Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1862,4,Mod(1,1862)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1862, 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("1862.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1862 = 2 \cdot 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1862.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: | \(109.861556431\) |
Analytic rank: | \(0\) |
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: | no (minimal twist has level 38) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1862.1 |
$q$-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 | ||||||||
\(3\) | −0.227998 | −0.0438783 | −0.0219391 | − | 0.999759i | \(-0.506984\pi\) | ||||
−0.0219391 | + | 0.999759i | \(0.506984\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −8.31601 | −0.743806 | −0.371903 | − | 0.928272i | \(-0.621295\pi\) | ||||
−0.371903 | + | 0.928272i | \(0.621295\pi\) | |||||||
\(6\) | −0.455996 | −0.0310266 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −26.9480 | −0.998075 | ||||||||
\(10\) | −16.6320 | −0.525950 | ||||||||
\(11\) | −12.7720 | −0.350082 | −0.175041 | − | 0.984561i | \(-0.556006\pi\) | ||||
−0.175041 | + | 0.984561i | \(0.556006\pi\) | |||||||
\(12\) | −0.911993 | −0.0219391 | ||||||||
\(13\) | 47.0360 | 1.00350 | 0.501748 | − | 0.865014i | \(-0.332691\pi\) | ||||
0.501748 | + | 0.865014i | \(0.332691\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.89603 | 0.0326369 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 31.4560 | 0.448776 | 0.224388 | − | 0.974500i | \(-0.427962\pi\) | ||||
0.224388 | + | 0.974500i | \(0.427962\pi\) | |||||||
\(18\) | −53.8960 | −0.705745 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | −33.2640 | −0.371903 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −25.5440 | −0.247545 | ||||||||
\(23\) | −19.0360 | −0.172578 | −0.0862888 | − | 0.996270i | \(-0.527501\pi\) | ||||
−0.0862888 | + | 0.996270i | \(0.527501\pi\) | |||||||
\(24\) | −1.82399 | −0.0155133 | ||||||||
\(25\) | −55.8441 | −0.446752 | ||||||||
\(26\) | 94.0720 | 0.709579 | ||||||||
\(27\) | 12.3000 | 0.0876720 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 91.2120 | 0.584057 | 0.292028 | − | 0.956410i | \(-0.405670\pi\) | ||||
0.292028 | + | 0.956410i | \(0.405670\pi\) | |||||||
\(30\) | 3.79207 | 0.0230778 | ||||||||
\(31\) | −293.968 | −1.70317 | −0.851584 | − | 0.524218i | \(-0.824358\pi\) | ||||
−0.851584 | + | 0.524218i | \(0.824358\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 2.91199 | 0.0153610 | ||||||||
\(34\) | 62.9120 | 0.317333 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −107.792 | −0.499037 | ||||||||
\(37\) | 215.616 | 0.958029 | 0.479014 | − | 0.877807i | \(-0.340994\pi\) | ||||
0.479014 | + | 0.877807i | \(0.340994\pi\) | |||||||
\(38\) | −38.0000 | −0.162221 | ||||||||
\(39\) | −10.7241 | −0.0440317 | ||||||||
\(40\) | −66.5280 | −0.262975 | ||||||||
\(41\) | 67.7200 | 0.257953 | 0.128977 | − | 0.991648i | \(-0.458831\pi\) | ||||
0.128977 | + | 0.991648i | \(0.458831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 308.596 | 1.09443 | 0.547214 | − | 0.836992i | \(-0.315688\pi\) | ||||
0.547214 | + | 0.836992i | \(0.315688\pi\) | |||||||
\(44\) | −51.0880 | −0.175041 | ||||||||
\(45\) | 224.100 | 0.742374 | ||||||||
\(46\) | −38.0720 | −0.122031 | ||||||||
\(47\) | −108.812 | −0.337700 | −0.168850 | − | 0.985642i | \(-0.554005\pi\) | ||||
−0.168850 | + | 0.985642i | \(0.554005\pi\) | |||||||
\(48\) | −3.64797 | −0.0109696 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −111.688 | −0.315902 | ||||||||
\(51\) | −7.17191 | −0.0196915 | ||||||||
\(52\) | 188.144 | 0.501748 | ||||||||
\(53\) | −682.124 | −1.76787 | −0.883933 | − | 0.467613i | \(-0.845114\pi\) | ||||
−0.883933 | + | 0.467613i | \(0.845114\pi\) | |||||||
\(54\) | 24.6001 | 0.0619935 | ||||||||
\(55\) | 106.212 | 0.260393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.33196 | 0.0100664 | ||||||||
\(58\) | 182.424 | 0.412991 | ||||||||
\(59\) | 250.300 | 0.552310 | 0.276155 | − | 0.961113i | \(-0.410940\pi\) | ||||
0.276155 | + | 0.961113i | \(0.410940\pi\) | |||||||
\(60\) | 7.58413 | 0.0163185 | ||||||||
\(61\) | 317.692 | 0.666825 | 0.333412 | − | 0.942781i | \(-0.391800\pi\) | ||||
0.333412 | + | 0.942781i | \(0.391800\pi\) | |||||||
\(62\) | −587.936 | −1.20432 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −391.152 | −0.746406 | ||||||||
\(66\) | 5.82399 | 0.0108619 | ||||||||
\(67\) | 940.444 | 1.71483 | 0.857414 | − | 0.514626i | \(-0.172069\pi\) | ||||
0.857414 | + | 0.514626i | \(0.172069\pi\) | |||||||
\(68\) | 125.824 | 0.224388 | ||||||||
\(69\) | 4.34018 | 0.00757241 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −395.552 | −0.661175 | −0.330587 | − | 0.943775i | \(-0.607247\pi\) | ||||
−0.330587 | + | 0.943775i | \(0.607247\pi\) | |||||||
\(72\) | −215.584 | −0.352873 | ||||||||
\(73\) | −975.048 | −1.56330 | −0.781649 | − | 0.623718i | \(-0.785621\pi\) | ||||
−0.781649 | + | 0.623718i | \(0.785621\pi\) | |||||||
\(74\) | 431.232 | 0.677429 | ||||||||
\(75\) | 12.7323 | 0.0196027 | ||||||||
\(76\) | −76.0000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −21.4483 | −0.0311351 | ||||||||
\(79\) | 922.776 | 1.31418 | 0.657091 | − | 0.753811i | \(-0.271787\pi\) | ||||
0.657091 | + | 0.753811i | \(0.271787\pi\) | |||||||
\(80\) | −133.056 | −0.185952 | ||||||||
\(81\) | 724.792 | 0.994228 | ||||||||
\(82\) | 135.440 | 0.182401 | ||||||||
\(83\) | 1163.77 | 1.53904 | 0.769519 | − | 0.638624i | \(-0.220496\pi\) | ||||
0.769519 | + | 0.638624i | \(0.220496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −261.588 | −0.333803 | ||||||||
\(86\) | 617.192 | 0.773878 | ||||||||
\(87\) | −20.7962 | −0.0256274 | ||||||||
\(88\) | −102.176 | −0.123773 | ||||||||
\(89\) | −685.136 | −0.816003 | −0.408002 | − | 0.912981i | \(-0.633774\pi\) | ||||
−0.408002 | + | 0.912981i | \(0.633774\pi\) | |||||||
\(90\) | 448.200 | 0.524938 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −76.1441 | −0.0862888 | ||||||||
\(93\) | 67.0242 | 0.0747321 | ||||||||
\(94\) | −217.624 | −0.238790 | ||||||||
\(95\) | 158.004 | 0.170641 | ||||||||
\(96\) | −7.29594 | −0.00775665 | ||||||||
\(97\) | −211.256 | −0.221132 | −0.110566 | − | 0.993869i | \(-0.535266\pi\) | ||||
−0.110566 | + | 0.993869i | \(0.535266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 344.180 | 0.349408 | ||||||||
\(100\) | −223.376 | −0.223376 | ||||||||
\(101\) | 1703.55 | 1.67831 | 0.839157 | − | 0.543889i | \(-0.183049\pi\) | ||||
0.839157 | + | 0.543889i | \(0.183049\pi\) | |||||||
\(102\) | −14.3438 | −0.0139240 | ||||||||
\(103\) | 1393.52 | 1.33308 | 0.666542 | − | 0.745468i | \(-0.267774\pi\) | ||||
0.666542 | + | 0.745468i | \(0.267774\pi\) | |||||||
\(104\) | 376.288 | 0.354789 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1364.25 | −1.25007 | ||||||||
\(107\) | 907.996 | 0.820367 | 0.410184 | − | 0.912003i | \(-0.365465\pi\) | ||||
0.410184 | + | 0.912003i | \(0.365465\pi\) | |||||||
\(108\) | 49.2002 | 0.0438360 | ||||||||
\(109\) | 862.077 | 0.757541 | 0.378770 | − | 0.925491i | \(-0.376347\pi\) | ||||
