Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, 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("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 411x^{4} + 1741x^{3} + 37570x^{2} - 116091x - 993528 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(12.6646\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 15.6646 | 1.40109 | 0.700544 | − | 0.713610i | \(-0.252941\pi\) | ||||
0.700544 | + | 0.713610i | \(0.252941\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 31.3293 | 0.990718 | ||||||||
\(11\) | −41.0616 | −1.12550 | −0.562752 | − | 0.826626i | \(-0.690257\pi\) | ||||
−0.562752 | + | 0.826626i | \(0.690257\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −14.2437 | −0.303884 | −0.151942 | − | 0.988389i | \(-0.548553\pi\) | ||||
−0.151942 | + | 0.988389i | \(0.548553\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 46.9939 | 0.808918 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 78.4383 | 1.11906 | 0.559532 | − | 0.828809i | \(-0.310981\pi\) | ||||
0.559532 | + | 0.828809i | \(0.310981\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 25.2024 | 0.304307 | 0.152154 | − | 0.988357i | \(-0.451379\pi\) | ||||
0.152154 | + | 0.988357i | \(0.451379\pi\) | |||||||
\(20\) | 62.6585 | 0.700544 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | −82.1233 | −0.795852 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 120.381 | 0.963046 | ||||||||
\(26\) | −28.4874 | −0.214879 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | 170.311 | 1.09055 | 0.545276 | − | 0.838257i | \(-0.316425\pi\) | ||||
0.545276 | + | 0.838257i | \(0.316425\pi\) | |||||||
\(30\) | 93.9878 | 0.571991 | ||||||||
\(31\) | −43.3112 | −0.250933 | −0.125466 | − | 0.992098i | \(-0.540043\pi\) | ||||
−0.125466 | + | 0.992098i | \(0.540043\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −123.185 | −0.649810 | ||||||||
\(34\) | 156.877 | 0.791297 | ||||||||
\(35\) | 109.652 | 0.529561 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 41.2032 | 0.183075 | 0.0915373 | − | 0.995802i | \(-0.470822\pi\) | ||||
0.0915373 | + | 0.995802i | \(0.470822\pi\) | |||||||
\(38\) | 50.4049 | 0.215178 | ||||||||
\(39\) | −42.7311 | −0.175448 | ||||||||
\(40\) | 125.317 | 0.495359 | ||||||||
\(41\) | −34.6183 | −0.131865 | −0.0659325 | − | 0.997824i | \(-0.521002\pi\) | ||||
−0.0659325 | + | 0.997824i | \(0.521002\pi\) | |||||||
\(42\) | 42.0000 | 0.154303 | ||||||||
\(43\) | 494.062 | 1.75218 | 0.876091 | − | 0.482146i | \(-0.160143\pi\) | ||||
0.876091 | + | 0.482146i | \(0.160143\pi\) | |||||||
\(44\) | −164.247 | −0.562752 | ||||||||
\(45\) | 140.982 | 0.467029 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 346.986 | 1.07688 | 0.538438 | − | 0.842665i | \(-0.319015\pi\) | ||||
0.538438 | + | 0.842665i | \(0.319015\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 240.761 | 0.680976 | ||||||||
\(51\) | 235.315 | 0.646091 | ||||||||
\(52\) | −56.9749 | −0.151942 | ||||||||
\(53\) | −507.897 | −1.31632 | −0.658161 | − | 0.752877i | \(-0.728665\pi\) | ||||
−0.658161 | + | 0.752877i | \(0.728665\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | −643.215 | −1.57693 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 75.6073 | 0.175692 | ||||||||
\(58\) | 340.622 | 0.771137 | ||||||||
\(59\) | 466.829 | 1.03010 | 0.515051 | − | 0.857160i | \(-0.327773\pi\) | ||||
0.515051 | + | 0.857160i | \(0.327773\pi\) | |||||||
\(60\) | 187.976 | 0.404459 | ||||||||
\(61\) | −58.6216 | −0.123045 | −0.0615223 | − | 0.998106i | \(-0.519596\pi\) | ||||
−0.0615223 | + | 0.998106i | \(0.519596\pi\) | |||||||
\(62\) | −86.6223 | −0.177436 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −223.123 | −0.425768 | ||||||||
\(66\) | −246.370 | −0.459485 | ||||||||
\(67\) | 880.363 | 1.60528 | 0.802638 | − | 0.596466i | \(-0.203429\pi\) | ||||
0.802638 | + | 0.596466i | \(0.203429\pi\) | |||||||
\(68\) | 313.753 | 0.559532 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | 219.305 | 0.374456 | ||||||||
\(71\) | −954.844 | −1.59604 | −0.798022 | − | 0.602629i | \(-0.794120\pi\) | ||||
−0.798022 | + | 0.602629i | \(0.794120\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −1187.49 | −1.90391 | −0.951953 | − | 0.306243i | \(-0.900928\pi\) | ||||
−0.951953 | + | 0.306243i | \(0.900928\pi\) | |||||||
\(74\) | 82.4064 | 0.129453 | ||||||||
\(75\) | 361.142 | 0.556015 | ||||||||
\(76\) | 100.810 | 0.152154 | ||||||||
\(77\) | −287.431 | −0.425401 | ||||||||
\(78\) | −85.4623 | −0.124060 | ||||||||
\(79\) | −545.186 | −0.776433 | −0.388217 | − | 0.921568i | \(-0.626909\pi\) | ||||
−0.388217 | + | 0.921568i | \(0.626909\pi\) | |||||||
\(80\) | 250.634 | 0.350272 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −69.2366 | −0.0932427 | ||||||||
\(83\) | −544.181 | −0.719658 | −0.359829 | − | 0.933018i | \(-0.617165\pi\) | ||||
−0.359829 | + | 0.933018i | \(0.617165\pi\) | |||||||
\(84\) | 84.0000 | 0.109109 | ||||||||
\(85\) | 1228.71 | 1.56791 | ||||||||
\(86\) | 988.125 | 1.23898 | ||||||||
\(87\) | 510.934 | 0.629630 | ||||||||
\(88\) | −328.493 | −0.397926 | ||||||||
\(89\) | −1160.71 | −1.38242 | −0.691208 | − | 0.722655i | \(-0.742921\pi\) | ||||
−0.691208 | + | 0.722655i | \(0.742921\pi\) | |||||||
\(90\) | 281.963 | 0.330239 | ||||||||
\(91\) | −99.7060 | −0.114857 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | −129.934 | −0.144876 | ||||||||
\(94\) | 693.973 | 0.761466 | ||||||||
\(95\) | 394.787 | 0.426361 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | −1543.79 | −1.61596 | −0.807982 | − | 0.589207i | \(-0.799440\pi\) | ||||
−0.807982 | + | 0.589207i | \(0.799440\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −369.555 | −0.375168 | ||||||||
\(100\) | 481.523 | 0.481523 | ||||||||
\(101\) | 1777.99 | 1.75165 | 0.875823 | − | 0.482632i | \(-0.160319\pi\) | ||||
0.875823 | + | 0.482632i | \(0.160319\pi\) | |||||||
\(102\) | 470.630 | 0.456856 | ||||||||
\(103\) | −1059.64 | −1.01368 | −0.506841 | − | 0.862040i | \(-0.669187\pi\) | ||||
−0.506841 | + | 0.862040i | \(0.669187\pi\) | |||||||
\(104\) | −113.950 | −0.107439 | ||||||||
\(105\) | 328.957 | 0.305742 | ||||||||
\(106\) | −1015.79 | −0.930780 | ||||||||
\(107\) | 1676.99 | 1.51514 | 0.757572 | − | 0.652751i | \(-0.226385\pi\) | ||||
0.757572 | + | 0.652751i | \(0.226385\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | −1238.47 | −1.08829 | −0.544145 | − | 0.838991i | \(-0.683146\pi\) | ||||
−0.544145 | + | 0.838991i | \(0.683146\pi\) | |||||||
\(110\) | −1286.43 | −1.11506 | ||||||||
\(111\) | 123.610 | 0.105698 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 708.275 | 0.589636 | 0.294818 | − | 0.955553i | \(-0.404741\pi\) | ||||
0.294818 | + | 0.955553i | \(0.404741\pi\) | |||||||
\(114\) | 151.215 | 0.124233 | ||||||||
\(115\) | 360.287 | 0.292147 | ||||||||
\(116\) | 681.245 | 0.545276 | ||||||||
\(117\) | −128.193 | −0.101295 | ||||||||
\(118\) | 933.658 | 0.728392 | ||||||||
\(119\) | 549.068 | 0.422966 | ||||||||
\(120\) | 375.951 | 0.285996 | ||||||||
