Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.41421 | −1.56066 | −0.780330 | − | 0.625368i | \(-0.784949\pi\) | ||||
−0.780330 | + | 0.625368i | \(0.784949\pi\) | |||||||
\(3\) | −3.24264 | −0.624046 | −0.312023 | − | 0.950074i | \(-0.601007\pi\) | ||||
−0.312023 | + | 0.950074i | \(0.601007\pi\) | |||||||
\(4\) | 11.4853 | 1.43566 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 14.3137 | 0.973925 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −15.3848 | −0.679917 | ||||||||
\(9\) | −16.4853 | −0.610566 | ||||||||
\(10\) | 22.0711 | 0.697948 | ||||||||
\(11\) | −0.142136 | −0.00389595 | −0.00194798 | − | 0.999998i | \(-0.500620\pi\) | ||||
−0.00194798 | + | 0.999998i | \(0.500620\pi\) | |||||||
\(12\) | −37.2426 | −0.895919 | ||||||||
\(13\) | 32.1421 | 0.685740 | 0.342870 | − | 0.939383i | \(-0.388601\pi\) | ||||
0.342870 | + | 0.939383i | \(0.388601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.2132 | 0.279082 | ||||||||
\(16\) | −23.9706 | −0.374540 | ||||||||
\(17\) | 114.368 | 1.63166 | 0.815829 | − | 0.578293i | \(-0.196281\pi\) | ||||
0.815829 | + | 0.578293i | \(0.196281\pi\) | |||||||
\(18\) | 72.7696 | 0.952886 | ||||||||
\(19\) | −43.2304 | −0.521987 | −0.260993 | − | 0.965341i | \(-0.584050\pi\) | ||||
−0.260993 | + | 0.965341i | \(0.584050\pi\) | |||||||
\(20\) | −57.4264 | −0.642047 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.627417 | 0.00608026 | ||||||||
\(23\) | 154.463 | 1.40034 | 0.700169 | − | 0.713977i | \(-0.253108\pi\) | ||||
0.700169 | + | 0.713977i | \(0.253108\pi\) | |||||||
\(24\) | 49.8873 | 0.424300 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −141.882 | −1.07021 | ||||||||
\(27\) | 141.007 | 1.00507 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −40.1472 | −0.257074 | −0.128537 | − | 0.991705i | \(-0.541028\pi\) | ||||
−0.128537 | + | 0.991705i | \(0.541028\pi\) | |||||||
\(30\) | −71.5685 | −0.435552 | ||||||||
\(31\) | −75.4214 | −0.436970 | −0.218485 | − | 0.975840i | \(-0.570112\pi\) | ||||
−0.218485 | + | 0.975840i | \(0.570112\pi\) | |||||||
\(32\) | 228.889 | 1.26445 | ||||||||
\(33\) | 0.460895 | 0.00243126 | ||||||||
\(34\) | −504.843 | −2.54647 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −189.338 | −0.876565 | ||||||||
\(37\) | −400.333 | −1.77877 | −0.889383 | − | 0.457163i | \(-0.848866\pi\) | ||||
−0.889383 | + | 0.457163i | \(0.848866\pi\) | |||||||
\(38\) | 190.828 | 0.814644 | ||||||||
\(39\) | −104.225 | −0.427934 | ||||||||
\(40\) | 76.9239 | 0.304068 | ||||||||
\(41\) | 95.4264 | 0.363490 | 0.181745 | − | 0.983346i | \(-0.441825\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −340.071 | −1.20605 | −0.603027 | − | 0.797721i | \(-0.706039\pi\) | ||||
−0.603027 | + | 0.797721i | \(0.706039\pi\) | |||||||
\(44\) | −1.63247 | −0.00559327 | ||||||||
\(45\) | 82.4264 | 0.273053 | ||||||||
\(46\) | −681.833 | −2.18545 | ||||||||
\(47\) | 7.49033 | 0.0232463 | 0.0116232 | − | 0.999932i | \(-0.496300\pi\) | ||||
0.0116232 | + | 0.999932i | \(0.496300\pi\) | |||||||
\(48\) | 77.7279 | 0.233730 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −110.355 | −0.312132 | ||||||||
\(51\) | −370.853 | −1.01823 | ||||||||
\(52\) | 369.161 | 0.984490 | ||||||||
\(53\) | −676.818 | −1.75412 | −0.877058 | − | 0.480385i | \(-0.840497\pi\) | ||||
−0.877058 | + | 0.480385i | \(0.840497\pi\) | |||||||
\(54\) | −622.436 | −1.56857 | ||||||||
\(55\) | 0.710678 | 0.00174232 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 140.181 | 0.325744 | ||||||||
\(58\) | 177.218 | 0.401205 | ||||||||
\(59\) | −796.181 | −1.75685 | −0.878423 | − | 0.477884i | \(-0.841404\pi\) | ||||
−0.878423 | + | 0.477884i | \(0.841404\pi\) | |||||||
\(60\) | 186.213 | 0.400667 | ||||||||
\(61\) | 757.102 | 1.58913 | 0.794565 | − | 0.607179i | \(-0.207699\pi\) | ||||
0.794565 | + | 0.607179i | \(0.207699\pi\) | |||||||
\(62\) | 332.926 | 0.681962 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −818.602 | −1.59883 | ||||||||
\(65\) | −160.711 | −0.306672 | ||||||||
\(66\) | −2.03449 | −0.00379437 | ||||||||
\(67\) | −740.581 | −1.35039 | −0.675197 | − | 0.737638i | \(-0.735941\pi\) | ||||
−0.675197 | + | 0.737638i | \(0.735941\pi\) | |||||||
\(68\) | 1313.54 | 2.34251 | ||||||||
\(69\) | −500.868 | −0.873876 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37.0253 | 0.0618886 | 0.0309443 | − | 0.999521i | \(-0.490149\pi\) | ||||
0.0309443 | + | 0.999521i | \(0.490149\pi\) | |||||||
\(72\) | 253.622 | 0.415134 | ||||||||
\(73\) | −80.8772 | −0.129671 | −0.0648353 | − | 0.997896i | \(-0.520652\pi\) | ||||
−0.0648353 | + | 0.997896i | \(0.520652\pi\) | |||||||
\(74\) | 1767.16 | 2.77605 | ||||||||
\(75\) | −81.0660 | −0.124809 | ||||||||
\(76\) | −496.514 | −0.749395 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 460.073 | 0.667859 | ||||||||
\(79\) | −317.358 | −0.451970 | −0.225985 | − | 0.974131i | \(-0.572560\pi\) | ||||
−0.225985 | + | 0.974131i | \(0.572560\pi\) | |||||||
\(80\) | 119.853 | 0.167499 | ||||||||
\(81\) | −12.1329 | −0.0166432 | ||||||||
\(82\) | −421.233 | −0.567285 | ||||||||
\(83\) | 945.929 | 1.25095 | 0.625477 | − | 0.780243i | \(-0.284904\pi\) | ||||
0.625477 | + | 0.780243i | \(0.284904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −571.838 | −0.729700 | ||||||||
\(86\) | 1501.15 | 1.88224 | ||||||||
\(87\) | 130.183 | 0.160426 | ||||||||
\(88\) | 2.18672 | 0.00264893 | ||||||||
\(89\) | −783.205 | −0.932804 | −0.466402 | − | 0.884573i | \(-0.654450\pi\) | ||||
−0.466402 | + | 0.884573i | \(0.654450\pi\) | |||||||
\(90\) | −363.848 | −0.426144 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1774.05 | 2.01041 | ||||||||
\(93\) | 244.564 | 0.272690 | ||||||||
\(94\) | −33.0639 | −0.0362796 | ||||||||
\(95\) | 216.152 | 0.233439 | ||||||||
\(96\) | −742.206 | −0.789074 | ||||||||
\(97\) | −393.107 | −0.411484 | −0.205742 | − | 0.978606i | \(-0.565961\pi\) | ||||
−0.205742 | + | 0.978606i | \(0.565961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.34315 | 0.00237874 | ||||||||
\(100\) | 287.132 | 0.287132 | ||||||||
\(101\) | −454.442 | −0.447709 | −0.223855 | − | 0.974623i | \(-0.571864\pi\) | ||||
−0.223855 | + | 0.974623i | \(0.571864\pi\) | |||||||
\(102\) | 1637.02 | 1.58911 | ||||||||
\(103\) | 703.699 | 0.673180 | 0.336590 | − | 0.941651i | \(-0.390726\pi\) | ||||
0.336590 | + | 0.941651i | \(0.390726\pi\) | |||||||
\(104\) | −494.500 | −0.466247 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2987.62 | 2.73758 | ||||||||
\(107\) | 954.997 | 0.862832 | 0.431416 | − | 0.902153i | \(-0.358014\pi\) | ||||
0.431416 | + | 0.902153i | \(0.358014\pi\) | |||||||
\(108\) | 1619.51 | 1.44294 | ||||||||
\(109\) | 288.927 | 0.253891 | 0.126946 | − | 0.991910i | \(-0.459483\pi\) | ||||
0.126946 | + | 0.991910i | \(0.459483\pi\) | |||||||
\(110\) | −3.13708 | −0.00271918 | ||||||||
\(111\) | 1298.14 | 1.11003 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1251.24 | 1.04165 | 0.520826 | − | 0.853663i | \(-0.325624\pi\) | ||||
0.520826 | + | 0.853663i | \(0.325624\pi\) | |||||||
\(114\) | −618.788 | −0.508376 | ||||||||
\(115\) | −772.315 | −0.626250 | ||||||||
\(116\) | −461.102 | −0.369071 | ||||||||