0.378770 | + | 0.925491i | \(0.376347\pi\) | |||||||
\(110\) | 212.424 | 0.184126 | ||||||||
\(111\) | −49.1601 | −0.0420366 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1502.72 | 1.25101 | 0.625505 | − | 0.780220i | \(-0.284893\pi\) | ||||
0.625505 | + | 0.780220i | \(0.284893\pi\) | |||||||
\(114\) | 8.66393 | 0.00711799 | ||||||||
\(115\) | 158.304 | 0.128364 | ||||||||
\(116\) | 364.848 | 0.292028 | ||||||||
\(117\) | −1267.53 | −1.00156 | ||||||||
\(118\) | 500.600 | 0.390542 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 15.1683 | 0.0115389 | ||||||||
\(121\) | −1167.88 | −0.877443 | ||||||||
\(122\) | 635.384 | 0.471516 | ||||||||
\(123\) | −15.4400 | −0.0113185 | ||||||||
\(124\) | −1175.87 | −0.851584 | ||||||||
\(125\) | 1503.90 | 1.07610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 389.280 | 0.271992 | 0.135996 | − | 0.990709i | \(-0.456577\pi\) | ||||
0.135996 | + | 0.990709i | \(0.456577\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −70.3593 | −0.0480216 | ||||||||
\(130\) | −782.304 | −0.527789 | ||||||||
\(131\) | 268.308 | 0.178948 | 0.0894739 | − | 0.995989i | \(-0.471481\pi\) | ||||
0.0894739 | + | 0.995989i | \(0.471481\pi\) | |||||||
\(132\) | 11.6480 | 0.00768050 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1880.89 | 1.21257 | ||||||||
\(135\) | −102.287 | −0.0652110 | ||||||||
\(136\) | 251.648 | 0.158666 | ||||||||
\(137\) | 2657.33 | 1.65716 | 0.828580 | − | 0.559871i | \(-0.189149\pi\) | ||||
0.828580 | + | 0.559871i | \(0.189149\pi\) | |||||||
\(138\) | 8.68036 | 0.00535450 | ||||||||
\(139\) | 2859.92 | 1.74514 | 0.872572 | − | 0.488486i | \(-0.162451\pi\) | ||||
0.872572 | + | 0.488486i | \(0.162451\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.8090 | 0.0148177 | ||||||||
\(142\) | −791.104 | −0.467521 | ||||||||
\(143\) | −600.744 | −0.351306 | ||||||||
\(144\) | −431.168 | −0.249519 | ||||||||
\(145\) | −758.520 | −0.434425 | ||||||||
\(146\) | −1950.10 | −1.10542 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 862.464 | 0.479014 | ||||||||
\(149\) | 311.812 | 0.171440 | 0.0857202 | − | 0.996319i | \(-0.472681\pi\) | ||||
0.0857202 | + | 0.996319i | \(0.472681\pi\) | |||||||
\(150\) | 25.4647 | 0.0138612 | ||||||||
\(151\) | −1462.32 | −0.788093 | −0.394046 | − | 0.919091i | \(-0.628925\pi\) | ||||
−0.394046 | + | 0.919091i | \(0.628925\pi\) | |||||||
\(152\) | −152.000 | −0.0811107 | ||||||||
\(153\) | −847.677 | −0.447912 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2444.64 | 1.26683 | ||||||||
\(156\) | −42.8965 | −0.0220158 | ||||||||
\(157\) | −4.38395 | −0.00222852 | −0.00111426 | − | 0.999999i | \(-0.500355\pi\) | ||||
−0.00111426 | + | 0.999999i | \(0.500355\pi\) | |||||||
\(158\) | 1845.55 | 0.929267 | ||||||||
\(159\) | 155.523 | 0.0775709 | ||||||||
\(160\) | −266.112 | −0.131488 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1449.58 | 0.703025 | ||||||||
\(163\) | −1777.89 | −0.854325 | −0.427162 | − | 0.904175i | \(-0.640487\pi\) | ||||
−0.427162 | + | 0.904175i | \(0.640487\pi\) | |||||||
\(164\) | 270.880 | 0.128977 | ||||||||
\(165\) | −24.2161 | −0.0114256 | ||||||||
\(166\) | 2327.54 | 1.08826 | ||||||||
\(167\) | −893.064 | −0.413817 | −0.206908 | − | 0.978360i | \(-0.566340\pi\) | ||||
−0.206908 | + | 0.978360i | \(0.566340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.3876 | 0.00700391 | ||||||||
\(170\) | −523.176 | −0.236034 | ||||||||
\(171\) | 512.012 | 0.228974 | ||||||||
\(172\) | 1234.38 | 0.547214 | ||||||||
\(173\) | 2452.56 | 1.07783 | 0.538915 | − | 0.842360i | \(-0.318834\pi\) | ||||
0.538915 | + | 0.842360i | \(0.318834\pi\) | |||||||
\(174\) | −41.5923 | −0.0181213 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −204.352 | −0.0875205 | ||||||||
\(177\) | −57.0679 | −0.0242344 | ||||||||
\(178\) | −1370.27 | −0.577002 | ||||||||
\(179\) | −2064.81 | −0.862185 | −0.431092 | − | 0.902308i | \(-0.641872\pi\) | ||||
−0.431092 | + | 0.902308i | \(0.641872\pi\) | |||||||
\(180\) | 896.399 | 0.371187 | ||||||||
\(181\) | 2518.54 | 1.03426 | 0.517132 | − | 0.855906i | \(-0.327000\pi\) | ||||
0.517132 | + | 0.855906i | \(0.327000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −72.4332 | −0.0292591 | ||||||||
\(184\) | −152.288 | −0.0610154 | ||||||||
\(185\) | −1793.06 | −0.712588 | ||||||||
\(186\) | 134.048 | 0.0528436 | ||||||||
\(187\) | −401.756 | −0.157109 | ||||||||
\(188\) | −435.249 | −0.168850 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 316.008 | 0.120661 | ||||||||
\(191\) | −4206.38 | −1.59352 | −0.796761 | − | 0.604294i | \(-0.793455\pi\) | ||||
−0.796761 | + | 0.604294i | \(0.793455\pi\) | |||||||
\(192\) | −14.5919 | −0.00548478 | ||||||||
\(193\) | 3245.82 | 1.21056 | 0.605282 | − | 0.796011i | \(-0.293060\pi\) | ||||
0.605282 | + | 0.796011i | \(0.293060\pi\) | |||||||
\(194\) | −422.512 | −0.156364 | ||||||||
\(195\) | 89.1819 | 0.0327510 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1734.71 | −0.627377 | −0.313688 | − | 0.949526i | \(-0.601565\pi\) | ||||
−0.313688 | + | 0.949526i | \(0.601565\pi\) | |||||||
\(198\) | 688.360 | 0.247069 | ||||||||
\(199\) | −380.792 | −0.135646 | −0.0678232 | − | 0.997697i | \(-0.521605\pi\) | ||||
−0.0678232 | + | 0.997697i | \(0.521605\pi\) | |||||||
\(200\) | −446.752 | −0.157951 | ||||||||
\(201\) | −214.420 | −0.0752437 | ||||||||
\(202\) | 3407.10 | 1.18675 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −28.6876 | −0.00984576 | ||||||||
\(205\) | −563.160 | −0.191867 | ||||||||
\(206\) | 2787.04 | 0.942633 | ||||||||
\(207\) | 512.983 | 0.172245 | ||||||||
\(208\) | 752.576 | 0.250874 | ||||||||
\(209\) | 242.668 | 0.0803143 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1010.44 | 0.329675 | 0.164837 | − | 0.986321i | \(-0.447290\pi\) | ||||
0.164837 | + | 0.986321i | \(0.447290\pi\) | |||||||
\(212\) | −2728.50 | −0.883933 | ||||||||
\(213\) | 90.1852 | 0.0290112 | ||||||||
\(214\) | 1815.99 | 0.580087 | ||||||||
\(215\) | −2566.29 | −0.814043 | ||||||||
\(216\) | 98.4004 | 0.0309967 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1724.15 | 0.535662 | ||||||||
\(219\) | 222.309 | 0.0685948 | ||||||||
\(220\) | 424.848 | 0.130197 | ||||||||
\(221\) | 1479.57 | 0.450345 | ||||||||
\(222\) | −98.3201 | −0.0297244 | ||||||||
\(223\) | −3398.70 | −1.02060 | −0.510301 | − | 0.859996i | \(-0.670466\pi\) | ||||
−0.510301 | + | 0.859996i | \(0.670466\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1504.89 | 0.445892 | ||||||||
\(226\) | 3005.44 | 0.884597 | ||||||||
\(227\) | −5760.80 | −1.68439 | −0.842197 | − | 0.539169i | \(-0.818738\pi\) | ||||
−0.842197 | + | 0.539169i | \(0.818738\pi\) | |||||||
\(228\) | 17.3279 | 0.00503318 | ||||||||
\(229\) | 2179.00 | 0.628786 | 0.314393 | − | 0.949293i | \(-0.398199\pi\) | ||||
0.314393 | + | 0.949293i | \(0.398199\pi\) | |||||||
\(230\) | 316.607 | 0.0907673 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 729.696 | 0.206495 | ||||||||
\(233\) | −2808.49 | −0.789659 | −0.394830 | − | 0.918754i | \(-0.629196\pi\) | ||||
−0.394830 | + | 0.918754i | \(0.629196\pi\) | |||||||
