Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(1025,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1025");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 34x^{6} + 345x^{4} + 1064x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 152) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1025.5 | ||
Root | \(0.512197i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1025 |
Dual form | 1216.3.e.n.1025.4 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.512197i | 0.170732i | 0.996350 | + | 0.0853661i | \(0.0272060\pi\) | ||||
−0.996350 | + | 0.0853661i | \(0.972794\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.30665 | 0.461329 | 0.230665 | − | 0.973033i | \(-0.425910\pi\) | ||||
0.230665 | + | 0.973033i | \(0.425910\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.59559 | −0.656513 | −0.328257 | − | 0.944589i | \(-0.606461\pi\) | ||||
−0.328257 | + | 0.944589i | \(0.606461\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.73765 | 0.970851 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.7820 | 1.25291 | 0.626453 | − | 0.779460i | \(-0.284506\pi\) | ||||
0.626453 | + | 0.779460i | \(0.284506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 22.2405i | − | 1.71081i | −0.517960 | − | 0.855405i | \(-0.673308\pi\) | ||
0.517960 | − | 0.855405i | \(-0.326692\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.18146i | 0.0787638i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.43101 | 0.319471 | 0.159736 | − | 0.987160i | \(-0.448936\pi\) | ||||
0.159736 | + | 0.987160i | \(0.448936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.35095 | − | 17.5204i | −0.386892 | − | 0.922125i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.35385i | − | 0.112088i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.9908 | −1.08656 | −0.543279 | − | 0.839552i | \(-0.682817\pi\) | ||||
−0.543279 | + | 0.839552i | \(0.682817\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.6794 | −0.787175 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.08517i | 0.336488i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 34.7357i | − | 1.19778i | −0.800830 | − | 0.598891i | \(-0.795608\pi\) | ||
0.800830 | − | 0.598891i | \(-0.204392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.2508i | 1.33067i | 0.746544 | + | 0.665336i | \(0.231712\pi\) | ||||
−0.746544 | + | 0.665336i | \(0.768288\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.05907i | 0.213911i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.6004 | −0.302869 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 20.5969i | 0.556674i | 0.960483 | + | 0.278337i | \(0.0897832\pi\) | ||||
−0.960483 | + | 0.278337i | \(0.910217\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.3915 | 0.292090 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 27.8883i | − | 0.680203i | −0.940389 | − | 0.340101i | \(-0.889539\pi\) | ||
0.940389 | − | 0.340101i | \(-0.110461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8491 | −0.252305 | −0.126153 | − | 0.992011i | \(-0.540263\pi\) | ||||
−0.126153 | + | 0.992011i | \(0.540263\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 20.1547 | 0.447882 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.8609 | 0.720445 | 0.360223 | − | 0.932866i | \(-0.382701\pi\) | ||||
0.360223 | + | 0.932866i | \(0.382701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −27.8805 | −0.568991 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.78174i | 0.0545440i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 29.2996i | − | 0.552823i | −0.961039 | − | 0.276411i | \(-0.910855\pi\) | ||
0.961039 | − | 0.276411i | \(-0.0891452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 31.7901 | 0.578002 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.97388 | − | 3.76513i | 0.157436 | − | 0.0660549i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 65.8291i | − | 1.11575i | −0.829926 | − | 0.557874i | \(-0.811617\pi\) | ||
0.829926 | − | 0.557874i | \(-0.188383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 107.373 | 1.76021 | 0.880103 | − | 0.474782i | \(-0.157473\pi\) | ||||
0.880103 | + | 0.474782i | \(0.157473\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −40.1547 | −0.637376 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 51.3010i | − | 0.789247i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.78720i | − | 0.0266746i | −0.999911 | − | 0.0133373i | \(-0.995754\pi\) | ||
0.999911 | − | 0.0133373i | \(-0.00424552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 12.8002i | − | 0.185511i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 95.8822i | − | 1.35045i | −0.737610 | − | 0.675227i | \(-0.764046\pi\) | ||
0.737610 | − | 0.675227i | \(-0.235954\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65.4556 | 0.896651 | 0.448326 | − | 0.893870i | \(-0.352020\pi\) | ||||
0.448326 | + | 0.893870i | \(0.352020\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 10.0797i | − | 0.134396i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −63.3362 | −0.822549 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 37.2168i | − | 0.471098i | −0.971862 | − | 0.235549i | \(-0.924311\pi\) | ||
0.971862 | − | 0.235549i | \(-0.0756888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 73.9855 | 0.913401 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −32.6916 | −0.393874 | −0.196937 | − | 0.980416i | \(-0.563099\pi\) | ||||
−0.196937 | + | 0.980416i | \(0.563099\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.5274 | 0.147381 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.7915 | 0.204500 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 74.3815i | − | 0.835747i | −0.908505 | − | 0.417874i | \(-0.862775\pi\) | ||
0.908505 | − | 0.417874i | \(-0.137225\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 102.208i | 1.12317i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.1285 | −0.227188 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.9560 | − | 40.4133i | −0.178485 | − | 0.425403i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 128.116i | − | 1.32078i | −0.750921 | − | 0.660392i | \(-0.770390\pi\) | ||
0.750921 | − | 0.660392i | \(-0.229610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 120.422 | 1.21638 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −66.1257 | −0.654710 | −0.327355 | − | 0.944902i | \(-0.606157\pi\) | ||||
−0.327355 | + | 0.944902i | \(0.606157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 68.6107i | 0.666123i | 0.942905 | + | 0.333061i | \(0.108082\pi\) | ||||
−0.942905 | + | 0.333061i | \(0.891918\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 5.42949i | − | 0.0517095i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 163.182i | 1.52507i | 0.646949 | + | 0.762534i | \(0.276045\pi\) | ||||
