Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,4,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, 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("1617.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(95.4060884793\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 30x^{3} + 11x^{2} + 185x + 162 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.28053\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.28053 | 0.452737 | 0.226369 | − | 0.974042i | \(-0.427315\pi\) | ||||
0.226369 | + | 0.974042i | \(0.427315\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −6.36023 | −0.795029 | ||||||||
\(5\) | −16.8824 | −1.51001 | −0.755004 | − | 0.655720i | \(-0.772365\pi\) | ||||
−0.755004 | + | 0.655720i | \(0.772365\pi\) | |||||||
\(6\) | 3.84160 | 0.261388 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −18.3888 | −0.812676 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −21.6185 | −0.683637 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −19.0807 | −0.459010 | ||||||||
\(13\) | 68.0397 | 1.45160 | 0.725801 | − | 0.687905i | \(-0.241469\pi\) | ||||
0.725801 | + | 0.687905i | \(0.241469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −50.6472 | −0.871804 | ||||||||
\(16\) | 27.3344 | 0.427100 | ||||||||
\(17\) | −119.045 | −1.69839 | −0.849197 | − | 0.528076i | \(-0.822913\pi\) | ||||
−0.849197 | + | 0.528076i | \(0.822913\pi\) | |||||||
\(18\) | 11.5248 | 0.150912 | ||||||||
\(19\) | −16.8404 | −0.203340 | −0.101670 | − | 0.994818i | \(-0.532419\pi\) | ||||
−0.101670 | + | 0.994818i | \(0.532419\pi\) | |||||||
\(20\) | 107.376 | 1.20050 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.0859 | 0.136505 | ||||||||
\(23\) | 199.722 | 1.81065 | 0.905323 | − | 0.424724i | \(-0.139629\pi\) | ||||
0.905323 | + | 0.424724i | \(0.139629\pi\) | |||||||
\(24\) | −55.1663 | −0.469199 | ||||||||
\(25\) | 160.016 | 1.28013 | ||||||||
\(26\) | 87.1272 | 0.657194 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 181.053 | 1.15933 | 0.579667 | − | 0.814853i | \(-0.303183\pi\) | ||||
0.579667 | + | 0.814853i | \(0.303183\pi\) | |||||||
\(30\) | −64.8555 | −0.394698 | ||||||||
\(31\) | 31.5474 | 0.182776 | 0.0913882 | − | 0.995815i | \(-0.470870\pi\) | ||||
0.0913882 | + | 0.995815i | \(0.470870\pi\) | |||||||
\(32\) | 182.113 | 1.00604 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −152.441 | −0.768926 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −57.2421 | −0.265010 | ||||||||
\(37\) | 75.9047 | 0.337261 | 0.168630 | − | 0.985679i | \(-0.446066\pi\) | ||||
0.168630 | + | 0.985679i | \(0.446066\pi\) | |||||||
\(38\) | −21.5647 | −0.0920594 | ||||||||
\(39\) | 204.119 | 0.838083 | ||||||||
\(40\) | 310.447 | 1.22715 | ||||||||
\(41\) | −408.485 | −1.55597 | −0.777983 | − | 0.628285i | \(-0.783757\pi\) | ||||
−0.777983 | + | 0.628285i | \(0.783757\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −97.8817 | −0.347135 | −0.173568 | − | 0.984822i | \(-0.555530\pi\) | ||||
−0.173568 | + | 0.984822i | \(0.555530\pi\) | |||||||
\(44\) | −69.9626 | −0.239710 | ||||||||
\(45\) | −151.942 | −0.503336 | ||||||||
\(46\) | 255.750 | 0.819747 | ||||||||
\(47\) | −41.8437 | −0.129862 | −0.0649311 | − | 0.997890i | \(-0.520683\pi\) | ||||
−0.0649311 | + | 0.997890i | \(0.520683\pi\) | |||||||
\(48\) | 82.0033 | 0.246586 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 204.906 | 0.579561 | ||||||||
\(51\) | −357.136 | −0.980568 | ||||||||
\(52\) | −432.748 | −1.15407 | ||||||||
\(53\) | −563.375 | −1.46010 | −0.730052 | − | 0.683392i | \(-0.760504\pi\) | ||||
−0.730052 | + | 0.683392i | \(0.760504\pi\) | |||||||
\(54\) | 34.5744 | 0.0871293 | ||||||||
\(55\) | −185.707 | −0.455285 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −50.5212 | −0.117398 | ||||||||
\(58\) | 231.845 | 0.524874 | ||||||||
\(59\) | 224.425 | 0.495213 | 0.247607 | − | 0.968861i | \(-0.420356\pi\) | ||||
0.247607 | + | 0.968861i | \(0.420356\pi\) | |||||||
\(60\) | 322.128 | 0.693109 | ||||||||
\(61\) | 622.237 | 1.30605 | 0.653027 | − | 0.757335i | \(-0.273499\pi\) | ||||
0.653027 | + | 0.757335i | \(0.273499\pi\) | |||||||
\(62\) | 40.3975 | 0.0827497 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 14.5263 | 0.0283716 | ||||||||
\(65\) | −1148.67 | −2.19193 | ||||||||
\(66\) | 42.2576 | 0.0788114 | ||||||||
\(67\) | −280.572 | −0.511603 | −0.255801 | − | 0.966729i | \(-0.582339\pi\) | ||||
−0.255801 | + | 0.966729i | \(0.582339\pi\) | |||||||
\(68\) | 757.155 | 1.35027 | ||||||||
\(69\) | 599.165 | 1.04538 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −807.229 | −1.34930 | −0.674651 | − | 0.738137i | \(-0.735706\pi\) | ||||
−0.674651 | + | 0.738137i | \(0.735706\pi\) | |||||||
\(72\) | −165.499 | −0.270892 | ||||||||
\(73\) | −1038.49 | −1.66501 | −0.832505 | − | 0.554017i | \(-0.813094\pi\) | ||||
−0.832505 | + | 0.554017i | \(0.813094\pi\) | |||||||
\(74\) | 97.1985 | 0.152691 | ||||||||
\(75\) | 480.047 | 0.739081 | ||||||||
\(76\) | 107.109 | 0.161661 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 261.382 | 0.379431 | ||||||||
\(79\) | 710.954 | 1.01251 | 0.506257 | − | 0.862383i | \(-0.331029\pi\) | ||||
0.506257 | + | 0.862383i | \(0.331029\pi\) | |||||||
\(80\) | −461.471 | −0.644925 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −523.079 | −0.704444 | ||||||||
\(83\) | 191.854 | 0.253719 | 0.126860 | − | 0.991921i | \(-0.459510\pi\) | ||||
0.126860 | + | 0.991921i | \(0.459510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2009.77 | 2.56459 | ||||||||
\(86\) | −125.341 | −0.157161 | ||||||||
\(87\) | 543.159 | 0.669342 | ||||||||
\(88\) | −202.276 | −0.245031 | ||||||||
\(89\) | −1562.10 | −1.86047 | −0.930236 | − | 0.366962i | \(-0.880398\pi\) | ||||
−0.930236 | + | 0.366962i | \(0.880398\pi\) | |||||||
\(90\) | −194.566 | −0.227879 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1270.28 | −1.43952 | ||||||||
\(93\) | 94.6421 | 0.105526 | ||||||||
\(94\) | −53.5822 | −0.0587935 | ||||||||
\(95\) | 284.307 | 0.307045 | ||||||||
\(96\) | 546.338 | 0.580838 | ||||||||
\(97\) | −816.513 | −0.854684 | −0.427342 | − | 0.904090i | \(-0.640550\pi\) | ||||
−0.427342 | + | 0.904090i | \(0.640550\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −1017.74 | −1.01774 | ||||||||
\(101\) | 990.633 | 0.975957 | 0.487979 | − | 0.872856i | \(-0.337734\pi\) | ||||
0.487979 | + | 0.872856i | \(0.337734\pi\) | |||||||
\(102\) | −457.324 | −0.443940 | ||||||||
\(103\) | 1947.55 | 1.86308 | 0.931542 | − | 0.363634i | \(-0.118464\pi\) | ||||
0.931542 | + | 0.363634i | \(0.118464\pi\) | |||||||
\(104\) | −1251.17 | −1.17968 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −721.421 | −0.661043 | ||||||||
\(107\) | −479.820 | −0.433513 | −0.216757 | − | 0.976226i | \(-0.569548\pi\) | ||||
−0.216757 | + | 0.976226i | \(0.569548\pi\) | |||||||
\(108\) | −171.726 | −0.153003 | ||||||||
\(109\) | −474.762 | −0.417192 | −0.208596 | − | 0.978002i | \(-0.566889\pi\) | ||||
−0.208596 | + | 0.978002i | \(0.566889\pi\) | |||||||