\(234\) | −2535.06 | −0.708213 | ||||||||
\(235\) | 904.882 | 0.251183 | ||||||||
\(236\) | 1001.20 | 0.276155 | ||||||||
\(237\) | −210.391 | −0.0576640 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6285.67 | 1.70120 | 0.850599 | − | 0.525815i | \(-0.176239\pi\) | ||||
0.850599 | + | 0.525815i | \(0.176239\pi\) | |||||||
\(240\) | 30.3365 | 0.00815923 | ||||||||
\(241\) | −1129.22 | −0.301825 | −0.150912 | − | 0.988547i | \(-0.548221\pi\) | ||||
−0.150912 | + | 0.988547i | \(0.548221\pi\) | |||||||
\(242\) | −2335.75 | −0.620446 | ||||||||
\(243\) | −497.352 | −0.131297 | ||||||||
\(244\) | 1270.77 | 0.333412 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −30.8801 | −0.00800342 | ||||||||
\(247\) | −893.684 | −0.230218 | ||||||||
\(248\) | −2351.74 | −0.602161 | ||||||||
\(249\) | −265.337 | −0.0675303 | ||||||||
\(250\) | 3007.80 | 0.760920 | ||||||||
\(251\) | 2873.73 | 0.722661 | 0.361331 | − | 0.932438i | \(-0.382323\pi\) | ||||
0.361331 | + | 0.932438i | \(0.382323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 243.128 | 0.0604163 | ||||||||
\(254\) | 778.559 | 0.192327 | ||||||||
\(255\) | 59.6416 | 0.0146467 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 3712.18 | 0.901008 | 0.450504 | − | 0.892774i | \(-0.351244\pi\) | ||||
0.450504 | + | 0.892774i | \(0.351244\pi\) | |||||||
\(258\) | −140.719 | −0.0339564 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1564.61 | −0.373203 | ||||||||
\(261\) | −2457.98 | −0.582932 | ||||||||
\(262\) | 536.616 | 0.126535 | ||||||||
\(263\) | 1263.04 | 0.296130 | 0.148065 | − | 0.988978i | \(-0.452696\pi\) | ||||
0.148065 | + | 0.988978i | \(0.452696\pi\) | |||||||
\(264\) | 23.2959 | 0.00543093 | ||||||||
\(265\) | 5672.55 | 1.31495 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 156.210 | 0.0358048 | ||||||||
\(268\) | 3761.78 | 0.857414 | ||||||||
\(269\) | 5484.39 | 1.24308 | 0.621541 | − | 0.783381i | \(-0.286507\pi\) | ||||
0.621541 | + | 0.783381i | \(0.286507\pi\) | |||||||
\(270\) | −204.575 | −0.0461111 | ||||||||
\(271\) | 3217.66 | 0.721251 | 0.360625 | − | 0.932711i | \(-0.382563\pi\) | ||||
0.360625 | + | 0.932711i | \(0.382563\pi\) | |||||||
\(272\) | 503.296 | 0.112194 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5314.66 | 1.17179 | ||||||||
\(275\) | 713.240 | 0.156400 | ||||||||
\(276\) | 17.3607 | 0.00378620 | ||||||||
\(277\) | 7668.13 | 1.66330 | 0.831649 | − | 0.555302i | \(-0.187397\pi\) | ||||
0.831649 | + | 0.555302i | \(0.187397\pi\) | |||||||
\(278\) | 5719.83 | 1.23400 | ||||||||
\(279\) | 7921.86 | 1.69989 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1126.81 | 0.239216 | 0.119608 | − | 0.992821i | \(-0.461836\pi\) | ||||
0.119608 | + | 0.992821i | \(0.461836\pi\) | |||||||
\(282\) | 49.6179 | 0.0104777 | ||||||||
\(283\) | 1502.63 | 0.315625 | 0.157813 | − | 0.987469i | \(-0.449556\pi\) | ||||
0.157813 | + | 0.987469i | \(0.449556\pi\) | |||||||
\(284\) | −1582.21 | −0.330587 | ||||||||
\(285\) | −36.0246 | −0.00748742 | ||||||||
\(286\) | −1201.49 | −0.248411 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −862.337 | −0.176436 | ||||||||
\(289\) | −3923.52 | −0.798600 | ||||||||
\(290\) | −1517.04 | −0.307185 | ||||||||
\(291\) | 48.1659 | 0.00970288 | ||||||||
\(292\) | −3900.19 | −0.781649 | ||||||||
\(293\) | 452.324 | 0.0901878 | 0.0450939 | − | 0.998983i | \(-0.485641\pi\) | ||||
0.0450939 | + | 0.998983i | \(0.485641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2081.50 | −0.410812 | ||||||||
\(296\) | 1724.93 | 0.338714 | ||||||||
\(297\) | −157.096 | −0.0306924 | ||||||||
\(298\) | 623.623 | 0.121227 | ||||||||
\(299\) | −895.379 | −0.173181 | ||||||||
\(300\) | 50.9294 | 0.00980136 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2924.64 | −0.557266 | ||||||||
\(303\) | −388.407 | −0.0736415 | ||||||||
\(304\) | −304.000 | −0.0573539 | ||||||||
\(305\) | −2641.93 | −0.495988 | ||||||||
\(306\) | −1695.35 | −0.316722 | ||||||||
\(307\) | 2333.46 | 0.433803 | 0.216901 | − | 0.976194i | \(-0.430405\pi\) | ||||
0.216901 | + | 0.976194i | \(0.430405\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −317.720 | −0.0584934 | ||||||||
\(310\) | 4889.28 | 0.895782 | ||||||||
\(311\) | −10476.1 | −1.91011 | −0.955055 | − | 0.296429i | \(-0.904204\pi\) | ||||
−0.955055 | + | 0.296429i | \(0.904204\pi\) | |||||||
\(312\) | −85.7930 | −0.0155675 | ||||||||
\(313\) | −4160.33 | −0.751297 | −0.375648 | − | 0.926762i | \(-0.622580\pi\) | ||||
−0.375648 | + | 0.926762i | \(0.622580\pi\) | |||||||
\(314\) | −8.76790 | −0.00157580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3691.10 | 0.657091 | ||||||||
\(317\) | −7508.56 | −1.33036 | −0.665178 | − | 0.746685i | \(-0.731644\pi\) | ||||
−0.665178 | + | 0.746685i | \(0.731644\pi\) | |||||||
\(318\) | 311.046 | 0.0548509 | ||||||||
\(319\) | −1164.96 | −0.204468 | ||||||||
\(320\) | −532.224 | −0.0929758 | ||||||||
\(321\) | −207.021 | −0.0359963 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −597.664 | −0.102956 | ||||||||
\(324\) | 2899.17 | 0.497114 | ||||||||
\(325\) | −2626.68 | −0.448314 | ||||||||
\(326\) | −3555.78 | −0.604099 | ||||||||
\(327\) | −196.552 | −0.0332396 | ||||||||
\(328\) | 541.760 | 0.0912003 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −48.4323 | −0.00807912 | ||||||||
\(331\) | 10386.8 | 1.72480 | 0.862400 | − | 0.506227i | \(-0.168960\pi\) | ||||
0.862400 | + | 0.506227i | \(0.168960\pi\) | |||||||
\(332\) | 4655.07 | 0.769519 | ||||||||
\(333\) | −5810.43 | −0.956184 | ||||||||
\(334\) | −1786.13 | −0.292613 | ||||||||
\(335\) | −7820.74 | −1.27550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5618.29 | 0.908153 | 0.454077 | − | 0.890963i | \(-0.349969\pi\) | ||||
0.454077 | + | 0.890963i | \(0.349969\pi\) | |||||||
\(338\) | 30.7752 | 0.00495251 | ||||||||
\(339\) | −342.617 | −0.0548921 | ||||||||
\(340\) | −1046.35 | −0.166901 | ||||||||
\(341\) | 3754.56 | 0.596249 | ||||||||
\(342\) | 1024.02 | 0.161909 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2468.77 | 0.386939 | ||||||||
\(345\) | −36.0929 | −0.00563240 | ||||||||
\(346\) | 4905.12 | 0.762142 | ||||||||
\(347\) | 1814.32 | 0.280686 | 0.140343 | − | 0.990103i | \(-0.455180\pi\) | ||||
0.140343 | + | 0.990103i | \(0.455180\pi\) | |||||||
\(348\) | −83.1847 | −0.0128137 | ||||||||
\(349\) | 816.757 | 0.125272 | 0.0626361 | − | 0.998036i | \(-0.480049\pi\) | ||||
0.0626361 | + | 0.998036i | \(0.480049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 578.545 | 0.0879785 | ||||||||
\(352\) | −408.704 | −0.0618864 | ||||||||
\(353\) | −11090.4 | −1.67219 | −0.836095 | − | 0.548585i | \(-0.815167\pi\) | ||||
−0.836095 | + | 0.548585i | \(0.815167\pi\) | |||||||
\(354\) | −114.136 | −0.0171363 | ||||||||
\(355\) | 3289.41 | 0.491786 | ||||||||
\(356\) | −2740.55 | −0.408002 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4129.62 | −0.609657 | ||||||||
\(359\) | −3211.68 | −0.472161 | −0.236081 | − | 0.971733i | \(-0.575863\pi\) | ||||
−0.236081 | + | 0.971733i | \(0.575863\pi\) | |||||||
\(360\) | 1792.80 | 0.262469 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 5037.09 | 0.731335 | ||||||||
