Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(91,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.e (of order \(2\), degree \(1\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.7465802011608416256.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.15 | ||
Root | \(-1.18353 - 0.774115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.91 |
Dual form | 460.2.e.a.91.14 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35760 | + | 0.396143i | 0.959966 | + | 0.280116i | ||||
\(3\) | 0.679463i | 0.392288i | 0.980575 | + | 0.196144i | \(0.0628420\pi\) | ||||
−0.980575 | + | 0.196144i | \(0.937158\pi\) | |||||||
\(4\) | 1.68614 | + | 1.07561i | 0.843070 | + | 0.537803i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −0.269165 | + | 0.922437i | −0.109886 | + | 0.376583i | ||||
\(7\) | −1.16300 | −0.439572 | −0.219786 | − | 0.975548i | \(-0.570536\pi\) | ||||
−0.219786 | + | 0.975548i | \(0.570536\pi\) | |||||||
\(8\) | 1.86301 | + | 2.12819i | 0.658672 | + | 0.752430i | ||||
\(9\) | 2.53833 | 0.846110 | ||||||||
\(10\) | 0.396143 | − | 1.35760i | 0.125272 | − | 0.429310i | ||||
\(11\) | 3.53986 | 1.06731 | 0.533654 | − | 0.845703i | \(-0.320819\pi\) | ||||
0.533654 | + | 0.845703i | \(0.320819\pi\) | |||||||
\(12\) | −0.730835 | + | 1.14567i | −0.210974 | + | 0.330727i | ||||
\(13\) | −2.38665 | −0.661938 | −0.330969 | − | 0.943642i | \(-0.607376\pi\) | ||||
−0.330969 | + | 0.943642i | \(0.607376\pi\) | |||||||
\(14\) | −1.57888 | − | 0.460714i | −0.421974 | − | 0.123131i | ||||
\(15\) | 0.679463 | 0.175437 | ||||||||
\(16\) | 1.68614 | + | 3.62725i | 0.421535 | + | 0.906812i | ||||
\(17\) | 3.19542i | 0.775002i | 0.921869 | + | 0.387501i | \(0.126662\pi\) | ||||
−0.921869 | + | 0.387501i | \(0.873338\pi\) | |||||||
\(18\) | 3.44603 | + | 1.00554i | 0.812237 | + | 0.237009i | ||||
\(19\) | 1.16300 | 0.266810 | 0.133405 | − | 0.991062i | \(-0.457409\pi\) | ||||
0.133405 | + | 0.991062i | \(0.457409\pi\) | |||||||
\(20\) | 1.07561 | − | 1.68614i | 0.240513 | − | 0.377033i | ||||
\(21\) | − | 0.790214i | − | 0.172439i | ||||||
\(22\) | 4.80570 | + | 1.40229i | 1.02458 | + | 0.298970i | ||||
\(23\) | −4.70285 | − | 0.939764i | −0.980613 | − | 0.195954i | ||||
\(24\) | −1.44603 | + | 1.26584i | −0.295170 | + | 0.258389i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −3.24011 | − | 0.945456i | −0.635438 | − | 0.185419i | ||||
\(27\) | 3.76309i | 0.724207i | ||||||||
\(28\) | −1.96098 | − | 1.25093i | −0.370590 | − | 0.236403i | ||||
\(29\) | −0.284805 | −0.0528870 | −0.0264435 | − | 0.999650i | \(-0.508418\pi\) | ||||
−0.0264435 | + | 0.999650i | \(0.508418\pi\) | |||||||
\(30\) | 0.922437 | + | 0.269165i | 0.168413 | + | 0.0491426i | ||||
\(31\) | − | 4.43358i | − | 0.796295i | −0.917321 | − | 0.398148i | \(-0.869653\pi\) | ||
0.917321 | − | 0.398148i | \(-0.130347\pi\) | |||||||
\(32\) | 0.852189 | + | 5.59230i | 0.150647 | + | 0.988588i | ||||
\(33\) | 2.40520i | 0.418692i | ||||||||
\(34\) | −1.26584 | + | 4.33809i | −0.217090 | + | 0.743976i | ||||
\(35\) | 1.16300i | 0.196582i | ||||||||
\(36\) | 4.27998 | + | 2.73024i | 0.713330 | + | 0.455041i | ||||
\(37\) | − | 8.93580i | − | 1.46904i | −0.678589 | − | 0.734518i | \(-0.737408\pi\) | ||
0.678589 | − | 0.734518i | \(-0.262592\pi\) | |||||||
\(38\) | 1.57888 | + | 0.460714i | 0.256128 | + | 0.0747376i | ||||
\(39\) | − | 1.62164i | − | 0.259670i | ||||||
\(40\) | 2.12819 | − | 1.86301i | 0.336497 | − | 0.294567i | ||||
\(41\) | −2.51978 | −0.393523 | −0.196762 | − | 0.980451i | \(-0.563042\pi\) | ||||
−0.196762 | + | 0.980451i | \(0.563042\pi\) | |||||||
\(42\) | 0.313038 | − | 1.07279i | 0.0483028 | − | 0.165535i | ||||
\(43\) | −6.07154 | −0.925902 | −0.462951 | − | 0.886384i | \(-0.653209\pi\) | ||||
−0.462951 | + | 0.886384i | \(0.653209\pi\) | |||||||
\(44\) | 5.96870 | + | 3.80749i | 0.899815 | + | 0.574001i | ||||
\(45\) | − | 2.53833i | − | 0.378392i | ||||||
\(46\) | −6.01230 | − | 3.13883i | −0.886466 | − | 0.462795i | ||||
\(47\) | − | 13.2344i | − | 1.93043i | −0.261456 | − | 0.965215i | \(-0.584203\pi\) | ||
0.261456 | − | 0.965215i | \(-0.415797\pi\) | |||||||
\(48\) | −2.46458 | + | 1.14567i | −0.355732 | + | 0.165363i | ||||
\(49\) | −5.64744 | −0.806777 | ||||||||
\(50\) | −1.35760 | − | 0.396143i | −0.191993 | − | 0.0560232i | ||||
\(51\) | −2.17117 | −0.304024 | ||||||||
\(52\) | −4.02423 | − | 2.56710i | −0.558060 | − | 0.355992i | ||||
\(53\) | 7.45202i | 1.02361i | 0.859100 | + | 0.511807i | \(0.171024\pi\) | ||||
−0.859100 | + | 0.511807i | \(0.828976\pi\) | |||||||
\(54\) | −1.49072 | + | 5.10876i | −0.202862 | + | 0.695214i | ||||
\(55\) | − | 3.53986i | − | 0.477314i | ||||||
\(56\) | −2.16667 | − | 2.47508i | −0.289533 | − | 0.330747i | ||||
\(57\) | 0.790214i | 0.104666i | ||||||||
\(58\) | −0.386651 | − | 0.112824i | −0.0507698 | − | 0.0148145i | ||||
\(59\) | − | 8.51278i | − | 1.10827i | −0.832427 | − | 0.554135i | \(-0.813049\pi\) | ||
0.832427 | − | 0.554135i | \(-0.186951\pi\) | |||||||
\(60\) | 1.14567 | + | 0.730835i | 0.147905 | + | 0.0943504i | ||||
\(61\) | 7.71164i | 0.987374i | 0.869640 | + | 0.493687i | \(0.164351\pi\) | ||||
−0.869640 | + | 0.493687i | \(0.835649\pi\) | |||||||
\(62\) | 1.75634 | − | 6.01902i | 0.223055 | − | 0.764416i | ||||
\(63\) | −2.95207 | −0.371926 | ||||||||
\(64\) | −1.05842 | + | 7.92967i | −0.132303 | + | 0.991209i | ||||
\(65\) | 2.38665i | 0.296028i | ||||||||
\(66\) | −0.952806 | + | 3.26530i | −0.117282 | + | 0.401930i | ||||
\(67\) | 11.4005 | 1.39279 | 0.696395 | − | 0.717659i | \(-0.254786\pi\) | ||||
0.696395 | + | 0.717659i | \(0.254786\pi\) | |||||||
\(68\) | −3.43701 | + | 5.38792i | −0.416799 | + | 0.653382i | ||||
\(69\) | 0.638535 | − | 3.19542i | 0.0768706 | − | 0.384683i | ||||
\(70\) | −0.460714 | + | 1.57888i | −0.0550658 | + | 0.188712i | ||||
\(71\) | − | 1.46199i | − | 0.173506i | −0.996230 | − | 0.0867529i | \(-0.972351\pi\) | ||
0.996230 | − | 0.0867529i | \(-0.0276491\pi\) | |||||||
\(72\) | 4.72892 | + | 5.40206i | 0.557309 | + | 0.636639i | ||||
\(73\) | 4.88851 | 0.572156 | 0.286078 | − | 0.958206i | \(-0.407648\pi\) | ||||
0.286078 | + | 0.958206i | \(0.407648\pi\) | |||||||
\(74\) | 3.53986 | − | 12.1312i | 0.411500 | − | 1.41022i | ||||
\(75\) | − | 0.679463i | − | 0.0784576i | ||||||
\(76\) | 1.96098 | + | 1.25093i | 0.224939 | + | 0.143491i | ||||
\(77\) | −4.11684 | −0.469158 | ||||||||
\(78\) | 0.642403 | − | 2.20154i | 0.0727378 | − | 0.249275i | ||||
\(79\) | 5.08495 | 0.572102 | 0.286051 | − | 0.958214i | \(-0.407657\pi\) | ||||
0.286051 | + | 0.958214i | \(0.407657\pi\) | |||||||
\(80\) | 3.62725 | − | 1.68614i | 0.405539 | − | 0.188516i | ||||
\(81\) | 5.05811 | 0.562012 | ||||||||
\(82\) | −3.42084 | − | 0.998194i | −0.377769 | − | 0.110232i | ||||
\(83\) | −15.1460 | −1.66249 | −0.831246 | − | 0.555904i | \(-0.812372\pi\) | ||||
−0.831246 | + | 0.555904i | \(0.812372\pi\) | |||||||
\(84\) | 0.849959 | − | 1.33241i | 0.0927381 | − | 0.145378i | ||||
\(85\) | 3.19542 | 0.346592 | ||||||||
\(86\) | −8.24271 | − | 2.40520i | −0.888835 | − | 0.259360i | ||||
\(87\) | − | 0.193515i | − | 0.0207470i | ||||||
\(88\) | 6.59477 | + | 7.53351i | 0.703005 | + | 0.803074i | ||||
\(89\) | − | 3.06420i | − | 0.324805i | −0.986725 | − | 0.162402i | \(-0.948076\pi\) | ||
0.986725 | − | 0.162402i | \(-0.0519243\pi\) | |||||||
\(90\) | 1.00554 | − | 3.44603i | 0.105994 | − | 0.363243i | ||||
\(91\) | 2.77567 | 0.290969 | ||||||||
\(92\) | −6.91886 | − | 6.64300i | −0.721341 | − | 0.692580i | ||||
\(93\) | 3.01246 | 0.312377 | ||||||||
\(94\) | 5.24271 | − | 17.9669i | 0.540744 | − | 1.85315i | ||||
\(95\) | − | 1.16300i | − | 0.119321i | ||||||
\(96\) | −3.79976 | + | 0.579031i | −0.387811 | + | 0.0590971i | ||||
\(97\) | − | 13.5832i | − | 1.37917i | −0.724205 | − | 0.689584i | \(-0.757793\pi\) | ||
0.724205 | − | 0.689584i | \(-0.242207\pi\) | |||||||
\(98\) | −7.66695 | − | 2.23720i | −0.774479 | − | 0.225991i | ||||
\(99\) | 8.98533 | 0.903059 | ||||||||
\(100\) | −1.68614 | − | 1.07561i | −0.168614 | − | 0.107561i | ||||
\(101\) | −13.8429 | −1.37742 | −0.688708 | − | 0.725039i | \(-0.741822\pi\) | ||||
−0.688708 | + | 0.725039i | \(0.741822\pi\) | |||||||
\(102\) | −2.94757 | − | 0.860094i | −0.291853 | − | 0.0851620i | ||||
\(103\) | −11.3622 | −1.11955 | −0.559775 | − | 0.828645i | \(-0.689112\pi\) | ||||
−0.559775 | + | 0.828645i | \(0.689112\pi\) | |||||||
\(104\) | −4.44634 | − | 5.07926i | −0.436000 | − | 0.498062i | ||||
\(105\) | −0.790214 | −0.0771169 | ||||||||
\(106\) | −2.95207 | + | 10.1168i | −0.286730 | + | 0.982635i | ||||
\(107\) | 6.07154 | 0.586958 | 0.293479 | − | 0.955965i | \(-0.405187\pi\) | ||||
0.293479 | + | 0.955965i | \(0.405187\pi\) | |||||||
\(108\) | −4.04761 | + | 6.34510i | −0.389481 | + | 0.610558i | ||||
\(109\) | 8.01437i | 0.767637i | 0.923408 | + | 0.383819i | \(0.125391\pi\) | ||||
−0.923408 | + | 0.383819i | \(0.874609\pi\) | |||||||
\(110\) | 1.40229 | − | 4.80570i | 0.133703 | − | 0.458206i | ||||
\(111\) | 6.07154 | 0.576286 | ||||||||
\(112\) | −1.96098 | − | 4.21848i | −0.185295 | − | 0.398609i | ||||
