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 | 1025.7 | ||
Root | \(3.20945i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1025 |
Dual form | 1216.3.e.n.1025.2 |
$q$-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 | ||||||||
\(3\) | 3.20945i | 1.06982i | 0.844911 | + | 0.534908i | \(0.179654\pi\) | ||||
−0.844911 | + | 0.534908i | \(0.820346\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.06310 | 0.612621 | 0.306310 | − | 0.951932i | \(-0.400905\pi\) | ||||
0.306310 | + | 0.951932i | \(0.400905\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.3151 | 1.75930 | 0.879651 | − | 0.475619i | \(-0.157776\pi\) | ||||
0.879651 | + | 0.475619i | \(0.157776\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.30054 | −0.144504 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.53798 | −0.503452 | −0.251726 | − | 0.967798i | \(-0.580998\pi\) | ||||
−0.251726 | + | 0.967798i | \(0.580998\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.70944i | 0.516111i | 0.966130 | + | 0.258055i | \(0.0830817\pi\) | ||||
−0.966130 | + | 0.258055i | \(0.916918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.83087i | 0.655391i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.36365 | −0.315509 | −0.157754 | − | 0.987478i | \(-0.550425\pi\) | ||||
−0.157754 | + | 0.987478i | \(0.550425\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.17433 | + | 18.9637i | 0.0618069 | + | 0.998088i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 39.5247i | 1.88213i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.72688 | 0.422908 | 0.211454 | − | 0.977388i | \(-0.432180\pi\) | ||||
0.211454 | + | 0.977388i | \(0.432180\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15.6174 | −0.624696 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 24.7110i | 0.915222i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 14.4351i | − | 0.497763i | −0.968534 | − | 0.248882i | \(-0.919937\pi\) | ||
0.968534 | − | 0.248882i | \(-0.0800630\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 36.0875i | − | 1.16411i | −0.813148 | − | 0.582057i | \(-0.802248\pi\) | ||
0.813148 | − | 0.582057i | \(-0.197752\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 17.7738i | − | 0.538601i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 37.7225 | 1.07779 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.4102i | 0.875951i | 0.898987 | + | 0.437976i | \(0.144304\pi\) | ||||
−0.898987 | + | 0.437976i | \(0.855696\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −21.5336 | −0.552143 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 60.2390i | 1.46924i | 0.678476 | + | 0.734622i | \(0.262641\pi\) | ||||
−0.678476 | + | 0.734622i | \(0.737359\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 60.5760 | 1.40874 | 0.704372 | − | 0.709831i | \(-0.251229\pi\) | ||||
0.704372 | + | 0.709831i | \(0.251229\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.98369 | −0.0885265 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58.8019 | 1.25110 | 0.625552 | − | 0.780182i | \(-0.284874\pi\) | ||||
0.625552 | + | 0.780182i | \(0.284874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 102.662 | 2.09515 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 17.2143i | − | 0.337536i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 24.4833i | 0.461949i | 0.972960 | + | 0.230974i | \(0.0741913\pi\) | ||||
−0.972960 | + | 0.230974i | \(0.925809\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.9634 | −0.308425 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −60.8629 | + | 3.76895i | −1.06777 | + | 0.0661219i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 107.312i | − | 1.81885i | −0.415869 | − | 0.909424i | \(-0.636523\pi\) | ||
0.415869 | − | 0.909424i | \(-0.363477\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −45.9998 | −0.754095 | −0.377048 | − | 0.926194i | \(-0.623061\pi\) | ||||
−0.377048 | + | 0.926194i | \(0.623061\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −16.0163 | −0.254227 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 20.5517i | 0.316180i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42.6265i | 0.636216i | 0.948054 | + | 0.318108i | \(0.103048\pi\) | ||||
−0.948054 | + | 0.318108i | \(0.896952\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 31.2179i | 0.452433i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 70.3493i | − | 0.990835i | −0.868655 | − | 0.495418i | \(-0.835015\pi\) | ||
0.868655 | − | 0.495418i | \(-0.164985\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 52.3089 | 0.716560 | 0.358280 | − | 0.933614i | \(-0.383363\pi\) | ||||
0.358280 | + | 0.933614i | \(0.383363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 50.1232i | − | 0.668309i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −68.2008 | −0.885725 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.68432i | 0.0339787i | 0.999856 | + | 0.0169893i | \(0.00540814\pi\) | ||||
−0.999856 | + | 0.0169893i | \(0.994592\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −91.0135 | −1.12362 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −138.135 | −1.66428 | −0.832140 | − | 0.554566i | \(-0.812884\pi\) | ||||
−0.832140 | + | 0.554566i | \(0.812884\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.4294 | −0.193287 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 46.3288 | 0.532515 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 106.061i | 1.19170i | 0.803096 | + | 0.595850i | \(0.203185\pi\) | ||||
−0.803096 | + | 0.595850i | \(0.796815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 82.6276i | 0.907995i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 115.821 | 1.24539 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.59710 | + | 58.0877i | 0.0378642 | + | 0.611450i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 79.3904i | 0.818457i | 0.912432 | + | 0.409229i | \(0.134202\pi\) | ||||
−0.912432 | + | 0.409229i | \(0.865798\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.20236 | 0.0727511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 170.345 | 1.68658 | 0.843290 | − | 0.537459i | \(-0.180616\pi\) | ||||
0.843290 | + | 0.537459i | \(0.180616\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 185.850i | 1.80437i | 0.431350 | + | 0.902185i | \(0.358037\pi\) | ||||
−0.431350 | + | 0.902185i | \(0.641963\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 121.068i | 1.15303i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 84.0434i | − | 0.785452i | −0.919655 | − | 0.392726i | \(-0.871532\pi\) | ||
0.919655 | − | 0.392726i | \(-0.128468\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 63.4658i | − | 0.582255i | −0.956684 | − | 0.291127i | \(-0.905970\pi\) | ||