−0.646949 | + | 0.762534i | \(0.723955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 98.8345i | − | 0.906738i | −0.891323 | − | 0.453369i | \(-0.850222\pi\) | ||
0.891323 | − | 0.453369i | \(-0.149778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.5497 | −0.0950422 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 94.2226i | − | 0.833829i | −0.908946 | − | 0.416914i | \(-0.863112\pi\) | ||
0.908946 | − | 0.416914i | \(-0.136888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −57.6451 | −0.501261 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 194.330i | − | 1.66094i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.9587 | −0.209737 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 68.9423 | 0.569771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.2843 | 0.116133 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −103.060 | −0.824477 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 119.017i | 0.937146i | 0.883425 | + | 0.468573i | \(0.155232\pi\) | ||||
−0.883425 | + | 0.468573i | \(0.844768\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 5.55689i | − | 0.0430766i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 126.661 | 0.966878 | 0.483439 | − | 0.875378i | \(-0.339387\pi\) | ||||
0.483439 | + | 0.875378i | \(0.339387\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 33.7820 | + | 80.5165i | 0.254000 | + | 0.605387i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.9563i | 0.155232i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 48.2645 | 0.352296 | 0.176148 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176148 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −243.120 | −1.74907 | −0.874534 | − | 0.484965i | \(-0.838832\pi\) | ||||
−0.874534 | + | 0.484965i | \(0.838832\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.3435i | 0.123003i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 306.518i | − | 2.14348i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 80.1230i | − | 0.552572i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 14.2803i | − | 0.0971450i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 131.025 | 0.879361 | 0.439681 | − | 0.898154i | \(-0.355092\pi\) | ||||
0.439681 | + | 0.898154i | \(0.355092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 173.521i | 1.14915i | 0.818453 | + | 0.574574i | \(0.194832\pi\) | ||||
−0.818453 | + | 0.574574i | \(0.805168\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 47.4543 | 0.310159 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 95.1511i | 0.613878i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 259.490 | 1.65280 | 0.826402 | − | 0.563081i | \(-0.190384\pi\) | ||||
0.826402 | + | 0.563081i | \(0.190384\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.0072 | 0.0943846 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114.848 | 0.713340 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 62.7264 | 0.384825 | 0.192412 | − | 0.981314i | \(-0.438369\pi\) | ||||
0.192412 | + | 0.981314i | \(0.438369\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16.2828i | 0.0986836i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 134.688i | 0.806518i | 0.915086 | + | 0.403259i | \(0.132123\pi\) | ||||
−0.915086 | + | 0.403259i | \(0.867877\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −325.641 | −1.92687 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −64.2301 | − | 153.087i | −0.375614 | − | 0.895246i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 90.4432i | 0.522793i | 0.965232 | + | 0.261397i | \(0.0841830\pi\) | ||||
−0.965232 | + | 0.261397i | \(0.915817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 90.4384 | 0.516791 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 33.7174 | 0.190494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 322.972i | − | 1.80431i | −0.431409 | − | 0.902156i | \(-0.641984\pi\) | ||
0.431409 | − | 0.902156i | \(-0.358016\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 241.679i | − | 1.33524i | −0.744502 | − | 0.667621i | \(-0.767313\pi\) | ||
0.744502 | − | 0.667621i | \(-0.232687\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 54.9959i | 0.300524i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 47.5099i | 0.256810i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 74.8499 | 0.400267 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 41.7517i | − | 0.220909i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 115.733 | 0.605931 | 0.302966 | − | 0.953001i | \(-0.402023\pi\) | ||||
0.302966 | + | 0.953001i | \(0.402023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 277.929i | 1.44005i | 0.693951 | + | 0.720023i | \(0.255869\pi\) | ||||
−0.693951 | + | 0.720023i | \(0.744131\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.2762 | 0.134750 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 78.7308 | 0.399649 | 0.199824 | − | 0.979832i | \(-0.435963\pi\) | ||||
0.199824 | + | 0.979832i | \(0.435963\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 93.6642 | 0.470674 | 0.235337 | − | 0.971914i | \(-0.424381\pi\) | ||||
0.235337 | + | 0.971914i | \(0.424381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.915397 | 0.00455422 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 159.631i | 0.786360i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 64.3285i | − | 0.313798i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −218.361 | −1.05489 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −101.310 | − | 241.465i | −0.484739 | − | 1.15534i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 362.818i | − | 1.71952i | −0.510701 | − | 0.859758i | \(-0.670614\pi\) | ||
0.510701 | − | 0.859758i | \(-0.329386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 49.1106 | 0.230566 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.0251 | −0.116396 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 189.572i | − | 0.873603i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 33.5261i | 0.153087i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 120.788i | − | 0.546554i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 221.055i | − | 0.991277i | −0.868529 | − | 0.495639i | \(-0.834934\pi\) | ||
0.868529 | − | 0.495639i | \(-0.165066\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −171.952 | −0.764229 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 46.2298i | 0.203656i | 0.994802 | + | 0.101828i | \(0.0324691\pi\) | ||||
−0.994802 | + | 0.101828i | \(0.967531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −44.5210 | −0.194415 | −0.0972075 | − | 0.995264i | \(-0.530991\pi\) | ||||
−0.0972075 | + | 0.995264i | \(0.530991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 32.4406i | − | 0.140436i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 276.616 | 1.18719 | 0.593596 | − | 0.804763i | \(-0.297708\pi\) | ||||
