Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (of order \(6\), 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: | \(4.41418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.3 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.107 |
Dual form | 162.3.d.c.53.3 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.34486 | + | 0.776457i | −0.268973 | + | 0.155291i | −0.628421 | − | 0.777874i | \(-0.716298\pi\) |
0.359448 | + | 0.933165i | \(0.382965\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.19615 | + | 10.7321i | −0.885165 | + | 1.53315i | −0.0396398 | + | 0.999214i | \(0.512621\pi\) |
−0.845525 | + | 0.533936i | \(0.820712\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.19615 | −0.219615 | ||||||||
\(11\) | 12.7279 | + | 7.34847i | 1.15708 | + | 0.668043i | 0.950603 | − | 0.310408i | \(-0.100466\pi\) |
0.206480 | + | 0.978451i | \(0.433799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.40192 | + | 9.35641i | 0.415533 | + | 0.719724i | 0.995484 | − | 0.0949274i | \(-0.0302619\pi\) |
−0.579952 | + | 0.814651i | \(0.696929\pi\) | |||||||
\(14\) | −15.1774 | + | 8.76268i | −1.08410 | + | 0.625906i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | − | 28.9778i | − | 1.70457i | −0.523074 | − | 0.852287i | \(-0.675215\pi\) | ||
0.523074 | − | 0.852287i | \(-0.324785\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.60770 | 0.189879 | 0.0949393 | − | 0.995483i | \(-0.469734\pi\) | ||||
0.0949393 | + | 0.995483i | \(0.469734\pi\) | |||||||
\(20\) | −2.68973 | − | 1.55291i | −0.134486 | − | 0.0776457i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.3923 | + | 18.0000i | 0.472377 | + | 0.818182i | ||||
\(23\) | 12.7279 | − | 7.34847i | 0.553388 | − | 0.319499i | −0.197099 | − | 0.980384i | \(-0.563152\pi\) |
0.750487 | + | 0.660885i | \(0.229819\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.2942 | + | 19.5622i | −0.451769 | + | 0.782487i | ||||
\(26\) | 15.2789i | 0.587652i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −24.7846 | −0.885165 | ||||||||
\(29\) | −24.3748 | − | 14.0728i | −0.840510 | − | 0.485268i | 0.0169278 | − | 0.999857i | \(-0.494611\pi\) |
−0.857437 | + | 0.514588i | \(0.827945\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 6.92820i | −0.129032 | − | 0.223490i | 0.794270 | − | 0.607565i | \(-0.207854\pi\) |
−0.923302 | + | 0.384075i | \(0.874520\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 20.4904 | − | 35.4904i | 0.602658 | − | 1.04383i | ||||
\(35\) | − | 19.2442i | − | 0.549834i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 22.5692 | 0.609979 | 0.304989 | − | 0.952356i | \(-0.401347\pi\) | ||||
0.304989 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(38\) | 4.41851 | + | 2.55103i | 0.116276 | + | 0.0671323i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.19615 | − | 3.80385i | −0.0549038 | − | 0.0950962i | ||||
\(41\) | 21.7816 | − | 12.5756i | 0.531259 | − | 0.306722i | −0.210270 | − | 0.977643i | \(-0.567434\pi\) |
0.741529 | + | 0.670921i | \(0.234101\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 26.5885 | − | 46.0526i | 0.618336 | − | 1.07099i | −0.371453 | − | 0.928452i | \(-0.621140\pi\) |
0.989789 | − | 0.142538i | \(-0.0455263\pi\) | |||||||
\(44\) | 29.3939i | 0.668043i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 20.7846 | 0.451839 | ||||||||
\(47\) | 14.6969 | + | 8.48528i | 0.312701 | + | 0.180538i | 0.648134 | − | 0.761526i | \(-0.275549\pi\) |
−0.335434 | + | 0.942064i | \(0.608883\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −52.2846 | − | 90.5596i | −1.06703 | − | 1.84816i | ||||
\(50\) | −27.6651 | + | 15.9725i | −0.553302 | + | 0.319449i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.8038 | + | 18.7128i | −0.207766 | + | 0.359862i | ||||
\(53\) | 84.5482i | 1.59525i | 0.603154 | + | 0.797625i | \(0.293910\pi\) | ||||
−0.603154 | + | 0.797625i | \(0.706090\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22.8231 | −0.414965 | ||||||||
\(56\) | −30.3548 | − | 17.5254i | −0.542050 | − | 0.312953i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.9019 | − | 34.4711i | −0.343137 | − | 0.594330i | ||||
\(59\) | 78.8641 | − | 45.5322i | 1.33668 | − | 0.771733i | 0.350367 | − | 0.936613i | \(-0.386057\pi\) |
0.986314 | + | 0.164880i | \(0.0527236\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.106557 | − | 0.184563i | −0.807816 | − | 0.589435i | \(-0.799351\pi\) |
0.914373 | + | 0.404872i | \(0.132684\pi\) | |||||||
\(62\) | − | 11.3137i | − | 0.182479i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −14.5297 | − | 8.38872i | −0.223534 | − | 0.129057i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.5885 | + | 35.6603i | 0.307290 | + | 0.532243i | 0.977769 | − | 0.209687i | \(-0.0672444\pi\) |
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(68\) | 50.1910 | − | 28.9778i | 0.738103 | − | 0.426144i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.6077 | − | 23.5692i | 0.194396 | − | 0.336703i | ||||
\(71\) | 16.3613i | 0.230442i | 0.993340 | + | 0.115221i | \(0.0367575\pi\) | ||||
−0.993340 | + | 0.115221i | \(0.963242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 71.5885 | 0.980664 | 0.490332 | − | 0.871536i | \(-0.336876\pi\) | ||||
0.490332 | + | 0.871536i | \(0.336876\pi\) | |||||||
\(74\) | 27.6415 | + | 15.9588i | 0.373534 | + | 0.215660i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.60770 | + | 6.24871i | 0.0474697 | + | 0.0822199i | ||||
\(77\) | −157.728 | + | 91.0645i | −2.04842 | + | 1.18266i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.3731 | − | 40.4833i | 0.295862 | − | 0.512447i | −0.679323 | − | 0.733839i | \(-0.737727\pi\) |
0.975185 | + | 0.221392i | \(0.0710599\pi\) | |||||||
\(80\) | − | 6.21166i | − | 0.0776457i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 35.5692 | 0.433771 | ||||||||
\(83\) | −13.2555 | − | 7.65308i | −0.159705 | − | 0.0922057i | 0.418017 | − | 0.908439i | \(-0.362725\pi\) |
−0.577723 | + | 0.816233i | \(0.696058\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.5000 | + | 38.9711i | 0.264706 | + | 0.458484i | ||||
\(86\) | 65.1282 | − | 37.6018i | 0.757304 | − | 0.437230i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20.7846 | + | 36.0000i | −0.236189 | + | 0.409091i | ||||
\(89\) | − | 78.9756i | − | 0.887367i | −0.896184 | − | 0.443683i | \(-0.853671\pi\) | ||
0.896184 | − | 0.443683i | \(-0.146329\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −133.885 | −1.47126 | ||||||||
\(92\) | 25.4558 | + | 14.6969i | 0.276694 | + | 0.159749i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0000 | + | 20.7846i | 0.127660 | + | 0.221113i | ||||
\(95\) | −4.85186 | + | 2.80122i | −0.0510722 | + | 0.0294865i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −45.5692 | + | 78.9282i | −0.469786 | + | 0.813693i | −0.999403 | − | 0.0345438i | \(-0.989002\pi\) |
0.529617 | + | 0.848237i | \(0.322336\pi\) | |||||||
\(98\) | − | 147.883i | − | 1.50901i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −45.1769 | −0.451769 | ||||||||
\(101\) | −76.6313 | − | 44.2431i | −0.758726 | − | 0.438051i | 0.0701121 | − | 0.997539i | \(-0.477664\pi\) |
−0.828838 | + | 0.559488i | \(0.810998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.3538 | + | 132.249i | 0.741299 | + | 1.28397i | 0.951904 | + | 0.306397i | \(0.0991234\pi\) |
−0.210605 | + | 0.977571i | \(0.567543\pi\) | |||||||
\(104\) | −26.4639 | + | 15.2789i | −0.254461 | + | 0.146913i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −59.7846 | + | 103.550i | −0.564006 | + | 0.976887i | ||||
\(107\) | 60.0062i | 0.560805i | 0.959882 | + | 0.280403i | \(0.0904680\pi\) | ||||
−0.959882 | + | 0.280403i | \(0.909532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −93.9423 | −0.861856 | −0.430928 | − | 0.902386i | \(-0.641814\pi\) | ||||
−0.430928 | + | 0.902386i | \(0.641814\pi\) | |||||||
\(110\) | −27.9525 | − | 16.1384i | −0.254113 | − | 0.146712i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −24.7846 | − | 42.9282i | −0.221291 | − | 0.383288i | ||||
\(113\) | −76.7279 | + | 44.2989i | −0.679008 | + | 0.392025i | −0.799481 | − | 0.600691i | \(-0.794892\pi\) |
0.120473 | + | 0.992717i | \(0.461559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.4115 | + | 19.7654i | −0.0992308 | + | 0.171873i | ||||
\(116\) | − | 56.2911i | − | 0.485268i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 128.785 | 1.09139 | ||||||||
