Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(91,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.4 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.5 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 5.52876i | 0.789822i | 0.918719 | + | 0.394911i | \(0.129225\pi\) | ||||
−0.918719 | + | 0.394911i | \(0.870775\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | 3.99843i | 0.363493i | 0.983345 | + | 0.181747i | \(0.0581751\pi\) | ||||
−0.983345 | + | 0.181747i | \(0.941825\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | 8.18275 | 0.629442 | 0.314721 | − | 0.949184i | \(-0.398089\pi\) | ||||
0.314721 | + | 0.949184i | \(0.398089\pi\) | |||||||
\(14\) | − | 7.81884i | − | 0.558489i | ||||||
\(15\) | 3.87298i | 0.258199i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 17.3987i | − | 1.02345i | −0.859148 | − | 0.511727i | \(-0.829006\pi\) | ||
0.859148 | − | 0.511727i | \(-0.170994\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 11.0934i | 0.583863i | 0.956439 | + | 0.291932i | \(0.0942980\pi\) | ||||
−0.956439 | + | 0.291932i | \(0.905702\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | − | 9.57609i | − | 0.456004i | ||||||
\(22\) | − | 5.65463i | − | 0.257029i | ||||||
\(23\) | −22.7880 | + | 3.11551i | −0.990783 | + | 0.135457i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −11.5722 | −0.445083 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 11.0575i | 0.394911i | ||||||||
\(29\) | 10.3250 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(30\) | − | 5.47723i | − | 0.182574i | ||||||
\(31\) | −20.6672 | −0.666684 | −0.333342 | − | 0.942806i | \(-0.608176\pi\) | ||||
−0.333342 | + | 0.942806i | \(0.608176\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − | 6.92548i | − | 0.209863i | ||||||
\(34\) | 24.6055i | 0.723691i | ||||||||
\(35\) | 12.3627 | 0.353219 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 39.0577i | 1.05561i | 0.849365 | + | 0.527806i | \(0.176985\pi\) | ||||
−0.849365 | + | 0.527806i | \(0.823015\pi\) | |||||||
\(38\) | − | 15.6884i | − | 0.412854i | ||||||
\(39\) | −14.1729 | −0.363409 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 73.4079 | 1.79044 | 0.895218 | − | 0.445629i | \(-0.147020\pi\) | ||||
0.895218 | + | 0.445629i | \(0.147020\pi\) | |||||||
\(42\) | 13.5426i | 0.322444i | ||||||||
\(43\) | − | 52.2098i | − | 1.21418i | −0.794632 | − | 0.607091i | \(-0.792336\pi\) | ||
0.794632 | − | 0.607091i | \(-0.207664\pi\) | |||||||
\(44\) | 7.99686i | 0.181747i | ||||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | 32.2271 | − | 4.40599i | 0.700590 | − | 0.0957825i | ||||
\(47\) | −74.9985 | −1.59571 | −0.797857 | − | 0.602847i | \(-0.794033\pi\) | ||||
−0.797857 | + | 0.602847i | \(0.794033\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 18.4329 | 0.376181 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | 30.1355i | 0.590892i | ||||||||
\(52\) | 16.3655 | 0.314721 | ||||||||
\(53\) | 18.2596i | 0.344521i | 0.985051 | + | 0.172260i | \(0.0551071\pi\) | ||||
−0.985051 | + | 0.172260i | \(0.944893\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | 8.94076 | 0.162559 | ||||||||
\(56\) | − | 15.6377i | − | 0.279244i | ||||||
\(57\) | − | 19.2143i | − | 0.337094i | ||||||
\(58\) | −14.6017 | −0.251754 | ||||||||
\(59\) | −6.77206 | −0.114781 | −0.0573904 | − | 0.998352i | \(-0.518278\pi\) | ||||
−0.0573904 | + | 0.998352i | \(0.518278\pi\) | |||||||
\(60\) | 7.74597i | 0.129099i | ||||||||
\(61\) | 115.117i | 1.88717i | 0.331130 | + | 0.943585i | \(0.392570\pi\) | ||||
−0.331130 | + | 0.943585i | \(0.607430\pi\) | |||||||
\(62\) | 29.2279 | 0.471417 | ||||||||
\(63\) | 16.5863i | 0.263274i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 18.2972i | − | 0.281495i | ||||||
\(66\) | 9.79411i | 0.148396i | ||||||||
\(67\) | 110.296i | 1.64621i | 0.567891 | + | 0.823104i | \(0.307759\pi\) | ||||
−0.567891 | + | 0.823104i | \(0.692241\pi\) | |||||||
\(68\) | − | 34.7974i | − | 0.511727i | ||||||
\(69\) | 39.4700 | − | 5.39622i | 0.572029 | − | 0.0782060i | ||||
\(70\) | −17.4835 | −0.249764 | ||||||||
\(71\) | 30.5113 | 0.429737 | 0.214868 | − | 0.976643i | \(-0.431068\pi\) | ||||
0.214868 | + | 0.976643i | \(0.431068\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | −89.5707 | −1.22700 | −0.613498 | − | 0.789696i | \(-0.710238\pi\) | ||||
−0.613498 | + | 0.789696i | \(0.710238\pi\) | |||||||
\(74\) | − | 55.2359i | − | 0.746431i | ||||||
\(75\) | 8.66025 | 0.115470 | ||||||||
\(76\) | 22.1868i | 0.291932i | ||||||||
\(77\) | −22.1063 | −0.287095 | ||||||||
\(78\) | 20.0436 | 0.256969 | ||||||||
\(79\) | 141.248i | 1.78795i | 0.448113 | + | 0.893977i | \(0.352096\pi\) | ||||
−0.448113 | + | 0.893977i | \(0.647904\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −103.814 | −1.26603 | ||||||||
\(83\) | 66.8139i | 0.804986i | 0.915423 | + | 0.402493i | \(0.131856\pi\) | ||||
−0.915423 | + | 0.402493i | \(0.868144\pi\) | |||||||
\(84\) | − | 19.1522i | − | 0.228002i | ||||||
\(85\) | −38.9047 | −0.457703 | ||||||||
\(86\) | 73.8359i | 0.858557i | ||||||||
\(87\) | −17.8834 | −0.205556 | ||||||||
\(88\) | − | 11.3093i | − | 0.128514i | ||||||
\(89\) | 54.8986i | 0.616838i | 0.951251 | + | 0.308419i | \(0.0997999\pi\) | ||||
−0.951251 | + | 0.308419i | \(0.900200\pi\) | |||||||
\(90\) | 9.48683i | 0.105409i | ||||||||
\(91\) | 45.2404i | 0.497148i | ||||||||
\(92\) | −45.5760 | + | 6.23102i | −0.495392 | + | 0.0677284i | ||||
\(93\) | 35.7967 | 0.384910 | ||||||||
\(94\) | 106.064 | 1.12834 | ||||||||
\(95\) | 24.8056 | 0.261112 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | − | 8.89570i | − | 0.0917083i | −0.998948 | − | 0.0458541i | \(-0.985399\pi\) | ||
0.998948 | − | 0.0458541i | \(-0.0146009\pi\) | |||||||
\(98\) | −26.0680 | −0.266000 | ||||||||
\(99\) | 11.9953i | 0.121164i | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −102.145 | −1.01133 | −0.505667 | − | 0.862729i | \(-0.668754\pi\) | ||||
−0.505667 | + | 0.862729i | \(0.668754\pi\) | |||||||
\(102\) | − | 42.6180i | − | 0.417823i | ||||||
\(103\) | 178.032i | 1.72847i | 0.503092 | + | 0.864233i | \(0.332196\pi\) | ||||
−0.503092 | + | 0.864233i | \(0.667804\pi\) | |||||||
\(104\) | −23.1443 | −0.222541 | ||||||||
\(105\) | −21.4128 | −0.203931 | ||||||||
\(106\) | − | 25.8230i | − | 0.243613i | ||||||
\(107\) | 5.45306i | 0.0509632i | 0.999675 | + | 0.0254816i | \(0.00811192\pi\) | ||||
−0.999675 | + | 0.0254816i | \(0.991888\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | 18.9658i | 0.173998i | 0.996208 | + | 0.0869989i | \(0.0277277\pi\) | ||||
−0.996208 | + | 0.0869989i | \(0.972272\pi\) | |||||||
\(110\) | −12.6441 | −0.114947 | ||||||||
\(111\) | − | 67.6498i | − | 0.609458i | ||||||
\(112\) | 22.1150i | 0.197456i | ||||||||
\(113\) | 55.6781i | 0.492727i | 0.969178 | + | 0.246363i | \(0.0792357\pi\) | ||||
−0.969178 | + | 0.246363i | \(0.920764\pi\) | |||||||
\(114\) | 27.1732i | 0.238361i | ||||||||
\(115\) | 6.96649 | + | 50.9555i | 0.0605781 | + | 0.443092i | ||||
\(116\) | 20.6500 | 0.178017 | ||||||||
\(117\) | 24.5482 | 0.209814 | ||||||||
\(118\) | 9.57714 | 0.0811622 | ||||||||
\(119\) | 96.1933 | 0.808347 | ||||||||
\(120\) | − | 10.9545i | − | 0.0912871i | ||||||
\(121\) | 105.013 | 0.867873 | ||||||||
\(122\) | − | 162.801i | − | 1.33443i | ||||||
\(123\) | −127.146 | −1.03371 | ||||||||
\(124\) | −41.3344 | −0.333342 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | − | 23.4565i | − | 0.186163i | ||||||