0.593596 | + | 0.804763i | \(0.297708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 78.1052 | 0.332363 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.0623 | 0.0804316 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 431.105 | 1.80379 | 0.901893 | − | 0.431959i | \(-0.142177\pi\) | ||||
0.901893 | + | 0.431959i | \(0.142177\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 90.5900i | 0.375892i | 0.982179 | + | 0.187946i | \(0.0601830\pi\) | ||||
−0.982179 | + | 0.187946i | \(0.939817\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 119.662i | 0.492435i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −64.3106 | −0.262492 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −389.662 | + | 163.489i | −1.57758 | + | 0.661899i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 16.7445i | − | 0.0672470i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 165.585 | 0.659702 | 0.329851 | − | 0.944033i | \(-0.393001\pi\) | ||||
0.329851 | + | 0.944033i | \(0.393001\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −344.423 | −1.36135 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.41650i | 0.0251628i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 500.700i | 1.94825i | 0.226011 | + | 0.974125i | \(0.427431\pi\) | ||||
−0.226011 | + | 0.974125i | \(0.572569\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 94.6551i | − | 0.365464i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 303.508i | − | 1.16287i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −370.994 | −1.41062 | −0.705312 | − | 0.708897i | \(-0.749193\pi\) | ||||
−0.705312 | + | 0.708897i | \(0.749193\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 67.5838i | − | 0.255033i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 38.0980 | 0.142689 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 273.479i | 1.01665i | 0.861165 | + | 0.508326i | \(0.169735\pi\) | ||||
−0.861165 | + | 0.508326i | \(0.830265\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −82.1566 | −0.303161 | −0.151580 | − | 0.988445i | \(-0.548436\pi\) | ||||
−0.151580 | + | 0.988445i | \(0.548436\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −52.3508 | −0.191761 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −271.220 | −0.986256 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −228.921 | −0.826430 | −0.413215 | − | 0.910633i | \(-0.635594\pi\) | ||||
−0.413215 | + | 0.910633i | \(0.635594\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 360.435i | 1.29188i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 170.230i | 0.605800i | 0.953022 | + | 0.302900i | \(0.0979549\pi\) | ||||
−0.953022 | + | 0.302900i | \(0.902045\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 37.0280 | 0.130841 | 0.0654205 | − | 0.997858i | \(-0.479161\pi\) | ||||
0.0654205 | + | 0.997858i | \(0.479161\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 20.6996 | − | 8.68483i | 0.0726301 | − | 0.0304731i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 128.163i | 0.446562i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −259.504 | −0.897938 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 65.6206 | 0.225500 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 379.390i | 1.29485i | 0.762130 | + | 0.647424i | \(0.224153\pi\) | ||||
−0.762130 | + | 0.647424i | \(0.775847\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 151.844i | − | 0.514727i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 125.211i | 0.421587i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 555.809i | 1.85889i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 49.8582 | 0.165642 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 33.8693i | − | 0.111780i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 247.671 | 0.812035 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 207.485i | 0.675846i | 0.941174 | + | 0.337923i | \(0.109724\pi\) | ||||
−0.941174 | + | 0.337923i | \(0.890276\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −35.1421 | −0.113729 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −250.191 | −0.804474 | −0.402237 | − | 0.915536i | \(-0.631767\pi\) | ||||
−0.402237 | + | 0.915536i | \(0.631767\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 490.013 | 1.56554 | 0.782768 | − | 0.622313i | \(-0.213807\pi\) | ||||
0.782768 | + | 0.622313i | \(0.213807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −92.6227 | −0.294040 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 193.572i | 0.610637i | 0.952250 | + | 0.305319i | \(0.0987630\pi\) | ||||
−0.952250 | + | 0.305319i | \(0.901237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 478.726i | − | 1.50071i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −83.5814 | −0.260378 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −39.9231 | − | 95.1533i | −0.123601 | − | 0.294592i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 437.680i | 1.34671i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 50.6227 | 0.154809 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −155.611 | −0.472982 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 77.3740i | 0.233758i | 0.993146 | + | 0.116879i | \(0.0372890\pi\) | ||||
−0.993146 | + | 0.116879i | \(0.962711\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 179.969i | 0.540447i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.12244i | − | 0.0123058i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 307.055i | 0.911143i | 0.890199 | + | 0.455571i | \(0.150565\pi\) | ||||
−0.890199 | + | 0.455571i | \(0.849435\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 48.2605 | 0.142361 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 568.517i | 1.66720i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 353.312 | 1.03006 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 29.5256i | − | 0.0855815i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −343.072 | −0.988679 | −0.494340 | − | 0.869269i | \(-0.664590\pi\) | ||||
−0.494340 | + | 0.869269i | \(0.664590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 135.313 | 0.387716 | 0.193858 | − | 0.981030i | \(-0.437900\pi\) | ||||
0.193858 | + | 0.981030i | \(0.437900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 202.059 | 0.575666 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 95.3649 | 0.270156 | 0.135078 | − | 0.990835i | \(-0.456872\pi\) | ||||
0.135078 | + | 0.990835i | \(0.456872\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 221.167i | − | 0.623004i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 12.7838i | − | 0.0358088i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 339.918 | 0.946846 | 0.473423 | − | 0.880835i | \(-0.343018\pi\) | ||||