\(113\) | 4.90706i | 0.461617i | 0.972999 | + | 0.230809i | \(0.0741371\pi\) | ||||
−0.972999 | + | 0.230809i | \(0.925863\pi\) | |||||||
\(114\) | −0.313038 | + | 1.07279i | −0.0293187 | + | 0.100476i | ||||
\(115\) | −0.939764 | + | 4.70285i | −0.0876334 | + | 0.438543i | ||||
\(116\) | −0.480222 | − | 0.306339i | −0.0445875 | − | 0.0284428i | ||||
\(117\) | −6.05811 | −0.560072 | ||||||||
\(118\) | 3.37228 | − | 11.5569i | 0.310444 | − | 1.06390i | ||||
\(119\) | − | 3.71626i | − | 0.340669i | ||||||
\(120\) | 1.26584 | + | 1.44603i | 0.115555 | + | 0.132004i | ||||
\(121\) | 1.53059 | 0.139145 | ||||||||
\(122\) | −3.05492 | + | 10.4693i | −0.276579 | + | 0.947846i | ||||
\(123\) | − | 1.71210i | − | 0.154375i | ||||||
\(124\) | 4.76879 | − | 7.47565i | 0.428250 | − | 0.671333i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −4.00772 | − | 1.16944i | −0.357036 | − | 0.104182i | ||||
\(127\) | 5.02137i | 0.445575i | 0.974867 | + | 0.222787i | \(0.0715156\pi\) | ||||
−0.974867 | + | 0.222787i | \(0.928484\pi\) | |||||||
\(128\) | −4.57820 | + | 10.3460i | −0.404660 | + | 0.914467i | ||||
\(129\) | − | 4.12539i | − | 0.363220i | ||||||
\(130\) | −0.945456 | + | 3.24011i | −0.0829220 | + | 0.284177i | ||||
\(131\) | − | 2.24289i | − | 0.195962i | −0.995188 | − | 0.0979810i | \(-0.968762\pi\) | ||
0.995188 | − | 0.0979810i | \(-0.0312385\pi\) | |||||||
\(132\) | −2.58705 | + | 4.05551i | −0.225174 | + | 0.352987i | ||||
\(133\) | −1.35256 | −0.117282 | ||||||||
\(134\) | 15.4773 | + | 4.51622i | 1.33703 | + | 0.390142i | ||||
\(135\) | 3.76309 | 0.323875 | ||||||||
\(136\) | −6.80047 | + | 5.95308i | −0.583135 | + | 0.510472i | ||||
\(137\) | − | 5.46941i | − | 0.467283i | −0.972323 | − | 0.233641i | \(-0.924936\pi\) | ||
0.972323 | − | 0.233641i | \(-0.0750642\pi\) | |||||||
\(138\) | 2.13272 | − | 4.08514i | 0.181549 | − | 0.347750i | ||||
\(139\) | 16.1962i | 1.37374i | 0.726779 | + | 0.686872i | \(0.241017\pi\) | ||||
−0.726779 | + | 0.686872i | \(0.758983\pi\) | |||||||
\(140\) | −1.25093 | + | 1.96098i | −0.105723 | + | 0.165733i | ||||
\(141\) | 8.99226 | 0.757285 | ||||||||
\(142\) | 0.579156 | − | 1.98479i | 0.0486017 | − | 0.166560i | ||||
\(143\) | −8.44841 | −0.706491 | ||||||||
\(144\) | 4.27998 | + | 9.20715i | 0.356665 | + | 0.767263i | ||||
\(145\) | 0.284805i | 0.0236518i | ||||||||
\(146\) | 6.63662 | + | 1.93655i | 0.549251 | + | 0.160270i | ||||
\(147\) | − | 3.83723i | − | 0.316489i | ||||||
\(148\) | 9.61140 | − | 15.0670i | 0.790052 | − | 1.23850i | ||||
\(149\) | − | 17.2126i | − | 1.41011i | −0.709152 | − | 0.705055i | \(-0.750922\pi\) | ||
0.709152 | − | 0.705055i | \(-0.249078\pi\) | |||||||
\(150\) | 0.269165 | − | 0.922437i | 0.0219772 | − | 0.0753167i | ||||
\(151\) | 3.80751i | 0.309851i | 0.987926 | + | 0.154925i | \(0.0495137\pi\) | ||||
−0.987926 | + | 0.154925i | \(0.950486\pi\) | |||||||
\(152\) | 2.16667 | + | 2.47508i | 0.175740 | + | 0.200756i | ||||
\(153\) | 8.11102i | 0.655737i | ||||||||
\(154\) | −5.58902 | − | 1.63086i | −0.450376 | − | 0.131419i | ||||
\(155\) | −4.43358 | −0.356114 | ||||||||
\(156\) | 1.74425 | − | 2.73432i | 0.139652 | − | 0.218920i | ||||
\(157\) | 16.7787i | 1.33908i | 0.742775 | + | 0.669541i | \(0.233509\pi\) | ||||
−0.742775 | + | 0.669541i | \(0.766491\pi\) | |||||||
\(158\) | 6.90331 | + | 2.01437i | 0.549198 | + | 0.160255i | ||||
\(159\) | −5.06337 | −0.401552 | ||||||||
\(160\) | 5.59230 | − | 0.852189i | 0.442110 | − | 0.0673715i | ||||
\(161\) | 5.46941 | + | 1.09294i | 0.431050 | + | 0.0861359i | ||||
\(162\) | 6.86687 | + | 2.00374i | 0.539513 | + | 0.157428i | ||||
\(163\) | 15.8341i | 1.24022i | 0.784515 | + | 0.620110i | \(0.212912\pi\) | ||||
−0.784515 | + | 0.620110i | \(0.787088\pi\) | |||||||
\(164\) | −4.24870 | − | 2.71029i | −0.331768 | − | 0.211638i | ||||
\(165\) | 2.40520 | 0.187245 | ||||||||
\(166\) | −20.5622 | − | 6.00000i | −1.59594 | − | 0.465690i | ||||
\(167\) | 8.51278i | 0.658738i | 0.944201 | + | 0.329369i | \(0.106836\pi\) | ||||
−0.944201 | + | 0.329369i | \(0.893164\pi\) | |||||||
\(168\) | 1.68173 | − | 1.47217i | 0.129748 | − | 0.113581i | ||||
\(169\) | −7.30390 | −0.561838 | ||||||||
\(170\) | 4.33809 | + | 1.26584i | 0.332716 | + | 0.0970858i | ||||
\(171\) | 2.95207 | 0.225750 | ||||||||
\(172\) | −10.2375 | − | 6.53059i | −0.780600 | − | 0.497953i | ||||
\(173\) | −3.19542 | −0.242943 | −0.121472 | − | 0.992595i | \(-0.538761\pi\) | ||||
−0.121472 | + | 0.992595i | \(0.538761\pi\) | |||||||
\(174\) | 0.0766596 | − | 0.262715i | 0.00581155 | − | 0.0199164i | ||||
\(175\) | 1.16300 | 0.0879143 | ||||||||
\(176\) | 5.96870 | + | 12.8399i | 0.449908 | + | 0.967847i | ||||
\(177\) | 5.78412 | 0.434761 | ||||||||
\(178\) | 1.21386 | − | 4.15995i | 0.0909830 | − | 0.311802i | ||||
\(179\) | 2.24289i | 0.167641i | 0.996481 | + | 0.0838207i | \(0.0267123\pi\) | ||||
−0.996481 | + | 0.0838207i | \(0.973288\pi\) | |||||||
\(180\) | 2.73024 | − | 4.27998i | 0.203500 | − | 0.319011i | ||||
\(181\) | 0.433943i | 0.0322547i | 0.999870 | + | 0.0161274i | \(0.00513372\pi\) | ||||
−0.999870 | + | 0.0161274i | \(0.994866\pi\) | |||||||
\(182\) | 3.76824 | + | 1.09956i | 0.279320 | + | 0.0815050i | ||||
\(183\) | −5.23978 | −0.387335 | ||||||||
\(184\) | −6.76144 | − | 11.7594i | −0.498460 | − | 0.866913i | ||||
\(185\) | −8.93580 | −0.656973 | ||||||||
\(186\) | 4.08970 | + | 1.19337i | 0.299872 | + | 0.0875018i | ||||
\(187\) | 11.3113i | 0.827166i | ||||||||
\(188\) | 14.2350 | − | 22.3150i | 1.03819 | − | 1.62749i | ||||
\(189\) | − | 4.37646i | − | 0.318341i | ||||||
\(190\) | 0.460714 | − | 1.57888i | 0.0334237 | − | 0.114544i | ||||
\(191\) | 15.1460 | 1.09593 | 0.547964 | − | 0.836502i | \(-0.315403\pi\) | ||||
0.547964 | + | 0.836502i | \(0.315403\pi\) | |||||||
\(192\) | −5.38792 | − | 0.719159i | −0.388840 | − | 0.0519008i | ||||
\(193\) | 12.1152 | 0.872071 | 0.436036 | − | 0.899929i | \(-0.356382\pi\) | ||||
0.436036 | + | 0.899929i | \(0.356382\pi\) | |||||||
\(194\) | 5.38091 | − | 18.4406i | 0.386327 | − | 1.32396i | ||||
\(195\) | −1.62164 | −0.116128 | ||||||||
\(196\) | −9.52238 | − | 6.07442i | −0.680170 | − | 0.433887i | ||||
\(197\) | 12.0252 | 0.856759 | 0.428380 | − | 0.903599i | \(-0.359085\pi\) | ||||
0.428380 | + | 0.903599i | \(0.359085\pi\) | |||||||
\(198\) | 12.1985 | + | 3.55948i | 0.866906 | + | 0.252961i | ||||
\(199\) | 26.5465 | 1.88183 | 0.940916 | − | 0.338641i | \(-0.109967\pi\) | ||||
0.940916 | + | 0.338641i | \(0.109967\pi\) | |||||||
\(200\) | −1.86301 | − | 2.12819i | −0.131734 | − | 0.150486i | ||||
\(201\) | 7.74620i | 0.546375i | ||||||||
\(202\) | −18.7930 | − | 5.48376i | −1.32227 | − | 0.385836i | ||||
\(203\) | 0.331228 | 0.0232476 | ||||||||
\(204\) | −3.66089 | − | 2.33532i | −0.256314 | − | 0.163505i | ||||
\(205\) | 2.51978i | 0.175989i | ||||||||
\(206\) | −15.4253 | − | 4.50106i | −1.07473 | − | 0.313603i | ||||
\(207\) | −11.9374 | − | 2.38543i | −0.829706 | − | 0.165799i | ||||
\(208\) | −4.02423 | − | 8.65698i | −0.279030 | − | 0.600253i | ||||
\(209\) | 4.11684 | 0.284768 | ||||||||
\(210\) | −1.07279 | − | 0.313038i | −0.0740297 | − | 0.0216017i | ||||
\(211\) | 14.7346i | 1.01437i | 0.861836 | + | 0.507187i | \(0.169315\pi\) | ||||
−0.861836 | + | 0.507187i | \(0.830685\pi\) | |||||||
\(212\) | −8.01544 | + | 12.5652i | −0.550503 | + | 0.862978i | ||||
\(213\) | 0.993366 | 0.0680643 | ||||||||
\(214\) | 8.24271 | + | 2.40520i | 0.563460 | + | 0.164416i | ||||
\(215\) | 6.07154i | 0.414076i | ||||||||
\(216\) | −8.00859 | + | 7.01066i | −0.544915 | + | 0.477015i | ||||
\(217\) | 5.15624i | 0.350029i | ||||||||
\(218\) | −3.17484 | + | 10.8803i | −0.215027 | + | 0.736906i | ||||
\(219\) | 3.32156i | 0.224450i | ||||||||
\(220\) | 3.80749 | − | 5.96870i | 0.256701 | − | 0.402410i | ||||
\(221\) | − | 7.62634i | − | 0.513003i | ||||||
\(222\) | 8.24271 | + | 2.40520i | 0.553215 | + | 0.161427i | ||||
\(223\) | 8.64152i | 0.578679i | 0.957227 | + | 0.289339i | \(0.0934356\pi\) | ||||
−0.957227 | + | 0.289339i | \(0.906564\pi\) | |||||||
\(224\) | −0.991093 | − | 6.50382i | −0.0662202 | − | 0.434555i | ||||
\(225\) | −2.53833 | −0.169222 | ||||||||
\(226\) | −1.94390 | + | 6.66181i | −0.129306 | + | 0.443137i | ||||
\(227\) | 3.55657 | 0.236058 | 0.118029 | − | 0.993010i | \(-0.462342\pi\) | ||||
0.118029 | + | 0.993010i | \(0.462342\pi\) | |||||||
\(228\) | −0.849959 | + | 1.33241i | −0.0562899 | + | 0.0882411i | ||||
\(229\) | 7.09294i | 0.468715i | 0.972151 | + | 0.234357i | \(0.0752986\pi\) | ||||
−0.972151 | + | 0.234357i | \(0.924701\pi\) | |||||||
\(230\) | −3.13883 | + | 6.01230i | −0.206968 | + | 0.396439i | ||||
\(231\) | − | 2.79724i | − | 0.184045i | ||||||
\(232\) | −0.530594 | − | 0.606121i | −0.0348352 | − | 0.0397938i | ||||
\(233\) | 3.48303 | 0.228181 | 0.114090 | − | 0.993470i | \(-0.463605\pi\) | ||||
0.114090 | + | 0.993470i | \(0.463605\pi\) | |||||||
\(234\) | −8.22447 | − | 2.39988i | −0.537650 | − | 0.156885i | ||||
\(235\) | −13.2344 | −0.863315 | ||||||||
\(236\) | 9.15640 | − | 14.3537i | 0.596031 | − | 0.934349i | ||||
\(237\) | 3.45504i | 0.224429i | ||||||||
