Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(199,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.b (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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(-2.17945 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.199 |
Dual form | 225.4.b.h.199.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.35890i | 1.89466i | 0.320264 | + | 0.947328i | \(0.396228\pi\) | ||||
−0.320264 | + | 0.947328i | \(0.603772\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −20.7178 | −2.58972 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.43560i | − 0.239500i | −0.992804 | − | 0.119750i | \(-0.961791\pi\) | ||||
0.992804 | − | 0.119750i | \(-0.0382092\pi\) | |||||||
\(8\) | − 68.1534i | − 3.01198i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.43560 | 0.0941701 | 0.0470851 | − | 0.998891i | \(-0.485007\pi\) | ||||
0.0470851 | + | 0.998891i | \(0.485007\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 78.7424i | − 1.67994i | −0.542634 | − | 0.839970i | \(-0.682573\pi\) | ||||
0.542634 | − | 0.839970i | \(-0.317427\pi\) | |||||||
\(14\) | 23.7699 | 0.453770 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 199.485 | 3.11695 | ||||||||
\(17\) | − 53.1780i | − 0.758680i | −0.925257 | − | 0.379340i | \(-0.876151\pi\) | ||||
0.925257 | − | 0.379340i | \(-0.123849\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.4356 | −0.246750 | −0.123375 | − | 0.992360i | \(-0.539372\pi\) | ||||
−0.123375 | + | 0.992360i | \(0.539372\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.4110i | 0.178420i | ||||||||
\(23\) | 118.307i | 1.07255i | 0.844043 | + | 0.536275i | \(0.180169\pi\) | ||||
−0.844043 | + | 0.536275i | \(0.819831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 421.972 | 3.18291 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 91.8958i | 0.620238i | ||||||||
\(29\) | 168.049 | 1.07607 | 0.538034 | − | 0.842923i | \(-0.319167\pi\) | ||||
0.538034 | + | 0.842923i | \(0.319167\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −61.0492 | −0.353702 | −0.176851 | − | 0.984238i | \(-0.556591\pi\) | ||||
−0.176851 | + | 0.984238i | \(0.556591\pi\) | |||||||
\(32\) | 523.792i | 2.89357i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 284.975 | 1.43744 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 246.614i | − 1.09576i | −0.836558 | − | 0.547879i | \(-0.815436\pi\) | ||||
0.836558 | − | 0.547879i | \(-0.184564\pi\) | |||||||
\(38\) | − 109.512i | − 0.467506i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −422.663 | −1.60997 | −0.804986 | − | 0.593294i | \(-0.797827\pi\) | ||||
−0.804986 | + | 0.593294i | \(0.797827\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 362.436i | − 1.28537i | −0.766131 | − | 0.642685i | \(-0.777820\pi\) | ||||
0.766131 | − | 0.642685i | \(-0.222180\pi\) | |||||||
\(44\) | −71.1780 | −0.243875 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −633.994 | −2.03212 | ||||||||
\(47\) | 170.515i | 0.529196i | 0.964359 | + | 0.264598i | \(0.0852392\pi\) | ||||
−0.964359 | + | 0.264598i | \(0.914761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 323.325 | 0.942640 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1631.37i | 4.35058i | ||||||||
\(53\) | − 546.049i | − 1.41520i | −0.706613 | − | 0.707600i | \(-0.749778\pi\) | ||||
0.706613 | − | 0.707600i | \(-0.250222\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −302.301 | −0.721369 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 900.559i | 2.03878i | ||||||||
\(59\) | −216.970 | −0.478763 | −0.239382 | − | 0.970926i | \(-0.576945\pi\) | ||||
−0.239382 | + | 0.970926i | \(0.576945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 130.902 | 0.274758 | 0.137379 | − | 0.990519i | \(-0.456132\pi\) | ||||
0.137379 | + | 0.990519i | \(0.456132\pi\) | |||||||
\(62\) | − 327.156i | − 0.670143i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1211.07 | −2.36537 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 614.890i | − 1.12121i | −0.828085 | − | 0.560603i | \(-0.810570\pi\) | ||||
0.828085 | − | 0.560603i | \(-0.189430\pi\) | |||||||
\(68\) | 1101.73i | 1.96477i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −324.822 | −0.542948 | −0.271474 | − | 0.962446i | \(-0.587511\pi\) | ||||
−0.271474 | + | 0.962446i | \(0.587511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 88.8712i | 0.142487i | 0.997459 | + | 0.0712437i | \(0.0226968\pi\) | ||||
−0.997459 | + | 0.0712437i | \(0.977303\pi\) | |||||||
\(74\) | 1321.58 | 2.07608 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 423.381 | 0.639014 | ||||||||
\(77\) | − 15.2389i | − 0.0225537i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1137.42 | 1.61988 | 0.809938 | − | 0.586516i | \(-0.199501\pi\) | ||||
0.809938 | + | 0.586516i | \(0.199501\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 2265.01i | − 3.05034i | ||||||||
\(83\) | − 758.909i | − 1.00363i | −0.864976 | − | 0.501813i | \(-0.832666\pi\) | ||||
0.864976 | − | 0.501813i | \(-0.167334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1942.26 | 2.43534 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 234.148i | − 0.283639i | ||||||||
\(89\) | 195.681 | 0.233058 | 0.116529 | − | 0.993187i | \(-0.462823\pi\) | ||||
0.116529 | + | 0.993187i | \(0.462823\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −349.269 | −0.402345 | ||||||||
\(92\) | − 2451.06i | − 2.77761i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −913.774 | −1.00264 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 521.000i | 0.545356i | 0.962105 | + | 0.272678i | \(0.0879094\pi\) | ||||
−0.962105 | + | 0.272678i | \(0.912091\pi\) | |||||||
\(98\) | 1732.67i | 1.78598i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −660.920 | −0.651129 | −0.325565 | − | 0.945520i | \(-0.605554\pi\) | ||||
−0.325565 | + | 0.945520i | \(0.605554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 1530.75i | − 1.46436i | −0.681110 | − | 0.732181i | \(-0.738503\pi\) | ||||
0.681110 | − | 0.732181i | \(-0.261497\pi\) | |||||||
\(104\) | −5366.56 | −5.05995 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2926.22 | 2.68132 | ||||||||
\(107\) | 264.625i | 0.239087i | 0.992829 | + | 0.119543i | \(0.0381431\pi\) | ||||
