Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(145,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.be (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: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 6.0.6967728.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Root | \(-1.13654 - 1.96854i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.145 |
Dual form | 912.3.be.d.673.3 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.27307 | + | 3.93708i | 0.454615 | + | 0.787416i | 0.998666 | − | 0.0516364i | \(-0.0164437\pi\) |
−0.544051 | + | 0.839052i | \(0.683110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.87987 | −1.41141 | −0.705705 | − | 0.708506i | \(-0.749369\pi\) | ||||
−0.705705 | + | 0.708506i | \(0.749369\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.6384 | 1.42168 | 0.710838 | − | 0.703356i | \(-0.248316\pi\) | ||||
0.710838 | + | 0.703356i | \(0.248316\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.3053 | + | 7.68182i | 1.02348 | + | 0.590909i | 0.915111 | − | 0.403201i | \(-0.132103\pi\) |
0.108373 | + | 0.994110i | \(0.465436\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.81922 | − | 3.93708i | −0.454615 | − | 0.262472i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.4260 | − | 21.5225i | −0.730942 | − | 1.26603i | −0.956481 | − | 0.291794i | \(-0.905748\pi\) |
0.225539 | − | 0.974234i | \(-0.427586\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.4260 | + | 4.63488i | 0.969790 | + | 0.243941i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.8198 | − | 8.55622i | 0.705705 | − | 0.407439i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.15294 | + | 7.19310i | −0.180563 | + | 0.312744i | −0.942072 | − | 0.335410i | \(-0.891125\pi\) |
0.761510 | + | 0.648154i | \(0.224458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.16628 | − | 3.75211i | 0.0866512 | − | 0.150084i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 27.3059 | + | 15.7651i | 0.941582 | + | 0.543623i | 0.890456 | − | 0.455070i | \(-0.150386\pi\) |
0.0511261 | + | 0.998692i | \(0.483719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 30.9353i | 0.997914i | 0.866627 | + | 0.498957i | \(0.166284\pi\) | ||||
−0.866627 | + | 0.498957i | \(0.833716\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −23.4577 | + | 13.5433i | −0.710838 | + | 0.410403i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −22.4577 | − | 38.8978i | −0.641647 | − | 1.11137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 17.3225i | 0.468176i | 0.972215 | + | 0.234088i | \(0.0752104\pi\) | ||||
−0.972215 | + | 0.234088i | \(0.924790\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −26.6106 | −0.682323 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −44.2502 | + | 25.5479i | −1.07927 | + | 0.623119i | −0.930700 | − | 0.365783i | \(-0.880801\pi\) |
−0.148573 | + | 0.988901i | \(0.547468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.773073 | + | 1.33900i | 0.0179784 | + | 0.0311396i | 0.874875 | − | 0.484349i | \(-0.160944\pi\) |
−0.856896 | + | 0.515489i | \(0.827610\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13.6384 | 0.303076 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.09113 | + | 8.81810i | −0.108322 | + | 0.187619i | −0.915091 | − | 0.403248i | \(-0.867881\pi\) |
0.806769 | + | 0.590867i | \(0.201214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.6118 | 0.992077 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 37.2780 | + | 21.5225i | 0.730942 | + | 0.422009i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.54002 | + | 2.62118i | 0.0856608 | + | 0.0494563i | 0.542219 | − | 0.840238i | \(-0.317584\pi\) |
−0.456558 | + | 0.889694i | \(0.650918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35.5473 | + | 61.5697i | 0.646315 | + | 1.11945i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −31.6529 | + | 9.00508i | −0.555315 | + | 0.157984i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −68.4321 | + | 39.5093i | −1.15987 | + | 0.669649i | −0.951272 | − | 0.308353i | \(-0.900222\pi\) |
−0.208595 | + | 0.978002i | \(0.566889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −53.9426 | + | 93.4313i | −0.884304 | + | 1.53166i | −0.0377957 | + | 0.999285i | \(0.512034\pi\) |
−0.846509 | + | 0.532375i | \(0.821300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.8198 | + | 25.6686i | −0.235235 | + | 0.407439i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 69.8453i | 1.07454i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.9843 | + | 9.80591i | 0.253498 | + | 0.146357i | 0.621365 | − | 0.783521i | \(-0.286579\pi\) |
−0.367867 | + | 0.929878i | \(0.619912\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 14.3862i | − | 0.208496i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 45.3604 | − | 26.1888i | 0.638879 | − | 0.368857i | −0.145304 | − | 0.989387i | \(-0.546416\pi\) |
0.784183 | + | 0.620530i | \(0.213083\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −36.6301 | − | 63.4451i | −0.501782 | − | 0.869111i | −0.999998 | − | 0.00205848i | \(-0.999345\pi\) |
0.498216 | − | 0.867053i | \(-0.333989\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.50421i | 0.100056i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −154.506 | −2.00657 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27.1512 | − | 15.6758i | 0.343686 | − | 0.198427i | −0.318215 | − | 0.948019i | \(-0.603083\pi\) |
0.661901 | + | 0.749591i | \(0.269750\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 42.6674 | 0.514066 | 0.257033 | − | 0.966403i | \(-0.417255\pi\) | ||||
0.257033 | + | 0.966403i | \(0.417255\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 56.4905 | − | 97.8443i | 0.664594 | − | 1.15111i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54.6118 | −0.627721 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 114.819 | + | 66.2909i | 1.29010 | + | 0.744842i | 0.978672 | − | 0.205427i | \(-0.0658583\pi\) |
0.311431 | + | 0.950269i | \(0.399192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −131.455 | − | 75.8953i | −1.44456 | − | 0.834015i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.7908 | − | 46.4030i | −0.288073 | − | 0.498957i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.6358 | + | 83.0801i | 0.248798 | + | 0.874527i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −70.2270 | + | 40.5456i | −0.723990 | + | 0.417996i | −0.816219 | − | 0.577742i | \(-0.803934\pi\) |
0.0922297 | + | 0.995738i | \(0.470601\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23.4577 | − | 40.6299i | 0.236946 | − | 0.410403i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −44.8242 | + | 77.6378i | −0.443804 | + | 0.768691i | −0.997968 | − | 0.0637166i | \(-0.979705\pi\) |
0.554164 | + | 0.832407i | \(0.313038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 59.2876i | − | 0.575608i | −0.957689 | − | 0.287804i | \(-0.907075\pi\) | ||
0.957689 | − | 0.287804i | \(-0.0929251\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 67.3730 | + | 38.8978i | 0.641647 | + | 0.370455i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 45.0373i | 0.420910i | 0.977604 | + | 0.210455i | \(0.0674945\pi\) | ||||
−0.977604 | + | 0.210455i | \(0.932505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.30356 | − | 2.48466i | 0.0394822 | − | 0.0227950i | −0.480129 | − | 0.877198i | \(-0.659410\pi\) |
0.519611 | + | 0.854403i | \(0.326077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0017 | − | 25.9838i | −0.135151 | − | 0.234088i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 124.048i | 1.09777i | 0.835898 | + | 0.548885i | \(0.184947\pi\) | ||||