\(238\) | 1.47217 | − | 5.04518i | 0.0954267 | − | 0.327031i | ||||
\(239\) | − | 4.98027i | − | 0.322147i | −0.986942 | − | 0.161073i | \(-0.948504\pi\) | ||
0.986942 | − | 0.161073i | \(-0.0514956\pi\) | |||||||
\(240\) | 1.14567 | + | 2.46458i | 0.0739527 | + | 0.159088i | ||||
\(241\) | − | 25.7144i | − | 1.65641i | −0.560423 | − | 0.828207i | \(-0.689361\pi\) | ||
0.560423 | − | 0.828207i | \(-0.310639\pi\) | |||||||
\(242\) | 2.07793 | + | 0.606335i | 0.133574 | + | 0.0389767i | ||||
\(243\) | 14.7261i | 0.944678i | ||||||||
\(244\) | −8.29469 | + | 13.0029i | −0.531013 | + | 0.832426i | ||||
\(245\) | 5.64744i | 0.360802i | ||||||||
\(246\) | 0.678236 | − | 2.32434i | 0.0432427 | − | 0.148194i | ||||
\(247\) | −2.77567 | −0.176612 | ||||||||
\(248\) | 9.43553 | − | 8.25979i | 0.599157 | − | 0.524497i | ||||
\(249\) | − | 10.2912i | − | 0.652176i | ||||||
\(250\) | −0.396143 | + | 1.35760i | −0.0250543 | + | 0.0858620i | ||||
\(251\) | 19.0680 | 1.20356 | 0.601780 | − | 0.798662i | \(-0.294458\pi\) | ||||
0.601780 | + | 0.798662i | \(0.294458\pi\) | |||||||
\(252\) | −4.97760 | − | 3.17527i | −0.313560 | − | 0.200023i | ||||
\(253\) | −16.6474 | − | 3.32663i | −1.04662 | − | 0.209143i | ||||
\(254\) | −1.98918 | + | 6.81700i | −0.124812 | + | 0.427737i | ||||
\(255\) | 2.17117i | 0.135964i | ||||||||
\(256\) | −10.3139 | + | 12.2321i | −0.644616 | + | 0.764506i | ||||
\(257\) | −13.6402 | −0.850851 | −0.425425 | − | 0.904994i | \(-0.639876\pi\) | ||||
−0.425425 | + | 0.904994i | \(0.639876\pi\) | |||||||
\(258\) | 1.63425 | − | 5.60062i | 0.101744 | − | 0.348679i | ||||
\(259\) | 10.3923i | 0.645746i | ||||||||
\(260\) | −2.56710 | + | 4.02423i | −0.159205 | + | 0.249572i | ||||
\(261\) | −0.722930 | −0.0447483 | ||||||||
\(262\) | 0.888506 | − | 3.04494i | 0.0548921 | − | 0.188117i | ||||
\(263\) | −17.2448 | −1.06336 | −0.531678 | − | 0.846946i | \(-0.678439\pi\) | ||||
−0.531678 | + | 0.846946i | \(0.678439\pi\) | |||||||
\(264\) | −5.11874 | + | 4.48091i | −0.315037 | + | 0.275781i | ||||
\(265\) | 7.45202 | 0.457774 | ||||||||
\(266\) | −1.83623 | − | 0.535809i | −0.112587 | − | 0.0328525i | ||||
\(267\) | 2.08201 | 0.127417 | ||||||||
\(268\) | 19.2228 | + | 12.2624i | 1.17422 | + | 0.749047i | ||||
\(269\) | 5.32436 | 0.324632 | 0.162316 | − | 0.986739i | \(-0.448104\pi\) | ||||
0.162316 | + | 0.986739i | \(0.448104\pi\) | |||||||
\(270\) | 5.10876 | + | 1.49072i | 0.310909 | + | 0.0907226i | ||||
\(271\) | 2.58255i | 0.156879i | 0.996919 | + | 0.0784395i | \(0.0249937\pi\) | ||||
−0.996919 | + | 0.0784395i | \(0.975006\pi\) | |||||||
\(272\) | −11.5906 | + | 5.38792i | −0.702781 | + | 0.326691i | ||||
\(273\) | 1.88596i | 0.114144i | ||||||||
\(274\) | 2.16667 | − | 7.42525i | 0.130893 | − | 0.448576i | ||||
\(275\) | −3.53986 | −0.213461 | ||||||||
\(276\) | 4.51367 | − | 4.70111i | 0.271691 | − | 0.282974i | ||||
\(277\) | 29.1509 | 1.75151 | 0.875755 | − | 0.482756i | \(-0.160364\pi\) | ||||
0.875755 | + | 0.482756i | \(0.160364\pi\) | |||||||
\(278\) | −6.41602 | + | 21.9879i | −0.384807 | + | 1.31875i | ||||
\(279\) | − | 11.2539i | − | 0.673753i | ||||||
\(280\) | −2.47508 | + | 2.16667i | −0.147915 | + | 0.129483i | ||||
\(281\) | − | 23.7749i | − | 1.41829i | −0.705061 | − | 0.709147i | \(-0.749080\pi\) | ||
0.705061 | − | 0.709147i | \(-0.250920\pi\) | |||||||
\(282\) | 12.2079 | + | 3.56223i | 0.726968 | + | 0.212128i | ||||
\(283\) | 4.07678 | 0.242339 | 0.121170 | − | 0.992632i | \(-0.461335\pi\) | ||||
0.121170 | + | 0.992632i | \(0.461335\pi\) | |||||||
\(284\) | 1.57252 | − | 2.46511i | 0.0933120 | − | 0.146278i | ||||
\(285\) | 0.790214 | 0.0468082 | ||||||||
\(286\) | −11.4695 | − | 3.34678i | −0.678208 | − | 0.197899i | ||||
\(287\) | 2.93049 | 0.172982 | ||||||||
\(288\) | 2.16314 | + | 14.1951i | 0.127464 | + | 0.836454i | ||||
\(289\) | 6.78931 | 0.399371 | ||||||||
\(290\) | −0.112824 | + | 0.386651i | −0.00662524 | + | 0.0227049i | ||||
\(291\) | 9.22931 | 0.541032 | ||||||||
\(292\) | 8.24271 | + | 5.25811i | 0.482368 | + | 0.307708i | ||||
\(293\) | 22.6820i | 1.32510i | 0.749019 | + | 0.662548i | \(0.230525\pi\) | ||||
−0.749019 | + | 0.662548i | \(0.769475\pi\) | |||||||
\(294\) | 1.52009 | − | 5.20941i | 0.0886536 | − | 0.303819i | ||||
\(295\) | −8.51278 | −0.495633 | ||||||||
\(296\) | 19.0171 | − | 16.6474i | 1.10535 | − | 0.967613i | ||||
\(297\) | 13.3208i | 0.772952i | ||||||||
\(298\) | 6.81866 | − | 23.3678i | 0.394994 | − | 1.35366i | ||||
\(299\) | 11.2241 | + | 2.24289i | 0.649105 | + | 0.129710i | ||||
\(300\) | 0.730835 | − | 1.14567i | 0.0421948 | − | 0.0661453i | ||||
\(301\) | 7.06119 | 0.407000 | ||||||||
\(302\) | −1.50832 | + | 5.16906i | −0.0867940 | + | 0.297446i | ||||
\(303\) | − | 9.40571i | − | 0.540344i | ||||||
\(304\) | 1.96098 | + | 4.21848i | 0.112470 | + | 0.241946i | ||||
\(305\) | 7.71164 | 0.441567 | ||||||||
\(306\) | −3.21313 | + | 11.0115i | −0.183682 | + | 0.629486i | ||||
\(307\) | 12.3488i | 0.704782i | 0.935853 | + | 0.352391i | \(0.114631\pi\) | ||||
−0.935853 | + | 0.352391i | \(0.885369\pi\) | |||||||
\(308\) | −6.94158 | − | 4.42810i | −0.395533 | − | 0.252315i | ||||
\(309\) | − | 7.72019i | − | 0.439186i | ||||||
\(310\) | −6.01902 | − | 1.75634i | −0.341857 | − | 0.0997531i | ||||
\(311\) | − | 23.9579i | − | 1.35853i | −0.733894 | − | 0.679264i | \(-0.762299\pi\) | ||
0.733894 | − | 0.679264i | \(-0.237701\pi\) | |||||||
\(312\) | 3.45117 | − | 3.02113i | 0.195384 | − | 0.171038i | ||||
\(313\) | 5.46941i | 0.309149i | 0.987981 | + | 0.154575i | \(0.0494007\pi\) | ||||
−0.987981 | + | 0.154575i | \(0.950599\pi\) | |||||||
\(314\) | −6.64675 | + | 22.7787i | −0.375098 | + | 1.28547i | ||||
\(315\) | 2.95207i | 0.166330i | ||||||||
\(316\) | 8.57394 | + | 5.46941i | 0.482322 | + | 0.307678i | ||||
\(317\) | −8.76428 | −0.492251 | −0.246126 | − | 0.969238i | \(-0.579158\pi\) | ||||
−0.246126 | + | 0.969238i | \(0.579158\pi\) | |||||||
\(318\) | −6.87402 | − | 2.00582i | −0.385476 | − | 0.112481i | ||||
\(319\) | −1.00817 | −0.0564467 | ||||||||
\(320\) | 7.92967 | + | 1.05842i | 0.443282 | + | 0.0591676i | ||||
\(321\) | 4.12539i | 0.230257i | ||||||||
\(322\) | 6.99229 | + | 3.65045i | 0.389665 | + | 0.203431i | ||||
\(323\) | 3.71626i | 0.206778i | ||||||||
\(324\) | 8.52868 | + | 5.44053i | 0.473816 | + | 0.302252i | ||||
\(325\) | 2.38665 | 0.132388 | ||||||||
\(326\) | −6.27256 | + | 21.4963i | −0.347405 | + | 1.19057i | ||||
\(327\) | −5.44547 | −0.301135 | ||||||||
\(328\) | −4.69436 | − | 5.36258i | −0.259203 | − | 0.296099i | ||||
\(329\) | 15.3915i | 0.848562i | ||||||||
\(330\) | 3.26530 | + | 0.952806i | 0.179749 | + | 0.0524502i | ||||
\(331\) | 32.3321i | 1.77713i | 0.458750 | + | 0.888565i | \(0.348297\pi\) | ||||
−0.458750 | + | 0.888565i | \(0.651703\pi\) | |||||||
\(332\) | −25.5383 | − | 16.2912i | −1.40160 | − | 0.894094i | ||||
\(333\) | − | 22.6820i | − | 1.24297i | ||||||
\(334\) | −3.37228 | + | 11.5569i | −0.184523 | + | 0.632367i | ||||
\(335\) | − | 11.4005i | − | 0.622875i | ||||||
\(336\) | 2.86630 | − | 1.33241i | 0.156370 | − | 0.0726890i | ||||
\(337\) | 15.3380i | 0.835513i | 0.908559 | + | 0.417757i | \(0.137184\pi\) | ||||
−0.908559 | + | 0.417757i | \(0.862816\pi\) | |||||||
\(338\) | −9.91575 | − | 2.89339i | −0.539346 | − | 0.157380i | ||||
\(339\) | −3.33416 | −0.181087 | ||||||||
\(340\) | 5.38792 | + | 3.43701i | 0.292201 | + | 0.186398i | ||||
\(341\) | − | 15.6943i | − | 0.849892i | ||||||
\(342\) | 4.00772 | + | 1.16944i | 0.216713 | + | 0.0632362i | ||||
\(343\) | 14.7089 | 0.794208 | ||||||||
\(344\) | −11.3113 | − | 12.9214i | −0.609866 | − | 0.696677i | ||||
\(345\) | −3.19542 | − | 0.638535i | −0.172035 | − | 0.0343776i | ||||
\(346\) | −4.33809 | − | 1.26584i | −0.233217 | − | 0.0680522i | ||||
\(347\) | − | 0.463178i | − | 0.0248647i | −0.999923 | − | 0.0124324i | \(-0.996043\pi\) | ||
0.999923 | − | 0.0124324i | \(-0.00395744\pi\) | |||||||
\(348\) | 0.208146 | − | 0.326293i | 0.0111578 | − | 0.0174912i | ||||
\(349\) | 3.91889 | 0.209773 | 0.104887 | − | 0.994484i | \(-0.466552\pi\) | ||||
0.104887 | + | 0.994484i | \(0.466552\pi\) | |||||||
\(350\) | 1.57888 | + | 0.460714i | 0.0843948 | + | 0.0246262i | ||||
\(351\) | − | 8.98119i | − | 0.479380i | ||||||
\(352\) | 3.01663 | + | 19.7959i | 0.160787 | + | 1.05513i | ||||
\(353\) | 7.58980 | 0.403964 | 0.201982 | − | 0.979389i | \(-0.435262\pi\) | ||||
0.201982 | + | 0.979389i | \(0.435262\pi\) | |||||||
\(354\) | 7.85250 | + | 2.29134i | 0.417356 | + | 0.121783i | ||||
\(355\) | −1.46199 | −0.0775942 | ||||||||
\(356\) | 3.29588 | − | 5.16668i | 0.174681 | − | 0.273833i | ||||
\(357\) | 2.52506 | 0.133640 | ||||||||
\(358\) | −0.888506 | + | 3.04494i | −0.0469590 | + | 0.160930i | ||||
\(359\) | 3.83280 | 0.202287 | 0.101144 | − | 0.994872i | \(-0.467750\pi\) | ||||
0.101144 | + | 0.994872i | \(0.467750\pi\) | |||||||
\(360\) | 5.40206 | − | 4.72892i | 0.284714 | − | 0.249236i | ||||
\(361\) | −17.6474 | −0.928813 | ||||||||
\(362\) | −0.171904 | + | 0.589119i | −0.00903505 | + | 0.0309634i | ||||
\(363\) | 1.03998i | 0.0545849i | ||||||||