0.956684 | − | 0.291127i | \(-0.0940304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −104.019 | −0.937106 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 81.8004i | − | 0.723897i | −0.932198 | − | 0.361949i | \(-0.882112\pi\) | ||
0.932198 | − | 0.361949i | \(-0.117888\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 29.7945 | 0.259082 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 8.72590i | − | 0.0745803i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −66.0539 | −0.555075 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −90.3308 | −0.746536 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −193.334 | −1.57182 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −124.415 | −0.995323 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 148.454i | 1.16893i | 0.811420 | + | 0.584464i | \(0.198695\pi\) | ||||
−0.811420 | + | 0.584464i | \(0.801305\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 194.415i | 1.50710i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 53.1636 | 0.405829 | 0.202915 | − | 0.979196i | \(-0.434959\pi\) | ||||
0.202915 | + | 0.979196i | \(0.434959\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.4620 | + | 233.540i | 0.108737 | + | 1.75594i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 75.6924i | 0.560684i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −152.424 | −1.11258 | −0.556292 | − | 0.830987i | \(-0.687776\pi\) | ||||
−0.556292 | + | 0.830987i | \(0.687776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.9384 | −0.129053 | −0.0645267 | − | 0.997916i | \(-0.520554\pi\) | ||||
−0.0645267 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 188.722i | 1.33845i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 37.1567i | − | 0.259837i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 44.2163i | − | 0.304940i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 329.489i | 2.24142i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 55.8636 | 0.374923 | 0.187462 | − | 0.982272i | \(-0.439974\pi\) | ||||
0.187462 | + | 0.982272i | \(0.439974\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 190.710i | − | 1.26298i | −0.775383 | − | 0.631491i | \(-0.782443\pi\) | ||
0.775383 | − | 0.631491i | \(-0.217557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.97564 | 0.0455924 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 110.540i | − | 0.713161i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −218.585 | −1.39226 | −0.696131 | − | 0.717915i | \(-0.745097\pi\) | ||||
−0.696131 | + | 0.717915i | \(0.745097\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −78.5777 | −0.494200 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 119.788 | 0.744023 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 43.3239 | 0.265791 | 0.132895 | − | 0.991130i | \(-0.457573\pi\) | ||||
0.132895 | + | 0.991130i | \(0.457573\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 54.4431i | − | 0.329958i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 162.852i | − | 0.975159i | −0.873078 | − | 0.487580i | \(-0.837880\pi\) | ||
0.873078 | − | 0.487580i | \(-0.162120\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 123.983 | 0.733630 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.52726 | − | 24.6630i | −0.00893137 | − | 0.144228i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 64.2618i | 0.371456i | 0.982601 | + | 0.185728i | \(0.0594643\pi\) | ||||
−0.982601 | + | 0.185728i | \(0.940536\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −192.330 | −1.09903 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 344.412 | 1.94583 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 103.185i | − | 0.576455i | −0.957562 | − | 0.288228i | \(-0.906934\pi\) | ||
0.957562 | − | 0.288228i | \(-0.0930659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 199.029i | − | 1.09961i | −0.835294 | − | 0.549804i | \(-0.814702\pi\) | ||
0.835294 | − | 0.549804i | \(-0.185298\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 147.634i | − | 0.806742i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 99.2758i | 0.536626i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 29.7037 | 0.158844 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 304.319i | 1.61015i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 180.081 | 0.942834 | 0.471417 | − | 0.881911i | \(-0.343743\pi\) | ||||
0.471417 | + | 0.881911i | \(0.343743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 320.709i | 1.66170i | 0.556493 | + | 0.830852i | \(0.312146\pi\) | ||||
−0.556493 | + | 0.830852i | \(0.687854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −65.9596 | −0.338255 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −126.793 | −0.643619 | −0.321809 | − | 0.946804i | \(-0.604291\pi\) | ||||
−0.321809 | + | 0.946804i | \(0.604291\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −94.6913 | −0.475836 | −0.237918 | − | 0.971285i | \(-0.576465\pi\) | ||||
−0.237918 | + | 0.971285i | \(0.576465\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −136.807 | −0.680634 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 177.770i | − | 0.875716i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 184.518i | 0.900090i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.6502 | −0.0611121 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.50342 | − | 105.020i | −0.0311168 | − | 0.502490i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 69.7789i | − | 0.330706i | −0.986234 | − | 0.165353i | \(-0.947124\pi\) | ||
0.986234 | − | 0.165353i | \(-0.0528763\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 225.782 | 1.06001 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 185.551 | 0.863026 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 444.422i | − | 2.04803i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 167.883i | 0.766587i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 35.9871i | − | 0.162837i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 152.781i | − | 0.685117i | −0.939496 | − | 0.342559i | \(-0.888706\pi\) | ||
0.939496 | − | 0.342559i | \(-0.111294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.3110 | 0.0902713 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 28.2692i | − | 0.124534i | −0.998060 | − | 0.0622670i | \(-0.980167\pi\) | ||
0.998060 | − | 0.0622670i | \(-0.0198330\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −308.715 | −1.34810 | −0.674050 | − | 0.738686i | \(-0.735447\pi\) | ||||
−0.674050 | + | 0.738686i | \(0.735447\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 218.887i | − | 0.947562i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −289.375 | −1.24195 | −0.620977 | − | 0.783828i | \(-0.713264\pi\) | ||||
−0.620977 | + | 0.783828i | \(0.713264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 180.116 | 0.766453 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.61517 | −0.0363509 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 62.7214 | 0.262433 | 0.131216 | − | 0.991354i | \(-0.458112\pi\) | ||||