−0.835898 | + | 0.548885i | \(0.815053\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −37.7597 | −0.328345 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 39.9159 | − | 23.0455i | 0.341161 | − | 0.196970i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 122.767 | + | 212.639i | 1.03166 | + | 1.78688i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 123.561 | 1.02116 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 44.2502 | − | 76.6436i | 0.359758 | − | 0.623119i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 133.350 | 1.06680 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −99.9211 | − | 57.6895i | −0.786780 | − | 0.454248i | 0.0520474 | − | 0.998645i | \(-0.483425\pi\) |
−0.838828 | + | 0.544397i | \(0.816759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.31922 | − | 1.33900i | −0.0179784 | − | 0.0103799i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 53.1834 | + | 92.1164i | 0.405980 | + | 0.703179i | 0.994435 | − | 0.105352i | \(-0.0335968\pi\) |
−0.588455 | + | 0.808530i | \(0.700263\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −182.047 | − | 45.7920i | −1.36877 | − | 0.344300i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −20.4577 | + | 11.8112i | −0.151538 | + | 0.0874906i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −58.9455 | + | 102.097i | −0.430259 | + | 0.745230i | −0.996895 | − | 0.0787376i | \(-0.974911\pi\) |
0.566636 | + | 0.823968i | \(0.308244\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −88.9275 | + | 154.027i | −0.639766 | + | 1.10811i | 0.345718 | + | 0.938339i | \(0.387635\pi\) |
−0.985484 | + | 0.169769i | \(0.945698\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 17.6362i | − | 0.125079i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 208.074 | + | 120.132i | 1.45506 | + | 0.840081i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 143.340i | 0.988555i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −72.9176 | + | 42.0990i | −0.496038 | + | 0.286388i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 89.8593 | + | 155.641i | 0.603083 | + | 1.04457i | 0.992351 | + | 0.123445i | \(0.0393944\pi\) |
−0.389269 | + | 0.921124i | \(0.627272\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 225.138i | 1.49098i | 0.666517 | + | 0.745490i | \(0.267785\pi\) | ||||
−0.666517 | + | 0.745490i | \(0.732215\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −74.5561 | −0.487295 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −121.795 | + | 70.3183i | −0.785773 | + | 0.453666i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.5101 | − | 23.4002i | −0.0860517 | − | 0.149046i | 0.819787 | − | 0.572668i | \(-0.194092\pi\) |
−0.905839 | + | 0.423622i | \(0.860758\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.08004 | −0.0571072 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 41.0305 | − | 71.0669i | 0.254848 | − | 0.441409i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 151.210 | 0.927667 | 0.463833 | − | 0.885922i | \(-0.346474\pi\) | ||||
0.463833 | + | 0.885922i | \(0.346474\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −106.642 | − | 61.5697i | −0.646315 | − | 0.373150i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −123.259 | − | 71.1638i | −0.738079 | − | 0.426130i | 0.0832911 | − | 0.996525i | \(-0.473457\pi\) |
−0.821371 | + | 0.570395i | \(0.806790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.5206 | + | 58.0594i | 0.198347 | + | 0.343547i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 39.6808 | − | 40.9199i | 0.232051 | − | 0.239297i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 205.442 | − | 118.612i | 1.18753 | − | 0.685620i | 0.229784 | − | 0.973242i | \(-0.426198\pi\) |
0.957744 | + | 0.287622i | \(0.0928646\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.4026 | + | 37.0703i | −0.122300 | + | 0.211830i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 68.4321 | − | 118.528i | 0.386622 | − | 0.669649i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.84122i | 0.0102862i | 0.999987 | + | 0.00514308i | \(0.00163710\pi\) | ||||
−0.999987 | + | 0.00514308i | \(0.998363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −30.9176 | − | 17.8503i | −0.170816 | − | 0.0986205i | 0.412155 | − | 0.911114i | \(-0.364776\pi\) |
−0.582970 | + | 0.812493i | \(0.698110\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 186.863i | − | 1.02111i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −68.2001 | + | 39.3753i | −0.368649 | + | 0.212840i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −194.323 | − | 336.578i | −1.03916 | − | 1.79988i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 51.3373i | − | 0.271626i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −166.346 | −0.870919 | −0.435460 | − | 0.900208i | \(-0.643414\pi\) | ||||
−0.435460 | + | 0.900208i | \(0.643414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 150.645 | − | 86.9747i | 0.780542 | − | 0.450646i | −0.0560803 | − | 0.998426i | \(-0.517860\pi\) |
0.836622 | + | 0.547780i | \(0.184527\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −60.4878 | − | 104.768i | −0.310194 | − | 0.537272i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −86.5637 | −0.439410 | −0.219705 | − | 0.975566i | \(-0.570509\pi\) | ||||
−0.219705 | + | 0.975566i | \(0.570509\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 125.922 | − | 218.103i | 0.632774 | − | 1.09600i | −0.354208 | − | 0.935167i | \(-0.615250\pi\) |
0.986982 | − | 0.160830i | \(-0.0514171\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.9687 | −0.168998 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −269.778 | − | 155.757i | −1.32896 | − | 0.767274i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −201.168 | − | 116.144i | −0.981306 | − | 0.566558i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.4588 | + | 21.5793i | 0.0601875 | + | 0.104248i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 288.154 | + | 72.4822i | 1.37873 | + | 0.346805i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 143.105 | − | 82.6215i | 0.678221 | − | 0.391571i | −0.120963 | − | 0.992657i | \(-0.538598\pi\) |
0.799184 | + | 0.601086i | \(0.205265\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −45.3604 | + | 78.5665i | −0.212960 | + | 0.368857i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.51450 | + | 6.08730i | −0.0163465 | + | 0.0283130i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 305.637i | − | 1.40847i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 109.890 | + | 63.4451i | 0.501782 | + | 0.289704i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 381.817i | − | 1.72768i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 178.604 | − | 103.117i | 0.800915 | − | 0.462408i | −0.0428761 | − | 0.999080i | \(-0.513652\pi\) |
0.843791 | + | 0.536672i | \(0.180319\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.49884 | − | 11.2563i | −0.0288837 | − | 0.0500281i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 329.381i | − | 1.45102i | −0.688213 | − | 0.725509i | \(-0.741605\pi\) | ||
0.688213 | − | 0.725509i | \(-0.258395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 109.771 | 0.479351 | 0.239676 | − | 0.970853i | \(-0.422959\pi\) | ||||
0.239676 | + | 0.970853i | \(0.422959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 231.759 | − | 133.806i | 1.00328 | − | 0.579246i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −107.428 | − | 186.071i | −0.461066 | − | 0.798589i | 0.537949 | − | 0.842978i | \(-0.319199\pi\) |
−0.999014 | + | 0.0443883i | \(0.985866\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −46.2900 | −0.196979 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −27.1512 | + | 47.0273i | −0.114562 | + | 0.198427i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 332.860 | 1.39272 | 0.696359 | − | 0.717694i | \(-0.254802\pi\) | ||||