−0.992829 | + | 0.119543i | \(0.961857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1117.61 | −0.982091 | −0.491046 | − | 0.871134i | \(-0.663385\pi\) | ||||
−0.491046 | + | 0.871134i | \(0.663385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 884.834i | − 0.746508i | ||||||||
\(113\) | − 934.061i | − 0.777602i | −0.921322 | − | 0.388801i | \(-0.872889\pi\) | ||||
0.921322 | − | 0.388801i | \(-0.127111\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3481.61 | −2.78672 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 1162.72i | − 0.907092i | ||||||||
\(119\) | −235.876 | −0.181704 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1319.20 | −0.991132 | ||||||||
\(122\) | 701.489i | 0.520572i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1264.80 | 0.915990 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 630.356i | 0.440433i | 0.975451 | + | 0.220217i | \(0.0706765\pi\) | ||||
−0.975451 | + | 0.220217i | \(0.929324\pi\) | |||||||
\(128\) | − 2299.66i | − 1.58799i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2163.06 | 1.44265 | 0.721325 | − | 0.692597i | \(-0.243534\pi\) | ||||
0.721325 | + | 0.692597i | \(0.243534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.6440i | 0.0590965i | ||||||||
\(134\) | 3295.13 | 2.12430 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3624.26 | −2.28513 | ||||||||
\(137\) | − 1118.61i | − 0.697588i | −0.937199 | − | 0.348794i | \(-0.886591\pi\) | ||||
0.937199 | − | 0.348794i | \(-0.113409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 166.478 | 0.101586 | 0.0507930 | − | 0.998709i | \(-0.483825\pi\) | ||||
0.0507930 | + | 0.998709i | \(0.483825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 1740.69i | − 1.02870i | ||||||||
\(143\) | − 270.527i | − 0.158200i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −476.252 | −0.269965 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5109.29i | 2.83771i | ||||||||
\(149\) | −653.143 | −0.359111 | −0.179555 | − | 0.983748i | \(-0.557466\pi\) | ||||
−0.179555 | + | 0.983748i | \(0.557466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1929.38 | −1.03981 | −0.519903 | − | 0.854225i | \(-0.674032\pi\) | ||||
−0.519903 | + | 0.854225i | \(0.674032\pi\) | |||||||
\(152\) | 1392.76i | 0.743206i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 81.6638 | 0.0427315 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2169.75i | 1.10296i | 0.834188 | + | 0.551480i | \(0.185937\pi\) | ||||
−0.834188 | + | 0.551480i | \(0.814063\pi\) | |||||||
\(158\) | 6095.34i | 3.06911i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 524.761 | 0.256876 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 763.738i | 0.366997i | 0.983020 | + | 0.183499i | \(0.0587423\pi\) | ||||
−0.983020 | + | 0.183499i | \(0.941258\pi\) | |||||||
\(164\) | 8756.64 | 4.16938 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4066.91 | 1.90153 | ||||||||
\(167\) | 2564.28i | 1.18820i | 0.804389 | + | 0.594102i | \(0.202493\pi\) | ||||
−0.804389 | + | 0.594102i | \(0.797507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4003.36 | −1.82220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7508.87i | 3.32875i | ||||||||
\(173\) | 51.8290i | 0.0227774i | 0.999935 | + | 0.0113887i | \(0.00362521\pi\) | ||||
−0.999935 | + | 0.0113887i | \(0.996375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 685.349 | 0.293523 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1048.64i | 0.441566i | ||||||||
\(179\) | −3956.63 | −1.65214 | −0.826068 | − | 0.563571i | \(-0.809427\pi\) | ||||
−0.826068 | + | 0.563571i | \(0.809427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1804.04 | 0.740848 | 0.370424 | − | 0.928863i | \(-0.379212\pi\) | ||||
0.370424 | + | 0.928863i | \(0.379212\pi\) | |||||||
\(182\) | − 1871.70i | − 0.762305i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8063.01 | 3.23050 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 182.698i | − 0.0714449i | ||||||||
\(188\) | − 3532.70i | − 1.37047i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3666.75 | −1.38909 | −0.694547 | − | 0.719448i | \(-0.744395\pi\) | ||||
−0.694547 | + | 0.719448i | \(0.744395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2716.98i | 1.01333i | 0.862144 | + | 0.506664i | \(0.169121\pi\) | ||||
−0.862144 | + | 0.506664i | \(0.830879\pi\) | |||||||
\(194\) | −2791.99 | −1.03326 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6698.59 | −2.44118 | ||||||||
\(197\) | − 2034.30i | − 0.735723i | −0.929881 | − | 0.367862i | \(-0.880090\pi\) | ||||
0.929881 | − | 0.367862i | \(-0.119910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1551.27 | 0.552596 | 0.276298 | − | 0.961072i | \(-0.410892\pi\) | ||||
0.276298 | + | 0.961072i | \(0.410892\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 3541.81i | − 1.23367i | ||||||||
\(203\) | − 745.398i | − 0.257718i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8203.13 | 2.77446 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 15707.9i | − 5.23629i | ||||||||
\(209\) | −70.2084 | −0.0232365 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3192.51 | 1.04162 | 0.520809 | − | 0.853673i | \(-0.325630\pi\) | ||||
0.520809 | + | 0.853673i | \(0.325630\pi\) | |||||||
\(212\) | 11312.9i | 3.66498i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1418.10 | −0.452988 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 270.789i | 0.0847115i | ||||||||
\(218\) | − 5989.18i | − 1.86073i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4187.36 | −1.27454 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1555.55i | 0.467120i | 0.972342 | + | 0.233560i | \(0.0750374\pi\) | ||||
−0.972342 | + | 0.233560i | \(0.924963\pi\) | |||||||
\(224\) | 2323.33 | 0.693008 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5005.54 | 1.47329 | ||||||||
\(227\) | 6206.86i | 1.81482i | 0.420248 | + | 0.907409i | \(0.361943\pi\) | ||||
−0.420248 | + | 0.907409i | \(0.638057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4679.51 | −1.35035 | −0.675176 | − | 0.737657i | \(-0.735932\pi\) | ||||
−0.675176 | + | 0.737657i | \(0.735932\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 11453.1i | − 3.24110i | ||||||||
