Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,3,Mod(17,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([33, 64]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.o (of order \(66\), degree \(20\), 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: | \(5.47685331364\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{66}]$ |
Embedding invariants
Embedding label | 170.1 | ||
Root | \(0.580057 + 0.814576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.170 |
Dual form | 201.3.o.a.188.1 |
$q$-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 \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).
\(n\) | \(68\) | \(136\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{33}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(3\) | 1.96458 | + | 2.26725i | 0.654861 | + | 0.755750i | ||||
\(4\) | 0.943036 | + | 3.88725i | 0.235759 | + | 0.971812i | ||||
\(5\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.84264 | − | 0.737681i | 0.263234 | − | 0.105383i | −0.236291 | − | 0.971682i | \(-0.575932\pi\) |
0.499525 | + | 0.866299i | \(0.333508\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.28083 | + | 8.90839i | −0.142315 | + | 0.989821i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(12\) | −6.96068 | + | 9.77491i | −0.580057 | + | 0.814576i | ||||
\(13\) | 15.2050 | + | 1.45190i | 1.16962 | + | 0.111685i | 0.661732 | − | 0.749740i | \(-0.269821\pi\) |
0.507885 | + | 0.861425i | \(0.330428\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.2214 | + | 7.33162i | −0.888835 | + | 0.458227i | ||||
\(17\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.2504 | − | 14.1121i | −1.85529 | − | 0.742744i | −0.942328 | − | 0.334691i | \(-0.891368\pi\) |
−0.912958 | − | 0.408054i | \(-0.866208\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.29252 | + | 2.72848i | 0.252025 | + | 0.129928i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.3854 | + | 22.7408i | 0.415415 | + | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −22.7138 | + | 14.5973i | −0.841254 | + | 0.540641i | ||||
\(28\) | 4.60522 | + | 6.46713i | 0.164472 | + | 0.230969i | ||||
\(29\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 43.5130 | − | 4.15499i | 1.40364 | − | 0.134032i | 0.634409 | − | 0.772997i | \(-0.281243\pi\) |
0.769235 | + | 0.638966i | \(0.220637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −35.8370 | + | 3.42202i | −0.995472 | + | 0.0950560i | ||||
\(37\) | 26.1102 | − | 45.2242i | 0.705681 | − | 1.22227i | −0.260765 | − | 0.965402i | \(-0.583975\pi\) |
0.966445 | − | 0.256872i | \(-0.0826920\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 26.5797 | + | 37.3260i | 0.681531 | + | 0.957076i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 77.2237 | − | 22.6749i | 1.79590 | − | 0.527324i | 0.798674 | − | 0.601764i | \(-0.205535\pi\) |
0.997225 | + | 0.0744407i | \(0.0237172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(48\) | −44.5617 | − | 17.8398i | −0.928368 | − | 0.371662i | ||||
\(49\) | −32.6118 | + | 31.0953i | −0.665547 | + | 0.634598i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.69497 | + | 60.4749i | 0.167211 | + | 1.16298i | ||||
\(53\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −37.2566 | − | 107.646i | −0.653625 | − | 1.88853i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.51299 | − | 115.732i | −0.0903770 | − | 1.89725i | −0.357999 | − | 0.933722i | \(-0.616541\pi\) |
0.267622 | − | 0.963524i | \(-0.413762\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.21144 | + | 17.3598i | 0.0668483 | + | 0.275552i | ||||
\(64\) | −41.9111 | − | 48.3680i | −0.654861 | − | 0.755750i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8093 | − | 65.7641i | 0.191183 | − | 0.981554i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.96661 | + | 104.262i | 0.0680357 | + | 1.42825i | 0.732419 | + | 0.680854i | \(0.238391\pi\) |
−0.664384 | + | 0.747392i | \(0.731306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −31.1561 | + | 68.2224i | −0.415415 | + | 0.909632i | ||||
\(76\) | 21.6150 | − | 150.335i | 0.284407 | − | 1.97810i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 78.1750 | − | 109.781i | 0.989558 | − | 1.38964i | 0.0696203 | − | 0.997574i | \(-0.477821\pi\) |
0.919937 | − | 0.392066i | \(-0.128239\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −77.7189 | − | 22.8203i | −0.959493 | − | 0.281733i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(84\) | −5.61525 | + | 23.1464i | −0.0668483 | + | 0.275552i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29.0884 | − | 8.54113i | 0.319653 | − | 0.0938585i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 94.9052 | + | 90.4919i | 1.02049 | + | 0.973032i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.3745 | − | 30.0935i | 0.179118 | − | 0.310242i | −0.762461 | − | 0.647035i | \(-0.776009\pi\) |