0.696359 | + | 0.717694i | \(0.254802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −243.721 | − | 140.712i | −1.01129 | − | 0.583869i | −0.0997218 | − | 0.995015i | \(-0.531795\pi\) |
−0.911569 | + | 0.411146i | \(0.865129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 110.498 | + | 191.388i | 0.451013 | + | 0.781177i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 209.559 | + | 203.214i | 0.848418 | + | 0.822727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −64.0012 | + | 36.9511i | −0.257033 | + | 0.148398i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −203.986 | + | 353.314i | −0.812694 | + | 1.40763i | 0.0982779 | + | 0.995159i | \(0.468667\pi\) |
−0.910972 | + | 0.412468i | \(0.864667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −64.9455 | + | 112.489i | −0.256701 | + | 0.444620i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 195.689i | 0.767407i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 37.5180 | + | 21.6610i | 0.145984 | + | 0.0842841i | 0.571213 | − | 0.820802i | \(-0.306473\pi\) |
−0.425229 | + | 0.905086i | \(0.639806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 171.144i | − | 0.660788i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 81.9176 | − | 47.2952i | 0.313861 | − | 0.181208i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 242.738 | + | 420.434i | 0.922958 | + | 1.59861i | 0.794813 | + | 0.606855i | \(0.207569\pi\) |
0.128145 | + | 0.991755i | \(0.459098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.8326i | 0.0899342i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −229.638 | −0.860069 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 335.484 | − | 193.692i | 1.24715 | − | 0.720044i | 0.276612 | − | 0.960982i | \(-0.410788\pi\) |
0.970540 | + | 0.240938i | \(0.0774551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −173.258 | − | 300.091i | −0.639328 | − | 1.10735i | −0.985581 | − | 0.169207i | \(-0.945879\pi\) |
0.346253 | − | 0.938141i | \(-0.387454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 262.909 | 0.963037 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 33.8772 | − | 58.6771i | 0.123190 | − | 0.213371i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −115.366 | −0.416484 | −0.208242 | − | 0.978077i | \(-0.566774\pi\) | ||||
−0.208242 | + | 0.978077i | \(0.566774\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 80.3724 | + | 46.4030i | 0.288073 | + | 0.166319i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −377.987 | − | 218.231i | −1.34515 | − | 0.776622i | −0.357591 | − | 0.933878i | \(-0.616402\pi\) |
−0.987558 | + | 0.157257i | \(0.949735\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −217.321 | − | 376.411i | −0.767919 | − | 1.33007i | −0.938689 | − | 0.344764i | \(-0.887959\pi\) |
0.170770 | − | 0.985311i | \(-0.445374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −107.403 | − | 104.151i | −0.376853 | − | 0.365442i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 437.186 | − | 252.409i | 1.52330 | − | 0.879475i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −164.312 | + | 284.596i | −0.568552 | + | 0.984761i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 70.2270 | − | 121.637i | 0.241330 | − | 0.417996i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 297.624i | 1.01578i | 0.861421 | + | 0.507891i | \(0.169575\pi\) | ||||
−0.861421 | + | 0.507891i | \(0.830425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −311.102 | − | 179.615i | −1.05458 | − | 0.608865i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 81.2597i | 0.273602i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −110.512 | + | 63.8042i | −0.369606 | + | 0.213392i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.63786 | − | 13.2292i | −0.0253749 | − | 0.0439507i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 155.276i | − | 0.512460i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −490.462 | −1.60807 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −69.6945 | + | 40.2381i | −0.227018 | + | 0.131069i | −0.609196 | − | 0.793020i | \(-0.708508\pi\) |
0.382178 | + | 0.924089i | \(0.375174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51.3445 | + | 88.9314i | 0.166164 | + | 0.287804i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 120.522 | 0.387529 | 0.193765 | − | 0.981048i | \(-0.437930\pi\) | ||||
0.193765 | + | 0.981048i | \(0.437930\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 189.243 | − | 327.778i | 0.604610 | − | 1.04721i | −0.387503 | − | 0.921868i | \(-0.626662\pi\) |
0.992113 | − | 0.125346i | \(-0.0400042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −134.746 | −0.427765 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 197.232 | + | 113.872i | 0.622182 | + | 0.359217i | 0.777718 | − | 0.628613i | \(-0.216377\pi\) |
−0.155536 | + | 0.987830i | \(0.549710\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 427.021 | + | 246.541i | 1.33862 | + | 0.772855i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.0035 | − | 67.5560i | −0.121506 | − | 0.210455i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −129.208 | − | 454.167i | −0.400024 | − | 1.40609i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 57.6460 | − | 33.2819i | 0.177372 | − | 0.102406i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.30356 | + | 7.45398i | −0.0131607 | + | 0.0227950i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 50.2997 | − | 87.1216i | 0.152887 | − | 0.264807i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 398.204i | 1.20303i | 0.798861 | + | 0.601516i | \(0.205436\pi\) | ||||
−0.798861 | + | 0.601516i | \(0.794564\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 45.0052 | + | 25.9838i | 0.135151 | + | 0.0780294i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 89.1582i | 0.266144i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 556.961 | − | 321.561i | 1.65270 | − | 0.954188i | 0.676747 | − | 0.736216i | \(-0.263389\pi\) |
0.975955 | − | 0.217972i | \(-0.0699442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −107.429 | − | 186.072i | −0.316899 | − | 0.548885i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 483.780i | 1.41871i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.83580 | 0.0111831 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 56.6396 | − | 32.7009i | 0.164173 | − | 0.0947852i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 64.6475 | + | 111.973i | 0.186304 | + | 0.322688i | 0.944015 | − | 0.329902i | \(-0.107016\pi\) |
−0.757711 | + | 0.652590i | \(0.773682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4853 | −0.0300438 | −0.0150219 | − | 0.999887i | \(-0.504782\pi\) | ||||
−0.0150219 | + | 0.999887i | \(0.504782\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −39.9159 | + | 69.1364i | −0.113720 | + | 0.196970i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −388.861 | −1.10159 | −0.550794 | − | 0.834641i | \(-0.685675\pi\) | ||||
−0.550794 | + | 0.834641i | \(0.685675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 206.215 | + | 119.058i | 0.580887 | + | 0.335375i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −368.302 | − | 212.639i | −1.03166 | − | 0.595628i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 142.019 | + | 245.985i | 0.395597 | + | 0.685194i | 0.993177 | − | 0.116615i | \(-0.0372045\pi\) |
−0.597580 | + | 0.801809i | \(0.703871\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 318.036 | + | 170.805i | 0.880986 | + | 0.473143i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −185.341 | + | 107.007i | −0.510581 | + | 0.294784i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 166.526 | − | 288.431i | 0.456234 | − | 0.790221i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −81.5487 | + | 141.247i | −0.222204 | + | 0.384868i | −0.955477 | − | 0.295066i | \(-0.904658\pi\) |