\(119\) | 310.991 | + | 179.551i | 2.61337 | + | 1.50883i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 47.5000 | + | 82.2724i | 0.392562 | + | 0.679937i | ||||
\(122\) | 15.9217 | − | 9.19239i | 0.130506 | − | 0.0753474i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.00000 | − | 13.8564i | 0.0645161 | − | 0.111745i | ||||
\(125\) | − | 73.9008i | − | 0.591206i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 78.8231 | 0.620654 | 0.310327 | − | 0.950630i | \(-0.399561\pi\) | ||||
0.310327 | + | 0.950630i | \(0.399561\pi\) | |||||||
\(128\) | −9.79796 | − | 5.65685i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.8634 | − | 20.5481i | −0.0912573 | − | 0.158062i | ||||
\(131\) | −71.5157 | + | 41.2896i | −0.545921 | + | 0.315188i | −0.747475 | − | 0.664290i | \(-0.768734\pi\) |
0.201554 | + | 0.979477i | \(0.435401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.3538 | + | 38.7180i | −0.168074 | + | 0.291113i | ||||
\(134\) | 58.2330i | 0.434574i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 81.9615 | 0.602658 | ||||||||
\(137\) | −185.970 | − | 107.370i | −1.35745 | − | 0.783723i | −0.368169 | − | 0.929759i | \(-0.620015\pi\) |
−0.989279 | + | 0.146036i | \(0.953349\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 30.3923 | + | 52.6410i | 0.218650 | + | 0.378712i | 0.954395 | − | 0.298546i | \(-0.0965015\pi\) |
−0.735746 | + | 0.677258i | \(0.763168\pi\) | |||||||
\(140\) | 33.3319 | − | 19.2442i | 0.238085 | − | 0.137458i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −11.5692 | + | 20.0385i | −0.0814734 | + | 0.141116i | ||||
\(143\) | 158.783i | 1.11037i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 43.7077 | 0.301432 | ||||||||
\(146\) | 87.6776 | + | 50.6207i | 0.600531 | + | 0.346717i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 22.5692 | + | 39.0910i | 0.152495 | + | 0.264129i | ||||
\(149\) | −26.5369 | + | 15.3211i | −0.178100 | + | 0.102826i | −0.586400 | − | 0.810022i | \(-0.699455\pi\) |
0.408300 | + | 0.912848i | \(0.366122\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | + | 27.7128i | −0.105960 | + | 0.183529i | −0.914130 | − | 0.405421i | \(-0.867125\pi\) |
0.808170 | + | 0.588949i | \(0.200458\pi\) | |||||||
\(152\) | 10.2041i | 0.0671323i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −257.569 | −1.67253 | ||||||||
\(155\) | 10.7589 | + | 6.21166i | 0.0694123 | + | 0.0400752i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −124.854 | − | 216.253i | −0.795247 | − | 1.37741i | −0.922682 | − | 0.385562i | \(-0.874008\pi\) |
0.127435 | − | 0.991847i | \(-0.459326\pi\) | |||||||
\(158\) | 57.2521 | − | 33.0545i | 0.362355 | − | 0.209206i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 4.39230 | − | 7.60770i | 0.0274519 | − | 0.0475481i | ||||
\(161\) | 182.129i | 1.13124i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.7846 | −0.0784332 | −0.0392166 | − | 0.999231i | \(-0.512486\pi\) | ||||
−0.0392166 | + | 0.999231i | \(0.512486\pi\) | |||||||
\(164\) | 43.5632 | + | 25.1512i | 0.265629 | + | 0.153361i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.8231 | − | 18.7461i | −0.0651993 | − | 0.112929i | ||||
\(167\) | 201.292 | − | 116.216i | 1.20534 | − | 0.695902i | 0.243601 | − | 0.969876i | \(-0.421671\pi\) |
0.961737 | + | 0.273973i | \(0.0883379\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.1384 | − | 45.2731i | 0.154665 | − | 0.267888i | ||||
\(170\) | 63.6396i | 0.374351i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 106.354 | 0.618336 | ||||||||
\(173\) | −18.6608 | − | 10.7738i | −0.107866 | − | 0.0622765i | 0.445096 | − | 0.895483i | \(-0.353169\pi\) |
−0.552963 | + | 0.833206i | \(0.686503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −139.962 | − | 242.420i | −0.799780 | − | 1.38526i | ||||
\(176\) | −50.9117 | + | 29.3939i | −0.289271 | + | 0.167011i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 55.8442 | − | 96.7250i | 0.313732 | − | 0.543399i | ||||
\(179\) | − | 277.741i | − | 1.55162i | −0.630964 | − | 0.775812i | \(-0.717341\pi\) | ||
0.630964 | − | 0.775812i | \(-0.282659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 174.277 | 0.962856 | 0.481428 | − | 0.876486i | \(-0.340118\pi\) | ||||
0.481428 | + | 0.876486i | \(0.340118\pi\) | |||||||
\(182\) | −163.974 | − | 94.6707i | −0.900958 | − | 0.520169i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 20.7846 | + | 36.0000i | 0.112960 | + | 0.195652i | ||||
\(185\) | −30.3525 | + | 17.5240i | −0.164068 | + | 0.0947245i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 212.942 | − | 368.827i | 1.13873 | − | 1.97234i | ||||
\(188\) | 33.9411i | 0.180538i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.92305 | −0.0417003 | ||||||||
\(191\) | −131.745 | − | 76.0629i | −0.689764 | − | 0.398235i | 0.113760 | − | 0.993508i | \(-0.463711\pi\) |
−0.803523 | + | 0.595273i | \(0.797044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.5000 | + | 47.6314i | 0.142487 | + | 0.246795i | 0.928433 | − | 0.371501i | \(-0.121157\pi\) |
−0.785946 | + | 0.618296i | \(0.787823\pi\) | |||||||
\(194\) | −111.621 | + | 64.4446i | −0.575368 | + | 0.332189i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 104.569 | − | 181.119i | 0.533516 | − | 0.924078i | ||||
\(197\) | − | 133.298i | − | 0.676638i | −0.941031 | − | 0.338319i | \(-0.890142\pi\) | ||
0.941031 | − | 0.338319i | \(-0.109858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −208.862 | −1.04956 | −0.524778 | − | 0.851239i | \(-0.675852\pi\) | ||||
−0.524778 | + | 0.851239i | \(0.675852\pi\) | |||||||
\(200\) | −55.3302 | − | 31.9449i | −0.276651 | − | 0.159725i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −62.5692 | − | 108.373i | −0.309749 | − | 0.536500i | ||||
\(203\) | 302.060 | − | 174.394i | 1.48798 | − | 0.859085i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.5289 | + | 33.8250i | −0.0952627 | + | 0.165000i | ||||
\(206\) | 215.961i | 1.04836i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −43.2154 | −0.207766 | ||||||||
\(209\) | 45.9185 | + | 26.5110i | 0.219706 | + | 0.126847i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 43.7269 | + | 75.7372i | 0.207236 | + | 0.358944i | 0.950843 | − | 0.309673i | \(-0.100220\pi\) |
−0.743607 | + | 0.668617i | \(0.766886\pi\) | |||||||
\(212\) | −146.442 | + | 84.5482i | −0.690763 | + | 0.398812i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −42.4308 | + | 73.4923i | −0.198275 | + | 0.343422i | ||||
\(215\) | 82.5792i | 0.384089i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 99.1384 | 0.456859 | ||||||||
\(218\) | −115.055 | − | 66.4272i | −0.527777 | − | 0.304712i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −22.8231 | − | 39.5307i | −0.103741 | − | 0.179685i | ||||
\(221\) | 271.128 | − | 156.536i | 1.22682 | − | 0.708306i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −111.296 | + | 192.771i | −0.499086 | + | 0.864442i | −0.999999 | − | 0.00105540i | \(-0.999664\pi\) |
0.500914 | + | 0.865497i | \(0.332997\pi\) | |||||||
\(224\) | − | 70.1015i | − | 0.312953i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −125.296 | −0.554408 | ||||||||
\(227\) | −260.079 | − | 150.157i | −1.14572 | − | 0.661484i | −0.197882 | − | 0.980226i | \(-0.563406\pi\) |
−0.947842 | + | 0.318742i | \(0.896740\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −114.971 | − | 199.136i | −0.502057 | − | 0.869589i | −0.999997 | − | 0.00237731i | \(-0.999243\pi\) |
0.497940 | − | 0.867212i | \(-0.334090\pi\) | |||||||
\(230\) | −27.9525 | + | 16.1384i | −0.121532 | + | 0.0701668i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 39.8038 | − | 68.9423i | 0.171568 | − | 0.297165i | ||||
\(233\) | 116.246i | 0.498908i | 0.968387 | + | 0.249454i | \(0.0802512\pi\) | ||||
−0.968387 | + | 0.249454i | \(0.919749\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.3538 | −0.112144 | ||||||||
\(236\) | 157.728 | + | 91.0645i | 0.668340 | + | 0.385866i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 253.923 | + | 439.808i | 1.06690 | + | 1.84793i | ||||
\(239\) | −142.362 | + | 82.1930i | −0.595659 | + | 0.343904i | −0.767332 | − | 0.641250i | \(-0.778416\pi\) |
0.171673 | + | 0.985154i | \(0.445083\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 40.6558 | − | 70.4179i | 0.168696 | − | 0.292190i | −0.769265 | − | 0.638929i | \(-0.779378\pi\) |
0.937962 | + | 0.346739i | \(0.112711\pi\) | |||||||
