.91218i | −0.780644 | + | 1.35212i | 0.150922 | + | 0.988546i | \(0.451776\pi\) |
−0.931567 | + | 0.363570i | \(0.881558\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.43762 | − | 2.49004i | −0.718812 | − | 1.24502i | ||||
\(5\) | −3.80779 | −1.70289 | −0.851447 | − | 0.524441i | \(-0.824274\pi\) | ||||
−0.851447 | + | 0.524441i | \(0.824274\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.57027 | − | 0.627473i | −0.971470 | − | 0.237163i | ||||
\(8\) | 1.93254 | 0.683256 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.20379 | − | 7.28117i | 1.32935 | − | 2.30251i | ||||
\(11\) | 4.32433 | 1.30384 | 0.651918 | − | 0.758290i | \(-0.273965\pi\) | ||||
0.651918 | + | 0.758290i | \(0.273965\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.43762 | − | 2.49004i | 0.398725 | − | 0.690612i | −0.594844 | − | 0.803841i | \(-0.702786\pi\) |
0.993569 | + | 0.113229i | \(0.0361195\pi\) | |||||||
\(14\) | 4.03741 | − | 4.22209i | 1.07904 | − | 1.12840i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.741726 | − | 1.28471i | 0.185432 | − | 0.321177i | ||||
\(17\) | −2.01297 | + | 3.48657i | −0.488218 | + | 0.845618i | −0.999908 | − | 0.0135517i | \(-0.995686\pi\) |
0.511690 | + | 0.859170i | \(0.329020\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.804103 | + | 1.39275i | 0.184474 | + | 0.319518i | 0.943399 | − | 0.331660i | \(-0.107609\pi\) |
−0.758925 | + | 0.651178i | \(0.774275\pi\) | |||||||
\(20\) | 5.47416 | + | 9.48152i | 1.22406 | + | 2.12013i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.77406 | + | 8.26891i | −1.01783 | + | 1.76294i | ||||
\(23\) | −2.66725 | −0.556160 | −0.278080 | − | 0.960558i | \(-0.589698\pi\) | ||||
−0.278080 | + | 0.960558i | \(0.589698\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.49923 | 1.89985 | ||||||||
\(26\) | 3.17427 | + | 5.49799i | 0.622525 | + | 1.07824i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.13264 | + | 7.30213i | 0.403032 | + | 1.37997i | ||||
\(29\) | −0.375246 | − | 0.649945i | −0.0696815 | − | 0.120692i | 0.829080 | − | 0.559131i | \(-0.188865\pi\) |
−0.898761 | + | 0.438439i | \(0.855532\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0702679 | − | 0.121708i | −0.0126205 | − | 0.0218593i | 0.859646 | − | 0.510890i | \(-0.170684\pi\) |
−0.872267 | + | 0.489031i | \(0.837351\pi\) | |||||||
\(32\) | 3.57027 | + | 6.18389i | 0.631140 | + | 1.09317i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.44464 | − | 7.69834i | −0.762249 | − | 1.32025i | ||||
\(35\) | 9.78703 | + | 2.38928i | 1.65431 | + | 0.403863i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.14141 | + | 7.17313i | 0.680844 | + | 1.17926i | 0.974724 | + | 0.223414i | \(0.0717201\pi\) |
−0.293880 | + | 0.955842i | \(0.594947\pi\) | |||||||
\(38\) | −3.55091 | −0.576034 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.35870 | −1.16351 | ||||||||
\(41\) | 5.18724 | − | 8.98456i | 0.810111 | − | 1.40315i | −0.102675 | − | 0.994715i | \(-0.532740\pi\) |
0.912786 | − | 0.408438i | \(-0.133926\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.133520 | − | 0.231264i | −0.0203616 | − | 0.0352674i | 0.855665 | − | 0.517530i | \(-0.173148\pi\) |
−0.876027 | + | 0.482263i | \(0.839815\pi\) | |||||||
\(44\) | −6.21676 | − | 10.7677i | −0.937212 | − | 1.62330i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.94464 | − | 5.10026i | 0.434163 | − | 0.751993i | ||||
\(47\) | 3.96627 | − | 6.86978i | 0.578540 | − | 1.00206i | −0.417107 | − | 0.908857i | \(-0.636956\pi\) |
0.995647 | − | 0.0932032i | \(-0.0297106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.21255 | + | 3.22555i | 0.887508 | + | 0.460793i | ||||
\(50\) | −10.4871 | + | 18.1643i | −1.48310 | + | 2.56881i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.26704 | −1.14643 | ||||||||
\(53\) | 5.61189 | − | 9.72008i | 0.770852 | − | 1.33516i | −0.166244 | − | 0.986085i | \(-0.553164\pi\) |
0.937096 | − | 0.349071i | \(-0.113503\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.4661 | −2.22029 | ||||||||
\(56\) | −4.96715 | − | 1.21262i | −0.663763 | − | 0.162043i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.65708 | 0.217586 | ||||||||
\(59\) | 0.346599 | + | 0.600327i | 0.0451234 | + | 0.0781560i | 0.887705 | − | 0.460413i | \(-0.152299\pi\) |
−0.842582 | + | 0.538569i | \(0.818965\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.05372 | + | 1.82510i | −0.134915 | + | 0.233680i | −0.925565 | − | 0.378589i | \(-0.876409\pi\) |
0.790650 | + | 0.612268i | \(0.209743\pi\) | |||||||
\(62\) | 0.310302 | 0.0394085 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.7994 | −1.59992 | ||||||||
\(65\) | −5.47416 | + | 9.48152i | −0.678986 | + | 1.17604i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.38314 | + | 9.32387i | 0.657655 | + | 1.13909i | 0.981221 | + | 0.192886i | \(0.0617848\pi\) |
−0.323566 | + | 0.946206i | \(0.604882\pi\) | |||||||
\(68\) | 11.5756 | 1.40375 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −15.3736 | + | 16.0768i | −1.83750 | + | 1.92155i | ||||
\(71\) | 3.62399 | 0.430088 | 0.215044 | − | 0.976604i | \(-0.431010\pi\) | ||||
0.215044 | + | 0.976604i | \(0.431010\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.78756 | − | 3.09614i | 0.209217 | − | 0.362375i | −0.742251 | − | 0.670122i | \(-0.766242\pi\) |
0.951468 | + | 0.307747i | \(0.0995750\pi\) | |||||||
\(74\) | −18.2884 | −2.12599 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.31199 | − | 4.00449i | 0.265204 | − | 0.459347i | ||||
\(77\) | −11.1147 | − | 2.71340i | −1.26664 | − | 0.309221i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.71168 | − | 13.3570i | 0.867632 | − | 1.50278i | 0.00322152 | − | 0.999995i | \(-0.498975\pi\) |
0.864410 | − | 0.502787i | \(-0.167692\pi\) | |||||||
\(80\) | −2.82433 | + | 4.89189i | −0.315770 | + | 0.546930i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.4534 | + | 19.8379i | 1.26482 | + | 2.19073i | ||||
\(83\) | −3.22034 | − | 5.57779i | −0.353478 | − | 0.612241i | 0.633378 | − | 0.773842i | \(-0.281668\pi\) |
−0.986856 | + | 0.161601i | \(0.948334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.66497 | − | 13.2761i | 0.831383 | − | 1.44000i | ||||
\(86\) | 0.589624 | 0.0635808 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.35695 | 0.890854 | ||||||||
\(89\) | −0.128437 | − | 0.222459i | −0.0136143 | − | 0.0235806i | 0.859138 | − | 0.511744i | \(-0.171000\pi\) |
−0.872752 | + | 0.488163i | \(0.837667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.25751 | + | 5.49799i | −0.551137 | + | 0.576346i | ||||
\(92\) | 3.83450 | + | 6.64155i | 0.399774 | + | 0.692429i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.75751 | + | 15.1684i | 0.903268 | + | 1.56451i | ||||
\(95\) | −3.06185 | − | 5.30328i | −0.314139 | − | 0.544105i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.529281 | − | 0.916742i | −0.0537403 | − | 0.0930810i | 0.837904 | − | 0.545818i | \(-0.183781\pi\) |
−0.891644 | + | 0.452737i | \(0.850448\pi\) | |||||||
\(98\) | −13.0265 | + | 8.31853i | −1.31587 | + | 0.840298i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −13.6563 | − | 23.6534i | −1.36563 | − | 2.36534i | ||||
\(101\) | −1.36585 | −0.135907 | −0.0679534 | − | 0.997688i | \(-0.521647\pi\) | ||||
−0.0679534 | + | 0.997688i | \(0.521647\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.9713 | −1.47516 | −0.737581 | − | 0.675259i | \(-0.764032\pi\) | ||||
−0.737581 | + | 0.675259i | \(0.764032\pi\) | |||||||
\(104\) | 2.77826 | − | 4.81209i | 0.272431 | − | 0.471865i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.3910 | + | 21.4619i | 1.20352 | + | 2.08456i | ||||
\(107\) | −4.04075 | − | 6.99878i | −0.390634 | − | 0.676597i | 0.601900 | − | 0.798572i | \(-0.294411\pi\) |
−0.992533 | + | 0.121974i | \(0.961077\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.55460 | − | 7.88879i | 0.436251 | − | 0.755609i | −0.561146 | − | 0.827717i | \(-0.689639\pi\) |
0.997397 | + | 0.0721080i | \(0.0229726\pi\) | |||||||
\(110\) | 18.1786 | − | 31.4862i | 1.73326 | − | 3.00209i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.71255 | + | 2.83663i | −0.256312 | + | 0.268036i | ||||
\(113\) | −1.38303 | + | 2.39547i | −0.130104 | + | 0.225347i | −0.923717 | − | 0.383077i | \(-0.874865\pi\) |
0.793612 | + | 0.608424i | \(0.208198\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.1563 | 0.947082 | ||||||||
\(116\) | −1.07892 | + | 1.86875i | −0.100176 | + | 0.173509i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.53058 | −0.140901 | ||||||||
