Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(2,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(156))
chi = DirichletCharacter(H, H._module([78, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.2");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.x (of order \(156\), degree \(48\), 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{156}]$ |
Embedding invariants
Embedding label | 176.1 | ||
Character | \(\chi\) | \(=\) | 507.176 |
Dual form | 507.2.x.a.314.1 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{107}{156}\right)\) |
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 | 0.551377 | − | 0.834256i | \(-0.314103\pi\) | ||||
−0.551377 | + | 0.834256i | \(0.685897\pi\) | |||||||
\(3\) | 1.70962 | + | 0.277840i | 0.987050 | + | 0.160411i | ||||
\(4\) | −0.783933 | − | 1.83996i | −0.391967 | − | 0.919979i | ||||
\(5\) | 0 | 0 | −0.855781 | − | 0.517338i | \(-0.826923\pi\) | ||||
0.855781 | + | 0.517338i | \(0.173077\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.45291 | + | 4.07679i | 0.549150 | + | 1.54088i | 0.816536 | + | 0.577294i | \(0.195891\pi\) |
−0.267386 | + | 0.963589i | \(0.586160\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.84561 | + | 0.950004i | 0.948536 | + | 0.316668i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.446798 | − | 0.894635i | \(-0.352564\pi\) | ||||
−0.446798 | + | 0.894635i | \(0.647436\pi\) | |||||||
\(12\) | −0.829014 | − | 3.36344i | −0.239316 | − | 0.970942i | ||||
\(13\) | 2.59808 | + | 2.50000i | 0.720577 | + | 0.693375i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.77090 | + | 2.88481i | −0.692724 | + | 0.721202i | ||||
\(17\) | 0 | 0 | −0.903450 | − | 0.428693i | \(-0.858974\pi\) | ||||
0.903450 | + | 0.428693i | \(0.141026\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.01264 | − | 7.51128i | 0.461731 | − | 1.72321i | −0.205773 | − | 0.978600i | \(-0.565971\pi\) |
0.667505 | − | 0.744606i | \(-0.267362\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.35124 | + | 7.37345i | 0.294864 | + | 1.60902i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.32362 | + | 4.42728i | 0.464723 | + | 0.885456i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.60096 | + | 2.41477i | 0.885456 | + | 0.464723i | ||||
\(28\) | 6.36215 | − | 5.86924i | 1.20233 | − | 1.10918i | ||||
\(29\) | 0 | 0 | −0.200026 | − | 0.979791i | \(-0.564103\pi\) | ||||
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.22827 | − | 10.3599i | −0.579815 | − | 1.86069i | −0.504264 | − | 0.863550i | \(-0.668236\pi\) |
−0.0755512 | − | 0.997142i | \(-0.524072\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.482799 | − | 5.98054i | −0.0804666 | − | 0.996757i | ||||
\(37\) | 1.88677 | − | 8.37752i | 0.310184 | − | 1.37726i | −0.535935 | − | 0.844260i | \(-0.680041\pi\) |
0.846118 | − | 0.532995i | \(-0.178934\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.74712 | + | 4.99590i | 0.600020 | + | 0.799985i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.584522 | − | 0.811378i | \(-0.698718\pi\) | ||||
0.584522 | + | 0.811378i | \(0.301282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24401 | + | 9.87411i | −0.952202 | + | 1.50579i | −0.0920473 | + | 0.995755i | \(0.529341\pi\) |
−0.860155 | + | 0.510033i | \(0.829633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.787183 | − | 0.616719i | \(-0.788462\pi\) | ||||
0.787183 | + | 0.616719i | \(0.211538\pi\) | |||||||
\(48\) | −5.53870 | + | 4.16206i | −0.799443 | + | 0.600742i | ||||
\(49\) | −9.08706 | + | 7.41935i | −1.29815 | + | 1.05991i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.56318 | − | 6.74019i | 0.355449 | − | 0.934696i | ||||
\(53\) | 0 | 0 | −0.568065 | − | 0.822984i | \(-0.692308\pi\) | ||||
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.52779 | − | 12.2822i | 0.732174 | − | 1.62682i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.999797 | − | 0.0201371i | \(-0.993590\pi\) | ||||
0.999797 | + | 0.0201371i | \(0.00641026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.9039 | − | 1.12244i | −1.78021 | − | 0.143713i | −0.853889 | − | 0.520455i | \(-0.825762\pi\) |
−0.926318 | + | 0.376742i | \(0.877044\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.261457 | + | 12.9812i | 0.0329405 | + | 1.63548i | ||||
\(64\) | 7.48013 | + | 2.83684i | 0.935016 | + | 0.354605i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.26774 | + | 13.0887i | 0.643557 | + | 1.59904i | 0.792279 | + | 0.610158i | \(0.208894\pi\) |
−0.148722 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.994935 | − | 0.100522i | \(-0.0320513\pi\) | ||||
−0.994935 | + | 0.100522i | \(0.967949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.6273 | + | 0.824301i | −1.59496 | + | 0.0964771i | −0.833791 | − | 0.552080i | \(-0.813834\pi\) |
−0.761166 | + | 0.648557i | \(0.775373\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.74243 | + | 8.21457i | 0.316668 | + | 0.948536i | ||||
\(76\) | −15.3982 | + | 2.18516i | −1.76630 | + | 0.250655i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.946919 | − | 7.79858i | −0.106537 | − | 0.877409i | −0.943779 | − | 0.330577i | \(-0.892757\pi\) |
0.837242 | − | 0.546832i | \(-0.184166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.19498 | + | 5.40668i | 0.799443 | + | 0.600742i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.911900 | − | 0.410413i | \(-0.134615\pi\) | ||||
