Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(76,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.76");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(14.3052138789\) |
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: | \( 2^{12}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.9 | ||
Root | \(0.198184 - 0.343264i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.76 |
Dual form | 525.3.h.d.76.10 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79155 | 1.39577 | 0.697887 | − | 0.716208i | \(-0.254124\pi\) | ||||
0.697887 | + | 0.716208i | \(0.254124\pi\) | |||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 3.79273 | 0.948184 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 4.83510i | − | 0.805850i | ||||||
\(7\) | −4.15782 | − | 5.63139i | −0.593975 | − | 0.804484i | ||||
\(8\) | −0.578591 | −0.0723239 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.9690 | −1.72445 | −0.862227 | − | 0.506522i | \(-0.830931\pi\) | ||||
−0.862227 | + | 0.506522i | \(0.830931\pi\) | |||||||
\(12\) | − | 6.56921i | − | 0.547434i | ||||||
\(13\) | − | 10.9807i | − | 0.844667i | −0.906441 | − | 0.422333i | \(-0.861211\pi\) | ||
0.906441 | − | 0.422333i | \(-0.138789\pi\) | |||||||
\(14\) | −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 | \(-0.227778\pi\) | |||||||
\(18\) | −8.37464 | −0.465258 | ||||||||
\(19\) | 19.6057i | 1.03188i | 0.856625 | + | 0.515939i | \(0.172557\pi\) | ||||
−0.856625 | + | 0.515939i | \(0.827443\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.75385 | + | 7.20156i | −0.464469 | + | 0.342932i | ||||
\(22\) | −52.9528 | −2.40695 | ||||||||
\(23\) | 31.9991 | 1.39126 | 0.695632 | − | 0.718399i | \(-0.255125\pi\) | ||||
0.695632 | + | 0.718399i | \(0.255125\pi\) | |||||||
\(24\) | 1.00215i | 0.0417562i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 30.6530i | − | 1.17896i | ||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −15.7695 | − | 21.3583i | −0.563197 | − | 0.762798i | ||||
\(29\) | 39.9967 | 1.37920 | 0.689598 | − | 0.724192i | \(-0.257787\pi\) | ||||
0.689598 | + | 0.724192i | \(0.257787\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 32.8553i | 0.995614i | ||||||||
\(34\) | − | 62.2683i | − | 1.83142i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.3782 | −0.316061 | ||||||||
\(37\) | −8.94699 | −0.241810 | −0.120905 | − | 0.992664i | \(-0.538580\pi\) | ||||
−0.120905 | + | 0.992664i | \(0.538580\pi\) | |||||||
\(38\) | 54.7302i | 1.44027i | ||||||||
\(39\) | −19.0191 | −0.487669 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 37.6320i | 0.917854i | 0.888474 | + | 0.458927i | \(0.151766\pi\) | ||||
−0.888474 | + | 0.458927i | \(0.848234\pi\) | |||||||
\(42\) | −27.2283 | + | 20.1035i | −0.648293 | + | 0.478655i | ||||
\(43\) | 18.8702 | 0.438841 | 0.219421 | − | 0.975630i | \(-0.429583\pi\) | ||||
0.219421 | + | 0.975630i | \(0.429583\pi\) | |||||||
\(44\) | −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 | \(-0.176048\pi\) | |||||||
\(48\) | 29.0744i | 0.605716i | ||||||||
\(49\) | −14.4250 | + | 46.8286i | −0.294388 | + | 0.955686i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −38.6352 | −0.757552 | ||||||||
\(52\) | − | 41.6468i | − | 0.800899i | ||||||
\(53\) | −49.2398 | −0.929052 | −0.464526 | − | 0.885559i | \(-0.653775\pi\) | ||||
−0.464526 | + | 0.885559i | \(0.653775\pi\) | |||||||
\(54\) | 14.5053i | 0.268617i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.40568 | + | 3.25827i | 0.0429586 | + | 0.0581834i | ||||
\(57\) | 33.9580 | 0.595755 | ||||||||
\(58\) | 111.653 | 1.92505 | ||||||||
\(59\) | − | 35.2173i | − | 0.596903i | −0.954425 | − | 0.298452i | \(-0.903530\pi\) | ||
0.954425 | − | 0.298452i | \(-0.0964701\pi\) | |||||||
\(60\) | 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 | ||||||
\(63\) | 12.4735 | + | 16.8942i | 0.197992 | + | 0.268161i | ||||
\(64\) | −57.2046 | −0.893821 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 91.7170i | 1.38965i | ||||||||
\(67\) | −21.3544 | −0.318723 | −0.159361 | − | 0.987220i | \(-0.550943\pi\) | ||||
−0.159361 | + | 0.987220i | \(0.550943\pi\) | |||||||
\(68\) | − | 84.6008i | − | 1.24413i | ||||||
\(69\) | − | 55.4240i | − | 0.803246i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.2998 | 0.511265 | 0.255632 | − | 0.966774i | \(-0.417716\pi\) | ||||
0.255632 | + | 0.966774i | \(0.417716\pi\) | |||||||
\(72\) | 1.73577 | 0.0241080 | ||||||||
\(73\) | − | 6.66818i | − | 0.0913449i | −0.998956 | − | 0.0456725i | \(-0.985457\pi\) | ||
0.998956 | − | 0.0456725i | \(-0.0145431\pi\) | |||||||
\(74\) | −24.9759 | −0.337513 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 74.3591i | 0.978409i | ||||||||
\(77\) | 78.8697 | + | 106.822i | 1.02428 | + | 1.38729i | ||||
\(78\) | −53.0926 | −0.680675 | ||||||||
\(79\) | −16.2015 | −0.205082 | −0.102541 | − | 0.994729i | \(-0.532697\pi\) | ||||
−0.102541 | + | 0.994729i | \(0.532697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 105.052i | 1.28112i | ||||||||
\(83\) | − | 36.7822i | − | 0.443159i | −0.975142 | − | 0.221579i | \(-0.928879\pi\) | ||
0.975142 | − | 0.221579i | \(-0.0711212\pi\) | |||||||
\(84\) | −36.9937 | + | 27.3136i | −0.440402 | + | 0.325162i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 52.6770 | 0.612523 | ||||||||
\(87\) | − | 69.2763i | − | 0.796279i | ||||||
\(88\) | 10.9753 | 0.124719 | ||||||||
\(89\) | 88.0954i | 0.989836i | 0.868940 | + | 0.494918i | \(0.164802\pi\) | ||||
−0.868940 | + | 0.494918i | \(0.835198\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −61.8364 | + | 45.6557i | −0.679520 | + | 0.501711i | ||||
\(92\) | 121.364 | 1.31917 | ||||||||
\(93\) | −63.5040 | −0.682839 | ||||||||
\(94\) | − | 137.843i | − | 1.46641i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 77.1539i | 0.803687i | ||||||||
\(97\) | 133.810i | 1.37948i | 0.724055 | + | 0.689742i | \(0.242276\pi\) | ||||
−0.724055 | + | 0.689742i | \(0.757724\pi\) | |||||||
\(98\) | −40.2681 | + | 130.724i | −0.410899 | + | 1.33392i | ||||
\(99\) | 56.9070 | 0.574818 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 194.903i | − | 1.92973i | −0.262743 | − | 0.964866i | \(-0.584627\pi\) | ||
0.262743 | − | 0.964866i | \(-0.415373\pi\) | |||||||
\(102\) | −107.852 | −1.05737 | ||||||||
\(103\) | − | 41.2629i | − | 0.400610i | −0.979734 | − | 0.200305i | \(-0.935807\pi\) | ||
0.979734 | − | 0.200305i | \(-0.0641933\pi\) | |||||||