0.473423 | + | 0.880835i | \(0.343018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −252.927 | + | 257.583i | −0.700629 | + | 0.713526i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 35.3120i | 0.0972783i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 150.983 | 0.413652 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 207.153 | 0.564449 | 0.282225 | − | 0.959348i | \(-0.408928\pi\) | ||||
0.282225 | + | 0.959348i | \(0.408928\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 243.678i | − | 0.660375i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 134.649i | 0.362935i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 221.266i | 0.593207i | 0.955001 | + | 0.296604i | \(0.0958540\pi\) | ||||
−0.955001 | + | 0.296604i | \(0.904146\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 52.7868i | − | 0.140765i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −772.540 | −2.04918 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 251.511i | − | 0.663619i | −0.943346 | − | 0.331809i | \(-0.892341\pi\) | ||
0.943346 | − | 0.331809i | \(-0.107659\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −60.9604 | −0.160001 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 367.906i | − | 0.960590i | −0.877107 | − | 0.480295i | \(-0.840530\pi\) | ||
0.877107 | − | 0.480295i | \(-0.159470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −146.094 | −0.379466 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −94.7959 | −0.244951 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −480.911 | −1.23628 | −0.618138 | − | 0.786070i | \(-0.712113\pi\) | ||||
−0.618138 | + | 0.786070i | \(0.712113\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −135.725 | −0.347124 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 64.8754i | 0.165077i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 85.8459i | − | 0.217331i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −432.964 | −1.09059 | −0.545294 | − | 0.838245i | \(-0.683582\pi\) | ||||
−0.545294 | + | 0.838245i | \(0.683582\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −41.2403 | + | 17.3030i | −0.103359 | + | 0.0433659i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 314.930i | − | 0.785361i | −0.919675 | − | 0.392680i | \(-0.871548\pi\) | ||
0.919675 | − | 0.392680i | \(-0.128452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 917.440 | 2.27653 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 170.658 | 0.421379 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 283.866i | 0.697460i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.2424i | − | 0.0323775i | −0.999869 | − | 0.0161888i | \(-0.994847\pi\) | ||
0.999869 | − | 0.0161888i | \(-0.00515327\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.7209i | 0.0601483i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 302.524i | 0.732503i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −75.4079 | −0.181706 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 124.525i | − | 0.298622i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −667.426 | −1.59290 | −0.796451 | − | 0.604703i | \(-0.793292\pi\) | ||||
−0.796451 | + | 0.604703i | \(0.793292\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 437.582i | − | 1.03939i | −0.854352 | − | 0.519694i | \(-0.826046\pi\) | ||
0.854352 | − | 0.519694i | \(-0.173954\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 295.865 | 0.699445 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −106.879 | −0.251480 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −493.441 | −1.15560 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 156.997 | 0.365961 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 680.592i | − | 1.57910i | −0.613686 | − | 0.789550i | \(-0.710314\pi\) | ||
0.613686 | − | 0.789550i | \(-0.289686\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 391.348i | 0.903807i | 0.892067 | + | 0.451904i | \(0.149255\pi\) | ||||
−0.892067 | + | 0.451904i | \(0.850745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 41.0387 | 0.0943419 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 183.706 | + | 437.849i | 0.420381 | + | 1.00194i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 433.093i | 0.986544i | 0.869875 | + | 0.493272i | \(0.164199\pi\) | ||||
−0.869875 | + | 0.493272i | \(0.835801\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −243.611 | −0.552405 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −372.634 | −0.841160 | −0.420580 | − | 0.907256i | \(-0.638173\pi\) | ||||
−0.420580 | + | 0.907256i | \(0.638173\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 171.572i | − | 0.385555i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 67.1105i | 0.150135i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 96.4188i | 0.214741i | 0.994219 | + | 0.107371i | \(0.0342431\pi\) | ||||
−0.994219 | + | 0.107371i | \(0.965757\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 384.355i | − | 0.852229i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −88.8770 | −0.196196 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 235.759i | 0.518151i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 741.777 | 1.62314 | 0.811572 | − | 0.584253i | \(-0.198612\pi\) | ||||
0.811572 | + | 0.584253i | \(0.198612\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 49.3416i | 0.107498i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −40.2016 | −0.0872053 | −0.0436026 | − | 0.999049i | \(-0.513884\pi\) | ||||
−0.0436026 | + | 0.999049i | \(0.513884\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −534.775 | −1.15502 | −0.577510 | − | 0.816383i | \(-0.695976\pi\) | ||||
−0.577510 | + | 0.816383i | \(0.695976\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −48.7361 | −0.104809 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 390.715 | 0.836649 | 0.418325 | − | 0.908298i | \(-0.362617\pi\) | ||||
0.418325 | + | 0.908298i | \(0.362617\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.21324i | 0.0175122i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 132.910i | 0.282187i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −149.522 | −0.316115 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 144.662 | + | 344.790i | 0.304552 | + | 0.725874i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 256.010i | − | 0.536708i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.79318 | 0.0100066 | 0.00500332 | − | 0.999987i | \(-0.498407\pi\) | ||||
0.00500332 | + | 0.999987i | \(0.498407\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 458.087 | 0.952364 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 58.8246i | 0.121790i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 295.518i | − | 0.609316i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 173.322i | − | 0.355898i | −0.984040 | − | 0.177949i | \(-0.943054\pi\) | ||
0.984040 | − | 0.177949i | \(-0.0569462\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.1283i | 0.0657020i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 522.057 | 1.06325 | 0.531626 | − | 0.846979i | \(-0.321581\pi\) | ||||
