Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(229,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.1 | ||
Character | \(\chi\) | \(=\) | 230.229 |
Dual form | 230.3.c.a.229.23 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | − | 5.45221i | − | 1.81740i | −0.417446 | − | 0.908702i | \(-0.637075\pi\) | ||
0.417446 | − | 0.908702i | \(-0.362925\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −3.90521 | + | 3.12239i | −0.781042 | + | 0.624479i | ||||
\(6\) | −7.71059 | −1.28510 | ||||||||
\(7\) | 0.770899 | 0.110128 | 0.0550642 | − | 0.998483i | \(-0.482464\pi\) | ||||
0.0550642 | + | 0.998483i | \(0.482464\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −20.7266 | −2.30296 | ||||||||
\(10\) | 4.41573 | + | 5.52280i | 0.441573 | + | 0.552280i | ||||
\(11\) | 8.45857i | 0.768961i | 0.923133 | + | 0.384481i | \(0.125619\pi\) | ||||
−0.923133 | + | 0.384481i | \(0.874381\pi\) | |||||||
\(12\) | 10.9044i | 0.908702i | ||||||||
\(13\) | − | 4.15908i | − | 0.319929i | −0.987123 | − | 0.159964i | \(-0.948862\pi\) | ||
0.987123 | − | 0.159964i | \(-0.0511380\pi\) | |||||||
\(14\) | − | 1.09022i | − | 0.0778725i | ||||||
\(15\) | 17.0239 | + | 21.2920i | 1.13493 | + | 1.41947i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −32.2680 | −1.89812 | −0.949059 | − | 0.315097i | \(-0.897963\pi\) | ||||
−0.949059 | + | 0.315097i | \(0.897963\pi\) | |||||||
\(18\) | 29.3118i | 1.62844i | ||||||||
\(19\) | − | 23.8163i | − | 1.25349i | −0.779224 | − | 0.626745i | \(-0.784387\pi\) | ||
0.779224 | − | 0.626745i | \(-0.215613\pi\) | |||||||
\(20\) | 7.81042 | − | 6.24479i | 0.390521 | − | 0.312239i | ||||
\(21\) | − | 4.20310i | − | 0.200148i | ||||||
\(22\) | 11.9622 | 0.543738 | ||||||||
\(23\) | 19.8603 | + | 11.6004i | 0.863489 | + | 0.504367i | ||||
\(24\) | 15.4212 | 0.642549 | ||||||||
\(25\) | 5.50131 | − | 24.3872i | 0.220052 | − | 0.975488i | ||||
\(26\) | −5.88182 | −0.226224 | ||||||||
\(27\) | 63.9359i | 2.36800i | ||||||||
\(28\) | −1.54180 | −0.0550642 | ||||||||
\(29\) | 21.7473 | 0.749907 | 0.374953 | − | 0.927044i | \(-0.377659\pi\) | ||||
0.374953 | + | 0.927044i | \(0.377659\pi\) | |||||||
\(30\) | 30.1115 | − | 24.0755i | 1.00372 | − | 0.802517i | ||||
\(31\) | −31.8764 | −1.02827 | −0.514136 | − | 0.857709i | \(-0.671887\pi\) | ||||
−0.514136 | + | 0.857709i | \(0.671887\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 46.1179 | 1.39751 | ||||||||
\(34\) | 45.6339i | 1.34217i | ||||||||
\(35\) | −3.01052 | + | 2.40705i | −0.0860149 | + | 0.0687729i | ||||
\(36\) | 41.4532 | 1.15148 | ||||||||
\(37\) | −6.03947 | −0.163229 | −0.0816145 | − | 0.996664i | \(-0.526008\pi\) | ||||
−0.0816145 | + | 0.996664i | \(0.526008\pi\) | |||||||
\(38\) | −33.6814 | −0.886352 | ||||||||
\(39\) | −22.6762 | −0.581440 | ||||||||
\(40\) | −8.83146 | − | 11.0456i | −0.220787 | − | 0.276140i | ||||
\(41\) | 16.9449 | 0.413289 | 0.206645 | − | 0.978416i | \(-0.433746\pi\) | ||||
0.206645 | + | 0.978416i | \(0.433746\pi\) | |||||||
\(42\) | −5.94408 | −0.141526 | ||||||||
\(43\) | −61.7107 | −1.43513 | −0.717566 | − | 0.696491i | \(-0.754744\pi\) | ||||
−0.717566 | + | 0.696491i | \(0.754744\pi\) | |||||||
\(44\) | − | 16.9171i | − | 0.384481i | ||||||
\(45\) | 80.9417 | − | 64.7166i | 1.79870 | − | 1.43815i | ||||
\(46\) | 16.4055 | − | 28.0866i | 0.356641 | − | 0.610579i | ||||
\(47\) | − | 45.0037i | − | 0.957525i | −0.877945 | − | 0.478762i | \(-0.841086\pi\) | ||
0.877945 | − | 0.478762i | \(-0.158914\pi\) | |||||||
\(48\) | − | 21.8088i | − | 0.454351i | ||||||
\(49\) | −48.4057 | −0.987872 | ||||||||
\(50\) | −34.4887 | − | 7.78003i | −0.689774 | − | 0.155601i | ||||
\(51\) | 175.932i | 3.44965i | ||||||||
\(52\) | 8.31815i | 0.159964i | ||||||||
\(53\) | −45.8817 | −0.865692 | −0.432846 | − | 0.901468i | \(-0.642491\pi\) | ||||
−0.432846 | + | 0.901468i | \(0.642491\pi\) | |||||||
\(54\) | 90.4190 | 1.67443 | ||||||||
\(55\) | −26.4110 | − | 33.0325i | −0.480200 | − | 0.600591i | ||||
\(56\) | 2.18043i | 0.0389363i | ||||||||
\(57\) | −129.852 | −2.27810 | ||||||||
\(58\) | − | 30.7553i | − | 0.530264i | ||||||
\(59\) | −93.6903 | −1.58797 | −0.793986 | − | 0.607937i | \(-0.791997\pi\) | ||||
−0.793986 | + | 0.607937i | \(0.791997\pi\) | |||||||
\(60\) | −34.0479 | − | 42.5840i | −0.567465 | − | 0.709734i | ||||
\(61\) | 37.1088i | 0.608341i | 0.952618 | + | 0.304170i | \(0.0983792\pi\) | ||||
−0.952618 | + | 0.304170i | \(0.901621\pi\) | |||||||
\(62\) | 45.0801i | 0.727099i | ||||||||
\(63\) | −15.9781 | −0.253621 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 12.9863 | + | 16.2421i | 0.199789 | + | 0.249878i | ||||
\(66\) | − | 65.2206i | − | 0.988191i | ||||||
\(67\) | 44.2092 | 0.659838 | 0.329919 | − | 0.944009i | \(-0.392978\pi\) | ||||
0.329919 | + | 0.944009i | \(0.392978\pi\) | |||||||
\(68\) | 64.5360 | 0.949059 | ||||||||
\(69\) | 63.2481 | − | 108.282i | 0.916639 | − | 1.56931i | ||||
\(70\) | 3.40408 | + | 4.25752i | 0.0486298 | + | 0.0608217i | ||||
\(71\) | 77.7931 | 1.09568 | 0.547839 | − | 0.836584i | \(-0.315451\pi\) | ||||
0.547839 | + | 0.836584i | \(0.315451\pi\) | |||||||
\(72\) | − | 58.6237i | − | 0.814218i | ||||||
\(73\) | − | 101.411i | − | 1.38919i | −0.719401 | − | 0.694595i | \(-0.755584\pi\) | ||
0.719401 | − | 0.694595i | \(-0.244416\pi\) | |||||||
\(74\) | 8.54110i | 0.115420i | ||||||||
\(75\) | −132.964 | − | 29.9943i | −1.77286 | − | 0.399924i | ||||
\(76\) | 47.6326i | 0.626745i | ||||||||
\(77\) | 6.52070i | 0.0846845i | ||||||||
\(78\) | 32.0689i | 0.411140i | ||||||||
\(79\) | 14.4772i | 0.183256i | 0.995793 | + | 0.0916278i | \(0.0292070\pi\) | ||||
−0.995793 | + | 0.0916278i | \(0.970793\pi\) | |||||||
\(80\) | −15.6208 | + | 12.4896i | −0.195260 | + | 0.156120i | ||||
\(81\) | 162.052 | 2.00065 | ||||||||
\(82\) | − | 23.9637i | − | 0.292240i | ||||||
\(83\) | 44.9529 | 0.541602 | 0.270801 | − | 0.962635i | \(-0.412712\pi\) | ||||
0.270801 | + | 0.962635i | \(0.412712\pi\) | |||||||
\(84\) | 8.40621i | 0.100074i | ||||||||
\(85\) | 126.013 | − | 100.753i | 1.48251 | − | 1.18534i | ||||
\(86\) | 87.2720i | 1.01479i | ||||||||
\(87\) | − | 118.571i | − | 1.36288i | ||||||
\(88\) | −23.9245 | −0.271869 | ||||||||
\(89\) | − | 74.0570i | − | 0.832102i | −0.909341 | − | 0.416051i | \(-0.863414\pi\) | ||
0.909341 | − | 0.416051i | \(-0.136586\pi\) | |||||||
\(90\) | −91.5231 | − | 114.469i | −1.01692 | − | 1.27188i | ||||
\(91\) | − | 3.20623i | − | 0.0352333i | ||||||
\(92\) | −39.7205 | − | 23.2009i | −0.431745 | − | 0.252184i | ||||
\(93\) | 173.797i | 1.86879i | ||||||||
\(94\) | −63.6448 | −0.677072 | ||||||||
\(95\) | 74.3639 | + | 93.0077i | 0.782778 | + | 0.979028i | ||||
\(96\) | −30.8424 | −0.321275 | ||||||||
\(97\) | 42.2048 | 0.435101 | 0.217551 | − | 0.976049i | \(-0.430193\pi\) | ||||
0.217551 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(98\) | 68.4560i | 0.698531i | ||||||||
\(99\) | − | 175.317i | − | 1.77088i | ||||||
\(100\) | −11.0026 | + | 48.7744i | −0.110026 | + | 0.487744i | ||||
\(101\) | 42.3218 | 0.419027 | 0.209514 | − | 0.977806i | \(-0.432812\pi\) | ||||
0.209514 | + | 0.977806i | \(0.432812\pi\) | |||||||
\(102\) | 248.805 | 2.43927 | ||||||||
\(103\) | −203.560 | −1.97632 | −0.988158 | − | 0.153443i | \(-0.950964\pi\) | ||||
−0.988158 | + | 0.153443i | \(0.950964\pi\) | |||||||
\(104\) | 11.7636 | 0.113112 | ||||||||
\(105\) | 13.1237 | + | 16.4140i | 0.124988 | + | 0.156324i | ||||
\(106\) | 64.8865i | 0.612137i | ||||||||
\(107\) | 141.946 | 1.32660 | 0.663301 | − | 0.748353i | \(-0.269155\pi\) | ||||
0.663301 | + | 0.748353i | \(0.269155\pi\) | |||||||
\(108\) | − | 127.872i | − | 1.18400i | ||||||
\(109\) | − | 82.8396i | − | 0.759997i | −0.924987 | − | 0.379998i | \(-0.875925\pi\) | ||
0.924987 | − | 0.379998i | \(-0.124075\pi\) | |||||||
\(110\) | −46.7150 | + | 37.3508i | −0.424682 | + | 0.339553i | ||||
\(111\) | 32.9285i | 0.296653i | ||||||||
\(112\) | 3.08360 | 0.0275321 | ||||||||
\(113\) | −88.6557 | −0.784564 | −0.392282 | − | 0.919845i | \(-0.628314\pi\) | ||||
−0.392282 | + | 0.919845i | \(0.628314\pi\) | |||||||
\(114\) | 183.638i | 1.61086i | ||||||||
\(115\) | −113.780 | + | 16.7094i | −0.989388 | + | 0.145299i | ||||
