Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} + \cdots - 6889792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7\cdot 13^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.685025\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.685025 | −0.242193 | −0.121096 | − | 0.992641i | \(-0.538641\pi\) | ||||
−0.121096 | + | 0.992641i | \(0.538641\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.53074 | −0.941343 | ||||||||
\(5\) | −9.28431 | −0.830414 | −0.415207 | − | 0.909727i | \(-0.636291\pi\) | ||||
−0.415207 | + | 0.909727i | \(0.636291\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.04730 | −0.326523 | −0.163262 | − | 0.986583i | \(-0.552201\pi\) | ||||
−0.163262 | + | 0.986583i | \(0.552201\pi\) | |||||||
\(8\) | 10.6389 | 0.470180 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.35999 | 0.201120 | ||||||||
\(11\) | −59.2146 | −1.62308 | −0.811539 | − | 0.584298i | \(-0.801370\pi\) | ||||
−0.811539 | + | 0.584298i | \(0.801370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 4.14255 | 0.0790817 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 52.9580 | 0.827468 | ||||||||
\(17\) | 117.407 | 1.67502 | 0.837512 | − | 0.546420i | \(-0.184010\pi\) | ||||
0.837512 | + | 0.546420i | \(0.184010\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −49.2492 | −0.594660 | −0.297330 | − | 0.954775i | \(-0.596096\pi\) | ||||
−0.297330 | + | 0.954775i | \(0.596096\pi\) | |||||||
\(20\) | 69.9177 | 0.781704 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 40.5635 | 0.393098 | ||||||||
\(23\) | −23.1522 | −0.209894 | −0.104947 | − | 0.994478i | \(-0.533467\pi\) | ||||
−0.104947 | + | 0.994478i | \(0.533467\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −38.8015 | −0.310412 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 45.5406 | 0.307370 | ||||||||
\(29\) | 145.028 | 0.928658 | 0.464329 | − | 0.885663i | \(-0.346296\pi\) | ||||
0.464329 | + | 0.885663i | \(0.346296\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 94.9826 | 0.550303 | 0.275151 | − | 0.961401i | \(-0.411272\pi\) | ||||
0.275151 | + | 0.961401i | \(0.411272\pi\) | |||||||
\(32\) | −121.389 | −0.670587 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −80.4268 | −0.405679 | ||||||||
\(35\) | 56.1450 | 0.271150 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 379.757 | 1.68734 | 0.843672 | − | 0.536860i | \(-0.180390\pi\) | ||||
0.843672 | + | 0.536860i | \(0.180390\pi\) | |||||||
\(38\) | 33.7370 | 0.144023 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −98.7753 | −0.390444 | ||||||||
\(41\) | 268.749 | 1.02370 | 0.511848 | − | 0.859076i | \(-0.328961\pi\) | ||||
0.511848 | + | 0.859076i | \(0.328961\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −23.6647 | −0.0839264 | −0.0419632 | − | 0.999119i | \(-0.513361\pi\) | ||||
−0.0419632 | + | 0.999119i | \(0.513361\pi\) | |||||||
\(44\) | 445.930 | 1.52787 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.8599 | 0.0508350 | ||||||||
\(47\) | −301.164 | −0.934666 | −0.467333 | − | 0.884081i | \(-0.654785\pi\) | ||||
−0.467333 | + | 0.884081i | \(0.654785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −306.430 | −0.893383 | ||||||||
\(50\) | 26.5800 | 0.0751797 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 391.713 | 1.01521 | 0.507603 | − | 0.861591i | \(-0.330532\pi\) | ||||
0.507603 | + | 0.861591i | \(0.330532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 549.767 | 1.34783 | ||||||||
\(56\) | −64.3369 | −0.153525 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −99.3480 | −0.224914 | ||||||||
\(59\) | −510.800 | −1.12713 | −0.563563 | − | 0.826073i | \(-0.690570\pi\) | ||||
−0.563563 | + | 0.826073i | \(0.690570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 520.734 | 1.09300 | 0.546501 | − | 0.837458i | \(-0.315959\pi\) | ||||
0.546501 | + | 0.837458i | \(0.315959\pi\) | |||||||
\(62\) | −65.0655 | −0.133279 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −340.509 | −0.665057 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 470.377 | 0.857697 | 0.428849 | − | 0.903376i | \(-0.358919\pi\) | ||||
0.428849 | + | 0.903376i | \(0.358919\pi\) | |||||||
\(68\) | −884.162 | −1.57677 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −38.4607 | −0.0656705 | ||||||||
\(71\) | 466.583 | 0.779905 | 0.389953 | − | 0.920835i | \(-0.372491\pi\) | ||||
0.389953 | + | 0.920835i | \(0.372491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −314.174 | −0.503716 | −0.251858 | − | 0.967764i | \(-0.581042\pi\) | ||||
−0.251858 | + | 0.967764i | \(0.581042\pi\) | |||||||
\(74\) | −260.143 | −0.408663 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 370.883 | 0.559779 | ||||||||
\(77\) | 358.088 | 0.529973 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 47.9136 | 0.0682368 | 0.0341184 | − | 0.999418i | \(-0.489138\pi\) | ||||
0.0341184 | + | 0.999418i | \(0.489138\pi\) | |||||||
\(80\) | −491.678 | −0.687141 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −184.100 | −0.247932 | ||||||||
\(83\) | −310.030 | −0.410003 | −0.205001 | − | 0.978762i | \(-0.565720\pi\) | ||||
−0.205001 | + | 0.978762i | \(0.565720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1090.04 | −1.39096 | ||||||||
\(86\) | 16.2109 | 0.0203264 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −629.981 | −0.763138 | ||||||||
\(89\) | −216.244 | −0.257549 | −0.128774 | − | 0.991674i | \(-0.541104\pi\) | ||||
−0.128774 | + | 0.991674i | \(0.541104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 174.353 | 0.197583 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 206.305 | 0.226369 | ||||||||
\(95\) | 457.245 | 0.493814 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −219.507 | −0.229768 | −0.114884 | − | 0.993379i | \(-0.536650\pi\) | ||||
−0.114884 | + | 0.993379i | \(0.536650\pi\) | |||||||
\(98\) | 209.912 | 0.216371 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 292.204 | 0.292204 | ||||||||
\(101\) | 921.359 | 0.907710 | 0.453855 | − | 0.891076i | \(-0.350048\pi\) | ||||
0.453855 | + | 0.891076i | \(0.350048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1277.55 | −1.22214 | −0.611072 | − | 0.791575i | \(-0.709262\pi\) | ||||
−0.611072 | + | 0.791575i | \(0.709262\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −268.333 | −0.245876 | ||||||||
\(107\) | 1626.78 | 1.46978 | 0.734892 | − | 0.678184i | \(-0.237233\pi\) | ||||
0.734892 | + | 0.678184i | \(0.237233\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1626.49 | −1.42926 | −0.714629 | − | 0.699504i | \(-0.753404\pi\) | ||||