\(364\) | 4.68017 | + | 2.98553i | 0.245307 | + | 0.156484i | ||||
\(365\) | − | 4.88851i | − | 0.255876i | ||||||
\(366\) | −7.11351 | − | 2.07570i | −0.371829 | − | 0.108499i | ||||
\(367\) | 11.9207 | 0.622255 | 0.311127 | − | 0.950368i | \(-0.399293\pi\) | ||||
0.311127 | + | 0.950368i | \(0.399293\pi\) | |||||||
\(368\) | −4.52092 | − | 18.6430i | −0.235669 | − | 0.971833i | ||||
\(369\) | −6.39603 | −0.332964 | ||||||||
\(370\) | −12.1312 | − | 3.53986i | −0.630672 | − | 0.184028i | ||||
\(371\) | − | 8.66668i | − | 0.449952i | ||||||
\(372\) | 5.07943 | + | 3.24022i | 0.263356 | + | 0.167998i | ||||
\(373\) | − | 30.2624i | − | 1.56693i | −0.621436 | − | 0.783465i | \(-0.713451\pi\) | ||
0.621436 | − | 0.783465i | \(-0.286549\pi\) | |||||||
\(374\) | −4.48091 | + | 15.3562i | −0.231702 | + | 0.794051i | ||||
\(375\) | −0.679463 | −0.0350873 | ||||||||
\(376\) | 28.1653 | − | 24.6557i | 1.45251 | − | 1.27152i | ||||
\(377\) | 0.679731 | 0.0350079 | ||||||||
\(378\) | 1.73371 | − | 5.94147i | 0.0891723 | − | 0.305596i | ||||
\(379\) | −17.4553 | −0.896619 | −0.448309 | − | 0.893878i | \(-0.647974\pi\) | ||||
−0.448309 | + | 0.893878i | \(0.647974\pi\) | |||||||
\(380\) | 1.25093 | − | 1.96098i | 0.0641712 | − | 0.100596i | ||||
\(381\) | −3.41184 | −0.174794 | ||||||||
\(382\) | 20.5622 | + | 6.00000i | 1.05205 | + | 0.306987i | ||||
\(383\) | −13.1513 | −0.671998 | −0.335999 | − | 0.941862i | \(-0.609074\pi\) | ||||
−0.335999 | + | 0.941862i | \(0.609074\pi\) | |||||||
\(384\) | −7.02974 | − | 3.11072i | −0.358735 | − | 0.158743i | ||||
\(385\) | 4.11684i | 0.209814i | ||||||||
\(386\) | 16.4476 | + | 4.79936i | 0.837159 | + | 0.244281i | ||||
\(387\) | −15.4116 | −0.783415 | ||||||||
\(388\) | 14.6102 | − | 22.9032i | 0.741721 | − | 1.16274i | ||||
\(389\) | 34.7815i | 1.76349i | 0.471726 | + | 0.881745i | \(0.343631\pi\) | ||||
−0.471726 | + | 0.881745i | \(0.656369\pi\) | |||||||
\(390\) | −2.20154 | − | 0.642403i | −0.111479 | − | 0.0325293i | ||||
\(391\) | 3.00294 | − | 15.0276i | 0.151865 | − | 0.759977i | ||||
\(392\) | −10.5212 | − | 12.0188i | −0.531401 | − | 0.607043i | ||||
\(393\) | 1.52396 | 0.0768736 | ||||||||
\(394\) | 16.3254 | + | 4.76370i | 0.822460 | + | 0.239992i | ||||
\(395\) | − | 5.08495i | − | 0.255852i | ||||||
\(396\) | 15.1505 | + | 9.66468i | 0.761343 | + | 0.485668i | ||||
\(397\) | −14.7914 | −0.742358 | −0.371179 | − | 0.928561i | \(-0.621046\pi\) | ||||
−0.371179 | + | 0.928561i | \(0.621046\pi\) | |||||||
\(398\) | 36.0395 | + | 10.5162i | 1.80649 | + | 0.527131i | ||||
\(399\) | − | 0.919016i | − | 0.0460083i | ||||||
\(400\) | −1.68614 | − | 3.62725i | −0.0843070 | − | 0.181362i | ||||
\(401\) | 16.6820i | 0.833059i | 0.909122 | + | 0.416530i | \(0.136754\pi\) | ||||
−0.909122 | + | 0.416530i | \(0.863246\pi\) | |||||||
\(402\) | −3.06861 | + | 10.5162i | −0.153048 | + | 0.524502i | ||||
\(403\) | 10.5814i | 0.527098i | ||||||||
\(404\) | −23.3410 | − | 14.8895i | −1.16126 | − | 0.740779i | ||||
\(405\) | − | 5.05811i | − | 0.251339i | ||||||
\(406\) | 0.449674 | + | 0.131214i | 0.0223170 | + | 0.00651203i | ||||
\(407\) | − | 31.6315i | − | 1.56791i | ||||||
\(408\) | −4.04490 | − | 4.62067i | −0.200252 | − | 0.228757i | ||||
\(409\) | 30.4207 | 1.50421 | 0.752104 | − | 0.659044i | \(-0.229039\pi\) | ||||
0.752104 | + | 0.659044i | \(0.229039\pi\) | |||||||
\(410\) | −0.998194 | + | 3.42084i | −0.0492973 | + | 0.168943i | ||||
\(411\) | 3.71626 | 0.183310 | ||||||||
\(412\) | −19.1582 | − | 12.2212i | −0.943859 | − | 0.602098i | ||||
\(413\) | 9.90033i | 0.487164i | ||||||||
\(414\) | −15.2612 | − | 7.96738i | −0.750047 | − | 0.391575i | ||||
\(415\) | 15.1460i | 0.743489i | ||||||||
\(416\) | −2.03388 | − | 13.3469i | −0.0997191 | − | 0.654384i | ||||
\(417\) | −11.0047 | −0.538904 | ||||||||
\(418\) | 5.58902 | + | 1.63086i | 0.273368 | + | 0.0797680i | ||||
\(419\) | −31.7989 | −1.55348 | −0.776738 | − | 0.629824i | \(-0.783127\pi\) | ||||
−0.776738 | + | 0.629824i | \(0.783127\pi\) | |||||||
\(420\) | −1.33241 | − | 0.849959i | −0.0650150 | − | 0.0414738i | ||||
\(421\) | 13.4089i | 0.653510i | 0.945109 | + | 0.326755i | \(0.105955\pi\) | ||||
−0.945109 | + | 0.326755i | \(0.894045\pi\) | |||||||
\(422\) | −5.83703 | + | 20.0037i | −0.284142 | + | 0.973765i | ||||
\(423\) | − | 33.5932i | − | 1.63336i | ||||||
\(424\) | −15.8593 | + | 13.8832i | −0.770198 | + | 0.674226i | ||||
\(425\) | − | 3.19542i | − | 0.155000i | ||||||
\(426\) | 1.34859 | + | 0.393515i | 0.0653394 | + | 0.0190659i | ||||
\(427\) | − | 8.96861i | − | 0.434022i | ||||||
\(428\) | 10.2375 | + | 6.53059i | 0.494847 | + | 0.315668i | ||||
\(429\) | − | 5.74038i | − | 0.277148i | ||||||
\(430\) | −2.40520 | + | 8.24271i | −0.115989 | + | 0.397499i | ||||
\(431\) | 15.6662 | 0.754616 | 0.377308 | − | 0.926088i | \(-0.376850\pi\) | ||||
0.377308 | + | 0.926088i | \(0.376850\pi\) | |||||||
\(432\) | −13.6497 | + | 6.34510i | −0.656720 | + | 0.305279i | ||||
\(433\) | − | 14.9789i | − | 0.719840i | −0.932983 | − | 0.359920i | \(-0.882804\pi\) | ||
0.932983 | − | 0.359920i | \(-0.117196\pi\) | |||||||
\(434\) | −2.04261 | + | 7.00010i | −0.0980485 | + | 0.336016i | ||||
\(435\) | −0.193515 | −0.00927833 | ||||||||
\(436\) | −8.62031 | + | 13.5134i | −0.412838 | + | 0.647172i | ||||
\(437\) | −5.46941 | − | 1.09294i | −0.261637 | − | 0.0522825i | ||||
\(438\) | −1.31581 | + | 4.50934i | −0.0628720 | + | 0.215465i | ||||
\(439\) | − | 23.2450i | − | 1.10942i | −0.832043 | − | 0.554712i | \(-0.812829\pi\) | ||
0.832043 | − | 0.554712i | \(-0.187171\pi\) | |||||||
\(440\) | 7.53351 | − | 6.59477i | 0.359146 | − | 0.314394i | ||||
\(441\) | −14.3351 | −0.682622 | ||||||||
\(442\) | 3.02113 | − | 10.3535i | 0.143700 | − | 0.492466i | ||||
\(443\) | − | 37.3633i | − | 1.77519i | −0.460629 | − | 0.887593i | \(-0.652376\pi\) | ||
0.460629 | − | 0.887593i | \(-0.347624\pi\) | |||||||
\(444\) | 10.2375 | + | 6.53059i | 0.485849 | + | 0.309928i | ||||
\(445\) | −3.06420 | −0.145257 | ||||||||
\(446\) | −3.42328 | + | 11.7317i | −0.162097 | + | 0.555512i | ||||
\(447\) | 11.6953 | 0.553170 | ||||||||
\(448\) | 1.23094 | − | 9.22219i | 0.0581565 | − | 0.435707i | ||||
\(449\) | −32.3734 | −1.52780 | −0.763899 | − | 0.645336i | \(-0.776717\pi\) | ||||
−0.763899 | + | 0.645336i | \(0.776717\pi\) | |||||||
\(450\) | −3.44603 | − | 1.00554i | −0.162447 | − | 0.0474017i | ||||
\(451\) | −8.91966 | −0.420010 | ||||||||
\(452\) | −5.27806 | + | 8.27399i | −0.248259 | + | 0.389176i | ||||
\(453\) | −2.58706 | −0.121551 | ||||||||
\(454\) | 4.82839 | + | 1.40891i | 0.226608 | + | 0.0661235i | ||||
\(455\) | − | 2.77567i | − | 0.130125i | ||||||
\(456\) | −1.68173 | + | 1.47217i | −0.0787541 | + | 0.0689408i | ||||
\(457\) | − | 12.6533i | − | 0.591895i | −0.955204 | − | 0.295947i | \(-0.904365\pi\) | ||
0.955204 | − | 0.295947i | \(-0.0956353\pi\) | |||||||
\(458\) | −2.80982 | + | 9.62936i | −0.131294 | + | 0.449950i | ||||
\(459\) | −12.0246 | −0.561262 | ||||||||
\(460\) | −6.64300 | + | 6.91886i | −0.309731 | + | 0.322593i | ||||
\(461\) | −26.8817 | −1.25200 | −0.626002 | − | 0.779821i | \(-0.715310\pi\) | ||||
−0.626002 | + | 0.779821i | \(0.715310\pi\) | |||||||
\(462\) | 1.10811 | − | 3.79753i | 0.0515539 | − | 0.176677i | ||||
\(463\) | − | 11.3203i | − | 0.526100i | −0.964782 | − | 0.263050i | \(-0.915272\pi\) | ||
0.964782 | − | 0.263050i | \(-0.0847284\pi\) | |||||||
\(464\) | −0.480222 | − | 1.03306i | −0.0222938 | − | 0.0479586i | ||||
\(465\) | − | 3.01246i | − | 0.139699i | ||||||
\(466\) | 4.72855 | + | 1.37978i | 0.219046 | + | 0.0639171i | ||||
\(467\) | 29.8807 | 1.38271 | 0.691356 | − | 0.722514i | \(-0.257014\pi\) | ||||
0.691356 | + | 0.722514i | \(0.257014\pi\) | |||||||
\(468\) | −10.2148 | − | 6.51614i | −0.472180 | − | 0.301209i | ||||
\(469\) | −13.2587 | −0.612231 | ||||||||
\(470\) | −17.9669 | − | 5.24271i | −0.828753 | − | 0.241828i | ||||
\(471\) | −11.4005 | −0.525306 | ||||||||
\(472\) | 18.1168 | − | 15.8593i | 0.833895 | − | 0.729986i | ||||
\(473\) | −21.4924 | −0.988222 | ||||||||
\(474\) | −1.36869 | + | 4.69055i | −0.0628660 | + | 0.215444i | ||||
\(475\) | −1.16300 | −0.0533620 | ||||||||
\(476\) | 3.99723 | − | 6.26614i | 0.183213 | − | 0.287208i | ||||
\(477\) | 18.9157i | 0.866090i | ||||||||
\(478\) | 1.97290 | − | 6.76120i | 0.0902384 | − | 0.309250i | ||||
\(479\) | −28.0533 | −1.28179 | −0.640894 | − | 0.767629i | \(-0.721436\pi\) | ||||
−0.640894 | + | 0.767629i | \(0.721436\pi\) | |||||||
\(480\) | 0.579031 | + | 3.79976i | 0.0264290 | + | 0.173434i | ||||
\(481\) | 21.3266i | 0.972411i | ||||||||
\(482\) | 10.1866 | − | 34.9099i | 0.463987 | − | 1.59010i | ||||
\(483\) | −0.742614 | + | 3.71626i | −0.0337901 | + | 0.169096i | ||||
\(484\) | 2.58080 | + | 1.64632i | 0.117309 | + | 0.0748326i | ||||
\(485\) | −13.5832 | −0.616783 | ||||||||
\(486\) | −5.83364 | + | 19.9921i | −0.264619 | + | 0.906859i | ||||
\(487\) | − | 31.1349i | − | 1.41086i | −0.708781 | − | 0.705429i | \(-0.750754\pi\) | ||
0.708781 | − | 0.705429i | \(-0.249246\pi\) | |||||||
\(488\) | −16.4119 | + | 14.3668i | −0.742930 | + | 0.650356i | ||||