0.733273 | + | 0.679934i | \(0.237992\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 153.287i | 0.415412i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −44.8548 | − | 25.8969i | −0.120902 | − | 0.0698031i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 329.361i | 0.883004i | 0.897260 | + | 0.441502i | \(0.145554\pi\) | ||||
−0.897260 | + | 0.441502i | \(0.854446\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −200.025 | + | 115.485i | −0.533400 | + | 0.307959i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 242.209 | + | 419.518i | 0.642463 | + | 1.11278i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 590.484i | − | 1.55801i | −0.627021 | − | 0.779003i | \(-0.715726\pi\) | ||
0.627021 | − | 0.779003i | \(-0.284274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 199.842 | 0.524520 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −417.346 | + | 240.955i | −1.08968 | + | 0.629125i | −0.933490 | − | 0.358602i | \(-0.883253\pi\) |
−0.156187 | + | 0.987728i | \(0.549920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −351.203 | − | 608.301i | −0.912215 | − | 1.58000i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.63844 | 0.0119856 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −86.5071 | + | 149.835i | −0.222383 | + | 0.385179i | −0.955531 | − | 0.294890i | \(-0.904717\pi\) |
0.733148 | + | 0.680069i | \(0.238050\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 206.418 | 0.527923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −159.550 | − | 92.1164i | −0.405980 | − | 0.234393i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 123.433 | + | 71.2642i | 0.312489 | + | 0.180416i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −80.0448 | − | 138.642i | −0.201624 | − | 0.349223i | 0.747428 | − | 0.664343i | \(-0.231289\pi\) |
−0.949052 | + | 0.315120i | \(0.897955\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 312.727 | − | 88.9690i | 0.783776 | − | 0.222980i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 83.3196 | − | 48.1046i | 0.207780 | − | 0.119962i | −0.392499 | − | 0.919752i | \(-0.628390\pi\) |
0.600279 | + | 0.799791i | \(0.295056\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −237.640 | + | 411.604i | −0.589677 | + | 1.02135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.4577 | − | 35.4337i | 0.0505127 | − | 0.0874906i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 270.897i | 0.665595i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −472.302 | − | 272.684i | −1.15477 | − | 0.666709i | −0.204728 | − | 0.978819i | \(-0.565631\pi\) |
−0.950046 | + | 0.312110i | \(0.898964\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 204.193i | − | 0.496820i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 676.100 | − | 390.347i | 1.63705 | − | 0.945149i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 96.9862 | + | 167.985i | 0.233702 | + | 0.404783i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 308.054i | − | 0.738738i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −81.4631 | −0.194423 | −0.0972114 | − | 0.995264i | \(-0.530992\pi\) | ||||
−0.0972114 | + | 0.995264i | \(0.530992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 326.092 | − | 188.269i | 0.774565 | − | 0.447196i | −0.0599354 | − | 0.998202i | \(-0.519089\pi\) |
0.834501 | + | 0.551007i | \(0.185756\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.2734 | + | 26.4543i | 0.0361073 | + | 0.0625397i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −107.673 | −0.253348 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 532.945 | − | 923.089i | 1.24812 | − | 2.16180i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −416.148 | −0.970042 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −504.983 | − | 291.552i | −1.17165 | − | 0.676454i | −0.217584 | − | 0.976042i | \(-0.569818\pi\) |
−0.954069 | + | 0.299587i | \(0.903151\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 552.877 | + | 319.204i | 1.27685 | + | 0.737191i | 0.976268 | − | 0.216564i | \(-0.0694849\pi\) |
0.300585 | + | 0.953755i | \(0.402818\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −124.137 | − | 215.011i | −0.285371 | − | 0.494278i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −109.861 | + | 113.292i | −0.251399 | + | 0.259249i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −267.855 | + | 154.646i | −0.610148 | + | 0.352269i | −0.773023 | − | 0.634378i | \(-0.781256\pi\) |
0.162875 | + | 0.986647i | \(0.447923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 72.9176 | − | 126.297i | 0.165346 | − | 0.286388i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 76.4634 | − | 132.438i | 0.172604 | − | 0.298958i | −0.766726 | − | 0.641975i | \(-0.778115\pi\) |
0.939329 | + | 0.343017i | \(0.111449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 602.736i | 1.35446i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −269.578 | − | 155.641i | −0.603083 | − | 0.348190i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 128.150i | 0.285413i | 0.989765 | + | 0.142706i | \(0.0455805\pi\) | ||||
−0.989765 | + | 0.142706i | \(0.954420\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −692.004 | + | 399.529i | −1.53438 | + | 0.885873i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −194.975 | − | 337.707i | −0.430409 | − | 0.745490i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 690.062i | − | 1.51662i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 338.690 | 0.741117 | 0.370558 | − | 0.928809i | \(-0.379166\pi\) | ||||
0.370558 | + | 0.928809i | \(0.379166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 111.834 | − | 64.5675i | 0.243647 | − | 0.140670i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 262.476 | + | 454.623i | 0.569363 | + | 0.986166i | 0.996629 | + | 0.0820401i | \(0.0261436\pi\) |
−0.427266 | + | 0.904126i | \(0.640523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −107.360 | −0.231879 | −0.115940 | − | 0.993256i | \(-0.536988\pi\) | ||||
−0.115940 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 121.795 | − | 210.955i | 0.261924 | − | 0.453666i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −60.2392 | −0.128992 | −0.0644959 | − | 0.997918i | \(-0.520544\pi\) | ||||
−0.0644959 | + | 0.997918i | \(0.520544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −167.803 | − | 96.8811i | −0.357789 | − | 0.206569i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.5304 | + | 23.4002i | 0.0860517 | + | 0.0496820i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0897 | + | 20.9399i | 0.0255595 | + | 0.0442704i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 57.3064 | − | 59.0959i | 0.120645 | − | 0.124412i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.6201 | − | 7.86355i | 0.0285536 | − | 0.0164854i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −38.8318 | + | 67.2586i | −0.0810684 | + | 0.140415i | −0.903709 | − | 0.428147i | \(-0.859167\pi\) |
0.822641 | + | 0.568562i | \(0.192500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −133.068 | + | 230.481i | −0.276650 | + | 0.479171i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 142.134i | 0.294273i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −319.262 | − | 184.326i | −0.658272 | − | 0.380054i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 248.267i | − | 0.509789i | −0.966969 | − | 0.254895i | \(-0.917959\pi\) | ||
0.966969 | − | 0.254895i | \(-0.0820408\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −226.815 | + | 130.951i | −0.463833 | + | 0.267794i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 176.358 | + | 305.461i | 0.359182 | + | 0.622121i | 0.987824 | − | 0.155573i | \(-0.0497225\pi\) |
