Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(181,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.181");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.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: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} + \cdots + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.10 | ||
Root | \(0.198184 + 0.343264i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.181 |
Dual form | 315.3.h.d.181.9 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79155 | 1.39577 | 0.697887 | − | 0.716208i | \(-0.254124\pi\) | ||||
0.697887 | + | 0.716208i | \(0.254124\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.79273 | 0.948184 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.15782 | + | 5.63139i | 0.593975 | + | 0.804484i | ||||
\(8\) | −0.578591 | −0.0723239 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.24209i | 0.624209i | ||||||||
\(11\) | 18.9690 | 1.72445 | 0.862227 | − | 0.506522i | \(-0.169069\pi\) | ||||
0.862227 | + | 0.506522i | \(0.169069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.9807i | 0.844667i | 0.906441 | + | 0.422333i | \(0.138789\pi\) | ||||
−0.906441 | + | 0.422333i | \(0.861211\pi\) | |||||||
\(14\) | 11.6068 | + | 15.7203i | 0.829054 | + | 1.12288i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.7861 | −1.04913 | ||||||||
\(17\) | − | 22.3060i | − | 1.31212i | −0.754709 | − | 0.656060i | \(-0.772222\pi\) | ||
0.754709 | − | 0.656060i | \(-0.227778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.6057i | 1.03188i | 0.856625 | + | 0.515939i | \(0.172557\pi\) | ||||
−0.856625 | + | 0.515939i | \(0.827443\pi\) | |||||||
\(20\) | 8.48081i | 0.424041i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 52.9528 | 2.40695 | ||||||||
\(23\) | 31.9991 | 1.39126 | 0.695632 | − | 0.718399i | \(-0.255125\pi\) | ||||
0.695632 | + | 0.718399i | \(0.255125\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 30.6530i | 1.17896i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15.7695 | + | 21.3583i | 0.563197 | + | 0.762798i | ||||
\(29\) | −39.9967 | −1.37920 | −0.689598 | − | 0.724192i | \(-0.742213\pi\) | ||||
−0.689598 | + | 0.724192i | \(0.742213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 36.6641i | − | 1.18271i | −0.806411 | − | 0.591356i | \(-0.798593\pi\) | ||
0.806411 | − | 0.591356i | \(-0.201407\pi\) | |||||||
\(32\) | −44.5448 | −1.39203 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 62.2683i | − | 1.83142i | ||||||
\(35\) | −12.5922 | + | 9.29718i | −0.359776 | + | 0.265634i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.94699 | 0.241810 | 0.120905 | − | 0.992664i | \(-0.461420\pi\) | ||||
0.120905 | + | 0.992664i | \(0.461420\pi\) | |||||||
\(38\) | 54.7302i | 1.44027i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1.29377i | − | 0.0323442i | ||||||
\(41\) | − | 37.6320i | − | 0.917854i | −0.888474 | − | 0.458927i | \(-0.848234\pi\) | ||
0.888474 | − | 0.458927i | \(-0.151766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18.8702 | −0.438841 | −0.219421 | − | 0.975630i | \(-0.570417\pi\) | ||||
−0.219421 | + | 0.975630i | \(0.570417\pi\) | |||||||
\(44\) | 71.9443 | 1.63510 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 89.3269 | 1.94189 | ||||||||
\(47\) | − | 49.3786i | − | 1.05061i | −0.850914 | − | 0.525304i | \(-0.823952\pi\) | ||
0.850914 | − | 0.525304i | \(-0.176048\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.4250 | + | 46.8286i | −0.294388 | + | 0.955686i | ||||
\(50\) | −13.9577 | −0.279155 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 41.6468i | 0.800899i | ||||||||
\(53\) | −49.2398 | −0.929052 | −0.464526 | − | 0.885559i | \(-0.653775\pi\) | ||||
−0.464526 | + | 0.885559i | \(0.653775\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 42.4160i | 0.771199i | ||||||||
\(56\) | −2.40568 | − | 3.25827i | −0.0429586 | − | 0.0581834i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −111.653 | −1.92505 | ||||||||
\(59\) | 35.2173i | 0.596903i | 0.954425 | + | 0.298452i | \(0.0964701\pi\) | ||||
−0.954425 | + | 0.298452i | \(0.903530\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 63.4723i | − | 1.04053i | −0.854005 | − | 0.520265i | \(-0.825833\pi\) | ||
0.854005 | − | 0.520265i | \(-0.174167\pi\) | |||||||
\(62\) | − | 102.349i | − | 1.65080i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −57.2046 | −0.893821 | ||||||||
\(65\) | −24.5535 | −0.377746 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21.3544 | 0.318723 | 0.159361 | − | 0.987220i | \(-0.449057\pi\) | ||||
0.159361 | + | 0.987220i | \(0.449057\pi\) | |||||||
\(68\) | − | 84.6008i | − | 1.24413i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −35.1516 | + | 25.9535i | −0.502166 | + | 0.370764i | ||||
\(71\) | −36.2998 | −0.511265 | −0.255632 | − | 0.966774i | \(-0.582284\pi\) | ||||
−0.255632 | + | 0.966774i | \(0.582284\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.66818i | 0.0913449i | 0.998956 | + | 0.0456725i | \(0.0145431\pi\) | ||||
−0.998956 | + | 0.0456725i | \(0.985457\pi\) | |||||||
\(74\) | 24.9759 | 0.337513 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 74.3591i | 0.978409i | ||||||||
\(77\) | 78.8697 | + | 106.822i | 1.02428 | + | 1.38729i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.2015 | −0.205082 | −0.102541 | − | 0.994729i | \(-0.532697\pi\) | ||||
−0.102541 | + | 0.994729i | \(0.532697\pi\) | |||||||
\(80\) | − | 37.5349i | − | 0.469186i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 105.052i | − | 1.28112i | ||||||
\(83\) | − | 36.7822i | − | 0.443159i | −0.975142 | − | 0.221579i | \(-0.928879\pi\) | ||
0.975142 | − | 0.221579i | \(-0.0711212\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49.8778 | 0.586798 | ||||||||
\(86\) | −52.6770 | −0.612523 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.9753 | −0.124719 | ||||||||
\(89\) | − | 88.0954i | − | 0.989836i | −0.868940 | − | 0.494918i | \(-0.835198\pi\) | ||
0.868940 | − | 0.494918i | \(-0.164802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61.8364 | + | 45.6557i | −0.679520 | + | 0.501711i | ||||
\(92\) | 121.364 | 1.31917 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 137.843i | − | 1.46641i | ||||||
\(95\) | −43.8396 | −0.461470 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 133.810i | − | 1.37948i | −0.724055 | − | 0.689742i | \(-0.757724\pi\) | ||
0.724055 | − | 0.689742i | \(-0.242276\pi\) | |||||||
\(98\) | −40.2681 | + | 130.724i | −0.410899 | + | 1.33392i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.9637 | −0.189637 | ||||||||
\(101\) | 194.903i | 1.92973i | 0.262743 | + | 0.964866i | \(0.415373\pi\) | ||||
−0.262743 | + | 0.964866i | \(0.584627\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 41.2629i | 0.400610i | 0.979734 | + | 0.200305i | \(0.0641933\pi\) | ||||
−0.979734 | + | 0.200305i | \(0.935807\pi\) | |||||||
\(104\) | − | 6.35332i | − | 0.0610896i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −137.455 | −1.29675 | ||||||||
\(107\) | −29.7031 | −0.277599 | −0.138799 | − | 0.990321i | \(-0.544324\pi\) | ||||
−0.138799 | + | 0.990321i | \(0.544324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 91.7028 | 0.841310 | 0.420655 | − | 0.907221i | \(-0.361800\pi\) | ||||
0.420655 | + | 0.907221i | \(0.361800\pi\) | |||||||
