Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 32x^{2} - 35x + 120 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 175) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(5.87199\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.87199 | 1.72251 | 0.861254 | − | 0.508175i | \(-0.169680\pi\) | ||||
0.861254 | + | 0.508175i | \(0.169680\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.7363 | 1.96703 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 37.6910 | 1.66572 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −36.9922 | −1.01396 | −0.506980 | − | 0.861958i | \(-0.669238\pi\) | ||||
−0.506980 | + | 0.861958i | \(0.669238\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.3165 | −1.30817 | −0.654083 | − | 0.756423i | \(-0.726945\pi\) | ||||
−0.654083 | + | 0.756423i | \(0.726945\pi\) | |||||||
\(14\) | 34.1039 | 0.651047 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 57.7401 | 0.902189 | ||||||||
\(17\) | 44.8345 | 0.639646 | 0.319823 | − | 0.947477i | \(-0.396377\pi\) | ||||
0.319823 | + | 0.947477i | \(0.396377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −139.701 | −1.68682 | −0.843408 | − | 0.537273i | \(-0.819455\pi\) | ||||
−0.843408 | + | 0.537273i | \(0.819455\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −180.226 | −1.74656 | ||||||||
\(23\) | −217.580 | −1.97255 | −0.986275 | − | 0.165110i | \(-0.947202\pi\) | ||||
−0.986275 | + | 0.165110i | \(0.947202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −298.733 | −2.25333 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 110.154 | 0.743469 | ||||||||
\(29\) | 33.8226 | 0.216576 | 0.108288 | − | 0.994120i | \(-0.465463\pi\) | ||||
0.108288 | + | 0.994120i | \(0.465463\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 124.437 | 0.720952 | 0.360476 | − | 0.932769i | \(-0.382614\pi\) | ||||
0.360476 | + | 0.932769i | \(0.382614\pi\) | |||||||
\(32\) | −20.2192 | −0.111697 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 218.433 | 1.10179 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 237.270 | 1.05424 | 0.527121 | − | 0.849790i | \(-0.323271\pi\) | ||||
0.527121 | + | 0.849790i | \(0.323271\pi\) | |||||||
\(38\) | −680.620 | −2.90556 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −195.117 | −0.743224 | −0.371612 | − | 0.928388i | \(-0.621195\pi\) | ||||
−0.371612 | + | 0.928388i | \(0.621195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −343.725 | −1.21901 | −0.609506 | − | 0.792781i | \(-0.708632\pi\) | ||||
−0.609506 | + | 0.792781i | \(0.708632\pi\) | |||||||
\(44\) | −582.119 | −1.99450 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1060.05 | −3.39773 | ||||||||
\(47\) | −16.8224 | −0.0522085 | −0.0261042 | − | 0.999659i | \(-0.508310\pi\) | ||||
−0.0261042 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −964.894 | −2.57321 | ||||||||
\(53\) | −346.965 | −0.899231 | −0.449616 | − | 0.893222i | \(-0.648439\pi\) | ||||
−0.449616 | + | 0.893222i | \(0.648439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 263.837 | 0.629584 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 164.783 | 0.373054 | ||||||||
\(59\) | −135.340 | −0.298640 | −0.149320 | − | 0.988789i | \(-0.547708\pi\) | ||||
−0.149320 | + | 0.988789i | \(0.547708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 490.414 | 1.02936 | 0.514681 | − | 0.857382i | \(-0.327911\pi\) | ||||
0.514681 | + | 0.857382i | \(0.327911\pi\) | |||||||
\(62\) | 606.255 | 1.24185 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −560.428 | −1.09459 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 477.969 | 0.871540 | 0.435770 | − | 0.900058i | \(-0.356476\pi\) | ||||
0.435770 | + | 0.900058i | \(0.356476\pi\) | |||||||
\(68\) | 705.529 | 1.25820 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45.2557 | −0.0756460 | −0.0378230 | − | 0.999284i | \(-0.512042\pi\) | ||||
−0.0378230 | + | 0.999284i | \(0.512042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 100.781 | 0.161583 | 0.0807913 | − | 0.996731i | \(-0.474255\pi\) | ||||
0.0807913 | + | 0.996731i | \(0.474255\pi\) | |||||||
\(74\) | 1155.98 | 1.81594 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2198.37 | −3.31803 | ||||||||
\(77\) | −258.945 | −0.383241 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 880.534 | 1.25402 | 0.627012 | − | 0.779010i | \(-0.284278\pi\) | ||||
0.627012 | + | 0.779010i | \(0.284278\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −950.609 | −1.28021 | ||||||||
\(83\) | 1155.03 | 1.52748 | 0.763739 | − | 0.645525i | \(-0.223362\pi\) | ||||
0.763739 | + | 0.645525i | \(0.223362\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1674.62 | −2.09976 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1394.27 | −1.68898 | ||||||||
\(89\) | −619.374 | −0.737680 | −0.368840 | − | 0.929493i | \(-0.620245\pi\) | ||||
−0.368840 | + | 0.929493i | \(0.620245\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −429.216 | −0.494440 | ||||||||
\(92\) | −3423.90 | −3.88007 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −81.9585 | −0.0899295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −231.195 | −0.242003 | −0.121001 | − | 0.992652i | \(-0.538611\pi\) | ||||
−0.121001 | + | 0.992652i | \(0.538611\pi\) | |||||||
\(98\) | 238.727 | 0.246073 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1875.99 | −1.84820 | −0.924101 | − | 0.382149i | \(-0.875184\pi\) | ||||
−0.924101 | + | 0.382149i | \(0.875184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1855.94 | 1.77545 | 0.887723 | − | 0.460377i | \(-0.152286\pi\) | ||||
0.887723 | + | 0.460377i | \(0.152286\pi\) | |||||||
\(104\) | −2311.08 | −2.17904 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1690.41 | −1.54893 | ||||||||
\(107\) | 218.016 | 0.196976 | 0.0984879 | − | 0.995138i | \(-0.468599\pi\) | ||||
0.0984879 | + | 0.995138i | \(0.468599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 847.217 | 0.744484 | 0.372242 | − | 0.928136i | \(-0.378589\pi\) | ||||
0.372242 | + | 0.928136i | \(0.378589\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 404.181 | 0.340995 | ||||||||
