Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.b (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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 10 x^{10} - 12 x^{9} + 290 x^{8} + 580 x^{7} + 3656 x^{6} + 5424 x^{5} + \cdots + 48312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.9 | ||
Root | \(4.48261 + 2.99036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.n.122.4 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16906i | 1.08453i | 0.840207 | + | 0.542266i | \(0.182433\pi\) | ||||
−0.840207 | + | 0.542266i | \(0.817567\pi\) | |||||||
\(3\) | 0.240294 | − | 2.99036i | 0.0800979 | − | 0.996787i | ||||
\(4\) | −0.704830 | −0.176208 | ||||||||
\(5\) | 5.33026i | 1.06605i | 0.846099 | + | 0.533026i | \(0.178945\pi\) | ||||
−0.846099 | + | 0.533026i | \(0.821055\pi\) | |||||||
\(6\) | 6.48628 | + | 0.521212i | 1.08105 | + | 0.0868687i | ||||
\(7\) | 12.4613 | 1.78019 | 0.890093 | − | 0.455778i | \(-0.150639\pi\) | ||||
0.890093 | + | 0.455778i | \(0.150639\pi\) | |||||||
\(8\) | 7.14743i | 0.893428i | ||||||||
\(9\) | −8.88452 | − | 1.43713i | −0.987169 | − | 0.159681i | ||||
\(10\) | −11.5617 | −1.15617 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.169366 | + | 2.10770i | −0.0141139 | + | 0.175641i | ||||
\(13\) | −3.85250 | −0.296346 | −0.148173 | − | 0.988961i | \(-0.547339\pi\) | ||||
−0.148173 | + | 0.988961i | \(0.547339\pi\) | |||||||
\(14\) | 27.0293i | 1.93067i | ||||||||
\(15\) | 15.9394 | + | 1.28083i | 1.06263 | + | 0.0853885i | ||||
\(16\) | −18.3225 | −1.14516 | ||||||||
\(17\) | − | 10.2747i | − | 0.604394i | −0.953245 | − | 0.302197i | \(-0.902280\pi\) | ||
0.953245 | − | 0.302197i | \(-0.0977201\pi\) | |||||||
\(18\) | 3.11723 | − | 19.2711i | 0.173179 | − | 1.07062i | ||||
\(19\) | 22.0768 | 1.16194 | 0.580969 | − | 0.813926i | \(-0.302674\pi\) | ||||
0.580969 | + | 0.813926i | \(0.302674\pi\) | |||||||
\(20\) | − | 3.75693i | − | 0.187846i | ||||||
\(21\) | 2.99438 | − | 37.2638i | 0.142589 | − | 1.77447i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.3094i | 0.969972i | 0.874522 | + | 0.484986i | \(0.161175\pi\) | ||||
−0.874522 | + | 0.484986i | \(0.838825\pi\) | |||||||
\(24\) | 21.3734 | + | 1.71748i | 0.890558 | + | 0.0715618i | ||||
\(25\) | −3.41164 | −0.136466 | ||||||||
\(26\) | − | 8.35631i | − | 0.321397i | ||||||
\(27\) | −6.43243 | + | 26.2226i | −0.238238 | + | 0.971207i | ||||
\(28\) | −8.78310 | −0.313682 | ||||||||
\(29\) | 10.8453i | 0.373976i | 0.982362 | + | 0.186988i | \(0.0598726\pi\) | ||||
−0.982362 | + | 0.186988i | \(0.940127\pi\) | |||||||
\(30\) | −2.77820 | + | 34.5735i | −0.0926065 | + | 1.15245i | ||||
\(31\) | −18.9176 | −0.610246 | −0.305123 | − | 0.952313i | \(-0.598698\pi\) | ||||
−0.305123 | + | 0.952313i | \(0.598698\pi\) | |||||||
\(32\) | − | 11.1530i | − | 0.348531i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 22.2865 | 0.655484 | ||||||||
\(35\) | 66.4220i | 1.89777i | ||||||||
\(36\) | 6.26208 | + | 1.01293i | 0.173947 | + | 0.0281370i | ||||
\(37\) | −5.71155 | −0.154366 | −0.0771831 | − | 0.997017i | \(-0.524593\pi\) | ||||
−0.0771831 | + | 0.997017i | \(0.524593\pi\) | |||||||
\(38\) | 47.8860i | 1.26016i | ||||||||
\(39\) | −0.925732 | + | 11.5204i | −0.0237367 | + | 0.295394i | ||||
\(40\) | −38.0976 | −0.952441 | ||||||||
\(41\) | 26.0142i | 0.634492i | 0.948343 | + | 0.317246i | \(0.102758\pi\) | ||||
−0.948343 | + | 0.317246i | \(0.897242\pi\) | |||||||
\(42\) | 80.8275 | + | 6.49499i | 1.92446 | + | 0.154643i | ||||
\(43\) | 62.1199 | 1.44465 | 0.722324 | − | 0.691555i | \(-0.243074\pi\) | ||||
0.722324 | + | 0.691555i | \(0.243074\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.66028 | − | 47.3568i | 0.170228 | − | 1.05237i | ||||
\(46\) | −48.3904 | −1.05196 | ||||||||
\(47\) | 57.0848i | 1.21457i | 0.794484 | + | 0.607285i | \(0.207741\pi\) | ||||
−0.794484 | + | 0.607285i | \(0.792259\pi\) | |||||||
\(48\) | −4.40279 | + | 54.7910i | −0.0917248 | + | 1.14148i | ||||
\(49\) | 106.284 | 2.16907 | ||||||||
\(50\) | − | 7.40007i | − | 0.148001i | ||||||
\(51\) | −30.7251 | − | 2.46895i | −0.602452 | − | 0.0484107i | ||||
\(52\) | 2.71536 | 0.0522184 | ||||||||
\(53\) | − | 55.7779i | − | 1.05241i | −0.850357 | − | 0.526207i | \(-0.823614\pi\) | ||
0.850357 | − | 0.526207i | \(-0.176386\pi\) | |||||||
\(54\) | −56.8784 | − | 13.9523i | −1.05330 | − | 0.258377i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 89.0663i | 1.59047i | ||||||||
\(57\) | 5.30492 | − | 66.0176i | 0.0930688 | − | 1.15820i | ||||
\(58\) | −23.5242 | −0.405589 | ||||||||
\(59\) | − | 67.0487i | − | 1.13642i | −0.822884 | − | 0.568209i | \(-0.807636\pi\) | ||
0.822884 | − | 0.568209i | \(-0.192364\pi\) | |||||||
\(60\) | −11.2346 | − | 0.902766i | −0.187243 | − | 0.0150461i | ||||
\(61\) | −20.3248 | −0.333194 | −0.166597 | − | 0.986025i | \(-0.553278\pi\) | ||||
−0.166597 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(62\) | − | 41.0335i | − | 0.661830i | ||||||
\(63\) | −110.713 | − | 17.9085i | −1.75734 | − | 0.284262i | ||||
\(64\) | −49.0986 | −0.767165 | ||||||||
\(65\) | − | 20.5348i | − | 0.315920i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −88.3646 | −1.31887 | −0.659437 | − | 0.751760i | \(-0.729205\pi\) | ||||
−0.659437 | + | 0.751760i | \(0.729205\pi\) | |||||||
\(68\) | 7.24192i | 0.106499i | ||||||||
\(69\) | 66.7130 | + | 5.36080i | 0.966855 | + | 0.0776927i | ||||
\(70\) | −144.073 | −2.05819 | ||||||||
\(71\) | − | 106.717i | − | 1.50305i | −0.659703 | − | 0.751526i | \(-0.729318\pi\) | ||
0.659703 | − | 0.751526i | \(-0.270682\pi\) | |||||||
\(72\) | 10.2718 | − | 63.5015i | 0.142664 | − | 0.881965i | ||||
\(73\) | 19.6558 | 0.269257 | 0.134629 | − | 0.990896i | \(-0.457016\pi\) | ||||
0.134629 | + | 0.990896i | \(0.457016\pi\) | |||||||
\(74\) | − | 12.3887i | − | 0.167415i | ||||||
\(75\) | −0.819797 | + | 10.2020i | −0.0109306 | + | 0.136027i | ||||
\(76\) | −15.5604 | −0.204742 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −24.9884 | − | 2.00797i | −0.320364 | − | 0.0257432i | ||||
\(79\) | 35.7157 | 0.452097 | 0.226049 | − | 0.974116i | \(-0.427419\pi\) | ||||
0.226049 | + | 0.974116i | \(0.427419\pi\) | |||||||
\(80\) | − | 97.6638i | − | 1.22080i | ||||||
\(81\) | 76.8693 | + | 25.5364i | 0.949004 | + | 0.315264i | ||||
\(82\) | −56.4263 | −0.688126 | ||||||||
\(83\) | 81.3571i | 0.980206i | 0.871665 | + | 0.490103i | \(0.163041\pi\) | ||||
−0.871665 | + | 0.490103i | \(0.836959\pi\) | |||||||
\(84\) | −2.11053 | + | 26.2647i | −0.0251253 | + | 0.312674i | ||||
\(85\) | 54.7668 | 0.644315 | ||||||||
\(86\) | 134.742i | 1.56677i | ||||||||
\(87\) | 32.4314 | + | 2.60606i | 0.372775 | + | 0.0299547i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 120.618i | − | 1.35526i | −0.735405 | − | 0.677628i | \(-0.763008\pi\) | ||
0.735405 | − | 0.677628i | \(-0.236992\pi\) | |||||||
\(90\) | 102.720 | + | 16.6156i | 1.14133 | + | 0.184618i | ||||
\(91\) | −48.0072 | −0.527552 | ||||||||
\(92\) | − | 15.7243i | − | 0.170916i | ||||||
\(93\) | −4.54579 | + | 56.5705i | −0.0488794 | + | 0.608285i | ||||
\(94\) | −123.820 | −1.31724 | ||||||||
\(95\) | 117.675i | 1.23869i | ||||||||
\(96\) | −33.3515 | − | 2.68000i | −0.347411 | − | 0.0279166i | ||||
\(97\) | −85.3365 | −0.879757 | −0.439879 | − | 0.898057i | \(-0.644979\pi\) | ||||
−0.439879 | + | 0.898057i | \(0.644979\pi\) | |||||||
\(98\) | 230.537i | 2.35242i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.40463 | 0.0240463 | ||||||||
\(101\) | − | 62.9870i | − | 0.623634i | −0.950142 | − | 0.311817i | \(-0.899062\pi\) | ||
0.950142 | − | 0.311817i | \(-0.100938\pi\) | |||||||
\(102\) | 5.35530 | − | 66.6446i | 0.0525029 | − | 0.653378i | ||||
\(103\) | 5.92433 | 0.0575178 | 0.0287589 | − | 0.999586i | \(-0.490844\pi\) | ||||
0.0287589 | + | 0.999586i | \(0.490844\pi\) | |||||||
\(104\) | − | 27.5355i | − | 0.264764i | ||||||
\(105\) | 198.626 | + | 15.9608i | 1.89167 | + | 0.152008i | ||||
\(106\) | 120.986 | 1.14137 | ||||||||
\(107\) | − | 132.855i | − | 1.24164i | −0.783954 | − | 0.620819i | \(-0.786800\pi\) | ||
0.783954 | − | 0.620819i | \(-0.213200\pi\) | |||||||
\(108\) | 4.53377 | − | 18.4825i | 0.0419794 | − | 0.171134i | ||||
\(109\) | −91.4741 | −0.839212 | −0.419606 | − | 0.907706i | \(-0.637832\pi\) | ||||
−0.419606 | + | 0.907706i | \(0.637832\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.37245 | + | 17.0796i | −0.0123644 | + | 0.153870i | ||||
\(112\) | −228.323 | −2.03860 | ||||||||