−0.911900 | + | 0.410413i | \(0.865385\pi\) | |||||||
\(84\) | 12.5076 | − | 8.26651i | 1.36469 | − | 0.901951i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.41720 | + | 14.2241i | −0.672706 | + | 1.49109i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.64073 | − | 18.6084i | −0.273831 | − | 1.92960i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.79404 | − | 8.70370i | 0.486761 | − | 0.883727i | −0.512920 | − | 0.858437i | \(-0.671436\pi\) |
0.999680 | − | 0.0252904i | \(-0.00805106\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.32445 | − | 7.74605i | 0.632445 | − | 0.774605i | ||||
\(101\) | 0 | 0 | −0.999189 | − | 0.0402659i | \(-0.987179\pi\) | ||||
0.999189 | + | 0.0402659i | \(0.0128205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.2430 | − | 4.26390i | 1.10780 | − | 0.420135i | 0.268217 | − | 0.963359i | \(-0.413566\pi\) |
0.839588 | + | 0.543224i | \(0.182796\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.278217 | − | 0.960518i | \(-0.410256\pi\) | ||||
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(108\) | 0.836233 | − | 10.3586i | 0.0804666 | − | 0.996757i | ||||
\(109\) | −16.4601 | − | 5.12916i | −1.57659 | − | 0.491285i | −0.620461 | − | 0.784238i | \(-0.713054\pi\) |
−0.956127 | + | 0.292953i | \(0.905362\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.55328 | − | 13.7982i | 0.527094 | − | 1.30966i | ||||
\(112\) | −15.7867 | − | 7.10500i | −1.49170 | − | 0.671359i | ||||
\(113\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.01810 | + | 9.58221i | 0.463924 | + | 0.885875i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.60816 | − | 8.79387i | −0.600742 | − | 0.799443i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −16.5310 | + | 14.0614i | −1.48453 | + | 1.26275i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.73157 | + | 4.06415i | −0.153652 | + | 0.360635i | −0.978961 | − | 0.204047i | \(-0.934591\pi\) |
0.825309 | + | 0.564681i | \(0.191001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.4183 | + | 15.1461i | −1.18142 | + | 1.33354i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 33.5461 | − | 2.70812i | 2.90882 | − | 0.234824i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.975564 | − | 0.219715i | \(-0.0705128\pi\) | ||||
−0.975564 | + | 0.219715i | \(0.929487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.18683 | + | 4.09740i | 0.100665 | + | 0.347537i | 0.995002 | − | 0.0998583i | \(-0.0318389\pi\) |
−0.894336 | + | 0.447395i | \(0.852352\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.6255 | + | 5.57668i | −0.885456 | + | 0.464723i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.5968 | + | 10.1595i | −1.45136 | + | 0.837944i | ||||
\(148\) | −16.8934 | + | 3.09583i | −1.38863 | + | 0.254476i | ||||
\(149\) | 0 | 0 | −0.990080 | − | 0.140502i | \(-0.955128\pi\) | ||||
0.990080 | + | 0.140502i | \(0.0448718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5436 | − | 17.2871i | −1.10216 | − | 1.40681i | −0.904467 | − | 0.426543i | \(-0.859731\pi\) |
−0.197696 | − | 0.980263i | \(-0.563346\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.25476 | − | 10.8110i | 0.500782 | − | 0.865574i | ||||
\(157\) | −20.4156 | + | 5.03199i | −1.62934 | + | 0.401597i | −0.944871 | − | 0.327444i | \(-0.893813\pi\) |
−0.684471 | + | 0.729040i | \(0.739967\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.82039 | + | 1.67935i | 0.142584 | + | 0.131537i | 0.746156 | − | 0.665771i | \(-0.231897\pi\) |
−0.603572 | + | 0.797309i | \(0.706256\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.834256 | − | 0.551377i | \(-0.814103\pi\) | ||||
0.834256 | + | 0.551377i | \(0.185897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.8629 | − | 19.4621i | 0.983653 | − | 1.48831i | ||||
\(172\) | 23.0628 | + | 3.74808i | 1.75852 | + | 0.285788i | ||||
\(173\) | 0 | 0 | −0.391967 | − | 0.919979i | \(-0.628205\pi\) | ||||
0.391967 | + | 0.919979i | \(0.371795\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.6731 | + | 15.9054i | −1.10918 | + | 1.20233i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.903450 | − | 0.428693i | \(-0.141026\pi\) | ||||
−0.903450 | + | 0.428693i | \(0.858974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.35971 | − | 17.6881i | −0.324055 | − | 1.31474i | −0.876584 | − | 0.481249i | \(-0.840183\pi\) |
0.552529 | − | 0.833494i | \(-0.313663\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.4585 | − | 5.78200i | −1.73410 | − | 0.427417i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.15972 | + | 22.2656i | −0.229836 | + | 1.61959i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | 18.3486 | + | 6.53918i | 1.32076 | + | 0.470701i | 0.899770 | − | 0.436365i | \(-0.143734\pi\) |
0.420989 | + | 0.907066i | \(0.361683\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.7750 | + | 10.9035i | 1.48393 | + | 0.778824i | ||||
\(197\) | 0 | 0 | 0.735006 | − | 0.678061i | \(-0.237179\pi\) | ||||
−0.735006 | + | 0.678061i | \(0.762821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.5641 | − | 7.69438i | 1.88308 | − | 0.545440i | 0.886505 | − | 0.462719i | \(-0.153126\pi\) |