\(113\) | −1430.05 | −1.19051 | −0.595254 | − | 0.803537i | \(-0.702949\pi\) | ||||
−0.595254 | + | 0.803537i | \(0.702949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 532.242 | 0.426012 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −659.374 | −0.514409 | ||||||||
\(119\) | 313.842 | 0.241763 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 37.4229 | 0.0281164 | ||||||||
\(122\) | 2389.29 | 1.77308 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1958.17 | 1.41814 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1732.84 | −1.21075 | −0.605374 | − | 0.795941i | \(-0.706976\pi\) | ||||
−0.605374 | + | 0.795941i | \(0.706976\pi\) | |||||||
\(128\) | −2568.65 | −1.77374 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2429.76 | 1.62052 | 0.810262 | − | 0.586068i | \(-0.199325\pi\) | ||||
0.810262 | + | 0.586068i | \(0.199325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −977.904 | −0.637557 | ||||||||
\(134\) | 2328.66 | 1.50123 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1689.86 | 1.06547 | ||||||||
\(137\) | −1452.84 | −0.906018 | −0.453009 | − | 0.891506i | \(-0.649649\pi\) | ||||
−0.453009 | + | 0.891506i | \(0.649649\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2927.47 | 1.78637 | 0.893183 | − | 0.449693i | \(-0.148467\pi\) | ||||
0.893183 | + | 0.449693i | \(0.148467\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −220.485 | −0.130301 | ||||||||
\(143\) | 2268.23 | 1.32643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 491.004 | 0.278327 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3733.75 | 2.07373 | ||||||||
\(149\) | −901.724 | −0.495786 | −0.247893 | − | 0.968787i | \(-0.579738\pi\) | ||||
−0.247893 | + | 0.968787i | \(0.579738\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1357.63 | −0.731669 | −0.365834 | − | 0.930680i | \(-0.619216\pi\) | ||||
−0.365834 | + | 0.930680i | \(0.619216\pi\) | |||||||
\(152\) | −5265.46 | −2.80977 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1261.58 | −0.660136 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2318.72 | −1.17869 | −0.589343 | − | 0.807883i | \(-0.700613\pi\) | ||||
−0.589343 | + | 0.807883i | \(0.700613\pi\) | |||||||
\(158\) | 4289.95 | 2.16006 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1523.06 | −0.745554 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1577.42 | −0.757996 | −0.378998 | − | 0.925397i | \(-0.623731\pi\) | ||||
−0.378998 | + | 0.925397i | \(0.623731\pi\) | |||||||
\(164\) | −3070.42 | −1.46195 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5627.28 | 2.63109 | ||||||||
\(167\) | −1038.02 | −0.480982 | −0.240491 | − | 0.970651i | \(-0.577309\pi\) | ||||
−0.240491 | + | 0.970651i | \(0.577309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1562.72 | 0.711296 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5408.95 | −2.39784 | ||||||||
\(173\) | 482.641 | 0.212107 | 0.106054 | − | 0.994360i | \(-0.466178\pi\) | ||||
0.106054 | + | 0.994360i | \(0.466178\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2135.93 | −0.914784 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3017.58 | −1.27066 | ||||||||
\(179\) | −2407.19 | −1.00515 | −0.502575 | − | 0.864534i | \(-0.667614\pi\) | ||||
−0.502575 | + | 0.864534i | \(0.667614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 532.600 | 0.218717 | 0.109359 | − | 0.994002i | \(-0.465120\pi\) | ||||
0.109359 | + | 0.994002i | \(0.465120\pi\) | |||||||
\(182\) | −2091.13 | −0.851677 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8200.83 | −3.28572 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1658.53 | −0.648575 | ||||||||
\(188\) | −264.722 | −0.102696 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −336.675 | −0.127544 | −0.0637721 | − | 0.997964i | \(-0.520313\pi\) | ||||
−0.0637721 | + | 0.997964i | \(0.520313\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.7366 | 0.00847988 | 0.00423994 | − | 0.999991i | \(-0.498650\pi\) | ||||
0.00423994 | + | 0.999991i | \(0.498650\pi\) | |||||||
\(194\) | −1126.38 | −0.416852 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 771.077 | 0.281005 | ||||||||
\(197\) | 1085.33 | 0.392520 | 0.196260 | − | 0.980552i | \(-0.437120\pi\) | ||||
0.196260 | + | 0.980552i | \(0.437120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2630.28 | −0.936963 | −0.468482 | − | 0.883473i | \(-0.655199\pi\) | ||||
−0.468482 | + | 0.883473i | \(0.655199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9139.82 | −3.18354 | ||||||||
\(203\) | 236.758 | 0.0818580 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9042.11 | 3.05822 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3540.42 | −1.18021 | ||||||||
\(209\) | 5167.83 | 1.71037 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 614.178 | 0.200388 | 0.100194 | − | 0.994968i | \(-0.468054\pi\) | ||||
0.100194 | + | 0.994968i | \(0.468054\pi\) | |||||||
\(212\) | −5459.93 | −1.76882 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1062.17 | 0.339292 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 871.057 | 0.272494 | ||||||||
\(218\) | 4127.63 | 1.28238 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2749.10 | −0.836762 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1930.30 | 0.579651 | 0.289826 | − | 0.957079i | \(-0.406403\pi\) | ||||
0.289826 | + | 0.957079i | \(0.406403\pi\) | |||||||
\(224\) | −141.535 | −0.0422173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6967.17 | −2.05066 | ||||||||
\(227\) | −765.365 | −0.223784 | −0.111892 | − | 0.993720i | \(-0.535691\pi\) | ||||
−0.111892 | + | 0.993720i | \(0.535691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5712.66 | −1.64849 | −0.824243 | − | 0.566237i | \(-0.808399\pi\) | ||||
−0.824243 | + | 0.566237i | \(0.808399\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1274.81 | 0.360756 | ||||||||
\(233\) | 864.418 | 0.243047 | 0.121523 | − | 0.992589i | \(-0.461222\pi\) | ||||
