Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(349,525)]
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, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.349");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.e (of order \(2\), degree \(1\), not 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: | \(24\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.8 | ||
Character | \(\chi\) | \(=\) | 525.349 |
Dual form | 525.3.e.c.349.7 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79155i | 1.39577i | 0.716208 | + | 0.697887i | \(0.245876\pi\) | ||||
−0.716208 | + | 0.697887i | \(0.754124\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −3.79273 | −0.948184 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 4.83510i | − | 0.805850i | ||||||
\(7\) | 5.63139 | − | 4.15782i | 0.804484 | − | 0.593975i | ||||
\(8\) | 0.578591i | 0.0723239i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.9690 | −1.72445 | −0.862227 | − | 0.506522i | \(-0.830931\pi\) | ||||
−0.862227 | + | 0.506522i | \(0.830931\pi\) | |||||||
\(12\) | 6.56921 | 0.547434 | ||||||||
\(13\) | −10.9807 | −0.844667 | −0.422333 | − | 0.906441i | \(-0.638789\pi\) | ||||
−0.422333 | + | 0.906441i | \(0.638789\pi\) | |||||||
\(14\) | 11.6068 | + | 15.7203i | 0.829054 | + | 1.12288i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −16.7861 | −1.04913 | ||||||||
\(17\) | 22.3060 | 1.31212 | 0.656060 | − | 0.754709i | \(-0.272222\pi\) | ||||
0.656060 | + | 0.754709i | \(0.272222\pi\) | |||||||
\(18\) | 8.37464i | 0.465258i | ||||||||
\(19\) | − | 19.6057i | − | 1.03188i | −0.856625 | − | 0.515939i | \(-0.827443\pi\) | ||
0.856625 | − | 0.515939i | \(-0.172557\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.75385 | + | 7.20156i | −0.464469 | + | 0.342932i | ||||
\(22\) | − | 52.9528i | − | 2.40695i | ||||||
\(23\) | − | 31.9991i | − | 1.39126i | −0.718399 | − | 0.695632i | \(-0.755125\pi\) | ||
0.718399 | − | 0.695632i | \(-0.244875\pi\) | |||||||
\(24\) | − | 1.00215i | − | 0.0417562i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 30.6530i | − | 1.17896i | ||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −21.3583 | + | 15.7695i | −0.762798 | + | 0.563197i | ||||
\(29\) | −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 | \(-0.201407\pi\) | |||||||
\(32\) | − | 44.5448i | − | 1.39203i | ||||||
\(33\) | 32.8553 | 0.995614 | ||||||||
\(34\) | 62.2683i | 1.83142i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.3782 | −0.316061 | ||||||||
\(37\) | − | 8.94699i | − | 0.241810i | −0.992664 | − | 0.120905i | \(-0.961420\pi\) | ||
0.992664 | − | 0.120905i | \(-0.0385797\pi\) | |||||||
\(38\) | 54.7302 | 1.44027 | ||||||||
\(39\) | 19.0191 | 0.487669 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 37.6320i | 0.917854i | 0.888474 | + | 0.458927i | \(0.151766\pi\) | ||||
−0.888474 | + | 0.458927i | \(0.848234\pi\) | |||||||
\(42\) | −20.1035 | − | 27.2283i | −0.478655 | − | 0.648293i | ||||
\(43\) | − | 18.8702i | − | 0.438841i | −0.975630 | − | 0.219421i | \(-0.929583\pi\) | ||
0.975630 | − | 0.219421i | \(-0.0704167\pi\) | |||||||
\(44\) | 71.9443 | 1.63510 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 89.3269 | 1.94189 | ||||||||
\(47\) | 49.3786 | 1.05061 | 0.525304 | − | 0.850914i | \(-0.323952\pi\) | ||||
0.525304 | + | 0.850914i | \(0.323952\pi\) | |||||||
\(48\) | 29.0744 | 0.605716 | ||||||||
\(49\) | 14.4250 | − | 46.8286i | 0.294388 | − | 0.955686i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −38.6352 | −0.757552 | ||||||||
\(52\) | 41.6468 | 0.800899 | ||||||||
\(53\) | 49.2398i | 0.929052i | 0.885559 | + | 0.464526i | \(0.153775\pi\) | ||||
−0.885559 | + | 0.464526i | \(0.846225\pi\) | |||||||
\(54\) | − | 14.5053i | − | 0.268617i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.40568 | + | 3.25827i | 0.0429586 | + | 0.0581834i | ||||
\(57\) | 33.9580i | 0.595755i | ||||||||
\(58\) | − | 111.653i | − | 1.92505i | ||||||
\(59\) | 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 | \(-0.174167\pi\) | |||||||
\(62\) | 102.349 | 1.65080 | ||||||||
\(63\) | 16.8942 | − | 12.4735i | 0.268161 | − | 0.197992i | ||||
\(64\) | 57.2046 | 0.893821 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 91.7170i | 1.38965i | ||||||||
\(67\) | − | 21.3544i | − | 0.318723i | −0.987220 | − | 0.159361i | \(-0.949057\pi\) | ||
0.987220 | − | 0.159361i | \(-0.0509435\pi\) | |||||||
\(68\) | −84.6008 | −1.24413 | ||||||||
\(69\) | 55.4240i | 0.803246i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.2998 | 0.511265 | 0.255632 | − | 0.966774i | \(-0.417716\pi\) | ||||
0.255632 | + | 0.966774i | \(0.417716\pi\) | |||||||
\(72\) | 1.73577i | 0.0241080i | ||||||||
\(73\) | −6.66818 | −0.0913449 | −0.0456725 | − | 0.998956i | \(-0.514543\pi\) | ||||
−0.0456725 | + | 0.998956i | \(0.514543\pi\) | |||||||
\(74\) | 24.9759 | 0.337513 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 74.3591i | 0.978409i | ||||||||
\(77\) | −106.822 | + | 78.8697i | −1.38729 | + | 1.02428i | ||||
\(78\) | 53.0926i | 0.680675i | ||||||||
\(79\) | 16.2015 | 0.205082 | 0.102541 | − | 0.994729i | \(-0.467303\pi\) | ||||
0.102541 | + | 0.994729i | \(0.467303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −105.052 | −1.28112 | ||||||||
\(83\) | −36.7822 | −0.443159 | −0.221579 | − | 0.975142i | \(-0.571121\pi\) | ||||
−0.221579 | + | 0.975142i | \(0.571121\pi\) | |||||||
\(84\) | 36.9937 | − | 27.3136i | 0.440402 | − | 0.325162i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 52.6770 | 0.612523 | ||||||||
\(87\) | 69.2763 | 0.796279 | ||||||||
\(88\) | − | 10.9753i | − | 0.124719i | ||||||
\(89\) | − | 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 | ||||
\(92\) | 121.364i | 1.31917i | ||||||||
\(93\) | 63.5040i | 0.682839i | ||||||||
\(94\) | 137.843i | 1.46641i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 77.1539i | 0.803687i | ||||||||
\(97\) | −133.810 | −1.37948 | −0.689742 | − | 0.724055i | \(-0.742276\pi\) | ||||
−0.689742 | + | 0.724055i | \(0.742276\pi\) | |||||||
\(98\) | 130.724 | + | 40.2681i | 1.33392 | + | 0.410899i | ||||
\(99\) | −56.9070 | −0.574818 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 194.903i | − | 1.92973i | −0.262743 | − | 0.964866i | \(-0.584627\pi\) | ||
0.262743 | − | 0.964866i | \(-0.415373\pi\) | |||||||
\(102\) | − | 107.852i | − | 1.05737i | ||||||
\(103\) | −41.2629 | −0.400610 | −0.200305 | − | 0.979734i | \(-0.564193\pi\) | ||||
−0.200305 | + | 0.979734i | \(0.564193\pi\) | |||||||
\(104\) | − | 6.35332i | − | 0.0610896i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −137.455 | −1.29675 | ||||||||
\(107\) | − | 29.7031i | − | 0.277599i | −0.990321 | − | 0.138799i | \(-0.955676\pi\) | ||
0.990321 | − | 0.138799i | \(-0.0443243\pi\) | |||||||
\(108\) | 19.7076 | 0.182478 | ||||||||
\(109\) | −91.7028 | −0.841310 | −0.420655 | − | 0.907221i | \(-0.638200\pi\) | ||||
−0.420655 | + | 0.907221i | \(0.638200\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.4966i | 0.139609i | ||||||||