\(242\) | 134.350i | 0.555166i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.0000 | 0.106557 | ||||||||
\(245\) | 140.631 | + | 81.1935i | 0.574005 | + | 0.331402i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.4885 | + | 33.7551i | 0.0789008 | + | 0.136660i | ||||
\(248\) | 19.5959 | − | 11.3137i | 0.0790158 | − | 0.0456198i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 52.2558 | − | 90.5096i | 0.209023 | − | 0.362038i | ||||
\(251\) | − | 396.371i | − | 1.57917i | −0.613642 | − | 0.789584i | \(-0.710296\pi\) | ||
0.613642 | − | 0.789584i | \(-0.289704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 216.000 | 0.853755 | ||||||||
\(254\) | 96.5382 | + | 55.7363i | 0.380072 | + | 0.219434i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −186.164 | + | 107.482i | −0.724372 | + | 0.418216i | −0.816360 | − | 0.577544i | \(-0.804011\pi\) |
0.0919879 | + | 0.995760i | \(0.470678\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −139.842 | + | 242.214i | −0.539932 | + | 0.935189i | ||||
\(260\) | − | 33.5549i | − | 0.129057i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −116.785 | −0.445743 | ||||||||
\(263\) | 275.304 | + | 158.947i | 1.04678 | + | 0.604360i | 0.921747 | − | 0.387792i | \(-0.126762\pi\) |
0.125036 | + | 0.992152i | \(0.460095\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −65.6481 | − | 113.706i | −0.247729 | − | 0.429078i | ||||
\(266\) | −54.7555 | + | 31.6131i | −0.205848 | + | 0.118846i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −41.1769 | + | 71.3205i | −0.153645 | + | 0.266121i | ||||
\(269\) | − | 208.528i | − | 0.775199i | −0.921828 | − | 0.387599i | \(-0.873304\pi\) | ||
0.921828 | − | 0.387599i | \(-0.126696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 409.885 | 1.51249 | 0.756245 | − | 0.654289i | \(-0.227032\pi\) | ||||
0.756245 | + | 0.654289i | \(0.227032\pi\) | |||||||
\(272\) | 100.382 | + | 57.9555i | 0.369051 | + | 0.213072i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −151.844 | − | 263.002i | −0.554176 | − | 0.959861i | ||||
\(275\) | −287.504 | + | 165.991i | −1.04547 | + | 0.603602i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −248.708 | + | 430.774i | −0.897862 | + | 1.55514i | −0.0676390 | + | 0.997710i | \(0.521547\pi\) |
−0.830223 | + | 0.557432i | \(0.811787\pi\) | |||||||
\(278\) | 85.9624i | 0.309217i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 54.4308 | 0.194396 | ||||||||
\(281\) | 186.427 | + | 107.634i | 0.663442 | + | 0.383039i | 0.793587 | − | 0.608456i | \(-0.208211\pi\) |
−0.130145 | + | 0.991495i | \(0.541544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 148.354 | + | 256.956i | 0.524218 | + | 0.907973i | 0.999602 | + | 0.0281946i | \(0.00897581\pi\) |
−0.475384 | + | 0.879778i | \(0.657691\pi\) | |||||||
\(284\) | −28.3387 | + | 16.3613i | −0.0997841 | + | 0.0576104i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −112.277 | + | 194.469i | −0.392576 | + | 0.679962i | ||||
\(287\) | 311.682i | 1.08600i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −550.711 | −1.90558 | ||||||||
\(290\) | 53.5307 | + | 30.9060i | 0.184589 | + | 0.106572i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 71.5885 | + | 123.995i | 0.245166 | + | 0.424640i | ||||
\(293\) | 295.284 | − | 170.482i | 1.00779 | − | 0.581850i | 0.0972490 | − | 0.995260i | \(-0.468996\pi\) |
0.910545 | + | 0.413410i | \(0.135662\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −70.7077 | + | 122.469i | −0.239687 | + | 0.415150i | ||||
\(296\) | 63.8354i | 0.215660i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −43.3346 | −0.145418 | ||||||||
\(299\) | 137.511 | + | 79.3917i | 0.459901 | + | 0.265524i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 329.492 | + | 570.697i | 1.09466 | + | 1.89600i | ||||
\(302\) | −39.1918 | + | 22.6274i | −0.129774 | + | 0.0749252i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.21539 | + | 12.4974i | −0.0237348 | + | 0.0411099i | ||||
\(305\) | 20.1879i | 0.0661898i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −114.354 | −0.372488 | −0.186244 | − | 0.982504i | \(-0.559632\pi\) | ||||
−0.186244 | + | 0.982504i | \(0.559632\pi\) | |||||||
\(308\) | −315.457 | − | 182.129i | −1.02421 | − | 0.591328i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.78461 | + | 15.2154i | 0.0283375 | + | 0.0490819i | ||||
\(311\) | −169.929 | + | 98.1083i | −0.546394 | + | 0.315461i | −0.747666 | − | 0.664074i | \(-0.768826\pi\) |
0.201272 | + | 0.979535i | \(0.435492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 73.3616 | − | 127.066i | 0.234382 | − | 0.405962i | −0.724711 | − | 0.689053i | \(-0.758027\pi\) |
0.959093 | + | 0.283092i | \(0.0913600\pi\) | |||||||
\(314\) | − | 353.140i | − | 1.12465i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 93.4923 | 0.295862 | ||||||||
\(317\) | −41.6908 | − | 24.0702i | −0.131517 | − | 0.0759311i | 0.432798 | − | 0.901491i | \(-0.357526\pi\) |
−0.564315 | + | 0.825560i | \(0.690860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −206.827 | − | 358.235i | −0.648360 | − | 1.12299i | ||||
\(320\) | 10.7589 | − | 6.21166i | 0.0336216 | − | 0.0194114i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −128.785 | + | 223.061i | −0.399952 | + | 0.692738i | ||||
\(323\) | − | 104.543i | − | 0.323662i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −244.042 | −0.750899 | ||||||||
\(326\) | −15.6579 | − | 9.04008i | −0.0480303 | − | 0.0277303i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 35.5692 | + | 61.6077i | 0.108443 | + | 0.187828i | ||||
\(329\) | −182.129 | + | 105.152i | −0.553583 | + | 0.319612i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 49.7269 | − | 86.1295i | 0.150232 | − | 0.260210i | −0.781080 | − | 0.624430i | \(-0.785331\pi\) |
0.931313 | + | 0.364220i | \(0.118665\pi\) | |||||||
\(332\) | − | 30.6123i | − | 0.0922057i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 328.708 | 0.984155 | ||||||||
\(335\) | −55.3773 | − | 31.9721i | −0.165305 | − | 0.0954391i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 212.631 | + | 368.287i | 0.630952 | + | 1.09284i | 0.987358 | + | 0.158509i | \(0.0506687\pi\) |
−0.356406 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(338\) | 64.0258 | − | 36.9653i | 0.189426 | − | 0.109365i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −45.0000 | + | 77.9423i | −0.132353 | + | 0.229242i | ||||
\(341\) | − | 117.576i | − | 0.344796i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 688.631 | 2.00767 | ||||||||
\(344\) | 130.256 | + | 75.2035i | 0.378652 | + | 0.218615i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.2365 | − | 26.3904i | −0.0440362 | − | 0.0762729i | ||||
\(347\) | 33.5768 | − | 19.3856i | 0.0967630 | − | 0.0558662i | −0.450838 | − | 0.892606i | \(-0.648875\pi\) |
0.547601 | + | 0.836740i | \(0.315541\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 325.985 | − | 564.622i | 0.934053 | − | 1.61783i | 0.157739 | − | 0.987481i | \(-0.449579\pi\) |
0.776314 | − | 0.630347i | \(-0.217087\pi\) | |||||||
\(350\) | − | 395.871i | − | 1.13106i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −83.1384 | −0.236189 | ||||||||
\(353\) | −1.03625 | − | 0.598281i | −0.00293556 | − | 0.00169485i | 0.498532 | − | 0.866872i | \(-0.333873\pi\) |
−0.501467 | + | 0.865177i | \(0.667206\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.7039 | − | 22.0038i | −0.0357856 | − | 0.0619825i | ||||
\(356\) | 136.790 | − | 78.9756i | 0.384241 | − | 0.221842i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 196.392 | − | 340.161i | 0.548582 | − | 0.950172i | ||||
\(359\) | 534.573i | 1.48906i | 0.667589 | + | 0.744530i | \(0.267326\pi\) | ||||
−0.667589 | + | 0.744530i | \(0.732674\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −347.985 | −0.963946 | ||||||||
\(362\) | 213.445 | + | 123.232i | 0.589626 | + | 0.340421i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −133.885 | − | 231.895i | −0.367815 | − | 0.637074i | ||||
\(365\) | −96.2767 | + | 55.5854i | −0.263772 | + | 0.152289i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −132.354 | + | 229.244i | −0.360637 | + | 0.624642i | −0.988066 | − | 0.154032i | \(-0.950774\pi\) |
0.627429 | + | 0.778674i | \(0.284107\pi\) | |||||||
\(368\) | 58.7878i | 0.159749i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −49.5654 | −0.133961 | ||||||||