\(233\) | − 3244.53i | − 0.912259i | −0.889913 | − | 0.456129i | \(-0.849235\pi\) | ||||
0.889913 | − | 0.456129i | \(-0.150765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4495.13 | 1.23986 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 1264.04i | − 0.344266i | ||||||||
\(239\) | −3658.62 | −0.990193 | −0.495097 | − | 0.868838i | \(-0.664867\pi\) | ||||
−0.495097 | + | 0.868838i | \(0.664867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1931.01 | 0.516131 | 0.258065 | − | 0.966127i | \(-0.416915\pi\) | ||||
0.258065 | + | 0.966127i | \(0.416915\pi\) | |||||||
\(242\) | − 7069.44i | − 1.87786i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2711.99 | −0.711548 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1609.15i | 0.414525i | ||||||||
\(248\) | 4160.71i | 1.06534i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5843.34 | 1.46944 | 0.734718 | − | 0.678373i | \(-0.237315\pi\) | ||||
0.734718 | + | 0.678373i | \(0.237315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 406.454i | 0.101002i | ||||||||
\(254\) | −3378.01 | −0.834470 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2635.09 | 0.643333 | ||||||||
\(257\) | − 4506.11i | − 1.09371i | −0.837227 | − | 0.546855i | \(-0.815825\pi\) | ||||
0.837227 | − | 0.546855i | \(-0.184175\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1093.88 | −0.262434 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11591.6i | 2.73333i | ||||||||
\(263\) | 5340.16i | 1.25205i | 0.779804 | + | 0.626024i | \(0.215319\pi\) | ||||
−0.779804 | + | 0.626024i | \(0.784681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −485.752 | −0.111968 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12739.2i | 2.90361i | ||||||||
\(269\) | 2809.79 | 0.636863 | 0.318431 | − | 0.947946i | \(-0.396844\pi\) | ||||
0.318431 | + | 0.947946i | \(0.396844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3102.95 | 0.695537 | 0.347769 | − | 0.937580i | \(-0.386940\pi\) | ||||
0.347769 | + | 0.937580i | \(0.386940\pi\) | |||||||
\(272\) | − 10608.2i | − 2.36477i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5994.54 | 1.32169 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4598.93i | − 0.997555i | −0.866730 | − | 0.498777i | \(-0.833783\pi\) | ||||
0.866730 | − | 0.498777i | \(-0.166217\pi\) | |||||||
\(278\) | 892.138i | 0.192471i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2571.83 | −0.545987 | −0.272994 | − | 0.962016i | \(-0.588014\pi\) | ||||
−0.272994 | + | 0.962016i | \(0.588014\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5575.31i | − 1.17109i | −0.810641 | − | 0.585544i | \(-0.800881\pi\) | ||||
0.810641 | − | 0.585544i | \(-0.199119\pi\) | |||||||
\(284\) | 6729.60 | 1.40608 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1449.73 | 0.299735 | ||||||||
\(287\) | 1874.76i | 0.385588i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2085.10 | 0.424405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 1841.22i | − 0.369003i | ||||||||
\(293\) | 5794.27i | 1.15531i | 0.816282 | + | 0.577654i | \(0.196032\pi\) | ||||
−0.816282 | + | 0.577654i | \(0.803968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16807.6 | −3.30040 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 3500.13i | − 0.680392i | ||||||||
\(299\) | 9315.76 | 1.80182 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1607.62 | −0.307846 | ||||||||
\(302\) | − 10339.4i | − 1.97008i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4076.59 | −0.769107 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1404.47i | − 0.261099i | −0.991442 | − | 0.130550i | \(-0.958326\pi\) | ||||
0.991442 | − | 0.130550i | \(-0.0416742\pi\) | |||||||
\(308\) | 315.717i | 0.0584079i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4096.75 | 0.746963 | 0.373481 | − | 0.927638i | \(-0.378164\pi\) | ||||
0.373481 | + | 0.927638i | \(0.378164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 974.611i | − 0.176001i | −0.996120 | − | 0.0880004i | \(-0.971952\pi\) | ||||
0.996120 | − | 0.0880004i | \(-0.0280477\pi\) | |||||||
\(314\) | −11627.5 | −2.08973 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23564.9 | −4.19503 | ||||||||
\(317\) | 2071.69i | 0.367058i | 0.983014 | + | 0.183529i | \(0.0587522\pi\) | ||||
−0.983014 | + | 0.183529i | \(0.941248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 577.349 | 0.101333 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2812.14i | 0.486691i | ||||||||
\(323\) | 1086.72i | 0.187204i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4092.79 | −0.695334 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28805.9i | 4.84921i | ||||||||
\(329\) | 756.337 | 0.126742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6159.17 | −1.02278 | −0.511388 | − | 0.859350i | \(-0.670868\pi\) | ||||
−0.511388 | + | 0.859350i | \(0.670868\pi\) | |||||||
\(332\) | 15722.9i | 2.59912i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13741.7 | −2.25124 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2791.26i | 0.451186i | 0.974222 | + | 0.225593i | \(0.0724320\pi\) | ||||
−0.974222 | + | 0.225593i | \(0.927568\pi\) | |||||||
\(338\) | − 21453.6i | − 3.45243i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −209.740 | −0.0333081 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2955.55i | − 0.465262i | ||||||||
\(344\) | −24701.2 | −3.87151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −277.746 | −0.0431553 | ||||||||
\(347\) | − 940.848i | − 0.145554i | −0.997348 | − | 0.0727772i | \(-0.976814\pi\) | ||||
0.997348 | − | 0.0727772i | \(-0.0231862\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3519.62 | 0.539831 | 0.269915 | − | 0.962884i | \(-0.413004\pi\) | ||||
0.269915 | + | 0.962884i | \(0.413004\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1799.54i | 0.272487i | ||||||||
\(353\) | 5021.60i | 0.757147i | 0.925571 | + | 0.378573i | \(0.123585\pi\) | ||||
−0.925571 | + | 0.378573i | \(0.876415\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4054.09 | −0.603557 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 21203.2i | − 3.13023i | ||||||||
\(359\) | 6811.99 | 1.00146 | 0.500728 | − | 0.865604i | \(-0.333066\pi\) | ||||
0.500728 | + | 0.865604i | \(0.333066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6441.39 | −0.939115 | ||||||||
