Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1940780862\) |
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: | \( x^{8} - 4x^{7} - 34x^{6} + 116x^{5} + 383x^{4} - 964x^{3} - 1476x^{2} + 1978x + 1028 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 544) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.427084\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.16565 | 0.224330 | 0.112165 | − | 0.993690i | \(-0.464222\pi\) | ||||
0.112165 | + | 0.993690i | \(0.464222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 16.7810 | 1.50094 | 0.750471 | − | 0.660904i | \(-0.229827\pi\) | ||||
0.750471 | + | 0.660904i | \(0.229827\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.7490 | −1.71428 | −0.857142 | − | 0.515080i | \(-0.827762\pi\) | ||||
−0.857142 | + | 0.515080i | \(0.827762\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.6413 | −0.949676 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.5557 | 0.289334 | 0.144667 | − | 0.989480i | \(-0.453789\pi\) | ||||
0.144667 | + | 0.989480i | \(0.453789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 53.0327 | 1.13143 | 0.565716 | − | 0.824600i | \(-0.308600\pi\) | ||||
0.565716 | + | 0.824600i | \(0.308600\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 19.5608 | 0.336705 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.0000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.4898 | 0.319852 | 0.159926 | − | 0.987129i | \(-0.448874\pi\) | ||||
0.159926 | + | 0.987129i | \(0.448874\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −37.0082 | −0.384565 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −200.849 | −1.82086 | −0.910432 | − | 0.413659i | \(-0.864251\pi\) | ||||
−0.910432 | + | 0.413659i | \(0.864251\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 156.603 | 1.25282 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −61.3613 | −0.437370 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00185 | 0.0256250 | 0.0128125 | − | 0.999918i | \(-0.495922\pi\) | ||||
0.0128125 | + | 0.999918i | \(0.495922\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 243.235 | 1.40924 | 0.704619 | − | 0.709586i | \(-0.251118\pi\) | ||||
0.704619 | + | 0.709586i | \(0.251118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.3043 | 0.0649061 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −532.781 | −2.57304 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 158.425 | 0.703916 | 0.351958 | − | 0.936016i | \(-0.385516\pi\) | ||||
0.351958 | + | 0.936016i | \(0.385516\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 61.8176 | 0.253814 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 360.289 | 1.37238 | 0.686192 | − | 0.727421i | \(-0.259281\pi\) | ||||
0.686192 | + | 0.727421i | \(0.259281\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 476.569 | 1.69014 | 0.845072 | − | 0.534653i | \(-0.179558\pi\) | ||||
0.845072 | + | 0.534653i | \(0.179558\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −430.287 | −1.42541 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −418.157 | −1.29776 | −0.648878 | − | 0.760893i | \(-0.724761\pi\) | ||||
−0.648878 | + | 0.760893i | \(0.724761\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 664.999 | 1.93877 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.8161 | 0.0544079 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 110.022 | 0.285146 | 0.142573 | − | 0.989784i | \(-0.454462\pi\) | ||||
0.142573 | + | 0.989784i | \(0.454462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 177.136 | 0.434273 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30.8779 | 0.0717523 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 455.621 | 1.00537 | 0.502685 | − | 0.864470i | \(-0.332346\pi\) | ||||
0.502685 | + | 0.864470i | \(0.332346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31.1780 | −0.0654416 | −0.0327208 | − | 0.999465i | \(-0.510417\pi\) | ||||
−0.0327208 | + | 0.999465i | \(0.510417\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 814.084 | 1.62802 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 889.943 | 1.69821 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 333.081 | 0.607348 | 0.303674 | − | 0.952776i | \(-0.401787\pi\) | ||||
0.303674 | + | 0.952776i | \(0.401787\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −234.120 | −0.408474 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −113.476 | −0.189677 | −0.0948386 | − | 0.995493i | \(-0.530234\pi\) | ||||
−0.0948386 | + | 0.995493i | \(0.530234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 124.858 | 0.200186 | 0.100093 | − | 0.994978i | \(-0.468086\pi\) | ||||
0.100093 | + | 0.994978i | \(0.468086\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 182.544 | 0.281045 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −335.134 | −0.496001 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38.8745 | 0.0553636 | 0.0276818 | − | 0.999617i | \(-0.491187\pi\) | ||||
0.0276818 | + | 0.999617i | \(0.491187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 620.788 | 0.851561 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1190.94 | 1.57498 | 0.787489 | − | 0.616329i | \(-0.211381\pi\) | ||||
0.787489 | + | 0.616329i | \(0.211381\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 285.278 | 0.364032 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.66476 | 0.00574844 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −978.287 | −1.16515 | −0.582574 | − | 0.812777i | \(-0.697954\pi\) | ||||
−0.582574 | + | 0.812777i | \(0.697954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1683.73 | −1.93960 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 283.527 | 0.316134 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 444.527 | 0.480079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 391.132 | 0.409417 | 0.204708 | − | 0.978823i | \(-0.434375\pi\) | ||||
0.204708 | + | 0.978823i | \(0.434375\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −270.662 | −0.274774 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1405.47 | −1.38465 | −0.692323 | − | 0.721588i | \(-0.743412\pi\) | ||||
−0.692323 | + | 0.721588i | \(0.743412\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −414.514 | −0.396536 | −0.198268 | − | 0.980148i | \(-0.563532\pi\) | ||||
−0.198268 | + | 0.980148i | \(0.563532\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −621.036 | −0.577209 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1029.42 | 0.930071 | 0.465035 | − | 0.885292i | \(-0.346042\pi\) | ||||