\(110\) | 118.406i | 1.07642i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −69.7937 | − | 94.5290i | −0.623158 | − | 0.844009i | ||||
\(113\) | −2.98301 | −0.0263983 | −0.0131992 | − | 0.999913i | \(-0.504202\pi\) | ||||
−0.0131992 | + | 0.999913i | \(0.504202\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 71.5521i | 0.622192i | ||||||||
\(116\) | −151.697 | −1.30773 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 98.3107i | 0.833142i | ||||||||
\(119\) | 125.614 | − | 92.7445i | 1.05558 | − | 0.779366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 238.823 | 1.97374 | ||||||||
\(122\) | − | 177.186i | − | 1.45234i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 139.057i | − | 1.12143i | ||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 104.651 | 0.824023 | 0.412012 | − | 0.911179i | \(-0.364826\pi\) | ||||
0.412012 | + | 0.911179i | \(0.364826\pi\) | |||||||
\(128\) | 18.4901 | 0.144454 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −68.5423 | −0.527248 | ||||||||
\(131\) | − | 70.8051i | − | 0.540497i | −0.962791 | − | 0.270249i | \(-0.912894\pi\) | ||
0.962791 | − | 0.270249i | \(-0.0871059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −110.407 | + | 81.5169i | −0.830129 | + | 0.612909i | ||||
\(134\) | 59.6118 | 0.444864 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.9061i | 0.0948976i | ||||||||
\(137\) | 158.673 | 1.15820 | 0.579100 | − | 0.815256i | \(-0.303404\pi\) | ||||
0.579100 | + | 0.815256i | \(0.303404\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 54.4253i | − | 0.391549i | −0.980649 | − | 0.195774i | \(-0.937278\pi\) | ||
0.980649 | − | 0.195774i | \(-0.0627220\pi\) | |||||||
\(140\) | −47.7587 | + | 35.2617i | −0.341134 | + | 0.251869i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −101.333 | −0.713610 | ||||||||
\(143\) | 208.292i | 1.45659i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 89.4353i | − | 0.616795i | ||||||
\(146\) | 18.6145i | 0.127497i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 33.9335 | 0.229281 | ||||||||
\(149\) | −229.102 | −1.53760 | −0.768799 | − | 0.639490i | \(-0.779146\pi\) | ||||
−0.768799 | + | 0.639490i | \(0.779146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −197.735 | −1.30950 | −0.654750 | − | 0.755845i | \(-0.727226\pi\) | ||||
−0.654750 | + | 0.755845i | \(0.727226\pi\) | |||||||
\(152\) | − | 11.3437i | − | 0.0746294i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 220.169 | + | 298.198i | 1.42967 | + | 1.93635i | ||||
\(155\) | 81.9833 | 0.528925 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 211.036i | 1.34418i | 0.740470 | + | 0.672089i | \(0.234603\pi\) | ||||
−0.740470 | + | 0.672089i | \(0.765397\pi\) | |||||||
\(158\) | −45.2271 | −0.286248 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 99.6053i | − | 0.622533i | ||||||
\(161\) | 133.046 | + | 180.199i | 0.826375 | + | 1.11925i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 181.823 | 1.11548 | 0.557741 | − | 0.830015i | \(-0.311668\pi\) | ||||
0.557741 | + | 0.830015i | \(0.311668\pi\) | |||||||
\(164\) | − | 142.728i | − | 0.870295i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 102.679i | − | 0.618549i | ||||||
\(167\) | − | 101.160i | − | 0.605751i | −0.953030 | − | 0.302876i | \(-0.902053\pi\) | ||
0.953030 | − | 0.302876i | \(-0.0979467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 48.4250 | 0.286538 | ||||||||
\(170\) | 139.236 | 0.819037 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −71.5696 | −0.416102 | ||||||||
\(173\) | − | 109.976i | − | 0.635702i | −0.948141 | − | 0.317851i | \(-0.897039\pi\) | ||
0.948141 | − | 0.317851i | \(-0.102961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.7891 | − | 28.1569i | −0.118795 | − | 0.160897i | ||||
\(176\) | −318.415 | −1.80918 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 245.922i | − | 1.38159i | ||||||
\(179\) | −91.8832 | −0.513314 | −0.256657 | − | 0.966503i | \(-0.582621\pi\) | ||||
−0.256657 | + | 0.966503i | \(0.582621\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 62.8649i | 0.347320i | 0.984806 | + | 0.173660i | \(0.0555594\pi\) | ||||
−0.984806 | + | 0.173660i | \(0.944441\pi\) | |||||||
\(182\) | −172.619 | + | 127.450i | −0.948457 | + | 0.700275i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.5144 | −0.100622 | ||||||||
\(185\) | 20.0061i | 0.108141i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 423.123i | − | 2.26269i | ||||||
\(188\) | − | 187.280i | − | 0.996170i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −122.380 | −0.644107 | ||||||||
\(191\) | 75.9925 | 0.397866 | 0.198933 | − | 0.980013i | \(-0.436252\pi\) | ||||
0.198933 | + | 0.980013i | \(0.436252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.7530 | 0.117891 | 0.0589456 | − | 0.998261i | \(-0.481226\pi\) | ||||
0.0589456 | + | 0.998261i | \(0.481226\pi\) | |||||||
\(194\) | − | 373.537i | − | 1.92545i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −54.7102 | + | 177.609i | −0.279134 | + | 0.906166i | ||||
\(197\) | 137.485 | 0.697891 | 0.348946 | − | 0.937143i | \(-0.386540\pi\) | ||||
0.348946 | + | 0.937143i | \(0.386540\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 267.299i | 1.34321i | 0.740909 | + | 0.671606i | \(0.234395\pi\) | ||||
−0.740909 | + | 0.671606i | \(0.765605\pi\) | |||||||
\(200\) | 2.89296 | 0.0144648 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 544.081i | 2.69347i | ||||||||
\(203\) | −166.299 | − | 225.237i | −0.819208 | − | 1.10954i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 84.1478 | 0.410477 | ||||||||
\(206\) | 115.187i | 0.559161i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 184.323i | − | 0.886166i | ||||||
\(209\) | 371.900i | 1.77943i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −366.610 | −1.73749 | −0.868744 | − | 0.495261i | \(-0.835073\pi\) | ||||
−0.868744 | + | 0.495261i | \(0.835073\pi\) | |||||||
\(212\) | −186.753 | −0.880912 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −82.9175 | −0.387465 | ||||||||
\(215\) | − | 42.1950i | − | 0.196256i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 206.469 | − | 152.443i | 0.951472 | − | 0.702501i | ||||
\(218\) | 255.993 | 1.17428 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 160.872i | 0.731238i | ||||||||
\(221\) | 244.935 | 1.10830 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 282.872i | 1.26848i | 0.773134 | + | 0.634242i | \(0.218688\pi\) | ||||
−0.773134 | + | 0.634242i | \(0.781312\pi\) | |||||||
\(224\) | −185.210 | − | 250.849i | −0.826828 | − | 1.11986i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.32722 | −0.0368461 | ||||||||
\(227\) | − | 210.777i | − | 0.928534i | −0.885695 | − | 0.464267i | \(-0.846318\pi\) | ||
0.885695 | − | 0.464267i | \(-0.153682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 137.506i | 0.600464i | 0.953866 | + | 0.300232i | \(0.0970641\pi\) | ||||
−0.953866 | + | 0.300232i | \(0.902936\pi\) | |||||||
\(230\) | 199.741i | 0.868439i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 23.1417 | 0.0997488 | ||||||||
\(233\) | 77.7682 | 0.333769 | 0.166884 | − | 0.985976i | \(-0.446629\pi\) | ||||
0.166884 | + | 0.985976i | \(0.446629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 110.414 | 0.469846 | ||||||||
