Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(809,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.18 | ||
Character | \(\chi\) | \(=\) | 810.809 |
Dual form | 810.3.b.c.809.17 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0.174155 | + | 4.99697i | 0.0348311 | + | 0.999393i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 9.47560i | − | 1.35366i | −0.736141 | − | 0.676828i | \(-0.763354\pi\) | ||
0.736141 | − | 0.676828i | \(-0.236646\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.246293 | + | 7.06678i | 0.0246293 | + | 0.706678i | ||||
\(11\) | − | 20.3859i | − | 1.85327i | −0.375966 | − | 0.926633i | \(-0.622689\pi\) | ||
0.375966 | − | 0.926633i | \(-0.377311\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.10986i | − | 0.469989i | −0.971997 | − | 0.234995i | \(-0.924493\pi\) | ||
0.971997 | − | 0.234995i | \(-0.0755072\pi\) | |||||||
\(14\) | − | 13.4005i | − | 0.957180i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −24.0002 | −1.41178 | −0.705888 | − | 0.708323i | \(-0.749452\pi\) | ||||
−0.705888 | + | 0.708323i | \(0.749452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.0752 | 0.846062 | 0.423031 | − | 0.906115i | \(-0.360966\pi\) | ||||
0.423031 | + | 0.906115i | \(0.360966\pi\) | |||||||
\(20\) | 0.348311 | + | 9.99393i | 0.0174155 | + | 0.499697i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 28.8301i | − | 1.31046i | ||||||
\(23\) | −43.2779 | −1.88165 | −0.940824 | − | 0.338896i | \(-0.889946\pi\) | ||||
−0.940824 | + | 0.338896i | \(0.889946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.9393 | + | 1.74050i | −0.997574 | + | 0.0696198i | ||||
\(26\) | − | 8.64064i | − | 0.332332i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 18.9512i | − | 0.676828i | ||||||
\(29\) | 19.6215i | 0.676602i | 0.941038 | + | 0.338301i | \(0.109852\pi\) | ||||
−0.941038 | + | 0.338301i | \(0.890148\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 30.5072 | 0.984105 | 0.492052 | − | 0.870566i | \(-0.336247\pi\) | ||||
0.492052 | + | 0.870566i | \(0.336247\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −33.9414 | −0.998277 | ||||||||
\(35\) | 47.3492 | − | 1.65023i | 1.35284 | − | 0.0471493i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 44.8335i | − | 1.21172i | −0.795573 | − | 0.605858i | \(-0.792830\pi\) | ||
0.795573 | − | 0.605858i | \(-0.207170\pi\) | |||||||
\(38\) | 22.7337 | 0.598256 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.492585 | + | 14.1336i | 0.0123146 | + | 0.353339i | ||||
\(41\) | − | 48.0908i | − | 1.17295i | −0.809968 | − | 0.586473i | \(-0.800516\pi\) | ||
0.809968 | − | 0.586473i | \(-0.199484\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 48.1045i | − | 1.11871i | −0.828929 | − | 0.559354i | \(-0.811049\pi\) | ||
0.828929 | − | 0.559354i | \(-0.188951\pi\) | |||||||
\(44\) | − | 40.7719i | − | 0.926633i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −61.2042 | −1.33053 | ||||||||
\(47\) | 68.0770 | 1.44845 | 0.724223 | − | 0.689565i | \(-0.242198\pi\) | ||||
0.724223 | + | 0.689565i | \(0.242198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −40.7869 | −0.832387 | ||||||||
\(50\) | −35.2696 | + | 2.46143i | −0.705391 | + | 0.0492287i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 12.2197i | − | 0.234995i | ||||||
\(53\) | 61.7484 | 1.16506 | 0.582532 | − | 0.812808i | \(-0.302062\pi\) | ||||
0.582532 | + | 0.812808i | \(0.302062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 101.868 | − | 3.55032i | 1.85214 | − | 0.0645512i | ||||
\(56\) | − | 26.8010i | − | 0.478590i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 27.7489i | 0.478430i | ||||||||
\(59\) | 50.4411i | 0.854934i | 0.904031 | + | 0.427467i | \(0.140594\pi\) | ||||
−0.904031 | + | 0.427467i | \(0.859406\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −48.9975 | −0.803237 | −0.401619 | − | 0.915807i | \(-0.631552\pi\) | ||||
−0.401619 | + | 0.915807i | \(0.631552\pi\) | |||||||
\(62\) | 43.1438 | 0.695867 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 30.5308 | − | 1.06406i | 0.469704 | − | 0.0163702i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 55.0907i | − | 0.822250i | −0.911579 | − | 0.411125i | \(-0.865136\pi\) | ||
0.911579 | − | 0.411125i | \(-0.134864\pi\) | |||||||
\(68\) | −48.0004 | −0.705888 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 66.9619 | − | 2.33377i | 0.956599 | − | 0.0333396i | ||||
\(71\) | 23.5982i | 0.332369i | 0.986095 | + | 0.166184i | \(0.0531447\pi\) | ||||
−0.986095 | + | 0.166184i | \(0.946855\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 40.4303i | − | 0.553840i | −0.960893 | − | 0.276920i | \(-0.910686\pi\) | ||
0.960893 | − | 0.276920i | \(-0.0893137\pi\) | |||||||
\(74\) | − | 63.4041i | − | 0.856812i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 32.1503 | 0.423031 | ||||||||
\(77\) | −193.169 | −2.50869 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 33.2338 | 0.420681 | 0.210340 | − | 0.977628i | \(-0.432543\pi\) | ||||
0.210340 | + | 0.977628i | \(0.432543\pi\) | |||||||
\(80\) | 0.696621 | + | 19.9879i | 0.00870776 | + | 0.249848i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 68.0107i | − | 0.829399i | ||||||
\(83\) | 22.7144 | 0.273668 | 0.136834 | − | 0.990594i | \(-0.456307\pi\) | ||||
0.136834 | + | 0.990594i | \(0.456307\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.17976 | − | 119.928i | −0.0491737 | − | 1.41092i | ||||
\(86\) | − | 68.0300i | − | 0.791046i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 57.6601i | − | 0.655229i | ||||||
\(89\) | 79.5266i | 0.893557i | 0.894644 | + | 0.446779i | \(0.147429\pi\) | ||||
−0.894644 | + | 0.446779i | \(0.852571\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −57.8946 | −0.636204 | ||||||||
\(92\) | −86.5558 | −0.940824 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 96.2754 | 1.02421 | ||||||||
\(95\) | 2.79958 | + | 80.3271i | 0.0294692 | + | 0.845548i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 119.886i | 1.23594i | 0.786202 | + | 0.617970i | \(0.212045\pi\) | ||||
−0.786202 | + | 0.617970i | \(0.787955\pi\) | |||||||
\(98\) | −57.6815 | −0.588586 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −49.8787 | + | 3.48099i | −0.498787 | + | 0.0348099i | ||||
\(101\) | 22.0774i | 0.218588i | 0.994009 | + | 0.109294i | \(0.0348591\pi\) | ||||
−0.994009 | + | 0.109294i | \(0.965141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3872i | 0.178516i | 0.996009 | + | 0.0892581i | \(0.0284496\pi\) | ||||
−0.996009 | + | 0.0892581i | \(0.971550\pi\) | |||||||
\(104\) | − | 17.2813i | − | 0.166166i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 87.3254 | 0.823825 | ||||||||
\(107\) | 60.8601 | 0.568786 | 0.284393 | − | 0.958708i | \(-0.408208\pi\) | ||||
0.284393 | + | 0.958708i | \(0.408208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.4892 | 0.738433 | 0.369216 | − | 0.929343i | \(-0.379626\pi\) | ||||
0.369216 | + | 0.929343i | \(0.379626\pi\) | |||||||
\(110\) | 144.063 | − | 5.02091i | 1.30966 | − | 0.0456446i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 37.9024i | − | 0.338414i | ||||||
\(113\) | −22.7556 | −0.201377 | −0.100689 | − | 0.994918i | \(-0.532105\pi\) | ||||
−0.100689 | + | 0.994918i | \(0.532105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.53707 | − | 216.258i | −0.0655398 | − | 1.88051i | ||||