\(119\) | 7.36162 | − | 7.69834i | 0.674838 | − | 0.705706i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.69986 | 0.699988 | ||||||||
\(122\) | −2.32661 | − | 4.02981i | −0.210641 | − | 0.364841i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.202038 | + | 0.349939i | −0.0181435 | + | 0.0314255i | ||||
\(125\) | −17.1321 | −1.53234 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.6573 | 1.21189 | 0.605945 | − | 0.795507i | \(-0.292795\pi\) | ||||
0.605945 | + | 0.795507i | \(0.292795\pi\) | |||||||
\(128\) | 6.98994 | − | 12.1069i | 0.617829 | − | 1.07011i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0869 | − | 20.9352i | −1.06009 | − | 1.83614i | ||||
\(131\) | 17.6138 | 1.53893 | 0.769463 | − | 0.638691i | \(-0.220524\pi\) | ||||
0.769463 | + | 0.638691i | \(0.220524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.19285 | − | 4.08429i | −0.103433 | − | 0.354153i | ||||
\(134\) | −23.7719 | −2.05358 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.89015 | + | 6.73794i | −0.333578 | + | 0.577774i | ||||
\(137\) | 8.66725 | 0.740493 | 0.370247 | − | 0.928934i | \(-0.379273\pi\) | ||||
0.370247 | + | 0.928934i | \(0.379273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.88303 | − | 3.26150i | 0.159716 | − | 0.276637i | −0.775050 | − | 0.631900i | \(-0.782275\pi\) |
0.934766 | + | 0.355263i | \(0.115609\pi\) | |||||||
\(140\) | −8.12066 | − | 27.8049i | −0.686321 | − | 2.34995i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00088 | + | 6.92972i | −0.335746 | + | 0.581529i | ||||
\(143\) | 6.21676 | − | 10.7677i | 0.519872 | − | 0.900444i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.42886 | + | 2.47485i | 0.118660 | + | 0.205525i | ||||
\(146\) | 3.94691 | + | 6.83626i | 0.326649 | + | 0.565773i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.9076 | − | 20.6245i | 0.978797 | − | 1.69533i | ||||
\(149\) | 4.61122 | 0.377766 | 0.188883 | − | 0.982000i | \(-0.439513\pi\) | ||||
0.188883 | + | 0.982000i | \(0.439513\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.79762 | 0.634561 | 0.317281 | − | 0.948332i | \(-0.397230\pi\) | ||||
0.317281 | + | 0.948332i | \(0.397230\pi\) | |||||||
\(152\) | 1.55396 | + | 2.69154i | 0.126043 | + | 0.218313i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.4591 | − | 18.2577i | 1.40690 | − | 1.47125i | ||||
\(155\) | 0.267565 | + | 0.463436i | 0.0214913 | + | 0.0372241i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6328 | − | 20.1485i | −0.928395 | − | 1.60803i | −0.786008 | − | 0.618216i | \(-0.787856\pi\) |
−0.142387 | − | 0.989811i | \(-0.545478\pi\) | |||||||
\(158\) | 17.0274 | + | 29.4922i | 1.35462 | + | 2.34628i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.5948 | − | 23.5469i | −1.07476 | − | 1.86155i | ||||
\(161\) | 6.85555 | + | 1.67363i | 0.540293 | + | 0.131900i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.05547 | − | 5.29223i | −0.239323 | − | 0.414519i | 0.721197 | − | 0.692730i | \(-0.243592\pi\) |
−0.960520 | + | 0.278210i | \(0.910259\pi\) | |||||||
\(164\) | −29.8292 | −2.32927 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.2210 | 1.10376 | ||||||||
\(167\) | −5.82076 | + | 10.0819i | −0.450424 | + | 0.780157i | −0.998412 | − | 0.0563288i | \(-0.982060\pi\) |
0.547988 | + | 0.836486i | \(0.315394\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.36648 | + | 4.09886i | 0.182037 | + | 0.315297i | ||||
\(170\) | 16.9242 | + | 29.3136i | 1.29803 | + | 2.24825i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.383903 | + | 0.664940i | −0.0292723 | + | 0.0507012i | ||||
\(173\) | −9.62855 | + | 16.6771i | −0.732045 | + | 1.26794i | 0.223963 | + | 0.974598i | \(0.428101\pi\) |
−0.956008 | + | 0.293341i | \(0.905233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.4156 | − | 5.96052i | −1.84564 | − | 0.450573i | ||||
\(176\) | 3.20747 | − | 5.55550i | 0.241772 | − | 0.418762i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.567176 | 0.0425117 | ||||||||
\(179\) | −1.67093 | + | 2.89414i | −0.124891 | + | 0.216318i | −0.921690 | − | 0.387926i | \(-0.873192\pi\) |
0.796799 | + | 0.604244i | \(0.206525\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.7358 | −1.46695 | −0.733474 | − | 0.679717i | \(-0.762103\pi\) | ||||
−0.733474 | + | 0.679717i | \(0.762103\pi\) | |||||||
\(182\) | −4.70887 | − | 16.1231i | −0.349045 | − | 1.19512i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.15457 | −0.380000 | ||||||||
\(185\) | −15.7696 | − | 27.3138i | −1.15940 | − | 2.00815i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.70477 | + | 15.0771i | −0.636556 | + | 1.10255i | ||||
\(188\) | −22.8080 | −1.66344 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.5211 | 0.980925 | ||||||||
\(191\) | −2.08745 | + | 3.61557i | −0.151043 | + | 0.261613i | −0.931611 | − | 0.363457i | \(-0.881596\pi\) |
0.780568 | + | 0.625070i | \(0.214930\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.93686 | + | 12.0150i | 0.499326 | + | 0.864858i | 1.00000 | 0.000778217i | \(-0.000247714\pi\) | |
−0.500674 | + | 0.865636i | \(0.666914\pi\) | |||||||
\(194\) | 2.33730 | 0.167808 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.899576 | − | 20.1066i | −0.0642554 | − | 1.43619i | ||||
\(197\) | 7.48520 | 0.533299 | 0.266649 | − | 0.963794i | \(-0.414083\pi\) | ||||
0.266649 | + | 0.963794i | \(0.414083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.32767 | − | 10.9598i | 0.448556 | − | 0.776922i | −0.549736 | − | 0.835338i | \(-0.685272\pi\) |
0.998292 | + | 0.0584160i | \(0.0186050\pi\) | |||||||
\(200\) | 18.3576 | 1.29808 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.50789 | − | 2.61174i | 0.106095 | − | 0.183762i | ||||
\(203\) | 0.556660 | + | 1.90599i | 0.0390698 | + | 0.133774i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.7519 | + | 34.2113i | −1.37953 | + | 2.38942i | ||||
\(206\) | 16.5282 | − | 28.6277i | 1.15158 | − | 1.99459i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.13264 | − | 3.69385i | −0.147872 | − | 0.256122i | ||||
\(209\) | 3.47721 | + | 6.02270i | 0.240524 | + | 0.416599i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.57599 | − | 4.46174i | 0.177338 | − | 0.307159i | −0.763630 | − | 0.645654i | \(-0.776585\pi\) |
0.940968 | + | 0.338496i | \(0.109918\pi\) | |||||||
\(212\) | −32.2711 | −2.21639 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.8439 | 1.21978 | ||||||||
\(215\) | 0.508416 | + | 0.880602i | 0.0346737 | + | 0.0600566i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.104239 | + | 0.356912i | 0.00707621 | + | 0.0242288i | ||||
\(218\) | 10.0565 | + | 17.4184i | 0.681114 | + | 1.17972i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 23.6721 | + | 41.0013i | 1.59597 | + | 2.76431i | ||||
\(221\) | 5.78780 | + | 10.0248i | 0.389329 | + | 0.674338i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.60832 | + | 13.1780i | 0.509490 | + | 0.882463i | 0.999940 | + | 0.0109935i | \(0.00349942\pi\) |
−0.490449 | + | 0.871470i | \(0.663167\pi\) | |||||||
\(224\) | −5.29632 | − | 18.1345i | −0.353875 | − | 1.21166i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.05372 | − | 5.28920i | −0.203130 | − | 0.351832i | ||||
\(227\) | 4.28949 | 0.284703 | 0.142352 | − | 0.989816i | \(-0.454534\pi\) | ||||
0.142352 | + | 0.989816i | \(0.454534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.971251 | 0.0641821 | 0.0320910 | − | 0.999485i | \(-0.489783\pi\) | ||||
0.0320910 | + | 0.999485i | \(0.489783\pi\) | |||||||
\(230\) | −11.2126 | + | 19.4207i | −0.739334 | + | 1.28056i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.725178 | − | 1.25605i | −0.0476103 | − | 0.0824634i | ||||
\(233\) | −1.88671 | − | 3.26788i | −0.123603 | − | 0.214086i | 0.797583 | − | 0.603209i | \(-0.206111\pi\) |
−0.921186 | + | 0.389123i | \(0.872778\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.1027 | + | 26.1587i | −0.985192 | + | 1.70640i | ||||
\(236\) | 0.996558 | − | 1.72609i | 0.0648704 | − | 0.112359i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.59341 | + | 22.5757i | 0.427387 | + | 1.46336i | ||||
\(239\) | 3.34520 | − | 5.79405i | 0.216383 | − | 0.374786i | −0.737317 | − | 0.675547i | \(-0.763907\pi\) |
0.953699 | + | 0.300761i | \(0.0972407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9713 | −0.964383 | −0.482192 | − | 0.876066i | \(-0.660159\pi\) | ||||
−0.482192 | + | 0.876066i | \(0.660159\pi\) | |||||||