\(236\) | 133.570i | 0.565974i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 350.657 | − | 258.901i | 1.47335 | − | 1.08782i | ||||
\(239\) | 123.843 | 0.518173 | 0.259086 | − | 0.965854i | \(-0.416579\pi\) | ||||
0.259086 | + | 0.965854i | \(0.416579\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 155.802i | 0.646481i | 0.946317 | + | 0.323240i | \(0.104772\pi\) | ||||
−0.946317 | + | 0.323240i | \(0.895228\pi\) | |||||||
\(242\) | 666.684 | 2.75489 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 240.734i | − | 0.986613i | ||||||
\(245\) | −104.712 | − | 32.2553i | −0.427396 | − | 0.131654i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −215.283 | −0.871593 | ||||||||
\(248\) | 21.2135i | 0.0855383i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 31.2104i | − | 0.124842i | ||||||
\(251\) | 278.340i | 1.10892i | 0.832210 | + | 0.554461i | \(0.187076\pi\) | ||||
−0.832210 | + | 0.554461i | \(0.812924\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 606.990 | 2.39917 | ||||||||
\(254\) | 292.138 | 1.15015 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 280.434 | 1.09545 | ||||||||
\(257\) | 220.802i | 0.859151i | 0.903031 | + | 0.429575i | \(0.141337\pi\) | ||||
−0.903031 | + | 0.429575i | \(0.858663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37.2000 | + | 50.3839i | 0.143629 | + | 0.194533i | ||||
\(260\) | −93.1250 | −0.358173 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 197.656i | − | 0.754412i | ||||||
\(263\) | 17.3477 | 0.0659609 | 0.0329804 | − | 0.999456i | \(-0.489500\pi\) | ||||
0.0329804 | + | 0.999456i | \(0.489500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 110.103i | − | 0.415485i | ||||||
\(266\) | −308.207 | + | 227.558i | −1.15867 | + | 0.855483i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 80.9916 | 0.302207 | ||||||||
\(269\) | 499.213i | 1.85581i | 0.372816 | + | 0.927905i | \(0.378392\pi\) | ||||
−0.372816 | + | 0.927905i | \(0.621608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 330.005i | 1.21773i | 0.793273 | + | 0.608866i | \(0.208375\pi\) | ||||
−0.793273 | + | 0.608866i | \(0.791625\pi\) | |||||||
\(272\) | 374.431i | 1.37659i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 442.944 | 1.61659 | ||||||||
\(275\) | −94.8449 | −0.344891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 147.766 | 0.533452 | 0.266726 | − | 0.963772i | \(-0.414058\pi\) | ||||
0.266726 | + | 0.963772i | \(0.414058\pi\) | |||||||
\(278\) | − | 151.931i | − | 0.546513i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.28571 | − | 5.37926i | 0.0260204 | − | 0.0192117i | ||||
\(281\) | −353.405 | −1.25767 | −0.628834 | − | 0.777540i | \(-0.716467\pi\) | ||||
−0.628834 | + | 0.777540i | \(0.716467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 428.203i | − | 1.51308i | −0.653945 | − | 0.756542i | \(-0.726887\pi\) | ||
0.653945 | − | 0.756542i | \(-0.273113\pi\) | |||||||
\(284\) | −137.675 | −0.484773 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 581.457i | 2.03307i | ||||||||
\(287\) | 211.920 | − | 156.467i | 0.738399 | − | 0.545182i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −208.559 | −0.721657 | ||||||||
\(290\) | − | 249.663i | − | 0.860906i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 25.2906i | 0.0866117i | ||||||||
\(293\) | − | 402.632i | − | 1.37417i | −0.726577 | − | 0.687085i | \(-0.758890\pi\) | ||
0.726577 | − | 0.687085i | \(-0.241110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −78.7483 | −0.266943 | ||||||||
\(296\) | −5.17665 | −0.0174887 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −639.550 | −2.14614 | ||||||||
\(299\) | 351.371i | 1.17515i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −78.4589 | − | 106.265i | −0.260661 | − | 0.353041i | ||||
\(302\) | −551.986 | −1.82777 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 329.103i | − | 1.08258i | ||||||
\(305\) | 141.928 | 0.465339 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 92.7330i | 0.302062i | 0.988529 | + | 0.151031i | \(0.0482593\pi\) | ||||
−0.988529 | + | 0.151031i | \(0.951741\pi\) | |||||||
\(308\) | 299.132 | + | 405.146i | 0.971207 | + | 1.31541i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 228.860 | 0.738259 | ||||||||
\(311\) | − | 218.118i | − | 0.701343i | −0.936498 | − | 0.350672i | \(-0.885953\pi\) | ||
0.936498 | − | 0.350672i | \(-0.114047\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 293.684i | − | 0.938288i | −0.883122 | − | 0.469144i | \(-0.844562\pi\) | ||
0.883122 | − | 0.469144i | \(-0.155438\pi\) | |||||||
\(314\) | 589.117i | 1.87617i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −61.4479 | −0.194455 | ||||||||
\(317\) | −109.074 | −0.344081 | −0.172041 | − | 0.985090i | \(-0.555036\pi\) | ||||
−0.172041 | + | 0.985090i | \(0.555036\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −758.697 | −2.37836 | ||||||||
\(320\) | − | 127.913i | − | 0.399729i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 371.405 | + | 503.034i | 1.15343 | + | 1.56222i | ||||
\(323\) | 437.325 | 1.35395 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 54.9033i | − | 0.168933i | ||||||
\(326\) | 507.569 | 1.55696 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 21.7736i | 0.0663828i | ||||||||
\(329\) | 278.070 | − | 205.308i | 0.845197 | − | 0.624035i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 408.913 | 1.23539 | 0.617694 | − | 0.786419i | \(-0.288067\pi\) | ||||
0.617694 | + | 0.786419i | \(0.288067\pi\) | |||||||
\(332\) | − | 139.505i | − | 0.420196i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 282.394i | − | 0.845492i | ||||||
\(335\) | 47.7499i | 0.142537i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −299.269 | −0.888040 | −0.444020 | − | 0.896017i | \(-0.646448\pi\) | ||||
−0.444020 | + | 0.896017i | \(0.646448\pi\) | |||||||
\(338\) | 135.181 | 0.399942 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 189.173 | 0.556392 | ||||||||
\(341\) | − | 695.480i | − | 2.03953i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −323.687 | + | 113.472i | −0.943693 | + | 0.330823i | ||||
\(344\) | 10.9181 | 0.0317387 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 307.004i | − | 0.887296i | ||||||
\(347\) | −567.731 | −1.63611 | −0.818056 | − | 0.575138i | \(-0.804948\pi\) | ||||
−0.818056 | + | 0.575138i | \(0.804948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 141.703i | 0.406025i | 0.979176 | + | 0.203012i | \(0.0650732\pi\) | ||||
−0.979176 | + | 0.203012i | \(0.934927\pi\) | |||||||
\(350\) | −58.0338 | − | 78.6014i | −0.165811 | − | 0.224575i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −844.970 | −2.40048 | ||||||||
\(353\) | − | 452.435i | − | 1.28169i | −0.767672 | − | 0.640843i | \(-0.778585\pi\) | ||
0.767672 | − | 0.640843i | \(-0.221415\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 81.1688i | − | 0.228644i | ||||||
\(356\) | − | 334.123i | − | 0.938546i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −256.496 | −0.716470 | ||||||||
\(359\) | −174.670 | −0.486546 | −0.243273 | − | 0.969958i | \(-0.578221\pi\) | ||||
−0.243273 | + | 0.969958i | \(0.578221\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.3825 | −0.0647714 | ||||||||
\(362\) | 175.490i | 0.484780i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −234.529 | + | 173.160i | −0.644310 | + | 0.475714i | ||||