\(121\) | 355.057 | 0.266760 | ||||||||
\(122\) | −117.243 | −0.0870057 | ||||||||
\(123\) | −103.855 | −0.0761323 | ||||||||
\(124\) | −173.245 | −0.125466 | ||||||||
\(125\) | −72.3597 | −0.0517764 | ||||||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | 1836.70 | 1.28331 | 0.641657 | − | 0.766992i | \(-0.278247\pi\) | ||||
0.641657 | + | 0.766992i | \(0.278247\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1482.19 | 1.01162 | ||||||||
\(130\) | −446.245 | −0.301064 | ||||||||
\(131\) | 302.385 | 0.201676 | 0.100838 | − | 0.994903i | \(-0.467848\pi\) | ||||
0.100838 | + | 0.994903i | \(0.467848\pi\) | |||||||
\(132\) | −492.740 | −0.324905 | ||||||||
\(133\) | 176.417 | 0.115017 | ||||||||
\(134\) | 1760.73 | 1.13510 | ||||||||
\(135\) | 422.945 | 0.269639 | ||||||||
\(136\) | 627.506 | 0.395649 | ||||||||
\(137\) | 1809.78 | 1.12861 | 0.564306 | − | 0.825566i | \(-0.309144\pi\) | ||||
0.564306 | + | 0.825566i | \(0.309144\pi\) | |||||||
\(138\) | 138.000 | 0.0851257 | ||||||||
\(139\) | −841.134 | −0.513267 | −0.256633 | − | 0.966509i | \(-0.582613\pi\) | ||||
−0.256633 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(140\) | 438.610 | 0.264781 | ||||||||
\(141\) | 1040.96 | 0.621734 | ||||||||
\(142\) | −1909.69 | −1.12857 | ||||||||
\(143\) | 584.870 | 0.342023 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 2667.86 | 1.52796 | ||||||||
\(146\) | −2374.98 | −1.34627 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 164.813 | 0.0915373 | ||||||||
\(149\) | −2554.77 | −1.40466 | −0.702331 | − | 0.711851i | \(-0.747857\pi\) | ||||
−0.702331 | + | 0.711851i | \(0.747857\pi\) | |||||||
\(150\) | 722.284 | 0.393162 | ||||||||
\(151\) | −1476.88 | −0.795939 | −0.397970 | − | 0.917399i | \(-0.630285\pi\) | ||||
−0.397970 | + | 0.917399i | \(0.630285\pi\) | |||||||
\(152\) | 201.620 | 0.107589 | ||||||||
\(153\) | 705.944 | 0.373021 | ||||||||
\(154\) | −574.863 | −0.300804 | ||||||||
\(155\) | −678.454 | −0.351579 | ||||||||
\(156\) | −170.925 | −0.0877238 | ||||||||
\(157\) | −833.186 | −0.423538 | −0.211769 | − | 0.977320i | \(-0.567922\pi\) | ||||
−0.211769 | + | 0.977320i | \(0.567922\pi\) | |||||||
\(158\) | −1090.37 | −0.549021 | ||||||||
\(159\) | −1523.69 | −0.759979 | ||||||||
\(160\) | 501.268 | 0.247680 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 576.389 | 0.276971 | 0.138485 | − | 0.990364i | \(-0.455777\pi\) | ||||
0.138485 | + | 0.990364i | \(0.455777\pi\) | |||||||
\(164\) | −138.473 | −0.0659325 | ||||||||
\(165\) | −1929.65 | −0.910441 | ||||||||
\(166\) | −1088.36 | −0.508875 | ||||||||
\(167\) | 1082.11 | 0.501416 | 0.250708 | − | 0.968063i | \(-0.419337\pi\) | ||||
0.250708 | + | 0.968063i | \(0.419337\pi\) | |||||||
\(168\) | 168.000 | 0.0771517 | ||||||||
\(169\) | −1994.12 | −0.907654 | ||||||||
\(170\) | 2457.41 | 1.10868 | ||||||||
\(171\) | 226.822 | 0.101436 | ||||||||
\(172\) | 1976.25 | 0.876091 | ||||||||
\(173\) | −2388.32 | −1.04960 | −0.524799 | − | 0.851226i | \(-0.675859\pi\) | ||||
−0.524799 | + | 0.851226i | \(0.675859\pi\) | |||||||
\(174\) | 1021.87 | 0.445216 | ||||||||
\(175\) | 842.665 | 0.363997 | ||||||||
\(176\) | −656.986 | −0.281376 | ||||||||
\(177\) | 1400.49 | 0.594729 | ||||||||
\(178\) | −2321.42 | −0.977516 | ||||||||
\(179\) | 2248.85 | 0.939033 | 0.469516 | − | 0.882924i | \(-0.344428\pi\) | ||||
0.469516 | + | 0.882924i | \(0.344428\pi\) | |||||||
\(180\) | 563.927 | 0.233515 | ||||||||
\(181\) | 2942.59 | 1.20840 | 0.604202 | − | 0.796831i | \(-0.293492\pi\) | ||||
0.604202 | + | 0.796831i | \(0.293492\pi\) | |||||||
\(182\) | −199.412 | −0.0812165 | ||||||||
\(183\) | −175.865 | −0.0710398 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 645.433 | 0.256504 | ||||||||
\(186\) | −259.867 | −0.102443 | ||||||||
\(187\) | −3220.80 | −1.25951 | ||||||||
\(188\) | 1387.95 | 0.538438 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 789.574 | 0.301483 | ||||||||
\(191\) | 2976.98 | 1.12778 | 0.563892 | − | 0.825848i | \(-0.309303\pi\) | ||||
0.563892 | + | 0.825848i | \(0.309303\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 1442.27 | 0.537911 | 0.268955 | − | 0.963153i | \(-0.413322\pi\) | ||||
0.268955 | + | 0.963153i | \(0.413322\pi\) | |||||||
\(194\) | −3087.59 | −1.14266 | ||||||||
\(195\) | −669.368 | −0.245817 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −4061.37 | −1.46884 | −0.734418 | − | 0.678698i | \(-0.762545\pi\) | ||||
−0.734418 | + | 0.678698i | \(0.762545\pi\) | |||||||
\(198\) | −739.109 | −0.265284 | ||||||||
\(199\) | 2311.84 | 0.823526 | 0.411763 | − | 0.911291i | \(-0.364913\pi\) | ||||
0.411763 | + | 0.911291i | \(0.364913\pi\) | |||||||
\(200\) | 963.046 | 0.340488 | ||||||||
\(201\) | 2641.09 | 0.926807 | ||||||||
\(202\) | 3555.97 | 1.23860 | ||||||||
\(203\) | 1192.18 | 0.412190 | ||||||||
\(204\) | 941.259 | 0.323046 | ||||||||
\(205\) | −542.283 | −0.184754 | ||||||||
\(206\) | −2119.27 | −0.716781 | ||||||||
\(207\) | 207.000 | 0.0695048 | ||||||||
\(208\) | −227.899 | −0.0759711 | ||||||||
\(209\) | −1034.85 | −0.342499 | ||||||||
\(210\) | 657.915 | 0.216192 | ||||||||
\(211\) | −3431.33 | −1.11954 | −0.559769 | − | 0.828649i | \(-0.689110\pi\) | ||||
−0.559769 | + | 0.828649i | \(0.689110\pi\) | |||||||
\(212\) | −2031.59 | −0.658161 | ||||||||
\(213\) | −2864.53 | −0.921476 | ||||||||
\(214\) | 3353.98 | 1.07137 | ||||||||
\(215\) | 7739.31 | 2.45496 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | −303.178 | −0.0948437 | ||||||||
\(218\) | −2476.93 | −0.769537 | ||||||||
\(219\) | −3562.47 | −1.09922 | ||||||||
\(220\) | −2572.86 | −0.788465 | ||||||||
\(221\) | −1117.25 | −0.340066 | ||||||||
\(222\) | 247.219 | 0.0747399 | ||||||||
\(223\) | 2032.48 | 0.610335 | 0.305167 | − | 0.952299i | \(-0.401288\pi\) | ||||
0.305167 | + | 0.952299i | \(0.401288\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 1083.43 | 0.321015 | ||||||||
\(226\) | 1416.55 | 0.416936 | ||||||||
\(227\) | 1319.50 | 0.385807 | 0.192904 | − | 0.981218i | \(-0.438210\pi\) | ||||
0.192904 | + | 0.981218i | \(0.438210\pi\) | |||||||
\(228\) | 302.429 | 0.0878459 | ||||||||
\(229\) | 5358.47 | 1.54628 | 0.773138 | − | 0.634237i | \(-0.218686\pi\) | ||||
0.773138 | + | 0.634237i | \(0.218686\pi\) | |||||||
\(230\) | 720.573 | 0.206579 | ||||||||
\(231\) | −862.294 | −0.245605 | ||||||||
\(232\) | 1362.49 | 0.385568 | ||||||||
\(233\) | −3621.29 | −1.01819 | −0.509096 | − | 0.860710i | \(-0.670020\pi\) | ||||
−0.509096 | + | 0.860710i | \(0.670020\pi\) | |||||||
\(234\) | −256.387 | −0.0716262 | ||||||||
\(235\) | 5435.41 | 1.50880 | ||||||||
\(236\) | 1867.32 | 0.515051 | ||||||||
\(237\) | −1635.56 | −0.448274 | ||||||||
\(238\) | 1098.14 | 0.299082 | ||||||||
\(239\) | −2373.71 | −0.642439 | −0.321219 | − | 0.947005i | \(-0.604093\pi\) | ||||
−0.321219 | + | 0.947005i | \(0.604093\pi\) | |||||||
\(240\) | 751.902 | 0.202230 | ||||||||
\(241\) | −672.233 | −0.179678 | −0.0898389 | − | 0.995956i | \(-0.528635\pi\) | ||||
−0.0898389 | + | 0.995956i | \(0.528635\pi\) | |||||||