0.131216 | + | 0.991354i | \(0.458112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 285.131i | − | 1.18311i | −0.806263 | − | 0.591557i | \(-0.798513\pi\) | ||
0.806263 | − | 0.591557i | \(-0.201487\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 69.7038i | − | 0.286847i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 314.465 | 1.28353 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −127.236 | + | 7.87911i | −0.515124 | + | 0.0318992i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 443.337i | − | 1.78047i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 444.455 | 1.77074 | 0.885370 | − | 0.464888i | \(-0.153905\pi\) | ||||
0.885370 | + | 0.464888i | \(0.153905\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −53.8673 | −0.212914 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 52.7293i | − | 0.206782i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 361.131i | 1.40518i | 0.711595 | + | 0.702590i | \(0.247973\pi\) | ||||
−0.711595 | + | 0.702590i | \(0.752027\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 399.135i | 1.54106i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.7735i | 0.0719290i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 283.913 | 1.07952 | 0.539759 | − | 0.841820i | \(-0.318515\pi\) | ||||
0.539759 | + | 0.841820i | \(0.318515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 74.9948i | 0.282999i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −340.398 | −1.27490 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 405.876i | − | 1.50883i | −0.656396 | − | 0.754416i | \(-0.727920\pi\) | ||
0.656396 | − | 0.754416i | \(-0.272080\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 528.781 | 1.95122 | 0.975610 | − | 0.219511i | \(-0.0704463\pi\) | ||||
0.975610 | + | 0.219511i | \(0.0704463\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −265.189 | −0.971387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 86.4887 | 0.314504 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 406.620 | 1.46794 | 0.733971 | − | 0.679181i | \(-0.237665\pi\) | ||||
0.733971 | + | 0.679181i | \(0.237665\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 46.9333i | 0.168220i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0317i | − | 0.0641697i | −0.999485 | − | 0.0320849i | \(-0.989785\pi\) | ||
0.999485 | − | 0.0320849i | \(-0.0102147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 106.244 | 0.375422 | 0.187711 | − | 0.982224i | \(-0.439893\pi\) | ||||
0.187711 | + | 0.982224i | \(0.439893\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −186.429 | + | 11.5447i | −0.654138 | + | 0.0405077i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 741.851i | 2.58485i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −260.231 | −0.900454 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −254.799 | −0.875598 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 473.502i | − | 1.61605i | −0.589149 | − | 0.808024i | \(-0.700537\pi\) | ||
0.589149 | − | 0.808024i | \(-0.299463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 328.708i | − | 1.11426i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 136.849i | − | 0.460771i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 65.2620i | 0.218267i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 746.001 | 2.47841 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 546.712i | 1.80433i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −140.902 | −0.461974 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 481.865i | 1.56959i | 0.619754 | + | 0.784796i | \(0.287232\pi\) | ||||
−0.619754 | + | 0.784796i | \(0.712768\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −596.476 | −1.93034 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −529.837 | −1.70366 | −0.851828 | − | 0.523822i | \(-0.824506\pi\) | ||||
−0.851828 | + | 0.523822i | \(0.824506\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 261.542 | 0.835598 | 0.417799 | − | 0.908539i | \(-0.362802\pi\) | ||||
0.417799 | + | 0.908539i | \(0.362802\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −49.0596 | −0.155745 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 265.379i | − | 0.837158i | −0.908180 | − | 0.418579i | \(-0.862528\pi\) | ||
0.908180 | − | 0.418579i | \(-0.137472\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 79.9414i | 0.250600i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 269.733 | 0.840289 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.29869 | − | 101.714i | −0.0195006 | − | 0.314905i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 104.784i | − | 0.322412i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 203.690 | 0.622905 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 724.152 | 2.20107 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 605.094i | − | 1.82808i | −0.405626 | − | 0.914039i | \(-0.632947\pi\) | ||
0.405626 | − | 0.914039i | \(-0.367053\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 42.1508i | − | 0.126579i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 130.569i | 0.389759i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 349.555i | − | 1.03726i | −0.855000 | − | 0.518628i | \(-0.826443\pi\) | ||
0.855000 | − | 0.518628i | \(-0.173557\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 262.534 | 0.774436 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 199.852i | 0.586076i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 660.856 | 1.92669 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 95.6237i | 0.277170i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 162.204 | 0.467447 | 0.233724 | − | 0.972303i | \(-0.424909\pi\) | ||||
0.233724 | + | 0.972303i | \(0.424909\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −273.918 | −0.784865 | −0.392433 | − | 0.919781i | \(-0.628366\pi\) | ||||
−0.392433 | + | 0.919781i | \(0.628366\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −165.797 | −0.472356 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 90.1452 | 0.255369 | 0.127684 | − | 0.991815i | \(-0.459246\pi\) | ||||
0.127684 | + | 0.991815i | \(0.459246\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 215.487i | − | 0.607006i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 211.996i | − | 0.593828i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −342.459 | −0.953925 | −0.476962 | − | 0.878924i | \(-0.658262\pi\) | ||||
−0.476962 | + | 0.878924i | \(0.658262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −358.242 | + | 44.5393i | −0.992360 | + | 0.123377i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 289.912i | − | 0.798655i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 160.228 | 0.438980 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 203.266 | 0.553858 | 0.276929 | − | 0.960890i | \(-0.410683\pi\) | ||||