\(112\) | −94.5290 | + | 69.7937i | −0.844009 | + | 0.623158i | ||||
\(113\) | 2.98301i | 0.0263983i | 0.999913 | + | 0.0131992i | \(0.00420155\pi\) | ||||
−0.999913 | + | 0.0131992i | \(0.995798\pi\) | |||||||
\(114\) | −94.7954 | −0.831539 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 151.697 | 1.30773 | ||||||||
\(117\) | −32.9420 | −0.281556 | ||||||||
\(118\) | −98.3107 | −0.833142 | ||||||||
\(119\) | 125.614 | − | 92.7445i | 1.05558 | − | 0.779366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 238.823 | 1.97374 | ||||||||
\(122\) | 177.186 | 1.45234 | ||||||||
\(123\) | − | 65.1806i | − | 0.529923i | ||||||
\(124\) | 139.057i | 1.12143i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 34.8203 | + | 47.1608i | 0.276351 | + | 0.374292i | ||||
\(127\) | − | 104.651i | − | 0.824023i | −0.911179 | − | 0.412012i | \(-0.864826\pi\) | ||
0.911179 | − | 0.412012i | \(-0.135174\pi\) | |||||||
\(128\) | − | 18.4901i | − | 0.144454i | ||||||
\(129\) | 32.6841i | 0.253365i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70.8051i | 0.540497i | 0.962791 | + | 0.270249i | \(0.0871059\pi\) | ||||
−0.962791 | + | 0.270249i | \(0.912894\pi\) | |||||||
\(132\) | −124.611 | −0.944025 | ||||||||
\(133\) | −81.5169 | − | 110.407i | −0.612909 | − | 0.830129i | ||||
\(134\) | 59.6118 | 0.444864 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.9061i | 0.0948976i | ||||||||
\(137\) | 158.673i | 1.15820i | 0.815256 | + | 0.579100i | \(0.196596\pi\) | ||||
−0.815256 | + | 0.579100i | \(0.803404\pi\) | |||||||
\(138\) | −154.719 | −1.12115 | ||||||||
\(139\) | 54.4253i | 0.391549i | 0.980649 | + | 0.195774i | \(0.0627220\pi\) | ||||
−0.980649 | + | 0.195774i | \(0.937278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −85.5262 | −0.606569 | ||||||||
\(142\) | 101.333i | 0.713610i | ||||||||
\(143\) | 208.292 | 1.45659 | ||||||||
\(144\) | −50.3583 | −0.349710 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 18.6145i | − | 0.127497i | ||||||
\(147\) | −24.9848 | + | 81.1095i | −0.169965 | + | 0.551766i | ||||
\(148\) | 33.9335i | 0.229281i | ||||||||
\(149\) | −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 | \(0.727226\pi\) | |||||||
\(152\) | 11.3437 | 0.0746294 | ||||||||
\(153\) | 66.9181 | 0.437373 | ||||||||
\(154\) | −220.169 | − | 298.198i | −1.42967 | − | 1.93635i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −72.1343 | −0.462399 | ||||||||
\(157\) | 211.036 | 1.34418 | 0.672089 | − | 0.740470i | \(-0.265397\pi\) | ||||
0.672089 | + | 0.740470i | \(0.265397\pi\) | |||||||
\(158\) | 45.2271i | 0.286248i | ||||||||
\(159\) | − | 85.2858i | − | 0.536389i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −133.046 | − | 180.199i | −0.826375 | − | 1.11925i | ||||
\(162\) | 25.1239i | 0.155086i | ||||||||
\(163\) | 181.823i | 1.11548i | 0.830015 | + | 0.557741i | \(0.188332\pi\) | ||||
−0.830015 | + | 0.557741i | \(0.811668\pi\) | |||||||
\(164\) | − | 142.728i | − | 0.870295i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 102.679i | − | 0.618549i | ||||||
\(167\) | 101.160 | 0.605751 | 0.302876 | − | 0.953030i | \(-0.402053\pi\) | ||||
0.302876 | + | 0.953030i | \(0.402053\pi\) | |||||||
\(168\) | −4.16676 | − | 5.64349i | −0.0248021 | − | 0.0335922i | ||||
\(169\) | −48.4250 | −0.286538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 58.8170i | − | 0.343959i | ||||||
\(172\) | 71.5696i | 0.416102i | ||||||||
\(173\) | −109.976 | −0.635702 | −0.317851 | − | 0.948141i | \(-0.602961\pi\) | ||||
−0.317851 | + | 0.948141i | \(0.602961\pi\) | |||||||
\(174\) | 193.388i | 1.11143i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 318.415 | 1.80918 | ||||||||
\(177\) | − | 60.9981i | − | 0.344622i | ||||||
\(178\) | 245.922 | 1.38159 | ||||||||
\(179\) | −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 | \(0.944441\pi\) | |||||||
\(182\) | −127.450 | − | 172.619i | −0.700275 | − | 0.948457i | ||||
\(183\) | 109.937i | 0.600750i | ||||||||
\(184\) | 18.5144 | 0.100622 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −177.274 | −0.953088 | ||||||||
\(187\) | −423.123 | −2.26269 | ||||||||
\(188\) | −187.280 | −0.996170 | ||||||||
\(189\) | −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 | \(0.563748\pi\) | |||||||
\(192\) | −99.0812 | −0.516048 | ||||||||
\(193\) | 22.7530i | 0.117891i | 0.998261 | + | 0.0589456i | \(0.0187738\pi\) | ||||
−0.998261 | + | 0.0589456i | \(0.981226\pi\) | |||||||
\(194\) | − | 373.537i | − | 1.92545i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −54.7102 | + | 177.609i | −0.279134 | + | 0.906166i | ||||
\(197\) | 137.485i | 0.697891i | 0.937143 | + | 0.348946i | \(0.113460\pi\) | ||||
−0.937143 | + | 0.348946i | \(0.886540\pi\) | |||||||
\(198\) | − | 158.858i | − | 0.802316i | ||||||
\(199\) | − | 267.299i | − | 1.34321i | −0.740909 | − | 0.671606i | \(-0.765605\pi\) | ||
0.740909 | − | 0.671606i | \(-0.234395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.9869i | 0.184015i | ||||||||
\(202\) | 544.081 | 2.69347 | ||||||||
\(203\) | −225.237 | + | 166.299i | −1.10954 | + | 0.819208i | ||||
\(204\) | 146.533 | 0.718299 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 115.187i | − | 0.559161i | ||||||
\(207\) | − | 95.9972i | − | 0.463754i | ||||||
\(208\) | 184.323 | 0.886166 | ||||||||
\(209\) | 371.900i | 1.77943i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −366.610 | −1.73749 | −0.868744 | − | 0.495261i | \(-0.835073\pi\) | ||||
−0.868744 | + | 0.495261i | \(0.835073\pi\) | |||||||
\(212\) | − | 186.753i | − | 0.880912i | ||||||
\(213\) | −62.8731 | −0.295179 | ||||||||
\(214\) | 82.9175 | 0.387465 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 3.00645i | − | 0.0139187i | ||||||
\(217\) | −152.443 | − | 206.469i | −0.702501 | − | 0.951472i | ||||
\(218\) | − | 255.993i | − | 1.17428i | ||||||
\(219\) | 11.5496 | 0.0527380 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −244.935 | −1.10830 | ||||||||
\(222\) | −43.2596 | −0.194863 | ||||||||
\(223\) | −282.872 | −1.26848 | −0.634242 | − | 0.773134i | \(-0.718688\pi\) | ||||
−0.634242 | + | 0.773134i | \(0.718688\pi\) | |||||||
\(224\) | −185.210 | − | 250.849i | −0.826828 | − | 1.11986i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.32722 | −0.0368461 | ||||||||
\(227\) | 210.777 | 0.928534 | 0.464267 | − | 0.885695i | \(-0.346318\pi\) | ||||
0.464267 | + | 0.885695i | \(0.346318\pi\) | |||||||
\(228\) | − | 128.794i | − | 0.564885i | ||||||
\(229\) | − | 137.506i | − | 0.600464i | −0.953866 | − | 0.300232i | \(-0.902936\pi\) | ||
0.953866 | − | 0.300232i | \(-0.0970641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 185.021 | − | 136.606i | 0.800955 | − | 0.591370i | ||||
\(232\) | − | 23.1417i | − | 0.0997488i | ||||||
\(233\) | − | 77.7682i | − | 0.333769i | −0.985976 | − | 0.166884i | \(-0.946629\pi\) | ||
0.985976 | − | 0.166884i | \(-0.0533707\pi\) | |||||||
\(234\) | − | 91.9591i | − | 0.392988i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 133.570i | − | 0.565974i | ||||||
\(237\) | −28.0618 | −0.118404 | ||||||||