\(113\) | − | 84.6038i | − | 0.748706i | −0.927286 | − | 0.374353i | \(-0.877865\pi\) | ||
0.927286 | − | 0.374353i | \(-0.122135\pi\) | |||||||
\(114\) | 143.196 | + | 11.5067i | 1.25611 | + | 0.100936i | ||||
\(115\) | −118.915 | −1.03404 | ||||||||
\(116\) | − | 7.64410i | − | 0.0658974i | ||||||
\(117\) | 34.2276 | + | 5.53655i | 0.292544 | + | 0.0473209i | ||||
\(118\) | 145.433 | 1.23248 | ||||||||
\(119\) | − | 128.036i | − | 1.07593i | ||||||
\(120\) | −9.15462 | + | 113.926i | −0.0762885 | + | 0.949381i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 44.0858i | − | 0.361359i | ||||||
\(123\) | 77.7917 | + | 6.25104i | 0.632453 | + | 0.0508215i | ||||
\(124\) | 13.3337 | 0.107530 | ||||||||
\(125\) | 115.071i | 0.920572i | ||||||||
\(126\) | 38.8447 | − | 240.143i | 0.308291 | − | 1.90589i | ||||
\(127\) | 35.2600 | 0.277638 | 0.138819 | − | 0.990318i | \(-0.455669\pi\) | ||||
0.138819 | + | 0.990318i | \(0.455669\pi\) | |||||||
\(128\) | − | 151.110i | − | 1.18055i | ||||||
\(129\) | 14.9270 | − | 185.761i | 0.115713 | − | 1.44001i | ||||
\(130\) | 44.5413 | 0.342625 | ||||||||
\(131\) | − | 119.526i | − | 0.912414i | −0.889874 | − | 0.456207i | \(-0.849208\pi\) | ||
0.889874 | − | 0.456207i | \(-0.150792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 275.106 | 2.06847 | ||||||||
\(134\) | − | 191.668i | − | 1.43036i | ||||||
\(135\) | −139.773 | − | 34.2865i | −1.03536 | − | 0.253974i | ||||
\(136\) | 73.4377 | 0.539983 | ||||||||
\(137\) | − | 67.5636i | − | 0.493165i | −0.969122 | − | 0.246582i | \(-0.920692\pi\) | ||
0.969122 | − | 0.246582i | \(-0.0793076\pi\) | |||||||
\(138\) | −11.6279 | + | 144.705i | −0.0842602 | + | 1.04858i | ||||
\(139\) | −40.8446 | −0.293846 | −0.146923 | − | 0.989148i | \(-0.546937\pi\) | ||||
−0.146923 | + | 0.989148i | \(0.546937\pi\) | |||||||
\(140\) | − | 46.8162i | − | 0.334401i | ||||||
\(141\) | 170.704 | + | 13.7171i | 1.21067 | + | 0.0972845i | ||||
\(142\) | 231.475 | 1.63011 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 162.787 | + | 26.3319i | 1.13046 | + | 0.182860i | ||||
\(145\) | −57.8083 | −0.398678 | ||||||||
\(146\) | 42.6346i | 0.292018i | ||||||||
\(147\) | 25.5394 | − | 317.828i | 0.173738 | − | 2.16210i | ||||
\(148\) | 4.02567 | 0.0272005 | ||||||||
\(149\) | − | 126.283i | − | 0.847535i | −0.905771 | − | 0.423768i | \(-0.860707\pi\) | ||
0.905771 | − | 0.423768i | \(-0.139293\pi\) | |||||||
\(150\) | −22.1289 | − | 1.77819i | −0.147526 | − | 0.0118546i | ||||
\(151\) | 144.453 | 0.956645 | 0.478322 | − | 0.878184i | \(-0.341245\pi\) | ||||
0.478322 | + | 0.878184i | \(0.341245\pi\) | |||||||
\(152\) | 157.792i | 1.03811i | ||||||||
\(153\) | −14.7661 | + | 91.2858i | −0.0965104 | + | 0.596639i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 100.836i | − | 0.650553i | ||||||
\(156\) | 0.652484 | − | 8.11990i | 0.00418259 | − | 0.0520507i | ||||
\(157\) | −21.7969 | −0.138834 | −0.0694168 | − | 0.997588i | \(-0.522114\pi\) | ||||
−0.0694168 | + | 0.997588i | \(0.522114\pi\) | |||||||
\(158\) | 77.4695i | 0.490313i | ||||||||
\(159\) | −166.796 | − | 13.4031i | −1.04903 | − | 0.0842961i | ||||
\(160\) | 59.4484 | 0.371552 | ||||||||
\(161\) | 278.004i | 1.72673i | ||||||||
\(162\) | −55.3901 | + | 166.734i | −0.341914 | + | 1.02922i | ||||
\(163\) | −116.768 | −0.716367 | −0.358184 | − | 0.933651i | \(-0.616604\pi\) | ||||
−0.358184 | + | 0.933651i | \(0.616604\pi\) | |||||||
\(164\) | − | 18.3356i | − | 0.111802i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −176.469 | −1.06306 | ||||||||
\(167\) | − | 7.56849i | − | 0.0453203i | −0.999743 | − | 0.0226602i | \(-0.992786\pi\) | ||
0.999743 | − | 0.0226602i | \(-0.00721357\pi\) | |||||||
\(168\) | 266.340 | + | 21.4021i | 1.58536 | + | 0.127393i | ||||
\(169\) | −154.158 | −0.912179 | ||||||||
\(170\) | 118.793i | 0.698780i | ||||||||
\(171\) | −196.142 | − | 31.7273i | −1.14703 | − | 0.185540i | ||||
\(172\) | −43.7840 | −0.254558 | ||||||||
\(173\) | 62.4526i | 0.360998i | 0.983575 | + | 0.180499i | \(0.0577712\pi\) | ||||
−0.983575 | + | 0.180499i | \(0.942229\pi\) | |||||||
\(174\) | −5.65271 | + | 70.3457i | −0.0324868 | + | 0.404286i | ||||
\(175\) | −42.5135 | −0.242935 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −200.500 | − | 16.1114i | −1.13277 | − | 0.0910247i | ||||
\(178\) | 261.627 | 1.46982 | ||||||||
\(179\) | − | 212.091i | − | 1.18486i | −0.805620 | − | 0.592432i | \(-0.798168\pi\) | ||
0.805620 | − | 0.592432i | \(-0.201832\pi\) | |||||||
\(180\) | −5.39919 | + | 33.3785i | −0.0299955 | + | 0.185436i | ||||
\(181\) | 192.168 | 1.06170 | 0.530852 | − | 0.847464i | \(-0.321872\pi\) | ||||
0.530852 | + | 0.847464i | \(0.321872\pi\) | |||||||
\(182\) | − | 104.131i | − | 0.572146i | ||||||
\(183\) | −4.88393 | + | 60.7785i | −0.0266881 | + | 0.332123i | ||||
\(184\) | −159.454 | −0.866601 | ||||||||
\(185\) | − | 30.4440i | − | 0.164562i | ||||||
\(186\) | −122.705 | − | 9.86009i | −0.659704 | − | 0.0530112i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 40.2351i | − | 0.214016i | ||||||
\(189\) | −80.1565 | + | 326.768i | −0.424109 | + | 1.72893i | ||||
\(190\) | −255.245 | −1.34339 | ||||||||
\(191\) | 215.925i | 1.13050i | 0.824920 | + | 0.565249i | \(0.191220\pi\) | ||||
−0.824920 | + | 0.565249i | \(0.808780\pi\) | |||||||
\(192\) | −11.7981 | + | 146.822i | −0.0614484 | + | 0.764700i | ||||
\(193\) | −118.484 | −0.613909 | −0.306954 | − | 0.951724i | \(-0.599310\pi\) | ||||
−0.306954 | + | 0.951724i | \(0.599310\pi\) | |||||||
\(194\) | − | 185.100i | − | 0.954124i | ||||||
\(195\) | −61.4065 | − | 4.93439i | −0.314905 | − | 0.0253046i | ||||
\(196\) | −74.9123 | −0.382206 | ||||||||
\(197\) | − | 78.5365i | − | 0.398662i | −0.979932 | − | 0.199331i | \(-0.936123\pi\) | ||
0.979932 | − | 0.199331i | \(-0.0638769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −223.166 | −1.12144 | −0.560719 | − | 0.828006i | \(-0.689475\pi\) | ||||
−0.560719 | + | 0.828006i | \(0.689475\pi\) | |||||||
\(200\) | − | 24.3845i | − | 0.121922i | ||||||
\(201\) | −21.2335 | + | 264.242i | −0.105639 | + | 1.31464i | ||||
\(202\) | 136.623 | 0.676350 | ||||||||
\(203\) | 135.147i | 0.665748i | ||||||||
\(204\) | 21.6559 | + | 1.74019i | 0.106157 | + | 0.00853033i | ||||
\(205\) | −138.662 | −0.676401 | ||||||||
\(206\) | 12.8502i | 0.0623799i | ||||||||
\(207\) | 32.0615 | − | 198.208i | 0.154886 | − | 0.957526i | ||||
\(208\) | 70.5876 | 0.339363 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −34.6199 | + | 430.831i | −0.164857 | + | 2.05158i | ||||
\(211\) | −68.8093 | −0.326110 | −0.163055 | − | 0.986617i | \(-0.552135\pi\) | ||||
−0.163055 | + | 0.986617i | \(0.552135\pi\) | |||||||
\(212\) | 39.3139i | 0.185443i | ||||||||
\(213\) | −319.122 | − | 25.6434i | −1.49822 | − | 0.120391i | ||||
\(214\) | 288.171 | 1.34659 | ||||||||
\(215\) | 331.115i | 1.54007i | ||||||||
\(216\) | −187.424 | − | 45.9754i | −0.867704 | − | 0.212849i | ||||
\(217\) | −235.738 | −1.08635 | ||||||||
\(218\) | − | 198.413i | − | 0.910151i | ||||||
\(219\) | 4.72316 | − | 58.7779i | 0.0215670 | − | 0.268392i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 39.5833i | 0.179110i | ||||||||
\(222\) | −37.0467 | − | 2.97693i | −0.166877 | − | 0.0134096i | ||||
\(223\) | 362.880 | 1.62726 | 0.813632 | − | 0.581380i | \(-0.197487\pi\) | ||||
0.813632 | + | 0.581380i | \(0.197487\pi\) | |||||||
\(224\) | − | 138.981i | − | 0.620451i | ||||||
\(225\) | 30.3108 | + | 4.90298i | 0.134715 | + | 0.0217910i | ||||
\(226\) | 183.511 | 0.811995 | ||||||||
\(227\) | − | 385.017i | − | 1.69611i | −0.529910 | − | 0.848054i | \(-0.677774\pi\) | ||
0.529910 | − | 0.848054i | \(-0.322226\pi\) | |||||||
\(228\) | −3.73907 | + | 46.5312i | −0.0163994 | + | 0.204084i | ||||
\(229\) | 114.821 | 0.501400 | 0.250700 | − | 0.968065i | \(-0.419339\pi\) | ||||
0.250700 | + | 0.968065i | \(0.419339\pi\) | |||||||
\(230\) | − | 257.933i | − | 1.12145i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −77.5161 | −0.334121 | ||||||||
\(233\) | − | 44.4204i | − | 0.190645i | −0.995446 | − | 0.0953227i | \(-0.969612\pi\) | ||
0.995446 | − | 0.0953227i | \(-0.0303883\pi\) | |||||||
\(234\) | −12.0091 | + | 74.2418i | −0.0513210 | + | 0.317273i | ||||
\(235\) | −304.276 | −1.29479 | ||||||||
\(236\) | 47.2579i | 0.200245i | ||||||||
\(237\) | 8.58226 | − | 106.803i | 0.0362121 | − | 0.450645i | ||||
\(238\) | 277.718 | 1.16688 | ||||||||
\(239\) | 463.337i | 1.93865i | 0.245789 | + | 0.969323i | \(0.420953\pi\) | ||||