0.465035 | + | 0.885292i | \(0.346042\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 846.834 | 0.744147 | 0.372073 | − | 0.928203i | \(-0.378647\pi\) | ||||
0.372073 | + | 0.928203i | \(0.378647\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 184.668 | 0.157909 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 868.186 | 0.722762 | 0.361381 | − | 0.932418i | \(-0.382305\pi\) | ||||
0.361381 | + | 0.932418i | \(0.382305\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3370.45 | −2.73301 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1359.83 | −1.07449 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −539.733 | −0.415775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1219.58 | −0.916286 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 419.971 | 0.307866 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 530.331 | 0.379474 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 404.863 | 0.282880 | 0.141440 | − | 0.989947i | \(-0.454827\pi\) | ||||
0.141440 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 555.514 | 0.379149 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −361.572 | −0.241151 | −0.120575 | − | 0.992704i | \(-0.538474\pi\) | ||||
−0.120575 | + | 0.992704i | \(0.538474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −841.026 | −0.548317 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1029.71 | −0.656467 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3072.27 | 1.91593 | 0.957963 | − | 0.286892i | \(-0.0926220\pi\) | ||||
0.957963 | + | 0.286892i | \(0.0926220\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −634.213 | −0.387002 | −0.193501 | − | 0.981100i | \(-0.561984\pi\) | ||||
−0.193501 | + | 0.981100i | \(0.561984\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −487.425 | −0.291125 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 559.799 | 0.327362 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 67.1551 | 0.0384616 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 775.156 | 0.434924 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2211.32 | 1.21583 | 0.607915 | − | 0.794002i | \(-0.292006\pi\) | ||||
0.607915 | + | 0.794002i | \(0.292006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2760.95 | −1.48796 | −0.743982 | − | 0.668200i | \(-0.767065\pi\) | ||||
−0.743982 | + | 0.668200i | \(0.767065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −435.901 | −0.230330 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4081.74 | 2.11518 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3327.61 | 1.69154 | 0.845771 | − | 0.533546i | \(-0.179141\pi\) | ||||
0.845771 | + | 0.533546i | \(0.179141\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 128.248 | 0.0639667 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6376.75 | 3.12148 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −454.281 | −0.218295 | −0.109147 | − | 0.994026i | \(-0.534812\pi\) | ||||
−0.109147 | + | 0.994026i | \(0.534812\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 206.479 | 0.0974203 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2146.91 | 0.994809 | 0.497405 | − | 0.867519i | \(-0.334286\pi\) | ||||
0.497405 | + | 0.867519i | \(0.334286\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 615.467 | 0.280140 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −679.233 | −0.303756 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1442.68 | 0.634018 | 0.317009 | − | 0.948423i | \(-0.397321\pi\) | ||||
0.317009 | + | 0.948423i | \(0.397321\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4971.99 | −2.14770 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 531.095 | 0.225534 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4377.52 | −1.82788 | −0.913941 | − | 0.405846i | \(-0.866977\pi\) | ||||
−0.913941 | + | 0.405846i | \(0.866977\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4095.15 | 1.68171 | 0.840857 | − | 0.541257i | \(-0.182051\pi\) | ||||
0.840857 | + | 0.541257i | \(0.182051\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −36.3427 | −0.0146805 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2658.53 | 1.05654 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 179.447 | 0.0701738 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1948.16 | 0.749777 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4643.64 | −1.75917 | −0.879587 | − | 0.475737i | \(-0.842181\pi\) | ||||
−0.879587 | + | 0.475737i | \(0.842181\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1341.79 | 0.500435 | 0.250217 | − | 0.968190i | \(-0.419498\pi\) | ||||
0.250217 | + | 0.968190i | \(0.419498\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1037.36 | 0.380960 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2202.95 | −0.796719 | −0.398359 | − | 0.917229i | \(-0.630420\pi\) | ||||
−0.398359 | + | 0.917229i | \(0.630420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2073.15 | 0.738502 | 0.369251 | − | 0.929330i | \(-0.379614\pi\) | ||||
0.369251 | + | 0.929330i | \(0.379614\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 388.256 | 0.136246 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −127.055 | −0.0439285 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6046.02 | 2.05987 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5150.02 | 1.72923 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 279.620 | 0.0925440 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5538.65 | 1.80709 | 0.903545 | − | 0.428493i | \(-0.140955\pi\) | ||||
0.903545 | + | 0.428493i | \(0.140955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −132.273 | −0.0425502 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7997.33 | 2.53681 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7722.48 | −2.41583 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 145.541 | 0.0449076 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 901.556 | 0.274413 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 845.390 | 0.253863 | 0.126932 | − | 0.991911i | \(-0.459487\pi\) | ||||
0.126932 | + | 0.991911i | \(0.459487\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4015.50 | −1.18978 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3854.89 | 1.12713 | 0.563565 | − | 0.826072i | \(-0.309430\pi\) | ||||
0.563565 | + | 0.826072i | \(0.309430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3996.61 | 1.15329 | 0.576646 | − | 0.816994i | \(-0.304361\pi\) | ||||