−0.714629 | + | 0.699504i | \(0.753404\pi\) | |||||||
\(110\) | −376.604 | −0.326434 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −320.253 | −0.270188 | ||||||||
\(113\) | 2003.32 | 1.66776 | 0.833878 | − | 0.551949i | \(-0.186116\pi\) | ||||
0.833878 | + | 0.551949i | \(0.186116\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 214.952 | 0.174299 | ||||||||
\(116\) | −1092.17 | −0.874185 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 349.911 | 0.272982 | ||||||||
\(119\) | −709.995 | −0.546934 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2175.36 | 1.63438 | ||||||||
\(122\) | −356.716 | −0.264717 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −715.290 | −0.518023 | ||||||||
\(125\) | 1520.78 | 1.08818 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1966.75 | −1.37418 | −0.687091 | − | 0.726571i | \(-0.741113\pi\) | ||||
−0.687091 | + | 0.726571i | \(0.741113\pi\) | |||||||
\(128\) | 1204.37 | 0.831659 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2863.90 | −1.91008 | −0.955039 | − | 0.296480i | \(-0.904187\pi\) | ||||
−0.955039 | + | 0.296480i | \(0.904187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 297.825 | 0.194171 | ||||||||
\(134\) | −322.220 | −0.207728 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1249.09 | 0.787562 | ||||||||
\(137\) | 1774.52 | 1.10663 | 0.553313 | − | 0.832974i | \(-0.313363\pi\) | ||||
0.553313 | + | 0.832974i | \(0.313363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1349.35 | −0.823382 | −0.411691 | − | 0.911324i | \(-0.635062\pi\) | ||||
−0.411691 | + | 0.911324i | \(0.635062\pi\) | |||||||
\(140\) | −422.813 | −0.255245 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −319.621 | −0.188888 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1346.49 | −0.771171 | ||||||||
\(146\) | 215.217 | 0.121996 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2859.85 | −1.58837 | ||||||||
\(149\) | 1267.51 | 0.696903 | 0.348452 | − | 0.937327i | \(-0.386708\pi\) | ||||
0.348452 | + | 0.937327i | \(0.386708\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2928.66 | −1.57835 | −0.789176 | − | 0.614168i | \(-0.789492\pi\) | ||||
−0.789176 | + | 0.614168i | \(0.789492\pi\) | |||||||
\(152\) | −523.960 | −0.279597 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −245.299 | −0.128356 | ||||||||
\(155\) | −881.849 | −0.456979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2520.07 | 1.28104 | 0.640521 | − | 0.767940i | \(-0.278718\pi\) | ||||
0.640521 | + | 0.767940i | \(0.278718\pi\) | |||||||
\(158\) | −32.8220 | −0.0165265 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1127.01 | 0.556865 | ||||||||
\(161\) | 140.008 | 0.0685354 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3596.35 | −1.72815 | −0.864073 | − | 0.503366i | \(-0.832095\pi\) | ||||
−0.864073 | + | 0.503366i | \(0.832095\pi\) | |||||||
\(164\) | −2023.88 | −0.963649 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 212.378 | 0.0992998 | ||||||||
\(167\) | −1988.55 | −0.921430 | −0.460715 | − | 0.887548i | \(-0.652407\pi\) | ||||
−0.460715 | + | 0.887548i | \(0.652407\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 746.707 | 0.336881 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 178.213 | 0.0790035 | ||||||||
\(173\) | −584.054 | −0.256675 | −0.128338 | − | 0.991731i | \(-0.540964\pi\) | ||||
−0.128338 | + | 0.991731i | \(0.540964\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 234.644 | 0.101357 | ||||||||
\(176\) | −3135.88 | −1.34305 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 148.133 | 0.0623765 | ||||||||
\(179\) | 1253.49 | 0.523409 | 0.261704 | − | 0.965148i | \(-0.415715\pi\) | ||||
0.261704 | + | 0.965148i | \(0.415715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3426.69 | −1.40720 | −0.703601 | − | 0.710595i | \(-0.748426\pi\) | ||||
−0.703601 | + | 0.710595i | \(0.748426\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −246.315 | −0.0986881 | ||||||||
\(185\) | −3525.78 | −1.40119 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6952.21 | −2.71869 | ||||||||
\(188\) | 2267.99 | 0.879840 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −313.225 | −0.119598 | ||||||||
\(191\) | −3100.81 | −1.17470 | −0.587348 | − | 0.809335i | \(-0.699828\pi\) | ||||
−0.587348 | + | 0.809335i | \(0.699828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −338.564 | −0.126271 | −0.0631357 | − | 0.998005i | \(-0.520110\pi\) | ||||
−0.0631357 | + | 0.998005i | \(0.520110\pi\) | |||||||
\(194\) | 150.368 | 0.0556482 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2307.65 | 0.840979 | ||||||||
\(197\) | −1317.22 | −0.476387 | −0.238193 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238193 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3454.89 | 1.23071 | 0.615354 | − | 0.788251i | \(-0.289013\pi\) | ||||
0.615354 | + | 0.788251i | \(0.289013\pi\) | |||||||
\(200\) | −412.808 | −0.145950 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −631.154 | −0.219841 | ||||||||
\(203\) | −877.029 | −0.303228 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2495.15 | −0.850092 | ||||||||
\(206\) | 875.155 | 0.295995 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2916.27 | 0.965181 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2391.57 | 0.780295 | 0.390148 | − | 0.920752i | \(-0.372424\pi\) | ||||
0.390148 | + | 0.920752i | \(0.372424\pi\) | |||||||
\(212\) | −2949.89 | −0.955657 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1114.39 | −0.355971 | ||||||||
\(215\) | 219.711 | 0.0696937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −574.388 | −0.179687 | ||||||||
\(218\) | 1114.18 | 0.346156 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4140.15 | −1.26877 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1389.30 | −0.417194 | −0.208597 | − | 0.978002i | \(-0.566890\pi\) | ||||
−0.208597 | + | 0.978002i | \(0.566890\pi\) | |||||||
\(224\) | 734.076 | 0.218962 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1372.32 | −0.403919 | ||||||||
\(227\) | −4465.41 | −1.30564 | −0.652818 | − | 0.757514i | \(-0.726414\pi\) | ||||
−0.652818 | + | 0.757514i | \(0.726414\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3605.58 | −1.04045 | −0.520226 | − | 0.854029i | \(-0.674152\pi\) | ||||
−0.520226 | + | 0.854029i | \(0.674152\pi\) | |||||||
\(230\) | −147.248 | −0.0422141 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1542.95 | 0.436636 | ||||||||