\(117\) | −529.872 | −0.418690 | ||||||||
\(118\) | 3514.51 | 2.74184 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −249.437 | −0.189753 | ||||||||
\(121\) | −1330.98 | −0.999985 | ||||||||
\(122\) | −3342.01 | −2.48009 | ||||||||
\(123\) | −309.434 | −0.226835 | ||||||||
\(124\) | −866.235 | −0.627341 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1947.62 | −1.36082 | −0.680408 | − | 0.732833i | \(-0.738198\pi\) | ||||
−0.680408 | + | 0.732833i | \(0.738198\pi\) | |||||||
\(128\) | 1782.37 | 1.23079 | ||||||||
\(129\) | 1102.73 | 0.752634 | ||||||||
\(130\) | 709.411 | 0.478611 | ||||||||
\(131\) | −1061.65 | −0.708064 | −0.354032 | − | 0.935233i | \(-0.615190\pi\) | ||||
−0.354032 | + | 0.935233i | \(0.615190\pi\) | |||||||
\(132\) | 5.29351 | 0.00349046 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3269.08 | 2.10750 | ||||||||
\(135\) | −705.036 | −0.449480 | ||||||||
\(136\) | −1759.52 | −1.10939 | ||||||||
\(137\) | −1439.34 | −0.897601 | −0.448800 | − | 0.893632i | \(-0.648149\pi\) | ||||
−0.448800 | + | 0.893632i | \(0.648149\pi\) | |||||||
\(138\) | 2210.94 | 1.36382 | ||||||||
\(139\) | −662.132 | −0.404038 | −0.202019 | − | 0.979382i | \(-0.564750\pi\) | ||||
−0.202019 | + | 0.979382i | \(0.564750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.2885 | −0.0145068 | ||||||||
\(142\) | −163.437 | −0.0965870 | ||||||||
\(143\) | −4.56854 | −0.00267161 | ||||||||
\(144\) | 395.161 | 0.228681 | ||||||||
\(145\) | 200.736 | 0.114967 | ||||||||
\(146\) | 357.009 | 0.202372 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4597.94 | −2.55370 | ||||||||
\(149\) | −787.110 | −0.432769 | −0.216384 | − | 0.976308i | \(-0.569426\pi\) | ||||
−0.216384 | + | 0.976308i | \(0.569426\pi\) | |||||||
\(150\) | 357.843 | 0.194785 | ||||||||
\(151\) | −848.355 | −0.457206 | −0.228603 | − | 0.973520i | \(-0.573416\pi\) | ||||
−0.228603 | + | 0.973520i | \(0.573416\pi\) | |||||||
\(152\) | 665.091 | 0.354908 | ||||||||
\(153\) | −1885.38 | −0.996235 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 377.107 | 0.195419 | ||||||||
\(156\) | −1197.06 | −0.614368 | ||||||||
\(157\) | −954.922 | −0.485421 | −0.242710 | − | 0.970099i | \(-0.578036\pi\) | ||||
−0.242710 | + | 0.970099i | \(0.578036\pi\) | |||||||
\(158\) | 1400.89 | 0.705371 | ||||||||
\(159\) | 2194.68 | 1.09465 | ||||||||
\(160\) | −1144.45 | −0.565478 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 53.5572 | 0.0259744 | ||||||||
\(163\) | −7.36421 | −0.00353871 | −0.00176936 | − | 0.999998i | \(-0.500563\pi\) | ||||
−0.00176936 | + | 0.999998i | \(0.500563\pi\) | |||||||
\(164\) | 1096.00 | 0.521848 | ||||||||
\(165\) | −2.30447 | −0.00108729 | ||||||||
\(166\) | −4175.53 | −1.95231 | ||||||||
\(167\) | −2921.40 | −1.35368 | −0.676841 | − | 0.736129i | \(-0.736651\pi\) | ||||
−0.676841 | + | 0.736129i | \(0.736651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1163.88 | −0.529760 | ||||||||
\(170\) | 2524.21 | 1.13881 | ||||||||
\(171\) | 712.666 | 0.318707 | ||||||||
\(172\) | −3905.81 | −1.73148 | ||||||||
\(173\) | 3969.57 | 1.74451 | 0.872256 | − | 0.489049i | \(-0.162656\pi\) | ||||
0.872256 | + | 0.489049i | \(0.162656\pi\) | |||||||
\(174\) | −574.655 | −0.250371 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.40707 | 0.00145919 | ||||||||
\(177\) | 2581.73 | 1.09635 | ||||||||
\(178\) | 3457.23 | 1.45579 | ||||||||
\(179\) | −1105.95 | −0.461803 | −0.230901 | − | 0.972977i | \(-0.574167\pi\) | ||||
−0.230901 | + | 0.972977i | \(0.574167\pi\) | |||||||
\(180\) | 946.690 | 0.392012 | ||||||||
\(181\) | 117.214 | 0.0481349 | 0.0240674 | − | 0.999710i | \(-0.492338\pi\) | ||||
0.0240674 | + | 0.999710i | \(0.492338\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2455.01 | −0.991691 | ||||||||
\(184\) | −2376.38 | −0.952114 | ||||||||
\(185\) | 2001.67 | 0.795488 | ||||||||
\(186\) | −1079.56 | −0.425576 | ||||||||
\(187\) | −16.2557 | −0.00635687 | ||||||||
\(188\) | 86.0286 | 0.0333738 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −954.142 | −0.364320 | ||||||||
\(191\) | 1002.60 | 0.379820 | 0.189910 | − | 0.981802i | \(-0.439180\pi\) | ||||
0.189910 | + | 0.981802i | \(0.439180\pi\) | |||||||
\(192\) | 2654.43 | 0.997746 | ||||||||
\(193\) | 3257.76 | 1.21502 | 0.607510 | − | 0.794312i | \(-0.292169\pi\) | ||||
0.607510 | + | 0.794312i | \(0.292169\pi\) | |||||||
\(194\) | 1735.26 | 0.642187 | ||||||||
\(195\) | 521.127 | 0.191378 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −41.6955 | −0.0150796 | −0.00753981 | − | 0.999972i | \(-0.502400\pi\) | ||||
−0.00753981 | + | 0.999972i | \(0.502400\pi\) | |||||||
\(198\) | −10.3431 | −0.00371240 | ||||||||
\(199\) | −2405.61 | −0.856932 | −0.428466 | − | 0.903558i | \(-0.640946\pi\) | ||||
−0.428466 | + | 0.903558i | \(0.640946\pi\) | |||||||
\(200\) | −384.619 | −0.135983 | ||||||||
\(201\) | 2401.44 | 0.842708 | ||||||||
\(202\) | 2006.00 | 0.698722 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4259.35 | −1.46183 | ||||||||
\(205\) | −477.132 | −0.162558 | ||||||||
\(206\) | −3106.28 | −1.05061 | ||||||||
\(207\) | −2546.37 | −0.854998 | ||||||||
\(208\) | −770.465 | −0.256837 | ||||||||
\(209\) | 6.14459 | 0.00203364 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1211.24 | 0.395190 | 0.197595 | − | 0.980284i | \(-0.436687\pi\) | ||||
0.197595 | + | 0.980284i | \(0.436687\pi\) | |||||||
\(212\) | −7773.45 | −2.51831 | ||||||||
\(213\) | −120.060 | −0.0386214 | ||||||||
\(214\) | −4215.56 | −1.34659 | ||||||||
\(215\) | 1700.36 | 0.539364 | ||||||||
\(216\) | −2169.36 | −0.683363 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1275.38 | −0.396238 | ||||||||
\(219\) | 262.256 | 0.0809205 | ||||||||
\(220\) | 8.16234 | 0.00250139 | ||||||||
\(221\) | 3676.02 | 1.11889 | ||||||||
\(222\) | −5730.25 | −1.73238 | ||||||||
\(223\) | −4164.99 | −1.25071 | −0.625354 | − | 0.780341i | \(-0.715046\pi\) | ||||
−0.625354 | + | 0.780341i | \(0.715046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −412.132 | −0.122113 | ||||||||
\(226\) | −5523.24 | −1.62566 | ||||||||
\(227\) | −2356.24 | −0.688940 | −0.344470 | − | 0.938797i | \(-0.611941\pi\) | ||||
−0.344470 | + | 0.938797i | \(0.611941\pi\) | |||||||
\(228\) | 1610.02 | 0.467658 | ||||||||
\(229\) | −4345.16 | −1.25387 | −0.626935 | − | 0.779071i | \(-0.715691\pi\) | ||||
−0.626935 | + | 0.779071i | \(0.715691\pi\) | |||||||
\(230\) | 3409.16 | 0.977363 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 617.655 | 0.174789 | ||||||||
\(233\) | 2458.25 | 0.691182 | 0.345591 | − | 0.938385i | \(-0.387679\pi\) | ||||
0.345591 | + | 0.938385i | \(0.387679\pi\) | |||||||
\(234\) | 2338.97 | 0.653432 | ||||||||
\(235\) | −37.4517 | −0.0103961 | ||||||||
\(236\) | −9144.36 | −2.52223 | ||||||||
\(237\) | 1029.08 | 0.282050 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 322.304 | 0.0872307 | 0.0436154 | − | 0.999048i | \(-0.486112\pi\) | ||||
0.0436154 | + | 0.999048i | \(0.486112\pi\) | |||||||
\(240\) | −388.640 | −0.104527 | ||||||||
\(241\) | 5011.24 | 1.33943 | 0.669714 | − | 0.742619i | \(-0.266417\pi\) | ||||
0.669714 | + | 0.742619i | \(0.266417\pi\) | |||||||