\(242\) | −8.50063 | + | 14.7235i | −0.546441 | + | 0.946464i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.05941 | 0.387914 | ||||||||
\(245\) | −23.6561 | − | 12.2822i | −1.51133 | − | 0.784681i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.62399 | 0.294217 | ||||||||
\(248\) | −0.135796 | − | 0.235205i | −0.00862302 | − | 0.0149355i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 18.9138 | − | 32.7597i | 1.19622 | − | 2.07191i | ||||
\(251\) | 17.0787 | 1.07800 | 0.538999 | − | 0.842307i | \(-0.318803\pi\) | ||||
0.538999 | + | 0.842307i | \(0.318803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.5341 | −0.725141 | ||||||||
\(254\) | −15.0776 | + | 26.1152i | −0.946055 | + | 1.63862i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.63440 | + | 4.56291i | 0.164650 | + | 0.285182i | ||||
\(257\) | −8.57231 | −0.534726 | −0.267363 | − | 0.963596i | \(-0.586152\pi\) | ||||
−0.267363 | + | 0.963596i | \(0.586152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.14358 | − | 21.0355i | −0.381744 | − | 1.30708i | ||||
\(260\) | 31.4791 | 1.95225 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.4456 | + | 33.6808i | −1.20135 | + | 2.08081i | ||||
\(263\) | 5.69685 | 0.351283 | 0.175641 | − | 0.984454i | \(-0.443800\pi\) | ||||
0.175641 | + | 0.984454i | \(0.443800\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.3689 | + | 37.0120i | −1.31268 | + | 2.27363i | ||||
\(266\) | 9.12680 | + | 2.22810i | 0.559600 | + | 0.136614i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.4778 | − | 26.8084i | 0.945460 | − | 1.63758i | ||||
\(269\) | 7.80077 | − | 13.5113i | 0.475621 | − | 0.823800i | −0.523989 | − | 0.851725i | \(-0.675557\pi\) |
0.999610 | + | 0.0279249i | \(0.00888992\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3688 | + | 26.6195i | 0.933586 | + | 1.61702i | 0.777136 | + | 0.629332i | \(0.216671\pi\) |
0.156449 | + | 0.987686i | \(0.449995\pi\) | |||||||
\(272\) | 2.98615 | + | 5.17216i | 0.181062 | + | 0.313609i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.56863 | + | 16.5733i | −0.578062 | + | 1.00123i | ||||
\(275\) | 41.0779 | 2.47709 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.5926 | −1.59780 | −0.798899 | − | 0.601466i | \(-0.794584\pi\) | ||||
−0.798899 | + | 0.601466i | \(0.794584\pi\) | |||||||
\(278\) | 4.15772 | + | 7.20138i | 0.249363 | + | 0.431910i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 18.9138 | + | 4.61739i | 1.13032 | + | 0.275942i | ||||
\(281\) | 8.68065 | + | 15.0353i | 0.517844 | + | 0.896932i | 0.999785 | + | 0.0207285i | \(0.00659857\pi\) |
−0.481941 | + | 0.876204i | \(0.660068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.17771 | − | 15.8963i | −0.545558 | − | 0.944934i | −0.998572 | − | 0.0534307i | \(-0.982984\pi\) |
0.453013 | − | 0.891504i | \(-0.350349\pi\) | |||||||
\(284\) | −5.20993 | − | 9.02386i | −0.309152 | − | 0.535468i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.7266 | + | 23.7751i | 0.811670 | + | 1.40585i | ||||
\(287\) | −18.9702 | + | 19.8379i | −1.11977 | + | 1.17099i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.395870 | + | 0.685667i | 0.0232865 | + | 0.0403334i | ||||
\(290\) | −6.30982 | −0.370525 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.2793 | −0.601552 | ||||||||
\(293\) | −5.34906 | + | 9.26484i | −0.312495 | + | 0.541258i | −0.978902 | − | 0.204331i | \(-0.934498\pi\) |
0.666407 | + | 0.745588i | \(0.267831\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.31978 | − | 2.28592i | −0.0768403 | − | 0.133091i | ||||
\(296\) | 8.00344 | + | 13.8624i | 0.465191 | + | 0.805734i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.09078 | + | 8.81749i | −0.294901 | + | 0.510784i | ||||
\(299\) | −3.83450 | + | 6.64155i | −0.221755 | + | 0.384091i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.198071 | + | 0.678190i | 0.0114166 | + | 0.0390902i | ||||
\(302\) | −8.60856 | + | 14.9105i | −0.495367 | + | 0.858000i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.38570 | 0.136829 | ||||||||
\(305\) | 4.01234 | − | 6.94958i | 0.229746 | − | 0.397932i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.3948 | 1.79180 | 0.895899 | − | 0.444258i | \(-0.146533\pi\) | ||||
0.895899 | + | 0.444258i | \(0.146533\pi\) | |||||||
\(308\) | 9.22227 | + | 31.5768i | 0.525488 | + | 1.79926i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.18157 | −0.0671084 | ||||||||
\(311\) | 6.74453 | + | 11.6819i | 0.382447 | + | 0.662418i | 0.991411 | − | 0.130779i | \(-0.0417480\pi\) |
−0.608964 | + | 0.793198i | \(0.708415\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.67069 | − | 16.7501i | 0.546620 | − | 0.946773i | −0.451883 | − | 0.892077i | \(-0.649248\pi\) |
0.998503 | − | 0.0546962i | \(-0.0174190\pi\) | |||||||
\(314\) | 51.3701 | 2.89899 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −44.3459 | −2.49465 | ||||||||
\(317\) | 7.67882 | − | 13.3001i | 0.431286 | − | 0.747009i | −0.565699 | − | 0.824612i | \(-0.691393\pi\) |
0.996984 | + | 0.0776033i | \(0.0247268\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.62269 | − | 2.81058i | −0.0908532 | − | 0.157362i | ||||
\(320\) | 48.7373 | 2.72450 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.7688 | + | 11.2614i | −0.600121 | + | 0.627571i | ||||
\(323\) | −6.47455 | −0.360254 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.6563 | − | 23.6534i | 0.757516 | − | 1.31206i | ||||
\(326\) | 13.4929 | 0.747304 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.0245 | − | 17.3630i | 0.553513 | − | 0.958713i | ||||
\(329\) | −14.5050 | + | 15.1684i | −0.799686 | + | 0.836264i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.619146 | − | 1.07239i | 0.0340313 | − | 0.0589440i | −0.848508 | − | 0.529182i | \(-0.822499\pi\) |
0.882539 | + | 0.470238i | \(0.155832\pi\) | |||||||
\(332\) | −9.25926 | + | 16.0375i | −0.508168 | + | 0.880172i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.8522 | − | 22.2607i | −0.703242 | − | 1.21805i | ||||
\(335\) | −20.4978 | − | 35.5033i | −1.11992 | − | 1.93975i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.95428 | + | 10.3131i | −0.324350 | + | 0.561791i | −0.981381 | − | 0.192073i | \(-0.938479\pi\) |
0.657030 | + | 0.753864i | \(0.271812\pi\) | |||||||
\(338\) | −10.4504 | −0.568424 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −44.0774 | −2.39043 | ||||||||
\(341\) | −0.303862 | − | 0.526304i | −0.0164550 | − | 0.0285010i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.9440 | − | 12.1887i | −0.752904 | − | 0.658130i | ||||
\(344\) | −0.258033 | − | 0.446926i | −0.0139122 | − | 0.0240966i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.2598 | − | 36.8230i | −1.14293 | − | 1.97962i | ||||
\(347\) | 2.17339 | + | 3.76442i | 0.116674 | + | 0.202085i | 0.918448 | − | 0.395543i | \(-0.129443\pi\) |
−0.801774 | + | 0.597628i | \(0.796110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.58780 | − | 6.21425i | −0.192051 | − | 0.332641i | 0.753879 | − | 0.657013i | \(-0.228180\pi\) |
−0.945930 | + | 0.324372i | \(0.894847\pi\) | |||||||
\(350\) | 38.3523 | − | 40.1066i | 2.05002 | − | 2.14379i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.4390 | + | 26.7412i | 0.822903 | + | 1.42531i | ||||
\(353\) | 25.0967 | 1.33576 | 0.667881 | − | 0.744268i | \(-0.267201\pi\) | ||||
0.667881 | + | 0.744268i | \(0.267201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7994 | −0.732395 | ||||||||
\(356\) | −0.369288 | + | 0.639625i | −0.0195722 | + | 0.0339001i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.68941 | − | 6.39025i | −0.194992 | − | 0.337735i | ||||
\(359\) | −15.9959 | − | 27.7057i | −0.844231 | − | 1.46225i | −0.886287 | − | 0.463136i | \(-0.846724\pi\) |
0.0420557 | − | 0.999115i | \(-0.486609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.20684 | − | 14.2147i | 0.431939 | − | 0.748140i | ||||
\(362\) | 21.7883 | − | 37.7384i | 1.14517 | − | 1.98348i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 21.2485 | + | 5.18735i | 1.11372 | + | 0.271891i | ||||
\(365\) | −6.80663 | + | 11.7894i | −0.356275 | + | 0.617087i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1248 | −0.580707 | −0.290354 | − | 0.956919i | \(-0.593773\pi\) | ||||
−0.290354 | + | 0.956919i | \(0.593773\pi\) | |||||||
\(368\) | −1.97837 | + | 3.42664i | −0.103130 | + | 0.178626i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 69.6385 | 3.62033 | ||||||||