\(127\) | −129.679 | −1.02109 | −0.510546 | − | 0.859850i | \(-0.670557\pi\) | ||||
−0.510546 | + | 0.859850i | \(0.670557\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 90.4301i | 0.701008i | ||||||||
\(130\) | 25.8761i | 0.199047i | ||||||||
\(131\) | 194.919 | 1.48793 | 0.743965 | − | 0.668218i | \(-0.232943\pi\) | ||||
0.743965 | + | 0.668218i | \(0.232943\pi\) | |||||||
\(132\) | − | 13.8510i | − | 0.104932i | ||||||
\(133\) | −61.3327 | −0.461148 | ||||||||
\(134\) | − | 155.982i | − | 1.16404i | ||||||
\(135\) | 11.6190i | 0.0860663i | ||||||||
\(136\) | 49.2110i | 0.361846i | ||||||||
\(137\) | 115.467i | 0.842825i | 0.906869 | + | 0.421412i | \(0.138466\pi\) | ||||
−0.906869 | + | 0.421412i | \(0.861534\pi\) | |||||||
\(138\) | −55.8190 | + | 7.63140i | −0.404486 | + | 0.0553000i | ||||
\(139\) | −248.366 | −1.78680 | −0.893401 | − | 0.449260i | \(-0.851688\pi\) | ||||
−0.893401 | + | 0.449260i | \(0.851688\pi\) | |||||||
\(140\) | 24.7253 | 0.176610 | ||||||||
\(141\) | 129.901 | 0.921285 | ||||||||
\(142\) | −43.1495 | −0.303870 | ||||||||
\(143\) | 32.7181i | 0.228798i | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | − | 23.0874i | − | 0.159223i | ||||||
\(146\) | 126.672 | 0.867617 | ||||||||
\(147\) | −31.9266 | −0.217188 | ||||||||
\(148\) | 78.1153i | 0.527806i | ||||||||
\(149\) | − | 224.035i | − | 1.50359i | −0.659397 | − | 0.751795i | \(-0.729188\pi\) | ||
0.659397 | − | 0.751795i | \(-0.270812\pi\) | |||||||
\(150\) | −12.2474 | −0.0816497 | ||||||||
\(151\) | 230.365 | 1.52560 | 0.762799 | − | 0.646636i | \(-0.223825\pi\) | ||||
0.762799 | + | 0.646636i | \(0.223825\pi\) | |||||||
\(152\) | − | 31.3769i | − | 0.206427i | ||||||
\(153\) | − | 52.1962i | − | 0.341151i | ||||||
\(154\) | 31.2631 | 0.203007 | ||||||||
\(155\) | 46.2133i | 0.298150i | ||||||||
\(156\) | −28.3459 | −0.181704 | ||||||||
\(157\) | 11.2242i | 0.0714920i | 0.999361 | + | 0.0357460i | \(0.0113807\pi\) | ||||
−0.999361 | + | 0.0357460i | \(0.988619\pi\) | |||||||
\(158\) | − | 199.755i | − | 1.26427i | ||||||
\(159\) | − | 31.6266i | − | 0.198909i | ||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | −17.2249 | − | 125.989i | −0.106987 | − | 0.782543i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 67.5155 | 0.414206 | 0.207103 | − | 0.978319i | \(-0.433597\pi\) | ||||
0.207103 | + | 0.978319i | \(0.433597\pi\) | |||||||
\(164\) | 146.816 | 0.895218 | ||||||||
\(165\) | −15.4858 | −0.0938536 | ||||||||
\(166\) | − | 94.4891i | − | 0.569211i | ||||||
\(167\) | 28.5518 | 0.170969 | 0.0854845 | − | 0.996339i | \(-0.472756\pi\) | ||||
0.0854845 | + | 0.996339i | \(0.472756\pi\) | |||||||
\(168\) | 27.0853i | 0.161222i | ||||||||
\(169\) | −102.043 | −0.603802 | ||||||||
\(170\) | 55.0196 | 0.323645 | ||||||||
\(171\) | 33.2802i | 0.194621i | ||||||||
\(172\) | − | 104.420i | − | 0.607091i | ||||||
\(173\) | −40.7348 | −0.235461 | −0.117731 | − | 0.993046i | \(-0.537562\pi\) | ||||
−0.117731 | + | 0.993046i | \(0.537562\pi\) | |||||||
\(174\) | 25.2909 | 0.145350 | ||||||||
\(175\) | − | 27.6438i | − | 0.157964i | ||||||
\(176\) | 15.9937i | 0.0908734i | ||||||||
\(177\) | 11.7296 | 0.0662687 | ||||||||
\(178\) | − | 77.6383i | − | 0.436170i | ||||||
\(179\) | −283.716 | −1.58500 | −0.792502 | − | 0.609869i | \(-0.791222\pi\) | ||||
−0.792502 | + | 0.609869i | \(0.791222\pi\) | |||||||
\(180\) | − | 13.4164i | − | 0.0745356i | ||||||
\(181\) | 23.5724i | 0.130234i | 0.997878 | + | 0.0651172i | \(0.0207421\pi\) | ||||
−0.997878 | + | 0.0651172i | \(0.979258\pi\) | |||||||
\(182\) | − | 63.9796i | − | 0.351536i | ||||||
\(183\) | − | 199.389i | − | 1.08956i | ||||||
\(184\) | 64.4542 | − | 8.81199i | 0.350295 | − | 0.0478912i | ||||
\(185\) | 87.3356 | 0.472084 | ||||||||
\(186\) | −50.6241 | −0.272173 | ||||||||
\(187\) | 69.5675 | 0.372019 | ||||||||
\(188\) | −149.997 | −0.797857 | ||||||||
\(189\) | − | 28.7283i | − | 0.152001i | ||||||
\(190\) | −35.0804 | −0.184634 | ||||||||
\(191\) | − | 39.2377i | − | 0.205433i | −0.994711 | − | 0.102717i | \(-0.967247\pi\) | ||
0.994711 | − | 0.102717i | \(-0.0327535\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | 215.075 | 1.11438 | 0.557188 | − | 0.830386i | \(-0.311880\pi\) | ||||
0.557188 | + | 0.830386i | \(0.311880\pi\) | |||||||
\(194\) | 12.5804i | 0.0648475i | ||||||||
\(195\) | 31.6917i | 0.162521i | ||||||||
\(196\) | 36.8657 | 0.188090 | ||||||||
\(197\) | 195.426 | 0.992009 | 0.496005 | − | 0.868320i | \(-0.334800\pi\) | ||||
0.496005 | + | 0.868320i | \(0.334800\pi\) | |||||||
\(198\) | − | 16.9639i | − | 0.0856762i | ||||||
\(199\) | 126.232i | 0.634334i | 0.948370 | + | 0.317167i | \(0.102732\pi\) | ||||
−0.948370 | + | 0.317167i | \(0.897268\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | − | 191.038i | − | 0.950438i | ||||||
\(202\) | 144.454 | 0.715121 | ||||||||
\(203\) | 57.0843i | 0.281204i | ||||||||
\(204\) | 60.2709i | 0.295446i | ||||||||
\(205\) | − | 164.145i | − | 0.800707i | ||||||
\(206\) | − | 251.775i | − | 1.22221i | ||||||
\(207\) | −68.3640 | + | 9.34652i | −0.330261 | + | 0.0451523i | ||||
\(208\) | 32.7310 | 0.157361 | ||||||||
\(209\) | −44.3562 | −0.212231 | ||||||||
\(210\) | 30.2822 | 0.144201 | ||||||||
\(211\) | 248.669 | 1.17853 | 0.589263 | − | 0.807941i | \(-0.299418\pi\) | ||||
0.589263 | + | 0.807941i | \(0.299418\pi\) | |||||||
\(212\) | 36.5192i | 0.172260i | ||||||||
\(213\) | −52.8472 | −0.248109 | ||||||||
\(214\) | − | 7.71179i | − | 0.0360364i | ||||||
\(215\) | −116.745 | −0.542999 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | − | 114.264i | − | 0.526562i | ||||||
\(218\) | − | 26.8216i | − | 0.123035i | ||||||
\(219\) | 155.141 | 0.708407 | ||||||||
\(220\) | 17.8815 | 0.0812796 | ||||||||
\(221\) | − | 142.369i | − | 0.644205i | ||||||
\(222\) | 95.6713i | 0.430952i | ||||||||
\(223\) | −211.066 | −0.946485 | −0.473243 | − | 0.880932i | \(-0.656917\pi\) | ||||
−0.473243 | + | 0.880932i | \(0.656917\pi\) | |||||||
\(224\) | − | 31.2754i | − | 0.139622i | ||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | − | 78.7407i | − | 0.348410i | ||||||
\(227\) | − | 273.698i | − | 1.20572i | −0.797848 | − | 0.602859i | \(-0.794028\pi\) | ||
0.797848 | − | 0.602859i | \(-0.205972\pi\) | |||||||
\(228\) | − | 38.4287i | − | 0.168547i | ||||||
\(229\) | − | 366.210i | − | 1.59917i | −0.600552 | − | 0.799586i | \(-0.705052\pi\) | ||
0.600552 | − | 0.799586i | \(-0.294948\pi\) | |||||||
\(230\) | −9.85210 | − | 72.0620i | −0.0428352 | − | 0.313313i | ||||
\(231\) | 38.2893 | 0.165754 | ||||||||
\(232\) | −29.2035 | −0.125877 | ||||||||
\(233\) | −232.825 | −0.999249 | −0.499624 | − | 0.866242i | \(-0.666529\pi\) | ||||
−0.499624 | + | 0.866242i | \(0.666529\pi\) | |||||||
\(234\) | −34.7165 | −0.148361 | ||||||||
\(235\) | 167.702i | 0.713625i | ||||||||
\(236\) | −13.5441 | −0.0573904 | ||||||||
\(237\) | − | 244.649i | − | 1.03228i | ||||||
\(238\) | −136.038 | −0.571588 | ||||||||
\(239\) | −103.855 | −0.434541 | −0.217270 | − | 0.976111i | \(-0.569715\pi\) | ||||
−0.217270 | + | 0.976111i | \(0.569715\pi\) | |||||||
\(240\) | 15.4919i | 0.0645497i | ||||||||
\(241\) | 206.595i | 0.857243i | 0.903484 | + | 0.428621i | \(0.141001\pi\) | ||||
−0.903484 | + | 0.428621i | \(0.858999\pi\) | |||||||
\(242\) | −148.510 | −0.613679 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 230.235i | 0.943585i | ||||||||
\(245\) | − | 41.2171i | − | 0.168233i | ||||||