0.531626 | + | 0.846979i | \(0.321581\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 188.650i | − | 0.382657i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 277.771 | 0.561154 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 440.636i | 0.886591i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 806.635 | 1.61650 | 0.808251 | − | 0.588838i | \(-0.200414\pi\) | ||||
0.808251 | + | 0.588838i | \(0.200414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −68.9870 | −0.137699 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −148.884 | −0.295992 | −0.147996 | − | 0.988988i | \(-0.547282\pi\) | ||||
−0.147996 | + | 0.988988i | \(0.547282\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −152.529 | −0.302037 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 166.792i | − | 0.328979i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 469.470i | 0.922339i | 0.887312 | + | 0.461169i | \(0.152570\pi\) | ||||
−0.887312 | + | 0.461169i | \(0.847430\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −300.807 | −0.588663 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 159.176 | − | 66.7846i | 0.310284 | − | 0.130184i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 158.261i | 0.307302i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 466.670 | 0.902650 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −46.3247 | −0.0892576 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 952.247i | 1.82773i | 0.406020 | + | 0.913864i | \(0.366916\pi\) | ||||
−0.406020 | + | 0.913864i | \(0.633084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 883.789i | 1.68985i | 0.534889 | + | 0.844923i | \(0.320354\pi\) | ||||
−0.534889 | + | 0.844923i | \(0.679646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 46.3222i | 0.0882328i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 224.033i | 0.425111i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 95.5422 | 0.180609 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 575.192i | − | 1.08322i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −620.251 | −1.16370 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 376.404i | 0.703558i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 165.425 | 0.308054 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −384.248 | −0.712891 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −370.690 | −0.685193 | −0.342597 | − | 0.939483i | \(-0.611306\pi\) | ||||
−0.342597 | + | 0.939483i | \(0.611306\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 123.787 | 0.227969 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 227.976i | − | 0.418305i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 361.146i | − | 0.660230i | −0.943941 | − | 0.330115i | \(-0.892912\pi\) | ||
0.943941 | − | 0.330115i | \(-0.107088\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 938.185 | 1.70890 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −608.582 | + | 255.340i | −1.10451 | + | 0.463413i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 171.033i | 0.309282i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.3344 | −0.0438458 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −935.225 | −1.67904 | −0.839519 | − | 0.543330i | \(-0.817163\pi\) | ||||
−0.839519 | + | 0.543330i | \(0.817163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 241.290i | 0.431646i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.3379i | 0.0683384i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 288.854i | − | 0.513062i | −0.966536 | − | 0.256531i | \(-0.917420\pi\) | ||
0.966536 | − | 0.256531i | \(-0.0825796\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 217.338i | − | 0.384670i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −340.007 | −0.599660 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1109.10i | 1.94921i | 0.223936 | + | 0.974604i | \(0.428109\pi\) | ||||
−0.223936 | + | 0.974604i | \(0.571891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 81.8698 | 0.143380 | 0.0716898 | − | 0.997427i | \(-0.477161\pi\) | ||||
0.0716898 | + | 0.997427i | \(0.477161\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 59.2780i | 0.103452i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 491.804 | 0.855312 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −282.577 | −0.489735 | −0.244867 | − | 0.969557i | \(-0.578744\pi\) | ||||
−0.244867 | + | 0.969557i | \(0.578744\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −142.354 | −0.245862 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 150.237 | 0.258584 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 403.806i | − | 0.692634i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 448.251i | − | 0.766241i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 732.036 | 1.24708 | 0.623540 | − | 0.781792i | \(-0.285694\pi\) | ||||
0.623540 | + | 0.781792i | \(0.285694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 722.730 | − | 303.233i | 1.22705 | − | 0.514826i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.3256i | 0.0682329i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −669.125 | −1.12837 | −0.564187 | − | 0.825647i | \(-0.690810\pi\) | ||||
−0.564187 | + | 0.825647i | \(0.690810\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −57.5709 | −0.0967578 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 47.9745i | 0.0803592i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 852.366i | 1.42298i | 0.702695 | + | 0.711491i | \(0.251980\pi\) | ||||
−0.702695 | + | 0.711491i | \(0.748020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 265.429i | − | 0.441646i | −0.975314 | − | 0.220823i | \(-0.929126\pi\) | ||
0.975314 | − | 0.220823i | \(-0.0708743\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 15.6159i | − | 0.0258971i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 159.026 | 0.262852 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 751.473i | − | 1.23801i | −0.785387 | − | 0.619005i | \(-0.787536\pi\) | ||
0.785387 | − | 0.619005i | \(-0.212464\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −81.7625 | −0.134257 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 753.085i | − | 1.23254i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −606.487 | −0.989376 | −0.494688 | − | 0.869071i | \(-0.664718\pi\) | ||||
−0.494688 | + | 0.869071i | \(0.664718\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.9488 | 0.0535754 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1020.39 | −1.65380 | −0.826900 | − | 0.562349i | \(-0.809898\pi\) | ||||
−0.826900 | + | 0.562349i | \(0.809898\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −886.720 | −1.43250 | −0.716252 | − | 0.697842i | \(-0.754144\pi\) | ||||