\(242\) | 710.115 | 0.188628 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −234.486 | −0.0615223 | ||||||||
\(245\) | 767.567 | 0.200155 | ||||||||
\(246\) | −207.710 | −0.0538337 | ||||||||
\(247\) | −358.976 | −0.0924742 | ||||||||
\(248\) | −346.489 | −0.0887181 | ||||||||
\(249\) | −1632.54 | −0.415495 | ||||||||
\(250\) | −144.719 | −0.0366114 | ||||||||
\(251\) | −6176.25 | −1.55315 | −0.776577 | − | 0.630022i | \(-0.783046\pi\) | ||||
−0.776577 | + | 0.630022i | \(0.783046\pi\) | |||||||
\(252\) | 252.000 | 0.0629941 | ||||||||
\(253\) | −944.417 | −0.234684 | ||||||||
\(254\) | 3673.40 | 0.907439 | ||||||||
\(255\) | 3686.12 | 0.905230 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2384.75 | −0.578821 | −0.289410 | − | 0.957205i | \(-0.593459\pi\) | ||||
−0.289410 | + | 0.957205i | \(0.593459\pi\) | |||||||
\(258\) | 2964.37 | 0.715325 | ||||||||
\(259\) | 288.422 | 0.0691957 | ||||||||
\(260\) | −892.490 | −0.212884 | ||||||||
\(261\) | 1532.80 | 0.363517 | ||||||||
\(262\) | 604.771 | 0.142606 | ||||||||
\(263\) | −5527.75 | −1.29603 | −0.648015 | − | 0.761628i | \(-0.724400\pi\) | ||||
−0.648015 | + | 0.761628i | \(0.724400\pi\) | |||||||
\(264\) | −985.479 | −0.229743 | ||||||||
\(265\) | −7956.03 | −1.84428 | ||||||||
\(266\) | 352.834 | 0.0813295 | ||||||||
\(267\) | −3482.13 | −0.798139 | ||||||||
\(268\) | 3521.45 | 0.802638 | ||||||||
\(269\) | −2778.55 | −0.629782 | −0.314891 | − | 0.949128i | \(-0.601968\pi\) | ||||
−0.314891 | + | 0.949128i | \(0.601968\pi\) | |||||||
\(270\) | 845.890 | 0.190664 | ||||||||
\(271\) | −3363.43 | −0.753925 | −0.376962 | − | 0.926229i | \(-0.623031\pi\) | ||||
−0.376962 | + | 0.926229i | \(0.623031\pi\) | |||||||
\(272\) | 1255.01 | 0.279766 | ||||||||
\(273\) | −299.118 | −0.0663130 | ||||||||
\(274\) | 3619.56 | 0.798049 | ||||||||
\(275\) | −4943.03 | −1.08391 | ||||||||
\(276\) | 276.000 | 0.0601929 | ||||||||
\(277\) | 4972.04 | 1.07849 | 0.539243 | − | 0.842150i | \(-0.318710\pi\) | ||||
0.539243 | + | 0.842150i | \(0.318710\pi\) | |||||||
\(278\) | −1682.27 | −0.362934 | ||||||||
\(279\) | −389.801 | −0.0836443 | ||||||||
\(280\) | 877.219 | 0.187228 | ||||||||
\(281\) | −8372.63 | −1.77747 | −0.888735 | − | 0.458422i | \(-0.848415\pi\) | ||||
−0.888735 | + | 0.458422i | \(0.848415\pi\) | |||||||
\(282\) | 2081.92 | 0.439633 | ||||||||
\(283\) | −945.767 | −0.198657 | −0.0993287 | − | 0.995055i | \(-0.531670\pi\) | ||||
−0.0993287 | + | 0.995055i | \(0.531670\pi\) | |||||||
\(284\) | −3819.37 | −0.798022 | ||||||||
\(285\) | 1184.36 | 0.246160 | ||||||||
\(286\) | 1169.74 | 0.241847 | ||||||||
\(287\) | −242.328 | −0.0498403 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 1239.56 | 0.252302 | ||||||||
\(290\) | 5335.73 | 1.08043 | ||||||||
\(291\) | −4631.38 | −0.932978 | ||||||||
\(292\) | −4749.96 | −0.951953 | ||||||||
\(293\) | −7149.99 | −1.42562 | −0.712810 | − | 0.701357i | \(-0.752578\pi\) | ||||
−0.712810 | + | 0.701357i | \(0.752578\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | 7312.71 | 1.44326 | ||||||||
\(296\) | 329.626 | 0.0647267 | ||||||||
\(297\) | −1108.66 | −0.216603 | ||||||||
\(298\) | −5109.53 | −0.993246 | ||||||||
\(299\) | −327.605 | −0.0633642 | ||||||||
\(300\) | 1444.57 | 0.278007 | ||||||||
\(301\) | 3458.44 | 0.662262 | ||||||||
\(302\) | −2953.76 | −0.562814 | ||||||||
\(303\) | 5333.96 | 1.01131 | ||||||||
\(304\) | 403.239 | 0.0760768 | ||||||||
\(305\) | −918.285 | −0.172396 | ||||||||
\(306\) | 1411.89 | 0.263766 | ||||||||
\(307\) | 162.739 | 0.0302541 | 0.0151271 | − | 0.999886i | \(-0.495185\pi\) | ||||
0.0151271 | + | 0.999886i | \(0.495185\pi\) | |||||||
\(308\) | −1149.73 | −0.212700 | ||||||||
\(309\) | −3178.91 | −0.585249 | ||||||||
\(310\) | −1356.91 | −0.248604 | ||||||||
\(311\) | 2925.90 | 0.533481 | 0.266740 | − | 0.963768i | \(-0.414053\pi\) | ||||
0.266740 | + | 0.963768i | \(0.414053\pi\) | |||||||
\(312\) | −341.849 | −0.0620301 | ||||||||
\(313\) | −3563.52 | −0.643521 | −0.321760 | − | 0.946821i | \(-0.604275\pi\) | ||||
−0.321760 | + | 0.946821i | \(0.604275\pi\) | |||||||
\(314\) | −1666.37 | −0.299487 | ||||||||
\(315\) | 986.872 | 0.176520 | ||||||||
\(316\) | −2180.74 | −0.388217 | ||||||||
\(317\) | 3735.00 | 0.661761 | 0.330881 | − | 0.943673i | \(-0.392654\pi\) | ||||
0.330881 | + | 0.943673i | \(0.392654\pi\) | |||||||
\(318\) | −3047.38 | −0.537386 | ||||||||
\(319\) | −6993.26 | −1.22742 | ||||||||
\(320\) | 1002.54 | 0.175136 | ||||||||
\(321\) | 5030.96 | 0.874769 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | 1976.84 | 0.340539 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −1714.67 | −0.292654 | ||||||||
\(326\) | 1152.78 | 0.195848 | ||||||||
\(327\) | −3715.40 | −0.628325 | ||||||||
\(328\) | −276.946 | −0.0466213 | ||||||||
\(329\) | 2428.90 | 0.407021 | ||||||||
\(330\) | −3859.29 | −0.643779 | ||||||||
\(331\) | −10583.2 | −1.75742 | −0.878712 | − | 0.477352i | \(-0.841597\pi\) | ||||
−0.878712 | + | 0.477352i | \(0.841597\pi\) | |||||||
\(332\) | −2176.72 | −0.359829 | ||||||||
\(333\) | 370.829 | 0.0610249 | ||||||||
\(334\) | 2164.23 | 0.354555 | ||||||||
\(335\) | 13790.6 | 2.24913 | ||||||||
\(336\) | 336.000 | 0.0545545 | ||||||||
\(337\) | 4282.53 | 0.692237 | 0.346119 | − | 0.938191i | \(-0.387499\pi\) | ||||
0.346119 | + | 0.938191i | \(0.387499\pi\) | |||||||
\(338\) | −3988.23 | −0.641809 | ||||||||
\(339\) | 2124.82 | 0.340426 | ||||||||
\(340\) | 4914.83 | 0.783953 | ||||||||
\(341\) | 1778.43 | 0.282426 | ||||||||
\(342\) | 453.644 | 0.0717259 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 3952.50 | 0.619490 | ||||||||
\(345\) | 1080.86 | 0.168671 | ||||||||
\(346\) | −4776.64 | −0.742178 | ||||||||
\(347\) | 10703.3 | 1.65586 | 0.827931 | − | 0.560829i | \(-0.189518\pi\) | ||||
0.827931 | + | 0.560829i | \(0.189518\pi\) | |||||||
\(348\) | 2043.73 | 0.314815 | ||||||||
\(349\) | −5781.60 | −0.886767 | −0.443384 | − | 0.896332i | \(-0.646222\pi\) | ||||
−0.443384 | + | 0.896332i | \(0.646222\pi\) | |||||||
\(350\) | 1685.33 | 0.257385 | ||||||||
\(351\) | −384.580 | −0.0584826 | ||||||||
\(352\) | −1313.97 | −0.198963 | ||||||||
\(353\) | −2252.26 | −0.339591 | −0.169796 | − | 0.985479i | \(-0.554311\pi\) | ||||
−0.169796 | + | 0.985479i | \(0.554311\pi\) | |||||||
\(354\) | 2800.98 | 0.420537 | ||||||||
\(355\) | −14957.3 | −2.23620 | ||||||||
\(356\) | −4642.84 | −0.691208 | ||||||||
\(357\) | 1647.20 | 0.244200 | ||||||||
\(358\) | 4497.70 | 0.663997 | ||||||||
\(359\) | −7819.05 | −1.14951 | −0.574754 | − | 0.818326i | \(-0.694902\pi\) | ||||
−0.574754 | + | 0.818326i | \(0.694902\pi\) | |||||||
\(360\) | 1127.85 | 0.165120 | ||||||||
\(361\) | −6223.84 | −0.907397 | ||||||||
\(362\) | 5885.18 | 0.854470 | ||||||||
\(363\) | 1065.17 | 0.154014 | ||||||||
\(364\) | −398.824 | −0.0574287 | ||||||||
\(365\) | −18601.6 | −2.66754 | ||||||||
\(366\) | −351.729 | −0.0502328 | ||||||||
\(367\) | 5845.51 | 0.831426 | 0.415713 | − | 0.909496i | \(-0.363532\pi\) | ||||
