Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(1,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("624.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{43}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 312) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.55744\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.11488 | −0.636374 | −0.318187 | − | 0.948028i | \(-0.603074\pi\) | ||||
−0.318187 | + | 0.948028i | \(0.603074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.88512 | −0.479752 | −0.239876 | − | 0.970804i | \(-0.577107\pi\) | ||||
−0.239876 | + | 0.970804i | \(0.577107\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.0000 | −0.712663 | −0.356332 | − | 0.934360i | \(-0.615973\pi\) | ||||
−0.356332 | + | 0.934360i | \(0.615973\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 21.3446 | 0.367411 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.2298 | 0.231547 | 0.115773 | − | 0.993276i | \(-0.463065\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.5744 | −0.429543 | −0.214772 | − | 0.976664i | \(-0.568901\pi\) | ||||
−0.214772 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 26.6554 | 0.276985 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −153.379 | −1.39051 | −0.695253 | − | 0.718765i | \(-0.744708\pi\) | ||||
−0.695253 | + | 0.718765i | \(0.744708\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −74.3785 | −0.595028 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 223.379 | 1.43036 | 0.715178 | − | 0.698942i | \(-0.246345\pi\) | ||||
0.715178 | + | 0.698942i | \(0.246345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −126.723 | −0.734198 | −0.367099 | − | 0.930182i | \(-0.619649\pi\) | ||||
−0.367099 | + | 0.930182i | \(0.619649\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 78.0000 | 0.411456 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 63.2166 | 0.305301 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 217.608 | 0.966881 | 0.483440 | − | 0.875377i | \(-0.339387\pi\) | ||||
0.483440 | + | 0.875377i | \(0.339387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 105.804 | 0.403020 | 0.201510 | − | 0.979486i | \(-0.435415\pi\) | ||||
0.201510 | + | 0.979486i | \(0.435415\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 183.608 | 0.651163 | 0.325581 | − | 0.945514i | \(-0.394440\pi\) | ||||
0.325581 | + | 0.945514i | \(0.394440\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −64.0339 | −0.212125 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −96.6893 | −0.300076 | −0.150038 | − | 0.988680i | \(-0.547940\pi\) | ||||
−0.150038 | + | 0.988680i | \(0.547940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −264.055 | −0.769838 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −48.6893 | −0.133684 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 386.460 | 1.00159 | 0.500795 | − | 0.865566i | \(-0.333041\pi\) | ||||
0.500795 | + | 0.865566i | \(0.333041\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 184.987 | 0.453520 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 106.723 | 0.247997 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −34.5273 | −0.0761876 | −0.0380938 | − | 0.999274i | \(-0.512129\pi\) | ||||
−0.0380938 | + | 0.999274i | \(0.512129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 274.919 | 0.577045 | 0.288523 | − | 0.957473i | \(-0.406836\pi\) | ||||
0.288523 | + | 0.957473i | \(0.406836\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −79.9661 | −0.159917 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 92.4934 | 0.176498 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −93.9397 | −0.171292 | −0.0856460 | − | 0.996326i | \(-0.527295\pi\) | ||||
−0.0856460 | + | 0.996326i | \(0.527295\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 460.136 | 0.802809 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 741.812 | 1.23996 | 0.619978 | − | 0.784619i | \(-0.287142\pi\) | ||||
0.619978 | + | 0.784619i | \(0.287142\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 640.689 | 1.02722 | 0.513610 | − | 0.858024i | \(-0.328308\pi\) | ||||
0.513610 | + | 0.858024i | \(0.328308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 223.136 | 0.343540 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 231.013 | 0.341901 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 182.945 | 0.260544 | 0.130272 | − | 0.991478i | \(-0.458415\pi\) | ||||
0.130272 | + | 0.991478i | \(0.458415\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 288.825 | 0.381960 | 0.190980 | − | 0.981594i | \(-0.438834\pi\) | ||||
0.190980 | + | 0.981594i | \(0.438834\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −115.473 | −0.147350 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −670.136 | −0.825817 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 963.115 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 115.507 | 0.133059 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 380.169 | 0.423890 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 253.107 | 0.273350 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −481.932 | −0.504462 | −0.252231 | − | 0.967667i | \(-0.581164\pi\) | ||||
−0.252231 | + | 0.967667i | \(0.581164\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −234.000 | −0.237554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1138.85 | 1.12198 | 0.560990 | − | 0.827823i | \(-0.310421\pi\) | ||||
0.560990 | + | 0.827823i | \(0.310421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1090.96 | 1.04365 | 0.521823 | − | 0.853054i | \(-0.325252\pi\) | ||||
0.521823 | + | 0.853054i | \(0.325252\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −189.650 | −0.176266 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −124.595 | −0.112571 | −0.0562853 | − | 0.998415i | \(-0.517926\pi\) | ||||
−0.0562853 | + | 0.998415i | \(0.517926\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1400.89 | −1.23102 | −0.615510 | − | 0.788129i | \(-0.711050\pi\) | ||||
−0.615510 | + | 0.788129i | \(0.711050\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −652.825 | −0.558229 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −541.812 | −0.451056 | −0.225528 | − | 0.974237i | \(-0.572411\pi\) | ||||