\(233\) | 559.829 | 0.157406 | 0.0787031 | − | 0.996898i | \(-0.474922\pi\) | ||||
0.0787031 | + | 0.996898i | \(0.474922\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2796.10 | 0.776159 | ||||||||
\(236\) | 3846.70 | 1.06101 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 486.365 | 0.132464 | ||||||||
\(239\) | 3411.14 | 0.923215 | 0.461607 | − | 0.887084i | \(-0.347273\pi\) | ||||
0.461607 | + | 0.887084i | \(0.347273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6188.58 | −1.65411 | −0.827057 | − | 0.562119i | \(-0.809986\pi\) | ||||
−0.827057 | + | 0.562119i | \(0.809986\pi\) | |||||||
\(242\) | −1490.18 | −0.395836 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3921.51 | −1.02889 | ||||||||
\(245\) | 2844.99 | 0.741877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1010.52 | 0.258741 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1041.78 | −0.263551 | ||||||||
\(251\) | 6493.27 | 1.63288 | 0.816438 | − | 0.577434i | \(-0.195946\pi\) | ||||
0.816438 | + | 0.577434i | \(0.195946\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1370.95 | 0.340675 | ||||||||
\(254\) | 1347.28 | 0.332817 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1899.05 | 0.463635 | ||||||||
\(257\) | −7490.26 | −1.81801 | −0.909007 | − | 0.416780i | \(-0.863159\pi\) | ||||
−0.909007 | + | 0.416780i | \(0.863159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2296.50 | −0.550957 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1961.84 | 0.462608 | ||||||||
\(263\) | 4040.55 | 0.947342 | 0.473671 | − | 0.880702i | \(-0.342929\pi\) | ||||
0.473671 | + | 0.880702i | \(0.342929\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3636.79 | −0.843041 | ||||||||
\(266\) | −204.017 | −0.0470267 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3542.29 | −0.807387 | ||||||||
\(269\) | 7720.88 | 1.75000 | 0.875001 | − | 0.484121i | \(-0.160860\pi\) | ||||
0.875001 | + | 0.484121i | \(0.160860\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6584.34 | 1.47590 | 0.737952 | − | 0.674853i | \(-0.235793\pi\) | ||||
0.737952 | + | 0.674853i | \(0.235793\pi\) | |||||||
\(272\) | 6217.64 | 1.38603 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1215.59 | −0.268017 | ||||||||
\(275\) | 2297.62 | 0.503824 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3790.56 | 0.822213 | 0.411106 | − | 0.911587i | \(-0.365142\pi\) | ||||
0.411106 | + | 0.911587i | \(0.365142\pi\) | |||||||
\(278\) | 924.336 | 0.199417 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 597.324 | 0.127489 | ||||||||
\(281\) | 6408.89 | 1.36058 | 0.680288 | − | 0.732945i | \(-0.261855\pi\) | ||||
0.680288 | + | 0.732945i | \(0.261855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7328.79 | −1.53940 | −0.769702 | − | 0.638403i | \(-0.779595\pi\) | ||||
−0.769702 | + | 0.638403i | \(0.779595\pi\) | |||||||
\(284\) | −3513.72 | −0.734158 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1625.20 | −0.334261 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8871.42 | 1.80570 | ||||||||
\(290\) | 922.378 | 0.186772 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2365.96 | 0.474169 | ||||||||
\(293\) | 527.824 | 0.105242 | 0.0526209 | − | 0.998615i | \(-0.483243\pi\) | ||||
0.0526209 | + | 0.998615i | \(0.483243\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4742.42 | 0.935981 | ||||||||
\(296\) | 4040.22 | 0.793354 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −868.277 | −0.168785 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 143.108 | 0.0274039 | ||||||||
\(302\) | 2006.21 | 0.382266 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2608.14 | −0.492063 | ||||||||
\(305\) | −4834.66 | −0.907645 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −827.031 | −0.153750 | −0.0768749 | − | 0.997041i | \(-0.524494\pi\) | ||||
−0.0768749 | + | 0.997041i | \(0.524494\pi\) | |||||||
\(308\) | −2696.67 | −0.498886 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 604.088 | 0.110677 | ||||||||
\(311\) | −2022.53 | −0.368769 | −0.184384 | − | 0.982854i | \(-0.559029\pi\) | ||||
−0.184384 | + | 0.982854i | \(0.559029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6839.50 | −1.23512 | −0.617559 | − | 0.786525i | \(-0.711878\pi\) | ||||
−0.617559 | + | 0.786525i | \(0.711878\pi\) | |||||||
\(314\) | −1726.31 | −0.310260 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −360.825 | −0.0642342 | ||||||||
\(317\) | −7535.31 | −1.33510 | −0.667548 | − | 0.744567i | \(-0.732656\pi\) | ||||
−0.667548 | + | 0.744567i | \(0.732656\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8587.79 | −1.50728 | ||||||||
\(320\) | 3161.39 | 0.552273 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −95.9092 | −0.0165988 | ||||||||
\(323\) | −5782.21 | −0.996070 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2463.59 | 0.418545 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2859.21 | 0.481321 | ||||||||
\(329\) | 1821.23 | 0.305190 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7616.11 | −1.26471 | −0.632355 | − | 0.774678i | \(-0.717912\pi\) | ||||
−0.632355 | + | 0.774678i | \(0.717912\pi\) | |||||||
\(332\) | 2334.76 | 0.385953 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1362.21 | 0.223164 | ||||||||
\(335\) | −4367.13 | −0.712244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5959.66 | −0.963334 | −0.481667 | − | 0.876354i | \(-0.659968\pi\) | ||||
−0.481667 | + | 0.876354i | \(0.659968\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8208.84 | 1.30937 | ||||||||
\(341\) | −5624.36 | −0.893185 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3927.30 | 0.618234 | ||||||||
\(344\) | −251.768 | −0.0394605 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 400.092 | 0.0621649 | ||||||||
\(347\) | −9976.27 | −1.54338 | −0.771692 | − | 0.635997i | \(-0.780589\pi\) | ||||
−0.771692 | + | 0.635997i | \(0.780589\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5660.84 | 0.868246 | 0.434123 | − | 0.900854i | \(-0.357058\pi\) | ||||
0.434123 | + | 0.900854i | \(0.357058\pi\) | |||||||
\(350\) | −160.737 | −0.0245479 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7188.01 | 1.08841 | ||||||||
\(353\) | −682.431 | −0.102896 | −0.0514478 | − | 0.998676i | \(-0.516384\pi\) | ||||
−0.0514478 | + | 0.998676i | \(0.516384\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4331.91 | −0.647644 | ||||||||
\(356\) | 1628.48 | 0.242442 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −858.672 | −0.126766 | ||||||||