−0.245789 | + | 0.969323i | \(0.579047\pi\) | |||||||
\(240\) | −292.050 | − | 23.4680i | −1.21688 | − | 0.0977834i | ||||
\(241\) | −345.385 | −1.43313 | −0.716566 | − | 0.697520i | \(-0.754287\pi\) | ||||
−0.716566 | + | 0.697520i | \(0.754287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 94.8343 | − | 223.731i | 0.390265 | − | 0.920703i | ||||
\(244\) | 14.3255 | 0.0587112 | ||||||||
\(245\) | 566.522i | 2.31234i | ||||||||
\(246\) | −13.5589 | + | 168.735i | −0.0551175 | + | 0.685915i | ||||
\(247\) | −85.0509 | −0.344336 | ||||||||
\(248\) | − | 135.212i | − | 0.545211i | ||||||
\(249\) | 243.287 | + | 19.5496i | 0.977056 | + | 0.0785125i | ||||
\(250\) | −249.597 | −0.998389 | ||||||||
\(251\) | 215.718i | 0.859436i | 0.902963 | + | 0.429718i | \(0.141387\pi\) | ||||
−0.902963 | + | 0.429718i | \(0.858613\pi\) | |||||||
\(252\) | 78.0336 | + | 12.6225i | 0.309657 | + | 0.0500892i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 76.4812i | 0.301107i | ||||||||
\(255\) | 13.1601 | − | 163.773i | 0.0516083 | − | 0.642245i | ||||
\(256\) | 131.372 | 0.513173 | ||||||||
\(257\) | − | 69.8784i | − | 0.271900i | −0.990716 | − | 0.135950i | \(-0.956591\pi\) | ||
0.990716 | − | 0.135950i | \(-0.0434087\pi\) | |||||||
\(258\) | 402.927 | + | 32.3776i | 1.56173 | + | 0.125495i | ||||
\(259\) | −71.1734 | −0.274801 | ||||||||
\(260\) | 14.4736i | 0.0556675i | ||||||||
\(261\) | 15.5861 | − | 96.3554i | 0.0597170 | − | 0.369178i | ||||
\(262\) | 259.260 | 0.989541 | ||||||||
\(263\) | − | 445.231i | − | 1.69290i | −0.532472 | − | 0.846448i | \(-0.678737\pi\) | ||
0.532472 | − | 0.846448i | \(-0.321263\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 297.311 | 1.12193 | ||||||||
\(266\) | 596.722i | 2.24332i | ||||||||
\(267\) | −360.691 | − | 28.9837i | −1.35090 | − | 0.108553i | ||||
\(268\) | 62.2820 | 0.232396 | ||||||||
\(269\) | 134.124i | 0.498603i | 0.968426 | + | 0.249301i | \(0.0802010\pi\) | ||||
−0.968426 | + | 0.249301i | \(0.919799\pi\) | |||||||
\(270\) | 74.3696 | − | 303.177i | 0.275443 | − | 1.12288i | ||||
\(271\) | −204.760 | −0.755573 | −0.377787 | − | 0.925893i | \(-0.623315\pi\) | ||||
−0.377787 | + | 0.925893i | \(0.623315\pi\) | |||||||
\(272\) | 188.259i | 0.692127i | ||||||||
\(273\) | −11.5358 | + | 143.559i | −0.0422558 | + | 0.525857i | ||||
\(274\) | 146.550 | 0.534853 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −47.0213 | − | 3.77845i | −0.170367 | − | 0.0136900i | ||||
\(277\) | −58.4995 | −0.211190 | −0.105595 | − | 0.994409i | \(-0.533675\pi\) | ||||
−0.105595 | + | 0.994409i | \(0.533675\pi\) | |||||||
\(278\) | − | 88.5944i | − | 0.318685i | ||||||
\(279\) | 168.074 | + | 27.1871i | 0.602415 | + | 0.0974447i | ||||
\(280\) | −474.746 | −1.69552 | ||||||||
\(281\) | − | 1.42405i | − | 0.00506781i | −0.999997 | − | 0.00253390i | \(-0.999193\pi\) | ||
0.999997 | − | 0.00253390i | \(-0.000806567\pi\) | |||||||
\(282\) | −29.7533 | + | 370.268i | −0.105508 | + | 1.31301i | ||||
\(283\) | 293.260 | 1.03625 | 0.518127 | − | 0.855304i | \(-0.326630\pi\) | ||||
0.518127 | + | 0.855304i | \(0.326630\pi\) | |||||||
\(284\) | 75.2172i | 0.264849i | ||||||||
\(285\) | 351.891 | + | 28.2766i | 1.23471 | + | 0.0992161i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 324.170i | 1.12951i | ||||||||
\(288\) | −16.0283 | + | 99.0890i | −0.0556539 | + | 0.344059i | ||||
\(289\) | 183.431 | 0.634708 | ||||||||
\(290\) | − | 125.390i | − | 0.432379i | ||||||
\(291\) | −20.5058 | + | 255.187i | −0.0704667 | + | 0.876931i | ||||
\(292\) | −13.8540 | −0.0474452 | ||||||||
\(293\) | 324.008i | 1.10583i | 0.833238 | + | 0.552914i | \(0.186484\pi\) | ||||
−0.833238 | + | 0.552914i | \(0.813516\pi\) | |||||||
\(294\) | 689.389 | + | 55.3966i | 2.34486 | + | 0.188424i | ||||
\(295\) | 357.387 | 1.21148 | ||||||||
\(296\) | − | 40.8229i | − | 0.137915i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 273.915 | 0.919178 | ||||||||
\(299\) | − | 85.9468i | − | 0.287448i | ||||||
\(300\) | 0.577818 | − | 7.19071i | 0.00192606 | − | 0.0239690i | ||||
\(301\) | 774.095 | 2.57174 | ||||||||
\(302\) | 313.328i | 1.03751i | ||||||||
\(303\) | −188.354 | − | 15.1354i | −0.621630 | − | 0.0499518i | ||||
\(304\) | −404.503 | −1.33060 | ||||||||
\(305\) | − | 108.336i | − | 0.355201i | ||||||
\(306\) | −198.004 | − | 32.0286i | −0.647073 | − | 0.104668i | ||||
\(307\) | −292.921 | −0.954140 | −0.477070 | − | 0.878865i | \(-0.658301\pi\) | ||||
−0.477070 | + | 0.878865i | \(0.658301\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.42358 | − | 17.7159i | 0.00460706 | − | 0.0573330i | ||||
\(310\) | 218.719 | 0.705545 | ||||||||
\(311\) | − | 338.912i | − | 1.08975i | −0.838517 | − | 0.544875i | \(-0.816577\pi\) | ||
0.838517 | − | 0.544875i | \(-0.183423\pi\) | |||||||
\(312\) | −82.3410 | − | 6.61660i | −0.263913 | − | 0.0212071i | ||||
\(313\) | −356.787 | −1.13989 | −0.569947 | − | 0.821681i | \(-0.693036\pi\) | ||||
−0.569947 | + | 0.821681i | \(0.693036\pi\) | |||||||
\(314\) | − | 47.2788i | − | 0.150569i | ||||||
\(315\) | 95.4570 | − | 590.127i | 0.303038 | − | 1.87342i | ||||
\(316\) | −25.1735 | −0.0796629 | ||||||||
\(317\) | − | 482.485i | − | 1.52204i | −0.648731 | − | 0.761018i | \(-0.724700\pi\) | ||
0.648731 | − | 0.761018i | \(-0.275300\pi\) | |||||||
\(318\) | 29.0721 | − | 361.791i | 0.0914217 | − | 1.13771i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 261.708i | − | 0.817838i | ||||||
\(321\) | −397.285 | − | 31.9243i | −1.23765 | − | 0.0994526i | ||||
\(322\) | −603.007 | −1.87269 | ||||||||
\(323\) | − | 226.833i | − | 0.702268i | ||||||
\(324\) | −54.1798 | − | 17.9988i | −0.167222 | − | 0.0555520i | ||||
\(325\) | 13.1434 | 0.0404411 | ||||||||
\(326\) | − | 253.277i | − | 0.776922i | ||||||
\(327\) | −21.9807 | + | 273.541i | −0.0672191 | + | 0.836516i | ||||
\(328\) | −185.934 | −0.566873 | ||||||||
\(329\) | 711.351i | 2.16216i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −131.863 | −0.398378 | −0.199189 | − | 0.979961i | \(-0.563831\pi\) | ||||
−0.199189 | + | 0.979961i | \(0.563831\pi\) | |||||||
\(332\) | − | 57.3429i | − | 0.172720i | ||||||
\(333\) | 50.7444 | + | 8.20825i | 0.152386 | + | 0.0246494i | ||||
\(334\) | 16.4165 | 0.0491513 | ||||||||
\(335\) | − | 471.006i | − | 1.40599i | ||||||
\(336\) | −54.8645 | + | 682.767i | −0.163287 | + | 2.03205i | ||||
\(337\) | 550.415 | 1.63328 | 0.816639 | − | 0.577149i | \(-0.195835\pi\) | ||||
0.816639 | + | 0.577149i | \(0.195835\pi\) | |||||||
\(338\) | − | 334.379i | − | 0.989286i | ||||||
\(339\) | −252.996 | − | 20.3298i | −0.746300 | − | 0.0599698i | ||||
\(340\) | −38.6013 | −0.113533 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 68.8184 | − | 425.444i | 0.201223 | − | 1.24399i | ||||
\(343\) | 713.836 | 2.08115 | ||||||||
\(344\) | 443.997i | 1.29069i | ||||||||
\(345\) | −28.5744 | + | 355.598i | −0.0828245 | + | 1.03072i | ||||
\(346\) | −135.463 | −0.391513 | ||||||||
\(347\) | 123.006i | 0.354484i | 0.984167 | + | 0.177242i | \(0.0567175\pi\) | ||||
−0.984167 | + | 0.177242i | \(0.943282\pi\) | |||||||
\(348\) | −22.8586 | − | 1.83683i | −0.0656857 | − | 0.00527825i | ||||
\(349\) | 123.310 | 0.353323 | 0.176662 | − | 0.984272i | \(-0.443470\pi\) | ||||
0.176662 | + | 0.984272i | \(0.443470\pi\) | |||||||
\(350\) | − | 92.2145i | − | 0.263470i | ||||||
\(351\) | 24.7810 | − | 101.023i | 0.0706010 | − | 0.287813i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 473.431i | 1.34116i | 0.741836 | + | 0.670582i | \(0.233956\pi\) | ||||
−0.741836 | + | 0.670582i | \(0.766044\pi\) | |||||||
\(354\) | 34.9466 | − | 434.896i | 0.0987192 | − | 1.22852i | ||||
\(355\) | 568.828 | 1.60233 | ||||||||
\(356\) | 85.0150i | 0.238806i | ||||||||
\(357\) | −382.874 | − | 30.7663i | −1.07248 | − | 0.0861801i | ||||
\(358\) | 460.038 | 1.28502 | ||||||||
\(359\) | 96.0299i | 0.267493i | 0.991016 | + | 0.133746i | \(0.0427007\pi\) | ||||
−0.991016 | + | 0.133746i | \(0.957299\pi\) | |||||||
\(360\) | 338.479 | + | 54.7513i | 0.940220 | + | 0.152087i | ||||
\(361\) | 126.386 | 0.350099 | ||||||||
\(362\) | 416.825i | 1.15145i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 33.8369 | 0.0929586 | ||||||||
\(365\) | 104.770i | 0.287042i | ||||||||
\(366\) | −131.832 | − | 10.5935i | −0.360198 | − | 0.0289441i | ||||
\(367\) | 450.970 | 1.22880 | 0.614400 | − | 0.788995i | \(-0.289398\pi\) | ||||
0.614400 | + | 0.788995i | \(0.289398\pi\) | |||||||
\(368\) | − | 408.764i | − | 1.11077i | ||||||