0.996573 | − | 0.0827210i | \(-0.0263610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.36928 | + | 23.8403i | 0.378720 | + | 1.68156i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.4110 | + | 0.567712i | −0.999225 | + | 0.0393638i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.7219 | − | 11.3851i | −1.83961 | − | 0.783786i | −0.927402 | − | 0.374067i | \(-0.877963\pi\) |
−0.912212 | − | 0.409719i | \(-0.865627\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37.5448 | − | 28.2130i | 2.54870 | − | 1.91523i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.5266 | − | 2.37698i | −1.58978 | − | 0.160621i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7790 | − | 13.0975i | 1.59236 | − | 0.877077i | 0.595053 | − | 0.803686i | \(-0.297131\pi\) |
0.997303 | − | 0.0733905i | \(-0.0233819\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.40617 | + | 14.8058i | 0.160411 | + | 0.987050i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.927686 | − | 0.373361i | \(-0.878205\pi\) | ||||
0.927686 | + | 0.373361i | \(0.121795\pi\) | |||||||
\(228\) | −26.9322 | − | 0.542446i | −1.78363 | − | 0.0359244i | ||||
\(229\) | 1.90570 | − | 6.11561i | 0.125932 | − | 0.404131i | −0.870126 | − | 0.492829i | \(-0.835963\pi\) |
0.996059 | + | 0.0886981i | \(0.0282706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.935016 | − | 0.354605i | \(-0.884615\pi\) | ||||
0.935016 | + | 0.354605i | \(0.115385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.547888 | − | 13.5957i | 0.0355892 | − | 0.883136i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5455 | + | 6.35930i | 0.743710 | + | 0.409638i | 0.808680 | − | 0.588249i | \(-0.200182\pi\) |
−0.0649701 | + | 0.997887i | \(0.520695\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7985 | + | 11.2424i | 0.692724 | + | 0.721202i | ||||
\(244\) | 8.83446 | + | 26.4624i | 0.565569 | + | 1.69408i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.0072 | − | 14.4833i | 1.52754 | − | 0.921548i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.999189 | − | 0.0402659i | \(-0.0128205\pi\) | ||||
−0.999189 | + | 0.0402659i | \(0.987179\pi\) | |||||||
\(252\) | 23.6800 | − | 10.6575i | 1.49170 | − | 0.671359i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.644255 | − | 15.9870i | −0.0402659 | − | 0.999189i | ||||
\(257\) | 0 | 0 | 0.600742 | − | 0.799443i | \(-0.294872\pi\) | ||||
−0.600742 | + | 0.799443i | \(0.705128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.8947 | − | 4.47983i | 2.29253 | − | 0.278363i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.948536 | − | 0.316668i | \(-0.102564\pi\) | ||||
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.9531 | − | 19.9531i | 1.21883 | − | 1.21883i | ||||
\(269\) | 0 | 0 | 0.632445 | − | 0.774605i | \(-0.282051\pi\) | ||||
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.20791 | − | 2.09600i | 0.316358 | − | 0.127323i | −0.209715 | − | 0.977763i | \(-0.567254\pi\) |
0.526073 | + | 0.850439i | \(0.323664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.9230 | + | 22.5349i | −0.903182 | + | 1.36387i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.54924 | + | 31.5780i | −0.153169 | + | 1.89734i | 0.229277 | + | 0.973361i | \(0.426364\pi\) |
−0.382446 | + | 0.923978i | \(0.624918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.655535 | − | 32.5471i | 0.0392459 | − | 1.94854i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.911900 | − | 0.410413i | \(-0.865385\pi\) | ||||
0.911900 | + | 0.410413i | \(0.134615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8534 | + | 25.0701i | 0.942387 | + | 1.49027i | 0.870096 | + | 0.492882i | \(0.164056\pi\) |
0.0722903 | + | 0.997384i | \(0.476969\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.7516 | + | 13.1683i | 0.632445 | + | 0.774605i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.6142 | − | 13.5481i | 0.622217 | − | 0.794201i | ||||
\(292\) | 12.1996 | + | 24.4275i | 0.713927 | + | 1.42951i | ||||
\(293\) | 0 | 0 | 0.761712 | − | 0.647915i | \(-0.224359\pi\) | ||||
−0.761712 | + | 0.647915i | \(0.775641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 12.9646 | − | 11.4856i | 0.748511 | − | 0.663123i | ||||
\(301\) | −49.3267 | − | 11.1093i | −2.84315 | − | 0.640329i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0918 | + | 26.6191i | 0.922927 | + | 1.52671i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.39673 | + | 1.37007i | −0.250934 | + | 0.0781943i | −0.420390 | − | 0.907344i | \(-0.638107\pi\) |
0.169456 | + | 0.985538i | \(0.445799\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.4059 | − | 4.16590i | 1.16085 | − | 0.236990i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.464723 | − | 0.885456i | \(-0.346154\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.0959 | + | 11.0720i | −1.19241 | + | 0.625825i | −0.939794 | − | 0.341741i | \(-0.888983\pi\) |
−0.252616 | + | 0.967567i | \(0.581291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.6067 | + | 7.85586i | −0.765439 | + | 0.441926i | ||||
\(317\) | 0 | 0 | 0.983620 | − | 0.180255i | \(-0.0576923\pi\) | ||||
−0.983620 | + | 0.180255i | \(0.942308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4.30768 | − | 17.4770i | 0.239316 | − | 0.970942i | ||||
\(325\) | −5.03127 | + | 17.3115i | −0.279085 | + | 0.960267i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.7154 | − | 13.3422i | −1.47736 | − | 0.737825i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5395 | − | 8.03279i | 1.23889 | − | 0.441522i | 0.366535 | − | 0.930404i | \(-0.380544\pi\) |