\(363\) | 266.274 | 0.0385007 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8108.51 | 1.16279 | ||||||||
\(366\) | −144.866 | −0.0206893 | ||||||||
\(367\) | −8077.81 | −1.14893 | −0.574466 | − | 0.818528i | \(-0.694790\pi\) | ||||
−0.574466 | + | 0.818528i | \(0.694790\pi\) | |||||||
\(368\) | −304.576 | −0.0431444 | ||||||||
\(369\) | −1824.92 | −0.257457 | ||||||||
\(370\) | −3586.13 | −0.503876 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 268.097 | 0.0373660 | ||||||||
\(373\) | −5088.15 | −0.706312 | −0.353156 | − | 0.935564i | \(-0.614892\pi\) | ||||
−0.353156 | + | 0.935564i | \(0.614892\pi\) | |||||||
\(374\) | −803.512 | −0.111093 | ||||||||
\(375\) | −342.886 | −0.0472175 | ||||||||
\(376\) | −870.497 | −0.119395 | ||||||||
\(377\) | 4290.25 | 0.586099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2547.00 | 0.345199 | 0.172600 | − | 0.984992i | \(-0.444783\pi\) | ||||
0.172600 | + | 0.984992i | \(0.444783\pi\) | |||||||
\(380\) | 632.016 | 0.0853204 | ||||||||
\(381\) | −88.7550 | −0.0119345 | ||||||||
\(382\) | −8412.76 | −1.12679 | ||||||||
\(383\) | 7056.11 | 0.941384 | 0.470692 | − | 0.882297i | \(-0.344004\pi\) | ||||
0.470692 | + | 0.882297i | \(0.344004\pi\) | |||||||
\(384\) | −29.1838 | −0.00387833 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6491.63 | 0.855999 | ||||||||
\(387\) | −8316.05 | −1.09232 | ||||||||
\(388\) | −845.023 | −0.110566 | ||||||||
\(389\) | 4728.25 | 0.616277 | 0.308138 | − | 0.951342i | \(-0.400294\pi\) | ||||
0.308138 | + | 0.951342i | \(0.400294\pi\) | |||||||
\(390\) | 178.364 | 0.0231585 | ||||||||
\(391\) | −598.797 | −0.0774488 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −61.1737 | −0.00785192 | ||||||||
\(394\) | −3469.43 | −0.443622 | ||||||||
\(395\) | −7673.81 | −0.977497 | ||||||||
\(396\) | 1376.72 | 0.174704 | ||||||||
\(397\) | −740.837 | −0.0936563 | −0.0468281 | − | 0.998903i | \(-0.514911\pi\) | ||||
−0.0468281 | + | 0.998903i | \(0.514911\pi\) | |||||||
\(398\) | −761.584 | −0.0959165 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −893.505 | −0.111688 | ||||||||
\(401\) | 1879.58 | 0.234070 | 0.117035 | − | 0.993128i | \(-0.462661\pi\) | ||||
0.117035 | + | 0.993128i | \(0.462661\pi\) | |||||||
\(402\) | −428.839 | −0.0532053 | ||||||||
\(403\) | −13827.1 | −1.70912 | ||||||||
\(404\) | 6814.21 | 0.839157 | ||||||||
\(405\) | −6027.37 | −0.739513 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2753.85 | −0.335389 | ||||||||
\(408\) | −57.3753 | −0.00696201 | ||||||||
\(409\) | 1715.45 | 0.207393 | 0.103697 | − | 0.994609i | \(-0.466933\pi\) | ||||
0.103697 | + | 0.994609i | \(0.466933\pi\) | |||||||
\(410\) | −1126.32 | −0.135671 | ||||||||
\(411\) | −605.866 | −0.0727133 | ||||||||
\(412\) | 5574.08 | 0.666542 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1025.97 | 0.121796 | ||||||||
\(415\) | −9677.90 | −1.14475 | ||||||||
\(416\) | 1505.15 | 0.177395 | ||||||||
\(417\) | −652.056 | −0.0765739 | ||||||||
\(418\) | 485.336 | 0.0567908 | ||||||||
\(419\) | −2497.15 | −0.291155 | −0.145578 | − | 0.989347i | \(-0.546504\pi\) | ||||
−0.145578 | + | 0.989347i | \(0.546504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6582.52 | 0.762024 | 0.381012 | − | 0.924570i | \(-0.375576\pi\) | ||||
0.381012 | + | 0.924570i | \(0.375576\pi\) | |||||||
\(422\) | 2020.87 | 0.233115 | ||||||||
\(423\) | 2932.27 | 0.337049 | ||||||||
\(424\) | −5456.99 | −0.625035 | ||||||||
\(425\) | −1756.63 | −0.200492 | ||||||||
\(426\) | 180.370 | 0.0205140 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3631.99 | 0.410184 | ||||||||
\(429\) | 136.969 | 0.0154147 | ||||||||
\(430\) | −5132.57 | −0.575615 | ||||||||
\(431\) | 8875.72 | 0.991946 | 0.495973 | − | 0.868338i | \(-0.334812\pi\) | ||||
0.495973 | + | 0.868338i | \(0.334812\pi\) | |||||||
\(432\) | 196.801 | 0.0219180 | ||||||||
\(433\) | 3636.90 | 0.403645 | 0.201822 | − | 0.979422i | \(-0.435314\pi\) | ||||
0.201822 | + | 0.979422i | \(0.435314\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 172.941 | 0.0190618 | ||||||||
\(436\) | 3448.31 | 0.378770 | ||||||||
\(437\) | 361.684 | 0.0395920 | ||||||||
\(438\) | 444.618 | 0.0485039 | ||||||||
\(439\) | 10979.4 | 1.19366 | 0.596829 | − | 0.802368i | \(-0.296427\pi\) | ||||
0.596829 | + | 0.802368i | \(0.296427\pi\) | |||||||
\(440\) | 849.696 | 0.0920629 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2959.13 | 0.318442 | ||||||||
\(443\) | 1300.16 | 0.139442 | 0.0697208 | − | 0.997567i | \(-0.477789\pi\) | ||||
0.0697208 | + | 0.997567i | \(0.477789\pi\) | |||||||
\(444\) | −196.640 | −0.0210183 | ||||||||
\(445\) | 5697.60 | 0.606948 | ||||||||
\(446\) | −6797.41 | −0.721674 | ||||||||
\(447\) | −71.0925 | −0.00752250 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15875.2 | −1.66859 | −0.834296 | − | 0.551317i | \(-0.814125\pi\) | ||||
−0.834296 | + | 0.551317i | \(0.814125\pi\) | |||||||
\(450\) | 3009.77 | 0.315293 | ||||||||
\(451\) | −864.920 | −0.0903049 | ||||||||
\(452\) | 6010.88 | 0.625505 | ||||||||
\(453\) | 333.406 | 0.0345801 | ||||||||
\(454\) | −11521.6 | −1.19105 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 34.6557 | 0.00355900 | ||||||||
\(457\) | 3115.66 | 0.318916 | 0.159458 | − | 0.987205i | \(-0.449025\pi\) | ||||
0.159458 | + | 0.987205i | \(0.449025\pi\) | |||||||
\(458\) | 4357.99 | 0.444619 | ||||||||
\(459\) | 386.910 | 0.0393451 | ||||||||
\(460\) | 633.215 | 0.0641822 | ||||||||
\(461\) | −13479.7 | −1.36185 | −0.680924 | − | 0.732354i | \(-0.738422\pi\) | ||||
−0.680924 | + | 0.732354i | \(0.738422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7946.19 | 0.797604 | 0.398802 | − | 0.917037i | \(-0.369426\pi\) | ||||
0.398802 | + | 0.917037i | \(0.369426\pi\) | |||||||
\(464\) | 1459.39 | 0.146014 | ||||||||
\(465\) | −557.373 | −0.0555862 | ||||||||
\(466\) | −5616.99 | −0.558373 | ||||||||
\(467\) | 9148.37 | 0.906501 | 0.453250 | − | 0.891383i | \(-0.350264\pi\) | ||||
0.453250 | + | 0.891383i | \(0.350264\pi\) | |||||||
\(468\) | −5070.11 | −0.500782 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1809.76 | 0.177613 | ||||||||
\(471\) | 0.999532 | 9.77834e−5 0 | ||||||||
\(472\) | 2002.40 | 0.195271 | ||||||||
\(473\) | −3941.39 | −0.383140 | ||||||||
\(474\) | −420.782 | −0.0407746 | ||||||||
\(475\) | 1061.04 | 0.102492 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18381.9 | 1.76446 | ||||||||
\(478\) | 12571.3 | 1.20293 | ||||||||
\(479\) | −7664.64 | −0.731120 | −0.365560 | − | 0.930788i | \(-0.619122\pi\) | ||||
−0.365560 | + | 0.930788i | \(0.619122\pi\) | |||||||
\(480\) | 60.6731 | 0.00576945 | ||||||||
\(481\) | 10141.7 | 0.961378 | ||||||||
\(482\) | −2258.45 | −0.213422 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4671.50 | −0.438721 | ||||||||
\(485\) | 1756.80 | 0.164479 | ||||||||
\(486\) | −994.705 | −0.0928410 | ||||||||
\(487\) | −5347.21 | −0.497547 | −0.248774 | − | 0.968562i | \(-0.580027\pi\) | ||||
−0.248774 | + | 0.968562i | \(0.580027\pi\) | |||||||
\(488\) | 2541.54 | 0.235758 | ||||||||