\(359\) | −8328.79 | −1.22445 | −0.612224 | − | 0.790685i | \(-0.709725\pi\) | ||||
−0.612224 | + | 0.790685i | \(0.709725\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4433.51 | −0.646379 | ||||||||
\(362\) | 2347.37 | 0.340815 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2916.89 | 0.418293 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 559.900 | 0.0796364 | 0.0398182 | − | 0.999207i | \(-0.487322\pi\) | ||||
0.0398182 | + | 0.999207i | \(0.487322\pi\) | |||||||
\(368\) | −1226.09 | −0.173681 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2415.25 | 0.339359 | ||||||||
\(371\) | −2368.80 | −0.331488 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 548.079 | 0.0760816 | 0.0380408 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380408 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(374\) | 4762.44 | 0.658449 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3204.07 | −0.439461 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4680.27 | −0.634325 | −0.317163 | − | 0.948371i | \(-0.602730\pi\) | ||||
−0.317163 | + | 0.948371i | \(0.602730\pi\) | |||||||
\(380\) | −3443.40 | −0.464849 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2124.13 | 0.284503 | ||||||||
\(383\) | 9174.13 | 1.22396 | 0.611979 | − | 0.790874i | \(-0.290374\pi\) | ||||
0.611979 | + | 0.790874i | \(0.290374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3324.60 | −0.440097 | ||||||||
\(386\) | 231.925 | 0.0305821 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1653.05 | 0.216291 | ||||||||
\(389\) | −346.645 | −0.0451816 | −0.0225908 | − | 0.999745i | \(-0.507191\pi\) | ||||
−0.0225908 | + | 0.999745i | \(0.507191\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2718.23 | −0.351578 | ||||||||
\(392\) | −3260.10 | −0.420050 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 902.331 | 0.115378 | ||||||||
\(395\) | −444.845 | −0.0566648 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −513.327 | −0.0648946 | −0.0324473 | − | 0.999473i | \(-0.510330\pi\) | ||||
−0.0324473 | + | 0.999473i | \(0.510330\pi\) | |||||||
\(398\) | −2366.69 | −0.298069 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2054.85 | −0.256856 | ||||||||
\(401\) | 11168.4 | 1.39083 | 0.695413 | − | 0.718610i | \(-0.255221\pi\) | ||||
0.695413 | + | 0.718610i | \(0.255221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −6938.52 | −0.854466 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 600.787 | 0.0734398 | ||||||||
\(407\) | −22487.2 | −2.73869 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4286.40 | −0.518212 | −0.259106 | − | 0.965849i | \(-0.583428\pi\) | ||||
−0.259106 | + | 0.965849i | \(0.583428\pi\) | |||||||
\(410\) | 1709.24 | 0.205886 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9620.91 | 1.15046 | ||||||||
\(413\) | 3088.96 | 0.368033 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2878.42 | 0.340472 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1997.72 | −0.233760 | ||||||||
\(419\) | 3822.03 | 0.445629 | 0.222814 | − | 0.974861i | \(-0.428476\pi\) | ||||
0.222814 | + | 0.974861i | \(0.428476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2751.33 | −0.318508 | −0.159254 | − | 0.987238i | \(-0.550909\pi\) | ||||
−0.159254 | + | 0.987238i | \(0.550909\pi\) | |||||||
\(422\) | −1638.28 | −0.188982 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4167.41 | 0.477329 | ||||||||
\(425\) | −4555.58 | −0.519948 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3149.03 | −0.356891 | ||||||||
\(428\) | −12250.9 | −1.38357 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −150.507 | −0.0168793 | ||||||||
\(431\) | 8079.52 | 0.902962 | 0.451481 | − | 0.892281i | \(-0.350896\pi\) | ||||
0.451481 | + | 0.892281i | \(0.350896\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3793.63 | 0.421040 | 0.210520 | − | 0.977590i | \(-0.432484\pi\) | ||||
0.210520 | + | 0.977590i | \(0.432484\pi\) | |||||||
\(434\) | 393.470 | 0.0435189 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12248.6 | 1.34542 | ||||||||
\(437\) | 1140.23 | 0.124816 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11525.0 | 1.25298 | 0.626491 | − | 0.779428i | \(-0.284490\pi\) | ||||
0.626491 | + | 0.779428i | \(0.284490\pi\) | |||||||
\(440\) | 5848.94 | 0.633721 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13127.4 | −1.40791 | −0.703954 | − | 0.710245i | \(-0.748584\pi\) | ||||
−0.703954 | + | 0.710245i | \(0.748584\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2007.68 | 0.213872 | ||||||||
\(446\) | 951.705 | 0.101042 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2059.16 | 0.217157 | ||||||||
\(449\) | −7763.80 | −0.816028 | −0.408014 | − | 0.912976i | \(-0.633779\pi\) | ||||
−0.408014 | + | 0.912976i | \(0.633779\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15913.9 | −1.66154 | ||||||||
\(452\) | −15086.5 | −1.56993 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3058.92 | 0.316216 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −291.436 | −0.0298311 | −0.0149156 | − | 0.999889i | \(-0.504748\pi\) | ||||
−0.0149156 | + | 0.999889i | \(0.504748\pi\) | |||||||
\(458\) | 2469.91 | 0.251990 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1618.75 | −0.164075 | ||||||||
\(461\) | 1612.08 | 0.162868 | 0.0814338 | − | 0.996679i | \(-0.474050\pi\) | ||||
0.0814338 | + | 0.996679i | \(0.474050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −916.747 | −0.0920191 | −0.0460095 | − | 0.998941i | \(-0.514650\pi\) | ||||
−0.0460095 | + | 0.998941i | \(0.514650\pi\) | |||||||
\(464\) | 7680.40 | 0.768435 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −383.497 | −0.0381227 | ||||||||
\(467\) | 3524.88 | 0.349277 | 0.174638 | − | 0.984633i | \(-0.444124\pi\) | ||||
0.174638 | + | 0.984633i | \(0.444124\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2844.51 | −0.280058 | ||||||||
\(470\) | −1915.40 | −0.187980 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5434.37 | −0.529952 | ||||||||
\(473\) | 1401.30 | 0.136219 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1910.95 | 0.184590 | ||||||||
\(476\) | 5346.79 | 0.514852 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2336.72 | −0.223596 | ||||||||
\(479\) | −12392.8 | −1.18213 | −0.591066 | − | 0.806623i | \(-0.701293\pi\) | ||||
−0.591066 | + | 0.806623i | \(0.701293\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 4239.33 | 0.400615 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16382.1 | −1.53851 | ||||||||