\(371\) | −907.376 | − | 523.874i | −2.44576 | − | 1.41206i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −35.5077 | − | 61.5012i | −0.0951950 | − | 0.164883i | 0.814495 | − | 0.580171i | \(-0.197014\pi\) |
−0.909690 | + | 0.415288i | \(0.863681\pi\) | |||||||
\(374\) | 521.600 | − | 301.146i | 1.39465 | − | 0.805203i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | + | 41.5692i | −0.0638298 | + | 0.110556i | ||||
\(377\) | − | 304.080i | − | 0.806579i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −696.785 | −1.83848 | −0.919241 | − | 0.393696i | \(-0.871196\pi\) | ||||
−0.919241 | + | 0.393696i | \(0.871196\pi\) | |||||||
\(380\) | −9.70371 | − | 5.60244i | −0.0255361 | − | 0.0147433i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −107.569 | − | 186.315i | −0.281595 | − | 0.487737i | ||||
\(383\) | −376.986 | + | 217.653i | −0.984297 | + | 0.568284i | −0.903565 | − | 0.428452i | \(-0.859059\pi\) |
−0.0807324 | + | 0.996736i | \(0.525726\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 141.415 | − | 244.939i | 0.367313 | − | 0.636204i | ||||
\(386\) | 77.7817i | 0.201507i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −182.277 | −0.469786 | ||||||||
\(389\) | −45.9374 | − | 26.5220i | −0.118091 | − | 0.0681799i | 0.439791 | − | 0.898100i | \(-0.355053\pi\) |
−0.557882 | + | 0.829920i | \(0.688386\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −212.942 | − | 368.827i | −0.544609 | − | 0.943291i | ||||
\(392\) | 256.141 | − | 147.883i | 0.653422 | − | 0.377253i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 94.2558 | − | 163.256i | 0.239228 | − | 0.414355i | ||||
\(395\) | 72.5927i | 0.183779i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 63.7077 | 0.160473 | 0.0802363 | − | 0.996776i | \(-0.474432\pi\) | ||||
0.0802363 | + | 0.996776i | \(0.474432\pi\) | |||||||
\(398\) | −255.802 | − | 147.687i | −0.642719 | − | 0.371074i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −45.1769 | − | 78.2487i | −0.112942 | − | 0.195622i | ||||
\(401\) | 544.463 | − | 314.346i | 1.35776 | − | 0.783904i | 0.368440 | − | 0.929651i | \(-0.379892\pi\) |
0.989322 | + | 0.145747i | \(0.0465586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 43.2154 | − | 74.8513i | 0.107234 | − | 0.185735i | ||||
\(404\) | − | 176.972i | − | 0.438051i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 493.261 | 1.21493 | ||||||||
\(407\) | 287.259 | + | 165.849i | 0.705797 | + | 0.407492i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −267.640 | − | 463.567i | −0.654377 | − | 1.13341i | −0.982050 | − | 0.188623i | \(-0.939597\pi\) |
0.327672 | − | 0.944791i | \(-0.393736\pi\) | |||||||
\(410\) | −47.8357 | + | 27.6180i | −0.116673 | + | 0.0673609i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −152.708 | + | 264.497i | −0.370650 | + | 0.641984i | ||||
\(413\) | 1128.50i | 2.73244i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.7691 | 0.0572750 | ||||||||
\(416\) | −52.9278 | − | 30.5579i | −0.127230 | − | 0.0734565i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 37.4923 | + | 64.9385i | 0.0896944 | + | 0.155355i | ||||
\(419\) | −333.705 | + | 192.665i | −0.796433 | + | 0.459821i | −0.842222 | − | 0.539130i | \(-0.818753\pi\) |
0.0457895 | + | 0.998951i | \(0.485420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 377.660 | − | 654.126i | 0.897054 | − | 1.55374i | 0.0658113 | − | 0.997832i | \(-0.479036\pi\) |
0.831242 | − | 0.555910i | \(-0.187630\pi\) | |||||||
\(422\) | 123.678i | 0.293077i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −239.138 | −0.564006 | ||||||||
\(425\) | 566.868 | + | 327.282i | 1.33381 | + | 0.770074i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 80.5500 | + | 139.517i | 0.188642 | + | 0.326737i | ||||
\(428\) | −103.934 | + | 60.0062i | −0.242836 | + | 0.140201i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −58.3923 | + | 101.138i | −0.135796 | + | 0.235206i | ||||
\(431\) | 107.709i | 0.249904i | 0.992163 | + | 0.124952i | \(0.0398777\pi\) | ||||
−0.992163 | + | 0.124952i | \(0.960122\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 655.123 | 1.51299 | 0.756493 | − | 0.654002i | \(-0.226911\pi\) | ||||
0.756493 | + | 0.654002i | \(0.226911\pi\) | |||||||
\(434\) | 121.419 | + | 70.1015i | 0.279768 | + | 0.161524i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −93.9423 | − | 162.713i | −0.215464 | − | 0.373195i | ||||
\(437\) | 45.9185 | − | 26.5110i | 0.105077 | − | 0.0606660i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 236.000 | − | 408.764i | 0.537585 | − | 0.931125i | −0.461448 | − | 0.887167i | \(-0.652670\pi\) |
0.999033 | − | 0.0439580i | \(-0.0139968\pi\) | |||||||
\(440\) | − | 64.5534i | − | 0.146712i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 442.750 | 1.00170 | ||||||||
\(443\) | −728.516 | − | 420.609i | −1.64451 | − | 0.949455i | −0.979203 | − | 0.202881i | \(-0.934970\pi\) |
−0.665302 | − | 0.746575i | \(-0.731697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 61.3212 | + | 106.211i | 0.137800 | + | 0.238677i | ||||
\(446\) | −272.619 | + | 157.396i | −0.611253 | + | 0.352907i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 49.5692 | − | 85.8564i | 0.110646 | − | 0.191644i | ||||
\(449\) | 382.751i | 0.852453i | 0.904616 | + | 0.426227i | \(0.140157\pi\) | ||||
−0.904616 | + | 0.426227i | \(0.859843\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 369.646 | 0.819615 | ||||||||
\(452\) | −153.456 | − | 88.5977i | −0.339504 | − | 0.196013i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −212.354 | − | 367.808i | −0.467740 | − | 0.810149i | ||||
\(455\) | 180.056 | − | 103.956i | 0.395728 | − | 0.228474i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −161.852 | + | 280.336i | −0.354162 | + | 0.613426i | −0.986974 | − | 0.160879i | \(-0.948567\pi\) |
0.632812 | + | 0.774305i | \(0.281900\pi\) | |||||||
\(458\) | − | 325.187i | − | 0.710016i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −45.6462 | −0.0992308 | ||||||||
\(461\) | 555.582 | + | 320.765i | 1.20517 | + | 0.695803i | 0.961700 | − | 0.274106i | \(-0.0883818\pi\) |
0.243467 | + | 0.969909i | \(0.421715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −64.7461 | − | 112.144i | −0.139840 | − | 0.242211i | 0.787596 | − | 0.616192i | \(-0.211326\pi\) |
−0.927436 | + | 0.373982i | \(0.877992\pi\) | |||||||
\(464\) | 97.4991 | − | 56.2911i | 0.210127 | − | 0.121317i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −82.1980 | + | 142.371i | −0.176391 | + | 0.305518i | ||||
\(467\) | − | 672.730i | − | 1.44054i | −0.693696 | − | 0.720268i | \(-0.744019\pi\) | ||
0.693696 | − | 0.720268i | \(-0.255981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −510.277 | −1.08801 | ||||||||
\(470\) | −32.2767 | − | 18.6350i | −0.0686739 | − | 0.0396489i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 128.785 | + | 223.061i | 0.272849 | + | 0.472588i | ||||
\(473\) | 676.832 | − | 390.769i | 1.43093 | − | 0.826150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −40.7461 | + | 70.5744i | −0.0857813 | + | 0.148578i | ||||
\(476\) | 718.203i | 1.50883i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −232.477 | −0.486353 | ||||||||
\(479\) | 108.786 | + | 62.8074i | 0.227110 | + | 0.131122i | 0.609238 | − | 0.792987i | \(-0.291475\pi\) |
−0.382128 | + | 0.924109i | \(0.624809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 121.917 | + | 211.167i | 0.253466 | + | 0.439016i | ||||
\(482\) | 99.5859 | − | 57.4960i | 0.206610 | − | 0.119286i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −95.0000 | + | 164.545i | −0.196281 | + | 0.339969i | ||||
\(485\) | − | 141.530i | − | 0.291815i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −448.631 | −0.921213 | −0.460606 | − | 0.887604i | \(-0.652368\pi\) | ||||
−0.460606 | + | 0.887604i | \(0.652368\pi\) | |||||||
\(488\) | 31.8434 | + | 18.3848i | 0.0652528 | + | 0.0376737i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 114.825 | + | 198.883i | 0.234337 | + | 0.405883i | ||||
\(491\) | −391.579 | + | 226.078i | −0.797514 | + | 0.460445i | −0.842601 | − | 0.538538i | \(-0.818977\pi\) |
0.0450873 | + | 0.998983i | \(0.485643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −407.798 | + | 706.327i | −0.827176 | + | 1.43271i | ||||
\(494\) | 55.1218i | 0.111583i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 0.0645161 | ||||||||
\(497\) | −175.591 | − | 101.377i | −0.353301 | − | 0.203979i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −63.2961 | − | 109.632i | −0.126846 | − | 0.219704i | 0.795607 | − | 0.605813i | \(-0.207152\pi\) |