0.941579 | + | 0.336793i | \(0.109342\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −78.6053 | + | 61.8159i | −0.786053 | + | 0.618159i | ||||
\(101\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −40.7823 | + | 3.89423i | −0.395944 | + | 0.0378081i | −0.291129 | − | 0.956684i | \(-0.594031\pi\) |
−0.104815 | + | 0.994492i | \(0.533425\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(108\) | −78.1633 | − | 74.5285i | −0.723734 | − | 0.690079i | ||||
\(109\) | 71.1035 | + | 155.695i | 0.652326 | + | 1.42839i | 0.889503 | + | 0.456928i | \(0.151050\pi\) |
−0.237177 | + | 0.971466i | \(0.576222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 153.830 | − | 29.6483i | 1.38586 | − | 0.267102i | ||||
\(112\) | −20.7964 | + | 24.0004i | −0.185682 | + | 0.214289i | ||||
\(113\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −32.4092 | + | 133.593i | −0.277002 | + | 1.14182i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −120.452 | − | 11.5018i | −0.995472 | − | 0.0950560i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 57.1857 | + | 165.227i | 0.461175 | + | 1.33248i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −78.5568 | + | 31.4494i | −0.618557 | + | 0.247633i | −0.659710 | − | 0.751520i | \(-0.729321\pi\) |
0.0411533 | + | 0.999153i | \(0.486897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 203.122 | + | 130.539i | 1.57459 | + | 1.01193i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −75.3641 | −0.566647 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 25.9480 | + | 16.6757i | 0.186676 | + | 0.119969i | 0.630641 | − | 0.776075i | \(-0.282792\pi\) |
−0.443965 | + | 0.896044i | \(0.646428\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −47.0978 | − | 136.080i | −0.327068 | − | 0.945001i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −134.569 | − | 12.8498i | −0.915438 | − | 0.0874138i | ||||
\(148\) | 200.420 | + | 58.8487i | 1.35419 | + | 0.397626i | ||||
\(149\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −26.0498 | + | 107.379i | −0.172515 | + | 0.711118i | 0.818173 | + | 0.574971i | \(0.194987\pi\) |
−0.990689 | + | 0.136146i | \(0.956528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −120.030 | + | 138.522i | −0.769420 | + | 0.887959i | ||||
\(157\) | −266.328 | + | 51.3305i | −1.69636 | + | 0.326946i | −0.943534 | − | 0.331276i | \(-0.892521\pi\) |
−0.752824 | + | 0.658222i | \(0.771309\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −63.3763 | − | 109.771i | −0.388812 | − | 0.673441i | 0.603478 | − | 0.797379i | \(-0.293781\pi\) |
−0.992290 | + | 0.123938i | \(0.960448\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 63.1388 | + | 12.1690i | 0.373603 | + | 0.0720060i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 170.866 | − | 295.949i | 0.999219 | − | 1.73070i | ||||
\(172\) | 160.968 | + | 278.804i | 0.935858 | + | 1.62095i | ||||
\(173\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 35.9120 | + | 34.2420i | 0.205211 | + | 0.195668i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −111.993 | + | 323.583i | −0.618748 | + | 1.78775i | −0.00276243 | + | 0.999996i | \(0.500879\pi\) |
−0.615985 | + | 0.787758i | \(0.711242\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 251.563 | − | 239.864i | 1.37466 | − | 1.31073i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −31.0853 | + | 43.6531i | −0.164472 | + | 0.230969i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(192\) | 27.3244 | − | 190.046i | 0.142315 | − | 0.989821i | ||||
\(193\) | 138.971 | − | 304.303i | 0.720054 | − | 1.57670i | −0.0937737 | − | 0.995594i | \(-0.529893\pi\) |
0.813828 | − | 0.581106i | \(-0.197380\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −151.629 | − | 97.4462i | −0.773619 | − | 0.497175i | ||||
\(197\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −272.207 | − | 214.066i | −1.36787 | − | 1.07571i | −0.988623 | − | 0.150412i | \(-0.951940\pi\) |
−0.379249 | − | 0.925295i | \(-0.623818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 174.269 | − | 100.157i | 0.867008 | − | 0.498295i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −226.881 | + | 90.8295i | −1.09077 | + | 0.436680i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.88915 | + | 28.5728i | 0.0468680 | + | 0.135416i | 0.966006 | − | 0.258519i | \(-0.0832346\pi\) |