0.121523 | + | 0.992589i | \(0.461222\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2129.74 | −0.587435 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1529.03 | 0.416439 | ||||||||
\(239\) | 1816.64 | 0.491669 | 0.245834 | − | 0.969312i | \(-0.420938\pi\) | ||||
0.245834 | + | 0.969312i | \(0.420938\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2354.53 | −0.629330 | −0.314665 | − | 0.949203i | \(-0.601892\pi\) | ||||
−0.314665 | + | 0.949203i | \(0.601892\pi\) | |||||||
\(242\) | 182.324 | 0.0484307 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7717.28 | 2.02479 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8565.96 | 2.20664 | ||||||||
\(248\) | 4690.15 | 1.20091 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2983.66 | 0.750306 | 0.375153 | − | 0.926963i | \(-0.377590\pi\) | ||||
0.375153 | + | 0.926963i | \(0.377590\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8048.78 | 2.00009 | ||||||||
\(254\) | −8442.39 | −2.08552 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8030.99 | −1.96069 | ||||||||
\(257\) | 5121.50 | 1.24307 | 0.621537 | − | 0.783385i | \(-0.286508\pi\) | ||||
0.621537 | + | 0.783385i | \(0.286508\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1660.89 | 0.398466 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11837.7 | 2.79137 | ||||||||
\(263\) | −4663.66 | −1.09344 | −0.546718 | − | 0.837317i | \(-0.684123\pi\) | ||||
−0.546718 | + | 0.837317i | \(0.684123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4764.34 | −1.09820 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7521.45 | 1.71435 | ||||||||
\(269\) | −5018.86 | −1.13757 | −0.568783 | − | 0.822488i | \(-0.692586\pi\) | ||||
−0.568783 | + | 0.822488i | \(0.692586\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2512.66 | −0.563222 | −0.281611 | − | 0.959529i | \(-0.590869\pi\) | ||||
−0.281611 | + | 0.959529i | \(0.590869\pi\) | |||||||
\(272\) | 2588.75 | 0.577081 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7078.21 | −1.56062 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6286.82 | 1.36368 | 0.681839 | − | 0.731503i | \(-0.261181\pi\) | ||||
0.681839 | + | 0.731503i | \(0.261181\pi\) | |||||||
\(278\) | 14262.6 | 3.07703 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8804.33 | −1.86912 | −0.934560 | − | 0.355807i | \(-0.884206\pi\) | ||||
−0.934560 | + | 0.355807i | \(0.884206\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 485.298 | 0.101936 | 0.0509681 | − | 0.998700i | \(-0.483769\pi\) | ||||
0.0509681 | + | 0.998700i | \(0.483769\pi\) | |||||||
\(284\) | −712.157 | −0.148798 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11050.8 | 2.28478 | ||||||||
\(287\) | −1365.82 | −0.280912 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2902.86 | −0.590854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1585.92 | 0.317838 | ||||||||
\(293\) | −4004.48 | −0.798444 | −0.399222 | − | 0.916854i | \(-0.630720\pi\) | ||||
−0.399222 | + | 0.916854i | \(0.630720\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8942.96 | 1.75608 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4393.19 | −0.853995 | ||||||||
\(299\) | 13341.3 | 2.58042 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2406.07 | −0.460743 | ||||||||
\(302\) | −6614.33 | −1.26031 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8066.32 | −1.52183 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3154.13 | 0.586370 | 0.293185 | − | 0.956056i | \(-0.405285\pi\) | ||||
0.293185 | + | 0.956056i | \(0.405285\pi\) | |||||||
\(308\) | −4074.84 | −0.753848 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1738.29 | 0.316944 | 0.158472 | − | 0.987363i | \(-0.449343\pi\) | ||||
0.158472 | + | 0.987363i | \(0.449343\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5092.30 | 0.919597 | 0.459799 | − | 0.888023i | \(-0.347922\pi\) | ||||
0.459799 | + | 0.888023i | \(0.347922\pi\) | |||||||
\(314\) | −11296.8 | −2.03030 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13856.3 | 2.46671 | ||||||||
\(317\) | 4874.67 | 0.863686 | 0.431843 | − | 0.901949i | \(-0.357863\pi\) | ||||
0.431843 | + | 0.901949i | \(0.357863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1251.17 | −0.219600 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7420.35 | −1.28422 | ||||||||
\(323\) | −6263.41 | −1.07896 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7685.19 | −1.30565 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7354.17 | −1.23801 | ||||||||
\(329\) | −117.757 | −0.0197329 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2448.46 | −0.406585 | −0.203292 | − | 0.979118i | \(-0.565164\pi\) | ||||
−0.203292 | + | 0.979118i | \(0.565164\pi\) | |||||||
\(332\) | 18175.8 | 3.00460 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5057.20 | −0.828496 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6271.50 | −1.01374 | −0.506870 | − | 0.862023i | \(-0.669197\pi\) | ||||
−0.506870 | + | 0.862023i | \(0.669197\pi\) | |||||||
\(338\) | 7613.54 | 1.22521 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4603.19 | −0.731017 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −12955.3 | −2.03054 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2351.42 | 0.365356 | ||||||||
\(347\) | −417.338 | −0.0645645 | −0.0322822 | − | 0.999479i | \(-0.510278\pi\) | ||||
−0.0322822 | + | 0.999479i | \(0.510278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5971.08 | 0.915829 | 0.457915 | − | 0.888996i | \(-0.348597\pi\) | ||||
0.457915 | + | 0.888996i | \(0.348597\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 747.954 | 0.113256 | ||||||||
\(353\) | 12012.6 | 1.81124 | 0.905620 | − | 0.424089i | \(-0.139406\pi\) | ||||
0.905620 | + | 0.424089i | \(0.139406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9746.64 | −1.45104 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11727.8 | −1.73138 | ||||||||
\(359\) | −6312.46 | −0.928020 | −0.464010 | − | 0.885830i | \(-0.653590\pi\) | ||||
−0.464010 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12657.3 | 1.84535 | ||||||||