\(362\) | 9667.69i | 1.40365i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7236.09 | 1.04196 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3748.07i | 0.533099i | 0.963821 | + | 0.266550i | \(0.0858836\pi\) | ||||
−0.963821 | + | 0.266550i | \(0.914116\pi\) | |||||||
\(368\) | 23600.4i | 3.34309i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2422.05 | −0.338940 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 898.302i | 0.124698i | 0.998054 | + | 0.0623489i | \(0.0198592\pi\) | ||||
−0.998054 | + | 0.0623489i | \(0.980141\pi\) | |||||||
\(374\) | 979.060 | 0.135364 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11621.2 | 1.59393 | ||||||||
\(377\) | − 13232.6i | − 1.80773i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9378.99 | 1.27115 | 0.635576 | − | 0.772038i | \(-0.280763\pi\) | ||||
0.635576 | + | 0.772038i | \(0.280763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 19649.8i | − 2.63186i | ||||||||
\(383\) | − 9446.29i | − 1.26027i | −0.776486 | − | 0.630134i | \(-0.783000\pi\) | ||||
0.776486 | − | 0.630134i | \(-0.217000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14560.0 | −1.91991 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 10794.0i | − 1.41232i | ||||||||
\(389\) | −7643.23 | −0.996214 | −0.498107 | − | 0.867116i | \(-0.665971\pi\) | ||||
−0.498107 | + | 0.867116i | \(0.665971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6291.32 | 0.813723 | ||||||||
\(392\) | − 22035.7i | − 2.83922i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10901.6 | 1.39394 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 12013.6i | − 1.51876i | −0.650650 | − | 0.759378i | \(-0.725503\pi\) | ||||
0.650650 | − | 0.759378i | \(-0.274497\pi\) | |||||||
\(398\) | 8313.10i | 1.04698i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8538.51 | 1.06332 | 0.531662 | − | 0.846957i | \(-0.321568\pi\) | ||||
0.531662 | + | 0.846957i | \(0.321568\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4807.16i | 0.594197i | ||||||||
\(404\) | 13692.8 | 1.68625 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3994.51 | 0.488287 | ||||||||
\(407\) | − 847.265i | − 0.103188i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12267.6 | 1.48312 | 0.741558 | − | 0.670889i | \(-0.234087\pi\) | ||||
0.741558 | + | 0.670889i | \(0.234087\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 31713.8i | 3.79229i | ||||||||
\(413\) | 962.389i | 0.114664i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 41244.6 | 4.86102 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 376.240i | − 0.0440251i | ||||||||
\(419\) | 15493.0 | 1.80641 | 0.903204 | − | 0.429212i | \(-0.141209\pi\) | ||||
0.903204 | + | 0.429212i | \(0.141209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7510.67 | 0.869472 | 0.434736 | − | 0.900558i | \(-0.356842\pi\) | ||||
0.434736 | + | 0.900558i | \(0.356842\pi\) | |||||||
\(422\) | 17108.3i | 1.97351i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −37215.1 | −4.26256 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 580.627i | − 0.0658045i | ||||||||
\(428\) | − 5482.45i | − 0.619169i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15675.3 | 1.75186 | 0.875932 | − | 0.482434i | \(-0.160247\pi\) | ||||
0.875932 | + | 0.482434i | \(0.160247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9604.78i | 1.06600i | 0.846117 | + | 0.532998i | \(0.178935\pi\) | ||||
−0.846117 | + | 0.532998i | \(0.821065\pi\) | |||||||
\(434\) | −1451.13 | −0.160499 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23154.5 | 2.54335 | ||||||||
\(437\) | − 2417.67i | − 0.264652i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6362.06 | 0.691673 | 0.345837 | − | 0.938295i | \(-0.387595\pi\) | ||||
0.345837 | + | 0.938295i | \(0.387595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 22439.6i | − 2.41481i | ||||||||
\(443\) | 931.658i | 0.0999196i | 0.998751 | + | 0.0499598i | \(0.0159093\pi\) | ||||
−0.998751 | + | 0.0499598i | \(0.984091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8336.06 | −0.885031 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5371.81i | 0.566505i | ||||||||
\(449\) | −18684.1 | −1.96383 | −0.981914 | − | 0.189329i | \(-0.939369\pi\) | ||||
−0.981914 | + | 0.189329i | \(0.939369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1452.10 | −0.151611 | ||||||||
\(452\) | 19351.7i | 2.01378i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −33261.9 | −3.43846 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 11565.9i | − 1.18387i | −0.805985 | − | 0.591936i | \(-0.798364\pi\) | ||||
0.805985 | − | 0.591936i | \(-0.201636\pi\) | |||||||
\(458\) | − 25077.0i | − 2.55845i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19401.0 | −1.96008 | −0.980039 | − | 0.198806i | \(-0.936294\pi\) | ||||
−0.980039 | + | 0.198806i | \(0.936294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1576.28i | − 0.158220i | −0.996866 | − | 0.0791099i | \(-0.974792\pi\) | ||||
0.996866 | − | 0.0791099i | \(-0.0252078\pi\) | |||||||
\(464\) | 33523.2 | 3.35405 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 17387.1 | 1.72842 | ||||||||
\(467\) | − 3256.55i | − 0.322687i | −0.986898 | − | 0.161344i | \(-0.948417\pi\) | ||||
0.986898 | − | 0.161344i | \(-0.0515827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2727.40 | −0.268528 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14787.2i | 1.44203i | ||||||||
\(473\) | − 1245.18i | − 0.121043i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4886.83 | 0.470562 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 19606.2i | − 1.87608i | ||||||||
\(479\) | 8291.59 | 0.790924 | 0.395462 | − | 0.918482i | \(-0.370585\pi\) | ||||
0.395462 | + | 0.918482i | \(0.370585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19418.9 | −1.84081 | ||||||||
\(482\) | 10348.1i | 0.977891i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27330.9 | 2.56676 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4758.55i | 0.442773i | 0.975186 | + | 0.221387i | \(0.0710583\pi\) | ||||
−0.975186 | + | 0.221387i | \(0.928942\pi\) | |||||||
\(488\) | − 8921.39i | − 0.827567i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3906.46 | −0.359055 | −0.179528 | − | 0.983753i | \(-0.557457\pi\) | ||||