\(238\) | 258.901 | + | 350.657i | 1.08782 | + | 1.47335i | ||||
\(239\) | 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 | \(0.895228\pi\) | |||||||
\(242\) | 666.684i | 2.75489i | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 240.734i | 0.986613i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 181.955 | 0.739653 | ||||||||
\(247\) | 215.283i | 0.871593i | ||||||||
\(248\) | 21.2135 | 0.0855383 | ||||||||
\(249\) | 63.7086 | 0.255858 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 278.340i | − | 1.10892i | −0.832210 | − | 0.554461i | \(-0.812924\pi\) | ||
0.832210 | − | 0.554461i | \(-0.187076\pi\) | |||||||
\(252\) | −64.0750 | + | 47.3086i | −0.254266 | + | 0.187732i | ||||
\(253\) | 606.990i | 2.39917i | ||||||||
\(254\) | 292.138 | 1.15015 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 280.434 | 1.09545 | ||||||||
\(257\) | −220.802 | −0.859151 | −0.429575 | − | 0.903031i | \(-0.641337\pi\) | ||||
−0.429575 | + | 0.903031i | \(0.641337\pi\) | |||||||
\(258\) | −91.2392 | −0.353640 | ||||||||
\(259\) | −37.2000 | − | 50.3839i | −0.143629 | − | 0.194533i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −119.990 | −0.459732 | ||||||||
\(262\) | −197.656 | −0.754412 | ||||||||
\(263\) | − | 17.3477i | − | 0.0659609i | −0.999456 | − | 0.0329804i | \(-0.989500\pi\) | ||
0.999456 | − | 0.0329804i | \(-0.0104999\pi\) | |||||||
\(264\) | 19.0098i | 0.0720067i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 308.207 | − | 227.558i | 1.15867 | − | 0.855483i | ||||
\(267\) | 152.586i | 0.571482i | ||||||||
\(268\) | 80.9916i | 0.302207i | ||||||||
\(269\) | 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 | \(0.791625\pi\) | |||||||
\(272\) | −374.431 | −1.37659 | ||||||||
\(273\) | 107.104 | − | 79.0780i | 0.392321 | − | 0.289663i | ||||
\(274\) | −442.944 | −1.61659 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 210.209i | − | 0.761625i | ||||||
\(277\) | − | 147.766i | − | 0.533452i | −0.963772 | − | 0.266726i | \(-0.914058\pi\) | ||
0.963772 | − | 0.266726i | \(-0.0859418\pi\) | |||||||
\(278\) | −151.931 | −0.546513 | ||||||||
\(279\) | − | 109.992i | − | 0.394237i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 353.405 | 1.25767 | 0.628834 | − | 0.777540i | \(-0.283533\pi\) | ||||
0.628834 | + | 0.777540i | \(0.283533\pi\) | |||||||
\(282\) | − | 238.751i | − | 0.846633i | ||||||
\(283\) | 428.203 | 1.51308 | 0.756542 | − | 0.653945i | \(-0.226887\pi\) | ||||
0.756542 | + | 0.653945i | \(0.226887\pi\) | |||||||
\(284\) | −137.675 | −0.484773 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 581.457i | 2.03307i | ||||||||
\(287\) | 156.467 | + | 211.920i | 0.545182 | + | 0.738399i | ||||
\(288\) | − | 133.634i | − | 0.464009i | ||||||
\(289\) | 208.559 | 0.721657 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 231.766 | 0.796446 | ||||||||
\(292\) | 25.2906 | 0.0866117 | ||||||||
\(293\) | −402.632 | −1.37417 | −0.687085 | − | 0.726577i | \(-0.741110\pi\) | ||||
−0.687085 | + | 0.726577i | \(0.741110\pi\) | |||||||
\(294\) | −226.421 | − | 69.7463i | −0.770140 | − | 0.237232i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.17665 | 0.0174887 | ||||||||
\(297\) | 98.5658 | 0.331871 | ||||||||
\(298\) | − | 639.550i | − | 2.14614i | ||||||
\(299\) | 351.371i | 1.17515i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −78.4589 | − | 106.265i | −0.260661 | − | 0.353041i | ||||
\(302\) | − | 551.986i | − | 1.82777i | ||||||
\(303\) | 337.582i | 1.11413i | ||||||||
\(304\) | 329.103i | 1.08258i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 186.805i | 0.610474i | ||||||||
\(307\) | 92.7330 | 0.302062 | 0.151031 | − | 0.988529i | \(-0.451741\pi\) | ||||
0.151031 | + | 0.988529i | \(0.451741\pi\) | |||||||
\(308\) | 405.146 | − | 299.132i | 1.31541 | − | 0.971207i | ||||
\(309\) | 71.4694 | 0.231292 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 218.118i | 0.701343i | 0.936498 | + | 0.350672i | \(0.114047\pi\) | ||||
−0.936498 | + | 0.350672i | \(0.885953\pi\) | |||||||
\(312\) | 11.0043i | 0.0352701i | ||||||||
\(313\) | 293.684 | 0.938288 | 0.469144 | − | 0.883122i | \(-0.344562\pi\) | ||||
0.469144 | + | 0.883122i | \(0.344562\pi\) | |||||||
\(314\) | 589.117i | 1.87617i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −61.4479 | −0.194455 | ||||||||
\(317\) | − | 109.074i | − | 0.344081i | −0.985090 | − | 0.172041i | \(-0.944964\pi\) | ||
0.985090 | − | 0.172041i | \(-0.0550361\pi\) | |||||||
\(318\) | 238.079 | 0.748677 | ||||||||
\(319\) | 758.697 | 2.37836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 51.4472i | 0.160272i | ||||||||
\(322\) | 503.034 | − | 371.405i | 1.56222 | − | 1.15343i | ||||
\(323\) | − | 437.325i | − | 1.35395i | ||||||
\(324\) | −34.1346 | −0.105354 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −507.569 | −1.55696 | ||||||||
\(327\) | 158.834 | 0.485731 | ||||||||
\(328\) | −21.7736 | −0.0663828 | ||||||||
\(329\) | 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 | \(0.288067\pi\) | |||||||
\(332\) | 139.505 | 0.420196 | ||||||||
\(333\) | − | 26.8410i | − | 0.0806035i | ||||||
\(334\) | 282.394i | 0.845492i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 163.729 | − | 120.886i | 0.487289 | − | 0.359780i | ||||
\(337\) | 299.269i | 0.888040i | 0.896017 | + | 0.444020i | \(0.146448\pi\) | ||||
−0.896017 | + | 0.444020i | \(0.853552\pi\) | |||||||
\(338\) | − | 135.181i | − | 0.399942i | ||||||
\(339\) | − | 5.16673i | − | 0.0152411i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 695.480i | 2.03953i | ||||||||
\(342\) | 164.190 | 0.480089 | ||||||||
\(343\) | −113.472 | − | 323.687i | −0.330823 | − | 0.943693i | ||||
\(344\) | 10.9181 | 0.0317387 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 307.004i | − | 0.887296i | ||||||
\(347\) | − | 567.731i | − | 1.63611i | −0.575138 | − | 0.818056i | \(-0.695052\pi\) | ||
0.575138 | − | 0.818056i | \(-0.304948\pi\) | |||||||
\(348\) | −262.747 | −0.755019 | ||||||||
\(349\) | − | 141.703i | − | 0.406025i | −0.979176 | − | 0.203012i | \(-0.934927\pi\) | ||
0.979176 | − | 0.203012i | \(-0.0650732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 57.0572 | 0.162556 | ||||||||
\(352\) | 844.970i | 2.40048i | ||||||||
\(353\) | −452.435 | −1.28169 | −0.640843 | − | 0.767672i | \(-0.721415\pi\) | ||||
−0.640843 | + | 0.767672i | \(0.721415\pi\) | |||||||
\(354\) | 170.279 | 0.481015 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 334.123i | 0.938546i | ||||||||
\(357\) | −217.570 | + | 160.638i | −0.609439 | + | 0.449967i | ||||
\(358\) | − | 256.496i | − | 0.716470i | ||||||
\(359\) | −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 | ||||||||
\(362\) | −175.490 | −0.484780 | ||||||||
\(363\) | −413.653 | −1.13954 | ||||||||
\(364\) | 234.529 | − | 173.160i | 0.644310 | − | 0.475714i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −306.895 | −0.838511 | ||||||||
\(367\) | −121.147 | −0.330101 | −0.165051 | − | 0.986285i | \(-0.552779\pi\) | ||||