−0.225528 | + | 0.974237i | \(0.572411\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1091.27 | 0.884882 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −144.203 | −0.111085 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −655.000 | −0.492111 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −317.412 | −0.232684 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1418.55 | 1.01503 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1552.07 | 1.08444 | 0.542219 | − | 0.840237i | \(-0.317584\pi\) | ||||
0.542219 | + | 0.840237i | \(0.317584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −550.825 | −0.375949 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2281.97 | 1.52196 | 0.760981 | − | 0.648774i | \(-0.224718\pi\) | ||||
0.760981 | + | 0.648774i | \(0.224718\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 316.083 | 0.206074 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 192.102 | 0.122470 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1443.06 | −0.899921 | −0.449960 | − | 0.893049i | \(-0.648562\pi\) | ||||
−0.449960 | + | 0.893049i | \(0.648562\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3060.41 | 1.86748 | 0.933742 | − | 0.357946i | \(-0.116523\pi\) | ||||
0.933742 | + | 0.357946i | \(0.116523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 290.068 | 0.173249 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 338.000 | 0.197657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1589.31 | −0.910242 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 792.164 | 0.444466 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 302.520 | 0.166331 | 0.0831657 | − | 0.996536i | \(-0.473497\pi\) | ||||
0.0831657 | + | 0.996536i | \(0.473497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −383.574 | −0.206721 | −0.103360 | − | 0.994644i | \(-0.532960\pi\) | ||||
−0.103360 | + | 0.994644i | \(0.532960\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 146.068 | 0.0771822 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 901.620 | 0.467225 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2583.38 | −1.31322 | −0.656612 | − | 0.754229i | \(-0.728011\pi\) | ||||
−0.656612 | + | 0.754229i | \(0.728011\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1159.38 | −0.578269 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1362.79 | 0.667097 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1303.45 | −0.626346 | −0.313173 | − | 0.949696i | \(-0.601392\pi\) | ||||
−0.313173 | + | 0.949696i | \(0.601392\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −554.960 | −0.261840 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1040.04 | −0.481921 | −0.240961 | − | 0.970535i | \(-0.577462\pi\) | ||||
−0.240961 | + | 0.970535i | \(0.577462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −320.169 | −0.143181 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2989.10 | 1.31362 | 0.656811 | − | 0.754055i | \(-0.271905\pi\) | ||||
0.656811 | + | 0.754055i | \(0.271905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 660.862 | 0.285466 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 103.582 | 0.0439870 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1786.06 | 0.745788 | 0.372894 | − | 0.927874i | \(-0.378365\pi\) | ||||
0.372894 | + | 0.927874i | \(0.378365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1320.84 | −0.542416 | −0.271208 | − | 0.962521i | \(-0.587423\pi\) | ||||
−0.271208 | + | 0.962521i | \(0.587423\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −824.757 | −0.333157 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1548.26 | −0.615298 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −421.974 | −0.165015 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 239.898 | 0.0923282 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 436.595 | 0.165397 | 0.0826987 | − | 0.996575i | \(-0.473646\pi\) | ||||
0.0826987 | + | 0.996575i | \(0.473646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2402.19 | −0.895924 | −0.447962 | − | 0.894053i | \(-0.647850\pi\) | ||||
−0.447962 | + | 0.894053i | \(0.647850\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −277.480 | −0.101901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1129.94 | 0.408654 | 0.204327 | − | 0.978903i | \(-0.434499\pi\) | ||||
0.204327 | + | 0.978903i | \(0.434499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1859.61 | −0.662433 | −0.331216 | − | 0.943555i | \(-0.607459\pi\) | ||||
−0.331216 | + | 0.943555i | \(0.607459\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 281.819 | 0.0988955 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1984.75 | −0.686216 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −752.783 | −0.256472 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1380.41 | −0.463502 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 924.934 | 0.306120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −859.729 | −0.280503 | −0.140252 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140252 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2225.43 | −0.715889 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1306.35 | −0.414383 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1125.95 | 0.352233 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1922.07 | −0.593065 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −210.987 | −0.0642195 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −265.345 | −0.0796807 | −0.0398403 | − | 0.999206i | \(-0.512685\pi\) | ||||
−0.0398403 | + | 0.999206i | \(0.512685\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −669.407 | −0.198343 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1519.43 | −0.444265 | −0.222133 | − | 0.975016i | \(-0.571302\pi\) | ||||
−0.222133 | + | 0.975016i | \(0.571302\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2069.00 | 0.597045 | 0.298522 | − | 0.954403i | \(-0.403506\pi\) | ||||
0.298522 | + | 0.954403i | \(0.403506\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −693.040 | −0.197397 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4624.94 | −1.30039 | −0.650193 | − | 0.759769i | \(-0.725312\pi\) | ||||
−0.650193 | + | 0.759769i | \(0.725312\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 687.932 | 0.190961 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −548.836 | −0.150425 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2098.35 | −0.567913 | −0.283957 | − | 0.958837i | \(-0.591647\pi\) | ||||
−0.283957 | + | 0.958837i | \(0.591647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1345.96 | −0.359755 | −0.179878 | − | 0.983689i | \(-0.557570\pi\) | ||||