\(116\) | −43.4946 | −0.374953 | ||||||||
\(117\) | 86.2035i | 0.736782i | ||||||||
\(118\) | 132.498i | 1.12287i | ||||||||
\(119\) | −24.8754 | −0.209037 | ||||||||
\(120\) | −60.2229 | + | 48.1510i | −0.501858 | + | 0.401258i | ||||
\(121\) | 49.4526 | 0.408699 | ||||||||
\(122\) | 52.4797 | 0.430162 | ||||||||
\(123\) | − | 92.3870i | − | 0.751114i | ||||||
\(124\) | 63.7529 | 0.514136 | ||||||||
\(125\) | 54.6627 | + | 112.414i | 0.437301 | + | 0.899315i | ||||
\(126\) | 22.5965i | 0.179337i | ||||||||
\(127\) | − | 211.003i | − | 1.66144i | −0.556689 | − | 0.830721i | \(-0.687929\pi\) | ||
0.556689 | − | 0.830721i | \(-0.312071\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 336.459i | 2.60821i | ||||||||
\(130\) | 22.9697 | − | 18.3654i | 0.176690 | − | 0.141272i | ||||
\(131\) | −17.0037 | −0.129799 | −0.0648997 | − | 0.997892i | \(-0.520673\pi\) | ||||
−0.0648997 | + | 0.997892i | \(0.520673\pi\) | |||||||
\(132\) | −92.2358 | −0.698756 | ||||||||
\(133\) | − | 18.3600i | − | 0.138045i | ||||||
\(134\) | − | 62.5212i | − | 0.466576i | ||||||
\(135\) | −199.633 | − | 249.683i | −1.47876 | − | 1.84950i | ||||
\(136\) | − | 91.2677i | − | 0.671086i | ||||||
\(137\) | 93.2792 | 0.680870 | 0.340435 | − | 0.940268i | \(-0.389426\pi\) | ||||
0.340435 | + | 0.940268i | \(0.389426\pi\) | |||||||
\(138\) | −153.134 | − | 89.4463i | −1.10967 | − | 0.648161i | ||||
\(139\) | 46.0137 | 0.331034 | 0.165517 | − | 0.986207i | \(-0.447071\pi\) | ||||
0.165517 | + | 0.986207i | \(0.447071\pi\) | |||||||
\(140\) | 6.02104 | − | 4.81410i | 0.0430074 | − | 0.0343864i | ||||
\(141\) | −245.369 | −1.74021 | ||||||||
\(142\) | − | 110.016i | − | 0.774761i | ||||||
\(143\) | 35.1798 | 0.246013 | ||||||||
\(144\) | −82.9064 | −0.575739 | ||||||||
\(145\) | −84.9278 | + | 67.9036i | −0.585709 | + | 0.468301i | ||||
\(146\) | −143.417 | −0.982305 | ||||||||
\(147\) | 263.918i | 1.79536i | ||||||||
\(148\) | 12.0789 | 0.0816145 | ||||||||
\(149\) | − | 173.780i | − | 1.16631i | −0.812362 | − | 0.583154i | \(-0.801818\pi\) | ||
0.812362 | − | 0.583154i | \(-0.198182\pi\) | |||||||
\(150\) | −42.4183 | + | 188.040i | −0.282789 | + | 1.25360i | ||||
\(151\) | 65.7314 | 0.435307 | 0.217654 | − | 0.976026i | \(-0.430160\pi\) | ||||
0.217654 | + | 0.976026i | \(0.430160\pi\) | |||||||
\(152\) | 67.3627 | 0.443176 | ||||||||
\(153\) | 668.806 | 4.37128 | ||||||||
\(154\) | 9.22167 | 0.0598810 | ||||||||
\(155\) | 124.484 | − | 99.5308i | 0.803124 | − | 0.642134i | ||||
\(156\) | 45.3523 | 0.290720 | ||||||||
\(157\) | −141.661 | −0.902301 | −0.451151 | − | 0.892448i | \(-0.648986\pi\) | ||||
−0.451151 | + | 0.892448i | \(0.648986\pi\) | |||||||
\(158\) | 20.4738 | 0.129581 | ||||||||
\(159\) | 250.157i | 1.57331i | ||||||||
\(160\) | 17.6629 | + | 22.0912i | 0.110393 | + | 0.138070i | ||||
\(161\) | 15.3102 | + | 8.94277i | 0.0950947 | + | 0.0555452i | ||||
\(162\) | − | 229.177i | − | 1.41467i | ||||||
\(163\) | 165.811i | 1.01724i | 0.860990 | + | 0.508621i | \(0.169845\pi\) | ||||
−0.860990 | + | 0.508621i | \(0.830155\pi\) | |||||||
\(164\) | −33.8897 | −0.206645 | ||||||||
\(165\) | −180.100 | + | 143.998i | −1.09152 | + | 0.872717i | ||||
\(166\) | − | 63.5730i | − | 0.382970i | ||||||
\(167\) | 197.607i | 1.18328i | 0.806203 | + | 0.591639i | \(0.201519\pi\) | ||||
−0.806203 | + | 0.591639i | \(0.798481\pi\) | |||||||
\(168\) | 11.8882 | 0.0707629 | ||||||||
\(169\) | 151.702 | 0.897645 | ||||||||
\(170\) | −142.487 | − | 178.210i | −0.838158 | − | 1.04829i | ||||
\(171\) | 493.631i | 2.88673i | ||||||||
\(172\) | 123.421 | 0.717566 | ||||||||
\(173\) | 129.325i | 0.747545i | 0.927520 | + | 0.373773i | \(0.121936\pi\) | ||||
−0.927520 | + | 0.373773i | \(0.878064\pi\) | |||||||
\(174\) | −167.685 | −0.963704 | ||||||||
\(175\) | 4.24095 | − | 18.8001i | 0.0242340 | − | 0.107429i | ||||
\(176\) | 33.8343i | 0.192240i | ||||||||
\(177\) | 510.819i | 2.88598i | ||||||||
\(178\) | −104.732 | −0.588385 | ||||||||
\(179\) | −53.7876 | −0.300489 | −0.150245 | − | 0.988649i | \(-0.548006\pi\) | ||||
−0.150245 | + | 0.988649i | \(0.548006\pi\) | |||||||
\(180\) | −161.883 | + | 129.433i | −0.899352 | + | 0.719073i | ||||
\(181\) | − | 294.478i | − | 1.62695i | −0.581599 | − | 0.813476i | \(-0.697573\pi\) | ||
0.581599 | − | 0.813476i | \(-0.302427\pi\) | |||||||
\(182\) | −4.53429 | −0.0249137 | ||||||||
\(183\) | 202.325 | 1.10560 | ||||||||
\(184\) | −32.8110 | + | 56.1733i | −0.178321 | + | 0.305290i | ||||
\(185\) | 23.5854 | − | 18.8576i | 0.127489 | − | 0.101933i | ||||
\(186\) | 245.786 | 1.32143 | ||||||||
\(187\) | − | 272.941i | − | 1.45958i | ||||||
\(188\) | 90.0073i | 0.478762i | ||||||||
\(189\) | 49.2881i | 0.260784i | ||||||||
\(190\) | 131.533 | − | 105.166i | 0.692278 | − | 0.553508i | ||||
\(191\) | 10.1786i | 0.0532913i | 0.999645 | + | 0.0266456i | \(0.00848258\pi\) | ||||
−0.999645 | + | 0.0266456i | \(0.991517\pi\) | |||||||
\(192\) | 43.6177i | 0.227175i | ||||||||
\(193\) | − | 6.11467i | − | 0.0316822i | −0.999875 | − | 0.0158411i | \(-0.994957\pi\) | ||
0.999875 | − | 0.0158411i | \(-0.00504259\pi\) | |||||||
\(194\) | − | 59.6866i | − | 0.307663i | ||||||
\(195\) | 88.5551 | − | 70.8039i | 0.454129 | − | 0.363097i | ||||
\(196\) | 96.8114 | 0.493936 | ||||||||
\(197\) | 176.222i | 0.894527i | 0.894402 | + | 0.447264i | \(0.147601\pi\) | ||||
−0.894402 | + | 0.447264i | \(0.852399\pi\) | |||||||
\(198\) | −247.936 | −1.25220 | ||||||||
\(199\) | − | 248.127i | − | 1.24687i | −0.781875 | − | 0.623435i | \(-0.785737\pi\) | ||
0.781875 | − | 0.623435i | \(-0.214263\pi\) | |||||||
\(200\) | 68.9774 | + | 15.5601i | 0.344887 | + | 0.0778003i | ||||
\(201\) | − | 241.038i | − | 1.19919i | ||||||
\(202\) | − | 59.8520i | − | 0.296297i | ||||||
\(203\) | 16.7650 | 0.0825861 | ||||||||
\(204\) | − | 351.864i | − | 1.72482i | ||||||
\(205\) | −66.1732 | + | 52.9085i | −0.322796 | + | 0.258090i | ||||
\(206\) | 287.878i | 1.39747i | ||||||||
\(207\) | −411.635 | − | 240.438i | −1.98858 | − | 1.16154i | ||||
\(208\) | − | 16.6363i | − | 0.0799822i | ||||||
\(209\) | 201.452 | 0.963885 | ||||||||
\(210\) | 23.2129 | − | 18.5598i | 0.110538 | − | 0.0883799i | ||||
\(211\) | 247.820 | 1.17450 | 0.587250 | − | 0.809405i | \(-0.300210\pi\) | ||||
0.587250 | + | 0.809405i | \(0.300210\pi\) | |||||||
\(212\) | 91.7633 | 0.432846 | ||||||||
\(213\) | − | 424.145i | − | 1.99129i | ||||||
\(214\) | − | 200.743i | − | 0.938049i | ||||||
\(215\) | 240.993 | − | 192.685i | 1.12090 | − | 0.896209i | ||||
\(216\) | −180.838 | −0.837213 | ||||||||
\(217\) | −24.5735 | −0.113242 | ||||||||
\(218\) | −117.153 | −0.537399 | ||||||||
\(219\) | −552.913 | −2.52472 | ||||||||
\(220\) | 52.8220 | + | 66.0650i | 0.240100 | + | 0.300295i | ||||
\(221\) | 134.205i | 0.607263i | ||||||||
\(222\) | 46.5679 | 0.209765 | ||||||||
\(223\) | − | 290.264i | − | 1.30163i | −0.759235 | − | 0.650817i | \(-0.774427\pi\) | ||
0.759235 | − | 0.650817i | \(-0.225573\pi\) | |||||||
\(224\) | − | 4.36086i | − | 0.0194681i | ||||||
\(225\) | −114.023 | + | 505.464i | −0.506771 | + | 2.24651i | ||||
\(226\) | 125.378i | 0.554770i | ||||||||
\(227\) | −310.686 | −1.36866 | −0.684331 | − | 0.729171i | \(-0.739906\pi\) | ||||
−0.684331 | + | 0.729171i | \(0.739906\pi\) | |||||||
\(228\) | 259.703 | 1.13905 | ||||||||
\(229\) | 267.722i | 1.16909i | 0.811361 | + | 0.584545i | \(0.198727\pi\) | ||||
−0.811361 | + | 0.584545i | \(0.801273\pi\) | |||||||
\(230\) | 23.6306 | + | 160.909i | 0.102742 | + | 0.699603i | ||||
\(231\) | 35.5522 | 0.153906 | ||||||||
\(232\) | 61.5107i | 0.265132i | ||||||||
\(233\) | 82.0593i | 0.352186i | 0.984374 | + | 0.176093i | \(0.0563459\pi\) | ||||
−0.984374 | + | 0.176093i | \(0.943654\pi\) | |||||||
\(234\) | 121.910 | 0.520984 | ||||||||
\(235\) | 140.519 | + | 175.749i | 0.597954 | + | 0.747867i | ||||
\(236\) | 187.381 | 0.793986 | ||||||||
\(237\) | 78.9327 | 0.333049 | ||||||||
\(238\) | 35.1791i | 0.147811i | ||||||||
\(239\) | 15.0646 | 0.0630316 | 0.0315158 | − | 0.999503i | \(-0.489967\pi\) | ||||
0.0315158 | + | 0.999503i | \(0.489967\pi\) | |||||||
\(240\) | 68.0958 | + | 85.1681i | 0.283732 | + | 0.354867i | ||||