0.415713 | + | 0.909496i | \(0.363532\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | −311.565 | −0.0439550 | ||||||||
\(370\) | 1290.87 | 0.181375 | ||||||||
\(371\) | −3555.28 | −0.497523 | ||||||||
\(372\) | −519.734 | −0.0724380 | ||||||||
\(373\) | 11575.4 | 1.60684 | 0.803422 | − | 0.595410i | \(-0.203010\pi\) | ||||
0.803422 | + | 0.595410i | \(0.203010\pi\) | |||||||
\(374\) | −6441.61 | −0.890608 | ||||||||
\(375\) | −217.079 | −0.0298931 | ||||||||
\(376\) | 2775.89 | 0.380733 | ||||||||
\(377\) | −2425.86 | −0.331402 | ||||||||
\(378\) | 378.000 | 0.0514344 | ||||||||
\(379\) | 4411.89 | 0.597951 | 0.298976 | − | 0.954261i | \(-0.403355\pi\) | ||||
0.298976 | + | 0.954261i | \(0.403355\pi\) | |||||||
\(380\) | 1579.15 | 0.213181 | ||||||||
\(381\) | 5510.10 | 0.740921 | ||||||||
\(382\) | 5953.96 | 0.797464 | ||||||||
\(383\) | −4878.61 | −0.650875 | −0.325438 | − | 0.945564i | \(-0.605512\pi\) | ||||
−0.325438 | + | 0.945564i | \(0.605512\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −4502.51 | −0.596023 | ||||||||
\(386\) | 2884.54 | 0.380360 | ||||||||
\(387\) | 4446.56 | 0.584061 | ||||||||
\(388\) | −6175.18 | −0.807982 | ||||||||
\(389\) | −5414.58 | −0.705733 | −0.352866 | − | 0.935674i | \(-0.614793\pi\) | ||||
−0.352866 | + | 0.935674i | \(0.614793\pi\) | |||||||
\(390\) | −1338.74 | −0.173819 | ||||||||
\(391\) | 1804.08 | 0.233341 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 907.156 | 0.116438 | ||||||||
\(394\) | −8122.74 | −1.03862 | ||||||||
\(395\) | −8540.14 | −1.08785 | ||||||||
\(396\) | −1478.22 | −0.187584 | ||||||||
\(397\) | 8484.39 | 1.07259 | 0.536296 | − | 0.844030i | \(-0.319823\pi\) | ||||
0.536296 | + | 0.844030i | \(0.319823\pi\) | |||||||
\(398\) | 4623.67 | 0.582321 | ||||||||
\(399\) | 529.251 | 0.0664053 | ||||||||
\(400\) | 1926.09 | 0.240761 | ||||||||
\(401\) | 14924.6 | 1.85860 | 0.929298 | − | 0.369332i | \(-0.120413\pi\) | ||||
0.929298 | + | 0.369332i | \(0.120413\pi\) | |||||||
\(402\) | 5282.18 | 0.655351 | ||||||||
\(403\) | 616.912 | 0.0762545 | ||||||||
\(404\) | 7111.95 | 0.875823 | ||||||||
\(405\) | 1268.84 | 0.155676 | ||||||||
\(406\) | 2384.36 | 0.291462 | ||||||||
\(407\) | −1691.87 | −0.206051 | ||||||||
\(408\) | 1882.52 | 0.228428 | ||||||||
\(409\) | 9025.61 | 1.09117 | 0.545584 | − | 0.838056i | \(-0.316308\pi\) | ||||
0.545584 | + | 0.838056i | \(0.316308\pi\) | |||||||
\(410\) | −1084.57 | −0.130641 | ||||||||
\(411\) | 5429.34 | 0.651605 | ||||||||
\(412\) | −4238.55 | −0.506841 | ||||||||
\(413\) | 3267.80 | 0.389342 | ||||||||
\(414\) | 414.000 | 0.0491473 | ||||||||
\(415\) | −8524.39 | −1.00830 | ||||||||
\(416\) | −455.799 | −0.0537197 | ||||||||
\(417\) | −2523.40 | −0.296335 | ||||||||
\(418\) | −2069.71 | −0.242183 | ||||||||
\(419\) | −10699.8 | −1.24754 | −0.623770 | − | 0.781608i | \(-0.714400\pi\) | ||||
−0.623770 | + | 0.781608i | \(0.714400\pi\) | |||||||
\(420\) | 1315.83 | 0.152871 | ||||||||
\(421\) | −2196.34 | −0.254259 | −0.127130 | − | 0.991886i | \(-0.540576\pi\) | ||||
−0.127130 | + | 0.991886i | \(0.540576\pi\) | |||||||
\(422\) | −6862.66 | −0.791633 | ||||||||
\(423\) | 3122.88 | 0.358959 | ||||||||
\(424\) | −4063.18 | −0.465390 | ||||||||
\(425\) | 9442.45 | 1.07771 | ||||||||
\(426\) | −5729.06 | −0.651582 | ||||||||
\(427\) | −410.351 | −0.0465065 | ||||||||
\(428\) | 6707.95 | 0.757572 | ||||||||
\(429\) | 1754.61 | 0.197467 | ||||||||
\(430\) | 15478.6 | 1.73592 | ||||||||
\(431\) | −12038.1 | −1.34537 | −0.672685 | − | 0.739929i | \(-0.734859\pi\) | ||||
−0.672685 | + | 0.739929i | \(0.734859\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 4919.60 | 0.546007 | 0.273003 | − | 0.962013i | \(-0.411983\pi\) | ||||
0.273003 | + | 0.962013i | \(0.411983\pi\) | |||||||
\(434\) | −606.356 | −0.0670646 | ||||||||
\(435\) | 8003.59 | 0.882167 | ||||||||
\(436\) | −4953.87 | −0.544145 | ||||||||
\(437\) | 579.656 | 0.0634525 | ||||||||
\(438\) | −7124.94 | −0.777267 | ||||||||
\(439\) | 1758.49 | 0.191180 | 0.0955902 | − | 0.995421i | \(-0.469526\pi\) | ||||
0.0955902 | + | 0.995421i | \(0.469526\pi\) | |||||||
\(440\) | −5145.72 | −0.557529 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −2234.50 | −0.240463 | ||||||||
\(443\) | −7385.45 | −0.792084 | −0.396042 | − | 0.918232i | \(-0.629617\pi\) | ||||
−0.396042 | + | 0.918232i | \(0.629617\pi\) | |||||||
\(444\) | 494.438 | 0.0528491 | ||||||||
\(445\) | −18182.1 | −1.93689 | ||||||||
\(446\) | 4064.95 | 0.431572 | ||||||||
\(447\) | −7664.30 | −0.810982 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | −3349.26 | −0.352029 | −0.176015 | − | 0.984388i | \(-0.556321\pi\) | ||||
−0.176015 | + | 0.984388i | \(0.556321\pi\) | |||||||
\(450\) | 2166.85 | 0.226992 | ||||||||
\(451\) | 1421.48 | 0.148415 | ||||||||
\(452\) | 2833.10 | 0.294818 | ||||||||
\(453\) | −4430.64 | −0.459536 | ||||||||
\(454\) | 2639.00 | 0.272807 | ||||||||
\(455\) | −1561.86 | −0.160925 | ||||||||
\(456\) | 604.859 | 0.0621165 | ||||||||
\(457\) | −9045.61 | −0.925899 | −0.462949 | − | 0.886385i | \(-0.653209\pi\) | ||||
−0.462949 | + | 0.886385i | \(0.653209\pi\) | |||||||
\(458\) | 10716.9 | 1.09338 | ||||||||
\(459\) | 2117.83 | 0.215364 | ||||||||
\(460\) | 1441.15 | 0.146073 | ||||||||
\(461\) | −1333.76 | −0.134749 | −0.0673745 | − | 0.997728i | \(-0.521462\pi\) | ||||
−0.0673745 | + | 0.997728i | \(0.521462\pi\) | |||||||
\(462\) | −1724.59 | −0.173669 | ||||||||
\(463\) | 4055.12 | 0.407035 | 0.203518 | − | 0.979071i | \(-0.434763\pi\) | ||||
0.203518 | + | 0.979071i | \(0.434763\pi\) | |||||||
\(464\) | 2724.98 | 0.272638 | ||||||||
\(465\) | −2035.36 | −0.202984 | ||||||||
\(466\) | −7242.59 | −0.719971 | ||||||||
\(467\) | 7723.31 | 0.765294 | 0.382647 | − | 0.923895i | \(-0.375013\pi\) | ||||
0.382647 | + | 0.923895i | \(0.375013\pi\) | |||||||
\(468\) | −512.774 | −0.0506474 | ||||||||
\(469\) | 6162.54 | 0.606737 | ||||||||
\(470\) | 10870.8 | 1.06688 | ||||||||
\(471\) | −2499.56 | −0.244530 | ||||||||
\(472\) | 3734.63 | 0.364196 | ||||||||
\(473\) | −20287.0 | −1.97209 | ||||||||
\(474\) | −3271.12 | −0.316978 | ||||||||
\(475\) | 3033.89 | 0.293062 | ||||||||
\(476\) | 2196.27 | 0.211483 | ||||||||
\(477\) | −4571.08 | −0.438774 | ||||||||
\(478\) | −4747.43 | −0.454273 | ||||||||
\(479\) | 1606.26 | 0.153219 | 0.0766095 | − | 0.997061i | \(-0.475591\pi\) | ||||
0.0766095 | + | 0.997061i | \(0.475591\pi\) | |||||||
\(480\) | 1503.80 | 0.142998 | ||||||||
\(481\) | −586.886 | −0.0556335 | ||||||||
\(482\) | −1344.47 | −0.127051 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | 1420.23 | 0.133380 | ||||||||
\(485\) | −24183.0 | −2.26411 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −425.512 | −0.0395930 | −0.0197965 | − | 0.999804i | \(-0.506302\pi\) | ||||
−0.0197965 | + | 0.999804i | \(0.506302\pi\) | |||||||
\(488\) | −468.972 | −0.0435028 | ||||||||
\(489\) | 1729.17 | 0.159909 | ||||||||
\(490\) | 1535.13 | 0.141531 | ||||||||
\(491\) | 1161.29 | 0.106738 | 0.0533690 | − | 0.998575i | \(-0.483004\pi\) | ||||