−0.179878 | + | 0.983689i | \(0.557570\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1878.72 | 0.489905 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 462.467 | 0.119134 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −866.475 | −0.220524 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4117.24 | −1.03537 | −0.517685 | − | 0.855571i | \(-0.673206\pi\) | ||||
−0.517685 | + | 0.855571i | \(0.673206\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3987.84 | 0.990962 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 346.418 | 0.0850727 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3393.64 | 0.823694 | 0.411847 | − | 0.911253i | \(-0.364884\pi\) | ||||
0.411847 | + | 0.911253i | \(0.364884\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1933.48 | −0.463862 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2010.41 | 0.476786 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6335.19 | 1.48534 | 0.742671 | − | 0.669657i | \(-0.233559\pi\) | ||||
0.742671 | + | 0.669657i | \(0.233559\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2749.61 | −0.637386 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2889.34 | −0.662266 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 619.702 | 0.140461 | 0.0702303 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702303 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5165.75 | −1.15792 | −0.578961 | − | 0.815355i | \(-0.696542\pi\) | ||||
−0.578961 | + | 0.815355i | \(0.696542\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −346.520 | −0.0768217 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1933.84 | 0.424055 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3534.38 | 0.766643 | 0.383322 | − | 0.923615i | \(-0.374780\pi\) | ||||
0.383322 | + | 0.923615i | \(0.374780\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1140.51 | −0.244733 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4115.81 | 0.873767 | 0.436883 | − | 0.899518i | \(-0.356082\pi\) | ||||
0.436883 | + | 0.899518i | \(0.356082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3944.56 | −0.828550 | −0.414275 | − | 0.910152i | \(-0.635965\pi\) | ||||
−0.414275 | + | 0.910152i | \(0.635965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −759.322 | −0.157819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −940.083 | −0.193350 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4649.60 | −0.946386 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1445.80 | 0.291251 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 772.441 | 0.154015 | 0.0770076 | − | 0.997031i | \(-0.475463\pi\) | ||||
0.0770076 | + | 0.997031i | \(0.475463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 245.657 | 0.0484838 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 702.000 | 0.137152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1993.92 | 0.385657 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1631.38 | −0.312396 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3416.55 | −0.647775 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1956.01 | −0.367217 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4885.74 | −0.908286 | −0.454143 | − | 0.890929i | \(-0.650054\pi\) | ||||
−0.454143 | + | 0.890929i | \(0.650054\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3272.88 | −0.602549 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −177.544 | −0.0323717 | −0.0161859 | − | 0.999869i | \(-0.505152\pi\) | ||||
−0.0161859 | + | 0.999869i | \(0.505152\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6677.03 | −1.20578 | −0.602888 | − | 0.797826i | \(-0.705983\pi\) | ||||
−0.602888 | + | 0.797826i | \(0.705983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 568.949 | 0.101767 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1806.53 | 0.320079 | 0.160040 | − | 0.987111i | \(-0.448838\pi\) | ||||
0.160040 | + | 0.987111i | \(0.448838\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5807.84 | −1.01936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 373.785 | 0.0649927 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −577.364 | −0.0994593 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 966.921 | 0.165031 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4202.68 | 0.710730 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 859.096 | 0.143962 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11447.2 | −1.90088 | −0.950442 | − | 0.310901i | \(-0.899369\pi\) | ||||
−0.950442 | + | 0.310901i | \(0.899369\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1958.47 | 0.322294 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 668.370 | 0.109006 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −821.752 | −0.132830 | −0.0664149 | − | 0.997792i | \(-0.521156\pi\) | ||||
−0.0664149 | + | 0.997792i | \(0.521156\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1625.43 | 0.260417 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3294.80 | 0.523236 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5393.75 | 0.849083 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3273.81 | −0.510887 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4819.55 | 0.745611 | 0.372805 | − | 0.927910i | \(-0.378396\pi\) | ||||
0.372805 | + | 0.927910i | \(0.378396\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7922.72 | 1.21517 | 0.607584 | − | 0.794255i | \(-0.292139\pi\) | ||||
0.607584 | + | 0.794255i | \(0.292139\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2860.73 | −0.431336 | −0.215668 | − | 0.976467i | \(-0.569193\pi\) | ||||
−0.215668 | + | 0.976467i | \(0.569193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5277.90 | −0.789075 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 432.610 | 0.0641349 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11785.8 | 1.73267 | 0.866334 | − | 0.499464i | \(-0.166470\pi\) | ||||
0.866334 | + | 0.499464i | \(0.166470\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5593.46 | −0.815493 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1965.00 | 0.284121 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4558.43 | −0.653696 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2017.19 | −0.286911 | −0.143456 | − | 0.989657i | \(-0.545821\pi\) | ||||