\(489\) | −10.7587 | −0.486523 | ||||||||
\(490\) | −2.23720 | + | 7.66695i | −0.101066 | + | 0.346357i | ||||
\(491\) | − | 30.9504i | − | 1.39677i | −0.715722 | − | 0.698385i | \(-0.753902\pi\) | ||
0.715722 | − | 0.698385i | \(-0.246098\pi\) | |||||||
\(492\) | 1.84154 | − | 2.88684i | 0.0830231 | − | 0.130149i | ||||
\(493\) | − | 0.910072i | − | 0.0409876i | ||||||
\(494\) | −3.76824 | − | 1.09956i | −0.169541 | − | 0.0494717i | ||||
\(495\) | − | 8.98533i | − | 0.403860i | ||||||
\(496\) | 16.0817 | − | 7.47565i | 0.722090 | − | 0.335666i | ||||
\(497\) | 1.70029i | 0.0762682i | ||||||||
\(498\) | 4.07678 | − | 13.9713i | 0.182685 | − | 0.626067i | ||||
\(499\) | 6.56809i | 0.294028i | 0.989134 | + | 0.147014i | \(0.0469662\pi\) | ||||
−0.989134 | + | 0.147014i | \(0.953034\pi\) | |||||||
\(500\) | −1.07561 | + | 1.68614i | −0.0481026 | + | 0.0754065i | ||||
\(501\) | −5.78412 | −0.258415 | ||||||||
\(502\) | 25.8866 | + | 7.55366i | 1.15538 | + | 0.337136i | ||||
\(503\) | −24.3969 | −1.08780 | −0.543902 | − | 0.839149i | \(-0.683054\pi\) | ||||
−0.543902 | + | 0.839149i | \(0.683054\pi\) | |||||||
\(504\) | −5.49972 | − | 6.28258i | −0.244977 | − | 0.279848i | ||||
\(505\) | 13.8429i | 0.615999i | ||||||||
\(506\) | −21.2827 | − | 11.1110i | −0.946131 | − | 0.493944i | ||||
\(507\) | − | 4.96273i | − | 0.220403i | ||||||
\(508\) | −5.40102 | + | 8.46674i | −0.239632 | + | 0.375651i | ||||
\(509\) | −12.1922 | −0.540412 | −0.270206 | − | 0.962803i | \(-0.587092\pi\) | ||||
−0.270206 | + | 0.962803i | \(0.587092\pi\) | |||||||
\(510\) | −0.860094 | + | 2.94757i | −0.0380856 | + | 0.130521i | ||||
\(511\) | −5.68532 | −0.251504 | ||||||||
\(512\) | −18.8477 | + | 12.5205i | −0.832960 | + | 0.553333i | ||||
\(513\) | 4.37646i | 0.193226i | ||||||||
\(514\) | −18.5179 | − | 5.40347i | −0.816788 | − | 0.238337i | ||||
\(515\) | 11.3622i | 0.500678i | ||||||||
\(516\) | 4.43730 | − | 6.95599i | 0.195341 | − | 0.306220i | ||||
\(517\) | − | 46.8478i | − | 2.06036i | ||||||
\(518\) | −4.11684 | + | 14.1086i | −0.180884 | + | 0.619895i | ||||
\(519\) | − | 2.17117i | − | 0.0953037i | ||||||
\(520\) | −5.07926 | + | 4.44634i | −0.222740 | + | 0.194985i | ||||
\(521\) | − | 15.2300i | − | 0.667237i | −0.942708 | − | 0.333619i | \(-0.891730\pi\) | ||
0.942708 | − | 0.333619i | \(-0.108270\pi\) | |||||||
\(522\) | −0.981448 | − | 0.286384i | −0.0429568 | − | 0.0125347i | ||||
\(523\) | 37.2916 | 1.63065 | 0.815324 | − | 0.579005i | \(-0.196559\pi\) | ||||
0.815324 | + | 0.579005i | \(0.196559\pi\) | |||||||
\(524\) | 2.41247 | − | 3.78183i | 0.105389 | − | 0.165210i | ||||
\(525\) | 0.790214i | 0.0344877i | ||||||||
\(526\) | −23.4114 | − | 6.83140i | −1.02079 | − | 0.297863i | ||||
\(527\) | 14.1671 | 0.617131 | ||||||||
\(528\) | −8.72427 | + | 4.05551i | −0.379675 | + | 0.176493i | ||||
\(529\) | 21.2337 | + | 8.83915i | 0.923204 | + | 0.384311i | ||||
\(530\) | 10.1168 | + | 2.95207i | 0.439448 | + | 0.128230i | ||||
\(531\) | − | 21.6082i | − | 0.937718i | ||||||
\(532\) | −2.28061 | − | 1.45482i | −0.0988770 | − | 0.0630746i | ||||
\(533\) | 6.01383 | 0.260488 | ||||||||
\(534\) | 2.82654 | + | 0.824776i | 0.122316 | + | 0.0356915i | ||||
\(535\) | − | 6.07154i | − | 0.262496i | ||||||
\(536\) | 21.2391 | + | 24.2624i | 0.917391 | + | 1.04798i | ||||
\(537\) | −1.52396 | −0.0657637 | ||||||||
\(538\) | 7.22834 | + | 2.10921i | 0.311636 | + | 0.0909345i | ||||
\(539\) | −19.9911 | −0.861079 | ||||||||
\(540\) | 6.34510 | + | 4.04761i | 0.273050 | + | 0.174181i | ||||
\(541\) | 45.1850 | 1.94266 | 0.971328 | − | 0.237744i | \(-0.0764078\pi\) | ||||
0.971328 | + | 0.237744i | \(0.0764078\pi\) | |||||||
\(542\) | −1.02306 | + | 3.50607i | −0.0439443 | + | 0.150599i | ||||
\(543\) | −0.294848 | −0.0126531 | ||||||||
\(544\) | −17.8697 | + | 2.72310i | −0.766158 | + | 0.116752i | ||||
\(545\) | 8.01437 | 0.343298 | ||||||||
\(546\) | −0.747112 | + | 2.56038i | −0.0319735 | + | 0.109574i | ||||
\(547\) | 16.1869i | 0.692100i | 0.938216 | + | 0.346050i | \(0.112477\pi\) | ||||
−0.938216 | + | 0.346050i | \(0.887523\pi\) | |||||||
\(548\) | 5.88293 | − | 9.22219i | 0.251306 | − | 0.393952i | ||||
\(549\) | 19.5747i | 0.835427i | ||||||||
\(550\) | −4.80570 | − | 1.40229i | −0.204916 | − | 0.0597939i | ||||
\(551\) | −0.331228 | −0.0141108 | ||||||||
\(552\) | 7.99006 | − | 4.59415i | 0.340080 | − | 0.195540i | ||||
\(553\) | −5.91378 | −0.251480 | ||||||||
\(554\) | 39.5752 | + | 11.5480i | 1.68139 | + | 0.490625i | ||||
\(555\) | − | 6.07154i | − | 0.257723i | ||||||
\(556\) | −17.4207 | + | 27.3091i | −0.738804 | + | 1.15816i | ||||
\(557\) | − | 30.6215i | − | 1.29747i | −0.761012 | − | 0.648737i | \(-0.775297\pi\) | ||
0.761012 | − | 0.648737i | \(-0.224703\pi\) | |||||||
\(558\) | 4.45816 | − | 15.2783i | 0.188729 | − | 0.646780i | ||||
\(559\) | 14.4907 | 0.612890 | ||||||||
\(560\) | −4.21848 | + | 1.96098i | −0.178263 | + | 0.0828664i | ||||
\(561\) | −7.68563 | −0.324487 | ||||||||
\(562\) | 9.41829 | − | 32.2768i | 0.397287 | − | 1.36151i | ||||
\(563\) | 12.1431 | 0.511770 | 0.255885 | − | 0.966707i | \(-0.417633\pi\) | ||||
0.255885 | + | 0.966707i | \(0.417633\pi\) | |||||||
\(564\) | 15.1622 | + | 9.67214i | 0.638445 | + | 0.407271i | ||||
\(565\) | 4.90706 | 0.206441 | ||||||||
\(566\) | 5.53462 | + | 1.61499i | 0.232638 | + | 0.0678831i | ||||
\(567\) | −5.88256 | −0.247044 | ||||||||
\(568\) | 3.11139 | − | 2.72369i | 0.130551 | − | 0.114283i | ||||
\(569\) | 37.5211i | 1.57297i | 0.617610 | + | 0.786484i | \(0.288101\pi\) | ||||
−0.617610 | + | 0.786484i | \(0.711899\pi\) | |||||||
\(570\) | 1.07279 | + | 0.313038i | 0.0449343 | + | 0.0131117i | ||||
\(571\) | 10.9508 | 0.458277 | 0.229138 | − | 0.973394i | \(-0.426409\pi\) | ||||
0.229138 | + | 0.973394i | \(0.426409\pi\) | |||||||
\(572\) | −14.2452 | − | 9.08716i | −0.595622 | − | 0.379953i | ||||
\(573\) | 10.2912i | 0.429920i | ||||||||
\(574\) | 3.97843 | + | 1.16090i | 0.166056 | + | 0.0484549i | ||||
\(575\) | 4.70285 | + | 0.939764i | 0.196123 | + | 0.0391909i | ||||
\(576\) | −2.68662 | + | 20.1281i | −0.111943 | + | 0.838672i | ||||
\(577\) | −19.1222 | −0.796067 | −0.398034 | − | 0.917371i | \(-0.630307\pi\) | ||||
−0.398034 | + | 0.917371i | \(0.630307\pi\) | |||||||
\(578\) | 9.21715 | + | 2.68954i | 0.383383 | + | 0.111870i | ||||
\(579\) | 8.23183i | 0.342103i | ||||||||
\(580\) | −0.306339 | + | 0.480222i | −0.0127200 | + | 0.0199401i | ||||
\(581\) | 17.6148 | 0.730784 | ||||||||
\(582\) | 12.5297 | + | 3.65613i | 0.519372 | + | 0.151551i | ||||
\(583\) | 26.3791i | 1.09251i | ||||||||
\(584\) | 9.10731 | + | 10.4037i | 0.376863 | + | 0.430508i | ||||
\(585\) | 6.05811i | 0.250472i | ||||||||
\(586\) | −8.98533 | + | 30.7930i | −0.371180 | + | 1.27205i | ||||
\(587\) | − | 15.3774i | − | 0.634695i | −0.948309 | − | 0.317347i | \(-0.897208\pi\) | ||
0.948309 | − | 0.317347i | \(-0.102792\pi\) | |||||||
\(588\) | 4.12735 | − | 6.47010i | 0.170209 | − | 0.266823i | ||||
\(589\) | − | 5.15624i | − | 0.212459i | ||||||
\(590\) | −11.5569 | − | 3.37228i | −0.475791 | − | 0.138835i | ||||
\(591\) | 8.17067i | 0.336096i | ||||||||
\(592\) | 32.4124 | − | 15.0670i | 1.33214 | − | 0.619250i | ||||
\(593\) | −9.29488 | −0.381695 | −0.190847 | − | 0.981620i | \(-0.561124\pi\) | ||||
−0.190847 | + | 0.981620i | \(0.561124\pi\) | |||||||
\(594\) | −5.27695 | + | 18.0843i | −0.216516 | + | 0.742007i | ||||
\(595\) | −3.71626 | −0.152352 | ||||||||
\(596\) | 18.5140 | − | 29.0229i | 0.758362 | − | 1.18882i | ||||
\(597\) | 18.0374i | 0.738220i | ||||||||
\(598\) | 14.3493 | + | 7.49128i | 0.586785 | + | 0.306341i | ||||
\(599\) | − | 25.4614i | − | 1.04032i | −0.854068 | − | 0.520162i | \(-0.825872\pi\) | ||
0.854068 | − | 0.520162i | \(-0.174128\pi\) | |||||||
\(600\) | 1.44603 | − | 1.26584i | 0.0590339 | − | 0.0516778i | ||||
\(601\) | 12.1583 | 0.495948 | 0.247974 | − | 0.968767i | \(-0.420235\pi\) | ||||
0.247974 | + | 0.968767i | \(0.420235\pi\) | |||||||
\(602\) | 9.58625 | + | 2.79724i | 0.390706 | + | 0.114007i | ||||
\(603\) | 28.9382 | 1.17845 | ||||||||
\(604\) | −4.09538 | + | 6.41999i | −0.166639 | + | 0.261226i | ||||
\(605\) | − | 1.53059i | − | 0.0622275i | ||||||
\(606\) | 3.72601 | − | 12.7692i | 0.151359 | − | 0.518712i | ||||
\(607\) | 37.2700i | 1.51274i | 0.654142 | + | 0.756372i | \(0.273030\pi\) | ||||
−0.654142 | + | 0.756372i | \(0.726970\pi\) | |||||||
\(608\) | 0.991093 | + | 6.50382i | 0.0401941 | + | 0.263765i | ||||
\(609\) | 0.225057i | 0.00911978i | ||||||||
\(610\) | 10.4693 | + | 3.05492i | 0.423890 | + | 0.123690i | ||||
\(611\) | 31.5858i | 1.27783i | ||||||||
\(612\) | −8.72427 | + | 13.6763i | −0.352658 | + | 0.552833i | ||||
\(613\) | − | 10.4845i | − | 0.423464i | −0.977328 | − | 0.211732i | \(-0.932090\pi\) | ||
0.977328 | − | 0.211732i | \(-0.0679104\pi\) | |||||||
\(614\) | −4.89189 | + | 16.7647i | −0.197421 | + | 0.676567i | ||||
\(615\) | −1.71210 | −0.0690384 | ||||||||
\(616\) | −7.66970 | − | 8.76144i | −0.309021 | − | 0.353009i | ||||
\(617\) | − | 47.6120i | − | 1.91679i | −0.285452 | − | 0.958393i | \(-0.592144\pi\) | ||