\(362\) | 2594.82 | 0.376743 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6754.26 | −0.972580 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12228.6 | 1.73932 | 0.869659 | − | 0.493652i | \(-0.164338\pi\) | ||||
0.869659 | + | 0.493652i | \(0.164338\pi\) | |||||||
\(368\) | −12563.1 | −1.77961 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2428.75 | −0.339877 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7876.24 | 1.09334 | 0.546671 | − | 0.837348i | \(-0.315895\pi\) | ||||
0.546671 | + | 0.837348i | \(0.315895\pi\) | |||||||
\(374\) | −8080.33 | −1.11718 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −634.053 | −0.0869649 | ||||||||
\(377\) | −2073.89 | −0.283317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5992.79 | 0.812214 | 0.406107 | − | 0.913826i | \(-0.366886\pi\) | ||||
0.406107 | + | 0.913826i | \(0.366886\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1640.28 | −0.219696 | ||||||||
\(383\) | −7373.61 | −0.983743 | −0.491872 | − | 0.870668i | \(-0.663687\pi\) | ||||
−0.491872 | + | 0.870668i | \(0.663687\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 110.772 | 0.0146067 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3638.14 | −0.476028 | ||||||||
\(389\) | −1896.88 | −0.247238 | −0.123619 | − | 0.992330i | \(-0.539450\pi\) | ||||
−0.123619 | + | 0.992330i | \(0.539450\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9755.12 | −1.26173 | ||||||||
\(392\) | 1846.86 | 0.237961 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5287.71 | 0.676119 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −791.156 | −0.100018 | −0.0500088 | − | 0.998749i | \(-0.515925\pi\) | ||||
−0.0500088 | + | 0.998749i | \(0.515925\pi\) | |||||||
\(398\) | −12814.7 | −1.61393 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4410.55 | −0.549258 | −0.274629 | − | 0.961550i | \(-0.588555\pi\) | ||||
−0.274629 | + | 0.961550i | \(0.588555\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7630.03 | −0.943124 | ||||||||
\(404\) | −29521.1 | −3.63548 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1153.48 | 0.141001 | ||||||||
\(407\) | −8777.14 | −1.06896 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4403.73 | −0.532397 | −0.266199 | − | 0.963918i | \(-0.585768\pi\) | ||||
−0.266199 | + | 0.963918i | \(0.585768\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 29205.5 | 3.49236 | ||||||||
\(413\) | −947.379 | −0.112875 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1239.77 | 0.146117 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25177.6 | 2.94612 | ||||||||
\(419\) | 14272.6 | 1.66411 | 0.832057 | − | 0.554691i | \(-0.187163\pi\) | ||||
0.832057 | + | 0.554691i | \(0.187163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15530.4 | −1.79788 | −0.898939 | − | 0.438074i | \(-0.855661\pi\) | ||||
−0.898939 | + | 0.438074i | \(0.855661\pi\) | |||||||
\(422\) | 2992.27 | 0.345169 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13077.5 | −1.49787 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3432.90 | 0.389062 | ||||||||
\(428\) | 3430.76 | 0.387458 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5260.75 | 0.587938 | 0.293969 | − | 0.955815i | \(-0.405024\pi\) | ||||
0.293969 | + | 0.955815i | \(0.405024\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6610.65 | 0.733690 | 0.366845 | − | 0.930282i | \(-0.380438\pi\) | ||||
0.366845 | + | 0.930282i | \(0.380438\pi\) | |||||||
\(434\) | 4243.78 | 0.469373 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13332.0 | 1.46442 | ||||||||
\(437\) | 30396.1 | 3.32733 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8870.46 | −0.964383 | −0.482191 | − | 0.876066i | \(-0.660159\pi\) | ||||
−0.482191 | + | 0.876066i | \(0.660159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13393.6 | −1.44133 | ||||||||
\(443\) | 13221.8 | 1.41802 | 0.709012 | − | 0.705196i | \(-0.249141\pi\) | ||||
0.709012 | + | 0.705196i | \(0.249141\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9404.38 | 0.998454 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3923.00 | −0.413715 | ||||||||
\(449\) | −4192.70 | −0.440681 | −0.220341 | − | 0.975423i | \(-0.570717\pi\) | ||||
−0.220341 | + | 0.975423i | \(0.570717\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7217.82 | 0.753600 | ||||||||
\(452\) | −22503.6 | −2.34177 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3728.85 | −0.385470 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4701.78 | −0.481270 | −0.240635 | − | 0.970616i | \(-0.577356\pi\) | ||||
−0.240635 | + | 0.970616i | \(0.577356\pi\) | |||||||
\(458\) | −27832.0 | −2.83953 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1949.82 | 0.196989 | 0.0984946 | − | 0.995138i | \(-0.468597\pi\) | ||||
0.0984946 | + | 0.995138i | \(0.468597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7315.85 | 0.734333 | 0.367166 | − | 0.930155i | \(-0.380328\pi\) | ||||
0.367166 | + | 0.930155i | \(0.380328\pi\) | |||||||
\(464\) | 1952.92 | 0.195392 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4211.43 | 0.418650 | ||||||||
\(467\) | 1897.54 | 0.188025 | 0.0940126 | − | 0.995571i | \(-0.470031\pi\) | ||||
0.0940126 | + | 0.995571i | \(0.470031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3345.78 | 0.329411 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5101.10 | −0.497451 | ||||||||
\(473\) | 12715.1 | 1.23603 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4938.70 | 0.475557 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8850.66 | 0.846903 | ||||||||
\(479\) | −10534.4 | −1.00486 | −0.502429 | − | 0.864619i | \(-0.667560\pi\) | ||||
−0.502429 | + | 0.864619i | \(0.667560\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14548.6 | −1.37912 | ||||||||
\(482\) | −11471.2 | −1.08403 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 588.897 | 0.0553058 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11937.0 | 1.11071 | 0.555355 | − | 0.831614i | \(-0.312583\pi\) | ||||
0.555355 | + | 0.831614i | \(0.312583\pi\) | |||||||