\(110\) | −237.803 | −0.206124 | ||||||||
\(111\) | 227.714 | 0.194718 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 486.828 | 0.405283 | 0.202641 | − | 0.979253i | \(-0.435047\pi\) | ||||
0.202641 | + | 0.979253i | \(0.435047\pi\) | |||||||
\(114\) | −64.6942 | −0.0531505 | ||||||||
\(115\) | −3371.78 | −2.73409 | ||||||||
\(116\) | −1151.54 | −0.921704 | ||||||||
\(117\) | 612.357 | 0.483867 | ||||||||
\(118\) | 287.383 | 0.224201 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 931.340 | 0.708494 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 796.795 | 0.591299 | ||||||||
\(123\) | −1225.45 | −0.898338 | ||||||||
\(124\) | −200.648 | −0.145313 | ||||||||
\(125\) | −591.150 | −0.422993 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1060.45 | −0.740943 | −0.370471 | − | 0.928844i | \(-0.620804\pi\) | ||||
−0.370471 | + | 0.928844i | \(0.620804\pi\) | |||||||
\(128\) | −1438.30 | −0.993196 | ||||||||
\(129\) | −293.645 | −0.200419 | ||||||||
\(130\) | −1470.92 | −0.992369 | ||||||||
\(131\) | −1988.88 | −1.32648 | −0.663242 | − | 0.748405i | \(-0.730820\pi\) | ||||
−0.663242 | + | 0.748405i | \(0.730820\pi\) | |||||||
\(132\) | −209.888 | −0.138397 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −359.283 | −0.231622 | ||||||||
\(135\) | −455.825 | −0.290601 | ||||||||
\(136\) | 2189.09 | 1.38024 | ||||||||
\(137\) | −1270.95 | −0.792590 | −0.396295 | − | 0.918123i | \(-0.629704\pi\) | ||||
−0.396295 | + | 0.918123i | \(0.629704\pi\) | |||||||
\(138\) | 767.251 | 0.473281 | ||||||||
\(139\) | 1086.86 | 0.663210 | 0.331605 | − | 0.943418i | \(-0.392410\pi\) | ||||
0.331605 | + | 0.943418i | \(0.392410\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −125.531 | −0.0749760 | ||||||||
\(142\) | −1033.68 | −0.610879 | ||||||||
\(143\) | 748.437 | 0.437674 | ||||||||
\(144\) | 246.010 | 0.142367 | ||||||||
\(145\) | −3056.61 | −1.75060 | ||||||||
\(146\) | −1329.82 | −0.753812 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −482.772 | −0.268132 | ||||||||
\(149\) | −811.871 | −0.446383 | −0.223192 | − | 0.974775i | \(-0.571648\pi\) | ||||
−0.223192 | + | 0.974775i | \(0.571648\pi\) | |||||||
\(150\) | 614.717 | 0.334609 | ||||||||
\(151\) | −719.203 | −0.387602 | −0.193801 | − | 0.981041i | \(-0.562082\pi\) | ||||
−0.193801 | + | 0.981041i | \(0.562082\pi\) | |||||||
\(152\) | 309.674 | 0.165249 | ||||||||
\(153\) | −1071.41 | −0.566131 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −532.595 | −0.275994 | ||||||||
\(156\) | −1298.25 | −0.666300 | ||||||||
\(157\) | −3411.37 | −1.73412 | −0.867061 | − | 0.498201i | \(-0.833994\pi\) | ||||
−0.867061 | + | 0.498201i | \(0.833994\pi\) | |||||||
\(158\) | 910.401 | 0.458402 | ||||||||
\(159\) | −1690.12 | −0.842991 | ||||||||
\(160\) | −3074.50 | −1.51913 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 103.723 | 0.0503041 | ||||||||
\(163\) | −2691.36 | −1.29327 | −0.646637 | − | 0.762798i | \(-0.723825\pi\) | ||||
−0.646637 | + | 0.762798i | \(0.723825\pi\) | |||||||
\(164\) | 2598.06 | 1.23704 | ||||||||
\(165\) | −557.120 | −0.262859 | ||||||||
\(166\) | 245.675 | 0.114868 | ||||||||
\(167\) | 2449.16 | 1.13486 | 0.567429 | − | 0.823422i | \(-0.307938\pi\) | ||||
0.567429 | + | 0.823422i | \(0.307938\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2432.40 | 1.10715 | ||||||||
\(170\) | 2573.58 | 1.16108 | ||||||||
\(171\) | −151.564 | −0.0677799 | ||||||||
\(172\) | 622.550 | 0.275983 | ||||||||
\(173\) | −914.239 | −0.401782 | −0.200891 | − | 0.979614i | \(-0.564384\pi\) | ||||
−0.200891 | + | 0.979614i | \(0.564384\pi\) | |||||||
\(174\) | 695.534 | 0.303036 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 300.679 | 0.128776 | ||||||||
\(177\) | 673.274 | 0.285912 | ||||||||
\(178\) | −2000.32 | −0.842305 | ||||||||
\(179\) | −3651.00 | −1.52452 | −0.762258 | − | 0.647273i | \(-0.775909\pi\) | ||||
−0.762258 | + | 0.647273i | \(0.775909\pi\) | |||||||
\(180\) | 966.384 | 0.400167 | ||||||||
\(181\) | 193.523 | 0.0794722 | 0.0397361 | − | 0.999210i | \(-0.487348\pi\) | ||||
0.0397361 | + | 0.999210i | \(0.487348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1866.71 | 0.754050 | ||||||||
\(184\) | −3672.64 | −1.47147 | ||||||||
\(185\) | −1281.45 | −0.509267 | ||||||||
\(186\) | 121.192 | 0.0477756 | ||||||||
\(187\) | −1309.50 | −0.512085 | ||||||||
\(188\) | 266.135 | 0.103244 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 364.064 | 0.139011 | ||||||||
\(191\) | 3300.22 | 1.25024 | 0.625119 | − | 0.780529i | \(-0.285050\pi\) | ||||
0.625119 | + | 0.780529i | \(0.285050\pi\) | |||||||
\(192\) | 43.5788 | 0.0163804 | ||||||||
\(193\) | 2659.32 | 0.991824 | 0.495912 | − | 0.868373i | \(-0.334834\pi\) | ||||
0.495912 | + | 0.868373i | \(0.334834\pi\) | |||||||
\(194\) | −1045.57 | −0.386947 | ||||||||
\(195\) | −3446.02 | −1.26551 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1318.61 | 0.476890 | 0.238445 | − | 0.971156i | \(-0.423362\pi\) | ||||
0.238445 | + | 0.971156i | \(0.423362\pi\) | |||||||
\(198\) | 126.773 | 0.0455018 | ||||||||
\(199\) | 1213.60 | 0.432309 | 0.216155 | − | 0.976359i | \(-0.430648\pi\) | ||||
0.216155 | + | 0.976359i | \(0.430648\pi\) | |||||||
\(200\) | −2942.49 | −1.04033 | ||||||||
\(201\) | −841.717 | −0.295374 | ||||||||
\(202\) | 1268.54 | 0.441852 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2271.46 | 0.779580 | ||||||||
\(205\) | 6896.21 | 2.34952 | ||||||||
\(206\) | 2493.90 | 0.843487 | ||||||||
\(207\) | 1797.50 | 0.603549 | ||||||||
\(208\) | 1859.83 | 0.619979 | ||||||||
\(209\) | −185.244 | −0.0613092 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −999.365 | −0.326062 | −0.163031 | − | 0.986621i | \(-0.552127\pi\) | ||||
−0.163031 | + | 0.986621i | \(0.552127\pi\) | |||||||
\(212\) | 3583.20 | 1.16083 | ||||||||
\(213\) | −2421.69 | −0.779020 | ||||||||
\(214\) | −614.425 | −0.196268 | ||||||||
\(215\) | 1652.48 | 0.524177 | ||||||||
\(216\) | −496.497 | −0.156400 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −607.949 | −0.188878 | ||||||||
\(219\) | −3115.46 | −0.961294 | ||||||||
\(220\) | 1181.14 | 0.361965 | ||||||||
\(221\) | −8099.80 | −2.46539 | ||||||||
\(222\) | 291.596 | 0.0881559 | ||||||||
\(223\) | −594.639 | −0.178565 | −0.0892825 | − | 0.996006i | \(-0.528457\pi\) | ||||
−0.0892825 | + | 0.996006i | \(0.528457\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1440.14 | 0.426709 | ||||||||
\(226\) | 623.400 | 0.183487 | ||||||||
\(227\) | −3854.66 | −1.12706 | −0.563531 | − | 0.826095i | \(-0.690557\pi\) | ||||
−0.563531 | + | 0.826095i | \(0.690557\pi\) | |||||||
\(228\) | 321.327 | 0.0933350 | ||||||||
\(229\) | 1878.04 | 0.541942 | 0.270971 | − | 0.962588i | \(-0.412655\pi\) | ||||
0.270971 | + | 0.962588i | \(0.412655\pi\) | |||||||
\(230\) | −4317.68 | −1.23782 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3329.34 | −0.942164 | ||||||||
\(233\) | −2960.57 | −0.832418 | −0.416209 | − | 0.909269i | \(-0.636641\pi\) | ||||