0.872350 | + | 0.488882i | \(0.162595\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.3277 | − | 22.0467i | 0.730353 | − | 1.20815i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −25.0151 | − | 16.5330i | −1.36469 | − | 0.901951i | ||||
\(337\) | − | 35.0047i | − | 1.90683i | −0.301663 | − | 0.953414i | \(-0.597542\pi\) | ||
0.301663 | − | 0.953414i | \(-0.402458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.5234 | − | 10.5933i | −0.946176 | − | 0.571983i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.948536 | − | 0.316668i | \(-0.897436\pi\) | ||||
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.5691 | + | 33.1767i | −0.886925 | + | 1.77591i | −0.334343 | + | 0.942451i | \(0.608514\pi\) |
−0.552582 | + | 0.833459i | \(0.686357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.91673 | + | 17.7762i | 0.315811 | + | 0.948822i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.761712 | − | 0.647915i | \(-0.775641\pi\) | ||||
0.761712 | + | 0.647915i | \(0.224359\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.180255 | − | 0.983620i | \(-0.557692\pi\) | ||||
0.180255 | + | 0.983620i | \(0.442308\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.9141 | − | 20.7350i | −1.89022 | − | 1.09132i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.85417 | − | 16.8702i | −0.464723 | − | 0.885456i | ||||
\(364\) | 31.2024 | + | 0.656637i | 1.63545 | + | 0.0344171i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.41006 | + | 31.3986i | 0.334603 | + | 1.63899i | 0.704345 | + | 0.709857i | \(0.251241\pi\) |
−0.369743 | + | 0.929134i | \(0.620554\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −32.1686 | + | 19.4466i | −1.66786 | + | 1.00826i | ||||
\(373\) | −1.70440 | + | 8.34872i | −0.0882507 | + | 0.432281i | 0.911528 | + | 0.411238i | \(0.134904\pi\) |
−0.999779 | + | 0.0210423i | \(0.993302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.37985 | + | 11.6321i | 0.430444 | + | 0.597501i | 0.969597 | − | 0.244706i | \(-0.0786916\pi\) |
−0.539153 | + | 0.842208i | \(0.681256\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.08951 | + | 6.46705i | −0.209512 | + | 0.331317i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.647915 | − | 0.761712i | \(-0.724359\pi\) | ||||
0.647915 | + | 0.761712i | \(0.275641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.1484 | + | 22.1660i | −1.38003 | + | 1.12676i | ||||
\(388\) | −19.7727 | − | 1.99771i | −1.00380 | − | 0.101418i | ||||
\(389\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.9694 | − | 0.643900i | −1.60450 | − | 0.0323164i | −0.790232 | − | 0.612808i | \(-0.790040\pi\) |
−0.814266 | + | 0.580492i | \(0.802860\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 58.1036 | + | 4.69061i | 2.90882 | + | 0.234824i | ||||
\(400\) | −19.2104 | − | 5.56435i | −0.960518 | − | 0.278217i | ||||
\(401\) | 0 | 0 | −0.0201371 | − | 0.999797i | \(-0.506410\pi\) | ||||
0.0201371 | + | 0.999797i | \(0.493590\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.5124 | − | 34.9865i | 0.872356 | − | 1.74280i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6643 | − | 2.79502i | 1.36791 | − | 0.138205i | 0.610951 | − | 0.791668i | \(-0.290787\pi\) |
0.756958 | + | 0.653463i | \(0.226685\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.6592 | − | 17.3440i | −0.820738 | − | 0.854479i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.890600 | + | 7.33475i | 0.0436129 | + | 0.359184i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.799443 | − | 0.600742i | \(-0.794872\pi\) | ||||
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.33202 | + | 1.04956i | −0.113656 | + | 0.0511522i | −0.466443 | − | 0.884551i | \(-0.654465\pi\) |
0.352787 | + | 0.935704i | \(0.385234\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.6252 | − | 58.3140i | −0.756156 | − | 2.82201i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.140502 | − | 0.990080i | \(-0.544872\pi\) | ||||
0.140502 | + | 0.990080i | \(0.455128\pi\) | |||||||
\(432\) | −19.7150 | + | 6.58182i | −0.948536 | + | 0.316668i | ||||
\(433\) | −8.12548 | + | 7.80463i | −0.390485 | + | 0.375066i | −0.862100 | − | 0.506739i | \(-0.830851\pi\) |
0.471614 | + | 0.881805i | \(0.343671\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.46614 | + | 34.3067i | 0.165998 | + | 1.64300i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.4080 | + | 1.54779i | 1.83311 | + | 0.0738719i | 0.932590 | − | 0.360938i | \(-0.117543\pi\) |
0.900522 | + | 0.434810i | \(0.143184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.9066 | + | 12.4798i | −1.56698 | + | 0.594278i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(444\) | −29.7414 | + | 0.599026i | −1.41147 | + | 0.0284285i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.697219 | + | 34.6166i | −0.0329405 | + | 1.63548i | ||||
\(449\) | 0 | 0 | 0.373361 | − | 0.927686i | \(-0.378205\pi\) | ||||
−0.373361 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18.3514 | − | 33.3174i | −0.862222 | − | 1.56539i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.08916 | + | 10.7802i | −0.0509488 | + | 0.504275i | 0.936982 | + | 0.349378i | \(0.113607\pi\) |
