Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, 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("147.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.57516.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 24x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.248072\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.248072 | 0.0877067 | 0.0438533 | − | 0.999038i | \(-0.486037\pi\) | ||||
0.0438533 | + | 0.999038i | \(0.486037\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −7.93846 | −0.992308 | ||||||||
\(5\) | 12.4346 | 1.11218 | 0.556092 | − | 0.831120i | \(-0.312300\pi\) | ||||
0.556092 | + | 0.831120i | \(0.312300\pi\) | |||||||
\(6\) | 0.744216 | 0.0506375 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.95388 | −0.174739 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 3.08468 | 0.0975460 | ||||||||
\(11\) | 60.3115 | 1.65315 | 0.826573 | − | 0.562829i | \(-0.190287\pi\) | ||||
0.826573 | + | 0.562829i | \(0.190287\pi\) | |||||||
\(12\) | −23.8154 | −0.572909 | ||||||||
\(13\) | −36.4269 | −0.777154 | −0.388577 | − | 0.921416i | \(-0.627033\pi\) | ||||
−0.388577 | + | 0.921416i | \(0.627033\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 37.3038 | 0.642120 | ||||||||
\(16\) | 62.5268 | 0.976982 | ||||||||
\(17\) | 48.7461 | 0.695451 | 0.347726 | − | 0.937596i | \(-0.386954\pi\) | ||||
0.347726 | + | 0.937596i | \(0.386954\pi\) | |||||||
\(18\) | 2.23265 | 0.0292356 | ||||||||
\(19\) | 50.5500 | 0.610366 | 0.305183 | − | 0.952294i | \(-0.401282\pi\) | ||||
0.305183 | + | 0.952294i | \(0.401282\pi\) | |||||||
\(20\) | −98.7116 | −1.10363 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 14.9616 | 0.144992 | ||||||||
\(23\) | 138.792 | 1.25827 | 0.629135 | − | 0.777296i | \(-0.283409\pi\) | ||||
0.629135 | + | 0.777296i | \(0.283409\pi\) | |||||||
\(24\) | −11.8617 | −0.100885 | ||||||||
\(25\) | 29.6194 | 0.236955 | ||||||||
\(26\) | −9.03649 | −0.0681616 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −61.1345 | −0.391462 | −0.195731 | − | 0.980658i | \(-0.562708\pi\) | ||||
−0.195731 | + | 0.980658i | \(0.562708\pi\) | |||||||
\(30\) | 9.25403 | 0.0563182 | ||||||||
\(31\) | 1.16935 | 0.00677490 | 0.00338745 | − | 0.999994i | \(-0.498922\pi\) | ||||
0.00338745 | + | 0.999994i | \(0.498922\pi\) | |||||||
\(32\) | 47.1422 | 0.260426 | ||||||||
\(33\) | 180.935 | 0.954444 | ||||||||
\(34\) | 12.0925 | 0.0609957 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −71.4461 | −0.330769 | ||||||||
\(37\) | 69.5268 | 0.308923 | 0.154461 | − | 0.987999i | \(-0.450636\pi\) | ||||
0.154461 | + | 0.987999i | \(0.450636\pi\) | |||||||
\(38\) | 12.5400 | 0.0535332 | ||||||||
\(39\) | −109.281 | −0.448690 | ||||||||
\(40\) | −49.1650 | −0.194342 | ||||||||
\(41\) | −308.115 | −1.17365 | −0.586823 | − | 0.809715i | \(-0.699622\pi\) | ||||
−0.586823 | + | 0.809715i | \(0.699622\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 174.443 | 0.618657 | 0.309329 | − | 0.950955i | \(-0.399896\pi\) | ||||
0.309329 | + | 0.950955i | \(0.399896\pi\) | |||||||
\(44\) | −478.781 | −1.64043 | ||||||||
\(45\) | 111.911 | 0.370728 | ||||||||
\(46\) | 34.4305 | 0.110359 | ||||||||
\(47\) | −389.362 | −1.20839 | −0.604194 | − | 0.796837i | \(-0.706505\pi\) | ||||