\(104\) | 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 | \(0.544324\pi\) | |||||||
\(108\) | 19.7076i | 0.182478i | ||||||||
\(109\) | 91.7028 | 0.841310 | 0.420655 | − | 0.907221i | \(-0.361800\pi\) | ||||
0.420655 | + | 0.907221i | \(0.361800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.4966i | 0.139609i | ||||||||
\(112\) | 69.7937 | + | 94.5290i | 0.623158 | + | 0.844009i | ||||
\(113\) | −2.98301 | −0.0263983 | −0.0131992 | − | 0.999913i | \(-0.504202\pi\) | ||||
−0.0131992 | + | 0.999913i | \(0.504202\pi\) | |||||||
\(114\) | 94.7954 | 0.831539 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 151.697 | 1.30773 | ||||||||
\(117\) | 32.9420i | 0.281556i | ||||||||
\(118\) | − | 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 | ||||||
\(123\) | 65.1806 | 0.529923 | ||||||||
\(124\) | − | 139.057i | − | 1.12143i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 34.8203 | + | 47.1608i | 0.276351 | + | 0.374292i | ||||
\(127\) | −104.651 | −0.824023 | −0.412012 | − | 0.911179i | \(-0.635174\pi\) | ||||
−0.412012 | + | 0.911179i | \(0.635174\pi\) | |||||||
\(128\) | 18.4901 | 0.144454 | ||||||||
\(129\) | − | 32.6841i | − | 0.253365i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70.8051i | 0.540497i | 0.962791 | + | 0.270249i | \(0.0871059\pi\) | ||||
−0.962791 | + | 0.270249i | \(0.912894\pi\) | |||||||
\(132\) | 124.611i | 0.944025i | ||||||||
\(133\) | 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 | \(0.303404\pi\) | |||||||
\(138\) | − | 154.719i | − | 1.12115i | ||||||
\(139\) | − | 54.4253i | − | 0.391549i | −0.980649 | − | 0.195774i | \(-0.937278\pi\) | ||
0.980649 | − | 0.195774i | \(-0.0627220\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −85.5262 | −0.606569 | ||||||||
\(142\) | 101.333 | 0.713610 | ||||||||
\(143\) | 208.292i | 1.45659i | ||||||||
\(144\) | 50.3583 | 0.349710 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 18.6145i | − | 0.127497i | ||||||
\(147\) | 81.1095 | + | 24.9848i | 0.551766 | + | 0.169965i | ||||
\(148\) | −33.9335 | −0.229281 | ||||||||
\(149\) | 229.102 | 1.53760 | 0.768799 | − | 0.639490i | \(-0.220854\pi\) | ||||
0.768799 | + | 0.639490i | \(0.220854\pi\) | |||||||
\(150\) | 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 | ||||||
\(153\) | 66.9181i | 0.437373i | ||||||||
\(154\) | 220.169 | + | 298.198i | 1.42967 | + | 1.93635i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −72.1343 | −0.462399 | ||||||||
\(157\) | − | 211.036i | − | 1.34418i | −0.740470 | − | 0.672089i | \(-0.765397\pi\) | ||
0.740470 | − | 0.672089i | \(-0.234603\pi\) | |||||||
\(158\) | −45.2271 | −0.286248 | ||||||||
\(159\) | 85.2858i | 0.536389i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −133.046 | − | 180.199i | −0.826375 | − | 1.11925i | ||||
\(162\) | 25.1239 | 0.155086 | ||||||||
\(163\) | −181.823 | −1.11548 | −0.557741 | − | 0.830015i | \(-0.688332\pi\) | ||||
−0.557741 | + | 0.830015i | \(0.688332\pi\) | |||||||
\(164\) | 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 | \(-0.0979467\pi\) | |||||||
\(168\) | 5.64349 | − | 4.16676i | 0.0335922 | − | 0.0248021i | ||||
\(169\) | 48.4250 | 0.286538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 58.8170i | − | 0.343959i | ||||||
\(172\) | 71.5696 | 0.416102 | ||||||||
\(173\) | − | 109.976i | − | 0.635702i | −0.948141 | − | 0.317851i | \(-0.897039\pi\) | ||
0.948141 | − | 0.317851i | \(-0.102961\pi\) | |||||||
\(174\) | − | 193.388i | − | 1.11143i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 318.415 | 1.80918 | ||||||||
\(177\) | −60.9981 | −0.344622 | ||||||||
\(178\) | 245.922i | 1.38159i | ||||||||
\(179\) | 91.8832 | 0.513314 | 0.256657 | − | 0.966503i | \(-0.417379\pi\) | ||||
0.256657 | + | 0.966503i | \(0.417379\pi\) | |||||||
\(180\) | 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 | ||||
\(183\) | −109.937 | −0.600750 | ||||||||
\(184\) | −18.5144 | −0.100622 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −177.274 | −0.953088 | ||||||||
\(187\) | 423.123i | 2.26269i | ||||||||
\(188\) | − | 187.280i | − | 0.996170i | ||||||
\(189\) | 29.2615 | − | 21.6047i | 0.154823 | − | 0.114311i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −75.9925 | −0.397866 | −0.198933 | − | 0.980013i | \(-0.563748\pi\) | ||||
−0.198933 | + | 0.980013i | \(0.563748\pi\) | |||||||
\(192\) | 99.0812i | 0.516048i | ||||||||
\(193\) | −22.7530 | −0.117891 | −0.0589456 | − | 0.998261i | \(-0.518774\pi\) | ||||
−0.0589456 | + | 0.998261i | \(0.518774\pi\) | |||||||
\(194\) | 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 | \(0.386540\pi\) | |||||||
\(198\) | 158.858 | 0.802316 | ||||||||
\(199\) | 267.299i | 1.34321i | 0.740909 | + | 0.671606i | \(0.234395\pi\) | ||||
−0.740909 | + | 0.671606i | \(0.765605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.9869i | 0.184015i | ||||||||
\(202\) | − | 544.081i | − | 2.69347i | ||||||
\(203\) | −166.299 | − | 225.237i | −0.819208 | − | 1.10954i | ||||
\(204\) | −146.533 | −0.718299 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 115.187i | − | 0.559161i | ||||||
\(207\) | −95.9972 | −0.463754 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | − | 62.8731i | − | 0.295179i | ||||||
\(214\) | −82.9175 | −0.387465 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 3.00645i | − | 0.0139187i | ||||||
\(217\) | −206.469 | + | 152.443i | −0.951472 | + | 0.702501i | ||||
\(218\) | 255.993 | 1.17428 | ||||||||
\(219\) | −11.5496 | −0.0527380 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −244.935 | −1.10830 | ||||||||
\(222\) | 43.2596i | 0.194863i | ||||||||
\(223\) | − | 282.872i | − | 1.26848i | −0.773134 | − | 0.634242i | \(-0.781312\pi\) | ||
0.773134 | − | 0.634242i | \(-0.218688\pi\) | |||||||
\(224\) | 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 | \(-0.153682\pi\) | |||||||
\(228\) | 128.794 | 0.564885 | ||||||||
\(229\) | 137.506i | 0.600464i | 0.953866 | + | 0.300232i | \(0.0970641\pi\) | ||||
−0.953866 | + | 0.300232i | \(0.902936\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 185.021 | − | 136.606i | 0.800955 | − | 0.591370i | ||||
\(232\) | −23.1417 | −0.0997488 | ||||||||
\(233\) | 77.7682 | 0.333769 | 0.166884 | − | 0.985976i | \(-0.446629\pi\) | ||||
0.166884 | + | 0.985976i | \(0.446629\pi\) | |||||||
\(234\) | 91.9591i | 0.392988i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 133.570i | − | 0.565974i | ||||||
\(237\) | 28.0618i | 0.118404i | ||||||||