\(365\) | −14.9105 | −0.0408507 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 121.147i | − | 0.330101i | −0.986285 | − | 0.165051i | \(-0.947221\pi\) | ||
0.986285 | − | 0.165051i | \(-0.0527788\pi\) | |||||||
\(368\) | −537.139 | −1.45962 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 55.8479i | 0.150940i | ||||||||
\(371\) | −204.730 | − | 277.288i | −0.551834 | − | 0.747407i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −90.9075 | −0.243720 | −0.121860 | − | 0.992547i | \(-0.538886\pi\) | ||||
−0.121860 | + | 0.992547i | \(0.538886\pi\) | |||||||
\(374\) | − | 1181.17i | − | 3.15820i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.5700i | 0.0759841i | ||||||||
\(377\) | − | 439.190i | − | 1.16496i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −638.344 | −1.68429 | −0.842143 | − | 0.539254i | \(-0.818706\pi\) | ||||
−0.842143 | + | 0.539254i | \(0.818706\pi\) | |||||||
\(380\) | −166.272 | −0.437558 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 212.137 | 0.555331 | ||||||||
\(383\) | 176.395i | 0.460561i | 0.973124 | + | 0.230281i | \(0.0739644\pi\) | ||||
−0.973124 | + | 0.230281i | \(0.926036\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −238.861 | + | 176.358i | −0.620417 | + | 0.458073i | ||||
\(386\) | 63.5160 | 0.164549 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 507.506i | − | 1.30800i | ||||||
\(389\) | −249.521 | −0.641442 | −0.320721 | − | 0.947174i | \(-0.603925\pi\) | ||||
−0.320721 | + | 0.947174i | \(0.603925\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 713.772i | − | 1.82550i | ||||||
\(392\) | 8.34618 | − | 27.0946i | 0.0212913 | − | 0.0691189i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 383.795 | 0.974098 | ||||||||
\(395\) | − | 36.2276i | − | 0.0917154i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 186.071i | 0.468694i | 0.972153 | + | 0.234347i | \(0.0752951\pi\) | ||||
−0.972153 | + | 0.234347i | \(0.924705\pi\) | |||||||
\(398\) | 746.178i | 1.87482i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 83.9305 | 0.209826 | ||||||||
\(401\) | 188.067 | 0.468996 | 0.234498 | − | 0.972117i | \(-0.424655\pi\) | ||||
0.234498 | + | 0.972117i | \(0.424655\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 402.596 | 0.998997 | ||||||||
\(404\) | 739.215i | 1.82974i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −464.232 | − | 628.759i | −1.14343 | − | 1.54867i | ||||
\(407\) | 169.715 | 0.416991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 512.173i | 1.25226i | 0.779720 | + | 0.626128i | \(0.215361\pi\) | ||||
−0.779720 | + | 0.626128i | \(0.784639\pi\) | |||||||
\(410\) | 234.902 | 0.572933 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 156.499i | 0.379852i | ||||||||
\(413\) | −198.322 | + | 146.427i | −0.480199 | + | 0.354545i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 82.2475 | 0.198187 | ||||||||
\(416\) | − | 489.132i | − | 1.17580i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1038.18i | 2.48367i | ||||||||
\(419\) | 323.661i | 0.772461i | 0.922402 | + | 0.386231i | \(0.126223\pi\) | ||||
−0.922402 | + | 0.386231i | \(0.873777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −503.872 | −1.19685 | −0.598423 | − | 0.801180i | \(-0.704206\pi\) | ||||
−0.598423 | + | 0.801180i | \(0.704206\pi\) | |||||||
\(422\) | −1023.41 | −2.42514 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 28.4897 | 0.0671927 | ||||||||
\(425\) | 111.530i | 0.262424i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 357.437 | − | 263.907i | 0.837089 | − | 0.618049i | ||||
\(428\) | −112.656 | −0.263215 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 117.789i | − | 0.273929i | ||||||
\(431\) | −317.731 | −0.737195 | −0.368597 | − | 0.929589i | \(-0.620162\pi\) | ||||
−0.368597 | + | 0.929589i | \(0.620162\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 261.387i | 0.603665i | 0.953361 | + | 0.301833i | \(0.0975984\pi\) | ||||
−0.953361 | + | 0.301833i | \(0.902402\pi\) | |||||||
\(434\) | 576.369 | − | 425.551i | 1.32804 | − | 0.980532i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 347.805 | 0.797717 | ||||||||
\(437\) | 627.363i | 1.43561i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 789.513i | − | 1.79844i | −0.437501 | − | 0.899218i | \(-0.644137\pi\) | ||
0.437501 | − | 0.899218i | \(-0.355863\pi\) | |||||||
\(440\) | − | 24.5415i | − | 0.0557761i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 683.748 | 1.54694 | ||||||||
\(443\) | −585.242 | −1.32109 | −0.660544 | − | 0.750787i | \(-0.729674\pi\) | ||||
−0.660544 | + | 0.750787i | \(0.729674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 196.987 | 0.442668 | ||||||||
\(446\) | 789.651i | 1.77052i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −237.847 | − | 322.141i | −0.530907 | − | 0.719065i | ||||
\(449\) | −528.147 | −1.17627 | −0.588137 | − | 0.808761i | \(-0.700138\pi\) | ||||
−0.588137 | + | 0.808761i | \(0.700138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 713.842i | − | 1.58280i | ||||||
\(452\) | −11.3138 | −0.0250305 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 588.395i | − | 1.29602i | ||||||
\(455\) | −102.089 | − | 138.270i | −0.224372 | − | 0.303891i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −164.041 | −0.358953 | −0.179476 | − | 0.983762i | \(-0.557440\pi\) | ||||
−0.179476 | + | 0.983762i | \(0.557440\pi\) | |||||||
\(458\) | 383.855i | 0.838112i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 271.378i | 0.589952i | ||||||||
\(461\) | 399.626i | 0.866867i | 0.901186 | + | 0.433434i | \(0.142698\pi\) | ||||
−0.901186 | + | 0.433434i | \(0.857302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −680.267 | −1.46926 | −0.734630 | − | 0.678468i | \(-0.762644\pi\) | ||||
−0.734630 | + | 0.678468i | \(0.762644\pi\) | |||||||
\(464\) | 671.388 | 1.44696 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 217.093 | 0.465866 | ||||||||
\(467\) | − | 725.217i | − | 1.55293i | −0.630162 | − | 0.776464i | \(-0.717011\pi\) | ||
0.630162 | − | 0.776464i | \(-0.282989\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 88.7879 | + | 120.255i | 0.189313 | + | 0.256407i | ||||
\(470\) | 308.226 | 0.655799 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 20.3764i | − | 0.0431704i | ||||||
\(473\) | −357.948 | −0.756762 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 98.0284i | − | 0.206376i | ||||||
\(476\) | 476.420 | − | 351.755i | 1.00088 | − | 0.738982i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 345.714 | 0.723252 | ||||||||
\(479\) | − | 317.103i | − | 0.662010i | −0.943629 | − | 0.331005i | \(-0.892612\pi\) | ||
0.943629 | − | 0.331005i | \(-0.107388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 98.2439i | 0.204249i | ||||||||
\(482\) | 434.928i | 0.902341i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 905.791 | 1.87147 | ||||||||
\(485\) | 299.208 | 0.616924 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 353.125 | 0.725103 | 0.362551 | − | 0.931964i | \(-0.381906\pi\) | ||||
0.362551 | + | 0.931964i | \(0.381906\pi\) | |||||||
\(488\) | 36.7245i | 0.0752552i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −292.308 | − | 90.0421i | −0.596548 | − | 0.183759i | ||||
\(491\) | 343.280 | 0.699145 | 0.349572 | − | 0.936909i | \(-0.386327\pi\) | ||||