0.276929 | + | 0.960890i | \(0.410683\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 78.3433i | − | 0.212312i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 301.514i | 0.812707i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 458.615i | − | 1.22953i | −0.788710 | − | 0.614765i | \(-0.789251\pi\) | ||
0.788710 | − | 0.614765i | \(-0.210749\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 399.304i | − | 1.06481i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 96.8517 | 0.256901 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 114.433i | 0.301934i | 0.988539 | + | 0.150967i | \(0.0482388\pi\) | ||||
−0.988539 | + | 0.150967i | \(0.951761\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −476.454 | −1.25054 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 357.223i | 0.932696i | 0.884601 | + | 0.466348i | \(0.154431\pi\) | ||||
−0.884601 | + | 0.466348i | \(0.845569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −208.906 | −0.542614 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −78.7815 | −0.203570 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −336.952 | −0.866200 | −0.433100 | − | 0.901346i | \(-0.642580\pi\) | ||||
−0.433100 | + | 0.901346i | \(0.642580\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −52.1716 | −0.133431 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 170.626i | 0.434162i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.22234i | 0.0208161i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 225.208 | 0.567274 | 0.283637 | − | 0.958932i | \(-0.408459\pi\) | ||||
0.283637 | + | 0.958932i | \(0.408459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −749.534 | + | 46.4151i | −1.87853 | + | 0.116329i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 488.538i | − | 1.21830i | −0.793055 | − | 0.609149i | \(-0.791511\pi\) | ||
0.793055 | − | 0.609149i | \(-0.208489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 242.127 | 0.600812 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −278.784 | −0.688355 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 179.487i | − | 0.441000i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 125.524i | 0.306905i | 0.988156 | + | 0.153452i | \(0.0490391\pi\) | ||||
−0.988156 | + | 0.153452i | \(0.950961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 489.196i | − | 1.19026i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1321.56i | − | 3.19991i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −423.122 | −1.01957 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 57.5724i | − | 0.138063i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 187.698 | 0.447967 | 0.223984 | − | 0.974593i | \(-0.428094\pi\) | ||||
0.223984 | + | 0.974593i | \(0.428094\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 146.182i | 0.347227i | 0.984814 | + | 0.173613i | \(0.0555443\pi\) | ||||
−0.984814 | + | 0.173613i | \(0.944456\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −76.4743 | −0.180790 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 83.7661 | 0.197097 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −566.493 | −1.32668 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 119.252 | 0.277978 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 470.285i | − | 1.09115i | −0.838063 | − | 0.545574i | \(-0.816312\pi\) | ||
0.838063 | − | 0.545574i | \(-0.183688\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 436.928i | 1.00907i | 0.863391 | + | 0.504536i | \(0.168336\pi\) | ||||
−0.863391 | + | 0.504536i | \(0.831664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 141.910 | 0.326230 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.4226 | + | 184.457i | 0.0261386 | + | 0.422099i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 518.542i | − | 1.18119i | −0.806968 | − | 0.590595i | \(-0.798893\pi\) | ||
0.806968 | − | 0.590595i | \(-0.201107\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −133.516 | −0.302758 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −107.645 | −0.242991 | −0.121495 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121495 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 324.877i | 0.730060i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 179.291i | 0.401099i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 643.806i | − | 1.43387i | −0.697142 | − | 0.716933i | \(-0.745545\pi\) | ||
0.697142 | − | 0.716933i | \(-0.254455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 333.602i | − | 0.739695i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 612.074 | 1.35116 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 253.097i | 0.556257i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.99715 | 0.0131229 | 0.00656144 | − | 0.999978i | \(-0.497911\pi\) | ||||
0.00656144 | + | 0.999978i | \(0.497911\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 132.541i | − | 0.288760i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 400.082 | 0.867858 | 0.433929 | − | 0.900947i | \(-0.357127\pi\) | ||||
0.433929 | + | 0.900947i | \(0.357127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −83.5840 | −0.180527 | −0.0902635 | − | 0.995918i | \(-0.528771\pi\) | ||||
−0.0902635 | + | 0.995918i | \(0.528771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 354.772 | 0.762950 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −601.132 | −1.28722 | −0.643610 | − | 0.765354i | \(-0.722564\pi\) | ||||
−0.643610 | + | 0.765354i | \(0.722564\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 524.950i | 1.11930i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 701.537i | − | 1.48946i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −335.468 | −0.709236 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.3400 | − | 296.163i | −0.0386105 | − | 0.623501i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 31.8415i | − | 0.0667536i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −394.710 | −0.824030 | −0.412015 | − | 0.911177i | \(-0.635175\pi\) | ||||
−0.412015 | + | 0.911177i | \(0.635175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −217.454 | −0.452088 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 384.452i | 0.795967i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 243.181i | 0.501404i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 454.916i | 0.934119i | 0.884226 | + | 0.467060i | \(0.154687\pi\) | ||||
−0.884226 | + | 0.467060i | \(0.845313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 139.046i | 0.284347i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 115.066 | 0.234351 | 0.117175 | − | 0.993111i | \(-0.462616\pi\) | ||||