−0.179528 | + | 0.983753i | \(0.557457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 8936.52i | − 0.816390i | ||||||||
\(494\) | −8623.26 | −0.785382 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12178.4 | −1.10247 | ||||||||
\(497\) | 1440.78i | 0.130036i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3093.31 | 0.277506 | 0.138753 | − | 0.990327i | \(-0.455691\pi\) | ||||
0.138753 | + | 0.990327i | \(0.455691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 31313.9i | 2.78408i | ||||||||
\(503\) | − 18153.9i | − 1.60923i | −0.593796 | − | 0.804616i | \(-0.702371\pi\) | ||||
0.593796 | − | 0.804616i | \(-0.297629\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2178.15 | −0.191365 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 13059.6i | − 1.14060i | ||||||||
\(509\) | 2281.32 | 0.198660 | 0.0993298 | − | 0.995055i | \(-0.468330\pi\) | ||||
0.0993298 | + | 0.995055i | \(0.468330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 394.197 | 0.0341257 | ||||||||
\(512\) | − 4276.07i | − 0.369097i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24147.8 | 2.07221 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 585.821i | 0.0498344i | ||||||||
\(518\) | − 5861.98i | − 0.497221i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16691.9 | 1.40362 | 0.701809 | − | 0.712366i | \(-0.252376\pi\) | ||||
0.701809 | + | 0.712366i | \(0.252376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17090.4i | 1.42889i | 0.699690 | + | 0.714446i | \(0.253321\pi\) | ||||
−0.699690 | + | 0.714446i | \(0.746679\pi\) | |||||||
\(524\) | −44813.8 | −3.73607 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −28617.4 | −2.37220 | ||||||||
\(527\) | 3246.47i | 0.268346i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1829.50 | −0.150365 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 1877.94i | − 0.153044i | ||||||||
\(533\) | 33281.5i | 2.70465i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −41906.8 | −3.37705 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15057.4i | 1.20664i | ||||||||
\(539\) | 1110.82 | 0.0887685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5271.40 | 0.418919 | 0.209459 | − | 0.977817i | \(-0.432830\pi\) | ||||
0.209459 | + | 0.977817i | \(0.432830\pi\) | |||||||
\(542\) | 16628.4i | 1.31780i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 27854.2 | 2.19529 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15182.2i | 1.18673i | 0.804933 | + | 0.593366i | \(0.202201\pi\) | ||||
−0.804933 | + | 0.593366i | \(0.797799\pi\) | |||||||
\(548\) | 23175.2i | 1.80656i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3434.18 | −0.265519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 5045.15i | − 0.387960i | ||||||||
\(554\) | 24645.2 | 1.89002 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3449.05 | −0.263080 | ||||||||
\(557\) | − 12241.2i | − 0.931198i | −0.884996 | − | 0.465599i | \(-0.845839\pi\) | ||||
0.884996 | − | 0.465599i | \(-0.154161\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28539.0 | −2.15934 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 13782.2i | − 1.03446i | ||||||||
\(563\) | 14196.4i | 1.06271i | 0.847149 | + | 0.531355i | \(0.178317\pi\) | ||||
−0.847149 | + | 0.531355i | \(0.821683\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 29877.5 | 2.21881 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22137.7i | 1.63535i | ||||||||
\(569\) | 9150.05 | 0.674148 | 0.337074 | − | 0.941478i | \(-0.390563\pi\) | ||||
0.337074 | + | 0.941478i | \(0.390563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23582.1 | 1.72833 | 0.864167 | − | 0.503206i | \(-0.167846\pi\) | ||||
0.864167 | + | 0.503206i | \(0.167846\pi\) | |||||||
\(572\) | 5604.72i | 0.409695i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10046.7 | −0.730556 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3906.22i | 0.281834i | 0.990021 | + | 0.140917i | \(0.0450050\pi\) | ||||
−0.990021 | + | 0.140917i | \(0.954995\pi\) | |||||||
\(578\) | 11173.9i | 0.804102i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3366.21 | −0.240368 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1876.00i | − 0.133270i | ||||||||
\(584\) | 6056.87 | 0.429170 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31050.9 | −2.18891 | ||||||||
\(587\) | 25938.0i | 1.82381i | 0.410401 | + | 0.911905i | \(0.365389\pi\) | ||||
−0.410401 | + | 0.911905i | \(0.634611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1247.58 | 0.0872759 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 49195.7i | − 3.41542i | ||||||||
\(593\) | 1908.23i | 0.132145i | 0.997815 | + | 0.0660723i | \(0.0210468\pi\) | ||||
−0.997815 | + | 0.0660723i | \(0.978953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13531.7 | 0.929999 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 49922.2i | 3.41383i | ||||||||
\(599\) | −3495.41 | −0.238429 | −0.119214 | − | 0.992869i | \(-0.538038\pi\) | ||||
−0.119214 | + | 0.992869i | \(0.538038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18267.2 | −1.23983 | −0.619913 | − | 0.784671i | \(-0.712832\pi\) | ||||
−0.619913 | + | 0.784671i | \(0.712832\pi\) | |||||||
\(602\) | − 8615.06i | − 0.583262i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 39972.5 | 2.69281 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11538.2i | 0.771534i | 0.922596 | + | 0.385767i | \(0.126063\pi\) | ||||
−0.922596 | + | 0.385767i | \(0.873937\pi\) | |||||||
\(608\) | − 10704.0i | − 0.713987i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13426.8 | 0.889017 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 21136.9i | − 1.39268i | −0.717713 | − | 0.696340i | \(-0.754811\pi\) | ||||
0.717713 | − | 0.696340i | \(-0.245189\pi\) | |||||||
\(614\) | 7526.43 | 0.494694 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1038.58 | −0.0679314 | ||||||||
\(617\) | − 15673.2i | − 1.02266i | −0.859385 | − | 0.511329i | \(-0.829153\pi\) | ||||
0.859385 | − | 0.511329i | \(-0.170847\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22923.7 | −1.48850 | −0.744249 | − | 0.667902i | \(-0.767193\pi\) | ||||
