Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,4,Mod(1,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(1.94706303019\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37228 | −0.838728 | −0.419364 | − | 0.907818i | \(-0.637747\pi\) | ||||
−0.419364 | + | 0.907818i | \(0.637747\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −2.37228 | −0.296535 | ||||||||
\(5\) | 19.4891 | 1.74316 | 0.871580 | − | 0.490253i | \(-0.163096\pi\) | ||||
0.871580 | + | 0.490253i | \(0.163096\pi\) | |||||||
\(6\) | −7.11684 | −0.484240 | ||||||||
\(7\) | 6.74456 | 0.364172 | 0.182086 | − | 0.983283i | \(-0.441715\pi\) | ||||
0.182086 | + | 0.983283i | \(0.441715\pi\) | |||||||
\(8\) | 24.6060 | 1.08744 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −46.2337 | −1.46204 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −7.11684 | −0.171205 | ||||||||
\(13\) | −60.9783 | −1.30095 | −0.650474 | − | 0.759529i | \(-0.725430\pi\) | ||||
−0.650474 | + | 0.759529i | \(0.725430\pi\) | |||||||
\(14\) | −16.0000 | −0.305441 | ||||||||
\(15\) | 58.4674 | 1.00641 | ||||||||
\(16\) | −39.3940 | −0.615532 | ||||||||
\(17\) | −99.1684 | −1.41482 | −0.707408 | − | 0.706805i | \(-0.750136\pi\) | ||||
−0.707408 | + | 0.706805i | \(0.750136\pi\) | |||||||
\(18\) | −21.3505 | −0.279576 | ||||||||
\(19\) | 24.7011 | 0.298253 | 0.149127 | − | 0.988818i | \(-0.452354\pi\) | ||||
0.149127 | + | 0.988818i | \(0.452354\pi\) | |||||||
\(20\) | −46.2337 | −0.516908 | ||||||||
\(21\) | 20.2337 | 0.210255 | ||||||||
\(22\) | −26.0951 | −0.252886 | ||||||||
\(23\) | 112.000 | 1.01537 | 0.507687 | − | 0.861541i | \(-0.330501\pi\) | ||||
0.507687 | + | 0.861541i | \(0.330501\pi\) | |||||||
\(24\) | 73.8179 | 0.627834 | ||||||||
\(25\) | 254.826 | 2.03861 | ||||||||
\(26\) | 144.658 | 1.09114 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −16.0000 | −0.107990 | ||||||||
\(29\) | −21.1249 | −0.135269 | −0.0676345 | − | 0.997710i | \(-0.521545\pi\) | ||||
−0.0676345 | + | 0.997710i | \(0.521545\pi\) | |||||||
\(30\) | −138.701 | −0.844108 | ||||||||
\(31\) | −318.717 | −1.84656 | −0.923279 | − | 0.384130i | \(-0.874502\pi\) | ||||
−0.923279 | + | 0.384130i | \(0.874502\pi\) | |||||||
\(32\) | −103.394 | −0.571177 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | 235.255 | 1.18665 | ||||||||
\(35\) | 131.446 | 0.634810 | ||||||||
\(36\) | −21.3505 | −0.0988451 | ||||||||
\(37\) | −150.380 | −0.668172 | −0.334086 | − | 0.942543i | \(-0.608428\pi\) | ||||
−0.334086 | + | 0.942543i | \(0.608428\pi\) | |||||||
\(38\) | −58.5979 | −0.250153 | ||||||||
\(39\) | −182.935 | −0.751103 | ||||||||
\(40\) | 479.549 | 1.89558 | ||||||||
\(41\) | −252.745 | −0.962733 | −0.481367 | − | 0.876519i | \(-0.659859\pi\) | ||||
−0.481367 | + | 0.876519i | \(0.659859\pi\) | |||||||
\(42\) | −48.0000 | −0.176347 | ||||||||
\(43\) | 214.016 | 0.759004 | 0.379502 | − | 0.925191i | \(-0.376095\pi\) | ||||
0.379502 | + | 0.925191i | \(0.376095\pi\) | |||||||
\(44\) | −26.0951 | −0.0894087 | ||||||||
\(45\) | 175.402 | 0.581053 | ||||||||
\(46\) | −265.696 | −0.851623 | ||||||||
\(47\) | 105.870 | 0.328567 | 0.164284 | − | 0.986413i | \(-0.447469\pi\) | ||||
0.164284 | + | 0.986413i | \(0.447469\pi\) | |||||||
\(48\) | −118.182 | −0.355377 | ||||||||
\(49\) | −297.511 | −0.867379 | ||||||||
\(50\) | −604.519 | −1.70984 | ||||||||
\(51\) | −297.505 | −0.816845 | ||||||||
\(52\) | 144.658 | 0.385777 | ||||||||
\(53\) | 325.652 | 0.843995 | 0.421998 | − | 0.906597i | \(-0.361329\pi\) | ||||
0.421998 | + | 0.906597i | \(0.361329\pi\) | |||||||
\(54\) | −64.0516 | −0.161413 | ||||||||
\(55\) | 214.380 | 0.525583 | ||||||||
\(56\) | 165.957 | 0.396016 | ||||||||
\(57\) | 74.1032 | 0.172197 | ||||||||
\(58\) | 50.1143 | 0.113454 | ||||||||
\(59\) | 196.000 | 0.432492 | 0.216246 | − | 0.976339i | \(-0.430619\pi\) | ||||
0.216246 | + | 0.976339i | \(0.430619\pi\) | |||||||
\(60\) | −138.701 | −0.298437 | ||||||||
\(61\) | −402.641 | −0.845130 | −0.422565 | − | 0.906333i | \(-0.638870\pi\) | ||||
−0.422565 | + | 0.906333i | \(0.638870\pi\) | |||||||
\(62\) | 756.087 | 1.54876 | ||||||||
\(63\) | 60.7011 | 0.121391 | ||||||||
\(64\) | 560.432 | 1.09459 | ||||||||
\(65\) | −1188.41 | −2.26776 | ||||||||
\(66\) | −78.2853 | −0.146004 | ||||||||
\(67\) | 27.4132 | 0.0499860 | 0.0249930 | − | 0.999688i | \(-0.492044\pi\) | ||||
0.0249930 | + | 0.999688i | \(0.492044\pi\) | |||||||
\(68\) | 235.255 | 0.419543 | ||||||||
\(69\) | 336.000 | 0.586227 | ||||||||
\(70\) | −311.826 | −0.532433 | ||||||||
\(71\) | −300.500 | −0.502292 | −0.251146 | − | 0.967949i | \(-0.580807\pi\) | ||||
−0.251146 | + | 0.967949i | \(0.580807\pi\) | |||||||
\(72\) | 221.454 | 0.362480 | ||||||||
\(73\) | 427.815 | 0.685917 | 0.342959 | − | 0.939351i | \(-0.388571\pi\) | ||||
0.342959 | + | 0.939351i | \(0.388571\pi\) | |||||||
\(74\) | 356.745 | 0.560415 | ||||||||
\(75\) | 764.478 | 1.17699 | ||||||||
\(76\) | −58.5979 | −0.0884426 | ||||||||
\(77\) | 74.1902 | 0.109802 | ||||||||
\(78\) | 433.973 | 0.629971 | ||||||||
\(79\) | 97.5488 | 0.138925 | 0.0694627 | − | 0.997585i | \(-0.477872\pi\) | ||||
0.0694627 | + | 0.997585i | \(0.477872\pi\) | |||||||
\(80\) | −767.755 | −1.07297 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 599.581 | 0.807472 | ||||||||
\(83\) | 1104.62 | 1.46082 | 0.730408 | − | 0.683011i | \(-0.239330\pi\) | ||||
0.730408 | + | 0.683011i | \(0.239330\pi\) | |||||||
\(84\) | −48.0000 | −0.0623480 | ||||||||
\(85\) | −1932.71 | −2.46625 | ||||||||
\(86\) | −507.707 | −0.636598 | ||||||||
\(87\) | −63.3748 | −0.0780976 | ||||||||
\(88\) | 270.666 | 0.327876 | ||||||||
\(89\) | 463.022 | 0.551463 | 0.275732 | − | 0.961235i | \(-0.411080\pi\) | ||||
0.275732 | + | 0.961235i | \(0.411080\pi\) | |||||||
\(90\) | −416.103 | −0.487346 | ||||||||
\(91\) | −411.272 | −0.473769 | ||||||||
\(92\) | −265.696 | −0.301094 | ||||||||
\(93\) | −956.152 | −1.06611 | ||||||||
\(94\) | −251.152 | −0.275578 | ||||||||
\(95\) | 481.402 | 0.519903 | ||||||||
\(96\) | −310.182 | −0.329769 | ||||||||
\(97\) | −1798.36 | −1.88243 | −0.941214 | − | 0.337810i | \(-0.890314\pi\) | ||||
−0.941214 | + | 0.337810i | \(0.890314\pi\) | |||||||
\(98\) | 705.779 | 0.727495 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −604.519 | −0.604519 | ||||||||
\(101\) | 741.918 | 0.730927 | 0.365463 | − | 0.930826i | \(-0.380911\pi\) | ||||
0.365463 | + | 0.930826i | \(0.380911\pi\) | |||||||
\(102\) | 705.766 | 0.685111 | ||||||||
\(103\) | 389.837 | 0.372930 | 0.186465 | − | 0.982462i | \(-0.440297\pi\) | ||||
0.186465 | + | 0.982462i | \(0.440297\pi\) | |||||||
\(104\) | −1500.43 | −1.41470 | ||||||||
\(105\) | 394.337 | 0.366508 | ||||||||
\(106\) | −772.538 | −0.707882 | ||||||||
\(107\) | 1538.42 | 1.38995 | 0.694977 | − | 0.719032i | \(-0.255415\pi\) | ||||
0.694977 | + | 0.719032i | \(0.255415\pi\) | |||||||
\(108\) | −64.0516 | −0.0570682 | ||||||||
\(109\) | 779.783 | 0.685226 | 0.342613 | − | 0.939477i | \(-0.388688\pi\) | ||||
0.342613 | + | 0.939477i | \(0.388688\pi\) | |||||||
\(110\) | −508.571 | −0.440821 | ||||||||
\(111\) | −451.141 | −0.385770 | ||||||||
\(112\) | −265.696 | −0.224160 | ||||||||
\(113\) | −1514.55 | −1.26086 | −0.630430 | − | 0.776246i | \(-0.717122\pi\) | ||||