0.285452 | − | 0.958393i | \(-0.407856\pi\) | |||||||
\(618\) | 3.05830 | − | 10.4809i | 0.123023 | − | 0.421604i | ||||
\(619\) | −27.8733 | −1.12032 | −0.560162 | − | 0.828383i | \(-0.689261\pi\) | ||||
−0.560162 | + | 0.828383i | \(0.689261\pi\) | |||||||
\(620\) | −7.47565 | − | 4.76879i | −0.300229 | − | 0.191519i | ||||
\(621\) | 3.53642 | − | 17.6973i | 0.141912 | − | 0.710167i | ||||
\(622\) | 9.49077 | − | 32.5252i | 0.380545 | − | 1.30414i | ||||
\(623\) | 3.56366i | 0.142775i | ||||||||
\(624\) | 5.88210 | − | 2.73432i | 0.235472 | − | 0.109460i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.16667 | + | 7.42525i | −0.0865975 | + | 0.296773i | ||||
\(627\) | 2.79724i | 0.111711i | ||||||||
\(628\) | −18.0472 | + | 28.2912i | −0.720163 | + | 1.12894i | ||||
\(629\) | 28.5536 | 1.13851 | ||||||||
\(630\) | −1.16944 | + | 4.00772i | −0.0465917 | + | 0.159671i | ||||
\(631\) | −37.1899 | −1.48051 | −0.740253 | − | 0.672329i | \(-0.765294\pi\) | ||||
−0.740253 | + | 0.672329i | \(0.765294\pi\) | |||||||
\(632\) | 9.47329 | + | 10.8218i | 0.376827 | + | 0.430467i | ||||
\(633\) | −10.0116 | −0.397927 | ||||||||
\(634\) | −11.8984 | − | 3.47191i | −0.472544 | − | 0.137887i | ||||
\(635\) | 5.02137 | 0.199267 | ||||||||
\(636\) | −8.53756 | − | 5.44620i | −0.338536 | − | 0.215956i | ||||
\(637\) | 13.4785 | 0.534036 | ||||||||
\(638\) | −1.36869 | − | 0.399380i | −0.0541870 | − | 0.0158116i | ||||
\(639\) | − | 3.71100i | − | 0.146805i | ||||||
\(640\) | 10.3460 | + | 4.57820i | 0.408962 | + | 0.180969i | ||||
\(641\) | − | 12.8783i | − | 0.508663i | −0.967117 | − | 0.254331i | \(-0.918145\pi\) | ||
0.967117 | − | 0.254331i | \(-0.0818554\pi\) | |||||||
\(642\) | −1.63425 | + | 5.60062i | −0.0644986 | + | 0.221039i | ||||
\(643\) | 26.8777 | 1.05995 | 0.529977 | − | 0.848012i | \(-0.322201\pi\) | ||||
0.529977 | + | 0.848012i | \(0.322201\pi\) | |||||||
\(644\) | 8.04661 | + | 7.72578i | 0.317081 | + | 0.304439i | ||||
\(645\) | −4.12539 | −0.162437 | ||||||||
\(646\) | −1.47217 | + | 5.04518i | −0.0579218 | + | 0.198500i | ||||
\(647\) | 0.572262i | 0.0224979i | 0.999937 | + | 0.0112490i | \(0.00358073\pi\) | ||||
−0.999937 | + | 0.0112490i | \(0.996419\pi\) | |||||||
\(648\) | 9.42328 | + | 10.7646i | 0.370181 | + | 0.422875i | ||||
\(649\) | − | 30.1340i | − | 1.18286i | ||||||
\(650\) | 3.24011 | + | 0.945456i | 0.127088 | + | 0.0370838i | ||||
\(651\) | −3.50348 | −0.137312 | ||||||||
\(652\) | −17.0312 | + | 26.6985i | −0.666994 | + | 1.04559i | ||||
\(653\) | 32.2544 | 1.26221 | 0.631106 | − | 0.775696i | \(-0.282601\pi\) | ||||
0.631106 | + | 0.775696i | \(0.282601\pi\) | |||||||
\(654\) | −7.39275 | − | 2.15719i | −0.289080 | − | 0.0843527i | ||||
\(655\) | −2.24289 | −0.0876369 | ||||||||
\(656\) | −4.24870 | − | 9.13986i | −0.165884 | − | 0.356852i | ||||
\(657\) | 12.4086 | 0.484107 | ||||||||
\(658\) | −6.09725 | + | 20.8955i | −0.237696 | + | 0.814591i | ||||
\(659\) | −12.4086 | −0.483372 | −0.241686 | − | 0.970354i | \(-0.577700\pi\) | ||||
−0.241686 | + | 0.970354i | \(0.577700\pi\) | |||||||
\(660\) | 4.05551 | + | 2.58705i | 0.157861 | + | 0.100701i | ||||
\(661\) | 43.3582i | 1.68644i | 0.537570 | + | 0.843219i | \(0.319342\pi\) | ||||
−0.537570 | + | 0.843219i | \(0.680658\pi\) | |||||||
\(662\) | −12.8081 | + | 43.8939i | −0.497802 | + | 1.70599i | ||||
\(663\) | 5.18182 | 0.201245 | ||||||||
\(664\) | −28.2171 | − | 32.2337i | −1.09504 | − | 1.25091i | ||||
\(665\) | 1.35256i | 0.0524501i | ||||||||
\(666\) | 8.98533 | − | 30.7930i | 0.348174 | − | 1.19321i | ||||
\(667\) | 1.33940 | + | 0.267650i | 0.0518617 | + | 0.0103634i | ||||
\(668\) | −9.15640 | + | 14.3537i | −0.354272 | + | 0.555363i | ||||
\(669\) | −5.87159 | −0.227009 | ||||||||
\(670\) | 4.51622 | − | 15.4773i | 0.174477 | − | 0.597939i | ||||
\(671\) | 27.2981i | 1.05383i | ||||||||
\(672\) | 4.41911 | − | 0.673411i | 0.170471 | − | 0.0259774i | ||||
\(673\) | 17.4027 | 0.670823 | 0.335412 | − | 0.942072i | \(-0.391125\pi\) | ||||
0.335412 | + | 0.942072i | \(0.391125\pi\) | |||||||
\(674\) | −6.07604 | + | 20.8228i | −0.234040 | + | 0.802065i | ||||
\(675\) | − | 3.76309i | − | 0.144841i | ||||||
\(676\) | −12.3154 | − | 7.85612i | −0.473669 | − | 0.302158i | ||||
\(677\) | 29.6092i | 1.13797i | 0.822347 | + | 0.568986i | \(0.192664\pi\) | ||||
−0.822347 | + | 0.568986i | \(0.807336\pi\) | |||||||
\(678\) | −4.52645 | − | 1.32081i | −0.173837 | − | 0.0507253i | ||||
\(679\) | 15.7973i | 0.606243i | ||||||||
\(680\) | 5.95308 | + | 6.80047i | 0.228290 | + | 0.260786i | ||||
\(681\) | 2.41656i | 0.0926027i | ||||||||
\(682\) | 6.21718 | − | 21.3065i | 0.238068 | − | 0.815867i | ||||
\(683\) | 25.8996i | 0.991020i | 0.868602 | + | 0.495510i | \(0.165019\pi\) | ||||
−0.868602 | + | 0.495510i | \(0.834981\pi\) | |||||||
\(684\) | 4.97760 | + | 3.17527i | 0.190323 | + | 0.121409i | ||||
\(685\) | −5.46941 | −0.208975 | ||||||||
\(686\) | 19.9688 | + | 5.82685i | 0.762413 | + | 0.222470i | ||||
\(687\) | −4.81939 | −0.183871 | ||||||||
\(688\) | −10.2375 | − | 22.0230i | −0.390300 | − | 0.839619i | ||||
\(689\) | − | 17.7854i | − | 0.677569i | ||||||
\(690\) | −4.08514 | − | 2.13272i | −0.155519 | − | 0.0811911i | ||||
\(691\) | 22.5354i | 0.857287i | 0.903474 | + | 0.428643i | \(0.141008\pi\) | ||||
−0.903474 | + | 0.428643i | \(0.858992\pi\) | |||||||
\(692\) | −5.38792 | − | 3.43701i | −0.204818 | − | 0.130656i | ||||
\(693\) | −10.4499 | −0.396959 | ||||||||
\(694\) | 0.183485 | − | 0.628810i | 0.00696500 | − | 0.0238693i | ||||
\(695\) | 16.1962 | 0.614357 | ||||||||
\(696\) | 0.411837 | − | 0.360519i | 0.0156106 | − | 0.0136654i | ||||
\(697\) | − | 8.05174i | − | 0.304981i | ||||||
\(698\) | 5.32027 | + | 1.55244i | 0.201375 | + | 0.0587608i | ||||
\(699\) | 2.36659i | 0.0895127i | ||||||||
\(700\) | 1.96098 | + | 1.25093i | 0.0741179 | + | 0.0472806i | ||||
\(701\) | 5.43765i | 0.205377i | 0.994714 | + | 0.102689i | \(0.0327445\pi\) | ||||
−0.994714 | + | 0.102689i | \(0.967255\pi\) | |||||||
\(702\) | 3.55784 | − | 12.1928i | 0.134282 | − | 0.460189i | ||||
\(703\) | − | 10.3923i | − | 0.391953i | ||||||
\(704\) | −3.74666 | + | 28.0699i | −0.141208 | + | 1.05793i | ||||
\(705\) | − | 8.99226i | − | 0.338668i | ||||||
\(706\) | 10.3039 | + | 3.00665i | 0.387792 | + | 0.113157i | ||||
\(707\) | 16.0992 | 0.605473 | ||||||||
\(708\) | 9.75284 | + | 6.22144i | 0.366534 | + | 0.233816i | ||||
\(709\) | 2.31710i | 0.0870205i | 0.999053 | + | 0.0435102i | \(0.0138541\pi\) | ||||
−0.999053 | + | 0.0435102i | \(0.986146\pi\) | |||||||
\(710\) | −1.98479 | − | 0.579156i | −0.0744878 | − | 0.0217354i | ||||
\(711\) | 12.9073 | 0.484061 | ||||||||
\(712\) | 6.52122 | − | 5.70863i | 0.244393 | − | 0.213940i | ||||
\(713\) | −4.16652 | + | 20.8505i | −0.156037 | + | 0.780857i | ||||
\(714\) | 3.42802 | + | 1.00029i | 0.128290 | + | 0.0374348i | ||||
\(715\) | 8.44841i | 0.315952i | ||||||||
\(716\) | −2.41247 | + | 3.78183i | −0.0901581 | + | 0.141333i | ||||
\(717\) | 3.38391 | 0.126374 | ||||||||
\(718\) | 5.20340 | + | 1.51834i | 0.194189 | + | 0.0566639i | ||||
\(719\) | 50.9154i | 1.89882i | 0.314032 | + | 0.949412i | \(0.398320\pi\) | ||||
−0.314032 | + | 0.949412i | \(0.601680\pi\) | |||||||
\(720\) | 9.20715 | − | 4.27998i | 0.343130 | − | 0.159505i | ||||
\(721\) | 13.2142 | 0.492122 | ||||||||
\(722\) | −23.9581 | − | 6.99092i | −0.891629 | − | 0.260175i | ||||
\(723\) | 17.4720 | 0.649791 | ||||||||
\(724\) | −0.466752 | + | 0.731688i | −0.0173467 | + | 0.0271930i | ||||
\(725\) | 0.284805 | 0.0105774 | ||||||||
\(726\) | −0.411982 | + | 1.41188i | −0.0152901 | + | 0.0523997i | ||||
\(727\) | −10.2883 | −0.381574 | −0.190787 | − | 0.981631i | \(-0.561104\pi\) | ||||
−0.190787 | + | 0.981631i | \(0.561104\pi\) | |||||||
\(728\) | 5.17108 | + | 5.90716i | 0.191653 | + | 0.218934i | ||||
\(729\) | 5.16850 | 0.191426 | ||||||||
\(730\) | 1.93655 | − | 6.63662i | 0.0716749 | − | 0.245632i | ||||
\(731\) | − | 19.4011i | − | 0.717576i | ||||||
\(732\) | −8.83500 | − | 5.63594i | −0.326551 | − | 0.208310i | ||||
\(733\) | 13.1896i | 0.487169i | 0.969880 | + | 0.243584i | \(0.0783233\pi\) | ||||
−0.969880 | + | 0.243584i | \(0.921677\pi\) | |||||||
\(734\) | 16.1835 | + | 4.72230i | 0.597343 | + | 0.174303i | ||||
\(735\) | −3.83723 | −0.141538 | ||||||||
\(736\) | 1.24772 | − | 27.1006i | 0.0459914 | − | 0.998942i | ||||
\(737\) | 40.3561 | 1.48653 | ||||||||
\(738\) | −8.68323 | − | 2.53374i | −0.319634 | − | 0.0932684i | ||||
\(739\) | 36.6567i | 1.34844i | 0.738532 | + | 0.674219i | \(0.235519\pi\) | ||||
−0.738532 | + | 0.674219i | \(0.764481\pi\) | |||||||
\(740\) | −15.0670 | − | 9.61140i | −0.553874 | − | 0.353322i | ||||
\(741\) | − | 1.88596i | − | 0.0692826i | ||||||
\(742\) | 3.43325 | − | 11.7659i | 0.126039 | − | 0.431938i | ||||
\(743\) | 6.92489 | 0.254050 | 0.127025 | − | 0.991900i | \(-0.459457\pi\) | ||||
0.127025 | + | 0.991900i | \(0.459457\pi\) | |||||||
\(744\) | 5.61222 | + | 6.41109i | 0.205754 | + | 0.235042i | ||||
\(745\) | −17.2126 | −0.630621 | ||||||||
\(746\) | 11.9883 | − | 41.0842i | 0.438922 | − | 1.50420i | ||||
\(747\) | −38.4456 | −1.40665 | ||||||||