−0.628643 | + | 0.777694i | \(0.716389\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 783.587i | − | 1.58943i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 213.284 | 0.430876 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −448.155 | + | 258.742i | −0.901720 | + | 0.520608i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −103.370 | − | 179.043i | −0.207155 | − | 0.358803i | 0.743662 | − | 0.668555i | \(-0.233087\pi\) |
−0.950817 | + | 0.309753i | \(0.899754\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 246.519 | 0.492053 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −292.748 | + | 507.055i | −0.582005 | + | 1.00806i | 0.413237 | + | 0.910624i | \(0.364398\pi\) |
−0.995242 | + | 0.0974382i | \(0.968935\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −407.555 | −0.807039 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −100.562 | − | 58.0594i | −0.198347 | − | 0.114516i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 436.147 | + | 251.810i | 0.856870 | + | 0.494714i | 0.862963 | − | 0.505267i | \(-0.168606\pi\) |
−0.00609272 | + | 0.999981i | \(0.501939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 361.900 | + | 626.829i | 0.708219 | + | 1.22667i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.0835 | + | 95.7444i | −0.0469464 | + | 0.186636i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 233.420 | − | 134.765i | 0.453242 | − | 0.261680i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −79.6173 | + | 137.901i | −0.153999 | + | 0.266734i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −205.442 | + | 355.837i | −0.395843 | + | 0.685620i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 622.860i | − | 1.19551i | −0.801679 | − | 0.597754i | \(-0.796060\pi\) | ||
0.801679 | − | 0.597754i | \(-0.203940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −197.688 | − | 114.136i | −0.377989 | − | 0.218232i | 0.298954 | − | 0.954268i | \(-0.403362\pi\) |
−0.676943 | + | 0.736035i | \(0.736696\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 74.1406i | − | 0.141220i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 665.805 | − | 384.403i | 1.26339 | − | 0.729417i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 230.006 | + | 398.382i | 0.434794 | + | 0.753086i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 237.056i | 0.446433i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −785.016 | −1.47283 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −177.316 | + | 102.373i | −0.331431 | + | 0.191352i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.59454 | − | 2.76183i | −0.00296936 | − | 0.00514308i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 760.212 | 1.41041 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 156.080 | − | 270.338i | 0.288502 | − | 0.499701i | −0.684950 | − | 0.728590i | \(-0.740176\pi\) |
0.973452 | + | 0.228889i | \(0.0735094\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 61.8353 | 0.113877 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.5646 | + | 11.2956i | 0.0358983 | + | 0.0207259i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 588.922 | + | 340.015i | 1.07664 | + | 0.621599i | 0.929988 | − | 0.367589i | \(-0.119817\pi\) |
0.146652 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 161.828 | + | 280.294i | 0.294768 | + | 0.510553i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 430.069 | + | 417.046i | 0.780525 | + | 0.756890i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −268.250 | + | 154.874i | −0.485082 | + | 0.280062i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 68.2001 | − | 118.126i | 0.122883 | − | 0.212840i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −452.880 | + | 784.411i | −0.813070 | + | 1.40828i | 0.0976363 | + | 0.995222i | \(0.468872\pi\) |
−0.910706 | + | 0.413056i | \(0.864462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.7544i | 0.0424945i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 582.970 | + | 336.578i | 1.03916 | + | 0.599961i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 190.842i | 0.338974i | 0.985532 | + | 0.169487i | \(0.0542110\pi\) | ||||
−0.985532 | + | 0.169487i | \(0.945789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −488.386 | + | 281.970i | −0.864401 | + | 0.499062i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 44.4594 | + | 77.0059i | 0.0784116 | + | 0.135813i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 283.587i | − | 0.498396i | −0.968453 | − | 0.249198i | \(-0.919833\pi\) | ||
0.968453 | − | 0.249198i | \(-0.0801669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 147.076 | 0.257576 | 0.128788 | − | 0.991672i | \(-0.458891\pi\) | ||||
0.128788 | + | 0.991672i | \(0.458891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 249.518 | − | 144.059i | 0.435460 | − | 0.251413i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.9929 | + | 31.1645i | 0.0312919 | + | 0.0541992i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 270.982 | 0.469639 | 0.234819 | − | 0.972039i | \(-0.424550\pi\) | ||||
0.234819 | + | 0.972039i | \(0.424550\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −150.645 | + | 260.924i | −0.260181 | + | 0.450646i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −421.549 | −0.725557 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 70.9988 | + | 40.9912i | 0.121782 | + | 0.0703108i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 181.463 | + | 104.768i | 0.310194 | + | 0.179091i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −83.4124 | − | 144.475i | −0.142100 | − | 0.246124i | 0.786188 | − | 0.617988i | \(-0.212052\pi\) |
−0.928287 | + | 0.371864i | \(0.878719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −143.382 | + | 570.015i | −0.243432 | + | 0.967767i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 129.846 | − | 74.9663i | 0.219705 | − | 0.126847i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −153.105 | + | 265.186i | −0.258188 | + | 0.447194i | −0.965756 | − | 0.259450i | \(-0.916459\pi\) |
0.707569 | + | 0.706644i | \(0.249792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −558.118 | + | 966.689i | −0.938014 | + | 1.62469i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 436.207i | 0.730664i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.3854 | + | 23.3165i | 0.0674213 | + | 0.0389257i | 0.533332 | − | 0.845906i | \(-0.320940\pi\) |
−0.465910 | + | 0.884832i | \(0.654273\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 47.7571i | − | 0.0794627i | −0.999210 | − | 0.0397314i | \(-0.987350\pi\) | ||
0.999210 | − | 0.0397314i | \(-0.0126502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 50.9530 | − | 29.4177i | 0.0844992 | − | 0.0487856i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 280.863 | + | 486.468i | 0.464236 | + | 0.804080i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 304.461i | 0.501583i | 0.968041 | + | 0.250792i | \(0.0806909\pi\) | ||||
−0.968041 | + | 0.250792i | \(0.919309\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 539.557 | 0.885972 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −135.478 | + | 78.2183i | −0.221732 | + | 0.128017i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −411.325 | − | 712.436i | −0.671004 | − | 1.16221i | −0.977620 | − | 0.210379i | \(-0.932530\pi\) |
0.306616 | − | 0.951833i | \(-0.400803\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 402.336 | 0.654204 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −279.527 | + | 484.154i | −0.453042 | + | 0.784691i | −0.998573 | − | 0.0533993i | \(-0.982994\pi\) |
0.545532 | + | 0.838090i | \(0.316328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −582.672 | −0.941311 | −0.470656 | − | 0.882317i | \(-0.655983\pi\) | ||||
