Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(343,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.343");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.g (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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 343.12 | ||
Root | \(-1.89728 - 0.632718i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.343 |
Dual form | 684.3.g.b.343.11 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89728 | + | 0.632718i | 0.948639 | + | 0.316359i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.19934 | + | 2.40089i | 0.799834 | + | 0.600222i | ||||
\(5\) | −5.79268 | −1.15854 | −0.579268 | − | 0.815137i | \(-0.696662\pi\) | ||||
−0.579268 | + | 0.815137i | \(0.696662\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.87536i | − | 0.839338i | −0.907677 | − | 0.419669i | \(-0.862146\pi\) | ||
0.907677 | − | 0.419669i | \(-0.137854\pi\) | |||||||
\(8\) | 4.55095 | + | 6.57943i | 0.568868 | + | 0.822429i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.9903 | − | 3.66514i | −1.09903 | − | 0.366514i | ||||
\(11\) | − | 8.07883i | − | 0.734439i | −0.930134 | − | 0.367219i | \(-0.880310\pi\) | ||
0.930134 | − | 0.367219i | \(-0.119690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.0396 | −1.07997 | −0.539983 | − | 0.841676i | \(-0.681569\pi\) | ||||
−0.539983 | + | 0.841676i | \(0.681569\pi\) | |||||||
\(14\) | 3.71745 | − | 11.1472i | 0.265532 | − | 0.796229i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.47149 | + | 15.3625i | 0.279468 | + | 0.960155i | ||||
\(17\) | −29.9906 | −1.76415 | −0.882077 | − | 0.471104i | \(-0.843855\pi\) | ||||
−0.882077 | + | 0.471104i | \(0.843855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.35890i | − | 0.229416i | ||||||
\(20\) | −18.5327 | − | 13.9076i | −0.926636 | − | 0.695378i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.11162 | − | 15.3278i | 0.232346 | − | 0.696718i | ||||
\(23\) | − | 8.74865i | − | 0.380376i | −0.981748 | − | 0.190188i | \(-0.939090\pi\) | ||
0.981748 | − | 0.190188i | \(-0.0609098\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.55515 | 0.342206 | ||||||||
\(26\) | −26.6370 | − | 8.88309i | −1.02450 | − | 0.341657i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 14.1061 | − | 18.7973i | 0.503789 | − | 0.671331i | ||||
\(29\) | −13.4473 | −0.463700 | −0.231850 | − | 0.972752i | \(-0.574478\pi\) | ||||
−0.231850 | + | 0.972752i | \(0.574478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.65793i | − | 0.247030i | −0.992343 | − | 0.123515i | \(-0.960583\pi\) | ||
0.992343 | − | 0.123515i | \(-0.0394167\pi\) | |||||||
\(32\) | −1.23646 | + | 31.9761i | −0.0386394 | + | 0.999253i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −56.9006 | − | 18.9756i | −1.67355 | − | 0.558107i | ||||
\(35\) | 34.0341i | 0.972403i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.1221 | 0.678975 | 0.339488 | − | 0.940611i | \(-0.389746\pi\) | ||||
0.339488 | + | 0.940611i | \(0.389746\pi\) | |||||||
\(38\) | 2.75796 | − | 8.27005i | 0.0725778 | − | 0.217633i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −26.3622 | − | 38.1125i | −0.659054 | − | 0.952813i | ||||
\(41\) | −49.6861 | −1.21186 | −0.605928 | − | 0.795519i | \(-0.707198\pi\) | ||||
−0.605928 | + | 0.795519i | \(0.707198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 47.2402i | − | 1.09861i | −0.835622 | − | 0.549305i | \(-0.814892\pi\) | ||
0.835622 | − | 0.549305i | \(-0.185108\pi\) | |||||||
\(44\) | 19.3963 | − | 25.8469i | 0.440826 | − | 0.587429i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.53543 | − | 16.5986i | 0.120336 | − | 0.360840i | ||||
\(47\) | − | 46.8391i | − | 0.996577i | −0.867011 | − | 0.498289i | \(-0.833962\pi\) | ||
0.867011 | − | 0.498289i | \(-0.166038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.4801 | 0.295512 | ||||||||
\(50\) | 16.2315 | + | 5.41300i | 0.324630 | + | 0.108260i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −44.9173 | − | 33.7074i | −0.863793 | − | 0.648219i | ||||
\(53\) | 14.1940 | 0.267811 | 0.133906 | − | 0.990994i | \(-0.457248\pi\) | ||||
0.133906 | + | 0.990994i | \(0.457248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46.7981i | 0.850874i | ||||||||
\(56\) | 38.6565 | − | 26.7385i | 0.690295 | − | 0.477473i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −25.5133 | − | 8.50835i | −0.439884 | − | 0.146696i | ||||
\(59\) | − | 100.107i | − | 1.69673i | −0.529415 | − | 0.848363i | \(-0.677589\pi\) | ||
0.529415 | − | 0.848363i | \(-0.322411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31.1928 | −0.511357 | −0.255678 | − | 0.966762i | \(-0.582299\pi\) | ||||
−0.255678 | + | 0.966762i | \(0.582299\pi\) | |||||||
\(62\) | 4.84532 | − | 14.5292i | 0.0781503 | − | 0.234343i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −22.5778 | + | 59.8853i | −0.352778 | + | 0.935707i | ||||
\(65\) | 81.3267 | 1.25118 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.5861i | 0.516210i | 0.966117 | + | 0.258105i | \(0.0830981\pi\) | ||||
−0.966117 | + | 0.258105i | \(0.916902\pi\) | |||||||
\(68\) | −95.9501 | − | 72.0041i | −1.41103 | − | 1.05888i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −21.5340 | + | 64.5722i | −0.307629 | + | 0.922460i | ||||
\(71\) | 66.0243i | 0.929919i | 0.885332 | + | 0.464960i | \(0.153931\pi\) | ||||
−0.885332 | + | 0.464960i | \(0.846069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −27.5063 | −0.376798 | −0.188399 | − | 0.982093i | \(-0.560330\pi\) | ||||
−0.188399 | + | 0.982093i | \(0.560330\pi\) | |||||||
\(74\) | 47.6636 | + | 15.8952i | 0.644103 | + | 0.214800i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.4652 | − | 13.9456i | 0.137700 | − | 0.183494i | ||||
\(77\) | −47.4661 | −0.616442 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 40.9739i | 0.518657i | 0.965789 | + | 0.259329i | \(0.0835013\pi\) | ||||
−0.965789 | + | 0.259329i | \(0.916499\pi\) | |||||||
\(80\) | −25.9019 | − | 88.9899i | −0.323774 | − | 1.11237i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −94.2684 | − | 31.4373i | −1.14961 | − | 0.383382i | ||||
\(83\) | 87.8564i | 1.05851i | 0.848463 | + | 0.529255i | \(0.177529\pi\) | ||||
−0.848463 | + | 0.529255i | \(0.822471\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 173.726 | 2.04384 | ||||||||
\(86\) | 29.8898 | − | 89.6279i | 0.347555 | − | 1.04219i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 53.1541 | − | 36.7663i | 0.604024 | − | 0.417799i | ||||
\(89\) | −28.6482 | −0.321890 | −0.160945 | − | 0.986963i | \(-0.551454\pi\) | ||||
−0.160945 | + | 0.986963i | \(0.551454\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 82.4875i | 0.906457i | ||||||||
\(92\) | 21.0045 | − | 27.9899i | 0.228310 | − | 0.304238i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 29.6360 | − | 88.8669i | 0.315276 | − | 0.945393i | ||||
\(95\) | 25.2497i | 0.265786i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.35629 | 0.0964566 | 0.0482283 | − | 0.998836i | \(-0.484642\pi\) | ||||
0.0482283 | + | 0.998836i | \(0.484642\pi\) | |||||||
\(98\) | 27.4728 | + | 9.16182i | 0.280334 | + | 0.0934879i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 27.3708 | + | 20.5399i | 0.273708 | + | 0.205399i | ||||
\(101\) | 86.6846 | 0.858263 | 0.429132 | − | 0.903242i | \(-0.358820\pi\) | ||||
0.429132 | + | 0.903242i | \(0.358820\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 139.602i | 1.35536i | 0.735358 | + | 0.677679i | \(0.237014\pi\) | ||||
−0.735358 | + | 0.677679i | \(0.762986\pi\) | |||||||
\(104\) | −63.8933 | − | 92.3723i | −0.614359 | − | 0.888195i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.9300 | + | 8.98081i | 0.254057 | + | 0.0847246i | ||||
\(107\) | 53.5627i | 0.500586i | 0.968170 | + | 0.250293i | \(0.0805269\pi\) | ||||
−0.968170 | + | 0.250293i | \(0.919473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −154.519 | −1.41760 | −0.708802 | − | 0.705408i | \(-0.750764\pi\) | ||||
−0.708802 | + | 0.705408i | \(0.750764\pi\) | |||||||