\(246\) | 179.812 | 0.730942 | ||||||||
\(247\) | 90.7746i | 0.367508i | ||||||||
\(248\) | 58.4557 | 0.235708 | ||||||||
\(249\) | − | 115.725i | − | 0.464759i | ||||||
\(250\) | − | 15.8114i | − | 0.0632456i | ||||||
\(251\) | 252.278i | 1.00509i | 0.864550 | + | 0.502547i | \(0.167603\pi\) | ||||
−0.864550 | + | 0.502547i | \(0.832397\pi\) | |||||||
\(252\) | 33.1725i | 0.131637i | ||||||||
\(253\) | −12.4571 | − | 91.1162i | −0.0492377 | − | 0.360143i | ||||
\(254\) | 183.393 | 0.722021 | ||||||||
\(255\) | 67.3850 | 0.264255 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −161.467 | −0.628277 | −0.314139 | − | 0.949377i | \(-0.601716\pi\) | ||||
−0.314139 | + | 0.949377i | \(0.601716\pi\) | |||||||
\(258\) | − | 127.887i | − | 0.495688i | ||||||
\(259\) | −215.940 | −0.833746 | ||||||||
\(260\) | − | 36.5944i | − | 0.140748i | ||||||
\(261\) | 30.9749 | 0.118678 | ||||||||
\(262\) | −275.657 | −1.05213 | ||||||||
\(263\) | − | 271.077i | − | 1.03071i | −0.856977 | − | 0.515355i | \(-0.827660\pi\) | ||
0.856977 | − | 0.515355i | \(-0.172340\pi\) | |||||||
\(264\) | 19.5882i | 0.0741978i | ||||||||
\(265\) | 40.8297 | 0.154074 | ||||||||
\(266\) | 86.7376 | 0.326081 | ||||||||
\(267\) | − | 95.0871i | − | 0.356132i | ||||||
\(268\) | 220.592i | 0.823104i | ||||||||
\(269\) | −164.713 | −0.612315 | −0.306158 | − | 0.951981i | \(-0.599043\pi\) | ||||
−0.306158 | + | 0.951981i | \(0.599043\pi\) | |||||||
\(270\) | − | 16.4317i | − | 0.0608581i | ||||||
\(271\) | 248.736 | 0.917845 | 0.458922 | − | 0.888476i | \(-0.348236\pi\) | ||||
0.458922 | + | 0.888476i | \(0.348236\pi\) | |||||||
\(272\) | − | 69.5949i | − | 0.255864i | ||||||
\(273\) | − | 78.3587i | − | 0.287028i | ||||||
\(274\) | − | 163.295i | − | 0.595967i | ||||||
\(275\) | − | 19.9921i | − | 0.0726987i | ||||||
\(276\) | 78.9400 | − | 10.7924i | 0.286014 | − | 0.0391030i | ||||
\(277\) | −134.521 | −0.485636 | −0.242818 | − | 0.970072i | \(-0.578072\pi\) | ||||
−0.242818 | + | 0.970072i | \(0.578072\pi\) | |||||||
\(278\) | 351.242 | 1.26346 | ||||||||
\(279\) | −62.0016 | −0.222228 | ||||||||
\(280\) | −34.9669 | −0.124882 | ||||||||
\(281\) | 244.802i | 0.871182i | 0.900145 | + | 0.435591i | \(0.143461\pi\) | ||||
−0.900145 | + | 0.435591i | \(0.856539\pi\) | |||||||
\(282\) | −183.708 | −0.651447 | ||||||||
\(283\) | − | 413.193i | − | 1.46005i | −0.683423 | − | 0.730023i | \(-0.739509\pi\) | ||
0.683423 | − | 0.730023i | \(-0.260491\pi\) | |||||||
\(284\) | 61.0226 | 0.214868 | ||||||||
\(285\) | −42.9646 | −0.150753 | ||||||||
\(286\) | − | 46.2704i | − | 0.161785i | ||||||
\(287\) | 405.854i | 1.41413i | ||||||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −13.7155 | −0.0474585 | ||||||||
\(290\) | 32.6505i | 0.112588i | ||||||||
\(291\) | 15.4078i | 0.0529478i | ||||||||
\(292\) | −179.141 | −0.613498 | ||||||||
\(293\) | − | 59.2551i | − | 0.202236i | −0.994874 | − | 0.101118i | \(-0.967758\pi\) | ||
0.994874 | − | 0.101118i | \(-0.0322419\pi\) | |||||||
\(294\) | 45.1511 | 0.153575 | ||||||||
\(295\) | 15.1428i | 0.0513315i | ||||||||
\(296\) | − | 110.472i | − | 0.373215i | ||||||
\(297\) | − | 20.7764i | − | 0.0699543i | ||||||
\(298\) | 316.833i | 1.06320i | ||||||||
\(299\) | −186.469 | + | 25.4934i | −0.623641 | + | 0.0852623i | ||||
\(300\) | 17.3205 | 0.0577350 | ||||||||
\(301\) | 288.655 | 0.958988 | ||||||||
\(302\) | −325.786 | −1.07876 | ||||||||
\(303\) | 176.920 | 0.583894 | ||||||||
\(304\) | 44.3736i | 0.145966i | ||||||||
\(305\) | 257.410 | 0.843968 | ||||||||
\(306\) | 73.8165i | 0.241230i | ||||||||
\(307\) | 163.557 | 0.532760 | 0.266380 | − | 0.963868i | \(-0.414172\pi\) | ||||
0.266380 | + | 0.963868i | \(0.414172\pi\) | |||||||
\(308\) | −44.2127 | −0.143548 | ||||||||
\(309\) | − | 308.360i | − | 0.997930i | ||||||
\(310\) | − | 65.3555i | − | 0.210824i | ||||||
\(311\) | 143.413 | 0.461134 | 0.230567 | − | 0.973056i | \(-0.425942\pi\) | ||||
0.230567 | + | 0.973056i | \(0.425942\pi\) | |||||||
\(312\) | 40.0871 | 0.128484 | ||||||||
\(313\) | 37.6949i | 0.120431i | 0.998185 | + | 0.0602155i | \(0.0191788\pi\) | ||||
−0.998185 | + | 0.0602155i | \(0.980821\pi\) | |||||||
\(314\) | − | 15.8735i | − | 0.0505525i | ||||||
\(315\) | 37.0880 | 0.117740 | ||||||||
\(316\) | 282.497i | 0.893977i | ||||||||
\(317\) | −123.519 | −0.389650 | −0.194825 | − | 0.980838i | \(-0.562414\pi\) | ||||
−0.194825 | + | 0.980838i | \(0.562414\pi\) | |||||||
\(318\) | 44.7267i | 0.140650i | ||||||||
\(319\) | 41.2837i | 0.129416i | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | − | 9.44497i | − | 0.0294236i | ||||||
\(322\) | 24.3597 | + | 178.176i | 0.0756511 | + | 0.553341i | ||||
\(323\) | 193.011 | 0.597557 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | −40.9137 | −0.125888 | ||||||||
\(326\) | −95.4814 | −0.292888 | ||||||||
\(327\) | − | 32.8496i | − | 0.100458i | ||||||
\(328\) | −207.629 | −0.633015 | ||||||||
\(329\) | − | 414.649i | − | 1.26033i | ||||||
\(330\) | 21.9003 | 0.0663645 | ||||||||
\(331\) | 139.163 | 0.420432 | 0.210216 | − | 0.977655i | \(-0.432583\pi\) | ||||
0.210216 | + | 0.977655i | \(0.432583\pi\) | |||||||
\(332\) | 133.628i | 0.402493i | ||||||||
\(333\) | 117.173i | 0.351871i | ||||||||
\(334\) | −40.3784 | −0.120893 | ||||||||
\(335\) | 246.629 | 0.736206 | ||||||||
\(336\) | − | 38.3043i | − | 0.114001i | ||||||
\(337\) | − | 441.284i | − | 1.30945i | −0.755868 | − | 0.654724i | \(-0.772785\pi\) | ||
0.755868 | − | 0.654724i | \(-0.227215\pi\) | |||||||
\(338\) | 144.310 | 0.426953 | ||||||||
\(339\) | − | 96.4373i | − | 0.284476i | ||||||
\(340\) | −77.8094 | −0.228851 | ||||||||
\(341\) | − | 82.6364i | − | 0.242335i | ||||||
\(342\) | − | 47.0653i | − | 0.137618i | ||||||
\(343\) | 372.820i | 1.08694i | ||||||||
\(344\) | 147.672i | 0.429278i | ||||||||
\(345\) | −12.0663 | − | 88.2576i | −0.0349748 | − | 0.255819i | ||||
\(346\) | 57.6077 | 0.166496 | ||||||||
\(347\) | 229.795 | 0.662233 | 0.331116 | − | 0.943590i | \(-0.392575\pi\) | ||||
0.331116 | + | 0.943590i | \(0.392575\pi\) | |||||||
\(348\) | −35.7668 | −0.102778 | ||||||||
\(349\) | −521.752 | −1.49499 | −0.747496 | − | 0.664266i | \(-0.768744\pi\) | ||||
−0.747496 | + | 0.664266i | \(0.768744\pi\) | |||||||
\(350\) | 39.0942i | 0.111698i | ||||||||
\(351\) | −42.5188 | −0.121136 | ||||||||
\(352\) | − | 22.6185i | − | 0.0642572i | ||||||
\(353\) | 214.638 | 0.608040 | 0.304020 | − | 0.952666i | \(-0.401671\pi\) | ||||
0.304020 | + | 0.952666i | \(0.401671\pi\) | |||||||
\(354\) | −16.5881 | −0.0468590 | ||||||||
\(355\) | − | 68.2254i | − | 0.192184i | ||||||
\(356\) | 109.797i | 0.308419i | ||||||||
\(357\) | −166.612 | −0.466699 | ||||||||
\(358\) | 401.235 | 1.12077 | ||||||||
\(359\) | 597.409i | 1.66409i | 0.554707 | + | 0.832045i | \(0.312830\pi\) | ||||
−0.554707 | + | 0.832045i | \(0.687170\pi\) | |||||||
\(360\) | 18.9737i | 0.0527046i | ||||||||
\(361\) | 237.936 | 0.659104 | ||||||||
\(362\) | − | 33.3364i | − | 0.0920896i | ||||||
\(363\) | −181.887 | −0.501066 | ||||||||
\(364\) | 90.4809i | 0.248574i | ||||||||
\(365\) | 200.286i | 0.548729i | ||||||||
\(366\) | 281.979i | 0.770434i | ||||||||
\(367\) | 99.3937i | 0.270828i | 0.990789 | + | 0.135414i | \(0.0432364\pi\) | ||||
−0.990789 | + | 0.135414i | \(0.956764\pi\) | |||||||
\(368\) | −91.1521 | + | 12.4620i | −0.247696 | + | 0.0338642i | ||||
\(369\) | 220.224 | 0.596812 | ||||||||
\(370\) | −123.511 | −0.333814 | ||||||||
\(371\) | −100.953 | −0.272110 | ||||||||
