Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,3,Mod(559,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.559");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.h (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: | \(17.1662566547\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 96 x^{14} - 532 x^{13} + 3236 x^{12} - 12864 x^{11} + 49526 x^{10} - 141436 x^{9} + \cdots + 33750 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 559.1 | ||
Root | \(0.500000 + 0.422343i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.559 |
Dual form | 630.3.h.e.559.9 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −4.91728 | + | 0.905717i | −0.983457 | + | 0.181143i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.91369 | − | 6.73333i | −0.273384 | − | 0.961905i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.28088 | + | 6.95409i | 0.128088 | + | 0.695409i | ||||
\(11\) | −17.5116 | −1.59196 | −0.795982 | − | 0.605321i | \(-0.793045\pi\) | ||||
−0.795982 | + | 0.605321i | \(0.793045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.83531 | 0.371947 | 0.185973 | − | 0.982555i | \(-0.440456\pi\) | ||||
0.185973 | + | 0.982555i | \(0.440456\pi\) | |||||||
\(14\) | −9.52237 | + | 2.70636i | −0.680170 | + | 0.193312i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 18.0284 | 1.06049 | 0.530247 | − | 0.847843i | \(-0.322099\pi\) | ||||
0.530247 | + | 0.847843i | \(0.322099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.13350i | 0.480711i | 0.970685 | + | 0.240355i | \(0.0772640\pi\) | ||||
−0.970685 | + | 0.240355i | \(0.922736\pi\) | |||||||
\(20\) | 9.83457 | − | 1.81143i | 0.491728 | − | 0.0905717i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 24.7651i | 1.12569i | ||||||||
\(23\) | 3.72515i | 0.161963i | 0.996716 | + | 0.0809816i | \(0.0258055\pi\) | ||||
−0.996716 | + | 0.0809816i | \(0.974194\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.3594 | − | 8.90734i | 0.934374 | − | 0.356294i | ||||
\(26\) | − | 6.83816i | − | 0.263006i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.82738 | + | 13.4667i | 0.136692 | + | 0.480952i | ||||
\(29\) | −1.12582 | −0.0388213 | −0.0194107 | − | 0.999812i | \(-0.506179\pi\) | ||||
−0.0194107 | + | 0.999812i | \(0.506179\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.0859i | 1.84148i | 0.390175 | + | 0.920741i | \(0.372415\pi\) | ||||
−0.390175 | + | 0.920741i | \(0.627585\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 25.4960i | − | 0.749882i | ||||||
\(35\) | 15.5086 | + | 31.3765i | 0.443104 | + | 0.896470i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 41.3624i | − | 1.11790i | −0.829200 | − | 0.558952i | \(-0.811204\pi\) | ||
0.829200 | − | 0.558952i | \(-0.188796\pi\) | |||||||
\(38\) | 12.9167 | 0.339914 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.56176 | − | 13.9082i | −0.0640439 | − | 0.347704i | ||||
\(41\) | − | 11.7156i | − | 0.285745i | −0.989741 | − | 0.142873i | \(-0.954366\pi\) | ||
0.989741 | − | 0.142873i | \(-0.0456340\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.4171i | 1.49807i | 0.662529 | + | 0.749036i | \(0.269483\pi\) | ||||
−0.662529 | + | 0.749036i | \(0.730517\pi\) | |||||||
\(44\) | 35.0232 | 0.795982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.26816 | 0.114525 | ||||||||
\(47\) | 77.6614 | 1.65237 | 0.826185 | − | 0.563399i | \(-0.190507\pi\) | ||||
0.826185 | + | 0.563399i | \(0.190507\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.6756 | + | 25.7710i | −0.850522 | + | 0.525939i | ||||
\(50\) | −12.5969 | − | 33.0351i | −0.251938 | − | 0.660702i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.67062 | −0.185973 | ||||||||
\(53\) | 77.5383i | 1.46299i | 0.681849 | + | 0.731493i | \(0.261176\pi\) | ||||
−0.681849 | + | 0.731493i | \(0.738824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 86.1095 | − | 15.8606i | 1.56563 | − | 0.288374i | ||||
\(56\) | 19.0447 | − | 5.41273i | 0.340085 | − | 0.0966559i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.59215i | 0.0274508i | ||||||||
\(59\) | 87.0651i | 1.47568i | 0.674976 | + | 0.737839i | \(0.264154\pi\) | ||||
−0.674976 | + | 0.737839i | \(0.735846\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.36957i | 0.0880258i | 0.999031 | + | 0.0440129i | \(0.0140143\pi\) | ||||
−0.999031 | + | 0.0440129i | \(0.985986\pi\) | |||||||
\(62\) | 80.7317 | 1.30212 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −23.7766 | + | 4.37942i | −0.365794 | + | 0.0673757i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 47.1879i | − | 0.704297i | −0.935944 | − | 0.352149i | \(-0.885451\pi\) | ||
0.935944 | − | 0.352149i | \(-0.114549\pi\) | |||||||
\(68\) | −36.0568 | −0.530247 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 44.3730 | − | 21.9325i | 0.633900 | − | 0.313322i | ||||
\(71\) | 58.3047 | 0.821193 | 0.410597 | − | 0.911817i | \(-0.365320\pi\) | ||||
0.410597 | + | 0.911817i | \(0.365320\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 53.4082 | 0.731619 | 0.365810 | − | 0.930690i | \(-0.380792\pi\) | ||||
0.365810 | + | 0.930690i | \(0.380792\pi\) | |||||||
\(74\) | −58.4953 | −0.790477 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 18.2670i | − | 0.240355i | ||||||
\(77\) | 33.5117 | + | 117.911i | 0.435217 | + | 1.53132i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −74.9637 | −0.948907 | −0.474454 | − | 0.880280i | \(-0.657354\pi\) | ||||
−0.474454 | + | 0.880280i | \(0.657354\pi\) | |||||||
\(80\) | −19.6691 | + | 3.62287i | −0.245864 | + | 0.0452859i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.5683 | −0.202053 | ||||||||
\(83\) | 28.7890 | 0.346855 | 0.173428 | − | 0.984847i | \(-0.444516\pi\) | ||||
0.173428 | + | 0.984847i | \(0.444516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −88.6507 | + | 16.3286i | −1.04295 | + | 0.192101i | ||||
\(86\) | 91.0996 | 1.05930 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 49.5303i | − | 0.562844i | ||||||
\(89\) | − | 101.499i | − | 1.14043i | −0.821494 | − | 0.570217i | \(-0.806859\pi\) | ||
0.821494 | − | 0.570217i | \(-0.193141\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.25327 | − | 32.5578i | −0.101684 | − | 0.357778i | ||||
\(92\) | − | 7.45031i | − | 0.0809816i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 109.830i | − | 1.16840i | ||||||
\(95\) | −8.27237 | − | 44.9120i | −0.0870776 | − | 0.472758i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −107.830 | −1.11165 | −0.555827 | − | 0.831298i | \(-0.687598\pi\) | ||||
−0.555827 | + | 0.831298i | \(0.687598\pi\) | |||||||
\(98\) | 36.4457 | + | 58.9382i | 0.371895 | + | 0.601410i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −46.7187 | + | 17.8147i | −0.467187 | + | 0.178147i | ||||
\(101\) | 52.6151i | 0.520941i | 0.965482 | + | 0.260471i | \(0.0838777\pi\) | ||||
−0.965482 | + | 0.260471i | \(0.916122\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −72.4002 | −0.702915 | −0.351457 | − | 0.936204i | \(-0.614314\pi\) | ||||
−0.351457 | + | 0.936204i | \(0.614314\pi\) | |||||||
\(104\) | 13.6763i | 0.131503i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 109.656 | 1.03449 | ||||||||
\(107\) | − | 173.562i | − | 1.62207i | −0.584994 | − | 0.811037i | \(-0.698903\pi\) | ||
0.584994 | − | 0.811037i | \(-0.301097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 49.9966 | 0.458684 | 0.229342 | − | 0.973346i | \(-0.426342\pi\) | ||||
0.229342 | + | 0.973346i | \(0.426342\pi\) | |||||||
\(110\) | −22.4302 | − | 121.777i | −0.203911 | − | 1.10707i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.65475 | − | 26.9333i | −0.0683460 | − | 0.240476i | ||||
\(113\) | − | 70.1536i | − | 0.620828i | −0.950601 | − | 0.310414i | \(-0.899532\pi\) | ||