\(116\) | 39.2429i | 0.338301i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 71.3345i | 0.604530i | ||||||||
\(119\) | 227.416i | 1.91106i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −294.586 | −2.43460 | ||||||||
\(122\) | −69.2929 | −0.567974 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 61.0145 | 0.492052 | ||||||||
\(125\) | −13.0405 | − | 124.318i | −0.104324 | − | 0.994543i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 73.3562i | 0.577608i | 0.957388 | + | 0.288804i | \(0.0932576\pi\) | ||||
−0.957388 | + | 0.288804i | \(0.906742\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 43.1770 | − | 1.50481i | 0.332131 | − | 0.0115755i | ||||
\(131\) | 91.0508i | 0.695045i | 0.937672 | + | 0.347522i | \(0.112977\pi\) | ||||
−0.937672 | + | 0.347522i | \(0.887023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 152.322i | − | 1.14528i | ||||||
\(134\) | − | 77.9101i | − | 0.581419i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −67.8828 | −0.499138 | ||||||||
\(137\) | −27.8837 | −0.203531 | −0.101765 | − | 0.994808i | \(-0.532449\pi\) | ||||
−0.101765 | + | 0.994808i | \(0.532449\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 34.7379 | 0.249913 | 0.124957 | − | 0.992162i | \(-0.460121\pi\) | ||||
0.124957 | + | 0.992162i | \(0.460121\pi\) | |||||||
\(140\) | 94.6985 | − | 3.30045i | 0.676418 | − | 0.0235746i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 33.3729i | 0.235020i | ||||||||
\(143\) | −124.555 | −0.871015 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −98.0477 | + | 3.41718i | −0.676191 | + | 0.0235668i | ||||
\(146\) | − | 57.1771i | − | 0.391624i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 89.6669i | − | 0.605858i | ||||||
\(149\) | − | 0.317069i | − | 0.00212798i | −0.999999 | − | 0.00106399i | \(-0.999661\pi\) | ||
0.999999 | − | 0.00106399i | \(-0.000338678\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −105.328 | −0.697534 | −0.348767 | − | 0.937209i | \(-0.613400\pi\) | ||||
−0.348767 | + | 0.937209i | \(0.613400\pi\) | |||||||
\(152\) | 45.4674 | 0.299128 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −273.182 | −1.77391 | ||||||||
\(155\) | 5.31300 | + | 152.444i | 0.0342774 | + | 0.983507i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 45.6023i | − | 0.290460i | −0.989398 | − | 0.145230i | \(-0.953608\pi\) | ||
0.989398 | − | 0.145230i | \(-0.0463923\pi\) | |||||||
\(158\) | 46.9997 | 0.297466 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.985171 | + | 28.2671i | 0.00615732 | + | 0.176669i | ||||
\(161\) | 410.084i | 2.54711i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 152.794i | − | 0.937384i | −0.883362 | − | 0.468692i | \(-0.844725\pi\) | ||
0.883362 | − | 0.468692i | \(-0.155275\pi\) | |||||||
\(164\) | − | 96.1816i | − | 0.586473i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 32.1230 | 0.193512 | ||||||||
\(167\) | −13.7284 | −0.0822060 | −0.0411030 | − | 0.999155i | \(-0.513087\pi\) | ||||
−0.0411030 | + | 0.999155i | \(0.513087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 131.670 | 0.779110 | ||||||||
\(170\) | −5.91107 | − | 169.604i | −0.0347710 | − | 0.997671i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 96.2089i | − | 0.559354i | ||||||
\(173\) | −10.4307 | −0.0602932 | −0.0301466 | − | 0.999545i | \(-0.509597\pi\) | ||||
−0.0301466 | + | 0.999545i | \(0.509597\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.4922 | + | 236.315i | 0.0942414 | + | 1.35037i | ||||
\(176\) | − | 81.5437i | − | 0.463317i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 112.468i | 0.631841i | ||||||||
\(179\) | − | 62.4650i | − | 0.348967i | −0.984660 | − | 0.174483i | \(-0.944174\pi\) | ||
0.984660 | − | 0.174483i | \(-0.0558255\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 343.029 | 1.89519 | 0.947594 | − | 0.319477i | \(-0.103507\pi\) | ||||
0.947594 | + | 0.319477i | \(0.103507\pi\) | |||||||
\(182\) | −81.8753 | −0.449864 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −122.408 | −0.665263 | ||||||||
\(185\) | 224.031 | − | 7.80799i | 1.21098 | − | 0.0422053i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 489.266i | 2.61640i | ||||||||
\(188\) | 136.154 | 0.724223 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.95920 | + | 113.600i | 0.0208379 | + | 0.597893i | ||||
\(191\) | − | 12.6376i | − | 0.0661657i | −0.999453 | − | 0.0330829i | \(-0.989467\pi\) | ||
0.999453 | − | 0.0330829i | \(-0.0105325\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 168.124i | 0.871111i | 0.900162 | + | 0.435556i | \(0.143448\pi\) | ||||
−0.900162 | + | 0.435556i | \(0.856552\pi\) | |||||||
\(194\) | 169.545i | 0.873942i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −81.5739 | −0.416193 | ||||||||
\(197\) | −372.044 | −1.88855 | −0.944275 | − | 0.329157i | \(-0.893235\pi\) | ||||
−0.944275 | + | 0.329157i | \(0.893235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 231.821 | 1.16493 | 0.582466 | − | 0.812855i | \(-0.302088\pi\) | ||||
0.582466 | + | 0.812855i | \(0.302088\pi\) | |||||||
\(200\) | −70.5391 | + | 4.92287i | −0.352696 | + | 0.0246143i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 31.2222i | 0.154565i | ||||||||
\(203\) | 185.925 | 0.915887 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 240.308 | − | 8.37527i | 1.17224 | − | 0.0408550i | ||||
\(206\) | 26.0034i | 0.126230i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 24.4394i | − | 0.117497i | ||||||
\(209\) | − | 327.707i | − | 1.56798i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9012 | 0.0990579 | 0.0495289 | − | 0.998773i | \(-0.484228\pi\) | ||||
0.0495289 | + | 0.998773i | \(0.484228\pi\) | |||||||
\(212\) | 123.497 | 0.582532 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 86.0692 | 0.402192 | ||||||||
\(215\) | 240.376 | − | 8.37765i | 1.11803 | − | 0.0389658i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 289.074i | − | 1.33214i | ||||||
\(218\) | 113.829 | 0.522151 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 203.736 | − | 7.10063i | 0.926071 | − | 0.0322756i | ||||
\(221\) | 146.638i | 0.663520i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.7730i | − | 0.0707311i | −0.999374 | − | 0.0353655i | \(-0.988740\pi\) | ||
0.999374 | − | 0.0353655i | \(-0.0112595\pi\) | |||||||
\(224\) | − | 53.6021i | − | 0.239295i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.1813 | −0.142395 | ||||||||
\(227\) | −341.346 | −1.50373 | −0.751863 | − | 0.659319i | \(-0.770845\pi\) | ||||
−0.751863 | + | 0.659319i | \(0.770845\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 120.453 | 0.525994 | 0.262997 | − | 0.964797i | \(-0.415289\pi\) | ||||
0.262997 | + | 0.964797i | \(0.415289\pi\) | |||||||
\(230\) | −10.6590 | − | 305.835i | −0.0463436 | − | 1.32972i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 55.4979i | 0.239215i | ||||||||
\(233\) | 307.400 | 1.31931 | 0.659657 | − | 0.751567i | \(-0.270702\pi\) | ||||
0.659657 | + | 0.751567i | \(0.270702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8560 | + | 340.178i | 0.0504509 | + | 1.44757i | ||||
\(236\) | 100.882i | 0.427467i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 321.615i | 1.35132i | ||||||||
\(239\) | − | 119.083i | − | 0.498257i | −0.968470 | − | 0.249128i | \(-0.919856\pi\) | ||
0.968470 | − | 0.249128i | \(-0.0801441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −314.600 | −1.30539 | −0.652697 | − | 0.757619i | \(-0.726362\pi\) | ||||