\(748\) | −12.1665 | + | 19.0725i | −0.444852 | + | 0.697359i | ||||
\(749\) | −7.06119 | −0.258010 | ||||||||
\(750\) | −0.922437 | − | 0.269165i | −0.0336826 | − | 0.00982851i | ||||
\(751\) | −30.6233 | −1.11746 | −0.558730 | − | 0.829350i | \(-0.688711\pi\) | ||||
−0.558730 | + | 0.829350i | \(0.688711\pi\) | |||||||
\(752\) | 48.0043 | − | 22.3150i | 1.75054 | − | 0.813744i | ||||
\(753\) | 12.9560i | 0.472143i | ||||||||
\(754\) | 0.922801 | + | 0.269271i | 0.0336064 | + | 0.00980628i | ||||
\(755\) | 3.80751 | 0.138569 | ||||||||
\(756\) | 4.70735 | − | 7.37933i | 0.171205 | − | 0.268384i | ||||
\(757\) | 14.3517i | 0.521620i | 0.965390 | + | 0.260810i | \(0.0839896\pi\) | ||||
−0.965390 | + | 0.260810i | \(0.916010\pi\) | |||||||
\(758\) | −23.6973 | − | 6.91481i | −0.860724 | − | 0.251157i | ||||
\(759\) | 2.26032 | − | 11.3113i | 0.0820445 | − | 0.410575i | ||||
\(760\) | 2.47508 | − | 2.16667i | 0.0897807 | − | 0.0785934i | ||||
\(761\) | 22.3858 | 0.811486 | 0.405743 | − | 0.913987i | \(-0.367013\pi\) | ||||
0.405743 | + | 0.913987i | \(0.367013\pi\) | |||||||
\(762\) | −4.63190 | − | 1.35158i | −0.167796 | − | 0.0489625i | ||||
\(763\) | − | 9.32069i | − | 0.337432i | ||||||
\(764\) | 25.5383 | + | 16.2912i | 0.923944 | + | 0.589394i | ||||
\(765\) | 8.11102 | 0.293255 | ||||||||
\(766\) | −17.8541 | − | 5.20979i | −0.645095 | − | 0.188237i | ||||
\(767\) | 20.3170i | 0.733605i | ||||||||
\(768\) | −8.31126 | − | 7.00789i | −0.299907 | − | 0.252875i | ||||
\(769\) | 32.6472i | 1.17729i | 0.808392 | + | 0.588645i | \(0.200338\pi\) | ||||
−0.808392 | + | 0.588645i | \(0.799662\pi\) | |||||||
\(770\) | −1.63086 | + | 5.58902i | −0.0587721 | + | 0.201414i | ||||
\(771\) | − | 9.26800i | − | 0.333779i | ||||||
\(772\) | 20.4279 | + | 13.0312i | 0.735218 | + | 0.469003i | ||||
\(773\) | − | 36.9053i | − | 1.32739i | −0.748003 | − | 0.663695i | \(-0.768987\pi\) | ||
0.748003 | − | 0.663695i | \(-0.231013\pi\) | |||||||
\(774\) | −20.9227 | − | 6.10520i | −0.752052 | − | 0.219447i | ||||
\(775\) | 4.43358i | 0.159259i | ||||||||
\(776\) | 28.9078 | − | 25.3056i | 1.03773 | − | 0.908420i | ||||
\(777\) | −7.06119 | −0.253319 | ||||||||
\(778\) | −13.7784 | + | 47.2192i | −0.493981 | + | 1.69289i | ||||
\(779\) | −2.93049 | −0.104996 | ||||||||
\(780\) | −2.73432 | − | 1.74425i | −0.0979042 | − | 0.0624541i | ||||
\(781\) | − | 5.17522i | − | 0.185184i | ||||||
\(782\) | 10.0299 | − | 19.2118i | 0.358667 | − | 0.687013i | ||||
\(783\) | − | 1.07175i | − | 0.0383012i | ||||||
\(784\) | −9.52238 | − | 20.4847i | −0.340085 | − | 0.731595i | ||||
\(785\) | 16.7787 | 0.598856 | ||||||||
\(786\) | 2.06892 | + | 0.603707i | 0.0737961 | + | 0.0215335i | ||||
\(787\) | −0.865924 | −0.0308669 | −0.0154334 | − | 0.999881i | \(-0.504913\pi\) | ||||
−0.0154334 | + | 0.999881i | \(0.504913\pi\) | |||||||
\(788\) | 20.2762 | + | 12.9344i | 0.722308 | + | 0.460768i | ||||
\(789\) | − | 11.7172i | − | 0.417142i | ||||||
\(790\) | 2.01437 | − | 6.90331i | 0.0716681 | − | 0.245609i | ||||
\(791\) | − | 5.70689i | − | 0.202914i | ||||||
\(792\) | 16.7397 | + | 19.1225i | 0.594820 | + | 0.679489i | ||||
\(793\) | − | 18.4050i | − | 0.653581i | ||||||
\(794\) | −20.0807 | − | 5.85951i | −0.712639 | − | 0.207946i | ||||
\(795\) | 5.06337i | 0.179579i | ||||||||
\(796\) | 44.7611 | + | 28.5536i | 1.58652 | + | 1.01206i | ||||
\(797\) | − | 4.60244i | − | 0.163027i | −0.996672 | − | 0.0815135i | \(-0.974025\pi\) | ||
0.996672 | − | 0.0815135i | \(-0.0259754\pi\) | |||||||
\(798\) | 0.364062 | − | 1.24765i | 0.0128877 | − | 0.0441665i | ||||
\(799\) | 42.2893 | 1.49609 | ||||||||
\(800\) | −0.852189 | − | 5.59230i | −0.0301294 | − | 0.197718i | ||||
\(801\) | − | 7.77796i | − | 0.274821i | ||||||
\(802\) | −6.60847 | + | 22.6474i | −0.233353 | + | 0.799709i | ||||
\(803\) | 17.3046 | 0.610667 | ||||||||
\(804\) | −8.33187 | + | 13.0612i | −0.293842 | + | 0.460633i | ||||
\(805\) | 1.09294 | − | 5.46941i | 0.0385212 | − | 0.192771i | ||||
\(806\) | −4.19176 | + | 14.3653i | −0.147648 | + | 0.505996i | ||||
\(807\) | 3.61771i | 0.127349i | ||||||||
\(808\) | −25.7893 | − | 29.4603i | −0.907265 | − | 1.03641i | ||||
\(809\) | 35.0439 | 1.23208 | 0.616039 | − | 0.787716i | \(-0.288736\pi\) | ||||
0.616039 | + | 0.787716i | \(0.288736\pi\) | |||||||
\(810\) | 2.00374 | − | 6.86687i | 0.0704041 | − | 0.241277i | ||||
\(811\) | − | 10.0046i | − | 0.351309i | −0.984452 | − | 0.175654i | \(-0.943796\pi\) | ||
0.984452 | − | 0.175654i | \(-0.0562041\pi\) | |||||||
\(812\) | 0.558497 | + | 0.356271i | 0.0195994 | + | 0.0125027i | ||||
\(813\) | −1.75475 | −0.0615418 | ||||||||
\(814\) | 12.5306 | − | 42.9428i | 0.439197 | − | 1.50514i | ||||
\(815\) | 15.8341 | 0.554643 | ||||||||
\(816\) | −3.66089 | − | 7.87536i | −0.128157 | − | 0.275693i | ||||
\(817\) | −7.06119 | −0.247040 | ||||||||
\(818\) | 41.2991 | + | 12.0510i | 1.44399 | + | 0.421353i | ||||
\(819\) | 7.04556 | 0.246192 | ||||||||
\(820\) | −2.71029 | + | 4.24870i | −0.0946474 | + | 0.148371i | ||||
\(821\) | −26.7107 | −0.932211 | −0.466106 | − | 0.884729i | \(-0.654343\pi\) | ||||
−0.466106 | + | 0.884729i | \(0.654343\pi\) | |||||||
\(822\) | 5.04518 | + | 1.47217i | 0.175971 | + | 0.0513479i | ||||
\(823\) | − | 19.0791i | − | 0.665055i | −0.943094 | − | 0.332527i | \(-0.892099\pi\) | ||
0.943094 | − | 0.332527i | \(-0.107901\pi\) | |||||||
\(824\) | −21.1678 | − | 24.1809i | −0.737416 | − | 0.842383i | ||||
\(825\) | − | 2.40520i | − | 0.0837384i | ||||||
\(826\) | −3.92195 | + | 13.4407i | −0.136462 | + | 0.467661i | ||||
\(827\) | −38.3439 | −1.33335 | −0.666674 | − | 0.745350i | \(-0.732283\pi\) | ||||
−0.666674 | + | 0.745350i | \(0.732283\pi\) | |||||||
\(828\) | −17.5623 | − | 16.8621i | −0.610334 | − | 0.585999i | ||||
\(829\) | −28.2337 | −0.980597 | −0.490298 | − | 0.871555i | \(-0.663112\pi\) | ||||
−0.490298 | + | 0.871555i | \(0.663112\pi\) | |||||||
\(830\) | −6.00000 | + | 20.5622i | −0.208263 | + | 0.713725i | ||||
\(831\) | 19.8070i | 0.687097i | ||||||||
\(832\) | 2.52608 | − | 18.9254i | 0.0875762 | − | 0.656119i | ||||
\(833\) | − | 18.0459i | − | 0.625254i | ||||||
\(834\) | −14.9400 | − | 4.35945i | −0.517329 | − | 0.150955i | ||||
\(835\) | 8.51278 | 0.294597 | ||||||||
\(836\) | 6.94158 | + | 4.42810i | 0.240079 | + | 0.153149i | ||||
\(837\) | 16.6840 | 0.576683 | ||||||||
\(838\) | −43.1700 | − | 12.5969i | −1.49128 | − | 0.435153i | ||||
\(839\) | 15.0659 | 0.520132 | 0.260066 | − | 0.965591i | \(-0.416256\pi\) | ||||
0.260066 | + | 0.965591i | \(0.416256\pi\) | |||||||
\(840\) | −1.47217 | − | 1.68173i | −0.0507948 | − | 0.0580251i | ||||
\(841\) | −28.9189 | −0.997203 | ||||||||
\(842\) | −5.31185 | + | 18.2039i | −0.183059 | + | 0.627348i | ||||
\(843\) | 16.1542 | 0.556380 | ||||||||
\(844\) | −15.8487 | + | 24.8447i | −0.545534 | + | 0.855189i | ||||
\(845\) | 7.30390i | 0.251262i | ||||||||
\(846\) | 13.3077 | − | 45.6060i | 0.457529 | − | 1.56797i | ||||
\(847\) | −1.78008 | −0.0611641 | ||||||||
\(848\) | −27.0303 | + | 12.5652i | −0.928225 | + | 0.431489i | ||||
\(849\) | 2.77002i | 0.0950669i | ||||||||
\(850\) | 1.26584 | − | 4.33809i | 0.0434181 | − | 0.148795i | ||||
\(851\) | −8.39754 | + | 42.0238i | −0.287864 | + | 1.44056i | ||||
\(852\) | 1.67495 | + | 1.06847i | 0.0573830 | + | 0.0366052i | ||||
\(853\) | 40.8505 | 1.39869 | 0.699347 | − | 0.714782i | \(-0.253474\pi\) | ||||
0.699347 | + | 0.714782i | \(0.253474\pi\) | |||||||
\(854\) | 3.55286 | − | 12.1758i | 0.121576 | − | 0.416646i | ||||
\(855\) | − | 2.95207i | − | 0.100959i | ||||||
\(856\) | 11.3113 | + | 12.9214i | 0.386613 | + | 0.441645i | ||||
\(857\) | −17.2146 | −0.588039 | −0.294019 | − | 0.955799i | \(-0.594993\pi\) | ||||
−0.294019 | + | 0.955799i | \(0.594993\pi\) | |||||||
\(858\) | 2.27401 | − | 7.79312i | 0.0776336 | − | 0.266053i | ||||
\(859\) | − | 23.8177i | − | 0.812649i | −0.913729 | − | 0.406325i | \(-0.866810\pi\) | ||
0.913729 | − | 0.406325i | \(-0.133190\pi\) | |||||||
\(860\) | −6.53059 | + | 10.2375i | −0.222691 | + | 0.349095i | ||||
\(861\) | 1.99116i | 0.0678586i | ||||||||
\(862\) | 21.2684 | + | 6.20608i | 0.724406 | + | 0.211380i | ||||
\(863\) | 47.1128i | 1.60374i | 0.597499 | + | 0.801870i | \(0.296161\pi\) | ||||
−0.597499 | + | 0.801870i | \(0.703839\pi\) | |||||||
\(864\) | −21.0443 | + | 3.20687i | −0.715942 | + | 0.109100i | ||||
\(865\) | 3.19542i | 0.108647i | ||||||||
\(866\) | 5.93380 | − | 20.3353i | 0.201639 | − | 0.691022i | ||||
\(867\) | 4.61309i | 0.156669i | ||||||||
\(868\) | −5.54609 | + | 8.69415i | −0.188247 | + | 0.295099i | ||||
\(869\) | 18.0000 | 0.610608 | ||||||||
\(870\) | −0.262715 | − | 0.0766596i | −0.00890688 | − | 0.00259901i | ||||
\(871\) | −27.2090 | −0.921940 | ||||||||
\(872\) | −17.0561 | + | 14.9308i | −0.577594 | + | 0.505621i | ||||
\(873\) | − | 34.4787i | − | 1.16693i | ||||||
\(874\) | −6.99229 | − | 3.65045i | −0.236518 | − | 0.123478i | ||||
\(875\) | − | 1.16300i | − | 0.0393165i | ||||||
\(876\) | −3.57269 | + | 5.60062i | −0.120710 | + | 0.189227i | ||||
\(877\) | −13.5862 | −0.458775 | −0.229388 | − | 0.973335i | \(-0.573672\pi\) | ||||