\(110\) | −29.6100 | + | 88.7890i | −0.269182 | + | 0.807173i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 90.2602 | − | 26.2716i | 0.805894 | − | 0.234568i | ||||
\(113\) | 66.0050 | 0.584115 | 0.292057 | − | 0.956401i | \(-0.405660\pi\) | ||||
0.292057 | + | 0.956401i | \(0.405660\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 50.6782i | 0.440680i | ||||||||
\(116\) | −43.0224 | − | 32.2854i | −0.370883 | − | 0.278323i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 63.3394 | − | 189.931i | 0.536775 | − | 1.60958i | ||||
\(119\) | 176.206i | 1.48072i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 55.7325 | 0.460600 | ||||||||
\(122\) | −59.1814 | − | 19.7362i | −0.485093 | − | 0.161772i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.3858 | − | 24.5003i | 0.148273 | − | 0.197583i | ||||
\(125\) | 95.2598 | 0.762078 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 222.988i | 1.75581i | 0.478833 | + | 0.877906i | \(0.341060\pi\) | ||||
−0.478833 | + | 0.877906i | \(0.658940\pi\) | |||||||
\(128\) | −80.7268 | + | 99.3337i | −0.630678 | + | 0.776044i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 154.299 | + | 51.4569i | 1.18692 | + | 0.395822i | ||||
\(131\) | − | 199.333i | − | 1.52163i | −0.648971 | − | 0.760813i | \(-0.724800\pi\) | ||
0.648971 | − | 0.760813i | \(-0.275200\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.6101 | −0.192557 | ||||||||
\(134\) | −21.8833 | + | 65.6195i | −0.163308 | + | 0.489698i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −136.486 | − | 197.321i | −1.00357 | − | 1.45089i | ||||
\(137\) | 6.01427 | 0.0438998 | 0.0219499 | − | 0.999759i | \(-0.493013\pi\) | ||||
0.0219499 | + | 0.999759i | \(0.493013\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 77.3080i | − | 0.556172i | −0.960556 | − | 0.278086i | \(-0.910300\pi\) | ||
0.960556 | − | 0.278086i | \(-0.0897001\pi\) | |||||||
\(140\) | −81.7120 | + | 108.887i | −0.583657 | + | 0.777761i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −41.7748 | + | 125.266i | −0.294188 | + | 0.882158i | ||||
\(143\) | 113.423i | 0.793169i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 77.8959 | 0.537213 | ||||||||
\(146\) | −52.1870 | − | 17.4037i | −0.357445 | − | 0.119203i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 80.3740 | + | 60.3153i | 0.543067 | + | 0.407536i | ||||
\(149\) | −250.996 | −1.68454 | −0.842270 | − | 0.539056i | \(-0.818781\pi\) | ||||
−0.842270 | + | 0.539056i | \(0.818781\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 62.0159i | − | 0.410701i | −0.978688 | − | 0.205351i | \(-0.934167\pi\) | ||
0.978688 | − | 0.205351i | \(-0.0658335\pi\) | |||||||
\(152\) | 28.6791 | − | 19.8371i | 0.188678 | − | 0.130507i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −90.0564 | − | 30.0326i | −0.584782 | − | 0.195017i | ||||
\(155\) | 44.3600i | 0.286193i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −100.150 | −0.637898 | −0.318949 | − | 0.947772i | \(-0.603330\pi\) | ||||
−0.318949 | + | 0.947772i | \(0.603330\pi\) | |||||||
\(158\) | −25.9250 | + | 77.7390i | −0.164082 | + | 0.492019i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.16242 | − | 185.227i | 0.0447651 | − | 1.15767i | ||||
\(161\) | −51.4015 | −0.319264 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 187.915i | − | 1.15285i | −0.817150 | − | 0.576425i | \(-0.804447\pi\) | ||
0.817150 | − | 0.576425i | \(-0.195553\pi\) | |||||||
\(164\) | −158.963 | − | 119.291i | −0.969284 | − | 0.727382i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −55.5883 | + | 166.688i | −0.334869 | + | 1.00414i | ||||
\(167\) | − | 24.2604i | − | 0.145272i | −0.997359 | − | 0.0726361i | \(-0.976859\pi\) | ||
0.997359 | − | 0.0726361i | \(-0.0231412\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.1093 | 0.166327 | ||||||||
\(170\) | 329.607 | + | 109.920i | 1.93886 | + | 0.646587i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 113.418 | − | 151.137i | 0.659410 | − | 0.878706i | ||||
\(173\) | 250.771 | 1.44954 | 0.724772 | − | 0.688989i | \(-0.241945\pi\) | ||||
0.724772 | + | 0.688989i | \(0.241945\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 50.2646i | − | 0.287226i | ||||||
\(176\) | 124.111 | − | 36.1244i | 0.705175 | − | 0.205252i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −54.3537 | − | 18.1263i | −0.305358 | − | 0.101833i | ||||
\(179\) | − | 62.4162i | − | 0.348694i | −0.984684 | − | 0.174347i | \(-0.944219\pi\) | ||
0.984684 | − | 0.174347i | \(-0.0557815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −66.6789 | −0.368392 | −0.184196 | − | 0.982890i | \(-0.558968\pi\) | ||||
−0.184196 | + | 0.982890i | \(0.558968\pi\) | |||||||
\(182\) | −52.1914 | + | 156.502i | −0.286766 | + | 0.859900i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 57.5612 | − | 39.8147i | 0.312832 | − | 0.216384i | ||||
\(185\) | −145.524 | −0.786617 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 242.289i | 1.29566i | ||||||||
\(188\) | 112.455 | − | 149.854i | 0.598167 | − | 0.797096i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.9760 | + | 47.9057i | −0.0840840 | + | 0.252135i | ||||
\(191\) | − | 218.487i | − | 1.14391i | −0.820285 | − | 0.571955i | \(-0.806185\pi\) | ||
0.820285 | − | 0.571955i | \(-0.193815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 61.9485 | 0.320977 | 0.160488 | − | 0.987038i | \(-0.448693\pi\) | ||||
0.160488 | + | 0.987038i | \(0.448693\pi\) | |||||||
\(194\) | 17.7515 | + | 5.91990i | 0.0915025 | + | 0.0305149i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 46.3267 | + | 34.7651i | 0.236361 | + | 0.177373i | ||||
\(197\) | 355.348 | 1.80380 | 0.901898 | − | 0.431950i | \(-0.142174\pi\) | ||||
0.901898 | + | 0.431950i | \(0.142174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 208.471i | 1.04759i | 0.851843 | + | 0.523797i | \(0.175485\pi\) | ||||
−0.851843 | + | 0.523797i | \(0.824515\pi\) | |||||||
\(200\) | 38.9340 | + | 56.2880i | 0.194670 | + | 0.281440i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 164.465 | + | 54.8469i | 0.814183 | + | 0.271519i | ||||
\(203\) | 79.0078i | 0.389201i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 287.816 | 1.40398 | ||||||||
\(206\) | −88.3286 | + | 264.864i | −0.428780 | + | 1.28575i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −62.7777 | − | 215.682i | −0.301816 | − | 1.03694i | ||||
\(209\) | −35.2148 | −0.168492 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 275.150i | − | 1.30403i | −0.758206 | − | 0.652015i | \(-0.773924\pi\) | ||
0.758206 | − | 0.652015i | \(-0.226076\pi\) | |||||||
\(212\) | 45.4114 | + | 34.0782i | 0.214205 | + | 0.160746i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −33.8901 | + | 101.623i | −0.158365 | + | 0.474876i | ||||
\(215\) | 273.648i | 1.27278i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44.9932 | −0.207342 | ||||||||
\(218\) | −293.165 | − | 97.7669i | −1.34479 | − | 0.448472i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −112.357 | + | 149.723i | −0.510713 | + | 0.680558i | ||||
\(221\) | 421.055 | 1.90523 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 237.911i | 1.06687i | 0.845842 | + | 0.533434i | \(0.179099\pi\) | ||||
−0.845842 | + | 0.533434i | \(0.820901\pi\) | |||||||
\(224\) | 187.871 | + | 7.26466i | 0.838711 | + | 0.0324315i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 125.230 | + | 41.7626i | 0.554114 | + | 0.184790i | ||||
\(227\) | 157.067i | 0.691924i | 0.938249 | + | 0.345962i | \(0.112447\pi\) | ||||
−0.938249 | + | 0.345962i | \(0.887553\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −177.569 | −0.775412 | −0.387706 | − | 0.921783i | \(-0.626732\pi\) | ||||
−0.387706 | + | 0.921783i | \(0.626732\pi\) | |||||||
\(230\) | −32.0650 | + | 96.1506i | −0.139413 | + | 0.418046i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −61.1979 | − | 88.4756i | −0.263784 | − | 0.381360i | ||||
\(233\) | −75.5890 | −0.324416 | −0.162208 | − | 0.986757i | \(-0.551862\pi\) | ||||
−0.162208 | + | 0.986757i | \(0.551862\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 271.324i | 1.15457i | ||||||||