−0.165051 | + | 0.986285i | \(0.552779\pi\) | |||||||
\(368\) | 537.139i | 1.45962i | ||||||||
\(369\) | 112.896i | 0.305951i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 204.730 | + | 277.288i | 0.551834 | + | 0.747407i | ||||
\(372\) | − | 240.854i | − | 0.647456i | ||||||
\(373\) | − | 90.9075i | − | 0.243720i | −0.992547 | − | 0.121860i | \(-0.961114\pi\) | ||
0.992547 | − | 0.121860i | \(-0.0388859\pi\) | |||||||
\(374\) | − | 1181.17i | − | 3.15820i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.5700i | 0.0759841i | ||||||||
\(377\) | 439.190 | 1.16496 | ||||||||
\(378\) | −60.3105 | − | 81.6850i | −0.159552 | − | 0.216098i | ||||
\(379\) | 638.344 | 1.68429 | 0.842143 | − | 0.539254i | \(-0.181294\pi\) | ||||
0.842143 | + | 0.539254i | \(0.181294\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 181.261i | 0.475750i | ||||||||
\(382\) | − | 212.137i | − | 0.555331i | ||||||
\(383\) | 176.395 | 0.460561 | 0.230281 | − | 0.973124i | \(-0.426036\pi\) | ||||
0.230281 | + | 0.973124i | \(0.426036\pi\) | |||||||
\(384\) | 32.0257i | 0.0834003i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −63.5160 | −0.164549 | ||||||||
\(387\) | − | 56.6105i | − | 0.146280i | ||||||
\(388\) | 507.506 | 1.30800 | ||||||||
\(389\) | −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 | ||||||
\(392\) | 27.0946 | + | 8.34618i | 0.0691189 | + | 0.0212913i | ||||
\(393\) | − | 122.638i | − | 0.312056i | ||||||
\(394\) | −383.795 | −0.974098 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 215.833 | 0.545033 | ||||||||
\(397\) | 186.071 | 0.468694 | 0.234347 | − | 0.972153i | \(-0.424705\pi\) | ||||
0.234347 | + | 0.972153i | \(0.424705\pi\) | |||||||
\(398\) | 746.178 | 1.87482 | ||||||||
\(399\) | 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 | \(0.575345\pi\) | |||||||
\(402\) | −103.251 | −0.256843 | ||||||||
\(403\) | 402.596i | 0.998997i | ||||||||
\(404\) | 739.215i | 1.82974i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −464.232 | − | 628.759i | −1.14343 | − | 1.54867i | ||||
\(407\) | 169.715i | 0.416991i | ||||||||
\(408\) | − | 22.3540i | − | 0.0547891i | ||||||
\(409\) | − | 512.173i | − | 1.25226i | −0.779720 | − | 0.626128i | \(-0.784639\pi\) | ||
0.779720 | − | 0.626128i | \(-0.215361\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 274.831i | − | 0.668687i | ||||||
\(412\) | 156.499 | 0.379852 | ||||||||
\(413\) | 146.427 | + | 198.322i | 0.354545 | + | 0.480199i | ||||
\(414\) | 267.981 | 0.647296 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 489.132i | 1.17580i | ||||||||
\(417\) | − | 94.2673i | − | 0.226061i | ||||||
\(418\) | −1038.18 | −2.48367 | ||||||||
\(419\) | 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 | \(0.704206\pi\) | |||||||
\(422\) | − | 1023.41i | − | 2.42514i | ||||||
\(423\) | 148.136 | 0.350203 | ||||||||
\(424\) | −28.4897 | −0.0671927 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 175.513i | − | 0.412003i | ||||||
\(427\) | −263.907 | − | 357.437i | −0.618049 | − | 0.837089i | ||||
\(428\) | 112.656i | 0.263215i | ||||||||
\(429\) | −360.773 | −0.840962 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 317.731 | 0.737195 | 0.368597 | − | 0.929589i | \(-0.379838\pi\) | ||||
0.368597 | + | 0.929589i | \(0.379838\pi\) | |||||||
\(432\) | 87.2231 | 0.201905 | ||||||||
\(433\) | −261.387 | −0.603665 | −0.301833 | − | 0.953361i | \(-0.597598\pi\) | ||||
−0.301833 | + | 0.953361i | \(0.597598\pi\) | |||||||
\(434\) | 576.369 | − | 425.551i | 1.32804 | − | 0.980532i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 347.805 | 0.797717 | ||||||||
\(437\) | −627.363 | −1.43561 | ||||||||
\(438\) | 32.2413i | 0.0736103i | ||||||||
\(439\) | 789.513i | 1.79844i | 0.437501 | + | 0.899218i | \(0.355863\pi\) | ||||
−0.437501 | + | 0.899218i | \(0.644137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 43.2750 | − | 140.486i | 0.0981293 | − | 0.318562i | ||||
\(442\) | − | 683.748i | − | 1.54694i | ||||||
\(443\) | 585.242i | 1.32109i | 0.750787 | + | 0.660544i | \(0.229674\pi\) | ||||
−0.750787 | + | 0.660544i | \(0.770326\pi\) | |||||||
\(444\) | − | 58.7746i | − | 0.132375i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 789.651i | − | 1.77052i | ||||||
\(447\) | 396.817 | 0.887733 | ||||||||
\(448\) | 322.141 | − | 237.847i | 0.719065 | − | 0.530907i | ||||
\(449\) | −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 | ||||||
\(452\) | − | 11.3138i | − | 0.0250305i | ||||||
\(453\) | 342.486 | 0.756041 | ||||||||
\(454\) | 588.395i | 1.29602i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −19.6478 | −0.0430873 | ||||||||
\(457\) | 164.041i | 0.358953i | 0.983762 | + | 0.179476i | \(0.0574404\pi\) | ||||
−0.983762 | + | 0.179476i | \(0.942560\pi\) | |||||||
\(458\) | 383.855 | 0.838112 | ||||||||
\(459\) | −115.906 | −0.252517 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 399.626i | − | 0.866867i | −0.901186 | − | 0.433434i | \(-0.857302\pi\) | ||
0.901186 | − | 0.433434i | \(-0.142698\pi\) | |||||||
\(462\) | 381.343 | + | 516.494i | 0.825418 | + | 1.11795i | ||||
\(463\) | − | 680.267i | − | 1.46926i | −0.678468 | − | 0.734630i | \(-0.737356\pi\) | ||
0.678468 | − | 0.734630i | \(-0.262644\pi\) | |||||||
\(464\) | 671.388 | 1.44696 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 217.093 | 0.465866 | ||||||||
\(467\) | 725.217 | 1.55293 | 0.776464 | − | 0.630162i | \(-0.217011\pi\) | ||||
0.776464 | + | 0.630162i | \(0.217011\pi\) | |||||||
\(468\) | 124.940 | 0.266966 | ||||||||
\(469\) | −88.7879 | − | 120.255i | −0.189313 | − | 0.256407i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −365.525 | −0.776062 | ||||||||
\(472\) | −20.3764 | −0.0431704 | ||||||||
\(473\) | 357.948i | 0.756762i | ||||||||
\(474\) | − | 78.3357i | − | 0.165265i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −476.420 | + | 351.755i | −1.00088 | + | 0.738982i | ||||
\(477\) | 147.719i | 0.309684i | ||||||||
\(478\) | 345.714i | 0.723252i | ||||||||
\(479\) | − | 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 | ||||||||
\(482\) | −434.928 | −0.902341 | ||||||||
\(483\) | 230.443 | + | 312.114i | 0.477108 | + | 0.646198i | ||||
\(484\) | −905.791 | −1.87147 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 43.5159i | − | 0.0895389i | ||||||
\(487\) | − | 353.125i | − | 0.725103i | −0.931964 | − | 0.362551i | \(-0.881906\pi\) | ||
0.931964 | − | 0.362551i | \(-0.118094\pi\) | |||||||
\(488\) | 36.7245 | 0.0752552 | ||||||||
\(489\) | − | 314.927i | − | 0.644023i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −343.280 | −0.699145 | −0.349572 | − | 0.936909i | \(-0.613673\pi\) | ||||
−0.349572 | + | 0.936909i | \(0.613673\pi\) | |||||||
\(492\) | 247.213i | 0.502465i | ||||||||
\(493\) | −892.167 | −1.80967 | ||||||||
\(494\) | −600.974 | −1.21655 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 615.447i | 1.24082i | ||||||||
\(497\) | 204.418 | − | 150.928i | 0.411304 | − | 0.303678i | ||||
\(498\) | 177.846i | 0.357120i | ||||||||