\(485\) | 2037.97 | 0.190803 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14186.4 | 1.32002 | 0.660009 | − | 0.751258i | \(-0.270552\pi\) | ||||
0.660009 | + | 0.751258i | \(0.270552\pi\) | |||||||
\(488\) | 5540.06 | 0.513907 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1948.89 | −0.179678 | ||||||||
\(491\) | 14559.4 | 1.33820 | 0.669101 | − | 0.743172i | \(-0.266680\pi\) | ||||
0.669101 | + | 0.743172i | \(0.266680\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17027.3 | 1.55552 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5030.09 | 0.455358 | ||||||||
\(497\) | −2821.57 | −0.254657 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8470.02 | 0.759860 | 0.379930 | − | 0.925015i | \(-0.375948\pi\) | ||||
0.379930 | + | 0.925015i | \(0.375948\pi\) | |||||||
\(500\) | −11452.6 | −1.02435 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4448.05 | −0.395471 | ||||||||
\(503\) | 7649.38 | 0.678070 | 0.339035 | − | 0.940774i | \(-0.389900\pi\) | ||||
0.339035 | + | 0.940774i | \(0.389900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8554.19 | −0.753775 | ||||||||
\(506\) | −939.134 | −0.0825091 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14811.1 | 1.29358 | ||||||||
\(509\) | −13019.8 | −1.13378 | −0.566889 | − | 0.823794i | \(-0.691853\pi\) | ||||
−0.566889 | + | 0.823794i | \(0.691853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1899.90 | 0.164475 | ||||||||
\(512\) | −10935.9 | −0.943948 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5131.02 | 0.440310 | ||||||||
\(515\) | 11861.2 | 1.01489 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17833.3 | 1.51704 | ||||||||
\(518\) | 1573.16 | 0.133438 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1003.37 | 0.0843734 | 0.0421867 | − | 0.999110i | \(-0.486568\pi\) | ||||
0.0421867 | + | 0.999110i | \(0.486568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4216.27 | −0.352514 | −0.176257 | − | 0.984344i | \(-0.556399\pi\) | ||||
−0.176257 | + | 0.984344i | \(0.556399\pi\) | |||||||
\(524\) | 21567.3 | 1.79804 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2767.88 | −0.229439 | ||||||||
\(527\) | 11151.6 | 0.921770 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11631.0 | −0.955944 | ||||||||
\(530\) | 2491.29 | 0.204179 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2242.84 | −0.182781 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15103.5 | −1.22053 | ||||||||
\(536\) | 5004.32 | 0.403272 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5289.00 | −0.423838 | ||||||||
\(539\) | 18145.1 | 1.45003 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23139.4 | 1.83889 | 0.919447 | − | 0.393213i | \(-0.128637\pi\) | ||||
0.919447 | + | 0.393213i | \(0.128637\pi\) | |||||||
\(542\) | −4510.44 | −0.357454 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −14251.9 | −1.12325 | ||||||||
\(545\) | 15100.8 | 1.18688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12532.9 | −0.979646 | −0.489823 | − | 0.871822i | \(-0.662939\pi\) | ||||
−0.489823 | + | 0.871822i | \(0.662939\pi\) | |||||||
\(548\) | −13363.5 | −1.04171 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1573.93 | −0.122023 | ||||||||
\(551\) | −7142.53 | −0.552236 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −289.748 | −0.0222809 | ||||||||
\(554\) | −2596.63 | −0.199134 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10161.6 | 0.775084 | ||||||||
\(557\) | −6240.38 | −0.474710 | −0.237355 | − | 0.971423i | \(-0.576280\pi\) | ||||
−0.237355 | + | 0.971423i | \(0.576280\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2973.32 | 0.224368 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4390.25 | −0.329522 | ||||||||
\(563\) | 6742.87 | 0.504756 | 0.252378 | − | 0.967629i | \(-0.418787\pi\) | ||||
0.252378 | + | 0.967629i | \(0.418787\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18599.4 | −1.38493 | ||||||||
\(566\) | 5020.41 | 0.372833 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4963.96 | 0.366695 | ||||||||
\(569\) | −2935.57 | −0.216283 | −0.108142 | − | 0.994135i | \(-0.534490\pi\) | ||||
−0.108142 | + | 0.994135i | \(0.534490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9709.50 | 0.711611 | 0.355805 | − | 0.934560i | \(-0.384207\pi\) | ||||
0.355805 | + | 0.934560i | \(0.384207\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1113.31 | 0.0809556 | ||||||||
\(575\) | 898.342 | 0.0651538 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18892.5 | 1.36309 | 0.681546 | − | 0.731775i | \(-0.261308\pi\) | ||||
0.681546 | + | 0.731775i | \(0.261308\pi\) | |||||||
\(578\) | −6077.14 | −0.437329 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10140.1 | 0.725936 | ||||||||
\(581\) | 1874.84 | 0.133875 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23195.1 | −1.64776 | ||||||||
\(584\) | −3342.48 | −0.236837 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −361.573 | −0.0254888 | ||||||||
\(587\) | 24642.6 | 1.73272 | 0.866362 | − | 0.499416i | \(-0.166452\pi\) | ||||
0.866362 | + | 0.499416i | \(0.166452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4677.82 | −0.327243 | ||||||||
\(590\) | −3248.68 | −0.226688 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 20111.2 | 1.39622 | ||||||||
\(593\) | −6433.11 | −0.445491 | −0.222745 | − | 0.974877i | \(-0.571502\pi\) | ||||
−0.222745 | + | 0.974877i | \(0.571502\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6591.82 | 0.454182 | ||||||||
\(596\) | −9545.30 | −0.656025 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19055.2 | 1.29979 | 0.649897 | − | 0.760023i | \(-0.274812\pi\) | ||||
0.649897 | + | 0.760023i | \(0.274812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20141.7 | −1.36705 | −0.683524 | − | 0.729928i | \(-0.739554\pi\) | ||||
−0.683524 | + | 0.729928i | \(0.739554\pi\) | |||||||
\(602\) | −98.0323 | −0.00663704 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22055.0 | 1.48577 | ||||||||
\(605\) | −20196.8 | −1.35722 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10627.2 | −0.710620 | −0.355310 | − | 0.934749i | \(-0.615625\pi\) | ||||
−0.355310 | + | 0.934749i | \(0.615625\pi\) | |||||||
\(608\) | 5978.32 | 0.398771 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3311.86 | 0.219825 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18460.9 | −1.21636 | −0.608181 | − | 0.793798i | \(-0.708101\pi\) | ||||
−0.608181 | + | 0.793798i | \(0.708101\pi\) | |||||||
\(614\) | 566.537 | 0.0372371 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3809.68 | 0.249182 | ||||||||