−0.744249 | + | 0.667902i | \(0.767193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21954.1i | 1.41524i | ||||||||
\(623\) | − 867.964i | − 0.0558174i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5222.84 | 0.333461 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 44952.4i | − 2.85636i | ||||||||
\(629\) | −13114.4 | −0.831329 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9108.23 | 0.574632 | 0.287316 | − | 0.957836i | \(-0.407237\pi\) | ||||
0.287316 | + | 0.957836i | \(0.407237\pi\) | |||||||
\(632\) | − 77519.3i | − 4.87904i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11102.0 | −0.695449 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 25459.4i | − 1.58358i | ||||||||
\(638\) | 3093.96i | 0.191992i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20103.5 | −1.23875 | −0.619375 | − | 0.785095i | \(-0.712614\pi\) | ||||
−0.619375 | + | 0.785095i | \(0.712614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5934.92i | − 0.363997i | −0.983299 | − | 0.181999i | \(-0.941743\pi\) | ||||
0.983299 | − | 0.181999i | \(-0.0582567\pi\) | |||||||
\(644\) | −10871.9 | −0.665237 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5823.64 | −0.354688 | ||||||||
\(647\) | 14193.7i | 0.862460i | 0.902242 | + | 0.431230i | \(0.141920\pi\) | ||||
−0.902242 | + | 0.431230i | \(0.858080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −745.420 | −0.0450852 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 15823.0i | − 0.950422i | ||||||||
\(653\) | − 4795.80i | − 0.287403i | −0.989621 | − | 0.143701i | \(-0.954100\pi\) | ||||
0.989621 | − | 0.143701i | \(-0.0459005\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −84314.8 | −5.01820 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4053.13i | 0.240133i | ||||||||
\(659\) | 4399.57 | 0.260065 | 0.130032 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130032 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24096.0 | 1.41789 | 0.708945 | − | 0.705263i | \(-0.249171\pi\) | ||||
0.708945 | + | 0.705263i | \(0.249171\pi\) | |||||||
\(662\) | − 33006.4i | − 1.93781i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −51722.2 | −3.02291 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19881.4i | 1.15414i | ||||||||
\(668\) | − 53126.3i | − 3.07712i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 449.725 | 0.0258740 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27648.3i | 1.58360i | 0.610781 | + | 0.791800i | \(0.290856\pi\) | ||||
−0.610781 | + | 0.791800i | \(0.709144\pi\) | |||||||
\(674\) | −14958.1 | −0.854843 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 82940.9 | 4.71898 | ||||||||
\(677\) | 27605.5i | 1.56716i | 0.621292 | + | 0.783580i | \(0.286608\pi\) | ||||
−0.621292 | + | 0.783580i | \(0.713392\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2310.95 | 0.130613 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 1123.98i | − 0.0631075i | ||||||||
\(683\) | − 14949.4i | − 0.837513i | −0.908099 | − | 0.418756i | \(-0.862466\pi\) | ||||
0.908099 | − | 0.418756i | \(-0.137534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15838.5 | 0.881511 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 72300.4i | − 4.00643i | ||||||||
\(689\) | −42997.2 | −2.37745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8884.30 | 0.489110 | 0.244555 | − | 0.969635i | \(-0.421358\pi\) | ||||
0.244555 | + | 0.969635i | \(0.421358\pi\) | |||||||
\(692\) | − 1073.78i | − 0.0589871i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5041.91 | 0.275775 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22476.4i | 1.22145i | ||||||||
\(698\) | 18861.3i | 1.02279i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10556.9 | −0.568798 | −0.284399 | − | 0.958706i | \(-0.591794\pi\) | ||||
−0.284399 | + | 0.958706i | \(0.591794\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5039.70i | 0.270378i | ||||||||
\(704\) | −4160.74 | −0.222747 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26910.2 | −1.43453 | ||||||||
\(707\) | 2931.58i | 0.155945i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25351.9 | −1.34289 | −0.671445 | − | 0.741055i | \(-0.734326\pi\) | ||||
−0.671445 | + | 0.741055i | \(0.734326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 13336.4i | − 0.701968i | ||||||||
\(713\) | − 7222.53i | − 0.379363i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 81972.6 | 4.27858 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 36504.8i | 1.89742i | ||||||||
\(719\) | 9719.94 | 0.504162 | 0.252081 | − | 0.967706i | \(-0.418885\pi\) | ||||
0.252081 | + | 0.967706i | \(0.418885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6789.79 | −0.350714 | ||||||||
\(722\) | − 34518.7i | − 1.77930i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −37375.8 | −1.91859 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 27509.3i | − 1.40339i | −0.712479 | − | 0.701694i | \(-0.752428\pi\) | ||||
0.712479 | − | 0.701694i | \(-0.247572\pi\) | |||||||
\(728\) | 23803.9i | 1.21186i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19273.6 | −0.975184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7240.49i | 0.364848i | 0.983220 | + | 0.182424i | \(0.0583944\pi\) | ||||
−0.983220 | + | 0.182424i | \(0.941606\pi\) | |||||||
\(734\) | −20085.5 | −1.01004 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −61968.1 | −3.10350 | ||||||||
\(737\) | − 2112.51i | − 0.105584i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15875.3 | 0.790234 | 0.395117 | − | 0.918631i | \(-0.370704\pi\) | ||||
0.395117 | + | 0.918631i | \(0.370704\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 12979.5i | − 0.642175i | ||||||||
\(743\) | − 25714.3i | − 1.26967i | −0.772647 | − | 0.634836i | \(-0.781068\pi\) | ||||
0.772647 | − | 0.634836i | \(-0.218932\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4813.91 | −0.236260 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3785.10i | 0.185023i | ||||||||
\(749\) | 1173.77 | 0.0572612 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9709.09 | −0.471757 | −0.235879 | − | 0.971783i | \(-0.575797\pi\) | ||||
−0.235879 | + | 0.971783i | \(0.575797\pi\) | |||||||