−0.416209 | + | 0.909269i | \(0.636641\pi\) | |||||||
\(234\) | 784.145 | 0.219065 | ||||||||
\(235\) | 706.422 | 0.196093 | ||||||||
\(236\) | −1427.39 | −0.393709 | ||||||||
\(237\) | 2132.86 | 0.584575 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1857.27 | −0.502664 | −0.251332 | − | 0.967901i | \(-0.580869\pi\) | ||||
−0.251332 | + | 0.967901i | \(0.580869\pi\) | |||||||
\(240\) | −1384.41 | −0.372348 | ||||||||
\(241\) | −3597.60 | −0.961583 | −0.480792 | − | 0.876835i | \(-0.659651\pi\) | ||||
−0.480792 | + | 0.876835i | \(0.659651\pi\) | |||||||
\(242\) | 154.945 | 0.0411579 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −3957.57 | −1.03835 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1569.24 | −0.406711 | ||||||||
\(247\) | −1145.82 | −0.295168 | ||||||||
\(248\) | −580.117 | −0.148538 | ||||||||
\(249\) | 575.562 | 0.146485 | ||||||||
\(250\) | −756.988 | −0.191504 | ||||||||
\(251\) | −910.320 | −0.228920 | −0.114460 | − | 0.993428i | \(-0.536514\pi\) | ||||
−0.114460 | + | 0.993428i | \(0.536514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2196.94 | 0.545930 | ||||||||
\(254\) | −1357.94 | −0.335452 | ||||||||
\(255\) | 6029.31 | 1.48067 | ||||||||
\(256\) | −1958.00 | −0.478028 | ||||||||
\(257\) | 669.516 | 0.162503 | 0.0812515 | − | 0.996694i | \(-0.474108\pi\) | ||||
0.0812515 | + | 0.996694i | \(0.474108\pi\) | |||||||
\(258\) | −376.022 | −0.0907369 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7305.84 | 1.74265 | ||||||||
\(261\) | 1629.48 | 0.386445 | ||||||||
\(262\) | −2546.83 | −0.600549 | ||||||||
\(263\) | 5046.95 | 1.18330 | 0.591651 | − | 0.806195i | \(-0.298477\pi\) | ||||
0.591651 | + | 0.806195i | \(0.298477\pi\) | |||||||
\(264\) | −606.829 | −0.141469 | ||||||||
\(265\) | 9511.13 | 2.20477 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4686.29 | −1.07414 | ||||||||
\(268\) | 1784.51 | 0.406739 | ||||||||
\(269\) | −7226.13 | −1.63786 | −0.818931 | − | 0.573892i | \(-0.805433\pi\) | ||||
−0.818931 | + | 0.573892i | \(0.805433\pi\) | |||||||
\(270\) | −583.699 | −0.131566 | ||||||||
\(271\) | 4741.05 | 1.06272 | 0.531362 | − | 0.847145i | \(-0.321680\pi\) | ||||
0.531362 | + | 0.847145i | \(0.321680\pi\) | |||||||
\(272\) | −3254.03 | −0.725384 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1627.50 | −0.358835 | ||||||||
\(275\) | 1760.17 | 0.385972 | ||||||||
\(276\) | −3810.83 | −0.831105 | ||||||||
\(277\) | −7997.89 | −1.73482 | −0.867412 | − | 0.497590i | \(-0.834218\pi\) | ||||
−0.867412 | + | 0.497590i | \(0.834218\pi\) | |||||||
\(278\) | 1391.76 | 0.300260 | ||||||||
\(279\) | 283.926 | 0.0609255 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −304.490 | −0.0646418 | −0.0323209 | − | 0.999478i | \(-0.510290\pi\) | ||||
−0.0323209 | + | 0.999478i | \(0.510290\pi\) | |||||||
\(282\) | −160.747 | −0.0339444 | ||||||||
\(283\) | −6994.49 | −1.46919 | −0.734593 | − | 0.678508i | \(-0.762627\pi\) | ||||
−0.734593 | + | 0.678508i | \(0.762627\pi\) | |||||||
\(284\) | 5134.16 | 1.07273 | ||||||||
\(285\) | 852.920 | 0.177272 | ||||||||
\(286\) | 958.399 | 0.198151 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1639.02 | 0.335347 | ||||||||
\(289\) | 9258.75 | 1.88454 | ||||||||
\(290\) | −3914.09 | −0.792564 | ||||||||
\(291\) | −2449.54 | −0.493452 | ||||||||
\(292\) | 6605.02 | 1.32373 | ||||||||
\(293\) | −3090.16 | −0.616141 | −0.308070 | − | 0.951364i | \(-0.599683\pi\) | ||||
−0.308070 | + | 0.951364i | \(0.599683\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3788.83 | −0.747776 | ||||||||
\(296\) | −1395.79 | −0.274084 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −1039.63 | −0.202094 | ||||||||
\(299\) | 13589.0 | 2.62834 | ||||||||
\(300\) | −3053.21 | −0.587591 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −920.964 | −0.175482 | ||||||||
\(303\) | 2971.90 | 0.563469 | ||||||||
\(304\) | −460.323 | −0.0868465 | ||||||||
\(305\) | −10504.9 | −1.97215 | ||||||||
\(306\) | −1371.97 | −0.256309 | ||||||||
\(307\) | −2816.61 | −0.523624 | −0.261812 | − | 0.965119i | \(-0.584320\pi\) | ||||
−0.261812 | + | 0.965119i | \(0.584320\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5842.64 | 1.07565 | ||||||||
\(310\) | −682.006 | −0.124953 | ||||||||
\(311\) | 1962.61 | 0.357844 | 0.178922 | − | 0.983863i | \(-0.442739\pi\) | ||||
0.178922 | + | 0.983863i | \(0.442739\pi\) | |||||||
\(312\) | −3753.50 | −0.681090 | ||||||||
\(313\) | 9270.94 | 1.67420 | 0.837100 | − | 0.547050i | \(-0.184249\pi\) | ||||
0.837100 | + | 0.547050i | \(0.184249\pi\) | |||||||
\(314\) | −4368.38 | −0.785102 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4521.83 | −0.804978 | ||||||||
\(317\) | −2929.73 | −0.519084 | −0.259542 | − | 0.965732i | \(-0.583572\pi\) | ||||
−0.259542 | + | 0.965732i | \(0.583572\pi\) | |||||||
\(318\) | −2164.26 | −0.381654 | ||||||||
\(319\) | 1991.58 | 0.349552 | ||||||||
\(320\) | −245.238 | −0.0428414 | ||||||||
\(321\) | −1439.46 | −0.250289 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2004.77 | 0.345351 | ||||||||
\(324\) | −515.179 | −0.0883366 | ||||||||
\(325\) | 10887.4 | 1.85823 | ||||||||
\(326\) | −3446.38 | −0.585513 | ||||||||
\(327\) | −1424.29 | −0.240866 | ||||||||
\(328\) | 7511.53 | 1.26450 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −713.410 | −0.119006 | ||||||||
\(331\) | −6024.72 | −1.00045 | −0.500224 | − | 0.865896i | \(-0.666749\pi\) | ||||
−0.500224 | + | 0.865896i | \(0.666749\pi\) | |||||||
\(332\) | −1220.24 | −0.201714 | ||||||||
\(333\) | 683.142 | 0.112420 | ||||||||
\(334\) | 3136.23 | 0.513793 | ||||||||
\(335\) | 4736.74 | 0.772524 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1851.77 | 0.299324 | 0.149662 | − | 0.988737i | \(-0.452181\pi\) | ||||
0.149662 | + | 0.988737i | \(0.452181\pi\) | |||||||
\(338\) | 3114.77 | 0.501247 | ||||||||
\(339\) | 1460.48 | 0.233990 | ||||||||
\(340\) | −12782.6 | −2.03892 | ||||||||
\(341\) | 347.021 | 0.0551092 | ||||||||
\(342\) | −194.082 | −0.0306865 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1799.92 | 0.282109 | ||||||||
\(345\) | −10115.4 | −1.57853 | ||||||||
\(346\) | −1170.71 | −0.181902 | ||||||||
\(347\) | 3931.79 | 0.608269 | 0.304134 | − | 0.952629i | \(-0.401633\pi\) | ||||
0.304134 | + | 0.952629i | \(0.401633\pi\) | |||||||
\(348\) | −3454.62 | −0.532146 | ||||||||
\(349\) | 746.311 | 0.114467 | 0.0572337 | − | 0.998361i | \(-0.481772\pi\) | ||||
0.0572337 | + | 0.998361i | \(0.481772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1837.07 | 0.279361 | ||||||||
\(352\) | 2003.24 | 0.303333 | ||||||||
\(353\) | 8623.77 | 1.30027 | 0.650137 | − | 0.759817i | \(-0.274711\pi\) | ||||
0.650137 | + | 0.759817i | \(0.274711\pi\) | |||||||
\(354\) | 862.150 | 0.129443 | ||||||||
\(355\) | 13628.0 | 2.03746 | ||||||||
\(356\) | 9935.30 | 1.47913 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4675.23 | −0.690205 | ||||||||
\(359\) | 4195.46 | 0.616791 | 0.308395 | − | 0.951258i | \(-0.400208\pi\) | ||||