−0.630430 | + | 0.776246i | \(0.717122\pi\) | |||||||
\(114\) | −175.794 | −0.144426 | ||||||||
\(115\) | 2182.78 | 1.76996 | ||||||||
\(116\) | 50.1143 | 0.0401120 | ||||||||
\(117\) | −548.804 | −0.433649 | ||||||||
\(118\) | −464.967 | −0.362743 | ||||||||
\(119\) | −668.848 | −0.515237 | ||||||||
\(120\) | 1438.65 | 1.09442 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 955.179 | 0.708834 | ||||||||
\(123\) | −758.234 | −0.555834 | ||||||||
\(124\) | 756.087 | 0.547569 | ||||||||
\(125\) | 2530.20 | 1.81046 | ||||||||
\(126\) | −144.000 | −0.101814 | ||||||||
\(127\) | 2302.74 | 1.60894 | 0.804471 | − | 0.593992i | \(-0.202449\pi\) | ||||
0.804471 | + | 0.593992i | \(0.202449\pi\) | |||||||
\(128\) | −502.350 | −0.346890 | ||||||||
\(129\) | 642.049 | 0.438211 | ||||||||
\(130\) | 2819.25 | 1.90203 | ||||||||
\(131\) | −2020.59 | −1.34763 | −0.673815 | − | 0.738900i | \(-0.735345\pi\) | ||||
−0.673815 | + | 0.738900i | \(0.735345\pi\) | |||||||
\(132\) | −78.2853 | −0.0516201 | ||||||||
\(133\) | 166.598 | 0.108616 | ||||||||
\(134\) | −65.0319 | −0.0419246 | ||||||||
\(135\) | 526.206 | 0.335471 | ||||||||
\(136\) | −2440.14 | −1.53853 | ||||||||
\(137\) | 1475.40 | 0.920088 | 0.460044 | − | 0.887896i | \(-0.347834\pi\) | ||||
0.460044 | + | 0.887896i | \(0.347834\pi\) | |||||||
\(138\) | −797.087 | −0.491685 | ||||||||
\(139\) | −1623.71 | −0.990802 | −0.495401 | − | 0.868665i | \(-0.664979\pi\) | ||||
−0.495401 | + | 0.868665i | \(0.664979\pi\) | |||||||
\(140\) | −311.826 | −0.188244 | ||||||||
\(141\) | 317.609 | 0.189698 | ||||||||
\(142\) | 712.870 | 0.421287 | ||||||||
\(143\) | −670.761 | −0.392251 | ||||||||
\(144\) | −354.546 | −0.205177 | ||||||||
\(145\) | −411.707 | −0.235796 | ||||||||
\(146\) | −1014.90 | −0.575298 | ||||||||
\(147\) | −892.533 | −0.500781 | ||||||||
\(148\) | 356.745 | 0.198137 | ||||||||
\(149\) | −1104.11 | −0.607064 | −0.303532 | − | 0.952821i | \(-0.598166\pi\) | ||||
−0.303532 | + | 0.952821i | \(0.598166\pi\) | |||||||
\(150\) | −1813.56 | −0.987175 | ||||||||
\(151\) | 2980.07 | 1.60606 | 0.803029 | − | 0.595940i | \(-0.203221\pi\) | ||||
0.803029 | + | 0.595940i | \(0.203221\pi\) | |||||||
\(152\) | 607.794 | 0.324333 | ||||||||
\(153\) | −892.516 | −0.471605 | ||||||||
\(154\) | −176.000 | −0.0920941 | ||||||||
\(155\) | −6211.52 | −3.21885 | ||||||||
\(156\) | 433.973 | 0.222728 | ||||||||
\(157\) | 2844.67 | 1.44605 | 0.723024 | − | 0.690823i | \(-0.242751\pi\) | ||||
0.723024 | + | 0.690823i | \(0.242751\pi\) | |||||||
\(158\) | −231.413 | −0.116521 | ||||||||
\(159\) | 976.956 | 0.487281 | ||||||||
\(160\) | −2015.06 | −0.995653 | ||||||||
\(161\) | 755.391 | 0.369771 | ||||||||
\(162\) | −192.155 | −0.0931920 | ||||||||
\(163\) | −1528.51 | −0.734492 | −0.367246 | − | 0.930124i | \(-0.619699\pi\) | ||||
−0.367246 | + | 0.930124i | \(0.619699\pi\) | |||||||
\(164\) | 599.581 | 0.285484 | ||||||||
\(165\) | 643.141 | 0.303445 | ||||||||
\(166\) | −2620.47 | −1.22523 | ||||||||
\(167\) | −383.881 | −0.177878 | −0.0889388 | − | 0.996037i | \(-0.528348\pi\) | ||||
−0.0889388 | + | 0.996037i | \(0.528348\pi\) | |||||||
\(168\) | 497.870 | 0.228640 | ||||||||
\(169\) | 1521.35 | 0.692466 | ||||||||
\(170\) | 4584.92 | 2.06851 | ||||||||
\(171\) | 222.310 | 0.0994178 | ||||||||
\(172\) | −507.707 | −0.225071 | ||||||||
\(173\) | 2702.85 | 1.18783 | 0.593914 | − | 0.804529i | \(-0.297582\pi\) | ||||
0.593914 | + | 0.804529i | \(0.297582\pi\) | |||||||
\(174\) | 150.343 | 0.0655027 | ||||||||
\(175\) | 1718.69 | 0.742404 | ||||||||
\(176\) | −433.334 | −0.185590 | ||||||||
\(177\) | 588.000 | 0.249699 | ||||||||
\(178\) | −1098.42 | −0.462528 | ||||||||
\(179\) | −2777.61 | −1.15982 | −0.579911 | − | 0.814680i | \(-0.696913\pi\) | ||||
−0.579911 | + | 0.814680i | \(0.696913\pi\) | |||||||
\(180\) | −416.103 | −0.172303 | ||||||||
\(181\) | −3993.61 | −1.64001 | −0.820007 | − | 0.572354i | \(-0.806030\pi\) | ||||
−0.820007 | + | 0.572354i | \(0.806030\pi\) | |||||||
\(182\) | 975.652 | 0.397363 | ||||||||
\(183\) | −1207.92 | −0.487936 | ||||||||
\(184\) | 2755.87 | 1.10416 | ||||||||
\(185\) | −2930.78 | −1.16473 | ||||||||
\(186\) | 2268.26 | 0.894177 | ||||||||
\(187\) | −1090.85 | −0.426583 | ||||||||
\(188\) | −251.152 | −0.0974317 | ||||||||
\(189\) | 182.103 | 0.0700850 | ||||||||
\(190\) | −1142.02 | −0.436058 | ||||||||
\(191\) | 895.587 | 0.339280 | 0.169640 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169640 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(192\) | 1681.30 | 0.631964 | ||||||||
\(193\) | 1328.24 | 0.495382 | 0.247691 | − | 0.968839i | \(-0.420328\pi\) | ||||
0.247691 | + | 0.968839i | \(0.420328\pi\) | |||||||
\(194\) | 4266.21 | 1.57885 | ||||||||
\(195\) | −3565.24 | −1.30929 | ||||||||
\(196\) | 705.779 | 0.257208 | ||||||||
\(197\) | 154.114 | 0.0557370 | 0.0278685 | − | 0.999612i | \(-0.491128\pi\) | ||||
0.0278685 | + | 0.999612i | \(0.491128\pi\) | |||||||
\(198\) | −234.856 | −0.0842953 | ||||||||
\(199\) | 1316.15 | 0.468842 | 0.234421 | − | 0.972135i | \(-0.424681\pi\) | ||||
0.234421 | + | 0.972135i | \(0.424681\pi\) | |||||||
\(200\) | 6270.24 | 2.21686 | ||||||||
\(201\) | 82.2397 | 0.0288594 | ||||||||
\(202\) | −1760.04 | −0.613049 | ||||||||
\(203\) | −142.478 | −0.0492612 | ||||||||
\(204\) | 705.766 | 0.242223 | ||||||||
\(205\) | −4925.77 | −1.67820 | ||||||||
\(206\) | −924.803 | −0.312787 | ||||||||
\(207\) | 1008.00 | 0.338458 | ||||||||
\(208\) | 2402.18 | 0.800775 | ||||||||
\(209\) | 271.712 | 0.0899268 | ||||||||
\(210\) | −935.478 | −0.307401 | ||||||||
\(211\) | −1735.76 | −0.566324 | −0.283162 | − | 0.959072i | \(-0.591383\pi\) | ||||
−0.283162 | + | 0.959072i | \(0.591383\pi\) | |||||||
\(212\) | −772.538 | −0.250274 | ||||||||
\(213\) | −901.499 | −0.289999 | ||||||||
\(214\) | −3649.57 | −1.16579 | ||||||||
\(215\) | 4170.99 | 1.32307 | ||||||||
\(216\) | 664.361 | 0.209278 | ||||||||
\(217\) | −2149.61 | −0.672465 | ||||||||
\(218\) | −1849.86 | −0.574718 | ||||||||
\(219\) | 1283.44 | 0.396014 | ||||||||
\(220\) | −508.571 | −0.155854 | ||||||||
\(221\) | 6047.12 | 1.84060 | ||||||||
\(222\) | 1070.23 | 0.323556 | ||||||||
\(223\) | 1663.71 | 0.499597 | 0.249798 | − | 0.968298i | \(-0.419636\pi\) | ||||
0.249798 | + | 0.968298i | \(0.419636\pi\) | |||||||
\(224\) | −697.348 | −0.208007 | ||||||||
\(225\) | 2293.43 | 0.679536 | ||||||||
\(226\) | 3592.95 | 1.05752 | ||||||||
\(227\) | −3658.84 | −1.06980 | −0.534902 | − | 0.844914i | \(-0.679651\pi\) | ||||
−0.534902 | + | 0.844914i | \(0.679651\pi\) | |||||||
\(228\) | −175.794 | −0.0510624 | ||||||||
\(229\) | 1927.07 | 0.556090 | 0.278045 | − | 0.960568i | \(-0.410314\pi\) | ||||
0.278045 | + | 0.960568i | \(0.410314\pi\) | |||||||
\(230\) | −5178.17 | −1.48452 | ||||||||
\(231\) | 222.571 | 0.0633942 | ||||||||
\(232\) | −519.800 | −0.147097 | ||||||||
\(233\) | −2784.27 | −0.782847 | −0.391423 | − | 0.920211i | \(-0.628017\pi\) | ||||
−0.391423 | + | 0.920211i | \(0.628017\pi\) | |||||||
\(234\) | 1301.92 | 0.363714 | ||||||||
\(235\) | 2063.30 | 0.572745 | ||||||||
\(236\) | −464.967 | −0.128249 | ||||||||
\(237\) | 292.646 | 0.0802086 | ||||||||
\(238\) | 1586.70 | 0.432144 | ||||||||
\(239\) | 1222.60 | 0.330892 | 0.165446 | − | 0.986219i | \(-0.447094\pi\) | ||||
0.165446 | + | 0.986219i | \(0.447094\pi\) | |||||||
\(240\) | −2303.27 | −0.619480 | ||||||||
\(241\) | −2013.01 | −0.538047 | −0.269024 | − | 0.963134i | \(-0.586701\pi\) | ||||
−0.269024 | + | 0.963134i | \(0.586701\pi\) | |||||||
\(242\) | −287.046 | −0.0762480 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 955.179 | 0.250611 | ||||||||
\(245\) | −5798.23 | −1.51198 | ||||||||
\(246\) | 1798.74 | 0.466194 | ||||||||
\(247\) | −1506.23 | −0.388012 | ||||||||
\(248\) | −7842.35 | −2.00802 | ||||||||
\(249\) | 3313.86 | 0.843402 | ||||||||
\(250\) | −6002.33 | −1.51848 | ||||||||
\(251\) | 2706.63 | 0.680641 | 0.340320 | − | 0.940310i | \(-0.389464\pi\) | ||||
0.340320 | + | 0.940310i | \(0.389464\pi\) | |||||||
\(252\) | −144.000 | −0.0359966 | ||||||||
\(253\) | 1232.00 | 0.306147 | ||||||||
\(254\) | −5462.76 | −1.34946 | ||||||||
\(255\) | −5798.12 | −1.42389 | ||||||||
\(256\) | −3291.74 | −0.803647 | ||||||||
\(257\) | 225.741 | 0.0547912 | 0.0273956 | − | 0.999625i | \(-0.491279\pi\) | ||||
0.0273956 | + | 0.999625i | \(0.491279\pi\) | |||||||
\(258\) | −1523.12 | −0.367540 | ||||||||
\(259\) | −1014.25 | −0.243330 | ||||||||
\(260\) | 2819.25 | 0.672471 | ||||||||
\(261\) | −190.124 | −0.0450897 | ||||||||
\(262\) | 4793.40 | 1.13029 | ||||||||
\(263\) | 1953.42 | 0.457997 | 0.228998 | − | 0.973427i | \(-0.426455\pi\) | ||||
0.228998 | + | 0.973427i | \(0.426455\pi\) | |||||||
\(264\) | 811.997 | 0.189299 | ||||||||
\(265\) | 6346.67 | 1.47122 | ||||||||
\(266\) | −395.217 | −0.0910989 | ||||||||
\(267\) | 1389.07 | 0.318387 | ||||||||
\(268\) | −65.0319 | −0.0148226 | ||||||||
\(269\) | −350.848 | −0.0795225 | −0.0397613 | − | 0.999209i | \(-0.512660\pi\) | ||||
−0.0397613 | + | 0.999209i | \(0.512660\pi\) | |||||||
\(270\) | −1248.31 | −0.281369 | ||||||||
\(271\) | 254.779 | 0.0571096 | 0.0285548 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285548 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(272\) | 3906.64 | 0.870864 | ||||||||
\(273\) | −1233.81 | −0.273531 | ||||||||
\(274\) | −3500.07 | −0.771704 | ||||||||
\(275\) | 2803.09 | 0.614663 | ||||||||
\(276\) | −797.087 | −0.173837 | ||||||||
\(277\) | 116.478 | 0.0252654 | 0.0126327 | − | 0.999920i | \(-0.495979\pi\) | ||||
0.0126327 | + | 0.999920i | \(0.495979\pi\) | |||||||
\(278\) | 3851.90 | 0.831013 | ||||||||
\(279\) | −2868.46 | −0.615519 | ||||||||
\(280\) | 3234.35 | 0.690319 | ||||||||
\(281\) | 8226.47 | 1.74644 | 0.873221 | − | 0.487325i | \(-0.162027\pi\) | ||||
0.873221 | + | 0.487325i | \(0.162027\pi\) | |||||||
\(282\) | −753.457 | −0.159105 | ||||||||
\(283\) | 1561.52 | 0.327995 | 0.163997 | − | 0.986461i | \(-0.447561\pi\) | ||||
0.163997 | + | 0.986461i | \(0.447561\pi\) | |||||||
\(284\) | 712.870 | 0.148947 | ||||||||
\(285\) | 1444.21 | 0.300166 | ||||||||
\(286\) | 1591.23 | 0.328992 | ||||||||
\(287\) | −1704.65 | −0.350601 | ||||||||
\(288\) | −930.546 | −0.190392 | ||||||||
\(289\) | 4921.38 | 1.00171 | ||||||||
\(290\) | 976.684 | 0.197768 | ||||||||
\(291\) | −5395.07 | −1.08682 | ||||||||
\(292\) | −1014.90 | −0.203399 | ||||||||
\(293\) | 9486.19 | 1.89143 | 0.945715 | − | 0.324997i | \(-0.105363\pi\) | ||||
0.945715 | + | 0.324997i | \(0.105363\pi\) | |||||||
\(294\) | 2117.34 | 0.420019 | ||||||||
\(295\) | 3819.87 | 0.753903 | ||||||||
\(296\) | −3700.25 | −0.726598 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | 2619.27 | 0.509161 | ||||||||
\(299\) | −6829.56 | −1.32095 | ||||||||
\(300\) | −1813.56 | −0.349019 | ||||||||
\(301\) | 1443.45 | 0.276408 | ||||||||
\(302\) | −7069.56 | −1.34705 | ||||||||
\(303\) | 2225.75 | 0.422001 | ||||||||
\(304\) | −973.074 | −0.183584 | ||||||||
\(305\) | −7847.13 | −1.47320 | ||||||||
\(306\) | 2117.30 | 0.395549 | ||||||||
\(307\) | −8443.06 | −1.56961 | −0.784806 | − | 0.619742i | \(-0.787237\pi\) | ||||
−0.784806 | + | 0.619742i | \(0.787237\pi\) | |||||||
\(308\) | −176.000 | −0.0325602 | ||||||||
\(309\) | 1169.51 | 0.215311 | ||||||||
\(310\) | 14735.5 | 2.69974 | ||||||||
\(311\) | 4447.17 | 0.810856 | 0.405428 | − | 0.914127i | \(-0.367123\pi\) | ||||
0.405428 | + | 0.914127i | \(0.367123\pi\) | |||||||
\(312\) | −4501.29 | −0.816779 | ||||||||
\(313\) | 6480.75 | 1.17033 | 0.585165 | − | 0.810914i | \(-0.301030\pi\) | ||||
0.585165 | + | 0.810914i | \(0.301030\pi\) | |||||||
\(314\) | −6748.36 | −1.21284 | ||||||||
\(315\) | 1183.01 | 0.211603 | ||||||||
\(316\) | −231.413 | −0.0411962 | ||||||||
\(317\) | −1252.75 | −0.221960 | −0.110980 | − | 0.993823i | \(-0.535399\pi\) | ||||
−0.110980 | + | 0.993823i | \(0.535399\pi\) | |||||||
\(318\) | −2317.61 | −0.408696 | ||||||||
\(319\) | −232.374 | −0.0407852 | ||||||||
\(320\) | 10922.3 | 1.90805 | ||||||||
\(321\) | 4615.27 | 0.802490 | ||||||||
\(322\) | −1792.00 | −0.310137 | ||||||||
\(323\) | −2449.57 | −0.421974 | ||||||||
\(324\) | −192.155 | −0.0329484 | ||||||||
\(325\) | −15538.8 | −2.65212 | ||||||||
\(326\) | 3626.06 | 0.616039 | ||||||||
\(327\) | 2339.35 | 0.395615 | ||||||||
\(328\) | −6219.02 | −1.04692 | ||||||||
\(329\) | 714.043 | 0.119655 | ||||||||
\(330\) | −1525.71 | −0.254508 | ||||||||
\(331\) | 3801.44 | 0.631258 | 0.315629 | − | 0.948883i | \(-0.397785\pi\) | ||||
0.315629 | + | 0.948883i | \(0.397785\pi\) | |||||||
\(332\) | −2620.47 | −0.433183 | ||||||||
\(333\) | −1353.42 | −0.222724 | ||||||||
\(334\) | 910.673 | 0.149191 | ||||||||
\(335\) | 534.260 | 0.0871336 | ||||||||
\(336\) | −797.087 | −0.129419 | ||||||||
\(337\) | −5456.53 | −0.882007 | −0.441003 | − | 0.897506i | \(-0.645377\pi\) | ||||
−0.441003 | + | 0.897506i | \(0.645377\pi\) | |||||||
\(338\) | −3609.06 | −0.580790 | ||||||||
\(339\) | −4543.66 | −0.727958 | ||||||||
\(340\) | 4584.92 | 0.731330 | ||||||||
\(341\) | −3505.89 | −0.556758 | ||||||||
\(342\) | −527.381 | −0.0833845 | ||||||||
\(343\) | −4319.97 | −0.680047 | ||||||||
\(344\) | 5266.08 | 0.825371 | ||||||||
\(345\) | 6548.35 | 1.02189 | ||||||||
\(346\) | −6411.93 | −0.996264 | ||||||||
\(347\) | −4240.53 | −0.656033 | −0.328017 | − | 0.944672i | \(-0.606380\pi\) | ||||
−0.328017 | + | 0.944672i | \(0.606380\pi\) | |||||||
\(348\) | 150.343 | 0.0231587 | ||||||||
\(349\) | −8471.53 | −1.29934 | −0.649672 | − | 0.760215i | \(-0.725094\pi\) | ||||
−0.649672 | + | 0.760215i | \(0.725094\pi\) | |||||||
\(350\) | −4077.22 | −0.622675 | ||||||||
\(351\) | −1646.41 | −0.250368 | ||||||||
\(352\) | −1137.33 | −0.172216 | ||||||||
\(353\) | 981.282 | 0.147956 | 0.0739778 | − | 0.997260i | \(-0.476431\pi\) | ||||
0.0739778 | + | 0.997260i | \(0.476431\pi\) | |||||||
\(354\) | −1394.90 | −0.209430 | ||||||||
\(355\) | −5856.48 | −0.875576 | ||||||||
\(356\) | −1098.42 | −0.163528 | ||||||||
\(357\) | −2006.54 | −0.297472 | ||||||||
\(358\) | 6589.27 | 0.972776 | ||||||||
\(359\) | −3020.09 | −0.443995 | −0.221997 | − | 0.975047i | \(-0.571258\pi\) | ||||
−0.221997 | + | 0.975047i | \(0.571258\pi\) | |||||||
\(360\) | 4315.94 | 0.631861 | ||||||||
\(361\) | −6248.86 | −0.911045 | ||||||||
\(362\) | 9473.96 | 1.37553 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 975.652 | 0.140489 | ||||||||
\(365\) | 8337.74 | 1.19566 | ||||||||
\(366\) | 2865.54 | 0.409246 | ||||||||
\(367\) | 8689.40 | 1.23592 | 0.617960 | − | 0.786209i | \(-0.287959\pi\) | ||||
0.617960 | + | 0.786209i | \(0.287959\pi\) | |||||||
\(368\) | −4412.13 | −0.624995 | ||||||||
\(369\) | −2274.70 | −0.320911 | ||||||||
\(370\) | 6952.64 | 0.976893 | ||||||||
\(371\) | 2196.38 | 0.307360 | ||||||||
\(372\) | 2268.26 | 0.316139 | ||||||||
\(373\) | 5340.53 | 0.741346 | 0.370673 | − | 0.928763i | \(-0.379127\pi\) | ||||
0.370673 | + | 0.928763i | \(0.379127\pi\) | |||||||
\(374\) | 2587.81 | 0.357787 | ||||||||
\(375\) | 7590.59 | 1.04527 | ||||||||
\(376\) | 2605.02 | 0.357297 | ||||||||
\(377\) | 1288.16 | 0.175978 | ||||||||
\(378\) | −432.000 | −0.0587822 | ||||||||
\(379\) | −1603.49 | −0.217324 | −0.108662 | − | 0.994079i | \(-0.534657\pi\) | ||||
−0.108662 | + | 0.994079i | \(0.534657\pi\) | |||||||
\(380\) | −1142.02 | −0.154170 | ||||||||
\(381\) | 6908.23 | 0.928923 | ||||||||
\(382\) | −2124.58 | −0.284563 | ||||||||
\(383\) | −830.236 | −0.110765 | −0.0553826 | − | 0.998465i | \(-0.517638\pi\) | ||||
−0.0553826 | + | 0.998465i | \(0.517638\pi\) | |||||||
\(384\) | −1507.05 | −0.200277 | ||||||||
\(385\) | 1445.90 | 0.191403 | ||||||||
\(386\) | −3150.96 | −0.415491 | ||||||||
\(387\) | 1926.15 | 0.253001 | ||||||||
\(388\) | 4266.21 | 0.558206 | ||||||||
\(389\) | −1746.12 | −0.227588 | −0.113794 | − | 0.993504i | \(-0.536300\pi\) | ||||
−0.113794 | + | 0.993504i | \(0.536300\pi\) | |||||||
\(390\) | 8457.75 | 1.09814 | ||||||||
\(391\) | −11106.9 | −1.43657 | ||||||||
\(392\) | −7320.54 | −0.943223 | ||||||||
\(393\) | −6061.76 | −0.778054 | ||||||||
\(394\) | −365.602 | −0.0467482 | ||||||||
\(395\) | 1901.14 | 0.242169 | ||||||||
\(396\) | −234.856 | −0.0298029 | ||||||||
\(397\) | −10016.2 | −1.26624 | −0.633119 | − | 0.774054i | \(-0.718226\pi\) | ||||
−0.633119 | + | 0.774054i | \(0.718226\pi\) | |||||||
\(398\) | −3122.28 | −0.393231 | ||||||||
\(399\) | 499.794 | 0.0627092 | ||||||||
\(400\) | −10038.6 | −1.25483 | ||||||||
\(401\) | 8228.38 | 1.02470 | 0.512351 | − | 0.858776i | \(-0.328775\pi\) | ||||
0.512351 | + | 0.858776i | \(0.328775\pi\) | |||||||
\(402\) | −195.096 | −0.0242052 | ||||||||
\(403\) | 19434.8 | 2.40228 | ||||||||
\(404\) | −1760.04 | −0.216746 | ||||||||
\(405\) | 1578.62 | 0.193684 | ||||||||
\(406\) | 337.999 | 0.0413168 | ||||||||
\(407\) | −1654.18 | −0.201462 | ||||||||
\(408\) | −7320.41 | −0.888270 | ||||||||
\(409\) | −12311.5 | −1.48843 | −0.744213 | − | 0.667943i | \(-0.767175\pi\) | ||||
−0.744213 | + | 0.667943i | \(0.767175\pi\) | |||||||
\(410\) | 11685.3 | 1.40755 | ||||||||
\(411\) | 4426.21 | 0.531213 | ||||||||
\(412\) | −924.803 | −0.110587 | ||||||||
\(413\) | 1321.93 | 0.157502 | ||||||||
\(414\) | −2391.26 | −0.283874 | ||||||||
\(415\) | 21528.1 | 2.54644 | ||||||||
\(416\) | 6304.79 | 0.743071 | ||||||||
\(417\) | −4871.14 | −0.572040 | ||||||||
\(418\) | −644.577 | −0.0754241 | ||||||||
\(419\) | 13260.4 | 1.54610 | 0.773048 | − | 0.634347i | \(-0.218731\pi\) | ||||
0.773048 | + | 0.634347i | \(0.218731\pi\) | |||||||
\(420\) | −935.478 | −0.108683 | ||||||||
\(421\) | −6177.74 | −0.715165 | −0.357583 | − | 0.933881i | \(-0.616399\pi\) | ||||
−0.357583 | + | 0.933881i | \(0.616399\pi\) | |||||||
\(422\) | 4117.70 | 0.474992 | ||||||||
\(423\) | 952.826 | 0.109522 | ||||||||
\(424\) | 8012.98 | 0.917795 | ||||||||
\(425\) | −25270.7 | −2.88426 | ||||||||
\(426\) | 2138.61 | 0.243230 | ||||||||
\(427\) | −2715.64 | −0.307773 | ||||||||
\(428\) | −3649.57 | −0.412170 | ||||||||
\(429\) | −2012.28 | −0.226466 | ||||||||
\(430\) | −9894.76 | −1.10969 | ||||||||
\(431\) | 1668.05 | 0.186421 | 0.0932103 | − | 0.995646i | \(-0.470287\pi\) | ||||
0.0932103 | + | 0.995646i | \(0.470287\pi\) | |||||||
\(432\) | −1063.64 | −0.118459 | ||||||||
\(433\) | −731.748 | −0.0812138 | −0.0406069 | − | 0.999175i | \(-0.512929\pi\) | ||||
−0.0406069 | + | 0.999175i | \(0.512929\pi\) | |||||||
\(434\) | 5099.48 | 0.564015 | ||||||||
\(435\) | −1235.12 | −0.136137 | ||||||||
\(436\) | −1849.86 | −0.203194 | ||||||||
\(437\) | 2766.52 | 0.302839 | ||||||||
\(438\) | −3044.69 | −0.332148 | ||||||||
\(439\) | −14248.0 | −1.54902 | −0.774508 | − | 0.632564i | \(-0.782002\pi\) | ||||
−0.774508 | + | 0.632564i | \(0.782002\pi\) | |||||||
\(440\) | 5275.04 | 0.571540 | ||||||||
\(441\) | −2677.60 | −0.289126 | ||||||||
\(442\) | −14345.5 | −1.54377 | ||||||||
\(443\) | 174.262 | 0.0186895 | 0.00934473 | − | 0.999956i | \(-0.497025\pi\) | ||||
0.00934473 | + | 0.999956i | \(0.497025\pi\) | |||||||
\(444\) | 1070.23 | 0.114394 | ||||||||
\(445\) | 9023.89 | 0.961288 | ||||||||
\(446\) | −3946.78 | −0.419026 | ||||||||
\(447\) | −3312.34 | −0.350488 | ||||||||
\(448\) | 3779.87 | 0.398621 | ||||||||
\(449\) | 7469.97 | 0.785144 | 0.392572 | − | 0.919721i | \(-0.371585\pi\) | ||||
0.392572 | + | 0.919721i | \(0.371585\pi\) | |||||||
\(450\) | −5440.67 | −0.569946 | ||||||||
\(451\) | −2780.19 | −0.290275 | ||||||||
\(452\) | 3592.95 | 0.373890 | ||||||||
\(453\) | 8940.21 | 0.927258 | ||||||||
\(454\) | 8679.79 | 0.897275 | ||||||||
\(455\) | −8015.32 | −0.825855 | ||||||||
\(456\) | 1823.38 | 0.187254 | ||||||||
\(457\) | 8762.68 | 0.896939 | 0.448469 | − | 0.893798i | \(-0.351969\pi\) | ||||
0.448469 | + | 0.893798i | \(0.351969\pi\) | |||||||
\(458\) | −4571.56 | −0.466409 | ||||||||
\(459\) | −2677.55 | −0.272282 | ||||||||
\(460\) | −5178.17 | −0.524856 | ||||||||
\(461\) | 4339.67 | 0.438435 | 0.219218 | − | 0.975676i | \(-0.429650\pi\) | ||||
0.219218 | + | 0.975676i | \(0.429650\pi\) | |||||||
\(462\) | −528.000 | −0.0531705 | ||||||||
\(463\) | −3932.49 | −0.394726 | −0.197363 | − | 0.980330i | \(-0.563238\pi\) | ||||
−0.197363 | + | 0.980330i | \(0.563238\pi\) | |||||||
\(464\) | 832.197 | 0.0832624 | ||||||||
\(465\) | −18634.6 | −1.85840 | ||||||||
\(466\) | 6605.06 | 0.656596 | ||||||||
\(467\) | −8383.97 | −0.830758 | −0.415379 | − | 0.909648i | \(-0.636351\pi\) | ||||
−0.415379 | + | 0.909648i | \(0.636351\pi\) | |||||||
\(468\) | 1301.92 | 0.128592 | ||||||||
\(469\) | 184.890 | 0.0182035 | ||||||||
\(470\) | −4894.74 | −0.480377 | ||||||||
\(471\) | 8534.02 | 0.834876 | ||||||||
\(472\) | 4822.77 | 0.470309 | ||||||||
\(473\) | 2354.18 | 0.228848 | ||||||||
\(474\) | −694.240 | −0.0672732 | ||||||||
\(475\) | 6294.47 | 0.608022 | ||||||||
\(476\) | 1586.70 | 0.152786 | ||||||||
\(477\) | 2930.87 | 0.281332 | ||||||||
\(478\) | −2900.35 | −0.277529 | ||||||||
\(479\) | 9534.10 | 0.909445 | 0.454722 | − | 0.890633i | \(-0.349739\pi\) | ||||
0.454722 | + | 0.890633i | \(0.349739\pi\) | |||||||
\(480\) | −6045.18 | −0.574840 | ||||||||
\(481\) | 9169.93 | 0.869258 | ||||||||
\(482\) | 4775.43 | 0.451275 | ||||||||
\(483\) | 2266.17 | 0.213487 | ||||||||
\(484\) | −287.046 | −0.0269577 | ||||||||
\(485\) | −35048.4 | −3.28138 | ||||||||
\(486\) | −576.464 | −0.0538044 | ||||||||
\(487\) | 4451.09 | 0.414164 | 0.207082 | − | 0.978324i | \(-0.433603\pi\) | ||||
0.207082 | + | 0.978324i | \(0.433603\pi\) | |||||||
\(488\) | −9907.38 | −0.919029 | ||||||||
\(489\) | −4585.53 | −0.424059 | ||||||||
\(490\) | 13755.0 | 1.26814 | ||||||||
\(491\) | −9757.40 | −0.896833 | −0.448417 | − | 0.893825i | \(-0.648012\pi\) | ||||
−0.448417 | + | 0.893825i | \(0.648012\pi\) | |||||||
\(492\) | 1798.74 | 0.164824 | ||||||||
\(493\) | 2094.93 | 0.191381 | ||||||||
\(494\) | 3573.20 | 0.325437 | ||||||||
\(495\) | 1929.42 | 0.175194 | ||||||||
\(496\) | 12555.6 | 1.13662 | ||||||||
\(497\) | −2026.74 | −0.182921 | ||||||||
\(498\) | −7861.40 | −0.707385 | ||||||||
\(499\) | −7173.69 | −0.643564 | −0.321782 | − | 0.946814i | \(-0.604282\pi\) | ||||
−0.321782 | + | 0.946814i | \(0.604282\pi\) | |||||||
\(500\) | −6002.33 | −0.536865 | ||||||||
\(501\) | −1151.64 | −0.102698 | ||||||||
\(502\) | −6420.88 | −0.570873 | ||||||||
\(503\) | −15617.0 | −1.38435 | −0.692177 | − | 0.721728i | \(-0.743348\pi\) | ||||
−0.692177 | + | 0.721728i | \(0.743348\pi\) | |||||||
\(504\) | 1493.61 | 0.132005 | ||||||||
\(505\) | 14459.3 | 1.27412 | ||||||||
\(506\) | −2922.65 | −0.256774 | ||||||||
\(507\) | 4564.04 | 0.399795 | ||||||||
\(508\) | −5462.76 | −0.477108 | ||||||||
\(509\) | −8789.23 | −0.765375 | −0.382688 | − | 0.923878i | \(-0.625001\pi\) | ||||
−0.382688 | + | 0.923878i | \(0.625001\pi\) | |||||||
\(510\) | 13754.8 | 1.19426 | ||||||||
\(511\) | 2885.42 | 0.249792 | ||||||||
\(512\) | 11827.7 | 1.02093 | ||||||||
\(513\) | 666.929 | 0.0573989 | ||||||||
\(514\) | −535.521 | −0.0459549 | ||||||||
\(515\) | 7597.58 | 0.650077 | ||||||||
\(516\) | −1523.12 | −0.129945 | ||||||||
\(517\) | 1164.56 | 0.0990667 | ||||||||
\(518\) | 2406.09 | 0.204088 | ||||||||
\(519\) | 8108.56 | 0.685792 | ||||||||
\(520\) | −29242.0 | −2.46606 | ||||||||
\(521\) | 13099.3 | 1.10152 | 0.550760 | − | 0.834664i | \(-0.314338\pi\) | ||||
0.550760 | + | 0.834664i | \(0.314338\pi\) | |||||||
\(522\) | 451.029 | 0.0378180 | ||||||||
\(523\) | 16824.2 | 1.40664 | 0.703318 | − | 0.710876i | \(-0.251701\pi\) | ||||
0.703318 | + | 0.710876i | \(0.251701\pi\) | |||||||
\(524\) | 4793.40 | 0.399620 | ||||||||
\(525\) | 5156.07 | 0.428627 | ||||||||
\(526\) | −4634.07 | −0.384135 | ||||||||
\(527\) | 31606.7 | 2.61254 | ||||||||
\(528\) | −1300.00 | −0.107150 | ||||||||
\(529\) | 377.000 | 0.0309855 | ||||||||
\(530\) | −15056.1 | −1.23395 | ||||||||
\(531\) | 1764.00 | 0.144164 | ||||||||
\(532\) | −395.217 | −0.0322083 | ||||||||
\(533\) | 15411.9 | 1.25247 | ||||||||
\(534\) | −3295.25 | −0.267040 | ||||||||
\(535\) | 29982.5 | 2.42291 | ||||||||
\(536\) | 674.529 | 0.0543568 | ||||||||
\(537\) | −8332.83 | −0.669624 | ||||||||
\(538\) | 832.310 | 0.0666978 | ||||||||
\(539\) | −3272.62 | −0.261525 | ||||||||
\(540\) | −1248.31 | −0.0994791 | ||||||||
\(541\) | 18863.1 | 1.49905 | 0.749527 | − | 0.661974i | \(-0.230281\pi\) | ||||
0.749527 | + | 0.661974i | \(0.230281\pi\) | |||||||
\(542\) | −604.407 | −0.0478995 | ||||||||
\(543\) | −11980.8 | −0.946862 | ||||||||
\(544\) | 10253.4 | 0.808110 | ||||||||
\(545\) | 15197.3 | 1.19446 | ||||||||
\(546\) | 2926.96 | 0.229418 | ||||||||
\(547\) | −12283.0 | −0.960119 | −0.480059 | − | 0.877236i | \(-0.659385\pi\) | ||||
−0.480059 | + | 0.877236i | \(0.659385\pi\) | |||||||
\(548\) | −3500.07 | −0.272839 | ||||||||
\(549\) | −3623.77 | −0.281710 | ||||||||
\(550\) | −6649.71 | −0.515536 | ||||||||
\(551\) | −521.809 | −0.0403444 | ||||||||
\(552\) | 8267.61 | 0.637487 | ||||||||
\(553\) | 657.924 | 0.0505927 | ||||||||
\(554\) | −276.320 | −0.0211908 | ||||||||
\(555\) | −8792.35 | −0.672458 | ||||||||
\(556\) | 3851.90 | 0.293808 | ||||||||
\(557\) | −9752.05 | −0.741845 | −0.370923 | − | 0.928664i | \(-0.620958\pi\) | ||||
−0.370923 | + | 0.928664i | \(0.620958\pi\) | |||||||
\(558\) | 6804.78 | 0.516253 | ||||||||
\(559\) | −13050.3 | −0.987424 | ||||||||
\(560\) | −5178.17 | −0.390746 | ||||||||
\(561\) | −3272.56 | −0.246288 | ||||||||
\(562\) | −19515.5 | −1.46479 | ||||||||
\(563\) | −3447.50 | −0.258072 | −0.129036 | − | 0.991640i | \(-0.541188\pi\) | ||||
−0.129036 | + | 0.991640i | \(0.541188\pi\) | |||||||
\(564\) | −753.457 | −0.0562522 | ||||||||
\(565\) | −29517.3 | −2.19788 | ||||||||
\(566\) | −3704.36 | −0.275098 | ||||||||
\(567\) | 546.310 | 0.0404636 | ||||||||
\(568\) | −7394.09 | −0.546213 | ||||||||
\(569\) | −3371.02 | −0.248366 | −0.124183 | − | 0.992259i | \(-0.539631\pi\) | ||||
−0.124183 | + | 0.992259i | \(0.539631\pi\) | |||||||
\(570\) | −3426.06 | −0.251758 | ||||||||
\(571\) | −15852.5 | −1.16183 | −0.580916 | − | 0.813964i | \(-0.697305\pi\) | ||||
−0.580916 | + | 0.813964i | \(0.697305\pi\) | |||||||
\(572\) | 1591.23 | 0.116316 | ||||||||
\(573\) | 2686.76 | 0.195883 | ||||||||
\(574\) | 4043.91 | 0.294059 | ||||||||
\(575\) | 28540.5 | 2.06995 | ||||||||
\(576\) | 5043.89 | 0.364865 | ||||||||
\(577\) | 1376.35 | 0.0993036 | 0.0496518 | − | 0.998767i | \(-0.484189\pi\) | ||||
0.0496518 | + | 0.998767i | \(0.484189\pi\) | |||||||
\(578\) | −11674.9 | −0.840159 | ||||||||
\(579\) | 3984.72 | 0.286009 | ||||||||
\(580\) | 976.684 | 0.0699217 | ||||||||
\(581\) | 7450.17 | 0.531988 | ||||||||
\(582\) | 12798.6 | 0.911547 | ||||||||
\(583\) | 3582.17 | 0.254474 | ||||||||
\(584\) | 10526.8 | 0.745894 | ||||||||
\(585\) | −10695.7 | −0.755920 | ||||||||
\(586\) | −22503.9 | −1.58640 | ||||||||
\(587\) | −23021.4 | −1.61873 | −0.809366 | − | 0.587304i | \(-0.800189\pi\) | ||||
−0.809366 | + | 0.587304i | \(0.800189\pi\) | |||||||
\(588\) | 2117.34 | 0.148499 | ||||||||
\(589\) | −7872.66 | −0.550742 | ||||||||
\(590\) | −9061.80 | −0.632320 | ||||||||
\(591\) | 462.343 | 0.0321798 | ||||||||
\(592\) | 5924.09 | 0.411281 | ||||||||
\(593\) | 2818.69 | 0.195194 | 0.0975968 | − | 0.995226i | \(-0.468884\pi\) | ||||
0.0975968 | + | 0.995226i | \(0.468884\pi\) | |||||||
\(594\) | −704.568 | −0.0486679 | ||||||||
\(595\) | −13035.3 | −0.898140 | ||||||||
\(596\) | 2619.27 | 0.180016 | ||||||||
\(597\) | 3948.46 | 0.270686 | ||||||||
\(598\) | 16201.6 | 1.10792 | ||||||||
\(599\) | −17691.4 | −1.20676 | −0.603380 | − | 0.797454i | \(-0.706180\pi\) | ||||
−0.603380 | + | 0.797454i | \(0.706180\pi\) | |||||||
\(600\) | 18810.7 | 1.27991 | ||||||||
\(601\) | −24516.1 | −1.66394 | −0.831972 | − | 0.554817i | \(-0.812788\pi\) | ||||
−0.831972 | + | 0.554817i | \(0.812788\pi\) | |||||||
\(602\) | −3424.26 | −0.231831 | ||||||||
\(603\) | 246.719 | 0.0166620 | ||||||||
\(604\) | −7069.56 | −0.476252 | ||||||||
\(605\) | 2358.18 | 0.158469 | ||||||||
\(606\) | −5280.12 | −0.353944 | ||||||||
\(607\) | 4288.59 | 0.286768 | 0.143384 | − | 0.989667i | \(-0.454202\pi\) | ||||
0.143384 | + | 0.989667i | \(0.454202\pi\) | |||||||
\(608\) | −2553.94 | −0.170355 | ||||||||
\(609\) | −427.435 | −0.0284410 | ||||||||
\(610\) | 18615.6 | 1.23561 | ||||||||
\(611\) | −6455.74 | −0.427449 | ||||||||
\(612\) | 2117.30 | 0.139848 | ||||||||
\(613\) | −8124.07 | −0.535283 | −0.267641 | − | 0.963519i | \(-0.586244\pi\) | ||||
−0.267641 | + | 0.963519i | \(0.586244\pi\) | |||||||
\(614\) | 20029.3 | 1.31648 | ||||||||
\(615\) | −14777.3 | −0.968908 | ||||||||
\(616\) | 1825.52 | 0.119403 | ||||||||
\(617\) | −14923.1 | −0.973714 | −0.486857 | − | 0.873482i | \(-0.661857\pi\) | ||||
−0.486857 | + | 0.873482i | \(0.661857\pi\) | |||||||
\(618\) | −2774.41 | −0.180588 | ||||||||
\(619\) | 3627.68 | 0.235556 | 0.117778 | − | 0.993040i | \(-0.462423\pi\) | ||||
0.117778 | + | 0.993040i | \(0.462423\pi\) | |||||||
\(620\) | 14735.5 | 0.954501 | ||||||||
\(621\) | 3024.00 | 0.195409 | ||||||||
\(622\) | −10549.9 | −0.680087 | ||||||||
\(623\) | 3122.88 | 0.200827 | ||||||||
\(624\) | 7206.54 | 0.462328 | ||||||||
\(625\) | 17458.0 | 1.11731 | ||||||||
\(626\) | −15374.2 | −0.981589 | ||||||||
\(627\) | 815.135 | 0.0519192 | ||||||||
\(628\) | −6748.36 | −0.428804 | ||||||||
\(629\) | 14913.0 | 0.945341 | ||||||||
\(630\) | −2806.43 | −0.177478 | ||||||||
\(631\) | 12576.5 | 0.793445 | 0.396723 | − | 0.917939i | \(-0.370147\pi\) | ||||
0.396723 | + | 0.917939i | \(0.370147\pi\) | |||||||
\(632\) | 2400.28 | 0.151073 | ||||||||
\(633\) | −5207.27 | −0.326967 | ||||||||
\(634\) | 2971.87 | 0.186164 | ||||||||
\(635\) | 44878.5 | 2.80464 | ||||||||
\(636\) | −2317.61 | −0.144496 | ||||||||
\(637\) | 18141.7 | 1.12841 | ||||||||
\(638\) | 551.257 | 0.0342077 | ||||||||
\(639\) | −2704.50 | −0.167431 | ||||||||
\(640\) | −9790.36 | −0.604685 | ||||||||
\(641\) | −7292.77 | −0.449371 | −0.224686 | − | 0.974431i | \(-0.572136\pi\) | ||||
−0.224686 | + | 0.974431i | \(0.572136\pi\) | |||||||
\(642\) | −10948.7 | −0.673071 | ||||||||
\(643\) | −12946.3 | −0.794016 | −0.397008 | − | 0.917815i | \(-0.629951\pi\) | ||||
−0.397008 | + | 0.917815i | \(0.629951\pi\) | |||||||
\(644\) | −1792.00 | −0.109650 | ||||||||
\(645\) | 12513.0 | 0.763872 | ||||||||
\(646\) | 5811.06 | 0.353921 | ||||||||
\(647\) | 21973.3 | 1.33518 | 0.667589 | − | 0.744530i | \(-0.267327\pi\) | ||||
0.667589 | + | 0.744530i | \(0.267327\pi\) | |||||||
\(648\) | 1993.08 | 0.120827 | ||||||||
\(649\) | 2156.00 | 0.130401 | ||||||||
\(650\) | 36862.5 | 2.22441 | ||||||||
\(651\) | −6448.83 | −0.388248 | ||||||||
\(652\) | 3626.06 | 0.217803 | ||||||||
\(653\) | −27495.6 | −1.64776 | −0.823880 | − | 0.566764i | \(-0.808195\pi\) | ||||
−0.823880 | + | 0.566764i | \(0.808195\pi\) | |||||||
\(654\) | −5549.59 | −0.331814 | ||||||||
\(655\) | −39379.5 | −2.34913 | ||||||||
\(656\) | 9956.63 | 0.592593 | ||||||||
\(657\) | 3850.33 | 0.228639 | ||||||||
\(658\) | −1693.91 | −0.100358 | ||||||||
\(659\) | 5156.28 | 0.304796 | 0.152398 | − | 0.988319i | \(-0.451301\pi\) | ||||
0.152398 | + | 0.988319i | \(0.451301\pi\) | |||||||
\(660\) | −1525.71 | −0.0899822 | ||||||||
\(661\) | 9328.59 | 0.548926 | 0.274463 | − | 0.961598i | \(-0.411500\pi\) | ||||
0.274463 | + | 0.961598i | \(0.411500\pi\) | |||||||
\(662\) | −9018.10 | −0.529454 | ||||||||
\(663\) | 18141.4 | 1.06267 | ||||||||
\(664\) | 27180.2 | 1.58855 | ||||||||
\(665\) | 3246.85 | 0.189334 | ||||||||
\(666\) | 3210.70 | 0.186805 | ||||||||
\(667\) | −2365.99 | −0.137349 | ||||||||
\(668\) | 910.673 | 0.0527470 | ||||||||
\(669\) | 4991.12 | 0.288442 | ||||||||
\(670\) | −1267.42 | −0.0730814 | ||||||||
\(671\) | −4429.06 | −0.254816 | ||||||||
\(672\) | −2092.04 | −0.120093 | ||||||||
\(673\) | 22182.4 | 1.27053 | 0.635267 | − | 0.772293i | \(-0.280890\pi\) | ||||
0.635267 | + | 0.772293i | \(0.280890\pi\) | |||||||
\(674\) | 12944.4 | 0.739764 | ||||||||
\(675\) | 6880.30 | 0.392330 | ||||||||
\(676\) | −3609.06 | −0.205340 | ||||||||
\(677\) | −13507.1 | −0.766797 | −0.383399 | − | 0.923583i | \(-0.625246\pi\) | ||||
−0.383399 | + | 0.923583i | \(0.625246\pi\) | |||||||
\(678\) | 10778.8 | 0.610559 | ||||||||
\(679\) | −12129.1 | −0.685528 | ||||||||
\(680\) | −47556.1 | −2.68190 | ||||||||
\(681\) | −10976.5 | −0.617652 | ||||||||
\(682\) | 8316.96 | 0.466969 | ||||||||
\(683\) | −19465.6 | −1.09053 | −0.545264 | − | 0.838264i | \(-0.683571\pi\) | ||||
−0.545264 | + | 0.838264i | \(0.683571\pi\) | |||||||
\(684\) | −527.381 | −0.0294809 | ||||||||
\(685\) | 28754.3 | 1.60386 | ||||||||
\(686\) | 10248.2 | 0.570375 | ||||||||
\(687\) | 5781.22 | 0.321059 | ||||||||
\(688\) | −8430.96 | −0.467191 | ||||||||
\(689\) | −19857.7 | −1.09799 | ||||||||
\(690\) | −15534.5 | −0.857086 | ||||||||
\(691\) | −19971.8 | −1.09951 | −0.549757 | − | 0.835324i | \(-0.685280\pi\) | ||||
−0.549757 | + | 0.835324i | \(0.685280\pi\) | |||||||
\(692\) | −6411.93 | −0.352233 | ||||||||
\(693\) | 667.712 | 0.0366007 | ||||||||
\(694\) | 10059.7 | 0.550234 | ||||||||
\(695\) | −31644.7 | −1.72713 | ||||||||
\(696\) | −1559.40 | −0.0849265 | ||||||||
\(697\) | 25064.3 | 1.36209 | ||||||||
\(698\) | 20096.9 | 1.08980 | ||||||||
\(699\) | −8352.80 | −0.451977 | ||||||||
\(700\) | −4077.22 | −0.220149 | ||||||||
\(701\) | −14180.1 | −0.764018 | −0.382009 | − | 0.924159i | \(-0.624768\pi\) | ||||
−0.382009 | + | 0.924159i | \(0.624768\pi\) | |||||||
\(702\) | 3905.75 | 0.209990 | ||||||||
\(703\) | −3714.56 | −0.199285 | ||||||||
\(704\) | 6164.75 | 0.330032 | ||||||||
\(705\) | 6189.91 | 0.330675 | ||||||||
\(706\) | −2327.88 | −0.124095 | ||||||||
\(707\) | 5003.91 | 0.266183 | ||||||||
\(708\) | −1394.90 | −0.0740446 | ||||||||
\(709\) | 15870.6 | 0.840667 | 0.420334 | − | 0.907370i | \(-0.361913\pi\) | ||||
0.420334 | + | 0.907370i | \(0.361913\pi\) | |||||||
\(710\) | 13893.2 | 0.734370 | ||||||||
\(711\) | 877.939 | 0.0463084 | ||||||||
\(712\) | 11393.1 | 0.599683 | ||||||||
\(713\) | −35696.3 | −1.87495 | ||||||||
\(714\) | 4760.09 | 0.249498 | ||||||||
\(715\) | −13072.5 | −0.683756 | ||||||||
\(716\) | 6589.27 | 0.343928 | ||||||||
\(717\) | 3667.79 | 0.191041 | ||||||||
\(718\) | 7164.50 | 0.372391 | ||||||||
\(719\) | −6040.05 | −0.313290 | −0.156645 | − | 0.987655i | \(-0.550068\pi\) | ||||
−0.156645 | + | 0.987655i | \(0.550068\pi\) | |||||||
\(720\) | −6909.80 | −0.357657 | ||||||||
\(721\) | 2629.28 | 0.135811 | ||||||||
\(722\) | 14824.0 | 0.764119 | ||||||||
\(723\) | −6039.03 | −0.310642 | ||||||||
\(724\) | 9473.96 | 0.486322 | ||||||||
\(725\) | −5383.18 | −0.275761 | ||||||||
\(726\) | −861.138 | −0.0440218 | ||||||||
\(727\) | 37252.3 | 1.90043 | 0.950213 | − | 0.311601i | \(-0.100865\pi\) | ||||
0.950213 | + | 0.311601i | \(0.100865\pi\) | |||||||
\(728\) | −10119.7 | −0.515196 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −19779.5 | −1.00284 | ||||||||
\(731\) | −21223.7 | −1.07385 | ||||||||
\(732\) | 2865.54 | 0.144690 | ||||||||
\(733\) | 6125.52 | 0.308665 | 0.154332 | − | 0.988019i | \(-0.450677\pi\) | ||||
0.154332 | + | 0.988019i | \(0.450677\pi\) | |||||||
\(734\) | −20613.7 | −1.03660 | ||||||||
\(735\) | −17394.7 | −0.872942 | ||||||||
\(736\) | −11580.1 | −0.579958 | ||||||||
\(737\) | 301.546 | 0.0150713 | ||||||||
\(738\) | 5396.23 | 0.269157 | ||||||||
\(739\) | −5225.97 | −0.260136 | −0.130068 | − | 0.991505i | \(-0.541520\pi\) | ||||
−0.130068 | + | 0.991505i | \(0.541520\pi\) | |||||||
\(740\) | 6952.64 | 0.345384 | ||||||||
\(741\) | −4518.68 | −0.224019 | ||||||||
\(742\) | −5210.43 | −0.257791 | ||||||||
\(743\) | 7062.96 | 0.348741 | 0.174371 | − | 0.984680i | \(-0.444211\pi\) | ||||
0.174371 | + | 0.984680i | \(0.444211\pi\) | |||||||
\(744\) | −23527.0 | −1.15933 | ||||||||
\(745\) | −21518.2 | −1.05821 | ||||||||
\(746\) | −12669.2 | −0.621788 | ||||||||
\(747\) | 9941.57 | 0.486939 | ||||||||
\(748\) | 2587.81 | 0.126497 | ||||||||
\(749\) | 10376.0 | 0.506182 | ||||||||
\(750\) | −18007.0 | −0.876697 | ||||||||
\(751\) | −20755.4 | −1.00849 | −0.504244 | − | 0.863561i | \(-0.668229\pi\) | ||||
−0.504244 | + | 0.863561i | \(0.668229\pi\) | |||||||
\(752\) | −4170.63 | −0.202243 | ||||||||
\(753\) | 8119.89 | 0.392968 | ||||||||
\(754\) | −3055.88 | −0.147598 | ||||||||
\(755\) | 58079.0 | 2.79962 | ||||||||
\(756\) | −432.000 | −0.0207827 | ||||||||
\(757\) | 31182.9 | 1.49717 | 0.748587 | − | 0.663037i | \(-0.230733\pi\) | ||||
0.748587 | + | 0.663037i | \(0.230733\pi\) | |||||||
\(758\) | 3803.93 | 0.182276 | ||||||||
\(759\) | 3696.00 | 0.176754 | ||||||||
\(760\) | 11845.4 | 0.565364 | ||||||||
\(761\) | 32047.8 | 1.52659 | 0.763293 | − | 0.646052i | \(-0.223581\pi\) | ||||
0.763293 | + | 0.646052i | \(0.223581\pi\) | |||||||
\(762\) | −16388.3 | −0.779114 | ||||||||
\(763\) | 5259.29 | 0.249540 | ||||||||
\(764\) | −2124.58 | −0.100608 | ||||||||
\(765\) | −17394.4 | −0.822084 | ||||||||
\(766\) | 1969.55 | 0.0929019 | ||||||||
\(767\) | −11951.7 | −0.562650 | ||||||||
\(768\) | −9875.22 | −0.463986 | ||||||||
\(769\) | 2215.88 | 0.103910 | 0.0519548 | − | 0.998649i | \(-0.483455\pi\) | ||||
0.0519548 | + | 0.998649i | \(0.483455\pi\) | |||||||
\(770\) | −3430.09 | −0.160535 | ||||||||
\(771\) | 677.223 | 0.0316337 | ||||||||
\(772\) | −3150.96 | −0.146898 | ||||||||
\(773\) | 5300.56 | 0.246634 | 0.123317 | − | 0.992367i | \(-0.460647\pi\) | ||||
0.123317 | + | 0.992367i | \(0.460647\pi\) | |||||||
\(774\) | −4569.36 | −0.212199 | ||||||||
\(775\) | −81217.4 | −3.76441 | ||||||||
\(776\) | −44250.3 | −2.04703 | ||||||||
\(777\) | −3042.75 | −0.140487 | ||||||||
\(778\) | 4142.29 | 0.190885 | ||||||||
\(779\) | −6243.06 | −0.287138 | ||||||||
\(780\) | 8457.75 | 0.388251 | ||||||||
\(781\) | −3305.50 | −0.151447 | ||||||||
\(782\) | 26348.6 | 1.20489 | ||||||||
\(783\) | −570.373 | −0.0260325 | ||||||||
\(784\) | 11720.2 | 0.533899 | ||||||||
\(785\) | 55440.2 | 2.52069 | ||||||||
\(786\) | 14380.2 | 0.652576 | ||||||||
\(787\) | 34374.1 | 1.55693 | 0.778466 | − | 0.627687i | \(-0.215998\pi\) | ||||
0.778466 | + | 0.627687i | \(0.215998\pi\) | |||||||
\(788\) | −365.602 | −0.0165280 | ||||||||
\(789\) | 5860.27 | 0.264425 | ||||||||
\(790\) | −4510.04 | −0.203114 | ||||||||
\(791\) | −10215.0 | −0.459170 | ||||||||
\(792\) | 2435.99 | 0.109292 | ||||||||
\(793\) | 24552.4 | 1.09947 | ||||||||
\(794\) | 23761.2 | 1.06203 | ||||||||
\(795\) | 19040.0 | 0.849409 | ||||||||
\(796\) | −3122.28 | −0.139028 | ||||||||
\(797\) | 29867.1 | 1.32741 | 0.663707 | − | 0.747993i | \(-0.268982\pi\) | ||||
0.663707 | + | 0.747993i | \(0.268982\pi\) | |||||||
\(798\) | −1185.65 | −0.0525960 | ||||||||
\(799\) | −10498.9 | −0.464862 | ||||||||
\(800\) | −26347.5 | −1.16441 | ||||||||
\(801\) | 4167.20 | 0.183821 | ||||||||
\(802\) | −19520.0 | −0.859447 | ||||||||
\(803\) | 4705.96 | 0.206812 | ||||||||
\(804\) | −195.096 | −0.00855783 | ||||||||
\(805\) | 14721.9 | 0.644570 | ||||||||
\(806\) | −46104.9 | −2.01486 | ||||||||
\(807\) | −1052.54 | −0.0459124 | ||||||||
\(808\) | 18255.6 | 0.794839 | ||||||||
\(809\) | −15857.2 | −0.689133 | −0.344566 | − | 0.938762i | \(-0.611974\pi\) | ||||
−0.344566 | + | 0.938762i | \(0.611974\pi\) | |||||||
\(810\) | −3744.93 | −0.162449 | ||||||||
\(811\) | 36122.6 | 1.56404 | 0.782020 | − | 0.623253i | \(-0.214189\pi\) | ||||
0.782020 | + | 0.623253i | \(0.214189\pi\) | |||||||
\(812\) | 337.999 | 0.0146077 | ||||||||
\(813\) | 764.337 | 0.0329723 | ||||||||
\(814\) | 3924.19 | 0.168971 | ||||||||
\(815\) | −29789.3 | −1.28034 | ||||||||
\(816\) | 11719.9 | 0.502794 | ||||||||
\(817\) | 5286.43 | 0.226375 | ||||||||
\(818\) | 29206.4 | 1.24838 | ||||||||
\(819\) | −3701.44 | −0.157923 | ||||||||
\(820\) | 11685.3 | 0.497645 | ||||||||
\(821\) | 25779.6 | 1.09588 | 0.547938 | − | 0.836519i | \(-0.315413\pi\) | ||||
0.547938 | + | 0.836519i | \(0.315413\pi\) | |||||||
\(822\) | −10500.2 | −0.445544 | ||||||||
\(823\) | −22130.2 | −0.937315 | −0.468658 | − | 0.883380i | \(-0.655262\pi\) | ||||
−0.468658 | + | 0.883380i | \(0.655262\pi\) | |||||||
\(824\) | 9592.32 | 0.405539 | ||||||||
\(825\) | 8409.26 | 0.354876 | ||||||||
\(826\) | −3136.00 | −0.132101 | ||||||||
\(827\) | 18288.6 | 0.768994 | 0.384497 | − | 0.923126i | \(-0.374375\pi\) | ||||
0.384497 | + | 0.923126i | \(0.374375\pi\) | |||||||
\(828\) | −2391.26 | −0.100365 | ||||||||
\(829\) | −34956.6 | −1.46453 | −0.732263 | − | 0.681022i | \(-0.761536\pi\) | ||||
−0.732263 | + | 0.681022i | \(0.761536\pi\) | |||||||
\(830\) | −51070.6 | −2.13577 | ||||||||
\(831\) | 349.435 | 0.0145870 | ||||||||
\(832\) | −34174.2 | −1.42401 | ||||||||
\(833\) | 29503.7 | 1.22718 | ||||||||
\(834\) | 11555.7 | 0.479786 | ||||||||
\(835\) | −7481.50 | −0.310069 | ||||||||
\(836\) | −644.577 | −0.0266664 | ||||||||
\(837\) | −8605.37 | −0.355370 | ||||||||
\(838\) | −31457.5 | −1.29675 | ||||||||
\(839\) | −14507.5 | −0.596965 | −0.298482 | − | 0.954415i | \(-0.596480\pi\) | ||||
−0.298482 | + | 0.954415i | \(0.596480\pi\) | |||||||
\(840\) | 9703.04 | 0.398556 | ||||||||
\(841\) | −23942.7 | −0.981702 | ||||||||
\(842\) | 14655.3 | 0.599829 | ||||||||
\(843\) | 24679.4 | 1.00831 | ||||||||
\(844\) | 4117.70 | 0.167935 | ||||||||
\(845\) | 29649.7 | 1.20708 | ||||||||
\(846\) | −2260.37 | −0.0918595 | ||||||||
\(847\) | 816.092 | 0.0331066 | ||||||||
\(848\) | −12828.7 | −0.519506 | ||||||||
\(849\) | 4684.55 | 0.189368 | ||||||||
\(850\) | 59949.2 | 2.41911 | ||||||||
\(851\) | −16842.6 | −0.678445 | ||||||||
\(852\) | 2138.61 | 0.0859948 | ||||||||
\(853\) | −44146.9 | −1.77205 | −0.886027 | − | 0.463634i | \(-0.846545\pi\) | ||||
−0.886027 | + | 0.463634i | \(0.846545\pi\) | |||||||
\(854\) | 6442.26 | 0.258138 | ||||||||
\(855\) | 4332.62 | 0.173301 | ||||||||
\(856\) | 37854.4 | 1.51149 | ||||||||
\(857\) | −47679.3 | −1.90046 | −0.950230 | − | 0.311549i | \(-0.899152\pi\) | ||||
−0.950230 | + | 0.311549i | \(0.899152\pi\) | |||||||
\(858\) | 4773.70 | 0.189943 | ||||||||
\(859\) | 7525.09 | 0.298897 | 0.149449 | − | 0.988769i | \(-0.452250\pi\) | ||||
0.149449 | + | 0.988769i | \(0.452250\pi\) | |||||||
\(860\) | −9894.76 | −0.392335 | ||||||||
\(861\) | −5113.95 | −0.202419 | ||||||||
\(862\) | −3957.09 | −0.156356 | ||||||||
\(863\) | 45816.1 | 1.80718 | 0.903591 | − | 0.428396i | \(-0.140921\pi\) | ||||
0.903591 | + | 0.428396i | \(0.140921\pi\) | |||||||
\(864\) | −2791.64 | −0.109923 | ||||||||
\(865\) | 52676.2 | 2.07057 | ||||||||
\(866\) | 1735.91 | 0.0681163 | ||||||||
\(867\) | 14764.1 | 0.578335 | ||||||||
\(868\) | 5099.48 | 0.199410 | ||||||||
\(869\) | 1073.04 | 0.0418876 | ||||||||
\(870\) | 2930.05 | 0.114182 | ||||||||
\(871\) | −1671.61 | −0.0650292 | ||||||||
\(872\) | 19187.3 | 0.745142 | ||||||||
\(873\) | −16185.2 | −0.627476 | ||||||||
\(874\) | −6562.96 | −0.253999 | ||||||||
\(875\) | 17065.1 | 0.659319 | ||||||||
\(876\) | −3044.69 | −0.117432 | ||||||||
\(877\) | −34168.3 | −1.31560 | −0.657801 | − | 0.753192i | \(-0.728513\pi\) | ||||
−0.657801 | + | 0.753192i | \(0.728513\pi\) | |||||||
\(878\) | 33800.2 | 1.29920 | ||||||||
\(879\) | 28458.6 | 1.09202 | ||||||||
\(880\) | −8445.31 | −0.323513 | ||||||||
\(881\) | −100.796 | −0.00385460 | −0.00192730 | − | 0.999998i | \(-0.500613\pi\) | ||||
−0.00192730 | + | 0.999998i | \(0.500613\pi\) | |||||||
\(882\) | 6352.02 | 0.242498 | ||||||||
\(883\) | −12346.1 | −0.470531 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(884\) | −14345.5 | −0.545803 | ||||||||
\(885\) | 11459.6 | 0.435266 | ||||||||
\(886\) | −413.398 | −0.0156754 | ||||||||
\(887\) | −37345.1 | −1.41367 | −0.706834 | − | 0.707379i | \(-0.749877\pi\) | ||||
−0.706834 | + | 0.707379i | \(0.749877\pi\) | |||||||
\(888\) | −11100.8 | −0.419501 | ||||||||
\(889\) | 15531.0 | 0.585932 | ||||||||
\(890\) | −21407.2 | −0.806260 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −3946.78 | −0.148148 | ||||||||
\(893\) | 2615.09 | 0.0979962 | ||||||||
\(894\) | 7857.80 | 0.293964 | ||||||||
\(895\) | −54133.2 | −2.02176 | ||||||||
\(896\) | −3388.13 | −0.126328 | ||||||||
\(897\) | −20488.7 | −0.762651 | ||||||||
\(898\) | −17720.9 | −0.658523 | ||||||||
\(899\) | 6732.88 | 0.249782 | ||||||||
\(900\) | −5440.67 | −0.201506 | ||||||||
\(901\) | −32294.4 | −1.19410 | ||||||||
\(902\) | 6595.39 | 0.243462 | ||||||||
\(903\) | 4330.34 | 0.159584 | ||||||||
\(904\) | −37267.1 | −1.37111 | ||||||||
\(905\) | −77831.9 | −2.85881 | ||||||||
\(906\) | −21208.7 | −0.777717 | ||||||||
\(907\) | 10308.6 | 0.377390 | 0.188695 | − | 0.982036i | \(-0.439574\pi\) | ||||
0.188695 | + | 0.982036i | \(0.439574\pi\) | |||||||
\(908\) | 8679.79 | 0.317235 | ||||||||
\(909\) | 6677.26 | 0.243642 | ||||||||
\(910\) | 19014.6 | 0.692668 | ||||||||
\(911\) | −22590.8 | −0.821589 | −0.410795 | − | 0.911728i | \(-0.634749\pi\) | ||||
−0.410795 | + | 0.911728i | \(0.634749\pi\) | |||||||
\(912\) | −2919.22 | −0.105992 | ||||||||
\(913\) | 12150.8 | 0.440453 | ||||||||
\(914\) | −20787.5 | −0.752288 | ||||||||
\(915\) | −23541.4 | −0.850551 | ||||||||
\(916\) | −4571.56 | −0.164900 | ||||||||
\(917\) | −13628.0 | −0.490769 | ||||||||
\(918\) | 6351.90 | 0.228370 | ||||||||
\(919\) | 47712.1 | 1.71260 | 0.856299 | − | 0.516481i | \(-0.172758\pi\) | ||||
0.856299 | + | 0.516481i | \(0.172758\pi\) | |||||||
\(920\) | 53709.5 | 1.92473 | ||||||||
\(921\) | −25329.2 | −0.906216 | ||||||||
\(922\) | −10294.9 | −0.367728 | ||||||||
\(923\) | 18323.9 | 0.653456 | ||||||||
\(924\) | −528.000 | −0.0187986 | ||||||||
\(925\) | −38320.8 | −1.36214 | ||||||||
\(926\) | 9328.96 | 0.331068 | ||||||||
\(927\) | 3508.53 | 0.124310 | ||||||||
\(928\) | 2184.19 | 0.0772625 | ||||||||
\(929\) | 10714.3 | 0.378391 | 0.189196 | − | 0.981939i | \(-0.439412\pi\) | ||||
0.189196 | + | 0.981939i | \(0.439412\pi\) | |||||||
\(930\) | 44206.4 | 1.55869 | ||||||||
\(931\) | −7348.84 | −0.258699 | ||||||||
\(932\) | 6605.06 | 0.232142 | ||||||||
\(933\) | 13341.5 | 0.468148 | ||||||||
\(934\) | 19889.1 | 0.696780 | ||||||||
\(935\) | −21259.8 | −0.743603 | ||||||||
\(936\) | −13503.9 | −0.471568 | ||||||||
\(937\) | −14719.5 | −0.513197 | −0.256599 | − | 0.966518i | \(-0.582602\pi\) | ||||
−0.256599 | + | 0.966518i | \(0.582602\pi\) | |||||||
\(938\) | −438.612 | −0.0152678 | ||||||||
\(939\) | 19442.2 | 0.675691 | ||||||||
\(940\) | −4894.74 | −0.169839 | ||||||||
\(941\) | 3694.44 | 0.127987 | 0.0639933 | − | 0.997950i | \(-0.479616\pi\) | ||||
0.0639933 | + | 0.997950i | \(0.479616\pi\) | |||||||
\(942\) | −20245.1 | −0.700234 | ||||||||
\(943\) | −28307.4 | −0.977535 | ||||||||
\(944\) | −7721.23 | −0.266213 | ||||||||
\(945\) | 3549.03 | 0.122169 | ||||||||
\(946\) | −5584.77 | −0.191941 | ||||||||
\(947\) | 36416.7 | 1.24961 | 0.624806 | − | 0.780780i | \(-0.285178\pi\) | ||||
0.624806 | + | 0.780780i | \(0.285178\pi\) | |||||||
\(948\) | −694.240 | −0.0237847 | ||||||||
\(949\) | −26087.4 | −0.892342 | ||||||||
\(950\) | −14932.3 | −0.509965 | ||||||||
\(951\) | −3758.25 | −0.128149 | ||||||||
\(952\) | −16457.6 | −0.560289 | ||||||||
\(953\) | 20779.4 | 0.706306 | 0.353153 | − | 0.935566i | \(-0.385110\pi\) | ||||
0.353153 | + | 0.935566i | \(0.385110\pi\) | |||||||
\(954\) | −6952.84 | −0.235961 | ||||||||
\(955\) | 17454.2 | 0.591419 | ||||||||
\(956\) | −2900.35 | −0.0981212 | ||||||||
\(957\) | −697.123 | −0.0235473 | ||||||||
\(958\) | −22617.6 | −0.762777 | ||||||||
\(959\) | 9950.94 | 0.335071 | ||||||||
\(960\) | 32767.0 | 1.10161 | ||||||||
\(961\) | 71789.7 | 2.40978 | ||||||||
\(962\) | −21753.7 | −0.729071 | ||||||||
\(963\) | 13845.8 | 0.463318 | ||||||||
\(964\) | 4775.43 | 0.159550 | ||||||||
\(965\) | 25886.2 | 0.863531 | ||||||||
\(966\) | −5376.00 | −0.179058 | ||||||||
\(967\) | 56812.8 | 1.88932 | 0.944662 | − | 0.328044i | \(-0.106389\pi\) | ||||
0.944662 | + | 0.328044i | \(0.106389\pi\) | |||||||
\(968\) | 2977.32 | 0.0988582 | ||||||||
\(969\) | −7348.70 | −0.243627 | ||||||||
\(970\) | 83144.7 | 2.75218 | ||||||||
\(971\) | −26459.7 | −0.874493 | −0.437247 | − | 0.899342i | \(-0.644046\pi\) | ||||
−0.437247 | + | 0.899342i | \(0.644046\pi\) | |||||||
\(972\) | −576.464 | −0.0190227 | ||||||||
\(973\) | −10951.2 | −0.360822 | ||||||||
\(974\) | −10559.2 | −0.347371 | ||||||||
\(975\) | −46616.5 | −1.53120 | ||||||||
\(976\) | 15861.7 | 0.520204 | ||||||||
\(977\) | −21009.2 | −0.687967 | −0.343984 | − | 0.938976i | \(-0.611776\pi\) | ||||
−0.343984 | + | 0.938976i | \(0.611776\pi\) | |||||||
\(978\) | 10878.2 | 0.355670 | ||||||||
\(979\) | 5093.24 | 0.166272 | ||||||||
\(980\) | 13755.0 | 0.448355 | ||||||||
\(981\) | 7018.04 | 0.228409 | ||||||||
\(982\) | 23147.3 | 0.752199 | ||||||||
\(983\) | −9076.80 | −0.294512 | −0.147256 | − | 0.989098i | \(-0.547044\pi\) | ||||
−0.147256 | + | 0.989098i | \(0.547044\pi\) | |||||||
\(984\) | −18657.1 | −0.604437 | ||||||||
\(985\) | 3003.55 | 0.0971585 | ||||||||
\(986\) | −4969.76 | −0.160517 | ||||||||
\(987\) | 2142.13 | 0.0690828 | ||||||||
\(988\) | 3573.20 | 0.115059 | ||||||||
\(989\) | 23969.8 | 0.770673 | ||||||||
\(990\) | −4577.14 | −0.146940 | ||||||||
\(991\) | 2629.24 | 0.0842791 | 0.0421395 | − | 0.999112i | \(-0.486583\pi\) | ||||
0.0421395 | + | 0.999112i | \(0.486583\pi\) | |||||||
\(992\) | 32953.5 | 1.05471 | ||||||||
\(993\) | 11404.3 | 0.364457 | ||||||||
\(994\) | 4808.00 | 0.153421 | ||||||||
\(995\) | 25650.6 | 0.817267 | ||||||||
\(996\) | −7861.40 | −0.250098 | ||||||||
\(997\) | −50423.9 | −1.60175 | −0.800874 | − | 0.598833i | \(-0.795631\pi\) | ||||
−0.800874 | + | 0.598833i | \(0.795631\pi\) | |||||||
\(998\) | 17018.0 | 0.539775 | ||||||||
\(999\) | −4060.27 | −0.128590 |
(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 | 33.4.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 99.4.a.e.1.2 | 2 | |||
4.3 | odd | 2 | 528.4.a.o.1.2 | 2 | |||
5.2 | odd | 4 | 825.4.c.i.199.2 | 4 | |||
5.3 | odd | 4 | 825.4.c.i.199.3 | 4 | |||
5.4 | even | 2 | 825.4.a.k.1.2 | 2 | |||
7.6 | odd | 2 | 1617.4.a.j.1.1 | 2 | |||
8.3 | odd | 2 | 2112.4.a.bh.1.1 | 2 | |||
8.5 | even | 2 | 2112.4.a.ba.1.1 | 2 | |||
11.10 | odd | 2 | 363.4.a.j.1.2 | 2 | |||
12.11 | even | 2 | 1584.4.a.x.1.1 | 2 | |||
15.14 | odd | 2 | 2475.4.a.o.1.1 | 2 | |||
33.32 | even | 2 | 1089.4.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.4.a.e.1.2 | 2 | 3.2 | odd | 2 | |||
363.4.a.j.1.2 | 2 | 11.10 | odd | 2 | |||
528.4.a.o.1.2 | 2 | 4.3 | odd | 2 | |||
825.4.a.k.1.2 | 2 | 5.4 | even | 2 | |||
825.4.c.i.199.2 | 4 | 5.2 | odd | 4 | |||
825.4.c.i.199.3 | 4 | 5.3 | odd | 4 | |||
1089.4.a.t.1.1 | 2 | 33.32 | even | 2 | |||
1584.4.a.x.1.1 | 2 | 12.11 | even | 2 | |||
1617.4.a.j.1.1 | 2 | 7.6 | odd | 2 | |||
2112.4.a.ba.1.1 | 2 | 8.5 | even | 2 | |||
2112.4.a.bh.1.1 | 2 | 8.3 | odd | 2 | |||
2475.4.a.o.1.1 | 2 | 15.14 | odd | 2 |