0.0533690 | + | 0.998575i | \(0.483004\pi\) | |||||||
\(492\) | −415.419 | −0.0380662 | ||||||||
\(493\) | 13358.9 | 1.22040 | ||||||||
\(494\) | −717.953 | −0.0653891 | ||||||||
\(495\) | −5788.94 | −0.525643 | ||||||||
\(496\) | −692.979 | −0.0627332 | ||||||||
\(497\) | −6683.90 | −0.603248 | ||||||||
\(498\) | −3265.08 | −0.293799 | ||||||||
\(499\) | −6226.43 | −0.558584 | −0.279292 | − | 0.960206i | \(-0.590100\pi\) | ||||
−0.279292 | + | 0.960206i | \(0.590100\pi\) | |||||||
\(500\) | −289.439 | −0.0258882 | ||||||||
\(501\) | 3246.34 | 0.289493 | ||||||||
\(502\) | −12352.5 | −1.09825 | ||||||||
\(503\) | 5054.24 | 0.448026 | 0.224013 | − | 0.974586i | \(-0.428084\pi\) | ||||
0.224013 | + | 0.974586i | \(0.428084\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | 27851.5 | 2.45421 | ||||||||
\(506\) | −1888.83 | −0.165947 | ||||||||
\(507\) | −5982.35 | −0.524034 | ||||||||
\(508\) | 7346.80 | 0.641657 | ||||||||
\(509\) | −4458.15 | −0.388220 | −0.194110 | − | 0.980980i | \(-0.562182\pi\) | ||||
−0.194110 | + | 0.980980i | \(0.562182\pi\) | |||||||
\(510\) | 7372.24 | 0.640095 | ||||||||
\(511\) | −8312.43 | −0.719609 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 680.466 | 0.0585640 | ||||||||
\(514\) | −4769.51 | −0.409288 | ||||||||
\(515\) | −16598.8 | −1.42026 | ||||||||
\(516\) | 5928.75 | 0.505811 | ||||||||
\(517\) | −14247.8 | −1.21203 | ||||||||
\(518\) | 576.845 | 0.0489288 | ||||||||
\(519\) | −7164.95 | −0.605986 | ||||||||
\(520\) | −1784.98 | −0.150532 | ||||||||
\(521\) | 4257.67 | 0.358027 | 0.179013 | − | 0.983847i | \(-0.442709\pi\) | ||||
0.179013 | + | 0.983847i | \(0.442709\pi\) | |||||||
\(522\) | 3065.60 | 0.257046 | ||||||||
\(523\) | −1216.85 | −0.101739 | −0.0508694 | − | 0.998705i | \(-0.516199\pi\) | ||||
−0.0508694 | + | 0.998705i | \(0.516199\pi\) | |||||||
\(524\) | 1209.54 | 0.100838 | ||||||||
\(525\) | 2527.99 | 0.210154 | ||||||||
\(526\) | −11055.5 | −0.916431 | ||||||||
\(527\) | −3397.25 | −0.280810 | ||||||||
\(528\) | −1970.96 | −0.162453 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −15912.1 | −1.30410 | ||||||||
\(531\) | 4201.46 | 0.343367 | ||||||||
\(532\) | 705.669 | 0.0575087 | ||||||||
\(533\) | 493.093 | 0.0400717 | ||||||||
\(534\) | −6964.27 | −0.564369 | ||||||||
\(535\) | 26269.4 | 2.12285 | ||||||||
\(536\) | 7042.91 | 0.567551 | ||||||||
\(537\) | 6746.55 | 0.542151 | ||||||||
\(538\) | −5557.11 | −0.445323 | ||||||||
\(539\) | −2012.02 | −0.160786 | ||||||||
\(540\) | 1691.78 | 0.134820 | ||||||||
\(541\) | −17106.2 | −1.35943 | −0.679715 | − | 0.733476i | \(-0.737897\pi\) | ||||
−0.679715 | + | 0.733476i | \(0.737897\pi\) | |||||||
\(542\) | −6726.85 | −0.533105 | ||||||||
\(543\) | 8827.77 | 0.697672 | ||||||||
\(544\) | 2510.02 | 0.197824 | ||||||||
\(545\) | −19400.1 | −1.52479 | ||||||||
\(546\) | −598.236 | −0.0468904 | ||||||||
\(547\) | 5856.10 | 0.457749 | 0.228875 | − | 0.973456i | \(-0.426495\pi\) | ||||
0.228875 | + | 0.973456i | \(0.426495\pi\) | |||||||
\(548\) | 7239.12 | 0.564306 | ||||||||
\(549\) | −527.594 | −0.0410149 | ||||||||
\(550\) | −9886.05 | −0.766441 | ||||||||
\(551\) | 4292.26 | 0.331863 | ||||||||
\(552\) | 552.000 | 0.0425628 | ||||||||
\(553\) | −3816.30 | −0.293464 | ||||||||
\(554\) | 9944.08 | 0.762605 | ||||||||
\(555\) | 1936.30 | 0.148092 | ||||||||
\(556\) | −3364.54 | −0.256633 | ||||||||
\(557\) | −20383.9 | −1.55062 | −0.775308 | − | 0.631584i | \(-0.782405\pi\) | ||||
−0.775308 | + | 0.631584i | \(0.782405\pi\) | |||||||
\(558\) | −779.601 | −0.0591454 | ||||||||
\(559\) | −7037.28 | −0.532460 | ||||||||
\(560\) | 1754.44 | 0.132390 | ||||||||
\(561\) | −9662.41 | −0.727179 | ||||||||
\(562\) | −16745.3 | −1.25686 | ||||||||
\(563\) | −13396.6 | −1.00284 | −0.501419 | − | 0.865205i | \(-0.667188\pi\) | ||||
−0.501419 | + | 0.865205i | \(0.667188\pi\) | |||||||
\(564\) | 4163.84 | 0.310867 | ||||||||
\(565\) | 11094.9 | 0.826131 | ||||||||
\(566\) | −1891.53 | −0.140472 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −7638.75 | −0.564287 | ||||||||
\(569\) | 14019.7 | 1.03293 | 0.516465 | − | 0.856309i | \(-0.327248\pi\) | ||||
0.516465 | + | 0.856309i | \(0.327248\pi\) | |||||||
\(570\) | 2368.72 | 0.174061 | ||||||||
\(571\) | −4704.66 | −0.344805 | −0.172403 | − | 0.985027i | \(-0.555153\pi\) | ||||
−0.172403 | + | 0.985027i | \(0.555153\pi\) | |||||||
\(572\) | 2339.48 | 0.171012 | ||||||||
\(573\) | 8930.94 | 0.651127 | ||||||||
\(574\) | −484.656 | −0.0352424 | ||||||||
\(575\) | 2768.76 | 0.200809 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 22638.1 | 1.63334 | 0.816668 | − | 0.577107i | \(-0.195819\pi\) | ||||
0.816668 | + | 0.577107i | \(0.195819\pi\) | |||||||
\(578\) | 2479.12 | 0.178405 | ||||||||
\(579\) | 4326.81 | 0.310563 | ||||||||
\(580\) | 10671.5 | 0.763979 | ||||||||
\(581\) | −3809.26 | −0.272005 | ||||||||
\(582\) | −9262.77 | −0.659715 | ||||||||
\(583\) | 20855.1 | 1.48153 | ||||||||
\(584\) | −9499.92 | −0.673133 | ||||||||
\(585\) | −2008.10 | −0.141923 | ||||||||
\(586\) | −14300.0 | −1.00807 | ||||||||
\(587\) | 4850.29 | 0.341044 | 0.170522 | − | 0.985354i | \(-0.445455\pi\) | ||||
0.170522 | + | 0.985354i | \(0.445455\pi\) | |||||||
\(588\) | 588.000 | 0.0412393 | ||||||||
\(589\) | −1091.55 | −0.0763607 | ||||||||
\(590\) | 14625.4 | 1.02054 | ||||||||
\(591\) | −12184.1 | −0.848032 | ||||||||
\(592\) | 659.251 | 0.0457687 | ||||||||
\(593\) | −11984.4 | −0.829915 | −0.414958 | − | 0.909841i | \(-0.636204\pi\) | ||||
−0.414958 | + | 0.909841i | \(0.636204\pi\) | |||||||
\(594\) | −2217.33 | −0.153162 | ||||||||
\(595\) | 8600.95 | 0.592612 | ||||||||
\(596\) | −10219.1 | −0.702331 | ||||||||
\(597\) | 6935.51 | 0.475463 | ||||||||
\(598\) | −655.211 | −0.0448053 | ||||||||
\(599\) | −13344.5 | −0.910256 | −0.455128 | − | 0.890426i | \(-0.650407\pi\) | ||||
−0.455128 | + | 0.890426i | \(0.650407\pi\) | |||||||
\(600\) | 2889.14 | 0.196581 | ||||||||
\(601\) | 17124.7 | 1.16228 | 0.581139 | − | 0.813804i | \(-0.302607\pi\) | ||||
0.581139 | + | 0.813804i | \(0.302607\pi\) | |||||||
\(602\) | 6916.87 | 0.468290 | ||||||||
\(603\) | 7923.27 | 0.535092 | ||||||||
\(604\) | −5907.52 | −0.397970 | ||||||||
\(605\) | 5561.84 | 0.373754 | ||||||||
\(606\) | 10667.9 | 0.715107 | ||||||||
\(607\) | 12470.8 | 0.833893 | 0.416946 | − | 0.908931i | \(-0.363100\pi\) | ||||
0.416946 | + | 0.908931i | \(0.363100\pi\) | |||||||
\(608\) | 806.478 | 0.0537944 | ||||||||
\(609\) | 3576.54 | 0.237978 | ||||||||
\(610\) | −1836.57 | −0.121903 | ||||||||
\(611\) | −4942.37 | −0.327246 | ||||||||
\(612\) | 2823.78 | 0.186511 | ||||||||
\(613\) | 8662.64 | 0.570768 | 0.285384 | − | 0.958413i | \(-0.407879\pi\) | ||||
0.285384 | + | 0.958413i | \(0.407879\pi\) | |||||||
\(614\) | 325.478 | 0.0213929 | ||||||||
\(615\) | −1626.85 | −0.106668 | ||||||||
\(616\) | −2299.45 | −0.150402 | ||||||||
\(617\) | −20138.9 | −1.31404 | −0.657020 | − | 0.753873i | \(-0.728183\pi\) | ||||
−0.657020 | + | 0.753873i | \(0.728183\pi\) | |||||||