0.308395 | + | 0.951258i | \(0.400208\pi\) | |||||||
\(360\) | 2794.02 | 0.409049 | ||||||||
\(361\) | −6575.40 | −0.958653 | ||||||||
\(362\) | 247.813 | 0.0359800 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17532.2 | 2.51418 | ||||||||
\(366\) | 2390.39 | 0.341386 | ||||||||
\(367\) | 11009.4 | 1.56590 | 0.782948 | − | 0.622087i | \(-0.213715\pi\) | ||||
0.782948 | + | 0.622087i | \(0.213715\pi\) | |||||||
\(368\) | 5459.28 | 0.773328 | ||||||||
\(369\) | −3676.36 | −0.518655 | ||||||||
\(370\) | −1640.95 | −0.230564 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −601.945 | −0.0838963 | ||||||||
\(373\) | −647.517 | −0.0898852 | −0.0449426 | − | 0.998990i | \(-0.514310\pi\) | ||||
−0.0449426 | + | 0.998990i | \(0.514310\pi\) | |||||||
\(374\) | −1676.86 | −0.231840 | ||||||||
\(375\) | −1773.45 | −0.244215 | ||||||||
\(376\) | 769.453 | 0.105536 | ||||||||
\(377\) | 12318.8 | 1.68289 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10934.0 | 1.48191 | 0.740955 | − | 0.671555i | \(-0.234373\pi\) | ||||
0.740955 | + | 0.671555i | \(0.234373\pi\) | |||||||
\(380\) | −1808.26 | −0.244109 | ||||||||
\(381\) | −3181.35 | −0.427783 | ||||||||
\(382\) | 4226.04 | 0.566029 | ||||||||
\(383\) | 662.006 | 0.0883210 | 0.0441605 | − | 0.999024i | \(-0.485939\pi\) | ||||
0.0441605 | + | 0.999024i | \(0.485939\pi\) | |||||||
\(384\) | −4314.90 | −0.573422 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3405.35 | 0.449036 | ||||||||
\(387\) | −880.935 | −0.115712 | ||||||||
\(388\) | 5193.21 | 0.679499 | ||||||||
\(389\) | 46.1336 | 0.00601302 | 0.00300651 | − | 0.999995i | \(-0.499043\pi\) | ||||
0.00300651 | + | 0.999995i | \(0.499043\pi\) | |||||||
\(390\) | −4412.75 | −0.572944 | ||||||||
\(391\) | −23775.9 | −3.07519 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5966.64 | −0.765846 | ||||||||
\(394\) | 1688.53 | 0.215906 | ||||||||
\(395\) | −12002.6 | −1.52890 | ||||||||
\(396\) | −629.663 | −0.0799034 | ||||||||
\(397\) | −11516.2 | −1.45587 | −0.727936 | − | 0.685645i | \(-0.759520\pi\) | ||||
−0.727936 | + | 0.685645i | \(0.759520\pi\) | |||||||
\(398\) | 1554.05 | 0.195723 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4373.94 | 0.546742 | ||||||||
\(401\) | −9201.87 | −1.14593 | −0.572967 | − | 0.819578i | \(-0.694208\pi\) | ||||
−0.572967 | + | 0.819578i | \(0.694208\pi\) | |||||||
\(402\) | −1077.85 | −0.133727 | ||||||||
\(403\) | 2146.47 | 0.265319 | ||||||||
\(404\) | −6300.66 | −0.775914 | ||||||||
\(405\) | −1367.48 | −0.167779 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 834.952 | 0.101688 | ||||||||
\(408\) | 6567.28 | 0.796884 | ||||||||
\(409\) | −5529.75 | −0.668529 | −0.334265 | − | 0.942479i | \(-0.608488\pi\) | ||||
−0.334265 | + | 0.942479i | \(0.608488\pi\) | |||||||
\(410\) | 8830.83 | 1.06372 | ||||||||
\(411\) | −3812.86 | −0.457602 | ||||||||
\(412\) | −12386.9 | −1.48121 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2301.75 | 0.273249 | ||||||||
\(415\) | −3238.96 | −0.383118 | ||||||||
\(416\) | 12390.9 | 1.46037 | ||||||||
\(417\) | 3260.58 | 0.382905 | ||||||||
\(418\) | −237.212 | −0.0277570 | ||||||||
\(419\) | 13372.9 | 1.55921 | 0.779604 | − | 0.626273i | \(-0.215420\pi\) | ||||
0.779604 | + | 0.626273i | \(0.215420\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6100.40 | −0.706213 | −0.353106 | − | 0.935583i | \(-0.614875\pi\) | ||||
−0.353106 | + | 0.935583i | \(0.614875\pi\) | |||||||
\(422\) | −1279.72 | −0.147620 | ||||||||
\(423\) | −376.593 | −0.0432874 | ||||||||
\(424\) | 10359.8 | 1.18659 | ||||||||
\(425\) | −19049.1 | −2.17416 | ||||||||
\(426\) | −3101.05 | −0.352691 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3051.76 | 0.344656 | ||||||||
\(429\) | 2245.31 | 0.252691 | ||||||||
\(430\) | 2116.05 | 0.237314 | ||||||||
\(431\) | −4465.34 | −0.499043 | −0.249522 | − | 0.968369i | \(-0.580273\pi\) | ||||
−0.249522 | + | 0.968369i | \(0.580273\pi\) | |||||||
\(432\) | 738.029 | 0.0821955 | ||||||||
\(433\) | 9331.67 | 1.03568 | 0.517842 | − | 0.855476i | \(-0.326735\pi\) | ||||
0.517842 | + | 0.855476i | \(0.326735\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9169.83 | −1.01071 | ||||||||
\(436\) | 3019.60 | 0.331680 | ||||||||
\(437\) | −3363.40 | −0.368176 | ||||||||
\(438\) | −3989.45 | −0.435214 | ||||||||
\(439\) | −2725.68 | −0.296332 | −0.148166 | − | 0.988963i | \(-0.547337\pi\) | ||||
−0.148166 | + | 0.988963i | \(0.547337\pi\) | |||||||
\(440\) | 3414.91 | 0.369999 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10372.1 | −1.11617 | ||||||||
\(443\) | −14731.7 | −1.57996 | −0.789980 | − | 0.613132i | \(-0.789909\pi\) | ||||
−0.789980 | + | 0.613132i | \(0.789909\pi\) | |||||||
\(444\) | −1448.31 | −0.154806 | ||||||||
\(445\) | 26372.0 | 2.80933 | ||||||||
\(446\) | −761.456 | −0.0808430 | ||||||||
\(447\) | −2435.61 | −0.257719 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1591.42 | −0.167269 | −0.0836345 | − | 0.996497i | \(-0.526653\pi\) | ||||
−0.0836345 | + | 0.996497i | \(0.526653\pi\) | |||||||
\(450\) | 1844.15 | 0.193187 | ||||||||
\(451\) | −4493.33 | −0.469141 | ||||||||
\(452\) | −3096.34 | −0.322212 | ||||||||
\(453\) | −2157.61 | −0.223782 | ||||||||
\(454\) | −4936.03 | −0.510263 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 929.023 | 0.0954068 | ||||||||
\(457\) | −9627.76 | −0.985487 | −0.492744 | − | 0.870175i | \(-0.664006\pi\) | ||||
−0.492744 | + | 0.870175i | \(0.664006\pi\) | |||||||
\(458\) | 2404.90 | 0.245357 | ||||||||
\(459\) | −3214.22 | −0.326856 | ||||||||
\(460\) | 21445.3 | 2.17368 | ||||||||
\(461\) | −15234.5 | −1.53913 | −0.769567 | − | 0.638566i | \(-0.779528\pi\) | ||||
−0.769567 | + | 0.638566i | \(0.779528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5534.70 | 0.555549 | 0.277775 | − | 0.960646i | \(-0.410403\pi\) | ||||
0.277775 | + | 0.960646i | \(0.410403\pi\) | |||||||
\(464\) | 4948.98 | 0.495152 | ||||||||
\(465\) | −1597.79 | −0.159345 | ||||||||
\(466\) | −3791.11 | −0.376866 | ||||||||
\(467\) | 2265.02 | 0.224438 | 0.112219 | − | 0.993683i | \(-0.464204\pi\) | ||||
0.112219 | + | 0.993683i | \(0.464204\pi\) | |||||||
\(468\) | −3894.74 | −0.384689 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 904.597 | 0.0887786 | ||||||||
\(471\) | −10234.1 | −1.00120 | ||||||||
\(472\) | −4126.89 | −0.402448 | ||||||||
\(473\) | −1076.70 | −0.104665 | ||||||||
\(474\) | 2731.20 | 0.264659 | ||||||||
\(475\) | −2694.73 | −0.260300 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5070.37 | −0.486701 | ||||||||
\(478\) | −2378.29 | −0.227575 | ||||||||
\(479\) | 2150.36 | 0.205120 | 0.102560 | − | 0.994727i | \(-0.467297\pi\) | ||||
0.102560 | + | 0.994727i | \(0.467297\pi\) | |||||||
\(480\) | −9223.51 | −0.877070 | ||||||||
\(481\) | 5164.53 | 0.489569 | ||||||||
\(482\) | −4606.84 | −0.435344 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −769.588 | −0.0722754 | ||||||||
\(485\) | 13784.7 | 1.29058 | ||||||||