\(241\) | − | 70.4867i | − | 0.292476i | −0.989249 | − | 0.146238i | \(-0.953283\pi\) | ||
0.989249 | − | 0.146238i | \(-0.0467165\pi\) | |||||||
\(242\) | − | 69.9365i | − | 0.288994i | ||||||
\(243\) | − | 308.121i | − | 1.26799i | ||||||
\(244\) | − | 74.2176i | − | 0.304170i | ||||||
\(245\) | 189.034 | − | 151.142i | 0.771569 | − | 0.616905i | ||||
\(246\) | −130.655 | −0.531117 | ||||||||
\(247\) | −99.0539 | −0.401028 | ||||||||
\(248\) | − | 90.1602i | − | 0.363549i | ||||||
\(249\) | − | 245.093i | − | 0.984309i | ||||||
\(250\) | 158.978 | − | 77.3047i | 0.635912 | − | 0.309219i | ||||
\(251\) | 210.853i | 0.840053i | 0.907512 | + | 0.420027i | \(0.137979\pi\) | ||||
−0.907512 | + | 0.420027i | \(0.862021\pi\) | |||||||
\(252\) | 31.9562 | 0.126810 | ||||||||
\(253\) | −98.1232 | + | 167.989i | −0.387839 | + | 0.663990i | ||||
\(254\) | −298.403 | −1.17482 | ||||||||
\(255\) | −549.329 | − | 687.051i | −2.15423 | − | 2.69432i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 224.082i | 0.871914i | 0.899967 | + | 0.435957i | \(0.143590\pi\) | ||||
−0.899967 | + | 0.435957i | \(0.856410\pi\) | |||||||
\(258\) | 475.826 | 1.84428 | ||||||||
\(259\) | −4.65582 | −0.0179761 | ||||||||
\(260\) | −25.9726 | − | 32.4841i | −0.0998944 | − | 0.124939i | ||||
\(261\) | −450.748 | −1.72700 | ||||||||
\(262\) | 24.0469i | 0.0917820i | ||||||||
\(263\) | −141.086 | −0.536448 | −0.268224 | − | 0.963357i | \(-0.586437\pi\) | ||||
−0.268224 | + | 0.963357i | \(0.586437\pi\) | |||||||
\(264\) | 130.441i | 0.494095i | ||||||||
\(265\) | 179.177 | − | 143.261i | 0.676141 | − | 0.540606i | ||||
\(266\) | −25.9649 | −0.0976125 | ||||||||
\(267\) | −403.775 | −1.51226 | ||||||||
\(268\) | −88.4183 | −0.329919 | ||||||||
\(269\) | −192.441 | −0.715394 | −0.357697 | − | 0.933838i | \(-0.616438\pi\) | ||||
−0.357697 | + | 0.933838i | \(0.616438\pi\) | |||||||
\(270\) | −353.105 | + | 282.324i | −1.30780 | + | 1.04564i | ||||
\(271\) | 138.386 | 0.510649 | 0.255324 | − | 0.966855i | \(-0.417818\pi\) | ||||
0.255324 | + | 0.966855i | \(0.417818\pi\) | |||||||
\(272\) | −129.072 | −0.474530 | ||||||||
\(273\) | −17.4810 | −0.0640331 | ||||||||
\(274\) | − | 131.917i | − | 0.481448i | ||||||
\(275\) | 206.281 | + | 46.5332i | 0.750112 | + | 0.169212i | ||||
\(276\) | −126.496 | + | 216.565i | −0.458319 | + | 0.784654i | ||||
\(277\) | − | 443.283i | − | 1.60030i | −0.599799 | − | 0.800151i | \(-0.704753\pi\) | ||
0.599799 | − | 0.800151i | \(-0.295247\pi\) | |||||||
\(278\) | − | 65.0732i | − | 0.234076i | ||||||
\(279\) | 660.690 | 2.36807 | ||||||||
\(280\) | −6.80817 | − | 8.51504i | −0.0243149 | − | 0.0304109i | ||||
\(281\) | − | 405.142i | − | 1.44178i | −0.693047 | − | 0.720892i | \(-0.743732\pi\) | ||
0.693047 | − | 0.720892i | \(-0.256268\pi\) | |||||||
\(282\) | 347.005i | 1.23051i | ||||||||
\(283\) | −161.101 | −0.569263 | −0.284631 | − | 0.958637i | \(-0.591871\pi\) | ||||
−0.284631 | + | 0.958637i | \(0.591871\pi\) | |||||||
\(284\) | −155.586 | −0.547839 | ||||||||
\(285\) | 507.098 | − | 405.448i | 1.77929 | − | 1.42262i | ||||
\(286\) | − | 49.7518i | − | 0.173957i | ||||||
\(287\) | 13.0628 | 0.0455149 | ||||||||
\(288\) | 117.247i | 0.407109i | ||||||||
\(289\) | 752.225 | 2.60286 | ||||||||
\(290\) | 96.0303 | + | 120.106i | 0.331139 | + | 0.414159i | ||||
\(291\) | − | 230.109i | − | 0.790754i | ||||||
\(292\) | 202.822i | 0.694595i | ||||||||
\(293\) | −187.936 | −0.641419 | −0.320709 | − | 0.947178i | \(-0.603921\pi\) | ||||
−0.320709 | + | 0.947178i | \(0.603921\pi\) | |||||||
\(294\) | 373.237 | 1.26951 | ||||||||
\(295\) | 365.880 | − | 292.538i | 1.24027 | − | 0.991654i | ||||
\(296\) | − | 17.0822i | − | 0.0577102i | ||||||
\(297\) | −540.806 | −1.82090 | ||||||||
\(298\) | −245.762 | −0.824704 | ||||||||
\(299\) | 48.2471 | − | 82.6003i | 0.161362 | − | 0.276255i | ||||
\(300\) | 265.928 | + | 59.9886i | 0.886428 | + | 0.199962i | ||||
\(301\) | −47.5727 | −0.158049 | ||||||||
\(302\) | − | 92.9583i | − | 0.307809i | ||||||
\(303\) | − | 230.747i | − | 0.761542i | ||||||
\(304\) | − | 95.2653i | − | 0.313373i | ||||||
\(305\) | −115.868 | − | 144.918i | −0.379896 | − | 0.475139i | ||||
\(306\) | − | 945.835i | − | 3.09096i | ||||||
\(307\) | 357.974i | 1.16604i | 0.812458 | + | 0.583020i | \(0.198129\pi\) | ||||
−0.812458 | + | 0.583020i | \(0.801871\pi\) | |||||||
\(308\) | − | 13.0414i | − | 0.0423422i | ||||||
\(309\) | 1109.85i | 3.59176i | ||||||||
\(310\) | −140.758 | − | 176.047i | −0.454058 | − | 0.567894i | ||||
\(311\) | 88.3106 | 0.283957 | 0.141978 | − | 0.989870i | \(-0.454654\pi\) | ||||
0.141978 | + | 0.989870i | \(0.454654\pi\) | |||||||
\(312\) | − | 64.1379i | − | 0.205570i | ||||||
\(313\) | 451.978 | 1.44402 | 0.722009 | − | 0.691883i | \(-0.243219\pi\) | ||||
0.722009 | + | 0.691883i | \(0.243219\pi\) | |||||||
\(314\) | 200.339i | 0.638023i | ||||||||
\(315\) | 62.3979 | − | 49.8900i | 0.198088 | − | 0.158381i | ||||
\(316\) | − | 28.9544i | − | 0.0916278i | ||||||
\(317\) | − | 545.035i | − | 1.71935i | −0.510838 | − | 0.859677i | \(-0.670665\pi\) | ||
0.510838 | − | 0.859677i | \(-0.329335\pi\) | |||||||
\(318\) | 353.775 | 1.11250 | ||||||||
\(319\) | 183.951i | 0.576649i | ||||||||
\(320\) | 31.2417 | − | 24.9792i | 0.0976302 | − | 0.0780599i | ||||
\(321\) | − | 773.922i | − | 2.41097i | ||||||
\(322\) | 12.6470 | − | 21.6520i | 0.0392764 | − | 0.0672421i | ||||
\(323\) | 768.506i | 2.37927i | ||||||||
\(324\) | −324.105 | −1.00032 | ||||||||
\(325\) | −101.428 | − | 22.8804i | −0.312087 | − | 0.0704011i | ||||
\(326\) | 234.492 | 0.719299 | ||||||||
\(327\) | −451.659 | −1.38122 | ||||||||
\(328\) | 47.9273i | 0.146120i | ||||||||
\(329\) | − | 34.6933i | − | 0.105451i | ||||||
\(330\) | 203.644 | + | 254.700i | 0.617104 | + | 0.771818i | ||||
\(331\) | −529.975 | −1.60113 | −0.800566 | − | 0.599244i | \(-0.795468\pi\) | ||||
−0.800566 | + | 0.599244i | \(0.795468\pi\) | |||||||
\(332\) | −89.9059 | −0.270801 | ||||||||
\(333\) | 125.178 | 0.375909 | ||||||||
\(334\) | 279.459 | 0.836704 | ||||||||
\(335\) | −172.646 | + | 138.038i | −0.515361 | + | 0.412055i | ||||
\(336\) | − | 16.8124i | − | 0.0500369i | ||||||
\(337\) | 278.285 | 0.825771 | 0.412886 | − | 0.910783i | \(-0.364521\pi\) | ||||
0.412886 | + | 0.910783i | \(0.364521\pi\) | |||||||
\(338\) | − | 214.539i | − | 0.634731i | ||||||
\(339\) | 483.369i | 1.42587i | ||||||||
\(340\) | −252.027 | + | 201.507i | −0.741255 | + | 0.592668i | ||||
\(341\) | − | 269.629i | − | 0.790702i | ||||||
\(342\) | 698.100 | 2.04123 | ||||||||
\(343\) | −75.0900 | −0.218921 | ||||||||
\(344\) | − | 174.544i | − | 0.507396i | ||||||
\(345\) | 91.1030 | + | 620.350i | 0.264067 | + | 1.79812i | ||||
\(346\) | 182.894 | 0.528594 | ||||||||
\(347\) | 641.622i | 1.84906i | 0.381114 | + | 0.924528i | \(0.375540\pi\) | ||||
−0.381114 | + | 0.924528i | \(0.624460\pi\) | |||||||
\(348\) | 237.142i | 0.681442i | ||||||||
\(349\) | −237.462 | −0.680408 | −0.340204 | − | 0.940352i | \(-0.610496\pi\) | ||||
−0.340204 | + | 0.940352i | \(0.610496\pi\) | |||||||
\(350\) | −26.5873 | − | 5.99761i | −0.0759637 | − | 0.0171360i | ||||
\(351\) | 265.914 | 0.757590 | ||||||||
\(352\) | 47.8489 | 0.135934 | ||||||||
\(353\) | − | 297.586i | − | 0.843020i | −0.906824 | − | 0.421510i | \(-0.861500\pi\) | ||
0.906824 | − | 0.421510i | \(-0.138500\pi\) | |||||||
\(354\) | 722.407 | 2.04070 | ||||||||
\(355\) | −303.798 | + | 242.901i | −0.855770 | + | 0.684228i | ||||
\(356\) | 148.114i | 0.416051i | ||||||||
\(357\) | 135.626i | 0.379904i | ||||||||
\(358\) | 76.0671i | 0.212478i | ||||||||
\(359\) | − | 145.988i | − | 0.406651i | −0.979111 | − | 0.203325i | \(-0.934825\pi\) | ||
0.979111 | − | 0.203325i | \(-0.0651749\pi\) | |||||||
\(360\) | 183.046 | + | 228.938i | 0.508462 | + | 0.635938i | ||||
\(361\) | −206.217 | −0.571239 | ||||||||
\(362\) | −416.455 | −1.15043 | ||||||||
\(363\) | − | 269.626i | − | 0.742771i | ||||||
\(364\) | 6.41246i | 0.0176166i | ||||||||
\(365\) | 316.645 | + | 396.030i | 0.867519 | + | 1.08501i | ||||
\(366\) | − | 286.131i | − | 0.781778i | ||||||
\(367\) | 687.079 | 1.87215 | 0.936075 | − | 0.351801i | \(-0.114431\pi\) | ||||