\(617\) | −21119.7 | −1.37804 | −0.689018 | − | 0.724744i | \(-0.741958\pi\) | ||||
−0.689018 | + | 0.724744i | \(0.741958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −571.628 | −0.0371174 | −0.0185587 | − | 0.999828i | \(-0.505908\pi\) | ||||
−0.0185587 | + | 0.999828i | \(0.505908\pi\) | |||||||
\(620\) | 6640.97 | 0.430174 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1385.48 | 0.0893132 | ||||||||
\(623\) | 1307.69 | 0.0840957 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9269.25 | −0.593232 | ||||||||
\(626\) | 4685.23 | 0.299137 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18978.0 | −1.20590 | ||||||||
\(629\) | 44586.2 | 2.82634 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7543.32 | 0.475903 | 0.237952 | − | 0.971277i | \(-0.423524\pi\) | ||||
0.237952 | + | 0.971277i | \(0.423524\pi\) | |||||||
\(632\) | 509.751 | 0.0320835 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5161.88 | 0.323351 | ||||||||
\(635\) | 18260.0 | 1.14114 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5882.85 | 0.365054 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11181.8 | −0.690621 | ||||||||
\(641\) | −6800.31 | −0.419027 | −0.209513 | − | 0.977806i | \(-0.567188\pi\) | ||||
−0.209513 | + | 0.977806i | \(0.567188\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11713.1 | −0.718380 | −0.359190 | − | 0.933265i | \(-0.616947\pi\) | ||||
−0.359190 | + | 0.933265i | \(0.616947\pi\) | |||||||
\(644\) | −1054.37 | −0.0645153 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3960.96 | 0.241241 | ||||||||
\(647\) | −12455.4 | −0.756835 | −0.378417 | − | 0.925635i | \(-0.623532\pi\) | ||||
−0.378417 | + | 0.925635i | \(0.623532\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30246.8 | 1.82941 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27083.2 | 1.62678 | ||||||||
\(653\) | −14073.0 | −0.843369 | −0.421685 | − | 0.906743i | \(-0.638561\pi\) | ||||
−0.421685 | + | 0.906743i | \(0.638561\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26589.4 | 1.58616 | ||||||||
\(656\) | 14232.4 | 0.847076 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1247.59 | −0.0739149 | ||||||||
\(659\) | 8037.27 | 0.475095 | 0.237548 | − | 0.971376i | \(-0.423656\pi\) | ||||
0.237548 | + | 0.971376i | \(0.423656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1994.71 | −0.117375 | −0.0586877 | − | 0.998276i | \(-0.518692\pi\) | ||||
−0.0586877 | + | 0.998276i | \(0.518692\pi\) | |||||||
\(662\) | 5217.23 | 0.306304 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3298.40 | −0.192775 | ||||||||
\(665\) | −2765.10 | −0.161242 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3357.73 | −0.194920 | ||||||||
\(668\) | 14975.3 | 0.867382 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2991.59 | 0.172500 | ||||||||
\(671\) | −30835.0 | −1.77403 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13886.1 | 0.795348 | 0.397674 | − | 0.917527i | \(-0.369817\pi\) | ||||
0.397674 | + | 0.917527i | \(0.369817\pi\) | |||||||
\(674\) | 4082.52 | 0.233313 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11024.0 | −0.625831 | −0.312915 | − | 0.949781i | \(-0.601306\pi\) | ||||
−0.312915 | + | 0.949781i | \(0.601306\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1327.42 | 0.0750247 | ||||||||
\(680\) | −11596.9 | −0.654002 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3852.83 | 0.216323 | ||||||||
\(683\) | −22696.5 | −1.27154 | −0.635768 | − | 0.771880i | \(-0.719317\pi\) | ||||
−0.635768 | + | 0.771880i | \(0.719317\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16475.2 | −0.918957 | ||||||||
\(686\) | −2690.30 | −0.149732 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1253.24 | −0.0694465 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3516.06 | 0.193570 | 0.0967852 | − | 0.995305i | \(-0.469144\pi\) | ||||
0.0967852 | + | 0.995305i | \(0.469144\pi\) | |||||||
\(692\) | 4398.36 | 0.241619 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6834.00 | 0.373797 | ||||||||
\(695\) | 12527.8 | 0.683748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31553.0 | 1.71471 | ||||||||
\(698\) | −3877.82 | −0.210283 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1767.05 | −0.0954115 | ||||||||
\(701\) | −26652.4 | −1.43602 | −0.718009 | − | 0.696034i | \(-0.754946\pi\) | ||||
−0.718009 | + | 0.696034i | \(0.754946\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18702.7 | −1.00340 | ||||||||
\(704\) | 20163.1 | 1.07944 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 467.482 | 0.0249206 | ||||||||
\(707\) | −5571.73 | −0.296388 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8938.91 | 0.473495 | 0.236747 | − | 0.971571i | \(-0.423919\pi\) | ||||
0.236747 | + | 0.971571i | \(0.423919\pi\) | |||||||
\(710\) | 2967.46 | 0.156855 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2300.61 | −0.121094 | ||||||||
\(713\) | −2199.06 | −0.115505 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9439.70 | −0.492707 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5705.43 | 0.296553 | ||||||||
\(719\) | 5294.09 | 0.274599 | 0.137299 | − | 0.990530i | \(-0.456158\pi\) | ||||
0.137299 | + | 0.990530i | \(0.456158\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7725.73 | 0.399059 | ||||||||
\(722\) | 3037.07 | 0.156548 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 25805.5 | 1.32466 | ||||||||
\(725\) | −5627.32 | −0.288267 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30010.0 | 1.53096 | 0.765480 | − | 0.643459i | \(-0.222501\pi\) | ||||
0.765480 | + | 0.643459i | \(0.222501\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1998.14 | −0.101308 | ||||||||
\(731\) | −2778.40 | −0.140579 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35185.8 | 1.77301 | 0.886505 | − | 0.462720i | \(-0.153126\pi\) | ||||
0.886505 | + | 0.462720i | \(0.153126\pi\) | |||||||
\(734\) | −383.546 | −0.0192874 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2810.43 | 0.140752 | ||||||||
\(737\) | −27853.2 | −1.39211 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16737.3 | 0.833140 | 0.416570 | − | 0.909104i | \(-0.363232\pi\) | ||||
0.416570 | + | 0.909104i | \(0.363232\pi\) | |||||||
\(740\) | 26551.8 | 1.31900 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1622.69 | 0.0802842 | ||||||||
\(743\) | −14564.0 | −0.719115 | −0.359558 | − | 0.933123i | \(-0.617072\pi\) | ||||
−0.359558 | + | 0.933123i | \(0.617072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11768.0 | −0.578718 | ||||||||