−0.716252 | + | 0.697842i | \(0.754144\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 227.046i | − | 0.365613i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 341.827i | 0.548679i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 254.262 | 0.406820 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 123.678 | − | 51.8909i | 0.197253 | − | 0.0827606i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 111.862i | 0.177841i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −737.311 | −1.16848 | −0.584240 | − | 0.811581i | \(-0.698607\pi\) | ||||
−0.584240 | + | 0.811581i | \(0.698607\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 185.834 | 0.293577 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 274.531i | 0.432333i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 620.078i | 0.973435i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 837.786i | − | 1.31109i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 267.570i | 0.417426i | 0.977977 | + | 0.208713i | \(0.0669274\pi\) | ||||
−0.977977 | + | 0.208713i | \(0.933073\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −567.693 | −0.882881 | −0.441441 | − | 0.897290i | \(-0.645532\pi\) | ||||
−0.441441 | + | 0.897290i | \(0.645532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 12.8178i | − | 0.0198725i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 543.577 | 0.840150 | 0.420075 | − | 0.907489i | \(-0.362004\pi\) | ||||
0.420075 | + | 0.907489i | \(0.362004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 907.254i | − | 1.39793i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 97.0981 | 0.149152 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.9308 | 0.0611498 | 0.0305749 | − | 0.999532i | \(-0.490266\pi\) | ||||
0.0305749 | + | 0.999532i | \(0.490266\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 292.162 | 0.446049 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 571.928 | 0.870515 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 779.029i | − | 1.18214i | −0.806621 | − | 0.591069i | \(-0.798706\pi\) | ||
0.806621 | − | 0.591069i | \(-0.201294\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 419.496i | − | 0.634638i | −0.948319 | − | 0.317319i | \(-0.897217\pi\) | ||
0.948319 | − | 0.317319i | \(-0.102783\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 61.8674 | 0.0933144 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 77.9231 | + | 185.723i | 0.117178 | + | 0.279283i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 868.074i | 1.30146i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 113.224 | 0.169243 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1479.80 | 2.20537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 997.533i | − | 1.48222i | −0.671385 | − | 0.741109i | \(-0.734300\pi\) | ||
0.671385 | − | 0.741109i | \(-0.265700\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 178.790i | − | 0.264875i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 441.407i | − | 0.652005i | −0.945369 | − | 0.326003i | \(-0.894298\pi\) | ||
0.945369 | − | 0.326003i | \(-0.105702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 588.769i | 0.867111i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.6788 | −0.0347706 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 907.324i | 1.32844i | 0.747537 | + | 0.664220i | \(0.231236\pi\) | ||||
−0.747537 | + | 0.664220i | \(0.768764\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 111.329 | 0.162525 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 22.8035i | − | 0.0331929i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −651.638 | −0.945774 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −928.930 | −1.34433 | −0.672164 | − | 0.740403i | \(-0.734635\pi\) | ||||
−0.672164 | + | 0.740403i | \(0.734635\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −553.410 | −0.798572 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −560.793 | −0.806896 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 151.462i | − | 0.217305i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 141.682i | 0.202692i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1104.52 | 1.57563 | 0.787814 | − | 0.615913i | \(-0.211213\pi\) | ||||
0.787814 | + | 0.615913i | \(0.211213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 360.866 | − | 151.407i | 0.513323 | − | 0.215373i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40.0052i | 0.0567450i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 303.886 | 0.429825 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 382.002 | 0.538790 | 0.269395 | − | 0.963030i | \(-0.413176\pi\) | ||||
0.269395 | + | 0.963030i | \(0.413176\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 325.187i | − | 0.457366i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1030.89i | − | 1.44585i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 707.029i | − | 0.988851i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 220.811i | 0.307964i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −784.961 | −1.09174 | −0.545870 | − | 0.837870i | \(-0.683801\pi\) | ||||
−0.545870 | + | 0.837870i | \(0.683801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 315.307i | − | 0.437318i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.3999 | −0.0641769 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 683.577i | 0.942865i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 776.412 | 1.06797 | 0.533983 | − | 0.845495i | \(-0.320694\pi\) | ||||
0.533983 | + | 0.845495i | \(0.320694\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 604.579 | 0.829327 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.9217 | −0.0806042 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −263.990 | −0.360150 | −0.180075 | − | 0.983653i | \(-0.557634\pi\) | ||||
−0.180075 | + | 0.983653i | \(0.557634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 32.9397i | − | 0.0448159i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 24.6311i | − | 0.0334208i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 696.550 | 0.942558 | 0.471279 | − | 0.881984i | \(-0.343792\pi\) | ||||
0.471279 | + | 0.881984i | \(0.343792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −83.7385 | − | 199.584i | −0.113007 | − | 0.269344i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 544.317i | − | 0.732593i | −0.930498 | − | 0.366297i | \(-0.880626\pi\) | ||
0.930498 | − | 0.366297i | \(-0.119374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 302.228 | 0.405675 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −285.648 | −0.382393 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 749.919i | − | 1.00123i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 648.270i | 0.863209i | 0.902063 | + | 0.431605i | \(0.142052\pi\) | ||||
−0.902063 | + | 0.431605i | \(0.857948\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 84.8122i | 0.112632i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 400.252i | 0.530136i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 726.694 | 0.959965 | 0.479983 | − | 0.877278i | \(-0.340643\pi\) | ||||