0.936075 | + | 0.351801i | \(0.114431\pi\) | |||||||
\(368\) | 79.4410 | + | 46.4018i | 0.215872 | + | 0.126092i | ||||
\(369\) | −351.209 | −0.951787 | ||||||||
\(370\) | −26.6687 | − | 33.3548i | −0.0720775 | − | 0.0901481i | ||||
\(371\) | −35.3701 | −0.0953373 | ||||||||
\(372\) | − | 347.594i | − | 0.934393i | ||||||
\(373\) | −703.379 | −1.88573 | −0.942867 | − | 0.333170i | \(-0.891882\pi\) | ||||
−0.942867 | + | 0.333170i | \(0.891882\pi\) | |||||||
\(374\) | −385.997 | −1.03208 | ||||||||
\(375\) | 612.907 | − | 298.032i | 1.63442 | − | 0.794753i | ||||
\(376\) | 127.290 | 0.338536 | ||||||||
\(377\) | − | 90.4487i | − | 0.239917i | ||||||
\(378\) | 69.7039 | 0.184402 | ||||||||
\(379\) | 602.990i | 1.59100i | 0.605952 | + | 0.795501i | \(0.292792\pi\) | ||||
−0.605952 | + | 0.795501i | \(0.707208\pi\) | |||||||
\(380\) | −148.728 | − | 186.015i | −0.391389 | − | 0.489514i | ||||
\(381\) | −1150.43 | −3.01951 | ||||||||
\(382\) | 14.3948 | 0.0376826 | ||||||||
\(383\) | −223.793 | −0.584315 | −0.292158 | − | 0.956370i | \(-0.594373\pi\) | ||||
−0.292158 | + | 0.956370i | \(0.594373\pi\) | |||||||
\(384\) | 61.6847 | 0.160637 | ||||||||
\(385\) | −20.3602 | − | 25.4647i | −0.0528837 | − | 0.0661421i | ||||
\(386\) | −8.64745 | −0.0224027 | ||||||||
\(387\) | 1279.05 | 3.30504 | ||||||||
\(388\) | −84.4096 | −0.217551 | ||||||||
\(389\) | − | 348.989i | − | 0.897145i | −0.893746 | − | 0.448572i | \(-0.851933\pi\) | ||
0.893746 | − | 0.448572i | \(-0.148067\pi\) | |||||||
\(390\) | −100.132 | − | 125.236i | −0.256748 | − | 0.321118i | ||||
\(391\) | −640.851 | − | 374.323i | −1.63901 | − | 0.957349i | ||||
\(392\) | − | 136.912i | − | 0.349265i | ||||||
\(393\) | 92.7078i | 0.235898i | ||||||||
\(394\) | 249.215 | 0.632526 | ||||||||
\(395\) | −45.2035 | − | 56.5364i | −0.114439 | − | 0.143130i | ||||
\(396\) | 350.635i | 0.885441i | ||||||||
\(397\) | 126.645i | 0.319005i | 0.987198 | + | 0.159503i | \(0.0509890\pi\) | ||||
−0.987198 | + | 0.159503i | \(0.949011\pi\) | |||||||
\(398\) | −350.905 | −0.881670 | ||||||||
\(399\) | −100.102 | −0.250883 | ||||||||
\(400\) | 22.0052 | − | 97.5488i | 0.0550131 | − | 0.243872i | ||||
\(401\) | 330.569i | 0.824362i | 0.911102 | + | 0.412181i | \(0.135233\pi\) | ||||
−0.911102 | + | 0.412181i | \(0.864767\pi\) | |||||||
\(402\) | −340.879 | −0.847957 | ||||||||
\(403\) | 132.577i | 0.328974i | ||||||||
\(404\) | −84.6435 | −0.209514 | ||||||||
\(405\) | −632.849 | + | 505.992i | −1.56259 | + | 1.24936i | ||||
\(406\) | − | 23.7092i | − | 0.0583972i | ||||||
\(407\) | − | 51.0853i | − | 0.125517i | ||||||
\(408\) | −497.611 | −1.21963 | ||||||||
\(409\) | −381.557 | −0.932903 | −0.466451 | − | 0.884547i | \(-0.654468\pi\) | ||||
−0.466451 | + | 0.884547i | \(0.654468\pi\) | |||||||
\(410\) | 74.8240 | + | 93.5831i | 0.182498 | + | 0.228251i | ||||
\(411\) | − | 508.578i | − | 1.23742i | ||||||
\(412\) | 407.121 | 0.988158 | ||||||||
\(413\) | −72.2257 | −0.174881 | ||||||||
\(414\) | −340.030 | + | 582.140i | −0.821329 | + | 1.40614i | ||||
\(415\) | −175.551 | + | 140.361i | −0.423013 | + | 0.338219i | ||||
\(416\) | −23.5273 | −0.0565560 | ||||||||
\(417\) | − | 250.876i | − | 0.601622i | ||||||
\(418\) | − | 284.896i | − | 0.681570i | ||||||
\(419\) | − | 125.759i | − | 0.300141i | −0.988675 | − | 0.150070i | \(-0.952050\pi\) | ||
0.988675 | − | 0.150070i | \(-0.0479501\pi\) | |||||||
\(420\) | −26.2475 | − | 32.8280i | −0.0624940 | − | 0.0781619i | ||||
\(421\) | 88.8050i | 0.210938i | 0.994423 | + | 0.105469i | \(0.0336344\pi\) | ||||
−0.994423 | + | 0.105469i | \(0.966366\pi\) | |||||||
\(422\) | − | 350.470i | − | 0.830497i | ||||||
\(423\) | 932.773i | 2.20514i | ||||||||
\(424\) | − | 129.773i | − | 0.306068i | ||||||
\(425\) | −177.516 | + | 786.927i | −0.417686 | + | 1.85159i | ||||
\(426\) | −599.831 | −1.40805 | ||||||||
\(427\) | 28.6071i | 0.0669956i | ||||||||
\(428\) | −283.893 | −0.663301 | ||||||||
\(429\) | − | 191.808i | − | 0.447105i | ||||||
\(430\) | −272.498 | − | 340.816i | −0.633716 | − | 0.792594i | ||||
\(431\) | 643.839i | 1.49383i | 0.664922 | + | 0.746913i | \(0.268465\pi\) | ||||
−0.664922 | + | 0.746913i | \(0.731535\pi\) | |||||||
\(432\) | 255.743i | 0.591999i | ||||||||
\(433\) | 137.912 | 0.318504 | 0.159252 | − | 0.987238i | \(-0.449092\pi\) | ||||
0.159252 | + | 0.987238i | \(0.449092\pi\) | |||||||
\(434\) | 34.7522i | 0.0800742i | ||||||||
\(435\) | 370.225 | + | 463.044i | 0.851092 | + | 1.06447i | ||||
\(436\) | 165.679i | 0.379998i | ||||||||
\(437\) | 276.280 | − | 472.998i | 0.632220 | − | 1.08238i | ||||
\(438\) | 781.937i | 1.78524i | ||||||||
\(439\) | −300.975 | −0.685593 | −0.342796 | − | 0.939410i | \(-0.611374\pi\) | ||||
−0.342796 | + | 0.939410i | \(0.611374\pi\) | |||||||
\(440\) | 93.4300 | − | 74.7016i | 0.212341 | − | 0.169776i | ||||
\(441\) | 1003.29 | 2.27502 | ||||||||
\(442\) | 189.795 | 0.429400 | ||||||||
\(443\) | 248.020i | 0.559864i | 0.960020 | + | 0.279932i | \(0.0903119\pi\) | ||||
−0.960020 | + | 0.279932i | \(0.909688\pi\) | |||||||
\(444\) | − | 65.8569i | − | 0.148326i | ||||||
\(445\) | 231.235 | + | 289.208i | 0.519630 | + | 0.649906i | ||||
\(446\) | −410.496 | −0.920394 | ||||||||
\(447\) | −947.484 | −2.11965 | ||||||||
\(448\) | −6.16719 | −0.0137661 | ||||||||
\(449\) | −576.186 | −1.28327 | −0.641633 | − | 0.767012i | \(-0.721743\pi\) | ||||
−0.641633 | + | 0.767012i | \(0.721743\pi\) | |||||||
\(450\) | 714.834 | + | 161.253i | 1.58852 | + | 0.358341i | ||||
\(451\) | 143.329i | 0.317803i | ||||||||
\(452\) | 177.311 | 0.392282 | ||||||||
\(453\) | − | 358.381i | − | 0.791129i | ||||||
\(454\) | 439.377i | 0.967790i | ||||||||
\(455\) | 10.0111 | + | 12.5210i | 0.0220024 | + | 0.0275187i | ||||
\(456\) | − | 367.276i | − | 0.805429i | ||||||
\(457\) | −104.755 | −0.229224 | −0.114612 | − | 0.993410i | \(-0.536563\pi\) | ||||
−0.114612 | + | 0.993410i | \(0.536563\pi\) | |||||||
\(458\) | 378.616 | 0.826672 | ||||||||
\(459\) | − | 2063.08i | − | 4.49474i | ||||||
\(460\) | 227.559 | − | 33.4187i | 0.494694 | − | 0.0726494i | ||||
\(461\) | 467.711 | 1.01456 | 0.507279 | − | 0.861782i | \(-0.330651\pi\) | ||||
0.507279 | + | 0.861782i | \(0.330651\pi\) | |||||||
\(462\) | − | 50.2785i | − | 0.108828i | ||||||
\(463\) | 502.838i | 1.08604i | 0.839719 | + | 0.543021i | \(0.182720\pi\) | ||||
−0.839719 | + | 0.543021i | \(0.817280\pi\) | |||||||
\(464\) | 86.9892 | 0.187477 | ||||||||
\(465\) | −542.663 | − | 678.714i | −1.16702 | − | 1.45960i | ||||
\(466\) | 116.049 | 0.249033 | ||||||||
\(467\) | 209.413 | 0.448422 | 0.224211 | − | 0.974541i | \(-0.428020\pi\) | ||||
0.224211 | + | 0.974541i | \(0.428020\pi\) | |||||||
\(468\) | − | 172.407i | − | 0.368391i | ||||||
\(469\) | 34.0808 | 0.0726670 | ||||||||
\(470\) | 248.546 | − | 198.724i | 0.528822 | − | 0.422817i | ||||
\(471\) | 772.367i | 1.63985i | ||||||||
\(472\) | − | 264.996i | − | 0.561433i | ||||||
\(473\) | − | 521.984i | − | 1.10356i | ||||||
\(474\) | − | 111.628i | − | 0.235501i | ||||||
\(475\) | −580.813 | − | 131.021i | −1.22277 | − | 0.275834i | ||||
\(476\) | 49.7508 | 0.104518 | ||||||||
\(477\) | 950.971 | 1.99365 | ||||||||
\(478\) | − | 21.3045i | − | 0.0445701i | ||||||
\(479\) | 446.153i | 0.931425i | 0.884936 | + | 0.465713i | \(0.154202\pi\) | ||||
−0.884936 | + | 0.465713i | \(0.845798\pi\) | |||||||
\(480\) | 120.446 | − | 96.3020i | 0.250929 | − | 0.200629i | ||||
\(481\) | 25.1186i | 0.0522217i | ||||||||
\(482\) | −99.6833 | −0.206812 | ||||||||
\(483\) | 48.7579 | − | 83.4747i | 0.100948 | − | 0.172825i | ||||
\(484\) | −98.9051 | −0.204349 | ||||||||
\(485\) | −164.819 | + | 131.780i | −0.339832 | + | 0.271711i | ||||
\(486\) | −435.749 | −0.896603 | ||||||||
\(487\) | 150.073i | 0.308158i | 0.988059 | + | 0.154079i | \(0.0492410\pi\) | ||||
−0.988059 | + | 0.154079i | \(0.950759\pi\) | |||||||
\(488\) | −104.959 | −0.215081 | ||||||||
\(489\) | 904.034 | 1.84874 | ||||||||
\(490\) | −213.747 | − | 267.335i | −0.436218 | − | 0.545582i | ||||
\(491\) | −823.267 | −1.67672 | −0.838358 | − | 0.545121i | \(-0.816484\pi\) | ||||
−0.838358 | + | 0.545121i | \(0.816484\pi\) | |||||||
\(492\) | 184.774i | 0.375557i | ||||||||