0.950601 | − | 0.310414i | \(-0.100468\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.37394 | − | 18.3176i | −0.0293386 | − | 0.159284i | ||||
\(116\) | 2.25164 | 0.0194107 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 123.129 | 1.04346 | ||||||||
\(119\) | −34.5007 | − | 121.391i | −0.289922 | − | 1.02009i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 185.656 | 1.53435 | ||||||||
\(122\) | 7.59373 | 0.0622436 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 114.172i | − | 0.920741i | ||||||
\(125\) | −106.797 | + | 64.9569i | −0.854376 | + | 0.519655i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 197.945i | 1.55863i | 0.626635 | + | 0.779313i | \(0.284432\pi\) | ||||
−0.626635 | + | 0.779313i | \(0.715568\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.19344 | + | 33.6252i | 0.0476418 | + | 0.258655i | ||||
\(131\) | 114.901i | 0.877105i | 0.898706 | + | 0.438552i | \(0.144509\pi\) | ||||
−0.898706 | + | 0.438552i | \(0.855491\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 61.4989 | − | 17.4787i | 0.462398 | − | 0.131419i | ||||
\(134\) | −66.7338 | −0.498013 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 50.9920i | 0.374941i | ||||||||
\(137\) | 95.3358i | 0.695882i | 0.937516 | + | 0.347941i | \(0.113119\pi\) | ||||
−0.937516 | + | 0.347941i | \(0.886881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 237.587i | 1.70926i | 0.519237 | + | 0.854630i | \(0.326216\pi\) | ||||
−0.519237 | + | 0.854630i | \(0.673784\pi\) | |||||||
\(140\) | −31.0173 | − | 62.7529i | −0.221552 | − | 0.448235i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 82.4553i | − | 0.580671i | ||||||
\(143\) | −84.6740 | −0.592126 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.53597 | − | 1.01967i | 0.0381791 | − | 0.00703223i | ||||
\(146\) | − | 75.5306i | − | 0.517333i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 82.7248i | 0.558952i | ||||||||
\(149\) | −133.844 | −0.898285 | −0.449142 | − | 0.893460i | \(-0.648270\pi\) | ||||
−0.449142 | + | 0.893460i | \(0.648270\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155.064 | 1.02691 | 0.513456 | − | 0.858116i | \(-0.328365\pi\) | ||||
0.513456 | + | 0.858116i | \(0.328365\pi\) | |||||||
\(152\) | −25.8335 | −0.169957 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 166.752 | − | 47.3928i | 1.08280 | − | 0.307745i | ||||
\(155\) | −51.7037 | − | 280.708i | −0.333572 | − | 1.81102i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −104.634 | −0.666459 | −0.333230 | − | 0.942846i | \(-0.608138\pi\) | ||||
−0.333230 | + | 0.942846i | \(0.608138\pi\) | |||||||
\(158\) | 106.015i | 0.670979i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.12351 | + | 27.8164i | 0.0320219 | + | 0.173852i | ||||
\(161\) | 25.0827 | − | 7.12878i | 0.155793 | − | 0.0442782i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 130.909i | 0.803120i | 0.915833 | + | 0.401560i | \(0.131532\pi\) | ||||
−0.915833 | + | 0.401560i | \(0.868468\pi\) | |||||||
\(164\) | 23.4311i | 0.142873i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 40.7138i | − | 0.245264i | ||||||
\(167\) | 102.845 | 0.615838 | 0.307919 | − | 0.951413i | \(-0.400367\pi\) | ||||
0.307919 | + | 0.951413i | \(0.400367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −145.620 | −0.861656 | ||||||||
\(170\) | 23.0922 | + | 125.371i | 0.135836 | + | 0.737477i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 128.834i | − | 0.749036i | ||||||
\(173\) | −197.432 | −1.14122 | −0.570612 | − | 0.821220i | \(-0.693294\pi\) | ||||
−0.570612 | + | 0.821220i | \(0.693294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −104.679 | − | 140.240i | −0.598163 | − | 0.801374i | ||||
\(176\) | −70.0464 | −0.397991 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −143.541 | −0.806409 | ||||||||
\(179\) | 118.822 | 0.663809 | 0.331904 | − | 0.943313i | \(-0.392309\pi\) | ||||
0.331904 | + | 0.943313i | \(0.392309\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.4148i | 0.0796399i | 0.999207 | + | 0.0398199i | \(0.0126784\pi\) | ||||
−0.999207 | + | 0.0398199i | \(0.987322\pi\) | |||||||
\(182\) | −46.0436 | + | 13.0861i | −0.252987 | + | 0.0719017i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.5363 | −0.0572626 | ||||||||
\(185\) | 37.4627 | + | 203.391i | 0.202501 | + | 1.09941i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −315.706 | −1.68827 | ||||||||
\(188\) | −155.323 | −0.826185 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −63.5152 | + | 11.6989i | −0.334291 | + | 0.0615732i | ||||
\(191\) | −59.9375 | −0.313809 | −0.156904 | − | 0.987614i | \(-0.550151\pi\) | ||||
−0.156904 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 245.948i | − | 1.27434i | −0.770723 | − | 0.637171i | \(-0.780105\pi\) | ||
0.770723 | − | 0.637171i | \(-0.219895\pi\) | |||||||
\(194\) | 152.495i | 0.786058i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 83.3512 | − | 51.5420i | 0.425261 | − | 0.262969i | ||||
\(197\) | 82.0594i | 0.416545i | 0.978071 | + | 0.208273i | \(0.0667842\pi\) | ||||
−0.978071 | + | 0.208273i | \(0.933216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 289.338i | 1.45396i | 0.686658 | + | 0.726981i | \(0.259077\pi\) | ||||
−0.686658 | + | 0.726981i | \(0.740923\pi\) | |||||||
\(200\) | 25.1938 | + | 66.0702i | 0.125969 | + | 0.330351i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 74.4089 | 0.368361 | ||||||||
\(203\) | 2.15447 | + | 7.58051i | 0.0106131 | + | 0.0373424i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.6110 | + | 57.6087i | 0.0517609 | + | 0.281018i | ||||
\(206\) | 102.389i | 0.497036i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 19.3412 | 0.0929867 | ||||||||
\(209\) | − | 159.942i | − | 0.765274i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 33.6995 | 0.159713 | 0.0798567 | − | 0.996806i | \(-0.474554\pi\) | ||||
0.0798567 | + | 0.996806i | \(0.474554\pi\) | |||||||
\(212\) | − | 155.077i | − | 0.731493i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −245.454 | −1.14698 | ||||||||
\(215\) | −58.3437 | − | 316.757i | −0.271366 | − | 1.47329i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 384.379 | − | 109.245i | 1.77133 | − | 0.503432i | ||||
\(218\) | − | 70.7059i | − | 0.324339i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −172.219 | + | 31.7211i | −0.782813 | + | 0.144187i | ||||
\(221\) | 87.1728 | 0.394447 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7556 | −0.0482313 | −0.0241156 | − | 0.999709i | \(-0.507677\pi\) | ||||
−0.0241156 | + | 0.999709i | \(0.507677\pi\) | |||||||
\(224\) | −38.0895 | + | 10.8255i | −0.170042 | + | 0.0483279i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −99.2121 | −0.438992 | ||||||||
\(227\) | −416.450 | −1.83458 | −0.917290 | − | 0.398219i | \(-0.869628\pi\) | ||||
−0.917290 | + | 0.398219i | \(0.869628\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 388.469i | − | 1.69637i | −0.529700 | − | 0.848185i | \(-0.677695\pi\) | ||
0.529700 | − | 0.848185i | \(-0.322305\pi\) | |||||||
\(230\) | −25.9051 | + | 4.77147i | −0.112631 | + | 0.0207455i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 3.18429i | − | 0.0137254i | ||||||
\(233\) | − | 70.4036i | − | 0.302162i | −0.988521 | − | 0.151081i | \(-0.951725\pi\) | ||
0.988521 | − | 0.151081i | \(-0.0482754\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −381.883 | + | 70.3393i | −1.62503 | + | 0.299316i | ||||
\(236\) | − | 174.130i | − | 0.737839i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −171.673 | + | 48.7914i | −0.721315 | + | 0.205006i | ||||
\(239\) | 313.133 | 1.31018 | 0.655091 | − | 0.755550i | \(-0.272630\pi\) | ||||
0.655091 | + | 0.755550i | \(0.272630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 198.727i | 0.824595i | 0.911049 | + | 0.412297i | \(0.135274\pi\) | ||||