\(242\) | 5875.23 | 1.56064 | ||||||||
\(243\) | −3767.85 | −0.994682 | ||||||||
\(244\) | 8695.53 | 2.28145 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1365.91 | 0.354012 | ||||||||
\(247\) | −1389.52 | −0.357947 | ||||||||
\(248\) | 1160.34 | 0.297104 | ||||||||
\(249\) | −3067.31 | −0.780654 | ||||||||
\(250\) | 551.777 | 0.139590 | ||||||||
\(251\) | −3936.95 | −0.990031 | −0.495015 | − | 0.868884i | \(-0.664838\pi\) | ||||
−0.495015 | + | 0.868884i | \(0.664838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.9547 | −0.00545565 | ||||||||
\(254\) | 8597.23 | 2.12377 | ||||||||
\(255\) | 1854.26 | 0.455367 | ||||||||
\(256\) | −1318.94 | −0.322008 | ||||||||
\(257\) | 3626.16 | 0.880131 | 0.440066 | − | 0.897966i | \(-0.354955\pi\) | ||||
0.440066 | + | 0.897966i | \(0.354955\pi\) | |||||||
\(258\) | −4867.68 | −1.17461 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1845.81 | −0.440277 | ||||||||
\(261\) | 661.838 | 0.156961 | ||||||||
\(262\) | 4686.33 | 1.10505 | ||||||||
\(263\) | −786.555 | −0.184415 | −0.0922074 | − | 0.995740i | \(-0.529392\pi\) | ||||
−0.0922074 | + | 0.995740i | \(0.529392\pi\) | |||||||
\(264\) | −7.09076 | −0.00165305 | ||||||||
\(265\) | 3384.09 | 0.784465 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2539.65 | 0.582113 | ||||||||
\(268\) | −8505.78 | −1.93871 | ||||||||
\(269\) | −4057.94 | −0.919766 | −0.459883 | − | 0.887979i | \(-0.652109\pi\) | ||||
−0.459883 | + | 0.887979i | \(0.652109\pi\) | |||||||
\(270\) | 3112.18 | 0.701486 | ||||||||
\(271\) | −2899.42 | −0.649916 | −0.324958 | − | 0.945728i | \(-0.605350\pi\) | ||||
−0.324958 | + | 0.945728i | \(0.605350\pi\) | |||||||
\(272\) | −2741.45 | −0.611122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6353.56 | 1.40085 | ||||||||
\(275\) | −3.55339 | −0.000779191 0 | ||||||||
\(276\) | −5752.61 | −1.25459 | ||||||||
\(277\) | 5293.96 | 1.14831 | 0.574157 | − | 0.818745i | \(-0.305330\pi\) | ||||
0.574157 | + | 0.818745i | \(0.305330\pi\) | |||||||
\(278\) | 2922.79 | 0.630566 | ||||||||
\(279\) | 1243.34 | 0.266799 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2359.40 | 0.500890 | 0.250445 | − | 0.968131i | \(-0.419423\pi\) | ||||
0.250445 | + | 0.968131i | \(0.419423\pi\) | |||||||
\(282\) | 107.214 | 0.0226402 | ||||||||
\(283\) | 2881.35 | 0.605224 | 0.302612 | − | 0.953114i | \(-0.402141\pi\) | ||||
0.302612 | + | 0.953114i | \(0.402141\pi\) | |||||||
\(284\) | 425.245 | 0.0888510 | ||||||||
\(285\) | −700.904 | −0.145677 | ||||||||
\(286\) | 20.1665 | 0.00416948 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3773.31 | −0.772028 | ||||||||
\(289\) | 8166.93 | 1.66231 | ||||||||
\(290\) | −886.091 | −0.179424 | ||||||||
\(291\) | 1274.70 | 0.256785 | ||||||||
\(292\) | −928.897 | −0.186163 | ||||||||
\(293\) | −760.730 | −0.151680 | −0.0758402 | − | 0.997120i | \(-0.524164\pi\) | ||||
−0.0758402 | + | 0.997120i | \(0.524164\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3980.90 | 0.785685 | ||||||||
\(296\) | 6159.03 | 1.20941 | ||||||||
\(297\) | −20.0421 | −0.00391570 | ||||||||
\(298\) | 3474.47 | 0.675405 | ||||||||
\(299\) | 4964.77 | 0.960268 | ||||||||
\(300\) | −931.066 | −0.179184 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3744.82 | 0.713544 | ||||||||
\(303\) | 1473.59 | 0.279391 | ||||||||
\(304\) | 1036.26 | 0.195505 | ||||||||
\(305\) | −3785.51 | −0.710681 | ||||||||
\(306\) | 8322.47 | 1.55478 | ||||||||
\(307\) | 4968.57 | 0.923685 | 0.461842 | − | 0.886962i | \(-0.347189\pi\) | ||||
0.461842 | + | 0.886962i | \(0.347189\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2281.84 | −0.420096 | ||||||||
\(310\) | −1664.63 | −0.304983 | ||||||||
\(311\) | 5033.96 | 0.917845 | 0.458922 | − | 0.888476i | \(-0.348236\pi\) | ||||
0.458922 | + | 0.888476i | \(0.348236\pi\) | |||||||
\(312\) | 1603.48 | 0.290960 | ||||||||
\(313\) | −3599.20 | −0.649965 | −0.324983 | − | 0.945720i | \(-0.605358\pi\) | ||||
−0.324983 | + | 0.945720i | \(0.605358\pi\) | |||||||
\(314\) | 4215.23 | 0.757577 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3644.95 | −0.648875 | ||||||||
\(317\) | 3541.56 | 0.627488 | 0.313744 | − | 0.949508i | \(-0.398417\pi\) | ||||
0.313744 | + | 0.949508i | \(0.398417\pi\) | |||||||
\(318\) | −9687.78 | −1.70838 | ||||||||
\(319\) | 5.70635 | 0.00100155 | ||||||||
\(320\) | 4093.01 | 0.715020 | ||||||||
\(321\) | −3096.71 | −0.538447 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4944.16 | −0.851704 | ||||||||
\(324\) | −139.350 | −0.0238940 | ||||||||
\(325\) | 803.553 | 0.137148 | ||||||||
\(326\) | 32.5072 | 0.00552272 | ||||||||
\(327\) | −936.886 | −0.158440 | ||||||||
\(328\) | −1468.11 | −0.247143 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 10.1724 | 0.00169689 | ||||||||
\(331\) | −7357.96 | −1.22184 | −0.610922 | − | 0.791691i | \(-0.709201\pi\) | ||||
−0.610922 | + | 0.791691i | \(0.709201\pi\) | |||||||
\(332\) | 10864.3 | 1.79594 | ||||||||
\(333\) | 6599.60 | 1.08605 | ||||||||
\(334\) | 12895.7 | 2.11264 | ||||||||
\(335\) | 3702.90 | 0.603914 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2323.24 | −0.375534 | −0.187767 | − | 0.982214i | \(-0.560125\pi\) | ||||
−0.187767 | + | 0.982214i | \(0.560125\pi\) | |||||||
\(338\) | 5137.63 | 0.826776 | ||||||||
\(339\) | −4057.32 | −0.650039 | ||||||||
\(340\) | −6567.72 | −1.04760 | ||||||||
\(341\) | 10.7201 | 0.00170242 | ||||||||
\(342\) | −3145.86 | −0.497394 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5231.92 | 0.820018 | ||||||||
\(345\) | 2504.34 | 0.390809 | ||||||||
\(346\) | −17522.5 | −2.72259 | ||||||||
\(347\) | −5447.79 | −0.842803 | −0.421401 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421401 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(348\) | 1495.19 | 0.230317 | ||||||||
\(349\) | 1227.84 | 0.188324 | 0.0941618 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941618 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4532.27 | 0.689216 | ||||||||
\(352\) | −32.5333 | −0.00492623 | ||||||||
\(353\) | −1981.86 | −0.298821 | −0.149411 | − | 0.988775i | \(-0.547738\pi\) | ||||
−0.149411 | + | 0.988775i | \(0.547738\pi\) | |||||||
\(354\) | −11396.3 | −1.71104 | ||||||||
\(355\) | −185.126 | −0.0276774 | ||||||||
\(356\) | −8995.33 | −1.33919 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4881.90 | 0.720717 | ||||||||
\(359\) | −12218.1 | −1.79622 | −0.898112 | − | 0.439768i | \(-0.855061\pi\) | ||||
−0.898112 | + | 0.439768i | \(0.855061\pi\) | |||||||
\(360\) | −1268.11 | −0.185654 | ||||||||
\(361\) | −4990.13 | −0.727530 | ||||||||
\(362\) | −517.406 | −0.0751222 | ||||||||
\(363\) | 4315.89 | 0.624037 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 404.386 | 0.0579905 | ||||||||
\(366\) | 10836.9 | 1.54769 | ||||||||
\(367\) | −13647.7 | −1.94115 | −0.970577 | − | 0.240789i | \(-0.922594\pi\) | ||||
−0.970577 | + | 0.240789i | \(0.922594\pi\) | |||||||
\(368\) | −3702.56 | −0.524482 | ||||||||
\(369\) | −1573.13 | −0.221935 | ||||||||
\(370\) | −8835.78 | −1.24149 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2808.89 | 0.391490 | ||||||||
\(373\) | −5544.03 | −0.769594 | −0.384797 | − | 0.923001i | \(-0.625729\pi\) | ||||