−0.919138 | + | 0.393935i | \(0.871113\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 77.1136 | − | 39.7548i | 0.355362 | − | 0.183202i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −226.630 | + | 216.092i | −1.03484 | + | 0.986720i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −181.280 | + | 209.209i | −0.812916 | + | 0.938155i | −0.999015 | − | 0.0443757i | \(-0.985870\pi\) |
0.186099 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −215.886 | + | 63.3898i | −0.959493 | + | 0.281733i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(228\) | 383.312 | − | 246.340i | 1.68119 | − | 1.08044i | ||||
\(229\) | 10.1993 | + | 14.3228i | 0.0445382 | + | 0.0625452i | 0.836245 | − | 0.548357i | \(-0.184746\pi\) |
−0.791706 | + | 0.610902i | \(0.790807\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 402.483 | − | 38.4325i | 1.69824 | − | 0.162162i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 208.484 | − | 133.984i | 0.865078 | − | 0.555952i | −0.0311655 | − | 0.999514i | \(-0.509922\pi\) |
0.896244 | + | 0.443562i | \(0.146286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −100.946 | − | 221.041i | −0.415415 | − | 0.909632i | ||||
\(244\) | 444.680 | − | 130.570i | 1.82246 | − | 0.535122i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −515.494 | − | 265.756i | −2.08702 | − | 1.07593i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(252\) | −63.5103 | + | 32.7418i | −0.252025 | + | 0.129928i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 148.495 | − | 208.531i | 0.580057 | − | 0.814576i | ||||
\(257\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.7506 | − | 102.593i | 0.0569522 | − | 0.396111i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 267.721 | − | 12.2251i | 0.998959 | − | 0.0456161i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −71.7507 | − | 82.8047i | −0.264763 | − | 0.305552i | 0.607765 | − | 0.794117i | \(-0.292066\pi\) |
−0.872528 | + | 0.488564i | \(0.837521\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 76.5114 | + | 49.1709i | 0.280262 | + | 0.180113i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −78.8324 | + | 548.291i | −0.284593 | + | 1.97939i | −0.126497 | + | 0.991967i | \(0.540373\pi\) |
−0.158096 | + | 0.987424i | \(0.550536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −18.7186 | + | 392.953i | −0.0670919 | + | 1.40843i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −80.4202 | − | 559.334i | −0.284170 | − | 1.97645i | −0.198306 | − | 0.980140i | \(-0.563544\pi\) |
−0.0858637 | − | 0.996307i | \(-0.527365\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −256.873 | − | 132.427i | −0.888835 | − | 0.458227i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 102.363 | − | 19.7288i | 0.351763 | − | 0.0677967i | ||||
\(292\) | −400.608 | + | 117.629i | −1.37195 | + | 0.402840i | ||||
\(293\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −294.579 | − | 56.7754i | −0.981929 | − | 0.189251i | ||||
\(301\) | 125.568 | − | 98.7481i | 0.417171 | − | 0.328067i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 604.774 | − | 57.7489i | 1.98939 | − | 0.189964i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −349.965 | − | 491.458i | −1.13995 | − | 1.60084i | −0.721180 | − | 0.692748i | \(-0.756400\pi\) |
−0.418772 | − | 0.908091i | \(-0.637539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −88.9493 | − | 84.8130i | −0.287862 | − | 0.274476i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −408.427 | + | 471.350i | −1.30488 | + | 1.50591i | −0.587503 | + | 0.809222i | \(0.699889\pi\) |
−0.717375 | + | 0.696687i | \(0.754657\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 500.470 | + | 200.358i | 1.58376 | + | 0.634044i | ||||
\(317\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 15.4165 | − | 323.633i | 0.0475819 | − | 0.998867i | ||||
\(325\) | 124.892 | + | 360.853i | 0.384284 | + | 1.11032i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −213.311 | + | 467.085i | −0.652326 | + | 1.42839i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 95.5705 | + | 393.947i | 0.288733 | + | 1.19017i | 0.912670 | + | 0.408698i | \(0.134017\pi\) |
−0.623937 | + | 0.781475i | \(0.714468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 369.432 | + | 290.524i | 1.10940 | + | 0.872446i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −95.2711 | −0.283545 | ||||||||
\(337\) | −521.427 | − | 410.055i | −1.54726 | − | 1.21678i | −0.883093 | − | 0.469198i | \(-0.844543\pi\) |
−0.664169 | − | 0.747583i | \(-0.731214\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −77.5550 | + | 169.822i | −0.226108 | + | 0.495107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.580057 | − | 0.814576i | \(-0.303030\pi\) | ||||
−0.580057 | + | 0.814576i | \(0.696970\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 274.217 | + | 80.5175i | 0.785723 | + | 0.230709i | 0.649896 | − | 0.760023i | \(-0.274813\pi\) |