\(746\) | −375.448 | −0.0184264 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 52355.3 | 2.55922 | ||||||||
\(749\) | −9837.63 | −0.479919 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22935.6 | 1.11442 | 0.557212 | − | 0.830370i | \(-0.311871\pi\) | ||||
0.557212 | + | 0.830370i | \(0.311871\pi\) | |||||||
\(752\) | −15949.0 | −0.773406 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27190.6 | 1.31069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15356.3 | 0.737296 | 0.368648 | − | 0.929569i | \(-0.379821\pi\) | ||||
0.368648 | + | 0.929569i | \(0.379821\pi\) | |||||||
\(758\) | 3206.10 | 0.153629 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4864.61 | 0.232181 | ||||||||
\(761\) | 25838.1 | 1.23079 | 0.615394 | − | 0.788219i | \(-0.288997\pi\) | ||||
0.615394 | + | 0.788219i | \(0.288997\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9835.84 | 0.466686 | ||||||||
\(764\) | 23351.4 | 1.10579 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6284.51 | −0.296434 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11315.0 | 0.530597 | 0.265299 | − | 0.964166i | \(-0.414529\pi\) | ||||
0.265299 | + | 0.964166i | \(0.414529\pi\) | |||||||
\(770\) | 2277.44 | 0.106588 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2549.64 | 0.118865 | ||||||||
\(773\) | −1991.25 | −0.0926524 | −0.0463262 | − | 0.998926i | \(-0.514751\pi\) | ||||
−0.0463262 | + | 0.998926i | \(0.514751\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3685.47 | −0.170821 | ||||||||
\(776\) | −2335.32 | −0.108032 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 237.461 | 0.0109427 | ||||||||
\(779\) | −13235.7 | −0.608752 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27628.5 | −1.26585 | ||||||||
\(782\) | 1862.06 | 0.0851497 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16227.9 | −0.739246 | ||||||||
\(785\) | −23397.1 | −1.06380 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13262.7 | −0.600717 | −0.300359 | − | 0.953826i | \(-0.597106\pi\) | ||||
−0.300359 | + | 0.953826i | \(0.597106\pi\) | |||||||
\(788\) | 9919.66 | 0.448443 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 304.730 | 0.0137238 | ||||||||
\(791\) | −12114.7 | −0.544561 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 351.642 | 0.0157170 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26017.9 | −1.15852 | ||||||||
\(797\) | 36462.7 | 1.62055 | 0.810273 | − | 0.586052i | \(-0.199319\pi\) | ||||
0.810273 | + | 0.586052i | \(0.199319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35358.8 | −1.56559 | ||||||||
\(800\) | 4710.09 | 0.208158 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7650.61 | −0.336848 | ||||||||
\(803\) | 18603.7 | 0.817570 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1299.88 | −0.0569128 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9802.29 | 0.426786 | ||||||||
\(809\) | −2469.45 | −0.107319 | −0.0536596 | − | 0.998559i | \(-0.517089\pi\) | ||||
−0.0536596 | + | 0.998559i | \(0.517089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42081.3 | 1.82204 | 0.911019 | − | 0.412363i | \(-0.135297\pi\) | ||||
0.911019 | + | 0.412363i | \(0.135297\pi\) | |||||||
\(812\) | 6604.68 | 0.285442 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15404.3 | 0.663292 | ||||||||
\(815\) | 33389.6 | 1.43508 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1165.47 | 0.0499077 | ||||||||
\(818\) | 2936.29 | 0.125507 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18790.3 | 0.800228 | ||||||||
\(821\) | −43282.1 | −1.83990 | −0.919949 | − | 0.392038i | \(-0.871770\pi\) | ||||
−0.919949 | + | 0.392038i | \(0.871770\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38193.7 | −1.61768 | −0.808838 | − | 0.588031i | \(-0.799903\pi\) | ||||
−0.808838 | + | 0.588031i | \(0.799903\pi\) | |||||||
\(824\) | −13591.8 | −0.574628 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2116.01 | −0.0891350 | ||||||||
\(827\) | 35724.1 | 1.50211 | 0.751057 | − | 0.660238i | \(-0.229544\pi\) | ||||
0.751057 | + | 0.660238i | \(0.229544\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7345.94 | 0.307762 | 0.153881 | − | 0.988089i | \(-0.450823\pi\) | ||||
0.153881 | + | 0.988089i | \(0.450823\pi\) | |||||||
\(830\) | −1971.79 | −0.0824600 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35977.1 | −1.49644 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18462.3 | 0.765169 | ||||||||
\(836\) | −21961.7 | −0.908566 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2618.19 | −0.107928 | ||||||||
\(839\) | 11691.7 | 0.481100 | 0.240550 | − | 0.970637i | \(-0.422672\pi\) | ||||
0.240550 | + | 0.970637i | \(0.422672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3355.80 | −0.137595 | ||||||||
\(842\) | 1884.73 | 0.0771404 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18010.3 | −0.734525 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13155.1 | −0.533664 | ||||||||
\(848\) | 20744.3 | 0.840051 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3120.68 | 0.125928 | ||||||||
\(851\) | −8792.22 | −0.354164 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15321.4 | −0.615000 | −0.307500 | − | 0.951548i | \(-0.599492\pi\) | ||||
−0.307500 | + | 0.951548i | \(0.599492\pi\) | |||||||
\(854\) | 2157.17 | 0.0864364 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17307.2 | 0.691063 | ||||||||
\(857\) | −32949.6 | −1.31335 | −0.656673 | − | 0.754176i | \(-0.728037\pi\) | ||||
−0.656673 | + | 0.754176i | \(0.728037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8132.72 | −0.323032 | −0.161516 | − | 0.986870i | \(-0.551638\pi\) | ||||
−0.161516 | + | 0.986870i | \(0.551638\pi\) | |||||||
\(860\) | −1654.58 | −0.0656056 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5534.67 | −0.218691 | ||||||||
\(863\) | −25770.4 | −1.01649 | −0.508247 | − | 0.861212i | \(-0.669706\pi\) | ||||
−0.508247 | + | 0.861212i | \(0.669706\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5422.54 | 0.213147 | ||||||||
\(866\) | −2598.73 | −0.101973 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4325.57 | 0.169147 | ||||||||
\(869\) | −2837.19 | −0.110754 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −17304.1 | −0.672008 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −781.086 | −0.0302295 | ||||||||
\(875\) | −9196.64 | −0.355318 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31715.4 | −1.22116 | −0.610578 | − | 0.791956i | \(-0.709063\pi\) | ||||