\(493\) | −701.742 | −1.42341 | ||||||||
\(494\) | 140.083i | 0.283570i | ||||||||
\(495\) | 547.410 | + | 684.651i | 1.10588 | + | 1.38313i | ||||
\(496\) | −127.506 | −0.257068 | ||||||||
\(497\) | 59.9706 | 0.120665 | ||||||||
\(498\) | −346.614 | −0.696011 | ||||||||
\(499\) | −403.544 | −0.808705 | −0.404353 | − | 0.914603i | \(-0.632503\pi\) | ||||
−0.404353 | + | 0.914603i | \(0.632503\pi\) | |||||||
\(500\) | −109.325 | − | 224.829i | −0.218651 | − | 0.449657i | ||||
\(501\) | 1077.40 | 2.15049 | ||||||||
\(502\) | 298.192 | 0.594007 | ||||||||
\(503\) | 467.899 | 0.930217 | 0.465108 | − | 0.885254i | \(-0.346015\pi\) | ||||
0.465108 | + | 0.885254i | \(0.346015\pi\) | |||||||
\(504\) | − | 45.1929i | − | 0.0896685i | ||||||
\(505\) | −165.275 | + | 132.145i | −0.327278 | + | 0.261674i | ||||
\(506\) | 237.573 | + | 138.767i | 0.469512 | + | 0.274243i | ||||
\(507\) | − | 827.112i | − | 1.63138i | ||||||
\(508\) | 422.006i | 0.830721i | ||||||||
\(509\) | 52.1092 | 0.102376 | 0.0511878 | − | 0.998689i | \(-0.483699\pi\) | ||||
0.0511878 | + | 0.998689i | \(0.483699\pi\) | |||||||
\(510\) | −971.637 | + | 776.869i | −1.90517 | + | 1.52327i | ||||
\(511\) | − | 78.1775i | − | 0.152989i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 1522.72 | 2.96826 | ||||||||
\(514\) | 316.900 | 0.616536 | ||||||||
\(515\) | 794.946 | − | 635.596i | 1.54358 | − | 1.23417i | ||||
\(516\) | − | 672.919i | − | 1.30411i | ||||||
\(517\) | 380.667 | 0.736299 | ||||||||
\(518\) | 6.58433i | 0.0127111i | ||||||||
\(519\) | 705.109 | 1.35859 | ||||||||
\(520\) | −45.9395 | + | 36.7307i | −0.0883452 | + | 0.0706360i | ||||
\(521\) | − | 978.566i | − | 1.87825i | −0.343581 | − | 0.939123i | \(-0.611640\pi\) | ||
0.343581 | − | 0.939123i | \(-0.388360\pi\) | |||||||
\(522\) | 637.453i | 1.22117i | ||||||||
\(523\) | 360.011 | 0.688358 | 0.344179 | − | 0.938904i | \(-0.388157\pi\) | ||||
0.344179 | + | 0.938904i | \(0.388157\pi\) | |||||||
\(524\) | 34.0074 | 0.0648997 | ||||||||
\(525\) | −102.502 | − | 23.1226i | −0.195242 | − | 0.0440430i | ||||
\(526\) | 199.526i | 0.379326i | ||||||||
\(527\) | 1028.59 | 1.95178 | ||||||||
\(528\) | 184.472 | 0.349378 | ||||||||
\(529\) | 259.859 | + | 460.776i | 0.491227 | + | 0.871031i | ||||
\(530\) | −202.601 | − | 253.395i | −0.382266 | − | 0.478104i | ||||
\(531\) | 1941.88 | 3.65703 | ||||||||
\(532\) | 36.7199i | 0.0690225i | ||||||||
\(533\) | − | 70.4750i | − | 0.132223i | ||||||
\(534\) | 571.024i | 1.06933i | ||||||||
\(535\) | −554.330 | + | 443.213i | −1.03613 | + | 0.828435i | ||||
\(536\) | 125.042i | 0.233288i | ||||||||
\(537\) | 293.261i | 0.546110i | ||||||||
\(538\) | 272.152i | 0.505860i | ||||||||
\(539\) | − | 409.443i | − | 0.759635i | ||||||
\(540\) | 399.266 | + | 499.366i | 0.739381 | + | 0.924751i | ||||
\(541\) | 142.266 | 0.262969 | 0.131484 | − | 0.991318i | \(-0.458026\pi\) | ||||
0.131484 | + | 0.991318i | \(0.458026\pi\) | |||||||
\(542\) | − | 195.707i | − | 0.361083i | ||||||
\(543\) | −1605.56 | −2.95683 | ||||||||
\(544\) | 182.535i | 0.335543i | ||||||||
\(545\) | 258.658 | + | 323.506i | 0.474602 | + | 0.593589i | ||||
\(546\) | 24.7219i | 0.0452782i | ||||||||
\(547\) | 405.389i | 0.741114i | 0.928810 | + | 0.370557i | \(0.120833\pi\) | ||||
−0.928810 | + | 0.370557i | \(0.879167\pi\) | |||||||
\(548\) | −186.558 | −0.340435 | ||||||||
\(549\) | − | 769.139i | − | 1.40098i | ||||||
\(550\) | 65.8079 | − | 291.725i | 0.119651 | − | 0.530410i | ||||
\(551\) | − | 517.941i | − | 0.940001i | ||||||
\(552\) | 306.269 | + | 178.893i | 0.554834 | + | 0.324081i | ||||
\(553\) | 11.1604i | 0.0201816i | ||||||||
\(554\) | −626.897 | −1.13158 | ||||||||
\(555\) | −102.816 | − | 128.593i | −0.185253 | − | 0.231698i | ||||
\(556\) | −92.0274 | −0.165517 | ||||||||
\(557\) | −726.195 | −1.30376 | −0.651881 | − | 0.758322i | \(-0.726020\pi\) | ||||
−0.651881 | + | 0.758322i | \(0.726020\pi\) | |||||||
\(558\) | − | 934.357i | − | 1.67448i | ||||||
\(559\) | 256.659i | 0.459140i | ||||||||
\(560\) | −12.0421 | + | 9.62820i | −0.0215037 | + | 0.0171932i | ||||
\(561\) | −1488.13 | −2.65264 | ||||||||
\(562\) | −572.957 | −1.01950 | ||||||||
\(563\) | −294.331 | −0.522790 | −0.261395 | − | 0.965232i | \(-0.584182\pi\) | ||||
−0.261395 | + | 0.965232i | \(0.584182\pi\) | |||||||
\(564\) | 490.739 | 0.870104 | ||||||||
\(565\) | 346.219 | − | 276.818i | 0.612777 | − | 0.489943i | ||||
\(566\) | 227.832i | 0.402529i | ||||||||
\(567\) | 124.926 | 0.220328 | ||||||||
\(568\) | 220.032i | 0.387381i | ||||||||
\(569\) | − | 573.397i | − | 1.00773i | −0.863783 | − | 0.503864i | \(-0.831911\pi\) | ||
0.863783 | − | 0.503864i | \(-0.168089\pi\) | |||||||
\(570\) | −573.390 | − | 717.144i | −1.00595 | − | 1.25815i | ||||
\(571\) | − | 139.152i | − | 0.243698i | −0.992549 | − | 0.121849i | \(-0.961118\pi\) | ||
0.992549 | − | 0.121849i | \(-0.0388824\pi\) | |||||||
\(572\) | −70.3597 | −0.123006 | ||||||||
\(573\) | 55.4961 | 0.0968518 | ||||||||
\(574\) | − | 18.4736i | − | 0.0321839i | ||||||
\(575\) | 392.160 | − | 420.518i | 0.682017 | − | 0.731336i | ||||
\(576\) | 165.813 | 0.287869 | ||||||||
\(577\) | − | 784.266i | − | 1.35921i | −0.733577 | − | 0.679606i | \(-0.762151\pi\) | ||
0.733577 | − | 0.679606i | \(-0.237849\pi\) | |||||||
\(578\) | − | 1063.81i | − | 1.84050i | ||||||
\(579\) | −33.3385 | −0.0575794 | ||||||||
\(580\) | 169.856 | − | 135.807i | 0.292854 | − | 0.234151i | ||||
\(581\) | 34.6542 | 0.0596457 | ||||||||
\(582\) | −325.424 | −0.559148 | ||||||||
\(583\) | − | 388.093i | − | 0.665683i | ||||||
\(584\) | 286.833 | 0.491153 | ||||||||
\(585\) | −269.161 | − | 336.643i | −0.460105 | − | 0.575458i | ||||
\(586\) | 265.781i | 0.453552i | ||||||||
\(587\) | 70.9458i | 0.120862i | 0.998172 | + | 0.0604308i | \(0.0192475\pi\) | ||||
−0.998172 | + | 0.0604308i | \(0.980753\pi\) | |||||||
\(588\) | − | 527.836i | − | 0.897681i | ||||||
\(589\) | 759.180i | 1.28893i | ||||||||
\(590\) | −413.711 | − | 517.433i | −0.701205 | − | 0.877005i | ||||
\(591\) | 960.798 | 1.62572 | ||||||||
\(592\) | −24.1579 | −0.0408072 | ||||||||
\(593\) | 519.409i | 0.875900i | 0.898999 | + | 0.437950i | \(0.144295\pi\) | ||||
−0.898999 | + | 0.437950i | \(0.855705\pi\) | |||||||
\(594\) | 764.815i | 1.28757i | ||||||||
\(595\) | 97.1436 | − | 77.6707i | 0.163266 | − | 0.130539i | ||||
\(596\) | 347.560i | 0.583154i | ||||||||
\(597\) | −1352.84 | −2.26607 | ||||||||
\(598\) | −116.814 | − | 68.2318i | −0.195342 | − | 0.114100i | ||||
\(599\) | 841.749 | 1.40526 | 0.702628 | − | 0.711557i | \(-0.252010\pi\) | ||||
0.702628 | + | 0.711557i | \(0.252010\pi\) | |||||||
\(600\) | 84.8367 | − | 376.079i | 0.141394 | − | 0.626799i | ||||
\(601\) | −465.116 | −0.773904 | −0.386952 | − | 0.922100i | \(-0.626472\pi\) | ||||
−0.386952 | + | 0.922100i | \(0.626472\pi\) | |||||||
\(602\) | 67.2779i | 0.111757i | ||||||||
\(603\) | −916.306 | −1.51958 | ||||||||
\(604\) | −131.463 | −0.217654 | ||||||||
\(605\) | −193.123 | + | 154.410i | −0.319211 | + | 0.255224i | ||||
\(606\) | −326.326 | −0.538491 | ||||||||
\(607\) | − | 725.814i | − | 1.19574i | −0.801593 | − | 0.597870i | \(-0.796014\pi\) | ||
0.801593 | − | 0.597870i | \(-0.203986\pi\) | |||||||
\(608\) | −134.725 | −0.221588 | ||||||||
\(609\) | − | 91.4061i | − | 0.150092i | ||||||
\(610\) | −204.944 | + | 163.862i | −0.335974 | + | 0.268627i | ||||
\(611\) | −187.174 | −0.306340 | ||||||||
\(612\) | −1337.61 | −2.18564 | ||||||||
\(613\) | 1054.37 | 1.72002 | 0.860011 | − | 0.510276i | \(-0.170457\pi\) | ||||
0.860011 | + | 0.510276i | \(0.170457\pi\) | |||||||
\(614\) | 506.252 | 0.824515 | ||||||||
\(615\) | 288.469 | + | 360.790i | 0.469055 | + | 0.586651i | ||||
\(616\) | −18.4433 | −0.0299405 | ||||||||
\(617\) | −966.001 | −1.56564 | −0.782821 | − | 0.622247i | \(-0.786220\pi\) | ||||
−0.782821 | + | 0.622247i | \(0.786220\pi\) | |||||||
\(618\) | 1569.57 | 2.53976 | ||||||||
\(619\) | 380.125i | 0.614096i | 0.951694 | + | 0.307048i | \(0.0993412\pi\) | ||||
−0.951694 | + | 0.307048i | \(0.900659\pi\) | |||||||
\(620\) | −248.968 | + | 199.062i | −0.401562 | + | 0.321067i | ||||
\(621\) | −741.685 | + | 1269.78i | −1.19434 | + | 2.04474i | ||||