\(372\) | 71.5933 | 0.192455 | ||||||||
\(373\) | 59.2285i | 0.158790i | 0.996843 | + | 0.0793948i | \(0.0252988\pi\) | ||||
−0.996843 | + | 0.0793948i | \(0.974701\pi\) | |||||||
\(374\) | −98.3833 | −0.263057 | ||||||||
\(375\) | − | 19.3649i | − | 0.0516398i | ||||||
\(376\) | 212.128 | 0.564170 | ||||||||
\(377\) | 84.4868 | 0.224103 | ||||||||
\(378\) | 40.6279i | 0.107481i | ||||||||
\(379\) | − | 127.161i | − | 0.335517i | −0.985828 | − | 0.167759i | \(-0.946347\pi\) | ||
0.985828 | − | 0.167759i | \(-0.0536529\pi\) | |||||||
\(380\) | 49.6112 | 0.130556 | ||||||||
\(381\) | 224.610 | 0.589528 | ||||||||
\(382\) | 55.4905i | 0.145263i | ||||||||
\(383\) | 354.837i | 0.926466i | 0.886236 | + | 0.463233i | \(0.153311\pi\) | ||||
−0.886236 | + | 0.463233i | \(0.846689\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | 49.4313i | 0.128393i | ||||||||
\(386\) | −304.161 | −0.787983 | ||||||||
\(387\) | − | 156.630i | − | 0.404727i | ||||||
\(388\) | − | 17.7914i | − | 0.0458541i | ||||||
\(389\) | 188.718i | 0.485136i | 0.970134 | + | 0.242568i | \(0.0779897\pi\) | ||||
−0.970134 | + | 0.242568i | \(0.922010\pi\) | |||||||
\(390\) | − | 44.8188i | − | 0.114920i | ||||||
\(391\) | 54.2058 | + | 396.482i | 0.138634 | + | 1.01402i | ||||
\(392\) | −52.1360 | −0.133000 | ||||||||
\(393\) | −337.609 | −0.859057 | ||||||||
\(394\) | −276.374 | −0.701457 | ||||||||
\(395\) | 315.841 | 0.799597 | ||||||||
\(396\) | 23.9906i | 0.0605822i | ||||||||
\(397\) | 110.983 | 0.279553 | 0.139777 | − | 0.990183i | \(-0.455362\pi\) | ||||
0.139777 | + | 0.990183i | \(0.455362\pi\) | |||||||
\(398\) | − | 178.520i | − | 0.448542i | ||||||
\(399\) | 106.231 | 0.266244 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 493.947i | 1.23179i | 0.787829 | + | 0.615894i | \(0.211205\pi\) | ||||
−0.787829 | + | 0.615894i | \(0.788795\pi\) | |||||||
\(402\) | 270.169i | 0.672061i | ||||||||
\(403\) | −169.115 | −0.419639 | ||||||||
\(404\) | −204.289 | −0.505667 | ||||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | − | 80.7294i | − | 0.198841i | ||||||
\(407\) | −156.169 | −0.383708 | ||||||||
\(408\) | − | 85.2360i | − | 0.208912i | ||||||
\(409\) | 65.1665 | 0.159331 | 0.0796656 | − | 0.996822i | \(-0.474615\pi\) | ||||
0.0796656 | + | 0.996822i | \(0.474615\pi\) | |||||||
\(410\) | 232.136i | 0.566185i | ||||||||
\(411\) | − | 199.995i | − | 0.486605i | ||||||
\(412\) | 356.064i | 0.864233i | ||||||||
\(413\) | − | 37.4411i | − | 0.0906564i | ||||||
\(414\) | 96.6814 | − | 13.2180i | 0.233530 | − | 0.0319275i | ||||
\(415\) | 149.400 | 0.360001 | ||||||||
\(416\) | −46.2886 | −0.111271 | ||||||||
\(417\) | 430.182 | 1.03161 | ||||||||
\(418\) | 62.7291 | 0.150070 | ||||||||
\(419\) | 330.658i | 0.789161i | 0.918861 | + | 0.394580i | \(0.129110\pi\) | ||||
−0.918861 | + | 0.394580i | \(0.870890\pi\) | |||||||
\(420\) | −42.8256 | −0.101966 | ||||||||
\(421\) | − | 775.522i | − | 1.84209i | −0.389451 | − | 0.921047i | \(-0.627335\pi\) | ||
0.389451 | − | 0.921047i | \(-0.372665\pi\) | |||||||
\(422\) | −351.671 | −0.833344 | ||||||||
\(423\) | −224.996 | −0.531904 | ||||||||
\(424\) | − | 51.6460i | − | 0.121807i | ||||||
\(425\) | 86.9936i | 0.204691i | ||||||||
\(426\) | 74.7372 | 0.175439 | ||||||||
\(427\) | −636.456 | −1.49053 | ||||||||
\(428\) | 10.9061i | 0.0254816i | ||||||||
\(429\) | − | 56.6695i | − | 0.132097i | ||||||
\(430\) | 165.102 | 0.383958 | ||||||||
\(431\) | − | 10.8609i | − | 0.0251993i | −0.999921 | − | 0.0125996i | \(-0.995989\pi\) | ||
0.999921 | − | 0.0125996i | \(-0.00401069\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | − | 693.229i | − | 1.60099i | −0.599338 | − | 0.800496i | \(-0.704570\pi\) | ||
0.599338 | − | 0.800496i | \(-0.295430\pi\) | |||||||
\(434\) | 161.594i | 0.372336i | ||||||||
\(435\) | 39.9885i | 0.0919276i | ||||||||
\(436\) | 37.9315i | 0.0869989i | ||||||||
\(437\) | −34.5616 | − | 252.797i | −0.0790883 | − | 0.578482i | ||||
\(438\) | −219.403 | −0.500919 | ||||||||
\(439\) | −631.383 | −1.43823 | −0.719115 | − | 0.694891i | \(-0.755453\pi\) | ||||
−0.719115 | + | 0.694891i | \(0.755453\pi\) | |||||||
\(440\) | −25.2883 | −0.0574734 | ||||||||
\(441\) | 55.2986 | 0.125394 | ||||||||
\(442\) | 201.341i | 0.455522i | ||||||||
\(443\) | −12.4244 | −0.0280460 | −0.0140230 | − | 0.999902i | \(-0.504464\pi\) | ||||
−0.0140230 | + | 0.999902i | \(0.504464\pi\) | |||||||
\(444\) | − | 135.300i | − | 0.304729i | ||||||
\(445\) | 122.757 | 0.275858 | ||||||||
\(446\) | 298.493 | 0.669266 | ||||||||
\(447\) | 388.040i | 0.868098i | ||||||||
\(448\) | 44.2300i | 0.0987278i | ||||||||
\(449\) | −712.745 | −1.58740 | −0.793702 | − | 0.608306i | \(-0.791849\pi\) | ||||
−0.793702 | + | 0.608306i | \(0.791849\pi\) | |||||||
\(450\) | 21.2132 | 0.0471405 | ||||||||
\(451\) | 293.516i | 0.650812i | ||||||||
\(452\) | 111.356i | 0.246363i | ||||||||
\(453\) | −399.004 | −0.880804 | ||||||||
\(454\) | 387.067i | 0.852571i | ||||||||
\(455\) | 101.161 | 0.222331 | ||||||||
\(456\) | 54.3464i | 0.119181i | ||||||||
\(457\) | 345.010i | 0.754946i | 0.926021 | + | 0.377473i | \(0.123207\pi\) | ||||
−0.926021 | + | 0.377473i | \(0.876793\pi\) | |||||||
\(458\) | 517.900i | 1.13079i | ||||||||
\(459\) | 90.4064i | 0.196964i | ||||||||
\(460\) | 13.9330 | + | 101.911i | 0.0302891 | + | 0.221546i | ||||
\(461\) | −208.968 | −0.453293 | −0.226646 | − | 0.973977i | \(-0.572776\pi\) | ||||
−0.226646 | + | 0.973977i | \(0.572776\pi\) | |||||||
\(462\) | −54.1492 | −0.117206 | ||||||||
\(463\) | 743.406 | 1.60563 | 0.802814 | − | 0.596229i | \(-0.203335\pi\) | ||||
0.802814 | + | 0.596229i | \(0.203335\pi\) | |||||||
\(464\) | 41.2999 | 0.0890085 | ||||||||
\(465\) | − | 80.0438i | − | 0.172137i | ||||||
\(466\) | 329.264 | 0.706575 | ||||||||
\(467\) | − | 409.810i | − | 0.877536i | −0.898600 | − | 0.438768i | \(-0.855415\pi\) | ||
0.898600 | − | 0.438768i | \(-0.144585\pi\) | |||||||
\(468\) | 49.0965 | 0.104907 | ||||||||
\(469\) | −609.799 | −1.30021 | ||||||||
\(470\) | − | 237.166i | − | 0.504609i | ||||||
\(471\) | − | 19.4410i | − | 0.0412759i | ||||||
\(472\) | 19.1543 | 0.0405811 | ||||||||
\(473\) | 208.757 | 0.441347 | ||||||||
\(474\) | 345.986i | 0.729929i | ||||||||
\(475\) | − | 55.4670i | − | 0.116773i | ||||||
\(476\) | 192.387 | 0.404173 | ||||||||
\(477\) | 54.7788i | 0.114840i | ||||||||
\(478\) | 146.873 | 0.307267 | ||||||||
\(479\) | − | 219.384i | − | 0.458004i | −0.973426 | − | 0.229002i | \(-0.926454\pi\) | ||
0.973426 | − | 0.229002i | \(-0.0735462\pi\) | |||||||
\(480\) | − | 21.9089i | − | 0.0456435i | ||||||
\(481\) | 319.599i | 0.664447i | ||||||||
\(482\) | − | 292.170i | − | 0.606162i | ||||||
\(483\) | 29.8344 | + | 218.220i | 0.0617689 | + | 0.451801i | ||||
\(484\) | 210.025 | 0.433936 | ||||||||
\(485\) | −19.8914 | −0.0410132 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 47.9454 | 0.0984506 | 0.0492253 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492253 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(488\) | − | 325.601i | − | 0.667216i | ||||||
\(489\) | −116.940 | −0.239142 | ||||||||
\(490\) | 58.2898i | 0.118959i | ||||||||
\(491\) | −734.556 | −1.49604 | −0.748020 | − | 0.663676i | \(-0.768995\pi\) | ||||
−0.748020 | + | 0.663676i | \(0.768995\pi\) | |||||||
\(492\) | −254.292 | −0.516854 | ||||||||
\(493\) | − | 179.641i | − | 0.364384i | ||||||
\(494\) | − | 128.375i | − | 0.259868i | ||||||
\(495\) | 26.8223 | 0.0541864 | ||||||||