\(371\) | −20.5231 | + | 21.4619i | −1.06551 | + | 1.11425i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1546 | 0.836452 | 0.418226 | − | 0.908343i | \(-0.362652\pi\) | ||||
0.418226 | + | 0.908343i | \(0.362652\pi\) | |||||||
\(374\) | −19.2201 | − | 33.2902i | −0.993848 | − | 1.72139i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.66497 | − | 13.2761i | 0.395291 | − | 0.684664i | ||||
\(377\) | −2.15785 | −0.111135 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.18485 | 0.163595 | 0.0817973 | − | 0.996649i | \(-0.473934\pi\) | ||||
0.0817973 | + | 0.996649i | \(0.473934\pi\) | |||||||
\(380\) | −8.80358 | + | 15.2482i | −0.451614 | + | 0.782218i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.60908 | − | 7.98316i | −0.235821 | − | 0.408454i | ||||
\(383\) | 16.4776 | 0.841968 | 0.420984 | − | 0.907068i | \(-0.361685\pi\) | ||||
0.420984 | + | 0.907068i | \(0.361685\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 42.3224 | + | 10.3321i | 2.15695 | + | 0.526571i | ||||
\(386\) | −30.6331 | −1.55918 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.52181 | + | 2.63586i | −0.0772584 | + | 0.133815i | ||||
\(389\) | −31.9771 | −1.62130 | −0.810651 | − | 0.585529i | \(-0.800887\pi\) | ||||
−0.810651 | + | 0.585529i | \(0.800887\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.36911 | − | 9.29956i | 0.271527 | − | 0.470299i | ||||
\(392\) | 12.0060 | + | 6.23350i | 0.606395 | + | 0.314839i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.26365 | + | 14.3131i | −0.416317 | + | 0.721081i | ||||
\(395\) | −29.3644 | + | 50.8607i | −1.47748 | + | 2.55908i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.9059 | − | 24.0858i | −0.697919 | − | 1.20883i | −0.969187 | − | 0.246327i | \(-0.920776\pi\) |
0.271268 | − | 0.962504i | \(-0.412557\pi\) | |||||||
\(398\) | 13.9715 | + | 24.1993i | 0.700326 | + | 1.21300i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.04583 | − | 12.2037i | 0.352291 | − | 0.610187i | ||||
\(401\) | −27.5883 | −1.37769 | −0.688847 | − | 0.724907i | \(-0.741883\pi\) | ||||
−0.688847 | + | 0.724907i | \(0.741883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.404075 | −0.0201284 | ||||||||
\(404\) | 1.96357 | + | 3.40101i | 0.0976913 | + | 0.169206i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.25915 | − | 1.03978i | −0.211378 | − | 0.0516032i | ||||
\(407\) | 17.9088 | + | 31.0190i | 0.887708 | + | 1.53756i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.91231 | + | 10.2404i | 0.292345 | + | 0.506356i | 0.974364 | − | 0.224978i | \(-0.0722312\pi\) |
−0.682019 | + | 0.731335i | \(0.738898\pi\) | |||||||
\(410\) | −43.6121 | − | 75.5384i | −2.15385 | − | 3.73058i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.5230 | + | 37.2790i | 1.06036 | + | 1.83660i | ||||
\(413\) | −0.514163 | − | 1.76048i | −0.0253003 | − | 0.0866278i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.2624 | + | 21.2390i | 0.601935 | + | 1.04258i | ||||
\(416\) | 20.5308 | 1.00661 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −15.3553 | −0.751054 | ||||||||
\(419\) | 4.40834 | − | 7.63547i | 0.215362 | − | 0.373017i | −0.738023 | − | 0.674776i | \(-0.764240\pi\) |
0.953384 | + | 0.301759i | \(0.0975737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.35004 | − | 16.1947i | −0.455693 | − | 0.789284i | 0.543035 | − | 0.839710i | \(-0.317275\pi\) |
−0.998728 | + | 0.0504267i | \(0.983942\pi\) | |||||||
\(422\) | 5.68776 | + | 9.85150i | 0.276876 | + | 0.479563i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.8452 | − | 18.7844i | 0.526689 | − | 0.912253i | ||||
\(425\) | −19.1217 | + | 33.1198i | −0.927539 | + | 1.60655i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.85354 | − | 4.02981i | 0.186486 | − | 0.195016i | ||||
\(428\) | −11.6181 | + | 20.1232i | −0.561584 | + | 0.972692i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.24516 | −0.108271 | ||||||||
\(431\) | −8.30972 | + | 14.3929i | −0.400265 | + | 0.693279i | −0.993758 | − | 0.111560i | \(-0.964415\pi\) |
0.593493 | + | 0.804839i | \(0.297749\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.3004 | −1.21586 | −0.607929 | − | 0.793992i | \(-0.707999\pi\) | ||||
−0.607929 | + | 0.793992i | \(0.707999\pi\) | |||||||
\(434\) | −0.797561 | − | 0.194707i | −0.0382841 | − | 0.00934621i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.1912 | −1.25433 | ||||||||
\(437\) | −2.14474 | − | 3.71481i | −0.102597 | − | 0.177703i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7262 | − | 25.5065i | 0.702841 | − | 1.21736i | −0.264624 | − | 0.964352i | \(-0.585248\pi\) |
0.967465 | − | 0.253005i | \(-0.0814190\pi\) | |||||||
\(440\) | −31.8215 | −1.51703 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −25.5589 | −1.21571 | ||||||||
\(443\) | 16.2783 | − | 28.1948i | 0.773404 | − | 1.33957i | −0.162284 | − | 0.986744i | \(-0.551886\pi\) |
0.935687 | − | 0.352830i | \(-0.114781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.489060 | + | 0.847077i | 0.0231837 | + | 0.0401553i | ||||
\(446\) | −33.5983 | −1.59092 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 32.8978 | + | 8.03126i | 1.55428 | + | 0.379442i | ||||
\(449\) | 0.171881 | 0.00811158 | 0.00405579 | − | 0.999992i | \(-0.498709\pi\) | ||||
0.00405579 | + | 0.999992i | \(0.498709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.4314 | − | 38.8523i | 1.05625 | − | 1.82948i | ||||
\(452\) | 7.95309 | 0.374082 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.73559 | + | 8.20227i | −0.222252 | + | 0.384952i | ||||
\(455\) | 20.0195 | − | 20.9352i | 0.938527 | − | 0.981456i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.2510 | + | 21.2194i | −0.573079 | + | 0.992602i | 0.423169 | + | 0.906051i | \(0.360918\pi\) |
−0.996247 | + | 0.0865506i | \(0.972416\pi\) | |||||||
\(458\) | −1.07226 | + | 1.85721i | −0.0501034 | + | 0.0867816i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.6010 | − | 25.2896i | −0.680773 | − | 1.17913i | ||||
\(461\) | −4.71554 | − | 8.16755i | −0.219624 | − | 0.380401i | 0.735069 | − | 0.677993i | \(-0.237150\pi\) |
−0.954693 | + | 0.297592i | \(0.903817\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.43061 | + | 2.47788i | −0.0664860 | + | 0.115157i | −0.897352 | − | 0.441315i | \(-0.854512\pi\) |
0.830866 | + | 0.556472i | \(0.187845\pi\) | |||||||
\(464\) | −1.11332 | −0.0516845 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.33170 | 0.385959 | ||||||||
\(467\) | −3.85144 | − | 6.67089i | −0.178223 | − | 0.308692i | 0.763049 | − | 0.646341i | \(-0.223702\pi\) |
−0.941272 | + | 0.337649i | \(0.890368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.98563 | − | 27.3426i | −0.368742 | − | 1.26256i | ||||
\(470\) | −33.3467 | − | 57.7582i | −1.53817 | − | 2.66419i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.669817 | + | 1.16016i | 0.0308308 | + | 0.0534005i | ||||
\(473\) | −0.577385 | − | 1.00006i | −0.0265482 | − | 0.0459829i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.63836 | + | 13.2300i | 0.350472 | + | 0.607035i | ||||
\(476\) | −29.7524 | − | 7.26338i | −1.36370 | − | 0.332916i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.38619 | + | 12.7932i | 0.337836 | + | 0.585150i | ||||
\(479\) | 34.5822 | 1.58010 | 0.790051 | − | 0.613041i | \(-0.210054\pi\) | ||||
0.790051 | + | 0.613041i | \(0.210054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23.8152 | 1.08588 | ||||||||
\(482\) | 16.5282 | − | 28.6277i | 0.752840 | − | 1.30396i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0695 | − | 19.1729i | −0.503159 | − | 0.871497i | ||||
\(485\) | 2.01539 | + | 3.49076i | 0.0915141 | + | 0.158507i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.21782 | + | 15.9657i | −0.417699 | + | 0.723476i | −0.995708 | − | 0.0925545i | \(-0.970497\pi\) |
0.578008 | + | 0.816031i | \(0.303830\pi\) | |||||||
\(488\) | −2.03636 | + | 3.52707i | −0.0921815 | + | 0.159663i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 49.6021 | − | 31.6752i | 2.24079 | − | 1.43094i | ||||
\(491\) | −1.57686 | + | 2.73120i | −0.0711627 | + | 0.123257i | −0.899411 | − | 0.437104i | \(-0.856004\pi\) |
0.828248 | + | 0.560361i | \(0.189338\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.02144 | 0.136079 | ||||||||
\(494\) | −5.10487 | + | 8.84190i | −0.229679 | + | 0.397816i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.208478 | −0.00936094 | ||||||||
\(497\) | −9.31462 | − | 2.27396i | −0.417818 | − | 0.102001i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.8798 | 1.29284 | 0.646419 | − | 0.762983i | \(-0.276266\pi\) | ||||