\(369\) | 37.3857 | − | 231.123i | 0.101316 | − | 0.626350i | ||||
\(370\) | 66.0350 | 0.178473 | ||||||||
\(371\) | − | 695.065i | − | 1.87349i | ||||||
\(372\) | 3.20401 | − | 39.8726i | 0.00861292 | − | 0.107184i | ||||
\(373\) | 522.030 | 1.39954 | 0.699772 | − | 0.714366i | \(-0.253285\pi\) | ||||
0.699772 | + | 0.714366i | \(0.253285\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 344.105 | + | 27.6510i | 0.917614 | + | 0.0737359i | ||||
\(376\) | −408.009 | −1.08513 | ||||||||
\(377\) | − | 41.7816i | − | 0.110826i | ||||||
\(378\) | −708.779 | − | 173.864i | −1.87508 | − | 0.459959i | ||||
\(379\) | 667.354 | 1.76083 | 0.880414 | − | 0.474206i | \(-0.157265\pi\) | ||||
0.880414 | + | 0.474206i | \(0.157265\pi\) | |||||||
\(380\) | − | 82.9409i | − | 0.218266i | ||||||
\(381\) | 8.47277 | − | 105.440i | 0.0222382 | − | 0.276746i | ||||
\(382\) | −468.355 | −1.22606 | ||||||||
\(383\) | 504.576i | 1.31743i | 0.752392 | + | 0.658716i | \(0.228900\pi\) | ||||
−0.752392 | + | 0.658716i | \(0.771100\pi\) | |||||||
\(384\) | −451.873 | − | 36.3108i | −1.17675 | − | 0.0945593i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 257.000i | − | 0.665803i | ||||||
\(387\) | −551.905 | − | 89.2744i | −1.42611 | − | 0.230683i | ||||
\(388\) | 60.1477 | 0.155020 | ||||||||
\(389\) | 92.4975i | 0.237783i | 0.992907 | + | 0.118891i | \(0.0379340\pi\) | ||||
−0.992907 | + | 0.118891i | \(0.962066\pi\) | |||||||
\(390\) | 10.7030 | − | 133.195i | 0.0274436 | − | 0.341525i | ||||
\(391\) | 229.222 | 0.586245 | ||||||||
\(392\) | 759.659i | 1.93790i | ||||||||
\(393\) | −357.426 | − | 28.7214i | −0.909482 | − | 0.0730825i | ||||
\(394\) | 170.350 | 0.432362 | ||||||||
\(395\) | 190.374i | 0.481959i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −97.3003 | −0.245089 | −0.122544 | − | 0.992463i | \(-0.539105\pi\) | ||||
−0.122544 | + | 0.992463i | \(0.539105\pi\) | |||||||
\(398\) | − | 484.061i | − | 1.21623i | ||||||
\(399\) | 66.1063 | − | 822.666i | 0.165680 | − | 2.06182i | ||||
\(400\) | 62.5100 | 0.156275 | ||||||||
\(401\) | 239.040i | 0.596109i | 0.954549 | + | 0.298054i | \(0.0963377\pi\) | ||||
−0.954549 | + | 0.298054i | \(0.903662\pi\) | |||||||
\(402\) | −573.157 | − | 46.0567i | −1.42576 | − | 0.114569i | ||||
\(403\) | 72.8801 | 0.180844 | ||||||||
\(404\) | 44.3951i | 0.109889i | ||||||||
\(405\) | −136.116 | + | 409.733i | −0.336088 | + | 1.01169i | ||||
\(406\) | −293.142 | −0.722024 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 17.6466 | − | 219.605i | 0.0432515 | − | 0.538248i | ||||
\(409\) | 469.742 | 1.14851 | 0.574256 | − | 0.818676i | \(-0.305291\pi\) | ||||
0.574256 | + | 0.818676i | \(0.305291\pi\) | |||||||
\(410\) | − | 300.767i | − | 0.733578i | ||||||
\(411\) | −202.039 | − | 16.2351i | −0.491580 | − | 0.0395015i | ||||
\(412\) | −4.17565 | −0.0101351 | ||||||||
\(413\) | − | 835.514i | − | 2.02304i | ||||||
\(414\) | 429.925 | + | 69.5433i | 1.03847 | + | 0.167979i | ||||
\(415\) | −433.654 | −1.04495 | ||||||||
\(416\) | 42.9670i | 0.103286i | ||||||||
\(417\) | −9.81470 | + | 122.140i | −0.0235365 | + | 0.292902i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.5367i | 0.0752667i | 0.999292 | + | 0.0376333i | \(0.0119819\pi\) | ||||
−0.999292 | + | 0.0376333i | \(0.988018\pi\) | |||||||
\(420\) | −139.997 | − | 11.2496i | −0.333327 | − | 0.0267849i | ||||
\(421\) | −558.710 | −1.32710 | −0.663551 | − | 0.748131i | \(-0.730951\pi\) | ||||
−0.663551 | + | 0.748131i | \(0.730951\pi\) | |||||||
\(422\) | − | 149.252i | − | 0.353677i | ||||||
\(423\) | 82.0382 | − | 507.171i | 0.193944 | − | 1.19898i | ||||
\(424\) | 398.668 | 0.940256 | ||||||||
\(425\) | 35.0536i | 0.0824791i | ||||||||
\(426\) | 55.6221 | − | 692.194i | 0.130568 | − | 1.62487i | ||||
\(427\) | −253.274 | −0.593147 | ||||||||
\(428\) | 93.6404i | 0.218786i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −718.209 | −1.67025 | ||||||||
\(431\) | 747.635i | 1.73465i | 0.497740 | + | 0.867326i | \(0.334163\pi\) | ||||
−0.497740 | + | 0.867326i | \(0.665837\pi\) | |||||||
\(432\) | 117.858 | − | 480.464i | 0.272821 | − | 1.11219i | ||||
\(433\) | −568.525 | −1.31299 | −0.656496 | − | 0.754330i | \(-0.727962\pi\) | ||||
−0.656496 | + | 0.754330i | \(0.727962\pi\) | |||||||
\(434\) | − | 511.331i | − | 1.17818i | ||||||
\(435\) | −13.8910 | + | 172.868i | −0.0319333 | + | 0.397397i | ||||
\(436\) | 64.4737 | 0.147875 | ||||||||
\(437\) | 492.519i | 1.12705i | ||||||||
\(438\) | 127.493 | + | 10.2448i | 0.291080 | + | 0.0233900i | ||||
\(439\) | −543.687 | −1.23847 | −0.619233 | − | 0.785207i | \(-0.712556\pi\) | ||||
−0.619233 | + | 0.785207i | \(0.712556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −944.284 | − | 152.744i | −2.14123 | − | 0.346359i | ||||
\(442\) | −85.8586 | −0.194250 | ||||||||
\(443\) | − | 15.9346i | − | 0.0359698i | −0.999838 | − | 0.0179849i | \(-0.994275\pi\) | ||
0.999838 | − | 0.0179849i | \(-0.00572507\pi\) | |||||||
\(444\) | 0.967344 | − | 12.0382i | 0.00217870 | − | 0.0271131i | ||||
\(445\) | 642.923 | 1.44477 | ||||||||
\(446\) | 787.109i | 1.76482i | ||||||||
\(447\) | −377.631 | − | 30.3450i | −0.844812 | − | 0.0678858i | ||||
\(448\) | −611.833 | −1.36570 | ||||||||
\(449\) | 369.861i | 0.823743i | 0.911242 | + | 0.411872i | \(0.135125\pi\) | ||||
−0.911242 | + | 0.411872i | \(0.864875\pi\) | |||||||
\(450\) | −10.6349 | + | 65.7460i | −0.0236330 | + | 0.146102i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 59.6313i | 0.131928i | ||||||||
\(453\) | 34.7112 | − | 431.968i | 0.0766253 | − | 0.953571i | ||||
\(454\) | 835.125 | 1.83948 | ||||||||
\(455\) | − | 255.891i | − | 0.562397i | ||||||
\(456\) | 471.856 | + | 37.9165i | 1.03477 | + | 0.0831503i | ||||
\(457\) | −47.1793 | −0.103237 | −0.0516185 | − | 0.998667i | \(-0.516438\pi\) | ||||
−0.0516185 | + | 0.998667i | \(0.516438\pi\) | |||||||
\(458\) | 249.053i | 0.543784i | ||||||||
\(459\) | 269.429 | + | 66.0913i | 0.586992 | + | 0.143990i | ||||
\(460\) | 83.8146 | 0.182206 | ||||||||
\(461\) | 731.265i | 1.58626i | 0.609053 | + | 0.793129i | \(0.291550\pi\) | ||||
−0.609053 | + | 0.793129i | \(0.708450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 247.761 | 0.535120 | 0.267560 | − | 0.963541i | \(-0.413783\pi\) | ||||
0.267560 | + | 0.963541i | \(0.413783\pi\) | |||||||
\(464\) | − | 198.714i | − | 0.428262i | ||||||
\(465\) | −301.535 | − | 24.2302i | −0.648463 | − | 0.0521080i | ||||
\(466\) | 96.3506 | 0.206761 | ||||||||
\(467\) | − | 222.607i | − | 0.476675i | −0.971182 | − | 0.238338i | \(-0.923398\pi\) | ||
0.971182 | − | 0.238338i | \(-0.0766024\pi\) | |||||||
\(468\) | −24.1247 | − | 3.90232i | −0.0515484 | − | 0.00833830i | ||||
\(469\) | −1101.14 | −2.34784 | ||||||||
\(470\) | − | 659.994i | − | 1.40424i | ||||||
\(471\) | −5.23765 | + | 65.1805i | −0.0111203 | + | 0.138388i | ||||
\(472\) | 479.226 | 1.01531 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 231.662 | + | 18.6154i | 0.488738 | + | 0.0392731i | ||||
\(475\) | −75.3182 | −0.158565 | ||||||||
\(476\) | 90.2438i | 0.189588i | ||||||||
\(477\) | −80.1601 | + | 495.560i | −0.168051 | + | 1.03891i | ||||
\(478\) | −1005.01 | −2.10252 | ||||||||
\(479\) | 788.075i | 1.64525i | 0.568583 | + | 0.822626i | \(0.307492\pi\) | ||||
−0.568583 | + | 0.822626i | \(0.692508\pi\) | |||||||
\(480\) | 14.2851 | − | 177.772i | 0.0297606 | − | 0.370359i | ||||
\(481\) | 22.0038 | 0.0457459 | ||||||||
\(482\) | − | 749.161i | − | 1.55428i | ||||||
\(483\) | 831.331 | + | 66.8026i | 1.72118 | + | 0.138308i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 454.865i | − | 0.937867i | ||||||
\(486\) | 485.286 | + | 205.702i | 0.998531 | + | 0.423254i | ||||
\(487\) | −314.723 | −0.646248 | −0.323124 | − | 0.946357i | \(-0.604733\pi\) | ||||
−0.323124 | + | 0.946357i | \(0.604733\pi\) | |||||||
\(488\) | − | 145.270i | − | 0.297685i | ||||||
\(489\) | −28.0586 | + | 349.178i | −0.0573795 | + | 0.714065i | ||||
\(490\) | −1228.82 | −2.50780 | ||||||||
\(491\) | − | 706.608i | − | 1.43912i | −0.694430 | − | 0.719560i | \(-0.744343\pi\) | ||
0.694430 | − | 0.719560i | \(-0.255657\pi\) | |||||||
\(492\) | −54.8300 | − | 4.40592i | −0.111443 | − | 0.00895513i | ||||
\(493\) | 111.432 | 0.226029 | ||||||||
\(494\) | − | 184.481i | − | 0.373443i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 346.619 | 0.698828 | ||||||||
\(497\) | − | 1329.83i | − | 2.67571i | ||||||
\(498\) | −42.4043 | + | 527.705i | −0.0851492 | + | 1.05965i | ||||
\(499\) | −223.148 | −0.447190 | −0.223595 | − | 0.974682i | \(-0.571779\pi\) | ||||