\(618\) | −6357.82 | −0.413834 | ||||||||
\(619\) | −11612.2 | −0.754013 | −0.377006 | − | 0.926211i | \(-0.623046\pi\) | ||||
−0.377006 | + | 0.926211i | \(0.623046\pi\) | |||||||
\(620\) | −2713.81 | −0.175789 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | 5851.80 | 0.377228 | ||||||||
\(623\) | −8124.98 | −0.522505 | ||||||||
\(624\) | −683.698 | −0.0438619 | ||||||||
\(625\) | −16181.1 | −1.03559 | ||||||||
\(626\) | −7127.04 | −0.455038 | ||||||||
\(627\) | −3104.56 | −0.197742 | ||||||||
\(628\) | −3332.74 | −0.211769 | ||||||||
\(629\) | 3231.91 | 0.204872 | ||||||||
\(630\) | 1973.74 | 0.124819 | ||||||||
\(631\) | 31294.9 | 1.97437 | 0.987187 | − | 0.159567i | \(-0.0510099\pi\) | ||||
0.987187 | + | 0.159567i | \(0.0510099\pi\) | |||||||
\(632\) | −4361.49 | −0.274511 | ||||||||
\(633\) | −10294.0 | −0.646365 | ||||||||
\(634\) | 7469.99 | 0.467936 | ||||||||
\(635\) | 28771.2 | 1.79803 | ||||||||
\(636\) | −6094.77 | −0.379990 | ||||||||
\(637\) | −697.942 | −0.0434120 | ||||||||
\(638\) | −13986.5 | −0.867918 | ||||||||
\(639\) | −8593.59 | −0.532014 | ||||||||
\(640\) | 2005.07 | 0.123840 | ||||||||
\(641\) | −14757.6 | −0.909344 | −0.454672 | − | 0.890659i | \(-0.650244\pi\) | ||||
−0.454672 | + | 0.890659i | \(0.650244\pi\) | |||||||
\(642\) | 10061.9 | 0.618555 | ||||||||
\(643\) | −23006.9 | −1.41105 | −0.705525 | − | 0.708685i | \(-0.749289\pi\) | ||||
−0.705525 | + | 0.708685i | \(0.749289\pi\) | |||||||
\(644\) | 644.000 | 0.0394055 | ||||||||
\(645\) | 23217.9 | 1.41737 | ||||||||
\(646\) | 3953.67 | 0.240797 | ||||||||
\(647\) | 17894.4 | 1.08733 | 0.543663 | − | 0.839304i | \(-0.317037\pi\) | ||||
0.543663 | + | 0.839304i | \(0.317037\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −19168.8 | −1.15938 | ||||||||
\(650\) | −3429.34 | −0.206938 | ||||||||
\(651\) | −909.535 | −0.0547580 | ||||||||
\(652\) | 2305.56 | 0.138485 | ||||||||
\(653\) | −13436.6 | −0.805230 | −0.402615 | − | 0.915369i | \(-0.631899\pi\) | ||||
−0.402615 | + | 0.915369i | \(0.631899\pi\) | |||||||
\(654\) | −7430.80 | −0.444293 | ||||||||
\(655\) | 4736.76 | 0.282565 | ||||||||
\(656\) | −553.892 | −0.0329663 | ||||||||
\(657\) | −10687.4 | −0.634636 | ||||||||
\(658\) | 4857.81 | 0.287807 | ||||||||
\(659\) | 6471.98 | 0.382568 | 0.191284 | − | 0.981535i | \(-0.438735\pi\) | ||||
0.191284 | + | 0.981535i | \(0.438735\pi\) | |||||||
\(660\) | −7718.58 | −0.455220 | ||||||||
\(661\) | 13545.5 | 0.797062 | 0.398531 | − | 0.917155i | \(-0.369520\pi\) | ||||
0.398531 | + | 0.917155i | \(0.369520\pi\) | |||||||
\(662\) | −21166.5 | −1.24269 | ||||||||
\(663\) | −3351.76 | −0.196337 | ||||||||
\(664\) | −4353.44 | −0.254437 | ||||||||
\(665\) | 2763.51 | 0.161149 | ||||||||
\(666\) | 741.657 | 0.0431511 | ||||||||
\(667\) | 3917.16 | 0.227396 | ||||||||
\(668\) | 4328.45 | 0.250708 | ||||||||
\(669\) | 6097.43 | 0.352377 | ||||||||
\(670\) | 27581.1 | 1.59038 | ||||||||
\(671\) | 2407.10 | 0.138487 | ||||||||
\(672\) | 672.000 | 0.0385758 | ||||||||
\(673\) | 9490.33 | 0.543574 | 0.271787 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271787 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(674\) | 8565.05 | 0.489486 | ||||||||
\(675\) | 3250.28 | 0.185338 | ||||||||
\(676\) | −7976.47 | −0.453827 | ||||||||
\(677\) | −1200.29 | −0.0681401 | −0.0340700 | − | 0.999419i | \(-0.510847\pi\) | ||||
−0.0340700 | + | 0.999419i | \(0.510847\pi\) | |||||||
\(678\) | 4249.65 | 0.240718 | ||||||||
\(679\) | −10806.6 | −0.610777 | ||||||||
\(680\) | 9829.65 | 0.554338 | ||||||||
\(681\) | 3958.50 | 0.222746 | ||||||||
\(682\) | 3556.85 | 0.199705 | ||||||||
\(683\) | −12270.6 | −0.687440 | −0.343720 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343720 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(684\) | 907.288 | 0.0507179 | ||||||||
\(685\) | 28349.5 | 1.58128 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 16075.4 | 0.892743 | ||||||||
\(688\) | 7905.00 | 0.438045 | ||||||||
\(689\) | 7234.35 | 0.400010 | ||||||||
\(690\) | 2161.72 | 0.119268 | ||||||||
\(691\) | 14926.5 | 0.821750 | 0.410875 | − | 0.911692i | \(-0.365223\pi\) | ||||
0.410875 | + | 0.911692i | \(0.365223\pi\) | |||||||
\(692\) | −9553.27 | −0.524799 | ||||||||
\(693\) | −2586.88 | −0.141800 | ||||||||
\(694\) | 21406.6 | 1.17087 | ||||||||
\(695\) | −13176.1 | −0.719132 | ||||||||
\(696\) | 4087.47 | 0.222608 | ||||||||
\(697\) | −2715.40 | −0.147565 | ||||||||
\(698\) | −11563.2 | −0.627039 | ||||||||
\(699\) | −10863.9 | −0.587854 | ||||||||
\(700\) | 3370.66 | 0.181999 | ||||||||
\(701\) | 2973.45 | 0.160208 | 0.0801038 | − | 0.996787i | \(-0.474475\pi\) | ||||
0.0801038 | + | 0.996787i | \(0.474475\pi\) | |||||||
\(702\) | −769.161 | −0.0413534 | ||||||||
\(703\) | 1038.42 | 0.0557110 | ||||||||
\(704\) | −2627.94 | −0.140688 | ||||||||
\(705\) | 16306.2 | 0.871104 | ||||||||
\(706\) | −4504.52 | −0.240127 | ||||||||
\(707\) | 12445.9 | 0.662060 | ||||||||
\(708\) | 5601.95 | 0.297365 | ||||||||
\(709\) | −1065.16 | −0.0564216 | −0.0282108 | − | 0.999602i | \(-0.508981\pi\) | ||||
−0.0282108 | + | 0.999602i | \(0.508981\pi\) | |||||||
\(710\) | −29914.5 | −1.58123 | ||||||||
\(711\) | −4906.68 | −0.258811 | ||||||||
\(712\) | −9285.69 | −0.488758 | ||||||||
\(713\) | −996.157 | −0.0523231 | ||||||||
\(714\) | 3294.41 | 0.172675 | ||||||||
\(715\) | 9161.77 | 0.479204 | ||||||||
\(716\) | 8995.40 | 0.469516 | ||||||||
\(717\) | −7121.14 | −0.370912 | ||||||||
\(718\) | −15638.1 | −0.812825 | ||||||||
\(719\) | −21596.5 | −1.12019 | −0.560093 | − | 0.828430i | \(-0.689234\pi\) | ||||
−0.560093 | + | 0.828430i | \(0.689234\pi\) | |||||||
\(720\) | 2255.71 | 0.116757 | ||||||||
\(721\) | −7417.46 | −0.383135 | ||||||||
\(722\) | −12447.7 | −0.641627 | ||||||||
\(723\) | −2016.70 | −0.103737 | ||||||||
\(724\) | 11770.4 | 0.604202 | ||||||||
\(725\) | 20502.2 | 1.05025 | ||||||||
\(726\) | 2130.34 | 0.108904 | ||||||||
\(727\) | 25240.0 | 1.28762 | 0.643810 | − | 0.765185i | \(-0.277353\pi\) | ||||
0.643810 | + | 0.765185i | \(0.277353\pi\) | |||||||
\(728\) | −797.648 | −0.0406082 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −37203.2 | −1.88624 | ||||||||
\(731\) | 38753.4 | 1.96080 | ||||||||
\(732\) | −703.459 | −0.0355199 | ||||||||
\(733\) | 15674.9 | 0.789859 | 0.394930 | − | 0.918711i | \(-0.370769\pi\) | ||||
0.394930 | + | 0.918711i | \(0.370769\pi\) | |||||||
\(734\) | 11691.0 | 0.587907 | ||||||||
\(735\) | 2302.70 | 0.115560 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −36149.2 | −1.80675 | ||||||||
\(738\) | −623.129 | −0.0310809 | ||||||||
\(739\) | −15214.4 | −0.757336 | −0.378668 | − | 0.925533i | \(-0.623618\pi\) | ||||
−0.378668 | + | 0.925533i | \(0.623618\pi\) | |||||||
\(740\) | 2581.73 | 0.128252 | ||||||||
\(741\) | −1076.93 | −0.0533900 | ||||||||
\(742\) | −7110.56 | −0.351802 | ||||||||
\(743\) | −5724.82 | −0.282669 | −0.141335 | − | 0.989962i | \(-0.545139\pi\) | ||||
−0.141335 | + | 0.989962i | \(0.545139\pi\) | |||||||
\(744\) | −1039.47 | −0.0512214 | ||||||||