0.135827 | + | 0.990733i | \(0.456631\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −366.558 | + | 188.974i | −1.04433 | + | 0.538388i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 782.172 | + | 745.800i | 2.16668 | + | 2.06593i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −210.561 | − | 295.691i | −0.580057 | − | 0.814576i | ||||
\(364\) | 60.6329 | + | 105.019i | 0.166574 | + | 0.288514i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −674.020 | − | 129.907i | −1.83657 | − | 0.353969i | −0.851258 | − | 0.524748i | \(-0.824160\pi\) |
−0.985309 | + | 0.170778i | \(0.945372\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −262.265 | + | 454.257i | −0.705015 | + | 1.22112i | ||||
\(373\) | 192.961 | + | 334.218i | 0.517321 | + | 0.896026i | 0.999798 | + | 0.0201171i | \(0.00640391\pi\) |
−0.482477 | + | 0.875909i | \(0.660263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 720.697 | − | 138.903i | 1.90158 | − | 0.366499i | 0.903505 | − | 0.428578i | \(-0.140985\pi\) |
0.998071 | + | 0.0620789i | \(0.0197730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −225.635 | − | 116.323i | −0.592217 | − | 0.305309i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.928368 | − | 0.371662i | \(-0.878788\pi\) | ||||
0.928368 | + | 0.371662i | \(0.121212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 103.086 | + | 716.982i | 0.266373 | + | 1.85267i | ||||
\(388\) | 133.365 | + | 39.1596i | 0.343725 | + | 0.100927i | ||||
\(389\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 630.649 | + | 405.294i | 1.58854 | + | 1.02089i | 0.972420 | + | 0.233237i | \(0.0749319\pi\) |
0.616118 | + | 0.787654i | \(0.288704\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −148.059 | − | 170.869i | −0.371075 | − | 0.428243i | ||||
\(400\) | −314.421 | − | 247.264i | −0.786053 | − | 0.618159i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 667.649 | 1.65670 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 224.622 | − | 89.9252i | 0.549198 | − | 0.219866i | −0.0804328 | − | 0.996760i | \(-0.525630\pi\) |
0.629631 | + | 0.776894i | \(0.283206\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −53.5970 | − | 154.858i | −0.130090 | − | 0.375870i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.1689 | + | 91.5914i | 0.0315800 | + | 0.219644i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −769.107 | − | 307.904i | −1.82686 | − | 0.731363i | −0.979836 | − | 0.199805i | \(-0.935969\pi\) |
−0.847022 | − | 0.531558i | \(-0.821607\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −95.5318 | − | 209.185i | −0.223728 | − | 0.489896i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | 216.000 | − | 374.123i | 0.500000 | − | 0.866025i | ||||
\(433\) | 281.183 | − | 26.8498i | 0.649384 | − | 0.0620087i | 0.234835 | − | 0.972035i | \(-0.424545\pi\) |
0.414550 | + | 0.910027i | \(0.363939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −538.172 | + | 423.223i | −1.23434 | + | 0.970695i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 435.254 | − | 753.882i | 0.991467 | − | 1.71727i | 0.382838 | − | 0.923815i | \(-0.374947\pi\) |
0.608629 | − | 0.793455i | \(-0.291720\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −235.239 | − | 330.347i | −0.533422 | − | 0.749086i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.723734 | − | 0.690079i | \(-0.757576\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(444\) | 260.317 | + | 570.016i | 0.586301 | + | 1.28382i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −112.907 | − | 58.2077i | −0.252025 | − | 0.129928i | ||||
\(449\) | 0 | 0 | 0.327068 | − | 0.945001i | \(-0.393939\pi\) | ||||
−0.327068 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −294.631 | + | 151.893i | −0.650400 | + | 0.335305i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −527.961 | + | 741.418i | −1.15528 | + | 1.62236i | −0.503326 | + | 0.864096i | \(0.667891\pi\) |
−0.651950 | + | 0.758262i | \(0.726049\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.3313 | − | 678.718i | −0.0698301 | − | 1.46591i | −0.713524 | − | 0.700631i | \(-0.752902\pi\) |
0.643694 | − | 0.765283i | \(-0.277401\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.786053 | − | 0.618159i | \(-0.787879\pi\) | ||||
0.786053 | + | 0.618159i | \(0.212121\pi\) | |||||||
\(468\) | −549.871 | −1.17494 | ||||||||