0.349572 | + | 0.936909i | \(0.386327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 892.167i | 1.80967i | ||||||||
\(494\) | −600.974 | −1.21655 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 615.447i | 1.24082i | ||||||||
\(497\) | −150.928 | − | 204.418i | −0.303678 | − | 0.411304i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −420.584 | −0.842853 | −0.421427 | − | 0.906863i | \(-0.638470\pi\) | ||||
−0.421427 | + | 0.906863i | \(0.638470\pi\) | |||||||
\(500\) | − | 42.4041i | − | 0.0848081i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 776.998i | 1.54780i | ||||||||
\(503\) | − | 183.030i | − | 0.363876i | −0.983310 | − | 0.181938i | \(-0.941763\pi\) | ||
0.983310 | − | 0.181938i | \(-0.0582370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −435.816 | −0.863002 | ||||||||
\(506\) | 1694.44 | 3.34870 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 396.913 | 0.781326 | ||||||||
\(509\) | − | 261.854i | − | 0.514448i | −0.966352 | − | 0.257224i | \(-0.917192\pi\) | ||
0.966352 | − | 0.257224i | \(-0.0828079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.5511 | + | 27.7251i | −0.0734855 | + | 0.0542566i | ||||
\(512\) | 708.885 | 1.38454 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 616.378i | 1.19918i | ||||||||
\(515\) | −92.2665 | −0.179158 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 936.662i | − | 1.81173i | ||||||
\(518\) | 103.846 | + | 140.649i | 0.200474 | + | 0.271523i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 14.2064 | 0.0273201 | ||||||||
\(521\) | 477.677i | 0.916846i | 0.888734 | + | 0.458423i | \(0.151586\pi\) | ||||
−0.888734 | + | 0.458423i | \(0.848414\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 770.784i | − | 1.47377i | −0.676016 | − | 0.736887i | \(-0.736295\pi\) | ||
0.676016 | − | 0.736887i | \(-0.263705\pi\) | |||||||
\(524\) | − | 268.545i | − | 0.512491i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.4269 | 0.0920664 | ||||||||
\(527\) | −817.829 | −1.55186 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 494.940 | 0.935614 | ||||||||
\(530\) | − | 307.359i | − | 0.579923i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −418.745 | + | 309.172i | −0.787114 | + | 0.581151i | ||||
\(533\) | 413.225 | 0.775281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 66.4181i | − | 0.124146i | ||||||
\(536\) | −12.3555 | −0.0230513 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1393.58i | 2.59029i | ||||||||
\(539\) | −273.628 | + | 888.292i | −0.507658 | + | 1.64804i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1054.53 | 1.94922 | 0.974609 | − | 0.223912i | \(-0.0718828\pi\) | ||||
0.974609 | + | 0.223912i | \(0.0718828\pi\) | |||||||
\(542\) | 921.225i | 1.69968i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 993.618i | 1.82650i | ||||||||
\(545\) | 205.054i | 0.376245i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 697.821 | 1.27572 | 0.637862 | − | 0.770151i | \(-0.279819\pi\) | ||||
0.637862 | + | 0.770151i | \(0.279819\pi\) | |||||||
\(548\) | 601.806 | 1.09819 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −264.764 | −0.481389 | ||||||||
\(551\) | − | 784.162i | − | 1.42316i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −67.3628 | − | 91.2367i | −0.121813 | − | 0.164985i | ||||
\(554\) | 412.496 | 0.744578 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 206.421i | − | 0.371260i | ||||||
\(557\) | 941.244 | 1.68985 | 0.844923 | − | 0.534888i | \(-0.179646\pi\) | ||||
0.844923 | + | 0.534888i | \(0.179646\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 207.207i | − | 0.370675i | ||||||
\(560\) | 211.373 | − | 156.063i | 0.377452 | − | 0.278685i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −986.545 | −1.75542 | ||||||||
\(563\) | 768.996i | 1.36589i | 0.730470 | + | 0.682945i | \(0.239301\pi\) | ||||
−0.730470 | + | 0.682945i | \(0.760699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.67022i | − | 0.0118057i | ||||||
\(566\) | − | 1195.35i | − | 2.11192i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.0027 | 0.0369766 | ||||||||
\(569\) | 46.4935 | 0.0817108 | 0.0408554 | − | 0.999165i | \(-0.486992\pi\) | ||||
0.0408554 | + | 0.999165i | \(0.486992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 774.153 | 1.35578 | 0.677892 | − | 0.735161i | \(-0.262894\pi\) | ||||
0.677892 | + | 0.735161i | \(0.262894\pi\) | |||||||
\(572\) | 789.997i | 1.38111i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 591.586 | − | 436.786i | 1.03064 | − | 0.760951i | ||||
\(575\) | −159.995 | −0.278253 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 66.7246i | 0.115641i | 0.998327 | + | 0.0578203i | \(0.0184150\pi\) | ||||
−0.998327 | + | 0.0578203i | \(0.981585\pi\) | |||||||
\(578\) | −582.202 | −1.00727 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 339.204i | − | 0.584835i | ||||||
\(581\) | 207.135 | − | 152.934i | 0.356514 | − | 0.263225i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −934.029 | −1.60211 | ||||||||
\(584\) | − | 3.85815i | − | 0.00660642i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1123.97i | − | 1.91803i | ||||||
\(587\) | 678.789i | 1.15637i | 0.815906 | + | 0.578185i | \(0.196239\pi\) | ||||
−0.815906 | + | 0.578185i | \(0.803761\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 718.823 | 1.22041 | ||||||||
\(590\) | −219.829 | −0.372592 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −150.185 | −0.253691 | ||||||||
\(593\) | 289.610i | 0.488381i | 0.969727 | + | 0.244190i | \(0.0785222\pi\) | ||||
−0.969727 | + | 0.244190i | \(0.921478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 207.383 | + | 280.881i | 0.348543 | + | 0.472069i | ||||
\(596\) | −868.924 | −1.45793 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 980.869i | 1.64025i | ||||||||
\(599\) | −384.076 | −0.641195 | −0.320598 | − | 0.947216i | \(-0.603884\pi\) | ||||
−0.320598 | + | 0.947216i | \(0.603884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.4083i | 0.0622434i | 0.999516 | + | 0.0311217i | \(0.00990794\pi\) | ||||
−0.999516 | + | 0.0311217i | \(0.990092\pi\) | |||||||
\(602\) | −219.022 | − | 296.644i | −0.363823 | − | 0.492765i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −749.955 | −1.24165 | ||||||||
\(605\) | 534.023i | 0.882683i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 876.691i | 1.44430i | 0.691736 | + | 0.722150i | \(0.256846\pi\) | ||||
−0.691736 | + | 0.722150i | \(0.743154\pi\) | |||||||
\(608\) | − | 873.331i | − | 1.43640i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 396.200 | 0.649508 | ||||||||
\(611\) | 542.210 | 0.887414 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −591.071 | −0.964226 | −0.482113 | − | 0.876109i | \(-0.660131\pi\) | ||||
−0.482113 | + | 0.876109i | \(0.660131\pi\) | |||||||
\(614\) | 258.868i | 0.421610i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −45.6333 | − | 61.8061i | −0.0740801 | − | 0.100335i | ||||
\(617\) | 744.668 | 1.20692 | 0.603459 | − | 0.797394i | \(-0.293789\pi\) | ||||
0.603459 | + | 0.797394i | \(0.293789\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 851.811i | 1.37611i | 0.725659 | + | 0.688054i | \(0.241535\pi\) | ||||
−0.725659 | + | 0.688054i | \(0.758465\pi\) | |||||||
\(620\) | 310.941 | 0.501518 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 608.886i | − | 0.978917i | ||||||