\(488\) | 18484.2 | 1.71463 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −100.060 | −0.00919683 | −0.00459841 | − | 0.999989i | \(-0.501464\pi\) | ||||
−0.00459841 | + | 0.999989i | \(0.501464\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1516.42 | 0.138532 | ||||||||
\(494\) | 41733.3 | 3.80095 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7184.99 | 0.650435 | ||||||||
\(497\) | −316.790 | −0.0285915 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15611.7 | −1.40055 | −0.700275 | − | 0.713874i | \(-0.746939\pi\) | ||||
−0.700275 | + | 0.713874i | \(0.746939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14536.3 | 1.29241 | ||||||||
\(503\) | −2270.39 | −0.201256 | −0.100628 | − | 0.994924i | \(-0.532085\pi\) | ||||
−0.100628 | + | 0.994924i | \(0.532085\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 39213.6 | 3.44517 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −27268.5 | −2.38158 | ||||||||
\(509\) | 2579.79 | 0.224651 | 0.112325 | − | 0.993671i | \(-0.464170\pi\) | ||||
0.112325 | + | 0.993671i | \(0.464170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 705.467 | 0.0610725 | ||||||||
\(512\) | −18577.7 | −1.60357 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24951.9 | 2.14121 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 622.297 | 0.0529373 | ||||||||
\(518\) | 8091.84 | 0.686361 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12793.9 | −1.07584 | −0.537918 | − | 0.842997i | \(-0.680789\pi\) | ||||
−0.537918 | + | 0.842997i | \(0.680789\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11273.4 | −0.942548 | −0.471274 | − | 0.881987i | \(-0.656206\pi\) | ||||
−0.471274 | + | 0.881987i | \(0.656206\pi\) | |||||||
\(524\) | 38235.3 | 3.18763 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22721.3 | −1.88345 | ||||||||
\(527\) | 5579.07 | 0.461154 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35174.2 | 2.89095 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15388.6 | −1.25410 | ||||||||
\(533\) | 11963.9 | 0.972260 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18015.1 | 1.45175 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24451.8 | −1.95947 | ||||||||
\(539\) | −1812.62 | −0.144852 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10282.9 | 0.817183 | 0.408591 | − | 0.912717i | \(-0.366020\pi\) | ||||
0.408591 | + | 0.912717i | \(0.366020\pi\) | |||||||
\(542\) | −12241.6 | −0.970154 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −906.520 | −0.0714462 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2160.94 | −0.168912 | −0.0844562 | − | 0.996427i | \(-0.526915\pi\) | ||||
−0.0844562 | + | 0.996427i | \(0.526915\pi\) | |||||||
\(548\) | −22862.3 | −1.78217 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4725.04 | −0.365324 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6163.74 | 0.473976 | ||||||||
\(554\) | 30629.3 | 2.34895 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 46067.5 | 3.51384 | ||||||||
\(557\) | −15648.4 | −1.19038 | −0.595190 | − | 0.803585i | \(-0.702923\pi\) | ||||
−0.595190 | + | 0.803585i | \(0.702923\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21076.0 | 1.59467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −42894.6 | −3.21957 | ||||||||
\(563\) | 21951.6 | 1.64325 | 0.821623 | − | 0.570031i | \(-0.193069\pi\) | ||||
0.821623 | + | 0.570031i | \(0.193069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2364.36 | 0.175586 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1705.74 | −0.126005 | ||||||||
\(569\) | −14019.2 | −1.03289 | −0.516445 | − | 0.856321i | \(-0.672745\pi\) | ||||
−0.516445 | + | 0.856321i | \(0.672745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21706.3 | −1.59086 | −0.795430 | − | 0.606045i | \(-0.792755\pi\) | ||||
−0.795430 | + | 0.606045i | \(0.792755\pi\) | |||||||
\(572\) | 35693.5 | 2.60913 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6654.26 | −0.483874 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12569.0 | 0.906853 | 0.453427 | − | 0.891294i | \(-0.350201\pi\) | ||||
0.453427 | + | 0.891294i | \(0.350201\pi\) | |||||||
\(578\) | −14142.7 | −1.01775 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8085.19 | 0.577332 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12835.0 | 0.911785 | ||||||||
\(584\) | 3798.54 | 0.269152 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19509.8 | −1.37533 | ||||||||
\(587\) | 1330.20 | 0.0935322 | 0.0467661 | − | 0.998906i | \(-0.485108\pi\) | ||||
0.0467661 | + | 0.998906i | \(0.485108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17383.9 | −1.21611 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13700.0 | 0.951126 | ||||||||
\(593\) | −9866.91 | −0.683281 | −0.341640 | − | 0.939831i | \(-0.610982\pi\) | ||||
−0.341640 | + | 0.939831i | \(0.610982\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −14189.8 | −0.975228 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 64998.6 | 4.44480 | ||||||||
\(599\) | −4185.17 | −0.285478 | −0.142739 | − | 0.989760i | \(-0.545591\pi\) | ||||
−0.142739 | + | 0.989760i | \(0.545591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10599.8 | 0.719426 | 0.359713 | − | 0.933063i | \(-0.382875\pi\) | ||||
0.359713 | + | 0.933063i | \(0.382875\pi\) | |||||||
\(602\) | −11722.4 | −0.793634 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21364.0 | −1.43922 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13290.1 | −0.888679 | −0.444340 | − | 0.895858i | \(-0.646562\pi\) | ||||
−0.444340 | + | 0.895858i | \(0.646562\pi\) | |||||||
\(608\) | 2824.64 | 0.188412 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1031.49 | 0.0682973 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21327.1 | 1.40521 | 0.702606 | − | 0.711579i | \(-0.252020\pi\) | ||||
0.702606 | + | 0.711579i | \(0.252020\pi\) | |||||||
\(614\) | 15366.9 | 1.01003 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9759.92 | −0.638374 | ||||||||
\(617\) | −13741.6 | −0.896622 | −0.448311 | − | 0.893878i | \(-0.647974\pi\) | ||||