0.576646 | + | 0.816994i | \(0.304361\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −390.649 | −0.111268 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2408.59 | −0.677220 | −0.338610 | − | 0.940927i | \(-0.609957\pi\) | ||||
−0.338610 | + | 0.940927i | \(0.609957\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7017.11 | −1.94785 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 45.3141 | 0.0124197 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5823.34 | 1.57607 | 0.788034 | − | 0.615631i | \(-0.211099\pi\) | ||||
0.788034 | + | 0.615631i | \(0.211099\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3082.74 | −0.823971 | −0.411985 | − | 0.911190i | \(-0.635165\pi\) | ||||
−0.411985 | + | 0.911190i | \(0.635165\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2380.38 | 0.628400 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11159.4 | 2.90998 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1404.83 | 0.361891 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1388.23 | 0.353314 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 36.0373 | 0.00906237 | 0.00453118 | − | 0.999990i | \(-0.498558\pi\) | ||||
0.00453118 | + | 0.999990i | \(0.498558\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2120.11 | −0.526838 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 332.534 | 0.0816631 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2437.56 | −0.591637 | −0.295819 | − | 0.955244i | \(-0.595592\pi\) | ||||
−0.295819 | + | 0.955244i | \(0.595592\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5029.83 | −1.20671 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −102.612 | −0.0243354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5240.19 | −1.22861 | −0.614305 | − | 0.789069i | \(-0.710563\pi\) | ||||
−0.614305 | + | 0.789069i | \(0.710563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1846.29 | 0.427987 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1140.34 | −0.261377 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 614.470 | 0.139275 | 0.0696374 | − | 0.997572i | \(-0.477816\pi\) | ||||
0.0696374 | + | 0.997572i | \(0.477816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3886.26 | −0.871121 | −0.435560 | − | 0.900160i | \(-0.643450\pi\) | ||||
−0.435560 | + | 0.900160i | \(0.643450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1962.65 | −0.435109 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1653.06 | 0.362484 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7086.52 | −1.53714 | −0.768570 | − | 0.639766i | \(-0.779031\pi\) | ||||
−0.768570 | + | 0.639766i | \(0.779031\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6236.86 | −1.33832 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2265.56 | −0.480967 | −0.240483 | − | 0.970653i | \(-0.577306\pi\) | ||||
−0.240483 | + | 0.970653i | \(0.577306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5024.39 | 1.05537 | 0.527684 | − | 0.849441i | \(-0.323061\pi\) | ||||
0.527684 | + | 0.849441i | \(0.323061\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 518.163 | 0.107696 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11438.8 | −2.35266 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 455.923 | 0.0918443 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3341.65 | 0.666285 | 0.333142 | − | 0.942876i | \(-0.391891\pi\) | ||||
0.333142 | + | 0.942876i | \(0.391891\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7645.80 | 1.50900 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −647.714 | −0.126546 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10651.6 | −2.06019 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15130.6 | −2.89739 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1638.28 | −0.310617 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −523.200 | −0.0982240 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3513.66 | 0.653209 | 0.326604 | − | 0.945161i | \(-0.394096\pi\) | ||||
0.326604 | + | 0.945161i | \(0.394096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −483.178 | −0.0889548 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5859.37 | 1.06834 | 0.534171 | − | 0.845376i | \(-0.320624\pi\) | ||||
0.534171 | + | 0.845376i | \(0.320624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7167.54 | −1.29436 | −0.647178 | − | 0.762339i | \(-0.724051\pi\) | ||||
−0.647178 | + | 0.762339i | \(0.724051\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13661.2 | 2.44356 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8474.00 | −1.50141 | −0.750705 | − | 0.660637i | \(-0.770286\pi\) | ||||
−0.750705 | + | 0.660637i | \(0.770286\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.2424 | 0.00741418 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1199.94 | 0.208642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 450.327 | 0.0775755 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8305.08 | 1.41749 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 987.112 | 0.166934 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13276.1 | 2.22472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8036.70 | −1.33455 | −0.667277 | − | 0.744810i | \(-0.732540\pi\) | ||||
−0.667277 | + | 0.744810i | \(0.732540\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4062.22 | −0.668493 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5589.44 | 0.911593 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8387.76 | 1.35582 | 0.677908 | − | 0.735146i | \(-0.262887\pi\) | ||||
0.677908 | + | 0.735146i | \(0.262887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1012.00 | 0.162137 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2567.53 | 0.407740 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10223.1 | −1.60932 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3928.77 | −0.613095 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6393.65 | −0.989133 | −0.494567 | − | 0.869140i | \(-0.664673\pi\) | ||||
−0.494567 | + | 0.869140i | \(0.664673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2803.61 | 0.430010 | 0.215005 | − | 0.976613i | \(-0.431023\pi\) | ||||
0.215005 | + | 0.976613i | \(0.431023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3254.16 | −0.494855 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5410.85 | −0.815837 | −0.407918 | − | 0.913018i | \(-0.633745\pi\) | ||||
−0.407918 | + | 0.913018i | \(0.633745\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1904.24 | −0.284694 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −629.140 | −0.0932707 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9090.49 | 1.33643 | 0.668214 | − | 0.743969i | \(-0.267059\pi\) | ||||