\(496\) | −82.6689 | −0.166671 | ||||||||
\(497\) | 168.690i | 0.339416i | ||||||||
\(498\) | 163.660i | 0.328634i | ||||||||
\(499\) | −391.502 | −0.784574 | −0.392287 | − | 0.919843i | \(-0.628316\pi\) | ||||
−0.392287 | + | 0.919843i | \(0.628316\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −49.4532 | −0.0987090 | ||||||||
\(502\) | − | 356.776i | − | 0.710708i | ||||||
\(503\) | 336.866i | 0.669713i | 0.942269 | + | 0.334856i | \(0.108688\pi\) | ||||
−0.942269 | + | 0.334856i | \(0.891312\pi\) | |||||||
\(504\) | − | 46.9131i | − | 0.0930815i | ||||||
\(505\) | 228.403i | 0.452282i | ||||||||
\(506\) | 17.6170 | + | 128.858i | 0.0348163 | + | 0.254660i | ||||
\(507\) | 176.743 | 0.348605 | ||||||||
\(508\) | −259.358 | −0.510546 | ||||||||
\(509\) | 345.754 | 0.679281 | 0.339641 | − | 0.940555i | \(-0.389695\pi\) | ||||
0.339641 | + | 0.940555i | \(0.389695\pi\) | |||||||
\(510\) | −95.2967 | −0.186856 | ||||||||
\(511\) | − | 495.215i | − | 0.969109i | ||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | − | 57.6430i | − | 0.112365i | ||||||
\(514\) | 228.349 | 0.444259 | ||||||||
\(515\) | 398.092 | 0.772993 | ||||||||
\(516\) | 180.860i | 0.350504i | ||||||||
\(517\) | − | 299.876i | − | 0.580031i | ||||||
\(518\) | 305.386 | 0.589548 | ||||||||
\(519\) | 70.5548 | 0.135944 | ||||||||
\(520\) | 51.7523i | 0.0995236i | ||||||||
\(521\) | − | 217.945i | − | 0.418320i | −0.977881 | − | 0.209160i | \(-0.932927\pi\) | ||
0.977881 | − | 0.209160i | \(-0.0670729\pi\) | |||||||
\(522\) | −43.8052 | −0.0839180 | ||||||||
\(523\) | 106.244i | 0.203144i | 0.994828 | + | 0.101572i | \(0.0323873\pi\) | ||||
−0.994828 | + | 0.101572i | \(0.967613\pi\) | |||||||
\(524\) | 389.838 | 0.743965 | ||||||||
\(525\) | 47.8804i | 0.0912008i | ||||||||
\(526\) | 383.360i | 0.728822i | ||||||||
\(527\) | 359.583i | 0.682321i | ||||||||
\(528\) | − | 27.7019i | − | 0.0524658i | ||||||
\(529\) | 509.587 | − | 141.992i | 0.963303 | − | 0.268417i | ||||
\(530\) | −57.7419 | −0.108947 | ||||||||
\(531\) | −20.3162 | −0.0382602 | ||||||||
\(532\) | −122.665 | −0.230574 | ||||||||
\(533\) | 600.678 | 1.12698 | ||||||||
\(534\) | 134.473i | 0.251823i | ||||||||
\(535\) | 12.1934 | 0.0227914 | ||||||||
\(536\) | − | 311.964i | − | 0.582022i | ||||||
\(537\) | 491.410 | 0.915103 | ||||||||
\(538\) | 232.939 | 0.432972 | ||||||||
\(539\) | 73.7024i | 0.136739i | ||||||||
\(540\) | 23.2379i | 0.0430331i | ||||||||
\(541\) | 547.119 | 1.01131 | 0.505656 | − | 0.862735i | \(-0.331251\pi\) | ||||
0.505656 | + | 0.862735i | \(0.331251\pi\) | |||||||
\(542\) | −351.766 | −0.649014 | ||||||||
\(543\) | − | 40.8286i | − | 0.0751908i | ||||||
\(544\) | 98.4220i | 0.180923i | ||||||||
\(545\) | 42.4087 | 0.0778142 | ||||||||
\(546\) | 110.816i | 0.202960i | ||||||||
\(547\) | −58.9612 | −0.107790 | −0.0538951 | − | 0.998547i | \(-0.517164\pi\) | ||||
−0.0538951 | + | 0.998547i | \(0.517164\pi\) | |||||||
\(548\) | 230.934i | 0.421412i | ||||||||
\(549\) | 345.352i | 0.629057i | ||||||||
\(550\) | 28.2732i | 0.0514057i | ||||||||
\(551\) | 114.539i | 0.207875i | ||||||||
\(552\) | −111.638 | + | 15.2628i | −0.202243 | + | 0.0276500i | ||||
\(553\) | −780.928 | −1.41217 | ||||||||
\(554\) | 190.242 | 0.343397 | ||||||||
\(555\) | −151.270 | −0.272558 | ||||||||
\(556\) | −496.731 | −0.893401 | ||||||||
\(557\) | 1000.83i | 1.79682i | 0.439157 | + | 0.898410i | \(0.355277\pi\) | ||||
−0.439157 | + | 0.898410i | \(0.644723\pi\) | |||||||
\(558\) | 87.6836 | 0.157139 | ||||||||
\(559\) | − | 427.220i | − | 0.764258i | ||||||
\(560\) | 49.4507 | 0.0883048 | ||||||||
\(561\) | −120.494 | −0.214785 | ||||||||
\(562\) | − | 346.202i | − | 0.616019i | ||||||
\(563\) | 308.329i | 0.547653i | 0.961779 | + | 0.273827i | \(0.0882895\pi\) | ||||
−0.961779 | + | 0.273827i | \(0.911711\pi\) | |||||||
\(564\) | 259.802 | 0.460643 | ||||||||
\(565\) | 124.500 | 0.220354 | ||||||||
\(566\) | 584.343i | 1.03241i | ||||||||
\(567\) | 49.7588i | 0.0877580i | ||||||||
\(568\) | −86.2991 | −0.151935 | ||||||||
\(569\) | 871.925i | 1.53238i | 0.642613 | + | 0.766191i | \(0.277850\pi\) | ||||
−0.642613 | + | 0.766191i | \(0.722150\pi\) | |||||||
\(570\) | 60.7611 | 0.106598 | ||||||||
\(571\) | 86.2852i | 0.151112i | 0.997142 | + | 0.0755562i | \(0.0240732\pi\) | ||||
−0.997142 | + | 0.0755562i | \(0.975927\pi\) | |||||||
\(572\) | 65.4363i | 0.114399i | ||||||||
\(573\) | 67.9617i | 0.118607i | ||||||||
\(574\) | − | 573.964i | − | 0.999938i | ||||||
\(575\) | 113.940 | − | 15.5775i | 0.198157 | − | 0.0270914i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 316.305 | 0.548189 | 0.274094 | − | 0.961703i | \(-0.411622\pi\) | ||||
0.274094 | + | 0.961703i | \(0.411622\pi\) | |||||||
\(578\) | 19.3967 | 0.0335582 | ||||||||
\(579\) | −372.520 | −0.643385 | ||||||||
\(580\) | − | 46.1747i | − | 0.0796116i | ||||||
\(581\) | −369.398 | −0.635796 | ||||||||
\(582\) | − | 21.7899i | − | 0.0374397i | ||||||
\(583\) | −73.0097 | −0.125231 | ||||||||
\(584\) | 253.344 | 0.433809 | ||||||||
\(585\) | − | 54.8916i | − | 0.0938317i | ||||||
\(586\) | 83.7994i | 0.143002i | ||||||||
\(587\) | 2.18581 | 0.00372369 | 0.00186185 | − | 0.999998i | \(-0.499407\pi\) | ||||
0.00186185 | + | 0.999998i | \(0.499407\pi\) | |||||||
\(588\) | −63.8533 | −0.108594 | ||||||||
\(589\) | − | 229.270i | − | 0.389253i | ||||||
\(590\) | − | 21.4151i | − | 0.0362969i | ||||||
\(591\) | −338.487 | −0.572737 | ||||||||
\(592\) | 156.231i | 0.263903i | ||||||||
\(593\) | 19.9467 | 0.0336369 | 0.0168185 | − | 0.999859i | \(-0.494646\pi\) | ||||
0.0168185 | + | 0.999859i | \(0.494646\pi\) | |||||||
\(594\) | 29.3823i | 0.0494652i | ||||||||
\(595\) | − | 215.095i | − | 0.361504i | ||||||
\(596\) | − | 448.070i | − | 0.751795i | ||||||
\(597\) | − | 218.641i | − | 0.366233i | ||||||
\(598\) | 263.706 | − | 36.0531i | 0.440981 | − | 0.0602895i | ||||
\(599\) | −455.182 | −0.759903 | −0.379952 | − | 0.925006i | \(-0.624059\pi\) | ||||
−0.379952 | + | 0.925006i | \(0.624059\pi\) | |||||||
\(600\) | −24.4949 | −0.0408248 | ||||||||
\(601\) | 374.525 | 0.623169 | 0.311584 | − | 0.950218i | \(-0.399140\pi\) | ||||
0.311584 | + | 0.950218i | \(0.399140\pi\) | |||||||
\(602\) | −408.220 | −0.678107 | ||||||||
\(603\) | 330.888i | 0.548736i | ||||||||
\(604\) | 460.730 | 0.762799 | ||||||||
\(605\) | − | 234.815i | − | 0.388124i | ||||||
\(606\) | −250.202 | −0.412875 | ||||||||
\(607\) | 613.993 | 1.01152 | 0.505760 | − | 0.862674i | \(-0.331212\pi\) | ||||
0.505760 | + | 0.862674i | \(0.331212\pi\) | |||||||
\(608\) | − | 62.7538i | − | 0.103213i | ||||||
\(609\) | − | 98.8729i | − | 0.162353i | ||||||
\(610\) | −364.033 | −0.596776 | ||||||||
\(611\) | −613.694 | −1.00441 | ||||||||
\(612\) | − | 104.392i | − | 0.170576i | ||||||
\(613\) | 633.738i | 1.03383i | 0.856037 | + | 0.516915i | \(0.172920\pi\) | ||||
−0.856037 | + | 0.516915i | \(0.827080\pi\) | |||||||
\(614\) | −231.305 | −0.376718 | ||||||||
\(615\) | 284.307i | 0.462288i | ||||||||
\(616\) | 62.5261 | 0.101503 | ||||||||
\(617\) | 209.518i | 0.339575i | 0.985481 | + | 0.169788i | \(0.0543082\pi\) | ||||
−0.985481 | + | 0.169788i | \(0.945692\pi\) | |||||||
\(618\) | 436.087i | 0.705643i | ||||||||
\(619\) | − | 82.5461i | − | 0.133354i | −0.997775 | − | 0.0666770i | \(-0.978760\pi\) | ||
0.997775 | − | 0.0666770i | \(-0.0212397\pi\) | |||||||
\(620\) | 92.4266i | 0.149075i | ||||||||
\(621\) | 118.410 | − | 16.1887i | 0.190676 | − | 0.0260687i | ||||