\(489\) | 405.355 | 0.0374863 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13647.2 | 1.25436 | 0.627178 | − | 0.778876i | \(-0.284210\pi\) | ||||
0.627178 | + | 0.778876i | \(0.284210\pi\) | |||||||
\(492\) | −61.7601 | −0.00565927 | ||||||||
\(493\) | 2869.17 | 0.262111 | ||||||||
\(494\) | −1787.37 | −0.162789 | ||||||||
\(495\) | −2862.20 | −0.259892 | ||||||||
\(496\) | −4703.49 | −0.425792 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −530.674 | −0.0477511 | ||||||||
\(499\) | −19351.6 | −1.73607 | −0.868034 | − | 0.496504i | \(-0.834617\pi\) | ||||
−0.868034 | + | 0.496504i | \(0.834617\pi\) | |||||||
\(500\) | 6015.60 | 0.538052 | ||||||||
\(501\) | 203.617 | 0.0181576 | ||||||||
\(502\) | 5747.45 | 0.510999 | ||||||||
\(503\) | 19259.1 | 1.70720 | 0.853600 | − | 0.520929i | \(-0.174414\pi\) | ||||
0.853600 | + | 0.520929i | \(0.174414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14166.7 | −1.24834 | ||||||||
\(506\) | 486.256 | 0.0427208 | ||||||||
\(507\) | −3.50834 | −0.000307319 0 | ||||||||
\(508\) | 1557.12 | 0.135996 | ||||||||
\(509\) | −3595.77 | −0.313123 | −0.156561 | − | 0.987668i | \(-0.550041\pi\) | ||||
−0.156561 | + | 0.987668i | \(0.550041\pi\) | |||||||
\(510\) | 119.283 | 0.0103568 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −233.701 | −0.0201133 | ||||||||
\(514\) | 7424.35 | 0.637109 | ||||||||
\(515\) | −11588.5 | −0.991556 | ||||||||
\(516\) | −281.437 | −0.0240108 | ||||||||
\(517\) | 1389.75 | 0.118223 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −559.179 | −0.0472933 | ||||||||
\(520\) | −3129.21 | −0.263895 | ||||||||
\(521\) | 15211.0 | 1.27909 | 0.639544 | − | 0.768754i | \(-0.279123\pi\) | ||||
0.639544 | + | 0.768754i | \(0.279123\pi\) | |||||||
\(522\) | −4915.97 | −0.412195 | ||||||||
\(523\) | −18307.1 | −1.53062 | −0.765310 | − | 0.643662i | \(-0.777414\pi\) | ||||
−0.765310 | + | 0.643662i | \(0.777414\pi\) | |||||||
\(524\) | 1073.23 | 0.0894739 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2526.07 | 0.209395 | ||||||||
\(527\) | −9247.06 | −0.764342 | ||||||||
\(528\) | 46.5919 | 0.00384025 | ||||||||
\(529\) | −11804.6 | −0.970217 | ||||||||
\(530\) | 11345.1 | 0.929810 | ||||||||
\(531\) | −6745.09 | −0.551247 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3185.28 | 0.258855 | ||||||||
\(534\) | 312.420 | 0.0253178 | ||||||||
\(535\) | −7550.90 | −0.610194 | ||||||||
\(536\) | 7523.55 | 0.606284 | ||||||||
\(537\) | 470.773 | 0.0378312 | ||||||||
\(538\) | 10968.8 | 0.878992 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −409.149 | −0.0326055 | ||||||||
\(541\) | 9102.17 | 0.723351 | 0.361676 | − | 0.932304i | \(-0.382205\pi\) | ||||
0.361676 | + | 0.932304i | \(0.382205\pi\) | |||||||
\(542\) | 6435.32 | 0.510001 | ||||||||
\(543\) | −574.223 | −0.0453817 | ||||||||
\(544\) | 1006.59 | 0.0793332 | ||||||||
\(545\) | −7169.03 | −0.563464 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9218.75 | −0.720595 | −0.360297 | − | 0.932837i | \(-0.617325\pi\) | ||||
−0.360297 | + | 0.932837i | \(0.617325\pi\) | |||||||
\(548\) | 10629.3 | 0.828580 | ||||||||
\(549\) | −8561.17 | −0.665541 | ||||||||
\(550\) | 1426.48 | 0.110592 | ||||||||
\(551\) | −1733.03 | −0.133992 | ||||||||
\(552\) | 34.7214 | 0.00267725 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15336.3 | 1.17613 | ||||||||
\(555\) | 408.815 | 0.0312671 | ||||||||
\(556\) | 11439.7 | 0.872572 | ||||||||
\(557\) | −13435.1 | −1.02202 | −0.511010 | − | 0.859575i | \(-0.670728\pi\) | ||||
−0.511010 | + | 0.859575i | \(0.670728\pi\) | |||||||
\(558\) | 15843.7 | 1.20200 | ||||||||
\(559\) | 14515.1 | 1.09825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 91.5996 | 0.00689365 | ||||||||
\(562\) | 2253.62 | 0.169151 | ||||||||
\(563\) | −11941.5 | −0.893916 | −0.446958 | − | 0.894555i | \(-0.647493\pi\) | ||||
−0.446958 | + | 0.894555i | \(0.647493\pi\) | |||||||
\(564\) | 99.2359 | 0.00740884 | ||||||||
\(565\) | −12496.6 | −0.930508 | ||||||||
\(566\) | 3005.26 | 0.223181 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3164.42 | −0.233761 | ||||||||
\(569\) | −6378.91 | −0.469979 | −0.234989 | − | 0.971998i | \(-0.575506\pi\) | ||||
−0.234989 | + | 0.971998i | \(0.575506\pi\) | |||||||
\(570\) | −72.0493 | −0.00529441 | ||||||||
\(571\) | 24903.9 | 1.82521 | 0.912605 | − | 0.408843i | \(-0.134068\pi\) | ||||
0.912605 | + | 0.408843i | \(0.134068\pi\) | |||||||
\(572\) | −2402.98 | −0.175653 | ||||||||
\(573\) | 959.046 | 0.0699210 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1063.05 | 0.0770995 | ||||||||
\(576\) | −1724.67 | −0.124759 | ||||||||
\(577\) | 11414.7 | 0.823568 | 0.411784 | − | 0.911281i | \(-0.364906\pi\) | ||||
0.411784 | + | 0.911281i | \(0.364906\pi\) | |||||||
\(578\) | −7847.04 | −0.564695 | ||||||||
\(579\) | −740.040 | −0.0531175 | ||||||||
\(580\) | −3034.08 | −0.217213 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 96.3319 | 0.00686097 | ||||||||
\(583\) | 8712.09 | 0.618899 | ||||||||
\(584\) | −7800.39 | −0.552709 | ||||||||
\(585\) | 10540.8 | 0.744969 | ||||||||
\(586\) | 904.648 | 0.0637724 | ||||||||
\(587\) | −20732.1 | −1.45776 | −0.728881 | − | 0.684641i | \(-0.759959\pi\) | ||||
−0.728881 | + | 0.684641i | \(0.759959\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5585.39 | 0.390734 | ||||||||
\(590\) | −4162.99 | −0.290488 | ||||||||
\(591\) | 395.511 | 0.0275282 | ||||||||
\(592\) | 3449.86 | 0.239507 | ||||||||
\(593\) | −18010.5 | −1.24722 | −0.623611 | − | 0.781735i | \(-0.714335\pi\) | ||||
−0.623611 | + | 0.781735i | \(0.714335\pi\) | |||||||
\(594\) | −314.192 | −0.0217028 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1247.25 | 0.0857202 | ||||||||
\(597\) | 86.8199 | 0.00595193 | ||||||||
\(598\) | −1790.76 | −0.122457 | ||||||||
\(599\) | 27944.7 | 1.90616 | 0.953080 | − | 0.302719i | \(-0.0978942\pi\) | ||||
0.953080 | + | 0.302719i | \(0.0978942\pi\) | |||||||
\(600\) | 101.859 | 0.00693061 | ||||||||
\(601\) | 11598.1 | 0.787179 | 0.393590 | − | 0.919286i | \(-0.371233\pi\) | ||||
0.393590 | + | 0.919286i | \(0.371233\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25343.1 | −1.71153 | ||||||||
\(604\) | −5849.28 | −0.394046 | ||||||||
\(605\) | 9712.06 | 0.652647 | ||||||||
\(606\) | −776.813 | −0.0520724 | ||||||||
\(607\) | −20170.5 | −1.34876 | −0.674379 | − | 0.738385i | \(-0.735589\pi\) | ||||
−0.674379 | + | 0.738385i | \(0.735589\pi\) | |||||||
\(608\) | −608.000 | −0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5283.86 | −0.350717 | ||||||||
\(611\) | −5118.09 | −0.338880 | ||||||||
\(612\) | −3390.71 | −0.223956 | ||||||||
\(613\) | 14618.3 | 0.963174 | 0.481587 | − | 0.876398i | \(-0.340061\pi\) | ||||
0.481587 | + | 0.876398i | \(0.340061\pi\) | |||||||
\(614\) | 4666.91 | 0.306745 | ||||||||
\(615\) | 128.399 | 0.00841880 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17538.1 | −1.14434 | −0.572171 | − | 0.820134i | \(-0.693899\pi\) | ||||
−0.572171 | + | 0.820134i | \(0.693899\pi\) | |||||||
\(618\) | −635.440 | −0.0413611 | ||||||||
\(619\) | 8815.75 | 0.572431 | 0.286216 | − | 0.958165i | \(-0.407603\pi\) | ||||
0.286216 | + | 0.958165i | \(0.407603\pi\) | |||||||