\(499\) | 420.584 | 0.842853 | 0.421427 | − | 0.906863i | \(-0.361530\pi\) | ||||
0.421427 | + | 0.906863i | \(0.361530\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −175.215 | −0.349731 | ||||||||
\(502\) | 776.998 | 1.54780 | ||||||||
\(503\) | −183.030 | −0.363876 | −0.181938 | − | 0.983310i | \(-0.558237\pi\) | ||||
−0.181938 | + | 0.983310i | \(0.558237\pi\) | |||||||
\(504\) | 7.21704 | + | 9.77481i | 0.0143195 | + | 0.0193945i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1694.44 | −3.34870 | ||||||||
\(507\) | 83.8745 | 0.165433 | ||||||||
\(508\) | 396.913i | 0.781326i | ||||||||
\(509\) | − | 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 | ||||
\(512\) | 708.885i | 1.38454i | ||||||||
\(513\) | 101.874i | 0.198585i | ||||||||
\(514\) | − | 616.378i | − | 1.19918i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 123.962i | − | 0.240237i | ||||||
\(517\) | −936.662 | −1.81173 | ||||||||
\(518\) | 140.649 | − | 103.846i | 0.271523 | − | 0.200474i | ||||
\(519\) | 190.485 | 0.367023 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 477.677i | − | 0.916846i | −0.888734 | − | 0.458423i | \(-0.848414\pi\) | ||
0.888734 | − | 0.458423i | \(-0.151586\pi\) | |||||||
\(522\) | − | 334.958i | − | 0.641682i | ||||||
\(523\) | 770.784 | 1.47377 | 0.736887 | − | 0.676016i | \(-0.236295\pi\) | ||||
0.736887 | + | 0.676016i | \(0.236295\pi\) | |||||||
\(524\) | − | 268.545i | − | 0.512491i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 48.4269 | 0.0920664 | ||||||||
\(527\) | − | 817.829i | − | 1.55186i | ||||||
\(528\) | −551.512 | −1.04453 | ||||||||
\(529\) | −494.940 | −0.935614 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105.652i | 0.198968i | ||||||||
\(532\) | 309.172 | + | 418.745i | 0.581151 | + | 0.787114i | ||||
\(533\) | − | 413.225i | − | 0.775281i | ||||||
\(534\) | −425.950 | −0.797660 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.3555 | 0.0230513 | ||||||||
\(537\) | 159.146 | 0.296362 | ||||||||
\(538\) | −1393.58 | −2.59029 | ||||||||
\(539\) | −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 | \(0.0718828\pi\) | |||||||
\(542\) | −921.225 | −1.69968 | ||||||||
\(543\) | − | 108.885i | − | 0.200525i | ||||||
\(544\) | − | 993.618i | − | 1.82650i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 220.750 | + | 298.985i | 0.404304 | + | 0.547592i | ||||
\(547\) | − | 697.821i | − | 1.27572i | −0.770151 | − | 0.637862i | \(-0.779819\pi\) | ||
0.770151 | − | 0.637862i | \(-0.220181\pi\) | |||||||
\(548\) | − | 601.806i | − | 1.09819i | ||||||
\(549\) | − | 190.417i | − | 0.346843i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 784.162i | 1.42316i | ||||||||
\(552\) | −32.0678 | −0.0580939 | ||||||||
\(553\) | 91.2367 | − | 67.3628i | 0.164985 | − | 0.121813i | ||||
\(554\) | 412.496 | 0.744578 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 206.421i | − | 0.371260i | ||||||
\(557\) | 941.244i | 1.68985i | 0.534888 | + | 0.844923i | \(0.320354\pi\) | ||||
−0.534888 | + | 0.844923i | \(0.679646\pi\) | |||||||
\(558\) | 307.048 | 0.550266 | ||||||||
\(559\) | 207.207i | 0.370675i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 732.870 | 1.30636 | ||||||||
\(562\) | 986.545i | 1.75542i | ||||||||
\(563\) | 768.996 | 1.36589 | 0.682945 | − | 0.730470i | \(-0.260699\pi\) | ||||
0.682945 | + | 0.730470i | \(0.260699\pi\) | |||||||
\(564\) | 324.378 | 0.575139 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1195.35i | 2.11192i | ||||||||
\(567\) | 50.6825 | − | 37.4204i | 0.0893871 | − | 0.0659972i | ||||
\(568\) | 21.0027i | 0.0369766i | ||||||||
\(569\) | 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 | \(0.262894\pi\) | |||||||
\(572\) | −789.997 | −1.38111 | ||||||||
\(573\) | 131.623 | 0.229708 | ||||||||
\(574\) | −591.586 | + | 436.786i | −1.03064 | + | 0.760951i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 171.614 | 0.297940 | ||||||||
\(577\) | 66.7246 | 0.115641 | 0.0578203 | − | 0.998327i | \(-0.481585\pi\) | ||||
0.0578203 | + | 0.998327i | \(0.481585\pi\) | |||||||
\(578\) | 582.202i | 1.00727i | ||||||||
\(579\) | − | 39.4093i | − | 0.0680645i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −207.135 | + | 152.934i | −0.356514 | + | 0.263225i | ||||
\(582\) | 646.985i | 1.11166i | ||||||||
\(583\) | − | 934.029i | − | 1.60211i | ||||||
\(584\) | − | 3.85815i | − | 0.00660642i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1123.97i | − | 1.91803i | ||||||
\(587\) | −678.789 | −1.15637 | −0.578185 | − | 0.815906i | \(-0.696239\pi\) | ||||
−0.578185 | + | 0.815906i | \(0.696239\pi\) | |||||||
\(588\) | 94.7608 | − | 307.627i | 0.161158 | − | 0.523175i | ||||
\(589\) | −718.823 | −1.22041 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 238.130i | − | 0.402928i | ||||||
\(592\) | 150.185i | 0.253691i | ||||||||
\(593\) | 289.610 | 0.488381 | 0.244190 | − | 0.969727i | \(-0.421478\pi\) | ||||
0.244190 | + | 0.969727i | \(0.421478\pi\) | |||||||
\(594\) | 275.151i | 0.463217i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 868.924 | 1.45793 | ||||||||
\(597\) | 462.976i | 0.775503i | ||||||||
\(598\) | −980.869 | −1.64025 | ||||||||
\(599\) | −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 | \(0.990092\pi\) | |||||||
\(602\) | 296.644 | − | 219.022i | 0.492765 | − | 0.363823i | ||||
\(603\) | − | 64.0632i | − | 0.106241i | ||||||
\(604\) | 749.955 | 1.24165 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −942.375 | −1.55507 | ||||||||
\(607\) | 876.691 | 1.44430 | 0.722150 | − | 0.691736i | \(-0.243154\pi\) | ||||
0.722150 | + | 0.691736i | \(0.243154\pi\) | |||||||
\(608\) | −873.331 | −1.43640 | ||||||||
\(609\) | 390.121 | − | 288.039i | 0.640594 | − | 0.472970i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −542.210 | −0.887414 | ||||||||
\(612\) | −253.803 | −0.414710 | ||||||||
\(613\) | − | 591.071i | − | 0.964226i | −0.876109 | − | 0.482113i | \(-0.839869\pi\) | ||
0.876109 | − | 0.482113i | \(-0.160131\pi\) | |||||||
\(614\) | 258.868i | 0.421610i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −45.6333 | − | 61.8061i | −0.0740801 | − | 0.100335i | ||||
\(617\) | 744.668i | 1.20692i | 0.797394 | + | 0.603459i | \(0.206211\pi\) | ||||
−0.797394 | + | 0.603459i | \(0.793789\pi\) | |||||||
\(618\) | 199.510i | 0.322832i | ||||||||
\(619\) | − | 851.811i | − | 1.37611i | −0.725659 | − | 0.688054i | \(-0.758465\pi\) | ||
0.725659 | − | 0.688054i | \(-0.241535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 166.272i | 0.267749i | ||||||||
\(622\) | −608.886 | −0.978917 | ||||||||
\(623\) | −366.285 | − | 496.099i | −0.587938 | − | 0.796307i | ||||
\(624\) | −319.256 | −0.511628 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 819.833i | 1.30964i | ||||||||
\(627\) | − | 644.149i | − | 1.02735i | ||||||
\(628\) | −800.404 | −1.27453 | ||||||||
\(629\) | − | 199.572i | − | 0.317284i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 316.625 | 0.501783 | 0.250891 | − | 0.968015i | \(-0.419276\pi\) | ||||
0.250891 | + | 0.968015i | \(0.419276\pi\) | |||||||