−0.922453 | + | 0.386109i | \(0.873819\pi\) | |||||||
\(500\) | 128.000 | − | 73.9008i | 0.256000 | − | 0.147802i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 280.277 | − | 485.454i | 0.558320 | − | 0.967039i | ||||
\(503\) | 296.822i | 0.590103i | 0.955481 | + | 0.295051i | \(0.0953367\pi\) | ||||
−0.955481 | + | 0.295051i | \(0.904663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 137.412 | 0.272102 | ||||||||
\(506\) | 264.545 | + | 152.735i | 0.522816 | + | 0.301848i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 78.8231 | + | 136.526i | 0.155164 | + | 0.268751i | ||||
\(509\) | −567.113 | + | 327.423i | −1.11417 | + | 0.643267i | −0.939907 | − | 0.341432i | \(-0.889088\pi\) |
−0.174265 | + | 0.984699i | \(0.555755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −443.573 | + | 768.291i | −0.868049 | + | 1.50350i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −304.004 | −0.591447 | ||||||||
\(515\) | −205.371 | − | 118.571i | −0.398778 | − | 0.230235i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 124.708 | + | 216.000i | 0.241214 | + | 0.417795i | ||||
\(518\) | −342.542 | + | 197.767i | −0.661279 | + | 0.381789i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.7269 | − | 41.0962i | 0.0456286 | − | 0.0790311i | ||||
\(521\) | − | 690.006i | − | 1.32439i | −0.749333 | − | 0.662193i | \(-0.769626\pi\) | ||
0.749333 | − | 0.662193i | \(-0.230374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 616.238 | 1.17828 | 0.589138 | − | 0.808032i | \(-0.299467\pi\) | ||||
0.589138 | + | 0.808032i | \(0.299467\pi\) | |||||||
\(524\) | −143.031 | − | 82.5792i | −0.272961 | − | 0.157594i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 224.785 | + | 389.338i | 0.427347 | + | 0.740187i | ||||
\(527\) | −200.764 | + | 115.911i | −0.380956 | + | 0.219945i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −156.500 | + | 271.066i | −0.295841 | + | 0.512412i | ||||
\(530\) | − | 185.681i | − | 0.350341i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −89.4153 | −0.168074 | ||||||||
\(533\) | 235.325 | + | 135.865i | 0.441511 | + | 0.254906i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.5922 | − | 80.7001i | −0.0870883 | − | 0.150841i | ||||
\(536\) | −100.862 | + | 58.2330i | −0.188176 | + | 0.108644i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 147.452 | − | 255.394i | 0.274074 | − | 0.474710i | ||||
\(539\) | − | 1536.85i | − | 2.85129i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −548.734 | −1.01430 | −0.507148 | − | 0.861859i | \(-0.669300\pi\) | ||||
−0.507148 | + | 0.861859i | \(0.669300\pi\) | |||||||
\(542\) | 502.004 | + | 289.832i | 0.926207 | + | 0.534746i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 81.9615 | + | 141.962i | 0.150665 | + | 0.260959i | ||||
\(545\) | 126.340 | − | 72.9422i | 0.231816 | − | 0.133839i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 409.885 | − | 709.941i | 0.749332 | − | 1.29788i | −0.198811 | − | 0.980038i | \(-0.563708\pi\) |
0.948143 | − | 0.317843i | \(-0.102959\pi\) | |||||||
\(548\) | − | 429.480i | − | 0.783723i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −469.492 | −0.853622 | ||||||||
\(551\) | −87.9368 | − | 50.7703i | −0.159595 | − | 0.0921421i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 289.646 | + | 501.682i | 0.523772 | + | 0.907201i | ||||
\(554\) | −609.207 | + | 351.726i | −1.09965 | + | 0.634884i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −60.7846 | + | 105.282i | −0.109325 | + | 0.189356i | ||||
\(557\) | − | 125.808i | − | 0.225867i | −0.993603 | − | 0.112934i | \(-0.963975\pi\) | ||
0.993603 | − | 0.112934i | \(-0.0360247\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 574.515 | 1.02776 | ||||||||
\(560\) | 66.6638 | + | 38.4884i | 0.119043 | + | 0.0687292i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 152.217 | + | 263.648i | 0.270849 | + | 0.469125i | ||||
\(563\) | 440.625 | − | 254.395i | 0.782638 | − | 0.451856i | −0.0547261 | − | 0.998501i | \(-0.517429\pi\) |
0.837365 | + | 0.546645i | \(0.184095\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 68.7923 | − | 119.152i | 0.121756 | − | 0.210888i | ||||
\(566\) | 419.608i | 0.741357i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −46.2769 | −0.0814734 | ||||||||
\(569\) | 83.8832 | + | 48.4300i | 0.147422 | + | 0.0851143i | 0.571897 | − | 0.820326i | \(-0.306208\pi\) |
−0.424474 | + | 0.905440i | \(0.639541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 227.100 | + | 393.349i | 0.397723 | + | 0.688877i | 0.993445 | − | 0.114314i | \(-0.0364671\pi\) |
−0.595721 | + | 0.803191i | \(0.703134\pi\) | |||||||
\(572\) | −275.021 | + | 158.783i | −0.480806 | + | 0.277594i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −220.392 | + | 381.731i | −0.383959 | + | 0.665036i | ||||
\(575\) | 331.981i | 0.577359i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.1230 | −0.0678041 | −0.0339021 | − | 0.999425i | \(-0.510793\pi\) | ||||
−0.0339021 | + | 0.999425i | \(0.510793\pi\) | |||||||
\(578\) | −674.481 | − | 389.412i | −1.16692 | − | 0.673723i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 43.7077 | + | 75.7039i | 0.0753580 | + | 0.130524i | ||||
\(581\) | 164.266 | − | 94.8393i | 0.282731 | − | 0.163235i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −621.300 | + | 1076.12i | −1.06569 | + | 1.84584i | ||||
\(584\) | 202.483i | 0.346717i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 482.196 | 0.822860 | ||||||||
\(587\) | 363.061 | + | 209.614i | 0.618503 | + | 0.357093i | 0.776286 | − | 0.630381i | \(-0.217101\pi\) |
−0.157783 | + | 0.987474i | \(0.550435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4308 | − | 24.9948i | −0.0245005 | − | 0.0424361i | ||||
\(590\) | −173.198 | + | 99.9957i | −0.293555 | + | 0.169484i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −45.1384 | + | 78.1821i | −0.0762474 | + | 0.132064i | ||||
\(593\) | − | 329.210i | − | 0.555160i | −0.960703 | − | 0.277580i | \(-0.910468\pi\) | ||
0.960703 | − | 0.277580i | \(-0.0895323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −557.654 | −0.937233 | ||||||||
\(596\) | −53.0738 | − | 30.6422i | −0.0890500 | − | 0.0514131i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 112.277 | + | 194.469i | 0.187754 | + | 0.325199i | ||||
\(599\) | 159.556 | − | 92.1197i | 0.266371 | − | 0.153789i | −0.360867 | − | 0.932617i | \(-0.617519\pi\) |
0.627237 | + | 0.778828i | \(0.284186\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −109.208 | + | 189.153i | −0.181710 | + | 0.314731i | −0.942463 | − | 0.334311i | \(-0.891497\pi\) |
0.760753 | + | 0.649041i | \(0.224830\pi\) | |||||||
\(602\) | 931.945i | 1.54808i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −64.0000 | −0.105960 | ||||||||
\(605\) | −127.762 | − | 73.7634i | −0.211177 | − | 0.121923i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.13467 | − | 8.89350i | −0.00845909 | − | 0.0146516i | 0.861765 | − | 0.507308i | \(-0.169359\pi\) |
−0.870224 | + | 0.492656i | \(0.836026\pi\) | |||||||
\(608\) | −17.6740 | + | 10.2041i | −0.0290691 | + | 0.0167831i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.2750 | + | 24.7250i | −0.0234016 | + | 0.0405328i | ||||
\(611\) | 183.347i | 0.300078i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −180.585 | −0.294592 | −0.147296 | − | 0.989092i | \(-0.547057\pi\) | ||||
−0.147296 | + | 0.989092i | \(0.547057\pi\) | |||||||
\(614\) | −140.054 | − | 80.8604i | −0.228101 | − | 0.131694i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −257.569 | − | 446.123i | −0.418132 | − | 0.724226i | ||||
\(617\) | 784.800 | − | 453.104i | 1.27196 | − | 0.734367i | 0.296604 | − | 0.955000i | \(-0.404146\pi\) |
0.975357 | + | 0.220633i | \(0.0708124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −380.823 | + | 659.605i | −0.615223 | + | 1.06560i | 0.375122 | + | 0.926975i | \(0.377601\pi\) |
−0.990345 | + | 0.138622i | \(0.955733\pi\) | |||||||
\(620\) | 24.8466i | 0.0400752i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −277.492 | −0.446129 | ||||||||
\(623\) | 847.571 | + | 489.345i | 1.36047 | + | 0.785466i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −224.975 | − | 389.668i | −0.359960 | − | 0.623469i | ||||
\(626\) | 179.698 | − | 103.749i | 0.287058 | − | 0.165733i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 249.708 | − | 432.506i | 0.397624 | − | 0.688704i | ||||