0.646419 | + | 0.762983i | \(0.276266\pi\) | |||||||
\(500\) | 24.6295 | + | 42.6596i | 1.10147 | + | 1.90780i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.8548 | + | 32.6575i | −0.841533 | + | 1.45758i | ||||
\(503\) | 21.4742 | 0.957487 | 0.478744 | − | 0.877955i | \(-0.341092\pi\) | ||||
0.478744 | + | 0.877955i | \(0.341092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.20085 | 0.231435 | ||||||||
\(506\) | 12.7336 | − | 22.0552i | 0.566078 | − | 0.980475i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.6341 | − | 34.0072i | −0.871120 | − | 1.50882i | ||||
\(509\) | 8.82435 | 0.391133 | 0.195566 | − | 0.980690i | \(-0.437346\pi\) | ||||
0.195566 | + | 0.980690i | \(0.437346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.53724 | + | 6.83626i | −0.289190 | + | 0.302418i | ||||
\(512\) | 16.3263 | 0.721527 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.46381 | − | 16.3918i | 0.417431 | − | 0.723011i | ||||
\(515\) | 57.0073 | 2.51204 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.1515 | − | 29.7072i | 0.754321 | − | 1.30652i | ||||
\(518\) | 47.0062 | + | 11.4755i | 2.06533 | + | 0.504205i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.5790 | + | 18.3234i | −0.463921 | + | 0.803535i | ||||
\(521\) | −14.8351 | + | 25.6952i | −0.649939 | + | 1.12573i | 0.333198 | + | 0.942857i | \(0.391872\pi\) |
−0.983137 | + | 0.182871i | \(0.941461\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.46995 | + | 6.01013i | 0.151730 | + | 0.262805i | 0.931864 | − | 0.362809i | \(-0.118182\pi\) |
−0.780133 | + | 0.625613i | \(0.784849\pi\) | |||||||
\(524\) | −25.3220 | − | 43.8591i | −1.10620 | − | 1.91599i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.28931 | + | 10.8934i | −0.274227 | + | 0.474975i | ||||
\(527\) | 0.565790 | 0.0246462 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.8858 | −0.690686 | ||||||||
\(530\) | −47.1824 | − | 81.7223i | −2.04947 | − | 3.54979i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.45516 | + | 8.84190i | −0.366577 | + | 0.383345i | ||||
\(533\) | −14.9146 | − | 25.8328i | −0.646023 | − | 1.11894i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.3863 | + | 26.6498i | 0.665208 | + | 1.15217i | ||||
\(536\) | 10.4031 | + | 18.0187i | 0.449347 | + | 0.778291i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.2241 | + | 29.8330i | 0.742582 | + | 1.28619i | ||||
\(539\) | 26.8652 | + | 13.9484i | 1.15716 | + | 0.600798i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.34520 | + | 14.4543i | 0.358788 | + | 0.621439i | 0.987759 | − | 0.155990i | \(-0.0498567\pi\) |
−0.628971 | + | 0.777429i | \(0.716523\pi\) | |||||||
\(542\) | −67.8683 | −2.91519 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.7474 | −1.23254 | ||||||||
\(545\) | −17.3429 | + | 30.0388i | −0.742889 | + | 1.28672i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.88962 | − | 3.27292i | −0.0807943 | − | 0.139940i | 0.822797 | − | 0.568335i | \(-0.192412\pi\) |
−0.903591 | + | 0.428395i | \(0.859079\pi\) | |||||||
\(548\) | −12.4602 | − | 21.5818i | −0.532275 | − | 0.921927i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −45.3499 | + | 78.5483i | −1.93373 | + | 3.34931i | ||||
\(551\) | 0.603473 | − | 1.04525i | 0.0257088 | − | 0.0445290i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.2023 | + | 29.4922i | −1.19928 | + | 1.25414i | ||||
\(554\) | 29.3582 | − | 50.8499i | 1.24731 | − | 2.16041i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.8283 | −0.459224 | ||||||||
\(557\) | 5.73458 | − | 9.93258i | 0.242982 | − | 0.420857i | −0.718580 | − | 0.695444i | \(-0.755208\pi\) |
0.961562 | + | 0.274587i | \(0.0885411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.767806 | −0.0324747 | ||||||||
\(560\) | 10.3288 | − | 10.8013i | 0.436473 | − | 0.456437i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −38.3337 | −1.61701 | ||||||||
\(563\) | 12.6908 | + | 21.9811i | 0.534854 | + | 0.926394i | 0.999170 | + | 0.0407249i | \(0.0129667\pi\) |
−0.464316 | + | 0.885669i | \(0.653700\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.26627 | − | 9.12145i | 0.221554 | − | 0.383742i | ||||
\(566\) | 40.5287 | 1.70355 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.00350 | 0.293860 | ||||||||
\(569\) | −4.34702 | + | 7.52926i | −0.182237 | + | 0.315643i | −0.942642 | − | 0.333806i | \(-0.891667\pi\) |
0.760405 | + | 0.649449i | \(0.225000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.06378 | − | 7.03868i | −0.170064 | − | 0.294560i | 0.768378 | − | 0.639996i | \(-0.221064\pi\) |
−0.938442 | + | 0.345437i | \(0.887731\pi\) | |||||||
\(572\) | −35.7494 | −1.49476 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.9906 | − | 58.1754i | −0.709173 | − | 2.42819i | ||||
\(575\) | −25.3368 | −1.05662 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.0420 | + | 19.1253i | −0.459683 | + | 0.796195i | −0.998944 | − | 0.0459441i | \(-0.985370\pi\) |
0.539261 | + | 0.842139i | \(0.318704\pi\) | |||||||
\(578\) | −1.74816 | −0.0727138 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.10832 | − | 7.11581i | 0.170589 | − | 0.295468i | ||||
\(581\) | 4.77721 | + | 16.3571i | 0.198192 | + | 0.678606i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.2677 | − | 42.0329i | 1.00506 | − | 1.74082i | ||||
\(584\) | 3.45452 | − | 5.98341i | 0.142949 | − | 0.247595i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.8107 | − | 20.4567i | −0.487895 | − | 0.845060i | ||||
\(587\) | −15.3600 | − | 26.6043i | −0.633975 | − | 1.09808i | −0.986731 | − | 0.162362i | \(-0.948089\pi\) |
0.352756 | − | 0.935715i | \(-0.385244\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.113005 | − | 0.195731i | 0.00465630 | − | 0.00806495i | ||||
\(590\) | 5.82812 | 0.239940 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.2872 | 0.505000 | ||||||||
\(593\) | 22.0358 | + | 38.1671i | 0.904901 | + | 1.56733i | 0.821050 | + | 0.570856i | \(0.193388\pi\) |
0.0838502 | + | 0.996478i | \(0.473278\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.0315 | + | 29.3136i | −1.14918 | + | 1.20174i | ||||
\(596\) | −6.62920 | − | 11.4821i | −0.271543 | − | 0.470326i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.46656 | − | 14.6645i | −0.346223 | − | 0.599677i | ||||
\(599\) | 13.6831 | + | 23.6999i | 0.559078 | + | 0.968351i | 0.997574 | + | 0.0696182i | \(0.0221781\pi\) |
−0.438496 | + | 0.898733i | \(0.644489\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.60908 | + | 6.25111i | 0.147217 | + | 0.254988i | 0.930198 | − | 0.367058i | \(-0.119635\pi\) |
−0.782981 | + | 0.622046i | \(0.786302\pi\) | |||||||
\(602\) | −1.51549 | − | 0.369973i | −0.0617668 | − | 0.0150790i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.2100 | − | 19.4164i | −0.456130 | − | 0.790040i | ||||
\(605\) | −29.3194 | −1.19200 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.0048 | 1.50198 | 0.750989 | − | 0.660315i | \(-0.229577\pi\) | ||||
0.750989 | + | 0.660315i | \(0.229577\pi\) | |||||||
\(608\) | −5.74173 | + | 9.94496i | −0.232858 | + | 0.403321i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.85923 | + | 15.3446i | 0.358700 | + | 0.621286i | ||||
\(611\) | −11.4040 | − | 19.7523i | −0.461357 | − | 0.799093i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.830292 | + | 1.43811i | −0.0335352 | + | 0.0580847i | −0.882306 | − | 0.470676i | \(-0.844010\pi\) |
0.848771 | + | 0.528761i | \(0.177343\pi\) | |||||||
\(614\) | −34.6598 | + | 60.0326i | −1.39876 | + | 2.42272i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −21.4796 | − | 5.24376i | −0.865438 | − | 0.211277i | ||||
\(617\) | 11.1209 | − | 19.2620i | 0.447710 | − | 0.775457i | −0.550526 | − | 0.834818i | \(-0.685573\pi\) |
0.998237 | + | 0.0593607i | \(0.0189062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.7805 | 0.795046 | 0.397523 | − | 0.917592i | \(-0.369870\pi\) | ||||
0.397523 | + | 0.917592i | \(0.369870\pi\) | |||||||
\(620\) | 0.769316 | − | 1.33249i | 0.0308965 | − | 0.0535142i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29.7838 | −1.19422 | ||||||||
\(623\) | 0.190530 | + | 0.652371i | 0.00763342 | + | 0.0261367i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.7393 | 0.709571 | ||||||||
\(626\) | 21.3528 | + | 36.9842i | 0.853431 | + | 1.47819i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −33.4470 | + | 57.9320i | −1.33468 | + | 2.31174i | ||||