−0.384797 | + | 0.923001i | \(0.625729\pi\) | |||||||
\(374\) | 71.7561 | 0.00992091 | ||||||||
\(375\) | 405.330 | 0.0558164 | ||||||||
\(376\) | −115.237 | −0.0158056 | ||||||||
\(377\) | −1290.42 | −0.176286 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −634.243 | −0.0859601 | −0.0429801 | − | 0.999076i | \(-0.513685\pi\) | ||||
−0.0429801 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(380\) | 2482.57 | 0.335140 | ||||||||
\(381\) | 6315.45 | 0.849213 | ||||||||
\(382\) | −4425.69 | −0.592769 | ||||||||
\(383\) | −5790.93 | −0.772592 | −0.386296 | − | 0.922375i | \(-0.626246\pi\) | ||||
−0.386296 | + | 0.922375i | \(0.626246\pi\) | |||||||
\(384\) | −5779.58 | −0.768068 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14380.5 | −1.89623 | ||||||||
\(387\) | 5606.17 | 0.736376 | ||||||||
\(388\) | −4514.94 | −0.590751 | ||||||||
\(389\) | 1516.99 | 0.197724 | 0.0988619 | − | 0.995101i | \(-0.468480\pi\) | ||||
0.0988619 | + | 0.995101i | \(0.468480\pi\) | |||||||
\(390\) | −2300.37 | −0.298676 | ||||||||
\(391\) | 17665.6 | 2.28487 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3442.53 | 0.441865 | ||||||||
\(394\) | 184.053 | 0.0235341 | ||||||||
\(395\) | 1586.79 | 0.202127 | ||||||||
\(396\) | 26.9117 | 0.00341506 | ||||||||
\(397\) | 7874.94 | 0.995547 | 0.497773 | − | 0.867307i | \(-0.334151\pi\) | ||||
0.497773 | + | 0.867307i | \(0.334151\pi\) | |||||||
\(398\) | 10618.9 | 1.33738 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −599.264 | −0.0749080 | ||||||||
\(401\) | −11111.3 | −1.38372 | −0.691859 | − | 0.722033i | \(-0.743208\pi\) | ||||
−0.691859 | + | 0.722033i | \(0.743208\pi\) | |||||||
\(402\) | −10600.5 | −1.31518 | ||||||||
\(403\) | −2424.20 | −0.299648 | ||||||||
\(404\) | −5219.39 | −0.642758 | ||||||||
\(405\) | 60.6645 | 0.00744307 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 56.9016 | 0.00692999 | ||||||||
\(408\) | 5705.49 | 0.692313 | ||||||||
\(409\) | 10710.1 | 1.29482 | 0.647411 | − | 0.762141i | \(-0.275852\pi\) | ||||
0.647411 | + | 0.762141i | \(0.275852\pi\) | |||||||
\(410\) | 2106.16 | 0.253697 | ||||||||
\(411\) | 4667.27 | 0.560145 | ||||||||
\(412\) | 8082.19 | 0.966458 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11240.2 | 1.33436 | ||||||||
\(415\) | −4729.64 | −0.559444 | ||||||||
\(416\) | 7356.99 | 0.867082 | ||||||||
\(417\) | 2147.06 | 0.252139 | ||||||||
\(418\) | −27.1235 | −0.00317381 | ||||||||
\(419\) | −8615.98 | −1.00458 | −0.502289 | − | 0.864700i | \(-0.667509\pi\) | ||||
−0.502289 | + | 0.864700i | \(0.667509\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6689.72 | 0.774435 | 0.387217 | − | 0.921988i | \(-0.373436\pi\) | ||||
0.387217 | + | 0.921988i | \(0.373436\pi\) | |||||||
\(422\) | −5346.67 | −0.616758 | ||||||||
\(423\) | −123.480 | −0.0141934 | ||||||||
\(424\) | 10412.7 | 1.19265 | ||||||||
\(425\) | 2859.19 | 0.326332 | ||||||||
\(426\) | 529.969 | 0.0602748 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10968.4 | 1.23873 | ||||||||
\(429\) | 14.8141 | 0.00166721 | ||||||||
\(430\) | −7505.73 | −0.841764 | ||||||||
\(431\) | 6170.64 | 0.689627 | 0.344814 | − | 0.938671i | \(-0.387942\pi\) | ||||
0.344814 | + | 0.938671i | \(0.387942\pi\) | |||||||
\(432\) | −3380.02 | −0.376438 | ||||||||
\(433\) | −14001.1 | −1.55392 | −0.776961 | − | 0.629548i | \(-0.783240\pi\) | ||||
−0.776961 | + | 0.629548i | \(0.783240\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −650.914 | −0.0717447 | ||||||||
\(436\) | 3318.41 | 0.364502 | ||||||||
\(437\) | −6677.50 | −0.730957 | ||||||||
\(438\) | −1157.65 | −0.126289 | ||||||||
\(439\) | −12207.0 | −1.32712 | −0.663562 | − | 0.748121i | \(-0.730956\pi\) | ||||
−0.663562 | + | 0.748121i | \(0.730956\pi\) | |||||||
\(440\) | −10.9336 | −0.00118464 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16226.7 | −1.74621 | ||||||||
\(443\) | 1227.76 | 0.131677 | 0.0658384 | − | 0.997830i | \(-0.479028\pi\) | ||||
0.0658384 | + | 0.997830i | \(0.479028\pi\) | |||||||
\(444\) | 14909.5 | 1.59363 | ||||||||
\(445\) | 3916.03 | 0.417163 | ||||||||
\(446\) | 18385.1 | 1.95193 | ||||||||
\(447\) | 2552.32 | 0.270068 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1151.70 | −0.121051 | −0.0605257 | − | 0.998167i | \(-0.519278\pi\) | ||||
−0.0605257 | + | 0.998167i | \(0.519278\pi\) | |||||||
\(450\) | 1819.24 | 0.190577 | ||||||||
\(451\) | −13.5635 | −0.00141614 | ||||||||
\(452\) | 14370.8 | 1.49546 | ||||||||
\(453\) | 2750.91 | 0.285318 | ||||||||
\(454\) | 10401.0 | 1.07520 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2156.65 | −0.221479 | ||||||||
\(457\) | 18713.8 | 1.91553 | 0.957763 | − | 0.287558i | \(-0.0928433\pi\) | ||||
0.957763 | + | 0.287558i | \(0.0928433\pi\) | |||||||
\(458\) | 19180.5 | 1.95687 | ||||||||
\(459\) | 16126.6 | 1.63993 | ||||||||
\(460\) | −8870.25 | −0.899082 | ||||||||
\(461\) | 3154.57 | 0.318705 | 0.159352 | − | 0.987222i | \(-0.449059\pi\) | ||||
0.159352 | + | 0.987222i | \(0.449059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4051.11 | 0.406633 | 0.203316 | − | 0.979113i | \(-0.434828\pi\) | ||||
0.203316 | + | 0.979113i | \(0.434828\pi\) | |||||||
\(464\) | 962.351 | 0.0962845 | ||||||||
\(465\) | −1222.82 | −0.121951 | ||||||||
\(466\) | −10851.2 | −1.07870 | ||||||||
\(467\) | −16341.6 | −1.61927 | −0.809635 | − | 0.586934i | \(-0.800335\pi\) | ||||
−0.809635 | + | 0.586934i | \(0.800335\pi\) | |||||||
\(468\) | −6085.73 | −0.601096 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 165.320 | 0.0162247 | ||||||||
\(471\) | 3096.47 | 0.302925 | ||||||||
\(472\) | 12249.1 | 1.19451 | ||||||||
\(473\) | 48.3362 | 0.00469873 | ||||||||
\(474\) | −4542.57 | −0.440184 | ||||||||
\(475\) | −1080.76 | −0.104397 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11157.5 | 1.07100 | ||||||||
\(478\) | −1422.72 | −0.136138 | ||||||||
\(479\) | −2531.45 | −0.241472 | −0.120736 | − | 0.992685i | \(-0.538525\pi\) | ||||
−0.120736 | + | 0.992685i | \(0.538525\pi\) | |||||||
\(480\) | 3711.03 | 0.352885 | ||||||||
\(481\) | −12867.6 | −1.21977 | ||||||||
\(482\) | −22120.7 | −2.09039 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15286.7 | −1.43564 | ||||||||
\(485\) | 1965.53 | 0.184021 | ||||||||
\(486\) | 16632.1 | 1.55236 | ||||||||
\(487\) | −8442.18 | −0.785527 | −0.392763 | − | 0.919640i | \(-0.628481\pi\) | ||||
−0.392763 | + | 0.919640i | \(0.628481\pi\) | |||||||
\(488\) | −11647.8 | −1.08048 | ||||||||
\(489\) | 23.8795 | 0.00220832 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15223.9 | −1.39928 | −0.699640 | − | 0.714496i | \(-0.746656\pi\) | ||||
−0.699640 | + | 0.714496i | \(0.746656\pi\) | |||||||
\(492\) | −3553.93 | −0.325658 | ||||||||
\(493\) | −4591.53 | −0.419457 | ||||||||
\(494\) | 6133.63 | 0.558634 | ||||||||
\(495\) | −11.7157 | −0.00106380 | ||||||||
\(496\) | 1807.89 | 0.163663 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 13539.8 | 1.21833 | ||||||||
\(499\) | −16622.6 | −1.49125 | −0.745623 | − | 0.666368i | \(-0.767848\pi\) | ||||
−0.745623 | + | 0.666368i | \(0.767848\pi\) | |||||||
\(500\) | −1435.66 | −0.128409 | ||||||||