0.117175 | + | 0.993111i | \(0.462616\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 77.4249i | 0.157049i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.0616 | 0.0445689 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 866.360i | − | 1.74318i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −196.082 | −0.392950 | −0.196475 | − | 0.980509i | \(-0.562950\pi\) | ||||
−0.196475 | + | 0.980509i | \(0.562950\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 522.663 | 1.04324 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 504.642 | 1.00327 | 0.501633 | − | 0.865081i | \(-0.332733\pi\) | ||||
0.501633 | + | 0.865081i | \(0.332733\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 521.783 | 1.03323 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 397.918i | 0.784848i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 48.7384i | 0.0957533i | 0.998853 | + | 0.0478766i | \(0.0152454\pi\) | ||||
−0.998853 | + | 0.0478766i | \(0.984755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 644.190 | 1.26065 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −468.611 | + | 29.0189i | −0.913472 | + | 0.0565670i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 569.278i | 1.10539i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −325.644 | −0.629872 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −206.245 | −0.397389 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 646.673i | − | 1.24121i | −0.784122 | − | 0.620607i | \(-0.786886\pi\) | ||
0.784122 | − | 0.620607i | \(-0.213114\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 257.895i | − | 0.493108i | −0.969129 | − | 0.246554i | \(-0.920702\pi\) | ||
0.969129 | − | 0.246554i | \(-0.0792982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 617.273i | − | 1.17576i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 193.561i | 0.367288i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −434.388 | −0.821149 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 139.564i | 0.262832i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −404.170 | −0.758293 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 257.434i | − | 0.481184i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 331.168 | 0.616700 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −568.540 | −1.05481 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −158.185 | −0.292393 | −0.146197 | − | 0.989256i | \(-0.546703\pi\) | ||||
−0.146197 | + | 0.989256i | \(0.546703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 638.773 | 1.17638 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 194.402i | − | 0.356701i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 483.829i | 0.884513i | 0.896889 | + | 0.442257i | \(0.145822\pi\) | ||||
−0.896889 | + | 0.442257i | \(0.854178\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 59.8246 | 0.108970 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 273.743 | − | 16.9516i | 0.496812 | − | 0.0307652i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.0577i | 0.0597788i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −318.620 | −0.574091 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 763.214 | 1.37022 | 0.685111 | − | 0.728438i | \(-0.259754\pi\) | ||||
0.685111 | + | 0.728438i | \(0.259754\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 406.431i | 0.727068i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 95.3325i | 0.169933i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 414.128i | 0.735573i | 0.929910 | + | 0.367787i | \(0.119884\pi\) | ||||
−0.929910 | + | 0.367787i | \(0.880116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 250.563i | − | 0.443475i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1120.84 | −1.97679 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 728.193i | 1.27978i | 0.768468 | + | 0.639888i | \(0.221019\pi\) | ||||
−0.768468 | + | 0.639888i | \(0.778981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −532.481 | −0.932541 | −0.466271 | − | 0.884642i | \(-0.654403\pi\) | ||||
−0.466271 | + | 0.884642i | \(0.654403\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 577.961i | 1.00866i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −151.909 | −0.264189 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −164.020 | −0.284264 | −0.142132 | − | 0.989848i | \(-0.545396\pi\) | ||||
−0.142132 | + | 0.989848i | \(0.545396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1029.30 | −1.77772 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1701.15 | −2.92797 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 135.588i | − | 0.232569i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 26.7283i | − | 0.0456895i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 934.356 | 1.59175 | 0.795874 | − | 0.605463i | \(-0.207012\pi\) | ||||
0.795874 | + | 0.605463i | \(0.207012\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 684.352 | − | 42.3787i | 1.16189 | − | 0.0719503i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 406.935i | − | 0.688553i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −387.798 | −0.653960 | −0.326980 | − | 0.945031i | \(-0.606031\pi\) | ||||
−0.326980 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −202.330 | −0.340051 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 303.906i | − | 0.509056i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 255.369i | − | 0.426325i | −0.977017 | − | 0.213162i | \(-0.931624\pi\) | ||
0.977017 | − | 0.213162i | \(-0.0683763\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 585.508i | − | 0.974223i | −0.873340 | − | 0.487112i | \(-0.838050\pi\) | ||
0.873340 | − | 0.487112i | \(-0.161950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 55.4375i | − | 0.0919361i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −276.693 | −0.457343 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 438.164i | − | 0.721852i | −0.932594 | − | 0.360926i | \(-0.882461\pi\) | ||
0.932594 | − | 0.360926i | \(-0.117539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 570.544 | 0.936854 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 394.528i | 0.645709i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 174.723 | 0.285030 | 0.142515 | − | 0.989793i | \(-0.454481\pi\) | ||||
0.142515 | + | 0.989793i | \(0.454481\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −592.202 | −0.962930 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 494.815 | 0.801969 | 0.400984 | − | 0.916085i | \(-0.368668\pi\) | ||||
0.400984 | + | 0.916085i | \(0.368668\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 788.206 | 1.27335 | 0.636677 | − | 0.771131i | \(-0.280308\pi\) | ||||