\(236\) | 240.345 | − | 320.275i | 1.01841 | − | 1.35710i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −111.489 | + | 334.312i | −0.468440 | + | 1.40467i | ||||
\(239\) | 1.99543i | 0.00834909i | 0.999991 | + | 0.00417454i | \(0.00132880\pi\) | ||||
−0.999991 | + | 0.00417454i | \(0.998671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −64.6551 | −0.268278 | −0.134139 | − | 0.990962i | \(-0.542827\pi\) | ||||
−0.134139 | + | 0.990962i | \(0.542827\pi\) | |||||||
\(242\) | 105.740 | + | 35.2630i | 0.436943 | + | 0.145715i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −99.7961 | − | 74.8903i | −0.409000 | − | 0.306927i | ||||
\(245\) | −83.8785 | −0.342361 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 61.1970i | 0.247761i | ||||||||
\(248\) | 50.3848 | − | 34.8508i | 0.203165 | − | 0.140528i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 180.734 | + | 60.2726i | 0.722937 | + | 0.241090i | ||||
\(251\) | − | 245.790i | − | 0.979245i | −0.871935 | − | 0.489622i | \(-0.837135\pi\) | ||
0.871935 | − | 0.489622i | \(-0.162865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −70.6789 | −0.279363 | ||||||||
\(254\) | −141.089 | + | 423.071i | −0.555467 | + | 1.66563i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −216.012 | + | 137.386i | −0.843795 | + | 0.536665i | ||||
\(257\) | −276.853 | −1.07725 | −0.538625 | − | 0.842546i | \(-0.681056\pi\) | ||||
−0.538625 | + | 0.842546i | \(0.681056\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 147.601i | − | 0.569890i | ||||||
\(260\) | 260.191 | + | 195.256i | 1.00074 | + | 0.750985i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 126.122 | − | 378.190i | 0.481380 | − | 1.44347i | ||||
\(263\) | 95.4157i | 0.362797i | 0.983410 | + | 0.181399i | \(0.0580624\pi\) | ||||
−0.983410 | + | 0.181399i | \(0.941938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −82.2213 | −0.310269 | ||||||||
\(266\) | −48.5895 | − | 16.2040i | −0.182667 | − | 0.0609173i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −83.0373 | + | 110.653i | −0.309841 | + | 0.412882i | ||||
\(269\) | 128.844 | 0.478974 | 0.239487 | − | 0.970900i | \(-0.423021\pi\) | ||||
0.239487 | + | 0.970900i | \(0.423021\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 317.491i | − | 1.17155i | −0.810472 | − | 0.585777i | \(-0.800789\pi\) | ||
0.810472 | − | 0.585777i | \(-0.199211\pi\) | |||||||
\(272\) | −134.103 | − | 460.730i | −0.493025 | − | 1.69386i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.4107 | + | 3.80534i | 0.0416450 | + | 0.0138881i | ||||
\(275\) | − | 69.1156i | − | 0.251329i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.1910 | −0.105383 | −0.0526913 | − | 0.998611i | \(-0.516780\pi\) | ||||
−0.0526913 | + | 0.998611i | \(0.516780\pi\) | |||||||
\(278\) | 48.9142 | − | 146.675i | 0.175950 | − | 0.527607i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −223.925 | + | 154.887i | −0.799732 | + | 0.553169i | ||||
\(281\) | −204.530 | −0.727866 | −0.363933 | − | 0.931425i | \(-0.618566\pi\) | ||||
−0.363933 | + | 0.931425i | \(0.618566\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 502.549i | − | 1.77579i | −0.460044 | − | 0.887896i | \(-0.652166\pi\) | ||
0.460044 | − | 0.887896i | \(-0.347834\pi\) | |||||||
\(284\) | −158.517 | + | 211.234i | −0.558158 | + | 0.743781i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −71.7649 | + | 215.195i | −0.250926 | + | 0.752432i | ||||
\(287\) | 291.924i | 1.01716i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 610.438 | 2.11224 | ||||||||
\(290\) | 147.790 | + | 49.2862i | 0.509622 | + | 0.169952i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −88.0017 | − | 66.0394i | −0.301376 | − | 0.226162i | ||||
\(293\) | −239.563 | −0.817623 | −0.408811 | − | 0.912619i | \(-0.634057\pi\) | ||||
−0.408811 | + | 0.912619i | \(0.634057\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 579.887i | 1.96572i | ||||||||
\(296\) | 114.329 | + | 165.289i | 0.386248 | + | 0.558409i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −476.210 | − | 158.810i | −1.59802 | − | 0.532919i | ||||
\(299\) | 122.827i | 0.410794i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −277.554 | −0.922105 | ||||||||
\(302\) | 39.2386 | − | 117.661i | 0.129929 | − | 0.389608i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 66.9635 | − | 19.4908i | 0.220275 | − | 0.0641144i | ||||
\(305\) | 180.690 | 0.592425 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 310.436i | − | 1.01119i | −0.862771 | − | 0.505595i | \(-0.831273\pi\) | ||
0.862771 | − | 0.505595i | \(-0.168727\pi\) | |||||||
\(308\) | −151.860 | − | 113.961i | −0.493051 | − | 0.370002i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.0674 | + | 84.1632i | −0.0905399 | + | 0.271494i | ||||
\(311\) | 219.552i | 0.705956i | 0.935632 | + | 0.352978i | \(0.114831\pi\) | ||||
−0.935632 | + | 0.352978i | \(0.885169\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 322.681 | 1.03093 | 0.515465 | − | 0.856911i | \(-0.327619\pi\) | ||||
0.515465 | + | 0.856911i | \(0.327619\pi\) | |||||||
\(314\) | −190.013 | − | 63.3668i | −0.605136 | − | 0.201805i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −98.3738 | + | 131.089i | −0.311309 | + | 0.414840i | ||||
\(317\) | 53.6396 | 0.169210 | 0.0846050 | − | 0.996415i | \(-0.473037\pi\) | ||||
0.0846050 | + | 0.996415i | \(0.473037\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 108.638i | 0.340559i | ||||||||
\(320\) | 130.786 | − | 346.896i | 0.408706 | − | 1.08405i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −97.5231 | − | 32.5227i | −0.302867 | − | 0.101002i | ||||
\(323\) | 130.726i | 0.404725i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −120.111 | −0.369571 | ||||||||
\(326\) | 118.897 | − | 356.526i | 0.364715 | − | 1.09364i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −226.119 | − | 326.906i | −0.689387 | − | 0.996665i | ||||
\(329\) | −275.197 | −0.836465 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 165.098i | 0.498786i | 0.968402 | + | 0.249393i | \(0.0802310\pi\) | ||||
−0.968402 | + | 0.249393i | \(0.919769\pi\) | |||||||
\(332\) | −210.933 | + | 281.082i | −0.635341 | + | 0.846632i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.3500 | − | 46.0288i | 0.0459582 | − | 0.137811i | ||||
\(335\) | − | 200.346i | − | 0.598048i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −374.211 | −1.11042 | −0.555210 | − | 0.831710i | \(-0.687362\pi\) | ||||
−0.555210 | + | 0.831710i | \(0.687362\pi\) | |||||||
\(338\) | 53.3312 | + | 17.7853i | 0.157785 | + | 0.0526191i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 555.808 | + | 417.097i | 1.63473 | + | 1.22676i | ||||
\(341\) | −61.8671 | −0.181429 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 372.969i | − | 1.08737i | ||||||
\(344\) | 310.814 | − | 214.988i | 0.903529 | − | 0.624965i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 475.783 | + | 158.667i | 1.37509 | + | 0.458577i | ||||
\(347\) | − | 442.710i | − | 1.27582i | −0.770110 | − | 0.637911i | \(-0.779799\pi\) | ||
0.770110 | − | 0.637911i | \(-0.220201\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −163.363 | −0.468090 | −0.234045 | − | 0.972226i | \(-0.575196\pi\) | ||||
−0.234045 | + | 0.972226i | \(0.575196\pi\) | |||||||
\(350\) | 31.8033 | − | 95.3660i | 0.0908667 | − | 0.272474i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 258.329 | + | 9.98915i | 0.733890 | + | 0.0283783i | ||||
\(353\) | −410.271 | −1.16224 | −0.581120 | − | 0.813818i | \(-0.697385\pi\) | ||||
−0.581120 | + | 0.813818i | \(0.697385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 382.457i | − | 1.07734i | ||||||
\(356\) | −91.6553 | − | 68.7812i | −0.257459 | − | 0.193206i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 39.4919 | − | 118.421i | 0.110313 | − | 0.330785i | ||||
\(359\) | − | 124.552i | − | 0.346941i | −0.984839 | − | 0.173470i | \(-0.944502\pi\) | ||