−0.470656 | + | 0.882317i | \(0.655983\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −37.3765 | − | 21.5793i | −0.0601875 | − | 0.0347493i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1134.40 | − | 654.945i | −1.82086 | − | 1.05128i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 248.957 | + | 431.207i | 0.398332 | + | 0.689931i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −495.002 | + | 140.825i | −0.789478 | + | 0.224602i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 372.824 | − | 215.250i | 0.592724 | − | 0.342210i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 421.987 | − | 730.904i | 0.668760 | − | 1.15833i | −0.309492 | − | 0.950902i | \(-0.600159\pi\) |
0.978251 | − | 0.207424i | \(-0.0665078\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −143.105 | + | 247.864i | −0.226074 | + | 0.391571i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 524.530i | − | 0.826031i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 646.794 | + | 373.427i | 1.01538 | + | 0.586227i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 157.133i | − | 0.245905i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 386.782 | − | 223.309i | 0.603404 | − | 0.348375i | −0.166976 | − | 0.985961i | \(-0.553400\pi\) |
0.770380 | + | 0.637586i | \(0.220067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −502.768 | − | 870.820i | −0.781910 | − | 1.35431i | −0.930828 | − | 0.365458i | \(-0.880912\pi\) |
0.148918 | − | 0.988850i | \(-0.452421\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 12.1746i | − | 0.0188753i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 189.919 | 0.293538 | 0.146769 | − | 0.989171i | \(-0.453113\pi\) | ||||
0.146769 | + | 0.989171i | \(0.453113\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1070.17 | + | 617.864i | −1.64895 | + | 0.952024i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 264.689 | + | 458.456i | 0.406589 | + | 0.704233i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1018.29 | 1.55940 | 0.779700 | − | 0.626153i | \(-0.215371\pi\) | ||||
0.779700 | + | 0.626153i | \(0.215371\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −241.780 | + | 418.775i | −0.369129 | + | 0.639350i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −219.780 | −0.334521 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 979.725 | + | 565.644i | 1.48668 | + | 0.858338i | 0.999885 | − | 0.0151763i | \(-0.00483095\pi\) |
0.486799 | + | 0.873514i | \(0.338164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 105.628 | + | 60.9841i | 0.159800 | + | 0.0922604i | 0.577767 | − | 0.816202i | \(-0.303924\pi\) |
−0.417968 | + | 0.908462i | \(0.637257\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 330.664 | + | 572.726i | 0.498738 | + | 0.863840i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −233.519 | − | 820.820i | −0.351156 | − | 1.23432i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −226.799 | + | 130.943i | −0.340029 | + | 0.196316i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −178.604 | + | 309.351i | −0.266972 | + | 0.462408i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −843.578 | + | 1461.12i | −1.25719 | + | 2.17752i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 353.592i | − | 0.525397i | −0.964878 | − | 0.262699i | \(-0.915387\pi\) | ||
0.964878 | − | 0.262699i | \(-0.0846125\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.4965 | + | 11.2563i | 0.0288837 | + | 0.0166760i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 333.896i | − | 0.493199i | −0.969118 | − | 0.246599i | \(-0.920687\pi\) | ||
0.969118 | − | 0.246599i | \(-0.0793132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 693.833 | − | 400.585i | 1.02185 | − | 0.589963i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 285.252 | + | 494.071i | 0.418873 | + | 0.725509i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 160.520i | − | 0.235022i | −0.993072 | − | 0.117511i | \(-0.962509\pi\) | ||
0.993072 | − | 0.117511i | \(-0.0374915\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −535.949 | −0.782408 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −164.657 | + | 95.0649i | −0.239676 | + | 0.138377i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.2709 | + | 69.7512i | 0.0584483 | + | 0.101235i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 417.343 | 0.603969 | 0.301985 | − | 0.953313i | \(-0.402351\pi\) | ||||
0.301985 | + | 0.953313i | \(0.402351\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −231.759 | + | 401.417i | −0.334428 | + | 0.579246i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −808.555 | −1.16339 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1099.71 | + | 634.916i | 1.57777 | + | 0.910927i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 322.285 | + | 186.071i | 0.461066 | + | 0.266196i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −546.106 | − | 945.883i | −0.779039 | − | 1.34933i | −0.932496 | − | 0.361179i | \(-0.882374\pi\) |
0.153458 | − | 0.988155i | \(-0.450959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −80.2877 | + | 319.185i | −0.114207 | + | 0.454033i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 69.4351 | − | 40.0883i | 0.0984894 | − | 0.0568629i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 442.857 | − | 767.051i | 0.626389 | − | 1.08494i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 255.378 | − | 442.327i | 0.360194 | − | 0.623875i | −0.627798 | − | 0.778376i | \(-0.716044\pi\) |
0.987993 | + | 0.154501i | \(0.0493771\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 94.0545i | − | 0.132285i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −222.521 | − | 128.473i | −0.312091 | − | 0.180186i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1092.27i | 1.52765i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −499.289 | + | 288.265i | −0.696359 | + | 0.402043i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −143.484 | − | 248.522i | −0.199561 | − | 0.345649i | 0.748825 | − | 0.662767i | \(-0.230618\pi\) |
−0.948386 | + | 0.317118i | \(0.897285\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 585.753i | 0.812418i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 487.442 | 0.674194 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 118.304 | − | 68.3030i | 0.163178 | − | 0.0942111i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 358.442 | + | 620.840i | 0.493043 | + | 0.853975i | 0.999968 | − | 0.00801511i | \(-0.00255132\pi\) |
−0.506925 | + | 0.861990i | \(0.669218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.2124 | − | 33.2769i | 0.0262824 | − | 0.0455224i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −534.712 | −0.729484 | −0.364742 | − | 0.931109i | \(-0.618843\pi\) | ||||
−0.364742 | + | 0.931109i | \(0.618843\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −331.494 | − | 191.388i | −0.451013 | − | 0.260392i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 265.608 | + | 153.349i | 0.360391 | + | 0.208072i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −337.022 | − | 583.739i | −0.456051 | − | 0.789904i | 0.542697 | − | 0.839929i | \(-0.317403\pi\) |
−0.998748 | + | 0.0500248i | \(0.984070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −490.327 | − | 123.337i | −0.661710 | − | 0.166446i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 794.193 | − | 458.527i | 1.06890 | − | 0.617130i | 0.141019 | − | 0.990007i | \(-0.454962\pi\) |
0.927881 | + | 0.372877i | \(0.121629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −408.514 | + | 707.566i | −0.548340 | + | 0.949753i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 64.0012 | − | 110.853i | 0.0856776 | − | 0.148398i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 444.963i | − | 0.594076i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 387.655 | + | 223.813i | 0.516185 | + | 0.298019i | 0.735372 | − | 0.677663i | \(-0.237007\pi\) |