−0.223595 | + | 0.974682i | \(0.571779\pi\) | |||||||
\(500\) | − | 81.1058i | − | 0.162212i | ||||||
\(501\) | −22.6325 | − | 1.81866i | −0.0451747 | − | 0.00363006i | ||||
\(502\) | −467.906 | −0.932085 | ||||||||
\(503\) | 285.889i | 0.568368i | 0.958770 | + | 0.284184i | \(0.0917226\pi\) | ||||
−0.958770 | + | 0.284184i | \(0.908277\pi\) | |||||||
\(504\) | 128.000 | − | 791.311i | 0.253968 | − | 1.57006i | ||||
\(505\) | 335.737 | 0.664826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.0433 | + | 460.989i | −0.0730636 | + | 0.909248i | ||||
\(508\) | −24.8523 | −0.0489219 | ||||||||
\(509\) | − | 291.204i | − | 0.572110i | −0.958213 | − | 0.286055i | \(-0.907656\pi\) | ||
0.958213 | − | 0.286055i | \(-0.0923439\pi\) | |||||||
\(510\) | 355.233 | + | 28.5451i | 0.696535 | + | 0.0559708i | ||||
\(511\) | 244.937 | 0.479328 | ||||||||
\(512\) | − | 319.485i | − | 0.623994i | ||||||
\(513\) | −142.008 | + | 578.911i | −0.276818 | + | 1.12848i | ||||
\(514\) | 151.570 | 0.294884 | ||||||||
\(515\) | 31.5782i | 0.0613169i | ||||||||
\(516\) | −10.5210 | + | 130.930i | −0.0203896 | + | 0.253740i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 154.380i | − | 0.298030i | ||||||
\(519\) | 186.756 | + | 15.0070i | 0.359838 | + | 0.0289152i | ||||
\(520\) | 146.771 | 0.282252 | ||||||||
\(521\) | 617.998i | 1.18618i | 0.805137 | + | 0.593088i | \(0.202092\pi\) | ||||
−0.805137 | + | 0.593088i | \(0.797908\pi\) | |||||||
\(522\) | 209.001 | + | 33.8073i | 0.400385 | + | 0.0647649i | ||||
\(523\) | 310.931 | 0.594514 | 0.297257 | − | 0.954798i | \(-0.403928\pi\) | ||||
0.297257 | + | 0.954798i | \(0.403928\pi\) | |||||||
\(524\) | 84.2457i | 0.160774i | ||||||||
\(525\) | −10.2157 | + | 127.131i | −0.0194586 | + | 0.242154i | ||||
\(526\) | 965.735 | 1.83600 | ||||||||
\(527\) | 194.373i | 0.368829i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.2927 | 0.0591545 | ||||||||
\(530\) | 644.885i | 1.21676i | ||||||||
\(531\) | −96.3577 | + | 595.695i | −0.181465 | + | 1.12184i | ||||
\(532\) | −193.903 | −0.364479 | ||||||||
\(533\) | − | 100.220i | − | 0.188029i | ||||||
\(534\) | 62.8674 | − | 782.360i | 0.117729 | − | 1.46509i | ||||
\(535\) | 708.153 | 1.32365 | ||||||||
\(536\) | − | 631.580i | − | 1.17832i | ||||||
\(537\) | −634.228 | − | 50.9641i | −1.18106 | − | 0.0949052i | ||||
\(538\) | −290.924 | −0.540750 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 98.5163 | + | 24.1662i | 0.182438 | + | 0.0447522i | ||||
\(541\) | −119.286 | −0.220491 | −0.110245 | − | 0.993904i | \(-0.535164\pi\) | ||||
−0.110245 | + | 0.993904i | \(0.535164\pi\) | |||||||
\(542\) | − | 444.138i | − | 0.819443i | ||||||
\(543\) | 46.1769 | − | 574.653i | 0.0850403 | − | 1.05829i | ||||
\(544\) | −114.594 | −0.210650 | ||||||||
\(545\) | − | 487.581i | − | 0.894643i | ||||||
\(546\) | −311.388 | − | 25.0219i | −0.570308 | − | 0.0458277i | ||||
\(547\) | 736.527 | 1.34649 | 0.673243 | − | 0.739422i | \(-0.264901\pi\) | ||||
0.673243 | + | 0.739422i | \(0.264901\pi\) | |||||||
\(548\) | 47.6208i | 0.0868993i | ||||||||
\(549\) | 180.576 | + | 29.2094i | 0.328918 | + | 0.0532047i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 239.430i | 0.434537i | ||||||||
\(552\) | −38.3159 | + | 476.827i | −0.0694129 | + | 0.863816i | ||||
\(553\) | 445.064 | 0.804818 | ||||||||
\(554\) | − | 126.889i | − | 0.229042i | ||||||
\(555\) | −91.0387 | − | 7.31552i | −0.164034 | − | 0.0131811i | ||||
\(556\) | 28.7885 | 0.0517779 | ||||||||
\(557\) | − | 409.020i | − | 0.734326i | −0.930157 | − | 0.367163i | \(-0.880329\pi\) | ||
0.930157 | − | 0.367163i | \(-0.119671\pi\) | |||||||
\(558\) | −58.9705 | + | 364.563i | −0.105682 | + | 0.653338i | ||||
\(559\) | −239.317 | −0.428116 | ||||||||
\(560\) | − | 1217.02i | − | 2.17325i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.08886 | 0.00549619 | ||||||||
\(563\) | 468.336i | 0.831859i | 0.909397 | + | 0.415929i | \(0.136544\pi\) | ||||
−0.909397 | + | 0.415929i | \(0.863456\pi\) | |||||||
\(564\) | −120.317 | − | 9.66823i | −0.213329 | − | 0.0171423i | ||||
\(565\) | 450.960 | 0.798159 | ||||||||
\(566\) | 636.098i | 1.12385i | ||||||||
\(567\) | 957.892 | + | 318.217i | 1.68940 | + | 0.561230i | ||||
\(568\) | 762.750 | 1.34287 | ||||||||
\(569\) | 208.533i | 0.366491i | 0.983067 | + | 0.183245i | \(0.0586603\pi\) | ||||
−0.983067 | + | 0.183245i | \(0.941340\pi\) | |||||||
\(570\) | −61.3337 | + | 763.273i | −0.107603 | + | 1.33908i | ||||
\(571\) | −177.630 | −0.311086 | −0.155543 | − | 0.987829i | \(-0.549713\pi\) | ||||
−0.155543 | + | 0.987829i | \(0.549713\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 645.694 | + | 51.8854i | 1.12687 | + | 0.0905505i | ||||
\(574\) | −703.146 | −1.22499 | ||||||||
\(575\) | − | 76.1116i | − | 0.132368i | ||||||
\(576\) | 436.217 | + | 70.5611i | 0.757322 | + | 0.122502i | ||||
\(577\) | −194.396 | −0.336908 | −0.168454 | − | 0.985709i | \(-0.553878\pi\) | ||||
−0.168454 | + | 0.985709i | \(0.553878\pi\) | |||||||
\(578\) | 397.872i | 0.688360i | ||||||||
\(579\) | −28.4711 | + | 354.311i | −0.0491728 | + | 0.611936i | ||||
\(580\) | 40.7450 | 0.0702500 | ||||||||
\(581\) | 1013.82i | 1.74495i | ||||||||
\(582\) | −553.516 | − | 44.4784i | −0.951058 | − | 0.0764234i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 140.488i | 0.240562i | ||||||||
\(585\) | −29.5112 | + | 182.442i | −0.0504465 | + | 0.311867i | ||||
\(586\) | −702.792 | −1.19930 | ||||||||
\(587\) | − | 439.156i | − | 0.748136i | −0.927401 | − | 0.374068i | \(-0.877963\pi\) | ||
0.927401 | − | 0.374068i | \(-0.122037\pi\) | |||||||
\(588\) | −18.0010 | + | 224.015i | −0.0306139 | + | 0.380978i | ||||
\(589\) | −417.641 | −0.709067 | ||||||||
\(590\) | 775.194i | 1.31389i | ||||||||
\(591\) | −234.852 | − | 18.8718i | −0.397381 | − | 0.0319320i | ||||
\(592\) | 104.650 | 0.176774 | ||||||||
\(593\) | − | 987.710i | − | 1.66561i | −0.553563 | − | 0.832807i | \(-0.686732\pi\) | ||
0.553563 | − | 0.832807i | \(-0.313268\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 682.466 | 1.14700 | ||||||||
\(596\) | 89.0079i | 0.149342i | ||||||||
\(597\) | −53.6255 | + | 667.348i | −0.0898249 | + | 1.11784i | ||||
\(598\) | 186.424 | 0.311746 | ||||||||
\(599\) | 317.730i | 0.530433i | 0.964189 | + | 0.265217i | \(0.0854435\pi\) | ||||
−0.964189 | + | 0.265217i | \(0.914557\pi\) | |||||||
\(600\) | −72.9184 | − | 5.85944i | −0.121531 | − | 0.00976573i | ||||
\(601\) | −176.924 | −0.294383 | −0.147192 | − | 0.989108i | \(-0.547023\pi\) | ||||
−0.147192 | + | 0.989108i | \(0.547023\pi\) | |||||||
\(602\) | 1679.06i | 2.78914i | ||||||||
\(603\) | 785.077 | + | 126.991i | 1.30195 | + | 0.210599i | ||||
\(604\) | −101.815 | −0.168568 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 32.8296 | − | 408.551i | 0.0541743 | − | 0.674177i | ||||
\(607\) | −423.517 | −0.697722 | −0.348861 | − | 0.937175i | \(-0.613431\pi\) | ||||
−0.348861 | + | 0.937175i | \(0.613431\pi\) | |||||||
\(608\) | − | 246.223i | − | 0.404972i | ||||||
\(609\) | 404.138 | + | 32.4749i | 0.663608 | + | 0.0533250i | ||||
\(610\) | 234.988 | 0.385227 | ||||||||
\(611\) | − | 219.919i | − | 0.359933i | ||||||
\(612\) | 10.4076 | − | 64.3409i | 0.0170059 | − | 0.105132i | ||||
\(613\) | 995.062 | 1.62327 | 0.811633 | − | 0.584168i | \(-0.198579\pi\) | ||||
0.811633 | + | 0.584168i | \(0.198579\pi\) | |||||||
\(614\) | − | 635.364i | − | 1.03479i | ||||||
\(615\) | −33.3197 | + | 414.650i | −0.0541783 | + | 0.674228i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 82.1697i | − | 0.133176i | −0.997781 | − | 0.0665881i | \(-0.978789\pi\) | ||
0.997781 | − | 0.0665881i | \(-0.0212113\pi\) | |||||||
\(618\) | 38.4269 | + | 3.08784i | 0.0621794 | + | 0.00499650i | ||||
\(619\) | −823.362 | −1.33015 | −0.665074 | − | 0.746777i | \(-0.731600\pi\) | ||||
−0.665074 | + | 0.746777i | \(0.731600\pi\) | |||||||
\(620\) | 71.0721i | 0.114632i | ||||||||
\(621\) | −585.009 | − | 143.503i | −0.942043 | − | 0.231084i | ||||
\(622\) | 735.122 | 1.18187 | ||||||||
\(623\) | − | 1503.05i | − | 2.41261i | ||||||
\(624\) | 16.9618 | − | 211.082i | 0.0271823 | − | 0.338273i | ||||
\(625\) | −698.652 | −1.11784 | ||||||||
\(626\) | − | 773.893i | − | 1.23625i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.3631 | 0.0244635 | ||||||||
\(629\) | 58.6845i | 0.0932981i | ||||||||
\(630\) | 1280.02 | + | 207.052i | 2.03178 | + | 0.328654i | ||||
\(631\) | −238.417 | −0.377840 | −0.188920 | − | 0.981993i | \(-0.560499\pi\) | ||||