−0.652697 | + | 0.757619i | \(0.726362\pi\) | |||||||
\(242\) | −416.608 | −1.72152 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −97.9949 | −0.401619 | ||||||||
\(245\) | −7.10326 | − | 203.811i | −0.0289929 | − | 0.831882i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 98.2170i | − | 0.397640i | ||||||
\(248\) | 86.2875 | 0.347933 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18.4421 | − | 175.812i | −0.0737683 | − | 0.703248i | ||||
\(251\) | 148.193i | 0.590411i | 0.955434 | + | 0.295206i | \(0.0953882\pi\) | ||||
−0.955434 | + | 0.295206i | \(0.904612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 882.260i | 3.48719i | ||||||||
\(254\) | 103.741i | 0.408431i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 294.316 | 1.14520 | 0.572598 | − | 0.819836i | \(-0.305935\pi\) | ||||
0.572598 | + | 0.819836i | \(0.305935\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −424.824 | −1.64025 | ||||||||
\(260\) | 61.0615 | − | 2.12813i | 0.234852 | − | 0.00818511i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 128.765i | 0.491471i | ||||||||
\(263\) | −69.4645 | −0.264123 | −0.132062 | − | 0.991241i | \(-0.542160\pi\) | ||||
−0.132062 | + | 0.991241i | \(0.542160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.7538 | + | 308.555i | 0.0405804 | + | 1.16436i | ||||
\(266\) | − | 215.416i | − | 0.809833i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 110.181i | − | 0.411125i | ||||||
\(269\) | − | 262.460i | − | 0.975687i | −0.872931 | − | 0.487844i | \(-0.837784\pi\) | ||
0.872931 | − | 0.487844i | \(-0.162216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −375.110 | −1.38417 | −0.692084 | − | 0.721817i | \(-0.743307\pi\) | ||||
−0.692084 | + | 0.721817i | \(0.743307\pi\) | |||||||
\(272\) | −96.0008 | −0.352944 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −39.4335 | −0.143918 | ||||||||
\(275\) | 35.4816 | + | 508.412i | 0.129024 | + | 1.84877i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 146.370i | 0.528412i | 0.964466 | + | 0.264206i | \(0.0851100\pi\) | ||||
−0.964466 | + | 0.264206i | \(0.914890\pi\) | |||||||
\(278\) | 49.1268 | 0.176715 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 133.924 | − | 4.66754i | 0.478300 | − | 0.0166698i | ||||
\(281\) | 79.1692i | 0.281741i | 0.990028 | + | 0.140870i | \(0.0449901\pi\) | ||||
−0.990028 | + | 0.140870i | \(0.955010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 216.326i | − | 0.764401i | −0.924079 | − | 0.382201i | \(-0.875166\pi\) | ||
0.924079 | − | 0.382201i | \(-0.124834\pi\) | |||||||
\(284\) | 47.1963i | 0.166184i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −176.148 | −0.615901 | ||||||||
\(287\) | −455.689 | −1.58777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 287.010 | 0.993113 | ||||||||
\(290\) | −138.660 | + | 4.83262i | −0.478140 | + | 0.0166642i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 80.8606i | − | 0.276920i | ||||||
\(293\) | 416.332 | 1.42093 | 0.710464 | − | 0.703734i | \(-0.248485\pi\) | ||||
0.710464 | + | 0.703734i | \(0.248485\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −252.053 | + | 8.78458i | −0.854415 | + | 0.0297783i | ||||
\(296\) | − | 126.808i | − | 0.428406i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 0.448403i | − | 0.00150471i | ||||||
\(299\) | 264.422i | 0.884354i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −455.819 | −1.51435 | ||||||||
\(302\) | −148.956 | −0.493231 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 64.3007 | 0.211515 | ||||||||
\(305\) | −8.53317 | − | 244.839i | −0.0279776 | − | 0.802750i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 331.571i | − | 1.08004i | −0.841653 | − | 0.540018i | \(-0.818417\pi\) | ||
0.841653 | − | 0.540018i | \(-0.181583\pi\) | |||||||
\(308\) | −386.338 | −1.25434 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.51371 | + | 215.588i | 0.0242378 | + | 0.695445i | ||||
\(311\) | − | 393.568i | − | 1.26549i | −0.774360 | − | 0.632745i | \(-0.781928\pi\) | ||
0.774360 | − | 0.632745i | \(-0.218072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 254.130i | 0.811917i | 0.913891 | + | 0.405959i | \(0.133062\pi\) | ||||
−0.913891 | + | 0.405959i | \(0.866938\pi\) | |||||||
\(314\) | − | 64.4914i | − | 0.205387i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 66.4675 | 0.210340 | ||||||||
\(317\) | −431.983 | −1.36272 | −0.681361 | − | 0.731947i | \(-0.738612\pi\) | ||||
−0.681361 | + | 0.731947i | \(0.738612\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 400.002 | 1.25392 | ||||||||
\(320\) | 1.39324 | + | 39.9757i | 0.00435388 | + | 0.124924i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 579.946i | 1.80108i | ||||||||
\(323\) | −385.807 | −1.19445 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6342 | + | 152.376i | 0.0327206 | + | 0.468849i | ||||
\(326\) | − | 216.083i | − | 0.662831i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 136.021i | − | 0.414699i | ||||||
\(329\) | − | 645.070i | − | 1.96070i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 191.732 | 0.579249 | 0.289625 | − | 0.957140i | \(-0.406469\pi\) | ||||
0.289625 | + | 0.957140i | \(0.406469\pi\) | |||||||
\(332\) | 45.4288 | 0.136834 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.4149 | −0.0581284 | ||||||||
\(335\) | 275.287 | − | 9.59434i | 0.821751 | − | 0.0286398i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 254.110i | − | 0.754035i | −0.926206 | − | 0.377017i | \(-0.876950\pi\) | ||
0.926206 | − | 0.377017i | \(-0.123050\pi\) | |||||||
\(338\) | 186.209 | 0.550914 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.35952 | − | 239.856i | −0.0245868 | − | 0.705460i | ||||
\(341\) | − | 621.919i | − | 1.82381i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 77.8236i | − | 0.226891i | ||||||
\(344\) | − | 136.060i | − | 0.395523i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.7513 | −0.0426337 | ||||||||
\(347\) | −320.795 | −0.924481 | −0.462241 | − | 0.886755i | \(-0.652954\pi\) | ||||
−0.462241 | + | 0.886755i | \(0.652954\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 304.524 | 0.872563 | 0.436281 | − | 0.899810i | \(-0.356295\pi\) | ||||
0.436281 | + | 0.899810i | \(0.356295\pi\) | |||||||
\(350\) | 23.3235 | + | 334.200i | 0.0666387 | + | 0.954857i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 115.320i | − | 0.327614i | ||||||
\(353\) | 215.758 | 0.611213 | 0.305607 | − | 0.952158i | \(-0.401141\pi\) | ||||
0.305607 | + | 0.952158i | \(0.401141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −117.919 | + | 4.10975i | −0.332167 | + | 0.0115767i | ||||
\(356\) | 159.053i | 0.446779i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 88.3389i | − | 0.246757i | ||||||
\(359\) | 638.110i | 1.77746i | 0.458427 | + | 0.888732i | \(0.348413\pi\) | ||||
−0.458427 | + | 0.888732i | \(0.651587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −102.589 | −0.284180 | ||||||||
\(362\) | 485.116 | 1.34010 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −115.789 | −0.318102 | ||||||||
\(365\) | 202.029 | − | 7.04115i | 0.553504 | − | 0.0192908i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 370.600i | 1.00981i | 0.863176 | + | 0.504904i | \(0.168472\pi\) | ||||
−0.863176 | + | 0.504904i | \(0.831528\pi\) | |||||||
\(368\) | −173.112 | −0.470412 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 316.828 | − | 11.0422i | 0.856292 | − | 0.0298437i | ||||