\(469\) | −24.9101 | − | 130.629i | −0.0531132 | − | 0.278526i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −639.603 | − | 502.989i | −1.35797 | − | 1.06792i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.1675 | − | 948.183i | −0.0950895 | − | 1.99617i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 462.667 | − | 649.725i | 0.961886 | − | 1.35078i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −68.8804 | − | 479.074i | −0.142315 | − | 0.989821i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 56.9406 | − | 54.2927i | 0.116921 | − | 0.111484i | −0.629363 | − | 0.777111i | \(-0.716684\pi\) |
0.746285 | + | 0.665627i | \(0.231836\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 124.370 | − | 359.344i | 0.254336 | − | 0.734855i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −588.351 | + | 378.110i | −1.18619 | + | 0.762319i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 448.352 | − | 776.568i | 0.898501 | − | 1.55625i | 0.0690896 | − | 0.997610i | \(-0.477991\pi\) |
0.829411 | − | 0.558639i | \(-0.188676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 96.4513 | + | 167.058i | 0.190239 | + | 0.329504i | ||||
\(508\) | −196.333 | − | 275.712i | −0.386483 | − | 0.542739i | ||||
\(509\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 86.0637 | + | 188.453i | 0.168422 | + | 0.368793i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1006.67 | − | 194.020i | 1.96232 | − | 0.378207i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −315.884 | + | 912.687i | −0.612179 | + | 1.76877i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 215.865 | + | 20.6126i | 0.412743 | + | 0.0394122i | 0.299362 | − | 0.954139i | \(-0.403226\pi\) |
0.113380 | + | 0.993552i | \(0.463832\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.08310 | + | 148.693i | −0.0134916 | + | 0.283224i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 491.107 | − | 196.609i | 0.928368 | − | 0.371662i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −71.0710 | − | 292.959i | −0.133592 | − | 0.550674i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 465.624 | + | 299.238i | 0.860673 | + | 0.553121i | 0.894887 | − | 0.446294i | \(-0.147256\pi\) |
−0.0342135 | + | 0.999415i | \(0.510893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −953.664 | + | 381.790i | −1.75629 | + | 0.703112i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.1748 | + | 822.381i | −0.0716176 | + | 1.50344i | 0.621956 | + | 0.783052i | \(0.286338\pi\) |
−0.693574 | + | 0.720386i | \(0.743965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1038.05 | + | 99.1215i | 1.89080 | + | 0.180549i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 63.0646 | − | 259.956i | 0.114041 | − | 0.470083i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −40.3529 | + | 116.592i | −0.0725771 | + | 0.209698i | ||||
\(557\) | 0 | 0 | −0.888835 | − | 0.458227i | \(-0.848485\pi\) | ||||
0.888835 | + | 0.458227i | \(0.151515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1207.11 | − | 232.651i | 2.15941 | − | 0.416192i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −160.042 | + | 15.2822i | −0.282261 | + | 0.0269527i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −384.054 | − | 74.0204i | −0.672599 | − | 0.129633i | −0.158494 | − | 0.987360i | \(-0.550664\pi\) |
−0.514105 | + | 0.857727i | \(0.671876\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 484.562 | − | 311.409i | 0.841254 | − | 0.540641i | ||||
\(577\) | −830.218 | − | 791.611i | −1.43885 | − | 1.37194i | −0.794608 | − | 0.607123i | \(-0.792324\pi\) |
−0.644244 | − | 0.764820i | \(-0.722828\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 962.949 | − | 282.747i | 1.66313 | − | 0.488338i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(588\) | −76.9534 | − | 535.222i | −0.130873 | − | 0.910242i | ||||
\(589\) | −1592.49 | − | 467.596i | −2.70371 | − | 0.793882i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −39.7559 | + | 834.579i | −0.0671553 | + | 1.40976i | ||||
\(593\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.4322 | − | 1037.71i | −0.0828010 | − | 1.73821i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.235759 | − | 0.971812i | \(-0.575758\pi\) | ||||
0.235759 | + | 0.971812i | \(0.424242\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 868.277 | + | 682.821i | 1.44472 | + | 1.13614i | 0.966115 | + | 0.258111i | \(0.0830999\pi\) |
0.478605 | + | 0.878030i | \(0.341143\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 569.446 | + | 198.343i | 0.944355 | + | 0.328927i | ||||
\(604\) | −441.974 | −0.731744 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 282.110 | + | 1162.87i | 0.464761 | + | 1.91577i | 0.396316 | + | 0.918114i | \(0.370289\pi\) |
0.0684450 | + | 0.997655i | \(0.478196\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 375.996 | + | 1086.37i | 0.613370 | + | 1.77222i | 0.635074 | + | 0.772451i | \(0.280970\pi\) |