\(629\) | −33.3462 | −1.32960 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.2569 | 1.96089 | 0.980443 | − | 0.196804i | \(-0.0630562\pi\) | ||||
0.980443 | + | 0.196804i | \(0.0630562\pi\) | |||||||
\(632\) | 14.9031 | − | 25.8130i | 0.592815 | − | 1.02678i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.9548 | + | 29.3666i | 0.673362 | + | 1.16630i | ||||
\(635\) | −52.0041 | −2.06372 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.9630 | − | 10.8324i | 0.672100 | − | 0.429194i | ||||
\(638\) | 7.16578 | 0.283696 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.6162 | + | 46.1006i | −1.05210 | + | 1.82229i | ||||
\(641\) | −8.65682 | −0.341924 | −0.170962 | − | 0.985278i | \(-0.554688\pi\) | ||||
−0.170962 | + | 0.985278i | \(0.554688\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.85782 | + | 15.3422i | −0.349318 | + | 0.605037i | −0.986129 | − | 0.165983i | \(-0.946920\pi\) |
0.636810 | + | 0.771021i | \(0.280254\pi\) | |||||||
\(644\) | −5.68830 | − | 19.4766i | −0.224150 | − | 0.767486i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.14789 | − | 12.3805i | 0.281230 | − | 0.487105i | ||||
\(647\) | 6.05092 | − | 10.4805i | 0.237886 | − | 0.412031i | −0.722221 | − | 0.691662i | \(-0.756879\pi\) |
0.960108 | + | 0.279631i | \(0.0902121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.49881 | + | 2.59602i | 0.0588335 | + | 0.101903i | ||||
\(650\) | 30.1531 | + | 52.2267i | 1.18270 | + | 2.04850i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.78523 | + | 15.2165i | −0.344056 | + | 0.595923i | ||||
\(653\) | −36.2140 | −1.41717 | −0.708583 | − | 0.705628i | \(-0.750665\pi\) | ||||
−0.708583 | + | 0.705628i | \(0.750665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −67.0697 | −2.62063 | ||||||||
\(656\) | −7.69502 | − | 13.3282i | −0.300440 | − | 0.520378i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.9913 | − | 44.4821i | −0.506455 | − | 1.73409i | ||||
\(659\) | −19.6707 | − | 34.0706i | −0.766261 | − | 1.32720i | −0.939577 | − | 0.342337i | \(-0.888781\pi\) |
0.173316 | − | 0.984866i | \(-0.444552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.830402 | + | 1.43830i | 0.0322989 | + | 0.0559433i | 0.881723 | − | 0.471767i | \(-0.156384\pi\) |
−0.849424 | + | 0.527711i | \(0.823050\pi\) | |||||||
\(662\) | 1.36707 | + | 2.36784i | 0.0531327 | + | 0.0920286i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.22343 | − | 10.7793i | −0.241516 | − | 0.418318i | ||||
\(665\) | 4.54211 | + | 15.5521i | 0.176135 | + | 0.603084i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00088 | + | 1.73357i | 0.0387540 | + | 0.0671240i | ||||
\(668\) | 33.4722 | 1.29508 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 90.5183 | 3.49703 | ||||||||
\(671\) | −4.55664 | + | 7.89233i | −0.175907 | + | 0.304680i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.4154 | − | 18.0399i | −0.401483 | − | 0.695388i | 0.592423 | − | 0.805627i | \(-0.298172\pi\) |
−0.993905 | + | 0.110239i | \(0.964838\pi\) | |||||||
\(674\) | −13.1470 | − | 22.7713i | −0.506405 | − | 0.877118i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.80421 | − | 11.7852i | 0.261700 | − | 0.453279i | ||||
\(677\) | 23.3654 | − | 40.4701i | 0.898006 | − | 1.55539i | 0.0679653 | − | 0.997688i | \(-0.478349\pi\) |
0.830040 | − | 0.557704i | \(-0.188317\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.785163 | + | 2.68838i | 0.0301318 | + | 0.103171i | ||||
\(680\) | 14.8129 | − | 25.6566i | 0.568048 | − | 0.983887i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.34185 | 0.0513822 | ||||||||
\(683\) | 10.5747 | − | 18.3159i | 0.404630 | − | 0.700840i | −0.589648 | − | 0.807660i | \(-0.700734\pi\) |
0.994278 | + | 0.106820i | \(0.0340669\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.0030 | −1.26098 | ||||||||
\(686\) | 38.7012 | − | 13.2071i | 1.47762 | − | 0.504248i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.396141 | −0.0151027 | ||||||||
\(689\) | −16.1356 | − | 27.9476i | −0.614716 | − | 1.06472i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7985 | − | 20.4356i | 0.448836 | − | 0.777407i | −0.549475 | − | 0.835510i | \(-0.685172\pi\) |
0.998311 | + | 0.0581038i | \(0.0185054\pi\) | |||||||
\(692\) | 55.3689 | 2.10481 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.59768 | −0.364323 | ||||||||
\(695\) | −7.17017 | + | 12.4191i | −0.271980 | + | 0.471083i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.8836 | + | 36.1714i | 0.791021 | + | 1.37009i | ||||
\(698\) | 15.8437 | 0.599693 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 20.2585 | + | 69.3646i | 0.765699 | + | 2.62174i | ||||
\(701\) | −42.1420 | −1.59168 | −0.795841 | − | 0.605505i | \(-0.792971\pi\) | ||||
−0.795841 | + | 0.605505i | \(0.792971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.66024 | + | 11.5359i | −0.251196 | + | 0.435084i | ||||
\(704\) | −55.3488 | −2.08603 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.7067 | + | 47.9894i | −1.04276 | + | 1.80611i | ||||
\(707\) | 3.51059 | + | 0.857032i | 0.132029 | + | 0.0322320i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9919 | + | 39.8231i | −0.863478 | + | 1.49559i | 0.00507252 | + | 0.999987i | \(0.498385\pi\) |
−0.868551 | + | 0.495601i | \(0.834948\pi\) | |||||||
\(710\) | 15.2345 | − | 26.3869i | 0.571740 | − | 0.990282i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.248209 | − | 0.429911i | −0.00930204 | − | 0.0161116i | ||||
\(713\) | 0.187422 | + | 0.324625i | 0.00701901 | + | 0.0121573i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.6721 | + | 41.0013i | −0.885286 | + | 1.53336i | ||||
\(716\) | 9.60869 | 0.359094 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 70.6378 | 2.63618 | ||||||||
\(719\) | 16.5249 | + | 28.6220i | 0.616275 | + | 1.06742i | 0.990159 | + | 0.139944i | \(0.0446922\pi\) |
−0.373885 | + | 0.927475i | \(0.621974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38.4801 | + | 9.39406i | 1.43307 | + | 0.349853i | ||||
\(722\) | 18.1207 | + | 31.3859i | 0.674381 | + | 1.16806i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28.3726 | + | 49.1428i | 1.05446 | + | 1.82638i | ||||
\(725\) | −3.56455 | − | 6.17398i | −0.132384 | − | 0.229296i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.5275 | + | 21.6982i | 0.464619 | + | 0.804743i | 0.999184 | − | 0.0403837i | \(-0.0128580\pi\) |
−0.534565 | + | 0.845127i | \(0.679525\pi\) | |||||||
\(728\) | −10.1603 | + | 10.6251i | −0.376567 | + | 0.393792i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.0290 | − | 26.0310i | −0.556248 | − | 0.963451i | ||||
\(731\) | 1.07509 | 0.0397636 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.0125 | 0.517563 | 0.258782 | − | 0.965936i | \(-0.416679\pi\) | ||||
0.258782 | + | 0.965936i | \(0.416679\pi\) | |||||||
\(734\) | 12.2817 | − | 21.2725i | 0.453326 | − | 0.785184i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.52280 | − | 16.4940i | −0.351015 | − | 0.607976i | ||||
\(737\) | 23.2785 | + | 40.3195i | 0.857474 | + | 1.48519i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.3007 | − | 33.4297i | 0.709987 | − | 1.22973i | −0.254875 | − | 0.966974i | \(-0.582034\pi\) |
0.964862 | − | 0.262759i | \(-0.0846323\pi\) | |||||||
\(740\) | −45.3415 | + | 78.5338i | −1.66679 | + | 2.88696i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.3815 | − | 62.9378i | −0.674806 | − | 2.31052i | ||||
\(743\) | 0.906592 | − | 1.57026i | 0.0332596 | − | 0.0576073i | −0.848916 | − | 0.528527i | \(-0.822745\pi\) |
0.882176 | + | 0.470920i | \(0.156078\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17.5586 | −0.643296 | ||||||||
\(746\) | −17.8346 | + | 30.8904i | −0.652971 | + | 1.13098i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 50.0567 | 1.83026 | ||||||||
\(749\) | 5.99425 | + | 20.5242i | 0.219025 | + | 0.749938i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.4262 | −1.07378 | −0.536888 | − | 0.843653i | \(-0.680400\pi\) | ||||
−0.536888 | + | 0.843653i | \(0.680400\pi\) | |||||||
\(752\) | −5.88377 | − | 10.1910i | −0.214559 | − | 0.371627i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.38226 | − | 4.12620i | 0.0867569 | − | 0.150267i | ||||
\(755\) | −29.6917 | −1.08059 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.5455 | 0.819431 | 0.409715 | − | 0.912213i | \(-0.365628\pi\) | ||||
0.409715 | + | 0.912213i | \(0.365628\pi\) | |||||||
\(758\) | −3.51607 | + | 6.09000i | −0.127709 | + | 0.221199i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.91715 | − | 10.2488i | −0.214638 | − | 0.371763i | ||||