\(238\) | −350.657 | + | 258.901i | −1.47335 | + | 1.08782i | ||||
\(239\) | −123.843 | −0.518173 | −0.259086 | − | 0.965854i | \(-0.583421\pi\) | ||||
−0.259086 | + | 0.965854i | \(0.583421\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 240.734i | − | 0.986613i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 181.955 | 0.739653 | ||||||||
\(247\) | 215.283 | 0.871593 | ||||||||
\(248\) | 21.2135i | 0.0855383i | ||||||||
\(249\) | −63.7086 | −0.255858 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 278.340i | − | 1.10892i | −0.832210 | − | 0.554461i | \(-0.812924\pi\) | ||
0.832210 | − | 0.554461i | \(-0.187076\pi\) | |||||||
\(252\) | 47.3086 | + | 64.0750i | 0.187732 | + | 0.254266i | ||||
\(253\) | −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 | \(0.858663\pi\) | |||||||
\(258\) | − | 91.2392i | − | 0.353640i | ||||||
\(259\) | 37.2000 | + | 50.3839i | 0.143629 | + | 0.194533i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −119.990 | −0.459732 | ||||||||
\(262\) | 197.656i | 0.754412i | ||||||||
\(263\) | 17.3477 | 0.0659609 | 0.0329804 | − | 0.999456i | \(-0.489500\pi\) | ||||
0.0329804 | + | 0.999456i | \(0.489500\pi\) | |||||||
\(264\) | − | 19.0098i | − | 0.0720067i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 308.207 | − | 227.558i | 1.15867 | − | 0.855483i | ||||
\(267\) | 152.586 | 0.571482 | ||||||||
\(268\) | −80.9916 | −0.302207 | ||||||||
\(269\) | − | 499.213i | − | 1.85581i | −0.372816 | − | 0.927905i | \(-0.621608\pi\) | ||
0.372816 | − | 0.927905i | \(-0.378392\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | 79.0780 | + | 107.104i | 0.289663 | + | 0.392321i | ||||
\(274\) | 442.944 | 1.61659 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 210.209i | − | 0.761625i | ||||||
\(277\) | −147.766 | −0.533452 | −0.266726 | − | 0.963772i | \(-0.585942\pi\) | ||||
−0.266726 | + | 0.963772i | \(0.585942\pi\) | |||||||
\(278\) | − | 151.931i | − | 0.546513i | ||||||
\(279\) | 109.992i | 0.394237i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 353.405 | 1.25767 | 0.628834 | − | 0.777540i | \(-0.283533\pi\) | ||||
0.628834 | + | 0.777540i | \(0.283533\pi\) | |||||||
\(282\) | −238.751 | −0.846633 | ||||||||
\(283\) | 428.203i | 1.51308i | 0.653945 | + | 0.756542i | \(0.273113\pi\) | ||||
−0.653945 | + | 0.756542i | \(0.726887\pi\) | |||||||
\(284\) | 137.675 | 0.484773 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 581.457i | 2.03307i | ||||||||
\(287\) | 211.920 | − | 156.467i | 0.738399 | − | 0.545182i | ||||
\(288\) | 133.634 | 0.464009 | ||||||||
\(289\) | −208.559 | −0.721657 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 231.766 | 0.796446 | ||||||||
\(292\) | − | 25.2906i | − | 0.0866117i | ||||||
\(293\) | − | 402.632i | − | 1.37417i | −0.726577 | − | 0.687085i | \(-0.758890\pi\) | ||
0.726577 | − | 0.687085i | \(-0.241110\pi\) | |||||||
\(294\) | 226.421 | + | 69.7463i | 0.770140 | + | 0.237232i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.17665 | 0.0174887 | ||||||||
\(297\) | − | 98.5658i | − | 0.331871i | ||||||
\(298\) | 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 | ||||||||
\(303\) | −337.582 | −1.11413 | ||||||||
\(304\) | − | 329.103i | − | 1.08258i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 186.805i | 0.610474i | ||||||||
\(307\) | − | 92.7330i | − | 0.302062i | −0.988529 | − | 0.151031i | \(-0.951741\pi\) | ||
0.988529 | − | 0.151031i | \(-0.0482593\pi\) | |||||||
\(308\) | 299.132 | + | 405.146i | 0.971207 | + | 1.31541i | ||||
\(309\) | −71.4694 | −0.231292 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 218.118i | 0.701343i | 0.936498 | + | 0.350672i | \(0.114047\pi\) | ||||
−0.936498 | + | 0.350672i | \(0.885953\pi\) | |||||||
\(312\) | 11.0043 | 0.0352701 | ||||||||
\(313\) | 293.684i | 0.938288i | 0.883122 | + | 0.469144i | \(0.155438\pi\) | ||||
−0.883122 | + | 0.469144i | \(0.844562\pi\) | |||||||
\(314\) | − | 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 | \(0.555036\pi\) | |||||||
\(318\) | 238.079i | 0.748677i | ||||||||
\(319\) | −758.697 | −2.37836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 51.4472i | 0.160272i | ||||||||
\(322\) | −371.405 | − | 503.034i | −1.15343 | − | 1.56222i | ||||
\(323\) | 437.325 | 1.35395 | ||||||||
\(324\) | 34.1346 | 0.105354 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −507.569 | −1.55696 | ||||||||
\(327\) | − | 158.834i | − | 0.485731i | ||||||
\(328\) | − | 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 | ||||||
\(333\) | 26.8410 | 0.0806035 | ||||||||
\(334\) | − | 282.394i | − | 0.845492i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 163.729 | − | 120.886i | 0.487289 | − | 0.359780i | ||||
\(337\) | 299.269 | 0.888040 | 0.444020 | − | 0.896017i | \(-0.353552\pi\) | ||||
0.444020 | + | 0.896017i | \(0.353552\pi\) | |||||||
\(338\) | 135.181 | 0.399942 | ||||||||
\(339\) | 5.16673i | 0.0152411i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 695.480i | 2.03953i | ||||||||
\(342\) | − | 164.190i | − | 0.480089i | ||||||
\(343\) | 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 | \(0.804948\pi\) | |||||||
\(348\) | − | 262.747i | − | 0.755019i | ||||||
\(349\) | 141.703i | 0.406025i | 0.979176 | + | 0.203012i | \(0.0650732\pi\) | ||||
−0.979176 | + | 0.203012i | \(0.934927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 57.0572 | 0.162556 | ||||||||
\(352\) | 844.970 | 2.40048 | ||||||||
\(353\) | − | 452.435i | − | 1.28169i | −0.767672 | − | 0.640843i | \(-0.778585\pi\) | ||
0.767672 | − | 0.640843i | \(-0.221415\pi\) | |||||||
\(354\) | −170.279 | −0.481015 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 334.123i | 0.938546i | ||||||||
\(357\) | 160.638 | + | 217.570i | 0.449967 | + | 0.609439i | ||||
\(358\) | 256.496 | 0.716470 | ||||||||
\(359\) | 174.670 | 0.486546 | 0.243273 | − | 0.969958i | \(-0.421779\pi\) | ||||
0.243273 | + | 0.969958i | \(0.421779\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −23.3825 | −0.0647714 | ||||||||
\(362\) | 175.490i | 0.484780i | ||||||||
\(363\) | − | 413.653i | − | 1.13954i | ||||||
\(364\) | −234.529 | + | 173.160i | −0.644310 | + | 0.475714i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −306.895 | −0.838511 | ||||||||
\(367\) | 121.147i | 0.330101i | 0.986285 | + | 0.165051i | \(0.0527788\pi\) | ||||
−0.986285 | + | 0.165051i | \(0.947221\pi\) | |||||||
\(368\) | −537.139 | −1.45962 | ||||||||