−0.448311 | + | 0.893878i | \(0.647974\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19444.3 | 1.26257 | 0.631285 | − | 0.775551i | \(-0.282528\pi\) | ||||
0.631285 | + | 0.775551i | \(0.282528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8468.94 | 0.545938 | ||||||||
\(623\) | −4335.62 | −0.278817 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24809.6 | 1.58401 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −36488.0 | −2.31852 | ||||||||
\(629\) | 10637.9 | 0.674341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27425.6 | −1.73026 | −0.865130 | − | 0.501547i | \(-0.832764\pi\) | ||||
−0.865130 | + | 0.501547i | \(0.832764\pi\) | |||||||
\(632\) | 33188.2 | 2.08886 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23749.3 | 1.48771 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3004.51 | −0.186881 | ||||||||
\(638\) | −6095.70 | −0.378262 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10053.8 | 0.619502 | 0.309751 | − | 0.950818i | \(-0.399754\pi\) | ||||
0.309751 | + | 0.950818i | \(0.399754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4044.18 | −0.248036 | −0.124018 | − | 0.992280i | \(-0.539578\pi\) | ||||
−0.124018 | + | 0.992280i | \(0.539578\pi\) | |||||||
\(644\) | −23967.3 | −1.46653 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30515.3 | −1.85853 | ||||||||
\(647\) | −1486.90 | −0.0903491 | −0.0451746 | − | 0.998979i | \(-0.514384\pi\) | ||||
−0.0451746 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5006.52 | 0.302809 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24822.8 | −1.49100 | ||||||||
\(653\) | −4269.30 | −0.255851 | −0.127925 | − | 0.991784i | \(-0.540832\pi\) | ||||
−0.127925 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11266.1 | −0.670528 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −573.710 | −0.0339902 | ||||||||
\(659\) | −1607.29 | −0.0950094 | −0.0475047 | − | 0.998871i | \(-0.515127\pi\) | ||||
−0.0475047 | + | 0.998871i | \(0.515127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8001.31 | 0.470824 | 0.235412 | − | 0.971896i | \(-0.424356\pi\) | ||||
0.235412 | + | 0.971896i | \(0.424356\pi\) | |||||||
\(662\) | −11928.9 | −0.700345 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 43534.1 | 2.54436 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7359.14 | −0.427207 | ||||||||
\(668\) | −16334.5 | −0.946109 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18141.5 | −1.04373 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3347.96 | 0.191760 | 0.0958800 | − | 0.995393i | \(-0.469433\pi\) | ||||
0.0958800 | + | 0.995393i | \(0.469433\pi\) | |||||||
\(674\) | −30554.7 | −1.74617 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24591.4 | 1.39914 | ||||||||
\(677\) | 7.91810 | 0.000449508 0 | 0.000224754 | − | 1.00000i | \(-0.499928\pi\) | ||||
0.000224754 | 1.00000i | \(0.499928\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1618.36 | −0.0914684 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22426.7 | −1.25918 | ||||||||
\(683\) | −32136.0 | −1.80036 | −0.900182 | − | 0.435513i | \(-0.856567\pi\) | ||||
−0.900182 | + | 0.435513i | \(0.856567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1671.09 | 0.0930067 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −19846.7 | −1.09978 | ||||||||
\(689\) | 21274.7 | 1.17634 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6196.84 | −0.341156 | −0.170578 | − | 0.985344i | \(-0.554563\pi\) | ||||
−0.170578 | + | 0.985344i | \(0.554563\pi\) | |||||||
\(692\) | 7594.98 | 0.417222 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2033.27 | −0.111213 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8747.99 | −0.475400 | ||||||||
\(698\) | 29091.0 | 1.57752 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1651.38 | −0.0889755 | −0.0444878 | − | 0.999010i | \(-0.514166\pi\) | ||||
−0.0444878 | + | 0.999010i | \(0.514166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33146.8 | −1.77831 | ||||||||
\(704\) | 20731.5 | 1.10987 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 58525.4 | 3.11988 | ||||||||
\(707\) | −13132.0 | −0.698555 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15399.8 | 0.815728 | 0.407864 | − | 0.913043i | \(-0.366274\pi\) | ||||
0.407864 | + | 0.913043i | \(0.366274\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23344.8 | −1.22877 | ||||||||
\(713\) | −27075.0 | −1.42211 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −37880.2 | −1.97716 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30754.3 | −1.59852 | ||||||||
\(719\) | −3507.31 | −0.181920 | −0.0909600 | − | 0.995855i | \(-0.528994\pi\) | ||||
−0.0909600 | + | 0.995855i | \(0.528994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12991.6 | 0.671056 | ||||||||
\(722\) | 61666.0 | 3.17863 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8381.14 | 0.430225 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22516.7 | 1.14869 | 0.574346 | − | 0.818613i | \(-0.305256\pi\) | ||||
0.574346 | + | 0.818613i | \(0.305256\pi\) | |||||||
\(728\) | −16177.6 | −0.823600 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15410.7 | −0.779736 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10964.7 | −0.552509 | −0.276255 | − | 0.961084i | \(-0.589093\pi\) | ||||
−0.276255 | + | 0.961084i | \(0.589093\pi\) | |||||||
\(734\) | 59577.8 | 2.99599 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4399.31 | 0.220327 | ||||||||
\(737\) | −17681.1 | −0.883707 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3029.33 | 0.150793 | 0.0753963 | − | 0.997154i | \(-0.475978\pi\) | ||||
0.0753963 | + | 0.997154i | \(0.475978\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11832.9 | −0.585442 | ||||||||
\(743\) | 8921.04 | 0.440486 | 0.220243 | − | 0.975445i | \(-0.429315\pi\) | ||||
0.220243 | + | 0.975445i | \(0.429315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 38373.0 | 1.88329 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −26099.1 | −1.27577 | ||||||||
\(749\) | 1526.11 | 0.0744498 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6202.64 | −0.301382 | −0.150691 | − | 0.988581i | \(-0.548150\pi\) | ||||