0.668214 | + | 0.743969i | \(0.267059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6157.29 | −0.897695 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1421.60 | −0.205550 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2095.25 | 0.300467 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13209.5 | −1.87883 | −0.939415 | − | 0.342782i | \(-0.888631\pi\) | ||||
−0.939415 | + | 0.342782i | \(0.888631\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9238.27 | −1.30332 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3493.10 | −0.488822 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1415.84 | 0.196540 | 0.0982700 | − | 0.995160i | \(-0.468669\pi\) | ||||
0.0982700 | + | 0.995160i | \(0.468669\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 618.181 | 0.0851272 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 212.229 | 0.0289929 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3342.97 | 0.453079 | 0.226539 | − | 0.974002i | \(-0.427259\pi\) | ||||
0.226539 | + | 0.974002i | \(0.427259\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 471.929 | 0.0634584 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9486.89 | 1.26569 | 0.632843 | − | 0.774280i | \(-0.281888\pi\) | ||||
0.632843 | + | 0.774280i | \(0.281888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5623.89 | −0.744468 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12219.8 | −1.60509 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5561.74 | −0.724914 | −0.362457 | − | 0.932001i | \(-0.618062\pi\) | ||||
−0.362457 | + | 0.932001i | \(0.618062\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3414.43 | −0.441624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −421.467 | −0.0540972 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 652.354 | 0.0830974 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7956.47 | −1.00585 | −0.502927 | − | 0.864329i | \(-0.667743\pi\) | ||||
−0.502927 | + | 0.864329i | \(0.667743\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −980.343 | −0.123004 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5835.73 | 0.726739 | 0.363370 | − | 0.931645i | \(-0.381626\pi\) | ||||
0.363370 | + | 0.931645i | \(0.381626\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12899.4 | 1.59446 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10417.5 | 1.27814 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1672.29 | 0.203667 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4161.62 | 0.503126 | 0.251563 | − | 0.967841i | \(-0.419055\pi\) | ||||
0.251563 | + | 0.967841i | \(0.419055\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3581.20 | 0.429799 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14465.5 | −1.72349 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19985.3 | 2.36395 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −739.271 | −0.0868159 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −526.799 | −0.0614220 | −0.0307110 | − | 0.999528i | \(-0.509777\pi\) | ||||
−0.0307110 | + | 0.999528i | \(0.509777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6302.16 | 0.729569 | 0.364785 | − | 0.931092i | \(-0.381143\pi\) | ||||
0.364785 | + | 0.931092i | \(0.381143\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10722.1 | 1.23245 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2662.25 | 0.303854 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 989.871 | 0.112186 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 652.530 | 0.0734369 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5624.67 | −0.628610 | −0.314305 | − | 0.949322i | \(-0.601771\pi\) | ||||
−0.314305 | + | 0.949322i | \(0.601771\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14364.6 | 1.59427 | 0.797133 | − | 0.603803i | \(-0.206349\pi\) | ||||
0.797133 | + | 0.603803i | \(0.206349\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 78.2794 | 0.00862807 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5320.46 | −0.582407 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4655.07 | −0.506092 | −0.253046 | − | 0.967454i | \(-0.581432\pi\) | ||||
−0.253046 | + | 0.967454i | \(0.581432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17051.4 | −1.84121 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12335.4 | 1.32296 | 0.661479 | − | 0.749963i | \(-0.269929\pi\) | ||||
0.661479 | + | 0.749963i | \(0.269929\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16416.7 | −1.74882 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2577.63 | 0.272746 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4298.43 | −0.451793 | −0.225897 | − | 0.974151i | \(-0.572531\pi\) | ||||
−0.225897 | + | 0.974151i | \(0.572531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3803.12 | 0.397077 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3218.30 | −0.333794 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −28254.8 | −2.91122 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1036.67 | 0.106113 | 0.0530564 | − | 0.998592i | \(-0.483104\pi\) | ||||
0.0530564 | + | 0.998592i | \(0.483104\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1043.14 | −0.106078 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7019.41 | −0.709168 | −0.354584 | − | 0.935024i | \(-0.615378\pi\) | ||||
−0.354584 | + | 0.935024i | \(0.615378\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4016.72 | 0.403181 | 0.201590 | − | 0.979470i | \(-0.435389\pi\) | ||||
0.201590 | + | 0.979470i | \(0.435389\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4757.88 | 0.474498 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 684.278 | 0.0678043 | 0.0339022 | − | 0.999425i | \(-0.489207\pi\) | ||||
0.0339022 | + | 0.999425i | \(0.489207\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10575.0 | −1.04117 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3878.83 | 0.379463 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5030.54 | 0.489016 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4148.39 | 0.400718 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2821.11 | −0.270796 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4168.81 | 0.397657 | 0.198829 | − | 0.980034i | \(-0.436286\pi\) | ||||
0.198829 | + | 0.980034i | \(0.436286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8401.70 | 0.796434 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7433.06 | 0.700240 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6563.60 | 0.614511 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1831.22 | −0.170391 | −0.0851957 | − | 0.996364i | \(-0.527152\pi\) | ||||