\(501\) | 9473.06 | 0.844760 | ||||||||
\(502\) | 17378.5 | 1.54510 | ||||||||
\(503\) | 17506.6 | 1.55185 | 0.775923 | − | 0.630828i | \(-0.217285\pi\) | ||||
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2272.21 | 0.200222 | ||||||||
\(506\) | 96.9127 | 0.00851442 | ||||||||
\(507\) | 3774.05 | 0.330595 | ||||||||
\(508\) | −22369.0 | −1.95367 | ||||||||
\(509\) | −12383.2 | −1.07834 | −0.539169 | − | 0.842198i | \(-0.681261\pi\) | ||||
−0.539169 | + | 0.842198i | \(0.681261\pi\) | |||||||
\(510\) | −8185.12 | −0.710673 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −8436.86 | −0.728242 | ||||||||
\(513\) | −6095.80 | −0.524632 | ||||||||
\(514\) | −16006.7 | −1.37359 | ||||||||
\(515\) | −3518.50 | −0.301055 | ||||||||
\(516\) | 12665.1 | 1.08053 | ||||||||
\(517\) | −1.06464 | −9.05666e−5 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12871.9 | −1.08866 | ||||||||
\(520\) | 2472.50 | 0.208512 | ||||||||
\(521\) | 14979.0 | 1.25958 | 0.629790 | − | 0.776765i | \(-0.283141\pi\) | ||||
0.629790 | + | 0.776765i | \(0.283141\pi\) | |||||||
\(522\) | −2921.49 | −0.244962 | ||||||||
\(523\) | −3719.11 | −0.310947 | −0.155474 | − | 0.987840i | \(-0.549690\pi\) | ||||
−0.155474 | + | 0.987840i | \(0.549690\pi\) | |||||||
\(524\) | −12193.3 | −1.01654 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3472.02 | 0.287809 | ||||||||
\(527\) | −8625.75 | −0.712986 | ||||||||
\(528\) | −11.0479 | −0.000910603 0 | ||||||||
\(529\) | 11691.8 | 0.960945 | ||||||||
\(530\) | −14938.1 | −1.22428 | ||||||||
\(531\) | 13125.3 | 1.07267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3067.21 | 0.249260 | ||||||||
\(534\) | −11210.6 | −0.908481 | ||||||||
\(535\) | −4774.99 | −0.385870 | ||||||||
\(536\) | 11393.7 | 0.918156 | ||||||||
\(537\) | 3586.20 | 0.288186 | ||||||||
\(538\) | 17912.6 | 1.43544 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8097.53 | −0.645301 | ||||||||
\(541\) | −244.726 | −0.0194484 | −0.00972420 | − | 0.999953i | \(-0.503095\pi\) | ||||
−0.00972420 | + | 0.999953i | \(0.503095\pi\) | |||||||
\(542\) | 12798.7 | 1.01430 | ||||||||
\(543\) | −380.081 | −0.0300384 | ||||||||
\(544\) | 26177.5 | 2.06315 | ||||||||
\(545\) | −1444.63 | −0.113544 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12685.4 | −0.991568 | −0.495784 | − | 0.868446i | \(-0.665119\pi\) | ||||
−0.495784 | + | 0.868446i | \(0.665119\pi\) | |||||||
\(548\) | −16531.3 | −1.28865 | ||||||||
\(549\) | −12481.0 | −0.970269 | ||||||||
\(550\) | 15.6854 | 0.00121605 | ||||||||
\(551\) | 1735.58 | 0.134189 | ||||||||
\(552\) | 7705.74 | 0.594163 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −23368.7 | −1.79213 | ||||||||
\(555\) | −6490.68 | −0.496422 | ||||||||
\(556\) | −7604.77 | −0.580062 | ||||||||
\(557\) | −22062.7 | −1.67833 | −0.839164 | − | 0.543879i | \(-0.816955\pi\) | ||||
−0.839164 | + | 0.543879i | \(0.816955\pi\) | |||||||
\(558\) | −5488.38 | −0.416383 | ||||||||
\(559\) | −10930.6 | −0.827040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.7114 | 0.00396698 | ||||||||
\(562\) | −10414.9 | −0.781719 | ||||||||
\(563\) | −7862.20 | −0.588547 | −0.294274 | − | 0.955721i | \(-0.595078\pi\) | ||||
−0.294274 | + | 0.955721i | \(0.595078\pi\) | |||||||
\(564\) | −278.960 | −0.0208268 | ||||||||
\(565\) | −6256.19 | −0.465841 | ||||||||
\(566\) | −12718.9 | −0.944549 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −569.625 | −0.0420791 | ||||||||
\(569\) | 20941.5 | 1.54291 | 0.771453 | − | 0.636286i | \(-0.219530\pi\) | ||||
0.771453 | + | 0.636286i | \(0.219530\pi\) | |||||||
\(570\) | 3093.94 | 0.227352 | ||||||||
\(571\) | −7131.66 | −0.522681 | −0.261341 | − | 0.965247i | \(-0.584165\pi\) | ||||
−0.261341 | + | 0.965247i | \(0.584165\pi\) | |||||||
\(572\) | −52.4710 | −0.00383553 | ||||||||
\(573\) | −3251.07 | −0.237025 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3861.57 | 0.280067 | ||||||||
\(576\) | 13494.9 | 0.976193 | ||||||||
\(577\) | 15633.0 | 1.12792 | 0.563961 | − | 0.825801i | \(-0.309277\pi\) | ||||
0.563961 | + | 0.825801i | \(0.309277\pi\) | |||||||
\(578\) | −36050.6 | −2.59430 | ||||||||
\(579\) | −10563.7 | −0.758229 | ||||||||
\(580\) | 2305.51 | 0.165054 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5626.82 | −0.400754 | ||||||||
\(583\) | 96.2000 | 0.00683396 | ||||||||
\(584\) | 1244.28 | 0.0881654 | ||||||||
\(585\) | 2649.36 | 0.187244 | ||||||||
\(586\) | 3358.03 | 0.236721 | ||||||||
\(587\) | 19406.2 | 1.36453 | 0.682266 | − | 0.731104i | \(-0.260995\pi\) | ||||
0.682266 | + | 0.731104i | \(0.260995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3260.50 | 0.228093 | ||||||||
\(590\) | −17572.6 | −1.22619 | ||||||||
\(591\) | 135.204 | 0.00941038 | ||||||||
\(592\) | 9596.21 | 0.666219 | ||||||||
\(593\) | 14859.6 | 1.02903 | 0.514513 | − | 0.857483i | \(-0.327973\pi\) | ||||
0.514513 | + | 0.857483i | \(0.327973\pi\) | |||||||
\(594\) | 88.4703 | 0.00611108 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9040.18 | −0.621309 | ||||||||
\(597\) | 7800.54 | 0.534765 | ||||||||
\(598\) | −21915.6 | −1.49865 | ||||||||
\(599\) | −10529.9 | −0.718261 | −0.359131 | − | 0.933287i | \(-0.616927\pi\) | ||||
−0.359131 | + | 0.933287i | \(0.616927\pi\) | |||||||
\(600\) | 1247.18 | 0.0848600 | ||||||||
\(601\) | −11595.2 | −0.786984 | −0.393492 | − | 0.919328i | \(-0.628733\pi\) | ||||
−0.393492 | + | 0.919328i | \(0.628733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12208.7 | 0.824504 | ||||||||
\(604\) | −9743.60 | −0.656393 | ||||||||
\(605\) | 6654.90 | 0.447207 | ||||||||
\(606\) | −6504.74 | −0.436035 | ||||||||
\(607\) | 23282.1 | 1.55682 | 0.778411 | − | 0.627755i | \(-0.216026\pi\) | ||||
0.778411 | + | 0.627755i | \(0.216026\pi\) | |||||||
\(608\) | −9894.99 | −0.660024 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16710.0 | 1.10913 | ||||||||
\(611\) | 240.755 | 0.0159409 | ||||||||
\(612\) | −21654.1 | −1.43026 | ||||||||
\(613\) | −7387.98 | −0.486782 | −0.243391 | − | 0.969928i | \(-0.578260\pi\) | ||||
−0.243391 | + | 0.969928i | \(0.578260\pi\) | |||||||
\(614\) | −21932.3 | −1.44156 | ||||||||
\(615\) | 1547.17 | 0.101444 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 667.085 | 0.0435265 | 0.0217632 | − | 0.999763i | \(-0.493072\pi\) | ||||
0.0217632 | + | 0.999763i | \(0.493072\pi\) | |||||||
\(618\) | 10072.5 | 0.655627 | ||||||||
\(619\) | 9425.78 | 0.612042 | 0.306021 | − | 0.952025i | \(-0.401002\pi\) | ||||
0.306021 | + | 0.952025i | \(0.401002\pi\) | |||||||
\(620\) | 4331.18 | 0.280555 | ||||||||
\(621\) | 21780.4 | 1.40743 | ||||||||
\(622\) | −22221.0 | −1.43244 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2498.34 | 0.160278 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 15887.7 | 1.01437 | ||||||||
\(627\) | −19.9247 | −0.00126908 | ||||||||
\(628\) | −10967.5 | −0.696899 | ||||||||
\(629\) | −45785.1 | −2.90234 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28047.3 | 1.76949 | 0.884744 | − | 0.466078i | \(-0.154333\pi\) | ||||
0.884744 | + | 0.466078i | \(0.154333\pi\) | |||||||
\(632\) | 4882.49 | 0.307302 | ||||||||
\(633\) | −3927.61 | −0.246617 | ||||||||