−0.188920 | + | 0.981993i | \(0.560499\pi\) | |||||||
\(632\) | 255.275i | 0.403917i | ||||||||
\(633\) | −16.5344 | + | 205.765i | −0.0261208 | + | 0.325062i | ||||
\(634\) | 1046.54 | 1.65069 | ||||||||
\(635\) | 187.945i | 0.295976i | ||||||||
\(636\) | 117.563 | + | 9.44690i | 0.184847 | + | 0.0148536i | ||||
\(637\) | −409.460 | −0.642794 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −153.366 | + | 948.127i | −0.240009 | + | 1.48377i | ||||
\(640\) | 805.455 | 1.25852 | ||||||||
\(641\) | 1102.21i | 1.71952i | 0.510701 | + | 0.859759i | \(0.329386\pi\) | ||||
−0.510701 | + | 0.859759i | \(0.670614\pi\) | |||||||
\(642\) | 69.2458 | − | 861.736i | 0.107859 | − | 1.34227i | ||||
\(643\) | −58.4417 | −0.0908892 | −0.0454446 | − | 0.998967i | \(-0.514470\pi\) | ||||
−0.0454446 | + | 0.998967i | \(0.514470\pi\) | |||||||
\(644\) | − | 195.945i | − | 0.304263i | ||||||
\(645\) | 990.153 | + | 79.5649i | 1.53512 | + | 0.123356i | ||||
\(646\) | 492.014 | 0.761632 | ||||||||
\(647\) | − | 957.445i | − | 1.47982i | −0.672704 | − | 0.739911i | \(-0.734867\pi\) | ||
0.672704 | − | 0.739911i | \(-0.265133\pi\) | |||||||
\(648\) | −182.520 | + | 549.418i | −0.281666 | + | 0.847867i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 28.5088i | 0.0438596i | ||||||||
\(651\) | −56.6464 | + | 704.942i | −0.0870145 | + | 1.08286i | ||||
\(652\) | 82.3015 | 0.126229 | ||||||||
\(653\) | 1063.77i | 1.62904i | 0.580132 | + | 0.814522i | \(0.303001\pi\) | ||||
−0.580132 | + | 0.814522i | \(0.696999\pi\) | |||||||
\(654\) | −593.327 | − | 47.6774i | −0.907227 | − | 0.0729012i | ||||
\(655\) | 637.105 | 0.972680 | ||||||||
\(656\) | − | 476.645i | − | 0.726594i | ||||||
\(657\) | −174.632 | − | 28.2479i | −0.265802 | − | 0.0429953i | ||||
\(658\) | −1542.96 | −2.34493 | ||||||||
\(659\) | − | 91.2998i | − | 0.138543i | −0.997598 | − | 0.0692715i | \(-0.977933\pi\) | ||
0.997598 | − | 0.0692715i | \(-0.0220675\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −700.759 | −1.06015 | −0.530075 | − | 0.847951i | \(-0.677836\pi\) | ||||
−0.530075 | + | 0.847951i | \(0.677836\pi\) | |||||||
\(662\) | − | 286.019i | − | 0.432053i | ||||||
\(663\) | 118.368 | + | 9.51162i | 0.178534 | + | 0.0143463i | ||||
\(664\) | −581.494 | −0.875744 | ||||||||
\(665\) | 1466.39i | 2.20509i | ||||||||
\(666\) | −17.8042 | + | 110.068i | −0.0267330 | + | 0.165267i | ||||
\(667\) | −241.952 | −0.362746 | ||||||||
\(668\) | 5.33450i | 0.00798578i | ||||||||
\(669\) | 87.1978 | − | 1085.14i | 0.130341 | − | 1.62204i | ||||
\(670\) | 1021.64 | 1.52484 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −415.603 | − | 33.3963i | −0.618457 | − | 0.0496968i | ||||
\(673\) | 986.110 | 1.46525 | 0.732623 | − | 0.680635i | \(-0.238296\pi\) | ||||
0.732623 | + | 0.680635i | \(0.238296\pi\) | |||||||
\(674\) | 1193.88i | 1.77134i | ||||||||
\(675\) | 21.9452 | − | 89.4621i | 0.0325114 | − | 0.132536i | ||||
\(676\) | 108.655 | 0.160733 | ||||||||
\(677\) | − | 806.842i | − | 1.19179i | −0.803062 | − | 0.595895i | \(-0.796797\pi\) | ||
0.803062 | − | 0.595895i | \(-0.203203\pi\) | |||||||
\(678\) | 44.0965 | − | 548.764i | 0.0650391 | − | 0.809386i | ||||
\(679\) | −1063.40 | −1.56613 | ||||||||
\(680\) | 391.442i | 0.575650i | ||||||||
\(681\) | −1151.34 | − | 92.5171i | −1.69066 | − | 0.135855i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 189.393i | 0.277295i | 0.990342 | + | 0.138648i | \(0.0442755\pi\) | ||||
−0.990342 | + | 0.138648i | \(0.955724\pi\) | |||||||
\(684\) | 138.247 | + | 22.3623i | 0.202115 | + | 0.0326935i | ||||
\(685\) | 360.131 | 0.525739 | ||||||||
\(686\) | 1548.35i | 2.25708i | ||||||||
\(687\) | 27.5907 | − | 343.355i | 0.0401611 | − | 0.499789i | ||||
\(688\) | −1138.19 | −1.65435 | ||||||||
\(689\) | 214.884i | 0.311879i | ||||||||
\(690\) | −771.313 | − | 61.9797i | −1.11785 | − | 0.0898257i | ||||
\(691\) | −1276.88 | −1.84787 | −0.923936 | − | 0.382547i | \(-0.875047\pi\) | ||||
−0.923936 | + | 0.382547i | \(0.875047\pi\) | |||||||
\(692\) | − | 44.0184i | − | 0.0636105i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −266.808 | −0.384449 | ||||||||
\(695\) | − | 217.712i | − | 0.313255i | ||||||
\(696\) | −18.6266 | + | 231.801i | −0.0267624 | + | 0.333047i | ||||
\(697\) | 267.288 | 0.383483 | ||||||||
\(698\) | 267.466i | 0.383190i | ||||||||
\(699\) | −132.833 | − | 10.6739i | −0.190033 | − | 0.0152703i | ||||
\(700\) | 29.9648 | 0.0428069 | ||||||||
\(701\) | − | 754.729i | − | 1.07665i | −0.842739 | − | 0.538323i | \(-0.819058\pi\) | ||
0.842739 | − | 0.538323i | \(-0.180942\pi\) | |||||||
\(702\) | 219.124 | + | 53.7514i | 0.312143 | + | 0.0765690i | ||||
\(703\) | −126.093 | −0.179364 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −73.1157 | + | 909.896i | −0.103710 | + | 1.29063i | ||||
\(706\) | −1026.90 | −1.45453 | ||||||||
\(707\) | − | 784.901i | − | 1.11018i | ||||||
\(708\) | 141.318 | + | 11.3558i | 0.199602 | + | 0.0160392i | ||||
\(709\) | −688.403 | −0.970949 | −0.485474 | − | 0.874251i | \(-0.661353\pi\) | ||||
−0.485474 | + | 0.874251i | \(0.661353\pi\) | |||||||
\(710\) | 1233.82i | 1.73778i | ||||||||
\(711\) | −317.317 | − | 51.3281i | −0.446296 | − | 0.0721914i | ||||
\(712\) | 862.106 | 1.21082 | ||||||||
\(713\) | − | 422.040i | − | 0.591921i | ||||||
\(714\) | 66.7340 | − | 830.479i | 0.0934650 | − | 1.16314i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 149.488i | 0.208782i | ||||||||
\(717\) | 1385.54 | + | 111.337i | 1.93242 | + | 0.155282i | ||||
\(718\) | −208.295 | −0.290104 | ||||||||
\(719\) | − | 762.189i | − | 1.06007i | −0.847976 | − | 0.530034i | \(-0.822179\pi\) | ||
0.847976 | − | 0.530034i | \(-0.177821\pi\) | |||||||
\(720\) | −140.356 | + | 867.696i | −0.194938 | + | 1.20513i | ||||
\(721\) | 73.8250 | 0.102392 | ||||||||
\(722\) | 274.138i | 0.379693i | ||||||||
\(723\) | −82.9938 | + | 1032.82i | −0.114791 | + | 1.42853i | ||||
\(724\) | −135.446 | −0.187080 | ||||||||
\(725\) | − | 37.0003i | − | 0.0510350i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 64.3444 | 0.0885067 | 0.0442534 | − | 0.999020i | \(-0.485909\pi\) | ||||
0.0442534 | + | 0.999020i | \(0.485909\pi\) | |||||||
\(728\) | − | 343.128i | − | 0.471330i | ||||||
\(729\) | −646.248 | − | 337.350i | −0.886485 | − | 0.462757i | ||||
\(730\) | −227.253 | −0.311306 | ||||||||
\(731\) | − | 638.263i | − | 0.873137i | ||||||
\(732\) | 3.44234 | − | 42.8385i | 0.00470265 | − | 0.0585226i | ||||
\(733\) | −792.311 | −1.08092 | −0.540458 | − | 0.841371i | \(-0.681749\pi\) | ||||
−0.540458 | + | 0.841371i | \(0.681749\pi\) | |||||||
\(734\) | 978.181i | 1.33267i | ||||||||
\(735\) | 1694.11 | + | 136.132i | 2.30491 | + | 0.185213i | ||||
\(736\) | 248.816 | 0.338066 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 501.321 | + | 81.0920i | 0.679296 | + | 0.109881i | ||||
\(739\) | −975.853 | −1.32050 | −0.660252 | − | 0.751044i | \(-0.729551\pi\) | ||||
−0.660252 | + | 0.751044i | \(0.729551\pi\) | |||||||
\(740\) | 21.4579i | 0.0289971i | ||||||||
\(741\) | −20.4372 | + | 254.333i | −0.0275806 | + | 0.343229i | ||||
\(742\) | 1507.64 | 2.03186 | ||||||||
\(743\) | − | 613.238i | − | 0.825354i | −0.910877 | − | 0.412677i | \(-0.864594\pi\) | ||
0.910877 | − | 0.412677i | \(-0.135406\pi\) | |||||||
\(744\) | −404.334 | − | 32.4907i | −0.543459 | − | 0.0436703i | ||||
\(745\) | 673.120 | 0.903516 | ||||||||
\(746\) | 1132.32i | 1.51785i | ||||||||
\(747\) | 116.921 | − | 722.818i | 0.156520 | − | 0.967628i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1655.55i | − | 2.21035i | ||||||
\(750\) | −59.9767 | + | 746.386i | −0.0799689 | + | 0.995181i | ||||
\(751\) | 986.977 | 1.31422 | 0.657108 | − | 0.753796i | \(-0.271779\pi\) | ||||
0.657108 | + | 0.753796i | \(0.271779\pi\) | |||||||
\(752\) | − | 1045.94i | − | 1.39087i | ||||||
\(753\) | 645.076 | + | 51.8358i | 0.856674 | + | 0.0688390i | ||||
\(754\) | 90.6268 | 0.120195 | ||||||||
\(755\) | 769.974i | 1.01983i | ||||||||
\(756\) | 56.4967 | − | 230.316i | 0.0747311 | − | 0.304650i | ||||
\(757\) | 1307.29 | 1.72694 | 0.863471 | − | 0.504399i | \(-0.168286\pi\) | ||||
0.863471 | + | 0.504399i | \(0.168286\pi\) | |||||||
\(758\) | 1447.53i | 1.90967i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −841.074 | −1.10668 | ||||||||
\(761\) | 487.251i | 0.640278i | 0.947371 | + | 0.320139i | \(0.103730\pi\) | ||||
−0.947371 | + | 0.320139i | \(0.896270\pi\) | |||||||
\(762\) | 228.706 | + | 18.3780i | 0.300140 | + | 0.0241181i | ||||