−0.610578 | + | 0.791956i | \(0.709063\pi\) | |||||||
\(878\) | −7894.93 | −0.303464 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 29114.5 | 1.11528 | ||||||||
\(881\) | −29755.9 | −1.13791 | −0.568957 | − | 0.822367i | \(-0.692653\pi\) | ||||
−0.568957 | + | 0.822367i | \(0.692653\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41818.4 | 1.59377 | 0.796886 | − | 0.604129i | \(-0.206479\pi\) | ||||
0.796886 | + | 0.604129i | \(0.206479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8992.63 | 0.340986 | ||||||||
\(887\) | 6514.49 | 0.246601 | 0.123301 | − | 0.992369i | \(-0.460652\pi\) | ||||
0.123301 | + | 0.992369i | \(0.460652\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11893.5 | 0.448703 | ||||||||
\(890\) | −1375.31 | −0.0517984 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10462.5 | 0.392723 | ||||||||
\(893\) | 14832.1 | 0.555809 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11637.8 | −0.434646 | ||||||||
\(896\) | −7283.19 | −0.271556 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5318.40 | 0.197636 | ||||||||
\(899\) | 13775.2 | 0.511043 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45989.9 | 1.70049 | ||||||||
\(902\) | 10901.4 | 0.402413 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 21313.2 | 0.784145 | ||||||||
\(905\) | 31814.4 | 1.16856 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1750.33 | −0.0640780 | −0.0320390 | − | 0.999487i | \(-0.510200\pi\) | ||||
−0.0320390 | + | 0.999487i | \(0.510200\pi\) | |||||||
\(908\) | 33627.8 | 1.22905 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14268.9 | −0.518936 | −0.259468 | − | 0.965752i | \(-0.583547\pi\) | ||||
−0.259468 | + | 0.965752i | \(0.583547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18358.3 | 0.665467 | ||||||||
\(914\) | 199.641 | 0.00722489 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27152.7 | 0.979421 | ||||||||
\(917\) | 17318.9 | 0.623685 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19466.2 | −0.698729 | −0.349364 | − | 0.936987i | \(-0.613602\pi\) | ||||
−0.349364 | + | 0.936987i | \(0.613602\pi\) | |||||||
\(920\) | 2286.87 | 0.0819520 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1104.31 | −0.0394454 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14735.2 | −0.523772 | ||||||||
\(926\) | 627.995 | 0.0222864 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −17604.9 | −0.622745 | ||||||||
\(929\) | 866.279 | 0.0305939 | 0.0152969 | − | 0.999883i | \(-0.495131\pi\) | ||||
0.0152969 | + | 0.999883i | \(0.495131\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15091.5 | 0.531259 | ||||||||
\(932\) | −4215.93 | −0.148173 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2414.63 | −0.0845924 | ||||||||
\(935\) | 64546.5 | 2.25764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33092.8 | −1.15378 | −0.576891 | − | 0.816821i | \(-0.695734\pi\) | ||||
−0.576891 | + | 0.816821i | \(0.695734\pi\) | |||||||
\(938\) | 1948.56 | 0.0678281 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −21056.7 | −0.730632 | ||||||||
\(941\) | 27089.5 | 0.938461 | 0.469231 | − | 0.883076i | \(-0.344531\pi\) | ||||
0.469231 | + | 0.883076i | \(0.344531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6222.14 | −0.214868 | ||||||||
\(944\) | −27050.9 | −0.932661 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −959.923 | −0.0329913 | ||||||||
\(947\) | 45146.5 | 1.54917 | 0.774586 | − | 0.632469i | \(-0.217958\pi\) | ||||
0.774586 | + | 0.632469i | \(0.217958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1309.05 | −0.0447064 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7553.60 | −0.257157 | ||||||||
\(953\) | −32600.5 | −1.10812 | −0.554058 | − | 0.832478i | \(-0.686921\pi\) | ||||
−0.554058 | + | 0.832478i | \(0.686921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28788.9 | 0.975484 | ||||||||
\(956\) | −25688.4 | −0.869062 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8489.38 | 0.286304 | ||||||||
\(959\) | −10731.1 | −0.361339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20769.3 | −0.697167 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46604.6 | 1.55709 | ||||||||
\(965\) | 3143.34 | 0.104858 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13124.6 | −0.436462 | −0.218231 | − | 0.975897i | \(-0.570029\pi\) | ||||
−0.218231 | + | 0.975897i | \(0.570029\pi\) | |||||||
\(968\) | 23143.6 | 0.768454 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1396.06 | −0.0462111 | ||||||||
\(971\) | −7776.85 | −0.257025 | −0.128512 | − | 0.991708i | \(-0.541020\pi\) | ||||
−0.128512 | + | 0.991708i | \(0.541020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8159.90 | 0.268853 | ||||||||
\(974\) | −9718.07 | −0.319699 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27577.0 | 0.904425 | ||||||||
\(977\) | 25662.3 | 0.840339 | 0.420169 | − | 0.907446i | \(-0.361971\pi\) | ||||
0.420169 | + | 0.907446i | \(0.361971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12804.8 | 0.418022 | ||||||||
\(980\) | −21424.9 | −0.698361 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9973.56 | −0.324103 | ||||||||
\(983\) | −1747.89 | −0.0567132 | −0.0283566 | − | 0.999598i | \(-0.509027\pi\) | ||||
−0.0283566 | + | 0.999598i | \(0.509027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12229.5 | 0.395598 | ||||||||
\(986\) | −11664.2 | −0.376737 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 547.891 | 0.0176157 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14983.4 | −0.480286 | −0.240143 | − | 0.970738i | \(-0.577194\pi\) | ||||
−0.240143 | + | 0.970738i | \(0.577194\pi\) | |||||||
\(992\) | −11529.9 | −0.369026 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1932.85 | 0.0616762 | ||||||||
\(995\) | −32076.3 | −1.02200 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51834.8 | −1.64656 | −0.823282 | − | 0.567632i | \(-0.807860\pi\) | ||||
−0.823282 | + | 0.567632i | \(0.807860\pi\) | |||||||
\(998\) | −5802.18 | −0.184033 | ||||||||
\(999\) | 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 | 1521.4.a.bm.1.9 | ✓ | 18 | |
3.2 | odd | 2 | inner | 1521.4.a.bm.1.10 | yes | 18 | |
13.12 | even | 2 | 1521.4.a.bn.1.10 | yes | 18 | ||
39.38 | odd | 2 | 1521.4.a.bn.1.9 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.4.a.bm.1.9 | ✓ | 18 | 1.1 | even | 1 | trivial | |
1521.4.a.bm.1.10 | yes | 18 | 3.2 | odd | 2 | inner | |
1521.4.a.bn.1.9 | yes | 18 | 39.38 | odd | 2 | ||
1521.4.a.bn.1.10 | yes | 18 | 13.12 | even | 2 |