\(623\) | 496.099 | − | 366.285i | 0.796307 | − | 0.587938i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 819.833i | − | 1.30964i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 800.404i | 1.27453i | ||||||||
\(629\) | − | 199.572i | − | 0.317284i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 316.625 | 0.501783 | 0.250891 | − | 0.968015i | \(-0.419276\pi\) | ||||
0.250891 | + | 0.968015i | \(0.419276\pi\) | |||||||
\(632\) | 9.37402 | 0.0148323 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −304.485 | −0.480260 | ||||||||
\(635\) | 234.007i | 0.368514i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −514.209 | − | 158.396i | −0.807236 | − | 0.248660i | ||||
\(638\) | −2117.94 | −3.31965 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 41.3450i | 0.0646016i | ||||||||
\(641\) | −173.979 | −0.271418 | −0.135709 | − | 0.990749i | \(-0.543331\pi\) | ||||
−0.135709 | + | 0.990749i | \(0.543331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 926.785i | − | 1.44135i | −0.693275 | − | 0.720673i | \(-0.743833\pi\) | ||
0.693275 | − | 0.720673i | \(-0.256167\pi\) | |||||||
\(644\) | 504.610 | + | 683.447i | 0.783556 | + | 1.06125i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1220.81 | 1.88980 | ||||||||
\(647\) | 429.625i | 0.664027i | 0.943275 | + | 0.332013i | \(0.107728\pi\) | ||||
−0.943275 | + | 0.332013i | \(0.892272\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 668.036i | 1.02933i | ||||||||
\(650\) | − | 153.265i | − | 0.235793i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 689.608 | 1.05768 | ||||||||
\(653\) | 927.100 | 1.41976 | 0.709878 | − | 0.704325i | \(-0.248750\pi\) | ||||
0.709878 | + | 0.704325i | \(0.248750\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 158.325 | 0.241718 | ||||||||
\(656\) | 631.695i | 0.962950i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 776.245 | − | 573.126i | 1.17970 | − | 0.871012i | ||||
\(659\) | −692.153 | −1.05031 | −0.525154 | − | 0.851007i | \(-0.675992\pi\) | ||||
−0.525154 | + | 0.851007i | \(0.675992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1101.42i | 1.66629i | 0.553053 | + | 0.833146i | \(0.313463\pi\) | ||||
−0.553053 | + | 0.833146i | \(0.686537\pi\) | |||||||
\(662\) | 1141.50 | 1.72432 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21.2818i | 0.0320510i | ||||||||
\(665\) | −182.277 | − | 246.878i | −0.274101 | − | 0.371245i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1279.86 | −1.91882 | ||||||||
\(668\) | − | 383.675i | − | 0.574364i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 133.296i | 0.198949i | ||||||||
\(671\) | − | 1204.01i | − | 1.79435i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 701.861 | 1.04288 | 0.521442 | − | 0.853287i | \(-0.325394\pi\) | ||||
0.521442 | + | 0.853287i | \(0.325394\pi\) | |||||||
\(674\) | −835.424 | −1.23950 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 183.663 | 0.271691 | ||||||||
\(677\) | − | 404.920i | − | 0.598110i | −0.954236 | − | 0.299055i | \(-0.903329\pi\) | ||
0.954236 | − | 0.299055i | \(-0.0966714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 753.535 | − | 556.358i | 1.10977 | − | 0.819379i | ||||
\(680\) | −28.8589 | −0.0424395 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 1941.47i | − | 2.84672i | ||||||
\(683\) | 766.177 | 1.12178 | 0.560891 | − | 0.827890i | \(-0.310459\pi\) | ||||
0.560891 | + | 0.827890i | \(0.310459\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 354.805i | 0.517963i | ||||||||
\(686\) | −903.586 | + | 316.764i | −1.31718 | + | 0.461754i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 316.757 | 0.460402 | ||||||||
\(689\) | − | 540.686i | − | 0.784740i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 162.333i | − | 0.234925i | −0.993077 | − | 0.117462i | \(-0.962524\pi\) | ||
0.993077 | − | 0.117462i | \(-0.0374760\pi\) | |||||||
\(692\) | − | 417.111i | − | 0.602762i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1584.85 | −2.28364 | ||||||||
\(695\) | 121.699 | 0.175106 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −839.421 | −1.20433 | ||||||||
\(698\) | 395.570i | 0.566719i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −78.8476 | − | 106.792i | −0.112639 | − | 0.152560i | ||||
\(701\) | 69.5098 | 0.0991581 | 0.0495790 | − | 0.998770i | \(-0.484212\pi\) | ||||
0.0495790 | + | 0.998770i | \(0.484212\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 175.412i | 0.249519i | ||||||||
\(704\) | −1085.11 | −1.54135 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1262.99i | − | 1.78894i | ||||||
\(707\) | −1097.57 | + | 810.372i | −1.55244 | + | 1.14621i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 134.839 | 0.190182 | 0.0950912 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950912 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(710\) | − | 226.586i | − | 0.319136i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 50.9712i | 0.0715888i | ||||||||
\(713\) | − | 1173.22i | − | 1.64546i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −465.755 | −0.651406 | ||||||||
\(716\) | −348.489 | −0.486716 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −487.600 | −0.679109 | ||||||||
\(719\) | 638.863i | 0.888544i | 0.895892 | + | 0.444272i | \(0.146538\pi\) | ||||
−0.895892 | + | 0.444272i | \(0.853462\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −232.367 | + | 171.564i | −0.322284 | + | 0.237952i | ||||
\(722\) | −65.2732 | −0.0904062 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 238.430i | 0.329323i | ||||||||
\(725\) | 199.983 | 0.275839 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 704.430i | 0.968955i | 0.874804 | + | 0.484477i | \(0.160990\pi\) | ||||
−0.874804 | + | 0.484477i | \(0.839010\pi\) | |||||||
\(728\) | 35.7780 | − | 26.4160i | 0.0491456 | − | 0.0362857i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −41.6234 | −0.0570183 | ||||||||
\(731\) | 420.919i | 0.575812i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 275.472i | − | 0.375815i | −0.982187 | − | 0.187907i | \(-0.939830\pi\) | ||
0.982187 | − | 0.187907i | \(-0.0601705\pi\) | |||||||
\(734\) | − | 338.188i | − | 0.460747i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1425.39 | −1.93667 | ||||||||
\(737\) | 405.072 | 0.549622 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 238.655 | 0.322943 | 0.161471 | − | 0.986877i | \(-0.448376\pi\) | ||||
0.161471 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(740\) | 75.8777i | 0.102537i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −571.514 | − | 774.063i | −0.770235 | − | 1.04321i | ||||
\(743\) | −221.162 | −0.297661 | −0.148831 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148831 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 512.288i | − | 0.687635i | ||||||
\(746\) | −253.773 | −0.340178 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1604.79i | − | 2.14544i | ||||||
\(749\) | −123.500 | − | 167.269i | −0.164887 | − | 0.223324i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −496.682 | −0.661361 | −0.330680 | − | 0.943743i | \(-0.607278\pi\) | ||||
−0.330680 | + | 0.943743i | \(0.607278\pi\) | |||||||
\(752\) | 828.874i | 1.10223i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1226.02i | − | 1.62602i | ||||||