0.479983 | + | 0.877278i | \(0.340643\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 176.412i | − | 0.232427i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 425.877 | 0.559629 | 0.279814 | − | 0.960054i | \(-0.409727\pi\) | ||||
0.279814 | + | 0.960054i | \(0.409727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 454.203i | 0.595286i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 109.460 | 0.143085 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1464.07 | −1.90883 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1060.37 | 1.37890 | 0.689448 | − | 0.724335i | \(-0.257853\pi\) | ||||
0.689448 | + | 0.724335i | \(0.257853\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −256.457 | −0.332629 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.03627i | 0.00651523i | 0.999995 | + | 0.00325761i | \(0.00103693\pi\) | ||||
−0.999995 | + | 0.00325761i | \(0.998963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 811.790i | − | 1.04747i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 48.4820 | 0.0623964 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −488.614 | + | 205.006i | −0.627232 | + | 0.263165i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1321.44i | − | 1.69199i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 315.580 | 0.403039 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 598.552 | 0.762487 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 284.035i | 0.360909i | 0.983583 | + | 0.180454i | \(0.0577568\pi\) | ||||
−0.983583 | + | 0.180454i | \(0.942243\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 190.022i | − | 0.240839i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 433.009i | 0.547419i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2388.02i | − | 3.01138i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.6162 | 0.0435424 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 262.594i | − | 0.329479i | −0.986337 | − | 0.164739i | \(-0.947322\pi\) | ||
0.986337 | − | 0.164739i | \(-0.0526783\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 183.899 | 0.230161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 649.920i | − | 0.811386i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 902.106 | 1.12342 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 264.913 | 0.329085 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −140.075 | −0.173575 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1302.72 | 1.61028 | 0.805142 | − | 0.593082i | \(-0.202089\pi\) | ||||
0.805142 | + | 0.593082i | \(0.202089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 603.977i | 0.744731i | 0.928086 | + | 0.372365i | \(0.121453\pi\) | ||||
−0.928086 | + | 0.372365i | \(0.878547\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 42.0803i | − | 0.0517593i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 144.688 | 0.177531 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 79.7514 | + | 190.081i | 0.0976149 | + | 0.232657i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 893.061i | 1.09043i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −137.526 | −0.167510 | −0.0837550 | − | 0.996486i | \(-0.526691\pi\) | ||||
−0.0837550 | + | 0.996486i | \(0.526691\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.1953 | −0.0221085 | −0.0110543 | − | 0.999939i | \(-0.503519\pi\) | ||||
−0.0110543 | + | 0.999939i | \(0.503519\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 138.918i | − | 0.168386i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1257.34i | − | 1.52036i | −0.649710 | − | 0.760182i | \(-0.725110\pi\) | ||
0.649710 | − | 0.760182i | \(-0.274890\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 103.574i | − | 0.124939i | −0.998047 | − | 0.0624695i | \(-0.980102\pi\) | ||
0.998047 | − | 0.0624695i | \(-0.0198976\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 117.253i | − | 0.141098i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −151.419 | −0.181776 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 310.679i | 0.372070i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −374.770 | −0.447754 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 343.417i | − | 0.409317i | −0.978833 | − | 0.204659i | \(-0.934392\pi\) | ||
0.978833 | − | 0.204659i | \(-0.0656084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −365.568 | −0.434683 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −87.1912 | −0.103430 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −751.139 | −0.888922 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −316.831 | −0.374062 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.9656i | 0.0223388i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 514.735i | − | 0.604859i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 260.020 | 0.304830 | 0.152415 | − | 0.988317i | \(-0.451295\pi\) | ||||
0.152415 | + | 0.988317i | \(0.451295\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −148.156 | − | 353.118i | −0.173282 | − | 0.413003i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1420.47i | 1.65749i | 0.559623 | + | 0.828747i | \(0.310946\pi\) | ||||
−0.559623 | + | 0.828747i | \(0.689054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 856.333 | 0.996895 | 0.498447 | − | 0.866920i | \(-0.333904\pi\) | ||||
0.498447 | + | 0.866920i | \(0.333904\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −65.6448 | −0.0762425 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1477.83i | − | 1.71243i | −0.516616 | − | 0.856217i | \(-0.672808\pi\) | ||
0.516616 | − | 0.856217i | \(-0.327192\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 208.621i | 0.241180i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 132.917i | − | 0.153307i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 512.920i | − | 0.590241i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.7483 | −0.0456352 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 1119.43i | − | 1.28228i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 473.620 | 0.541280 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 160.901i | 0.183467i | 0.995784 | + | 0.0917337i | \(0.0292408\pi\) | ||||
−0.995784 | + | 0.0917337i | \(0.970759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −194.322 | −0.221072 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −711.737 | −0.807874 | −0.403937 | − | 0.914787i | \(-0.632359\pi\) | ||||
−0.403937 | + | 0.914787i | \(0.632359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1690.91 | −1.91496 | −0.957481 | − | 0.288496i | \(-0.906845\pi\) | ||||
−0.957481 | + | 0.288496i | \(0.906845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 77.7742 | 0.0878805 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.1528i | 0.0587968i | 0.999568 | + | 0.0293984i | \(0.00935916\pi\) | ||||