\(634\) | −15633.2 | −0.979295 | ||||||||
\(635\) | 9738.12 | 0.608576 | ||||||||
\(636\) | 25206.5 | 1.57155 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.1890 | −0.00156308 | ||||||||
\(639\) | −610.372 | −0.0377871 | ||||||||
\(640\) | −8911.85 | −0.550425 | ||||||||
\(641\) | 23208.3 | 1.43007 | 0.715034 | − | 0.699090i | \(-0.246411\pi\) | ||||
0.715034 | + | 0.699090i | \(0.246411\pi\) | |||||||
\(642\) | 13669.5 | 0.840333 | ||||||||
\(643\) | 4294.22 | 0.263371 | 0.131686 | − | 0.991292i | \(-0.457961\pi\) | ||||
0.131686 | + | 0.991292i | \(0.457961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5513.64 | −0.336588 | ||||||||
\(646\) | 21824.6 | 1.32922 | ||||||||
\(647\) | 17393.4 | 1.05689 | 0.528443 | − | 0.848969i | \(-0.322776\pi\) | ||||
0.528443 | + | 0.848969i | \(0.322776\pi\) | |||||||
\(648\) | 186.662 | 0.0113160 | ||||||||
\(649\) | 113.166 | 0.00684459 | ||||||||
\(650\) | −3547.06 | −0.214042 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −84.5801 | −0.00508039 | ||||||||
\(653\) | 14475.4 | 0.867486 | 0.433743 | − | 0.901037i | \(-0.357193\pi\) | ||||
0.433743 | + | 0.901037i | \(0.357193\pi\) | |||||||
\(654\) | 4135.61 | 0.247271 | ||||||||
\(655\) | 5308.23 | 0.316656 | ||||||||
\(656\) | −2287.42 | −0.136142 | ||||||||
\(657\) | 1333.28 | 0.0791725 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 620.113 | 0.0366558 | 0.0183279 | − | 0.999832i | \(-0.494166\pi\) | ||||
0.0183279 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(660\) | −26.4675 | −0.00156098 | ||||||||
\(661\) | −6105.50 | −0.359268 | −0.179634 | − | 0.983733i | \(-0.557491\pi\) | ||||
−0.179634 | + | 0.983733i | \(0.557491\pi\) | |||||||
\(662\) | 32479.6 | 1.90688 | ||||||||
\(663\) | −11920.0 | −0.698242 | ||||||||
\(664\) | −14552.9 | −0.850546 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −29132.1 | −1.69496 | ||||||||
\(667\) | −6201.25 | −0.359990 | ||||||||
\(668\) | −33553.1 | −1.94343 | ||||||||
\(669\) | 13505.6 | 0.780500 | ||||||||
\(670\) | −16345.4 | −0.942505 | ||||||||
\(671\) | −107.611 | −0.00619118 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16302.5 | −0.933754 | −0.466877 | − | 0.884322i | \(-0.654621\pi\) | ||||
−0.466877 | + | 0.884322i | \(0.654621\pi\) | |||||||
\(674\) | 10255.3 | 0.586081 | ||||||||
\(675\) | 3525.18 | 0.201014 | ||||||||
\(676\) | −13367.5 | −0.760556 | ||||||||
\(677\) | 4819.09 | 0.273579 | 0.136789 | − | 0.990600i | \(-0.456322\pi\) | ||||
0.136789 | + | 0.990600i | \(0.456322\pi\) | |||||||
\(678\) | 17909.9 | 1.01449 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8797.59 | 0.496136 | ||||||||
\(681\) | 7640.45 | 0.429930 | ||||||||
\(682\) | −47.3206 | −0.00265689 | ||||||||
\(683\) | −8190.32 | −0.458849 | −0.229425 | − | 0.973326i | \(-0.573684\pi\) | ||||
−0.229425 | + | 0.973326i | \(0.573684\pi\) | |||||||
\(684\) | 8185.17 | 0.457555 | ||||||||
\(685\) | 7196.71 | 0.401419 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14089.8 | 0.782473 | ||||||||
\(688\) | 8151.69 | 0.451716 | ||||||||
\(689\) | −21754.4 | −1.20287 | ||||||||
\(690\) | −11054.7 | −0.609920 | ||||||||
\(691\) | −476.973 | −0.0262589 | −0.0131295 | − | 0.999914i | \(-0.504179\pi\) | ||||
−0.0131295 | + | 0.999914i | \(0.504179\pi\) | |||||||
\(692\) | 45591.6 | 2.50453 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24047.7 | 1.31533 | ||||||||
\(695\) | 3310.66 | 0.180691 | ||||||||
\(696\) | −2002.83 | −0.109077 | ||||||||
\(697\) | 10913.7 | 0.593092 | ||||||||
\(698\) | −5419.96 | −0.293909 | ||||||||
\(699\) | −7971.22 | −0.431329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20366.7 | −1.09735 | −0.548673 | − | 0.836037i | \(-0.684867\pi\) | ||||
−0.548673 | + | 0.836037i | \(0.684867\pi\) | |||||||
\(702\) | −20006.4 | −1.07563 | ||||||||
\(703\) | 17306.6 | 0.928492 | ||||||||
\(704\) | 116.353 | 0.00622898 | ||||||||
\(705\) | 121.442 | 0.00648763 | ||||||||
\(706\) | 8748.36 | 0.466358 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 29651.9 | 1.57399 | ||||||||
\(709\) | 22415.1 | 1.18733 | 0.593664 | − | 0.804713i | \(-0.297681\pi\) | ||||
0.593664 | + | 0.804713i | \(0.297681\pi\) | |||||||
\(710\) | 817.187 | 0.0431950 | ||||||||
\(711\) | 5231.74 | 0.275957 | ||||||||
\(712\) | 12049.4 | 0.634230 | ||||||||
\(713\) | −11649.8 | −0.611906 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.8427 | 0.00119478 | ||||||||
\(716\) | −12702.2 | −0.662992 | ||||||||
\(717\) | −1045.12 | −0.0544360 | ||||||||
\(718\) | 53933.1 | 2.80329 | ||||||||
\(719\) | 26156.0 | 1.35668 | 0.678340 | − | 0.734748i | \(-0.262700\pi\) | ||||
0.678340 | + | 0.734748i | \(0.262700\pi\) | |||||||
\(720\) | −1975.81 | −0.102269 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 22027.5 | 1.13543 | ||||||||
\(723\) | −16249.6 | −0.835866 | ||||||||
\(724\) | 1346.23 | 0.0691053 | ||||||||
\(725\) | −1003.68 | −0.0514148 | ||||||||
\(726\) | −19051.3 | −0.973910 | ||||||||
\(727\) | 13666.2 | 0.697184 | 0.348592 | − | 0.937275i | \(-0.386660\pi\) | ||||
0.348592 | + | 0.937275i | \(0.386660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12545.4 | 0.637371 | ||||||||
\(730\) | −1785.05 | −0.0905035 | ||||||||
\(731\) | −38893.1 | −1.96787 | ||||||||
\(732\) | −28196.5 | −1.42373 | ||||||||
\(733\) | −25038.2 | −1.26167 | −0.630836 | − | 0.775916i | \(-0.717288\pi\) | ||||
−0.630836 | + | 0.775916i | \(0.717288\pi\) | |||||||
\(734\) | 60243.8 | 3.02948 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35354.9 | 1.77065 | ||||||||
\(737\) | 105.263 | 0.00526107 | ||||||||
\(738\) | 6944.14 | 0.346365 | ||||||||
\(739\) | 3255.20 | 0.162036 | 0.0810178 | − | 0.996713i | \(-0.474183\pi\) | ||||
0.0810178 | + | 0.996713i | \(0.474183\pi\) | |||||||
\(740\) | 22989.7 | 1.14205 | ||||||||
\(741\) | 4505.71 | 0.223376 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8366.48 | −0.413104 | −0.206552 | − | 0.978436i | \(-0.566224\pi\) | ||||
−0.206552 | + | 0.978436i | \(0.566224\pi\) | |||||||
\(744\) | −3762.57 | −0.185406 | ||||||||
\(745\) | 3935.55 | 0.193540 | ||||||||
\(746\) | 24472.5 | 1.20108 | ||||||||
\(747\) | −15593.9 | −0.763790 | ||||||||
\(748\) | −186.701 | −0.00912630 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1789.21 | −0.0871105 | ||||||||
\(751\) | −10164.5 | −0.493884 | −0.246942 | − | 0.969030i | \(-0.579426\pi\) | ||||
−0.246942 | + | 0.969030i | \(0.579426\pi\) | |||||||
\(752\) | −179.547 | −0.00870668 | ||||||||
\(753\) | 12766.1 | 0.617825 | ||||||||
\(754\) | 5696.17 | 0.275123 | ||||||||
\(755\) | 4241.77 | 0.204469 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9031.23 | 0.433614 | 0.216807 | − | 0.976214i | \(-0.430436\pi\) | ||||
0.216807 | + | 0.976214i | \(0.430436\pi\) | |||||||
\(758\) | 2799.68 | 0.134155 | ||||||||
\(759\) | 71.1912 | 0.00340458 | ||||||||
\(760\) | −3325.45 | −0.158720 | ||||||||
\(761\) | 32434.7 | 1.54502 | 0.772508 | − | 0.635005i | \(-0.219002\pi\) | ||||
0.772508 | + | 0.635005i | \(0.219002\pi\) | |||||||
\(762\) | −27877.7 | −1.32533 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 11515.1 | 0.545292 | ||||||||
\(765\) | 9426.90 | 0.445530 | ||||||||