\(369\) | − | 112.896i | − | 0.305951i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 204.730 | + | 277.288i | 0.551834 | + | 0.747407i | ||||
\(372\) | −240.854 | −0.647456 | ||||||||
\(373\) | 90.9075 | 0.243720 | 0.121860 | − | 0.992547i | \(-0.461114\pi\) | ||||
0.121860 | + | 0.992547i | \(0.461114\pi\) | |||||||
\(374\) | 1181.17i | 3.15820i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.5700i | 0.0759841i | ||||||||
\(377\) | − | 439.190i | − | 1.16496i | ||||||
\(378\) | 81.6850 | − | 60.3105i | 0.216098 | − | 0.159552i | ||||
\(379\) | −638.344 | −1.68429 | −0.842143 | − | 0.539254i | \(-0.818706\pi\) | ||||
−0.842143 | + | 0.539254i | \(0.818706\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 181.261i | 0.475750i | ||||||||
\(382\) | −212.137 | −0.555331 | ||||||||
\(383\) | 176.395i | 0.460561i | 0.973124 | + | 0.230281i | \(0.0739644\pi\) | ||||
−0.973124 | + | 0.230281i | \(0.926036\pi\) | |||||||
\(384\) | − | 32.0257i | − | 0.0834003i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −63.5160 | −0.164549 | ||||||||
\(387\) | −56.6105 | −0.146280 | ||||||||
\(388\) | 507.506i | 1.30800i | ||||||||
\(389\) | 249.521 | 0.641442 | 0.320721 | − | 0.947174i | \(-0.396075\pi\) | ||||
0.320721 | + | 0.947174i | \(0.396075\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 713.772i | − | 1.82550i | ||||||
\(392\) | 8.34618 | − | 27.0946i | 0.0212913 | − | 0.0691189i | ||||
\(393\) | 122.638 | 0.312056 | ||||||||
\(394\) | 383.795 | 0.974098 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 215.833 | 0.545033 | ||||||||
\(397\) | − | 186.071i | − | 0.468694i | −0.972153 | − | 0.234347i | \(-0.924705\pi\) | ||
0.972153 | − | 0.234347i | \(-0.0752951\pi\) | |||||||
\(398\) | 746.178i | 1.87482i | ||||||||
\(399\) | −141.191 | − | 191.231i | −0.353863 | − | 0.479275i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −188.067 | −0.468996 | −0.234498 | − | 0.972117i | \(-0.575345\pi\) | ||||
−0.234498 | + | 0.972117i | \(0.575345\pi\) | |||||||
\(402\) | 103.251i | 0.256843i | ||||||||
\(403\) | −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 | ||||||||
\(408\) | 22.3540 | 0.0547891 | ||||||||
\(409\) | 512.173i | 1.25226i | 0.779720 | + | 0.626128i | \(0.215361\pi\) | ||||
−0.779720 | + | 0.626128i | \(0.784639\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 274.831i | − | 0.668687i | ||||||
\(412\) | − | 156.499i | − | 0.379852i | ||||||
\(413\) | −198.322 | + | 146.427i | −0.480199 | + | 0.354545i | ||||
\(414\) | −267.981 | −0.647296 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 489.132i | 1.17580i | ||||||||
\(417\) | −94.2673 | −0.226061 | ||||||||
\(418\) | − | 1038.18i | − | 2.48367i | ||||||
\(419\) | − | 323.661i | − | 0.772461i | −0.922402 | − | 0.386231i | \(-0.873777\pi\) | ||
0.922402 | − | 0.386231i | \(-0.126223\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 148.136i | 0.350203i | ||||||||
\(424\) | 28.4897 | 0.0671927 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 175.513i | − | 0.412003i | ||||||
\(427\) | −357.437 | + | 263.907i | −0.837089 | + | 0.618049i | ||||
\(428\) | −112.656 | −0.263215 | ||||||||
\(429\) | 360.773 | 0.840962 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 317.731 | 0.737195 | 0.368597 | − | 0.929589i | \(-0.379838\pi\) | ||||
0.368597 | + | 0.929589i | \(0.379838\pi\) | |||||||
\(432\) | − | 87.2231i | − | 0.201905i | ||||||
\(433\) | − | 261.387i | − | 0.603665i | −0.953361 | − | 0.301833i | \(-0.902402\pi\) | ||
0.953361 | − | 0.301833i | \(-0.0975984\pi\) | |||||||
\(434\) | −576.369 | + | 425.551i | −1.32804 | + | 0.980532i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 347.805 | 0.797717 | ||||||||
\(437\) | 627.363i | 1.43561i | ||||||||
\(438\) | −32.2413 | −0.0736103 | ||||||||
\(439\) | − | 789.513i | − | 1.79844i | −0.437501 | − | 0.899218i | \(-0.644137\pi\) | ||
0.437501 | − | 0.899218i | \(-0.355863\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.2750 | − | 140.486i | 0.0981293 | − | 0.318562i | ||||
\(442\) | −683.748 | −1.54694 | ||||||||
\(443\) | −585.242 | −1.32109 | −0.660544 | − | 0.750787i | \(-0.729674\pi\) | ||||
−0.660544 | + | 0.750787i | \(0.729674\pi\) | |||||||
\(444\) | 58.7746i | 0.132375i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 789.651i | − | 1.77052i | ||||||
\(447\) | − | 396.817i | − | 0.887733i | ||||||
\(448\) | 237.847 | + | 322.141i | 0.530907 | + | 0.719065i | ||||
\(449\) | 528.147 | 1.17627 | 0.588137 | − | 0.808761i | \(-0.299862\pi\) | ||||
0.588137 | + | 0.808761i | \(0.299862\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 713.842i | − | 1.58280i | ||||||
\(452\) | −11.3138 | −0.0250305 | ||||||||
\(453\) | 342.486i | 0.756041i | ||||||||
\(454\) | − | 588.395i | − | 1.29602i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −19.6478 | −0.0430873 | ||||||||
\(457\) | 164.041 | 0.358953 | 0.179476 | − | 0.983762i | \(-0.442560\pi\) | ||||
0.179476 | + | 0.983762i | \(0.442560\pi\) | |||||||
\(458\) | 383.855i | 0.838112i | ||||||||
\(459\) | 115.906 | 0.252517 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 399.626i | − | 0.866867i | −0.901186 | − | 0.433434i | \(-0.857302\pi\) | ||
0.901186 | − | 0.433434i | \(-0.142698\pi\) | |||||||
\(462\) | 516.494 | − | 381.343i | 1.11795 | − | 0.825418i | ||||
\(463\) | 680.267 | 1.46926 | 0.734630 | − | 0.678468i | \(-0.237356\pi\) | ||||
0.734630 | + | 0.678468i | \(0.237356\pi\) | |||||||
\(464\) | −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 | \(-0.282989\pi\) | |||||||
\(468\) | 124.940i | 0.266966i | ||||||||
\(469\) | 88.7879 | + | 120.255i | 0.189313 | + | 0.256407i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −365.525 | −0.776062 | ||||||||
\(472\) | 20.3764i | 0.0431704i | ||||||||
\(473\) | −357.948 | −0.756762 | ||||||||
\(474\) | 78.3357i | 0.165265i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −476.420 | + | 351.755i | −1.00088 | + | 0.738982i | ||||
\(477\) | 147.719 | 0.309684 | ||||||||
\(478\) | −345.714 | −0.723252 | ||||||||
\(479\) | 317.103i | 0.662010i | 0.943629 | + | 0.331005i | \(0.107388\pi\) | ||||
−0.943629 | + | 0.331005i | \(0.892612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 98.2439i | 0.204249i | ||||||||
\(482\) | 434.928i | 0.902341i | ||||||||
\(483\) | −312.114 | + | 230.443i | −0.646198 | + | 0.477108i | ||||
\(484\) | 905.791 | 1.87147 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 43.5159i | − | 0.0895389i | ||||||