\(622\) | − | 124.890i | − | 0.200788i | ||||||
\(623\) | − | 57.0905i | − | 0.0916380i | ||||||
\(624\) | −90.7046 | −0.145360 | ||||||||
\(625\) | −564.471 | − | 268.323i | −0.903154 | − | 0.429317i | ||||
\(626\) | − | 639.193i | − | 1.02108i | ||||||
\(627\) | − | 1098.36i | − | 1.75177i | ||||||
\(628\) | 283.323 | 0.451151 | ||||||||
\(629\) | 194.882 | 0.309828 | ||||||||
\(630\) | −70.5551 | − | 88.2439i | −0.111992 | − | 0.140070i | ||||
\(631\) | − | 639.891i | − | 1.01409i | −0.861920 | − | 0.507045i | \(-0.830738\pi\) | ||
0.861920 | − | 0.507045i | \(-0.169262\pi\) | |||||||
\(632\) | −40.9477 | −0.0647906 | ||||||||
\(633\) | − | 1351.16i | − | 2.13454i | ||||||
\(634\) | −770.796 | −1.21577 | ||||||||
\(635\) | 658.835 | + | 824.011i | 1.03753 | + | 1.29766i | ||||
\(636\) | − | 500.313i | − | 0.786656i | ||||||
\(637\) | 201.323i | 0.316049i | ||||||||
\(638\) | 260.146 | 0.407753 | ||||||||
\(639\) | −1612.39 | −2.52330 | ||||||||
\(640\) | −35.3259 | − | 44.1824i | −0.0551967 | − | 0.0690350i | ||||
\(641\) | 871.493i | 1.35958i | 0.733405 | + | 0.679792i | \(0.237930\pi\) | ||||
−0.733405 | + | 0.679792i | \(0.762070\pi\) | |||||||
\(642\) | −1094.49 | −1.70481 | ||||||||
\(643\) | −252.302 | −0.392383 | −0.196191 | − | 0.980566i | \(-0.562857\pi\) | ||||
−0.196191 | + | 0.980566i | \(0.562857\pi\) | |||||||
\(644\) | −30.6205 | − | 17.8855i | −0.0475473 | − | 0.0277726i | ||||
\(645\) | −1050.56 | − | 1313.94i | −1.62877 | − | 2.03712i | ||||
\(646\) | 1086.83 | 1.68240 | ||||||||
\(647\) | 502.810i | 0.777140i | 0.921419 | + | 0.388570i | \(0.127031\pi\) | ||||
−0.921419 | + | 0.388570i | \(0.872969\pi\) | |||||||
\(648\) | 458.353i | 0.707336i | ||||||||
\(649\) | − | 792.486i | − | 1.22109i | ||||||
\(650\) | −32.3577 | + | 143.441i | −0.0497811 | + | 0.220679i | ||||
\(651\) | 133.980i | 0.205806i | ||||||||
\(652\) | − | 331.621i | − | 0.508621i | ||||||
\(653\) | 325.768i | 0.498879i | 0.968390 | + | 0.249439i | \(0.0802464\pi\) | ||||
−0.968390 | + | 0.249439i | \(0.919754\pi\) | |||||||
\(654\) | 638.742i | 0.976670i | ||||||||
\(655\) | 66.4030 | − | 53.0923i | 0.101379 | − | 0.0810569i | ||||
\(656\) | 67.7795 | 0.103322 | ||||||||
\(657\) | 2101.90i | 3.19924i | ||||||||
\(658\) | −49.0637 | −0.0745649 | ||||||||
\(659\) | − | 877.338i | − | 1.33132i | −0.746256 | − | 0.665659i | \(-0.768151\pi\) | ||
0.746256 | − | 0.665659i | \(-0.231849\pi\) | |||||||
\(660\) | 360.200 | − | 287.997i | 0.545758 | − | 0.436358i | ||||
\(661\) | − | 471.430i | − | 0.713207i | −0.934256 | − | 0.356603i | \(-0.883935\pi\) | ||
0.934256 | − | 0.356603i | \(-0.116065\pi\) | |||||||
\(662\) | 749.498i | 1.13217i | ||||||||
\(663\) | 731.715 | 1.10364 | ||||||||
\(664\) | 127.146i | 0.191485i | ||||||||
\(665\) | 57.3271 | + | 71.6995i | 0.0862061 | + | 0.107819i | ||||
\(666\) | − | 177.028i | − | 0.265808i | ||||||
\(667\) | 431.907 | + | 252.278i | 0.647537 | + | 0.378229i | ||||
\(668\) | − | 395.215i | − | 0.591639i | ||||||
\(669\) | −1582.58 | −2.36559 | ||||||||
\(670\) | 195.216 | + | 244.158i | 0.291367 | + | 0.364415i | ||||
\(671\) | −313.887 | −0.467790 | ||||||||
\(672\) | −23.7763 | −0.0353815 | ||||||||
\(673\) | 465.176i | 0.691198i | 0.938382 | + | 0.345599i | \(0.112324\pi\) | ||||
−0.938382 | + | 0.345599i | \(0.887676\pi\) | |||||||
\(674\) | − | 393.554i | − | 0.583908i | ||||||
\(675\) | 1559.22 | + | 351.731i | 2.30995 | + | 0.521083i | ||||
\(676\) | −303.404 | −0.448823 | ||||||||
\(677\) | −157.617 | −0.232816 | −0.116408 | − | 0.993201i | \(-0.537138\pi\) | ||||
−0.116408 | + | 0.993201i | \(0.537138\pi\) | |||||||
\(678\) | 683.588 | 1.00824 | ||||||||
\(679\) | 32.5356 | 0.0479170 | ||||||||
\(680\) | 284.974 | + | 356.420i | 0.419079 | + | 0.524146i | ||||
\(681\) | 1693.93i | 2.48741i | ||||||||
\(682\) | −381.313 | −0.559110 | ||||||||
\(683\) | 387.721i | 0.567674i | 0.958873 | + | 0.283837i | \(0.0916074\pi\) | ||||
−0.958873 | + | 0.283837i | \(0.908393\pi\) | |||||||
\(684\) | − | 987.263i | − | 1.44337i | ||||||
\(685\) | −364.275 | + | 291.255i | −0.531788 | + | 0.425189i | ||||
\(686\) | 106.193i | 0.154801i | ||||||||
\(687\) | 1459.68 | 2.12471 | ||||||||
\(688\) | −246.843 | −0.358783 | ||||||||
\(689\) | 190.825i | 0.276960i | ||||||||
\(690\) | 877.308 | − | 128.839i | 1.27146 | − | 0.186723i | ||||
\(691\) | −443.591 | −0.641954 | −0.320977 | − | 0.947087i | \(-0.604011\pi\) | ||||
−0.320977 | + | 0.947087i | \(0.604011\pi\) | |||||||
\(692\) | − | 258.651i | − | 0.373773i | ||||||
\(693\) | − | 135.152i | − | 0.195025i | ||||||
\(694\) | 907.391 | 1.30748 | ||||||||
\(695\) | −179.693 | + | 143.673i | −0.258551 | + | 0.206723i | ||||
\(696\) | 335.369 | 0.481852 | ||||||||
\(697\) | −546.777 | −0.784472 | ||||||||
\(698\) | 335.822i | 0.481121i | ||||||||
\(699\) | 447.405 | 0.640064 | ||||||||
\(700\) | −8.48191 | + | 37.6001i | −0.0121170 | + | 0.0537145i | ||||
\(701\) | − | 546.567i | − | 0.779696i | −0.920879 | − | 0.389848i | \(-0.872528\pi\) | ||
0.920879 | − | 0.389848i | \(-0.127472\pi\) | |||||||
\(702\) | − | 376.059i | − | 0.535697i | ||||||
\(703\) | 143.838i | 0.204606i | ||||||||
\(704\) | − | 67.6686i | − | 0.0961201i | ||||||
\(705\) | 958.219 | − | 766.140i | 1.35918 | − | 1.08672i | ||||
\(706\) | −420.850 | −0.596105 | ||||||||
\(707\) | 32.6258 | 0.0461468 | ||||||||
\(708\) | − | 1021.64i | − | 1.44299i | ||||||
\(709\) | 448.985i | 0.633265i | 0.948548 | + | 0.316633i | \(0.102552\pi\) | ||||
−0.948548 | + | 0.316633i | \(0.897448\pi\) | |||||||
\(710\) | 343.514 | + | 429.636i | 0.483822 | + | 0.605121i | ||||
\(711\) | − | 300.063i | − | 0.422029i | ||||||
\(712\) | 209.465 | 0.294192 | ||||||||
\(713\) | −633.074 | − | 369.781i | −0.887902 | − | 0.518627i | ||||
\(714\) | 191.804 | 0.268633 | ||||||||
\(715\) | −137.385 | + | 109.845i | −0.192146 | + | 0.153630i | ||||
\(716\) | 107.575 | 0.150245 | ||||||||
\(717\) | − | 82.1351i | − | 0.114554i | ||||||
\(718\) | −206.458 | −0.287545 | ||||||||
\(719\) | 575.714 | 0.800715 | 0.400357 | − | 0.916359i | \(-0.368886\pi\) | ||||
0.400357 | + | 0.916359i | \(0.368886\pi\) | |||||||
\(720\) | 323.767 | − | 258.866i | 0.449676 | − | 0.359537i | ||||
\(721\) | −156.925 | −0.217648 | ||||||||
\(722\) | 291.635i | 0.403927i | ||||||||
\(723\) | −384.308 | −0.531547 | ||||||||
\(724\) | 588.956i | 0.813476i | ||||||||
\(725\) | 119.639 | − | 530.356i | 0.165019 | − | 0.731525i | ||||
\(726\) | −381.308 | −0.525218 | ||||||||
\(727\) | 178.666 | 0.245758 | 0.122879 | − | 0.992422i | \(-0.460787\pi\) | ||||
0.122879 | + | 0.992422i | \(0.460787\pi\) | |||||||
\(728\) | 9.06858 | 0.0124568 | ||||||||
\(729\) | −221.469 | −0.303798 | ||||||||
\(730\) | 560.072 | − | 447.803i | 0.767221 | − | 0.613429i | ||||
\(731\) | 1991.28 | 2.72405 | ||||||||
\(732\) | −404.650 | −0.552800 | ||||||||
\(733\) | 912.345 | 1.24467 | 0.622336 | − | 0.782750i | \(-0.286184\pi\) | ||||
0.622336 | + | 0.782750i | \(0.286184\pi\) | |||||||
\(734\) | − | 971.676i | − | 1.32381i | ||||||
\(735\) | −824.056 | − | 1030.66i | −1.12117 | − | 1.40225i | ||||
\(736\) | 65.6220 | − | 112.347i | 0.0891604 | − | 0.152645i | ||||
\(737\) | 373.946i | 0.507390i | ||||||||
\(738\) | 496.685i | 0.673015i | ||||||||
\(739\) | −274.866 | −0.371942 | −0.185971 | − | 0.982555i | \(-0.559543\pi\) | ||||
−0.185971 | + | 0.982555i | \(0.559543\pi\) | |||||||
\(740\) | −47.1708 | + | 37.7152i | −0.0637443 | + | 0.0509665i | ||||
\(741\) | 540.063i | 0.728830i | ||||||||
\(742\) | 50.0209i | 0.0674136i | ||||||||
\(743\) | −175.014 | −0.235550 | −0.117775 | − | 0.993040i | \(-0.537576\pi\) | ||||
−0.117775 | + | 0.993040i | \(0.537576\pi\) | |||||||
\(744\) | −491.572 | −0.660716 | ||||||||
\(745\) | 542.609 | + | 678.647i | 0.728335 | + | 0.910935i | ||||
\(746\) | 994.728i | 1.33342i | ||||||||
\(747\) | −931.721 | −1.24728 | ||||||||
\(748\) | 545.883i | 0.729790i | ||||||||
\(749\) | 109.426 | 0.146097 | ||||||||
\(750\) | −421.482 | − | 866.781i | −0.561975 | − | 1.15571i | ||||
\(751\) | − | 28.7906i | − | 0.0383364i | −0.999816 | − | 0.0191682i | \(-0.993898\pi\) | ||
0.999816 | − | 0.0191682i | \(-0.00610180\pi\) | |||||||