−0.0851957 | + | 0.996364i | \(0.527152\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −529.533 | −0.0489700 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9449.95 | −0.868575 | −0.434287 | − | 0.900774i | \(-0.643000\pi\) | ||||
−0.434287 | + | 0.900774i | \(0.643000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 68.0314 | 0.00621497 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4541.99 | −0.412419 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3602.74 | 0.325161 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6524.39 | 0.585315 | 0.292657 | − | 0.956217i | \(-0.405461\pi\) | ||||
0.292657 | + | 0.956217i | \(0.405461\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2502.55 | 0.223165 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 385.856 | 0.0342037 | 0.0171019 | − | 0.999854i | \(-0.494556\pi\) | ||||
0.0171019 | + | 0.999854i | \(0.494556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23585.2 | −2.07827 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 717.420 | 0.0628436 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16377.7 | −1.42619 | −0.713094 | − | 0.701068i | \(-0.752707\pi\) | ||||
−0.713094 | + | 0.701068i | \(0.752707\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3964.12 | −0.343175 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1625.45 | −0.139894 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6955.97 | −0.595178 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4413.96 | −0.375485 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1681.66 | 0.142229 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20078.7 | 1.68841 | 0.844205 | − | 0.536020i | \(-0.180073\pi\) | ||||
0.844205 | + | 0.536020i | \(0.180073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2073.49 | 0.173360 | 0.0866801 | − | 0.996236i | \(-0.472374\pi\) | ||||
0.0866801 | + | 0.996236i | \(0.472374\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5795.60 | −0.481792 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4135.00 | 0.341790 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28173.3 | 2.31555 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11682.7 | −0.954776 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19107.1 | 1.55276 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17274.7 | 1.39598 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5102.66 | −0.410048 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7019.55 | 0.560952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12600.1 | −1.00133 | −0.500665 | − | 0.865641i | \(-0.666911\pi\) | ||||
−0.500665 | + | 0.865641i | \(0.666911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4773.52 | 0.377258 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14210.7 | 1.11692 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25467.7 | −1.99071 | −0.995357 | − | 0.0962488i | \(-0.969316\pi\) | ||||
−0.995357 | + | 0.0962488i | \(0.969316\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 799.444 | 0.0621483 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 106.008 | 0.00819620 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1234.23 | −0.0949089 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3098.92 | 0.237012 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17825.0 | −1.35596 | −0.677980 | − | 0.735081i | \(-0.737144\pi\) | ||||
−0.677980 | + | 0.735081i | \(0.737144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25273.8 | 1.91228 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 209.173 | 0.0157421 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1662.34 | −0.124439 | −0.0622196 | − | 0.998062i | \(-0.519818\pi\) | ||||
−0.0622196 | + | 0.998062i | \(0.519818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14569.1 | 1.08482 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19709.4 | −1.45982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6076.82 | −0.447721 | −0.223861 | − | 0.974621i | \(-0.571866\pi\) | ||||
−0.223861 | + | 0.974621i | \(0.571866\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17112.8 | −1.25420 | −0.627099 | − | 0.778939i | \(-0.715758\pi\) | ||||
−0.627099 | + | 0.778939i | \(0.715758\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5412.87 | −0.394635 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31453.5 | −2.28122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 86.2098 | 0.00622004 | 0.00311002 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00311002 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1564.05 | 0.112262 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37811.3 | −2.69996 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1161.37 | 0.0825024 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22819.3 | −1.61275 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5264.07 | 0.370139 | 0.185070 | − | 0.982725i | \(-0.440749\pi\) | ||||
0.185070 | + | 0.982725i | \(0.440749\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6443.27 | 0.450747 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2567.87 | −0.178728 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8460.14 | −0.585863 | −0.292931 | − | 0.956133i | \(-0.594631\pi\) | ||||
−0.292931 | + | 0.956133i | \(0.594631\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9057.28 | −0.624054 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2416.57 | 0.165668 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21638.6 | −1.47601 | −0.738004 | − | 0.674796i | \(-0.764231\pi\) | ||||
−0.738004 | + | 0.674796i | \(0.764231\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26366.0 | −1.78950 | −0.894750 | − | 0.446567i | \(-0.852647\pi\) | ||||
−0.894750 | + | 0.446567i | \(0.852647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8540.61 | −0.576784 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20465.8 | −1.37529 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20621.8 | −1.37893 | −0.689467 | − | 0.724317i | \(-0.742155\pi\) | ||||
−0.689467 | + | 0.724317i | \(0.742155\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −148.101 | −0.00985447 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22176.0 | −1.46832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26254.2 | −1.72985 | −0.864926 | − | 0.501900i | \(-0.832635\pi\) | ||||