0.984839 | − | 0.173470i | \(-0.0554981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | −126.508 | − | 42.1890i | −0.349471 | − | 0.116544i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −198.043 | + | 263.905i | −0.544075 | + | 0.725015i | ||||
\(365\) | 159.335 | 0.436534 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 288.749i | − | 0.786782i | −0.919371 | − | 0.393391i | \(-0.871302\pi\) | ||
0.919371 | − | 0.393391i | \(-0.128698\pi\) | |||||||
\(368\) | 134.401 | − | 39.1195i | 0.365220 | − | 0.106303i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −276.100 | − | 92.0758i | −0.746216 | − | 0.248854i | ||||
\(371\) | − | 83.3950i | − | 0.224784i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 380.740 | 1.02075 | 0.510376 | − | 0.859952i | \(-0.329506\pi\) | ||||
0.510376 | + | 0.859952i | \(0.329506\pi\) | |||||||
\(374\) | −153.301 | + | 459.690i | −0.409895 | + | 1.22912i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 308.175 | − | 213.162i | 0.819614 | − | 0.566921i | ||||
\(377\) | 188.794 | 0.500780 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 176.366i | 0.465345i | 0.972555 | + | 0.232673i | \(0.0747471\pi\) | ||||
−0.972555 | + | 0.232673i | \(0.925253\pi\) | |||||||
\(380\) | −60.6217 | + | 80.7823i | −0.159531 | + | 0.212585i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 138.241 | − | 414.530i | 0.361886 | − | 1.08516i | ||||
\(383\) | 389.993i | 1.01826i | 0.860690 | + | 0.509129i | \(0.170032\pi\) | ||||
−0.860690 | + | 0.509129i | \(0.829968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 274.956 | 0.714171 | ||||||||
\(386\) | 117.534 | + | 39.1960i | 0.304491 | + | 0.101544i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 29.9339 | + | 22.4634i | 0.0771493 | + | 0.0578953i | ||||
\(389\) | −5.08380 | −0.0130689 | −0.00653445 | − | 0.999979i | \(-0.502080\pi\) | ||||
−0.00653445 | + | 0.999979i | \(0.502080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 262.378i | 0.671043i | ||||||||
\(392\) | 65.8981 | + | 95.2707i | 0.168107 | + | 0.243038i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 674.194 | + | 224.835i | 1.71115 | + | 0.570647i | ||||
\(395\) | − | 237.349i | − | 0.600883i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 320.541 | 0.807409 | 0.403705 | − | 0.914889i | \(-0.367722\pi\) | ||||
0.403705 | + | 0.914889i | \(0.367722\pi\) | |||||||
\(398\) | −131.904 | + | 395.528i | −0.331416 | + | 0.993789i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 38.2543 | + | 131.428i | 0.0956356 | + | 0.328571i | ||||
\(401\) | 428.362 | 1.06823 | 0.534117 | − | 0.845410i | \(-0.320644\pi\) | ||||
0.534117 | + | 0.845410i | \(0.320644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 107.514i | 0.266784i | ||||||||
\(404\) | 277.333 | + | 208.120i | 0.686468 | + | 0.515148i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −49.9897 | + | 149.900i | −0.123127 | + | 0.369211i | ||||
\(407\) | − | 202.957i | − | 0.498666i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 109.550 | 0.267849 | 0.133925 | − | 0.990992i | \(-0.457242\pi\) | ||||
0.133925 | + | 0.990992i | \(0.457242\pi\) | |||||||
\(410\) | 546.067 | + | 182.106i | 1.33187 | + | 0.444162i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −335.168 | + | 446.633i | −0.813515 | + | 1.08406i | ||||
\(413\) | −588.164 | −1.42413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 508.924i | − | 1.22632i | ||||||
\(416\) | 17.3594 | − | 448.930i | 0.0417292 | − | 1.07916i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −66.8123 | − | 22.2810i | −0.159838 | − | 0.0533039i | ||||
\(419\) | − | 305.115i | − | 0.728199i | −0.931360 | − | 0.364099i | \(-0.881377\pi\) | ||
0.931360 | − | 0.364099i | \(-0.118623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −721.115 | −1.71286 | −0.856431 | − | 0.516261i | \(-0.827323\pi\) | ||||
−0.856431 | + | 0.516261i | \(0.827323\pi\) | |||||||
\(422\) | 174.093 | − | 522.037i | 0.412542 | − | 1.23705i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 64.5962 | + | 93.3885i | 0.152349 | + | 0.220256i | ||||
\(425\) | −256.574 | −0.603704 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 183.269i | 0.429201i | ||||||||
\(428\) | −128.598 | + | 171.365i | −0.300462 | + | 0.400386i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −173.142 | + | 519.186i | −0.402656 | + | 1.20741i | ||||
\(431\) | − | 275.396i | − | 0.638971i | −0.947591 | − | 0.319485i | \(-0.896490\pi\) | ||
0.947591 | − | 0.319485i | \(-0.103510\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −445.559 | −1.02900 | −0.514502 | − | 0.857489i | \(-0.672023\pi\) | ||||
−0.514502 | + | 0.857489i | \(0.672023\pi\) | |||||||
\(434\) | −85.3646 | − | 28.4680i | −0.196693 | − | 0.0655945i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −494.357 | − | 370.982i | −1.13385 | − | 0.850876i | ||||
\(437\) | −38.1345 | −0.0872643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 501.542i | − | 1.14246i | −0.820788 | − | 0.571232i | \(-0.806466\pi\) | ||
0.820788 | − | 0.571232i | \(-0.193534\pi\) | |||||||
\(440\) | −307.905 | + | 212.975i | −0.699783 | + | 0.484035i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 798.859 | + | 266.409i | 1.80737 | + | 0.602736i | ||||
\(443\) | 297.237i | 0.670964i | 0.942047 | + | 0.335482i | \(0.108899\pi\) | ||||
−0.942047 | + | 0.335482i | \(0.891101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 165.950 | 0.372922 | ||||||||
\(446\) | −150.531 | + | 451.384i | −0.337513 | + | 1.01207i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 351.848 | + | 132.653i | 0.785374 | + | 0.296100i | ||||
\(449\) | 286.813 | 0.638782 | 0.319391 | − | 0.947623i | \(-0.396522\pi\) | ||||
0.319391 | + | 0.947623i | \(0.396522\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 401.405i | 0.890034i | ||||||||
\(452\) | 211.172 | + | 158.470i | 0.467195 | + | 0.350598i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −99.3789 | + | 297.999i | −0.218896 | + | 0.656386i | ||||
\(455\) | − | 477.824i | − | 1.05016i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 254.383 | 0.556637 | 0.278318 | − | 0.960489i | \(-0.410223\pi\) | ||||
0.278318 | + | 0.960489i | \(0.410223\pi\) | |||||||
\(458\) | −336.899 | − | 112.351i | −0.735587 | − | 0.245309i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −121.673 | + | 162.136i | −0.264505 | + | 0.352470i | ||||
\(461\) | 77.6648 | 0.168470 | 0.0842351 | − | 0.996446i | \(-0.473155\pi\) | ||||
0.0842351 | + | 0.996446i | \(0.473155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 543.071i | − | 1.17294i | −0.809971 | − | 0.586470i | \(-0.800517\pi\) | ||
0.809971 | − | 0.586470i | \(-0.199483\pi\) | |||||||
\(464\) | −60.1295 | − | 206.584i | −0.129589 | − | 0.445224i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −143.413 | − | 47.8265i | −0.307754 | − | 0.102632i | ||||
\(467\) | 384.665i | 0.823694i | 0.911253 | + | 0.411847i | \(0.135116\pi\) | ||||
−0.911253 | + | 0.411847i | \(0.864884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 203.206 | 0.433275 | ||||||||
\(470\) | −171.672 | + | 514.778i | −0.365259 | + | 1.09527i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 658.646 | − | 455.581i | 1.39544 | − | 0.965213i | ||||
\(473\) | −381.646 | −0.806862 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 37.2910i | − | 0.0785074i | ||||||
\(476\) | −423.050 | + | 563.742i | −0.888761 | + | 1.18433i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.26255 | + | 3.78589i | −0.00264131 | + | 0.00792027i | ||||
\(479\) | 661.184i | 1.38034i | 0.723646 | + | 0.690171i | \(0.242465\pi\) | ||||
−0.723646 | + | 0.690171i | \(0.757535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −352.703 | −0.733270 | ||||||||
\(482\) | −122.669 | − | 40.9085i | −0.254500 | − | 0.0848724i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 178.307 | + | 133.808i | 0.368403 | + | 0.276462i | ||||
\(485\) | −54.1980 | −0.111748 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 626.822i | − | 1.28711i | −0.765401 | − | 0.643554i | \(-0.777459\pi\) | ||
0.765401 | − | 0.643554i | \(-0.222541\pi\) | |||||||