\(752\) | 34015.2i | 1.64948i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 70912.1 | 3.42502 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9567.13i | − 0.459344i | −0.973268 | − | 0.229672i | \(-0.926235\pi\) | ||||
0.973268 | − | 0.229672i | \(-0.0737653\pi\) | |||||||
\(758\) | 50261.1i | 2.40840i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12322.5 | 0.586980 | 0.293490 | − | 0.955962i | \(-0.405183\pi\) | ||||
0.293490 | + | 0.955962i | \(0.405183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4957.28i | 0.235211i | ||||||||
\(764\) | 75967.0 | 3.59737 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50621.7 | 2.38778 | ||||||||
\(767\) | 17084.7i | 0.804293i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2575.56 | −0.120776 | −0.0603881 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603881 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 56289.8i | − 2.62424i | ||||||||
\(773\) | − 6606.23i | − 0.307386i | −0.988119 | − | 0.153693i | \(-0.950883\pi\) | ||||
0.988119 | − | 0.153693i | \(-0.0491167\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 35507.9 | 1.64260 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 40959.3i | − 1.88748i | ||||||||
\(779\) | 8637.37 | 0.397260 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1115.96 | −0.0511294 | ||||||||
\(782\) | 33714.5i | 1.54173i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 64498.5 | 2.93816 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16417.0i | 0.743587i | 0.928315 | + | 0.371793i | \(0.121257\pi\) | ||||
−0.928315 | + | 0.371793i | \(0.878743\pi\) | |||||||
\(788\) | 42146.1i | 1.90532i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4143.12 | −0.186235 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 10307.5i | − 0.461577i | ||||||||
\(794\) | 64379.8 | 2.87752 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −32138.9 | −1.43107 | ||||||||
\(797\) | 3944.19i | 0.175295i | 0.996152 | + | 0.0876477i | \(0.0279350\pi\) | ||||
−0.996152 | + | 0.0876477i | \(0.972065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9067.66 | 0.401490 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 45757.0i | 2.01463i | ||||||||
\(803\) | 305.325i | 0.0134181i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −25761.1 | −1.12580 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 45044.0i | 1.96119i | ||||||||
\(809\) | −17960.7 | −0.780549 | −0.390275 | − | 0.920699i | \(-0.627620\pi\) | ||||
−0.390275 | + | 0.920699i | \(0.627620\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13162.5 | −0.569912 | −0.284956 | − | 0.958541i | \(-0.591979\pi\) | ||||
−0.284956 | + | 0.958541i | \(0.591979\pi\) | |||||||
\(812\) | 15443.0i | 0.667418i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4540.41 | 0.195505 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7406.59i | 0.317165i | ||||||||
\(818\) | 65740.9i | 2.81000i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26502.4 | −1.12660 | −0.563302 | − | 0.826251i | \(-0.690469\pi\) | ||||
−0.563302 | + | 0.826251i | \(0.690469\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 6937.86i | − 0.293850i | −0.989148 | − | 0.146925i | \(-0.953062\pi\) | ||||
0.989148 | − | 0.146925i | \(-0.0469376\pi\) | |||||||
\(824\) | −104326. | −4.41063 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5157.35 | −0.217248 | ||||||||
\(827\) | − 41197.9i | − 1.73228i | −0.499805 | − | 0.866138i | \(-0.666595\pi\) | ||||
0.499805 | − | 0.866138i | \(-0.333405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 693.324 | 0.0290472 | 0.0145236 | − | 0.999895i | \(-0.495377\pi\) | ||||
0.0145236 | + | 0.999895i | \(0.495377\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 95362.4i | 3.97367i | ||||||||
\(833\) | − 17193.8i | − 0.715162i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1454.56 | 0.0601760 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 83025.7i | 3.42252i | ||||||||
\(839\) | −6491.28 | −0.267108 | −0.133554 | − | 0.991042i | \(-0.542639\pi\) | ||||
−0.133554 | + | 0.991042i | \(0.542639\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3851.52 | 0.157921 | ||||||||
\(842\) | 40248.9i | 1.64735i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −66141.8 | −2.69750 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5851.42i | 0.237376i | ||||||||
\(848\) | − 108928.i | − 4.41111i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29176.1 | 1.17526 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1116.68i | 0.0448233i | 0.999749 | + | 0.0224117i | \(0.00713445\pi\) | ||||
−0.999749 | + | 0.0224117i | \(0.992866\pi\) | |||||||
\(854\) | 3111.52 | 0.124677 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18035.1 | 0.720126 | ||||||||
\(857\) | − 44383.9i | − 1.76911i | −0.466438 | − | 0.884554i | \(-0.654463\pi\) | ||||
0.466438 | − | 0.884554i | \(-0.345537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25579.3 | 1.01601 | 0.508006 | − | 0.861354i | \(-0.330383\pi\) | ||||
0.508006 | + | 0.861354i | \(0.330383\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 84002.5i | 3.31918i | ||||||||
\(863\) | − 11194.8i | − 0.441570i | −0.975323 | − | 0.220785i | \(-0.929138\pi\) | ||||
0.975323 | − | 0.220785i | \(-0.0708619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −51471.0 | −2.01970 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 5610.16i | − 0.219379i | ||||||||
\(869\) | 3907.73 | 0.152544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48417.9 | −1.88356 | ||||||||
\(872\) | 76169.2i | 2.95804i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12956.0 | 0.501424 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 5721.75i | − 0.220308i | −0.993915 | − | 0.110154i | \(-0.964866\pi\) | ||||
0.993915 | − | 0.110154i | \(-0.0351344\pi\) | |||||||
\(878\) | 34093.6i | 1.31048i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34682.8 | 1.32633 | 0.663163 | − | 0.748475i | \(-0.269214\pi\) | ||||
0.663163 | + | 0.748475i | \(0.269214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 37990.4i | − 1.44788i | −0.689862 | − | 0.723941i | \(-0.742329\pi\) | ||||
0.689862 | − | 0.723941i | \(-0.257671\pi\) | |||||||
\(884\) | 86752.9 | 3.30070 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4992.66 | −0.189313 | ||||||||
\(887\) | 28299.0i | 1.07124i | 0.844460 | + | 0.535618i | \(0.179921\pi\) | ||||