0.636677 | + | 0.771131i | \(0.280308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 240.361i | 0.387055i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1306.16i | 2.09656i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.33758 | 0.0149401 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 337.057 | − | 20.8724i | 0.537571 | − | 0.0332893i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 173.837i | − | 0.276370i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 371.925 | 0.589421 | 0.294710 | − | 0.955587i | \(-0.404777\pi\) | ||||
0.294710 | + | 0.955587i | \(0.404777\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 223.952 | 0.353794 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 454.729i | 0.716109i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 688.806i | 1.08133i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 91.4921i | 0.143180i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1239.81i | − | 1.93419i | −0.254423 | − | 0.967093i | \(-0.581886\pi\) | ||
0.254423 | − | 0.967093i | \(-0.418114\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 545.751 | 0.848757 | 0.424378 | − | 0.905485i | \(-0.360493\pi\) | ||||
0.424378 | + | 0.905485i | \(0.360493\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 595.515i | 0.923278i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 402.170 | 0.621593 | 0.310796 | − | 0.950477i | \(-0.399404\pi\) | ||||
0.310796 | + | 0.950477i | \(0.399404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 594.292i | 0.915704i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1426.35 | 2.19101 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −59.6101 | −0.0912866 | −0.0456433 | − | 0.998958i | \(-0.514534\pi\) | ||||
−0.0456433 | + | 0.998958i | \(0.514534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 162.846 | 0.248619 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −68.0298 | −0.103546 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 556.858i | 0.845004i | 0.906362 | + | 0.422502i | \(0.138848\pi\) | ||||
−0.906362 | + | 0.422502i | \(0.861152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 282.675i | 0.427647i | 0.976872 | + | 0.213824i | \(0.0685918\pi\) | ||||
−0.976872 | + | 0.213824i | \(0.931408\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 115.499 | 0.174206 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 44.2987 | + | 715.357i | 0.0666146 | + | 1.07573i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 140.409i | − | 0.210508i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 490.343 | 0.732949 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 254.746 | 0.379651 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 580.225i | 0.862147i | 0.902317 | + | 0.431073i | \(0.141865\pi\) | ||||
−0.902317 | + | 0.431073i | \(0.858135\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 385.921i | − | 0.571735i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 669.862i | − | 0.989457i | −0.869048 | − | 0.494728i | \(-0.835268\pi\) | ||
0.869048 | − | 0.494728i | \(-0.164732\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 977.702i | 1.43991i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 90.7284 | 0.133228 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 938.331i | − | 1.37384i | −0.726734 | − | 0.686919i | \(-0.758963\pi\) | ||
0.726734 | − | 0.686919i | \(-0.241037\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −466.890 | −0.681592 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 990.803i | − | 1.44222i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −164.269 | −0.238417 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −952.665 | −1.37868 | −0.689338 | − | 0.724440i | \(-0.742098\pi\) | ||||
−0.689338 | + | 0.724440i | \(0.742098\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 88.6979 | 0.127991 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −54.9472 | −0.0790608 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 323.101i | − | 0.463559i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 928.735i | − | 1.32866i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 99.3497 | 0.141726 | 0.0708628 | − | 0.997486i | \(-0.477425\pi\) | ||||
0.0708628 | + | 0.997486i | \(0.477425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −614.616 | + | 38.0603i | −0.874277 | + | 0.0541398i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 578.074i | 0.819963i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2097.81 | 2.96720 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3478 | 0.0202366 | 0.0101183 | − | 0.999949i | \(-0.496779\pi\) | ||||
0.0101183 | + | 0.999949i | \(0.496779\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3.49106i | − | 0.00491007i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 351.019i | − | 0.492313i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 113.815i | − | 0.159182i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 201.301i | 0.280755i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −68.9065 | −0.0958365 | −0.0479183 | − | 0.998851i | \(-0.515259\pi\) | ||||
−0.0479183 | + | 0.998851i | \(0.515259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2288.77i | 3.17443i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 915.111 | 1.26571 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 225.439i | 0.310950i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 250.027 | 0.343916 | 0.171958 | − | 0.985104i | \(-0.444991\pi\) | ||||
0.171958 | + | 0.985104i | \(0.444991\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −595.411 | −0.816750 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −324.908 | −0.444471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −65.2029 | −0.0889535 | −0.0444768 | − | 0.999010i | \(-0.514162\pi\) | ||||
−0.0444768 | + | 0.999010i | \(0.514162\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1009.26i | 1.37314i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 236.064i | − | 0.320305i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 108.182 | 0.146389 | 0.0731945 | − | 0.997318i | \(-0.476681\pi\) | ||||
0.0731945 | + | 0.997318i | \(0.476681\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.2876 | − | 408.356i | −0.0341263 | − | 0.551088i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 824.780i | − | 1.11007i | −0.831828 | − | 0.555034i | \(-0.812705\pi\) | ||
0.831828 | − | 0.555034i | \(-0.187295\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 171.116 | 0.229686 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 179.650 | 0.240496 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1035.00i | − | 1.38185i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 529.661i | − | 0.705274i | −0.935760 | − | 0.352637i | \(-0.885285\pi\) | ||
0.935760 | − | 0.352637i | \(-0.114715\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1426.46i | 1.89436i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 584.166i | − | 0.773729i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −808.792 | −1.06842 | −0.534209 | − | 0.845352i | \(-0.679390\pi\) | ||||