\(629\) | − | 654.006i | − | 1.03975i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 601.108 | 0.952627 | 0.476313 | − | 0.879276i | \(-0.341973\pi\) | ||||
0.476313 | + | 0.879276i | \(0.341973\pi\) | |||||||
\(632\) | 114.504 | + | 66.1090i | 0.181177 | + | 0.104603i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −34.0404 | − | 58.9596i | −0.0536914 | − | 0.0929963i | ||||
\(635\) | −106.006 | + | 61.2027i | −0.166939 | + | 0.0963823i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 564.875 | − | 978.392i | 0.886774 | − | 1.53594i | ||||
\(638\) | − | 584.995i | − | 0.916920i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.5692 | 0.0274519 | ||||||||
\(641\) | −500.089 | − | 288.727i | −0.780170 | − | 0.450431i | 0.0563204 | − | 0.998413i | \(-0.482063\pi\) |
−0.836491 | + | 0.547981i | \(0.815396\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −65.0615 | − | 112.690i | −0.101184 | − | 0.175256i | 0.810989 | − | 0.585062i | \(-0.198930\pi\) |
−0.912173 | + | 0.409806i | \(0.865597\pi\) | |||||||
\(644\) | −315.457 | + | 182.129i | −0.489839 | + | 0.282809i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 73.9230 | − | 128.038i | 0.114432 | − | 0.198202i | ||||
\(647\) | 985.467i | 1.52313i | 0.648087 | + | 0.761567i | \(0.275570\pi\) | ||||
−0.648087 | + | 0.761567i | \(0.724430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1338.37 | 2.06220 | ||||||||
\(650\) | −298.889 | − | 172.564i | −0.459830 | − | 0.265483i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.7846 | − | 22.1436i | −0.0196083 | − | 0.0339626i | ||||
\(653\) | −519.895 | + | 300.161i | −0.796163 | + | 0.459665i | −0.842128 | − | 0.539278i | \(-0.818697\pi\) |
0.0459644 | + | 0.998943i | \(0.485364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 64.1192 | − | 111.058i | 0.0978919 | − | 0.169554i | ||||
\(656\) | 100.605i | 0.153361i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −297.415 | −0.451999 | ||||||||
\(659\) | 13.5004 | + | 7.79445i | 0.0204862 | + | 0.0118277i | 0.510208 | − | 0.860051i | \(-0.329568\pi\) |
−0.489722 | + | 0.871879i | \(0.662902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −203.915 | − | 353.192i | −0.308495 | − | 0.534329i | 0.669538 | − | 0.742778i | \(-0.266492\pi\) |
−0.978033 | + | 0.208448i | \(0.933159\pi\) | |||||||
\(662\) | 121.806 | − | 70.3245i | 0.183996 | − | 0.106230i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.6462 | − | 37.4923i | 0.0325997 | − | 0.0564643i | ||||
\(665\) | − | 69.4272i | − | 0.104402i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −413.654 | −0.620170 | ||||||||
\(668\) | 402.583 | + | 232.431i | 0.602669 | + | 0.347951i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −45.2154 | − | 78.3154i | −0.0674857 | − | 0.116889i | ||||
\(671\) | 165.463 | − | 95.5301i | 0.246592 | − | 0.142370i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 237.285 | − | 410.989i | 0.352577 | − | 0.610682i | −0.634123 | − | 0.773232i | \(-0.718639\pi\) |
0.986700 | + | 0.162550i | \(0.0519720\pi\) | |||||||
\(674\) | 601.410i | 0.892300i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 104.554 | 0.154665 | ||||||||
\(677\) | −244.346 | − | 141.073i | −0.360925 | − | 0.208380i | 0.308562 | − | 0.951204i | \(-0.400152\pi\) |
−0.669486 | + | 0.742824i | \(0.733486\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −564.708 | − | 978.102i | −0.831675 | − | 1.44050i | ||||
\(680\) | −110.227 | + | 63.6396i | −0.162099 | + | 0.0935877i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 83.1384 | − | 144.000i | 0.121904 | − | 0.211144i | ||||
\(683\) | 1085.46i | 1.58926i | 0.607095 | + | 0.794629i | \(0.292335\pi\) | ||||
−0.607095 | + | 0.794629i | \(0.707665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 333.473 | 0.486822 | ||||||||
\(686\) | 843.397 | + | 486.935i | 1.22944 | + | 0.709818i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 106.354 | + | 184.210i | 0.154584 | + | 0.267747i | ||||
\(689\) | −791.067 | + | 456.723i | −1.14814 | + | 0.662878i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 503.888 | − | 872.760i | 0.729216 | − | 1.26304i | −0.227999 | − | 0.973661i | \(-0.573218\pi\) |
0.957215 | − | 0.289378i | \(-0.0934484\pi\) | |||||||
\(692\) | − | 43.0954i | − | 0.0622765i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 54.8306 | 0.0790067 | ||||||||
\(695\) | −81.7470 | − | 47.1966i | −0.117622 | − | 0.0679088i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −364.413 | − | 631.183i | −0.522831 | − | 0.905570i | ||||
\(698\) | 798.496 | − | 461.012i | 1.14398 | − | 0.660475i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 279.923 | − | 484.841i | 0.399890 | − | 0.692630i | ||||
\(701\) | 216.731i | 0.309174i | 0.987979 | + | 0.154587i | \(0.0494047\pi\) | ||||
−0.987979 | + | 0.154587i | \(0.950595\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 81.4229 | 0.115822 | ||||||||
\(704\) | −101.823 | − | 58.7878i | −0.144635 | − | 0.0835053i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.846097 | − | 1.46548i | −0.00119844 | − | 0.00207575i | ||||
\(707\) | 949.639 | − | 548.274i | 1.34319 | − | 0.775494i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −497.248 | + | 861.259i | −0.701337 | + | 1.21475i | 0.266660 | + | 0.963791i | \(0.414080\pi\) |
−0.967997 | + | 0.250961i | \(0.919253\pi\) | |||||||
\(710\) | − | 35.9320i | − | 0.0506085i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 223.377 | 0.313732 | ||||||||
\(713\) | −101.823 | − | 58.7878i | −0.142810 | − | 0.0824513i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −123.289 | − | 213.542i | −0.172432 | − | 0.298660i | ||||
\(716\) | 481.061 | − | 277.741i | 0.671873 | − | 0.387906i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −378.000 | + | 654.715i | −0.526462 | + | 0.911860i | ||||
\(719\) | − | 340.912i | − | 0.474148i | −0.971492 | − | 0.237074i | \(-0.923812\pi\) | ||
0.971492 | − | 0.237074i | \(-0.0761884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1892.40 | −2.62469 | ||||||||
\(722\) | −426.192 | − | 246.062i | −0.590294 | − | 0.340806i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 174.277 | + | 301.856i | 0.240714 | + | 0.416929i | ||||
\(725\) | 550.589 | − | 317.883i | 0.759433 | − | 0.438459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 485.888 | − | 841.583i | 0.668347 | − | 1.15761i | −0.310019 | − | 0.950730i | \(-0.600335\pi\) |
0.978366 | − | 0.206881i | \(-0.0663312\pi\) | |||||||
\(728\) | − | 378.683i | − | 0.520169i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −157.219 | −0.215369 | ||||||||
\(731\) | −1334.50 | − | 770.474i | −1.82558 | − | 1.05400i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −114.585 | − | 198.466i | −0.156323 | − | 0.270759i | 0.777217 | − | 0.629233i | \(-0.216631\pi\) |
−0.933540 | + | 0.358473i | \(0.883297\pi\) | |||||||
\(734\) | −324.199 | + | 187.177i | −0.441688 | + | 0.255009i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −41.5692 | + | 72.0000i | −0.0564799 | + | 0.0978261i | ||||
\(737\) | 605.175i | 0.821132i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −629.892 | −0.852357 | −0.426179 | − | 0.904639i | \(-0.640141\pi\) | ||||
−0.426179 | + | 0.904639i | \(0.640141\pi\) | |||||||
\(740\) | −60.7050 | − | 35.0481i | −0.0820338 | − | 0.0473622i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −740.869 | − | 1283.22i | −0.998476 | − | 1.72941i | ||||
\(743\) | −162.825 | + | 94.0071i | −0.219145 | + | 0.126524i | −0.605554 | − | 0.795804i | \(-0.707049\pi\) |
0.386409 | + | 0.922327i | \(0.373715\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.7923 | − | 41.2095i | 0.0319360 | − | 0.0553148i | ||||
\(746\) | − | 100.431i | − | 0.134626i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 851.769 | 1.13873 | ||||||||
\(749\) | −643.989 | − | 371.807i | −0.859799 | − | 0.496405i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 693.335 | + | 1200.89i | 0.923215 | + | 1.59906i | 0.794407 | + | 0.607386i | \(0.207782\pi\) |
0.128808 | + | 0.991670i | \(0.458885\pi\) | |||||||
\(752\) | −58.7878 | + | 33.9411i | −0.0781752 | + | 0.0451345i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 215.017 | − | 372.421i | 0.285169 | − | 0.493927i | ||||
\(755\) | − | 49.6933i | − | 0.0658189i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1222.12 | 1.61443 | 0.807215 | − | 0.590258i | \(-0.200974\pi\) | ||||