−0.143456 | + | 0.989657i | \(0.545821\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 952.237 | 0.134340 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3433.74 | −0.480515 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5148.21 | 0.714650 | 0.357325 | − | 0.933980i | \(-0.383689\pi\) | ||||
0.357325 | + | 0.933980i | \(0.383689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4255.66 | −0.586030 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2903.92 | −0.396710 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3419.10 | 0.463397 | 0.231698 | − | 0.972788i | \(-0.425572\pi\) | ||||
0.231698 | + | 0.972788i | \(0.425572\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4656.20 | −0.626101 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5427.04 | 0.724044 | 0.362022 | − | 0.932170i | \(-0.382087\pi\) | ||||
0.362022 | + | 0.932170i | \(0.382087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1643.63 | −0.217577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1652.47 | 0.217054 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6843.88 | 0.892027 | 0.446014 | − | 0.895026i | \(-0.352843\pi\) | ||||
0.446014 | + | 0.895026i | \(0.352843\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2489.30 | −0.321967 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6845.92 | −0.878705 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1301.63 | −0.165803 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8382.62 | −1.05973 | −0.529863 | − | 0.848083i | \(-0.677757\pi\) | ||||
−0.529863 | + | 0.848083i | \(0.677757\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −948.248 | −0.118977 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3525.30 | 0.439015 | 0.219508 | − | 0.975611i | \(-0.429555\pi\) | ||||
0.219508 | + | 0.975611i | \(0.429555\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1647.40 | 0.203630 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −576.305 | −0.0707082 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5657.82 | −0.689060 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 940.772 | 0.113736 | 0.0568682 | − | 0.998382i | \(-0.481889\pi\) | ||||
0.0568682 | + | 0.998382i | \(0.481889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4329.19 | 0.519569 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 306.779 | 0.0365511 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2054.95 | −0.243069 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9181.22 | −1.07819 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −532.791 | −0.0621206 | −0.0310603 | − | 0.999518i | \(-0.509888\pi\) | ||||
−0.0310603 | + | 0.999518i | \(0.509888\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14425.3 | 1.66994 | 0.834970 | − | 0.550295i | \(-0.185485\pi\) | ||||
0.834970 | + | 0.550295i | \(0.185485\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −870.203 | −0.100025 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1207.15 | −0.137777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2442.69 | −0.276838 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1014.00 | −0.114117 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15224.9 | 1.70152 | 0.850762 | − | 0.525551i | \(-0.176141\pi\) | ||||
0.850762 | + | 0.525551i | \(0.176141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10115.5 | 1.12268 | 0.561338 | − | 0.827587i | \(-0.310287\pi\) | ||||
0.561338 | + | 0.827587i | \(0.310287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4767.93 | 0.525528 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5456.35 | 0.597283 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15925.0 | 1.73134 | 0.865669 | − | 0.500617i | \(-0.166894\pi\) | ||||
0.865669 | + | 0.500617i | \(0.166894\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2376.49 | −0.256613 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2387.09 | −0.256014 | −0.128007 | − | 0.991773i | \(-0.540858\pi\) | ||||
−0.128007 | + | 0.991773i | \(0.540858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6852.44 | −0.729971 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −907.559 | −0.0960315 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13985.3 | −1.46995 | −0.734973 | − | 0.678096i | \(-0.762805\pi\) | ||||
−0.734973 | + | 0.678096i | \(0.762805\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2750.91 | −0.287218 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1150.72 | 0.119350 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −821.815 | −0.0846754 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6520.34 | −0.667414 | −0.333707 | − | 0.942677i | \(-0.608300\pi\) | ||||
−0.333707 | + | 0.942677i | \(0.608300\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −438.203 | −0.0445612 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6543.86 | 0.661124 | 0.330562 | − | 0.943784i | \(-0.392762\pi\) | ||||
0.330562 | + | 0.943784i | \(0.392762\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13172.7 | −1.32221 | −0.661107 | − | 0.750292i | \(-0.729913\pi\) | ||||
−0.661107 | + | 0.750292i | \(0.729913\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2704.86 | −0.269752 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3166.27 | 0.313742 | 0.156871 | − | 0.987619i | \(-0.449859\pi\) | ||||
0.156871 | + | 0.987619i | \(0.449859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 834.666 | 0.0821776 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7750.14 | 0.758190 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4773.82 | −0.464060 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2645.97 | 0.255590 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3478.14 | 0.333863 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6470.71 | 0.617232 | 0.308616 | − | 0.951187i | \(-0.400134\pi\) | ||||
0.308616 | + | 0.951187i | \(0.400134\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2828.91 | −0.268164 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4088.36 | −0.385149 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3428.89 | 0.321026 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7620.36 | −0.709058 | −0.354529 | − | 0.935045i | \(-0.615359\pi\) | ||||
−0.354529 | + | 0.935045i | \(0.615359\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3910.36 | 0.361621 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14472.0 | 1.33017 | 0.665084 | − | 0.746769i | \(-0.268396\pi\) | ||||