−0.534209 | + | 0.845352i | \(0.679390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 172.884i | − | 0.227779i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 749.782 | 0.985259 | 0.492629 | − | 0.870239i | \(-0.336036\pi\) | ||||
0.492629 | + | 0.870239i | \(0.336036\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 781.589i | − | 1.02436i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.3671 | 0.0279309 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 720.004 | 0.938728 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 500.547 | 0.650906 | 0.325453 | − | 0.945558i | \(-0.394483\pi\) | ||||
0.325453 | + | 0.945558i | \(0.394483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1159.03 | −1.50328 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 208.556i | 0.269801i | 0.990859 | + | 0.134900i | \(0.0430715\pi\) | ||||
−0.990859 | + | 0.134900i | \(0.956929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 563.593i | 0.727217i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1281.00 | −1.64865 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1142.35 | + | 70.7405i | −1.46644 | + | 0.0908094i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 389.593i | 0.498838i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 356.707 | 0.455564 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −669.549 | −0.852928 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 400.393i | 0.508758i | 0.967105 | + | 0.254379i | \(0.0818711\pi\) | ||||
−0.967105 | + | 0.254379i | \(0.918129\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 911.204i | 1.15488i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1007.38i | − | 1.27355i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 308.633i | − | 0.389197i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −240.692 | −0.302757 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 211.793i | − | 0.265738i | −0.991134 | − | 0.132869i | \(-0.957581\pi\) | ||
0.991134 | − | 0.132869i | \(-0.0424190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −315.393 | −0.394734 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 137.937i | − | 0.172206i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −289.685 | −0.360754 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 366.922 | 0.455804 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1302.64 | 1.61417 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 111.836 | 0.138240 | 0.0691199 | − | 0.997608i | \(-0.477981\pi\) | ||||
0.0691199 | + | 0.997608i | \(0.477981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 643.996i | 0.794077i | 0.917802 | + | 0.397038i | \(0.129962\pi\) | ||||
−0.917802 | + | 0.397038i | \(0.870038\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1697.09i | 2.08744i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 132.706 | 0.162829 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 71.1363 | + | 1148.74i | 0.0870701 | + | 1.40605i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 107.460i | − | 0.131209i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1540.49 | 1.87636 | 0.938182 | − | 0.346144i | \(-0.112509\pi\) | ||||
0.938182 | + | 0.346144i | \(0.112509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 789.808 | 0.959670 | 0.479835 | − | 0.877359i | \(-0.340697\pi\) | ||||
0.479835 | + | 0.877359i | \(0.340697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 277.581i | 0.336462i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 329.463i | − | 0.398384i | −0.979961 | − | 0.199192i | \(-0.936168\pi\) | ||
0.979961 | − | 0.199192i | \(-0.0638317\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 727.661i | 0.877757i | 0.898546 | + | 0.438879i | \(0.144624\pi\) | ||||
−0.898546 | + | 0.438879i | \(0.855376\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1305.02i | 1.57043i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −550.643 | −0.661036 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 498.832i | − | 0.597403i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 891.759 | 1.06542 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 593.731i | 0.707665i | 0.935309 | + | 0.353833i | \(0.115122\pi\) | ||||
−0.935309 | + | 0.353833i | \(0.884878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 632.627 | 0.752232 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 57.8717 | 0.0686498 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 379.774 | 0.449437 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1112.43 | −1.31338 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 340.985i | 0.401632i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 315.250i | 0.370447i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −675.336 | −0.791719 | −0.395860 | − | 0.918311i | \(-0.629553\pi\) | ||||
−0.395860 | + | 0.918311i | \(0.629553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.67817 | − | 75.5454i | −0.00547155 | − | 0.0883572i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 69.5952i | − | 0.0812079i | −0.999175 | − | 0.0406040i | \(-0.987072\pi\) | ||
0.999175 | − | 0.0406040i | \(-0.0129282\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 388.824 | 0.452647 | 0.226324 | − | 0.974052i | \(-0.427329\pi\) | ||||
0.226324 | + | 0.974052i | \(0.427329\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2380.93 | −2.76531 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 671.642i | − | 0.778264i | −0.921182 | − | 0.389132i | \(-0.872775\pi\) | ||
0.921182 | − | 0.389132i | \(-0.127225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 196.841i | 0.227561i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 835.198i | − | 0.963320i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 14.8657i | − | 0.0171067i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −286.000 | −0.328358 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 103.250i | − | 0.118271i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1532.19 | −1.75107 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 291.049i | 0.331869i | 0.986137 | + | 0.165934i | \(0.0530640\pi\) | ||||
−0.986137 | + | 0.165934i | \(0.946936\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1519.68 | 1.72887 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1021.90 | 1.15993 | 0.579965 | − | 0.814641i | \(-0.303066\pi\) | ||||
0.579965 | + | 0.814641i | \(0.303066\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1029.33 | 1.16572 | 0.582859 | − | 0.812574i | \(-0.301934\pi\) | ||||
0.582859 | + | 0.812574i | \(0.301934\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1054.97 | 1.19206 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 316.096i | − | 0.356366i | −0.983997 | − | 0.178183i | \(-0.942978\pi\) | ||