\(371\) | − | 585.103i | − | 1.57710i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 514.661i | 1.37979i | 0.723911 | + | 0.689894i | \(0.242343\pi\) | ||||
−0.723911 | + | 0.689894i | \(0.757657\pi\) | |||||||
\(374\) | 691.927i | 1.85007i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 192.551 | 0.512103 | ||||||||
\(377\) | 119.884 | 0.317996 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −159.583 | −0.421063 | −0.210532 | − | 0.977587i | \(-0.567519\pi\) | ||||
−0.210532 | + | 0.977587i | \(0.567519\pi\) | |||||||
\(380\) | 5.59915 | + | 160.654i | 0.0147346 | + | 0.422774i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 17.8723i | − | 0.0467862i | ||||||
\(383\) | 448.043 | 1.16983 | 0.584913 | − | 0.811096i | \(-0.301129\pi\) | ||||
0.584913 | + | 0.811096i | \(0.301129\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −33.6414 | − | 965.258i | −0.0873802 | − | 2.50716i | ||||
\(386\) | 237.764i | 0.615969i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 239.772i | 0.617970i | ||||||||
\(389\) | 558.830i | 1.43658i | 0.695743 | + | 0.718291i | \(0.255075\pi\) | ||||
−0.695743 | + | 0.718291i | \(0.744925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1038.68 | 2.65647 | ||||||||
\(392\) | −115.363 | −0.294293 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −526.150 | −1.33541 | ||||||||
\(395\) | 5.78784 | + | 166.068i | 0.0146527 | + | 0.420425i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 266.143i | − | 0.670385i | −0.942150 | − | 0.335192i | \(-0.891199\pi\) | ||
0.942150 | − | 0.335192i | \(-0.108801\pi\) | |||||||
\(398\) | 327.845 | 0.823731 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −99.7574 | + | 6.96198i | −0.249393 | + | 0.0174050i | ||||
\(401\) | 17.4204i | 0.0434423i | 0.999764 | + | 0.0217212i | \(0.00691460\pi\) | ||||
−0.999764 | + | 0.0217212i | \(0.993085\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 186.395i | − | 0.462518i | ||||||
\(404\) | 44.1549i | 0.109294i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 262.938 | 0.647630 | ||||||||
\(407\) | −913.972 | −2.24563 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −445.763 | −1.08989 | −0.544943 | − | 0.838473i | \(-0.683449\pi\) | ||||
−0.544943 | + | 0.838473i | \(0.683449\pi\) | |||||||
\(410\) | 339.847 | − | 11.8444i | 0.828895 | − | 0.0288888i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 36.7743i | 0.0892581i | ||||||||
\(413\) | 477.960 | 1.15729 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.95583 | + | 113.503i | 0.00953213 | + | 0.273502i | ||||
\(416\) | − | 34.5626i | − | 0.0830831i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 463.448i | − | 1.10873i | ||||||
\(419\) | 357.460i | 0.853127i | 0.904458 | + | 0.426563i | \(0.140276\pi\) | ||||
−0.904458 | + | 0.426563i | \(0.859724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 575.027 | 1.36586 | 0.682930 | − | 0.730484i | \(-0.260705\pi\) | ||||
0.682930 | + | 0.730484i | \(0.260705\pi\) | |||||||
\(422\) | 29.5588 | 0.0700445 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 174.651 | 0.411912 | ||||||||
\(425\) | 598.549 | − | 41.7722i | 1.40835 | − | 0.0982876i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 464.280i | 1.08731i | ||||||||
\(428\) | 121.720 | 0.284393 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 339.944 | − | 11.8478i | 0.790566 | − | 0.0275530i | ||||
\(431\) | 181.318i | 0.420691i | 0.977627 | + | 0.210346i | \(0.0674589\pi\) | ||||
−0.977627 | + | 0.210346i | \(0.932541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 705.627i | − | 1.62962i | −0.579726 | − | 0.814811i | \(-0.696840\pi\) | ||
0.579726 | − | 0.814811i | \(-0.303160\pi\) | |||||||
\(434\) | − | 408.813i | − | 0.941965i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 160.978 | 0.369216 | ||||||||
\(437\) | −695.700 | −1.59199 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 285.553 | 0.650463 | 0.325231 | − | 0.945634i | \(-0.394558\pi\) | ||||
0.325231 | + | 0.945634i | \(0.394558\pi\) | |||||||
\(440\) | 288.126 | − | 10.0418i | 0.654831 | − | 0.0228223i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 207.377i | 0.469179i | ||||||||
\(443\) | 706.104 | 1.59391 | 0.796957 | − | 0.604036i | \(-0.206442\pi\) | ||||
0.796957 | + | 0.604036i | \(0.206442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −397.392 | + | 13.8500i | −0.893015 | + | 0.0311235i | ||||
\(446\) | − | 22.3064i | − | 0.0500144i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 75.8048i | − | 0.169207i | ||||||
\(449\) | − | 505.807i | − | 1.12652i | −0.826280 | − | 0.563260i | \(-0.809547\pi\) | ||
0.826280 | − | 0.563260i | \(-0.190453\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −980.376 | −2.17378 | ||||||||
\(452\) | −45.5113 | −0.100689 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −482.736 | −1.06330 | ||||||||
\(455\) | −10.0826 | − | 289.297i | −0.0221597 | − | 0.635818i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 710.680i | 1.55510i | 0.628822 | + | 0.777550i | \(0.283538\pi\) | ||||
−0.628822 | + | 0.777550i | \(0.716462\pi\) | |||||||
\(458\) | 170.346 | 0.371934 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.0741 | − | 432.516i | −0.0327699 | − | 0.940253i | ||||
\(461\) | − | 137.615i | − | 0.298513i | −0.988799 | − | 0.149257i | \(-0.952312\pi\) | ||
0.988799 | − | 0.149257i | \(-0.0476880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 344.162i | − | 0.743330i | −0.928367 | − | 0.371665i | \(-0.878787\pi\) | ||
0.928367 | − | 0.371665i | \(-0.121213\pi\) | |||||||
\(464\) | 78.4858i | 0.169150i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 434.730 | 0.932896 | ||||||||
\(467\) | 322.715 | 0.691038 | 0.345519 | − | 0.938412i | \(-0.387703\pi\) | ||||
0.345519 | + | 0.938412i | \(0.387703\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −522.018 | −1.11304 | ||||||||
\(470\) | 16.7669 | + | 481.085i | 0.0356742 | + | 1.02359i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 142.669i | 0.302265i | ||||||||
\(473\) | −980.654 | −2.07327 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −400.904 | + | 27.9788i | −0.844009 | + | 0.0589027i | ||||
\(476\) | 454.832i | 0.955530i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 168.409i | − | 0.352321i | ||||||
\(479\) | 85.1304i | 0.177725i | 0.996044 | + | 0.0888626i | \(0.0283232\pi\) | ||||
−0.996044 | + | 0.0888626i | \(0.971677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −273.926 | −0.569493 | ||||||||
\(482\) | −444.911 | −0.923053 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −589.173 | −1.21730 | ||||||||
\(485\) | −599.067 | + | 20.8788i | −1.23519 | + | 0.0430491i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 437.344i | − | 0.898037i | −0.893522 | − | 0.449018i | \(-0.851774\pi\) | ||
0.893522 | − | 0.449018i | \(-0.148226\pi\) | |||||||
\(488\) | −138.586 | −0.283987 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.0455 | − | 288.232i | −0.0205011 | − | 0.588229i | ||||
\(491\) | 679.475i | 1.38386i | 0.721965 | + | 0.691930i | \(0.243239\pi\) | ||||
−0.721965 | + | 0.691930i | \(0.756761\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 470.919i | − | 0.955211i | ||||||
\(494\) | − | 138.900i | − | 0.281174i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 122.029 | 0.246026 | ||||||||