\(487\) | −353.125 | −0.725103 | −0.362551 | − | 0.931964i | \(-0.618094\pi\) | ||||
−0.362551 | + | 0.931964i | \(0.618094\pi\) | |||||||
\(488\) | 36.7245i | 0.0752552i | ||||||||
\(489\) | 314.927i | 0.644023i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −343.280 | −0.699145 | −0.349572 | − | 0.936909i | \(-0.613673\pi\) | ||||
−0.349572 | + | 0.936909i | \(0.613673\pi\) | |||||||
\(492\) | 247.213 | 0.502465 | ||||||||
\(493\) | − | 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 | ||||
\(498\) | −177.846 | −0.357120 | ||||||||
\(499\) | −420.584 | −0.842853 | −0.421427 | − | 0.906863i | \(-0.638470\pi\) | ||||
−0.421427 | + | 0.906863i | \(0.638470\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −175.215 | −0.349731 | ||||||||
\(502\) | − | 776.998i | − | 1.54780i | ||||||
\(503\) | − | 183.030i | − | 0.363876i | −0.983310 | − | 0.181938i | \(-0.941763\pi\) | ||
0.983310 | − | 0.181938i | \(-0.0582370\pi\) | |||||||
\(504\) | −7.21704 | − | 9.77481i | −0.0143195 | − | 0.0193945i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1694.44 | −3.34870 | ||||||||
\(507\) | − | 83.8745i | − | 0.165433i | ||||||
\(508\) | −396.913 | −0.781326 | ||||||||
\(509\) | 261.854i | 0.514448i | 0.966352 | + | 0.257224i | \(0.0828079\pi\) | ||||
−0.966352 | + | 0.257224i | \(0.917192\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37.5511 | + | 27.7251i | −0.0734855 | + | 0.0542566i | ||||
\(512\) | 708.885 | 1.38454 | ||||||||
\(513\) | −101.874 | −0.198585 | ||||||||
\(514\) | 616.378i | 1.19918i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 123.962i | − | 0.240237i | ||||||
\(517\) | 936.662i | 1.81173i | ||||||||
\(518\) | 103.846 | + | 140.649i | 0.200474 | + | 0.271523i | ||||
\(519\) | −190.485 | −0.367023 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 477.677i | − | 0.916846i | −0.888734 | − | 0.458423i | \(-0.848414\pi\) | ||
0.888734 | − | 0.458423i | \(-0.151586\pi\) | |||||||
\(522\) | −334.958 | −0.641682 | ||||||||
\(523\) | 770.784i | 1.47377i | 0.676016 | + | 0.736887i | \(0.263705\pi\) | ||||
−0.676016 | + | 0.736887i | \(0.736295\pi\) | |||||||
\(524\) | 268.545i | 0.512491i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.4269 | 0.0920664 | ||||||||
\(527\) | −817.829 | −1.55186 | ||||||||
\(528\) | − | 551.512i | − | 1.04453i | ||||||
\(529\) | 494.940 | 0.935614 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105.652i | 0.198968i | ||||||||
\(532\) | 418.745 | − | 309.172i | 0.787114 | − | 0.581151i | ||||
\(533\) | 413.225 | 0.775281 | ||||||||
\(534\) | 425.950 | 0.797660 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.3555 | 0.0230513 | ||||||||
\(537\) | − | 159.146i | − | 0.296362i | ||||||
\(538\) | − | 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 | ||||||||
\(543\) | 108.885 | 0.200525 | ||||||||
\(544\) | 993.618i | 1.82650i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 220.750 | + | 298.985i | 0.404304 | + | 0.547592i | ||||
\(547\) | −697.821 | −1.27572 | −0.637862 | − | 0.770151i | \(-0.720181\pi\) | ||||
−0.637862 | + | 0.770151i | \(0.720181\pi\) | |||||||
\(548\) | 601.806 | 1.09819 | ||||||||
\(549\) | 190.417i | 0.346843i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 784.162i | 1.42316i | ||||||||
\(552\) | 32.0678i | 0.0580939i | ||||||||
\(553\) | 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 | \(0.179646\pi\) | |||||||
\(558\) | 307.048i | 0.550266i | ||||||||
\(559\) | − | 207.207i | − | 0.370675i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 732.870 | 1.30636 | ||||||||
\(562\) | 986.545 | 1.75542 | ||||||||
\(563\) | 768.996i | 1.36589i | 0.730470 | + | 0.682945i | \(0.239301\pi\) | ||||
−0.730470 | + | 0.682945i | \(0.760699\pi\) | |||||||
\(564\) | −324.378 | −0.575139 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1195.35i | 2.11192i | ||||||||
\(567\) | −37.4204 | − | 50.6825i | −0.0659972 | − | 0.0893871i | ||||
\(568\) | −21.0027 | −0.0369766 | ||||||||
\(569\) | −46.4935 | −0.0817108 | −0.0408554 | − | 0.999165i | \(-0.513008\pi\) | ||||
−0.0408554 | + | 0.999165i | \(0.513008\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 131.623i | 0.229708i | ||||||||
\(574\) | 591.586 | − | 436.786i | 1.03064 | − | 0.760951i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 171.614 | 0.297940 | ||||||||
\(577\) | − | 66.7246i | − | 0.115641i | −0.998327 | − | 0.0578203i | \(-0.981585\pi\) | ||
0.998327 | − | 0.0578203i | \(-0.0184150\pi\) | |||||||
\(578\) | −582.202 | −1.00727 | ||||||||
\(579\) | 39.4093i | 0.0680645i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −207.135 | + | 152.934i | −0.356514 | + | 0.263225i | ||||
\(582\) | 646.985 | 1.11166 | ||||||||
\(583\) | 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 | \(0.803761\pi\) | |||||||
\(588\) | 307.627 | + | 94.7608i | 0.523175 | + | 0.161158i | ||||
\(589\) | 718.823 | 1.22041 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 238.130i | − | 0.402928i | ||||||
\(592\) | 150.185 | 0.253691 | ||||||||
\(593\) | 289.610i | 0.488381i | 0.969727 | + | 0.244190i | \(0.0785222\pi\) | ||||
−0.969727 | + | 0.244190i | \(0.921478\pi\) | |||||||
\(594\) | − | 275.151i | − | 0.463217i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 868.924 | 1.45793 | ||||||||
\(597\) | 462.976 | 0.775503 | ||||||||
\(598\) | − | 980.869i | − | 1.64025i | ||||||
\(599\) | 384.076 | 0.641195 | 0.320598 | − | 0.947216i | \(-0.396116\pi\) | ||||
0.320598 | + | 0.947216i | \(0.396116\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | 64.0632 | 0.106241 | ||||||||
\(604\) | −749.955 | −1.24165 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −942.375 | −1.55507 | ||||||||
\(607\) | − | 876.691i | − | 1.44430i | −0.691736 | − | 0.722150i | \(-0.743154\pi\) | ||
0.691736 | − | 0.722150i | \(-0.256846\pi\) | |||||||
\(608\) | − | 873.331i | − | 1.43640i | ||||||
\(609\) | −390.121 | + | 288.039i | −0.640594 | + | 0.472970i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −542.210 | −0.887414 | ||||||||
\(612\) | 253.803i | 0.414710i | ||||||||
\(613\) | 591.071 | 0.964226 | 0.482113 | − | 0.876109i | \(-0.339869\pi\) | ||||
0.482113 | + | 0.876109i | \(0.339869\pi\) | |||||||
\(614\) | − | 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 | \(0.293789\pi\) | |||||||
\(618\) | −199.510 | −0.322832 | ||||||||
\(619\) | 851.811i | 1.37611i | 0.725659 | + | 0.688054i | \(0.241535\pi\) | ||||