−0.150691 | + | 0.988581i | \(0.548150\pi\) | |||||||
\(752\) | −971.326 | −0.0471019 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10104.0 | −0.488016 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12099.3 | −0.580922 | −0.290461 | − | 0.956887i | \(-0.593809\pi\) | ||||
−0.290461 | + | 0.956887i | \(0.593809\pi\) | |||||||
\(758\) | 29196.8 | 1.39905 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29332.7 | −1.39725 | −0.698626 | − | 0.715487i | \(-0.746205\pi\) | ||||
−0.698626 | + | 0.715487i | \(0.746205\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5930.52 | 0.281388 | ||||||||
\(764\) | −5298.01 | −0.250884 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −35924.1 | −1.69451 | ||||||||
\(767\) | 8298.57 | 0.390670 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13280.1 | −0.622748 | −0.311374 | − | 0.950287i | \(-0.600789\pi\) | ||||
−0.311374 | + | 0.950287i | \(0.600789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 357.789 | 0.0166802 | ||||||||
\(773\) | −11248.1 | −0.523370 | −0.261685 | − | 0.965153i | \(-0.584278\pi\) | ||||
−0.261685 | + | 0.965153i | \(0.584278\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8713.96 | −0.403110 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9241.57 | −0.425869 | ||||||||
\(779\) | 27258.0 | 1.25368 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1674.11 | 0.0767021 | ||||||||
\(782\) | −47526.8 | −2.17335 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2829.26 | 0.128884 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −436.193 | −0.0197568 | −0.00987839 | − | 0.999951i | \(-0.503144\pi\) | ||||
−0.00987839 | + | 0.999951i | \(0.503144\pi\) | |||||||
\(788\) | 17079.0 | 0.772100 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10010.3 | −0.449970 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30070.5 | −1.34657 | ||||||||
\(794\) | −3854.50 | −0.172281 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −41390.8 | −1.84304 | ||||||||
\(797\) | 24034.0 | 1.06816 | 0.534082 | − | 0.845433i | \(-0.320657\pi\) | ||||
0.534082 | + | 0.845433i | \(0.320657\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −754.224 | −0.0333949 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21488.1 | −0.946101 | ||||||||
\(803\) | −3728.11 | −0.163838 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −37173.4 | −1.62454 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −70708.1 | −3.07859 | ||||||||
\(809\) | −16188.0 | −0.703509 | −0.351754 | − | 0.936092i | \(-0.614415\pi\) | ||||
−0.351754 | + | 0.936092i | \(0.614415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3732.42 | 0.161607 | 0.0808033 | − | 0.996730i | \(-0.474251\pi\) | ||||
0.0808033 | + | 0.996730i | \(0.474251\pi\) | |||||||
\(812\) | 3725.69 | 0.161018 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −42762.1 | −1.84129 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48018.6 | 2.05625 | ||||||||
\(818\) | −21454.9 | −0.917058 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37226.4 | −1.58247 | −0.791237 | − | 0.611510i | \(-0.790562\pi\) | ||||
−0.791237 | + | 0.611510i | \(0.790562\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21355.7 | 0.904511 | 0.452256 | − | 0.891888i | \(-0.350620\pi\) | ||||
0.452256 | + | 0.891888i | \(0.350620\pi\) | |||||||
\(824\) | 69952.2 | 2.95740 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4615.62 | −0.194428 | ||||||||
\(827\) | 18852.9 | 0.792718 | 0.396359 | − | 0.918096i | \(-0.370274\pi\) | ||||
0.396359 | + | 0.918096i | \(0.370274\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43227.9 | −1.81106 | −0.905528 | − | 0.424286i | \(-0.860525\pi\) | ||||
−0.905528 | + | 0.424286i | \(0.860525\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 34363.5 | 1.43190 | ||||||||
\(833\) | 2196.89 | 0.0913779 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 81322.4 | 3.36435 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 69536.1 | 2.86645 | ||||||||
\(839\) | −30311.3 | −1.24727 | −0.623637 | − | 0.781714i | \(-0.714346\pi\) | ||||
−0.623637 | + | 0.781714i | \(0.714346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23245.0 | −0.953095 | ||||||||
\(842\) | −75664.0 | −3.09686 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9664.88 | 0.394169 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 261.960 | 0.0106270 | ||||||||
\(848\) | −20033.8 | −0.811276 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51625.3 | −2.07955 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22797.0 | −0.915071 | −0.457535 | − | 0.889191i | \(-0.651268\pi\) | ||||
−0.457535 | + | 0.889191i | \(0.651268\pi\) | |||||||
\(854\) | 16725.0 | 0.670162 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8217.25 | 0.328107 | ||||||||
\(857\) | 11280.3 | 0.449625 | 0.224813 | − | 0.974402i | \(-0.427823\pi\) | ||||
0.224813 | + | 0.974402i | \(0.427823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43369.3 | 1.72263 | 0.861315 | − | 0.508071i | \(-0.169641\pi\) | ||||
0.861315 | + | 0.508071i | \(0.169641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25630.3 | 1.01273 | ||||||||
\(863\) | −9846.22 | −0.388377 | −0.194189 | − | 0.980964i | \(-0.562207\pi\) | ||||
−0.194189 | + | 0.980964i | \(0.562207\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32207.0 | 1.26379 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13707.2 | 0.536005 | ||||||||
\(869\) | −32572.9 | −1.27153 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29307.4 | −1.14012 | ||||||||
\(872\) | 31932.5 | 1.24010 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 148090. | 5.73136 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15229.8 | −0.586400 | −0.293200 | − | 0.956051i | \(-0.594720\pi\) | ||||
−0.293200 | + | 0.956051i | \(0.594720\pi\) | |||||||
\(878\) | −43216.8 | −1.66116 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27891.7 | −1.06662 | −0.533311 | − | 0.845919i | \(-0.679052\pi\) | ||||