\(497\) | 223.607 | 0.449913 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 300.560 | 0.602325 | 0.301162 | − | 0.953573i | \(-0.402625\pi\) | ||||
0.301162 | + | 0.953573i | \(0.402625\pi\) | |||||||
\(500\) | −26.0810 | − | 248.636i | −0.0521621 | − | 0.497272i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 209.577i | 0.417484i | ||||||||
\(503\) | 371.067 | 0.737707 | 0.368853 | − | 0.929488i | \(-0.379750\pi\) | ||||
0.368853 | + | 0.929488i | \(0.379750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −110.320 | + | 3.84490i | −0.218456 | + | 0.00761367i | ||||
\(506\) | 1247.70i | 2.46582i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 146.712i | 0.288804i | ||||||||
\(509\) | − | 581.653i | − | 1.14274i | −0.820693 | − | 0.571369i | \(-0.806413\pi\) | ||
0.820693 | − | 0.571369i | \(-0.193587\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −383.101 | −0.749709 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 416.225 | 0.809777 | ||||||||
\(515\) | −91.8800 | + | 3.20222i | −0.178408 | + | 0.00621791i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1387.81i | − | 2.68436i | ||||||
\(518\) | −600.792 | −1.15983 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 86.3540 | − | 3.00963i | 0.166065 | − | 0.00578775i | ||||
\(521\) | − | 1006.68i | − | 1.93222i | −0.258138 | − | 0.966108i | \(-0.583109\pi\) | ||
0.258138 | − | 0.966108i | \(-0.416891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 674.227i | 1.28915i | 0.764540 | + | 0.644576i | \(0.222966\pi\) | ||||
−0.764540 | + | 0.644576i | \(0.777034\pi\) | |||||||
\(524\) | 182.102i | 0.347522i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −98.2376 | −0.186763 | ||||||||
\(527\) | −732.180 | −1.38934 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1343.98 | 2.54060 | ||||||||
\(530\) | 15.2082 | + | 436.362i | 0.0286947 | + | 0.823325i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 304.644i | − | 0.572639i | ||||||
\(533\) | −293.828 | −0.551272 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.5991 | + | 304.116i | 0.0198114 | + | 0.568441i | ||||
\(536\) | − | 155.820i | − | 0.290709i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 371.174i | − | 0.689915i | ||||||
\(539\) | 831.480i | 1.54263i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 178.075 | 0.329159 | 0.164579 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164579 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(542\) | −530.485 | −0.978755 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −135.766 | −0.249569 | ||||||||
\(545\) | 14.0176 | + | 402.202i | 0.0257204 | + | 0.737985i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 206.149i | − | 0.376873i | −0.982085 | − | 0.188436i | \(-0.939658\pi\) | ||
0.982085 | − | 0.188436i | \(-0.0603419\pi\) | |||||||
\(548\) | −55.7674 | −0.101765 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.1786 | + | 719.003i | 0.0912338 | + | 1.30728i | ||||
\(551\) | 315.418i | 0.572447i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 314.910i | − | 0.569457i | ||||||
\(554\) | 206.999i | 0.373644i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 69.4759 | 0.124957 | ||||||||
\(557\) | 37.8724 | 0.0679935 | 0.0339968 | − | 0.999422i | \(-0.489176\pi\) | ||||
0.0339968 | + | 0.999422i | \(0.489176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −293.911 | −0.525781 | ||||||||
\(560\) | 189.397 | − | 6.60090i | 0.338209 | − | 0.0117873i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 111.962i | 0.199221i | ||||||||
\(563\) | −317.255 | −0.563508 | −0.281754 | − | 0.959487i | \(-0.590916\pi\) | ||||
−0.281754 | + | 0.959487i | \(0.590916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.96301 | − | 113.709i | −0.00701418 | − | 0.201255i | ||||
\(566\) | − | 305.931i | − | 0.540513i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 66.7457i | 0.117510i | ||||||||
\(569\) | − | 403.753i | − | 0.709584i | −0.934945 | − | 0.354792i | \(-0.884552\pi\) | ||
0.934945 | − | 0.354792i | \(-0.115448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 284.074 | 0.497502 | 0.248751 | − | 0.968567i | \(-0.419980\pi\) | ||||
0.248751 | + | 0.968567i | \(0.419980\pi\) | |||||||
\(572\) | −249.110 | −0.435508 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −644.442 | −1.12272 | ||||||||
\(575\) | 1079.32 | − | 75.3250i | 1.87708 | − | 0.131000i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 105.236i | 0.182386i | 0.995833 | + | 0.0911928i | \(0.0290679\pi\) | ||||
−0.995833 | + | 0.0911928i | \(0.970932\pi\) | |||||||
\(578\) | 405.893 | 0.702237 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −196.095 | + | 6.83436i | −0.338096 | + | 0.0117834i | ||||
\(581\) | − | 215.233i | − | 0.370452i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1258.80i | − | 2.15917i | ||||||
\(584\) | − | 114.354i | − | 0.195812i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 588.782 | 1.00475 | ||||||||
\(587\) | 877.574 | 1.49502 | 0.747508 | − | 0.664253i | \(-0.231250\pi\) | ||||
0.747508 | + | 0.664253i | \(0.231250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 490.409 | 0.832613 | ||||||||
\(590\) | −356.456 | + | 12.4233i | −0.604163 | + | 0.0210564i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 179.334i | − | 0.302929i | ||||||
\(593\) | 47.7971 | 0.0806022 | 0.0403011 | − | 0.999188i | \(-0.487168\pi\) | ||||
0.0403011 | + | 0.999188i | \(0.487168\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1136.39 | + | 39.6057i | −1.90990 | + | 0.0665643i | ||||
\(596\) | − | 0.634137i | − | 0.00106399i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 373.949i | 0.625333i | ||||||||
\(599\) | − | 1137.50i | − | 1.89900i | −0.313761 | − | 0.949502i | \(-0.601589\pi\) | ||
0.313761 | − | 0.949502i | \(-0.398411\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 190.726 | 0.317348 | 0.158674 | − | 0.987331i | \(-0.449278\pi\) | ||||
0.158674 | + | 0.987331i | \(0.449278\pi\) | |||||||
\(602\) | −644.625 | −1.07081 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −210.655 | −0.348767 | ||||||||
\(605\) | −51.3037 | − | 1472.04i | −0.0847996 | − | 2.43312i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 988.920i | − | 1.62919i | −0.580028 | − | 0.814597i | \(-0.696958\pi\) | ||
0.580028 | − | 0.814597i | \(-0.303042\pi\) | |||||||
\(608\) | 90.9349 | 0.149564 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0677 | − | 346.254i | −0.0197831 | − | 0.567630i | ||||
\(611\) | − | 415.941i | − | 0.680754i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 131.155i | − | 0.213956i | −0.994261 | − | 0.106978i | \(-0.965882\pi\) | ||
0.994261 | − | 0.106978i | \(-0.0341175\pi\) | |||||||
\(614\) | − | 468.912i | − | 0.763701i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −546.364 | −0.886955 | ||||||||
\(617\) | 433.317 | 0.702296 | 0.351148 | − | 0.936320i | \(-0.385791\pi\) | ||||
0.351148 | + | 0.936320i | \(0.385791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 579.893 | 0.936823 | 0.468411 | − | 0.883511i | \(-0.344827\pi\) | ||||
0.468411 | + | 0.883511i | \(0.344827\pi\) | |||||||
\(620\) | 10.6260 | + | 304.887i | 0.0171387 | + | 0.491754i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 556.589i | − | 0.894837i | ||||||
\(623\) | 753.562 | 1.20957 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 618.941 | − | 86.8136i | 0.990306 | − | 0.138902i | ||||