\(488\) | −141.957 | − | 205.231i | −0.290895 | − | 0.420555i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −159.141 | − | 53.0715i | −0.324778 | − | 0.108309i | ||||
\(491\) | − | 973.335i | − | 1.98235i | −0.132555 | − | 0.991176i | \(-0.542318\pi\) | ||
0.132555 | − | 0.991176i | \(-0.457682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 403.293 | 0.818039 | ||||||||
\(494\) | −38.7205 | + | 116.108i | −0.0783815 | + | 0.235036i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 117.645 | − | 34.2424i | 0.237187 | − | 0.0690370i | ||||
\(497\) | 387.917 | 0.780516 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 171.966i | − | 0.344621i | −0.985043 | − | 0.172311i | \(-0.944877\pi\) | ||
0.985043 | − | 0.172311i | \(-0.0551233\pi\) | |||||||
\(500\) | 304.768 | + | 228.708i | 0.609536 | + | 0.457416i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 155.516 | − | 466.333i | 0.309793 | − | 0.928950i | ||||
\(503\) | − | 806.197i | − | 1.60278i | −0.598145 | − | 0.801388i | \(-0.704095\pi\) | ||
0.598145 | − | 0.801388i | \(-0.295905\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −502.136 | −0.994329 | ||||||||
\(506\) | −134.098 | − | 44.7198i | −0.265015 | − | 0.0883791i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −535.369 | + | 713.414i | −1.05388 | + | 1.40436i | ||||
\(509\) | −944.065 | −1.85475 | −0.927373 | − | 0.374139i | \(-0.877938\pi\) | ||||
−0.927373 | + | 0.374139i | \(0.877938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 161.609i | 0.316261i | ||||||||
\(512\) | −496.761 | + | 123.986i | −0.970236 | + | 0.242160i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −525.268 | − | 175.170i | −1.02192 | − | 0.340798i | ||||
\(515\) | − | 808.669i | − | 1.57023i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −378.405 | −0.731925 | ||||||||
\(518\) | 93.3901 | − | 280.041i | 0.180290 | − | 0.540620i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 370.113 | + | 535.083i | 0.711757 | + | 1.02901i | ||||
\(521\) | −168.936 | −0.324253 | −0.162126 | − | 0.986770i | \(-0.551835\pi\) | ||||
−0.162126 | + | 0.986770i | \(0.551835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 391.361i | − | 0.748300i | −0.927368 | − | 0.374150i | \(-0.877935\pi\) | ||
0.927368 | − | 0.374150i | \(-0.122065\pi\) | |||||||
\(524\) | 478.576 | − | 637.733i | 0.913313 | − | 1.21705i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −60.3712 | + | 181.030i | −0.114774 | + | 0.344164i | ||||
\(527\) | 229.666i | 0.435799i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 452.461 | 0.855314 | ||||||||
\(530\) | −155.997 | − | 52.0230i | −0.294334 | − | 0.0981565i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −81.9354 | − | 61.4870i | −0.154014 | − | 0.115577i | ||||
\(533\) | 697.571 | 1.30876 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 310.272i | − | 0.579947i | ||||||
\(536\) | −227.557 | + | 157.399i | −0.424546 | + | 0.293656i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 244.453 | + | 81.5220i | 0.454374 | + | 0.151528i | ||||
\(539\) | − | 116.982i | − | 0.217036i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −561.849 | −1.03854 | −0.519269 | − | 0.854611i | \(-0.673796\pi\) | ||||
−0.519269 | + | 0.854611i | \(0.673796\pi\) | |||||||
\(542\) | 200.883 | − | 602.370i | 0.370632 | − | 1.11138i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 37.0822 | − | 958.984i | 0.0681659 | − | 1.76284i | ||||
\(545\) | 895.078 | 1.64234 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 630.789i | − | 1.15318i | −0.817034 | − | 0.576590i | \(-0.804383\pi\) | ||
0.817034 | − | 0.576590i | \(-0.195617\pi\) | |||||||
\(548\) | 19.2417 | + | 14.4396i | 0.0351125 | + | 0.0263496i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 43.7307 | − | 131.132i | 0.0795103 | − | 0.238421i | ||||
\(551\) | 58.6154i | 0.106380i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 240.737 | 0.435329 | ||||||||
\(554\) | −55.3834 | − | 18.4697i | −0.0999700 | − | 0.0333387i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 185.608 | − | 247.334i | 0.333827 | − | 0.444845i | ||||
\(557\) | −123.847 | −0.222346 | −0.111173 | − | 0.993801i | \(-0.535461\pi\) | ||||
−0.111173 | + | 0.993801i | \(0.535461\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 663.232i | 1.18646i | ||||||||
\(560\) | −522.848 | + | 152.183i | −0.933658 | + | 0.271756i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −388.051 | − | 129.410i | −0.690483 | − | 0.230267i | ||||
\(563\) | − | 935.582i | − | 1.66178i | −0.556437 | − | 0.830890i | \(-0.687832\pi\) | ||
0.556437 | − | 0.830890i | \(-0.312168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −382.346 | −0.676718 | ||||||||
\(566\) | 317.972 | − | 953.476i | 0.561788 | − | 1.68459i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −434.402 | + | 300.473i | −0.764792 | + | 0.529001i | ||||
\(569\) | −373.028 | −0.655586 | −0.327793 | − | 0.944750i | \(-0.606305\pi\) | ||||
−0.327793 | + | 0.944750i | \(0.606305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 435.521i | 0.762733i | 0.924424 | + | 0.381367i | \(0.124546\pi\) | ||||
−0.924424 | + | 0.381367i | \(0.875454\pi\) | |||||||
\(572\) | −272.316 | + | 362.879i | −0.476077 | + | 0.634404i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −184.706 | + | 553.861i | −0.321787 | + | 0.964915i | ||||
\(575\) | − | 74.8460i | − | 0.130167i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −807.758 | −1.39993 | −0.699964 | − | 0.714178i | \(-0.746801\pi\) | ||||
−0.699964 | + | 0.714178i | \(0.746801\pi\) | |||||||
\(578\) | 1158.17 | + | 386.235i | 2.00376 | + | 0.668227i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 249.215 | + | 187.019i | 0.429681 | + | 0.322447i | ||||
\(581\) | 516.188 | 0.888448 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 114.671i | − | 0.196691i | ||||||
\(584\) | −125.179 | − | 180.975i | −0.214348 | − | 0.309889i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −454.519 | − | 151.576i | −0.775629 | − | 0.258662i | ||||
\(587\) | 311.402i | 0.530498i | 0.964180 | + | 0.265249i | \(0.0854542\pi\) | ||||
−0.964180 | + | 0.265249i | \(0.914546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.3802 | −0.0566726 | ||||||||
\(590\) | −366.905 | + | 1100.21i | −0.621873 | + | 1.86476i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 112.333 | + | 385.938i | 0.189752 | + | 0.651922i | ||||
\(593\) | 1048.73 | 1.76851 | 0.884255 | − | 0.467005i | \(-0.154667\pi\) | ||||
0.884255 | + | 0.467005i | \(0.154667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1020.70i | − | 1.71547i | ||||||
\(596\) | −803.021 | − | 602.614i | −1.34735 | − | 1.01110i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −77.7151 | + | 233.038i | −0.129958 | + | 0.389695i | ||||
\(599\) | − | 20.9544i | − | 0.0349822i | −0.999847 | − | 0.0174911i | \(-0.994432\pi\) | ||
0.999847 | − | 0.0174911i | \(-0.00556788\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.04669 | 0.00673326 | 0.00336663 | − | 0.999994i | \(-0.498928\pi\) | ||||
0.00336663 | + | 0.999994i | \(0.498928\pi\) | |||||||
\(602\) | −526.597 | − | 175.613i | −0.874745 | − | 0.291716i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 148.893 | − | 198.410i | 0.246512 | − | 0.328493i | ||||
\(605\) | −322.841 | −0.533621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 718.845i | 1.18426i | 0.805843 | + | 0.592129i | \(0.201712\pi\) | ||||
−0.805843 | + | 0.592129i | \(0.798288\pi\) | |||||||
\(608\) | 139.381 | + | 5.38961i | 0.229244 | + | 0.00886449i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 342.819 | + | 114.326i | 0.561998 | + | 0.187419i | ||||
\(611\) | 657.601i | 1.07627i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −568.157 | −0.926847 | −0.463424 | − | 0.886137i | \(-0.653379\pi\) | ||||
−0.463424 | + | 0.886137i | \(0.653379\pi\) | |||||||
\(614\) | 196.418 | − | 588.983i | 0.319899 | − | 0.959255i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −216.015 | − | 312.300i | −0.350674 | − | 0.506980i | ||||
\(617\) | −344.297 | −0.558017 | −0.279009 | − | 0.960289i | \(-0.590006\pi\) | ||||