\(486\) | 311.170 | 0.0290431 | ||||||||
\(487\) | −19739.0 | −1.83667 | −0.918336 | − | 0.395801i | \(-0.870467\pi\) | ||||
−0.918336 | + | 0.395801i | \(0.870467\pi\) | |||||||
\(488\) | −11442.2 | −1.06140 | ||||||||
\(489\) | −8074.08 | −0.746672 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18494.8 | 1.69992 | 0.849958 | − | 0.526850i | \(-0.176627\pi\) | ||||
0.849958 | + | 0.526850i | \(0.176627\pi\) | |||||||
\(492\) | 7794.18 | 0.714204 | ||||||||
\(493\) | −21553.5 | −1.96901 | ||||||||
\(494\) | −1467.26 | −0.133634 | ||||||||
\(495\) | −1671.36 | −0.151762 | ||||||||
\(496\) | 862.329 | 0.0780639 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 737.026 | 0.0663191 | ||||||||
\(499\) | 1228.36 | 0.110199 | 0.0550993 | − | 0.998481i | \(-0.482452\pi\) | ||||
0.0550993 | + | 0.998481i | \(0.482452\pi\) | |||||||
\(500\) | 3759.85 | 0.336291 | ||||||||
\(501\) | 7347.47 | 0.655211 | ||||||||
\(502\) | −1165.70 | −0.103641 | ||||||||
\(503\) | −17887.6 | −1.58562 | −0.792812 | − | 0.609466i | \(-0.791384\pi\) | ||||
−0.792812 | + | 0.609466i | \(0.791384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16724.3 | −1.47370 | ||||||||
\(506\) | 2813.26 | 0.247163 | ||||||||
\(507\) | 7297.21 | 0.639212 | ||||||||
\(508\) | 6744.71 | 0.589071 | ||||||||
\(509\) | −6755.97 | −0.588317 | −0.294158 | − | 0.955757i | \(-0.595039\pi\) | ||||
−0.294158 | + | 0.955757i | \(0.595039\pi\) | |||||||
\(510\) | 7720.73 | 0.670353 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8999.12 | 0.776775 | ||||||||
\(513\) | −454.691 | −0.0391327 | ||||||||
\(514\) | 857.339 | 0.0735712 | ||||||||
\(515\) | −32879.3 | −2.81327 | ||||||||
\(516\) | 1867.65 | 0.159339 | ||||||||
\(517\) | −460.280 | −0.0391549 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2742.72 | −0.231969 | ||||||||
\(520\) | 21122.7 | 1.78133 | ||||||||
\(521\) | −10300.4 | −0.866158 | −0.433079 | − | 0.901356i | \(-0.642573\pi\) | ||||
−0.433079 | + | 0.901356i | \(0.642573\pi\) | |||||||
\(522\) | 2086.60 | 0.174958 | ||||||||
\(523\) | 1205.75 | 0.100811 | 0.0504053 | − | 0.998729i | \(-0.483949\pi\) | ||||
0.0504053 | + | 0.998729i | \(0.483949\pi\) | |||||||
\(524\) | 12649.7 | 1.05459 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6462.79 | 0.535724 | ||||||||
\(527\) | −3755.56 | −0.310426 | ||||||||
\(528\) | 902.036 | 0.0743486 | ||||||||
\(529\) | 27721.8 | 2.27844 | ||||||||
\(530\) | 12179.3 | 0.998181 | ||||||||
\(531\) | 2019.82 | 0.165071 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27793.2 | −2.25864 | ||||||||
\(534\) | −6000.96 | −0.486305 | ||||||||
\(535\) | 8100.51 | 0.654609 | ||||||||
\(536\) | 5159.38 | 0.415767 | ||||||||
\(537\) | −10953.0 | −0.880180 | ||||||||
\(538\) | −9253.31 | −0.741521 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2899.15 | 0.231036 | ||||||||
\(541\) | 3970.16 | 0.315509 | 0.157755 | − | 0.987478i | \(-0.449575\pi\) | ||||
0.157755 | + | 0.987478i | \(0.449575\pi\) | |||||||
\(542\) | 6071.08 | 0.481135 | ||||||||
\(543\) | 580.570 | 0.0458833 | ||||||||
\(544\) | −21679.6 | −1.70865 | ||||||||
\(545\) | 8015.13 | 0.629964 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24218.7 | −1.89308 | −0.946541 | − | 0.322584i | \(-0.895449\pi\) | ||||
−0.946541 | + | 0.322584i | \(0.895449\pi\) | |||||||
\(548\) | 8083.56 | 0.630132 | ||||||||
\(549\) | 5600.13 | 0.435351 | ||||||||
\(550\) | 2253.96 | 0.174744 | ||||||||
\(551\) | −3049.01 | −0.235739 | ||||||||
\(552\) | −11017.9 | −0.849553 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10241.6 | −0.785420 | ||||||||
\(555\) | −3844.36 | −0.294025 | ||||||||
\(556\) | −6912.68 | −0.527271 | ||||||||
\(557\) | −15753.5 | −1.19838 | −0.599190 | − | 0.800607i | \(-0.704511\pi\) | ||||
−0.599190 | + | 0.800607i | \(0.704511\pi\) | |||||||
\(558\) | 363.577 | 0.0275832 | ||||||||
\(559\) | −6659.84 | −0.503902 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3928.49 | −0.295652 | ||||||||
\(562\) | −389.910 | −0.0292658 | ||||||||
\(563\) | 7797.63 | 0.583714 | 0.291857 | − | 0.956462i | \(-0.405727\pi\) | ||||
0.291857 | + | 0.956462i | \(0.405727\pi\) | |||||||
\(564\) | 798.406 | 0.0596081 | ||||||||
\(565\) | −8218.83 | −0.611980 | ||||||||
\(566\) | −8956.69 | −0.665155 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14843.9 | 1.09655 | ||||||||
\(569\) | 5074.55 | 0.373877 | 0.186939 | − | 0.982372i | \(-0.440143\pi\) | ||||
0.186939 | + | 0.982372i | \(0.440143\pi\) | |||||||
\(570\) | 1092.19 | 0.0802578 | ||||||||
\(571\) | 19247.4 | 1.41065 | 0.705323 | − | 0.708886i | \(-0.250802\pi\) | ||||
0.705323 | + | 0.708886i | \(0.250802\pi\) | |||||||
\(572\) | −4760.23 | −0.347964 | ||||||||
\(573\) | 9900.66 | 0.721826 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31958.6 | 2.31786 | ||||||||
\(576\) | 130.736 | 0.00945720 | ||||||||
\(577\) | −13981.0 | −1.00873 | −0.504364 | − | 0.863491i | \(-0.668273\pi\) | ||||
−0.504364 | + | 0.863491i | \(0.668273\pi\) | |||||||
\(578\) | 11856.1 | 0.853202 | ||||||||
\(579\) | 7977.96 | 0.572630 | ||||||||
\(580\) | 19440.8 | 1.39178 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3136.72 | −0.223404 | ||||||||
\(583\) | −6197.12 | −0.440238 | ||||||||
\(584\) | 19096.5 | 1.35311 | ||||||||
\(585\) | −10338.1 | −0.730644 | ||||||||
\(586\) | −3957.06 | −0.278950 | ||||||||
\(587\) | 864.831 | 0.0608099 | 0.0304049 | − | 0.999538i | \(-0.490320\pi\) | ||||
0.0304049 | + | 0.999538i | \(0.490320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −531.270 | −0.0371657 | ||||||||
\(590\) | −4851.72 | −0.338546 | ||||||||
\(591\) | 3955.84 | 0.275333 | ||||||||
\(592\) | 2074.81 | 0.144044 | ||||||||
\(593\) | −3157.59 | −0.218662 | −0.109331 | − | 0.994005i | \(-0.534871\pi\) | ||||
−0.109331 | + | 0.994005i | \(0.534871\pi\) | |||||||
\(594\) | 380.319 | 0.0262705 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5163.69 | 0.354888 | ||||||||
\(597\) | 3640.79 | 0.249594 | ||||||||
\(598\) | 17401.2 | 1.18995 | ||||||||
\(599\) | 11270.2 | 0.768758 | 0.384379 | − | 0.923175i | \(-0.374416\pi\) | ||||
0.384379 | + | 0.923175i | \(0.374416\pi\) | |||||||
\(600\) | −8827.48 | −0.600634 | ||||||||
\(601\) | 22222.4 | 1.50827 | 0.754135 | − | 0.656719i | \(-0.228056\pi\) | ||||
0.754135 | + | 0.656719i | \(0.228056\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2525.15 | −0.170534 | ||||||||
\(604\) | 4574.30 | 0.308155 | ||||||||
\(605\) | −2042.77 | −0.137274 | ||||||||
\(606\) | 3805.62 | 0.255103 | ||||||||
\(607\) | −1829.17 | −0.122312 | −0.0611562 | − | 0.998128i | \(-0.519479\pi\) | ||||
−0.0611562 | + | 0.998128i | \(0.519479\pi\) | |||||||
\(608\) | −3066.85 | −0.204568 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13451.8 | −0.892866 | ||||||||
\(611\) | −2847.03 | −0.188508 | ||||||||
\(612\) | 6814.39 | 0.450091 | ||||||||
\(613\) | 11172.5 | 0.736136 | 0.368068 | − | 0.929799i | \(-0.380019\pi\) | ||||
0.368068 | + | 0.929799i | \(0.380019\pi\) | |||||||