\(622\) | −202.816 | −0.326071 | ||||||||
\(623\) | −303.521 | −0.487192 | ||||||||
\(624\) | −56.6918 | −0.0908522 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 53.3086i | − | 0.0851575i | ||||||
\(627\) | 76.8271 | 0.122531 | ||||||||
\(628\) | 22.4485i | 0.0357460i | ||||||||
\(629\) | 679.553 | 1.08037 | ||||||||
\(630\) | −52.4504 | −0.0832546 | ||||||||
\(631\) | − | 382.762i | − | 0.606596i | −0.952896 | − | 0.303298i | \(-0.901912\pi\) | ||
0.952896 | − | 0.303298i | \(-0.0980877\pi\) | |||||||
\(632\) | − | 399.511i | − | 0.632137i | ||||||
\(633\) | −430.707 | −0.680422 | ||||||||
\(634\) | 174.682 | 0.275524 | ||||||||
\(635\) | 289.971i | 0.456646i | ||||||||
\(636\) | − | 63.2531i | − | 0.0994546i | ||||||
\(637\) | 150.831 | 0.236784 | ||||||||
\(638\) | − | 58.3840i | − | 0.0915109i | ||||||
\(639\) | 91.5340 | 0.143246 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | − | 336.338i | − | 0.524708i | −0.964972 | − | 0.262354i | \(-0.915501\pi\) | ||
0.964972 | − | 0.262354i | \(-0.0844988\pi\) | |||||||
\(642\) | 13.3572i | 0.0208056i | ||||||||
\(643\) | − | 135.912i | − | 0.211371i | −0.994400 | − | 0.105686i | \(-0.966296\pi\) | ||
0.994400 | − | 0.105686i | \(-0.0337037\pi\) | |||||||
\(644\) | −34.4498 | − | 251.979i | −0.0534934 | − | 0.391271i | ||||
\(645\) | 202.208 | 0.313501 | ||||||||
\(646\) | −272.959 | −0.422537 | ||||||||
\(647\) | −586.820 | −0.906986 | −0.453493 | − | 0.891260i | \(-0.649822\pi\) | ||||
−0.453493 | + | 0.891260i | \(0.649822\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | − | 27.0776i | − | 0.0417220i | ||||||
\(650\) | 57.8608 | 0.0890166 | ||||||||
\(651\) | 197.911i | 0.304011i | ||||||||
\(652\) | 135.031 | 0.207103 | ||||||||
\(653\) | −99.3991 | −0.152219 | −0.0761095 | − | 0.997099i | \(-0.524250\pi\) | ||||
−0.0761095 | + | 0.997099i | \(0.524250\pi\) | |||||||
\(654\) | 46.4564i | 0.0710343i | ||||||||
\(655\) | − | 435.852i | − | 0.665423i | ||||||
\(656\) | 293.631 | 0.447609 | ||||||||
\(657\) | −268.712 | −0.408999 | ||||||||
\(658\) | 586.402i | 0.891188i | ||||||||
\(659\) | − | 838.897i | − | 1.27299i | −0.771283 | − | 0.636493i | \(-0.780385\pi\) | ||
0.771283 | − | 0.636493i | \(-0.219615\pi\) | |||||||
\(660\) | −30.9717 | −0.0469268 | ||||||||
\(661\) | − | 1079.24i | − | 1.63274i | −0.577529 | − | 0.816370i | \(-0.695983\pi\) | ||
0.577529 | − | 0.816370i | \(-0.304017\pi\) | |||||||
\(662\) | −196.806 | −0.297290 | ||||||||
\(663\) | 246.591i | 0.371932i | ||||||||
\(664\) | − | 188.978i | − | 0.284606i | ||||||
\(665\) | 137.144i | 0.206232i | ||||||||
\(666\) | − | 165.708i | − | 0.248810i | ||||||
\(667\) | −235.286 | + | 32.1676i | −0.352752 | + | 0.0482272i | ||||
\(668\) | 57.1037 | 0.0854845 | ||||||||
\(669\) | 365.577 | 0.546453 | ||||||||
\(670\) | −348.786 | −0.520576 | ||||||||
\(671\) | −460.289 | −0.685974 | ||||||||
\(672\) | 54.1705i | 0.0806109i | ||||||||
\(673\) | 175.116 | 0.260202 | 0.130101 | − | 0.991501i | \(-0.458470\pi\) | ||||
0.130101 | + | 0.991501i | \(0.458470\pi\) | |||||||
\(674\) | 624.070i | 0.925919i | ||||||||
\(675\) | 25.9808 | 0.0384900 | ||||||||
\(676\) | −204.085 | −0.301901 | ||||||||
\(677\) | − | 708.732i | − | 1.04687i | −0.852065 | − | 0.523435i | \(-0.824650\pi\) | ||
0.852065 | − | 0.523435i | \(-0.175350\pi\) | |||||||
\(678\) | 136.383i | 0.201155i | ||||||||
\(679\) | 49.1822 | 0.0724332 | ||||||||
\(680\) | 110.039 | 0.161822 | ||||||||
\(681\) | 474.059i | 0.696121i | ||||||||
\(682\) | 116.865i | 0.171357i | ||||||||
\(683\) | 1323.41 | 1.93764 | 0.968819 | − | 0.247768i | \(-0.0796970\pi\) | ||||
0.968819 | + | 0.247768i | \(0.0796970\pi\) | |||||||
\(684\) | 66.5604i | 0.0973106i | ||||||||
\(685\) | 258.192 | 0.376923 | ||||||||
\(686\) | − | 527.247i | − | 0.768581i | ||||||
\(687\) | 634.295i | 0.923282i | ||||||||
\(688\) | − | 208.839i | − | 0.303546i | ||||||
\(689\) | 149.414i | 0.216856i | ||||||||
\(690\) | 17.0643 | + | 124.815i | 0.0247309 | + | 0.180891i | ||||
\(691\) | 1044.51 | 1.51159 | 0.755794 | − | 0.654809i | \(-0.227251\pi\) | ||||
0.755794 | + | 0.654809i | \(0.227251\pi\) | |||||||
\(692\) | −81.4696 | −0.117731 | ||||||||
\(693\) | −66.3190 | −0.0956984 | ||||||||
\(694\) | −324.979 | −0.468269 | ||||||||
\(695\) | 555.362i | 0.799082i | ||||||||
\(696\) | 50.5819 | 0.0726751 | ||||||||
\(697\) | − | 1277.20i | − | 1.83243i | ||||||
\(698\) | 737.869 | 1.05712 | ||||||||
\(699\) | 403.265 | 0.576916 | ||||||||
\(700\) | − | 55.2876i | − | 0.0789822i | ||||||
\(701\) | − | 745.468i | − | 1.06344i | −0.846922 | − | 0.531718i | \(-0.821547\pi\) | ||
0.846922 | − | 0.531718i | \(-0.178453\pi\) | |||||||
\(702\) | 60.1307 | 0.0856562 | ||||||||
\(703\) | −433.282 | −0.616333 | ||||||||
\(704\) | 31.9874i | 0.0454367i | ||||||||
\(705\) | − | 290.468i | − | 0.412011i | ||||||
\(706\) | −303.544 | −0.429949 | ||||||||
\(707\) | − | 564.733i | − | 0.798774i | ||||||
\(708\) | 23.4591 | 0.0331343 | ||||||||
\(709\) | − | 831.513i | − | 1.17280i | −0.810023 | − | 0.586398i | \(-0.800545\pi\) | ||
0.810023 | − | 0.586398i | \(-0.199455\pi\) | |||||||
\(710\) | 96.4853i | 0.135895i | ||||||||
\(711\) | 423.745i | 0.595984i | ||||||||
\(712\) | − | 155.277i | − | 0.218085i | ||||||
\(713\) | 470.965 | − | 64.3889i | 0.660540 | − | 0.0903070i | ||||
\(714\) | 235.624 | 0.330006 | ||||||||
\(715\) | 73.1600 | 0.102322 | ||||||||
\(716\) | −567.431 | −0.792502 | ||||||||
\(717\) | 179.883 | 0.250882 | ||||||||
\(718\) | − | 844.863i | − | 1.17669i | ||||||
\(719\) | 1233.84 | 1.71605 | 0.858027 | − | 0.513605i | \(-0.171690\pi\) | ||||
0.858027 | + | 0.513605i | \(0.171690\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | −984.295 | −1.36518 | ||||||||
\(722\) | −336.493 | −0.466057 | ||||||||
\(723\) | − | 357.834i | − | 0.494929i | ||||||
\(724\) | 47.1448i | 0.0651172i | ||||||||
\(725\) | −51.6249 | −0.0712068 | ||||||||
\(726\) | 257.227 | 0.354307 | ||||||||
\(727\) | − | 250.846i | − | 0.345042i | −0.985006 | − | 0.172521i | \(-0.944809\pi\) | ||
0.985006 | − | 0.172521i | \(-0.0551913\pi\) | |||||||
\(728\) | − | 127.959i | − | 0.175768i | ||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 283.247i | − | 0.388010i | ||||||
\(731\) | −908.384 | −1.24266 | ||||||||
\(732\) | − | 398.778i | − | 0.544779i | ||||||
\(733\) | − | 1346.25i | − | 1.83662i | −0.395857 | − | 0.918312i | \(-0.629552\pi\) | ||
0.395857 | − | 0.918312i | \(-0.370448\pi\) | |||||||
\(734\) | − | 140.564i | − | 0.191504i | ||||||
\(735\) | 71.3901i | 0.0971294i | ||||||||
\(736\) | 128.908 | − | 17.6240i | 0.175147 | − | 0.0239456i | ||||
\(737\) | −441.010 | −0.598385 | ||||||||
\(738\) | −311.443 | −0.422010 | ||||||||
\(739\) | −192.468 | −0.260444 | −0.130222 | − | 0.991485i | \(-0.541569\pi\) | ||||
−0.130222 | + | 0.991485i | \(0.541569\pi\) | |||||||
\(740\) | 174.671 | 0.236042 | ||||||||
\(741\) | − | 157.226i | − | 0.212181i | ||||||
\(742\) | 142.769 | 0.192411 | ||||||||
\(743\) | − | 1291.03i | − | 1.73759i | −0.495171 | − | 0.868796i | \(-0.664894\pi\) | ||
0.495171 | − | 0.868796i | \(-0.335106\pi\) | |||||||
\(744\) | −101.248 | −0.136086 | ||||||||
\(745\) | −500.957 | −0.672426 | ||||||||
\(746\) | − | 83.7617i | − | 0.112281i | ||||||
\(747\) | 200.442i | 0.268329i | ||||||||
\(748\) | 139.135 | 0.186009 | ||||||||
\(749\) | −30.1486 | −0.0402518 | ||||||||
\(750\) | 27.3861i | 0.0365148i | ||||||||