−0.219188 | + | 0.975683i | \(0.570341\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 706.629i | − | 0.938418i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −886.386 | + | 511.755i | −1.17402 | + | 0.677821i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −118.319 | − | 204.934i | −0.156299 | − | 0.270718i | 0.777232 | − | 0.629214i | \(-0.216623\pi\) |
−0.933531 | + | 0.358496i | \(0.883290\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 224.978i | − | 0.296413i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −213.593 | −0.280674 | −0.140337 | − | 0.990104i | \(-0.544819\pi\) | ||||
−0.140337 | + | 0.990104i | \(0.544819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42.5186 | + | 24.5481i | −0.0557255 | + | 0.0321731i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −169.471 | − | 293.533i | −0.221531 | − | 0.383703i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1214.01 | −1.58281 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 442.292 | − | 766.072i | 0.575152 | − | 0.996192i | −0.420873 | − | 0.907119i | \(-0.638276\pi\) |
0.996025 | − | 0.0890727i | \(-0.0283903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −75.0360 | −0.0973229 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1110.22 | + | 640.988i | 1.43625 | + | 0.829222i | 0.997587 | − | 0.0694281i | \(-0.0221174\pi\) |
0.438667 | + | 0.898650i | \(0.355451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 116.073 | + | 67.0146i | 0.149771 | + | 0.0864705i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 148.215 | + | 256.716i | 0.190753 | + | 0.330394i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −933.766 | + | 265.651i | −1.19867 | + | 0.341015i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 709.366 | − | 409.553i | 0.908279 | − | 0.524395i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −81.9176 | + | 141.886i | −0.104620 | + | 0.181208i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 61.4190 | − | 106.381i | 0.0782407 | − | 0.135517i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 282.196i | 0.358572i | 0.983797 | + | 0.179286i | \(0.0573787\pi\) | ||||
−0.983797 | + | 0.179286i | \(0.942621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −728.214 | − | 420.434i | −0.922958 | − | 0.532870i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1225.58i | − | 1.54940i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1435.44 | + | 828.754i | −1.81014 | + | 1.04509i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.6396 | − | 35.7488i | −0.0259618 | − | 0.0449671i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1021.78i | − | 1.28203i | −0.767527 | − | 0.641016i | \(-0.778513\pi\) | ||
0.767527 | − | 0.641016i | \(-0.221487\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 253.050 | 0.316708 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 344.458 | − | 198.873i | 0.430035 | − | 0.248281i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −572.837 | − | 992.183i | −0.713371 | − | 1.23559i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 373.061 | 0.463430 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −335.484 | + | 581.075i | −0.415717 | + | 0.720044i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.57043 | −0.00812167 | −0.00406083 | − | 0.999992i | \(-0.501293\pi\) | ||||
−0.00406083 | + | 0.999992i | \(0.501293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −127.276 | − | 73.4831i | −0.156938 | − | 0.0906080i | 0.419474 | − | 0.907767i | \(-0.362214\pi\) |
−0.576412 | + | 0.817159i | \(0.695548\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 519.773 | + | 300.091i | 0.639328 | + | 0.369116i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 343.711 | + | 595.324i | 0.421731 | + | 0.730459i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.03854 | + | 28.2556i | 0.00983910 | + | 0.0345845i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −394.364 | + | 227.686i | −0.481519 | + | 0.278005i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −120.857 | + | 209.330i | −0.147206 | + | 0.254969i | −0.930194 | − | 0.367068i | \(-0.880362\pi\) |
0.782987 | + | 0.622037i | \(0.213695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 148.726 | − | 257.601i | 0.180712 | − | 0.313003i | −0.761411 | − | 0.648269i | \(-0.775493\pi\) |
0.942123 | + | 0.335267i | \(0.108826\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 117.354i | 0.142247i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 587.474 | + | 339.179i | 0.710368 | + | 0.410131i | 0.811197 | − | 0.584773i | \(-0.198816\pi\) |
−0.100829 | + | 0.994904i | \(0.532150\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 924.892i | 1.11567i | 0.829951 | + | 0.557836i | \(0.188368\pi\) | ||||
−0.829951 | + | 0.557836i | \(0.811632\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 173.049 | − | 99.9099i | 0.208242 | − | 0.120229i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −604.050 | − | 1046.25i | −0.725150 | − | 1.25600i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 647.042i | − | 0.774900i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −160.745 | −0.192049 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −294.467 | + | 170.011i | −0.350974 | + | 0.202635i | −0.665114 | − | 0.746742i | \(-0.731617\pi\) |
0.314140 | + | 0.949377i | \(0.398284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 76.5740 | + | 132.630i | 0.0910511 | + | 0.157705i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 755.973 | 0.896766 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −152.390 | + | 263.947i | −0.180343 | + | 0.312363i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1220.76 | −1.44128 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 651.963 | + | 376.411i | 0.767919 | + | 0.443358i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −124.603 | − | 71.9394i | −0.146419 | − | 0.0845351i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −436.122 | − | 755.386i | −0.511280 | − | 0.885564i | −0.999915 | − | 0.0130749i | \(-0.995838\pi\) |
0.488634 | − | 0.872489i | \(-0.337495\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 251.302 | + | 63.2125i | 0.293920 | + | 0.0739327i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −429.491 | + | 247.967i | −0.501156 | + | 0.289343i | −0.729191 | − | 0.684310i | \(-0.760103\pi\) |
0.228035 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −707.860 | + | 1226.05i | −0.824051 | + | 1.42730i | 0.0785919 | + | 0.996907i | \(0.474958\pi\) |
−0.902643 | + | 0.430391i | \(0.858376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −437.186 | + | 757.228i | −0.507765 | + | 0.879475i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1132.56i | − | 1.31236i | −0.754605 | − | 0.656179i | \(-0.772172\pi\) | ||
0.754605 | − | 0.656179i | \(-0.227828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 933.971 | + | 539.228i | 1.07974 | + | 0.623385i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 569.192i | − | 0.656507i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 424.602 | − | 245.144i | 0.488610 | − | 0.282099i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 150.654 | + | 260.941i | 0.172967 | + | 0.299588i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 243.273i | 0.278664i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1317.48 | −1.50569 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −879.491 | + | 507.775i | −1.00284 | + | 0.578990i | −0.909088 | − | 0.416605i | \(-0.863220\pi\) |