\(763\) | −1139.89 | −1.49395 | ||||||||
\(764\) | − | 152.190i | − | 0.199202i | ||||||
\(765\) | −486.577 | − | 78.7070i | −0.636048 | − | 0.102885i | ||||
\(766\) | −1094.46 | −1.42879 | ||||||||
\(767\) | 258.305i | 0.336773i | ||||||||
\(768\) | 31.5680 | − | 392.851i | 0.0411041 | − | 0.511525i | ||||
\(769\) | 887.598 | 1.15422 | 0.577112 | − | 0.816665i | \(-0.304180\pi\) | ||||
0.577112 | + | 0.816665i | \(0.304180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −208.962 | − | 16.7913i | −0.271027 | − | 0.0217786i | ||||
\(772\) | 83.5113 | 0.108175 | ||||||||
\(773\) | − | 299.226i | − | 0.387097i | −0.981091 | − | 0.193548i | \(-0.938000\pi\) | ||
0.981091 | − | 0.193548i | \(-0.0619996\pi\) | |||||||
\(774\) | 193.642 | − | 1197.12i | 0.250183 | − | 1.54666i | ||||
\(775\) | 64.5402 | 0.0832776 | ||||||||
\(776\) | − | 609.936i | − | 0.786000i | ||||||
\(777\) | −17.1025 | + | 212.834i | −0.0220110 | + | 0.273918i | ||||
\(778\) | −200.633 | −0.257883 | ||||||||
\(779\) | 574.310i | 0.737240i | ||||||||
\(780\) | 43.2812 | + | 3.47791i | 0.0554887 | + | 0.00445885i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 497.197i | 0.635801i | ||||||||
\(783\) | −284.392 | − | 69.7617i | −0.363208 | − | 0.0890954i | ||||
\(784\) | −1947.40 | −2.48392 | ||||||||
\(785\) | − | 116.183i | − | 0.148004i | ||||||
\(786\) | 62.2985 | − | 775.280i | 0.0792602 | − | 0.986362i | ||||
\(787\) | −1451.63 | −1.84451 | −0.922253 | − | 0.386587i | \(-0.873654\pi\) | ||||
−0.922253 | + | 0.386587i | \(0.873654\pi\) | |||||||
\(788\) | 55.3549i | 0.0702473i | ||||||||
\(789\) | −1331.40 | − | 106.986i | −1.68746 | − | 0.135597i | ||||
\(790\) | −412.933 | −0.522699 | ||||||||
\(791\) | − | 1054.27i | − | 1.33284i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 78.3013 | 0.0987407 | ||||||||
\(794\) | − | 211.050i | − | 0.265807i | ||||||
\(795\) | 71.4419 | − | 889.066i | 0.0898640 | − | 1.11832i | ||||
\(796\) | 157.294 | 0.197606 | ||||||||
\(797\) | − | 375.053i | − | 0.470581i | −0.971925 | − | 0.235290i | \(-0.924396\pi\) | ||
0.971925 | − | 0.235290i | \(-0.0756041\pi\) | |||||||
\(798\) | 1784.41 | + | 143.389i | 2.23611 | + | 0.179685i | ||||
\(799\) | 586.529 | 0.734079 | ||||||||
\(800\) | 38.0501i | 0.0475626i | ||||||||
\(801\) | −173.343 | + | 1071.63i | −0.216409 | + | 1.33787i | ||||
\(802\) | −518.492 | −0.646499 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 14.9660 | − | 186.246i | 0.0186144 | − | 0.231649i | ||||
\(805\) | −1481.83 | −1.84078 | ||||||||
\(806\) | 158.081i | 0.196131i | ||||||||
\(807\) | 401.080 | + | 32.2292i | 0.497001 | + | 0.0399371i | ||||
\(808\) | 450.195 | 0.557172 | ||||||||
\(809\) | 795.417i | 0.983210i | 0.870818 | + | 0.491605i | \(0.163590\pi\) | ||||
−0.870818 | + | 0.491605i | \(0.836410\pi\) | |||||||
\(810\) | −888.737 | − | 295.243i | −1.09721 | − | 0.364498i | ||||
\(811\) | −941.339 | −1.16071 | −0.580357 | − | 0.814362i | \(-0.697087\pi\) | ||||
−0.580357 | + | 0.814362i | \(0.697087\pi\) | |||||||
\(812\) | − | 95.2555i | − | 0.117310i | ||||||
\(813\) | −49.2027 | + | 612.308i | −0.0605199 | + | 0.753146i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 622.403i | − | 0.763684i | ||||||
\(816\) | 562.961 | + | 45.2374i | 0.689903 | + | 0.0554380i | ||||
\(817\) | 1371.41 | 1.67859 | ||||||||
\(818\) | 1018.90i | 1.24560i | ||||||||
\(819\) | 426.521 | + | 68.9926i | 0.520782 | + | 0.0842401i | ||||
\(820\) | 97.7333 | 0.119187 | ||||||||
\(821\) | 881.769i | 1.07402i | 0.843576 | + | 0.537009i | \(0.180446\pi\) | ||||
−0.843576 | + | 0.537009i | \(0.819554\pi\) | |||||||
\(822\) | 35.2150 | − | 438.236i | 0.0428406 | − | 0.533134i | ||||
\(823\) | 784.531 | 0.953257 | 0.476629 | − | 0.879105i | \(-0.341859\pi\) | ||||
0.476629 | + | 0.879105i | \(0.341859\pi\) | |||||||
\(824\) | 42.3438i | 0.0513881i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1812.28 | 2.19405 | ||||||||
\(827\) | − | 631.410i | − | 0.763495i | −0.924267 | − | 0.381747i | \(-0.875322\pi\) | ||
0.924267 | − | 0.381747i | \(-0.124678\pi\) | |||||||
\(828\) | −22.5979 | + | 139.703i | −0.0272921 | + | 0.168723i | ||||
\(829\) | −873.984 | −1.05426 | −0.527132 | − | 0.849784i | \(-0.676733\pi\) | ||||
−0.527132 | + | 0.849784i | \(0.676733\pi\) | |||||||
\(830\) | − | 940.623i | − | 1.13328i | ||||||
\(831\) | −14.0571 | + | 174.935i | −0.0169159 | + | 0.210511i | ||||
\(832\) | 189.152 | 0.227347 | ||||||||
\(833\) | − | 1092.04i | − | 1.31097i | ||||||
\(834\) | −264.929 | − | 21.2887i | −0.317661 | − | 0.0255260i | ||||
\(835\) | 40.3420 | 0.0483138 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 121.686 | − | 496.069i | 0.145384 | − | 0.592675i | ||||
\(838\) | −68.4051 | −0.0816290 | ||||||||
\(839\) | 130.049i | 0.155005i | 0.996992 | + | 0.0775025i | \(0.0246946\pi\) | ||||
−0.996992 | + | 0.0775025i | \(0.975305\pi\) | |||||||
\(840\) | −114.079 | + | 1419.66i | −0.135808 | + | 1.69007i | ||||
\(841\) | 723.379 | 0.860142 | ||||||||
\(842\) | − | 1211.88i | − | 1.43928i | ||||||
\(843\) | −4.25843 | − | 0.342191i | −0.00505152 | − | 0.000405921i | ||||
\(844\) | 48.4988 | 0.0574631 | ||||||||
\(845\) | − | 821.703i | − | 0.972430i | ||||||
\(846\) | 1100.08 | + | 177.946i | 1.30034 | + | 0.210338i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1021.99i | 1.20518i | ||||||||
\(849\) | 70.4685 | − | 876.952i | 0.0830018 | − | 1.03292i | ||||
\(850\) | −76.0335 | −0.0894512 | ||||||||
\(851\) | − | 127.421i | − | 0.149731i | ||||||
\(852\) | 224.926 | + | 18.0742i | 0.263998 | + | 0.0212139i | ||||
\(853\) | −955.546 | −1.12022 | −0.560109 | − | 0.828419i | \(-0.689241\pi\) | ||||
−0.560109 | + | 0.828419i | \(0.689241\pi\) | |||||||
\(854\) | − | 549.366i | − | 0.643286i | ||||||
\(855\) | 169.114 | − | 1045.49i | 0.197795 | − | 1.22279i | ||||
\(856\) | 949.573 | 1.10931 | ||||||||
\(857\) | 884.890i | 1.03254i | 0.856425 | + | 0.516272i | \(0.172681\pi\) | ||||
−0.856425 | + | 0.516272i | \(0.827319\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −248.741 | −0.289570 | −0.144785 | − | 0.989463i | \(-0.546249\pi\) | ||||
−0.144785 | + | 0.989463i | \(0.546249\pi\) | |||||||
\(860\) | − | 233.380i | − | 0.271372i | ||||||
\(861\) | 969.387 | + | 77.8962i | 1.12588 | + | 0.0904717i | ||||
\(862\) | −1621.67 | −1.88128 | ||||||||
\(863\) | 990.278i | 1.14748i | 0.819036 | + | 0.573742i | \(0.194509\pi\) | ||||
−0.819036 | + | 0.573742i | \(0.805491\pi\) | |||||||
\(864\) | 292.461 | + | 71.7409i | 0.338496 | + | 0.0830335i | ||||
\(865\) | −332.888 | −0.384842 | ||||||||
\(866\) | − | 1233.17i | − | 1.42398i | ||||||
\(867\) | 44.0772 | − | 548.523i | 0.0508388 | − | 0.632668i | ||||
\(868\) | 166.155 | 0.191423 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −374.961 | − | 30.1304i | −0.430989 | − | 0.0346326i | ||||
\(871\) | 340.425 | 0.390843 | ||||||||
\(872\) | − | 653.805i | − | 0.749776i | ||||||
\(873\) | 758.173 | + | 122.640i | 0.868469 | + | 0.140481i | ||||
\(874\) | −1068.31 | −1.22232 | ||||||||
\(875\) | 1433.94i | 1.63879i | ||||||||
\(876\) | −3.32903 | + | 41.4284i | −0.00380026 | + | 0.0472927i | ||||
\(877\) | 1073.75 | 1.22435 | 0.612173 | − | 0.790724i | \(-0.290296\pi\) | ||||
0.612173 | + | 0.790724i | \(0.290296\pi\) | |||||||
\(878\) | − | 1179.29i | − | 1.34316i | ||||||
\(879\) | 968.899 | + | 77.8570i | 1.10227 | + | 0.0885745i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1093.03i | 1.24067i | 0.784337 | + | 0.620335i | \(0.213003\pi\) | ||||
−0.784337 | + | 0.620335i | \(0.786997\pi\) | |||||||
\(882\) | 331.312 | − | 2048.21i | 0.375637 | − | 2.32223i | ||||
\(883\) | −1362.62 | −1.54317 | −0.771586 | − | 0.636125i | \(-0.780536\pi\) | ||||
−0.771586 | + | 0.636125i | \(0.780536\pi\) | |||||||
\(884\) | − | 27.8995i | − | 0.0315605i | ||||||
\(885\) | 85.8778 | − | 1068.72i | 0.0970371 | − | 1.20759i | ||||
\(886\) | 34.5631 | 0.0390103 | ||||||||
\(887\) | − | 207.746i | − | 0.234212i | −0.993119 | − | 0.117106i | \(-0.962638\pi\) | ||
0.993119 | − | 0.117106i | \(-0.0373617\pi\) | |||||||
\(888\) | −122.075 | − | 9.80949i | −0.137472 | − | 0.0110467i | ||||
\(889\) | 439.386 | 0.494248 | ||||||||
\(890\) | 1394.54i | 1.56690i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −255.769 | −0.286736 | ||||||||
\(893\) | 1260.25i | 1.41125i | ||||||||
\(894\) | 65.8201 | − | 819.105i | 0.0736243 | − | 0.916225i | ||||
\(895\) | 1130.50 | 1.26313 | ||||||||
\(896\) | − | 1883.03i | − | 2.10159i | ||||||