\(620\) | 9778.56 | 0.633414 | ||||||||
\(621\) | −234.144 | −0.0151302 | ||||||||
\(622\) | −20952.2 | −1.35065 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −171.586 | −0.0110079 | ||||||||
\(625\) | −5525.94 | −0.353660 | ||||||||
\(626\) | −8320.66 | −0.531247 | ||||||||
\(627\) | −55.3279 | −0.00352405 | ||||||||
\(628\) | −17.5358 | −0.00111426 | ||||||||
\(629\) | 6782.42 | 0.429941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22170.8 | −1.39874 | −0.699370 | − | 0.714759i | \(-0.746536\pi\) | ||||
−0.699370 | + | 0.714759i | \(0.746536\pi\) | |||||||
\(632\) | 7382.21 | 0.464634 | ||||||||
\(633\) | −230.378 | −0.0144655 | ||||||||
\(634\) | −15017.1 | −0.940703 | ||||||||
\(635\) | −3237.25 | −0.202309 | ||||||||
\(636\) | 622.092 | 0.0387855 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2329.92 | −0.144581 | ||||||||
\(639\) | 10659.3 | 0.659902 | ||||||||
\(640\) | −1064.45 | −0.0657438 | ||||||||
\(641\) | −22067.7 | −1.35978 | −0.679891 | − | 0.733313i | \(-0.737973\pi\) | ||||
−0.679891 | + | 0.733313i | \(0.737973\pi\) | |||||||
\(642\) | −414.043 | −0.0254532 | ||||||||
\(643\) | 11795.4 | 0.723428 | 0.361714 | − | 0.932289i | \(-0.382192\pi\) | ||||
0.361714 | + | 0.932289i | \(0.382192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 585.108 | 0.0357188 | ||||||||
\(646\) | −1195.33 | −0.0728012 | ||||||||
\(647\) | 9716.04 | 0.590382 | 0.295191 | − | 0.955438i | \(-0.404617\pi\) | ||||
0.295191 | + | 0.955438i | \(0.404617\pi\) | |||||||
\(648\) | 5798.34 | 0.351513 | ||||||||
\(649\) | −3196.83 | −0.193354 | ||||||||
\(650\) | −5253.36 | −0.317006 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7111.55 | −0.427162 | ||||||||
\(653\) | −10311.9 | −0.617969 | −0.308985 | − | 0.951067i | \(-0.599989\pi\) | ||||
−0.308985 | + | 0.951067i | \(0.599989\pi\) | |||||||
\(654\) | −393.104 | −0.0235039 | ||||||||
\(655\) | −2231.25 | −0.133102 | ||||||||
\(656\) | 1083.52 | 0.0644884 | ||||||||
\(657\) | 26275.6 | 1.56029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4019.80 | 0.237616 | 0.118808 | − | 0.992917i | \(-0.462093\pi\) | ||||
0.118808 | + | 0.992917i | \(0.462093\pi\) | |||||||
\(660\) | −96.8646 | −0.00571280 | ||||||||
\(661\) | 22702.6 | 1.33590 | 0.667951 | − | 0.744206i | \(-0.267172\pi\) | ||||
0.667951 | + | 0.744206i | \(0.267172\pi\) | |||||||
\(662\) | 20773.6 | 1.21962 | ||||||||
\(663\) | −337.338 | −0.0197604 | ||||||||
\(664\) | 9310.15 | 0.544132 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11620.9 | −0.676124 | ||||||||
\(667\) | −1736.31 | −0.100795 | ||||||||
\(668\) | −3572.26 | −0.206908 | ||||||||
\(669\) | 774.898 | 0.0447822 | ||||||||
\(670\) | −15641.5 | −0.901915 | ||||||||
\(671\) | −4057.57 | −0.233443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11132.8 | 0.637652 | 0.318826 | − | 0.947813i | \(-0.396711\pi\) | ||||
0.318826 | + | 0.947813i | \(0.396711\pi\) | |||||||
\(674\) | 11236.6 | 0.642161 | ||||||||
\(675\) | −686.884 | −0.0391677 | ||||||||
\(676\) | 61.5503 | 0.00350195 | ||||||||
\(677\) | 13967.0 | 0.792903 | 0.396452 | − | 0.918056i | \(-0.370241\pi\) | ||||
0.396452 | + | 0.918056i | \(0.370241\pi\) | |||||||
\(678\) | −685.235 | −0.0388146 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2092.71 | −0.118017 | ||||||||
\(681\) | 1313.45 | 0.0739083 | ||||||||
\(682\) | 7509.12 | 0.421612 | ||||||||
\(683\) | 1173.88 | 0.0657648 | 0.0328824 | − | 0.999459i | \(-0.489531\pi\) | ||||
0.0328824 | + | 0.999459i | \(0.489531\pi\) | |||||||
\(684\) | 2048.05 | 0.114487 | ||||||||
\(685\) | −22098.4 | −1.23261 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −496.807 | −0.0275901 | ||||||||
\(688\) | 4937.54 | 0.273607 | ||||||||
\(689\) | −32084.4 | −1.77405 | ||||||||
\(690\) | −72.1859 | −0.00398271 | ||||||||
\(691\) | −8713.33 | −0.479697 | −0.239849 | − | 0.970810i | \(-0.577098\pi\) | ||||
−0.239849 | + | 0.970810i | \(0.577098\pi\) | |||||||
\(692\) | 9810.24 | 0.538915 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3628.64 | 0.198475 | ||||||||
\(695\) | −23783.1 | −1.29805 | ||||||||
\(696\) | −166.369 | −0.00906065 | ||||||||
\(697\) | 2130.20 | 0.115763 | ||||||||
\(698\) | 1633.51 | 0.0885809 | ||||||||
\(699\) | 640.331 | 0.0346489 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31003.4 | −1.67045 | −0.835223 | − | 0.549912i | \(-0.814661\pi\) | ||||
−0.835223 | + | 0.549912i | \(0.814661\pi\) | |||||||
\(702\) | 1157.09 | 0.0622102 | ||||||||
\(703\) | −4096.70 | −0.219787 | ||||||||
\(704\) | −817.408 | −0.0437603 | ||||||||
\(705\) | −206.311 | −0.0110215 | ||||||||
\(706\) | −22180.8 | −1.18242 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −228.272 | −0.0121172 | ||||||||
\(709\) | −12145.1 | −0.643328 | −0.321664 | − | 0.946854i | \(-0.604242\pi\) | ||||
−0.321664 | + | 0.946854i | \(0.604242\pi\) | |||||||
\(710\) | 6578.83 | 0.347745 | ||||||||
\(711\) | −24867.0 | −1.31165 | ||||||||
\(712\) | −5481.09 | −0.288501 | ||||||||
\(713\) | 5595.98 | 0.293929 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4995.79 | 0.261304 | ||||||||
\(716\) | −8259.24 | −0.431092 | ||||||||
\(717\) | −1433.12 | −0.0746456 | ||||||||
\(718\) | −6423.36 | −0.333868 | ||||||||
\(719\) | −24787.8 | −1.28572 | −0.642858 | − | 0.765985i | \(-0.722252\pi\) | ||||
−0.642858 | + | 0.765985i | \(0.722252\pi\) | |||||||
\(720\) | 3585.60 | 0.185594 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 722.000 | 0.0372161 | ||||||||
\(723\) | 257.461 | 0.0132435 | ||||||||
\(724\) | 10074.2 | 0.517132 | ||||||||
\(725\) | −5093.65 | −0.260929 | ||||||||
\(726\) | 532.547 | 0.0272241 | ||||||||
\(727\) | −19335.6 | −0.986409 | −0.493204 | − | 0.869914i | \(-0.664174\pi\) | ||||
−0.493204 | + | 0.869914i | \(0.664174\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19456.0 | −0.988467 | ||||||||
\(730\) | 16217.0 | 0.822217 | ||||||||
\(731\) | 9707.19 | 0.491154 | ||||||||
\(732\) | −289.733 | −0.0146296 | ||||||||
\(733\) | −20204.5 | −1.01810 | −0.509052 | − | 0.860735i | \(-0.670004\pi\) | ||||
−0.509052 | + | 0.860735i | \(0.670004\pi\) | |||||||
\(734\) | −16155.6 | −0.812418 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −609.153 | −0.0305077 | ||||||||
\(737\) | −12011.4 | −0.600331 | ||||||||
\(738\) | −3649.84 | −0.182049 | ||||||||
\(739\) | 15643.7 | 0.778706 | 0.389353 | − | 0.921089i | \(-0.372699\pi\) | ||||
0.389353 | + | 0.921089i | \(0.372699\pi\) | |||||||
\(740\) | −7172.26 | −0.356294 | ||||||||
\(741\) | 203.758 | 0.0101016 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4500.20 | −0.222202 | −0.111101 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111101 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(744\) | 536.193 | 0.0264218 | ||||||||
\(745\) | −2593.03 | −0.127518 | ||||||||
\(746\) | −10176.3 | −0.499438 | ||||||||
\(747\) | −31361.2 | −1.53608 | ||||||||
\(748\) | −1607.02 | −0.0785543 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −685.773 | −0.0333878 | ||||||||
\(751\) | 35080.2 | 1.70452 | 0.852261 | − | 0.523117i | \(-0.175231\pi\) | ||||
0.852261 | + | 0.523117i | \(0.175231\pi\) | |||||||