\(626\) | 359.394i | 0.574112i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 91.2046i | − | 0.145230i | ||||||
\(629\) | 1076.01i | 1.71067i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1026.45 | 1.62671 | 0.813354 | − | 0.581768i | \(-0.197639\pi\) | ||||
0.813354 | + | 0.581768i | \(0.197639\pi\) | |||||||
\(632\) | 93.9993 | 0.148733 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −610.916 | −0.963591 | ||||||||
\(635\) | −366.559 | + | 12.7754i | −0.577258 | + | 0.0201187i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 249.202i | 0.391213i | ||||||||
\(638\) | 565.688 | 0.886658 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.97034 | + | 56.5342i | 0.00307866 | + | 0.0883347i | ||||
\(641\) | − | 326.380i | − | 0.509173i | −0.967050 | − | 0.254586i | \(-0.918061\pi\) | ||
0.967050 | − | 0.254586i | \(-0.0819394\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 558.564i | 0.868685i | 0.900748 | + | 0.434342i | \(0.143019\pi\) | ||||
−0.900748 | + | 0.434342i | \(0.856981\pi\) | |||||||
\(644\) | 820.168i | 1.27355i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −545.614 | −0.844604 | ||||||||
\(647\) | −404.040 | −0.624483 | −0.312241 | − | 0.950003i | \(-0.601080\pi\) | ||||
−0.312241 | + | 0.950003i | \(0.601080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1028.29 | 1.58442 | ||||||||
\(650\) | 15.0390 | + | 215.492i | 0.0231369 | + | 0.331526i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 305.587i | − | 0.468692i | ||||||
\(653\) | −714.002 | −1.09342 | −0.546709 | − | 0.837323i | \(-0.684120\pi\) | ||||
−0.546709 | + | 0.837323i | \(0.684120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −454.978 | + | 15.8570i | −0.694623 | + | 0.0242091i | ||||
\(656\) | − | 192.363i | − | 0.293237i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 912.267i | − | 1.38642i | ||||||
\(659\) | 127.690i | 0.193763i | 0.995296 | + | 0.0968817i | \(0.0308868\pi\) | ||||
−0.995296 | + | 0.0968817i | \(0.969113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −404.692 | −0.612242 | −0.306121 | − | 0.951993i | \(-0.599031\pi\) | ||||
−0.306121 | + | 0.951993i | \(0.599031\pi\) | |||||||
\(662\) | 271.149 | 0.409591 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 64.2461 | 0.0967561 | ||||||||
\(665\) | 761.147 | − | 26.5277i | 1.14458 | − | 0.0398912i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 849.175i | − | 1.27313i | ||||||
\(668\) | −27.4568 | −0.0411030 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 389.314 | − | 13.5685i | 0.581066 | − | 0.0202514i | ||||
\(671\) | 998.859i | 1.48861i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1239.08i | 1.84112i | 0.390595 | + | 0.920562i | \(0.372269\pi\) | ||||
−0.390595 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(674\) | − | 359.365i | − | 0.533183i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 263.339 | 0.389555 | ||||||||
\(677\) | 679.087 | 1.00308 | 0.501541 | − | 0.865134i | \(-0.332766\pi\) | ||||
0.501541 | + | 0.865134i | \(0.332766\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1135.99 | 1.67304 | ||||||||
\(680\) | −11.8221 | − | 339.208i | −0.0173855 | − | 0.498835i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 879.526i | − | 1.28963i | ||||||
\(683\) | −439.600 | −0.643632 | −0.321816 | − | 0.946802i | \(-0.604293\pi\) | ||||
−0.321816 | + | 0.946802i | \(0.604293\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85610 | − | 139.334i | −0.00708919 | − | 0.203407i | ||||
\(686\) | − | 110.059i | − | 0.160436i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 192.418i | − | 0.279677i | ||||||
\(689\) | − | 377.274i | − | 0.547567i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −324.689 | −0.469883 | −0.234941 | − | 0.972010i | \(-0.575490\pi\) | ||||
−0.234941 | + | 0.972010i | \(0.575490\pi\) | |||||||
\(692\) | −20.8614 | −0.0301466 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −453.673 | −0.653707 | ||||||||
\(695\) | 6.04979 | + | 173.584i | 0.00870474 | + | 0.249761i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1154.19i | 1.65594i | ||||||||
\(698\) | 430.662 | 0.616995 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 32.9845 | + | 472.630i | 0.0471207 | + | 0.675186i | ||||
\(701\) | − | 319.512i | − | 0.455795i | −0.973685 | − | 0.227898i | \(-0.926815\pi\) | ||
0.973685 | − | 0.227898i | \(-0.0731851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 720.706i | − | 1.02519i | ||||||
\(704\) | − | 163.087i | − | 0.231658i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 305.128 | 0.432193 | ||||||||
\(707\) | 209.197 | 0.295894 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1106.62 | −1.56082 | −0.780411 | − | 0.625267i | \(-0.784990\pi\) | ||||
−0.780411 | + | 0.625267i | \(0.784990\pi\) | |||||||
\(710\) | −166.763 | + | 5.81206i | −0.234877 | + | 0.00818600i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 224.935i | 0.315920i | ||||||||
\(713\) | −1320.29 | −1.85174 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.6919 | − | 622.398i | −0.0303384 | − | 0.870487i | ||||
\(716\) | − | 124.930i | − | 0.174483i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 902.424i | 1.25686i | ||||||||
\(719\) | − | 992.085i | − | 1.37981i | −0.723899 | − | 0.689906i | \(-0.757652\pi\) | ||
0.723899 | − | 0.689906i | \(-0.242348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 174.229 | 0.241650 | ||||||||
\(722\) | −145.083 | −0.200945 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 686.058 | 0.947594 | ||||||||
\(725\) | −34.1511 | − | 489.346i | −0.0471049 | − | 0.674960i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.95114i | − | 0.00956140i | −0.999989 | − | 0.00478070i | \(-0.998478\pi\) | ||
0.999989 | − | 0.00478070i | \(-0.00152175\pi\) | |||||||
\(728\) | −163.751 | −0.224932 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 285.712 | − | 9.95769i | 0.391386 | − | 0.0136407i | ||||
\(731\) | 1154.52i | 1.57937i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 249.539i | − | 0.340436i | −0.985406 | − | 0.170218i | \(-0.945553\pi\) | ||
0.985406 | − | 0.170218i | \(-0.0544471\pi\) | |||||||
\(734\) | 524.107i | 0.714042i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −244.817 | −0.332631 | ||||||||
\(737\) | −1123.08 | −1.52385 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −961.297 | −1.30081 | −0.650404 | − | 0.759588i | \(-0.725400\pi\) | ||||
−0.650404 | + | 0.759588i | \(0.725400\pi\) | |||||||
\(740\) | 448.063 | − | 15.6160i | 0.605490 | − | 0.0211027i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 827.460i | − | 1.11518i | ||||||
\(743\) | 796.752 | 1.07234 | 0.536172 | − | 0.844108i | \(-0.319870\pi\) | ||||
0.536172 | + | 0.844108i | \(0.319870\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.58438 | − | 0.0552192i | 0.00212669 | − | 7.41197e-5i | ||||
\(746\) | 727.840i | 0.975657i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 978.533i | 1.30820i | ||||||||
\(749\) | − | 576.686i | − | 0.769941i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 306.137 | 0.407639 | 0.203820 | − | 0.979008i | \(-0.434664\pi\) | ||||
0.203820 | + | 0.979008i | \(0.434664\pi\) | |||||||
\(752\) | 272.308 | 0.362112 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 169.542 | 0.224857 | ||||||||
\(755\) | −18.3434 | − | 526.319i | −0.0242958 | − | 0.697111i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 411.616i | − | 0.543746i | −0.962333 | − | 0.271873i | \(-0.912357\pi\) | ||