\(614\) | −3606.77 | −0.237064 | ||||||||
\(615\) | 20688.6 | 1.35650 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14278.2 | −0.931634 | −0.465817 | − | 0.884881i | \(-0.654240\pi\) | ||||
−0.465817 | + | 0.884881i | \(0.654240\pi\) | |||||||
\(618\) | 7481.70 | 0.486988 | ||||||||
\(619\) | 12918.1 | 0.838809 | 0.419405 | − | 0.907799i | \(-0.362239\pi\) | ||||
0.419405 | + | 0.907799i | \(0.362239\pi\) | |||||||
\(620\) | 3387.43 | 0.219423 | ||||||||
\(621\) | 5392.49 | 0.348459 | ||||||||
\(622\) | 2513.19 | 0.162009 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5579.48 | 0.357945 | ||||||||
\(625\) | −10021.9 | −0.641404 | ||||||||
\(626\) | 11871.8 | 0.757973 | ||||||||
\(627\) | −555.733 | −0.0353969 | ||||||||
\(628\) | 21697.1 | 1.37868 | ||||||||
\(629\) | −9036.09 | −0.572802 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17365.6 | −1.09558 | −0.547792 | − | 0.836614i | \(-0.684532\pi\) | ||||
−0.547792 | + | 0.836614i | \(0.684532\pi\) | |||||||
\(632\) | −13073.6 | −0.822846 | ||||||||
\(633\) | −2998.09 | −0.188252 | ||||||||
\(634\) | −3751.61 | −0.235009 | ||||||||
\(635\) | 17902.9 | 1.11883 | ||||||||
\(636\) | 10749.6 | 0.670203 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2550.29 | 0.158255 | ||||||||
\(639\) | −7265.06 | −0.449767 | ||||||||
\(640\) | 24282.0 | 1.49973 | ||||||||
\(641\) | −3234.39 | −0.199299 | −0.0996494 | − | 0.995023i | \(-0.531772\pi\) | ||||
−0.0996494 | + | 0.995023i | \(0.531772\pi\) | |||||||
\(642\) | −1843.28 | −0.113315 | ||||||||
\(643\) | 4372.53 | 0.268174 | 0.134087 | − | 0.990970i | \(-0.457190\pi\) | ||||
0.134087 | + | 0.990970i | \(0.457190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4957.43 | 0.302634 | ||||||||
\(646\) | 2567.18 | 0.156353 | ||||||||
\(647\) | −9149.07 | −0.555930 | −0.277965 | − | 0.960591i | \(-0.589660\pi\) | ||||
−0.277965 | + | 0.960591i | \(0.589660\pi\) | |||||||
\(648\) | −1489.49 | −0.0902974 | ||||||||
\(649\) | 2468.67 | 0.149312 | ||||||||
\(650\) | 13941.7 | 0.841291 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17117.7 | 1.02819 | ||||||||
\(653\) | −33267.8 | −1.99367 | −0.996837 | − | 0.0794734i | \(-0.974676\pi\) | ||||
−0.996837 | + | 0.0794734i | \(0.974676\pi\) | |||||||
\(654\) | −1823.85 | −0.109049 | ||||||||
\(655\) | 33577.1 | 2.00300 | ||||||||
\(656\) | −11165.7 | −0.664554 | ||||||||
\(657\) | −9346.38 | −0.555003 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15125.2 | −0.894073 | −0.447037 | − | 0.894516i | \(-0.647521\pi\) | ||||
−0.447037 | + | 0.894516i | \(0.647521\pi\) | |||||||
\(660\) | 3543.41 | 0.208980 | ||||||||
\(661\) | −12789.3 | −0.752568 | −0.376284 | − | 0.926504i | \(-0.622798\pi\) | ||||
−0.376284 | + | 0.926504i | \(0.622798\pi\) | |||||||
\(662\) | −7714.86 | −0.452940 | ||||||||
\(663\) | −24299.4 | −1.42339 | ||||||||
\(664\) | −3527.96 | −0.206192 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 874.787 | 0.0508969 | ||||||||
\(667\) | 36160.2 | 2.09914 | ||||||||
\(668\) | −15577.2 | −0.902246 | ||||||||
\(669\) | −1783.92 | −0.103095 | ||||||||
\(670\) | 6065.55 | 0.349750 | ||||||||
\(671\) | 6844.60 | 0.393790 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18730.3 | −1.07281 | −0.536404 | − | 0.843962i | \(-0.680217\pi\) | ||||
−0.536404 | + | 0.843962i | \(0.680217\pi\) | |||||||
\(674\) | 2371.25 | 0.135515 | ||||||||
\(675\) | 4320.42 | 0.246360 | ||||||||
\(676\) | −15470.6 | −0.880214 | ||||||||
\(677\) | 6160.79 | 0.349747 | 0.174873 | − | 0.984591i | \(-0.444048\pi\) | ||||
0.174873 | + | 0.984591i | \(0.444048\pi\) | |||||||
\(678\) | 1870.20 | 0.105936 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −36957.2 | −2.08418 | ||||||||
\(681\) | −11564.0 | −0.650709 | ||||||||
\(682\) | 444.372 | 0.0249500 | ||||||||
\(683\) | 3050.21 | 0.170883 | 0.0854415 | − | 0.996343i | \(-0.472770\pi\) | ||||
0.0854415 | + | 0.996343i | \(0.472770\pi\) | |||||||
\(684\) | 963.980 | 0.0538870 | ||||||||
\(685\) | 21456.7 | 1.19682 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5634.13 | 0.312890 | ||||||||
\(688\) | −2675.54 | −0.148262 | ||||||||
\(689\) | −38331.9 | −2.11949 | ||||||||
\(690\) | −12953.1 | −0.714658 | ||||||||
\(691\) | 12418.3 | 0.683668 | 0.341834 | − | 0.939760i | \(-0.388952\pi\) | ||||
0.341834 | + | 0.939760i | \(0.388952\pi\) | |||||||
\(692\) | 5814.77 | 0.319428 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5034.79 | 0.275386 | ||||||||
\(695\) | −18348.8 | −1.00145 | ||||||||
\(696\) | −9988.02 | −0.543958 | ||||||||
\(697\) | 48628.1 | 2.64264 | ||||||||
\(698\) | 955.676 | 0.0518236 | ||||||||
\(699\) | −8881.71 | −0.480597 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15271.1 | −0.822796 | −0.411398 | − | 0.911456i | \(-0.634959\pi\) | ||||
−0.411398 | + | 0.911456i | \(0.634959\pi\) | |||||||
\(702\) | 2352.43 | 0.126477 | ||||||||
\(703\) | −1278.27 | −0.0685785 | ||||||||
\(704\) | 159.789 | 0.00855436 | ||||||||
\(705\) | 2119.27 | 0.113214 | ||||||||
\(706\) | 11043.0 | 0.588682 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4282.18 | −0.227308 | ||||||||
\(709\) | 24174.5 | 1.28052 | 0.640262 | − | 0.768157i | \(-0.278826\pi\) | ||||
0.640262 | + | 0.768157i | \(0.278826\pi\) | |||||||
\(710\) | 17451.1 | 0.922433 | ||||||||
\(711\) | 6398.59 | 0.337504 | ||||||||
\(712\) | 28725.0 | 1.51196 | ||||||||
\(713\) | 6300.69 | 0.330944 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12635.4 | −0.660892 | ||||||||
\(716\) | 23221.2 | 1.21203 | ||||||||
\(717\) | −5571.80 | −0.290213 | ||||||||
\(718\) | 5372.43 | 0.279244 | ||||||||
\(719\) | −21724.7 | −1.12683 | −0.563416 | − | 0.826173i | \(-0.690513\pi\) | ||||
−0.563416 | + | 0.826173i | \(0.690513\pi\) | |||||||
\(720\) | −4153.24 | −0.214975 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8420.02 | −0.434018 | ||||||||
\(723\) | −10792.8 | −0.555170 | ||||||||
\(724\) | −1230.85 | −0.0631827 | ||||||||
\(725\) | 28971.3 | 1.48409 | ||||||||
\(726\) | 464.834 | 0.0237625 | ||||||||
\(727\) | 32751.2 | 1.67081 | 0.835403 | − | 0.549638i | \(-0.185234\pi\) | ||||
0.835403 | + | 0.549638i | \(0.185234\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 22450.5 | 1.13826 | ||||||||
\(731\) | 11652.3 | 0.589572 | ||||||||
\(732\) | −11872.7 | −0.599492 | ||||||||
\(733\) | 5646.65 | 0.284535 | 0.142267 | − | 0.989828i | \(-0.454561\pi\) | ||||
0.142267 | + | 0.989828i | \(0.454561\pi\) | |||||||
\(734\) | 14097.9 | 0.708940 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 36371.9 | 1.82158 | ||||||||
\(737\) | −3086.30 | −0.154254 | ||||||||
\(738\) | −4707.71 | −0.234815 | ||||||||
\(739\) | 34189.8 | 1.70188 | 0.850942 | − | 0.525260i | \(-0.176032\pi\) | ||||
0.850942 | + | 0.525260i | \(0.176032\pi\) | |||||||
\(740\) | 8150.35 | 0.404882 | ||||||||
\(741\) | −3437.45 | −0.170415 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15998.8 | −0.789960 | −0.394980 | − | 0.918690i | \(-0.629249\pi\) | ||||