\(752\) | −1740.99 | −0.0844249 | ||||||||
\(753\) | −655.204 | −0.0317091 | ||||||||
\(754\) | 8580.50 | 0.414434 | ||||||||
\(755\) | 12160.7 | 0.586188 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10391.8 | −0.498938 | −0.249469 | − | 0.968383i | \(-0.580256\pi\) | ||||
−0.249469 | + | 0.968383i | \(0.580256\pi\) | |||||||
\(758\) | 5094.00 | 0.244093 | ||||||||
\(759\) | −55.4328 | −0.00265096 | ||||||||
\(760\) | 1264.03 | 0.0603306 | ||||||||
\(761\) | −11810.5 | −0.562590 | −0.281295 | − | 0.959621i | \(-0.590764\pi\) | ||||
−0.281295 | + | 0.959621i | \(0.590764\pi\) | |||||||
\(762\) | −177.510 | −0.00843899 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16825.5 | −0.796761 | ||||||||
\(765\) | 7049.28 | 0.333160 | ||||||||
\(766\) | 14112.2 | 0.665659 | ||||||||
\(767\) | 11773.1 | 0.554241 | ||||||||
\(768\) | −58.3675 | −0.00274239 | ||||||||
\(769\) | −35125.5 | −1.64715 | −0.823574 | − | 0.567209i | \(-0.808023\pi\) | ||||
−0.823574 | + | 0.567209i | \(0.808023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −846.369 | −0.0395347 | ||||||||
\(772\) | 12983.3 | 0.605282 | ||||||||
\(773\) | −20001.5 | −0.930665 | −0.465332 | − | 0.885136i | \(-0.654065\pi\) | ||||
−0.465332 | + | 0.885136i | \(0.654065\pi\) | |||||||
\(774\) | −16632.1 | −0.772388 | ||||||||
\(775\) | 16416.4 | 0.760895 | ||||||||
\(776\) | −1690.05 | −0.0781819 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9456.49 | 0.435773 | ||||||||
\(779\) | −1286.68 | −0.0591786 | ||||||||
\(780\) | 356.728 | 0.0163755 | ||||||||
\(781\) | 5051.99 | 0.231465 | ||||||||
\(782\) | −1197.59 | −0.0547646 | ||||||||
\(783\) | 1121.91 | 0.0512055 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.4569 | 0.00165758 | ||||||||
\(786\) | −122.347 | −0.00555214 | ||||||||
\(787\) | −13593.3 | −0.615690 | −0.307845 | − | 0.951437i | \(-0.599608\pi\) | ||||
−0.307845 | + | 0.951437i | \(0.599608\pi\) | |||||||
\(788\) | −6938.85 | −0.313688 | ||||||||
\(789\) | −287.970 | −0.0129937 | ||||||||
\(790\) | −15347.6 | −0.691195 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2753.44 | 0.123534 | ||||||||
\(793\) | 14943.0 | 0.669156 | ||||||||
\(794\) | −1481.67 | −0.0662250 | ||||||||
\(795\) | −1293.33 | −0.0576977 | ||||||||
\(796\) | −1523.17 | −0.0678232 | ||||||||
\(797\) | 6946.75 | 0.308741 | 0.154370 | − | 0.988013i | \(-0.450665\pi\) | ||||
0.154370 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3422.79 | −0.151552 | ||||||||
\(800\) | −1787.01 | −0.0789754 | ||||||||
\(801\) | 18463.1 | 0.814432 | ||||||||
\(802\) | 3759.17 | 0.165512 | ||||||||
\(803\) | 12453.3 | 0.547283 | ||||||||
\(804\) | −857.678 | −0.0376219 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27654.2 | −1.20853 | ||||||||
\(807\) | −1250.43 | −0.0545443 | ||||||||
\(808\) | 13628.4 | 0.593374 | ||||||||
\(809\) | 24987.2 | 1.08591 | 0.542955 | − | 0.839762i | \(-0.317305\pi\) | ||||
0.542955 | + | 0.839762i | \(0.317305\pi\) | |||||||
\(810\) | −12054.7 | −0.522914 | ||||||||
\(811\) | 23172.5 | 1.00332 | 0.501662 | − | 0.865064i | \(-0.332722\pi\) | ||||
0.501662 | + | 0.865064i | \(0.332722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −733.621 | −0.0316472 | ||||||||
\(814\) | −5507.70 | −0.237156 | ||||||||
\(815\) | 14784.9 | 0.635452 | ||||||||
\(816\) | −114.751 | −0.00492288 | ||||||||
\(817\) | −5863.32 | −0.251079 | ||||||||
\(818\) | 3430.91 | 0.146649 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2252.64 | −0.0959337 | ||||||||
\(821\) | 30703.8 | 1.30520 | 0.652600 | − | 0.757703i | \(-0.273678\pi\) | ||||
0.652600 | + | 0.757703i | \(0.273678\pi\) | |||||||
\(822\) | −1211.73 | −0.0514161 | ||||||||
\(823\) | −15940.1 | −0.675135 | −0.337568 | − | 0.941301i | \(-0.609604\pi\) | ||||
−0.337568 | + | 0.941301i | \(0.609604\pi\) | |||||||
\(824\) | 11148.2 | 0.471316 | ||||||||
\(825\) | −162.617 | −0.00686256 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6662.20 | −0.280130 | −0.140065 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140065 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(828\) | 2051.93 | 0.0861227 | ||||||||
\(829\) | 20606.0 | 0.863299 | 0.431649 | − | 0.902041i | \(-0.357932\pi\) | ||||
0.431649 | + | 0.902041i | \(0.357932\pi\) | |||||||
\(830\) | −19355.8 | −0.809458 | ||||||||
\(831\) | −1748.32 | −0.0729826 | ||||||||
\(832\) | 3010.31 | 0.125437 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1304.11 | −0.0541459 | ||||||||
\(835\) | 7426.73 | 0.307799 | ||||||||
\(836\) | 970.672 | 0.0401572 | ||||||||
\(837\) | −3615.82 | −0.149320 | ||||||||
\(838\) | −4994.31 | −0.205878 | ||||||||
\(839\) | 45717.9 | 1.88124 | 0.940618 | − | 0.339468i | \(-0.110247\pi\) | ||||
0.940618 | + | 0.339468i | \(0.110247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16069.4 | −0.658878 | ||||||||
\(842\) | 13165.0 | 0.538833 | ||||||||
\(843\) | −256.910 | −0.0104964 | ||||||||
\(844\) | 4041.75 | 0.164837 | ||||||||
\(845\) | −127.963 | −0.00520955 | ||||||||
\(846\) | 5864.54 | 0.238330 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10914.0 | −0.441967 | ||||||||
\(849\) | −342.597 | −0.0138491 | ||||||||
\(850\) | −3513.26 | −0.141769 | ||||||||
\(851\) | −4104.47 | −0.165334 | ||||||||
\(852\) | 360.741 | 0.0145056 | ||||||||
\(853\) | −17230.4 | −0.691626 | −0.345813 | − | 0.938303i | \(-0.612397\pi\) | ||||
−0.345813 | + | 0.938303i | \(0.612397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4257.90 | −0.170312 | ||||||||
\(856\) | 7263.97 | 0.290044 | ||||||||
\(857\) | −44484.4 | −1.77311 | −0.886557 | − | 0.462619i | \(-0.846910\pi\) | ||||
−0.886557 | + | 0.462619i | \(0.846910\pi\) | |||||||
\(858\) | 273.937 | 0.0108998 | ||||||||
\(859\) | 23213.4 | 0.922039 | 0.461019 | − | 0.887390i | \(-0.347484\pi\) | ||||
0.461019 | + | 0.887390i | \(0.347484\pi\) | |||||||
\(860\) | −10265.1 | −0.407022 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17751.4 | 0.701411 | ||||||||
\(863\) | −9640.68 | −0.380270 | −0.190135 | − | 0.981758i | \(-0.560893\pi\) | ||||
−0.190135 | + | 0.981758i | \(0.560893\pi\) | |||||||
\(864\) | 393.601 | 0.0154984 | ||||||||
\(865\) | −20395.5 | −0.801697 | ||||||||
\(866\) | 7273.79 | 0.285420 | ||||||||
\(867\) | 894.555 | 0.0350412 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11785.7 | −0.460072 | ||||||||
\(870\) | 345.882 | 0.0134787 | ||||||||
\(871\) | 44234.8 | 1.72082 | ||||||||
\(872\) | 6896.61 | 0.267831 | ||||||||
\(873\) | 5692.93 | 0.220706 | ||||||||
\(874\) | 723.369 | 0.0279958 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 889.237 | 0.0342974 | ||||||||
\(877\) | −9499.62 | −0.365769 | −0.182885 | − | 0.983134i | \(-0.558543\pi\) | ||||
−0.182885 | + | 0.983134i | \(0.558543\pi\) | |||||||
\(878\) | 21958.7 | 0.844044 | ||||||||
\(879\) | −103.129 | −0.00395729 | ||||||||
\(880\) | 1699.39 | 0.0650983 | ||||||||
\(881\) | 8252.54 | 0.315590 | 0.157795 | − | 0.987472i | \(-0.449561\pi\) | ||||
0.157795 | + | 0.987472i | \(0.449561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34768.9 | −1.32510 | −0.662552 | − | 0.749016i | \(-0.730526\pi\) | ||||