0.962333 | − | 0.271873i | \(-0.0876431\pi\) | |||||||
\(758\) | −225.684 | −0.297737 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.91840 | + | 227.199i | 0.0104189 | + | 0.298946i | ||||
\(761\) | − | 535.619i | − | 0.703835i | −0.936031 | − | 0.351918i | \(-0.885530\pi\) | ||
0.936031 | − | 0.351918i | \(-0.114470\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 762.683i | − | 0.999584i | ||||||
\(764\) | − | 25.2753i | − | 0.0330829i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 633.629 | 0.827192 | ||||||||
\(767\) | 308.188 | 0.401810 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1081.83 | −1.40680 | −0.703402 | − | 0.710792i | \(-0.748337\pi\) | ||||
−0.703402 | + | 0.710792i | \(0.748337\pi\) | |||||||
\(770\) | −47.5761 | − | 1365.08i | −0.0617871 | − | 1.77283i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 336.249i | 0.435556i | ||||||||
\(773\) | −166.623 | −0.215554 | −0.107777 | − | 0.994175i | \(-0.534373\pi\) | ||||
−0.107777 | + | 0.994175i | \(0.534373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −760.830 | + | 53.0977i | −0.981717 | + | 0.0685132i | ||||
\(776\) | 339.089i | 0.436971i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 790.306i | 1.01582i | ||||||||
\(779\) | − | 773.068i | − | 0.992385i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 481.071 | 0.615968 | ||||||||
\(782\) | 1468.91 | 1.87841 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −163.148 | −0.208097 | ||||||||
\(785\) | 227.873 | − | 7.94188i | 0.290284 | − | 0.0101170i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 406.762i | 0.516852i | 0.966031 | + | 0.258426i | \(0.0832038\pi\) | ||||
−0.966031 | + | 0.258426i | \(0.916796\pi\) | |||||||
\(788\) | −744.089 | −0.944275 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.18524 | + | 234.856i | 0.0103611 | + | 0.297286i | ||||
\(791\) | 215.623i | 0.272596i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 299.368i | 0.377513i | ||||||||
\(794\) | − | 376.383i | − | 0.474034i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 463.643 | 0.582466 | ||||||||
\(797\) | −103.236 | −0.129530 | −0.0647652 | − | 0.997901i | \(-0.520630\pi\) | ||||
−0.0647652 | + | 0.997901i | \(0.520630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1633.86 | −2.04488 | ||||||||
\(800\) | −141.078 | + | 9.84573i | −0.176348 | + | 0.0123072i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.6361i | 0.0307184i | ||||||||
\(803\) | −824.210 | −1.02641 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2049.18 | + | 71.4183i | −2.54556 | + | 0.0887183i | ||||
\(806\) | − | 263.602i | − | 0.327050i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 62.4444i | 0.0772827i | ||||||||
\(809\) | − | 833.545i | − | 1.03034i | −0.857088 | − | 0.515170i | \(-0.827729\pi\) | ||
0.857088 | − | 0.515170i | \(-0.172271\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 814.193 | 1.00394 | 0.501968 | − | 0.864886i | \(-0.332609\pi\) | ||||
0.501968 | + | 0.864886i | \(0.332609\pi\) | |||||||
\(812\) | 371.850 | 0.457943 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1292.55 | −1.58790 | ||||||||
\(815\) | 763.504 | − | 26.6098i | 0.936815 | − | 0.0326501i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 773.287i | − | 0.946496i | ||||||
\(818\) | −630.405 | −0.770666 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 480.616 | − | 16.7505i | 0.586118 | − | 0.0204275i | ||||
\(821\) | − | 154.644i | − | 0.188361i | −0.995555 | − | 0.0941803i | \(-0.969977\pi\) | ||
0.995555 | − | 0.0941803i | \(-0.0300230\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1103.86i | 1.34127i | 0.741788 | + | 0.670635i | \(0.233978\pi\) | ||||
−0.741788 | + | 0.670635i | \(0.766022\pi\) | |||||||
\(824\) | 52.0068i | 0.0631150i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 675.937 | 0.818326 | ||||||||
\(827\) | 423.629 | 0.512248 | 0.256124 | − | 0.966644i | \(-0.417554\pi\) | ||||
0.256124 | + | 0.966644i | \(0.417554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 325.734 | 0.392924 | 0.196462 | − | 0.980511i | \(-0.437055\pi\) | ||||
0.196462 | + | 0.980511i | \(0.437055\pi\) | |||||||
\(830\) | 5.59439 | + | 160.518i | 0.00674023 | + | 0.193395i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 48.8789i | − | 0.0587486i | ||||||
\(833\) | 978.895 | 1.17514 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.39087 | − | 68.6003i | −0.00286332 | − | 0.0821561i | ||||
\(836\) | − | 655.415i | − | 0.783989i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 505.525i | 0.603252i | ||||||||
\(839\) | 1213.40i | 1.44624i | 0.690721 | + | 0.723121i | \(0.257293\pi\) | ||||
−0.690721 | + | 0.723121i | \(0.742707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 455.998 | 0.542210 | ||||||||
\(842\) | 813.211 | 0.965809 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 41.8024 | 0.0495289 | ||||||||
\(845\) | 22.9310 | + | 657.949i | 0.0271372 | + | 0.778637i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2791.38i | 3.29561i | ||||||||
\(848\) | 246.994 | 0.291266 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 846.476 | − | 59.0749i | 0.995855 | − | 0.0694999i | ||||
\(851\) | 1940.30i | 2.28002i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0492i | 0.0410893i | 0.999789 | + | 0.0205446i | \(0.00654002\pi\) | ||||
−0.999789 | + | 0.0205446i | \(0.993460\pi\) | |||||||
\(854\) | 656.591i | 0.768842i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 172.138 | 0.201096 | ||||||||
\(857\) | −1097.41 | −1.28053 | −0.640265 | − | 0.768154i | \(-0.721175\pi\) | ||||
−0.640265 | + | 0.768154i | \(0.721175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 904.289 | 1.05272 | 0.526362 | − | 0.850261i | \(-0.323556\pi\) | ||||
0.526362 | + | 0.850261i | \(0.323556\pi\) | |||||||
\(860\) | 480.753 | − | 16.7553i | 0.559015 | − | 0.0194829i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 256.422i | 0.297473i | ||||||||
\(863\) | 179.328 | 0.207796 | 0.103898 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103898 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.81656 | − | 52.1219i | −0.00210007 | − | 0.0602566i | ||||
\(866\) | − | 997.907i | − | 1.15232i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 578.149i | − | 0.666070i | ||||||
\(869\) | − | 677.501i | − | 0.779633i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −336.597 | −0.386449 | ||||||||
\(872\) | 227.658 | 0.261075 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −983.868 | −1.12571 | ||||||||
\(875\) | −1177.99 | + | 123.567i | −1.34627 | + | 0.141219i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1207.53i | 1.37689i | 0.725290 | + | 0.688443i | \(0.241706\pi\) | ||||
−0.725290 | + | 0.688443i | \(0.758294\pi\) | |||||||
\(878\) | 403.833 | 0.459947 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 407.471 | − | 14.2013i | 0.463036 | − | 0.0161378i | ||||
\(881\) | − | 407.569i | − | 0.462621i | −0.972880 | − | 0.231311i | \(-0.925699\pi\) | ||
0.972880 | − | 0.231311i | \(-0.0743013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 85.9086i | 0.0972918i | 0.998816 | + | 0.0486459i | \(0.0154906\pi\) | ||||
−0.998816 | + | 0.0486459i | \(0.984509\pi\) | |||||||
\(884\) | 293.276i | 0.331760i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 998.582 | 1.12707 | ||||||||