−0.911049 | + | 0.412297i | \(0.864726\pi\) | |||||||
\(242\) | − | 262.557i | − | 1.08495i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 10.7391i | − | 0.0440129i | ||||||
\(245\) | 181.589 | − | 164.470i | 0.741181 | − | 0.671305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.1633i | 0.178799i | ||||||||
\(248\) | −161.463 | −0.651062 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 91.8629 | + | 151.034i | 0.367452 | + | 0.604135i | ||||
\(251\) | 300.878i | 1.19872i | 0.800480 | + | 0.599359i | \(0.204578\pi\) | ||||
−0.800480 | + | 0.599359i | \(0.795422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 65.2334i | − | 0.257839i | ||||||
\(254\) | 279.937 | 1.10211 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −306.052 | −1.19087 | −0.595433 | − | 0.803405i | \(-0.703019\pi\) | ||||
−0.595433 | + | 0.803405i | \(0.703019\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −278.507 | + | 79.1548i | −1.07532 | + | 0.305617i | ||||
\(260\) | 47.5532 | − | 8.75885i | 0.182897 | − | 0.0336879i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 162.494 | 0.620207 | ||||||||
\(263\) | 286.135i | 1.08797i | 0.839096 | + | 0.543984i | \(0.183085\pi\) | ||||
−0.839096 | + | 0.543984i | \(0.816915\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −70.2278 | − | 381.278i | −0.265010 | − | 1.43878i | ||||
\(266\) | −24.7186 | − | 86.9726i | −0.0929270 | − | 0.326965i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 94.3758i | 0.352149i | ||||||||
\(269\) | 188.412i | 0.700415i | 0.936672 | + | 0.350208i | \(0.113889\pi\) | ||||
−0.936672 | + | 0.350208i | \(0.886111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.59288i | 0.0353981i | 0.999843 | + | 0.0176990i | \(0.00563408\pi\) | ||||
−0.999843 | + | 0.0176990i | \(0.994366\pi\) | |||||||
\(272\) | 72.1136 | 0.265123 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 134.825 | 0.492063 | ||||||||
\(275\) | −409.060 | + | 155.982i | −1.48749 | + | 0.567206i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 161.066i | 0.581464i | 0.956804 | + | 0.290732i | \(0.0938989\pi\) | ||||
−0.956804 | + | 0.290732i | \(0.906101\pi\) | |||||||
\(278\) | 335.999 | 1.20863 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −88.7460 | + | 43.8651i | −0.316950 | + | 0.156661i | ||||
\(281\) | 343.107 | 1.22102 | 0.610510 | − | 0.792008i | \(-0.290964\pi\) | ||||
0.610510 | + | 0.792008i | \(0.290964\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −324.748 | −1.14752 | −0.573759 | − | 0.819024i | \(-0.694516\pi\) | ||||
−0.573759 | + | 0.819024i | \(0.694516\pi\) | |||||||
\(284\) | −116.609 | −0.410597 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 119.747i | 0.418696i | ||||||||
\(287\) | −78.8848 | + | 22.4199i | −0.274860 | + | 0.0781182i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.0229 | 0.124647 | ||||||||
\(290\) | −1.44204 | − | 7.82904i | −0.00497254 | − | 0.0269967i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −106.816 | −0.365810 | ||||||||
\(293\) | −100.918 | −0.344429 | −0.172215 | − | 0.985059i | \(-0.555092\pi\) | ||||
−0.172215 | + | 0.985059i | \(0.555092\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −78.8563 | − | 428.124i | −0.267310 | − | 1.45127i | ||||
\(296\) | 116.991 | 0.395238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 189.285i | 0.635183i | ||||||||
\(299\) | 18.0123i | 0.0602417i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 433.742 | − | 123.274i | 1.44100 | − | 0.409549i | ||||
\(302\) | − | 219.293i | − | 0.726136i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 36.5340i | 0.120178i | ||||||||
\(305\) | −4.86332 | − | 26.4037i | −0.0159453 | − | 0.0865696i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 41.3057 | 0.134546 | 0.0672732 | − | 0.997735i | \(-0.478570\pi\) | ||||
0.0672732 | + | 0.997735i | \(0.478570\pi\) | |||||||
\(308\) | −67.0235 | − | 235.823i | −0.217609 | − | 0.765659i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −396.981 | + | 73.1201i | −1.28058 | + | 0.235871i | ||||
\(311\) | 470.341i | 1.51235i | 0.654369 | + | 0.756176i | \(0.272934\pi\) | ||||
−0.654369 | + | 0.756176i | \(0.727066\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −160.220 | −0.511884 | −0.255942 | − | 0.966692i | \(-0.582386\pi\) | ||||
−0.255942 | + | 0.966692i | \(0.582386\pi\) | |||||||
\(314\) | 147.975i | 0.471258i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 149.927 | 0.474454 | ||||||||
\(317\) | 268.766i | 0.847843i | 0.905699 | + | 0.423922i | \(0.139347\pi\) | ||||
−0.905699 | + | 0.423922i | \(0.860653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.7149 | 0.0618021 | ||||||||
\(320\) | 39.3383 | − | 7.24574i | 0.122932 | − | 0.0226429i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.0816 | − | 35.4723i | −0.0313094 | − | 0.110162i | ||||
\(323\) | 164.662i | 0.509791i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 112.950 | − | 43.0697i | 0.347537 | − | 0.132522i | ||||
\(326\) | 185.133 | 0.567891 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 33.1366 | 0.101026 | ||||||||
\(329\) | −148.620 | − | 522.920i | −0.451732 | − | 1.58942i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 555.018 | 1.67679 | 0.838395 | − | 0.545063i | \(-0.183494\pi\) | ||||
0.838395 | + | 0.545063i | \(0.183494\pi\) | |||||||
\(332\) | −57.5780 | −0.173428 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 145.445i | − | 0.435463i | ||||||
\(335\) | 42.7389 | + | 232.036i | 0.127579 | + | 0.692646i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 47.7972i | − | 0.141831i | −0.997482 | − | 0.0709157i | \(-0.977408\pi\) | ||
0.997482 | − | 0.0709157i | \(-0.0225921\pi\) | |||||||
\(338\) | 205.937i | 0.609282i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 177.301 | − | 32.6573i | 0.521475 | − | 0.0960507i | ||||
\(341\) | − | 999.666i | − | 2.93157i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 253.279 | + | 231.298i | 0.738422 | + | 0.674338i | ||||
\(344\) | −182.199 | −0.529649 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 279.211i | 0.806967i | ||||||||
\(347\) | − | 283.766i | − | 0.817771i | −0.912586 | − | 0.408885i | \(-0.865918\pi\) | ||
0.912586 | − | 0.408885i | \(-0.134082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0321i | 0.0573987i | 0.999588 | + | 0.0286993i | \(0.00913653\pi\) | ||||
−0.999588 | + | 0.0286993i | \(0.990863\pi\) | |||||||
\(350\) | −198.330 | + | 148.038i | −0.566657 | + | 0.422965i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 99.0605i | 0.281422i | ||||||||
\(353\) | 595.015 | 1.68559 | 0.842797 | − | 0.538231i | \(-0.180907\pi\) | ||||
0.842797 | + | 0.538231i | \(0.180907\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −286.701 | + | 52.8076i | −0.807608 | + | 0.148754i | ||||
\(356\) | 202.997i | 0.570217i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 168.039i | − | 0.469384i | ||||||
\(359\) | −588.390 | −1.63897 | −0.819485 | − | 0.573101i | \(-0.805740\pi\) | ||||
−0.819485 | + | 0.573101i | \(0.805740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 277.579 | 0.768917 | ||||||||
\(362\) | 20.3856 | 0.0563139 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.5065 | + | 65.1155i | 0.0508422 | + | 0.178889i | ||||
\(365\) | −262.623 | + | 48.3727i | −0.719516 | + | 0.132528i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 662.601 | 1.80545 | 0.902726 | − | 0.430215i | \(-0.141562\pi\) | ||||
0.902726 | + | 0.430215i | \(0.141562\pi\) | |||||||
\(368\) | 14.9006i | 0.0404908i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 287.638 | − | 52.9802i | 0.777400 | − | 0.143190i | ||||