−0.864926 | + | 0.501900i | \(0.832635\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7047.55 | 0.462089 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1009.02 | 0.0658371 | 0.0329185 | − | 0.999458i | \(-0.489520\pi\) | ||||
0.0329185 | + | 0.999458i | \(0.489520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13650.9 | 0.886392 | 0.443196 | − | 0.896425i | \(-0.353845\pi\) | ||||
0.443196 | + | 0.896425i | \(0.353845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12324.3 | 0.796391 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31059.6 | 1.99740 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10675.9 | −0.683256 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 325.939 | 0.0207604 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2693.22 | 0.170725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23738.3 | 1.49763 | 0.748816 | − | 0.662778i | \(-0.230622\pi\) | ||||
0.748816 | + | 0.662778i | \(0.230622\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6456.13 | 0.405384 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6794.02 | 0.424586 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35266.7 | 2.19359 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2909.66 | 0.180132 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18313.9 | −1.12848 | −0.564240 | − | 0.825611i | \(-0.690831\pi\) | ||||
−0.564240 | + | 0.825611i | \(0.690831\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14535.0 | 0.891451 | 0.445725 | − | 0.895170i | \(-0.352946\pi\) | ||||
0.445725 | + | 0.895170i | \(0.352946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9322.09 | 0.569081 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23237.7 | −1.41201 | −0.706004 | − | 0.708207i | \(-0.749504\pi\) | ||||
−0.706004 | + | 0.708207i | \(0.749504\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4809.42 | 0.290888 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9001.71 | −0.541943 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24776.7 | −1.48482 | −0.742410 | − | 0.669946i | \(-0.766317\pi\) | ||||
−0.742410 | + | 0.669946i | \(0.766317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6067.56 | −0.361953 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3201.52 | −0.190112 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11063.6 | 0.653987 | 0.326994 | − | 0.945027i | \(-0.393964\pi\) | ||||
0.326994 | + | 0.945027i | \(0.393964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11086.1 | −0.652341 | −0.326171 | − | 0.945311i | \(-0.605758\pi\) | ||||
−0.326171 | + | 0.945311i | \(0.605758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1050.90 | 0.0615589 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14113.3 | −0.822992 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −803.767 | −0.0466596 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 985.429 | 0.0569490 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −329.107 | −0.0189345 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30924.7 | −1.77126 | −0.885632 | − | 0.464388i | \(-0.846274\pi\) | ||||
−0.885632 | + | 0.464388i | \(0.846274\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9609.37 | −0.547948 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16434.3 | 0.932970 | 0.466485 | − | 0.884529i | \(-0.345520\pi\) | ||||
0.466485 | + | 0.884529i | \(0.345520\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12418.1 | −0.701857 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4493.46 | 0.252848 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25129.7 | 1.40785 | 0.703926 | − | 0.710273i | \(-0.251429\pi\) | ||||
0.703926 | + | 0.710273i | \(0.251429\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51555.9 | 2.87569 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4658.66 | 0.258717 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5834.79 | 0.322624 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20139.5 | 1.10874 | 0.554371 | − | 0.832269i | \(-0.312959\pi\) | ||||
0.554371 | + | 0.832269i | \(0.312959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8593.25 | 0.471040 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10642.7 | −0.580867 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6124.92 | 0.332852 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2807.58 | −0.151920 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14457.6 | −0.778965 | −0.389482 | − | 0.921034i | \(-0.627346\pi\) | ||||
−0.389482 | + | 0.921034i | \(0.627346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4196.65 | 0.225149 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8179.50 | −0.436961 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44622.2 | 2.37368 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11418.8 | 0.604855 | 0.302427 | − | 0.953172i | \(-0.402203\pi\) | ||||
0.302427 | + | 0.953172i | \(0.402203\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −996.791 | −0.0525775 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48853.5 | −2.56603 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9394.00 | 0.491351 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6787.98 | 0.353559 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7890.05 | 0.409248 | 0.204624 | − | 0.978841i | \(-0.434403\pi\) | ||||
0.204624 | + | 0.978841i | \(0.434403\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13160.4 | 0.679776 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3593.40 | −0.184841 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 626.701 | 0.0321036 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5368.41 | 0.273870 | 0.136935 | − | 0.990580i | \(-0.456275\pi\) | ||||
0.136935 | + | 0.990580i | \(0.456275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13986.6 | −0.710592 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8101.68 | 0.409920 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34845.6 | 1.75587 | 0.877935 | − | 0.478780i | \(-0.158921\pi\) | ||||
0.877935 | + | 0.478780i | \(0.158921\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13007.9 | 0.652795 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3515.91 | 0.175726 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14670.5 | 0.730264 | 0.365132 | − | 0.930956i | \(-0.381024\pi\) | ||||
0.365132 | + | 0.930956i | \(0.381024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1637.54 | 0.0811829 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12358.7 | 0.610226 | 0.305113 | − | 0.952316i | \(-0.401306\pi\) | ||||