−0.999568 | + | 0.0293984i | \(0.990641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 546.956i | − | 0.615248i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1019.66 | 1.14441 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −248.910 | − | 593.256i | −0.278735 | − | 0.664341i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 744.982i | − | 0.832383i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −284.684 | −0.317373 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1432.88 | 1.59385 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 159.126i | − | 0.176611i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.5372i | 0.0282804i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 557.467i | − | 0.615986i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1447.89i | − | 1.59635i | −0.602425 | − | 0.798176i | \(-0.705799\pi\) | ||
0.602425 | − | 0.798176i | \(-0.294201\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −577.783 | −0.635625 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 946.717i | 1.03921i | 0.854408 | + | 0.519603i | \(0.173920\pi\) | ||||
−0.854408 | + | 0.519603i | \(0.826080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −450.554 | −0.493487 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 126.856i | 0.138641i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −582.082 | −0.634768 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 236.916 | 0.257797 | 0.128899 | − | 0.991658i | \(-0.458856\pi\) | ||||
0.128899 | + | 0.991658i | \(0.458856\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −106.273 | −0.115389 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2132.47 | −2.31037 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 405.335i | − | 0.438200i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 599.496i | 0.646706i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1000.34 | 1.07680 | 0.538398 | − | 0.842691i | \(-0.319030\pi\) | ||||
0.538398 | + | 0.842691i | \(0.319030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 204.948 | + | 488.478i | 0.220138 | + | 0.524681i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 128.147i | − | 0.137350i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 172.652 | 0.184655 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −440.075 | −0.469664 | −0.234832 | − | 0.972036i | \(-0.575454\pi\) | ||||
−0.234832 | + | 0.972036i | \(0.575454\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 250.983i | 0.267287i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1176.64i | 1.25042i | 0.780457 | + | 0.625209i | \(0.214986\pi\) | ||||
−0.780457 | + | 0.625209i | \(0.785014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 696.952i | 0.739080i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 96.3065i | − | 0.101912i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 225.120 | 0.237719 | 0.118860 | − | 0.992911i | \(-0.462076\pi\) | ||||
0.118860 | + | 0.992911i | \(0.462076\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1455.77i | − | 1.53400i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −99.1469 | −0.104255 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 589.549i | 0.618624i | 0.950961 | + | 0.309312i | \(0.100099\pi\) | ||||
−0.950961 | + | 0.309312i | \(0.899901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 266.955 | 0.279534 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 245.202 | 0.256219 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −221.804 | −0.231287 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −740.629 | −0.770686 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1425.83i | 1.48061i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 641.084i | 0.664335i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1641.09 | 1.69709 | 0.848545 | − | 0.529124i | \(-0.177479\pi\) | ||||
0.848545 | + | 0.529124i | \(0.177479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.7372 | − | 20.4485i | 0.0502964 | − | 0.0211026i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 721.099i | − | 0.742636i | −0.928506 | − | 0.371318i | \(-0.878906\pi\) | ||
0.928506 | − | 0.371318i | \(-0.121094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1117.28 | 1.14829 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −224.178 | −0.229926 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1222.67i | 1.25145i | 0.780043 | + | 0.625725i | \(0.215197\pi\) | ||||
−0.780043 | + | 0.625725i | \(0.784803\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1025.12i | − | 1.04711i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 863.582i | − | 0.880308i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1493.88i | 1.51971i | 0.650090 | + | 0.759857i | \(0.274731\pi\) | ||||
−0.650090 | + | 0.759857i | \(0.725269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 181.604 | 0.184370 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 79.7034i | − | 0.0807532i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 271.129 | 0.274144 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1461.21i | 1.47448i | 0.675631 | + | 0.737240i | \(0.263871\pi\) | ||||
−0.675631 | + | 0.737240i | \(0.736129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −39.6307 | −0.0399101 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 216.050 | 0.217136 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 963.569 | 0.966469 | 0.483234 | − | 0.875491i | \(-0.339462\pi\) | ||||
0.483234 | + | 0.875491i | \(0.339462\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −187.127 | −0.187314 |
(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 | 1216.3.e.n.1025.5 | 8 | ||
4.3 | odd | 2 | 1216.3.e.m.1025.4 | 8 | |||
8.3 | odd | 2 | 152.3.e.b.113.5 | yes | 8 | ||
8.5 | even | 2 | 304.3.e.g.113.4 | 8 | |||
19.18 | odd | 2 | inner | 1216.3.e.n.1025.4 | 8 | ||
24.5 | odd | 2 | 2736.3.o.p.721.4 | 8 | |||
24.11 | even | 2 | 1368.3.o.b.721.4 | 8 | |||
76.75 | even | 2 | 1216.3.e.m.1025.5 | 8 | |||
152.37 | odd | 2 | 304.3.e.g.113.5 | 8 | |||
152.75 | even | 2 | 152.3.e.b.113.4 | ✓ | 8 | ||
456.227 | odd | 2 | 1368.3.o.b.721.3 | 8 | |||
456.341 | even | 2 | 2736.3.o.p.721.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.3.e.b.113.4 | ✓ | 8 | 152.75 | even | 2 | ||
152.3.e.b.113.5 | yes | 8 | 8.3 | odd | 2 | ||
304.3.e.g.113.4 | 8 | 8.5 | even | 2 | |||
304.3.e.g.113.5 | 8 | 152.37 | odd | 2 | |||
1216.3.e.m.1025.4 | 8 | 4.3 | odd | 2 | |||
1216.3.e.m.1025.5 | 8 | 76.75 | even | 2 | |||
1216.3.e.n.1025.4 | 8 | 19.18 | odd | 2 | inner | ||
1216.3.e.n.1025.5 | 8 | 1.1 | even | 1 | trivial | ||
1368.3.o.b.721.3 | 8 | 456.227 | odd | 2 | |||
1368.3.o.b.721.4 | 8 | 24.11 | even | 2 | |||
2736.3.o.p.721.3 | 8 | 456.341 | even | 2 | |||
2736.3.o.p.721.4 | 8 | 24.5 | odd | 2 |