\(632\) | 9.37402i | 0.0148323i | ||||||||
\(633\) | 634.987 | 1.00314 | ||||||||
\(634\) | 304.485 | 0.480260 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 323.466i | 0.508595i | ||||||||
\(637\) | −158.396 | + | 514.209i | −0.248660 | + | 0.807236i | ||||
\(638\) | 2117.94i | 3.31965i | ||||||||
\(639\) | 108.899 | 0.170422 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 173.979 | 0.271418 | 0.135709 | − | 0.990749i | \(-0.456669\pi\) | ||||
0.135709 | + | 0.990749i | \(0.456669\pi\) | |||||||
\(642\) | −143.617 | −0.223703 | ||||||||
\(643\) | 926.785 | 1.44135 | 0.720673 | − | 0.693275i | \(-0.243833\pi\) | ||||
0.720673 | + | 0.693275i | \(0.243833\pi\) | |||||||
\(644\) | 504.610 | + | 683.447i | 0.783556 | + | 1.06125i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1220.81 | 1.88980 | ||||||||
\(647\) | −429.625 | −0.664027 | −0.332013 | − | 0.943275i | \(-0.607728\pi\) | ||||
−0.332013 | + | 0.943275i | \(0.607728\pi\) | |||||||
\(648\) | 5.20732i | 0.00803599i | ||||||||
\(649\) | − | 668.036i | − | 1.02933i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 264.038 | + | 357.615i | 0.405589 | + | 0.549333i | ||||
\(652\) | − | 689.608i | − | 1.05768i | ||||||
\(653\) | − | 927.100i | − | 1.41976i | −0.704325 | − | 0.709878i | \(-0.748750\pi\) | ||
0.704325 | − | 0.709878i | \(-0.251250\pi\) | |||||||
\(654\) | 443.392i | 0.677970i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 631.695i | − | 0.962950i | ||||||
\(657\) | −20.0045 | −0.0304483 | ||||||||
\(658\) | 573.126 | + | 776.245i | 0.871012 | + | 1.17970i | ||||
\(659\) | −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 | \(0.686537\pi\) | |||||||
\(662\) | 1141.50i | 1.72432i | ||||||||
\(663\) | 424.240 | 0.639879 | ||||||||
\(664\) | − | 21.2818i | − | 0.0320510i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 74.9278 | 0.112504 | ||||||||
\(667\) | 1279.86i | 1.91882i | ||||||||
\(668\) | −383.675 | −0.574364 | ||||||||
\(669\) | 489.949 | 0.732360 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1204.01i | 1.79435i | ||||||||
\(672\) | 320.792 | + | 434.483i | 0.477370 | + | 0.646553i | ||||
\(673\) | 701.861i | 1.04288i | 0.853287 | + | 0.521442i | \(0.174606\pi\) | ||||
−0.853287 | + | 0.521442i | \(0.825394\pi\) | |||||||
\(674\) | −835.424 | −1.23950 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 183.663 | 0.271691 | ||||||||
\(677\) | 404.920 | 0.598110 | 0.299055 | − | 0.954236i | \(-0.403329\pi\) | ||||
0.299055 | + | 0.954236i | \(0.403329\pi\) | |||||||
\(678\) | 14.4232 | 0.0212731 | ||||||||
\(679\) | −753.535 | + | 556.358i | −1.10977 | + | 0.819379i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −365.077 | −0.536090 | ||||||||
\(682\) | −1941.47 | −2.84672 | ||||||||
\(683\) | − | 766.177i | − | 1.12178i | −0.827890 | − | 0.560891i | \(-0.810459\pi\) | ||
0.827890 | − | 0.560891i | \(-0.189541\pi\) | |||||||
\(684\) | 223.077i | 0.326136i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 903.586 | − | 316.764i | 1.31718 | − | 0.461754i | ||||
\(687\) | 238.168i | 0.346678i | ||||||||
\(688\) | 316.757i | 0.460402i | ||||||||
\(689\) | − | 540.686i | − | 0.784740i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 162.333i | − | 0.234925i | −0.993077 | − | 0.117462i | \(-0.962524\pi\) | ||
0.993077 | − | 0.117462i | \(-0.0374760\pi\) | |||||||
\(692\) | 417.111 | 0.602762 | ||||||||
\(693\) | −320.465 | + | 236.609i | −0.462432 | + | 0.341427i | ||||
\(694\) | 1584.85 | 2.28364 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.0826i | 0.0575900i | ||||||||
\(697\) | 839.421i | 1.20433i | ||||||||
\(698\) | 395.570 | 0.566719 | ||||||||
\(699\) | 134.698i | 0.192702i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −69.5098 | −0.0991581 | −0.0495790 | − | 0.998770i | \(-0.515788\pi\) | ||||
−0.0495790 | + | 0.998770i | \(0.515788\pi\) | |||||||
\(702\) | 159.278i | 0.226892i | ||||||||
\(703\) | −175.412 | −0.249519 | ||||||||
\(704\) | −1085.11 | −1.54135 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1262.99i | − | 1.78894i | ||||||
\(707\) | −810.372 | − | 1097.57i | −1.14621 | − | 1.55244i | ||||
\(708\) | 231.350i | 0.326765i | ||||||||
\(709\) | −134.839 | −0.190182 | −0.0950912 | − | 0.995469i | \(-0.530314\pi\) | ||||
−0.0950912 | + | 0.995469i | \(0.530314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.6044 | 0.0683606 | ||||||||
\(712\) | 50.9712 | 0.0715888 | ||||||||
\(713\) | −1173.22 | −1.64546 | ||||||||
\(714\) | −448.429 | − | 607.356i | −0.628052 | − | 0.850638i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 348.489 | 0.486716 | ||||||||
\(717\) | −214.503 | −0.299167 | ||||||||
\(718\) | − | 487.600i | − | 0.679109i | ||||||
\(719\) | 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 | ||||
\(722\) | − | 65.2732i | − | 0.0904062i | ||||||
\(723\) | − | 269.857i | − | 0.373246i | ||||||
\(724\) | − | 238.430i | − | 0.329323i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 1154.73i | − | 1.59054i | ||||||
\(727\) | 704.430 | 0.968955 | 0.484477 | − | 0.874804i | \(-0.339010\pi\) | ||||
0.484477 | + | 0.874804i | \(0.339010\pi\) | |||||||
\(728\) | −26.4160 | − | 35.7780i | −0.0362857 | − | 0.0491456i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 420.919i | − | 0.575812i | ||||||
\(732\) | − | 416.963i | − | 0.569622i | ||||||
\(733\) | 275.472 | 0.375815 | 0.187907 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187907 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(734\) | − | 338.188i | − | 0.460747i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1425.39 | −1.93667 | ||||||||
\(737\) | 405.072i | 0.549622i | ||||||||
\(738\) | −315.155 | −0.427039 | ||||||||
\(739\) | −238.655 | −0.322943 | −0.161471 | − | 0.986877i | \(-0.551624\pi\) | ||||
−0.161471 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 372.882i | − | 0.503214i | ||||||
\(742\) | −774.063 | + | 571.514i | −1.04321 | + | 0.770235i | ||||
\(743\) | 221.162i | 0.297661i | 0.988863 | + | 0.148831i | \(0.0475509\pi\) | ||||
−0.988863 | + | 0.148831i | \(0.952449\pi\) | |||||||
\(744\) | −36.7429 | −0.0493856 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 253.773 | 0.340178 | ||||||||
\(747\) | −110.347 | −0.147720 | ||||||||
\(748\) | 1604.79 | 2.14544 | ||||||||
\(749\) | −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 | \(0.607278\pi\) | |||||||
\(752\) | −828.874 | −1.10223 | ||||||||
\(753\) | 482.098i | 0.640237i | ||||||||
\(754\) | 1226.02i | 1.62602i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 110.981 | − | 81.9408i | 0.146801 | − | 0.108387i | ||||
\(757\) | − | 866.706i | − | 1.14492i | −0.819932 | − | 0.572461i | \(-0.805989\pi\) | ||
0.819932 | − | 0.572461i | \(-0.194011\pi\) | |||||||
\(758\) | 1781.97i | 2.35088i | ||||||||
\(759\) | − | 1051.34i | − | 1.38516i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 621.621i | 0.816847i | 0.912793 | + | 0.408424i | \(0.133921\pi\) | ||||
−0.912793 | + | 0.408424i | \(0.866079\pi\) | |||||||
\(762\) | −505.998 | −0.664039 | ||||||||