0.665084 | + | 0.746769i | \(0.268396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3625.38 | 0.331194 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1664.88 | 0.151173 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6591.09 | −0.594871 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12338.1 | 1.10687 | 0.553436 | − | 0.832892i | \(-0.313316\pi\) | ||||
0.553436 | + | 0.832892i | \(0.313316\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3120.12 | 0.278237 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12491.1 | 1.10725 | 0.553627 | − | 0.832765i | \(-0.313243\pi\) | ||||
0.553627 | + | 0.832765i | \(0.313243\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8102.79 | −0.713999 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21986.9 | −1.91464 | −0.957318 | − | 0.289036i | \(-0.906665\pi\) | ||||
−0.957318 | + | 0.289036i | \(0.906665\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5692.60 | −0.492810 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 960.508 | 0.0826657 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7762.05 | −0.664149 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2513.92 | 0.213853 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8967.29 | −0.758421 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6385.80 | −0.536981 | −0.268491 | − | 0.963282i | \(-0.586525\pi\) | ||||
−0.268491 | + | 0.963282i | \(0.586525\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11858.5 | 0.991467 | 0.495733 | − | 0.868475i | \(-0.334899\pi\) | ||||
0.495733 | + | 0.868475i | \(0.334899\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1982.59 | −0.164814 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2056.69 | −0.170001 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11358.0 | 0.933506 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −310.746 | −0.0253959 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1375.45 | −0.111778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 886.479 | 0.0716370 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5358.17 | −0.430581 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6865.42 | 0.548636 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19726.4 | 1.56766 | 0.783829 | − | 0.620976i | \(-0.213264\pi\) | ||||
0.783829 | + | 0.620976i | \(0.213264\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3962.52 | 0.313164 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9967.18 | 0.783389 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9070.36 | 0.708996 | 0.354498 | − | 0.935057i | \(-0.384652\pi\) | ||||
0.354498 | + | 0.935057i | \(0.384652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2474.27 | 0.192348 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7946.55 | −0.614400 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1625.49 | −0.124996 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4644.77 | 0.355242 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21557.9 | 1.63992 | 0.819961 | − | 0.572419i | \(-0.193995\pi\) | ||||
0.819961 | + | 0.572419i | \(0.193995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2386.91 | −0.180600 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1265.92 | 0.0952713 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22899.8 | −1.71423 | −0.857113 | − | 0.515128i | \(-0.827745\pi\) | ||||
−0.857113 | + | 0.515128i | \(0.827745\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3854.92 | 0.287040 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −719.695 | −0.0533057 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14009.0 | −1.03214 | −0.516071 | − | 0.856546i | \(-0.672606\pi\) | ||||
−0.516071 | + | 0.856546i | \(0.672606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22800.2 | 1.67103 | 0.835517 | − | 0.549465i | \(-0.185168\pi\) | ||||
0.835517 | + | 0.549465i | \(0.185168\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1309.79 | −0.0954923 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11408.1 | 0.827390 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16722.7 | 1.20655 | 0.603273 | − | 0.797535i | \(-0.293863\pi\) | ||||
0.603273 | + | 0.797535i | \(0.293863\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7206.57 | 0.517262 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2566.24 | −0.183246 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10047.9 | −0.713797 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 832.441 | 0.0588328 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4728.47 | −0.332479 | −0.166239 | − | 0.986085i | \(-0.553162\pi\) | ||||
−0.166239 | + | 0.986085i | \(0.553162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4508.10 | 0.315370 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3389.82 | −0.235937 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15903.8 | 1.10133 | 0.550667 | − | 0.834725i | \(-0.314374\pi\) | ||||
0.550667 | + | 0.834725i | \(0.314374\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1025.99 | 0.0706915 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5578.82 | 0.382456 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7515.22 | 0.512627 | 0.256313 | − | 0.966594i | \(-0.417492\pi\) | ||||
0.256313 | + | 0.966594i | \(0.417492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26704.5 | 1.81247 | 0.906237 | − | 0.422769i | \(-0.138942\pi\) | ||||
0.906237 | + | 0.422769i | \(0.138942\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −845.457 | −0.0570973 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4660.24 | 0.313167 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1113.76 | 0.0744748 | 0.0372374 | − | 0.999306i | \(-0.488144\pi\) | ||||
0.0372374 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5954.24 | 0.396187 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1256.96 | 0.0832261 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12195.8 | −0.803559 | −0.401780 | − | 0.915736i | \(-0.631608\pi\) | ||||
−0.401780 | + | 0.915736i | \(0.631608\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2258.35 | 0.148074 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −447.009 | −0.0291668 | −0.0145834 | − | 0.999894i | \(-0.504642\pi\) | ||||
−0.0145834 | + | 0.999894i | \(0.504642\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22476.3 | 1.45945 | 0.729725 | − | 0.683740i | \(-0.239648\pi\) | ||||