−0.662552 | + | 0.749016i | \(0.730526\pi\) | |||||||
\(884\) | 5918.26 | 0.225173 | ||||||||
\(885\) | 474.577 | 0.0180257 | ||||||||
\(886\) | 2600.33 | 0.0986000 | ||||||||
\(887\) | 3288.58 | 0.124487 | 0.0622433 | − | 0.998061i | \(-0.480175\pi\) | ||||
0.0622433 | + | 0.998061i | \(0.480175\pi\) | |||||||
\(888\) | −393.280 | −0.0148622 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11395.2 | 0.429177 | ||||||||
\(891\) | −9257.05 | −0.348061 | ||||||||
\(892\) | −13594.8 | −0.510301 | ||||||||
\(893\) | 2067.43 | 0.0774736 | ||||||||
\(894\) | −142.185 | −0.00531921 | ||||||||
\(895\) | 17171.0 | 0.641298 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 204.145 | 0.00759888 | ||||||||
\(898\) | −31750.4 | −1.17987 | ||||||||
\(899\) | −26813.4 | −0.994747 | ||||||||
\(900\) | 6019.55 | 0.222946 | ||||||||
\(901\) | −21456.9 | −0.793377 | ||||||||
\(902\) | −1729.84 | −0.0638552 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12021.8 | 0.442299 | ||||||||
\(905\) | −20944.2 | −0.769292 | ||||||||
\(906\) | 666.813 | 0.0244518 | ||||||||
\(907\) | 37686.1 | 1.37966 | 0.689828 | − | 0.723973i | \(-0.257686\pi\) | ||||
0.689828 | + | 0.723973i | \(0.257686\pi\) | |||||||
\(908\) | −23043.2 | −0.842197 | ||||||||
\(909\) | −45907.4 | −1.67508 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15090.9 | 0.548828 | 0.274414 | − | 0.961612i | \(-0.411516\pi\) | ||||
0.274414 | + | 0.961612i | \(0.411516\pi\) | |||||||
\(912\) | 69.3114 | 0.00251659 | ||||||||
\(913\) | −14863.7 | −0.538790 | ||||||||
\(914\) | 6231.32 | 0.225508 | ||||||||
\(915\) | 602.355 | 0.0217631 | ||||||||
\(916\) | 8715.98 | 0.314393 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 773.820 | 0.0278212 | ||||||||
\(919\) | 43617.4 | 1.56562 | 0.782810 | − | 0.622261i | \(-0.213786\pi\) | ||||
0.782810 | + | 0.622261i | \(0.213786\pi\) | |||||||
\(920\) | 1266.43 | 0.0453836 | ||||||||
\(921\) | −532.024 | −0.0190345 | ||||||||
\(922\) | −26959.4 | −0.962972 | ||||||||
\(923\) | −18605.2 | −0.663486 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12040.9 | −0.428002 | ||||||||
\(926\) | 15892.4 | 0.563991 | ||||||||
\(927\) | −37552.6 | −1.33052 | ||||||||
\(928\) | 2918.79 | 0.103248 | ||||||||
\(929\) | −32446.2 | −1.14588 | −0.572942 | − | 0.819596i | \(-0.694198\pi\) | ||||
−0.572942 | + | 0.819596i | \(0.694198\pi\) | |||||||
\(930\) | −1114.75 | −0.0393054 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −11234.0 | −0.394830 | ||||||||
\(933\) | 2388.53 | 0.0838123 | ||||||||
\(934\) | 18296.7 | 0.640993 | ||||||||
\(935\) | 3341.01 | 0.116858 | ||||||||
\(936\) | −10140.2 | −0.354106 | ||||||||
\(937\) | 28355.4 | 0.988614 | 0.494307 | − | 0.869287i | \(-0.335422\pi\) | ||||
0.494307 | + | 0.869287i | \(0.335422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 948.548 | 0.0329656 | ||||||||
\(940\) | 3619.53 | 0.125592 | ||||||||
\(941\) | 48970.8 | 1.69650 | 0.848248 | − | 0.529599i | \(-0.177658\pi\) | ||||
0.848248 | + | 0.529599i | \(0.177658\pi\) | |||||||
\(942\) | 1.99906 | 6.91433e−5 0 | ||||||||
\(943\) | −1289.12 | −0.0445170 | ||||||||
\(944\) | 4004.80 | 0.138078 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7882.78 | −0.270921 | ||||||||
\(947\) | −9198.84 | −0.315652 | −0.157826 | − | 0.987467i | \(-0.550448\pi\) | ||||
−0.157826 | + | 0.987467i | \(0.550448\pi\) | |||||||
\(948\) | −841.565 | −0.0288320 | ||||||||
\(949\) | −45862.4 | −1.56876 | ||||||||
\(950\) | 2122.07 | 0.0724728 | ||||||||
\(951\) | 1711.94 | 0.0583737 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28428.9 | 0.966321 | 0.483160 | − | 0.875532i | \(-0.339489\pi\) | ||||
0.483160 | + | 0.875532i | \(0.339489\pi\) | |||||||
\(954\) | 36763.8 | 1.24766 | ||||||||
\(955\) | 34980.3 | 1.18527 | ||||||||
\(956\) | 25142.7 | 0.850599 | ||||||||
\(957\) | 265.609 | 0.00897170 | ||||||||
\(958\) | −15329.3 | −0.516980 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 121.346 | 0.00407961 | ||||||||
\(961\) | 56626.2 | 1.90078 | ||||||||
\(962\) | 20283.4 | 0.679797 | ||||||||
\(963\) | −24468.7 | −0.818788 | ||||||||
\(964\) | −4516.90 | −0.150912 | ||||||||
\(965\) | −26992.2 | −0.900426 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22315.5 | −0.742109 | −0.371054 | − | 0.928611i | \(-0.621004\pi\) | ||||
−0.371054 | + | 0.928611i | \(0.621004\pi\) | |||||||
\(968\) | −9343.01 | −0.310223 | ||||||||
\(969\) | 136.266 | 0.00451755 | ||||||||
\(970\) | 3513.61 | 0.116304 | ||||||||
\(971\) | −208.410 | −0.00688795 | −0.00344398 | − | 0.999994i | \(-0.501096\pi\) | ||||
−0.00344398 | + | 0.999994i | \(0.501096\pi\) | |||||||
\(972\) | −1989.41 | −0.0656485 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10694.4 | −0.351819 | ||||||||
\(975\) | 598.879 | 0.0196712 | ||||||||
\(976\) | 5083.08 | 0.166706 | ||||||||
\(977\) | 35744.3 | 1.17048 | 0.585241 | − | 0.810860i | \(-0.301000\pi\) | ||||
0.585241 | + | 0.810860i | \(0.301000\pi\) | |||||||
\(978\) | 810.710 | 0.0265068 | ||||||||
\(979\) | 8750.56 | 0.285668 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23231.3 | −0.756082 | ||||||||
\(982\) | 27294.3 | 0.886963 | ||||||||
\(983\) | 36175.5 | 1.17377 | 0.586887 | − | 0.809669i | \(-0.300353\pi\) | ||||
0.586887 | + | 0.809669i | \(0.300353\pi\) | |||||||
\(984\) | −123.520 | −0.00400171 | ||||||||
\(985\) | 14425.9 | 0.466647 | ||||||||
\(986\) | 5738.33 | 0.185340 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3574.74 | −0.115109 | ||||||||
\(989\) | −5874.44 | −0.188874 | ||||||||
\(990\) | −5724.41 | −0.183771 | ||||||||
\(991\) | 34654.3 | 1.11083 | 0.555413 | − | 0.831575i | \(-0.312560\pi\) | ||||
0.555413 | + | 0.831575i | \(0.312560\pi\) | |||||||
\(992\) | −9406.98 | −0.301081 | ||||||||
\(993\) | −2368.17 | −0.0756812 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3166.67 | 0.100895 | ||||||||
\(996\) | −1061.35 | −0.0337652 | ||||||||
\(997\) | −4756.72 | −0.151100 | −0.0755501 | − | 0.997142i | \(-0.524071\pi\) | ||||
−0.0755501 | + | 0.997142i | \(0.524071\pi\) | |||||||
\(998\) | −38703.3 | −1.22759 | ||||||||
\(999\) | 2652.09 | 0.0839923 |
(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 | 1862.4.a.e.1.2 | 2 | ||
7.6 | odd | 2 | 38.4.a.c.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 342.4.a.h.1.1 | 2 | |||
28.27 | even | 2 | 304.4.a.c.1.2 | 2 | |||
35.13 | even | 4 | 950.4.b.i.799.1 | 4 | |||
35.27 | even | 4 | 950.4.b.i.799.4 | 4 | |||
35.34 | odd | 2 | 950.4.a.e.1.2 | 2 | |||
56.13 | odd | 2 | 1216.4.a.g.1.2 | 2 | |||
56.27 | even | 2 | 1216.4.a.p.1.1 | 2 | |||
133.132 | even | 2 | 722.4.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.a.c.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
304.4.a.c.1.2 | 2 | 28.27 | even | 2 | |||
342.4.a.h.1.1 | 2 | 21.20 | even | 2 | |||
722.4.a.f.1.2 | 2 | 133.132 | even | 2 | |||
950.4.a.e.1.2 | 2 | 35.34 | odd | 2 | |||
950.4.b.i.799.1 | 4 | 35.13 | even | 4 | |||
950.4.b.i.799.4 | 4 | 35.27 | even | 4 | |||
1216.4.a.g.1.2 | 2 | 56.13 | odd | 2 | |||
1216.4.a.p.1.1 | 2 | 56.27 | even | 2 | |||
1862.4.a.e.1.2 | 2 | 1.1 | even | 1 | trivial |