\(761\) | −12.8626 | −0.466270 | −0.233135 | − | 0.972444i | \(-0.574898\pi\) | ||||
−0.233135 | + | 0.972444i | \(0.574898\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.6565 | + | 17.4184i | −0.603007 | + | 0.630589i | ||||
\(764\) | 12.0039 | 0.434285 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.1913 | + | 31.5082i | −0.657277 | + | 1.13844i | ||||
\(767\) | 1.99312 | 0.0719673 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.3611 | − | 38.7305i | 0.806362 | − | 1.39666i | −0.109007 | − | 0.994041i | \(-0.534767\pi\) |
0.915368 | − | 0.402618i | \(-0.131900\pi\) | |||||||
\(770\) | −66.4806 | + | 69.5215i | −2.39579 | + | 2.50538i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.9452 | − | 34.5460i | 0.717842 | − | 1.24334i | ||||
\(773\) | 5.24400 | − | 9.08288i | 0.188614 | − | 0.326688i | −0.756175 | − | 0.654370i | \(-0.772934\pi\) |
0.944788 | + | 0.327681i | \(0.106267\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.667491 | − | 1.15613i | −0.0239770 | − | 0.0415294i | ||||
\(776\) | −1.02286 | − | 1.77164i | −0.0367184 | − | 0.0635982i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 35.3026 | − | 61.1460i | 1.26566 | − | 2.19219i | ||||
\(779\) | 16.6843 | 0.597777 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.6713 | 0.560764 | ||||||||
\(782\) | 11.8550 | + | 20.5334i | 0.423933 | + | 0.734273i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.75190 | − | 5.58884i | 0.312568 | − | 0.199601i | ||||
\(785\) | 44.2950 | + | 76.7213i | 1.58096 | + | 2.73830i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.1037 | − | 27.8924i | −0.574035 | − | 0.994257i | −0.996146 | − | 0.0877130i | \(-0.972044\pi\) |
0.422111 | − | 0.906544i | \(-0.361289\pi\) | |||||||
\(788\) | −10.7609 | − | 18.6384i | −0.383341 | − | 0.663966i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −64.8365 | − | 112.300i | −2.30678 | − | 3.99546i | ||||
\(791\) | 5.05785 | − | 5.28920i | 0.179836 | − | 0.188062i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.02970 | + | 5.24760i | 0.107588 | + | 0.186348i | ||||
\(794\) | 61.4085 | 2.17931 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.3872 | −1.28971 | ||||||||
\(797\) | 16.1389 | − | 27.9534i | 0.571669 | − | 0.990160i | −0.424726 | − | 0.905322i | \(-0.639629\pi\) |
0.996395 | − | 0.0848377i | \(-0.0270372\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.9680 | + | 27.6574i | 0.564907 | + | 0.978448i | ||||
\(800\) | 33.9148 | + | 58.7422i | 1.19907 | + | 2.07685i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.4574 | − | 52.7538i | 1.07549 | − | 1.86280i | ||||
\(803\) | 7.72998 | − | 13.3887i | 0.272785 | − | 0.472478i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.1045 | − | 6.37282i | −0.920061 | − | 0.224612i | ||||
\(806\) | 0.446098 | − | 0.772664i | 0.0157131 | − | 0.0272159i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.63955 | −0.0928591 | ||||||||
\(809\) | 14.9820 | − | 25.9495i | 0.526737 | − | 0.912336i | −0.472777 | − | 0.881182i | \(-0.656748\pi\) |
0.999515 | − | 0.0311538i | \(-0.00991818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1971 | −0.463414 | −0.231707 | − | 0.972786i | \(-0.574431\pi\) | ||||
−0.231707 | + | 0.972786i | \(0.574431\pi\) | |||||||
\(812\) | 3.94572 | − | 4.12620i | 0.138468 | − | 0.144801i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −79.0853 | −2.77194 | ||||||||
\(815\) | 11.6346 | + | 20.1517i | 0.407541 | + | 0.705883i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.214728 | − | 0.371919i | 0.00751237 | − | 0.0130118i | ||||
\(818\) | −26.1087 | −0.912870 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 113.583 | 3.96650 | ||||||||
\(821\) | −4.01806 | + | 6.95948i | −0.140231 | + | 0.242888i | −0.927584 | − | 0.373616i | \(-0.878118\pi\) |
0.787352 | + | 0.616503i | \(0.211451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.78282 | − | 16.9443i | −0.341008 | − | 0.590643i | 0.643612 | − | 0.765352i | \(-0.277435\pi\) |
−0.984620 | + | 0.174709i | \(0.944102\pi\) | |||||||
\(824\) | −28.9325 | −1.00791 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.93400 | + | 0.960398i | 0.136881 | + | 0.0334165i | ||||
\(827\) | 45.8218 | 1.59338 | 0.796690 | − | 0.604389i | \(-0.206583\pi\) | ||||
0.796690 | + | 0.604389i | \(0.206583\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.0773 | + | 29.5787i | −0.593119 | + | 1.02731i | 0.400691 | + | 0.916213i | \(0.368770\pi\) |
−0.993809 | + | 0.111098i | \(0.964563\pi\) | |||||||
\(830\) | −54.1504 | −1.87959 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −18.4007 | + | 31.8709i | −0.637928 | + | 1.10492i | ||||
\(833\) | −23.7518 | + | 15.1676i | −0.822952 | + | 0.525525i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.1642 | − | 38.3895i | 0.767024 | − | 1.32852i | ||||
\(836\) | 9.99783 | − | 17.3168i | 0.345782 | − | 0.598913i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.73360 | + | 16.8591i | 0.336242 | + | 0.582388i | ||||
\(839\) | −17.7986 | − | 30.8281i | −0.614476 | − | 1.06430i | −0.990476 | − | 0.137684i | \(-0.956034\pi\) |
0.376000 | − | 0.926620i | \(-0.377299\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.2184 | − | 24.6270i | 0.490289 | − | 0.849205i | ||||
\(842\) | 41.2897 | 1.42294 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.8132 | −0.509891 | ||||||||
\(845\) | −9.01105 | − | 15.6076i | −0.309990 | − | 0.536918i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.7907 | − | 4.83146i | −0.680017 | − | 0.166011i | ||||
\(848\) | −8.32497 | − | 14.4193i | −0.285881 | − | 0.495160i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −42.2207 | − | 73.1283i | −1.44816 | − | 2.50828i | ||||
\(851\) | −11.0462 | − | 19.1325i | −0.378658 | − | 0.655855i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.6973 | − | 28.9206i | −0.571705 | − | 0.990222i | −0.996391 | − | 0.0848812i | \(-0.972949\pi\) |
0.424686 | − | 0.905341i | \(-0.360384\pi\) | |||||||
\(854\) | 3.45141 | + | 11.8176i | 0.118105 | + | 0.404389i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.80890 | − | 13.5254i | −0.266903 | − | 0.462289i | ||||
\(857\) | 25.8147 | 0.881814 | 0.440907 | − | 0.897553i | \(-0.354657\pi\) | ||||
0.440907 | + | 0.897553i | \(0.354657\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.0007 | −1.46716 | −0.733582 | − | 0.679601i | \(-0.762153\pi\) | ||||
−0.733582 | + | 0.679601i | \(0.762153\pi\) | |||||||
\(860\) | 1.46182 | − | 2.53195i | 0.0498477 | − | 0.0863387i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.3478 | − | 31.7794i | −0.624929 | − | 1.08241i | ||||
\(863\) | 10.7483 | + | 18.6166i | 0.365877 | + | 0.633718i | 0.988917 | − | 0.148473i | \(-0.0474357\pi\) |
−0.623039 | + | 0.782191i | \(0.714102\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.6634 | − | 63.5029i | 1.24659 | − | 2.15916i | ||||
\(866\) | 27.9315 | − | 48.3788i | 0.949152 | − | 1.64398i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.738868 | − | 0.772664i | 0.0250788 | − | 0.0262259i | ||||
\(869\) | 33.3479 | − | 57.7602i | 1.13125 | − | 1.95938i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.9557 | 1.04889 | ||||||||
\(872\) | 8.80194 | − | 15.2454i | 0.298071 | − | 0.516274i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.47117 | 0.320367 | ||||||||
\(875\) | 44.0341 | + | 10.7500i | 1.48863 | + | 0.363415i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.6841 | 0.495846 | 0.247923 | − | 0.968780i | \(-0.420252\pi\) | ||||
0.247923 | + | 0.968780i | \(0.420252\pi\) | |||||||
\(878\) | 32.5153 | + | 56.3182i | 1.09734 | + | 1.90065i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.2134 | + | 21.1542i | −0.411712 | + | 0.713107i | ||||
\(881\) | −37.6060 | −1.26698 | −0.633490 | − | 0.773751i | \(-0.718378\pi\) | ||||
−0.633490 | + | 0.773751i | \(0.718378\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.9989 | −1.58164 | −0.790820 | − | 0.612049i | \(-0.790345\pi\) | ||||
−0.790820 | + | 0.612049i | \(0.790345\pi\) | |||||||
\(884\) | 16.6413 | − | 28.8236i | 0.559709 | − | 0.969444i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.9423 | + | 62.2540i | 1.20751 | + | 2.09146i | ||||
\(887\) | 26.4248 | 0.887259 | 0.443630 | − | 0.896210i | \(-0.353691\pi\) | ||||
0.443630 | + | 0.896210i | \(0.353691\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.1029 | − | 8.56959i | −1.17731 | − | 0.287415i | ||||