−0.0217041 | + | 0.999764i | \(0.506909\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1073.54 | + | 553.446i | −1.73431 | + | 0.894097i | −0.766559 | + | 0.642174i | \(0.778033\pi\) |
−0.967747 | + | 0.251923i | \(0.918937\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −651.660 | − | 335.954i | −1.04433 | − | 0.538388i | ||||
\(625\) | −409.288 | + | 472.343i | −0.654861 | + | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −450.691 | − | 986.876i | −0.717661 | − | 1.57146i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 211.701 | + | 297.292i | 0.335501 | + | 0.471145i | 0.947519 | − | 0.319699i | \(-0.103582\pi\) |
−0.612019 | + | 0.790843i | \(0.709642\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −45.3536 | + | 78.5548i | −0.0716487 | + | 0.124099i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −541.011 | + | 425.456i | −0.849311 | + | 0.667905i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.1142 | − | 27.0652i | 0.0654965 | − | 0.0420920i | −0.507483 | − | 0.861662i | \(-0.669424\pi\) |
0.572979 | + | 0.819570i | \(0.305788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 241.630 | + | 96.7341i | 0.371168 | + | 0.148593i | ||||
\(652\) | 366.941 | − | 349.877i | 0.562792 | − | 0.536621i | ||||
\(653\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −935.168 | − | 89.2977i | −1.42339 | − | 0.135917i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.0475819 | − | 0.998867i | \(-0.484848\pi\) | ||||
−0.0475819 | + | 0.998867i | \(0.515152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 177.963 | − | 1237.76i | 0.269233 | − | 1.87256i | −0.186517 | − | 0.982452i | \(-0.559720\pi\) |
0.455750 | − | 0.890108i | \(-0.349371\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −830.468 | −1.24136 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 417.229 | + | 481.508i | 0.619954 | + | 0.715465i | 0.975698 | − | 0.219119i | \(-0.0703181\pi\) |
−0.355745 | + | 0.934583i | \(0.615773\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −567.846 | − | 364.933i | −0.841254 | − | 0.540641i | ||||
\(676\) | 12.2382 | + | 256.912i | 0.0181039 | + | 0.380047i | ||||
\(677\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.81548 | − | 68.2682i | 0.0144558 | − | 0.100542i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.995472 | − | 0.0950560i | \(-0.969697\pi\) | ||||
0.995472 | + | 0.0950560i | \(0.0303030\pi\) | |||||||
\(684\) | 1311.56 | + | 385.109i | 1.91749 | + | 0.563025i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.4362 | + | 51.2626i | −0.0181022 | + | 0.0746181i | ||||
\(688\) | −931.982 | + | 888.643i | −1.35463 | + | 1.29163i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 822.745 | + | 424.155i | 1.19066 | + | 0.613827i | 0.935587 | − | 0.353095i | \(-0.114871\pi\) |
0.255071 | + | 0.966922i | \(0.417901\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −99.2407 | + | 171.890i | −0.141772 | + | 0.245557i | ||||
\(701\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1558.61 | + | 1225.70i | −2.21708 | + | 1.74353i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 822.510 | + | 1155.05i | 1.16010 | + | 1.62913i | 0.584169 | + | 0.811632i | \(0.301421\pi\) |
0.575930 | + | 0.817499i | \(0.304640\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 877.847 | + | 837.026i | 1.23467 | + | 1.17725i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
−0.723734 | + | 0.690079i | \(0.757576\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −72.2743 | + | 37.2600i | −0.100242 | + | 0.0516782i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 713.360 | + | 209.461i | 0.986666 | + | 0.289711i | ||||
\(724\) | −1363.46 | − | 130.195i | −1.88324 | − | 0.179827i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −423.710 | − | 1224.23i | −0.582820 | − | 1.68395i | −0.720487 | − | 0.693468i | \(-0.756082\pi\) |
0.137668 | − | 0.990478i | \(-0.456039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 302.838 | − | 663.122i | 0.415415 | − | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1169.64 | + | 751.685i | 1.59787 | + | 1.02689i | ||||
\(733\) | 207.821 | + | 856.651i | 0.283522 | + | 1.16869i | 0.918264 | + | 0.395968i | \(0.129591\pi\) |
−0.634743 | + | 0.772724i | \(0.718894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1146.16 | + | 901.352i | 1.55096 | + | 1.21969i | 0.876519 | + | 0.481368i | \(0.159860\pi\) |
0.674446 | + | 0.738324i | \(0.264383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −410.196 | − | 1690.85i | −0.553571 | − | 2.28185i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.0475819 | − | 0.998867i | \(-0.515152\pi\) | ||||