−0.987931 | + | 0.154897i | \(0.950495\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.446798 | − | 0.894635i | \(-0.647436\pi\) | ||||
0.446798 | + | 0.894635i | \(0.352564\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0523714 | + | 0.865802i | −0.00243390 | + | 0.0402372i | −0.999190 | − | 0.0402476i | \(-0.987185\pi\) |
0.996756 | + | 0.0804849i | \(0.0256469\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.663123 | − | 0.748511i | \(-0.269231\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(468\) | 13.6970 | − | 16.7449i | 0.633145 | − | 0.774034i | ||||
\(469\) | −45.7063 | + | 40.4923i | −2.11052 | + | 1.86976i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.3010 | + | 2.93052i | −1.67266 | + | 0.135031i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.9311 | − | 8.54280i | 1.74040 | − | 0.391971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.678061 | − | 0.735006i | \(-0.737179\pi\) | ||||
0.678061 | + | 0.735006i | \(0.262821\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.8458 | − | 17.0485i | 1.17847 | − | 0.777344i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.0000 | + | 19.0526i | −0.500000 | + | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.1666 | − | 3.42949i | −1.09509 | − | 0.155405i | −0.430486 | − | 0.902597i | \(-0.641658\pi\) |
−0.664608 | + | 0.747192i | \(0.731401\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.64558 | + | 3.37684i | 0.119637 | + | 0.152706i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.721202 | − | 0.692724i | \(-0.756410\pi\) | ||||
0.721202 | + | 0.692724i | \(0.243590\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 38.8315 | + | 19.3932i | 1.74359 | + | 0.870782i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.84362 | − | 42.8012i | 0.351129 | − | 1.91605i | −0.0473700 | − | 0.998877i | \(-0.515084\pi\) |
0.398499 | − | 0.917169i | \(-0.369531\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.75444 | + | 22.3476i | −0.122329 | + | 0.992490i | ||||
\(508\) | 8.83530 | 0.392003 | ||||||||
\(509\) | 0 | 0 | 0.551377 | − | 0.834256i | \(-0.314103\pi\) | ||||
−0.551377 | + | 0.834256i | \(0.685897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.1598 | − | 54.3581i | −1.02453 | − | 2.40466i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.3981 | − | 29.6991i | 1.20966 | − | 1.31125i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 38.3874 | + | 12.8156i | 1.68991 | + | 0.564174i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8347 | − | 25.8556i | 1.08594 | − | 1.13059i | 0.0951145 | − | 0.995466i | \(-0.469678\pi\) |
0.990829 | − | 0.135121i | \(-0.0431422\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −29.5046 | + | 23.1154i | −1.28769 | + | 1.00884i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −31.2808 | − | 59.6005i | −1.35619 | − | 2.58401i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.7067 | − | 24.0035i | 1.70712 | − | 1.03199i | 0.816329 | − | 0.577587i | \(-0.196006\pi\) |
0.890795 | − | 0.454405i | \(-0.150148\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.53900 | − | 31.4512i | −0.108959 | − | 1.34970i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4302 | − | 18.0996i | −0.873533 | − | 0.773883i | 0.101757 | − | 0.994809i | \(-0.467553\pi\) |
−0.975290 | + | 0.220926i | \(0.929092\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −38.4986 | − | 16.4027i | −1.64308 | − | 0.700052i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.4174 | − | 15.1911i | 1.29348 | − | 0.645990i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.60865 | − | 5.39580i | 0.280269 | − | 0.228833i | ||||
\(557\) | 0 | 0 | −0.994935 | − | 0.100522i | \(-0.967949\pi\) | ||||
0.994935 | + | 0.100522i | \(0.0320513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.9077 | + | 10.0437i | −1.73021 | + | 0.424802i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
0.160411 | + | 0.987050i | \(0.448718\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.5882 | + | 37.1879i | −0.486660 | + | 1.56175i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.960518 | − | 0.278217i | \(-0.910256\pi\) | ||||
0.960518 | + | 0.278217i | \(0.0897436\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.0656 | + | 12.9194i | 1.42560 | + | 0.540660i | 0.942293 | − | 0.334790i | \(-0.108665\pi\) |
0.483310 | + | 0.875449i | \(0.339434\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 18.5905 | + | 15.1787i | 0.774605 | + | 0.632445i | ||||
\(577\) | −19.0312 | − | 19.0312i | −0.792278 | − | 0.792278i | 0.189586 | − | 0.981864i | \(-0.439285\pi\) |
−0.981864 | + | 0.189586i | \(0.939285\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 29.5522 | + | 16.2775i | 1.22815 | + | 0.676470i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(588\) | 32.4879 | + | 24.4130i | 1.33978 | + | 1.00678i | ||||
\(589\) | −84.3134 | + | 3.39771i | −3.47407 | + | 0.140000i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.9395 | + | 28.6562i | 0.778408 | + | 1.17776i | ||||
\(593\) | 0 | 0 | −0.410413 | − | 0.911900i | \(-0.634615\pi\) | ||||
0.410413 | + | 0.911900i | \(0.365385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 47.5523 | − | 5.77390i | 1.94619 | − | 0.236310i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.10236 | + | 0.701872i | −0.0857571 | + | 0.0286299i | −0.359223 | − | 0.933252i | \(-0.616958\pi\) |