−0.844460 | + | 0.535618i | \(0.820079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2796.00 | 0.105484 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 32227.7i | − 1.20971i | ||||||||
\(893\) | − 3484.58i | − 0.130579i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10200.4 | −0.380324 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 100126.i | − 3.72078i | ||||||||
\(899\) | −10259.3 | −0.380607 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29037.8 | −1.07368 | ||||||||
\(902\) | − 7781.65i | − 0.287251i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −63659.4 | −2.34212 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 17388.0i | − 0.636559i | −0.947997 | − | 0.318280i | \(-0.896895\pi\) | ||||
0.947997 | − | 0.318280i | \(-0.103105\pi\) | |||||||
\(908\) | − 128592.i | − 4.69988i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23555.3 | −0.856663 | −0.428332 | − | 0.903622i | \(-0.640899\pi\) | ||||
−0.428332 | + | 0.903622i | \(0.640899\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 2607.30i | − 0.0945117i | ||||||||
\(914\) | 61980.4 | 2.24303 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 96949.1 | 3.49704 | ||||||||
\(917\) | − 9594.44i | − 0.345514i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5983.09 | 0.214760 | 0.107380 | − | 0.994218i | \(-0.465754\pi\) | ||||
0.107380 | + | 0.994218i | \(0.465754\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 103968.i | − 3.71368i | ||||||||
\(923\) | 25577.3i | 0.912119i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8447.10 | 0.299772 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 88022.7i | 3.11367i | ||||||||
\(929\) | 20576.7 | 0.726694 | 0.363347 | − | 0.931654i | \(-0.381634\pi\) | ||||
0.363347 | + | 0.931654i | \(0.381634\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6607.35 | −0.232596 | ||||||||
\(932\) | 67219.5i | 2.36250i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17451.5 | 0.611382 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 11228.6i | − 0.391485i | −0.980655 | − | 0.195743i | \(-0.937288\pi\) | ||||
0.980655 | − | 0.195743i | \(-0.0627117\pi\) | |||||||
\(938\) | − 14615.9i | − 0.508769i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38567.6 | −1.33610 | −0.668049 | − | 0.744118i | \(-0.732870\pi\) | ||||
−0.668049 | + | 0.744118i | \(0.732870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 50003.9i | − 1.72678i | ||||||||
\(944\) | −43282.1 | −1.49228 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6672.81 | 0.229336 | ||||||||
\(947\) | − 4606.17i | − 0.158057i | −0.996872 | − | 0.0790287i | \(-0.974818\pi\) | ||||
0.996872 | − | 0.0790287i | \(-0.0251819\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6997.93 | 0.239370 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 16075.8i | 0.547288i | ||||||||
\(953\) | − 25559.7i | − 0.868795i | −0.900721 | − | 0.434397i | \(-0.856961\pi\) | ||||
0.900721 | − | 0.434397i | \(-0.143039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 75798.5 | 2.56433 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 44433.8i | 1.49853i | ||||||||
\(959\) | −4961.72 | −0.167072 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26064.0 | −0.874895 | ||||||||
\(962\) | − 104064.i | − 3.48769i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40006.4 | −1.33664 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37895.8i | 1.26023i | 0.776500 | + | 0.630117i | \(0.216993\pi\) | ||||
−0.776500 | + | 0.630117i | \(0.783007\pi\) | |||||||
\(968\) | 89907.7i | 2.98527i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46761.0 | 1.54545 | 0.772726 | − | 0.634740i | \(-0.218893\pi\) | ||||
0.772726 | + | 0.634740i | \(0.218893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 738.428i | − 0.0243298i | ||||||||
\(974\) | −25500.6 | −0.838903 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26112.9 | 0.856407 | ||||||||
\(977\) | − 3070.29i | − 0.100540i | −0.998736 | − | 0.0502698i | \(-0.983992\pi\) | ||||
0.998736 | − | 0.0502698i | \(-0.0160081\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 672.282 | 0.0219471 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 20934.3i | − 0.680287i | ||||||||
\(983\) | 16319.0i | 0.529498i | 0.964317 | + | 0.264749i | \(0.0852891\pi\) | ||||
−0.964317 | + | 0.264749i | \(0.914711\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 47889.9 | 1.54678 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 33338.0i | − 1.07350i | ||||||||
\(989\) | 42878.6 | 1.37862 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5105.79 | 0.163664 | 0.0818319 | − | 0.996646i | \(-0.473923\pi\) | ||||
0.0818319 | + | 0.996646i | \(0.473923\pi\) | |||||||
\(992\) | − 31977.0i | − 1.02346i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7720.99 | −0.246373 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7206.97i | 0.228934i | 0.993427 | + | 0.114467i | \(0.0365160\pi\) | ||||
−0.993427 | + | 0.114467i | \(0.963484\pi\) | |||||||
\(998\) | 16576.7i | 0.525779i | ||||||||
\(999\) | 0 | 0 |
(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 | 225.4.b.h.199.4 | 4 | ||
3.2 | odd | 2 | 75.4.b.c.49.1 | 4 | |||
5.2 | odd | 4 | 225.4.a.j.1.1 | 2 | |||
5.3 | odd | 4 | 225.4.a.n.1.2 | 2 | |||
5.4 | even | 2 | inner | 225.4.b.h.199.1 | 4 | ||
12.11 | even | 2 | 1200.4.f.v.49.4 | 4 | |||
15.2 | even | 4 | 75.4.a.e.1.2 | yes | 2 | ||
15.8 | even | 4 | 75.4.a.d.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 75.4.b.c.49.4 | 4 | |||
60.23 | odd | 4 | 1200.4.a.bl.1.2 | 2 | |||
60.47 | odd | 4 | 1200.4.a.bu.1.1 | 2 | |||
60.59 | even | 2 | 1200.4.f.v.49.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.a.d.1.1 | ✓ | 2 | 15.8 | even | 4 | ||
75.4.a.e.1.2 | yes | 2 | 15.2 | even | 4 | ||
75.4.b.c.49.1 | 4 | 3.2 | odd | 2 | |||
75.4.b.c.49.4 | 4 | 15.14 | odd | 2 | |||
225.4.a.j.1.1 | 2 | 5.2 | odd | 4 | |||
225.4.a.n.1.2 | 2 | 5.3 | odd | 4 | |||
225.4.b.h.199.1 | 4 | 5.4 | even | 2 | inner | ||
225.4.b.h.199.4 | 4 | 1.1 | even | 1 | trivial | ||
1200.4.a.bl.1.2 | 2 | 60.23 | odd | 4 | |||
1200.4.a.bu.1.1 | 2 | 60.47 | odd | 4 | |||
1200.4.f.v.49.1 | 4 | 60.59 | even | 2 | |||
1200.4.f.v.49.4 | 4 | 12.11 | even | 2 |