−0.0937531 | + | 0.995595i | \(0.529886\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −257.750 | − | 446.436i | −0.293231 | − | 0.507891i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 356.912 | 0.405121 | 0.202561 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202561 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −466.592 | + | 808.161i | −0.528416 | + | 0.915244i | 0.471035 | + | 0.882115i | \(0.343881\pi\) |
−0.999451 | + | 0.0331294i | \(0.989453\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 622.205 | 0.703056 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 610.275 | + | 352.343i | 0.688022 | + | 0.397229i | 0.802870 | − | 0.596154i | \(-0.203305\pi\) |
−0.114849 | + | 0.993383i | \(0.536638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 987.207 | + | 569.964i | 1.11047 | + | 0.641130i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −70.3730 | − | 121.890i | −0.0789820 | − | 0.136801i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −134.680 | + | 138.886i | −0.150817 | + | 0.155527i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.24903 | + | 4.18523i | −0.00809948 | + | 0.00467624i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 110.512 | − | 191.413i | 0.123202 | − | 0.213392i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −487.697 | + | 844.717i | −0.542489 | + | 0.939618i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 130.283i | − | 0.144599i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.9136 | + | 13.2292i | 0.0253749 | + | 0.0146502i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 162.300i | − | 0.179337i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1101.29 | − | 635.829i | 1.21421 | − | 0.701024i | 0.250535 | − | 0.968107i | \(-0.419393\pi\) |
0.963673 | + | 0.267084i | \(0.0860600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 134.473 | + | 232.913i | 0.147935 | + | 0.256230i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 340.787i | 0.374080i | 0.982352 | + | 0.187040i | \(0.0598894\pi\) | ||||
−0.982352 | + | 0.187040i | \(0.940111\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 667.252 | 0.730835 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 735.692 | − | 424.752i | 0.804035 | − | 0.464210i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −525.445 | − | 910.098i | −0.573004 | − | 0.992473i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −204.788 | −0.222837 | −0.111419 | − | 0.993774i | \(-0.535539\pi\) | ||||
−0.111419 | + | 0.993774i | \(0.535539\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 69.6945 | − | 120.714i | 0.0756726 | − | 0.131069i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 804.712 | 0.871843 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 64.9959 | + | 37.5254i | 0.0702659 | + | 0.0405680i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −154.034 | − | 88.9314i | −0.166164 | − | 0.0959346i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −807.733 | − | 1399.03i | −0.869465 | − | 1.50596i | −0.862545 | − | 0.505981i | \(-0.831131\pi\) |
−0.00692012 | − | 0.999976i | \(-0.502203\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 895.721 | + | 225.310i | 0.962106 | + | 0.242008i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −180.782 | + | 104.375i | −0.193765 | + | 0.111870i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 883.423 | − | 1530.13i | 0.944837 | − | 1.63651i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −269.027 | + | 465.968i | −0.287115 | + | 0.497298i | −0.973120 | − | 0.230299i | \(-0.926030\pi\) |
0.686005 | + | 0.727597i | \(0.259363\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 655.556i | 0.698143i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 389.138 | + | 224.669i | 0.413537 | + | 0.238756i | 0.692308 | − | 0.721602i | \(-0.256594\pi\) |
−0.278771 | + | 0.960358i | \(0.589927\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 424.395i | − | 0.450048i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 202.119 | − | 116.693i | 0.213882 | − | 0.123485i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 767.818 | + | 1329.90i | 0.810789 | + | 1.40433i | 0.912312 | + | 0.409495i | \(0.134295\pi\) |
−0.101523 | + | 0.994833i | \(0.532371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1125.54i | − | 1.18603i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −394.464 | −0.414788 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1343.91 | + | 775.904i | −1.41018 | + | 0.814170i | −0.995405 | − | 0.0957525i | \(-0.969474\pi\) |
−0.414779 | + | 0.909922i | \(0.636141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −378.116 | − | 654.915i | −0.395933 | − | 0.685775i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −854.043 | −0.892416 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 582.373 | − | 1008.70i | 0.607272 | − | 1.05183i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.00437 | 0.00416687 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 117.010 | + | 67.5560i | 0.121506 | + | 0.0701516i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 684.852 | + | 395.400i | 0.709692 | + | 0.409741i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −379.617 | − | 657.515i | −0.392571 | − | 0.679954i | 0.600217 | − | 0.799838i | \(-0.295081\pi\) |
−0.992788 | + | 0.119884i | \(0.961748\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 587.131 | + | 569.353i | 0.605915 | + | 0.587567i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −691.147 | + | 399.034i | −0.711788 | + | 0.410951i | −0.811723 | − | 0.584043i | \(-0.801470\pi\) |
0.0999344 | + | 0.994994i | \(0.468137\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 878.592 | − | 1521.77i | 0.902972 | − | 1.56399i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −57.6460 | + | 99.8458i | −0.0591241 | + | 0.102406i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1031.50i | − | 1.05578i | −0.849313 | − | 0.527889i | \(-0.822984\pi\) | ||
0.849313 | − | 0.527889i | \(-0.177016\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1795.59 | + | 1036.69i | 1.83411 | + | 1.05892i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.9080i | − | 0.0151967i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 630.248 | − | 363.874i | 0.641148 | − | 0.370167i | −0.143909 | − | 0.989591i | \(-0.545967\pi\) |
0.785056 | + | 0.619424i | \(0.212634\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −196.766 | − | 340.808i | −0.199762 | − | 0.345998i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 174.243i | 0.176538i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.8421 | −0.0129849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 122.900 | − | 70.9565i | 0.124016 | − | 0.0716009i | −0.436708 | − | 0.899603i | \(-0.643856\pi\) |
0.560725 | + | 0.828002i | \(0.310523\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −344.854 | − | 597.305i | −0.347285 | − | 0.601516i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1144.92 | 1.15067 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −908.384 | + | 1573.37i | −0.911118 | + | 1.57810i | −0.0986299 | + | 0.995124i | \(0.531446\pi\) |
−0.812488 | + | 0.582978i | \(0.801887\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −90.0105 | −0.0901006 |
(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 | 912.3.be.d.145.3 | 6 | ||
4.3 | odd | 2 | 57.3.g.a.31.2 | ✓ | 6 | ||
12.11 | even | 2 | 171.3.p.e.145.2 | 6 | |||
19.8 | odd | 6 | inner | 912.3.be.d.673.3 | 6 | ||
76.27 | even | 6 | 57.3.g.a.46.2 | yes | 6 | ||
228.179 | odd | 6 | 171.3.p.e.46.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.g.a.31.2 | ✓ | 6 | 4.3 | odd | 2 | ||
57.3.g.a.46.2 | yes | 6 | 76.27 | even | 6 | ||
171.3.p.e.46.2 | 6 | 228.179 | odd | 6 | |||
171.3.p.e.145.2 | 6 | 12.11 | even | 2 | |||
912.3.be.d.145.3 | 6 | 1.1 | even | 1 | trivial | ||
912.3.be.d.673.3 | 6 | 19.8 | odd | 6 | inner |