\(751\) | 43.3403i | 0.0577101i | 0.999584 | + | 0.0288550i | \(0.00918612\pi\) | ||||
−0.999584 | + | 0.0288550i | \(0.990814\pi\) | |||||||
\(752\) | −299.994 | −0.398928 | ||||||||
\(753\) | − | 436.959i | − | 0.580291i | ||||||
\(754\) | −119.482 | −0.158465 | ||||||||
\(755\) | − | 515.112i | − | 0.682268i | ||||||
\(756\) | − | 57.4565i | − | 0.0760007i | ||||||
\(757\) | 1237.39i | 1.63460i | 0.576211 | + | 0.817301i | \(0.304531\pi\) | ||||
−0.576211 | + | 0.817301i | \(0.695469\pi\) | |||||||
\(758\) | 179.833i | 0.237247i | ||||||||
\(759\) | 21.5764 | + | 157.818i | 0.0284274 | + | 0.207929i | ||||
\(760\) | −70.1609 | −0.0923169 | ||||||||
\(761\) | −505.115 | −0.663751 | −0.331876 | − | 0.943323i | \(-0.607681\pi\) | ||||
−0.331876 | + | 0.943323i | \(0.607681\pi\) | |||||||
\(762\) | −317.647 | −0.416859 | ||||||||
\(763\) | −104.857 | −0.137427 | ||||||||
\(764\) | − | 78.4754i | − | 0.102717i | ||||||
\(765\) | −116.714 | −0.152568 | ||||||||
\(766\) | − | 501.815i | − | 0.655110i | ||||||
\(767\) | −55.4141 | −0.0722478 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | − | 1237.03i | − | 1.60862i | −0.594208 | − | 0.804311i | \(-0.702534\pi\) | ||
0.594208 | − | 0.804311i | \(-0.297466\pi\) | |||||||
\(770\) | − | 69.9064i | − | 0.0907875i | ||||||
\(771\) | 279.669 | 0.362736 | ||||||||
\(772\) | 430.149 | 0.557188 | ||||||||
\(773\) | 1016.69i | 1.31526i | 0.753342 | + | 0.657629i | \(0.228441\pi\) | ||||
−0.753342 | + | 0.657629i | \(0.771559\pi\) | |||||||
\(774\) | 221.508i | 0.286186i | ||||||||
\(775\) | 103.336 | 0.133337 | ||||||||
\(776\) | 25.1608i | 0.0324238i | ||||||||
\(777\) | 374.020 | 0.481364 | ||||||||
\(778\) | − | 266.887i | − | 0.343043i | ||||||
\(779\) | 814.343i | 1.04537i | ||||||||
\(780\) | 63.3833i | 0.0812607i | ||||||||
\(781\) | 121.997i | 0.156207i | ||||||||
\(782\) | −76.6586 | − | 560.711i | −0.0980290 | − | 0.717021i | ||||
\(783\) | −53.6502 | −0.0685188 | ||||||||
\(784\) | 73.7314 | 0.0940452 | ||||||||
\(785\) | 25.0982 | 0.0319722 | ||||||||
\(786\) | 477.452 | 0.607445 | ||||||||
\(787\) | − | 654.021i | − | 0.831030i | −0.909586 | − | 0.415515i | \(-0.863601\pi\) | ||
0.909586 | − | 0.415515i | \(-0.136399\pi\) | |||||||
\(788\) | 390.852 | 0.496005 | ||||||||
\(789\) | 469.519i | 0.595081i | ||||||||
\(790\) | −446.666 | −0.565401 | ||||||||
\(791\) | −307.831 | −0.389167 | ||||||||
\(792\) | − | 33.9278i | − | 0.0428381i | ||||||
\(793\) | 941.977i | 1.18786i | ||||||||
\(794\) | −156.953 | −0.197674 | ||||||||
\(795\) | −70.7191 | −0.0889549 | ||||||||
\(796\) | 252.465i | 0.317167i | ||||||||
\(797\) | − | 495.519i | − | 0.621730i | −0.950454 | − | 0.310865i | \(-0.899381\pi\) | ||
0.950454 | − | 0.310865i | \(-0.100619\pi\) | |||||||
\(798\) | −150.234 | −0.188263 | ||||||||
\(799\) | 1304.88i | 1.63314i | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | 164.696i | 0.205613i | ||||||||
\(802\) | − | 698.547i | − | 0.871006i | ||||||
\(803\) | − | 358.142i | − | 0.446005i | ||||||
\(804\) | − | 382.076i | − | 0.475219i | ||||||
\(805\) | −281.721 | + | 38.5160i | −0.349964 | + | 0.0478460i | ||||
\(806\) | 239.164 | 0.296730 | ||||||||
\(807\) | 285.291 | 0.353520 | ||||||||
\(808\) | 288.909 | 0.357561 | ||||||||
\(809\) | 763.784 | 0.944109 | 0.472055 | − | 0.881569i | \(-0.343512\pi\) | ||||
0.472055 | + | 0.881569i | \(0.343512\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | −103.645 | −0.127799 | −0.0638996 | − | 0.997956i | \(-0.520354\pi\) | ||||
−0.0638996 | + | 0.997956i | \(0.520354\pi\) | |||||||
\(812\) | 114.169i | 0.140602i | ||||||||
\(813\) | −430.823 | −0.529918 | ||||||||
\(814\) | 220.857 | 0.271323 | ||||||||
\(815\) | − | 150.969i | − | 0.185238i | ||||||
\(816\) | 120.542i | 0.147723i | ||||||||
\(817\) | 579.185 | 0.708917 | ||||||||
\(818\) | −92.1593 | −0.112664 | ||||||||
\(819\) | 135.721i | 0.165716i | ||||||||
\(820\) | − | 328.290i | − | 0.400354i | ||||||
\(821\) | −483.043 | −0.588359 | −0.294179 | − | 0.955750i | \(-0.595046\pi\) | ||||
−0.294179 | + | 0.955750i | \(0.595046\pi\) | |||||||
\(822\) | 282.835i | 0.344082i | ||||||||
\(823\) | 1017.90 | 1.23681 | 0.618406 | − | 0.785859i | \(-0.287779\pi\) | ||||
0.618406 | + | 0.785859i | \(0.287779\pi\) | |||||||
\(824\) | − | 503.550i | − | 0.611105i | ||||||
\(825\) | 34.6274i | 0.0419726i | ||||||||
\(826\) | 52.9497i | 0.0641037i | ||||||||
\(827\) | 77.9864i | 0.0943004i | 0.998888 | + | 0.0471502i | \(0.0150139\pi\) | ||||
−0.998888 | + | 0.0471502i | \(0.984986\pi\) | |||||||
\(828\) | −136.728 | + | 18.6930i | −0.165131 | + | 0.0225761i | ||||
\(829\) | 800.569 | 0.965704 | 0.482852 | − | 0.875702i | \(-0.339601\pi\) | ||||
0.482852 | + | 0.875702i | \(0.339601\pi\) | |||||||
\(830\) | −211.284 | −0.254559 | ||||||||
\(831\) | 232.998 | 0.280382 | ||||||||
\(832\) | 65.4620 | 0.0786803 | ||||||||
\(833\) | − | 320.708i | − | 0.385004i | ||||||
\(834\) | −608.369 | −0.729459 | ||||||||
\(835\) | − | 63.8438i | − | 0.0764597i | ||||||
\(836\) | −88.7124 | −0.106115 | ||||||||
\(837\) | 107.390 | 0.128303 | ||||||||
\(838\) | − | 467.622i | − | 0.558021i | ||||||
\(839\) | − | 1458.57i | − | 1.73846i | −0.494407 | − | 0.869231i | \(-0.664615\pi\) | ||
0.494407 | − | 0.869231i | \(-0.335385\pi\) | |||||||
\(840\) | 60.5645 | 0.0721006 | ||||||||
\(841\) | −734.395 | −0.873240 | ||||||||
\(842\) | 1096.75i | 1.30256i | ||||||||
\(843\) | − | 424.010i | − | 0.502977i | ||||||
\(844\) | 497.338 | 0.589263 | ||||||||
\(845\) | 228.174i | 0.270029i | ||||||||
\(846\) | 318.192 | 0.376113 | ||||||||
\(847\) | 580.589i | 0.685465i | ||||||||
\(848\) | 73.0384i | 0.0861302i | ||||||||
\(849\) | 715.671i | 0.842958i | ||||||||
\(850\) | − | 123.028i | − | 0.144738i | ||||||
\(851\) | −121.684 | − | 890.046i | −0.142990 | − | 1.04588i | ||||
\(852\) | −105.694 | −0.124054 | ||||||||
\(853\) | −604.635 | −0.708833 | −0.354417 | − | 0.935088i | \(-0.615321\pi\) | ||||
−0.354417 | + | 0.935088i | \(0.615321\pi\) | |||||||
\(854\) | 900.085 | 1.05396 | ||||||||
\(855\) | 74.4168 | 0.0870372 | ||||||||
\(856\) | − | 15.4236i | − | 0.0180182i | ||||||
\(857\) | 1061.96 | 1.23916 | 0.619582 | − | 0.784932i | \(-0.287302\pi\) | ||||
0.619582 | + | 0.784932i | \(0.287302\pi\) | |||||||
\(858\) | 80.1427i | 0.0934064i | ||||||||
\(859\) | −196.838 | −0.229148 | −0.114574 | − | 0.993415i | \(-0.536550\pi\) | ||||
−0.114574 | + | 0.993415i | \(0.536550\pi\) | |||||||
\(860\) | −233.489 | −0.271499 | ||||||||
\(861\) | − | 702.960i | − | 0.816446i | ||||||
\(862\) | 15.3596i | 0.0178186i | ||||||||
\(863\) | 183.759 | 0.212931 | 0.106465 | − | 0.994316i | \(-0.466047\pi\) | ||||
0.106465 | + | 0.994316i | \(0.466047\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | 91.0858i | 0.105302i | ||||||||
\(866\) | 980.374i | 1.13207i | ||||||||
\(867\) | 23.7560 | 0.0274002 | ||||||||
\(868\) | − | 228.528i | − | 0.263281i | ||||||
\(869\) | −564.771 | −0.649909 | ||||||||
\(870\) | − | 56.5523i | − | 0.0650026i | ||||||
\(871\) | 902.524i | 1.03619i | ||||||||
\(872\) | − | 53.6433i | − | 0.0615175i | ||||||
\(873\) | − | 26.6871i | − | 0.0305694i | ||||||
\(874\) | 48.8775 | + | 357.508i | 0.0559239 | + | 0.409049i | ||||
\(875\) | −61.8134 | −0.0706439 | ||||||||
\(876\) | 310.282 | 0.354203 | ||||||||
\(877\) | 394.360 | 0.449670 | 0.224835 | − | 0.974397i | \(-0.427816\pi\) | ||||
0.224835 | + | 0.974397i | \(0.427816\pi\) | |||||||
\(878\) | 892.911 | 1.01698 | ||||||||
\(879\) | 102.633i | 0.116761i | ||||||||