0.729725 | + | 0.683740i | \(0.239648\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4141.22 | 0.267603 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8557.39 | −0.550313 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −795.520 | −0.0509132 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2774.80 | −0.176738 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3531.73 | 0.223878 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7165.04 | 0.452037 | 0.226019 | − | 0.974123i | \(-0.427429\pi\) | ||||
0.226019 | + | 0.974123i | \(0.427429\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2579.19 | 0.161949 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11042.8 | −0.690109 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3432.71 | 0.213515 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6676.30 | 0.413319 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12463.4 | 0.767980 | 0.383990 | − | 0.923337i | \(-0.374550\pi\) | ||||
0.383990 | + | 0.923337i | \(0.374550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11009.8 | −0.675249 | −0.337625 | − | 0.941281i | \(-0.609623\pi\) | ||||
−0.337625 | + | 0.941281i | \(0.609623\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3919.05 | 0.239244 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30825.9 | 1.87309 | 0.936547 | − | 0.350541i | \(-0.114002\pi\) | ||||
0.936547 | + | 0.350541i | \(0.114002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 897.710 | 0.0542961 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3377.85 | −0.203362 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15675.9 | 0.939426 | 0.469713 | − | 0.882819i | \(-0.344357\pi\) | ||||
0.469713 | + | 0.882819i | \(0.344357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16236.0 | −0.968537 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5766.20 | 0.342406 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22568.8 | −1.33408 | −0.667038 | − | 0.745024i | \(-0.732438\pi\) | ||||
−0.667038 | + | 0.745024i | \(0.732438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31243.5 | 1.83847 | 0.919237 | − | 0.393705i | \(-0.128807\pi\) | ||||
0.919237 | + | 0.393705i | \(0.128807\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 632.960 | 0.0370771 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2248.89 | −0.131140 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34261.5 | −1.98892 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 796.034 | 0.0460037 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7147.89 | −0.411239 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19818.1 | −1.13511 | −0.567556 | − | 0.823335i | \(-0.692111\pi\) | ||||
−0.567556 | + | 0.823335i | \(0.692111\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2008.22 | 0.114513 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3421.40 | 0.194232 | 0.0971159 | − | 0.995273i | \(-0.469038\pi\) | ||||
0.0971159 | + | 0.995273i | \(0.469038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4282.03 | 0.242016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4558.29 | 0.256497 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11002.1 | −0.616373 | −0.308186 | − | 0.951326i | \(-0.599722\pi\) | ||||
−0.308186 | + | 0.951326i | \(0.599722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10267.2 | 0.572686 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6206.99 | −0.344704 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5023.97 | −0.277791 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9817.44 | 0.540482 | 0.270241 | − | 0.962793i | \(-0.412897\pi\) | ||||
0.270241 | + | 0.962793i | \(0.412897\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2079.12 | 0.113967 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21774.4 | −1.18842 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1717.18 | 0.0933180 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13874.8 | 0.750778 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5776.14 | −0.311215 | −0.155608 | − | 0.987819i | \(-0.549734\pi\) | ||||
−0.155608 | + | 0.987819i | \(0.549734\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7741.28 | −0.415317 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2063.80 | −0.110251 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10118.8 | −0.538271 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35654.9 | −1.88864 | −0.944322 | − | 0.329022i | \(-0.893281\pi\) | ||||
−0.944322 | + | 0.329022i | \(0.893281\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1646.51 | 0.0868480 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19436.6 | 1.02091 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2404.83 | −0.125784 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6295.06 | 0.327885 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14353.1 | −0.744478 | −0.372239 | − | 0.928137i | \(-0.621410\pi\) | ||||
−0.372239 | + | 0.928137i | \(0.621410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9693.32 | −0.500691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4037.89 | 0.207705 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16614.6 | −0.851103 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28167.8 | 1.43698 | 0.718491 | − | 0.695536i | \(-0.244833\pi\) | ||||
0.718491 | + | 0.695536i | \(0.244833\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2979.92 | 0.150775 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23945.2 | −1.20660 | −0.603299 | − | 0.797515i | \(-0.706147\pi\) | ||||
−0.603299 | + | 0.797515i | \(0.706147\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5636.15 | −0.282847 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2442.43 | 0.122073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4021.49 | 0.200180 | 0.100090 | − | 0.994978i | \(-0.468087\pi\) | ||||
0.100090 | + | 0.994978i | \(0.468087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1387.40 | −0.0687820 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13584.9 | −0.670770 | −0.335385 | − | 0.942081i | \(-0.608866\pi\) | ||||
−0.335385 | + | 0.942081i | \(0.608866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2152.39 | −0.105849 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2599.42 | 0.127320 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1107.04 | 0.0540060 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3537.89 | −0.171903 | −0.0859517 | − | 0.996299i | \(-0.527393\pi\) | ||||