0.807215 | + | 0.590258i | \(0.200974\pi\) | |||||||
\(758\) | −853.383 | − | 492.701i | −1.12584 | − | 0.650001i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.92305 | − | 13.7231i | −0.0104251 | − | 0.0180567i | ||||
\(761\) | −489.896 | + | 282.841i | −0.643752 | + | 0.371671i | −0.786059 | − | 0.618152i | \(-0.787882\pi\) |
0.142306 | + | 0.989823i | \(0.454548\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 582.081 | − | 1008.19i | 0.762884 | − | 1.32135i | ||||
\(764\) | − | 304.252i | − | 0.398235i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −615.615 | −0.803675 | ||||||||
\(767\) | 852.036 | + | 491.923i | 1.11087 | + | 0.641360i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 299.408 | + | 518.589i | 0.389347 | + | 0.674368i | 0.992362 | − | 0.123362i | \(-0.0393675\pi\) |
−0.603015 | + | 0.797730i | \(0.706034\pi\) | |||||||
\(770\) | 346.395 | − | 199.991i | 0.449864 | − | 0.259729i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −55.0000 | + | 95.2628i | −0.0712435 | + | 0.123397i | ||||
\(773\) | 446.970i | 0.578228i | 0.957295 | + | 0.289114i | \(0.0933607\pi\) | ||||
−0.957295 | + | 0.289114i | \(0.906639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 180.708 | 0.233171 | ||||||||
\(776\) | −223.243 | − | 128.889i | −0.287684 | − | 0.166094i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.5077 | − | 64.9653i | −0.0482105 | − | 0.0835030i | ||||
\(779\) | 78.5814 | − | 45.3690i | 0.100875 | − | 0.0582400i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −120.231 | + | 208.246i | −0.153945 | + | 0.266640i | ||||
\(782\) | − | 602.292i | − | 0.770194i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 418.277 | 0.533516 | ||||||||
\(785\) | 335.823 | + | 193.887i | 0.427800 | + | 0.246990i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 477.650 | + | 827.314i | 0.606925 | + | 1.05122i | 0.991744 | + | 0.128233i | \(0.0409305\pi\) |
−0.384819 | + | 0.922992i | \(0.625736\pi\) | |||||||
\(788\) | 230.878 | − | 133.298i | 0.292993 | − | 0.169160i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −51.3308 | + | 88.9076i | −0.0649757 | + | 0.112541i | ||||
\(791\) | − | 1097.93i | − | 1.38803i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 140.450 | 0.177112 | ||||||||
\(794\) | 78.0256 | + | 45.0481i | 0.0982691 | + | 0.0567357i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −208.862 | − | 361.759i | −0.262389 | − | 0.454471i | ||||
\(797\) | 192.141 | − | 110.933i | 0.241081 | − | 0.139188i | −0.374593 | − | 0.927189i | \(-0.622217\pi\) |
0.615673 | + | 0.788002i | \(0.288884\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 245.885 | − | 425.885i | 0.307740 | − | 0.533022i | ||||
\(800\) | − | 127.780i | − | 0.159725i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 889.104 | 1.10861 | ||||||||
\(803\) | 911.172 | + | 526.066i | 1.13471 | + | 0.655125i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −141.415 | − | 244.939i | −0.175671 | − | 0.304271i | ||||
\(806\) | 105.856 | − | 61.1158i | 0.131335 | − | 0.0758260i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 125.138 | − | 216.746i | 0.154874 | − | 0.268250i | ||||
\(809\) | 1180.17i | 1.45881i | 0.684084 | + | 0.729403i | \(0.260202\pi\) | ||||
−0.684084 | + | 0.729403i | \(0.739798\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −627.307 | −0.773499 | −0.386749 | − | 0.922185i | \(-0.626402\pi\) | ||||
−0.386749 | + | 0.922185i | \(0.626402\pi\) | |||||||
\(812\) | 604.119 | + | 348.788i | 0.743989 | + | 0.429542i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 234.546 | + | 406.246i | 0.288140 | + | 0.499074i | ||||
\(815\) | 17.1936 | − | 9.92670i | 0.0210964 | − | 0.0121800i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 95.9230 | − | 166.144i | 0.117409 | − | 0.203358i | ||||
\(818\) | − | 757.001i | − | 0.925429i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −78.1154 | −0.0952627 | ||||||||
\(821\) | −338.512 | − | 195.440i | −0.412317 | − | 0.238051i | 0.279468 | − | 0.960155i | \(-0.409842\pi\) |
−0.691785 | + | 0.722104i | \(0.743175\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −163.100 | − | 282.497i | −0.198177 | − | 0.343253i | 0.749760 | − | 0.661710i | \(-0.230169\pi\) |
−0.947937 | + | 0.318456i | \(0.896836\pi\) | |||||||
\(824\) | −374.056 | + | 215.961i | −0.453951 | + | 0.262089i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −797.969 | + | 1382.12i | −0.966064 | + | 1.67327i | ||||
\(827\) | − | 1103.70i | − | 1.33458i | −0.744799 | − | 0.667289i | \(-0.767455\pi\) | ||
0.744799 | − | 0.667289i | \(-0.232545\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −441.569 | −0.532653 | −0.266326 | − | 0.963883i | \(-0.585810\pi\) | ||||
−0.266326 | + | 0.963883i | \(0.585810\pi\) | |||||||
\(830\) | 29.1111 | + | 16.8073i | 0.0350737 | + | 0.0202498i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −43.2154 | − | 74.8513i | −0.0519416 | − | 0.0899654i | ||||
\(833\) | −2624.22 | + | 1515.09i | −3.15032 | + | 1.81884i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −180.473 | + | 312.588i | −0.216135 | + | 0.374357i | ||||
\(836\) | 106.044i | 0.126847i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −544.939 | −0.650285 | ||||||||
\(839\) | −436.443 | − | 251.980i | −0.520194 | − | 0.300334i | 0.216820 | − | 0.976212i | \(-0.430431\pi\) |
−0.737014 | + | 0.675878i | \(0.763765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.4134 | − | 42.2853i | −0.0290290 | − | 0.0502798i | ||||
\(842\) | 925.073 | − | 534.091i | 1.09866 | − | 0.634313i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −87.4538 | + | 151.474i | −0.103618 | + | 0.179472i | ||||
\(845\) | 81.1815i | 0.0960728i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1177.27 | −1.38993 | ||||||||
\(848\) | −292.884 | − | 169.096i | −0.345382 | − | 0.199406i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 462.846 | + | 801.673i | 0.544525 | + | 0.943145i | ||||
\(851\) | 287.259 | − | 165.849i | 0.337555 | − | 0.194887i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −472.415 | + | 818.247i | −0.553828 | + | 0.959258i | 0.444166 | + | 0.895945i | \(0.353500\pi\) |
−0.997994 | + | 0.0633136i | \(0.979833\pi\) | |||||||
\(854\) | 227.830i | 0.266780i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −169.723 | −0.198275 | ||||||||
\(857\) | −642.051 | − | 370.689i | −0.749185 | − | 0.432542i | 0.0762145 | − | 0.997091i | \(-0.475717\pi\) |
−0.825399 | + | 0.564549i | \(0.809050\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 680.631 | + | 1178.89i | 0.792352 | + | 1.37239i | 0.924507 | + | 0.381165i | \(0.124477\pi\) |
−0.132154 | + | 0.991229i | \(0.542189\pi\) | |||||||
\(860\) | −143.031 | + | 82.5792i | −0.166316 | + | 0.0960223i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −76.1615 | + | 131.916i | −0.0883544 | + | 0.153034i | ||||
\(863\) | 805.003i | 0.932796i | 0.884575 | + | 0.466398i | \(0.154449\pi\) | ||||
−0.884575 | + | 0.466398i | \(0.845551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.4617 | 0.0386841 | ||||||||
\(866\) | 802.359 | + | 463.242i | 0.926511 | + | 0.534921i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 99.1384 | + | 171.713i | 0.114215 | + | 0.197826i | ||||
\(869\) | 594.981 | − | 343.513i | 0.684673 | − | 0.395296i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −222.435 | + | 385.268i | −0.255378 | + | 0.442328i | ||||
\(872\) | − | 265.709i | − | 0.304712i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 74.9845 | 0.0857947 | ||||||||
\(875\) | 793.107 | + | 457.901i | 0.906408 | + | 0.523315i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.3461 | − | 36.9725i | −0.0243399 | − | 0.0421580i | 0.853599 | − | 0.520931i | \(-0.174415\pi\) |
−0.877939 | + | 0.478773i | \(0.841082\pi\) | |||||||
\(878\) | 578.080 | − | 333.754i | 0.658405 | − | 0.380130i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 45.6462 | − | 79.0615i | 0.0518706 | − | 0.0898426i | ||||
\(881\) | 264.567i | 0.300303i | 0.988663 | + | 0.150151i | \(0.0479761\pi\) | ||||
−0.988663 | + | 0.150151i | \(0.952024\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −393.338 | −0.445457 | −0.222728 | − | 0.974881i | \(-0.571496\pi\) | ||||
−0.222728 | + | 0.974881i | \(0.571496\pi\) | |||||||