0.273466 | + | 0.961882i | \(0.411830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.55563 | + | 42.2497i | 0.104073 | + | 1.72054i | ||||
\(604\) | −21.1903 | + | 38.4716i | −0.862222 | + | 1.56539i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.2541 | + | 19.9077i | −0.659734 | + | 0.808027i | −0.990765 | − | 0.135593i | \(-0.956706\pi\) |
0.331031 | + | 0.943620i | \(0.392604\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.3174 | + | 0.852320i | −1.70918 | + | 0.0344249i | −0.865043 | − | 0.501699i | \(-0.832709\pi\) |
−0.844140 | + | 0.536123i | \(0.819888\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.0201371 | − | 0.999797i | \(-0.493590\pi\) | ||||
−0.0201371 | + | 0.999797i | \(0.506410\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9354 | + | 10.3224i | 0.921852 | + | 0.414892i | 0.815051 | − | 0.579389i | \(-0.196709\pi\) |
0.106800 | + | 0.994280i | \(0.465939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −24.7951 | − | 3.03339i | −0.992600 | − | 0.121433i | ||||
\(625\) | −14.2016 | + | 20.5746i | −0.568065 | + | 0.822984i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 25.2631 | + | 33.6191i | 1.00811 | + | 1.34155i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.4964 | + | 31.8946i | −1.49271 | + | 1.26970i | −0.616902 | + | 0.787040i | \(0.711612\pi\) |
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −42.5211 | − | 26.8887i | −1.69006 | − | 1.06873i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −42.1573 | − | 3.44160i | −1.67033 | − | 0.136361i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.979791 | − | 0.200026i | \(-0.935897\pi\) | ||||
0.979791 | + | 0.200026i | \(0.0641026\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.33162 | − | 6.00216i | −0.328567 | − | 0.236702i | 0.408131 | − | 0.912923i | \(-0.366180\pi\) |
−0.736699 | + | 0.676221i | \(0.763616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) | ||||
−0.979791 | + | 0.200026i | \(0.935897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 72.0260 | − | 37.8022i | 2.82292 | − | 1.48158i | ||||
\(652\) | 1.66288 | − | 4.66594i | 0.0651234 | − | 0.182732i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39.5611 | − | 10.6004i | −1.54343 | − | 0.413560i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.428693 | − | 0.903450i | \(-0.358974\pi\) | ||||
−0.428693 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.16469 | − | 9.59870i | 0.317570 | − | 0.373346i | −0.579699 | − | 0.814830i | \(-0.696830\pi\) |
0.897269 | + | 0.441484i | \(0.145548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 44.2920 | − | 15.7851i | 1.71243 | − | 0.610287i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.64819 | + | 28.6015i | −0.179175 | + | 1.10251i | 0.729185 | + | 0.684316i | \(0.239899\pi\) |
−0.908360 | + | 0.418189i | \(0.862665\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 25.9808i | 1.00000i | ||||||||
\(676\) | 23.5098 | − | 11.1036i | 0.904223 | − | 0.427060i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 42.4485 | + | 6.89856i | 1.62903 | + | 0.264742i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.335705 | − | 0.941967i | \(-0.608974\pi\) | ||||
0.335705 | + | 0.941967i | \(0.391026\pi\) | |||||||
\(684\) | −45.8932 | − | 8.41025i | −1.75477 | − | 0.321574i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.95719 | − | 9.92589i | 0.189129 | − | 0.378696i | ||||
\(688\) | −11.1834 | − | 45.3729i | −0.426364 | − | 1.72983i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.12451 | − | 7.76134i | −0.347113 | − | 0.295255i | 0.457316 | − | 0.889304i | \(-0.348811\pi\) |
−0.804429 | + | 0.594049i | \(0.797529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 40.7679 | + | 14.5291i | 1.54088 | + | 0.549150i | ||||
\(701\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −59.1285 | − | 31.0330i | −2.23007 | − | 1.17043i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.4805 | − | 42.3102i | 1.14472 | − | 1.58899i | 0.407708 | − | 0.913112i | \(-0.366328\pi\) |
0.737012 | − | 0.675880i | \(-0.236236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.71412 | − | 23.0913i | 0.176793 | − | 0.865991i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.534466 | − | 0.845190i | \(-0.320513\pi\) | ||||
−0.534466 | + | 0.845190i | \(0.679487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.7182 | + | 39.6403i | 1.25573 | + | 1.47628i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.9715 | + | 14.0798i | 0.668368 | + | 0.523633i | ||||
\(724\) | −29.1276 | + | 21.8880i | −1.08252 | + | 0.813459i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.65731 | + | 5.28546i | 0.283994 | + | 0.196027i | 0.701542 | − | 0.712628i | \(-0.252495\pi\) |
−0.417548 | + | 0.908655i | \(0.637111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.3377 | + | 22.2206i | 0.568065 | + | 0.822984i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 7.75125 | + | 47.6953i | 0.286494 | + | 1.76287i | ||||
\(733\) | −6.79803 | + | 15.1046i | −0.251091 | + | 0.557901i | −0.993732 | − | 0.111789i | \(-0.964342\pi\) |
0.742641 | + | 0.669690i | \(0.233573\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.02237 | + | 50.7605i | 0.0376086 | + | 1.86725i | 0.376485 | + | 0.926423i | \(0.377133\pi\) |