\(752\) | − | 180.015i | − | 0.239381i | ||||||
\(753\) | 1149.62 | 1.52672 | ||||||||
\(754\) | −127.914 | −0.169647 | ||||||||
\(755\) | −256.695 | + | 205.239i | −0.339993 | + | 0.271840i | ||||
\(756\) | − | 98.5762i | − | 0.130392i | ||||||
\(757\) | 522.188 | 0.689812 | 0.344906 | − | 0.938637i | \(-0.387911\pi\) | ||||
0.344906 | + | 0.938637i | \(0.387911\pi\) | |||||||
\(758\) | 852.756 | 1.12501 | ||||||||
\(759\) | 915.913 | + | 534.988i | 1.20674 | + | 0.704860i | ||||
\(760\) | −263.066 | + | 210.333i | −0.346139 | + | 0.276754i | ||||
\(761\) | 613.477 | 0.806145 | 0.403073 | − | 0.915168i | \(-0.367942\pi\) | ||||
0.403073 | + | 0.915168i | \(0.367942\pi\) | |||||||
\(762\) | 1626.96i | 2.13512i | ||||||||
\(763\) | − | 63.8610i | − | 0.0836972i | ||||||
\(764\) | − | 20.3573i | − | 0.0266456i | ||||||
\(765\) | −2611.83 | + | 2088.28i | −3.41415 | + | 2.72977i | ||||
\(766\) | 316.491i | 0.413173i | ||||||||
\(767\) | 389.665i | 0.508038i | ||||||||
\(768\) | − | 87.2354i | − | 0.113588i | ||||||
\(769\) | − | 938.756i | − | 1.22075i | −0.792113 | − | 0.610374i | \(-0.791019\pi\) | ||
0.792113 | − | 0.610374i | \(-0.208981\pi\) | |||||||
\(770\) | −36.0125 | + | 28.7937i | −0.0467695 | + | 0.0373944i | ||||
\(771\) | 1221.74 | 1.58462 | ||||||||
\(772\) | 12.2293i | 0.0158411i | ||||||||
\(773\) | 121.364 | 0.157004 | 0.0785020 | − | 0.996914i | \(-0.474986\pi\) | ||||
0.0785020 | + | 0.996914i | \(0.474986\pi\) | |||||||
\(774\) | − | 1808.85i | − | 2.33702i | ||||||
\(775\) | −175.362 | + | 777.377i | −0.226274 | + | 1.00307i | ||||
\(776\) | 119.373i | 0.153831i | ||||||||
\(777\) | 25.3845i | 0.0326699i | ||||||||
\(778\) | −493.546 | −0.634377 | ||||||||
\(779\) | − | 403.564i | − | 0.518054i | ||||||
\(780\) | −177.110 | + | 141.608i | −0.227064 | + | 0.181548i | ||||
\(781\) | 658.019i | 0.842534i | ||||||||
\(782\) | −529.373 | + | 906.300i | −0.676948 | + | 1.15895i | ||||
\(783\) | 1390.43i | 1.77578i | ||||||||
\(784\) | −193.623 | −0.246968 | ||||||||
\(785\) | 553.217 | − | 442.322i | 0.704735 | − | 0.563468i | ||||
\(786\) | 131.109 | 0.166805 | ||||||||
\(787\) | 200.567 | 0.254850 | 0.127425 | − | 0.991848i | \(-0.459329\pi\) | ||||
0.127425 | + | 0.991848i | \(0.459329\pi\) | |||||||
\(788\) | − | 352.444i | − | 0.447264i | ||||||
\(789\) | 769.230i | 0.974943i | ||||||||
\(790\) | −79.9546 | + | 63.9274i | −0.101208 | + | 0.0809207i | ||||
\(791\) | −68.3446 | −0.0864027 | ||||||||
\(792\) | 495.872 | 0.626102 | ||||||||
\(793\) | 154.338 | 0.194626 | ||||||||
\(794\) | 179.103 | 0.225571 | ||||||||
\(795\) | −781.087 | − | 976.913i | −0.982500 | − | 1.22882i | ||||
\(796\) | 496.254i | 0.623435i | ||||||||
\(797\) | 291.655 | 0.365941 | 0.182970 | − | 0.983118i | \(-0.441429\pi\) | ||||
0.182970 | + | 0.983118i | \(0.441429\pi\) | |||||||
\(798\) | 141.566i | 0.177401i | ||||||||
\(799\) | 1452.18i | 1.81750i | ||||||||
\(800\) | −137.955 | − | 31.1201i | −0.172444 | − | 0.0389001i | ||||
\(801\) | 1534.95i | 1.91629i | ||||||||
\(802\) | 467.496 | 0.582912 | ||||||||
\(803\) | 857.791 | 1.06823 | ||||||||
\(804\) | 482.075i | 0.599596i | ||||||||
\(805\) | −87.7126 | + | 12.8812i | −0.108960 | + | 0.0160015i | ||||
\(806\) | 187.492 | 0.232620 | ||||||||
\(807\) | 1049.23i | 1.30016i | ||||||||
\(808\) | 119.704i | 0.148149i | ||||||||
\(809\) | −1151.04 | −1.42279 | −0.711394 | − | 0.702793i | \(-0.751936\pi\) | ||||
−0.711394 | + | 0.702793i | \(0.751936\pi\) | |||||||
\(810\) | 715.580 | + | 894.983i | 0.883432 | + | 1.10492i | ||||
\(811\) | −443.021 | −0.546266 | −0.273133 | − | 0.961976i | \(-0.588060\pi\) | ||||
−0.273133 | + | 0.961976i | \(0.588060\pi\) | |||||||
\(812\) | −33.5299 | −0.0412930 | ||||||||
\(813\) | − | 754.509i | − | 0.928055i | ||||||
\(814\) | −72.2455 | −0.0887537 | ||||||||
\(815\) | −517.726 | − | 647.525i | −0.635247 | − | 0.794509i | ||||
\(816\) | 703.728i | 0.862412i | ||||||||
\(817\) | 1469.72i | 1.79892i | ||||||||
\(818\) | 539.603i | 0.659662i | ||||||||
\(819\) | 66.4542i | 0.0811406i | ||||||||
\(820\) | 132.346 | − | 105.817i | 0.161398 | − | 0.129045i | ||||
\(821\) | 86.5798 | 0.105456 | 0.0527282 | − | 0.998609i | \(-0.483208\pi\) | ||||
0.0527282 | + | 0.998609i | \(0.483208\pi\) | |||||||
\(822\) | −719.238 | −0.874985 | ||||||||
\(823\) | − | 1231.62i | − | 1.49651i | −0.663414 | − | 0.748253i | \(-0.730893\pi\) | ||
0.663414 | − | 0.748253i | \(-0.269107\pi\) | |||||||
\(824\) | − | 575.756i | − | 0.698733i | ||||||
\(825\) | 253.709 | − | 1124.69i | 0.307526 | − | 1.36326i | ||||
\(826\) | 102.143i | 0.123659i | ||||||||
\(827\) | −174.508 | −0.211014 | −0.105507 | − | 0.994419i | \(-0.533647\pi\) | ||||
−0.105507 | + | 0.994419i | \(0.533647\pi\) | |||||||
\(828\) | 823.271 | + | 480.876i | 0.994288 | + | 0.580768i | ||||
\(829\) | 106.709 | 0.128720 | 0.0643600 | − | 0.997927i | \(-0.479499\pi\) | ||||
0.0643600 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(830\) | 198.500 | + | 248.266i | 0.239157 | + | 0.299116i | ||||
\(831\) | −2416.87 | −2.90839 | ||||||||
\(832\) | 33.2726i | 0.0399911i | ||||||||
\(833\) | 1561.96 | 1.87510 | ||||||||
\(834\) | −354.793 | −0.425411 | ||||||||
\(835\) | −617.008 | − | 771.698i | −0.738932 | − | 0.924190i | ||||
\(836\) | −402.904 | −0.481943 | ||||||||
\(837\) | − | 2038.05i | − | 2.43494i | ||||||
\(838\) | −177.850 | −0.212232 | ||||||||
\(839\) | 62.4957i | 0.0744883i | 0.999306 | + | 0.0372441i | \(0.0118579\pi\) | ||||
−0.999306 | + | 0.0372441i | \(0.988142\pi\) | |||||||
\(840\) | −46.4258 | + | 37.1196i | −0.0552688 | + | 0.0441899i | ||||
\(841\) | −368.055 | −0.437640 | ||||||||
\(842\) | 125.589 | 0.149156 | ||||||||
\(843\) | −2208.92 | −2.62030 | ||||||||
\(844\) | −495.639 | −0.587250 | ||||||||
\(845\) | −592.428 | + | 473.674i | −0.701099 | + | 0.560561i | ||||
\(846\) | 1319.14 | 1.55927 | ||||||||
\(847\) | 38.1229 | 0.0450094 | ||||||||
\(848\) | −183.527 | −0.216423 | ||||||||
\(849\) | 878.358i | 1.03458i | ||||||||
\(850\) | 1112.88 | + | 251.046i | 1.30927 | + | 0.295348i | ||||
\(851\) | −119.945 | − | 70.0606i | −0.140946 | − | 0.0823273i | ||||
\(852\) | 848.289i | 0.995644i | ||||||||
\(853\) | − | 615.419i | − | 0.721476i | −0.932667 | − | 0.360738i | \(-0.882525\pi\) | ||
0.932667 | − | 0.360738i | \(-0.117475\pi\) | |||||||
\(854\) | 40.4566 | 0.0473730 | ||||||||
\(855\) | −1541.31 | − | 1927.73i | −1.80270 | − | 2.25466i | ||||
\(856\) | 401.485i | 0.469025i | ||||||||
\(857\) | − | 1189.16i | − | 1.38758i | −0.720177 | − | 0.693790i | \(-0.755940\pi\) | ||
0.720177 | − | 0.693790i | \(-0.244060\pi\) | |||||||
\(858\) | −271.257 | −0.316151 | ||||||||
\(859\) | 1006.72 | 1.17196 | 0.585982 | − | 0.810324i | \(-0.300709\pi\) | ||||
0.585982 | + | 0.810324i | \(0.300709\pi\) | |||||||
\(860\) | −481.986 | + | 385.370i | −0.560449 | + | 0.448105i | ||||
\(861\) | − | 71.2210i | − | 0.0827189i | ||||||
\(862\) | 910.526 | 1.05629 | ||||||||
\(863\) | 66.2541i | 0.0767719i | 0.999263 | + | 0.0383859i | \(0.0122216\pi\) | ||||
−0.999263 | + | 0.0383859i | \(0.987778\pi\) | |||||||
\(864\) | 361.676 | 0.418606 | ||||||||
\(865\) | −403.805 | − | 505.042i | −0.466826 | − | 0.583864i | ||||
\(866\) | − | 195.037i | − | 0.225216i | ||||||
\(867\) | − | 4101.29i | − | 4.73044i | ||||||
\(868\) | 49.1470 | 0.0566210 | ||||||||
\(869\) | −122.456 | −0.140916 | ||||||||
\(870\) | 654.843 | − | 523.577i | 0.752693 | − | 0.601813i | ||||
\(871\) | − | 183.869i | − | 0.211101i | ||||||
\(872\) | 234.306 | 0.268699 | ||||||||
\(873\) | −874.762 | −1.00202 | ||||||||
\(874\) | −668.920 | − | 390.719i | −0.765355 | − | 0.447047i | ||||
\(875\) | 42.1394 | + | 86.6601i | 0.0481593 | + | 0.0990401i | ||||
\(876\) | 1105.83 | 1.26236 | ||||||||
\(877\) | 527.609i | 0.601607i | 0.953686 | + | 0.300803i | \(0.0972548\pi\) | ||||
−0.953686 | + | 0.300803i | \(0.902745\pi\) | |||||||
\(878\) | 425.643i | 0.484787i | ||||||||
\(879\) | 1024.67i | 1.16572i | ||||||||
\(880\) | −105.644 | − | 132.130i | −0.120050 | − | 0.150148i | ||||
\(881\) | − | 601.457i | − | 0.682698i | −0.939937 | − | 0.341349i | \(-0.889116\pi\) | ||
0.939937 | − | 0.341349i | \(-0.110884\pi\) | |||||||