\(371\) | 522.091 | − | 148.384i | 1.40725 | − | 0.399957i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 236.349i | − | 0.633644i | −0.948485 | − | 0.316822i | \(-0.897384\pi\) | ||
0.948485 | − | 0.316822i | \(-0.102616\pi\) | |||||||
\(374\) | 446.476i | 1.19378i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 219.660i | 0.584201i | ||||||||
\(377\) | −5.44368 | −0.0144395 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 344.235 | 0.908272 | 0.454136 | − | 0.890932i | \(-0.349948\pi\) | ||||
0.454136 | + | 0.890932i | \(0.349948\pi\) | |||||||
\(380\) | 16.5447 | + | 89.8241i | 0.0435388 | + | 0.236379i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 84.7644i | 0.221896i | ||||||||
\(383\) | 65.7097 | 0.171566 | 0.0857828 | − | 0.996314i | \(-0.472661\pi\) | ||||
0.0857828 | + | 0.996314i | \(0.472661\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −271.581 | − | 549.452i | −0.705406 | − | 1.42715i | ||||
\(386\) | −347.823 | −0.901095 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 215.661 | 0.555827 | ||||||||
\(389\) | −161.296 | −0.414642 | −0.207321 | − | 0.978273i | \(-0.566474\pi\) | ||||
−0.207321 | + | 0.978273i | \(0.566474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 67.1585i | 0.171761i | ||||||||
\(392\) | −72.8914 | − | 117.876i | −0.185947 | − | 0.300705i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 116.050 | 0.294542 | ||||||||
\(395\) | 368.618 | − | 67.8959i | 0.933209 | − | 0.171888i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 667.752 | 1.68200 | 0.840998 | − | 0.541039i | \(-0.181969\pi\) | ||||
0.840998 | + | 0.541039i | \(0.181969\pi\) | |||||||
\(398\) | 409.186 | 1.02811 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 93.4374 | − | 35.6294i | 0.233594 | − | 0.0890734i | ||||
\(401\) | 593.826 | 1.48086 | 0.740431 | − | 0.672132i | \(-0.234621\pi\) | ||||
0.740431 | + | 0.672132i | \(0.234621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 276.028i | 0.684933i | ||||||||
\(404\) | − | 105.230i | − | 0.260471i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.7205 | − | 3.04687i | 0.0264051 | − | 0.00750461i | ||||
\(407\) | 724.322i | 1.77966i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 569.625i | − | 1.39273i | −0.717690 | − | 0.696363i | \(-0.754800\pi\) | ||
0.717690 | − | 0.696363i | \(-0.245200\pi\) | |||||||
\(410\) | 81.4711 | − | 15.0062i | 0.198710 | − | 0.0366005i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 144.800 | 0.351457 | ||||||||
\(413\) | 586.238 | − | 166.615i | 1.41946 | − | 0.403427i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −141.564 | + | 26.0747i | −0.341117 | + | 0.0628306i | ||||
\(416\) | − | 27.3526i | − | 0.0657515i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −226.192 | −0.541130 | ||||||||
\(419\) | − | 209.456i | − | 0.499894i | −0.968260 | − | 0.249947i | \(-0.919587\pi\) | ||
0.968260 | − | 0.249947i | \(-0.0804132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −169.713 | −0.403119 | −0.201560 | − | 0.979476i | \(-0.564601\pi\) | ||||
−0.201560 | + | 0.979476i | \(0.564601\pi\) | |||||||
\(422\) | − | 47.6583i | − | 0.112934i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −219.311 | −0.517244 | ||||||||
\(425\) | 421.132 | − | 160.585i | 0.990898 | − | 0.377847i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 36.1551 | − | 10.2757i | 0.0846725 | − | 0.0240649i | ||||
\(428\) | 347.124i | 0.811037i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −447.962 | + | 82.5104i | −1.04177 | + | 0.191885i | ||||
\(431\) | −538.427 | −1.24925 | −0.624625 | − | 0.780925i | \(-0.714748\pi\) | ||||
−0.624625 | + | 0.780925i | \(0.714748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 118.314 | 0.273243 | 0.136622 | − | 0.990623i | \(-0.456376\pi\) | ||||
0.136622 | + | 0.990623i | \(0.456376\pi\) | |||||||
\(434\) | −154.495 | − | 543.593i | −0.355980 | − | 1.25252i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −99.9932 | −0.229342 | ||||||||
\(437\) | −34.0237 | −0.0778575 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 434.834i | − | 0.990510i | −0.868748 | − | 0.495255i | \(-0.835075\pi\) | ||
0.868748 | − | 0.495255i | \(-0.164925\pi\) | |||||||
\(440\) | 44.8604 | + | 243.554i | 0.101956 | + | 0.553533i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 123.281i | − | 0.278916i | ||||||
\(443\) | − | 555.005i | − | 1.25283i | −0.779488 | − | 0.626417i | \(-0.784521\pi\) | ||
0.779488 | − | 0.626417i | \(-0.215479\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 91.9291 | + | 499.098i | 0.206582 | + | 1.12157i | ||||
\(446\) | 15.2107i | 0.0341047i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15.3095 | + | 53.8667i | 0.0341730 | + | 0.120238i | ||||
\(449\) | 66.8926 | 0.148981 | 0.0744906 | − | 0.997222i | \(-0.476267\pi\) | ||||
0.0744906 | + | 0.997222i | \(0.476267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 205.158i | 0.454896i | ||||||||
\(452\) | 140.307i | 0.310414i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 588.949i | 1.29724i | ||||||||
\(455\) | 74.9891 | + | 151.715i | 0.164811 | + | 0.333439i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 750.939i | 1.64319i | 0.570070 | + | 0.821596i | \(0.306916\pi\) | ||||
−0.570070 | + | 0.821596i | \(0.693084\pi\) | |||||||
\(458\) | −549.378 | −1.19951 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.74787 | + | 36.6353i | 0.0146693 | + | 0.0796419i | ||||
\(461\) | 395.377i | 0.857651i | 0.903387 | + | 0.428826i | \(0.141072\pi\) | ||||
−0.903387 | + | 0.428826i | \(0.858928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 423.981i | − | 0.915726i | −0.889023 | − | 0.457863i | \(-0.848615\pi\) | ||
0.889023 | − | 0.457863i | \(-0.151385\pi\) | |||||||
\(464\) | −4.50327 | −0.00970533 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −99.5658 | −0.213660 | ||||||||
\(467\) | 584.408 | 1.25141 | 0.625705 | − | 0.780060i | \(-0.284812\pi\) | ||||
0.625705 | + | 0.780060i | \(0.284812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −317.732 | + | 90.3030i | −0.677467 | + | 0.192544i | ||||
\(470\) | 99.4747 | + | 540.064i | 0.211648 | + | 1.14907i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −246.257 | −0.521731 | ||||||||
\(473\) | − | 1128.05i | − | 2.38488i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 81.3552 | + | 213.353i | 0.171274 | + | 0.449164i | ||||
\(476\) | 69.0014 | + | 242.782i | 0.144961 | + | 0.510047i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 442.837i | − | 0.926438i | ||||||
\(479\) | 734.511i | 1.53343i | 0.641990 | + | 0.766713i | \(0.278109\pi\) | ||||
−0.641990 | + | 0.766713i | \(0.721891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 200.000i | − | 0.415801i | ||||||
\(482\) | 281.043 | 0.583077 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −371.312 | −0.767174 | ||||||||
\(485\) | 530.232 | − | 97.6638i | 1.09326 | − | 0.201369i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 91.6643i | − | 0.188222i | −0.995562 | − | 0.0941111i | \(-0.969999\pi\) | ||
0.995562 | − | 0.0941111i | \(-0.0300009\pi\) | |||||||
\(488\) | −15.1875 | −0.0311218 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −232.595 | − | 256.806i | −0.474684 | − | 0.524094i | ||||
\(491\) | −460.086 | −0.937038 | −0.468519 | − | 0.883453i | \(-0.655212\pi\) | ||||
−0.468519 | + | 0.883453i | \(0.655212\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.2967 | −0.0411698 | ||||||||
\(494\) | 62.4564 | 0.126430 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 228.344i | 0.460370i | ||||||||
\(497\) | −111.577 | − | 392.585i | −0.224501 | − | 0.789910i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −487.126 | −0.976204 | −0.488102 | − | 0.872786i | \(-0.662311\pi\) | ||||