−0.725659 | + | 0.688054i | \(0.758465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 166.272i | 0.267749i | ||||||||
\(622\) | 608.886i | 0.978917i | ||||||||
\(623\) | 496.099 | − | 366.285i | 0.796307 | − | 0.587938i | ||||
\(624\) | 319.256 | 0.511628 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 819.833i | 1.30964i | ||||||||
\(627\) | −644.149 | −1.02735 | ||||||||
\(628\) | − | 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 | ||||||||
\(633\) | 634.987i | 1.00314i | ||||||||
\(634\) | −304.485 | −0.480260 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 323.466i | 0.508595i | ||||||||
\(637\) | 514.209 | + | 158.396i | 0.807236 | + | 0.248660i | ||||
\(638\) | −2117.94 | −3.31965 | ||||||||
\(639\) | −108.899 | −0.170422 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 173.979 | 0.271418 | 0.135709 | − | 0.990749i | \(-0.456669\pi\) | ||||
0.135709 | + | 0.990749i | \(0.456669\pi\) | |||||||
\(642\) | 143.617i | 0.223703i | ||||||||
\(643\) | 926.785i | 1.44135i | 0.693275 | + | 0.720673i | \(0.256167\pi\) | ||||
−0.693275 | + | 0.720673i | \(0.743833\pi\) | |||||||
\(644\) | −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 | \(0.892272\pi\) | |||||||
\(648\) | −5.20732 | −0.00803599 | ||||||||
\(649\) | 668.036i | 1.02933i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 264.038 | + | 357.615i | 0.405589 | + | 0.549333i | ||||
\(652\) | −689.608 | −1.05768 | ||||||||
\(653\) | 927.100 | 1.41976 | 0.709878 | − | 0.704325i | \(-0.248750\pi\) | ||||
0.709878 | + | 0.704325i | \(0.248750\pi\) | |||||||
\(654\) | − | 443.392i | − | 0.677970i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 631.695i | − | 0.962950i | ||||||
\(657\) | 20.0045i | 0.0304483i | ||||||||
\(658\) | −776.245 | + | 573.126i | −1.17970 | + | 0.871012i | ||||
\(659\) | 692.153 | 1.05031 | 0.525154 | − | 0.851007i | \(-0.324008\pi\) | ||||
0.525154 | + | 0.851007i | \(0.324008\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 424.240i | 0.639879i | ||||||||
\(664\) | 21.2818i | 0.0320510i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 74.9278 | 0.112504 | ||||||||
\(667\) | 1279.86 | 1.91882 | ||||||||
\(668\) | − | 383.675i | − | 0.574364i | ||||||
\(669\) | −489.949 | −0.732360 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1204.01i | 1.79435i | ||||||||
\(672\) | 434.483 | − | 320.792i | 0.646553 | − | 0.477370i | ||||
\(673\) | −701.861 | −1.04288 | −0.521442 | − | 0.853287i | \(-0.674606\pi\) | ||||
−0.521442 | + | 0.853287i | \(0.674606\pi\) | |||||||
\(674\) | 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 | \(-0.0966714\pi\) | |||||||
\(678\) | 14.4232i | 0.0212731i | ||||||||
\(679\) | 753.535 | − | 556.358i | 1.10977 | − | 0.819379i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −365.077 | −0.536090 | ||||||||
\(682\) | 1941.47i | 2.84672i | ||||||||
\(683\) | 766.177 | 1.12178 | 0.560891 | − | 0.827890i | \(-0.310459\pi\) | ||||
0.560891 | + | 0.827890i | \(0.310459\pi\) | |||||||
\(684\) | − | 223.077i | − | 0.326136i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 903.586 | − | 316.764i | 1.31718 | − | 0.461754i | ||||
\(687\) | 238.168 | 0.346678 | ||||||||
\(688\) | −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 | ||||||
\(693\) | −236.609 | − | 320.465i | −0.341427 | − | 0.462432i | ||||
\(694\) | −1584.85 | −2.28364 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.0826i | 0.0575900i | ||||||||
\(697\) | 839.421 | 1.20433 | ||||||||
\(698\) | 395.570i | 0.566719i | ||||||||
\(699\) | − | 134.698i | − | 0.192702i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −69.5098 | −0.0991581 | −0.0495790 | − | 0.998770i | \(-0.515788\pi\) | ||||
−0.0495790 | + | 0.998770i | \(0.515788\pi\) | |||||||
\(702\) | 159.278 | 0.226892 | ||||||||
\(703\) | − | 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 | ||||
\(708\) | −231.350 | −0.326765 | ||||||||
\(709\) | 134.839 | 0.190182 | 0.0950912 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950912 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.6044 | 0.0683606 | ||||||||
\(712\) | − | 50.9712i | − | 0.0715888i | ||||||
\(713\) | − | 1173.22i | − | 1.64546i | ||||||
\(714\) | 448.429 | + | 607.356i | 0.628052 | + | 0.850638i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 348.489 | 0.486716 | ||||||||
\(717\) | 214.503i | 0.299167i | ||||||||
\(718\) | 487.600 | 0.679109 | ||||||||
\(719\) | − | 638.863i | − | 0.888544i | −0.895892 | − | 0.444272i | \(-0.853462\pi\) | ||
0.895892 | − | 0.444272i | \(-0.146538\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −232.367 | + | 171.564i | −0.322284 | + | 0.237952i | ||||
\(722\) | −65.2732 | −0.0904062 | ||||||||
\(723\) | 269.857 | 0.373246 | ||||||||
\(724\) | 238.430i | 0.329323i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 1154.73i | − | 1.59054i | ||||||
\(727\) | − | 704.430i | − | 0.968955i | −0.874804 | − | 0.484477i | \(-0.839010\pi\) | ||
0.874804 | − | 0.484477i | \(-0.160990\pi\) | |||||||
\(728\) | 35.7780 | − | 26.4160i | 0.0491456 | − | 0.0362857i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 420.919i | − | 0.575812i | ||||||
\(732\) | −416.963 | −0.569622 | ||||||||
\(733\) | 275.472i | 0.375815i | 0.982187 | + | 0.187907i | \(0.0601705\pi\) | ||||
−0.982187 | + | 0.187907i | \(0.939830\pi\) | |||||||
\(734\) | 338.188i | 0.460747i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1425.39 | −1.93667 | ||||||||
\(737\) | 405.072 | 0.549622 | ||||||||
\(738\) | − | 315.155i | − | 0.427039i | ||||||
\(739\) | 238.655 | 0.322943 | 0.161471 | − | 0.986877i | \(-0.448376\pi\) | ||||
0.161471 | + | 0.986877i | \(0.448376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 372.882i | − | 0.503214i | ||||||
\(742\) | 571.514 | + | 774.063i | 0.770235 | + | 1.04321i | ||||
\(743\) | −221.162 | −0.297661 | −0.148831 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148831 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(744\) | 36.7429 | 0.0493856 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 253.773 | 0.340178 | ||||||||
\(747\) | 110.347i | 0.147720i | ||||||||
\(748\) | 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 | ||||||||
\(753\) | −482.098 | −0.640237 | ||||||||
\(754\) | − | 1226.02i | − | 1.62602i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 110.981 | − | 81.9408i | 0.146801 | − | 0.108387i | ||||