\(882\) | − | 1418.86i | − | 1.60869i | ||||||
\(883\) | 692.293i | 0.784024i | 0.919960 | + | 0.392012i | \(0.128221\pi\) | ||||
−0.919960 | + | 0.392012i | \(0.871779\pi\) | |||||||
\(884\) | − | 268.410i | − | 0.303632i | ||||||
\(885\) | −1594.98 | − | 1994.86i | −1.80224 | − | 2.25407i | ||||
\(886\) | 350.753 | 0.395884 | ||||||||
\(887\) | − | 658.875i | − | 0.742813i | −0.928470 | − | 0.371406i | \(-0.878876\pi\) | ||
0.928470 | − | 0.371406i | \(-0.121124\pi\) | |||||||
\(888\) | −93.1358 | −0.104883 | ||||||||
\(889\) | − | 162.662i | − | 0.182972i | ||||||
\(890\) | 409.002 | − | 327.016i | 0.459553 | − | 0.367434i | ||||
\(891\) | 1370.73i | 1.53842i | ||||||||
\(892\) | 580.529i | 0.650817i | ||||||||
\(893\) | −1071.82 | −1.20025 | ||||||||
\(894\) | 1339.95i | 1.49882i | ||||||||
\(895\) | 210.052 | − | 167.946i | 0.234695 | − | 0.187649i | ||||
\(896\) | 8.72173i | 0.00973407i | ||||||||
\(897\) | −450.354 | − | 263.054i | −0.502067 | − | 0.293259i | ||||
\(898\) | 814.850i | 0.907406i | ||||||||
\(899\) | −693.227 | −0.771109 | ||||||||
\(900\) | 228.047 | − | 1010.93i | 0.253385 | − | 1.12325i | ||||
\(901\) | 1480.51 | 1.64319 | ||||||||
\(902\) | 202.698 | 0.224721 | ||||||||
\(903\) | 259.376i | 0.287238i | ||||||||
\(904\) | − | 250.756i | − | 0.277385i | ||||||
\(905\) | 919.477 | + | 1150.00i | 1.01600 | + | 1.27072i | ||||
\(906\) | −506.828 | −0.559413 | ||||||||
\(907\) | −608.891 | −0.671324 | −0.335662 | − | 0.941982i | \(-0.608960\pi\) | ||||
−0.335662 | + | 0.941982i | \(0.608960\pi\) | |||||||
\(908\) | 621.373 | 0.684331 | ||||||||
\(909\) | −877.186 | −0.965001 | ||||||||
\(910\) | 17.7074 | − | 14.1578i | 0.0194586 | − | 0.0155581i | ||||
\(911\) | − | 1653.04i | − | 1.81453i | −0.420557 | − | 0.907266i | \(-0.638165\pi\) | ||
0.420557 | − | 0.907266i | \(-0.361835\pi\) | |||||||
\(912\) | −519.406 | −0.569525 | ||||||||
\(913\) | 380.238i | 0.416471i | ||||||||
\(914\) | 148.147i | 0.162086i | ||||||||
\(915\) | −790.121 | + | 631.738i | −0.863520 | + | 0.690424i | ||||
\(916\) | − | 535.444i | − | 0.584545i | ||||||
\(917\) | −13.1081 | −0.0142946 | ||||||||
\(918\) | −2917.64 | −3.17826 | ||||||||
\(919\) | 1645.72i | 1.79077i | 0.445295 | + | 0.895384i | \(0.353099\pi\) | ||||
−0.445295 | + | 0.895384i | \(0.646901\pi\) | |||||||
\(920\) | −47.2612 | − | 321.817i | −0.0513709 | − | 0.349801i | ||||
\(921\) | 1951.75 | 2.11917 | ||||||||
\(922\) | − | 661.443i | − | 0.717401i | ||||||
\(923\) | − | 323.548i | − | 0.350539i | ||||||
\(924\) | −71.1045 | −0.0769529 | ||||||||
\(925\) | −33.2250 | + | 147.286i | −0.0359189 | + | 0.159228i | ||||
\(926\) | 711.120 | 0.767948 | ||||||||
\(927\) | 4219.12 | 4.55137 | ||||||||
\(928\) | − | 123.021i | − | 0.132566i | ||||||
\(929\) | −430.062 | −0.462930 | −0.231465 | − | 0.972843i | \(-0.574352\pi\) | ||||
−0.231465 | + | 0.972843i | \(0.574352\pi\) | |||||||
\(930\) | −959.847 | + | 767.441i | −1.03209 | + | 0.825206i | ||||
\(931\) | 1152.85i | 1.23829i | ||||||||
\(932\) | − | 164.119i | − | 0.176093i | ||||||
\(933\) | − | 481.488i | − | 0.516064i | ||||||
\(934\) | − | 296.155i | − | 0.317082i | ||||||
\(935\) | 852.231 | + | 1065.89i | 0.911477 | + | 1.13999i | ||||
\(936\) | −243.820 | −0.260492 | ||||||||
\(937\) | −300.016 | −0.320188 | −0.160094 | − | 0.987102i | \(-0.551180\pi\) | ||||
−0.160094 | + | 0.987102i | \(0.551180\pi\) | |||||||
\(938\) | − | 48.1975i | − | 0.0513833i | ||||||
\(939\) | − | 2464.28i | − | 2.62436i | ||||||
\(940\) | −281.038 | − | 351.497i | −0.298977 | − | 0.373933i | ||||
\(941\) | 1207.88i | 1.28361i | 0.766867 | + | 0.641806i | \(0.221815\pi\) | ||||
−0.766867 | + | 0.641806i | \(0.778185\pi\) | |||||||
\(942\) | 1092.29 | 1.15955 | ||||||||
\(943\) | 336.529 | + | 196.568i | 0.356871 | + | 0.208450i | ||||
\(944\) | −374.761 | −0.396993 | ||||||||
\(945\) | −153.897 | − | 192.480i | −0.162854 | − | 0.203683i | ||||
\(946\) | −738.197 | −0.780335 | ||||||||
\(947\) | − | 146.471i | − | 0.154669i | −0.997005 | − | 0.0773344i | \(-0.975359\pi\) | ||
0.997005 | − | 0.0773344i | \(-0.0246409\pi\) | |||||||
\(948\) | −157.865 | −0.166525 | ||||||||
\(949\) | −421.775 | −0.444442 | ||||||||
\(950\) | −185.292 | + | 821.394i | −0.195044 | + | 0.864625i | ||||
\(951\) | −2971.65 | −3.12476 | ||||||||
\(952\) | − | 70.3582i | − | 0.0739057i | ||||||
\(953\) | 224.831 | 0.235919 | 0.117960 | − | 0.993018i | \(-0.462365\pi\) | ||||
0.117960 | + | 0.993018i | \(0.462365\pi\) | |||||||
\(954\) | − | 1344.88i | − | 1.40972i | ||||||
\(955\) | −31.7817 | − | 39.7497i | −0.0332793 | − | 0.0416227i | ||||
\(956\) | −30.1291 | −0.0315158 | ||||||||
\(957\) | 1002.94 | 1.04800 | ||||||||
\(958\) | 630.955 | 0.658617 | ||||||||
\(959\) | 71.9088 | 0.0749832 | ||||||||
\(960\) | −136.192 | − | 170.336i | −0.141866 | − | 0.177433i | ||||
\(961\) | 55.1081 | 0.0573445 | ||||||||
\(962\) | 35.5231 | 0.0369263 | ||||||||
\(963\) | −2942.07 | −3.05510 | ||||||||
\(964\) | 140.973i | 0.146238i | ||||||||
\(965\) | 19.0924 | + | 23.8791i | 0.0197849 | + | 0.0247451i | ||||
\(966\) | −118.051 | − | 68.9540i | −0.122206 | − | 0.0713810i | ||||
\(967\) | 867.622i | 0.897230i | 0.893725 | + | 0.448615i | \(0.148083\pi\) | ||||
−0.893725 | + | 0.448615i | \(0.851917\pi\) | |||||||
\(968\) | 139.873i | 0.144497i | ||||||||
\(969\) | 4190.05 | 4.32410 | ||||||||
\(970\) | 186.365 | + | 233.089i | 0.192129 | + | 0.240298i | ||||
\(971\) | − | 520.260i | − | 0.535799i | −0.963447 | − | 0.267899i | \(-0.913671\pi\) | ||
0.963447 | − | 0.267899i | \(-0.0863295\pi\) | |||||||
\(972\) | 616.242i | 0.633994i | ||||||||
\(973\) | 35.4719 | 0.0364562 | ||||||||
\(974\) | 212.235 | 0.217900 | ||||||||
\(975\) | −124.749 | + | 553.008i | −0.127947 | + | 0.567188i | ||||
\(976\) | 148.435i | 0.152085i | ||||||||
\(977\) | −324.476 | −0.332115 | −0.166057 | − | 0.986116i | \(-0.553104\pi\) | ||||
−0.166057 | + | 0.986116i | \(0.553104\pi\) | |||||||
\(978\) | − | 1278.50i | − | 1.30726i | ||||||
\(979\) | 626.417 | 0.639854 | ||||||||
\(980\) | −378.069 | + | 302.283i | −0.385785 | + | 0.308452i | ||||
\(981\) | 1716.98i | 1.75024i | ||||||||
\(982\) | 1164.28i | 1.18562i | ||||||||
\(983\) | −1278.01 | −1.30011 | −0.650055 | − | 0.759887i | \(-0.725254\pi\) | ||||
−0.650055 | + | 0.759887i | \(0.725254\pi\) | |||||||
\(984\) | 261.310 | 0.265559 | ||||||||
\(985\) | −550.234 | − | 688.183i | −0.558613 | − | 0.698663i | ||||
\(986\) | 992.414i | 1.00650i | ||||||||
\(987\) | −189.155 | −0.191646 | ||||||||
\(988\) | 198.108 | 0.200514 | ||||||||
\(989\) | −1225.59 | − | 715.871i | −1.23922 | − | 0.723833i | ||||
\(990\) | 968.243 | − | 774.155i | 0.978023 | − | 0.781974i | ||||
\(991\) | 977.654 | 0.986533 | 0.493266 | − | 0.869878i | \(-0.335803\pi\) | ||||
0.493266 | + | 0.869878i | \(0.335803\pi\) | |||||||
\(992\) | 180.320i | 0.181775i | ||||||||
\(993\) | 2889.53i | 2.90990i | ||||||||
\(994\) | − | 84.8113i | − | 0.0853232i | ||||||
\(995\) | 774.751 | + | 968.988i | 0.778644 | + | 0.973857i | ||||
\(996\) | 490.186i | 0.492154i | ||||||||
\(997\) | − | 575.147i | − | 0.576877i | −0.957498 | − | 0.288439i | \(-0.906864\pi\) | ||
0.957498 | − | 0.288439i | \(-0.0931362\pi\) | |||||||
\(998\) | 570.697i | 0.571841i | ||||||||
\(999\) | − | 386.139i | − | 0.386525i |
(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 | 230.3.c.a.229.1 | ✓ | 24 | |
5.2 | odd | 4 | 1150.3.d.e.551.21 | 24 | |||
5.3 | odd | 4 | 1150.3.d.e.551.4 | 24 | |||
5.4 | even | 2 | inner | 230.3.c.a.229.24 | yes | 24 | |
23.22 | odd | 2 | inner | 230.3.c.a.229.2 | yes | 24 | |
115.22 | even | 4 | 1150.3.d.e.551.16 | 24 | |||
115.68 | even | 4 | 1150.3.d.e.551.9 | 24 | |||
115.114 | odd | 2 | inner | 230.3.c.a.229.23 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.c.a.229.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
230.3.c.a.229.2 | yes | 24 | 23.22 | odd | 2 | inner | |
230.3.c.a.229.23 | yes | 24 | 115.114 | odd | 2 | inner | |
230.3.c.a.229.24 | yes | 24 | 5.4 | even | 2 | inner | |
1150.3.d.e.551.4 | 24 | 5.3 | odd | 4 | |||
1150.3.d.e.551.9 | 24 | 115.68 | even | 4 | |||
1150.3.d.e.551.16 | 24 | 115.22 | even | 4 | |||
1150.3.d.e.551.21 | 24 | 5.2 | odd | 4 |