−0.488102 | + | 0.872786i | \(0.662311\pi\) | |||||||
\(500\) | 213.594 | − | 129.914i | 0.427188 | − | 0.259828i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 425.506 | 0.847622 | ||||||||
\(503\) | −305.145 | −0.606650 | −0.303325 | − | 0.952887i | \(-0.598097\pi\) | ||||
−0.303325 | + | 0.952887i | \(0.598097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.6544 | − | 258.723i | −0.0943651 | − | 0.512323i | ||||
\(506\) | −92.2539 | −0.182320 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 395.891i | − | 0.779313i | ||||||
\(509\) | 800.434i | 1.57256i | 0.617869 | + | 0.786281i | \(0.287996\pi\) | ||||
−0.617869 | + | 0.786281i | \(0.712004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −102.207 | − | 359.615i | −0.200013 | − | 0.703748i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 432.824i | 0.842069i | ||||||||
\(515\) | 356.012 | − | 65.5741i | 0.691286 | − | 0.127328i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1359.97 | −2.63051 | ||||||||
\(518\) | 111.942 | + | 393.868i | 0.216104 | + | 0.760364i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.3869 | − | 67.2503i | −0.0238209 | − | 0.129328i | ||||
\(521\) | − | 21.4194i | − | 0.0411121i | −0.999789 | − | 0.0205560i | \(-0.993456\pi\) | ||
0.999789 | − | 0.0205560i | \(-0.00654365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 842.290 | 1.61050 | 0.805249 | − | 0.592937i | \(-0.202032\pi\) | ||||
0.805249 | + | 0.592937i | \(0.202032\pi\) | |||||||
\(524\) | − | 229.801i | − | 0.438552i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 404.657 | 0.769309 | ||||||||
\(527\) | 1029.17i | 1.95288i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 515.123 | 0.973768 | ||||||||
\(530\) | −539.208 | + | 99.3171i | −1.01737 | + | 0.187391i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −122.998 | + | 34.9574i | −0.231199 | + | 0.0657093i | ||||
\(533\) | − | 56.6484i | − | 0.106282i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 157.198 | + | 853.453i | 0.293828 | + | 1.59524i | ||||
\(536\) | 133.468 | 0.249007 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 266.454 | 0.495268 | ||||||||
\(539\) | 729.806 | − | 451.291i | 1.35400 | − | 0.837275i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.6795 | −0.0289824 | −0.0144912 | − | 0.999895i | \(-0.504613\pi\) | ||||
−0.0144912 | + | 0.999895i | \(0.504613\pi\) | |||||||
\(542\) | 13.5664 | 0.0250302 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 101.984i | − | 0.187471i | ||||||
\(545\) | −245.847 | + | 45.2828i | −0.451096 | + | 0.0830877i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 315.792i | 0.577317i | 0.957432 | + | 0.288659i | \(0.0932092\pi\) | ||||
−0.957432 | + | 0.288659i | \(0.906791\pi\) | |||||||
\(548\) | − | 190.672i | − | 0.347941i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 220.591 | + | 578.498i | 0.401075 | + | 1.05181i | ||||
\(551\) | − | 10.2827i | − | 0.0186618i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 143.457 | + | 504.756i | 0.259416 | + | 0.912759i | ||||
\(554\) | 227.781 | 0.411157 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 475.174i | − | 0.854630i | ||||||
\(557\) | 358.421i | 0.643484i | 0.946827 | + | 0.321742i | \(0.104268\pi\) | ||||
−0.946827 | + | 0.321742i | \(0.895732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 311.477i | 0.557203i | ||||||||
\(560\) | 62.0346 | + | 125.506i | 0.110776 | + | 0.224118i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 485.226i | − | 0.863392i | ||||||
\(563\) | 622.834 | 1.10628 | 0.553138 | − | 0.833089i | \(-0.313430\pi\) | ||||
0.553138 | + | 0.833089i | \(0.313430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 63.5393 | + | 344.965i | 0.112459 | + | 0.610557i | ||||
\(566\) | 459.263i | 0.811418i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 164.911i | 0.290336i | ||||||||
\(569\) | 185.789 | 0.326518 | 0.163259 | − | 0.986583i | \(-0.447799\pi\) | ||||
0.163259 | + | 0.986583i | \(0.447799\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −486.258 | −0.851589 | −0.425795 | − | 0.904820i | \(-0.640005\pi\) | ||||
−0.425795 | + | 0.904820i | \(0.640005\pi\) | |||||||
\(572\) | 169.348 | 0.296063 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 31.7066 | + | 111.560i | 0.0552379 | + | 0.194355i | ||||
\(575\) | 33.1812 | + | 87.0172i | 0.0577064 | + | 0.151334i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 270.057 | 0.468037 | 0.234018 | − | 0.972232i | \(-0.424812\pi\) | ||||
0.234018 | + | 0.972232i | \(0.424812\pi\) | |||||||
\(578\) | − | 50.9440i | − | 0.0881385i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.0719 | + | 2.03935i | −0.0190895 | + | 0.00351611i | ||||
\(581\) | −55.0932 | − | 193.846i | −0.0948247 | − | 0.333642i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1357.82i | − | 2.32902i | ||||||
\(584\) | 151.061i | 0.258666i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 142.719i | 0.243548i | ||||||||
\(587\) | −400.613 | −0.682476 | −0.341238 | − | 0.939977i | \(-0.610846\pi\) | ||||
−0.341238 | + | 0.939977i | \(0.610846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −521.395 | −0.885220 | ||||||||
\(590\) | −605.458 | + | 111.520i | −1.02620 | + | 0.189016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 165.450i | − | 0.279476i | ||||||
\(593\) | 157.686 | 0.265912 | 0.132956 | − | 0.991122i | \(-0.457553\pi\) | ||||
0.132956 | + | 0.991122i | \(0.457553\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 279.596 | + | 565.667i | 0.469909 | + | 0.950701i | ||||
\(596\) | 267.689 | 0.449142 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 25.4732 | 0.0425973 | ||||||||
\(599\) | 468.940 | 0.782872 | 0.391436 | − | 0.920205i | \(-0.371978\pi\) | ||||
0.391436 | + | 0.920205i | \(0.371978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 255.932i | − | 0.425844i | −0.977069 | − | 0.212922i | \(-0.931702\pi\) | ||
0.977069 | − | 0.212922i | \(-0.0682980\pi\) | |||||||
\(602\) | −174.336 | − | 613.404i | −0.289595 | − | 1.01894i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −310.127 | −0.513456 | ||||||||
\(605\) | −912.923 | + | 168.152i | −1.50896 | + | 0.277937i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −773.553 | −1.27439 | −0.637194 | − | 0.770704i | \(-0.719905\pi\) | ||||
−0.637194 | + | 0.770704i | \(0.719905\pi\) | |||||||
\(608\) | 51.6669 | 0.0849785 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −37.3405 | + | 6.87777i | −0.0612139 | + | 0.0112750i | ||||
\(611\) | 375.517 | 0.614594 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 443.208i | 0.723015i | 0.932369 | + | 0.361507i | \(0.117738\pi\) | ||||
−0.932369 | + | 0.361507i | \(0.882262\pi\) | |||||||
\(614\) | − | 58.4151i | − | 0.0951386i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −333.504 | + | 94.7855i | −0.541402 | + | 0.153873i | ||||
\(617\) | 363.298i | 0.588813i | 0.955680 | + | 0.294407i | \(0.0951220\pi\) | ||||
−0.955680 | + | 0.294407i | \(0.904878\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 292.211i | 0.472069i | 0.971745 | + | 0.236035i | \(0.0758479\pi\) | ||||
−0.971745 | + | 0.236035i | \(0.924152\pi\) | |||||||
\(620\) | 103.407 | + | 561.415i | 0.166786 | + | 0.905509i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 665.163 | 1.06939 | ||||||||
\(623\) | −683.425 | + | 194.237i | −1.09699 | + | 0.311777i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 466.319 | − | 416.139i | 0.746110 | − | 0.665823i | ||||
\(626\) | 226.585i | 0.361956i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 209.268 | 0.333230 | ||||||||
\(629\) | − | 745.698i | − | 1.18553i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 189.221 | 0.299874 | 0.149937 | − | 0.988696i | \(-0.452093\pi\) | ||||