\(757\) | −866.706 | −1.14492 | −0.572461 | − | 0.819932i | \(-0.694011\pi\) | ||||
−0.572461 | + | 0.819932i | \(0.694011\pi\) | |||||||
\(758\) | −1781.97 | −2.35088 | ||||||||
\(759\) | 1051.34i | 1.38516i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 621.621i | 0.816847i | 0.912793 | + | 0.408424i | \(0.133921\pi\) | ||||
−0.912793 | + | 0.408424i | \(0.866079\pi\) | |||||||
\(762\) | 505.998i | 0.664039i | ||||||||
\(763\) | −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 | ||||||||
\(768\) | − | 485.726i | − | 0.632456i | ||||||
\(769\) | − | 316.574i | − | 0.411669i | −0.978587 | − | 0.205835i | \(-0.934009\pi\) | ||
0.978587 | − | 0.205835i | \(-0.0659909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 382.440 | 0.496031 | ||||||||
\(772\) | −86.2961 | −0.111782 | ||||||||
\(773\) | 710.993i | 0.919784i | 0.887975 | + | 0.459892i | \(0.152112\pi\) | ||||
−0.887975 | + | 0.459892i | \(0.847888\pi\) | |||||||
\(774\) | −158.031 | −0.204174 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 77.4213i | − | 0.0997697i | ||||||
\(777\) | 87.2675 | − | 64.4323i | 0.112313 | − | 0.0829244i | ||||
\(778\) | 696.550 | 0.895308 | ||||||||
\(779\) | −737.801 | −0.947113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −688.570 | −0.881652 | ||||||||
\(782\) | − | 1992.53i | − | 2.54799i | ||||||
\(783\) | 207.829i | 0.265426i | ||||||||
\(784\) | 242.140 | − | 786.070i | 0.308851 | − | 1.00264i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 342.350 | 0.435560 | ||||||||
\(787\) | − | 845.181i | − | 1.07393i | −0.843605 | − | 0.536964i | \(-0.819571\pi\) | ||
0.843605 | − | 0.536964i | \(-0.180429\pi\) | |||||||
\(788\) | 521.443 | 0.661729 | ||||||||
\(789\) | − | 30.0471i | − | 0.0380825i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.4028 | + | 16.7985i | 0.0156799 | + | 0.0212370i | ||||
\(792\) | −32.9259 | −0.0415731 | ||||||||
\(793\) | −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 | \(0.889663\pi\) | |||||||
\(798\) | −394.143 | − | 533.830i | −0.493913 | − | 0.668959i | ||||
\(799\) | −1101.44 | −1.37852 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 264.286i | − | 0.329945i | ||||||
\(802\) | −524.999 | −0.654612 | ||||||||
\(803\) | 126.489i | 0.157520i | ||||||||
\(804\) | 140.282i | 0.174480i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1123.86 | −1.39437 | ||||||||
\(807\) | −864.662 | −1.07145 | ||||||||
\(808\) | 112.769i | 0.139566i | ||||||||
\(809\) | −363.991 | −0.449927 | −0.224963 | − | 0.974367i | \(-0.572226\pi\) | ||||
−0.224963 | + | 0.974367i | \(0.572226\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | 571.586 | 0.703057 | ||||||||
\(814\) | 473.768 | 0.582025 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 648.534 | 0.794772 | ||||||||
\(817\) | 369.963i | 0.452831i | ||||||||
\(818\) | 1429.76i | 1.74787i | ||||||||
\(819\) | 185.509 | − | 136.967i | 0.226507 | − | 0.167237i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 681.271 | 0.829806 | 0.414903 | − | 0.909866i | \(-0.363815\pi\) | ||||
0.414903 | + | 0.909866i | \(0.363815\pi\) | |||||||
\(822\) | − | 767.202i | − | 0.933336i | ||||||
\(823\) | 360.544 | 0.438085 | 0.219042 | − | 0.975715i | \(-0.429707\pi\) | ||||
0.219042 | + | 0.975715i | \(0.429707\pi\) | |||||||
\(824\) | 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 | \(0.345840\pi\) | |||||||
\(828\) | −364.092 | −0.439724 | ||||||||
\(829\) | 128.381i | 0.154862i | 0.996998 | + | 0.0774312i | \(0.0246718\pi\) | ||||
−0.996998 | + | 0.0774312i | \(0.975328\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 255.938i | 0.307988i | ||||||||
\(832\) | 628.144i | 0.754981i | ||||||||
\(833\) | 1044.56 | + | 321.764i | 1.25397 | + | 0.386272i | ||||
\(834\) | −263.152 | −0.315530 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 1410.52i | − | 1.68722i | ||||||
\(837\) | 190.512 | 0.227613 | ||||||||
\(838\) | − | 903.515i | − | 1.07818i | ||||||
\(839\) | 1367.14i | 1.62949i | 0.579823 | + | 0.814743i | \(0.303122\pi\) | ||||
−0.579823 | + | 0.814743i | \(0.696878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 758.735 | 0.902182 | ||||||||
\(842\) | −1406.58 | −1.67053 | ||||||||
\(843\) | − | 612.115i | − | 0.726115i | ||||||
\(844\) | −1390.46 | −1.64746 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 413.528i | 0.488804i | ||||||||
\(847\) | −992.982 | − | 1344.90i | −1.17235 | − | 1.58784i | ||||
\(848\) | 826.544 | 0.974698 | ||||||||
\(849\) | 741.669 | 0.873580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −286.295 | −0.336422 | ||||||||
\(852\) | − | 238.461i | − | 0.279884i | ||||||
\(853\) | 797.415i | 0.934836i | 0.884036 | + | 0.467418i | \(0.154816\pi\) | ||||
−0.884036 | + | 0.467418i | \(0.845184\pi\) | |||||||
\(854\) | −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 | \(-0.175702\pi\) | |||||||
\(858\) | 1007.11 | 1.17379 | ||||||||
\(859\) | 915.157i | 1.06537i | 0.846312 | + | 0.532687i | \(0.178818\pi\) | ||||
−0.846312 | + | 0.532687i | \(0.821182\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −271.009 | − | 367.057i | −0.314761 | − | 0.426315i | ||||
\(862\) | 886.961 | 1.02896 | ||||||||
\(863\) | 1357.85 | 1.57341 | 0.786703 | − | 0.617332i | \(-0.211786\pi\) | ||||
0.786703 | + | 0.617332i | \(0.211786\pi\) | |||||||
\(864\) | − | 231.462i | − | 0.267896i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 729.674i | − | 0.842580i | ||||||
\(867\) | 361.235i | 0.416649i | ||||||||
\(868\) | −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 | ||||||||
\(873\) | − | 401.430i | − | 0.459828i | ||||||
\(874\) | 1751.31i | 2.00379i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −43.8047 | −0.0500053 | ||||||||
\(877\) | −1513.27 | −1.72550 | −0.862752 | − | 0.505627i | \(-0.831261\pi\) | ||||
−0.862752 | + | 0.505627i | \(0.831261\pi\) | |||||||
\(878\) | − | 2203.96i | − | 2.51021i | ||||||
\(879\) | −697.379 | −0.793377 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 677.970i | − | 0.769546i | −0.923011 | − | 0.384773i | \(-0.874280\pi\) | ||
0.923011 | − | 0.384773i | \(-0.125720\pi\) | |||||||
\(882\) | 120.804 | − | 392.173i | 0.136966 | − | 0.444640i | ||||
\(883\) | −155.548 | −0.176159 | −0.0880793 | − | 0.996113i | \(-0.528073\pi\) | ||||
−0.0880793 | + | 0.996113i | \(0.528073\pi\) | |||||||
\(884\) | −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 | \(0.836553\pi\) | |||||||
\(888\) | − | 8.96622i | − | 0.0100971i | ||||||