\(763\) | −516.414 | + | 381.284i | −0.676820 | + | 0.499717i | ||||
\(764\) | 288.219 | 0.377250 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 492.415i | 0.642839i | ||||||||
\(767\) | − | 386.709i | − | 0.504184i | ||||||
\(768\) | −485.726 | −0.632456 | ||||||||
\(769\) | 316.574i | 0.411669i | 0.978587 | + | 0.205835i | \(0.0659909\pi\) | ||||
−0.978587 | + | 0.205835i | \(0.934009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 382.440 | 0.496031 | ||||||||
\(772\) | − | 86.2961i | − | 0.111782i | ||||||
\(773\) | 710.993 | 0.919784 | 0.459892 | − | 0.887975i | \(-0.347888\pi\) | ||||
0.459892 | + | 0.887975i | \(0.347888\pi\) | |||||||
\(774\) | 158.031 | 0.204174 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 77.4213i | − | 0.0997697i | ||||||
\(777\) | 64.4323 | + | 87.2675i | 0.0829244 | + | 0.112313i | ||||
\(778\) | − | 696.550i | − | 0.895308i | ||||||
\(779\) | 737.801 | 0.947113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −688.570 | −0.881652 | ||||||||
\(782\) | 1992.53 | 2.54799 | ||||||||
\(783\) | 207.829 | 0.265426 | ||||||||
\(784\) | −242.140 | + | 786.070i | −0.308851 | + | 1.00264i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 342.350 | 0.435560 | ||||||||
\(787\) | 845.181 | 1.07393 | 0.536964 | − | 0.843605i | \(-0.319571\pi\) | ||||
0.536964 | + | 0.843605i | \(0.319571\pi\) | |||||||
\(788\) | − | 521.443i | − | 0.661729i | ||||||
\(789\) | 30.0471i | 0.0380825i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.4028 | + | 16.7985i | 0.0156799 | + | 0.0212370i | ||||
\(792\) | − | 32.9259i | − | 0.0415731i | ||||||
\(793\) | 696.968i | 0.878901i | ||||||||
\(794\) | 519.427i | 0.654190i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1013.79i | 1.27361i | ||||||||
\(797\) | −541.537 | −0.679469 | −0.339734 | − | 0.940521i | \(-0.610337\pi\) | ||||
−0.339734 | + | 0.940521i | \(0.610337\pi\) | |||||||
\(798\) | −533.830 | + | 394.143i | −0.668959 | + | 0.493913i | ||||
\(799\) | 1101.44 | 1.37852 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 264.286i | − | 0.329945i | ||||||
\(802\) | − | 524.999i | − | 0.654612i | ||||||
\(803\) | 126.489 | 0.157520 | ||||||||
\(804\) | − | 140.282i | − | 0.174480i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1123.86 | −1.39437 | ||||||||
\(807\) | − | 864.662i | − | 1.07145i | ||||||
\(808\) | 112.769 | 0.139566 | ||||||||
\(809\) | 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 | \(-0.183055\pi\) | |||||||
\(812\) | 854.263 | − | 630.729i | 1.05205 | − | 0.776759i | ||||
\(813\) | − | 571.586i | − | 0.703057i | ||||||
\(814\) | −473.768 | −0.582025 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 648.534 | 0.794772 | ||||||||
\(817\) | −369.963 | −0.452831 | ||||||||
\(818\) | 1429.76 | 1.74787 | ||||||||
\(819\) | −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 | \(0.363815\pi\) | |||||||
\(822\) | 767.202 | 0.933336 | ||||||||
\(823\) | − | 360.544i | − | 0.438085i | −0.975715 | − | 0.219042i | \(-0.929707\pi\) | ||
0.975715 | − | 0.219042i | \(-0.0702933\pi\) | |||||||
\(824\) | − | 23.8743i | − | 0.0289737i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −553.626 | + | 408.759i | −0.670249 | + | 0.494865i | ||||
\(827\) | 770.095i | 0.931191i | 0.884998 | + | 0.465596i | \(0.154160\pi\) | ||||
−0.884998 | + | 0.465596i | \(0.845840\pi\) | |||||||
\(828\) | 364.092i | 0.439724i | ||||||||
\(829\) | − | 128.381i | − | 0.154862i | −0.996998 | − | 0.0774312i | \(-0.975328\pi\) | ||
0.996998 | − | 0.0774312i | \(-0.0246718\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 255.938i | 0.307988i | ||||||||
\(832\) | −628.144 | −0.754981 | ||||||||
\(833\) | 321.764 | − | 1044.56i | 0.386272 | − | 1.25397i | ||||
\(834\) | 263.152 | 0.315530 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 1410.52i | − | 1.68722i | ||||||
\(837\) | 190.512i | 0.227613i | ||||||||
\(838\) | −903.515 | −1.07818 | ||||||||
\(839\) | − | 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 | ||||||||
\(842\) | − | 1406.58i | − | 1.67053i | ||||||
\(843\) | −612.115 | −0.726115 | ||||||||
\(844\) | 1390.46 | 1.64746 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 413.528i | 0.488804i | ||||||||
\(847\) | 1344.90 | − | 992.982i | 1.58784 | − | 1.17235i | ||||
\(848\) | − | 826.544i | − | 0.974698i | ||||||
\(849\) | −741.669 | −0.873580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −286.295 | −0.336422 | ||||||||
\(852\) | 238.461 | 0.279884 | ||||||||
\(853\) | 797.415 | 0.934836 | 0.467418 | − | 0.884036i | \(-0.345184\pi\) | ||||
0.467418 | + | 0.884036i | \(0.345184\pi\) | |||||||
\(854\) | 997.803 | − | 736.708i | 1.16839 | − | 0.862656i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.1859 | 0.0200770 | ||||||||
\(857\) | 898.781 | 1.04875 | 0.524377 | − | 0.851486i | \(-0.324298\pi\) | ||||
0.524377 | + | 0.851486i | \(0.324298\pi\) | |||||||
\(858\) | − | 1007.11i | − | 1.17379i | ||||||
\(859\) | − | 915.157i | − | 1.06537i | −0.846312 | − | 0.532687i | \(-0.821182\pi\) | ||
0.846312 | − | 0.532687i | \(-0.178818\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −271.009 | − | 367.057i | −0.314761 | − | 0.426315i | ||||
\(862\) | 886.961i | 1.02896i | ||||||||
\(863\) | − | 1357.85i | − | 1.57341i | −0.617332 | − | 0.786703i | \(-0.711786\pi\) | ||
0.617332 | − | 0.786703i | \(-0.288214\pi\) | |||||||
\(864\) | 231.462i | 0.267896i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 729.674i | − | 0.842580i | ||||||
\(867\) | −361.235 | −0.416649 | ||||||||
\(868\) | 578.175 | + | 783.084i | 0.666100 | + | 0.902170i | ||||
\(869\) | −307.325 | −0.353654 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 234.486i | 0.269214i | ||||||||
\(872\) | − | 53.0584i | − | 0.0608468i | ||||||
\(873\) | −401.430 | −0.459828 | ||||||||
\(874\) | − | 1751.31i | − | 2.00379i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −43.8047 | −0.0500053 | ||||||||
\(877\) | − | 1513.27i | − | 1.72550i | −0.505627 | − | 0.862752i | \(-0.668739\pi\) | ||
0.505627 | − | 0.862752i | \(-0.331261\pi\) | |||||||
\(878\) | −2203.96 | −2.51021 | ||||||||
\(879\) | 697.379 | 0.793377 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 677.970i | − | 0.769546i | −0.923011 | − | 0.384773i | \(-0.874280\pi\) | ||
0.923011 | − | 0.384773i | \(-0.125720\pi\) | |||||||
\(882\) | 392.173 | + | 120.804i | 0.444640 | + | 0.136966i | ||||
\(883\) | 155.548i | 0.176159i | 0.996113 | + | 0.0880793i | \(0.0280729\pi\) | ||||
−0.996113 | + | 0.0880793i | \(0.971927\pi\) | |||||||
\(884\) | 928.974 | 1.05088 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1633.73 | −1.84394 | ||||||||
\(887\) | −871.417 | −0.982432 | −0.491216 | − | 0.871038i | \(-0.663447\pi\) | ||||
−0.491216 | + | 0.871038i | \(0.663447\pi\) | |||||||
\(888\) | −8.96622 | −0.0100971 | ||||||||
\(889\) | −435.120 | − | 589.330i | −0.489449 | − | 0.662913i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −170.721 | −0.191606 | ||||||||
\(892\) | 1072.86 | 1.20276 | ||||||||