−0.0859517 | + | 0.996299i | \(0.527393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12351.7 | 0.597772 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2729.08 | 0.131552 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4421.46 | −0.212286 | −0.106143 | − | 0.994351i | \(-0.533850\pi\) | ||||
−0.106143 | + | 0.994351i | \(0.533850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11963.5 | −0.572132 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1093.63 | 0.0520947 | 0.0260473 | − | 0.999661i | \(-0.491708\pi\) | ||||
0.0260473 | + | 0.999661i | \(0.491708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12447.1 | 0.590584 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1039.25 | −0.0491168 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 448.855 | 0.0211307 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15814.2 | −0.741580 | −0.370790 | − | 0.928717i | \(-0.620913\pi\) | ||||
−0.370790 | + | 0.928717i | \(0.620913\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10180.9 | −0.475560 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37380.8 | −1.73932 | −0.869659 | − | 0.493653i | \(-0.835661\pi\) | ||||
−0.869659 | + | 0.493653i | \(0.835661\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9425.48 | 0.436869 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5800.43 | 0.267811 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3763.92 | −0.173115 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19287.1 | −0.883671 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6031.22 | −0.275272 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18380.4 | 0.835701 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1979.23 | −0.0896469 | −0.0448234 | − | 0.998995i | \(-0.514273\pi\) | ||||
−0.0448234 | + | 0.998995i | \(0.514273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19005.6 | −0.857562 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4814.06 | 0.216395 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3573.95 | −0.160044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8248.84 | 0.367995 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23575.5 | −1.04779 | −0.523894 | − | 0.851783i | \(-0.675521\pi\) | ||||
−0.523894 | + | 0.851783i | \(0.675521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1569.24 | −0.0694816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8668.03 | 0.382359 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16657.9 | −0.732061 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9696.06 | −0.424523 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1859.11 | −0.0810950 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39145.7 | −1.70122 | −0.850611 | − | 0.525796i | \(-0.823768\pi\) | ||||
−0.850611 | + | 0.525796i | \(0.823768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39342.9 | 1.70347 | 0.851735 | − | 0.523973i | \(-0.175551\pi\) | ||||
0.851735 | + | 0.523973i | \(0.175551\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15497.3 | 0.668527 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9273.91 | 0.398590 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6531.75 | −0.279703 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1039.56 | 0.0443530 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 216.569 | 0.00920622 | 0.00460311 | − | 0.999989i | \(-0.498535\pi\) | ||||
0.00460311 | + | 0.999989i | \(0.498535\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −45061.7 | −1.90857 | −0.954284 | − | 0.298901i | \(-0.903380\pi\) | ||||
−0.954284 | + | 0.298901i | \(0.903380\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5801.52 | −0.244828 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1228.67 | −0.0516625 | −0.0258313 | − | 0.999666i | \(-0.508223\pi\) | ||||
−0.0258313 | + | 0.999666i | \(0.508223\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29560.3 | −1.23845 | −0.619224 | − | 0.785215i | \(-0.712553\pi\) | ||||
−0.619224 | + | 0.785215i | \(0.712553\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10603.1 | −0.442622 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4285.54 | −0.178254 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7399.77 | 0.306682 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3421.53 | 0.141297 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23680.0 | −0.974402 | −0.487201 | − | 0.873290i | \(-0.661982\pi\) | ||||
−0.487201 | + | 0.873290i | \(0.661982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25509.0 | 1.04592 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12347.4 | −0.504470 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1202.41 | −0.0489518 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5819.76 | 0.236091 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11833.7 | 0.478363 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33376.4 | −1.34445 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15779.1 | 0.633374 | 0.316687 | − | 0.948530i | \(-0.397430\pi\) | ||||
0.316687 | + | 0.948530i | \(0.397430\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2277.97 | 0.0911167 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6759.13 | −0.269414 | −0.134707 | − | 0.990886i | \(-0.543009\pi\) | ||||
−0.134707 | + | 0.990886i | \(0.543009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20653.1 | 0.820344 | 0.410172 | − | 0.912008i | \(-0.365469\pi\) | ||||
0.410172 | + | 0.912008i | \(0.365469\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2820.25 | 0.111630 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6087.19 | −0.240105 | −0.120052 | − | 0.992768i | \(-0.538306\pi\) | ||||
−0.120052 | + | 0.992768i | \(0.538306\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21267.1 | −0.835955 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13948.8 | 0.546396 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4756.58 | −0.185680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1221.22 | 0.0475078 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4337.39 | −0.168154 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12604.0 | −0.486964 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6841.87 | −0.263436 | −0.131718 | − | 0.991287i | \(-0.542049\pi\) | ||||
−0.131718 | + | 0.991287i | \(0.542049\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2317.32 | −0.0889207 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9416.61 | 0.360106 | 0.180053 | − | 0.983657i | \(-0.442373\pi\) | ||||