0.0475819 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 863.125 | + | 253.436i | 1.14930 | + | 0.337465i | 0.800266 | − | 0.599645i | \(-0.204691\pi\) |
0.349034 | + | 0.937110i | \(0.386510\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −199.005 | − | 79.6696i | −0.263234 | − | 0.105383i | ||||
\(757\) | −398.902 | + | 1152.55i | −0.526951 | + | 1.52253i | 0.296439 | + | 0.955052i | \(0.404201\pi\) |
−0.823391 | + | 0.567475i | \(0.807920\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 245.871 | + | 234.438i | 0.322243 | + | 0.307258i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 764.522 | − | 73.0030i | 0.995472 | − | 0.0950560i | ||||
\(769\) | −785.062 | − | 151.308i | −1.02089 | − | 0.196760i | −0.348773 | − | 0.937207i | \(-0.613402\pi\) |
−0.672114 | + | 0.740447i | \(0.734614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1313.95 | + | 253.244i | 1.70201 | + | 0.328036i | ||||
\(773\) | 0 | 0 | 0.995472 | − | 0.0950560i | \(-0.0303030\pi\) | ||||
−0.995472 | + | 0.0950560i | \(0.969697\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 546.386 | + | 946.369i | 0.705015 | + | 1.22112i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 261.582 | − | 168.109i | 0.336657 | − | 0.216356i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 235.806 | − | 681.316i | 0.300772 | − | 0.869025i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 194.581 | − | 802.073i | 0.247244 | − | 1.01915i | −0.703875 | − | 0.710324i | \(-0.748548\pi\) |
0.951118 | − | 0.308828i | \(-0.0999366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 84.2065 | − | 1767.71i | 0.106187 | − | 2.22915i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 575.425 | − | 1260.01i | 0.722896 | − | 1.58292i | ||||
\(797\) | 0 | 0 | 0.928368 | − | 0.371662i | \(-0.121212\pi\) | ||||
−0.928368 | + | 0.371662i | \(0.878788\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 553.677 | + | 582.973i | 0.688653 | + | 0.725091i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1450.54 | + | 580.709i | −1.78858 | + | 0.716041i | −0.794521 | + | 0.607237i | \(0.792278\pi\) |
−0.994063 | + | 0.108804i | \(0.965298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.7787 | − | 325.353i | 0.0575384 | − | 0.400189i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3042.16 | − | 290.491i | −3.72357 | − | 0.355558i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 38.8303 | + | 270.071i | 0.0474119 | + | 0.329757i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.235759 | − | 0.971812i | \(-0.424242\pi\) | ||||
−0.235759 | + | 0.971812i | \(0.575758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.4488 | − | 19.3960i | −0.0588686 | − | 0.0235674i | 0.342041 | − | 0.939685i | \(-0.388882\pi\) |
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.981929 | − | 0.189251i | \(-0.0606061\pi\) | ||||
−0.981929 | + | 0.189251i | \(0.939394\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −598.443 | − | 1310.41i | −0.721886 | − | 1.58071i | −0.811243 | − | 0.584710i | \(-0.801208\pi\) |
0.0893571 | − | 0.996000i | \(-0.471519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1397.99 | + | 898.431i | −1.68229 | + | 1.08114i | ||||
\(832\) | −567.034 | − | 796.287i | −0.681531 | − | 0.957076i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −927.695 | + | 729.548i | −1.10836 | + | 0.871622i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.981929 | − | 0.189251i | \(-0.939394\pi\) | ||||
0.981929 | + | 0.189251i | \(0.0606061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −420.500 | + | 728.327i | −0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −101.744 | + | 65.3867i | −0.120549 | + | 0.0774724i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −230.434 | + | 67.6616i | −0.272059 | + | 0.0798839i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1110.16 | − | 1281.19i | 1.30761 | − | 1.50906i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 459.143 | − | 437.792i | 0.538269 | − | 0.513238i | −0.371456 | − | 0.928451i | \(-0.621141\pi\) |
0.909724 | + | 0.415213i | \(0.136293\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 935.410 | − | 1313.60i | 1.08895 | − | 1.52922i | 0.263574 | − | 0.964639i | \(-0.415099\pi\) |
0.825378 | − | 0.564580i | \(-0.190962\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −204.403 | − | 842.561i | −0.235759 | − | 0.971812i | ||||
\(868\) | 227.258 | + | 262.269i | 0.261818 | + | 0.302154i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 290.249 | − | 981.348i | 0.333236 | − | 1.12669i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 245.831 | + | 193.323i | 0.281593 | + | 0.221447i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1053.72 | − | 677.186i | −1.20288 | − | 0.773043i | ||||