0.149937 | + | 0.988696i | \(0.452093\pi\) | |||||||
\(632\) | − | 212.029i | − | 0.335489i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 380.093 | 0.599516 | ||||||||
\(635\) | −179.283 | − | 973.354i | −0.282335 | − | 1.53284i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −201.514 | + | 124.611i | −0.316349 | + | 0.195621i | ||||
\(638\) | − | 27.8810i | − | 0.0437007i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.2470 | − | 55.6327i | −0.0160110 | − | 0.0869261i | ||||
\(641\) | −1162.94 | −1.81425 | −0.907127 | − | 0.420857i | \(-0.861729\pi\) | ||||
−0.907127 | + | 0.420857i | \(0.861729\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1096.08 | −1.70464 | −0.852320 | − | 0.523021i | \(-0.824805\pi\) | ||||
−0.852320 | + | 0.523021i | \(0.824805\pi\) | |||||||
\(644\) | −50.1654 | + | 14.2576i | −0.0778966 | + | 0.0221391i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 232.868 | 0.360476 | ||||||||
\(647\) | −262.877 | −0.406302 | −0.203151 | − | 0.979147i | \(-0.565118\pi\) | ||||
−0.203151 | + | 0.979147i | \(0.565118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1524.65i | − | 2.34923i | ||||||
\(650\) | −60.9098 | − | 159.735i | −0.0937074 | − | 0.245746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 261.817i | − | 0.401560i | ||||||
\(653\) | − | 242.905i | − | 0.371983i | −0.982551 | − | 0.185992i | \(-0.940450\pi\) | ||
0.982551 | − | 0.185992i | \(-0.0595498\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −104.068 | − | 564.999i | −0.158882 | − | 0.862594i | ||||
\(656\) | − | 46.8622i | − | 0.0714364i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −739.521 | + | 210.180i | −1.12389 | + | 0.319422i | ||||
\(659\) | −1176.49 | −1.78527 | −0.892634 | − | 0.450783i | \(-0.851145\pi\) | ||||
−0.892634 | + | 0.450783i | \(0.851145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 246.444i | 0.372835i | 0.982471 | + | 0.186418i | \(0.0596877\pi\) | ||||
−0.982471 | + | 0.186418i | \(0.940312\pi\) | |||||||
\(662\) | − | 784.914i | − | 1.18567i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 81.4276i | 0.122632i | ||||||||
\(665\) | −286.577 | + | 141.648i | −0.430943 | + | 0.213005i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.19385i | − | 0.00628763i | ||||||
\(668\) | −205.690 | −0.307919 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 328.149 | − | 60.4420i | 0.489775 | − | 0.0902119i | ||||
\(671\) | − | 94.0298i | − | 0.140134i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 76.3328i | − | 0.113422i | −0.998391 | − | 0.0567109i | \(-0.981939\pi\) | ||
0.998391 | − | 0.0567109i | \(-0.0180613\pi\) | |||||||
\(674\) | −67.5954 | −0.100290 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 291.240 | 0.430828 | ||||||||
\(677\) | 310.277 | 0.458312 | 0.229156 | − | 0.973390i | \(-0.426403\pi\) | ||||
0.229156 | + | 0.973390i | \(0.426403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 206.354 | + | 726.058i | 0.303908 | + | 1.06930i | ||||
\(680\) | −46.1843 | − | 250.742i | −0.0679181 | − | 0.368738i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1413.74 | −2.07293 | ||||||||
\(683\) | − | 157.333i | − | 0.230356i | −0.993345 | − | 0.115178i | \(-0.963256\pi\) | ||
0.993345 | − | 0.115178i | \(-0.0367438\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −86.3473 | − | 468.793i | −0.126054 | − | 0.684370i | ||||
\(686\) | 327.105 | − | 358.190i | 0.476829 | − | 0.522144i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 257.668i | 0.374518i | ||||||||
\(689\) | 374.921i | 0.544153i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 683.565i | 0.989240i | 0.869109 | + | 0.494620i | \(0.164693\pi\) | ||||
−0.869109 | + | 0.494620i | \(0.835307\pi\) | |||||||
\(692\) | 394.863 | 0.570612 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −401.306 | −0.578251 | ||||||||
\(695\) | −215.187 | − | 1168.28i | −0.309621 | − | 1.68098i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 211.213i | − | 0.303031i | ||||||
\(698\) | 28.3297 | 0.0405870 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 209.357 | + | 280.481i | 0.299082 | + | 0.400687i | ||||
\(701\) | 306.153 | 0.436738 | 0.218369 | − | 0.975866i | \(-0.429926\pi\) | ||||
0.218369 | + | 0.975866i | \(0.429926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 377.784 | 0.537388 | ||||||||
\(704\) | 140.093 | 0.198995 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 841.478i | − | 1.19190i | ||||||
\(707\) | 354.275 | − | 100.689i | 0.501096 | − | 0.142417i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 444.082 | 0.626350 | 0.313175 | − | 0.949695i | \(-0.398607\pi\) | ||||
0.313175 | + | 0.949695i | \(0.398607\pi\) | |||||||
\(710\) | 74.6812 | + | 405.456i | 0.105185 | + | 0.571065i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 287.082 | 0.403205 | ||||||||
\(713\) | −212.654 | −0.298252 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 416.366 | − | 76.6907i | 0.582330 | − | 0.107260i | ||||
\(716\) | −237.643 | −0.331904 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 832.109i | 1.15893i | ||||||||
\(719\) | 672.926i | 0.935919i | 0.883750 | + | 0.467960i | \(0.155011\pi\) | ||||
−0.883750 | + | 0.467960i | \(0.844989\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 138.551 | + | 487.495i | 0.192166 | + | 0.676137i | ||||
\(722\) | − | 392.556i | − | 0.543707i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 28.8296i | − | 0.0398199i | ||||||
\(725\) | −26.2984 | + | 10.0280i | −0.0362736 | + | 0.0138318i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −675.927 | −0.929748 | −0.464874 | − | 0.885377i | \(-0.653900\pi\) | ||||
−0.464874 | + | 0.885377i | \(0.653900\pi\) | |||||||
\(728\) | 92.0872 | − | 26.1722i | 0.126493 | − | 0.0359508i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 68.4094 | + | 371.405i | 0.0937115 | + | 0.508775i | ||||
\(731\) | 1161.34i | 1.58870i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 387.908 | 0.529206 | 0.264603 | − | 0.964357i | \(-0.414759\pi\) | ||||
0.264603 | + | 0.964357i | \(0.414759\pi\) | |||||||
\(734\) | − | 937.059i | − | 1.27665i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.0727 | 0.0286313 | ||||||||
\(737\) | 826.336i | 1.12122i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −394.643 | −0.534024 | −0.267012 | − | 0.963693i | \(-0.586036\pi\) | ||||
−0.267012 | + | 0.963693i | \(0.586036\pi\) | |||||||
\(740\) | −74.9253 | − | 406.781i | −0.101250 | − | 0.549705i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −209.847 | − | 738.348i | −0.282812 | − | 0.995079i | ||||
\(743\) | − | 147.027i | − | 0.197883i | −0.995093 | − | 0.0989414i | \(-0.968454\pi\) | ||
0.995093 | − | 0.0989414i | \(-0.0315456\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 658.151 | − | 121.225i | 0.883424 | − | 0.162718i | ||||
\(746\) | −334.248 | −0.448054 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 631.412 | 0.844133 | ||||||||
\(749\) | −1168.65 | + | 332.144i | −1.56028 | + | 0.443449i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 103.003 | 0.137154 | 0.0685771 | − | 0.997646i | \(-0.478154\pi\) | ||||
0.0685771 | + | 0.997646i | \(0.478154\pi\) | |||||||
\(752\) | 310.646 | 0.413092 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.69852i | 0.0102102i | ||||||||
\(755\) | −762.492 | + | 140.444i | −1.00992 | + | 0.186018i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 547.747i | 0.723575i | 0.932261 | + | 0.361788i | \(0.117833\pi\) | ||||
−0.932261 | + | 0.361788i | \(0.882167\pi\) | |||||||
\(758\) | − | 486.822i | − | 0.642246i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 127.030 | − | 23.3978i | 0.167145 | − | 0.0307866i | ||||