\(755\) | − | 442.148i | − | 0.585627i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 866.706 | 1.14492 | 0.572461 | − | 0.819932i | \(-0.305989\pi\) | ||||
0.572461 | + | 0.819932i | \(0.305989\pi\) | |||||||
\(758\) | −1781.97 | −2.35088 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 25.3652 | 0.0333753 | ||||||||
\(761\) | − | 621.621i | − | 0.816847i | −0.912793 | − | 0.408424i | \(-0.866079\pi\) | ||
0.912793 | − | 0.408424i | \(-0.133921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 381.284 | + | 516.414i | 0.499717 | + | 0.676820i | ||||
\(764\) | 288.219 | 0.377250 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 492.415i | 0.642839i | ||||||||
\(767\) | −386.709 | −0.504184 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 316.574i | − | 0.411669i | −0.978587 | − | 0.205835i | \(-0.934009\pi\) | ||
0.978587 | − | 0.205835i | \(-0.0659909\pi\) | |||||||
\(770\) | −666.790 | + | 492.312i | −0.865962 | + | 0.639366i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 86.2961 | 0.111782 | ||||||||
\(773\) | 710.993i | 0.919784i | 0.887975 | + | 0.459892i | \(0.152112\pi\) | ||||
−0.887975 | + | 0.459892i | \(0.847888\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 183.320i | 0.236542i | ||||||||
\(776\) | 77.4213i | 0.0997697i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −696.550 | −0.895308 | ||||||||
\(779\) | 737.801 | 0.947113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −688.570 | −0.881652 | ||||||||
\(782\) | − | 1992.53i | − | 2.54799i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 242.140 | − | 786.070i | 0.308851 | − | 1.00264i | ||||
\(785\) | −471.891 | −0.601135 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 845.181i | 1.07393i | 0.843605 | + | 0.536964i | \(0.180429\pi\) | ||||
−0.843605 | + | 0.536964i | \(0.819571\pi\) | |||||||
\(788\) | 521.443 | 0.661729 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 101.131i | − | 0.128014i | ||||||
\(791\) | −12.4028 | − | 16.7985i | −0.0156799 | − | 0.0212370i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 696.968 | 0.878901 | ||||||||
\(794\) | 519.427i | 0.654190i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1013.79i | 1.27361i | ||||||||
\(797\) | 541.537i | 0.679469i | 0.940521 | + | 0.339734i | \(0.110337\pi\) | ||||
−0.940521 | + | 0.339734i | \(0.889663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1101.44 | −1.37852 | ||||||||
\(800\) | 222.724 | 0.278405 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 524.999 | 0.654612 | ||||||||
\(803\) | 126.489i | 0.157520i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −402.937 | + | 297.501i | −0.500543 | + | 0.369566i | ||||
\(806\) | 1123.86 | 1.39437 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 112.769i | − | 0.139566i | ||||||
\(809\) | 363.991 | 0.449927 | 0.224963 | − | 0.974367i | \(-0.427774\pi\) | ||||
0.224963 | + | 0.974367i | \(0.427774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 882.216i | − | 1.08781i | −0.839146 | − | 0.543906i | \(-0.816945\pi\) | ||
0.839146 | − | 0.543906i | \(-0.183055\pi\) | |||||||
\(812\) | −630.729 | − | 854.263i | −0.776759 | − | 1.05205i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 473.768 | 0.582025 | ||||||||
\(815\) | 406.570i | 0.498858i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 369.963i | − | 0.452831i | ||||||
\(818\) | 1429.76i | 1.74787i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 319.150 | 0.389208 | ||||||||
\(821\) | −681.271 | −0.829806 | −0.414903 | − | 0.909866i | \(-0.636185\pi\) | ||||
−0.414903 | + | 0.909866i | \(0.636185\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −360.544 | −0.438085 | −0.219042 | − | 0.975715i | \(-0.570293\pi\) | ||||
−0.219042 | + | 0.975715i | \(0.570293\pi\) | |||||||
\(824\) | − | 23.8743i | − | 0.0289737i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −553.626 | + | 408.759i | −0.670249 | + | 0.494865i | ||||
\(827\) | 770.095 | 0.931191 | 0.465596 | − | 0.884998i | \(-0.345840\pi\) | ||||
0.465596 | + | 0.884998i | \(0.345840\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 128.381i | 0.154862i | 0.996998 | + | 0.0774312i | \(0.0246718\pi\) | ||||
−0.996998 | + | 0.0774312i | \(0.975328\pi\) | |||||||
\(830\) | 229.598 | 0.276624 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 628.144i | − | 0.754981i | ||||||
\(833\) | 1044.56 | + | 321.764i | 1.25397 | + | 0.386272i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 226.202 | 0.270900 | ||||||||
\(836\) | 1410.52i | 1.68722i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 903.515i | 1.07818i | ||||||||
\(839\) | − | 1367.14i | − | 1.62949i | −0.579823 | − | 0.814743i | \(-0.696878\pi\) | ||
0.579823 | − | 0.814743i | \(-0.303122\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 758.735 | 0.902182 | ||||||||
\(842\) | −1406.58 | −1.67053 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1390.46 | −1.64746 | ||||||||
\(845\) | 108.281i | 0.128144i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 992.982 | + | 1344.90i | 1.17235 | + | 1.58784i | ||||
\(848\) | 826.544 | 0.974698 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 311.342i | 0.366284i | ||||||||
\(851\) | 286.295 | 0.336422 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 797.415i | − | 0.934836i | −0.884036 | − | 0.467418i | \(-0.845184\pi\) | ||
0.884036 | − | 0.467418i | \(-0.154816\pi\) | |||||||
\(854\) | 997.803 | − | 736.708i | 1.16839 | − | 0.862656i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.1859 | 0.0200770 | ||||||||
\(857\) | − | 898.781i | − | 1.04875i | −0.851486 | − | 0.524377i | \(-0.824298\pi\) | ||
0.851486 | − | 0.524377i | \(-0.175702\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 915.157i | 1.06537i | 0.846312 | + | 0.532687i | \(0.178818\pi\) | ||||
−0.846312 | + | 0.532687i | \(0.821182\pi\) | |||||||
\(860\) | − | 160.034i | − | 0.186087i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −886.961 | −1.02896 | ||||||||
\(863\) | 1357.85 | 1.57341 | 0.786703 | − | 0.617332i | \(-0.211786\pi\) | ||||
0.786703 | + | 0.617332i | \(0.211786\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 245.915 | 0.284294 | ||||||||
\(866\) | 729.674i | 0.842580i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 783.084 | − | 578.175i | 0.902170 | − | 0.666100i | ||||
\(869\) | −307.325 | −0.353654 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 234.486i | 0.269214i | ||||||||
\(872\) | −53.0584 | −0.0608468 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1751.31i | 2.00379i | ||||||||
\(875\) | 62.9608 | − | 46.4859i | 0.0719552 | − | 0.0531267i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1513.27 | 1.72550 | 0.862752 | − | 0.505627i | \(-0.168739\pi\) | ||||
0.862752 | + | 0.505627i | \(0.168739\pi\) | |||||||
\(878\) | − | 2203.96i | − | 2.51021i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 711.998i | − | 0.809089i | ||||||
\(881\) | 677.970i | 0.769546i | 0.923011 | + | 0.384773i | \(0.125720\pi\) | ||||
−0.923011 | + | 0.384773i | \(0.874280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 155.548 | 0.176159 | 0.0880793 | − | 0.996113i | \(-0.471927\pi\) | ||||
0.0880793 | + | 0.996113i | \(0.471927\pi\) | |||||||
\(884\) | 928.974 | 1.05088 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1633.73 | −1.84394 | ||||||||