\(893\) | − | 968.101i | − | 1.08410i | ||||||
\(894\) | 1107.73i | 1.23907i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −76.8784 | − | 104.125i | −0.0858018 | − | 0.116211i | ||||
\(897\) | − | 608.592i | − | 0.678475i | ||||||
\(898\) | − | 1474.35i | − | 1.64181i | ||||||
\(899\) | 1466.44i | 1.63119i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1098.34i | 1.21903i | ||||||||
\(902\) | 1992.72 | 2.20923 | ||||||||
\(903\) | 135.895 | + | 184.057i | 0.150493 | + | 0.203828i | ||||
\(904\) | −1.72594 | −0.00190923 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 956.067i | 1.05526i | ||||||||
\(907\) | 473.129i | 0.521642i | 0.965387 | + | 0.260821i | \(0.0839932\pi\) | ||||
−0.965387 | + | 0.260821i | \(0.916007\pi\) | |||||||
\(908\) | −799.422 | −0.880421 | ||||||||
\(909\) | − | 584.709i | − | 0.643244i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −676.153 | −0.742210 | −0.371105 | − | 0.928591i | \(-0.621021\pi\) | ||||
−0.371105 | + | 0.928591i | \(0.621021\pi\) | |||||||
\(912\) | − | 570.023i | − | 0.625025i | ||||||
\(913\) | 697.721 | 0.764207 | ||||||||
\(914\) | −457.929 | −0.501017 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 521.525i | 0.569350i | ||||||||
\(917\) | 294.395 | + | 398.731i | 0.321042 | + | 0.434821i | ||||
\(918\) | − | 323.556i | − | 0.352457i | ||||||
\(919\) | −1204.50 | −1.31066 | −0.655331 | − | 0.755342i | \(-0.727471\pi\) | ||||
−0.655331 | + | 0.755342i | \(0.727471\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −160.618 | −0.174395 | ||||||||
\(922\) | 1115.57 | 1.20995 | ||||||||
\(923\) | −398.596 | −0.431848 | ||||||||
\(924\) | −701.734 | + | 518.112i | −0.759452 | + | 0.560727i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1899.00 | 2.05075 | ||||||||
\(927\) | −123.789 | −0.133537 | ||||||||
\(928\) | 1781.65i | 1.91988i | ||||||||
\(929\) | 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 | ||||
\(932\) | 294.954i | 0.316474i | ||||||||
\(933\) | − | 377.791i | − | 0.404921i | ||||||
\(934\) | 2024.48i | 2.16754i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 19.0599i | − | 0.0203632i | ||||||
\(937\) | −449.053 | −0.479245 | −0.239623 | − | 0.970866i | \(-0.577024\pi\) | ||||
−0.239623 | + | 0.970866i | \(0.577024\pi\) | |||||||
\(938\) | 335.697 | − | 247.856i | 0.357886 | − | 0.264238i | ||||
\(939\) | −508.676 | −0.541721 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 904.538i | − | 0.961252i | −0.876926 | − | 0.480626i | \(-0.840409\pi\) | ||
0.876926 | − | 0.480626i | \(-0.159591\pi\) | |||||||
\(942\) | − | 1020.38i | − | 1.08321i | ||||||
\(943\) | 1204.19 | 1.27698 | ||||||||
\(944\) | − | 591.161i | − | 0.626230i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −999.229 | −1.05627 | ||||||||
\(947\) | − | 1631.56i | − | 1.72288i | −0.507861 | − | 0.861439i | \(-0.669564\pi\) | ||
0.507861 | − | 0.861439i | \(-0.330436\pi\) | |||||||
\(948\) | 106.431 | 0.112269 | ||||||||
\(949\) | 73.2210 | 0.0771560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 188.921i | 0.198656i | ||||||||
\(952\) | 53.6612 | + | 72.6791i | 0.0563668 | + | 0.0763435i | ||||
\(953\) | 1547.14i | 1.62344i | 0.584046 | + | 0.811721i | \(0.301469\pi\) | ||||
−0.584046 | + | 0.811721i | \(0.698531\pi\) | |||||||
\(954\) | −412.365 | −0.432249 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −469.705 | −0.491323 | ||||||||
\(957\) | −1314.10 | −1.37315 | ||||||||
\(958\) | 885.207 | 0.924015 | ||||||||
\(959\) | 659.736 | + | 893.552i | 0.687942 | + | 0.931753i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −383.253 | −0.398806 | ||||||||
\(962\) | −274.252 | −0.285086 | ||||||||
\(963\) | − | 89.1092i | − | 0.0925329i | ||||||
\(964\) | − | 590.915i | − | 0.612982i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −871.281 | + | 643.293i | −0.901947 | + | 0.665935i | ||||
\(967\) | − | 282.618i | − | 0.292263i | −0.989265 | − | 0.146131i | \(-0.953318\pi\) | ||
0.989265 | − | 0.146131i | \(-0.0466822\pi\) | |||||||
\(968\) | 138.181i | 0.142749i | ||||||||
\(969\) | 757.469i | 0.781701i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 586.935i | − | 0.604465i | −0.953234 | − | 0.302232i | \(-0.902268\pi\) | ||
0.953234 | − | 0.302232i | \(-0.0977319\pi\) | |||||||
\(972\) | 59.1229 | 0.0608260 | ||||||||
\(973\) | 226.291 | + | 306.490i | 0.232570 | + | 0.314994i | ||||
\(974\) | 985.765 | 1.01208 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1065.45i | 1.09165i | ||||||||
\(977\) | 651.703i | 0.667045i | 0.942742 | + | 0.333523i | \(0.108237\pi\) | ||||
−0.942742 | + | 0.333523i | \(0.891763\pi\) | |||||||
\(978\) | 879.135 | 0.898911 | ||||||||
\(979\) | 1671.08i | 1.70693i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −275.109 | −0.280437 | ||||||||
\(982\) | − | 958.283i | − | 0.975848i | ||||||
\(983\) | −583.048 | −0.593131 | −0.296565 | − | 0.955013i | \(-0.595841\pi\) | ||||
−0.296565 | + | 0.955013i | \(0.595841\pi\) | |||||||
\(984\) | 37.7129 | 0.0383261 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2490.53i | − | 2.52589i | ||||||
\(987\) | −481.631 | + | 355.603i | −0.487975 | + | 0.360287i | ||||
\(988\) | − | 816.513i | − | 0.826430i | ||||||
\(989\) | −603.828 | −0.610544 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 377.146 | 0.380572 | 0.190286 | − | 0.981729i | \(-0.439059\pi\) | ||||
0.190286 | + | 0.981729i | \(0.439059\pi\) | |||||||
\(992\) | −1633.19 | −1.64636 | ||||||||
\(993\) | −708.259 | −0.713251 | ||||||||
\(994\) | 421.323 | + | 570.643i | 0.423866 | + | 0.574087i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −241.630 | −0.242600 | ||||||||
\(997\) | 1586.82 | 1.59159 | 0.795795 | − | 0.605565i | \(-0.207053\pi\) | ||||
0.795795 | + | 0.605565i | \(0.207053\pi\) | |||||||
\(998\) | 1174.08i | 1.17643i | ||||||||
\(999\) | 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.e.c.349.8 | 24 | ||
5.2 | odd | 4 | 105.3.h.a.76.4 | yes | 12 | ||
5.3 | odd | 4 | 525.3.h.d.76.9 | 12 | |||
5.4 | even | 2 | inner | 525.3.e.c.349.21 | 24 | ||
7.6 | odd | 2 | inner | 525.3.e.c.349.22 | 24 | ||
15.2 | even | 4 | 315.3.h.d.181.10 | 12 | |||
20.7 | even | 4 | 1680.3.s.c.1441.1 | 12 | |||
35.13 | even | 4 | 525.3.h.d.76.10 | 12 | |||
35.27 | even | 4 | 105.3.h.a.76.3 | ✓ | 12 | ||
35.34 | odd | 2 | inner | 525.3.e.c.349.7 | 24 | ||
105.62 | odd | 4 | 315.3.h.d.181.9 | 12 | |||
140.27 | odd | 4 | 1680.3.s.c.1441.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.3 | ✓ | 12 | 35.27 | even | 4 | ||
105.3.h.a.76.4 | yes | 12 | 5.2 | odd | 4 | ||
315.3.h.d.181.9 | 12 | 105.62 | odd | 4 | |||
315.3.h.d.181.10 | 12 | 15.2 | even | 4 | |||
525.3.e.c.349.7 | 24 | 35.34 | odd | 2 | inner | ||
525.3.e.c.349.8 | 24 | 1.1 | even | 1 | trivial | ||
525.3.e.c.349.21 | 24 | 5.4 | even | 2 | inner | ||
525.3.e.c.349.22 | 24 | 7.6 | odd | 2 | inner | ||
525.3.h.d.76.9 | 12 | 5.3 | odd | 4 | |||
525.3.h.d.76.10 | 12 | 35.13 | even | 4 | |||
1680.3.s.c.1441.1 | 12 | 20.7 | even | 4 | |||
1680.3.s.c.1441.10 | 12 | 140.27 | odd | 4 |