0.305113 | + | 0.952316i | \(0.401306\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37108.3 | 1.82489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30537.3 | −1.49572 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32683.0 | −1.59441 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27659.8 | −1.34397 | −0.671984 | − | 0.740566i | \(-0.734557\pi\) | ||||
−0.671984 | + | 0.740566i | \(0.734557\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42.0069 | 0.00203296 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46331.5 | −2.23335 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1662.45 | −0.0798188 | −0.0399094 | − | 0.999203i | \(-0.512707\pi\) | ||||
−0.0399094 | + | 0.999203i | \(0.512707\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2471.30 | −0.118185 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13399.0 | −0.638255 | −0.319128 | − | 0.947712i | \(-0.603390\pi\) | ||||
−0.319128 | + | 0.947712i | \(0.603390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26886.1 | −1.27568 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7314.87 | −0.345712 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24162.8 | 1.13751 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11257.8 | 0.527917 | 0.263958 | − | 0.964534i | \(-0.414972\pi\) | ||||
0.263958 | + | 0.964534i | \(0.414972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2841.34 | −0.132722 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13596.8 | 0.632658 | 0.316329 | − | 0.948650i | \(-0.397550\pi\) | ||||
0.316329 | + | 0.948650i | \(0.397550\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38091.4 | 1.76553 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5863.03 | −0.270701 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9544.01 | 0.438960 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1197.82 | −0.0548800 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −245.559 | −0.0112076 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 55840.7 | 2.53890 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8294.83 | −0.375704 | −0.187852 | − | 0.982197i | \(-0.560152\pi\) | ||||
−0.187852 | + | 0.982197i | \(0.560152\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6108.24 | −0.275613 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27564.0 | −1.23902 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1653.46 | −0.0740428 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2152.13 | 0.0960102 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12296.9 | −0.546522 | −0.273261 | − | 0.961940i | \(-0.588102\pi\) | ||||
−0.273261 | + | 0.961940i | \(0.588102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7108.67 | −0.314752 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 25084.5 | 1.10651 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1317.97 | 0.0579205 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 107008. | 4.68516 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 716.258 | 0.0312434 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9058.67 | −0.393679 | −0.196839 | − | 0.980436i | \(-0.563068\pi\) | ||||
−0.196839 | + | 0.980436i | \(0.563068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12695.8 | 0.549706 | 0.274853 | − | 0.961486i | \(-0.411371\pi\) | ||||
0.274853 | + | 0.961486i | \(0.411371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4530.03 | −0.195418 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7623.31 | −0.327648 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12624.3 | 0.540596 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 43173.1 | 1.84199 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22827.6 | −0.970387 | −0.485193 | − | 0.874407i | \(-0.661251\pi\) | ||||
−0.485193 | + | 0.874407i | \(0.661251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27839.6 | 1.17913 | 0.589567 | − | 0.807719i | \(-0.299298\pi\) | ||||
0.589567 | + | 0.807719i | \(0.299298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1926.89 | 0.0813160 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7309.12 | −0.307331 | −0.153666 | − | 0.988123i | \(-0.549108\pi\) | ||||
−0.153666 | + | 0.988123i | \(0.549108\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36503.0 | 1.52931 | 0.764656 | − | 0.644438i | \(-0.222909\pi\) | ||||
0.764656 | + | 0.644438i | \(0.222909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8260.41 | −0.344826 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11305.0 | 0.470221 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36027.4 | 1.49315 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14925.2 | −0.616358 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11483.7 | 0.472542 | 0.236271 | − | 0.971687i | \(-0.424075\pi\) | ||||
0.236271 | + | 0.971687i | \(0.424075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24373.0 | −0.999343 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2640.85 | −0.107895 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10328.2 | 0.420473 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38720.3 | 1.57077 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5856.68 | 0.236750 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31819.5 | −1.28174 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14099.2 | 0.565939 | 0.282970 | − | 0.959129i | \(-0.408680\pi\) | ||||
0.282970 | + | 0.959129i | \(0.408680\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11398.2 | −0.455920 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15633.7 | −0.623148 | −0.311574 | − | 0.950222i | \(-0.600856\pi\) | ||||
−0.311574 | + | 0.950222i | \(0.600856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25320.8 | −1.00574 | −0.502872 | − | 0.864361i | \(-0.667723\pi\) | ||||
−0.502872 | + | 0.864361i | \(0.667723\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13333.7 | −0.527770 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31444.7 | 1.24031 | 0.620156 | − | 0.784479i | \(-0.287069\pi\) | ||||
0.620156 | + | 0.784479i | \(0.287069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24209.7 | 0.951623 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 336.873 | 0.0131959 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 410.349 | 0.0160186 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17664.2 | 0.687173 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10029.1 | −0.388814 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16837.5 | −0.650526 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32359.1 | 1.24594 | 0.622969 | − | 0.782246i | \(-0.285926\pi\) | ||||