\(877\) | −55.5758 | − | 1166.68i | −0.0633704 | − | 1.33031i | −0.776874 | − | 0.629656i | \(-0.783196\pi\) |
0.713504 | − | 0.700652i | \(-0.247107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.327068 | − | 0.945001i | \(-0.606061\pi\) | ||||
0.327068 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 439.988 | − | 617.877i | 0.498288 | − | 0.699747i | −0.486466 | − | 0.873699i | \(-0.661714\pi\) |
0.984754 | + | 0.173952i | \(0.0556537\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.888835 | − | 0.458227i | \(-0.151515\pi\) | ||||
−0.888835 | + | 0.458227i | \(0.848485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −121.552 | + | 115.900i | −0.136729 | + | 0.130371i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −984.199 | − | 507.390i | −1.10336 | − | 0.568823i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −450.000 | − | 779.423i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 470.576 | + | 90.6961i | 0.521125 | + | 0.100439i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1148.68 | − | 109.685i | 1.26646 | − | 0.120932i | 0.559884 | − | 0.828571i | \(-0.310846\pi\) |
0.706574 | + | 0.707639i | \(0.250240\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(912\) | 1319.06 | + | 1257.72i | 1.44634 | + | 1.37908i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.0582 | + | 53.1540i | −0.0502818 | + | 0.0580283i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −137.362 | − | 54.9916i | −0.149469 | − | 0.0598385i | 0.295722 | − | 0.955274i | \(-0.404440\pi\) |
−0.445191 | + | 0.895436i | \(0.646864\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 426.721 | − | 1758.97i | 0.463323 | − | 1.90985i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1299.60 | + | 124.097i | 1.40497 | + | 0.134158i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.5439 | − | 368.292i | 0.0189255 | − | 0.397295i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1588.40 | − | 635.900i | 1.70613 | − | 0.683029i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1861.48 | −1.98664 | −0.993321 | − | 0.115386i | \(-0.963189\pi\) | ||||
−0.993321 | + | 0.115386i | \(0.963189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1871.05 | −1.99260 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(948\) | 528.953 | + | 1528.31i | 0.557967 | + | 1.61214i | ||||
\(949\) | −75.8609 | + | 1592.52i | −0.0799377 | + | 1.67810i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 932.482 | − | 179.721i | 0.970324 | − | 0.187015i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 717.438 | + | 684.076i | 0.744230 | + | 0.709622i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 641.690 | + | 1111.44i | 0.663588 | + | 1.14937i | 0.979666 | + | 0.200635i | \(0.0643006\pi\) |
−0.316078 | + | 0.948733i | \(0.602366\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.786053 | − | 0.618159i | \(-0.212121\pi\) | ||||
−0.786053 | + | 0.618159i | \(0.787879\pi\) | |||||||
\(972\) | 764.044 | − | 600.851i | 0.786053 | − | 0.618159i | ||||
\(973\) | 60.1141 | + | 11.5860i | 0.0617822 | + | 0.0119075i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −572.782 | + | 992.088i | −0.587469 | + | 1.01753i | ||||
\(976\) | 926.906 | + | 1605.45i | 0.949699 | + | 1.64493i | ||||
\(977\) | 0 | 0 | −0.580057 | − | 0.814576i | \(-0.696970\pi\) | ||||
0.580057 | + | 0.814576i | \(0.303030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1478.06 | + | 433.999i | −1.50669 | + | 0.442405i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 546.929 | − | 2254.47i | 0.553571 | − | 2.28185i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −990.738 | − | 290.907i | −0.999735 | − | 0.293549i | −0.259388 | − | 0.965773i | \(-0.583521\pi\) |
−0.740347 | + | 0.672224i | \(0.765339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −705.420 | + | 990.624i | −0.710393 | + | 0.997607i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 319.482 | − | 699.568i | 0.320443 | − | 0.701673i | −0.679030 | − | 0.734110i | \(-0.737600\pi\) |
0.999474 | + | 0.0324369i | \(0.0103268\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 67.0881 | + | 1408.35i | 0.0671553 | + | 1.40976i |
(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 | 201.3.o.a.170.1 | ✓ | 20 | |
3.2 | odd | 2 | CM | 201.3.o.a.170.1 | ✓ | 20 | |
67.54 | even | 33 | inner | 201.3.o.a.188.1 | yes | 20 | |
201.188 | odd | 66 | inner | 201.3.o.a.188.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.3.o.a.170.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
201.3.o.a.170.1 | ✓ | 20 | 3.2 | odd | 2 | CM | |
201.3.o.a.188.1 | yes | 20 | 67.54 | even | 33 | inner | |
201.3.o.a.188.1 | yes | 20 | 201.188 | odd | 66 | inner |