−0.394980 | + | 0.918690i | \(0.629249\pi\) | |||||||
\(744\) | −1740.35 | −0.0857585 | ||||||||
\(745\) | 13706.3 | 0.674042 | ||||||||
\(746\) | −829.168 | −0.0406944 | ||||||||
\(747\) | 1726.68 | 0.0845731 | ||||||||
\(748\) | 8328.70 | 0.407122 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2270.96 | −0.110565 | ||||||||
\(751\) | −18097.7 | −0.879354 | −0.439677 | − | 0.898156i | \(-0.644907\pi\) | ||||
−0.439677 | + | 0.898156i | \(0.644907\pi\) | |||||||
\(752\) | −1143.77 | −0.0554642 | ||||||||
\(753\) | −2730.96 | −0.132167 | ||||||||
\(754\) | 15774.6 | 0.761908 | ||||||||
\(755\) | 12141.9 | 0.585282 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8597.91 | 0.412809 | 0.206404 | − | 0.978467i | \(-0.433824\pi\) | ||||
0.206404 | + | 0.978467i | \(0.433824\pi\) | |||||||
\(758\) | 14001.4 | 0.670915 | ||||||||
\(759\) | 6590.82 | 0.315193 | ||||||||
\(760\) | −5228.05 | −0.249528 | ||||||||
\(761\) | −31479.9 | −1.49953 | −0.749767 | − | 0.661702i | \(-0.769835\pi\) | ||||
−0.749767 | + | 0.661702i | \(0.769835\pi\) | |||||||
\(762\) | −4073.83 | −0.193673 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −20990.2 | −0.993976 | ||||||||
\(765\) | 18087.9 | 0.854863 | ||||||||
\(766\) | 847.721 | 0.0399862 | ||||||||
\(767\) | 15269.8 | 0.718853 | ||||||||
\(768\) | −5874.01 | −0.275990 | ||||||||
\(769\) | −31854.0 | −1.49374 | −0.746868 | − | 0.664972i | \(-0.768443\pi\) | ||||
−0.746868 | + | 0.664972i | \(0.768443\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2008.55 | 0.0938212 | ||||||||
\(772\) | −16913.9 | −0.788529 | ||||||||
\(773\) | 27.0929 | 0.00126062 | 0.000630312 | − | 1.00000i | \(-0.499799\pi\) | ||||
0.000630312 | 1.00000i | \(0.499799\pi\) | ||||||||
\(774\) | −1128.07 | −0.0523870 | ||||||||
\(775\) | 5048.07 | 0.233977 | ||||||||
\(776\) | 15014.7 | 0.694582 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 59.0756 | 0.00272232 | ||||||||
\(779\) | 6879.05 | 0.316390 | ||||||||
\(780\) | 21917.5 | 1.00612 | ||||||||
\(781\) | −8879.52 | −0.406830 | ||||||||
\(782\) | −30445.9 | −1.39225 | ||||||||
\(783\) | 4888.43 | 0.223114 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 57592.2 | 2.61854 | ||||||||
\(786\) | −7640.49 | −0.346727 | ||||||||
\(787\) | 6357.30 | 0.287946 | 0.143973 | − | 0.989582i | \(-0.454012\pi\) | ||||
0.143973 | + | 0.989582i | \(0.454012\pi\) | |||||||
\(788\) | −8386.69 | −0.379142 | ||||||||
\(789\) | 15140.8 | 0.683179 | ||||||||
\(790\) | −15369.8 | −0.692192 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1820.49 | −0.0816770 | ||||||||
\(793\) | 42336.8 | 1.89587 | ||||||||
\(794\) | −14746.9 | −0.659127 | ||||||||
\(795\) | 28533.4 | 1.27292 | ||||||||
\(796\) | −7718.76 | −0.343699 | ||||||||
\(797\) | 9946.90 | 0.442079 | 0.221040 | − | 0.975265i | \(-0.429055\pi\) | ||||
0.221040 | + | 0.975265i | \(0.429055\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4981.28 | 0.220557 | ||||||||
\(800\) | 29140.9 | 1.28786 | ||||||||
\(801\) | −14058.9 | −0.620157 | ||||||||
\(802\) | −11783.3 | −0.518807 | ||||||||
\(803\) | −11423.4 | −0.502019 | ||||||||
\(804\) | 5353.52 | 0.234831 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2748.63 | 0.120120 | ||||||||
\(807\) | −21678.4 | −0.945620 | ||||||||
\(808\) | −18216.5 | −0.793137 | ||||||||
\(809\) | 21882.2 | 0.950972 | 0.475486 | − | 0.879723i | \(-0.342272\pi\) | ||||
0.475486 | + | 0.879723i | \(0.342272\pi\) | |||||||
\(810\) | −1751.10 | −0.0759597 | ||||||||
\(811\) | 5407.69 | 0.234143 | 0.117071 | − | 0.993124i | \(-0.462649\pi\) | ||||
0.117071 | + | 0.993124i | \(0.462649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14223.2 | 0.613564 | ||||||||
\(814\) | 1069.18 | 0.0460379 | ||||||||
\(815\) | 45436.7 | 1.95285 | ||||||||
\(816\) | −9762.09 | −0.418801 | ||||||||
\(817\) | 1648.37 | 0.0705864 | ||||||||
\(818\) | −7081.03 | −0.302668 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −43861.5 | −1.86794 | ||||||||
\(821\) | 5294.69 | 0.225074 | 0.112537 | − | 0.993648i | \(-0.464102\pi\) | ||||
0.112537 | + | 0.993648i | \(0.464102\pi\) | |||||||
\(822\) | −4882.50 | −0.207173 | ||||||||
\(823\) | 7539.03 | 0.319312 | 0.159656 | − | 0.987173i | \(-0.448961\pi\) | ||||
0.159656 | + | 0.987173i | \(0.448961\pi\) | |||||||
\(824\) | −35813.0 | −1.51408 | ||||||||
\(825\) | 5280.52 | 0.222841 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18827.2 | −0.791640 | −0.395820 | − | 0.918328i | \(-0.629540\pi\) | ||||
−0.395820 | + | 0.918328i | \(0.629540\pi\) | |||||||
\(828\) | −11432.5 | −0.479839 | ||||||||
\(829\) | 5480.45 | 0.229607 | 0.114803 | − | 0.993388i | \(-0.463376\pi\) | ||||
0.114803 | + | 0.993388i | \(0.463376\pi\) | |||||||
\(830\) | −4147.59 | −0.173452 | ||||||||
\(831\) | −23993.7 | −1.00160 | ||||||||
\(832\) | 988.363 | 0.0411843 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4175.28 | 0.173355 | ||||||||
\(835\) | −41347.7 | −1.71365 | ||||||||
\(836\) | 1178.20 | 0.0487426 | ||||||||
\(837\) | 851.778 | 0.0351754 | ||||||||
\(838\) | 17124.4 | 0.705911 | ||||||||
\(839\) | 32885.7 | 1.35321 | 0.676603 | − | 0.736348i | \(-0.263451\pi\) | ||||
0.676603 | + | 0.736348i | \(0.263451\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8391.18 | 0.344056 | ||||||||
\(842\) | −7811.78 | −0.319729 | ||||||||
\(843\) | −913.470 | −0.0373210 | ||||||||
\(844\) | 6356.19 | 0.259229 | ||||||||
\(845\) | −41064.8 | −1.67180 | ||||||||
\(846\) | −482.240 | −0.0195978 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15399.5 | −0.623611 | ||||||||
\(849\) | −20983.5 | −0.848235 | ||||||||
\(850\) | −24393.0 | −0.984322 | ||||||||
\(851\) | 15159.8 | 0.610660 | ||||||||
\(852\) | 15402.5 | 0.619344 | ||||||||
\(853\) | 24852.9 | 0.997593 | 0.498797 | − | 0.866719i | \(-0.333775\pi\) | ||||
0.498797 | + | 0.866719i | \(0.333775\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2558.76 | 0.102348 | ||||||||
\(856\) | 8823.29 | 0.352306 | ||||||||
\(857\) | 26129.7 | 1.04151 | 0.520755 | − | 0.853706i | \(-0.325651\pi\) | ||||
0.520755 | + | 0.853706i | \(0.325651\pi\) | |||||||
\(858\) | 2875.20 | 0.114403 | ||||||||
\(859\) | −3354.66 | −0.133248 | −0.0666238 | − | 0.997778i | \(-0.521223\pi\) | ||||
−0.0666238 | + | 0.997778i | \(0.521223\pi\) | |||||||
\(860\) | −10510.1 | −0.416736 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5718.02 | −0.225936 | ||||||||
\(863\) | −37414.5 | −1.47579 | −0.737893 | − | 0.674918i | \(-0.764179\pi\) | ||||
−0.737893 | + | 0.674918i | \(0.764179\pi\) | |||||||
\(864\) | 4917.05 | 0.193613 | ||||||||
\(865\) | 15434.6 | 0.606694 | ||||||||
\(866\) | 11949.5 | 0.468893 | ||||||||
\(867\) | 27776.3 | 1.08804 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7820.49 | 0.305284 | ||||||||
\(870\) | −11742.3 | −0.457587 | ||||||||
\(871\) | −19090.1 | −0.742643 | ||||||||
\(872\) | 8730.29 | 0.339042 | ||||||||
\(873\) | −7348.62 | −0.284895 | ||||||||
\(874\) | −4306.94 | −0.166687 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19815.1 | 0.764257 | ||||||||