\(889\) | 435.120 | + | 589.330i | 0.489449 | + | 0.662913i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −170.721 | −0.191606 | ||||||||
\(892\) | − | 1072.86i | − | 1.20276i | ||||||
\(893\) | 968.101 | 1.08410 | ||||||||
\(894\) | − | 1107.73i | − | 1.23907i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −76.8784 | − | 104.125i | −0.0858018 | − | 0.116211i | ||||
\(897\) | −608.592 | −0.678475 | ||||||||
\(898\) | 1474.35 | 1.64181 | ||||||||
\(899\) | − | 1466.44i | − | 1.63119i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1098.34i | 1.21903i | ||||||||
\(902\) | − | 1992.72i | − | 2.20923i | ||||||
\(903\) | −184.057 | + | 135.895i | −0.203828 | + | 0.150493i | ||||
\(904\) | 1.72594 | 0.00190923 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 956.067i | 1.05526i | ||||||||
\(907\) | 473.129 | 0.521642 | 0.260821 | − | 0.965387i | \(-0.416007\pi\) | ||||
0.260821 | + | 0.965387i | \(0.416007\pi\) | |||||||
\(908\) | − | 799.422i | − | 0.880421i | ||||||
\(909\) | 584.709i | 0.643244i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −676.153 | −0.742210 | −0.371105 | − | 0.928591i | \(-0.621021\pi\) | ||||
−0.371105 | + | 0.928591i | \(0.621021\pi\) | |||||||
\(912\) | −570.023 | −0.625025 | ||||||||
\(913\) | 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 | ||||
\(918\) | 323.556 | 0.352457 | ||||||||
\(919\) | 1204.50 | 1.31066 | 0.655331 | − | 0.755342i | \(-0.272529\pi\) | ||||
0.655331 | + | 0.755342i | \(0.272529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −160.618 | −0.174395 | ||||||||
\(922\) | − | 1115.57i | − | 1.20995i | ||||||
\(923\) | − | 398.596i | − | 0.431848i | ||||||
\(924\) | 701.734 | − | 518.112i | 0.759452 | − | 0.560727i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1899.00 | 2.05075 | ||||||||
\(927\) | 123.789i | 0.133537i | ||||||||
\(928\) | −1781.65 | −1.91988 | ||||||||
\(929\) | − | 586.143i | − | 0.630940i | −0.948936 | − | 0.315470i | \(-0.897838\pi\) | ||
0.948936 | − | 0.315470i | \(-0.102162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −918.107 | − | 282.812i | −0.986151 | − | 0.303772i | ||||
\(932\) | 294.954 | 0.316474 | ||||||||
\(933\) | 377.791 | 0.404921 | ||||||||
\(934\) | − | 2024.48i | − | 2.16754i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 19.0599i | − | 0.0203632i | ||||||
\(937\) | 449.053i | 0.479245i | 0.970866 | + | 0.239623i | \(0.0770237\pi\) | ||||
−0.970866 | + | 0.239623i | \(0.922976\pi\) | |||||||
\(938\) | 247.856 | + | 335.697i | 0.264238 | + | 0.357886i | ||||
\(939\) | 508.676 | 0.541721 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 904.538i | − | 0.961252i | −0.876926 | − | 0.480626i | \(-0.840409\pi\) | ||
0.876926 | − | 0.480626i | \(-0.159591\pi\) | |||||||
\(942\) | −1020.38 | −1.08321 | ||||||||
\(943\) | 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 | \(0.830436\pi\) | |||||||
\(948\) | 106.431i | 0.112269i | ||||||||
\(949\) | −73.2210 | −0.0771560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 188.921i | 0.198656i | ||||||||
\(952\) | 72.6791 | − | 53.6612i | 0.0763435 | − | 0.0563668i | ||||
\(953\) | −1547.14 | −1.62344 | −0.811721 | − | 0.584046i | \(-0.801469\pi\) | ||||
−0.811721 | + | 0.584046i | \(0.801469\pi\) | |||||||
\(954\) | 412.365 | 0.432249 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −469.705 | −0.491323 | ||||||||
\(957\) | 1314.10i | 1.37315i | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 89.1092 | 0.0925329 | ||||||||
\(964\) | 590.915i | 0.612982i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −871.281 | + | 643.293i | −0.901947 | + | 0.665935i | ||||
\(967\) | −282.618 | −0.292263 | −0.146131 | − | 0.989265i | \(-0.546682\pi\) | ||||
−0.146131 | + | 0.989265i | \(0.546682\pi\) | |||||||
\(968\) | −138.181 | −0.142749 | ||||||||
\(969\) | − | 757.469i | − | 0.781701i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 586.935i | − | 0.604465i | −0.953234 | − | 0.302232i | \(-0.902268\pi\) | ||
0.953234 | − | 0.302232i | \(-0.0977319\pi\) | |||||||
\(972\) | − | 59.1229i | − | 0.0608260i | ||||||
\(973\) | −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 | \(0.391763\pi\) | |||||||
\(978\) | 879.135i | 0.898911i | ||||||||
\(979\) | − | 1671.08i | − | 1.70693i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −275.109 | −0.280437 | ||||||||
\(982\) | −958.283 | −0.975848 | ||||||||
\(983\) | − | 583.048i | − | 0.593131i | −0.955013 | − | 0.296565i | \(-0.904159\pi\) | ||
0.955013 | − | 0.296565i | \(-0.0958413\pi\) | |||||||
\(984\) | −37.7129 | −0.0383261 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2490.53i | − | 2.52589i | ||||||
\(987\) | 355.603 | + | 481.631i | 0.360287 | + | 0.487975i | ||||
\(988\) | 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 | ||||||||
\(993\) | − | 708.259i | − | 0.713251i | ||||||
\(994\) | −421.323 | − | 570.643i | −0.423866 | − | 0.574087i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −241.630 | −0.242600 | ||||||||
\(997\) | − | 1586.82i | − | 1.59159i | −0.605565 | − | 0.795795i | \(-0.707053\pi\) | ||
0.605565 | − | 0.795795i | \(-0.292947\pi\) | |||||||
\(998\) | −1174.08 | −1.17643 | ||||||||
\(999\) | − | 46.4899i | − | 0.0465364i |
(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 | 525.3.h.d.76.9 | 12 | ||
5.2 | odd | 4 | 525.3.e.c.349.8 | 24 | |||
5.3 | odd | 4 | 525.3.e.c.349.21 | 24 | |||
5.4 | even | 2 | 105.3.h.a.76.4 | yes | 12 | ||
7.6 | odd | 2 | inner | 525.3.h.d.76.10 | 12 | ||
15.14 | odd | 2 | 315.3.h.d.181.10 | 12 | |||
20.19 | odd | 2 | 1680.3.s.c.1441.1 | 12 | |||
35.13 | even | 4 | 525.3.e.c.349.7 | 24 | |||
35.27 | even | 4 | 525.3.e.c.349.22 | 24 | |||
35.34 | odd | 2 | 105.3.h.a.76.3 | ✓ | 12 | ||
105.104 | even | 2 | 315.3.h.d.181.9 | 12 | |||
140.139 | even | 2 | 1680.3.s.c.1441.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.3 | ✓ | 12 | 35.34 | odd | 2 | ||
105.3.h.a.76.4 | yes | 12 | 5.4 | even | 2 | ||
315.3.h.d.181.9 | 12 | 105.104 | even | 2 | |||
315.3.h.d.181.10 | 12 | 15.14 | odd | 2 | |||
525.3.e.c.349.7 | 24 | 35.13 | even | 4 | |||
525.3.e.c.349.8 | 24 | 5.2 | odd | 4 | |||
525.3.e.c.349.21 | 24 | 5.3 | odd | 4 | |||
525.3.e.c.349.22 | 24 | 35.27 | even | 4 | |||
525.3.h.d.76.9 | 12 | 1.1 | even | 1 | trivial | ||
525.3.h.d.76.10 | 12 | 7.6 | odd | 2 | inner | ||
1680.3.s.c.1441.1 | 12 | 20.19 | odd | 2 | |||
1680.3.s.c.1441.10 | 12 | 140.139 | even | 2 |