\(745\) | −40019.5 | −1.96805 | ||||||||
\(746\) | 23150.9 | 1.13621 | ||||||||
\(747\) | −4897.63 | −0.239886 | ||||||||
\(748\) | −12883.2 | −0.629755 | ||||||||
\(749\) | 11738.9 | 0.572671 | ||||||||
\(750\) | −434.158 | −0.0211376 | ||||||||
\(751\) | −12154.2 | −0.590565 | −0.295282 | − | 0.955410i | \(-0.595414\pi\) | ||||
−0.295282 | + | 0.955410i | \(0.595414\pi\) | |||||||
\(752\) | 5551.78 | 0.269219 | ||||||||
\(753\) | −18528.8 | −0.896714 | ||||||||
\(754\) | −4851.73 | −0.234336 | ||||||||
\(755\) | −23134.8 | −1.11518 | ||||||||
\(756\) | 756.000 | 0.0363696 | ||||||||
\(757\) | 23567.7 | 1.13155 | 0.565775 | − | 0.824559i | \(-0.308577\pi\) | ||||
0.565775 | + | 0.824559i | \(0.308577\pi\) | |||||||
\(758\) | 8823.78 | 0.422815 | ||||||||
\(759\) | −2833.25 | −0.135495 | ||||||||
\(760\) | 3158.30 | 0.150741 | ||||||||
\(761\) | −3502.26 | −0.166829 | −0.0834145 | − | 0.996515i | \(-0.526583\pi\) | ||||
−0.0834145 | + | 0.996515i | \(0.526583\pi\) | |||||||
\(762\) | 11020.2 | 0.523910 | ||||||||
\(763\) | −8669.27 | −0.411335 | ||||||||
\(764\) | 11907.9 | 0.563892 | ||||||||
\(765\) | 11058.4 | 0.522635 | ||||||||
\(766\) | −9757.21 | −0.460238 | ||||||||
\(767\) | −6649.38 | −0.313032 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 11792.9 | 0.553008 | 0.276504 | − | 0.961013i | \(-0.410824\pi\) | ||||
0.276504 | + | 0.961013i | \(0.410824\pi\) | |||||||
\(770\) | −9005.01 | −0.421452 | ||||||||
\(771\) | −7154.26 | −0.334182 | ||||||||
\(772\) | 5769.07 | 0.268955 | ||||||||
\(773\) | 39556.2 | 1.84054 | 0.920269 | − | 0.391286i | \(-0.127970\pi\) | ||||
0.920269 | + | 0.391286i | \(0.127970\pi\) | |||||||
\(774\) | 8893.12 | 0.412993 | ||||||||
\(775\) | −5213.83 | −0.241660 | ||||||||
\(776\) | −12350.4 | −0.571330 | ||||||||
\(777\) | 865.267 | 0.0399502 | ||||||||
\(778\) | −10829.2 | −0.499028 | ||||||||
\(779\) | −872.465 | −0.0401275 | ||||||||
\(780\) | −2677.47 | −0.122909 | ||||||||
\(781\) | 39207.4 | 1.79635 | ||||||||
\(782\) | 3608.16 | 0.164997 | ||||||||
\(783\) | 4598.40 | 0.209877 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −13051.5 | −0.593414 | ||||||||
\(786\) | 1814.31 | 0.0823338 | ||||||||
\(787\) | 35601.9 | 1.61254 | 0.806270 | − | 0.591547i | \(-0.201483\pi\) | ||||
0.806270 | + | 0.591547i | \(0.201483\pi\) | |||||||
\(788\) | −16245.5 | −0.734418 | ||||||||
\(789\) | −16583.3 | −0.748263 | ||||||||
\(790\) | −17080.3 | −0.769227 | ||||||||
\(791\) | 4957.92 | 0.222861 | ||||||||
\(792\) | −2956.44 | −0.132642 | ||||||||
\(793\) | 834.989 | 0.0373913 | ||||||||
\(794\) | 16968.8 | 0.758437 | ||||||||
\(795\) | −23868.1 | −1.06480 | ||||||||
\(796\) | 9247.34 | 0.411763 | ||||||||
\(797\) | 15044.7 | 0.668644 | 0.334322 | − | 0.942459i | \(-0.391493\pi\) | ||||
0.334322 | + | 0.942459i | \(0.391493\pi\) | |||||||
\(798\) | 1058.50 | 0.0469556 | ||||||||
\(799\) | 27217.0 | 1.20509 | ||||||||
\(800\) | 3852.18 | 0.170244 | ||||||||
\(801\) | −10446.4 | −0.460806 | ||||||||
\(802\) | 29849.1 | 1.31423 | ||||||||
\(803\) | 48760.3 | 2.14285 | ||||||||
\(804\) | 10564.4 | 0.463403 | ||||||||
\(805\) | 2522.01 | 0.110421 | ||||||||
\(806\) | 1233.82 | 0.0539201 | ||||||||
\(807\) | −8335.66 | −0.363605 | ||||||||
\(808\) | 14223.9 | 0.619300 | ||||||||
\(809\) | 14290.7 | 0.621054 | 0.310527 | − | 0.950565i | \(-0.399495\pi\) | ||||
0.310527 | + | 0.950565i | \(0.399495\pi\) | |||||||
\(810\) | 2537.67 | 0.110080 | ||||||||
\(811\) | 38093.6 | 1.64938 | 0.824691 | − | 0.565584i | \(-0.191349\pi\) | ||||
0.824691 | + | 0.565584i | \(0.191349\pi\) | |||||||
\(812\) | 4768.71 | 0.206095 | ||||||||
\(813\) | −10090.3 | −0.435279 | ||||||||
\(814\) | −3383.74 | −0.145700 | ||||||||
\(815\) | 9028.92 | 0.388060 | ||||||||
\(816\) | 3765.04 | 0.161523 | ||||||||
\(817\) | 12451.6 | 0.533202 | ||||||||
\(818\) | 18051.2 | 0.771572 | ||||||||
\(819\) | −897.354 | −0.0382858 | ||||||||
\(820\) | −2169.13 | −0.0923772 | ||||||||
\(821\) | −25271.4 | −1.07427 | −0.537136 | − | 0.843496i | \(-0.680494\pi\) | ||||
−0.537136 | + | 0.843496i | \(0.680494\pi\) | |||||||
\(822\) | 10858.7 | 0.460754 | ||||||||
\(823\) | 2865.28 | 0.121358 | 0.0606788 | − | 0.998157i | \(-0.480673\pi\) | ||||
0.0606788 | + | 0.998157i | \(0.480673\pi\) | |||||||
\(824\) | −8477.10 | −0.358390 | ||||||||
\(825\) | −14829.1 | −0.625797 | ||||||||
\(826\) | 6535.61 | 0.275306 | ||||||||
\(827\) | 29292.8 | 1.23169 | 0.615846 | − | 0.787866i | \(-0.288814\pi\) | ||||
0.615846 | + | 0.787866i | \(0.288814\pi\) | |||||||
\(828\) | 828.000 | 0.0347524 | ||||||||
\(829\) | −8064.04 | −0.337848 | −0.168924 | − | 0.985629i | \(-0.554029\pi\) | ||||
−0.168924 | + | 0.985629i | \(0.554029\pi\) | |||||||
\(830\) | −17048.8 | −0.712978 | ||||||||
\(831\) | 14916.1 | 0.622665 | ||||||||
\(832\) | −911.598 | −0.0379855 | ||||||||
\(833\) | 3843.47 | 0.159866 | ||||||||
\(834\) | −5046.81 | −0.209540 | ||||||||
\(835\) | 16950.9 | 0.702527 | ||||||||
\(836\) | −4139.41 | −0.171250 | ||||||||
\(837\) | −1169.40 | −0.0482920 | ||||||||
\(838\) | −21399.6 | −0.882144 | ||||||||
\(839\) | 25900.2 | 1.06576 | 0.532881 | − | 0.846190i | \(-0.321109\pi\) | ||||
0.532881 | + | 0.846190i | \(0.321109\pi\) | |||||||
\(840\) | 2631.66 | 0.108096 | ||||||||
\(841\) | 4616.92 | 0.189303 | ||||||||
\(842\) | −4392.68 | −0.179788 | ||||||||
\(843\) | −25117.9 | −1.02622 | ||||||||
\(844\) | −13725.3 | −0.559769 | ||||||||
\(845\) | −31237.1 | −1.27170 | ||||||||
\(846\) | 6245.75 | 0.253822 | ||||||||
\(847\) | 2485.40 | 0.100826 | ||||||||
\(848\) | −8126.36 | −0.329081 | ||||||||
\(849\) | −2837.30 | −0.114695 | ||||||||
\(850\) | 18884.9 | 0.762055 | ||||||||
\(851\) | 947.673 | 0.0381737 | ||||||||
\(852\) | −11458.1 | −0.460738 | ||||||||
\(853\) | 6335.92 | 0.254323 | 0.127162 | − | 0.991882i | \(-0.459413\pi\) | ||||
0.127162 | + | 0.991882i | \(0.459413\pi\) | |||||||
\(854\) | −820.702 | −0.0328851 | ||||||||
\(855\) | 3553.08 | 0.142120 | ||||||||
\(856\) | 13415.9 | 0.535685 | ||||||||
\(857\) | −28071.1 | −1.11889 | −0.559446 | − | 0.828867i | \(-0.688986\pi\) | ||||
−0.559446 | + | 0.828867i | \(0.688986\pi\) | |||||||
\(858\) | 3509.22 | 0.139630 | ||||||||
\(859\) | −24241.4 | −0.962869 | −0.481434 | − | 0.876482i | \(-0.659884\pi\) | ||||
−0.481434 | + | 0.876482i | \(0.659884\pi\) | |||||||
\(860\) | 30957.2 | 1.22748 | ||||||||
\(861\) | −726.984 | −0.0287753 | ||||||||
\(862\) | −24076.2 | −0.951320 | ||||||||
\(863\) | −33031.3 | −1.30290 | −0.651448 | − | 0.758693i | \(-0.725838\pi\) | ||||
−0.651448 | + | 0.758693i | \(0.725838\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −37412.1 | −1.47058 | ||||||||
\(866\) | 9839.20 | 0.386085 | ||||||||
\(867\) | 3718.68 | 0.145667 | ||||||||
\(868\) | −1212.71 | −0.0474218 | ||||||||
\(869\) | 22386.2 | 0.873879 | ||||||||
\(870\) | 16007.2 | 0.623786 | ||||||||
\(871\) | −12539.6 | −0.487818 | ||||||||
\(872\) | −9907.73 | −0.384769 | ||||||||
\(873\) | −13894.2 | −0.538655 | ||||||||