−0.279009 | + | 0.960289i | \(0.590006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 269.442i | − | 0.435286i | −0.976028 | − | 0.217643i | \(-0.930163\pi\) | ||
0.976028 | − | 0.217643i | \(-0.0698368\pi\) | |||||||
\(620\) | −106.503 | + | 141.922i | −0.171779 | + | 0.228907i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −138.915 | + | 416.552i | −0.223336 | + | 0.669698i | ||||
\(623\) | 168.319i | 0.270175i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −765.688 | −1.22510 | ||||||||
\(626\) | 612.216 | + | 204.166i | 0.977980 | + | 0.326144i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −320.414 | − | 240.449i | −0.510213 | − | 0.382880i | ||||
\(629\) | −753.427 | −1.19782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 916.217i | − | 1.45201i | −0.687691 | − | 0.726004i | \(-0.741375\pi\) | ||
0.687691 | − | 0.726004i | \(-0.258625\pi\) | |||||||
\(632\) | −269.585 | + | 186.470i | −0.426559 | + | 0.295048i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 101.769 | + | 33.9387i | 0.160519 | + | 0.0535311i | ||||
\(635\) | − | 1291.70i | − | 2.03417i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −203.294 | −0.319143 | ||||||||
\(638\) | −68.7375 | + | 206.117i | −0.107739 | + | 0.323068i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 467.625 | − | 575.408i | 0.730664 | − | 0.899075i | ||||
\(641\) | −809.161 | −1.26234 | −0.631171 | − | 0.775644i | \(-0.717425\pi\) | ||||
−0.631171 | + | 0.775644i | \(0.717425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 611.403i | 0.950859i | 0.879754 | + | 0.475430i | \(0.157707\pi\) | ||||
−0.879754 | + | 0.475430i | \(0.842293\pi\) | |||||||
\(644\) | −164.451 | − | 123.409i | −0.255358 | − | 0.191629i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −82.7128 | + | 248.024i | −0.128038 | + | 0.383938i | ||||
\(647\) | 375.179i | 0.579875i | 0.957046 | + | 0.289938i | \(0.0936345\pi\) | ||||
−0.957046 | + | 0.289938i | \(0.906365\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −808.746 | −1.24614 | ||||||||
\(650\) | −227.883 | − | 75.9961i | −0.350590 | − | 0.116917i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 451.161 | − | 601.202i | 0.691965 | − | 0.922088i | ||||
\(653\) | −122.859 | −0.188146 | −0.0940729 | − | 0.995565i | \(-0.529989\pi\) | ||||
−0.0940729 | + | 0.995565i | \(0.529989\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1154.67i | 1.76286i | ||||||||
\(656\) | −222.171 | − | 763.302i | −0.338675 | − | 1.16357i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −522.125 | − | 174.122i | −0.793504 | − | 0.264623i | ||||
\(659\) | 104.791i | 0.159015i | 0.996834 | + | 0.0795074i | \(0.0253347\pi\) | ||||
−0.996834 | + | 0.0795074i | \(0.974665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1185.52 | −1.79352 | −0.896762 | − | 0.442514i | \(-0.854087\pi\) | ||||
−0.896762 | + | 0.442514i | \(0.854087\pi\) | |||||||
\(662\) | −104.461 | + | 313.237i | −0.157795 | + | 0.473168i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −578.045 | + | 399.830i | −0.870549 | + | 0.602153i | ||||
\(665\) | 148.351 | 0.223085 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 117.646i | 0.176381i | ||||||||
\(668\) | 58.2466 | − | 77.6173i | 0.0871955 | − | 0.116194i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 126.763 | − | 380.113i | 0.189198 | − | 0.567332i | ||||
\(671\) | 252.001i | 0.375560i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 86.7624 | 0.128919 | 0.0644594 | − | 0.997920i | \(-0.479468\pi\) | ||||
0.0644594 | + | 0.997920i | \(0.479468\pi\) | |||||||
\(674\) | −709.983 | − | 236.770i | −1.05339 | − | 0.351291i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 89.9310 | + | 67.4872i | 0.133034 | + | 0.0998332i | ||||
\(677\) | 566.786 | 0.837202 | 0.418601 | − | 0.908170i | \(-0.362521\pi\) | ||||
0.418601 | + | 0.908170i | \(0.362521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 54.9716i | − | 0.0809597i | ||||||
\(680\) | 790.618 | + | 1143.02i | 1.16267 | + | 1.68091i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −117.379 | − | 39.1445i | −0.172110 | − | 0.0573966i | ||||
\(683\) | 192.839i | 0.282341i | 0.989985 | + | 0.141170i | \(0.0450865\pi\) | ||||
−0.989985 | + | 0.141170i | \(0.954913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.8387 | −0.0508595 | ||||||||
\(686\) | 235.984 | − | 707.626i | 0.344000 | − | 1.03152i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 725.727 | − | 211.234i | 1.05484 | − | 0.307026i | ||||
\(689\) | −199.278 | −0.289227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 639.216i | 0.925059i | 0.886604 | + | 0.462530i | \(0.153058\pi\) | ||||
−0.886604 | + | 0.462530i | \(0.846942\pi\) | |||||||
\(692\) | 802.301 | + | 602.073i | 1.15939 | + | 0.870048i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 280.111 | − | 839.945i | 0.403618 | − | 1.21029i | ||||
\(695\) | 447.820i | 0.644346i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1490.12 | 2.13790 | ||||||||
\(698\) | −309.946 | − | 103.363i | −0.444049 | − | 0.148085i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 120.680 | − | 160.813i | 0.172399 | − | 0.229733i | ||||
\(701\) | −109.111 | −0.155650 | −0.0778250 | − | 0.996967i | \(-0.524798\pi\) | ||||
−0.0778250 | + | 0.996967i | \(0.524798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 109.505i | − | 0.155768i | ||||||
\(704\) | 483.803 | + | 182.402i | 0.687220 | + | 0.259094i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −778.398 | − | 259.586i | −1.10255 | − | 0.367685i | ||||
\(707\) | − | 509.304i | − | 0.720373i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1381.83 | 1.94898 | 0.974489 | − | 0.224434i | \(-0.0720532\pi\) | ||||
0.974489 | + | 0.224434i | \(0.0720532\pi\) | |||||||
\(710\) | 241.988 | − | 725.628i | 0.340828 | − | 1.02201i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −130.377 | − | 188.489i | −0.183113 | − | 0.264732i | ||||
\(713\) | −66.9966 | −0.0939644 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 657.024i | − | 0.918915i | ||||||
\(716\) | 149.854 | − | 199.690i | 0.209294 | − | 0.278897i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 78.8062 | − | 236.309i | 0.109758 | − | 0.329122i | ||||
\(719\) | 844.528i | 1.17459i | 0.809374 | + | 0.587293i | \(0.199806\pi\) | ||||
−0.809374 | + | 0.587293i | \(0.800194\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 820.211 | 1.13760 | ||||||||
\(722\) | −36.0483 | − | 12.0216i | −0.0499284 | − | 0.0166505i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −213.328 | − | 160.088i | −0.294652 | − | 0.221117i | ||||
\(725\) | −115.044 | −0.158681 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 926.186i | 1.27398i | 0.770871 | + | 0.636992i | \(0.219821\pi\) | ||||
−0.770871 | + | 0.636992i | \(0.780179\pi\) | |||||||
\(728\) | −542.721 | + | 375.396i | −0.745496 | + | 0.515654i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 302.303 | + | 100.814i | 0.414113 | + | 0.138102i | ||||
\(731\) | 1416.76i | 1.93812i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 108.418 | 0.147910 | 0.0739551 | − | 0.997262i | \(-0.476438\pi\) | ||||
0.0739551 | + | 0.997262i | \(0.476438\pi\) | |||||||
\(734\) | 182.697 | − | 547.837i | 0.248906 | − | 0.746372i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 279.748 | + | 10.8174i | 0.380092 | + | 0.0146975i | ||||
\(737\) | 279.415 | 0.379125 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 209.058i | 0.282893i | 0.989946 | + | 0.141447i | \(0.0451753\pi\) | ||||
−0.989946 | + | 0.141447i | \(0.954825\pi\) | |||||||
\(740\) | −465.581 | − | 349.387i | −0.629163 | − | 0.472145i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 52.7655 | − | 158.224i | 0.0711126 | − | 0.213239i | ||||
\(743\) | 862.421i | 1.16073i | 0.814357 | + | 0.580364i | \(0.197090\pi\) | ||||
−0.814357 | + | 0.580364i | \(0.802910\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1453.94 | 1.95160 | ||||||||