\(897\) | −257.012 | − | 20.6525i | −0.286524 | − | 0.0230240i | ||||
\(898\) | −802.251 | −0.893375 | ||||||||
\(899\) | − | 205.167i | − | 0.228217i | ||||||
\(900\) | −21.3640 | − | 3.45577i | −0.0237377 | − | 0.00383974i | ||||
\(901\) | −573.101 | −0.636072 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 186.010 | − | 2314.82i | 0.205991 | − | 2.56348i | ||||
\(904\) | 604.699 | 0.668915 | ||||||||
\(905\) | 1024.31i | 1.13183i | ||||||||
\(906\) | 936.965 | + | 75.2908i | 1.03418 | + | 0.0831025i | ||||
\(907\) | −966.468 | −1.06557 | −0.532783 | − | 0.846252i | \(-0.678854\pi\) | ||||
−0.532783 | + | 0.846252i | \(0.678854\pi\) | |||||||
\(908\) | 271.371i | 0.298867i | ||||||||
\(909\) | −90.5206 | + | 559.609i | −0.0995826 | + | 0.615632i | ||||
\(910\) | 555.043 | 0.609937 | ||||||||
\(911\) | 107.416i | 0.117910i | 0.998261 | + | 0.0589548i | \(0.0187768\pi\) | ||||
−0.998261 | + | 0.0589548i | \(0.981223\pi\) | |||||||
\(912\) | −97.1996 | + | 1209.61i | −0.106579 | + | 1.32633i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 102.335i | − | 0.111964i | ||||||
\(915\) | −323.965 | − | 26.0326i | −0.354060 | − | 0.0284509i | ||||
\(916\) | −80.9290 | −0.0883504 | ||||||||
\(917\) | − | 1489.45i | − | 1.62427i | ||||||
\(918\) | −143.356 | + | 584.409i | −0.156161 | + | 0.636611i | ||||
\(919\) | 41.7982 | 0.0454823 | 0.0227411 | − | 0.999741i | \(-0.492761\pi\) | ||||
0.0227411 | + | 0.999741i | \(0.492761\pi\) | |||||||
\(920\) | − | 849.934i | − | 0.923841i | ||||||
\(921\) | −70.3871 | + | 875.940i | −0.0764247 | + | 0.951075i | ||||
\(922\) | −1586.16 | −1.72035 | ||||||||
\(923\) | 411.126i | 0.445424i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.4858 | 0.0210657 | ||||||||
\(926\) | 537.408i | 0.580354i | ||||||||
\(927\) | −52.6349 | − | 8.51404i | −0.0567798 | − | 0.00918451i | ||||
\(928\) | 120.958 | 0.130342 | ||||||||
\(929\) | − | 96.9891i | − | 0.104402i | −0.998637 | − | 0.0522008i | \(-0.983376\pi\) | ||
0.998637 | − | 0.0522008i | \(-0.0166236\pi\) | |||||||
\(930\) | 52.5568 | − | 654.049i | 0.0565127 | − | 0.703278i | ||||
\(931\) | 2346.42 | 2.52032 | ||||||||
\(932\) | 31.3088i | 0.0335932i | ||||||||
\(933\) | −1013.47 | − | 81.4385i | −1.08625 | − | 0.0872868i | ||||
\(934\) | 482.849 | 0.516969 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −39.5721 | + | 244.639i | −0.0422778 | + | 0.261367i | ||||
\(937\) | −438.349 | −0.467821 | −0.233911 | − | 0.972258i | \(-0.575152\pi\) | ||||
−0.233911 | + | 0.972258i | \(0.575152\pi\) | |||||||
\(938\) | − | 2388.44i | − | 2.54631i | ||||||
\(939\) | −85.7337 | + | 1066.92i | −0.0913032 | + | 1.13623i | ||||
\(940\) | 214.463 | 0.228152 | ||||||||
\(941\) | 1152.48i | 1.22474i | 0.790571 | + | 0.612370i | \(0.209784\pi\) | ||||
−0.790571 | + | 0.612370i | \(0.790216\pi\) | |||||||
\(942\) | −141.381 | − | 11.3608i | −0.150086 | − | 0.0120603i | ||||
\(943\) | −580.359 | −0.615439 | ||||||||
\(944\) | 1228.50i | 1.30138i | ||||||||
\(945\) | −1741.76 | − | 427.255i | −1.84313 | − | 0.452122i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 654.797i | − | 0.691443i | −0.938337 | − | 0.345722i | \(-0.887634\pi\) | ||
0.938337 | − | 0.345722i | \(-0.112366\pi\) | |||||||
\(948\) | −6.04903 | + | 75.2778i | −0.00638084 | + | 0.0794070i | ||||
\(949\) | −75.7239 | −0.0797934 | ||||||||
\(950\) | − | 163.370i | − | 0.171968i | ||||||
\(951\) | −1442.81 | − | 115.938i | −1.51715 | − | 0.121912i | ||||
\(952\) | 915.130 | 0.961271 | ||||||||
\(953\) | 1074.05i | 1.12702i | 0.826111 | + | 0.563508i | \(0.190548\pi\) | ||||
−0.826111 | + | 0.563508i | \(0.809452\pi\) | |||||||
\(954\) | −1074.90 | − | 173.872i | −1.12673 | − | 0.182256i | ||||
\(955\) | −1150.94 | −1.20517 | ||||||||
\(956\) | − | 326.573i | − | 0.341604i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1709.38 | −1.78433 | ||||||||
\(959\) | − | 841.931i | − | 0.877925i | ||||||
\(960\) | −782.602 | − | 62.8868i | −0.815210 | − | 0.0655071i | ||||
\(961\) | −603.124 | −0.627600 | ||||||||
\(962\) | 47.7275i | 0.0496128i | ||||||||
\(963\) | −190.930 | + | 1180.35i | −0.198266 | + | 1.22571i | ||||
\(964\) | 243.437 | 0.252529 | ||||||||
\(965\) | − | 631.552i | − | 0.654458i | ||||||
\(966\) | −144.899 | + | 1803.21i | −0.149999 | + | 1.86668i | ||||
\(967\) | −981.769 | −1.01527 | −0.507636 | − | 0.861571i | \(-0.669481\pi\) | ||||
−0.507636 | + | 0.861571i | \(0.669481\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −678.312 | − | 54.5065i | −0.700012 | − | 0.0562502i | ||||
\(970\) | 986.631 | 1.01715 | ||||||||
\(971\) | − | 1094.95i | − | 1.12765i | −0.825893 | − | 0.563827i | \(-0.809328\pi\) | ||
0.825893 | − | 0.563827i | \(-0.190672\pi\) | |||||||
\(972\) | −66.8421 | + | 157.692i | −0.0687676 | + | 0.162235i | ||||
\(973\) | −508.977 | −0.523101 | ||||||||
\(974\) | − | 682.653i | − | 0.700876i | ||||||
\(975\) | 3.15827 | − | 39.3034i | 0.00323925 | − | 0.0403112i | ||||
\(976\) | 372.402 | 0.381559 | ||||||||
\(977\) | 710.323i | 0.727045i | 0.931585 | + | 0.363523i | \(0.118426\pi\) | ||||
−0.931585 | + | 0.363523i | \(0.881574\pi\) | |||||||
\(978\) | −757.389 | − | 60.8608i | −0.774426 | − | 0.0622299i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 399.302i | − | 0.407451i | ||||||
\(981\) | 812.703 | + | 131.460i | 0.828444 | + | 0.134006i | ||||
\(982\) | 1532.68 | 1.56077 | ||||||||
\(983\) | − | 1520.74i | − | 1.54703i | −0.633775 | − | 0.773517i | \(-0.718495\pi\) | ||
0.633775 | − | 0.773517i | \(-0.281505\pi\) | |||||||
\(984\) | −44.6789 | + | 556.011i | −0.0454054 | + | 0.565052i | ||||
\(985\) | 418.620 | 0.424994 | ||||||||
\(986\) | 241.704i | 0.245136i | ||||||||
\(987\) | 2127.20 | + | 170.933i | 2.15521 | + | 0.173185i | ||||
\(988\) | 59.9465 | 0.0606746 | ||||||||
\(989\) | 1385.85i | 1.40127i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −339.543 | −0.342627 | −0.171313 | − | 0.985217i | \(-0.554801\pi\) | ||||
−0.171313 | + | 0.985217i | \(0.554801\pi\) | |||||||
\(992\) | 210.988i | 0.212690i | ||||||||
\(993\) | −31.6859 | + | 394.318i | −0.0319092 | + | 0.397098i | ||||
\(994\) | 2884.48 | 2.90190 | ||||||||
\(995\) | − | 1189.53i | − | 1.19551i | ||||||
\(996\) | −171.476 | − | 13.7791i | −0.172165 | − | 0.0138345i | ||||
\(997\) | 903.470 | 0.906189 | 0.453094 | − | 0.891463i | \(-0.350320\pi\) | ||||
0.453094 | + | 0.891463i | \(0.350320\pi\) | |||||||
\(998\) | − | 484.022i | − | 0.484992i | ||||||
\(999\) | 36.7392 | − | 149.772i | 0.0367760 | − | 0.149922i |
(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 | 363.3.b.n.122.9 | yes | 12 | |
3.2 | odd | 2 | inner | 363.3.b.n.122.4 | yes | 12 | |
11.2 | odd | 10 | 363.3.h.r.323.3 | 48 | |||
11.3 | even | 5 | 363.3.h.r.251.10 | 48 | |||
11.4 | even | 5 | 363.3.h.r.269.3 | 48 | |||
11.5 | even | 5 | 363.3.h.r.245.4 | 48 | |||
11.6 | odd | 10 | 363.3.h.r.245.10 | 48 | |||
11.7 | odd | 10 | 363.3.h.r.269.9 | 48 | |||
11.8 | odd | 10 | 363.3.h.r.251.4 | 48 | |||
11.9 | even | 5 | 363.3.h.r.323.9 | 48 | |||
11.10 | odd | 2 | inner | 363.3.b.n.122.3 | ✓ | 12 | |
33.2 | even | 10 | 363.3.h.r.323.10 | 48 | |||
33.5 | odd | 10 | 363.3.h.r.245.9 | 48 | |||
33.8 | even | 10 | 363.3.h.r.251.9 | 48 | |||
33.14 | odd | 10 | 363.3.h.r.251.3 | 48 | |||
33.17 | even | 10 | 363.3.h.r.245.3 | 48 | |||
33.20 | odd | 10 | 363.3.h.r.323.4 | 48 | |||
33.26 | odd | 10 | 363.3.h.r.269.10 | 48 | |||
33.29 | even | 10 | 363.3.h.r.269.4 | 48 | |||
33.32 | even | 2 | inner | 363.3.b.n.122.10 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.b.n.122.3 | ✓ | 12 | 11.10 | odd | 2 | inner | |
363.3.b.n.122.4 | yes | 12 | 3.2 | odd | 2 | inner | |
363.3.b.n.122.9 | yes | 12 | 1.1 | even | 1 | trivial | |
363.3.b.n.122.10 | yes | 12 | 33.32 | even | 2 | inner | |
363.3.h.r.245.3 | 48 | 33.17 | even | 10 | |||
363.3.h.r.245.4 | 48 | 11.5 | even | 5 | |||
363.3.h.r.245.9 | 48 | 33.5 | odd | 10 | |||
363.3.h.r.245.10 | 48 | 11.6 | odd | 10 | |||
363.3.h.r.251.3 | 48 | 33.14 | odd | 10 | |||
363.3.h.r.251.4 | 48 | 11.8 | odd | 10 | |||
363.3.h.r.251.9 | 48 | 33.8 | even | 10 | |||
363.3.h.r.251.10 | 48 | 11.3 | even | 5 | |||
363.3.h.r.269.3 | 48 | 11.4 | even | 5 | |||
363.3.h.r.269.4 | 48 | 33.29 | even | 10 | |||
363.3.h.r.269.9 | 48 | 11.7 | odd | 10 | |||
363.3.h.r.269.10 | 48 | 33.26 | odd | 10 | |||
363.3.h.r.323.3 | 48 | 11.2 | odd | 10 | |||
363.3.h.r.323.4 | 48 | 33.20 | odd | 10 | |||
363.3.h.r.323.9 | 48 | 11.9 | even | 5 | |||
363.3.h.r.323.10 | 48 | 33.2 | even | 10 |