−0.338876 | + | 0.940831i | \(0.610047\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.0672 | − | 18.0907i | 1.65559 | − | 0.664580i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.373361 | − | 0.927686i | \(-0.621795\pi\) | ||||
0.373361 | + | 0.927686i | \(0.378205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.38472 | − | 4.14775i | −0.0505293 | − | 0.151354i | 0.920248 | − | 0.391335i | \(-0.127987\pi\) |
−0.970777 | + | 0.239982i | \(0.922859\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 43.4449 | − | 11.6410i | 1.58008 | − | 0.423380i | ||||
\(757\) | 39.1305 | + | 29.4047i | 1.42222 | + | 1.06873i | 0.985601 | + | 0.169086i | \(0.0540817\pi\) |
0.436622 | + | 0.899645i | \(0.356175\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.551377 | − | 0.834256i | \(-0.685897\pi\) | ||||
0.551377 | + | 0.834256i | \(0.314103\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.00452 | − | 74.5565i | −0.108771 | − | 2.69913i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 3.34041 | − | 27.5108i | 0.120537 | − | 0.992709i | ||||
\(769\) | 2.58507 | + | 18.2162i | 0.0932199 | + | 0.656894i | 0.980624 | + | 0.195901i | \(0.0627631\pi\) |
−0.887404 | + | 0.460993i | \(0.847493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.35222 | − | 38.8869i | −0.0846584 | − | 1.39957i | ||||
\(773\) | 0 | 0 | 0.482459 | − | 0.875918i | \(-0.339744\pi\) | ||||
−0.482459 | + | 0.875918i | \(0.660256\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.3649 | − | 38.3649i | 1.37811 | − | 1.37811i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 64.3207 | + | 2.59204i | 2.30749 | + | 0.0929888i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.77588 | − | 46.7727i | 0.134853 | − | 1.67045i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2203 | − | 27.8788i | 0.399959 | − | 0.993772i | −0.583414 | − | 0.812175i | \(-0.698283\pi\) |
0.983373 | − | 0.181598i | \(-0.0581268\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.3172 | − | 37.6758i | −1.18313 | − | 1.33791i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.9818 | − | 42.8449i | −1.23990 | − | 1.51860i | ||||
\(797\) | 0 | 0 | −0.600742 | − | 0.799443i | \(-0.705128\pi\) | ||||
0.600742 | + | 0.799443i | \(0.294872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 39.6560 | − | 28.5684i | 1.39856 | − | 1.00753i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.3205 | + | 46.8479i | 0.994468 | + | 1.64505i | 0.733482 | + | 0.679708i | \(0.237894\pi\) |
0.260986 | + | 0.965343i | \(0.415952\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.48591 | − | 2.13640i | 0.332685 | − | 0.0749269i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 61.6002 | + | 66.7735i | 2.15512 | + | 2.33611i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −31.7738 | + | 34.3799i | −1.11027 | + | 1.20133i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.335705 | − | 0.941967i | \(-0.391026\pi\) | ||||
−0.335705 | + | 0.941967i | \(0.608974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.5813 | − | 26.3164i | 1.58887 | − | 0.917332i | 0.595371 | − | 0.803451i | \(-0.297005\pi\) |
0.993494 | − | 0.113881i | \(-0.0363284\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.616719 | − | 0.787183i | \(-0.711538\pi\) | ||||
0.616719 | + | 0.787183i | \(0.288462\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.2268 | + | 31.9147i | 1.15401 | + | 1.10844i | 0.992584 | + | 0.121560i | \(0.0387897\pi\) |
0.161429 | + | 0.986884i | \(0.448390\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.1319 | + | 53.2782i | −0.455540 | + | 1.84820i | ||||
\(832\) | 12.3418 | + | 26.0706i | 0.427877 | + | 0.903837i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1636 | − | 55.4610i | 0.351306 | − | 1.91701i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.735006 | − | 0.678061i | \(-0.762821\pi\) | ||||
0.735006 | + | 0.678061i | \(0.237179\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.6794 | + | 11.3670i | −0.919979 | + | 0.391967i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 58.0924i | 1.99962i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.2497 | − | 39.7169i | 0.901951 | − | 1.36469i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.1378 | + | 47.2652i | 0.691128 | + | 1.62214i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −57.1756 | − | 10.4778i | −1.95766 | − | 0.358754i | −0.996599 | − | 0.0824022i | \(-0.973741\pi\) |
−0.961057 | − | 0.276352i | \(-0.910875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.87743 | − | 1.94161i | −0.268774 | − | 0.0662469i | 0.102625 | − | 0.994720i | \(-0.467276\pi\) |
−0.371399 | + | 0.928473i | \(0.621122\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.787183 | − | 0.616719i | \(-0.211538\pi\) | ||||
−0.787183 | + | 0.616719i | \(0.788462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.7224 | + | 25.5000i | 0.500000 | + | 0.866025i | ||||
\(868\) | −81.3434 | − | 46.9637i | −2.76098 | − | 1.59405i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.0357 | + | 47.1748i | −0.645001 | + | 1.59846i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.9105 | − | 20.2130i | 0.741558 | − | 0.684106i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.0697 | + | 45.1513i | 0.475372 | + | 1.52552i | ||||