\(746\) | 722.371 | + | 240.901i | 0.968325 | + | 0.322924i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −581.709 | + | 775.164i | −0.777685 | + | 1.03632i | ||||
\(749\) | 314.700 | 0.420161 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 167.423i | 0.222933i | 0.993768 | + | 0.111467i | \(0.0355548\pi\) | ||||
−0.993768 | + | 0.111467i | \(0.964445\pi\) | |||||||
\(752\) | 719.565 | − | 209.441i | 0.956869 | − | 0.278512i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 358.195 | + | 119.454i | 0.475060 | + | 0.158426i | ||||
\(755\) | 359.238i | 0.475812i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 347.592 | 0.459171 | 0.229586 | − | 0.973288i | \(-0.426263\pi\) | ||||
0.229586 | + | 0.973288i | \(0.426263\pi\) | |||||||
\(758\) | −111.590 | + | 334.615i | −0.147216 | + | 0.441445i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −166.129 | + | 114.910i | −0.218590 | + | 0.151197i | ||||
\(761\) | −1395.24 | −1.83343 | −0.916714 | − | 0.399544i | \(-0.869168\pi\) | ||||
−0.916714 | + | 0.399544i | \(0.869168\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 907.854i | 1.18985i | ||||||||
\(764\) | 524.562 | − | 699.012i | 0.686599 | − | 0.914937i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −246.756 | + | 739.925i | −0.322135 | + | 0.965960i | ||||
\(767\) | 1405.46i | 1.83241i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1104.80 | 1.43667 | 0.718333 | − | 0.695700i | \(-0.244906\pi\) | ||||
0.718333 | + | 0.695700i | \(0.244906\pi\) | |||||||
\(770\) | 521.668 | + | 173.970i | 0.677490 | + | 0.225934i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 198.194 | + | 148.731i | 0.256728 | + | 0.192657i | ||||
\(773\) | 1508.32 | 1.95125 | 0.975627 | − | 0.219436i | \(-0.0704217\pi\) | ||||
0.975627 | + | 0.219436i | \(0.0704217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 65.5148i | − | 0.0845352i | ||||||
\(776\) | 42.5800 | + | 61.5591i | 0.0548711 | + | 0.0793287i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.64539 | − | 3.21661i | −0.0123977 | − | 0.00413447i | ||||
\(779\) | 216.577i | 0.278019i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 533.399 | 0.682969 | ||||||||
\(782\) | −166.011 | + | 497.804i | −0.212290 | + | 0.636578i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 64.7476 | + | 222.450i | 0.0825862 | + | 0.283737i | ||||
\(785\) | 580.137 | 0.739028 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 964.500i | 1.22554i | 0.790261 | + | 0.612770i | \(0.209945\pi\) | ||||
−0.790261 | + | 0.612770i | \(0.790055\pi\) | |||||||
\(788\) | 1136.88 | + | 853.149i | 1.44274 | + | 1.08268i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 150.175 | − | 450.317i | 0.190095 | − | 0.570022i | ||||
\(791\) | − | 387.803i | − | 0.490270i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 437.933 | 0.552248 | ||||||||
\(794\) | 608.157 | + | 202.812i | 0.765940 | + | 0.255431i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −500.516 | + | 666.969i | −0.628789 | + | 0.837901i | ||||
\(797\) | 237.493 | 0.297984 | 0.148992 | − | 0.988838i | \(-0.452397\pi\) | ||||
0.148992 | + | 0.988838i | \(0.452397\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1404.74i | 1.75812i | ||||||||
\(800\) | −10.5781 | + | 273.560i | −0.0132226 | + | 0.341950i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 812.722 | + | 271.032i | 1.01337 | + | 0.337946i | ||||
\(803\) | 222.218i | 0.276735i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 297.753 | 0.369879 | ||||||||
\(806\) | −68.0261 | + | 203.984i | −0.0843996 | + | 0.253082i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 394.497 | + | 570.335i | 0.488239 | + | 0.705860i | ||||
\(809\) | 1195.19 | 1.47736 | 0.738681 | − | 0.674056i | \(-0.235449\pi\) | ||||
0.738681 | + | 0.674056i | \(0.235449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1407.36i | − | 1.73534i | −0.497140 | − | 0.867670i | \(-0.665616\pi\) | ||
0.497140 | − | 0.867670i | \(-0.334384\pi\) | |||||||
\(812\) | −189.689 | + | 252.772i | −0.233607 | + | 0.311296i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 128.415 | − | 385.066i | 0.157758 | − | 0.473054i | ||||
\(815\) | 1088.53i | 1.33562i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −205.915 | −0.252038 | ||||||||
\(818\) | 207.848 | + | 69.3145i | 0.254092 | + | 0.0847366i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 920.819 | + | 691.013i | 1.12295 | + | 0.842699i | ||||
\(821\) | −336.476 | −0.409836 | −0.204918 | − | 0.978779i | \(-0.565693\pi\) | ||||
−0.204918 | + | 0.978779i | \(0.565693\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 260.242i | − | 0.316211i | −0.987422 | − | 0.158106i | \(-0.949461\pi\) | ||
0.987422 | − | 0.158106i | \(-0.0505386\pi\) | |||||||
\(824\) | −918.500 | + | 635.320i | −1.11468 | + | 0.771020i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1115.91 | − | 372.142i | −1.35098 | − | 0.450535i | ||||
\(827\) | − | 424.028i | − | 0.512730i | −0.966580 | − | 0.256365i | \(-0.917475\pi\) | ||
0.966580 | − | 0.256365i | \(-0.0825249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1148.21 | 1.38506 | 0.692529 | − | 0.721390i | \(-0.256496\pi\) | ||||
0.692529 | + | 0.721390i | \(0.256496\pi\) | |||||||
\(830\) | 322.005 | − | 965.570i | 0.387958 | − | 1.16334i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 316.982 | − | 840.763i | 0.380988 | − | 1.01053i | ||||
\(833\) | −434.267 | −0.521329 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 140.533i | 0.168303i | ||||||||
\(836\) | −112.664 | − | 84.5467i | −0.134765 | − | 0.101132i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 193.052 | − | 578.889i | 0.230372 | − | 0.690798i | ||||
\(839\) | 1071.72i | 1.27737i | 0.769467 | + | 0.638686i | \(0.220522\pi\) | ||||
−0.769467 | + | 0.638686i | \(0.779478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −660.170 | −0.784982 | ||||||||
\(842\) | −1368.16 | − | 456.263i | −1.62489 | − | 0.541880i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 660.604 | − | 880.297i | 0.782706 | − | 1.04301i | ||||
\(845\) | −162.828 | −0.192696 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 327.449i | − | 0.386599i | ||||||
\(848\) | 63.4683 | + | 218.055i | 0.0748447 | + | 0.257140i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −486.793 | − | 162.339i | −0.572698 | − | 0.190987i | ||||
\(851\) | − | 219.784i | − | 0.258266i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.0568 | −0.0129622 | −0.00648110 | − | 0.999979i | \(-0.502063\pi\) | ||||
−0.00648110 | + | 0.999979i | \(0.502063\pi\) | |||||||
\(854\) | −115.958 | + | 347.712i | −0.135782 | + | 0.407157i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −352.412 | + | 243.761i | −0.411696 | + | 0.284767i | ||||
\(857\) | 612.058 | 0.714187 | 0.357094 | − | 0.934069i | \(-0.383768\pi\) | ||||
0.357094 | + | 0.934069i | \(0.383768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1496.82i | − | 1.74252i | −0.490826 | − | 0.871258i | \(-0.663305\pi\) | ||
0.490826 | − | 0.871258i | \(-0.336695\pi\) | |||||||
\(860\) | −656.997 | + | 875.490i | −0.763950 | + | 1.01801i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 174.248 | − | 522.504i | 0.202144 | − | 0.606153i | ||||
\(863\) | 482.163i | 0.558706i | 0.960189 | + | 0.279353i | \(0.0901199\pi\) | ||||
−0.960189 | + | 0.279353i | \(0.909880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1452.64 | −1.67935 | ||||||||
\(866\) | −845.350 | − | 281.913i | −0.976154 | − | 0.325535i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −143.948 | − | 108.023i | −0.165839 | − | 0.124451i | ||||
\(869\) | 331.021 | 0.380922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 485.574i | − | 0.557490i | ||||||
\(872\) | −703.207 | − | 1016.65i | −0.806430 | − | 1.16588i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −72.3518 | − | 24.1284i | −0.0827824 | − | 0.0276069i | ||||
\(875\) | − | 559.686i | − | 0.639641i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 321.889 | 0.367034 | 0.183517 | − | 0.983017i | \(-0.441252\pi\) | ||||
0.183517 | + | 0.983017i | \(0.441252\pi\) | |||||||