\(877\) | 5518.99 | 0.212501 | 0.106250 | − | 0.994339i | \(-0.466115\pi\) | ||||
0.106250 | + | 0.994339i | \(0.466115\pi\) | |||||||
\(878\) | −3490.33 | −0.134160 | ||||||||
\(879\) | −9270.49 | −0.355729 | ||||||||
\(880\) | −5076.18 | −0.194452 | ||||||||
\(881\) | −35273.5 | −1.34892 | −0.674458 | − | 0.738313i | \(-0.735623\pi\) | ||||
−0.674458 | + | 0.738313i | \(0.735623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34154.4 | 1.30168 | 0.650842 | − | 0.759213i | \(-0.274416\pi\) | ||||
0.650842 | + | 0.759213i | \(0.274416\pi\) | |||||||
\(884\) | 51516.6 | 1.96006 | ||||||||
\(885\) | −11366.5 | −0.431729 | ||||||||
\(886\) | −18864.4 | −0.715307 | ||||||||
\(887\) | 31925.4 | 1.20851 | 0.604257 | − | 0.796790i | \(-0.293470\pi\) | ||||
0.604257 | + | 0.796790i | \(0.293470\pi\) | |||||||
\(888\) | −4187.38 | −0.158242 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 33770.2 | 1.27189 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 3782.04 | 0.141964 | ||||||||
\(893\) | 704.664 | 0.0264061 | ||||||||
\(894\) | −3118.89 | −0.116679 | ||||||||
\(895\) | 61637.7 | 2.30203 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 40767.0 | 1.51747 | ||||||||
\(898\) | −2037.87 | −0.0757288 | ||||||||
\(899\) | 5711.74 | 0.211899 | ||||||||
\(900\) | −9159.64 | −0.339246 | ||||||||
\(901\) | 67067.1 | 2.47983 | ||||||||
\(902\) | −5753.87 | −0.212398 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8952.17 | −0.329364 | ||||||||
\(905\) | −3267.14 | −0.120004 | ||||||||
\(906\) | −2762.89 | −0.101314 | ||||||||
\(907\) | 21299.4 | 0.779751 | 0.389875 | − | 0.920868i | \(-0.372518\pi\) | ||||
0.389875 | + | 0.920868i | \(0.372518\pi\) | |||||||
\(908\) | 24516.5 | 0.896046 | ||||||||
\(909\) | 8915.70 | 0.325319 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25231.7 | 0.917631 | 0.458816 | − | 0.888531i | \(-0.348274\pi\) | ||||
0.458816 | + | 0.888531i | \(0.348274\pi\) | |||||||
\(912\) | −1380.97 | −0.0501408 | ||||||||
\(913\) | 2110.39 | 0.0764992 | ||||||||
\(914\) | −12328.7 | −0.446167 | ||||||||
\(915\) | −31514.6 | −1.13862 | ||||||||
\(916\) | −11944.8 | −0.430859 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4115.92 | −0.147980 | ||||||||
\(919\) | 17335.9 | 0.622263 | 0.311131 | − | 0.950367i | \(-0.399292\pi\) | ||||
0.311131 | + | 0.950367i | \(0.399292\pi\) | |||||||
\(920\) | 62003.0 | 2.22193 | ||||||||
\(921\) | −8449.84 | −0.302314 | ||||||||
\(922\) | −19508.3 | −0.696824 | ||||||||
\(923\) | −54923.6 | −1.95865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12145.9 | 0.431736 | ||||||||
\(926\) | 7087.37 | 0.251518 | ||||||||
\(927\) | 17527.9 | 0.621028 | ||||||||
\(928\) | 32972.1 | 1.16634 | ||||||||
\(929\) | −22981.2 | −0.811614 | −0.405807 | − | 0.913959i | \(-0.633009\pi\) | ||||
−0.405807 | + | 0.913959i | \(0.633009\pi\) | |||||||
\(930\) | −2046.02 | −0.0721415 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 18829.9 | 0.661796 | ||||||||
\(933\) | 5887.83 | 0.206601 | ||||||||
\(934\) | 2900.43 | 0.101611 | ||||||||
\(935\) | 22107.5 | 0.773253 | ||||||||
\(936\) | −11260.5 | −0.393227 | ||||||||
\(937\) | 15884.3 | 0.553809 | 0.276904 | − | 0.960897i | \(-0.410691\pi\) | ||||
0.276904 | + | 0.960897i | \(0.410691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27812.8 | 0.966600 | ||||||||
\(940\) | −4493.01 | −0.155900 | ||||||||
\(941\) | −22366.2 | −0.774832 | −0.387416 | − | 0.921905i | \(-0.626632\pi\) | ||||
−0.387416 | + | 0.921905i | \(0.626632\pi\) | |||||||
\(942\) | −13105.1 | −0.453279 | ||||||||
\(943\) | −81583.3 | −2.81730 | ||||||||
\(944\) | 6134.51 | 0.211506 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1378.75 | −0.0473858 | ||||||||
\(947\) | −26760.3 | −0.918261 | −0.459130 | − | 0.888369i | \(-0.651839\pi\) | ||||
−0.459130 | + | 0.888369i | \(0.651839\pi\) | |||||||
\(948\) | −13565.5 | −0.464754 | ||||||||
\(949\) | −70658.4 | −2.41693 | ||||||||
\(950\) | −3450.69 | −0.117848 | ||||||||
\(951\) | −8789.18 | −0.299694 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33171.7 | −1.12753 | −0.563766 | − | 0.825935i | \(-0.690648\pi\) | ||||
−0.563766 | + | 0.825935i | \(0.690648\pi\) | |||||||
\(954\) | −6492.79 | −0.220348 | ||||||||
\(955\) | −55715.7 | −1.88787 | ||||||||
\(956\) | 11812.7 | 0.399632 | ||||||||
\(957\) | 5974.75 | 0.201814 | ||||||||
\(958\) | 2753.60 | 0.0928652 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −735.715 | −0.0247345 | ||||||||
\(961\) | −28795.8 | −0.966593 | ||||||||
\(962\) | 6613.36 | 0.221646 | ||||||||
\(963\) | −4318.38 | −0.144504 | ||||||||
\(964\) | 22881.6 | 0.764487 | ||||||||
\(965\) | −44895.7 | −1.49766 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7857.98 | 0.261319 | 0.130660 | − | 0.991427i | \(-0.458291\pi\) | ||||
0.130660 | + | 0.991427i | \(0.458291\pi\) | |||||||
\(968\) | −2225.04 | −0.0738797 | ||||||||
\(969\) | 6014.31 | 0.199388 | ||||||||
\(970\) | 17651.8 | 0.584294 | ||||||||
\(971\) | 434.865 | 0.0143723 | 0.00718614 | − | 0.999974i | \(-0.497713\pi\) | ||||
0.00718614 | + | 0.999974i | \(0.497713\pi\) | |||||||
\(972\) | −1545.54 | −0.0510011 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −25276.5 | −0.831530 | ||||||||
\(975\) | 32662.3 | 1.07285 | ||||||||
\(976\) | 17008.5 | 0.557816 | ||||||||
\(977\) | 19558.5 | 0.640463 | 0.320232 | − | 0.947339i | \(-0.396239\pi\) | ||||
0.320232 | + | 0.947339i | \(0.396239\pi\) | |||||||
\(978\) | −10339.1 | −0.338046 | ||||||||
\(979\) | −17183.1 | −0.560953 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4272.86 | −0.139064 | ||||||||
\(982\) | 23683.2 | 0.769615 | ||||||||
\(983\) | 59419.8 | 1.92797 | 0.963987 | − | 0.265950i | \(-0.0856854\pi\) | ||||
0.963987 | + | 0.265950i | \(0.0856854\pi\) | |||||||
\(984\) | 22534.6 | 0.730058 | ||||||||
\(985\) | −22261.4 | −0.720108 | ||||||||
\(986\) | −27600.0 | −0.891442 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7287.66 | 0.234667 | ||||||||
\(989\) | −19549.1 | −0.628539 | ||||||||
\(990\) | −2140.23 | −0.0687081 | ||||||||
\(991\) | −25376.7 | −0.813439 | −0.406719 | − | 0.913553i | \(-0.633327\pi\) | ||||
−0.406719 | + | 0.913553i | \(0.633327\pi\) | |||||||
\(992\) | 5745.18 | 0.183881 | ||||||||
\(993\) | −18074.2 | −0.577609 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20488.4 | −0.652791 | ||||||||
\(996\) | −3660.71 | −0.116460 | ||||||||
\(997\) | 38621.4 | 1.22683 | 0.613416 | − | 0.789760i | \(-0.289795\pi\) | ||||
0.613416 | + | 0.789760i | \(0.289795\pi\) | |||||||
\(998\) | 1572.96 | 0.0498910 | ||||||||
\(999\) | 2049.43 | 0.0649059 |
(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 | 1617.4.a.n.1.3 | 5 | ||
7.6 | odd | 2 | 231.4.a.k.1.3 | ✓ | 5 | ||
21.20 | even | 2 | 693.4.a.p.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.4.a.k.1.3 | ✓ | 5 | 7.6 | odd | 2 | ||
693.4.a.p.1.3 | 5 | 21.20 | even | 2 | |||
1617.4.a.n.1.3 | 5 | 1.1 | even | 1 | trivial |