0.983997 | − | 0.178183i | \(-0.0570218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1828.23i | 2.05650i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 504.030 | 0.565691 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 69.0529 | + | 1115.10i | 0.0773269 | + | 1.24871i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 316.068i | − | 0.353148i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −209.455 | −0.233506 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −520.928 | −0.579453 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 131.320i | − | 0.145749i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2394.25i | 2.65144i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 609.647i | − | 0.673643i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 805.455i | − | 0.888043i | −0.896016 | − | 0.444021i | \(-0.853551\pi\) | ||
0.896016 | − | 0.444021i | \(-0.146449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −221.540 | −0.243718 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1340.38i | − | 1.47132i | −0.677348 | − | 0.735662i | \(-0.736871\pi\) | ||
0.677348 | − | 0.735662i | \(-0.263129\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 764.989 | 0.837885 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 452.218i | − | 0.494227i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 654.716 | 0.713976 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1708.81 | −1.85942 | −0.929710 | − | 0.368291i | \(-0.879943\pi\) | ||||
−0.929710 | + | 0.368291i | \(0.879943\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1546.52 | −1.67917 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 472.005 | 0.511381 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 506.163i | − | 0.547203i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 241.706i | − | 0.260739i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −976.889 | −1.05155 | −0.525774 | − | 0.850624i | \(-0.676224\pi\) | ||||
−0.525774 | + | 0.850624i | \(0.676224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 120.559 | + | 1946.85i | 0.129494 | + | 2.09114i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1700.48i | − | 1.82260i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 90.9857 | 0.0973109 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −765.004 | −0.816439 | −0.408220 | − | 0.912884i | \(-0.633850\pi\) | ||||
−0.408220 | + | 0.912884i | \(0.633850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 839.406i | 0.893936i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 720.166i | 0.765320i | 0.923889 | + | 0.382660i | \(0.124992\pi\) | ||||
−0.923889 | + | 0.382660i | \(0.875008\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 585.938i | 0.621355i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 932.160i | 0.986413i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1659.17 | −1.75203 | −0.876015 | − | 0.482284i | \(-0.839807\pi\) | ||||
−0.876015 | + | 0.482284i | \(0.839807\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 350.963i | 0.369824i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 851.720 | 0.895605 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 422.810i | − | 0.443662i | −0.975085 | − | 0.221831i | \(-0.928797\pi\) | ||
0.975085 | − | 0.221831i | \(-0.0712033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 551.608 | 0.577600 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −256.568 | −0.268096 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1877.12 | −1.95737 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −341.310 | −0.355161 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 109.302i | 0.113501i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 982.365i | 1.01799i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −786.215 | −0.813046 | −0.406523 | − | 0.913641i | \(-0.633259\pi\) | ||||
−0.406523 | + | 0.913641i | \(0.633259\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 326.447 | − | 20.2153i | 0.336890 | − | 0.0208620i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1397.18i | 1.43891i | 0.694538 | + | 0.719456i | \(0.255609\pi\) | ||||
−0.694538 | + | 0.719456i | \(0.744391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −220.914 | −0.227044 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 336.298 | 0.344921 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 396.287i | − | 0.405616i | −0.979218 | − | 0.202808i | \(-0.934993\pi\) | ||
0.979218 | − | 0.202808i | \(-0.0650068\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 587.365i | − | 0.599964i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 82.5398i | 0.0841384i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1271.91i | − | 1.29391i | −0.762530 | − | 0.646953i | \(-0.776043\pi\) | ||
0.762530 | − | 0.646953i | \(-0.223957\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −388.380 | −0.394294 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2324.13i | 2.35474i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 589.216 | 0.595769 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1721.90i | 1.73753i | 0.495220 | + | 0.868767i | \(0.335087\pi\) | ||||
−0.495220 | + | 0.868767i | \(0.664913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1942.02 | 1.95571 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −290.049 | −0.291507 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1153.53 | −1.15700 | −0.578500 | − | 0.815683i | \(-0.696362\pi\) | ||||
−0.578500 | + | 0.815683i | \(0.696362\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −800.888 | −0.801690 |
(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.1025.7 | 8 | ||
4.3 | odd | 2 | 1216.3.e.m.1025.2 | 8 | |||
8.3 | odd | 2 | 152.3.e.b.113.7 | yes | 8 | ||
8.5 | even | 2 | 304.3.e.g.113.2 | 8 | |||
19.18 | odd | 2 | inner | 1216.3.e.n.1025.2 | 8 | ||
24.5 | odd | 2 | 2736.3.o.p.721.5 | 8 | |||
24.11 | even | 2 | 1368.3.o.b.721.5 | 8 | |||
76.75 | even | 2 | 1216.3.e.m.1025.7 | 8 | |||
152.37 | odd | 2 | 304.3.e.g.113.7 | 8 | |||
152.75 | even | 2 | 152.3.e.b.113.2 | ✓ | 8 | ||
456.227 | odd | 2 | 1368.3.o.b.721.6 | 8 | |||
456.341 | even | 2 | 2736.3.o.p.721.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.3.e.b.113.2 | ✓ | 8 | 152.75 | even | 2 | ||
152.3.e.b.113.7 | yes | 8 | 8.3 | odd | 2 | ||
304.3.e.g.113.2 | 8 | 8.5 | even | 2 | |||
304.3.e.g.113.7 | 8 | 152.37 | odd | 2 | |||
1216.3.e.m.1025.2 | 8 | 4.3 | odd | 2 | |||
1216.3.e.m.1025.7 | 8 | 76.75 | even | 2 | |||
1216.3.e.n.1025.2 | 8 | 19.18 | odd | 2 | inner | ||
1216.3.e.n.1025.7 | 8 | 1.1 | even | 1 | trivial | ||
1368.3.o.b.721.5 | 8 | 24.11 | even | 2 | |||
1368.3.o.b.721.6 | 8 | 456.227 | odd | 2 | |||
2736.3.o.p.721.5 | 8 | 24.5 | odd | 2 | |||
2736.3.o.p.721.6 | 8 | 456.341 | even | 2 |