0.622969 | + | 0.782246i | \(0.285926\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3895.20 | 0.149467 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17110.9 | 0.654348 | 0.327174 | − | 0.944964i | \(-0.393904\pi\) | ||||
0.327174 | + | 0.944964i | \(0.393904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24437.9 | 0.931369 | 0.465685 | − | 0.884951i | \(-0.345808\pi\) | ||||
0.465685 | + | 0.884951i | \(0.345808\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8912.33 | 0.338514 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27679.7 | 1.04779 | 0.523897 | − | 0.851781i | \(-0.324478\pi\) | ||||
0.523897 | + | 0.851781i | \(0.324478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12854.0 | −0.484937 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6552.87 | 0.246386 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11076.9 | −0.415090 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −73459.3 | −2.74354 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12416.0 | −0.462160 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 973.391 | 0.0361117 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1870.38 | 0.0691581 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17637.0 | −0.649970 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 68720.9 | 2.52415 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23724.5 | 0.868531 | 0.434266 | − | 0.900785i | \(-0.357008\pi\) | ||||
0.434266 | + | 0.900785i | \(0.357008\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36037.9 | 1.31496 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12782.2 | −0.464866 | −0.232433 | − | 0.972612i | \(-0.574669\pi\) | ||||
−0.232433 | + | 0.972612i | \(0.574669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12571.3 | 0.455695 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −609.868 | −0.0220345 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11479.6 | 0.413401 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14177.2 | −0.508881 | −0.254441 | − | 0.967088i | \(-0.581891\pi\) | ||||
−0.254441 | + | 0.967088i | \(0.581891\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4095.70 | 0.146534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6017.92 | −0.214607 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24809.8 | 0.881883 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10628.7 | 0.376581 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27706.5 | −0.978492 | −0.489246 | − | 0.872146i | \(-0.662728\pi\) | ||||
−0.489246 | + | 0.872146i | \(0.662728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17615.7 | 0.620120 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6829.98 | 0.239661 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3011.31 | 0.105327 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6043.38 | −0.210703 | −0.105351 | − | 0.994435i | \(-0.533597\pi\) | ||||
−0.105351 | + | 0.994435i | \(0.533597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8354.85 | −0.290362 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48734.8 | 1.68832 | 0.844160 | − | 0.536092i | \(-0.180100\pi\) | ||||
0.844160 | + | 0.536092i | \(0.180100\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −72363.7 | −2.49892 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32692.1 | 1.12537 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16251.6 | −0.557661 | −0.278831 | − | 0.960340i | \(-0.589947\pi\) | ||||
−0.278831 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6621.57 | 0.226497 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9877.72 | −0.336811 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3428.14 | −0.116525 | −0.0582625 | − | 0.998301i | \(-0.518556\pi\) | ||||
−0.0582625 | + | 0.998301i | \(0.518556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −77925.1 | −2.64042 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 49.2399 | 0.00166322 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −97541.5 | −3.28444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29372.4 | 0.985950 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26395.6 | −0.883266 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22516.6 | 0.751123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8400.92 | −0.279375 | −0.139687 | − | 0.990196i | \(-0.544610\pi\) | ||||
−0.139687 | + | 0.990196i | \(0.544610\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 524.924 | 0.0174025 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43523.7 | −1.43846 | −0.719229 | − | 0.694773i | \(-0.755505\pi\) | ||||
−0.719229 | + | 0.694773i | \(0.755505\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20135.6 | 0.663431 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9680.82 | 0.317984 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15850.0 | −0.519024 | −0.259512 | − | 0.965740i | \(-0.583562\pi\) | ||||
−0.259512 | + | 0.965740i | \(0.583562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10326.5 | −0.337117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21713.9 | −0.706698 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34943.1 | 1.13379 | 0.566894 | − | 0.823791i | \(-0.308145\pi\) | ||||
0.566894 | + | 0.823791i | \(0.308145\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36967.8 | −1.19583 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15475.3 | 0.499071 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −95718.4 | −3.07752 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33028.6 | 1.05872 | 0.529358 | − | 0.848399i | \(-0.322433\pi\) | ||||
0.529358 | + | 0.848399i | \(0.322433\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9367.99 | −0.299380 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34789.6 | 1.10845 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22849.2 | 0.725819 | 0.362910 | − | 0.931824i | \(-0.381783\pi\) | ||||
0.362910 | + | 0.931824i | \(0.381783\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9721.17 | −0.307872 |
(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 | 1088.4.a.bi.1.5 | 8 | ||
4.3 | odd | 2 | inner | 1088.4.a.bi.1.4 | 8 | ||
8.3 | odd | 2 | 544.4.a.m.1.5 | yes | 8 | ||
8.5 | even | 2 | 544.4.a.m.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
544.4.a.m.1.4 | ✓ | 8 | 8.5 | even | 2 | ||
544.4.a.m.1.5 | yes | 8 | 8.3 | odd | 2 | ||
1088.4.a.bi.1.4 | 8 | 4.3 | odd | 2 | inner | ||
1088.4.a.bi.1.5 | 8 | 1.1 | even | 1 | trivial |