\(761\) | − | 1223.78i | − | 1.60813i | −0.594544 | − | 0.804063i | \(-0.702668\pi\) | ||
0.594544 | − | 0.804063i | \(-0.297332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −95.6779 | − | 336.644i | −0.125397 | − | 0.441211i | ||||
\(764\) | 119.875 | 0.156904 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 92.9275i | − | 0.121315i | ||||||
\(767\) | 420.986i | 0.548874i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 194.874i | − | 0.253413i | −0.991940 | − | 0.126706i | \(-0.959559\pi\) | ||
0.991940 | − | 0.126706i | \(-0.0404406\pi\) | |||||||
\(770\) | −777.042 | + | 384.074i | −1.00915 | + | 0.498797i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 491.896i | 0.637171i | ||||||||
\(773\) | −1017.59 | −1.31642 | −0.658209 | − | 0.752835i | \(-0.728686\pi\) | ||||
−0.658209 | + | 0.752835i | \(0.728686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 508.484 | + | 1333.49i | 0.656108 | + | 1.72063i | ||||
\(776\) | − | 304.990i | − | 0.393029i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 228.107i | 0.293196i | ||||||||
\(779\) | 107.004 | 0.137361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1021.01 | −1.30731 | ||||||||
\(782\) | 94.9765 | 0.121453 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −166.702 | + | 103.084i | −0.212631 | + | 0.131485i | ||||
\(785\) | 514.515 | − | 94.7689i | 0.655434 | − | 0.120725i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 222.094 | 0.282203 | 0.141101 | − | 0.989995i | \(-0.454936\pi\) | ||||
0.141101 | + | 0.989995i | \(0.454936\pi\) | |||||||
\(788\) | − | 164.119i | − | 0.208273i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −96.0193 | − | 521.304i | −0.121543 | − | 0.659879i | ||||
\(791\) | −472.367 | + | 134.252i | −0.597178 | + | 0.169724i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.9636i | 0.0327409i | ||||||||
\(794\) | − | 944.344i | − | 1.18935i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 578.677i | − | 0.726981i | ||||||
\(797\) | −340.349 | −0.427038 | −0.213519 | − | 0.976939i | \(-0.568493\pi\) | ||||
−0.213519 | + | 0.976939i | \(0.568493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1400.11 | 1.75233 | ||||||||
\(800\) | −50.3875 | − | 132.140i | −0.0629844 | − | 0.165176i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 839.796i | − | 1.04713i | ||||||
\(803\) | −935.263 | −1.16471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −116.882 | + | 57.7721i | −0.145195 | + | 0.0717666i | ||||
\(806\) | 390.363 | 0.484321 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −148.818 | −0.184181 | ||||||||
\(809\) | 462.403 | 0.571573 | 0.285787 | − | 0.958293i | \(-0.407745\pi\) | ||||
0.285787 | + | 0.958293i | \(0.407745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1420.09i | − | 1.75103i | −0.483190 | − | 0.875516i | \(-0.660522\pi\) | ||
0.483190 | − | 0.875516i | \(-0.339478\pi\) | |||||||
\(812\) | −4.30893 | − | 15.1610i | −0.00530656 | − | 0.0186712i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1024.35 | 1.25841 | ||||||||
\(815\) | −118.566 | − | 643.714i | −0.145480 | − | 0.789833i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −588.354 | −0.720140 | ||||||||
\(818\) | −805.571 | −0.984806 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.2220 | − | 115.217i | −0.0258805 | − | 0.140509i | ||||
\(821\) | 651.695 | 0.793782 | 0.396891 | − | 0.917866i | \(-0.370089\pi\) | ||||
0.396891 | + | 0.917866i | \(0.370089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 604.705i | − | 0.734756i | −0.930072 | − | 0.367378i | \(-0.880255\pi\) | ||
0.930072 | − | 0.367378i | \(-0.119745\pi\) | |||||||
\(824\) | − | 204.779i | − | 0.248518i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −235.630 | − | 829.066i | −0.285266 | − | 1.00371i | ||||
\(827\) | − | 504.280i | − | 0.609771i | −0.952389 | − | 0.304885i | \(-0.901382\pi\) | ||
0.952389 | − | 0.304885i | \(-0.0986181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 814.575i | 0.982599i | 0.870991 | + | 0.491300i | \(0.163478\pi\) | ||||
−0.870991 | + | 0.491300i | \(0.836522\pi\) | |||||||
\(830\) | 36.8752 | + | 200.201i | 0.0444279 | + | 0.241206i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −38.6825 | −0.0464934 | ||||||||
\(833\) | −751.344 | + | 464.610i | −0.901973 | + | 0.557755i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −505.718 | + | 93.1484i | −0.605650 | + | 0.111555i | ||||
\(836\) | 319.884i | 0.382637i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −296.215 | −0.353478 | ||||||||
\(839\) | 128.459i | 0.153109i | 0.997065 | + | 0.0765547i | \(0.0243920\pi\) | ||||
−0.997065 | + | 0.0765547i | \(0.975608\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −839.733 | −0.998493 | ||||||||
\(842\) | 240.011i | 0.285048i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −67.3991 | −0.0798567 | ||||||||
\(845\) | 716.054 | − | 131.890i | 0.847401 | − | 0.156083i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −355.288 | − | 1250.08i | −0.419466 | − | 1.47590i | ||||
\(848\) | 310.153i | 0.365747i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −227.101 | − | 595.570i | −0.267178 | − | 0.700670i | ||||
\(851\) | 154.081 | 0.181059 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −636.175 | −0.745808 | −0.372904 | − | 0.927870i | \(-0.621638\pi\) | ||||
−0.372904 | + | 0.927870i | \(0.621638\pi\) | |||||||
\(854\) | −14.5320 | − | 51.1311i | −0.0170164 | − | 0.0598725i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 490.907 | 0.573490 | ||||||||
\(857\) | 494.679 | 0.577221 | 0.288611 | − | 0.957447i | \(-0.406807\pi\) | ||||
0.288611 | + | 0.957447i | \(0.406807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 745.414i | − | 0.867770i | −0.900968 | − | 0.433885i | \(-0.857142\pi\) | ||
0.900968 | − | 0.433885i | \(-0.142858\pi\) | |||||||
\(860\) | 116.687 | + | 633.514i | 0.135683 | + | 0.736645i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 761.450i | 0.883353i | ||||||||
\(863\) | 593.451i | 0.687661i | 0.939032 | + | 0.343830i | \(0.111725\pi\) | ||||
−0.939032 | + | 0.343830i | \(0.888275\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 970.828 | − | 178.817i | 1.12234 | − | 0.206725i | ||||
\(866\) | − | 167.322i | − | 0.193212i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −768.757 | + | 218.489i | −0.885665 | + | 0.251716i | ||||
\(869\) | 1312.73 | 1.51063 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 228.168i | − | 0.261961i | ||||||
\(872\) | 141.412i | 0.162169i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 48.1168i | 0.0550535i | ||||||||
\(875\) | 641.753 | + | 594.793i | 0.733432 | + | 0.679763i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 291.879i | 0.332815i | 0.986057 | + | 0.166407i | \(0.0532167\pi\) | ||||
−0.986057 | + | 0.166407i | \(0.946783\pi\) | |||||||
\(878\) | −614.948 | −0.700396 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 344.438 | − | 63.4422i | 0.391407 | − | 0.0720934i | ||||
\(881\) | − | 1226.42i | − | 1.39208i | −0.718004 | − | 0.696039i | \(-0.754944\pi\) | ||
0.718004 | − | 0.696039i | \(-0.245056\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1132.03i | 1.28202i | 0.767531 | + | 0.641012i | \(0.221485\pi\) | ||||
−0.767531 | + | 0.641012i | \(0.778515\pi\) | |||||||
\(884\) | −174.346 | −0.197224 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −784.896 | −0.885887 | ||||||||
\(887\) | −959.088 | −1.08127 | −0.540636 | − | 0.841257i | \(-0.681816\pi\) | ||||
−0.540636 | + | 0.841257i | \(0.681816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1332.83 | − | 378.806i | 1.49925 | − | 0.426103i | ||||
\(890\) | 705.831 | − | 130.007i | 0.793068 | − | 0.146076i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.5112 | 0.0241156 | ||||||||