−0.229388 | + | 0.973335i | \(0.573672\pi\) | |||||||
\(878\) | 9.20836 | − | 31.5574i | 0.310767 | − | 1.06501i | ||||
\(879\) | −15.4116 | −0.519820 | ||||||||
\(880\) | 12.8399 | − | 5.96870i | 0.432834 | − | 0.201205i | ||||
\(881\) | − | 0.390833i | − | 0.0131675i | −0.999978 | − | 0.00658375i | \(-0.997904\pi\) | ||
0.999978 | − | 0.00658375i | \(-0.00209569\pi\) | |||||||
\(882\) | −19.4612 | − | 5.67874i | −0.655294 | − | 0.191213i | ||||
\(883\) | − | 41.1920i | − | 1.38622i | −0.720831 | − | 0.693110i | \(-0.756240\pi\) | ||
0.720831 | − | 0.693110i | \(-0.243760\pi\) | |||||||
\(884\) | 8.20295 | − | 12.8591i | 0.275895 | − | 0.432498i | ||||
\(885\) | − | 5.78412i | − | 0.194431i | ||||||
\(886\) | 14.8012 | − | 50.7244i | 0.497257 | − | 1.70412i | ||||
\(887\) | 28.5670i | 0.959186i | 0.877491 | + | 0.479593i | \(0.159216\pi\) | ||||
−0.877491 | + | 0.479593i | \(0.840784\pi\) | |||||||
\(888\) | 11.3113 | + | 12.9214i | 0.379583 | + | 0.433615i | ||||
\(889\) | − | 5.83984i | − | 0.195862i | ||||||
\(890\) | −4.15995 | − | 1.21386i | −0.139442 | − | 0.0406888i | ||||
\(891\) | 17.9050 | 0.599839 | ||||||||
\(892\) | −9.29488 | + | 14.5708i | −0.311215 | + | 0.487867i | ||||
\(893\) | − | 15.3915i | − | 0.515058i | ||||||
\(894\) | 15.8775 | + | 4.63303i | 0.531024 | + | 0.154952i | ||||
\(895\) | 2.24289 | 0.0749715 | ||||||||
\(896\) | 5.32443 | − | 12.0324i | 0.177877 | − | 0.401974i | ||||
\(897\) | −1.52396 | + | 7.62634i | −0.0508835 | + | 0.254636i | ||||
\(898\) | −43.9501 | − | 12.8245i | −1.46663 | − | 0.427960i | ||||
\(899\) | 1.26271i | 0.0421137i | ||||||||
\(900\) | −4.27998 | − | 2.73024i | −0.142666 | − | 0.0910081i | ||||
\(901\) | −23.8123 | −0.793303 | ||||||||
\(902\) | −12.1093 | − | 3.53346i | −0.403196 | − | 0.117651i | ||||
\(903\) | 4.79782i | 0.159661i | ||||||||
\(904\) | −10.4432 | + | 9.14187i | −0.347335 | + | 0.304054i | ||||
\(905\) | 0.433943 | 0.0144247 | ||||||||
\(906\) | −3.51219 | − | 1.02485i | −0.116685 | − | 0.0340483i | ||||
\(907\) | 11.2367 | 0.373107 | 0.186553 | − | 0.982445i | \(-0.440268\pi\) | ||||
0.186553 | + | 0.982445i | \(0.440268\pi\) | |||||||
\(908\) | 5.99688 | + | 3.82547i | 0.199013 | + | 0.126953i | ||||
\(909\) | −35.1377 | −1.16544 | ||||||||
\(910\) | 1.09956 | − | 3.76824i | 0.0364502 | − | 0.124916i | ||||
\(911\) | −11.5022 | −0.381085 | −0.190543 | − | 0.981679i | \(-0.561025\pi\) | ||||
−0.190543 | + | 0.981679i | \(0.561025\pi\) | |||||||
\(912\) | −2.86630 | + | 1.33241i | −0.0949127 | + | 0.0441205i | ||||
\(913\) | −53.6148 | −1.77439 | ||||||||
\(914\) | 5.01251 | − | 17.1780i | 0.165799 | − | 0.568199i | ||||
\(915\) | 5.23978i | 0.173222i | ||||||||
\(916\) | −7.62922 | + | 11.9597i | −0.252076 | + | 0.395160i | ||||
\(917\) | 2.60847i | 0.0861393i | ||||||||
\(918\) | −16.3246 | − | 4.76348i | −0.538793 | − | 0.157218i | ||||
\(919\) | 38.1765 | 1.25933 | 0.629663 | − | 0.776869i | \(-0.283193\pi\) | ||||
0.629663 | + | 0.776869i | \(0.283193\pi\) | |||||||
\(920\) | −11.7594 | + | 6.76144i | −0.387695 | + | 0.222918i | ||||
\(921\) | −8.39054 | −0.276478 | ||||||||
\(922\) | −36.4945 | − | 10.6490i | −1.20188 | − | 0.350706i | ||||
\(923\) | 3.48925i | 0.114850i | ||||||||
\(924\) | 3.00873 | − | 4.71655i | 0.0989801 | − | 0.155163i | ||||
\(925\) | 8.93580i | 0.293807i | ||||||||
\(926\) | 4.48447 | − | 15.3684i | 0.147369 | − | 0.505038i | ||||
\(927\) | −28.8410 | −0.947262 | ||||||||
\(928\) | −0.242708 | − | 1.59272i | −0.00796728 | − | 0.0522835i | ||||
\(929\) | −8.03510 | −0.263623 | −0.131812 | − | 0.991275i | \(-0.542079\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542079\pi\) | |||||||
\(930\) | 1.19337 | − | 4.08970i | 0.0391320 | − | 0.134107i | ||||
\(931\) | −6.56795 | −0.215256 | ||||||||
\(932\) | 5.87288 | + | 3.74637i | 0.192373 | + | 0.122716i | ||||
\(933\) | 16.2785 | 0.532934 | ||||||||
\(934\) | 40.5659 | + | 11.8370i | 1.32736 | + | 0.387320i | ||||
\(935\) | 11.3113 | 0.369920 | ||||||||
\(936\) | −11.2863 | − | 12.8928i | −0.368904 | − | 0.421415i | ||||
\(937\) | 36.5045i | 1.19255i | 0.802781 | + | 0.596274i | \(0.203353\pi\) | ||||
−0.802781 | + | 0.596274i | \(0.796647\pi\) | |||||||
\(938\) | −18.0000 | − | 5.25236i | −0.587721 | − | 0.171495i | ||||
\(939\) | −3.71626 | −0.121276 | ||||||||
\(940\) | −22.3150 | − | 14.2350i | −0.727835 | − | 0.464294i | ||||
\(941\) | 17.5802i | 0.573099i | 0.958065 | + | 0.286549i | \(0.0925083\pi\) | ||||
−0.958065 | + | 0.286549i | \(0.907492\pi\) | |||||||
\(942\) | −15.4773 | − | 4.51622i | −0.504276 | − | 0.147147i | ||||
\(943\) | 11.8501 | + | 2.36800i | 0.385894 | + | 0.0771126i | ||||
\(944\) | 30.8780 | − | 14.3537i | 1.00499 | − | 0.467174i | ||||
\(945\) | −4.37646 | −0.142366 | ||||||||
\(946\) | −29.1780 | − | 8.51408i | −0.948660 | − | 0.276817i | ||||
\(947\) | 46.1938i | 1.50110i | 0.660815 | + | 0.750549i | \(0.270211\pi\) | ||||
−0.660815 | + | 0.750549i | \(0.729789\pi\) | |||||||
\(948\) | −3.71626 | + | 5.82568i | −0.120699 | + | 0.189209i | ||||
\(949\) | −11.6672 | −0.378732 | ||||||||
\(950\) | −1.57888 | − | 0.460714i | −0.0512257 | − | 0.0149475i | ||||
\(951\) | − | 5.95501i | − | 0.193104i | ||||||
\(952\) | 7.90892 | − | 6.92341i | 0.256330 | − | 0.224389i | ||||
\(953\) | 52.9790i | 1.71616i | 0.513518 | + | 0.858079i | \(0.328342\pi\) | ||||
−0.513518 | + | 0.858079i | \(0.671658\pi\) | |||||||
\(954\) | −7.49333 | + | 25.6799i | −0.242605 | + | 0.831417i | ||||
\(955\) | − | 15.1460i | − | 0.490114i | ||||||
\(956\) | 5.35681 | − | 8.39743i | 0.173252 | − | 0.271592i | ||||
\(957\) | − | 0.685015i | − | 0.0221434i | ||||||
\(958\) | −38.0851 | − | 11.1131i | −1.23047 | − | 0.359049i | ||||
\(959\) | 6.36090i | 0.205404i | ||||||||
\(960\) | −0.719159 | + | 5.38792i | −0.0232107 | + | 0.173894i | ||||
\(961\) | 11.3433 | 0.365914 | ||||||||
\(962\) | −8.44841 | + | 28.9530i | −0.272388 | + | 0.933481i | ||||
\(963\) | 15.4116 | 0.496631 | ||||||||
\(964\) | 27.6586 | − | 43.3582i | 0.890825 | − | 1.39647i | ||||
\(965\) | − | 12.1152i | − | 0.390002i | ||||||
\(966\) | −2.48034 | + | 4.75100i | −0.0798037 | + | 0.152861i | ||||
\(967\) | − | 51.8494i | − | 1.66737i | −0.552244 | − | 0.833683i | \(-0.686228\pi\) | ||
0.552244 | − | 0.833683i | \(-0.313772\pi\) | |||||||
\(968\) | 2.85151 | + | 3.25740i | 0.0916508 | + | 0.104697i | ||||
\(969\) | −2.52506 | −0.0811167 | ||||||||
\(970\) | −18.4406 | − | 5.38091i | −0.592091 | − | 0.172771i | ||||
\(971\) | −8.84721 | −0.283921 | −0.141960 | − | 0.989872i | \(-0.545341\pi\) | ||||
−0.141960 | + | 0.989872i | \(0.545341\pi\) | |||||||
\(972\) | −15.8395 | + | 24.8302i | −0.508051 | + | 0.796430i | ||||
\(973\) | − | 18.8361i | − | 0.603859i | ||||||
\(974\) | 12.3339 | − | 42.2687i | 0.395203 | − | 1.35438i | ||||
\(975\) | 1.62164i | 0.0519341i | ||||||||
\(976\) | −27.9720 | + | 13.0029i | −0.895363 | + | 0.416213i | ||||
\(977\) | 27.4493i | 0.878181i | 0.898443 | + | 0.439090i | \(0.144699\pi\) | ||||
−0.898443 | + | 0.439090i | \(0.855301\pi\) | |||||||
\(978\) | −14.6059 | − | 4.26197i | −0.467046 | − | 0.136283i | ||||
\(979\) | − | 10.8468i | − | 0.346667i | ||||||
\(980\) | −6.07442 | + | 9.52238i | −0.194040 | + | 0.304181i | ||||
\(981\) | 20.3431i | 0.649506i | ||||||||
\(982\) | 12.2608 | − | 42.0181i | 0.391257 | − | 1.34085i | ||||
\(983\) | 6.62295 | 0.211239 | 0.105620 | − | 0.994407i | \(-0.466317\pi\) | ||||
0.105620 | + | 0.994407i | \(0.466317\pi\) | |||||||
\(984\) | 3.64367 | − | 3.18964i | 0.116156 | − | 0.101682i | ||||
\(985\) | − | 12.0252i | − | 0.383154i | ||||||
\(986\) | 0.360519 | − | 1.23551i | 0.0114813 | − | 0.0393467i | ||||
\(987\) | −10.4580 | −0.332881 | ||||||||
\(988\) | −4.68017 | − | 2.98553i | −0.148896 | − | 0.0949823i | ||||
\(989\) | 28.5536 | + | 5.70582i | 0.907951 | + | 0.181434i | ||||
\(990\) | 3.55948 | − | 12.1985i | 0.113128 | − | 0.387692i | ||||
\(991\) | 26.6720i | 0.847265i | 0.905834 | + | 0.423633i | \(0.139245\pi\) | ||||
−0.905834 | + | 0.423633i | \(0.860755\pi\) | |||||||
\(992\) | 24.7939 | − | 3.77825i | 0.787208 | − | 0.119960i | ||||
\(993\) | −21.9684 | −0.697148 | ||||||||
\(994\) | −0.673557 | + | 2.30830i | −0.0213639 | + | 0.0732149i | ||||
\(995\) | − | 26.5465i | − | 0.841581i | ||||||
\(996\) | 11.0692 | − | 17.3524i | 0.350743 | − | 0.549830i | ||||
\(997\) | −56.5898 | −1.79222 | −0.896108 | − | 0.443837i | \(-0.853617\pi\) | ||||
−0.896108 | + | 0.443837i | \(0.853617\pi\) | |||||||
\(998\) | −2.60190 | + | 8.91681i | −0.0823618 | + | 0.282257i | ||||
\(999\) | 33.6262 | 1.06389 |
(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 | 460.2.e.a.91.15 | yes | 16 | |
4.3 | odd | 2 | inner | 460.2.e.a.91.13 | ✓ | 16 | |
23.22 | odd | 2 | inner | 460.2.e.a.91.16 | yes | 16 | |
92.91 | even | 2 | inner | 460.2.e.a.91.14 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.e.a.91.13 | ✓ | 16 | 4.3 | odd | 2 | inner | |
460.2.e.a.91.14 | yes | 16 | 92.91 | even | 2 | inner | |
460.2.e.a.91.15 | yes | 16 | 1.1 | even | 1 | trivial | |
460.2.e.a.91.16 | yes | 16 | 23.22 | odd | 2 | inner |