\(887\) | 871.417i | 0.982432i | 0.871038 | + | 0.491216i | \(0.163447\pi\) | ||||
−0.871038 | + | 0.491216i | \(0.836553\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 435.120 | + | 589.330i | 0.489449 | + | 0.662913i | ||||
\(890\) | 549.899 | 0.617864 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1072.86i | 1.20276i | ||||||||
\(893\) | 968.101 | 1.08410 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 205.457i | − | 0.229561i | ||||||
\(896\) | 76.8784 | + | 104.125i | 0.0858018 | + | 0.116211i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1474.35 | −1.64181 | ||||||||
\(899\) | 1466.44i | 1.63119i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1098.34i | 1.21903i | ||||||||
\(902\) | − | 1992.72i | − | 2.20923i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.72594 | 0.00190923 | ||||||||
\(905\) | −140.570 | −0.155326 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −473.129 | −0.521642 | −0.260821 | − | 0.965387i | \(-0.583993\pi\) | ||||
−0.260821 | + | 0.965387i | \(0.583993\pi\) | |||||||
\(908\) | − | 799.422i | − | 0.880421i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −284.987 | − | 385.988i | −0.313172 | − | 0.424163i | ||||
\(911\) | 676.153 | 0.742210 | 0.371105 | − | 0.928591i | \(-0.378979\pi\) | ||||
0.371105 | + | 0.928591i | \(0.378979\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 697.721i | − | 0.764207i | ||||||
\(914\) | −457.929 | −0.501017 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 521.525i | 0.569350i | ||||||||
\(917\) | 398.731 | − | 294.395i | 0.434821 | − | 0.321042i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1204.50 | 1.31066 | 0.655331 | − | 0.755342i | \(-0.272529\pi\) | ||||
0.655331 | + | 0.755342i | \(0.272529\pi\) | |||||||
\(920\) | − | 41.3994i | − | 0.0449993i | ||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1115.57i | 1.20995i | ||||||||
\(923\) | − | 398.596i | − | 0.431848i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.7349 | −0.0483621 | ||||||||
\(926\) | −1899.00 | −2.05075 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1781.65 | 1.91988 | ||||||||
\(929\) | 586.143i | 0.630940i | 0.948936 | + | 0.315470i | \(0.102162\pi\) | ||||
−0.948936 | + | 0.315470i | \(0.897838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −918.107 | − | 282.812i | −0.986151 | − | 0.303772i | ||||
\(932\) | 294.954 | 0.316474 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 2024.48i | − | 2.16754i | ||||||
\(935\) | 946.131 | 1.01191 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 449.053i | − | 0.479245i | −0.970866 | − | 0.239623i | \(-0.922976\pi\) | ||
0.970866 | − | 0.239623i | \(-0.0770237\pi\) | |||||||
\(938\) | 247.856 | + | 335.697i | 0.264238 | + | 0.357886i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 418.771 | 0.445501 | ||||||||
\(941\) | 904.538i | 0.961252i | 0.876926 | + | 0.480626i | \(0.159591\pi\) | ||||
−0.876926 | + | 0.480626i | \(0.840409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1204.19i | − | 1.27698i | ||||||
\(944\) | − | 591.161i | − | 0.626230i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −999.229 | −1.05627 | ||||||||
\(947\) | −1631.56 | −1.72288 | −0.861439 | − | 0.507861i | \(-0.830436\pi\) | ||||
−0.861439 | + | 0.507861i | \(0.830436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −73.2210 | −0.0771560 | ||||||||
\(950\) | − | 273.651i | − | 0.288053i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −72.6791 | + | 53.6612i | −0.0763435 | + | 0.0563668i | ||||
\(953\) | −1547.14 | −1.62344 | −0.811721 | − | 0.584046i | \(-0.801469\pi\) | ||||
−0.811721 | + | 0.584046i | \(0.801469\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 169.924i | 0.177931i | ||||||||
\(956\) | 469.705 | 0.491323 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 885.207i | − | 0.924015i | ||||||
\(959\) | 659.736 | + | 893.552i | 0.687942 | + | 0.931753i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −383.253 | −0.398806 | ||||||||
\(962\) | 274.252i | 0.285086i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 590.915i | 0.612982i | ||||||||
\(965\) | 50.8772i | 0.0527225i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 282.618 | 0.292263 | 0.146131 | − | 0.989265i | \(-0.453318\pi\) | ||||
0.146131 | + | 0.989265i | \(0.453318\pi\) | |||||||
\(968\) | −138.181 | −0.142749 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 835.254 | 0.861086 | ||||||||
\(971\) | 586.935i | 0.604465i | 0.953234 | + | 0.302232i | \(0.0977319\pi\) | ||||
−0.953234 | + | 0.302232i | \(0.902268\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 306.490 | − | 226.291i | 0.314994 | − | 0.232570i | ||||
\(974\) | 985.765 | 1.01208 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1065.45i | 1.09165i | ||||||||
\(977\) | 651.703 | 0.667045 | 0.333523 | − | 0.942742i | \(-0.391763\pi\) | ||||
0.333523 | + | 0.942742i | \(0.391763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1671.08i | − | 1.70693i | ||||||
\(980\) | −397.145 | − | 122.336i | −0.405250 | − | 0.124832i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 958.283 | 0.975848 | ||||||||
\(983\) | − | 583.048i | − | 0.593131i | −0.955013 | − | 0.296565i | \(-0.904159\pi\) | ||
0.955013 | − | 0.296565i | \(-0.0958413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 307.425i | 0.312106i | ||||||||
\(986\) | 2490.53i | 2.52589i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −816.513 | −0.826430 | ||||||||
\(989\) | −603.828 | −0.610544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 377.146 | 0.380572 | 0.190286 | − | 0.981729i | \(-0.439059\pi\) | ||||
0.190286 | + | 0.981729i | \(0.439059\pi\) | |||||||
\(992\) | 1633.19i | 1.64636i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −421.323 | − | 570.643i | −0.423866 | − | 0.574087i | ||||
\(995\) | −597.699 | −0.600702 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1586.82i | 1.59159i | 0.605565 | + | 0.795795i | \(0.292947\pi\) | ||||
−0.605565 | + | 0.795795i | \(0.707053\pi\) | |||||||
\(998\) | −1174.08 | −1.17643 | ||||||||
\(999\) | 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 | 315.3.h.d.181.10 | 12 | ||
3.2 | odd | 2 | 105.3.h.a.76.4 | yes | 12 | ||
7.6 | odd | 2 | inner | 315.3.h.d.181.9 | 12 | ||
12.11 | even | 2 | 1680.3.s.c.1441.1 | 12 | |||
15.2 | even | 4 | 525.3.e.c.349.21 | 24 | |||
15.8 | even | 4 | 525.3.e.c.349.8 | 24 | |||
15.14 | odd | 2 | 525.3.h.d.76.9 | 12 | |||
21.20 | even | 2 | 105.3.h.a.76.3 | ✓ | 12 | ||
84.83 | odd | 2 | 1680.3.s.c.1441.10 | 12 | |||
105.62 | odd | 4 | 525.3.e.c.349.7 | 24 | |||
105.83 | odd | 4 | 525.3.e.c.349.22 | 24 | |||
105.104 | even | 2 | 525.3.h.d.76.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.3 | ✓ | 12 | 21.20 | even | 2 | ||
105.3.h.a.76.4 | yes | 12 | 3.2 | odd | 2 | ||
315.3.h.d.181.9 | 12 | 7.6 | odd | 2 | inner | ||
315.3.h.d.181.10 | 12 | 1.1 | even | 1 | trivial | ||
525.3.e.c.349.7 | 24 | 105.62 | odd | 4 | |||
525.3.e.c.349.8 | 24 | 15.8 | even | 4 | |||
525.3.e.c.349.21 | 24 | 15.2 | even | 4 | |||
525.3.e.c.349.22 | 24 | 105.83 | odd | 4 | |||
525.3.h.d.76.9 | 12 | 15.14 | odd | 2 | |||
525.3.h.d.76.10 | 12 | 105.104 | even | 2 | |||
1680.3.s.c.1441.1 | 12 | 12.11 | even | 2 | |||
1680.3.s.c.1441.10 | 12 | 84.83 | odd | 2 |