\(878\) | 317.335 | − | 951.565i | 0.361429 | − | 1.08379i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −718.934 | + | 209.257i | −0.816971 | + | 0.237792i | ||||
\(881\) | −1053.56 | −1.19587 | −0.597934 | − | 0.801545i | \(-0.704012\pi\) | ||||
−0.597934 | + | 0.801545i | \(0.704012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 152.797i | 0.173043i | 0.996250 | + | 0.0865213i | \(0.0275751\pi\) | ||||
−0.996250 | + | 0.0865213i | \(0.972425\pi\) | |||||||
\(884\) | 1347.10 | + | 1010.91i | 1.52387 | + | 1.14356i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −188.067 | + | 563.941i | −0.212266 | + | 0.636503i | ||||
\(887\) | − | 1486.18i | − | 1.67551i | −0.546044 | − | 0.837756i | \(-0.683867\pi\) | ||
0.546044 | − | 0.837756i | \(-0.316133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1310.14 | 1.47372 | ||||||||
\(890\) | 314.854 | + | 105.000i | 0.353768 | + | 0.117977i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −571.198 | + | 761.158i | −0.640357 | + | 0.853317i | ||||
\(893\) | −204.167 | −0.228631 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 361.557i | 0.403975i | ||||||||
\(896\) | 583.621 | + | 474.300i | 0.651363 | + | 0.529352i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 544.165 | + | 181.472i | 0.605974 | + | 0.202085i | ||||
\(899\) | 102.979i | 0.114548i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −425.687 | −0.472461 | ||||||||
\(902\) | −253.977 | + | 761.578i | −0.281571 | + | 0.844322i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 300.385 | + | 434.275i | 0.332284 | + | 0.480393i | ||||
\(905\) | 386.249 | 0.426795 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 805.225i | 0.887790i | 0.896079 | + | 0.443895i | \(0.146404\pi\) | ||||
−0.896079 | + | 0.443895i | \(0.853596\pi\) | |||||||
\(908\) | −377.099 | + | 502.509i | −0.415307 | + | 0.553424i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 302.328 | − | 906.565i | 0.332229 | − | 0.996226i | ||||
\(911\) | − | 1424.24i | − | 1.56339i | −0.623664 | − | 0.781693i | \(-0.714357\pi\) | ||
0.623664 | − | 0.781693i | \(-0.285643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 709.776 | 0.777411 | ||||||||
\(914\) | 482.635 | + | 160.953i | 0.528047 | + | 0.176097i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −568.104 | − | 426.324i | −0.620201 | − | 0.465419i | ||||
\(917\) | −1171.15 | −1.27716 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 798.305i | 0.868667i | 0.900752 | + | 0.434334i | \(0.143016\pi\) | ||||
−0.900752 | + | 0.434334i | \(0.856984\pi\) | |||||||
\(920\) | −333.433 | + | 230.634i | −0.362428 | + | 0.250689i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 147.352 | + | 49.1399i | 0.159817 | + | 0.0532971i | ||||
\(923\) | − | 926.952i | − | 1.00428i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 214.923 | 0.232349 | ||||||||
\(926\) | 343.611 | − | 1030.36i | 0.371070 | − | 1.11270i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16.6271 | − | 429.992i | 0.0179171 | − | 0.463354i | ||||
\(929\) | 1237.61 | 1.33220 | 0.666099 | − | 0.745864i | \(-0.267963\pi\) | ||||
0.666099 | + | 0.745864i | \(0.267963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 63.1173i | − | 0.0677951i | ||||||
\(932\) | −241.835 | − | 181.481i | −0.259479 | − | 0.194722i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −243.385 | + | 729.817i | −0.260583 | + | 0.781388i | ||||
\(935\) | − | 1403.50i | − | 1.50107i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1445.92 | −1.54313 | −0.771567 | − | 0.636148i | \(-0.780527\pi\) | ||||
−0.771567 | + | 0.636148i | \(0.780527\pi\) | |||||||
\(938\) | 385.538 | + | 128.572i | 0.411022 | + | 0.137070i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −651.418 | + | 868.057i | −0.692998 | + | 0.923465i | ||||
\(941\) | 165.774 | 0.176168 | 0.0880840 | − | 0.996113i | \(-0.471926\pi\) | ||||
0.0880840 | + | 0.996113i | \(0.471926\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 434.687i | 0.460961i | ||||||||
\(944\) | 1537.89 | − | 447.626i | 1.62912 | − | 0.474181i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −724.088 | − | 241.474i | −0.765421 | − | 0.255258i | ||||
\(947\) | 1229.50i | 1.29831i | 0.760655 | + | 0.649156i | \(0.224878\pi\) | ||||
−0.760655 | + | 0.649156i | \(0.775122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 386.176 | 0.406929 | ||||||||
\(950\) | 23.5947 | − | 70.7515i | 0.0248365 | − | 0.0744752i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1159.33 | + | 801.904i | −1.21779 | + | 0.842336i | ||||
\(953\) | −1664.37 | −1.74646 | −0.873229 | − | 0.487310i | \(-0.837978\pi\) | ||||
−0.873229 | + | 0.487310i | \(0.837978\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1265.62i | 1.32526i | ||||||||
\(956\) | −4.79080 | + | 6.38405i | −0.00501130 | + | 0.00667788i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −418.343 | + | 1254.45i | −0.436684 | + | 1.30945i | ||||
\(959\) | − | 35.3360i | − | 0.0368467i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 902.356 | 0.938976 | ||||||||
\(962\) | −669.176 | − | 223.162i | −0.695609 | − | 0.231977i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −206.853 | − | 155.230i | −0.214578 | − | 0.161027i | ||||
\(965\) | −358.848 | −0.371863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 70.9865i | − | 0.0734090i | −0.999326 | − | 0.0367045i | \(-0.988314\pi\) | ||
0.999326 | − | 0.0367045i | \(-0.0116860\pi\) | |||||||
\(968\) | 253.636 | + | 366.688i | 0.262020 | + | 0.378810i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −102.829 | − | 34.2921i | −0.106009 | − | 0.0353527i | ||||
\(971\) | 925.687i | 0.953334i | 0.879084 | + | 0.476667i | \(0.158155\pi\) | ||||
−0.879084 | + | 0.476667i | \(0.841845\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −454.212 | −0.466817 | ||||||||
\(974\) | 396.602 | − | 1189.26i | 0.407188 | − | 1.22100i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −139.478 | − | 479.198i | −0.142908 | − | 0.490982i | ||||
\(977\) | 720.813 | 0.737782 | 0.368891 | − | 0.929473i | \(-0.379738\pi\) | ||||
0.368891 | + | 0.929473i | \(0.379738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 231.444i | 0.236409i | ||||||||
\(980\) | −268.356 | − | 201.383i | −0.273832 | − | 0.205493i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 615.847 | − | 1846.69i | 0.627135 | − | 1.88054i | ||||
\(983\) | 802.902i | 0.816787i | 0.912806 | + | 0.408394i | \(0.133911\pi\) | ||||
−0.912806 | + | 0.408394i | \(0.866089\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2058.42 | −2.08976 | ||||||||
\(986\) | 765.160 | + | 255.171i | 0.776024 | + | 0.258794i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −146.927 | + | 195.790i | −0.148712 | + | 0.198168i | ||||
\(989\) | −413.289 | −0.417885 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 117.656i | − | 0.118725i | −0.998236 | − | 0.0593624i | \(-0.981093\pi\) | ||
0.998236 | − | 0.0593624i | \(-0.0189068\pi\) | |||||||
\(992\) | 244.871 | + | 9.46874i | 0.246846 | + | 0.00954510i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 735.986 | + | 245.442i | 0.740429 | + | 0.246923i | ||||
\(995\) | − | 1207.61i | − | 1.21368i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1165.44 | −1.16894 | −0.584472 | − | 0.811414i | \(-0.698698\pi\) | ||||
−0.584472 | + | 0.811414i | \(0.698698\pi\) | |||||||
\(998\) | 108.806 | − | 326.267i | 0.109024 | − | 0.326921i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.3.g.b.343.12 | 14 | ||
3.2 | odd | 2 | 76.3.b.b.39.3 | ✓ | 14 | ||
4.3 | odd | 2 | inner | 684.3.g.b.343.11 | 14 | ||
12.11 | even | 2 | 76.3.b.b.39.4 | yes | 14 | ||
24.5 | odd | 2 | 1216.3.d.d.191.13 | 14 | |||
24.11 | even | 2 | 1216.3.d.d.191.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.b.b.39.3 | ✓ | 14 | 3.2 | odd | 2 | ||
76.3.b.b.39.4 | yes | 14 | 12.11 | even | 2 | ||
684.3.g.b.343.11 | 14 | 4.3 | odd | 2 | inner | ||
684.3.g.b.343.12 | 14 | 1.1 | even | 1 | trivial | ||
1216.3.d.d.191.2 | 14 | 24.11 | even | 2 | |||
1216.3.d.d.191.13 | 14 | 24.5 | odd | 2 |