\(766\) | 25562.4 | 1.20575 | ||||||||
\(767\) | −25591.0 | −1.20474 | ||||||||
\(768\) | 4276.86 | 0.200948 | ||||||||
\(769\) | 22629.4 | 1.06117 | 0.530583 | − | 0.847633i | \(-0.321973\pi\) | ||||
0.530583 | + | 0.847633i | \(0.321973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11758.3 | −0.549243 | ||||||||
\(772\) | 37416.3 | 1.74436 | ||||||||
\(773\) | −2707.01 | −0.125956 | −0.0629782 | − | 0.998015i | \(-0.520060\pi\) | ||||
−0.0629782 | + | 0.998015i | \(0.520060\pi\) | |||||||
\(774\) | −24746.8 | −1.14923 | ||||||||
\(775\) | −1885.53 | −0.0873940 | ||||||||
\(776\) | 6047.86 | 0.279775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6696.33 | −0.308580 | ||||||||
\(779\) | −4125.33 | −0.189737 | ||||||||
\(780\) | 5985.29 | 0.274754 | ||||||||
\(781\) | −5.26261 | −0.000241115 0 | ||||||||
\(782\) | −77979.5 | −3.56591 | ||||||||
\(783\) | −5661.04 | −0.258377 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4774.61 | 0.217087 | ||||||||
\(786\) | −15196.1 | −0.689601 | ||||||||
\(787\) | 25084.6 | 1.13618 | 0.568088 | − | 0.822968i | \(-0.307683\pi\) | ||||
0.568088 | + | 0.822968i | \(0.307683\pi\) | |||||||
\(788\) | −478.885 | −0.0216492 | ||||||||
\(789\) | 2550.52 | 0.115083 | ||||||||
\(790\) | −7004.44 | −0.315451 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −36.0488 | −0.00161735 | ||||||||
\(793\) | 24334.9 | 1.08973 | ||||||||
\(794\) | −34761.7 | −1.55371 | ||||||||
\(795\) | −10973.4 | −0.489542 | ||||||||
\(796\) | −27629.1 | −1.23026 | ||||||||
\(797\) | −7374.99 | −0.327774 | −0.163887 | − | 0.986479i | \(-0.552403\pi\) | ||||
−0.163887 | + | 0.986479i | \(0.552403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 856.651 | 0.0379301 | ||||||||
\(800\) | 5722.23 | 0.252889 | ||||||||
\(801\) | 12911.4 | 0.569539 | ||||||||
\(802\) | 49047.5 | 2.15951 | ||||||||
\(803\) | 11.4955 | 0.000505191 0 | ||||||||
\(804\) | 27581.2 | 1.20984 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10701.0 | 0.467649 | ||||||||
\(807\) | 13158.5 | 0.573977 | ||||||||
\(808\) | 6991.48 | 0.304405 | ||||||||
\(809\) | 2314.37 | 0.100580 | 0.0502899 | − | 0.998735i | \(-0.483985\pi\) | ||||
0.0502899 | + | 0.998735i | \(0.483985\pi\) | |||||||
\(810\) | −267.786 | −0.0116161 | ||||||||
\(811\) | −38300.1 | −1.65832 | −0.829160 | − | 0.559011i | \(-0.811181\pi\) | ||||
−0.829160 | + | 0.559011i | \(0.811181\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9401.78 | 0.405578 | ||||||||
\(814\) | −251.176 | −0.0108154 | ||||||||
\(815\) | 36.8211 | 0.00158256 | ||||||||
\(816\) | 8889.55 | 0.381368 | ||||||||
\(817\) | 14701.4 | 0.629544 | ||||||||
\(818\) | −47276.8 | −2.02078 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5480.00 | −0.233378 | ||||||||
\(821\) | 3942.93 | 0.167612 | 0.0838059 | − | 0.996482i | \(-0.473292\pi\) | ||||
0.0838059 | + | 0.996482i | \(0.473292\pi\) | |||||||
\(822\) | −20602.3 | −0.874195 | ||||||||
\(823\) | 18502.8 | 0.783679 | 0.391839 | − | 0.920034i | \(-0.371839\pi\) | ||||
0.391839 | + | 0.920034i | \(0.371839\pi\) | |||||||
\(824\) | −10826.3 | −0.457707 | ||||||||
\(825\) | 11.5224 | 0.000486251 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11965.2 | −0.503110 | −0.251555 | − | 0.967843i | \(-0.580942\pi\) | ||||
−0.251555 | + | 0.967843i | \(0.580942\pi\) | |||||||
\(828\) | −29245.7 | −1.22749 | ||||||||
\(829\) | 35962.9 | 1.50669 | 0.753344 | − | 0.657626i | \(-0.228439\pi\) | ||||
0.753344 | + | 0.657626i | \(0.228439\pi\) | |||||||
\(830\) | 20877.7 | 0.873101 | ||||||||
\(831\) | −17166.4 | −0.716602 | ||||||||
\(832\) | −26311.6 | −1.09638 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9477.56 | −0.393503 | ||||||||
\(835\) | 14607.0 | 0.605385 | ||||||||
\(836\) | 70.5723 | 0.00291961 | ||||||||
\(837\) | −10634.9 | −0.439185 | ||||||||
\(838\) | 38032.8 | 1.56780 | ||||||||
\(839\) | 20174.0 | 0.830137 | 0.415069 | − | 0.909790i | \(-0.363758\pi\) | ||||
0.415069 | + | 0.909790i | \(0.363758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22777.2 | −0.933913 | ||||||||
\(842\) | −29529.9 | −1.20863 | ||||||||
\(843\) | −7650.69 | −0.312579 | ||||||||
\(844\) | 13911.4 | 0.567359 | ||||||||
\(845\) | 5819.42 | 0.236916 | ||||||||
\(846\) | 545.068 | 0.0221511 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16223.7 | 0.656987 | ||||||||
\(849\) | −9343.17 | −0.377688 | ||||||||
\(850\) | −12621.1 | −0.509293 | ||||||||
\(851\) | −61836.6 | −2.49087 | ||||||||
\(852\) | −1378.92 | −0.0554471 | ||||||||
\(853\) | −25297.5 | −1.01544 | −0.507719 | − | 0.861523i | \(-0.669511\pi\) | ||||
−0.507719 | + | 0.861523i | \(0.669511\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3563.33 | −0.142530 | ||||||||
\(856\) | −14692.4 | −0.586655 | ||||||||
\(857\) | −39269.1 | −1.56523 | −0.782617 | − | 0.622504i | \(-0.786116\pi\) | ||||
−0.782617 | + | 0.622504i | \(0.786116\pi\) | |||||||
\(858\) | −65.3928 | −0.00260195 | ||||||||
\(859\) | 14499.1 | 0.575905 | 0.287953 | − | 0.957645i | \(-0.407025\pi\) | ||||
0.287953 | + | 0.957645i | \(0.407025\pi\) | |||||||
\(860\) | 19529.1 | 0.774343 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27238.5 | −1.07627 | ||||||||
\(863\) | −24411.3 | −0.962884 | −0.481442 | − | 0.876478i | \(-0.659887\pi\) | ||||
−0.481442 | + | 0.876478i | \(0.659887\pi\) | |||||||
\(864\) | 32275.0 | 1.27086 | ||||||||
\(865\) | −19847.8 | −0.780170 | ||||||||
\(866\) | 61803.7 | 2.42515 | ||||||||
\(867\) | −26482.4 | −1.03736 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45.1079 | 0.00176085 | ||||||||
\(870\) | 2873.28 | 0.111969 | ||||||||
\(871\) | −23803.8 | −0.926019 | ||||||||
\(872\) | −4445.07 | −0.172625 | ||||||||
\(873\) | 6480.48 | 0.251238 | ||||||||
\(874\) | 29475.9 | 1.14078 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3012.08 | 0.116174 | ||||||||
\(877\) | −5056.65 | −0.194699 | −0.0973494 | − | 0.995250i | \(-0.531036\pi\) | ||||
−0.0973494 | + | 0.995250i | \(0.531036\pi\) | |||||||
\(878\) | 53884.2 | 2.07119 | ||||||||
\(879\) | 2466.77 | 0.0946556 | ||||||||
\(880\) | −17.0354 | −0.000652570 0 | ||||||||
\(881\) | −13233.9 | −0.506086 | −0.253043 | − | 0.967455i | \(-0.581431\pi\) | ||||
−0.253043 | + | 0.967455i | \(0.581431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13824.2 | −0.526866 | −0.263433 | − | 0.964678i | \(-0.584855\pi\) | ||||
−0.263433 | + | 0.964678i | \(0.584855\pi\) | |||||||
\(884\) | 42220.1 | 1.60635 | ||||||||
\(885\) | −12908.6 | −0.490304 | ||||||||
\(886\) | −5419.61 | −0.205503 | ||||||||
\(887\) | 37819.3 | 1.43162 | 0.715811 | − | 0.698294i | \(-0.246057\pi\) | ||||
0.715811 | + | 0.698294i | \(0.246057\pi\) | |||||||
\(888\) | −19971.5 | −0.754731 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −17286.2 | −0.651049 | ||||||||
\(891\) | 1.72452 | 6.48412e−5 0 | ||||||||
\(892\) | −47836.0 | −1.79559 | ||||||||
\(893\) | −323.810 | −0.0121343 | ||||||||
\(894\) | −11266.5 | −0.421484 | ||||||||
\(895\) | 5529.76 | 0.206524 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16099.0 | −0.599252 | ||||||||
\(898\) | 5083.85 | 0.188920 | ||||||||
\(899\) | 3027.96 | 0.112334 | ||||||||