−0.533311 | + | 0.845919i | \(0.679052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18300.3 | 0.697456 | 0.348728 | − | 0.937224i | \(-0.386614\pi\) | ||||
0.348728 | + | 0.937224i | \(0.386614\pi\) | |||||||
\(884\) | −43260.6 | −1.64594 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64416.3 | 2.44256 | ||||||||
\(887\) | 19104.8 | 0.723197 | 0.361598 | − | 0.932334i | \(-0.382231\pi\) | ||||
0.361598 | + | 0.932334i | \(0.382231\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12129.9 | −0.457620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30375.7 | 1.14019 | ||||||||
\(893\) | 2350.10 | 0.0880661 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17980.5 | −0.670410 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20426.8 | −0.759077 | ||||||||
\(899\) | 4208.78 | 0.156141 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15556.0 | −0.575189 | ||||||||
\(902\) | 35165.1 | 1.29808 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −53899.9 | −1.98306 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29518.8 | −1.08066 | −0.540328 | − | 0.841455i | \(-0.681700\pi\) | ||||
−0.540328 | + | 0.841455i | \(0.681700\pi\) | |||||||
\(908\) | −12044.0 | −0.440191 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30322.2 | 1.10277 | 0.551383 | − | 0.834253i | \(-0.314100\pi\) | ||||
0.551383 | + | 0.834253i | \(0.314100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42727.0 | −1.54880 | ||||||||
\(914\) | −22907.0 | −0.828991 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −89895.9 | −3.24263 | ||||||||
\(917\) | 17008.3 | 0.612501 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37780.9 | −1.35612 | −0.678062 | − | 0.735005i | \(-0.737180\pi\) | ||||
−0.678062 | + | 0.735005i | \(0.737180\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9499.48 | 0.339315 | ||||||||
\(923\) | 2774.93 | 0.0989575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 35642.7 | 1.26489 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −683.867 | −0.0241908 | ||||||||
\(929\) | −48493.3 | −1.71261 | −0.856305 | − | 0.516470i | \(-0.827246\pi\) | ||||
−0.856305 | + | 0.516470i | \(0.827246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6845.33 | −0.240974 | ||||||||
\(932\) | 13602.7 | 0.478081 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9244.81 | 0.323875 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18661.7 | 0.650641 | 0.325320 | − | 0.945604i | \(-0.394528\pi\) | ||||
0.325320 | + | 0.945604i | \(0.394528\pi\) | |||||||
\(938\) | 16300.6 | 0.567413 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31270.1 | 1.08329 | 0.541644 | − | 0.840608i | \(-0.317802\pi\) | ||||
0.541644 | + | 0.840608i | \(0.317802\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42453.7 | 1.46605 | ||||||||
\(944\) | −7814.53 | −0.269429 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 61948.0 | 2.12907 | ||||||||
\(947\) | 22405.3 | 0.768823 | 0.384412 | − | 0.923162i | \(-0.374404\pi\) | ||||
0.384412 | + | 0.923162i | \(0.374404\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6179.55 | −0.211377 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11829.0 | 0.402711 | ||||||||
\(953\) | −21777.9 | −0.740247 | −0.370123 | − | 0.928983i | \(-0.620685\pi\) | ||||
−0.370123 | + | 0.928983i | \(0.620685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 28587.2 | 0.967129 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −51323.3 | −1.73088 | ||||||||
\(959\) | −10169.9 | −0.342442 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14306.5 | −0.480229 | ||||||||
\(962\) | −70880.5 | −2.37555 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37051.5 | −1.23791 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14432.2 | −0.479945 | −0.239973 | − | 0.970780i | \(-0.577138\pi\) | ||||
−0.239973 | + | 0.970780i | \(0.577138\pi\) | |||||||
\(968\) | 1410.51 | 0.0468341 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6672.57 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20492.3 | 0.675183 | ||||||||
\(974\) | 58156.7 | 1.91321 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28316.5 | 0.928678 | ||||||||
\(977\) | 33300.2 | 1.09045 | 0.545224 | − | 0.838290i | \(-0.316444\pi\) | ||||
0.545224 | + | 0.838290i | \(0.316444\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22912.0 | 0.747979 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −487.491 | −0.0158416 | ||||||||
\(983\) | −17243.3 | −0.559486 | −0.279743 | − | 0.960075i | \(-0.590249\pi\) | ||||
−0.279743 | + | 0.960075i | \(0.590249\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7387.99 | 0.238622 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 134796. | 4.34053 | ||||||||
\(989\) | 74787.8 | 2.40456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32266.7 | −1.03429 | −0.517147 | − | 0.855897i | \(-0.673006\pi\) | ||||
−0.517147 | + | 0.855897i | \(0.673006\pi\) | |||||||
\(992\) | −2516.02 | −0.0805278 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1543.40 | −0.0492491 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14339.8 | −0.455514 | −0.227757 | − | 0.973718i | \(-0.573139\pi\) | ||||
−0.227757 | + | 0.973718i | \(0.573139\pi\) | |||||||
\(998\) | −76059.8 | −2.41246 | ||||||||
\(999\) | 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 | 1575.4.a.bg.1.4 | 4 | ||
3.2 | odd | 2 | 175.4.a.h.1.1 | yes | 4 | ||
5.4 | even | 2 | 1575.4.a.bl.1.1 | 4 | |||
15.2 | even | 4 | 175.4.b.f.99.1 | 8 | |||
15.8 | even | 4 | 175.4.b.f.99.8 | 8 | |||
15.14 | odd | 2 | 175.4.a.g.1.4 | ✓ | 4 | ||
21.20 | even | 2 | 1225.4.a.bd.1.1 | 4 | |||
105.104 | even | 2 | 1225.4.a.z.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.4.a.g.1.4 | ✓ | 4 | 15.14 | odd | 2 | ||
175.4.a.h.1.1 | yes | 4 | 3.2 | odd | 2 | ||
175.4.b.f.99.1 | 8 | 15.2 | even | 4 | |||
175.4.b.f.99.8 | 8 | 15.8 | even | 4 | |||
1225.4.a.z.1.4 | 4 | 105.104 | even | 2 | |||
1225.4.a.bd.1.1 | 4 | 21.20 | even | 2 | |||
1575.4.a.bg.1.4 | 4 | 1.1 | even | 1 | trivial | ||
1575.4.a.bl.1.1 | 4 | 5.4 | even | 2 |