\(884\) | 542.256 | + | 313.071i | 0.613411 | + | 0.354153i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −594.831 | − | 1030.28i | −0.671366 | − | 1.16284i | ||||
\(887\) | −1340.65 | + | 774.026i | −1.51145 | + | 0.872634i | −0.511535 | + | 0.859262i | \(0.670923\pi\) |
−0.999911 | + | 0.0133715i | \(0.995744\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −488.400 | + | 845.933i | −0.549381 | + | 0.951556i | ||||
\(890\) | 173.443i | 0.194879i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −445.184 | −0.499086 | ||||||||
\(893\) | 53.0221 | + | 30.6123i | 0.0593752 | + | 0.0342803i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 215.654 | + | 373.523i | 0.240954 | + | 0.417344i | ||||
\(896\) | 121.419 | − | 70.1015i | 0.135513 | − | 0.0782382i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −270.646 | + | 468.773i | −0.301388 | + | 0.522019i | ||||
\(899\) | 225.165i | 0.250461i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2450.02 | 2.71922 | ||||||||
\(902\) | 452.722 | + | 261.379i | 0.501909 | + | 0.289778i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −125.296 | − | 217.019i | −0.138602 | − | 0.240066i | ||||
\(905\) | −234.379 | + | 135.319i | −0.258982 | + | 0.149523i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −688.746 | + | 1192.94i | −0.759367 | + | 1.31526i | 0.183806 | + | 0.982962i | \(0.441158\pi\) |
−0.943174 | + | 0.332300i | \(0.892175\pi\) | |||||||
\(908\) | − | 600.627i | − | 0.661484i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 294.031 | 0.323111 | ||||||||
\(911\) | 1217.70 | + | 703.038i | 1.33666 | + | 0.771721i | 0.986311 | − | 0.164898i | \(-0.0527294\pi\) |
0.350350 | + | 0.936619i | \(0.386063\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −112.477 | − | 194.816i | −0.123195 | − | 0.213380i | ||||
\(914\) | −396.455 | + | 228.893i | −0.433758 | + | 0.250430i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 229.942 | − | 398.272i | 0.251029 | − | 0.434794i | ||||
\(917\) | − | 1023.35i | − | 1.11597i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 479.992 | 0.522299 | 0.261149 | − | 0.965298i | \(-0.415899\pi\) | ||||
0.261149 | + | 0.965298i | \(0.415899\pi\) | |||||||
\(920\) | −55.9049 | − | 32.2767i | −0.0607662 | − | 0.0350834i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 453.631 | + | 785.711i | 0.492007 | + | 0.852182i | ||||
\(923\) | −153.083 | + | 88.3827i | −0.165854 | + | 0.0957560i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −254.902 | + | 441.503i | −0.275570 | + | 0.477301i | ||||
\(926\) | − | 183.130i | − | 0.197764i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 159.215 | 0.171568 | ||||||||
\(929\) | 587.800 | + | 339.366i | 0.632723 | + | 0.365303i | 0.781806 | − | 0.623522i | \(-0.214299\pi\) |
−0.149083 | + | 0.988825i | \(0.547632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −188.627 | − | 326.711i | −0.202607 | − | 0.350925i | ||||
\(932\) | −201.343 | + | 116.246i | −0.216034 | + | 0.124727i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 475.692 | − | 823.923i | 0.509306 | − | 0.882145i | ||||
\(935\) | 661.362i | 0.707339i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −666.600 | −0.711420 | −0.355710 | − | 0.934596i | \(-0.615761\pi\) | ||||
−0.355710 | + | 0.934596i | \(0.615761\pi\) | |||||||
\(938\) | −624.959 | − | 360.820i | −0.666268 | − | 0.384670i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26.3538 | − | 45.6462i | −0.0280360 | − | 0.0485598i | ||||
\(941\) | −1037.46 | + | 598.978i | −1.10251 | + | 0.636533i | −0.936879 | − | 0.349655i | \(-0.886299\pi\) |
−0.165629 | + | 0.986188i | \(0.552966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 184.823 | − | 320.123i | 0.195995 | − | 0.339473i | ||||
\(944\) | 364.258i | 0.385866i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1105.26 | 1.16835 | ||||||||
\(947\) | 393.793 | + | 227.357i | 0.415832 | + | 0.240081i | 0.693293 | − | 0.720656i | \(-0.256159\pi\) |
−0.277460 | + | 0.960737i | \(0.589493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 386.715 | + | 669.811i | 0.407498 | + | 0.705807i | ||||
\(950\) | −99.8072 | + | 57.6237i | −0.105060 | + | 0.0606566i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −507.846 | + | 879.615i | −0.533452 | + | 0.923966i | ||||
\(953\) | − | 1060.16i | − | 1.11245i | −0.831033 | − | 0.556224i | \(-0.812250\pi\) | ||
0.831033 | − | 0.556224i | \(-0.187750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 236.238 | 0.247370 | ||||||||
\(956\) | −284.725 | − | 164.386i | −0.297829 | − | 0.171952i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 88.8231 | + | 153.846i | 0.0927172 | + | 0.160591i | ||||
\(959\) | 2304.60 | − | 1330.56i | 2.40313 | − | 1.38745i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 448.500 | − | 776.825i | 0.466701 | − | 0.808350i | ||||
\(962\) | 344.834i | 0.358455i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 162.623 | 0.168696 | ||||||||
\(965\) | −73.9675 | − | 42.7051i | −0.0766502 | − | 0.0442540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 827.657 | + | 1433.54i | 0.855902 | + | 1.48247i | 0.875805 | + | 0.482664i | \(0.160331\pi\) |
−0.0199032 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(968\) | −232.702 | + | 134.350i | −0.240394 | + | 0.138792i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 100.077 | − | 173.338i | 0.103172 | − | 0.178699i | ||||
\(971\) | 797.780i | 0.821606i | 0.911724 | + | 0.410803i | \(0.134752\pi\) | ||||
−0.911724 | + | 0.410803i | \(0.865248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −753.261 | −0.774164 | ||||||||
\(974\) | −549.458 | − | 317.230i | −0.564125 | − | 0.325698i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.0000 | + | 45.0333i | 0.0266393 | + | 0.0461407i | ||||
\(977\) | 270.574 | − | 156.216i | 0.276944 | − | 0.159894i | −0.355095 | − | 0.934830i | \(-0.615552\pi\) |
0.632039 | + | 0.774936i | \(0.282218\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 580.350 | − | 1005.20i | 0.592799 | − | 1.02676i | ||||
\(980\) | 324.774i | 0.331402i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −639.446 | −0.651167 | ||||||||
\(983\) | 320.553 | + | 185.072i | 0.326097 | + | 0.188272i | 0.654107 | − | 0.756402i | \(-0.273045\pi\) |
−0.328010 | + | 0.944674i | \(0.606378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 103.500 | + | 179.267i | 0.105076 | + | 0.181997i | ||||
\(986\) | −998.897 | + | 576.713i | −1.01308 | + | 0.584902i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.9770 | + | 67.5101i | −0.0394504 | + | 0.0683301i | ||||
\(989\) | − | 781.538i | − | 0.790230i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1324.48 | −1.33651 | −0.668256 | − | 0.743931i | \(-0.732959\pi\) | ||||
−0.668256 | + | 0.743931i | \(0.732959\pi\) | |||||||
\(992\) | 39.1918 | + | 22.6274i | 0.0395079 | + | 0.0228099i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −143.369 | − | 248.323i | −0.144235 | − | 0.249822i | ||||
\(995\) | 280.890 | − | 162.172i | 0.282302 | − | 0.162987i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −439.623 | + | 761.449i | −0.440946 | + | 0.763741i | −0.997760 | − | 0.0668966i | \(-0.978690\pi\) |
0.556814 | + | 0.830637i | \(0.312024\pi\) | |||||||
\(998\) | − | 179.028i | − | 0.179387i | ||||||
\(999\) | 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 | 162.3.d.c.107.3 | 8 | ||
3.2 | odd | 2 | inner | 162.3.d.c.107.2 | 8 | ||
4.3 | odd | 2 | 1296.3.q.o.593.2 | 8 | |||
9.2 | odd | 6 | 162.3.b.b.161.4 | yes | 4 | ||
9.4 | even | 3 | inner | 162.3.d.c.53.2 | 8 | ||
9.5 | odd | 6 | inner | 162.3.d.c.53.3 | 8 | ||
9.7 | even | 3 | 162.3.b.b.161.1 | ✓ | 4 | ||
12.11 | even | 2 | 1296.3.q.o.593.3 | 8 | |||
36.7 | odd | 6 | 1296.3.e.d.161.2 | 4 | |||
36.11 | even | 6 | 1296.3.e.d.161.3 | 4 | |||
36.23 | even | 6 | 1296.3.q.o.1025.2 | 8 | |||
36.31 | odd | 6 | 1296.3.q.o.1025.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.3.b.b.161.1 | ✓ | 4 | 9.7 | even | 3 | ||
162.3.b.b.161.4 | yes | 4 | 9.2 | odd | 6 | ||
162.3.d.c.53.2 | 8 | 9.4 | even | 3 | inner | ||
162.3.d.c.53.3 | 8 | 9.5 | odd | 6 | inner | ||
162.3.d.c.107.2 | 8 | 3.2 | odd | 2 | inner | ||
162.3.d.c.107.3 | 8 | 1.1 | even | 1 | trivial | ||
1296.3.e.d.161.2 | 4 | 36.7 | odd | 6 | |||
1296.3.e.d.161.3 | 4 | 36.11 | even | 6 | |||
1296.3.q.o.593.2 | 8 | 4.3 | odd | 2 | |||
1296.3.q.o.593.3 | 8 | 12.11 | even | 2 | |||
1296.3.q.o.1025.2 | 8 | 36.23 | even | 6 | |||
1296.3.q.o.1025.3 | 8 | 36.31 | odd | 6 |