\(880\) | 35.7630 | 0.0406398 | ||||||||
\(881\) | 27.3381i | 0.0310307i | 0.999880 | + | 0.0155154i | \(0.00493889\pi\) | ||||
−0.999880 | + | 0.0155154i | \(0.995061\pi\) | |||||||
\(882\) | −78.2040 | −0.0886666 | ||||||||
\(883\) | −178.579 | −0.202242 | −0.101121 | − | 0.994874i | \(-0.532243\pi\) | ||||
−0.101121 | + | 0.994874i | \(0.532243\pi\) | |||||||
\(884\) | − | 284.739i | − | 0.322103i | ||||||
\(885\) | − | 26.2281i | − | 0.0296363i | ||||||
\(886\) | 17.5707 | 0.0198315 | ||||||||
\(887\) | −816.646 | −0.920684 | −0.460342 | − | 0.887742i | \(-0.652273\pi\) | ||||
−0.460342 | + | 0.887742i | \(0.652273\pi\) | |||||||
\(888\) | 191.343i | 0.215476i | ||||||||
\(889\) | − | 716.962i | − | 0.806482i | ||||||
\(890\) | −173.605 | −0.195061 | ||||||||
\(891\) | 35.9858i | 0.0403882i | ||||||||
\(892\) | −422.132 | −0.473243 | ||||||||
\(893\) | − | 831.989i | − | 0.931678i | ||||||
\(894\) | − | 548.771i | − | 0.613838i | ||||||
\(895\) | 634.408i | 0.708835i | ||||||||
\(896\) | − | 62.5507i | − | 0.0698111i | ||||||
\(897\) | 322.973 | − | 44.1559i | 0.360059 | − | 0.0492262i | ||||
\(898\) | 1007.97 | 1.12246 | ||||||||
\(899\) | −213.389 | −0.237362 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | 317.694 | 0.352601 | ||||||||
\(902\) | − | 415.094i | − | 0.460193i | ||||||
\(903\) | −499.966 | −0.553672 | ||||||||
\(904\) | − | 157.481i | − | 0.174205i | ||||||
\(905\) | 52.7095 | 0.0582426 | ||||||||
\(906\) | 564.277 | 0.622823 | ||||||||
\(907\) | − | 799.677i | − | 0.881672i | −0.897588 | − | 0.440836i | \(-0.854682\pi\) | ||
0.897588 | − | 0.440836i | \(-0.145318\pi\) | |||||||
\(908\) | − | 547.396i | − | 0.602859i | ||||||
\(909\) | −306.434 | −0.337111 | ||||||||
\(910\) | −143.063 | −0.157212 | ||||||||
\(911\) | 591.347i | 0.649118i | 0.945865 | + | 0.324559i | \(0.105216\pi\) | ||||
−0.945865 | + | 0.324559i | \(0.894784\pi\) | |||||||
\(912\) | − | 76.8574i | − | 0.0842734i | ||||||
\(913\) | −267.150 | −0.292607 | ||||||||
\(914\) | − | 487.918i | − | 0.533828i | ||||||
\(915\) | −445.848 | −0.487265 | ||||||||
\(916\) | − | 732.421i | − | 0.799586i | ||||||
\(917\) | 1077.66i | 1.17520i | ||||||||
\(918\) | − | 127.854i | − | 0.139274i | ||||||
\(919\) | 1669.69i | 1.81686i | 0.418040 | + | 0.908429i | \(0.362717\pi\) | ||||
−0.418040 | + | 0.908429i | \(0.637283\pi\) | |||||||
\(920\) | −19.7042 | − | 144.124i | −0.0214176 | − | 0.156657i | ||||
\(921\) | −283.290 | −0.307589 | ||||||||
\(922\) | 295.525 | 0.320526 | ||||||||
\(923\) | 249.667 | 0.270495 | ||||||||
\(924\) | 76.5786 | 0.0828772 | ||||||||
\(925\) | − | 195.288i | − | 0.211122i | ||||||
\(926\) | −1051.34 | −1.13535 | ||||||||
\(927\) | 534.096i | 0.576155i | ||||||||
\(928\) | −58.4069 | −0.0629385 | ||||||||
\(929\) | −475.381 | −0.511713 | −0.255856 | − | 0.966715i | \(-0.582357\pi\) | ||||
−0.255856 | + | 0.966715i | \(0.582357\pi\) | |||||||
\(930\) | 113.199i | 0.121719i | ||||||||
\(931\) | 204.483i | 0.219638i | ||||||||
\(932\) | −465.650 | −0.499624 | ||||||||
\(933\) | −248.398 | −0.266236 | ||||||||
\(934\) | 579.558i | 0.620512i | ||||||||
\(935\) | − | 155.558i | − | 0.166372i | ||||||
\(936\) | −69.4329 | −0.0741805 | ||||||||
\(937\) | 257.934i | 0.275277i | 0.990483 | + | 0.137638i | \(0.0439512\pi\) | ||||
−0.990483 | + | 0.137638i | \(0.956049\pi\) | |||||||
\(938\) | 862.386 | 0.919388 | ||||||||
\(939\) | − | 65.2895i | − | 0.0695308i | ||||||
\(940\) | 335.404i | 0.356812i | ||||||||
\(941\) | 1799.03i | 1.91183i | 0.293645 | + | 0.955915i | \(0.405132\pi\) | ||||
−0.293645 | + | 0.955915i | \(0.594868\pi\) | |||||||
\(942\) | 27.4937i | 0.0291865i | ||||||||
\(943\) | −1672.82 | + | 228.703i | −1.77393 | + | 0.242527i | ||||
\(944\) | −27.0883 | −0.0286952 | ||||||||
\(945\) | −64.2383 | −0.0679771 | ||||||||
\(946\) | −295.227 | −0.312080 | ||||||||
\(947\) | 641.887 | 0.677811 | 0.338906 | − | 0.940820i | \(-0.389943\pi\) | ||||
0.338906 | + | 0.940820i | \(0.389943\pi\) | |||||||
\(948\) | − | 489.299i | − | 0.516138i | ||||||
\(949\) | −732.935 | −0.772323 | ||||||||
\(950\) | 78.4422i | 0.0825708i | ||||||||
\(951\) | 213.941 | 0.224964 | ||||||||
\(952\) | −272.076 | −0.285794 | ||||||||
\(953\) | 1570.71i | 1.64817i | 0.566464 | + | 0.824087i | \(0.308311\pi\) | ||||
−0.566464 | + | 0.824087i | \(0.691689\pi\) | |||||||
\(954\) | − | 77.4689i | − | 0.0812043i | ||||||
\(955\) | −87.7382 | −0.0918724 | ||||||||
\(956\) | −207.710 | −0.217270 | ||||||||
\(957\) | − | 71.5055i | − | 0.0747183i | ||||||
\(958\) | 310.256i | 0.323858i | ||||||||
\(959\) | −638.389 | −0.665682 | ||||||||
\(960\) | 30.9839i | 0.0322749i | ||||||||
\(961\) | −533.866 | −0.555532 | ||||||||
\(962\) | − | 451.981i | − | 0.469835i | ||||||
\(963\) | 16.3592i | 0.0169877i | ||||||||
\(964\) | 413.191i | 0.428621i | ||||||||
\(965\) | − | 480.921i | − | 0.498364i | ||||||
\(966\) | −42.1922 | − | 308.610i | −0.0436772 | − | 0.319472i | ||||
\(967\) | 587.140 | 0.607177 | 0.303588 | − | 0.952803i | \(-0.401815\pi\) | ||||
0.303588 | + | 0.952803i | \(0.401815\pi\) | |||||||
\(968\) | −297.020 | −0.306839 | ||||||||
\(969\) | −334.305 | −0.345000 | ||||||||
\(970\) | 28.1307 | 0.0290007 | ||||||||
\(971\) | 153.291i | 0.157869i | 0.996880 | + | 0.0789347i | \(0.0251519\pi\) | ||||
−0.996880 | + | 0.0789347i | \(0.974848\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | − | 1373.15i | − | 1.41126i | ||||||
\(974\) | −67.8051 | −0.0696151 | ||||||||
\(975\) | 70.8647 | 0.0726817 | ||||||||
\(976\) | 460.470i | 0.471793i | ||||||||
\(977\) | − | 367.786i | − | 0.376444i | −0.982126 | − | 0.188222i | \(-0.939728\pi\) | ||
0.982126 | − | 0.188222i | \(-0.0602725\pi\) | |||||||
\(978\) | 165.379 | 0.169099 | ||||||||
\(979\) | −219.508 | −0.224217 | ||||||||
\(980\) | − | 82.4342i | − | 0.0841166i | ||||||
\(981\) | 56.8973i | 0.0579992i | ||||||||
\(982\) | 1038.82 | 1.05786 | ||||||||
\(983\) | 662.007i | 0.673455i | 0.941602 | + | 0.336728i | \(0.109320\pi\) | ||||
−0.941602 | + | 0.336728i | \(0.890680\pi\) | |||||||
\(984\) | 359.624 | 0.365471 | ||||||||
\(985\) | − | 436.985i | − | 0.443640i | ||||||
\(986\) | 254.051i | 0.257659i | ||||||||
\(987\) | 718.192i | 0.727652i | ||||||||
\(988\) | 181.549i | 0.183754i | ||||||||
\(989\) | 162.660 | + | 1189.76i | 0.164469 | + | 1.20299i | ||||
\(990\) | −37.9324 | −0.0383156 | ||||||||
\(991\) | −934.673 | −0.943161 | −0.471581 | − | 0.881823i | \(-0.656316\pi\) | ||||
−0.471581 | + | 0.881823i | \(0.656316\pi\) | |||||||
\(992\) | 116.911 | 0.117854 | ||||||||
\(993\) | −241.037 | −0.242736 | ||||||||
\(994\) | − | 238.563i | − | 0.240003i | ||||||
\(995\) | 282.264 | 0.283683 | ||||||||
\(996\) | − | 231.450i | − | 0.232380i | ||||||
\(997\) | 994.775 | 0.997768 | 0.498884 | − | 0.866669i | \(-0.333743\pi\) | ||||
0.498884 | + | 0.866669i | \(0.333743\pi\) | |||||||
\(998\) | 553.668 | 0.554777 | ||||||||
\(999\) | − | 202.950i | − | 0.203153i |
(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 | 690.3.c.a.91.4 | ✓ | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.31 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.5 | yes | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.18 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.4 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.3.c.a.91.5 | yes | 32 | 23.22 | odd | 2 | inner | |
2070.3.c.b.91.18 | 32 | 69.68 | even | 2 | |||
2070.3.c.b.91.31 | 32 | 3.2 | odd | 2 |