0.180053 | + | 0.983657i | \(0.442373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21561.3 | 0.821740 | 0.410870 | − | 0.911694i | \(-0.365225\pi\) | ||||
0.410870 | + | 0.911694i | \(0.365225\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −736.972 | −0.0279922 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25672.9 | 0.971828 | 0.485914 | − | 0.874007i | \(-0.338487\pi\) | ||||
0.485914 | + | 0.874007i | \(0.338487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13790.3 | −0.520261 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2106.00 | −0.0791848 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3439.66 | 0.128896 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12707.6 | −0.474600 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5981.76 | −0.222659 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28307.2 | −1.05017 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6272.14 | 0.231915 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4894.15 | 0.180362 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9397.61 | 0.345179 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17612.3 | 0.644770 | 0.322385 | − | 0.946609i | \(-0.395515\pi\) | ||||
0.322385 | + | 0.946609i | \(0.395515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10249.7 | 0.373993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8830.95 | 0.321166 | 0.160583 | − | 0.987022i | \(-0.448663\pi\) | ||||
0.160583 | + | 0.987022i | \(0.448663\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7509.45 | −0.272209 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5868.04 | 0.212013 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20275.6 | −0.730163 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30983.7 | 1.11214 | 0.556071 | − | 0.831135i | \(-0.312308\pi\) | ||||
0.556071 | + | 0.831135i | \(0.312308\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14657.2 | 0.524399 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9643.55 | −0.343902 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16185.4 | −0.575321 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9818.64 | 0.347882 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15131.2 | −0.534378 | −0.267189 | − | 0.963644i | \(-0.586095\pi\) | ||||
−0.267189 | + | 0.963644i | \(0.586095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9393.58 | 0.330679 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 532.632 | 0.0186898 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3002.29 | 0.105011 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40264.3 | 1.40382 | 0.701909 | − | 0.712267i | \(-0.252331\pi\) | ||||
0.701909 | + | 0.712267i | \(0.252331\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20031.1 | 0.696155 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36254.5 | −1.25597 | −0.627983 | − | 0.778227i | \(-0.716119\pi\) | ||||
−0.627983 | + | 0.778227i | \(0.716119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16228.1 | −0.560402 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1706.85 | −0.0587553 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47707.4 | −1.63705 | −0.818524 | − | 0.574473i | \(-0.805207\pi\) | ||||
−0.818524 | + | 0.574473i | \(0.805207\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8328.96 | −0.284899 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5419.60 | −0.184798 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28934.4 | −0.983502 | −0.491751 | − | 0.870736i | \(-0.663643\pi\) | ||||
−0.491751 | + | 0.870736i | \(0.663643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3106.32 | −0.105255 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 17423.5 | 0.588529 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12821.8 | 0.431738 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13732.2 | −0.460953 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1121.36 | −0.0375236 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17091.3 | 0.570143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9108.15 | −0.302894 | −0.151447 | − | 0.988465i | \(-0.548393\pi\) | ||||
−0.151447 | + | 0.988465i | \(0.548393\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1732.09 | 0.0574229 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34912.3 | 1.15385 | 0.576925 | − | 0.816797i | \(-0.304252\pi\) | ||||
0.576925 | + | 0.816797i | \(0.304252\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27192.1 | −0.895928 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2900.76 | −0.0952808 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41510.7 | −1.35931 | −0.679655 | − | 0.733532i | \(-0.737870\pi\) | ||||
−0.679655 | + | 0.733532i | \(0.737870\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25041.0 | −0.817480 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12608.0 | −0.410340 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18673.8 | 0.605901 | 0.302950 | − | 0.953006i | \(-0.402028\pi\) | ||||
0.302950 | + | 0.953006i | \(0.402028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8039.38 | −0.260057 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2577.29 | −0.0831165 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28161.6 | −0.905446 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5954.58 | 0.190871 | 0.0954356 | − | 0.995436i | \(-0.469576\pi\) | ||||
0.0954356 | + | 0.995436i | \(0.469576\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34341.5 | 1.09748 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13230.9 | 0.421555 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8918.13 | −0.283290 | −0.141645 | − | 0.989918i | \(-0.545239\pi\) | ||||
−0.141645 | + | 0.989918i | \(0.545239\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5875.42 | −0.186076 |
(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 | 624.4.a.l.1.1 | 2 | ||
3.2 | odd | 2 | 1872.4.a.v.1.2 | 2 | |||
4.3 | odd | 2 | 312.4.a.f.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 2496.4.a.u.1.2 | 2 | |||
8.5 | even | 2 | 2496.4.a.bd.1.2 | 2 | |||
12.11 | even | 2 | 936.4.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.4.a.f.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
624.4.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
936.4.a.c.1.2 | 2 | 12.11 | even | 2 | |||
1872.4.a.v.1.2 | 2 | 3.2 | odd | 2 | |||
2496.4.a.u.1.2 | 2 | 8.3 | odd | 2 | |||
2496.4.a.bd.1.2 | 2 | 8.5 | even | 2 |