\(900\) | −4733.45 | −0.175313 | ||||||||
\(901\) | −77406.0 | −2.86212 | ||||||||
\(902\) | 59.8721 | 0.00221012 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19250.0 | −0.708237 | ||||||||
\(905\) | −586.068 | −0.0215266 | ||||||||
\(906\) | −12143.1 | −0.445284 | ||||||||
\(907\) | 1052.75 | 0.0385404 | 0.0192702 | − | 0.999814i | \(-0.493866\pi\) | ||||
0.0192702 | + | 0.999814i | \(0.493866\pi\) | |||||||
\(908\) | −27062.1 | −0.989083 | ||||||||
\(909\) | 7491.60 | 0.273356 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7854.40 | 0.285651 | 0.142825 | − | 0.989748i | \(-0.454381\pi\) | ||||
0.142825 | + | 0.989748i | \(0.454381\pi\) | |||||||
\(912\) | −3360.21 | −0.122004 | ||||||||
\(913\) | −134.450 | −0.00487366 | ||||||||
\(914\) | −82606.8 | −2.98949 | ||||||||
\(915\) | 12275.0 | 0.443498 | ||||||||
\(916\) | −49905.4 | −1.80013 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −71186.4 | −2.55937 | ||||||||
\(919\) | 4935.85 | 0.177169 | 0.0885846 | − | 0.996069i | \(-0.471766\pi\) | ||||
0.0885846 | + | 0.996069i | \(0.471766\pi\) | |||||||
\(920\) | 11881.9 | 0.425798 | ||||||||
\(921\) | −16111.3 | −0.576422 | ||||||||
\(922\) | −13924.9 | −0.497390 | ||||||||
\(923\) | 1190.07 | 0.0424395 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10008.3 | −0.355753 | ||||||||
\(926\) | −17882.4 | −0.634615 | ||||||||
\(927\) | −11600.7 | −0.411021 | ||||||||
\(928\) | −9189.27 | −0.325056 | ||||||||
\(929\) | 15705.0 | 0.554645 | 0.277322 | − | 0.960777i | \(-0.410553\pi\) | ||||
0.277322 | + | 0.960777i | \(0.410553\pi\) | |||||||
\(930\) | 5397.80 | 0.190323 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 28233.7 | 0.992302 | ||||||||
\(933\) | −16323.3 | −0.572778 | ||||||||
\(934\) | 72135.3 | 2.52713 | ||||||||
\(935\) | 81.2785 | 0.00284288 | ||||||||
\(936\) | 8151.96 | 0.284674 | ||||||||
\(937\) | 43806.5 | 1.52732 | 0.763658 | − | 0.645621i | \(-0.223401\pi\) | ||||
0.763658 | + | 0.645621i | \(0.223401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11670.9 | 0.405608 | ||||||||
\(940\) | −430.143 | −0.0149252 | ||||||||
\(941\) | −4062.42 | −0.140734 | −0.0703672 | − | 0.997521i | \(-0.522417\pi\) | ||||
−0.0703672 | + | 0.997521i | \(0.522417\pi\) | |||||||
\(942\) | −13668.5 | −0.472763 | ||||||||
\(943\) | 14739.8 | 0.509009 | ||||||||
\(944\) | 19084.9 | 0.658009 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −213.366 | −0.00733313 | ||||||||
\(947\) | −4860.13 | −0.166772 | −0.0833859 | − | 0.996517i | \(-0.526573\pi\) | ||||
−0.0833859 | + | 0.996517i | \(0.526573\pi\) | |||||||
\(948\) | 11819.3 | 0.404928 | ||||||||
\(949\) | −2599.57 | −0.0889204 | ||||||||
\(950\) | 4770.71 | 0.162929 | ||||||||
\(951\) | −11484.0 | −0.391581 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18999.6 | −0.645811 | −0.322906 | − | 0.946431i | \(-0.604660\pi\) | ||||
−0.322906 | + | 0.946431i | \(0.604660\pi\) | |||||||
\(954\) | −49251.8 | −1.67147 | ||||||||
\(955\) | −5013.00 | −0.169861 | ||||||||
\(956\) | 3701.76 | 0.125234 | ||||||||
\(957\) | −18.5036 | −0.000625013 0 | ||||||||
\(958\) | 11174.4 | 0.376855 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −13272.2 | −0.446205 | ||||||||
\(961\) | −24102.6 | −0.809057 | ||||||||
\(962\) | 56800.2 | 1.90365 | ||||||||
\(963\) | −15743.4 | −0.526816 | ||||||||
\(964\) | 57555.5 | 1.92296 | ||||||||
\(965\) | −16288.8 | −0.543373 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32695.1 | −1.08728 | −0.543641 | − | 0.839318i | \(-0.682955\pi\) | ||||
−0.543641 | + | 0.839318i | \(0.682955\pi\) | |||||||
\(968\) | 20476.8 | 0.679907 | ||||||||
\(969\) | 16032.1 | 0.531503 | ||||||||
\(970\) | −8676.29 | −0.287195 | ||||||||
\(971\) | 6189.69 | 0.204569 | 0.102285 | − | 0.994755i | \(-0.467385\pi\) | ||||
0.102285 | + | 0.994755i | \(0.467385\pi\) | |||||||
\(972\) | −43274.8 | −1.42803 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37265.6 | 1.22594 | ||||||||
\(975\) | −2605.63 | −0.0855868 | ||||||||
\(976\) | −18148.2 | −0.595193 | ||||||||
\(977\) | 2142.44 | 0.0701563 | 0.0350782 | − | 0.999385i | \(-0.488832\pi\) | ||||
0.0350782 | + | 0.999385i | \(0.488832\pi\) | |||||||
\(978\) | −105.409 | −0.00344644 | ||||||||
\(979\) | 111.321 | 0.00363416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4763.04 | −0.155018 | ||||||||
\(982\) | 67201.7 | 2.18380 | ||||||||
\(983\) | −16808.2 | −0.545371 | −0.272685 | − | 0.962103i | \(-0.587912\pi\) | ||||
−0.272685 | + | 0.962103i | \(0.587912\pi\) | |||||||
\(984\) | 4760.57 | 0.154229 | ||||||||
\(985\) | 208.478 | 0.00674381 | ||||||||
\(986\) | 20268.0 | 0.654630 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15959.0 | −0.513891 | ||||||||
\(989\) | −52528.4 | −1.68888 | ||||||||
\(990\) | 51.7157 | 0.00166024 | ||||||||
\(991\) | 21250.8 | 0.681185 | 0.340593 | − | 0.940211i | \(-0.389372\pi\) | ||||
0.340593 | + | 0.940211i | \(0.389372\pi\) | |||||||
\(992\) | −17263.1 | −0.552526 | ||||||||
\(993\) | 23859.2 | 0.762487 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12028.1 | 0.383231 | ||||||||
\(996\) | −35228.9 | −1.12075 | ||||||||
\(997\) | 37639.9 | 1.19566 | 0.597828 | − | 0.801624i | \(-0.296031\pi\) | ||||
0.597828 | + | 0.801624i | \(0.296031\pi\) | |||||||
\(998\) | 73375.9 | 2.32733 | ||||||||
\(999\) | −56449.8 | −1.78778 |
(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 | 245.4.a.h.1.1 | 2 | ||
3.2 | odd | 2 | 2205.4.a.bg.1.2 | 2 | |||
5.4 | even | 2 | 1225.4.a.v.1.2 | 2 | |||
7.2 | even | 3 | 245.4.e.l.116.2 | 4 | |||
7.3 | odd | 6 | 35.4.e.b.16.2 | yes | 4 | ||
7.4 | even | 3 | 245.4.e.l.226.2 | 4 | |||
7.5 | odd | 6 | 35.4.e.b.11.2 | ✓ | 4 | ||
7.6 | odd | 2 | 245.4.a.g.1.1 | 2 | |||
21.5 | even | 6 | 315.4.j.c.46.1 | 4 | |||
21.17 | even | 6 | 315.4.j.c.226.1 | 4 | |||
21.20 | even | 2 | 2205.4.a.bf.1.2 | 2 | |||
28.3 | even | 6 | 560.4.q.i.401.2 | 4 | |||
28.19 | even | 6 | 560.4.q.i.81.2 | 4 | |||
35.3 | even | 12 | 175.4.k.c.149.1 | 8 | |||
35.12 | even | 12 | 175.4.k.c.74.1 | 8 | |||
35.17 | even | 12 | 175.4.k.c.149.4 | 8 | |||
35.19 | odd | 6 | 175.4.e.c.151.1 | 4 | |||
35.24 | odd | 6 | 175.4.e.c.51.1 | 4 | |||
35.33 | even | 12 | 175.4.k.c.74.4 | 8 | |||
35.34 | odd | 2 | 1225.4.a.x.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.b.11.2 | ✓ | 4 | 7.5 | odd | 6 | ||
35.4.e.b.16.2 | yes | 4 | 7.3 | odd | 6 | ||
175.4.e.c.51.1 | 4 | 35.24 | odd | 6 | |||
175.4.e.c.151.1 | 4 | 35.19 | odd | 6 | |||
175.4.k.c.74.1 | 8 | 35.12 | even | 12 | |||
175.4.k.c.74.4 | 8 | 35.33 | even | 12 | |||
175.4.k.c.149.1 | 8 | 35.3 | even | 12 | |||
175.4.k.c.149.4 | 8 | 35.17 | even | 12 | |||
245.4.a.g.1.1 | 2 | 7.6 | odd | 2 | |||
245.4.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
245.4.e.l.116.2 | 4 | 7.2 | even | 3 | |||
245.4.e.l.226.2 | 4 | 7.4 | even | 3 | |||
315.4.j.c.46.1 | 4 | 21.5 | even | 6 | |||
315.4.j.c.226.1 | 4 | 21.17 | even | 6 | |||
560.4.q.i.81.2 | 4 | 28.19 | even | 6 | |||
560.4.q.i.401.2 | 4 | 28.3 | even | 6 | |||
1225.4.a.v.1.2 | 2 | 5.4 | even | 2 | |||
1225.4.a.x.1.2 | 2 | 35.34 | odd | 2 | |||
2205.4.a.bf.1.2 | 2 | 21.20 | even | 2 | |||
2205.4.a.bg.1.2 | 2 | 3.2 | odd | 2 |