\(893\) | 709.321i | 0.794312i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −584.280 | + | 107.619i | −0.652827 | + | 0.120245i | ||||
\(896\) | 76.1790 | − | 21.6509i | 0.0850212 | − | 0.0241640i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 94.6004i | − | 0.105346i | ||||||
\(899\) | − | 64.2684i | − | 0.0714887i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1397.89i | 1.55149i | ||||||||
\(902\) | 290.137 | 0.321660 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 198.424 | 0.219496 | ||||||||
\(905\) | −13.0558 | − | 70.8817i | −0.0144262 | − | 0.0783224i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 989.799i | − | 1.09129i | −0.838017 | − | 0.545644i | \(-0.816285\pi\) | ||
0.838017 | − | 0.545644i | \(-0.183715\pi\) | |||||||
\(908\) | 832.900 | 0.917290 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 214.557 | − | 106.051i | 0.235777 | − | 0.116539i | ||||
\(911\) | −994.781 | −1.09197 | −0.545983 | − | 0.837796i | \(-0.683844\pi\) | ||||
−0.545983 | + | 0.837796i | \(0.683844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −504.141 | −0.552181 | ||||||||
\(914\) | 1061.99 | 1.16191 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 776.938i | 0.848185i | ||||||||
\(917\) | 773.665 | − | 219.884i | 0.843691 | − | 0.239786i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −887.212 | −0.965410 | −0.482705 | − | 0.875783i | \(-0.660346\pi\) | ||||
−0.482705 | + | 0.875783i | \(0.660346\pi\) | |||||||
\(920\) | 51.8101 | − | 9.54293i | 0.0563153 | − | 0.0103728i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 559.148 | 0.606451 | ||||||||
\(923\) | 281.921 | 0.305440 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −368.429 | − | 966.199i | −0.398302 | − | 1.04454i | ||||
\(926\) | −599.600 | −0.647516 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.36859i | 0.00686270i | ||||||||
\(929\) | 1224.49i | 1.31808i | 0.752109 | + | 0.659039i | \(0.229037\pi\) | ||||
−0.752109 | + | 0.659039i | \(0.770963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −235.380 | − | 380.644i | −0.252825 | − | 0.408855i | ||||
\(932\) | 140.807i | 0.151081i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 826.478i | − | 0.884880i | ||||||
\(935\) | 1552.42 | − | 285.940i | 1.66034 | − | 0.305819i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 807.001 | 0.861260 | 0.430630 | − | 0.902529i | \(-0.358291\pi\) | ||||
0.430630 | + | 0.902529i | \(0.358291\pi\) | |||||||
\(938\) | 127.708 | + | 449.341i | 0.136149 | + | 0.479042i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 763.766 | − | 140.679i | 0.812517 | − | 0.149658i | ||||
\(941\) | − | 1246.48i | − | 1.32464i | −0.749223 | − | 0.662318i | \(-0.769573\pi\) | ||
0.749223 | − | 0.662318i | \(-0.230427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.6423 | 0.0462802 | ||||||||
\(944\) | 348.260i | 0.368920i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1595.30 | −1.68636 | ||||||||
\(947\) | − | 675.978i | − | 0.713810i | −0.934141 | − | 0.356905i | \(-0.883832\pi\) | ||
0.934141 | − | 0.356905i | \(-0.116168\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 258.245 | 0.272123 | ||||||||
\(950\) | 301.726 | − | 115.054i | 0.317607 | − | 0.121109i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 343.346 | − | 97.5828i | 0.360658 | − | 0.102503i | ||||
\(953\) | − | 1098.24i | − | 1.15240i | −0.817308 | − | 0.576201i | \(-0.804534\pi\) | ||
0.817308 | − | 0.576201i | \(-0.195466\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 294.730 | − | 54.2864i | 0.308618 | − | 0.0568444i | ||||
\(956\) | −626.267 | −0.655091 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1038.76 | 1.08430 | ||||||||
\(959\) | 641.928 | − | 182.443i | 0.669372 | − | 0.190243i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2297.80 | −2.39105 | ||||||||
\(962\) | −282.843 | −0.294015 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 397.455i | − | 0.412297i | ||||||
\(965\) | 222.759 | + | 1209.40i | 0.230839 | + | 1.25326i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1345.41i | 1.39132i | 0.718370 | + | 0.695661i | \(0.244889\pi\) | ||||
−0.718370 | + | 0.695661i | \(0.755111\pi\) | |||||||
\(968\) | 525.114i | 0.542474i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −138.118 | − | 749.862i | −0.142389 | − | 0.773054i | ||||
\(971\) | 1230.36i | 1.26710i | 0.773701 | + | 0.633551i | \(0.218403\pi\) | ||||
−0.773701 | + | 0.633551i | \(0.781597\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1599.75 | − | 454.668i | 1.64415 | − | 0.467284i | ||||
\(974\) | −129.633 | −0.133093 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.4783i | 0.0220065i | ||||||||
\(977\) | 228.116i | 0.233487i | 0.993162 | + | 0.116743i | \(0.0372455\pi\) | ||||
−0.993162 | + | 0.116743i | \(0.962755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1777.40i | 1.81553i | ||||||||
\(980\) | −363.179 | + | 328.939i | −0.370591 | + | 0.335652i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 650.659i | 0.662586i | ||||||||
\(983\) | 1721.09 | 1.75085 | 0.875425 | − | 0.483354i | \(-0.160582\pi\) | ||||
0.875425 | + | 0.483354i | \(0.160582\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −74.3227 | − | 403.510i | −0.0754545 | − | 0.409654i | ||||
\(986\) | 28.7039i | 0.0291114i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 88.3266i | − | 0.0893994i | ||||||
\(989\) | −239.964 | −0.242633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1911.05 | −1.92841 | −0.964205 | − | 0.265159i | \(-0.914576\pi\) | ||||
−0.964205 | + | 0.265159i | \(0.914576\pi\) | |||||||
\(992\) | 322.927 | 0.325531 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −555.199 | + | 157.794i | −0.558550 | + | 0.158746i | ||||
\(995\) | −262.059 | − | 1422.76i | −0.263376 | − | 1.42991i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.3627 | −0.0314571 | −0.0157285 | − | 0.999876i | \(-0.505007\pi\) | ||||
−0.0157285 | + | 0.999876i | \(0.505007\pi\) | |||||||
\(998\) | 688.900i | 0.690281i | ||||||||
\(999\) | 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 | 630.3.h.e.559.1 | 16 | ||
3.2 | odd | 2 | 210.3.h.a.139.16 | yes | 16 | ||
5.4 | even | 2 | inner | 630.3.h.e.559.16 | 16 | ||
7.6 | odd | 2 | inner | 630.3.h.e.559.8 | 16 | ||
12.11 | even | 2 | 1680.3.bd.a.769.7 | 16 | |||
15.2 | even | 4 | 1050.3.f.e.601.4 | 16 | |||
15.8 | even | 4 | 1050.3.f.e.601.13 | 16 | |||
15.14 | odd | 2 | 210.3.h.a.139.1 | ✓ | 16 | ||
21.20 | even | 2 | 210.3.h.a.139.9 | yes | 16 | ||
35.34 | odd | 2 | inner | 630.3.h.e.559.9 | 16 | ||
60.59 | even | 2 | 1680.3.bd.a.769.9 | 16 | |||
84.83 | odd | 2 | 1680.3.bd.a.769.10 | 16 | |||
105.62 | odd | 4 | 1050.3.f.e.601.8 | 16 | |||
105.83 | odd | 4 | 1050.3.f.e.601.9 | 16 | |||
105.104 | even | 2 | 210.3.h.a.139.8 | yes | 16 | ||
420.419 | odd | 2 | 1680.3.bd.a.769.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.h.a.139.1 | ✓ | 16 | 15.14 | odd | 2 | ||
210.3.h.a.139.8 | yes | 16 | 105.104 | even | 2 | ||
210.3.h.a.139.9 | yes | 16 | 21.20 | even | 2 | ||
210.3.h.a.139.16 | yes | 16 | 3.2 | odd | 2 | ||
630.3.h.e.559.1 | 16 | 1.1 | even | 1 | trivial | ||
630.3.h.e.559.8 | 16 | 7.6 | odd | 2 | inner | ||
630.3.h.e.559.9 | 16 | 35.34 | odd | 2 | inner | ||
630.3.h.e.559.16 | 16 | 5.4 | even | 2 | inner | ||
1050.3.f.e.601.4 | 16 | 15.2 | even | 4 | |||
1050.3.f.e.601.8 | 16 | 105.62 | odd | 4 | |||
1050.3.f.e.601.9 | 16 | 105.83 | odd | 4 | |||
1050.3.f.e.601.13 | 16 | 15.8 | even | 4 | |||
1680.3.bd.a.769.7 | 16 | 12.11 | even | 2 | |||
1680.3.bd.a.769.8 | 16 | 420.419 | odd | 2 | |||
1680.3.bd.a.769.9 | 16 | 60.59 | even | 2 | |||
1680.3.bd.a.769.10 | 16 | 84.83 | odd | 2 |