\(887\) | −398.565 | −0.449340 | −0.224670 | − | 0.974435i | \(-0.572130\pi\) | ||||
−0.224670 | + | 0.974435i | \(0.572130\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 695.094 | 0.781883 | ||||||||
\(890\) | −561.997 | + | 19.5868i | −0.631457 | + | 0.0220077i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 31.5461i | − | 0.0353655i | ||||||
\(893\) | 1094.35 | 1.22548 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 312.136 | − | 10.8786i | 0.348755 | − | 0.0121549i | ||||
\(896\) | − | 107.204i | − | 0.119647i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 715.320i | − | 0.796570i | ||||||
\(899\) | 598.596i | 0.665847i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1481.97 | −1.64481 | ||||||||
\(902\) | −1386.46 | −1.53710 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −64.3626 | −0.0711976 | ||||||||
\(905\) | 59.7403 | + | 1714.10i | 0.0660114 | + | 1.89404i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1194.39i | 1.31686i | 0.752643 | + | 0.658429i | \(0.228779\pi\) | ||||
−0.752643 | + | 0.658429i | \(0.771221\pi\) | |||||||
\(908\) | −682.692 | −0.751863 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.2590 | − | 409.128i | −0.0156692 | − | 0.449591i | ||||
\(911\) | − | 1348.96i | − | 1.48074i | −0.672199 | − | 0.740371i | \(-0.734650\pi\) | ||
0.672199 | − | 0.740371i | \(-0.265350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 463.054i | − | 0.507179i | ||||||
\(914\) | 1005.05i | 1.09962i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 240.905 | 0.262997 | ||||||||
\(917\) | 862.761 | 0.940852 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1571.32 | 1.70982 | 0.854908 | − | 0.518780i | \(-0.173614\pi\) | ||||
0.854908 | + | 0.518780i | \(0.173614\pi\) | |||||||
\(920\) | −21.3181 | − | 611.670i | −0.0231718 | − | 0.664859i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 194.616i | − | 0.211081i | ||||||
\(923\) | 144.181 | 0.156210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 78.0325 | + | 1118.12i | 0.0843594 | + | 1.20878i | ||||
\(926\) | − | 486.718i | − | 0.525614i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 110.996i | 0.119607i | ||||||||
\(929\) | 251.609i | 0.270839i | 0.990788 | + | 0.135420i | \(0.0432382\pi\) | ||||
−0.990788 | + | 0.135420i | \(0.956762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −655.657 | −0.704250 | ||||||||
\(932\) | 614.800 | 0.659657 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 456.388 | 0.488638 | ||||||||
\(935\) | −2444.85 | + | 85.2083i | −2.61481 | + | 0.0911319i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1592.01i | 1.69905i | 0.527546 | + | 0.849526i | \(0.323112\pi\) | ||||
−0.527546 | + | 0.849526i | \(0.676888\pi\) | |||||||
\(938\) | −738.245 | −0.787041 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.7119 | + | 680.357i | 0.0252255 | + | 0.723784i | ||||
\(941\) | − | 1020.39i | − | 1.08437i | −0.840260 | − | 0.542184i | \(-0.817598\pi\) | ||
0.840260 | − | 0.542184i | \(-0.182402\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2081.27i | 2.20707i | ||||||||
\(944\) | 201.764i | 0.213734i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1386.85 | −1.46602 | ||||||||
\(947\) | −674.066 | −0.711791 | −0.355895 | − | 0.934526i | \(-0.615824\pi\) | ||||
−0.355895 | + | 0.934526i | \(0.615824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −247.024 | −0.260299 | ||||||||
\(950\) | −566.964 | + | 39.5680i | −0.596804 | + | 0.0416505i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 643.230i | 0.675662i | ||||||||
\(953\) | −836.522 | −0.877778 | −0.438889 | − | 0.898541i | \(-0.644628\pi\) | ||||
−0.438889 | + | 0.898541i | \(0.644628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.1499 | − | 2.20091i | 0.0661256 | − | 0.00230462i | ||||
\(956\) | − | 238.167i | − | 0.249128i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 120.393i | 0.125671i | ||||||||
\(959\) | 264.215i | 0.275511i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3083 | −0.0315383 | ||||||||
\(962\) | −387.390 | −0.402692 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −629.200 | −0.652697 | ||||||||
\(965\) | −840.112 | + | 29.2798i | −0.870583 | + | 0.0303417i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1018.19i | 1.05294i | 0.850194 | + | 0.526470i | \(0.176485\pi\) | ||||
−0.850194 | + | 0.526470i | \(0.823515\pi\) | |||||||
\(968\) | −833.216 | −0.860760 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −847.209 | + | 29.5271i | −0.873412 | + | 0.0304403i | ||||
\(971\) | 997.549i | 1.02734i | 0.857987 | + | 0.513671i | \(0.171715\pi\) | ||||
−0.857987 | + | 0.513671i | \(0.828285\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 329.163i | − | 0.338297i | ||||||
\(974\) | − | 618.498i | − | 0.635008i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −195.990 | −0.200809 | ||||||||
\(977\) | 1104.02 | 1.13001 | 0.565003 | − | 0.825089i | \(-0.308875\pi\) | ||||
0.565003 | + | 0.825089i | \(0.308875\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1621.22 | 1.65600 | ||||||||
\(980\) | −14.2065 | − | 407.622i | −0.0144965 | − | 0.415941i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 960.923i | 0.978537i | ||||||||
\(983\) | −1216.60 | −1.23764 | −0.618822 | − | 0.785531i | \(-0.712390\pi\) | ||||
−0.618822 | + | 0.785531i | \(0.712390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −64.7935 | − | 1859.09i | −0.0657802 | − | 1.88740i | ||||
\(986\) | − | 665.980i | − | 0.675436i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 196.434i | − | 0.198820i | ||||||
\(989\) | 2081.86i | 2.10502i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 736.595 | 0.743285 | 0.371642 | − | 0.928376i | \(-0.378795\pi\) | ||||
0.371642 | + | 0.928376i | \(0.378795\pi\) | |||||||
\(992\) | 172.575 | 0.173967 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 316.228 | 0.318137 | ||||||||
\(995\) | 40.3729 | + | 1158.40i | 0.0405758 | + | 1.16422i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 751.131i | − | 0.753391i | −0.926337 | − | 0.376696i | \(-0.877060\pi\) | ||
0.926337 | − | 0.376696i | \(-0.122940\pi\) | |||||||
\(998\) | 425.056 | 0.425908 | ||||||||
\(999\) | 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 | 810.3.b.c.809.18 | yes | 24 | |
3.2 | odd | 2 | inner | 810.3.b.c.809.7 | ✓ | 24 | |
5.4 | even | 2 | inner | 810.3.b.c.809.8 | yes | 24 | |
9.2 | odd | 6 | 810.3.j.g.539.12 | 24 | |||
9.4 | even | 3 | 810.3.j.h.269.6 | 24 | |||
9.5 | odd | 6 | 810.3.j.h.269.12 | 24 | |||
9.7 | even | 3 | 810.3.j.g.539.6 | 24 | |||
15.14 | odd | 2 | inner | 810.3.b.c.809.17 | yes | 24 | |
45.4 | even | 6 | 810.3.j.g.269.12 | 24 | |||
45.14 | odd | 6 | 810.3.j.g.269.6 | 24 | |||
45.29 | odd | 6 | 810.3.j.h.539.6 | 24 | |||
45.34 | even | 6 | 810.3.j.h.539.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
810.3.b.c.809.7 | ✓ | 24 | 3.2 | odd | 2 | inner | |
810.3.b.c.809.8 | yes | 24 | 5.4 | even | 2 | inner | |
810.3.b.c.809.17 | yes | 24 | 15.14 | odd | 2 | inner | |
810.3.b.c.809.18 | yes | 24 | 1.1 | even | 1 | trivial | |
810.3.j.g.269.6 | 24 | 45.14 | odd | 6 | |||
810.3.j.g.269.12 | 24 | 45.4 | even | 6 | |||
810.3.j.g.539.6 | 24 | 9.7 | even | 3 | |||
810.3.j.g.539.12 | 24 | 9.2 | odd | 6 | |||
810.3.j.h.269.6 | 24 | 9.4 | even | 3 | |||
810.3.j.h.269.12 | 24 | 9.5 | odd | 6 | |||
810.3.j.h.539.6 | 24 | 45.29 | odd | 6 | |||
810.3.j.h.539.12 | 24 | 45.34 | even | 6 |