\(890\) | −2.15969 | −0.0723928 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.8758 | − | 37.8900i | 0.732455 | − | 1.26865i | ||||
\(893\) | 12.7572 | 0.426902 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.36256 | − | 11.0203i | 0.212677 | − | 0.368367i | ||||
\(896\) | −25.5628 | + | 26.7321i | −0.853993 | + | 0.893056i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.189757 | + | 0.328668i | −0.00633226 | + | 0.0109678i | ||||
\(899\) | −0.0527355 | + | 0.0913406i | −0.00175883 | + | 0.00304638i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.5932 | + | 39.1325i | 0.752688 | + | 1.30369i | ||||
\(902\) | 49.5283 | + | 85.7856i | 1.64911 | + | 2.85635i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.67276 | + | 4.62935i | −0.0888946 | + | 0.153970i | ||||
\(905\) | 75.1496 | 2.49806 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.450052 | −0.0149437 | −0.00747187 | − | 0.999972i | \(-0.502378\pi\) | ||||
−0.00747187 | + | 0.999972i | \(0.502378\pi\) | |||||||
\(908\) | −6.16667 | − | 10.6810i | −0.204648 | − | 0.354461i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.9304 | + | 61.3932i | 0.594386 | + | 2.03517i | ||||
\(911\) | −2.37220 | − | 4.10877i | −0.0785944 | − | 0.136129i | 0.824049 | − | 0.566518i | \(-0.191710\pi\) |
−0.902644 | + | 0.430389i | \(0.858377\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.9258 | − | 24.1202i | −0.460877 | − | 0.798262i | ||||
\(914\) | −27.0502 | − | 46.8523i | −0.894742 | − | 1.54974i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.39629 | − | 2.41845i | −0.0461348 | − | 0.0799079i | ||||
\(917\) | −45.2722 | − | 11.0522i | −1.49502 | − | 0.364976i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2103 | − | 36.7372i | −0.699662 | − | 1.21185i | −0.968584 | − | 0.248688i | \(-0.920001\pi\) |
0.268922 | − | 0.963162i | \(-0.413333\pi\) | |||||||
\(920\) | 19.6275 | 0.647099 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.8238 | 0.685794 | ||||||||
\(923\) | 5.20993 | − | 9.02386i | 0.171487 | − | 0.297024i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.3402 | + | 68.1393i | 1.29350 | + | 2.24041i | ||||
\(926\) | −3.15878 | − | 5.47116i | −0.103804 | − | 0.179793i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.67946 | − | 4.64096i | 0.0879575 | − | 0.152347i | ||||
\(929\) | −22.5409 | + | 39.0419i | −0.739541 | + | 1.28092i | 0.213160 | + | 0.977017i | \(0.431624\pi\) |
−0.952702 | + | 0.303906i | \(0.901709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.503158 | + | 11.2462i | 0.0164903 | + | 0.368579i | ||||
\(932\) | −5.42476 | + | 9.39596i | −0.177694 | + | 0.307775i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.0079 | 0.556517 | ||||||||
\(935\) | 33.1459 | − | 57.4104i | 1.08399 | − | 1.87752i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.3045 | 0.630650 | 0.315325 | − | 0.948984i | \(-0.397886\pi\) | ||||
0.315325 | + | 0.948984i | \(0.397886\pi\) | |||||||
\(938\) | 61.1001 | + | 14.9162i | 1.99499 | + | 0.487032i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 86.8480 | 2.83267 | ||||||||
\(941\) | −5.27697 | − | 9.13997i | −0.172024 | − | 0.297955i | 0.767103 | − | 0.641524i | \(-0.221697\pi\) |
−0.939127 | + | 0.343569i | \(0.888364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.8357 | + | 23.9641i | −0.450551 | + | 0.780378i | ||||
\(944\) | 1.02833 | 0.0334692 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.54973 | 0.0828989 | ||||||||
\(947\) | −23.8800 | + | 41.3614i | −0.775996 | + | 1.34407i | 0.158236 | + | 0.987401i | \(0.449419\pi\) |
−0.934233 | + | 0.356664i | \(0.883914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.13966 | − | 8.90215i | −0.166840 | − | 0.288976i | ||||
\(950\) | −33.7309 | −1.09438 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 14.2266 | − | 14.8773i | 0.461087 | − | 0.482178i | ||||
\(953\) | 53.8101 | 1.74308 | 0.871540 | − | 0.490324i | \(-0.163121\pi\) | ||||
0.871540 | + | 0.490324i | \(0.163121\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.94856 | − | 13.7673i | 0.257209 | − | 0.445500i | ||||
\(956\) | −19.2365 | −0.622154 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.1787 | + | 66.1274i | −1.23350 | + | 2.13648i | ||||
\(959\) | −22.2772 | − | 5.43847i | −0.719367 | − | 0.175617i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.4901 | − | 26.8297i | 0.499681 | − | 0.865474i | ||||
\(962\) | −26.2919 | + | 45.5389i | −0.847684 | + | 1.46823i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 21.5230 | + | 37.2790i | 0.693210 | + | 1.20067i | ||||
\(965\) | −26.4141 | − | 45.7505i | −0.850299 | − | 1.47276i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.90887 | − | 8.50242i | 0.157859 | − | 0.273419i | −0.776238 | − | 0.630441i | \(-0.782874\pi\) |
0.934096 | + | 0.357021i | \(0.116208\pi\) | |||||||
\(968\) | 14.8803 | 0.478271 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.89994 | −0.285760 | ||||||||
\(971\) | 11.8993 | + | 20.6102i | 0.381867 | + | 0.661413i | 0.991329 | − | 0.131402i | \(-0.0419479\pi\) |
−0.609462 | + | 0.792815i | \(0.708615\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.88639 | + | 7.20138i | −0.220768 | + | 0.230866i | ||||
\(974\) | −20.3529 | − | 35.2523i | −0.652149 | − | 1.12956i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.56314 | + | 2.70744i | 0.0500350 | + | 0.0866631i | ||||
\(977\) | 19.9951 | + | 34.6326i | 0.639701 | + | 1.10799i | 0.985498 | + | 0.169685i | \(0.0542752\pi\) |
−0.345797 | + | 0.938309i | \(0.612391\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.555404 | − | 0.961988i | −0.0177508 | − | 0.0307453i | ||||
\(980\) | 3.42539 | + | 76.5617i | 0.109420 | + | 2.44567i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.48170 | − | 6.03048i | −0.111106 | − | 0.192440i | ||||
\(983\) | −46.2286 | −1.47446 | −0.737231 | − | 0.675641i | \(-0.763867\pi\) | ||||
−0.737231 | + | 0.675641i | \(0.763867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.5020 | −0.908151 | ||||||||
\(986\) | −3.33567 | + | 5.77754i | −0.106229 | + | 0.183994i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.64755 | − | 11.5139i | −0.211487 | − | 0.366306i | ||||
\(989\) | 0.356131 | + | 0.616838i | 0.0113243 | + | 0.0196143i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.19818 | + | 12.4676i | −0.228658 | + | 0.396047i | −0.957411 | − | 0.288730i | \(-0.906767\pi\) |
0.728753 | + | 0.684777i | \(0.240100\pi\) | |||||||
\(992\) | 0.501750 | − | 0.869057i | 0.0159306 | − | 0.0275926i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.6315 | − | 15.3008i | 0.464084 | − | 0.485312i | ||||
\(995\) | −24.0944 | + | 41.7327i | −0.763844 | + | 1.32302i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.8546 | 1.38889 | 0.694444 | − | 0.719547i | \(-0.255650\pi\) | ||||
0.694444 | + | 0.719547i | \(0.255650\pi\) | |||||||
\(998\) | −31.8833 | + | 55.2234i | −1.00925 | + | 1.74807i | ||||
\(999\) | 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 | 567.2.g.j.109.1 | 8 | ||
3.2 | odd | 2 | 567.2.g.k.109.4 | 8 | |||
7.2 | even | 3 | 567.2.h.k.352.4 | 8 | |||
9.2 | odd | 6 | 567.2.h.j.298.1 | 8 | |||
9.4 | even | 3 | 567.2.e.c.487.1 | yes | 8 | ||
9.5 | odd | 6 | 567.2.e.d.487.4 | yes | 8 | ||
9.7 | even | 3 | 567.2.h.k.298.4 | 8 | |||
21.2 | odd | 6 | 567.2.h.j.352.1 | 8 | |||
63.2 | odd | 6 | 567.2.g.k.541.4 | 8 | |||
63.4 | even | 3 | 3969.2.a.x.1.4 | 4 | |||
63.16 | even | 3 | inner | 567.2.g.j.541.1 | 8 | ||
63.23 | odd | 6 | 567.2.e.d.163.4 | yes | 8 | ||
63.31 | odd | 6 | 3969.2.a.w.1.4 | 4 | |||
63.32 | odd | 6 | 3969.2.a.s.1.1 | 4 | |||
63.58 | even | 3 | 567.2.e.c.163.1 | ✓ | 8 | ||
63.59 | even | 6 | 3969.2.a.t.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
567.2.e.c.163.1 | ✓ | 8 | 63.58 | even | 3 | ||
567.2.e.c.487.1 | yes | 8 | 9.4 | even | 3 | ||
567.2.e.d.163.4 | yes | 8 | 63.23 | odd | 6 | ||
567.2.e.d.487.4 | yes | 8 | 9.5 | odd | 6 | ||
567.2.g.j.109.1 | 8 | 1.1 | even | 1 | trivial | ||
567.2.g.j.541.1 | 8 | 63.16 | even | 3 | inner | ||
567.2.g.k.109.4 | 8 | 3.2 | odd | 2 | |||
567.2.g.k.541.4 | 8 | 63.2 | odd | 6 | |||
567.2.h.j.298.1 | 8 | 9.2 | odd | 6 | |||
567.2.h.j.352.1 | 8 | 21.2 | odd | 6 | |||
567.2.h.k.298.4 | 8 | 9.7 | even | 3 | |||
567.2.h.k.352.4 | 8 | 7.2 | even | 3 | |||
3969.2.a.s.1.1 | 4 | 63.32 | odd | 6 | |||
3969.2.a.t.1.1 | 4 | 63.59 | even | 6 | |||
3969.2.a.w.1.4 | 4 | 63.31 | odd | 6 | |||
3969.2.a.x.1.4 | 4 | 63.4 | even | 3 |