\(874\) | 1159.31 | 0.0448677 | ||||||||
\(875\) | −506.518 | −0.0195696 | ||||||||
\(876\) | −14249.9 | −0.549610 | ||||||||
\(877\) | −31569.6 | −1.21554 | −0.607771 | − | 0.794112i | \(-0.707936\pi\) | ||||
−0.607771 | + | 0.794112i | \(0.707936\pi\) | |||||||
\(878\) | 3516.98 | 0.135185 | ||||||||
\(879\) | −21450.0 | −0.823082 | ||||||||
\(880\) | −10291.4 | −0.394232 | ||||||||
\(881\) | 14117.9 | 0.539892 | 0.269946 | − | 0.962875i | \(-0.412994\pi\) | ||||
0.269946 | + | 0.962875i | \(0.412994\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 18516.7 | 0.705705 | 0.352852 | − | 0.935679i | \(-0.385212\pi\) | ||||
0.352852 | + | 0.935679i | \(0.385212\pi\) | |||||||
\(884\) | −4469.01 | −0.170033 | ||||||||
\(885\) | 21938.1 | 0.833268 | ||||||||
\(886\) | −14770.9 | −0.560088 | ||||||||
\(887\) | 19958.0 | 0.755494 | 0.377747 | − | 0.925909i | \(-0.376699\pi\) | ||||
0.377747 | + | 0.925909i | \(0.376699\pi\) | |||||||
\(888\) | 988.877 | 0.0373700 | ||||||||
\(889\) | 12856.9 | 0.485047 | ||||||||
\(890\) | −36364.2 | −1.36959 | ||||||||
\(891\) | −3325.99 | −0.125056 | ||||||||
\(892\) | 8129.90 | 0.305167 | ||||||||
\(893\) | 8744.90 | 0.327701 | ||||||||
\(894\) | −15328.6 | −0.573451 | ||||||||
\(895\) | 35227.4 | 1.31567 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | −982.816 | −0.0365834 | ||||||||
\(898\) | −6698.51 | −0.248922 | ||||||||
\(899\) | −7376.38 | −0.273655 | ||||||||
\(900\) | 4333.71 | 0.160508 | ||||||||
\(901\) | −39838.6 | −1.47305 | ||||||||
\(902\) | 2842.97 | 0.104945 | ||||||||
\(903\) | 10375.3 | 0.382357 | ||||||||
\(904\) | 5666.20 | 0.208468 | ||||||||
\(905\) | 46094.6 | 1.69308 | ||||||||
\(906\) | −8861.28 | −0.324941 | ||||||||
\(907\) | 5992.05 | 0.219363 | 0.109682 | − | 0.993967i | \(-0.465017\pi\) | ||||
0.109682 | + | 0.993967i | \(0.465017\pi\) | |||||||
\(908\) | 5277.99 | 0.192904 | ||||||||
\(909\) | 16001.9 | 0.583882 | ||||||||
\(910\) | −3123.72 | −0.113791 | ||||||||
\(911\) | 46442.8 | 1.68904 | 0.844522 | − | 0.535520i | \(-0.179884\pi\) | ||||
0.844522 | + | 0.535520i | \(0.179884\pi\) | |||||||
\(912\) | 1209.72 | 0.0439230 | ||||||||
\(913\) | 22344.9 | 0.809978 | ||||||||
\(914\) | −18091.2 | −0.654709 | ||||||||
\(915\) | −2754.86 | −0.0995330 | ||||||||
\(916\) | 21433.9 | 0.773138 | ||||||||
\(917\) | 2116.70 | 0.0762263 | ||||||||
\(918\) | 4235.67 | 0.152285 | ||||||||
\(919\) | 28341.6 | 1.01731 | 0.508653 | − | 0.860972i | \(-0.330144\pi\) | ||||
0.508653 | + | 0.860972i | \(0.330144\pi\) | |||||||
\(920\) | 2882.29 | 0.103290 | ||||||||
\(921\) | 488.217 | 0.0174672 | ||||||||
\(922\) | −2667.51 | −0.0952819 | ||||||||
\(923\) | 13600.5 | 0.485012 | ||||||||
\(924\) | −3449.18 | −0.122803 | ||||||||
\(925\) | 4960.07 | 0.176309 | ||||||||
\(926\) | 8110.23 | 0.287817 | ||||||||
\(927\) | −9536.73 | −0.337894 | ||||||||
\(928\) | 5449.96 | 0.192784 | ||||||||
\(929\) | 21328.8 | 0.753256 | 0.376628 | − | 0.926365i | \(-0.377083\pi\) | ||||
0.376628 | + | 0.926365i | \(0.377083\pi\) | |||||||
\(930\) | −4070.72 | −0.143531 | ||||||||
\(931\) | 1234.92 | 0.0434725 | ||||||||
\(932\) | −14485.2 | −0.509096 | ||||||||
\(933\) | 8777.70 | 0.308005 | ||||||||
\(934\) | 15446.6 | 0.541144 | ||||||||
\(935\) | −50452.7 | −1.76468 | ||||||||
\(936\) | −1025.55 | −0.0358131 | ||||||||
\(937\) | 21171.3 | 0.738141 | 0.369070 | − | 0.929401i | \(-0.379676\pi\) | ||||
0.369070 | + | 0.929401i | \(0.379676\pi\) | |||||||
\(938\) | 12325.1 | 0.429028 | ||||||||
\(939\) | −10690.6 | −0.371537 | ||||||||
\(940\) | 21741.7 | 0.754398 | ||||||||
\(941\) | 36049.9 | 1.24888 | 0.624439 | − | 0.781074i | \(-0.285328\pi\) | ||||
0.624439 | + | 0.781074i | \(0.285328\pi\) | |||||||
\(942\) | −4999.11 | −0.172909 | ||||||||
\(943\) | −796.220 | −0.0274958 | ||||||||
\(944\) | 7469.27 | 0.257525 | ||||||||
\(945\) | 2960.62 | 0.101914 | ||||||||
\(946\) | −40574.0 | −1.39448 | ||||||||
\(947\) | −53347.8 | −1.83059 | −0.915296 | − | 0.402783i | \(-0.868043\pi\) | ||||
−0.915296 | + | 0.402783i | \(0.868043\pi\) | |||||||
\(948\) | −6542.23 | −0.224137 | ||||||||
\(949\) | 16914.3 | 0.578567 | ||||||||
\(950\) | 6067.78 | 0.207226 | ||||||||
\(951\) | 11205.0 | 0.382068 | ||||||||
\(952\) | 4392.54 | 0.149541 | ||||||||
\(953\) | 38206.3 | 1.29866 | 0.649330 | − | 0.760507i | \(-0.275049\pi\) | ||||
0.649330 | + | 0.760507i | \(0.275049\pi\) | |||||||
\(954\) | −9142.15 | −0.310260 | ||||||||
\(955\) | 46633.3 | 1.58012 | ||||||||
\(956\) | −9494.86 | −0.321219 | ||||||||
\(957\) | −20979.8 | −0.708652 | ||||||||
\(958\) | 3212.52 | 0.108342 | ||||||||
\(959\) | 12668.5 | 0.426575 | ||||||||
\(960\) | 3007.61 | 0.101115 | ||||||||
\(961\) | −27915.1 | −0.937033 | ||||||||
\(962\) | −1173.77 | −0.0393388 | ||||||||
\(963\) | 15092.9 | 0.505048 | ||||||||
\(964\) | −2688.93 | −0.0898389 | ||||||||
\(965\) | 22592.6 | 0.753660 | ||||||||
\(966\) | 966.000 | 0.0321745 | ||||||||
\(967\) | −34937.5 | −1.16185 | −0.580927 | − | 0.813956i | \(-0.697310\pi\) | ||||
−0.580927 | + | 0.813956i | \(0.697310\pi\) | |||||||
\(968\) | 2840.46 | 0.0943138 | ||||||||
\(969\) | 5930.51 | 0.196610 | ||||||||
\(970\) | −48365.9 | −1.60097 | ||||||||
\(971\) | −9345.45 | −0.308867 | −0.154434 | − | 0.988003i | \(-0.549355\pi\) | ||||
−0.154434 | + | 0.988003i | \(0.549355\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −5887.94 | −0.193997 | ||||||||
\(974\) | −851.024 | −0.0279965 | ||||||||
\(975\) | −5144.00 | −0.168964 | ||||||||
\(976\) | −937.945 | −0.0307612 | ||||||||
\(977\) | −58593.9 | −1.91871 | −0.959357 | − | 0.282195i | \(-0.908938\pi\) | ||||
−0.959357 | + | 0.282195i | \(0.908938\pi\) | |||||||
\(978\) | 3458.33 | 0.113073 | ||||||||
\(979\) | 47660.7 | 1.55592 | ||||||||
\(980\) | 3070.27 | 0.100078 | ||||||||
\(981\) | −11146.2 | −0.362763 | ||||||||
\(982\) | 2322.58 | 0.0754752 | ||||||||
\(983\) | 11642.3 | 0.377755 | 0.188877 | − | 0.982001i | \(-0.439515\pi\) | ||||
0.188877 | + | 0.982001i | \(0.439515\pi\) | |||||||
\(984\) | −830.839 | −0.0269168 | ||||||||
\(985\) | −63619.8 | −2.05797 | ||||||||
\(986\) | 26717.8 | 0.862950 | ||||||||
\(987\) | 7286.71 | 0.234994 | ||||||||
\(988\) | −1435.91 | −0.0462371 | ||||||||
\(989\) | 11363.4 | 0.365355 | ||||||||
\(990\) | −11577.9 | −0.371686 | ||||||||
\(991\) | −5953.15 | −0.190825 | −0.0954127 | − | 0.995438i | \(-0.530417\pi\) | ||||
−0.0954127 | + | 0.995438i | \(0.530417\pi\) | |||||||
\(992\) | −1385.96 | −0.0443591 | ||||||||
\(993\) | −31749.7 | −1.01465 | ||||||||
\(994\) | −13367.8 | −0.426561 | ||||||||
\(995\) | 36214.0 | 1.15383 | ||||||||
\(996\) | −6530.17 | −0.207747 | ||||||||
\(997\) | 22143.4 | 0.703399 | 0.351700 | − | 0.936113i | \(-0.385604\pi\) | ||||
0.351700 | + | 0.936113i | \(0.385604\pi\) | |||||||
\(998\) | −12452.9 | −0.394978 | ||||||||
\(999\) | 1112.49 | 0.0352327 |
(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 | 966.4.a.r.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.r.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial |