Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,4,Mod(1,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, 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("230.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.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: | \(13.5704393013\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 18 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −5.77200 | −1.11082 | −0.555411 | − | 0.831576i | \(-0.687439\pi\) | ||||
−0.555411 | + | 0.831576i | \(0.687439\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 11.5440 | 0.785470 | ||||||||
\(7\) | −12.7720 | −0.689623 | −0.344812 | − | 0.938672i | \(-0.612057\pi\) | ||||
−0.344812 | + | 0.938672i | \(0.612057\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 6.31601 | 0.233926 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | 51.7200 | 1.41765 | 0.708826 | − | 0.705383i | \(-0.249225\pi\) | ||||
0.708826 | + | 0.705383i | \(0.249225\pi\) | |||||||
\(12\) | −23.0880 | −0.555411 | ||||||||
\(13\) | 33.9480 | 0.724268 | 0.362134 | − | 0.932126i | \(-0.382048\pi\) | ||||
0.362134 | + | 0.932126i | \(0.382048\pi\) | |||||||
\(14\) | 25.5440 | 0.487637 | ||||||||
\(15\) | −28.8600 | −0.496775 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −86.4920 | −1.23396 | −0.616982 | − | 0.786977i | \(-0.711645\pi\) | ||||
−0.616982 | + | 0.786977i | \(0.711645\pi\) | |||||||
\(18\) | −12.6320 | −0.165411 | ||||||||
\(19\) | 59.7200 | 0.721090 | 0.360545 | − | 0.932742i | \(-0.382591\pi\) | ||||
0.360545 | + | 0.932742i | \(0.382591\pi\) | |||||||
\(20\) | 20.0000 | 0.223607 | ||||||||
\(21\) | 73.7200 | 0.766049 | ||||||||
\(22\) | −103.440 | −1.00243 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 46.1760 | 0.392735 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −67.8960 | −0.512135 | ||||||||
\(27\) | 119.388 | 0.850972 | ||||||||
\(28\) | −51.0880 | −0.344812 | ||||||||
\(29\) | −64.5440 | −0.413294 | −0.206647 | − | 0.978416i | \(-0.566255\pi\) | ||||
−0.206647 | + | 0.978416i | \(0.566255\pi\) | |||||||
\(30\) | 57.7200 | 0.351273 | ||||||||
\(31\) | −157.072 | −0.910031 | −0.455016 | − | 0.890483i | \(-0.650366\pi\) | ||||
−0.455016 | + | 0.890483i | \(0.650366\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −298.528 | −1.57476 | ||||||||
\(34\) | 172.984 | 0.872545 | ||||||||
\(35\) | −63.8600 | −0.308409 | ||||||||
\(36\) | 25.2640 | 0.116963 | ||||||||
\(37\) | −275.404 | −1.22368 | −0.611840 | − | 0.790982i | \(-0.709570\pi\) | ||||
−0.611840 | + | 0.790982i | \(0.709570\pi\) | |||||||
\(38\) | −119.440 | −0.509888 | ||||||||
\(39\) | −195.948 | −0.804533 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | −482.128 | −1.83648 | −0.918241 | − | 0.396022i | \(-0.870390\pi\) | ||||
−0.918241 | + | 0.396022i | \(0.870390\pi\) | |||||||
\(42\) | −147.440 | −0.541678 | ||||||||
\(43\) | −270.984 | −0.961039 | −0.480520 | − | 0.876984i | \(-0.659552\pi\) | ||||
−0.480520 | + | 0.876984i | \(0.659552\pi\) | |||||||
\(44\) | 206.880 | 0.708826 | ||||||||
\(45\) | 31.5800 | 0.104615 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | −320.860 | −0.995792 | −0.497896 | − | 0.867237i | \(-0.665894\pi\) | ||||
−0.497896 | + | 0.867237i | \(0.665894\pi\) | |||||||
\(48\) | −92.3520 | −0.277706 | ||||||||
\(49\) | −179.876 | −0.524420 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 499.232 | 1.37072 | ||||||||
\(52\) | 135.792 | 0.362134 | ||||||||
\(53\) | −122.596 | −0.317733 | −0.158867 | − | 0.987300i | \(-0.550784\pi\) | ||||
−0.158867 | + | 0.987300i | \(0.550784\pi\) | |||||||
\(54\) | −238.776 | −0.601728 | ||||||||
\(55\) | 258.600 | 0.633993 | ||||||||
\(56\) | 102.176 | 0.243819 | ||||||||
\(57\) | −344.704 | −0.801003 | ||||||||
\(58\) | 129.088 | 0.292243 | ||||||||
\(59\) | 627.060 | 1.38367 | 0.691833 | − | 0.722058i | \(-0.256803\pi\) | ||||
0.691833 | + | 0.722058i | \(0.256803\pi\) | |||||||
\(60\) | −115.440 | −0.248387 | ||||||||
\(61\) | −34.7360 | −0.0729096 | −0.0364548 | − | 0.999335i | \(-0.511606\pi\) | ||||
−0.0364548 | + | 0.999335i | \(0.511606\pi\) | |||||||
\(62\) | 314.144 | 0.643489 | ||||||||
\(63\) | −80.6680 | −0.161321 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 169.740 | 0.323903 | ||||||||
\(66\) | 597.056 | 1.11352 | ||||||||
\(67\) | −90.3479 | −0.164743 | −0.0823713 | − | 0.996602i | \(-0.526249\pi\) | ||||
−0.0823713 | + | 0.996602i | \(0.526249\pi\) | |||||||
\(68\) | −345.968 | −0.616982 | ||||||||
\(69\) | 132.756 | 0.231622 | ||||||||
\(70\) | 127.720 | 0.218078 | ||||||||
\(71\) | 182.712 | 0.305407 | 0.152704 | − | 0.988272i | \(-0.451202\pi\) | ||||
0.152704 | + | 0.988272i | \(0.451202\pi\) | |||||||
\(72\) | −50.5280 | −0.0827054 | ||||||||
\(73\) | −73.2440 | −0.117432 | −0.0587161 | − | 0.998275i | \(-0.518701\pi\) | ||||
−0.0587161 | + | 0.998275i | \(0.518701\pi\) | |||||||
\(74\) | 550.808 | 0.865272 | ||||||||
\(75\) | −144.300 | −0.222164 | ||||||||
\(76\) | 238.880 | 0.360545 | ||||||||
\(77\) | −660.568 | −0.977646 | ||||||||
\(78\) | 391.896 | 0.568891 | ||||||||
\(79\) | −283.232 | −0.403368 | −0.201684 | − | 0.979451i | \(-0.564641\pi\) | ||||
−0.201684 | + | 0.979451i | \(0.564641\pi\) | |||||||
\(80\) | 80.0000 | 0.111803 | ||||||||
\(81\) | −859.640 | −1.17920 | ||||||||
\(82\) | 964.256 | 1.29859 | ||||||||
\(83\) | 1136.32 | 1.50274 | 0.751372 | − | 0.659879i | \(-0.229392\pi\) | ||||
0.751372 | + | 0.659879i | \(0.229392\pi\) | |||||||
\(84\) | 294.880 | 0.383024 | ||||||||
\(85\) | −432.460 | −0.551846 | ||||||||
\(86\) | 541.968 | 0.679557 | ||||||||
\(87\) | 372.548 | 0.459096 | ||||||||
\(88\) | −413.760 | −0.501216 | ||||||||
\(89\) | 476.104 | 0.567044 | 0.283522 | − | 0.958966i | \(-0.408497\pi\) | ||||
0.283522 | + | 0.958966i | \(0.408497\pi\) | |||||||
\(90\) | −63.1601 | −0.0739739 | ||||||||
\(91\) | −433.584 | −0.499472 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 906.620 | 1.01088 | ||||||||
\(94\) | 641.720 | 0.704132 | ||||||||
\(95\) | 298.600 | 0.322481 | ||||||||
\(96\) | 184.704 | 0.196367 | ||||||||
\(97\) | −1820.61 | −1.90572 | −0.952860 | − | 0.303412i | \(-0.901874\pi\) | ||||
−0.952860 | + | 0.303412i | \(0.901874\pi\) | |||||||
\(98\) | 359.752 | 0.370821 | ||||||||
\(99\) | 326.664 | 0.331626 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 184.836 | 0.182098 | 0.0910488 | − | 0.995846i | \(-0.470978\pi\) | ||||
0.0910488 | + | 0.995846i | \(0.470978\pi\) | |||||||
\(102\) | −998.464 | −0.969242 | ||||||||
\(103\) | −1249.78 | −1.19557 | −0.597787 | − | 0.801655i | \(-0.703953\pi\) | ||||
−0.597787 | + | 0.801655i | \(0.703953\pi\) | |||||||
\(104\) | −271.584 | −0.256067 | ||||||||
\(105\) | 368.600 | 0.342587 | ||||||||
\(106\) | 245.192 | 0.224671 | ||||||||
\(107\) | 816.820 | 0.737991 | 0.368995 | − | 0.929431i | \(-0.379702\pi\) | ||||
0.368995 | + | 0.929431i | \(0.379702\pi\) | |||||||
\(108\) | 477.552 | 0.425486 | ||||||||
\(109\) | −259.264 | −0.227826 | −0.113913 | − | 0.993491i | \(-0.536338\pi\) | ||||
−0.113913 | + | 0.993491i | \(0.536338\pi\) | |||||||
\(110\) | −517.200 | −0.448301 | ||||||||
\(111\) | 1589.63 | 1.35929 | ||||||||
\(112\) | −204.352 | −0.172406 | ||||||||
\(113\) | 890.876 | 0.741651 | 0.370825 | − | 0.928703i | \(-0.379075\pi\) | ||||
0.370825 | + | 0.928703i | \(0.379075\pi\) | |||||||
\(114\) | 689.408 | 0.566395 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | −258.176 | −0.206647 | ||||||||
\(117\) | 214.416 | 0.169425 | ||||||||
\(118\) | −1254.12 | −0.978399 | ||||||||
\(119\) | 1104.68 | 0.850971 | ||||||||
\(120\) | 230.880 | 0.175636 | ||||||||
\(121\) | 1343.96 | 1.00974 | ||||||||
\(122\) | 69.4720 | 0.0515549 | ||||||||
\(123\) | 2782.84 | 2.04001 | ||||||||
\(124\) | −628.288 | −0.455016 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 161.336 | 0.114071 | ||||||||
\(127\) | −2176.69 | −1.52087 | −0.760434 | − | 0.649415i | \(-0.775014\pi\) | ||||
−0.760434 | + | 0.649415i | \(0.775014\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 1564.12 | 1.06754 | ||||||||
\(130\) | −339.480 | −0.229034 | ||||||||
\(131\) | −1604.85 | −1.07036 | −0.535178 | − | 0.844739i | \(-0.679755\pi\) | ||||
−0.535178 | + | 0.844739i | \(0.679755\pi\) | |||||||
\(132\) | −1194.11 | −0.787380 | ||||||||
\(133\) | −762.744 | −0.497281 | ||||||||
\(134\) | 180.696 | 0.116491 | ||||||||
\(135\) | 596.940 | 0.380566 | ||||||||
\(136\) | 691.936 | 0.436272 | ||||||||
\(137\) | −1734.60 | −1.08173 | −0.540865 | − | 0.841110i | \(-0.681903\pi\) | ||||
−0.540865 | + | 0.841110i | \(0.681903\pi\) | |||||||
\(138\) | −265.512 | −0.163782 | ||||||||
\(139\) | −993.824 | −0.606439 | −0.303220 | − | 0.952921i | \(-0.598062\pi\) | ||||
−0.303220 | + | 0.952921i | \(0.598062\pi\) | |||||||
\(140\) | −255.440 | −0.154204 | ||||||||
\(141\) | 1852.00 | 1.10615 | ||||||||
\(142\) | −365.424 | −0.215955 | ||||||||
\(143\) | 1755.79 | 1.02676 | ||||||||
\(144\) | 101.056 | 0.0584815 | ||||||||
\(145\) | −322.720 | −0.184831 | ||||||||
\(146\) | 146.488 | 0.0830372 | ||||||||
\(147\) | 1038.24 | 0.582537 | ||||||||
\(148\) | −1101.62 | −0.611840 | ||||||||
\(149\) | −1023.08 | −0.562510 | −0.281255 | − | 0.959633i | \(-0.590751\pi\) | ||||
−0.281255 | + | 0.959633i | \(0.590751\pi\) | |||||||
\(150\) | 288.600 | 0.157094 | ||||||||
\(151\) | −1309.40 | −0.705677 | −0.352838 | − | 0.935684i | \(-0.614783\pi\) | ||||
−0.352838 | + | 0.935684i | \(0.614783\pi\) | |||||||
\(152\) | −477.760 | −0.254944 | ||||||||
\(153\) | −546.284 | −0.288657 | ||||||||
\(154\) | 1321.14 | 0.691300 | ||||||||
\(155\) | −785.360 | −0.406978 | ||||||||
\(156\) | −783.792 | −0.402267 | ||||||||
\(157\) | −1648.70 | −0.838093 | −0.419046 | − | 0.907965i | \(-0.637636\pi\) | ||||
−0.419046 | + | 0.907965i | \(0.637636\pi\) | |||||||
\(158\) | 566.464 | 0.285225 | ||||||||
\(159\) | 707.624 | 0.352945 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 293.756 | 0.143796 | ||||||||
\(162\) | 1719.28 | 0.833824 | ||||||||
\(163\) | 3964.26 | 1.90494 | 0.952469 | − | 0.304636i | \(-0.0985347\pi\) | ||||
0.952469 | + | 0.304636i | \(0.0985347\pi\) | |||||||
\(164\) | −1928.51 | −0.918241 | ||||||||
\(165\) | −1492.64 | −0.704254 | ||||||||
\(166\) | −2272.65 | −1.06260 | ||||||||
\(167\) | 3484.96 | 1.61482 | 0.807408 | − | 0.589993i | \(-0.200869\pi\) | ||||
0.807408 | + | 0.589993i | \(0.200869\pi\) | |||||||
\(168\) | −589.760 | −0.270839 | ||||||||
\(169\) | −1044.53 | −0.475436 | ||||||||
\(170\) | 864.920 | 0.390214 | ||||||||
\(171\) | 377.192 | 0.168682 | ||||||||
\(172\) | −1083.94 | −0.480520 | ||||||||
\(173\) | 2239.51 | 0.984202 | 0.492101 | − | 0.870538i | \(-0.336229\pi\) | ||||
0.492101 | + | 0.870538i | \(0.336229\pi\) | |||||||
\(174\) | −745.096 | −0.324630 | ||||||||
\(175\) | −319.300 | −0.137925 | ||||||||
\(176\) | 827.520 | 0.354413 | ||||||||
\(177\) | −3619.39 | −1.53701 | ||||||||
\(178\) | −952.208 | −0.400961 | ||||||||
\(179\) | −2402.86 | −1.00334 | −0.501671 | − | 0.865058i | \(-0.667281\pi\) | ||||
−0.501671 | + | 0.865058i | \(0.667281\pi\) | |||||||
\(180\) | 126.320 | 0.0523075 | ||||||||
\(181\) | 4314.39 | 1.77174 | 0.885872 | − | 0.463929i | \(-0.153561\pi\) | ||||
0.885872 | + | 0.463929i | \(0.153561\pi\) | |||||||
\(182\) | 867.168 | 0.353180 | ||||||||
\(183\) | 200.496 | 0.0809896 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −1377.02 | −0.547246 | ||||||||
\(186\) | −1813.24 | −0.714802 | ||||||||
\(187\) | −4473.37 | −1.74933 | ||||||||
\(188\) | −1283.44 | −0.497896 | ||||||||
\(189\) | −1524.82 | −0.586850 | ||||||||
\(190\) | −597.200 | −0.228029 | ||||||||
\(191\) | −1930.75 | −0.731434 | −0.365717 | − | 0.930726i | \(-0.619176\pi\) | ||||
−0.365717 | + | 0.930726i | \(0.619176\pi\) | |||||||
\(192\) | −369.408 | −0.138853 | ||||||||
\(193\) | 4302.32 | 1.60460 | 0.802299 | − | 0.596922i | \(-0.203610\pi\) | ||||
0.802299 | + | 0.596922i | \(0.203610\pi\) | |||||||
\(194\) | 3641.22 | 1.34755 | ||||||||
\(195\) | −979.740 | −0.359798 | ||||||||
\(196\) | −719.504 | −0.262210 | ||||||||
\(197\) | −5436.48 | −1.96616 | −0.983079 | − | 0.183184i | \(-0.941360\pi\) | ||||
−0.983079 | + | 0.183184i | \(0.941360\pi\) | |||||||
\(198\) | −653.328 | −0.234495 | ||||||||
\(199\) | 1071.03 | 0.381525 | 0.190762 | − | 0.981636i | \(-0.438904\pi\) | ||||
0.190762 | + | 0.981636i | \(0.438904\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 521.488 | 0.183000 | ||||||||
\(202\) | −369.672 | −0.128762 | ||||||||
\(203\) | 824.356 | 0.285017 | ||||||||
\(204\) | 1996.93 | 0.685358 | ||||||||
\(205\) | −2410.64 | −0.821300 | ||||||||
\(206\) | 2499.55 | 0.845399 | ||||||||
\(207\) | −145.268 | −0.0487770 | ||||||||
\(208\) | 543.168 | 0.181067 | ||||||||
\(209\) | 3088.72 | 1.02225 | ||||||||
\(210\) | −737.200 | −0.242246 | ||||||||
\(211\) | −2350.65 | −0.766946 | −0.383473 | − | 0.923552i | \(-0.625272\pi\) | ||||
−0.383473 | + | 0.923552i | \(0.625272\pi\) | |||||||
\(212\) | −490.384 | −0.158867 | ||||||||
\(213\) | −1054.61 | −0.339253 | ||||||||
\(214\) | −1633.64 | −0.521838 | ||||||||
\(215\) | −1354.92 | −0.429790 | ||||||||
\(216\) | −955.104 | −0.300864 | ||||||||
\(217\) | 2006.12 | 0.627579 | ||||||||
\(218\) | 518.528 | 0.161097 | ||||||||
\(219\) | 422.764 | 0.130446 | ||||||||
\(220\) | 1034.40 | 0.316997 | ||||||||
\(221\) | −2936.23 | −0.893721 | ||||||||
\(222\) | −3179.26 | −0.961163 | ||||||||
\(223\) | −2443.32 | −0.733708 | −0.366854 | − | 0.930279i | \(-0.619565\pi\) | ||||
−0.366854 | + | 0.930279i | \(0.619565\pi\) | |||||||
\(224\) | 408.704 | 0.121909 | ||||||||
\(225\) | 157.900 | 0.0467852 | ||||||||
\(226\) | −1781.75 | −0.524426 | ||||||||
\(227\) | 997.432 | 0.291638 | 0.145819 | − | 0.989311i | \(-0.453418\pi\) | ||||
0.145819 | + | 0.989311i | \(0.453418\pi\) | |||||||
\(228\) | −1378.82 | −0.400501 | ||||||||
\(229\) | −4084.76 | −1.17873 | −0.589364 | − | 0.807868i | \(-0.700621\pi\) | ||||
−0.589364 | + | 0.807868i | \(0.700621\pi\) | |||||||
\(230\) | 230.000 | 0.0659380 | ||||||||
\(231\) | 3812.80 | 1.08599 | ||||||||
\(232\) | 516.352 | 0.146121 | ||||||||
\(233\) | −1079.76 | −0.303593 | −0.151797 | − | 0.988412i | \(-0.548506\pi\) | ||||
−0.151797 | + | 0.988412i | \(0.548506\pi\) | |||||||
\(234\) | −428.832 | −0.119802 | ||||||||
\(235\) | −1604.30 | −0.445332 | ||||||||
\(236\) | 2508.24 | 0.691833 | ||||||||
\(237\) | 1634.82 | 0.448071 | ||||||||
\(238\) | −2209.35 | −0.601727 | ||||||||
\(239\) | 3678.78 | 0.995652 | 0.497826 | − | 0.867277i | \(-0.334132\pi\) | ||||
0.497826 | + | 0.867277i | \(0.334132\pi\) | |||||||
\(240\) | −461.760 | −0.124194 | ||||||||
\(241\) | −3127.15 | −0.835841 | −0.417920 | − | 0.908484i | \(-0.637241\pi\) | ||||
−0.417920 | + | 0.908484i | \(0.637241\pi\) | |||||||
\(242\) | −2687.92 | −0.713992 | ||||||||
\(243\) | 1738.37 | 0.458915 | ||||||||
\(244\) | −138.944 | −0.0364548 | ||||||||
\(245\) | −899.380 | −0.234528 | ||||||||
\(246\) | −5565.69 | −1.44250 | ||||||||
\(247\) | 2027.38 | 0.522263 | ||||||||
\(248\) | 1256.58 | 0.321745 | ||||||||
\(249\) | −6558.87 | −1.66928 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | −1585.51 | −0.398712 | −0.199356 | − | 0.979927i | \(-0.563885\pi\) | ||||
−0.199356 | + | 0.979927i | \(0.563885\pi\) | |||||||
\(252\) | −322.672 | −0.0806605 | ||||||||
\(253\) | −1189.56 | −0.295601 | ||||||||
\(254\) | 4353.38 | 1.07542 | ||||||||
\(255\) | 2496.16 | 0.613002 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 7046.41 | 1.71028 | 0.855142 | − | 0.518394i | \(-0.173470\pi\) | ||||
0.855142 | + | 0.518394i | \(0.173470\pi\) | |||||||
\(258\) | −3128.24 | −0.754867 | ||||||||
\(259\) | 3517.46 | 0.843878 | ||||||||
\(260\) | 678.960 | 0.161951 | ||||||||
\(261\) | −407.660 | −0.0966802 | ||||||||
\(262\) | 3209.71 | 0.756856 | ||||||||
\(263\) | 4990.01 | 1.16995 | 0.584976 | − | 0.811051i | \(-0.301104\pi\) | ||||
0.584976 | + | 0.811051i | \(0.301104\pi\) | |||||||
\(264\) | 2388.22 | 0.556762 | ||||||||
\(265\) | −612.980 | −0.142095 | ||||||||
\(266\) | 1525.49 | 0.351630 | ||||||||
\(267\) | −2748.07 | −0.629885 | ||||||||
\(268\) | −361.392 | −0.0823713 | ||||||||
\(269\) | 4842.06 | 1.09749 | 0.548746 | − | 0.835989i | \(-0.315105\pi\) | ||||
0.548746 | + | 0.835989i | \(0.315105\pi\) | |||||||
\(270\) | −1193.88 | −0.269101 | ||||||||
\(271\) | −2580.28 | −0.578379 | −0.289189 | − | 0.957272i | \(-0.593386\pi\) | ||||
−0.289189 | + | 0.957272i | \(0.593386\pi\) | |||||||
\(272\) | −1383.87 | −0.308491 | ||||||||
\(273\) | 2502.65 | 0.554825 | ||||||||
\(274\) | 3469.20 | 0.764898 | ||||||||
\(275\) | 1293.00 | 0.283530 | ||||||||
\(276\) | 531.024 | 0.115811 | ||||||||
\(277\) | 5444.79 | 1.18103 | 0.590516 | − | 0.807026i | \(-0.298924\pi\) | ||||
0.590516 | + | 0.807026i | \(0.298924\pi\) | |||||||
\(278\) | 1987.65 | 0.428817 | ||||||||
\(279\) | −992.068 | −0.212880 | ||||||||
\(280\) | 510.880 | 0.109039 | ||||||||
\(281\) | −2473.91 | −0.525199 | −0.262599 | − | 0.964905i | \(-0.584580\pi\) | ||||
−0.262599 | + | 0.964905i | \(0.584580\pi\) | |||||||
\(282\) | −3704.01 | −0.782165 | ||||||||
\(283\) | −1854.11 | −0.389454 | −0.194727 | − | 0.980858i | \(-0.562382\pi\) | ||||
−0.194727 | + | 0.980858i | \(0.562382\pi\) | |||||||
\(284\) | 730.847 | 0.152704 | ||||||||
\(285\) | −1723.52 | −0.358219 | ||||||||
\(286\) | −3511.58 | −0.726029 | ||||||||
\(287\) | 6157.74 | 1.26648 | ||||||||
\(288\) | −202.112 | −0.0413527 | ||||||||
\(289\) | 2567.87 | 0.522668 | ||||||||
\(290\) | 645.440 | 0.130695 | ||||||||
\(291\) | 10508.6 | 2.11692 | ||||||||
\(292\) | −292.976 | −0.0587161 | ||||||||
\(293\) | −4603.24 | −0.917829 | −0.458915 | − | 0.888480i | \(-0.651762\pi\) | ||||
−0.458915 | + | 0.888480i | \(0.651762\pi\) | |||||||
\(294\) | −2076.49 | −0.411916 | ||||||||
\(295\) | 3135.30 | 0.618794 | ||||||||
\(296\) | 2203.23 | 0.432636 | ||||||||
\(297\) | 6174.75 | 1.20638 | ||||||||
\(298\) | 2046.16 | 0.397755 | ||||||||
\(299\) | −780.804 | −0.151020 | ||||||||
\(300\) | −577.200 | −0.111082 | ||||||||
\(301\) | 3461.01 | 0.662755 | ||||||||
\(302\) | 2618.79 | 0.498989 | ||||||||
\(303\) | −1066.87 | −0.202278 | ||||||||
\(304\) | 955.520 | 0.180273 | ||||||||
\(305\) | −173.680 | −0.0326062 | ||||||||
\(306\) | 1092.57 | 0.204111 | ||||||||
\(307\) | 1076.46 | 0.200119 | 0.100060 | − | 0.994981i | \(-0.468097\pi\) | ||||
0.100060 | + | 0.994981i | \(0.468097\pi\) | |||||||
\(308\) | −2642.27 | −0.488823 | ||||||||
\(309\) | 7213.71 | 1.32807 | ||||||||
\(310\) | 1570.72 | 0.287777 | ||||||||
\(311\) | 8141.36 | 1.48442 | 0.742209 | − | 0.670168i | \(-0.233778\pi\) | ||||
0.742209 | + | 0.670168i | \(0.233778\pi\) | |||||||
\(312\) | 1567.58 | 0.284445 | ||||||||
\(313\) | −8180.24 | −1.47724 | −0.738618 | − | 0.674124i | \(-0.764521\pi\) | ||||
−0.738618 | + | 0.674124i | \(0.764521\pi\) | |||||||
\(314\) | 3297.40 | 0.592621 | ||||||||
\(315\) | −403.340 | −0.0721449 | ||||||||
\(316\) | −1132.93 | −0.201684 | ||||||||
\(317\) | −3229.21 | −0.572146 | −0.286073 | − | 0.958208i | \(-0.592350\pi\) | ||||
−0.286073 | + | 0.958208i | \(0.592350\pi\) | |||||||
\(318\) | −1415.25 | −0.249570 | ||||||||
\(319\) | −3338.22 | −0.585907 | ||||||||
\(320\) | 320.000 | 0.0559017 | ||||||||
\(321\) | −4714.69 | −0.819776 | ||||||||
\(322\) | −587.512 | −0.101679 | ||||||||
\(323\) | −5165.31 | −0.889800 | ||||||||
\(324\) | −3438.56 | −0.589602 | ||||||||
\(325\) | 848.700 | 0.144854 | ||||||||
\(326\) | −7928.52 | −1.34699 | ||||||||
\(327\) | 1496.47 | 0.253074 | ||||||||
\(328\) | 3857.03 | 0.649294 | ||||||||
\(329\) | 4098.02 | 0.686722 | ||||||||
\(330\) | 2985.28 | 0.497983 | ||||||||
\(331\) | −3414.79 | −0.567052 | −0.283526 | − | 0.958965i | \(-0.591504\pi\) | ||||
−0.283526 | + | 0.958965i | \(0.591504\pi\) | |||||||
\(332\) | 4545.30 | 0.751372 | ||||||||
\(333\) | −1739.45 | −0.286251 | ||||||||
\(334\) | −6969.92 | −1.14185 | ||||||||
\(335\) | −451.740 | −0.0736751 | ||||||||
\(336\) | 1179.52 | 0.191512 | ||||||||
\(337\) | −2157.79 | −0.348791 | −0.174395 | − | 0.984676i | \(-0.555797\pi\) | ||||
−0.174395 | + | 0.984676i | \(0.555797\pi\) | |||||||
\(338\) | 2089.06 | 0.336184 | ||||||||
\(339\) | −5142.14 | −0.823842 | ||||||||
\(340\) | −1729.84 | −0.275923 | ||||||||
\(341\) | −8123.77 | −1.29011 | ||||||||
\(342\) | −754.384 | −0.119276 | ||||||||
\(343\) | 6678.17 | 1.05128 | ||||||||
\(344\) | 2167.87 | 0.339779 | ||||||||
\(345\) | 663.780 | 0.103585 | ||||||||
\(346\) | −4479.03 | −0.695936 | ||||||||
\(347\) | −1920.53 | −0.297116 | −0.148558 | − | 0.988904i | \(-0.547463\pi\) | ||||
−0.148558 | + | 0.988904i | \(0.547463\pi\) | |||||||
\(348\) | 1490.19 | 0.229548 | ||||||||
\(349\) | 3086.66 | 0.473424 | 0.236712 | − | 0.971580i | \(-0.423930\pi\) | ||||
0.236712 | + | 0.971580i | \(0.423930\pi\) | |||||||
\(350\) | 638.600 | 0.0975275 | ||||||||
\(351\) | 4052.99 | 0.616332 | ||||||||
\(352\) | −1655.04 | −0.250608 | ||||||||
\(353\) | −350.901 | −0.0529082 | −0.0264541 | − | 0.999650i | \(-0.508422\pi\) | ||||
−0.0264541 | + | 0.999650i | \(0.508422\pi\) | |||||||
\(354\) | 7238.79 | 1.08683 | ||||||||
\(355\) | 913.559 | 0.136582 | ||||||||
\(356\) | 1904.42 | 0.283522 | ||||||||
\(357\) | −6376.19 | −0.945277 | ||||||||
\(358\) | 4805.72 | 0.709470 | ||||||||
\(359\) | −6536.65 | −0.960979 | −0.480489 | − | 0.877000i | \(-0.659541\pi\) | ||||
−0.480489 | + | 0.877000i | \(0.659541\pi\) | |||||||
\(360\) | −252.640 | −0.0369870 | ||||||||
\(361\) | −3292.52 | −0.480029 | ||||||||
\(362\) | −8628.77 | −1.25281 | ||||||||
\(363\) | −7757.34 | −1.12164 | ||||||||
\(364\) | −1734.34 | −0.249736 | ||||||||
\(365\) | −366.220 | −0.0525173 | ||||||||
\(366\) | −400.992 | −0.0572683 | ||||||||
\(367\) | 3858.89 | 0.548863 | 0.274431 | − | 0.961607i | \(-0.411510\pi\) | ||||
0.274431 | + | 0.961607i | \(0.411510\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −3045.12 | −0.429601 | ||||||||
\(370\) | 2754.04 | 0.386961 | ||||||||
\(371\) | 1565.80 | 0.219116 | ||||||||
\(372\) | 3626.48 | 0.505442 | ||||||||
\(373\) | 7132.34 | 0.990076 | 0.495038 | − | 0.868871i | \(-0.335154\pi\) | ||||
0.495038 | + | 0.868871i | \(0.335154\pi\) | |||||||
\(374\) | 8946.74 | 1.23696 | ||||||||
\(375\) | −721.500 | −0.0993550 | ||||||||
\(376\) | 2566.88 | 0.352066 | ||||||||
\(377\) | −2191.14 | −0.299336 | ||||||||
\(378\) | 3049.65 | 0.414966 | ||||||||
\(379\) | −10560.1 | −1.43123 | −0.715613 | − | 0.698497i | \(-0.753853\pi\) | ||||
−0.715613 | + | 0.698497i | \(0.753853\pi\) | |||||||
\(380\) | 1194.40 | 0.161241 | ||||||||
\(381\) | 12563.9 | 1.68941 | ||||||||
\(382\) | 3861.49 | 0.517202 | ||||||||
\(383\) | 343.459 | 0.0458222 | 0.0229111 | − | 0.999738i | \(-0.492707\pi\) | ||||
0.0229111 | + | 0.999738i | \(0.492707\pi\) | |||||||
\(384\) | 738.816 | 0.0981837 | ||||||||
\(385\) | −3302.84 | −0.437217 | ||||||||
\(386\) | −8604.63 | −1.13462 | ||||||||
\(387\) | −1711.54 | −0.224812 | ||||||||
\(388\) | −7282.43 | −0.952860 | ||||||||
\(389\) | 6173.29 | 0.804623 | 0.402312 | − | 0.915503i | \(-0.368207\pi\) | ||||
0.402312 | + | 0.915503i | \(0.368207\pi\) | |||||||
\(390\) | 1959.48 | 0.254416 | ||||||||
\(391\) | 1989.32 | 0.257299 | ||||||||
\(392\) | 1439.01 | 0.185410 | ||||||||
\(393\) | 9263.21 | 1.18898 | ||||||||
\(394\) | 10873.0 | 1.39028 | ||||||||
\(395\) | −1416.16 | −0.180392 | ||||||||
\(396\) | 1306.66 | 0.165813 | ||||||||
\(397\) | −1490.04 | −0.188371 | −0.0941853 | − | 0.995555i | \(-0.530025\pi\) | ||||
−0.0941853 | + | 0.995555i | \(0.530025\pi\) | |||||||
\(398\) | −2142.06 | −0.269779 | ||||||||
\(399\) | 4402.56 | 0.552390 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | 2227.87 | 0.277443 | 0.138721 | − | 0.990331i | \(-0.455701\pi\) | ||||
0.138721 | + | 0.990331i | \(0.455701\pi\) | |||||||
\(402\) | −1042.98 | −0.129400 | ||||||||
\(403\) | −5332.28 | −0.659107 | ||||||||
\(404\) | 739.343 | 0.0910488 | ||||||||
\(405\) | −4298.20 | −0.527356 | ||||||||
\(406\) | −1648.71 | −0.201537 | ||||||||
\(407\) | −14243.9 | −1.73475 | ||||||||
\(408\) | −3993.86 | −0.484621 | ||||||||
\(409\) | −469.656 | −0.0567799 | −0.0283900 | − | 0.999597i | \(-0.509038\pi\) | ||||
−0.0283900 | + | 0.999597i | \(0.509038\pi\) | |||||||
\(410\) | 4821.28 | 0.580747 | ||||||||
\(411\) | 10012.1 | 1.20161 | ||||||||
\(412\) | −4999.11 | −0.597787 | ||||||||
\(413\) | −8008.81 | −0.954208 | ||||||||
\(414\) | 290.536 | 0.0344905 | ||||||||
\(415\) | 5681.62 | 0.672048 | ||||||||
\(416\) | −1086.34 | −0.128034 | ||||||||
\(417\) | 5736.36 | 0.673647 | ||||||||
\(418\) | −6177.44 | −0.722843 | ||||||||
\(419\) | −14957.6 | −1.74398 | −0.871991 | − | 0.489522i | \(-0.837171\pi\) | ||||
−0.871991 | + | 0.489522i | \(0.837171\pi\) | |||||||
\(420\) | 1474.40 | 0.171294 | ||||||||
\(421\) | −10830.8 | −1.25382 | −0.626912 | − | 0.779090i | \(-0.715682\pi\) | ||||
−0.626912 | + | 0.779090i | \(0.715682\pi\) | |||||||
\(422\) | 4701.31 | 0.542313 | ||||||||
\(423\) | −2026.55 | −0.232942 | ||||||||
\(424\) | 980.768 | 0.112336 | ||||||||
\(425\) | −2162.30 | −0.246793 | ||||||||
\(426\) | 2109.23 | 0.239888 | ||||||||
\(427\) | 443.648 | 0.0502802 | ||||||||
\(428\) | 3267.28 | 0.368995 | ||||||||
\(429\) | −10134.4 | −1.14055 | ||||||||
\(430\) | 2709.84 | 0.303907 | ||||||||
\(431\) | 1774.70 | 0.198339 | 0.0991695 | − | 0.995071i | \(-0.468381\pi\) | ||||
0.0991695 | + | 0.995071i | \(0.468381\pi\) | |||||||
\(432\) | 1910.21 | 0.212743 | ||||||||
\(433\) | 4750.64 | 0.527254 | 0.263627 | − | 0.964625i | \(-0.415081\pi\) | ||||
0.263627 | + | 0.964625i | \(0.415081\pi\) | |||||||
\(434\) | −4012.25 | −0.443765 | ||||||||
\(435\) | 1862.74 | 0.205314 | ||||||||
\(436\) | −1037.06 | −0.113913 | ||||||||
\(437\) | −1373.56 | −0.150358 | ||||||||
\(438\) | −845.529 | −0.0922395 | ||||||||
\(439\) | 8283.27 | 0.900544 | 0.450272 | − | 0.892891i | \(-0.351327\pi\) | ||||
0.450272 | + | 0.892891i | \(0.351327\pi\) | |||||||
\(440\) | −2068.80 | −0.224150 | ||||||||
\(441\) | −1136.10 | −0.122675 | ||||||||
\(442\) | 5872.47 | 0.631956 | ||||||||
\(443\) | 13646.4 | 1.46357 | 0.731785 | − | 0.681536i | \(-0.238688\pi\) | ||||
0.731785 | + | 0.681536i | \(0.238688\pi\) | |||||||
\(444\) | 6358.53 | 0.679645 | ||||||||
\(445\) | 2380.52 | 0.253590 | ||||||||
\(446\) | 4886.64 | 0.518810 | ||||||||
\(447\) | 5905.22 | 0.624849 | ||||||||
\(448\) | −817.408 | −0.0862029 | ||||||||
\(449\) | −1904.70 | −0.200197 | −0.100098 | − | 0.994978i | \(-0.531916\pi\) | ||||
−0.100098 | + | 0.994978i | \(0.531916\pi\) | |||||||
\(450\) | −315.800 | −0.0330822 | ||||||||
\(451\) | −24935.7 | −2.60349 | ||||||||
\(452\) | 3563.50 | 0.370825 | ||||||||
\(453\) | 7557.84 | 0.783881 | ||||||||
\(454\) | −1994.86 | −0.206219 | ||||||||
\(455\) | −2167.92 | −0.223371 | ||||||||
\(456\) | 2757.63 | 0.283197 | ||||||||
\(457\) | −10056.3 | −1.02935 | −0.514676 | − | 0.857385i | \(-0.672088\pi\) | ||||
−0.514676 | + | 0.857385i | \(0.672088\pi\) | |||||||
\(458\) | 8169.52 | 0.833486 | ||||||||
\(459\) | −10326.1 | −1.05007 | ||||||||
\(460\) | −460.000 | −0.0466252 | ||||||||
\(461\) | 9219.60 | 0.931453 | 0.465726 | − | 0.884929i | \(-0.345793\pi\) | ||||
0.465726 | + | 0.884929i | \(0.345793\pi\) | |||||||
\(462\) | −7625.60 | −0.767911 | ||||||||
\(463\) | 2892.39 | 0.290326 | 0.145163 | − | 0.989408i | \(-0.453629\pi\) | ||||
0.145163 | + | 0.989408i | \(0.453629\pi\) | |||||||
\(464\) | −1032.70 | −0.103323 | ||||||||
\(465\) | 4533.10 | 0.452081 | ||||||||
\(466\) | 2159.51 | 0.214673 | ||||||||
\(467\) | 16773.0 | 1.66201 | 0.831007 | − | 0.556263i | \(-0.187765\pi\) | ||||
0.831007 | + | 0.556263i | \(0.187765\pi\) | |||||||
\(468\) | 857.663 | 0.0847126 | ||||||||
\(469\) | 1153.92 | 0.113610 | ||||||||
\(470\) | 3208.60 | 0.314897 | ||||||||
\(471\) | 9516.30 | 0.930972 | ||||||||
\(472\) | −5016.48 | −0.489200 | ||||||||
\(473\) | −14015.3 | −1.36242 | ||||||||
\(474\) | −3269.63 | −0.316834 | ||||||||
\(475\) | 1493.00 | 0.144218 | ||||||||
\(476\) | 4418.70 | 0.425485 | ||||||||
\(477\) | −774.317 | −0.0743261 | ||||||||
\(478\) | −7357.57 | −0.704032 | ||||||||
\(479\) | −1361.07 | −0.129831 | −0.0649153 | − | 0.997891i | \(-0.520678\pi\) | ||||
−0.0649153 | + | 0.997891i | \(0.520678\pi\) | |||||||
\(480\) | 923.520 | 0.0878182 | ||||||||
\(481\) | −9349.42 | −0.886272 | ||||||||
\(482\) | 6254.31 | 0.591029 | ||||||||
\(483\) | −1695.56 | −0.159732 | ||||||||
\(484\) | 5375.84 | 0.504869 | ||||||||
\(485\) | −9103.04 | −0.852264 | ||||||||
\(486\) | −3476.74 | −0.324502 | ||||||||
\(487\) | 10820.7 | 1.00684 | 0.503420 | − | 0.864042i | \(-0.332075\pi\) | ||||
0.503420 | + | 0.864042i | \(0.332075\pi\) | |||||||
\(488\) | 277.888 | 0.0257774 | ||||||||
\(489\) | −22881.7 | −2.11605 | ||||||||
\(490\) | 1798.76 | 0.165836 | ||||||||
\(491\) | 18702.3 | 1.71899 | 0.859496 | − | 0.511143i | \(-0.170778\pi\) | ||||
0.859496 | + | 0.511143i | \(0.170778\pi\) | |||||||
\(492\) | 11131.4 | 1.02000 | ||||||||
\(493\) | 5582.54 | 0.509990 | ||||||||
\(494\) | −4054.75 | −0.369295 | ||||||||
\(495\) | 1633.32 | 0.148308 | ||||||||
\(496\) | −2513.15 | −0.227508 | ||||||||
\(497\) | −2333.60 | −0.210616 | ||||||||
\(498\) | 13117.7 | 1.18036 | ||||||||
\(499\) | −3824.46 | −0.343099 | −0.171549 | − | 0.985176i | \(-0.554877\pi\) | ||||
−0.171549 | + | 0.985176i | \(0.554877\pi\) | |||||||
\(500\) | 500.000 | 0.0447214 | ||||||||
\(501\) | −20115.2 | −1.79377 | ||||||||
\(502\) | 3171.03 | 0.281932 | ||||||||
\(503\) | −11021.2 | −0.976961 | −0.488481 | − | 0.872575i | \(-0.662449\pi\) | ||||
−0.488481 | + | 0.872575i | \(0.662449\pi\) | |||||||
\(504\) | 645.344 | 0.0570356 | ||||||||
\(505\) | 924.179 | 0.0814365 | ||||||||
\(506\) | 2379.12 | 0.209021 | ||||||||
\(507\) | 6029.04 | 0.528125 | ||||||||
\(508\) | −8706.77 | −0.760434 | ||||||||
\(509\) | −16626.6 | −1.44786 | −0.723932 | − | 0.689872i | \(-0.757667\pi\) | ||||
−0.723932 | + | 0.689872i | \(0.757667\pi\) | |||||||
\(510\) | −4992.32 | −0.433458 | ||||||||
\(511\) | 935.472 | 0.0809840 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 7129.86 | 0.613627 | ||||||||
\(514\) | −14092.8 | −1.20935 | ||||||||
\(515\) | −6248.88 | −0.534677 | ||||||||
\(516\) | 6256.48 | 0.533772 | ||||||||
\(517\) | −16594.9 | −1.41169 | ||||||||
\(518\) | −7034.92 | −0.596712 | ||||||||
\(519\) | −12926.5 | −1.09327 | ||||||||
\(520\) | −1357.92 | −0.114517 | ||||||||
\(521\) | 1808.00 | 0.152035 | 0.0760174 | − | 0.997106i | \(-0.475780\pi\) | ||||
0.0760174 | + | 0.997106i | \(0.475780\pi\) | |||||||
\(522\) | 815.321 | 0.0683632 | ||||||||
\(523\) | 988.509 | 0.0826472 | 0.0413236 | − | 0.999146i | \(-0.486843\pi\) | ||||
0.0413236 | + | 0.999146i | \(0.486843\pi\) | |||||||
\(524\) | −6419.41 | −0.535178 | ||||||||
\(525\) | 1843.00 | 0.153210 | ||||||||
\(526\) | −9980.02 | −0.827281 | ||||||||
\(527\) | 13585.5 | 1.12295 | ||||||||
\(528\) | −4776.45 | −0.393690 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 1225.96 | 0.100476 | ||||||||
\(531\) | 3960.52 | 0.323676 | ||||||||
\(532\) | −3050.98 | −0.248640 | ||||||||
\(533\) | −16367.3 | −1.33011 | ||||||||
\(534\) | 5496.15 | 0.445396 | ||||||||
\(535\) | 4084.10 | 0.330039 | ||||||||
\(536\) | 722.783 | 0.0582453 | ||||||||
\(537\) | 13869.3 | 1.11453 | ||||||||
\(538\) | −9684.12 | −0.776044 | ||||||||
\(539\) | −9303.19 | −0.743445 | ||||||||
\(540\) | 2387.76 | 0.190283 | ||||||||
\(541\) | −16521.4 | −1.31296 | −0.656480 | − | 0.754344i | \(-0.727955\pi\) | ||||
−0.656480 | + | 0.754344i | \(0.727955\pi\) | |||||||
\(542\) | 5160.55 | 0.408976 | ||||||||
\(543\) | −24902.6 | −1.96809 | ||||||||
\(544\) | 2767.74 | 0.218136 | ||||||||
\(545\) | −1296.32 | −0.101887 | ||||||||
\(546\) | −5005.30 | −0.392320 | ||||||||
\(547\) | 14111.8 | 1.10307 | 0.551533 | − | 0.834153i | \(-0.314043\pi\) | ||||
0.551533 | + | 0.834153i | \(0.314043\pi\) | |||||||
\(548\) | −6938.40 | −0.540865 | ||||||||
\(549\) | −219.393 | −0.0170555 | ||||||||
\(550\) | −2586.00 | −0.200486 | ||||||||
\(551\) | −3854.57 | −0.298022 | ||||||||
\(552\) | −1062.05 | −0.0818909 | ||||||||
\(553\) | 3617.44 | 0.278172 | ||||||||
\(554\) | −10889.6 | −0.835115 | ||||||||
\(555\) | 7948.16 | 0.607893 | ||||||||
\(556\) | −3975.30 | −0.303220 | ||||||||
\(557\) | 3746.67 | 0.285012 | 0.142506 | − | 0.989794i | \(-0.454484\pi\) | ||||
0.142506 | + | 0.989794i | \(0.454484\pi\) | |||||||
\(558\) | 1984.14 | 0.150529 | ||||||||
\(559\) | −9199.37 | −0.696050 | ||||||||
\(560\) | −1021.76 | −0.0771022 | ||||||||
\(561\) | 25820.3 | 1.94320 | ||||||||
\(562\) | 4947.81 | 0.371372 | ||||||||
\(563\) | 11239.5 | 0.841365 | 0.420683 | − | 0.907208i | \(-0.361791\pi\) | ||||
0.420683 | + | 0.907208i | \(0.361791\pi\) | |||||||
\(564\) | 7408.02 | 0.553074 | ||||||||
\(565\) | 4454.38 | 0.331676 | ||||||||
\(566\) | 3708.22 | 0.275385 | ||||||||
\(567\) | 10979.3 | 0.813207 | ||||||||
\(568\) | −1461.69 | −0.107978 | ||||||||
\(569\) | 1870.13 | 0.137786 | 0.0688928 | − | 0.997624i | \(-0.478053\pi\) | ||||
0.0688928 | + | 0.997624i | \(0.478053\pi\) | |||||||
\(570\) | 3447.04 | 0.253299 | ||||||||
\(571\) | 23604.9 | 1.73001 | 0.865003 | − | 0.501766i | \(-0.167316\pi\) | ||||
0.865003 | + | 0.501766i | \(0.167316\pi\) | |||||||
\(572\) | 7023.17 | 0.513380 | ||||||||
\(573\) | 11144.3 | 0.812493 | ||||||||
\(574\) | −12315.5 | −0.895537 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 404.224 | 0.0292408 | ||||||||
\(577\) | 16572.9 | 1.19573 | 0.597866 | − | 0.801596i | \(-0.296015\pi\) | ||||
0.597866 | + | 0.801596i | \(0.296015\pi\) | |||||||
\(578\) | −5135.74 | −0.369582 | ||||||||
\(579\) | −24833.0 | −1.78242 | ||||||||
\(580\) | −1290.88 | −0.0924153 | ||||||||
\(581\) | −14513.1 | −1.03633 | ||||||||
\(582\) | −21017.1 | −1.49689 | ||||||||
\(583\) | −6340.67 | −0.450435 | ||||||||
\(584\) | 585.952 | 0.0415186 | ||||||||
\(585\) | 1072.08 | 0.0757693 | ||||||||
\(586\) | 9206.47 | 0.649003 | ||||||||
\(587\) | −27505.5 | −1.93403 | −0.967015 | − | 0.254721i | \(-0.918017\pi\) | ||||
−0.967015 | + | 0.254721i | \(0.918017\pi\) | |||||||
\(588\) | 4152.98 | 0.291269 | ||||||||
\(589\) | −9380.35 | −0.656215 | ||||||||
\(590\) | −6270.60 | −0.437554 | ||||||||
\(591\) | 31379.4 | 2.18405 | ||||||||
\(592\) | −4406.46 | −0.305920 | ||||||||
\(593\) | 21998.3 | 1.52338 | 0.761689 | − | 0.647943i | \(-0.224370\pi\) | ||||
0.761689 | + | 0.647943i | \(0.224370\pi\) | |||||||
\(594\) | −12349.5 | −0.853041 | ||||||||
\(595\) | 5523.38 | 0.380566 | ||||||||
\(596\) | −4092.32 | −0.281255 | ||||||||
\(597\) | −6182.00 | −0.423806 | ||||||||
\(598\) | 1561.61 | 0.106788 | ||||||||
\(599\) | −13628.2 | −0.929605 | −0.464802 | − | 0.885415i | \(-0.653875\pi\) | ||||
−0.464802 | + | 0.885415i | \(0.653875\pi\) | |||||||
\(600\) | 1154.40 | 0.0785470 | ||||||||
\(601\) | −14029.2 | −0.952182 | −0.476091 | − | 0.879396i | \(-0.657947\pi\) | ||||
−0.476091 | + | 0.879396i | \(0.657947\pi\) | |||||||
\(602\) | −6922.02 | −0.468638 | ||||||||
\(603\) | −570.638 | −0.0385376 | ||||||||
\(604\) | −5237.59 | −0.352838 | ||||||||
\(605\) | 6719.80 | 0.451568 | ||||||||
\(606\) | 2133.75 | 0.143032 | ||||||||
\(607\) | −3276.29 | −0.219079 | −0.109539 | − | 0.993982i | \(-0.534938\pi\) | ||||
−0.109539 | + | 0.993982i | \(0.534938\pi\) | |||||||
\(608\) | −1911.04 | −0.127472 | ||||||||
\(609\) | −4758.19 | −0.316603 | ||||||||
\(610\) | 347.360 | 0.0230560 | ||||||||
\(611\) | −10892.6 | −0.721221 | ||||||||
\(612\) | −2185.14 | −0.144328 | ||||||||
\(613\) | 5419.49 | 0.357082 | 0.178541 | − | 0.983932i | \(-0.442862\pi\) | ||||
0.178541 | + | 0.983932i | \(0.442862\pi\) | |||||||
\(614\) | −2152.91 | −0.141506 | ||||||||
\(615\) | 13914.2 | 0.912318 | ||||||||
\(616\) | 5284.55 | 0.345650 | ||||||||
\(617\) | 2820.18 | 0.184013 | 0.0920067 | − | 0.995758i | \(-0.470672\pi\) | ||||
0.0920067 | + | 0.995758i | \(0.470672\pi\) | |||||||
\(618\) | −14427.4 | −0.939088 | ||||||||
\(619\) | 22656.3 | 1.47113 | 0.735567 | − | 0.677452i | \(-0.236916\pi\) | ||||
0.735567 | + | 0.677452i | \(0.236916\pi\) | |||||||
\(620\) | −3141.44 | −0.203489 | ||||||||
\(621\) | −2745.93 | −0.177440 | ||||||||
\(622\) | −16282.7 | −1.04964 | ||||||||
\(623\) | −6080.80 | −0.391047 | ||||||||
\(624\) | −3135.17 | −0.201133 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 16360.5 | 1.04456 | ||||||||
\(627\) | −17828.1 | −1.13554 | ||||||||
\(628\) | −6594.80 | −0.419046 | ||||||||
\(629\) | 23820.2 | 1.50998 | ||||||||
\(630\) | 806.680 | 0.0510142 | ||||||||
\(631\) | −4336.70 | −0.273600 | −0.136800 | − | 0.990599i | \(-0.543682\pi\) | ||||
−0.136800 | + | 0.990599i | \(0.543682\pi\) | |||||||
\(632\) | 2265.86 | 0.142612 | ||||||||
\(633\) | 13568.0 | 0.851941 | ||||||||
\(634\) | 6458.41 | 0.404568 | ||||||||
\(635\) | −10883.5 | −0.680153 | ||||||||
\(636\) | 2830.50 | 0.176472 | ||||||||
\(637\) | −6106.43 | −0.379821 | ||||||||
\(638\) | 6676.43 | 0.414299 | ||||||||
\(639\) | 1154.01 | 0.0714427 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | 27123.4 | 1.67131 | 0.835654 | − | 0.549255i | \(-0.185089\pi\) | ||||
0.835654 | + | 0.549255i | \(0.185089\pi\) | |||||||
\(642\) | 9429.38 | 0.579670 | ||||||||
\(643\) | 20845.2 | 1.27847 | 0.639234 | − | 0.769012i | \(-0.279252\pi\) | ||||
0.639234 | + | 0.769012i | \(0.279252\pi\) | |||||||
\(644\) | 1175.02 | 0.0718982 | ||||||||
\(645\) | 7820.60 | 0.477420 | ||||||||
\(646\) | 10330.6 | 0.629183 | ||||||||
\(647\) | −3035.99 | −0.184478 | −0.0922388 | − | 0.995737i | \(-0.529402\pi\) | ||||
−0.0922388 | + | 0.995737i | \(0.529402\pi\) | |||||||
\(648\) | 6877.12 | 0.416912 | ||||||||
\(649\) | 32431.6 | 1.96156 | ||||||||
\(650\) | −1697.40 | −0.102427 | ||||||||
\(651\) | −11579.4 | −0.697129 | ||||||||
\(652\) | 15857.0 | 0.952469 | ||||||||
\(653\) | 3794.77 | 0.227413 | 0.113707 | − | 0.993514i | \(-0.463728\pi\) | ||||
0.113707 | + | 0.993514i | \(0.463728\pi\) | |||||||
\(654\) | −2992.94 | −0.178950 | ||||||||
\(655\) | −8024.26 | −0.478678 | ||||||||
\(656\) | −7714.05 | −0.459121 | ||||||||
\(657\) | −462.609 | −0.0274705 | ||||||||
\(658\) | −8196.05 | −0.485586 | ||||||||
\(659\) | 22291.8 | 1.31770 | 0.658849 | − | 0.752275i | \(-0.271043\pi\) | ||||
0.658849 | + | 0.752275i | \(0.271043\pi\) | |||||||
\(660\) | −5970.56 | −0.352127 | ||||||||
\(661\) | 30545.5 | 1.79740 | 0.898700 | − | 0.438565i | \(-0.144513\pi\) | ||||
0.898700 | + | 0.438565i | \(0.144513\pi\) | |||||||
\(662\) | 6829.59 | 0.400966 | ||||||||
\(663\) | 16947.9 | 0.992765 | ||||||||
\(664\) | −9090.59 | −0.531300 | ||||||||
\(665\) | −3813.72 | −0.222391 | ||||||||
\(666\) | 3478.91 | 0.202410 | ||||||||
\(667\) | 1484.51 | 0.0861777 | ||||||||
\(668\) | 13939.8 | 0.807408 | ||||||||
\(669\) | 14102.9 | 0.815019 | ||||||||
\(670\) | 903.479 | 0.0520962 | ||||||||
\(671\) | −1796.55 | −0.103360 | ||||||||
\(672\) | −2359.04 | −0.135420 | ||||||||
\(673\) | 482.978 | 0.0276633 | 0.0138317 | − | 0.999904i | \(-0.495597\pi\) | ||||
0.0138317 | + | 0.999904i | \(0.495597\pi\) | |||||||
\(674\) | 4315.59 | 0.246632 | ||||||||
\(675\) | 2984.70 | 0.170194 | ||||||||
\(676\) | −4178.13 | −0.237718 | ||||||||
\(677\) | 33458.8 | 1.89945 | 0.949725 | − | 0.313085i | \(-0.101363\pi\) | ||||
0.949725 | + | 0.313085i | \(0.101363\pi\) | |||||||
\(678\) | 10284.3 | 0.582545 | ||||||||
\(679\) | 23252.8 | 1.31423 | ||||||||
\(680\) | 3459.68 | 0.195107 | ||||||||
\(681\) | −5757.18 | −0.323958 | ||||||||
\(682\) | 16247.5 | 0.912244 | ||||||||
\(683\) | −12633.5 | −0.707770 | −0.353885 | − | 0.935289i | \(-0.615140\pi\) | ||||
−0.353885 | + | 0.935289i | \(0.615140\pi\) | |||||||
\(684\) | 1508.77 | 0.0843409 | ||||||||
\(685\) | −8673.00 | −0.483764 | ||||||||
\(686\) | −13356.3 | −0.743364 | ||||||||
\(687\) | 23577.2 | 1.30936 | ||||||||
\(688\) | −4335.74 | −0.240260 | ||||||||
\(689\) | −4161.89 | −0.230124 | ||||||||
\(690\) | −1327.56 | −0.0732455 | ||||||||
\(691\) | −15067.1 | −0.829491 | −0.414745 | − | 0.909938i | \(-0.636129\pi\) | ||||
−0.414745 | + | 0.909938i | \(0.636129\pi\) | |||||||
\(692\) | 8958.05 | 0.492101 | ||||||||
\(693\) | −4172.15 | −0.228697 | ||||||||
\(694\) | 3841.06 | 0.210093 | ||||||||
\(695\) | −4969.12 | −0.271208 | ||||||||
\(696\) | −2980.38 | −0.162315 | ||||||||
\(697\) | 41700.2 | 2.26615 | ||||||||
\(698\) | −6173.32 | −0.334762 | ||||||||
\(699\) | 6232.36 | 0.337238 | ||||||||
\(700\) | −1277.20 | −0.0689623 | ||||||||
\(701\) | −16517.0 | −0.889927 | −0.444964 | − | 0.895549i | \(-0.646783\pi\) | ||||
−0.444964 | + | 0.895549i | \(0.646783\pi\) | |||||||
\(702\) | −8105.98 | −0.435812 | ||||||||
\(703\) | −16447.1 | −0.882383 | ||||||||
\(704\) | 3310.08 | 0.177207 | ||||||||
\(705\) | 9260.02 | 0.494685 | ||||||||
\(706\) | 701.802 | 0.0374117 | ||||||||
\(707\) | −2360.72 | −0.125579 | ||||||||
\(708\) | −14477.6 | −0.768503 | ||||||||
\(709\) | −3206.99 | −0.169874 | −0.0849372 | − | 0.996386i | \(-0.527069\pi\) | ||||
−0.0849372 | + | 0.996386i | \(0.527069\pi\) | |||||||
\(710\) | −1827.12 | −0.0965782 | ||||||||
\(711\) | −1788.90 | −0.0943584 | ||||||||
\(712\) | −3808.83 | −0.200480 | ||||||||
\(713\) | 3612.66 | 0.189755 | ||||||||
\(714\) | 12752.4 | 0.668412 | ||||||||
\(715\) | 8778.96 | 0.459181 | ||||||||
\(716\) | −9611.44 | −0.501671 | ||||||||
\(717\) | −21233.9 | −1.10599 | ||||||||
\(718\) | 13073.3 | 0.679515 | ||||||||
\(719\) | −26482.4 | −1.37361 | −0.686806 | − | 0.726841i | \(-0.740988\pi\) | ||||
−0.686806 | + | 0.726841i | \(0.740988\pi\) | |||||||
\(720\) | 505.280 | 0.0261537 | ||||||||
\(721\) | 15962.1 | 0.824496 | ||||||||
\(722\) | 6585.04 | 0.339432 | ||||||||
\(723\) | 18049.9 | 0.928471 | ||||||||
\(724\) | 17257.5 | 0.885872 | ||||||||
\(725\) | −1613.60 | −0.0826588 | ||||||||
\(726\) | 15514.7 | 0.793118 | ||||||||
\(727\) | 3270.55 | 0.166848 | 0.0834238 | − | 0.996514i | \(-0.473414\pi\) | ||||
0.0834238 | + | 0.996514i | \(0.473414\pi\) | |||||||
\(728\) | 3468.67 | 0.176590 | ||||||||
\(729\) | 13176.4 | 0.669432 | ||||||||
\(730\) | 732.440 | 0.0371353 | ||||||||
\(731\) | 23438.0 | 1.18589 | ||||||||
\(732\) | 801.985 | 0.0404948 | ||||||||
\(733\) | −25182.1 | −1.26892 | −0.634462 | − | 0.772954i | \(-0.718778\pi\) | ||||
−0.634462 | + | 0.772954i | \(0.718778\pi\) | |||||||
\(734\) | −7717.79 | −0.388105 | ||||||||
\(735\) | 5191.22 | 0.260519 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −4672.80 | −0.233548 | ||||||||
\(738\) | 6090.25 | 0.303774 | ||||||||
\(739\) | −19406.3 | −0.965999 | −0.483000 | − | 0.875621i | \(-0.660453\pi\) | ||||
−0.483000 | + | 0.875621i | \(0.660453\pi\) | |||||||
\(740\) | −5508.08 | −0.273623 | ||||||||
\(741\) | −11702.0 | −0.580141 | ||||||||
\(742\) | −3131.59 | −0.154939 | ||||||||
\(743\) | −11547.0 | −0.570146 | −0.285073 | − | 0.958506i | \(-0.592018\pi\) | ||||
−0.285073 | + | 0.958506i | \(0.592018\pi\) | |||||||
\(744\) | −7252.96 | −0.357401 | ||||||||
\(745\) | −5115.40 | −0.251562 | ||||||||
\(746\) | −14264.7 | −0.700090 | ||||||||
\(747\) | 7177.03 | 0.351531 | ||||||||
\(748\) | −17893.5 | −0.874666 | ||||||||
\(749\) | −10432.4 | −0.508936 | ||||||||
\(750\) | 1443.00 | 0.0702546 | ||||||||
\(751\) | −30113.3 | −1.46318 | −0.731591 | − | 0.681744i | \(-0.761222\pi\) | ||||
−0.731591 | + | 0.681744i | \(0.761222\pi\) | |||||||
\(752\) | −5133.76 | −0.248948 | ||||||||
\(753\) | 9151.58 | 0.442898 | ||||||||
\(754\) | 4382.28 | 0.211662 | ||||||||
\(755\) | −6546.98 | −0.315588 | ||||||||
\(756\) | −6099.30 | −0.293425 | ||||||||
\(757\) | −26192.3 | −1.25756 | −0.628782 | − | 0.777582i | \(-0.716446\pi\) | ||||
−0.628782 | + | 0.777582i | \(0.716446\pi\) | |||||||
\(758\) | 21120.2 | 1.01203 | ||||||||
\(759\) | 6866.15 | 0.328360 | ||||||||
\(760\) | −2388.80 | −0.114014 | ||||||||
\(761\) | −5051.36 | −0.240620 | −0.120310 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120310 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(762\) | −25127.7 | −1.19460 | ||||||||
\(763\) | 3311.32 | 0.157114 | ||||||||
\(764\) | −7722.98 | −0.365717 | ||||||||
\(765\) | −2731.42 | −0.129091 | ||||||||
\(766\) | −686.917 | −0.0324012 | ||||||||
\(767\) | 21287.5 | 1.00215 | ||||||||
\(768\) | −1477.63 | −0.0694264 | ||||||||
\(769\) | 41142.8 | 1.92932 | 0.964661 | − | 0.263494i | \(-0.0848749\pi\) | ||||
0.964661 | + | 0.263494i | \(0.0848749\pi\) | |||||||
\(770\) | 6605.68 | 0.309159 | ||||||||
\(771\) | −40671.9 | −1.89982 | ||||||||
\(772\) | 17209.3 | 0.802299 | ||||||||
\(773\) | 3087.82 | 0.143675 | 0.0718376 | − | 0.997416i | \(-0.477114\pi\) | ||||
0.0718376 | + | 0.997416i | \(0.477114\pi\) | |||||||
\(774\) | 3423.07 | 0.158966 | ||||||||
\(775\) | −3926.80 | −0.182006 | ||||||||
\(776\) | 14564.9 | 0.673773 | ||||||||
\(777\) | −20302.8 | −0.937398 | ||||||||
\(778\) | −12346.6 | −0.568954 | ||||||||
\(779\) | −28792.7 | −1.32427 | ||||||||
\(780\) | −3918.96 | −0.179899 | ||||||||
\(781\) | 9449.86 | 0.432961 | ||||||||
\(782\) | −3978.63 | −0.181938 | ||||||||
\(783\) | −7705.78 | −0.351701 | ||||||||
\(784\) | −2878.02 | −0.131105 | ||||||||
\(785\) | −8243.50 | −0.374807 | ||||||||
\(786\) | −18526.4 | −0.840732 | ||||||||
\(787\) | 31166.9 | 1.41167 | 0.705833 | − | 0.708378i | \(-0.250573\pi\) | ||||
0.705833 | + | 0.708378i | \(0.250573\pi\) | |||||||
\(788\) | −21745.9 | −0.983079 | ||||||||
\(789\) | −28802.4 | −1.29961 | ||||||||
\(790\) | 2832.32 | 0.127556 | ||||||||
\(791\) | −11378.3 | −0.511460 | ||||||||
\(792\) | −2613.31 | −0.117247 | ||||||||
\(793\) | −1179.22 | −0.0528061 | ||||||||
\(794\) | 2980.09 | 0.133198 | ||||||||
\(795\) | 3538.12 | 0.157842 | ||||||||
\(796\) | 4284.13 | 0.190762 | ||||||||
\(797\) | 27495.3 | 1.22200 | 0.611000 | − | 0.791631i | \(-0.290768\pi\) | ||||
0.611000 | + | 0.791631i | \(0.290768\pi\) | |||||||
\(798\) | −8805.12 | −0.390599 | ||||||||
\(799\) | 27751.8 | 1.22877 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | 3007.08 | 0.132646 | ||||||||
\(802\) | −4455.74 | −0.196182 | ||||||||
\(803\) | −3788.18 | −0.166478 | ||||||||
\(804\) | 2085.95 | 0.0914999 | ||||||||
\(805\) | 1468.78 | 0.0643077 | ||||||||
\(806\) | 10664.6 | 0.466059 | ||||||||
\(807\) | −27948.4 | −1.21912 | ||||||||
\(808\) | −1478.69 | −0.0643812 | ||||||||
\(809\) | −1773.85 | −0.0770893 | −0.0385447 | − | 0.999257i | \(-0.512272\pi\) | ||||
−0.0385447 | + | 0.999257i | \(0.512272\pi\) | |||||||
\(810\) | 8596.40 | 0.372897 | ||||||||
\(811\) | −17.8982 | −0.000774956 0 | −0.000387478 | − | 1.00000i | \(-0.500123\pi\) | ||||
−0.000387478 | 1.00000i | \(0.500123\pi\) | ||||||||
\(812\) | 3297.42 | 0.142509 | ||||||||
\(813\) | 14893.4 | 0.642476 | ||||||||
\(814\) | 28487.8 | 1.22665 | ||||||||
\(815\) | 19821.3 | 0.851914 | ||||||||
\(816\) | 7987.71 | 0.342679 | ||||||||
\(817\) | −16183.2 | −0.692996 | ||||||||
\(818\) | 939.311 | 0.0401495 | ||||||||
\(819\) | −2738.52 | −0.116840 | ||||||||
\(820\) | −9642.56 | −0.410650 | ||||||||
\(821\) | −15459.5 | −0.657173 | −0.328587 | − | 0.944474i | \(-0.606572\pi\) | ||||
−0.328587 | + | 0.944474i | \(0.606572\pi\) | |||||||
\(822\) | −20024.2 | −0.849666 | ||||||||
\(823\) | −29737.4 | −1.25951 | −0.629757 | − | 0.776792i | \(-0.716845\pi\) | ||||
−0.629757 | + | 0.776792i | \(0.716845\pi\) | |||||||
\(824\) | 9998.21 | 0.422699 | ||||||||
\(825\) | −7463.20 | −0.314952 | ||||||||
\(826\) | 16017.6 | 0.674727 | ||||||||
\(827\) | −33405.8 | −1.40463 | −0.702317 | − | 0.711864i | \(-0.747851\pi\) | ||||
−0.702317 | + | 0.711864i | \(0.747851\pi\) | |||||||
\(828\) | −581.073 | −0.0243885 | ||||||||
\(829\) | 45802.5 | 1.91892 | 0.959460 | − | 0.281844i | \(-0.0909459\pi\) | ||||
0.959460 | + | 0.281844i | \(0.0909459\pi\) | |||||||
\(830\) | −11363.2 | −0.475210 | ||||||||
\(831\) | −31427.3 | −1.31192 | ||||||||
\(832\) | 2172.67 | 0.0905335 | ||||||||
\(833\) | 15557.8 | 0.647115 | ||||||||
\(834\) | −11472.7 | −0.476340 | ||||||||
\(835\) | 17424.8 | 0.722168 | ||||||||
\(836\) | 12354.9 | 0.511127 | ||||||||
\(837\) | −18752.5 | −0.774411 | ||||||||
\(838\) | 29915.3 | 1.23318 | ||||||||
\(839\) | 5331.64 | 0.219391 | 0.109695 | − | 0.993965i | \(-0.465013\pi\) | ||||
0.109695 | + | 0.993965i | \(0.465013\pi\) | |||||||
\(840\) | −2948.80 | −0.121123 | ||||||||
\(841\) | −20223.1 | −0.829188 | ||||||||
\(842\) | 21661.6 | 0.886588 | ||||||||
\(843\) | 14279.4 | 0.583402 | ||||||||
\(844\) | −9402.61 | −0.383473 | ||||||||
\(845\) | −5222.66 | −0.212621 | ||||||||
\(846\) | 4053.11 | 0.164715 | ||||||||
\(847\) | −17165.1 | −0.696338 | ||||||||
\(848\) | −1961.54 | −0.0794333 | ||||||||
\(849\) | 10701.9 | 0.432614 | ||||||||
\(850\) | 4324.60 | 0.174509 | ||||||||
\(851\) | 6334.29 | 0.255155 | ||||||||
\(852\) | −4218.45 | −0.169626 | ||||||||
\(853\) | −5792.08 | −0.232494 | −0.116247 | − | 0.993220i | \(-0.537086\pi\) | ||||
−0.116247 | + | 0.993220i | \(0.537086\pi\) | |||||||
\(854\) | −887.296 | −0.0355534 | ||||||||
\(855\) | 1885.96 | 0.0754368 | ||||||||
\(856\) | −6534.56 | −0.260919 | ||||||||
\(857\) | −22502.2 | −0.896918 | −0.448459 | − | 0.893803i | \(-0.648027\pi\) | ||||
−0.448459 | + | 0.893803i | \(0.648027\pi\) | |||||||
\(858\) | 20268.9 | 0.806489 | ||||||||
\(859\) | 92.1371 | 0.00365969 | 0.00182985 | − | 0.999998i | \(-0.499418\pi\) | ||||
0.00182985 | + | 0.999998i | \(0.499418\pi\) | |||||||
\(860\) | −5419.68 | −0.214895 | ||||||||
\(861\) | −35542.5 | −1.40684 | ||||||||
\(862\) | −3549.39 | −0.140247 | ||||||||
\(863\) | −33877.4 | −1.33627 | −0.668134 | − | 0.744041i | \(-0.732907\pi\) | ||||
−0.668134 | + | 0.744041i | \(0.732907\pi\) | |||||||
\(864\) | −3820.42 | −0.150432 | ||||||||
\(865\) | 11197.6 | 0.440149 | ||||||||
\(866\) | −9501.27 | −0.372825 | ||||||||
\(867\) | −14821.7 | −0.580592 | ||||||||
\(868\) | 8024.50 | 0.313789 | ||||||||
\(869\) | −14648.8 | −0.571836 | ||||||||
\(870\) | −3725.48 | −0.145179 | ||||||||
\(871\) | −3067.13 | −0.119318 | ||||||||
\(872\) | 2074.11 | 0.0805485 | ||||||||
\(873\) | −11499.0 | −0.445798 | ||||||||
\(874\) | 2747.12 | 0.106319 | ||||||||
\(875\) | −1596.50 | −0.0616818 | ||||||||
\(876\) | 1691.06 | 0.0652232 | ||||||||
\(877\) | 31434.6 | 1.21034 | 0.605172 | − | 0.796094i | \(-0.293104\pi\) | ||||
0.605172 | + | 0.796094i | \(0.293104\pi\) | |||||||
\(878\) | −16566.5 | −0.636781 | ||||||||
\(879\) | 26569.9 | 1.01955 | ||||||||
\(880\) | 4137.60 | 0.158498 | ||||||||
\(881\) | −15812.0 | −0.604676 | −0.302338 | − | 0.953201i | \(-0.597767\pi\) | ||||
−0.302338 | + | 0.953201i | \(0.597767\pi\) | |||||||
\(882\) | 2272.20 | 0.0867447 | ||||||||
\(883\) | 786.986 | 0.0299934 | 0.0149967 | − | 0.999888i | \(-0.495226\pi\) | ||||
0.0149967 | + | 0.999888i | \(0.495226\pi\) | |||||||
\(884\) | −11744.9 | −0.446861 | ||||||||
\(885\) | −18097.0 | −0.687370 | ||||||||
\(886\) | −27292.9 | −1.03490 | ||||||||
\(887\) | −52830.3 | −1.99985 | −0.999925 | − | 0.0122640i | \(-0.996096\pi\) | ||||
−0.999925 | + | 0.0122640i | \(0.996096\pi\) | |||||||
\(888\) | −12717.1 | −0.480582 | ||||||||
\(889\) | 27800.7 | 1.04883 | ||||||||
\(890\) | −4761.04 | −0.179315 | ||||||||
\(891\) | −44460.6 | −1.67170 | ||||||||
\(892\) | −9773.28 | −0.366854 | ||||||||
\(893\) | −19161.8 | −0.718056 | ||||||||
\(894\) | −11810.4 | −0.441835 | ||||||||
\(895\) | −12014.3 | −0.448708 | ||||||||
\(896\) | 1634.82 | 0.0609547 | ||||||||
\(897\) | 4506.80 | 0.167757 | ||||||||
\(898\) | 3809.40 | 0.141560 | ||||||||
\(899\) | 10138.1 | 0.376110 | ||||||||
\(900\) | 631.601 | 0.0233926 | ||||||||
\(901\) | 10603.6 | 0.392071 | ||||||||
\(902\) | 49871.4 | 1.84095 | ||||||||
\(903\) | −19976.9 | −0.736203 | ||||||||
\(904\) | −7127.01 | −0.262213 | ||||||||
\(905\) | 21571.9 | 0.792348 | ||||||||
\(906\) | −15115.7 | −0.554288 | ||||||||
\(907\) | −31587.2 | −1.15638 | −0.578189 | − | 0.815903i | \(-0.696240\pi\) | ||||
−0.578189 | + | 0.815903i | \(0.696240\pi\) | |||||||
\(908\) | 3989.73 | 0.145819 | ||||||||
\(909\) | 1167.42 | 0.0425974 | ||||||||
\(910\) | 4335.84 | 0.157947 | ||||||||
\(911\) | 5713.89 | 0.207804 | 0.103902 | − | 0.994588i | \(-0.466867\pi\) | ||||
0.103902 | + | 0.994588i | \(0.466867\pi\) | |||||||
\(912\) | −5515.26 | −0.200251 | ||||||||
\(913\) | 58770.7 | 2.13037 | ||||||||
\(914\) | 20112.6 | 0.727861 | ||||||||
\(915\) | 1002.48 | 0.0362197 | ||||||||
\(916\) | −16339.0 | −0.589364 | ||||||||
\(917\) | 20497.2 | 0.738142 | ||||||||
\(918\) | 20652.2 | 0.742511 | ||||||||
\(919\) | −52580.9 | −1.88736 | −0.943680 | − | 0.330860i | \(-0.892661\pi\) | ||||
−0.943680 | + | 0.330860i | \(0.892661\pi\) | |||||||
\(920\) | 920.000 | 0.0329690 | ||||||||
\(921\) | −6213.30 | −0.222297 | ||||||||
\(922\) | −18439.2 | −0.658636 | ||||||||
\(923\) | 6202.70 | 0.221197 | ||||||||
\(924\) | 15251.2 | 0.542995 | ||||||||
\(925\) | −6885.10 | −0.244736 | ||||||||
\(926\) | −5784.79 | −0.205291 | ||||||||
\(927\) | −7893.60 | −0.279676 | ||||||||
\(928\) | 2065.41 | 0.0730607 | ||||||||
\(929\) | 51129.0 | 1.80569 | 0.902845 | − | 0.429965i | \(-0.141474\pi\) | ||||
0.902845 | + | 0.429965i | \(0.141474\pi\) | |||||||
\(930\) | −9066.20 | −0.319669 | ||||||||
\(931\) | −10742.2 | −0.378154 | ||||||||
\(932\) | −4319.03 | −0.151797 | ||||||||
\(933\) | −46991.9 | −1.64893 | ||||||||
\(934\) | −33545.9 | −1.17522 | ||||||||
\(935\) | −22366.8 | −0.782325 | ||||||||
\(936\) | −1715.33 | −0.0599009 | ||||||||
\(937\) | −5328.37 | −0.185774 | −0.0928870 | − | 0.995677i | \(-0.529610\pi\) | ||||
−0.0928870 | + | 0.995677i | \(0.529610\pi\) | |||||||
\(938\) | −2307.85 | −0.0803346 | ||||||||
\(939\) | 47216.4 | 1.64095 | ||||||||
\(940\) | −6417.20 | −0.222666 | ||||||||
\(941\) | 41912.5 | 1.45198 | 0.725988 | − | 0.687708i | \(-0.241383\pi\) | ||||
0.725988 | + | 0.687708i | \(0.241383\pi\) | |||||||
\(942\) | −19032.6 | −0.658297 | ||||||||
\(943\) | 11088.9 | 0.382933 | ||||||||
\(944\) | 10033.0 | 0.345916 | ||||||||
\(945\) | −7624.12 | −0.262447 | ||||||||
\(946\) | 28030.6 | 0.963376 | ||||||||
\(947\) | −32175.8 | −1.10409 | −0.552045 | − | 0.833814i | \(-0.686152\pi\) | ||||
−0.552045 | + | 0.833814i | \(0.686152\pi\) | |||||||
\(948\) | 6539.26 | 0.224035 | ||||||||
\(949\) | −2486.49 | −0.0850525 | ||||||||
\(950\) | −2986.00 | −0.101978 | ||||||||
\(951\) | 18639.0 | 0.635553 | ||||||||
\(952\) | −8837.41 | −0.300864 | ||||||||
\(953\) | −22469.7 | −0.763763 | −0.381882 | − | 0.924211i | \(-0.624724\pi\) | ||||
−0.381882 | + | 0.924211i | \(0.624724\pi\) | |||||||
\(954\) | 1548.63 | 0.0525565 | ||||||||
\(955\) | −9653.73 | −0.327107 | ||||||||
\(956\) | 14715.1 | 0.497826 | ||||||||
\(957\) | 19268.2 | 0.650838 | ||||||||
\(958\) | 2722.14 | 0.0918042 | ||||||||
\(959\) | 22154.3 | 0.745986 | ||||||||
\(960\) | −1847.04 | −0.0620969 | ||||||||
\(961\) | −5119.37 | −0.171843 | ||||||||
\(962\) | 18698.8 | 0.626689 | ||||||||
\(963\) | 5159.04 | 0.172635 | ||||||||
\(964\) | −12508.6 | −0.417920 | ||||||||
\(965\) | 21511.6 | 0.717598 | ||||||||
\(966\) | 3391.12 | 0.112948 | ||||||||
\(967\) | 15967.7 | 0.531009 | 0.265504 | − | 0.964110i | \(-0.414462\pi\) | ||||
0.265504 | + | 0.964110i | \(0.414462\pi\) | |||||||
\(968\) | −10751.7 | −0.356996 | ||||||||
\(969\) | 29814.2 | 0.988409 | ||||||||
\(970\) | 18206.1 | 0.602641 | ||||||||
\(971\) | 58395.0 | 1.92995 | 0.964977 | − | 0.262334i | \(-0.0844923\pi\) | ||||
0.964977 | + | 0.262334i | \(0.0844923\pi\) | |||||||
\(972\) | 6953.47 | 0.229457 | ||||||||
\(973\) | 12693.1 | 0.418215 | ||||||||
\(974\) | −21641.3 | −0.711944 | ||||||||
\(975\) | −4898.70 | −0.160907 | ||||||||
\(976\) | −555.776 | −0.0182274 | ||||||||
\(977\) | 32548.6 | 1.06584 | 0.532918 | − | 0.846167i | \(-0.321095\pi\) | ||||
0.532918 | + | 0.846167i | \(0.321095\pi\) | |||||||
\(978\) | 45763.4 | 1.49627 | ||||||||
\(979\) | 24624.1 | 0.803871 | ||||||||
\(980\) | −3597.52 | −0.117264 | ||||||||
\(981\) | −1637.51 | −0.0532944 | ||||||||
\(982\) | −37404.7 | −1.21551 | ||||||||
\(983\) | −19691.8 | −0.638933 | −0.319466 | − | 0.947598i | \(-0.603504\pi\) | ||||
−0.319466 | + | 0.947598i | \(0.603504\pi\) | |||||||
\(984\) | −22262.8 | −0.721251 | ||||||||
\(985\) | −27182.4 | −0.879292 | ||||||||
\(986\) | −11165.1 | −0.360617 | ||||||||
\(987\) | −23653.8 | −0.762826 | ||||||||
\(988\) | 8109.50 | 0.261131 | ||||||||
\(989\) | 6232.63 | 0.200390 | ||||||||
\(990\) | −3266.64 | −0.104869 | ||||||||
\(991\) | 31329.5 | 1.00425 | 0.502127 | − | 0.864794i | \(-0.332551\pi\) | ||||
0.502127 | + | 0.864794i | \(0.332551\pi\) | |||||||
\(992\) | 5026.31 | 0.160872 | ||||||||
\(993\) | 19710.2 | 0.629893 | ||||||||
\(994\) | 4667.19 | 0.148928 | ||||||||
\(995\) | 5355.16 | 0.170623 | ||||||||
\(996\) | −26235.5 | −0.834641 | ||||||||
\(997\) | 10050.3 | 0.319254 | 0.159627 | − | 0.987177i | \(-0.448971\pi\) | ||||
0.159627 | + | 0.987177i | \(0.448971\pi\) | |||||||
\(998\) | 7648.91 | 0.242607 | ||||||||
\(999\) | −32879.9 | −1.04132 |
(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 | 230.4.a.f.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 2070.4.a.s.1.1 | 2 | |||
4.3 | odd | 2 | 1840.4.a.i.1.2 | 2 | |||
5.2 | odd | 4 | 1150.4.b.k.599.2 | 4 | |||
5.3 | odd | 4 | 1150.4.b.k.599.3 | 4 | |||
5.4 | even | 2 | 1150.4.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.f.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1150.4.a.l.1.2 | 2 | 5.4 | even | 2 | |||
1150.4.b.k.599.2 | 4 | 5.2 | odd | 4 | |||
1150.4.b.k.599.3 | 4 | 5.3 | odd | 4 | |||
1840.4.a.i.1.2 | 2 | 4.3 | odd | 2 | |||
2070.4.a.s.1.1 | 2 | 3.2 | odd | 2 |