\(877\) | −11.8276 | − | 52.5163i | −0.399391 | − | 1.77335i | −0.606554 | − | 0.795042i | \(-0.707449\pi\) |
0.207163 | − | 0.978306i | \(-0.433577\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.0804666 | − | 0.996757i | \(-0.525641\pi\) | ||||
0.0804666 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.0065 | + | 37.2567i | 1.11076 | + | 1.25379i | 0.964369 | + | 0.264560i | \(0.0852267\pi\) |
0.146389 | + | 0.989227i | \(0.453235\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.919979 | − | 0.391967i | \(-0.871795\pi\) | ||||
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.0845 | − | 1.15440i | −0.640074 | − | 0.0387173i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −42.7401 | − | 33.4847i | −1.43104 | − | 1.12115i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 25.3557 | − | 16.0340i | 0.845190 | − | 0.534466i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −81.2434 | − | 32.6977i | −2.70361 | − | 1.08811i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.9181 | − | 4.03143i | −0.462143 | − | 0.133861i | 0.0389751 | − | 0.999240i | \(-0.487591\pi\) |
−0.501118 | + | 0.865379i | \(0.667078\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(912\) | 20.1150 | + | 49.9795i | 0.666074 | + | 1.65499i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.7464 | + | 1.28782i | −0.421153 | + | 0.0425507i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.38310 | + | 2.48107i | 0.0786111 | + | 0.0818429i | 0.759346 | − | 0.650687i | \(-0.225519\pi\) |
−0.680735 | + | 0.732530i | \(0.738339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.89740 | + | 1.12072i | −0.260228 | + | 0.0369290i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.4737 | − | 11.1129i | 1.36365 | − | 0.365388i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.0439 | − | 1.45252i | 1.18384 | − | 0.0477070i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.834256 | − | 0.551377i | \(-0.185897\pi\) | ||||
−0.834256 | + | 0.551377i | \(0.814103\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 37.4398 | + | 83.1879i | 1.22704 | + | 2.72637i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.92247 | + | 24.0687i | −0.0954730 | + | 0.786291i | 0.863805 | + | 0.503826i | \(0.168075\pi\) |
−0.959278 | + | 0.282464i | \(0.908848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −39.1422 | + | 13.0676i | −1.27736 | + | 0.426445i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.0603785 | − | 0.998176i | \(-0.519231\pi\) | ||||
0.0603785 | + | 0.998176i | \(0.480769\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.927686 | − | 0.373361i | \(-0.121795\pi\) | ||||
−0.927686 | + | 0.373361i | \(0.878205\pi\) | |||||||
\(948\) | −25.4450 | + | 9.65003i | −0.826417 | + | 0.313419i | ||||
\(949\) | −37.4656 | − | 31.9267i | −1.21618 | − | 1.03638i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.0804666 | − | 0.996757i | \(-0.474359\pi\) | ||||
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −71.3931 | + | 49.2791i | −2.30300 | + | 1.58965i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.64996 | − | 26.2285i | 0.0853495 | − | 0.844762i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6888 | + | 16.1961i | −0.408045 | + | 0.520831i | −0.946883 | − | 0.321578i | \(-0.895787\pi\) |
0.538838 | + | 0.842410i | \(0.318864\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.845190 | − | 0.534466i | \(-0.820513\pi\) | ||||
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(972\) | 12.2203 | − | 28.6821i | 0.391967 | − | 0.919979i | ||||
\(973\) | −14.9799 | + | 10.7916i | −0.480233 | + | 0.345963i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.4114 | + | 28.1981i | −0.429508 | + | 0.903063i | ||||
\(976\) | 41.7642 | − | 36.9998i | 1.33684 | − | 1.18434i | ||||
\(977\) | 0 | 0 | −0.975564 | − | 0.219715i | \(-0.929487\pi\) | ||||
0.975564 | + | 0.219715i | \(0.0705128\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41.9662 | − | 30.2327i | −1.33988 | − | 0.965256i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.954721 | − | 0.297503i | \(-0.0961538\pi\) | ||||
−0.954721 | + | 0.297503i | \(0.903846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −45.4687 | − | 32.8183i | −1.44655 | − | 1.04409i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.53593 | − | 2.66031i | 0.0487904 | − | 0.0845074i | −0.840599 | − | 0.541658i | \(-0.817797\pi\) |
0.889389 | + | 0.457151i | \(0.151130\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 40.7659 | − | 7.47063i | 1.29367 | − | 0.237073i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9099 | + | 37.7443i | −0.567211 | + | 1.19537i | 0.393885 | + | 0.919160i | \(0.371131\pi\) |
−0.961096 | + | 0.276213i | \(0.910921\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 28.9108 | − | 33.9885i | 0.914696 | − | 1.07535i |
(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 | 507.2.x.a.176.1 | ✓ | 48 | |
3.2 | odd | 2 | CM | 507.2.x.a.176.1 | ✓ | 48 | |
169.145 | odd | 156 | inner | 507.2.x.a.314.1 | yes | 48 | |
507.314 | even | 156 | inner | 507.2.x.a.314.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.x.a.176.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
507.2.x.a.176.1 | ✓ | 48 | 3.2 | odd | 2 | CM | |
507.2.x.a.314.1 | yes | 48 | 169.145 | odd | 156 | inner | |
507.2.x.a.314.1 | yes | 48 | 507.314 | even | 156 | inner |