−0.604194 | + | 0.796837i | \(0.706505\pi\) | |||||||
\(48\) | 187.581 | 0.564061 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 7.34774 | 0.0207825 | ||||||||
\(51\) | 146.238 | 0.401519 | ||||||||
\(52\) | 289.173 | 0.771176 | ||||||||
\(53\) | 314.935 | 0.816220 | 0.408110 | − | 0.912933i | \(-0.366188\pi\) | ||||
0.408110 | + | 0.912933i | \(0.366188\pi\) | |||||||
\(54\) | 6.69794 | 0.0168792 | ||||||||
\(55\) | 749.950 | 1.83860 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 151.650 | 0.352395 | ||||||||
\(58\) | −15.1657 | −0.0343338 | ||||||||
\(59\) | −844.526 | −1.86352 | −0.931762 | − | 0.363068i | \(-0.881729\pi\) | ||||
−0.931762 | + | 0.363068i | \(0.881729\pi\) | |||||||
\(60\) | −296.135 | −0.637181 | ||||||||
\(61\) | 338.538 | 0.710579 | 0.355290 | − | 0.934756i | \(-0.384382\pi\) | ||||
0.355290 | + | 0.934756i | \(0.384382\pi\) | |||||||
\(62\) | 0.290084 | 0.000594204 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −488.520 | −0.954141 | ||||||||
\(65\) | −452.954 | −0.864339 | ||||||||
\(66\) | 44.8848 | 0.0837111 | ||||||||
\(67\) | −971.550 | −1.77155 | −0.885774 | − | 0.464117i | \(-0.846372\pi\) | ||||
−0.885774 | + | 0.464117i | \(0.846372\pi\) | |||||||
\(68\) | −386.969 | −0.690102 | ||||||||
\(69\) | 416.377 | 0.726463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −98.4698 | −0.164595 | −0.0822973 | − | 0.996608i | \(-0.526226\pi\) | ||||
−0.0822973 | + | 0.996608i | \(0.526226\pi\) | |||||||
\(72\) | −35.5850 | −0.0582462 | ||||||||
\(73\) | −710.235 | −1.13872 | −0.569361 | − | 0.822088i | \(-0.692809\pi\) | ||||
−0.569361 | + | 0.822088i | \(0.692809\pi\) | |||||||
\(74\) | 17.2477 | 0.0270946 | ||||||||
\(75\) | 88.8581 | 0.136806 | ||||||||
\(76\) | −401.289 | −0.605671 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −27.1095 | −0.0393531 | ||||||||
\(79\) | −486.884 | −0.693402 | −0.346701 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346701 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(80\) | 777.496 | 1.08658 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −76.4348 | −0.102937 | ||||||||
\(83\) | −605.688 | −0.800999 | −0.400499 | − | 0.916297i | \(-0.631163\pi\) | ||||
−0.400499 | + | 0.916297i | \(0.631163\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 606.139 | 0.773470 | ||||||||
\(86\) | 43.2743 | 0.0542604 | ||||||||
\(87\) | −183.403 | −0.226010 | ||||||||
\(88\) | −238.465 | −0.288869 | ||||||||
\(89\) | −218.069 | −0.259722 | −0.129861 | − | 0.991532i | \(-0.541453\pi\) | ||||
−0.129861 | + | 0.991532i | \(0.541453\pi\) | |||||||
\(90\) | 27.7621 | 0.0325153 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1101.80 | −1.24859 | ||||||||
\(93\) | 3.50806 | 0.00391149 | ||||||||
\(94\) | −96.5897 | −0.105984 | ||||||||
\(95\) | 628.569 | 0.678840 | ||||||||
\(96\) | 141.427 | 0.150357 | ||||||||
\(97\) | 782.288 | 0.818859 | 0.409429 | − | 0.912342i | \(-0.365728\pi\) | ||||
0.409429 | + | 0.912342i | \(0.365728\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 542.804 | 0.551049 | ||||||||
\(100\) | −235.132 | −0.235132 | ||||||||
\(101\) | 311.646 | 0.307029 | 0.153514 | − | 0.988146i | \(-0.450941\pi\) | ||||
0.153514 | + | 0.988146i | \(0.450941\pi\) | |||||||
\(102\) | 36.2776 | 0.0352159 | ||||||||
\(103\) | 149.258 | 0.142784 | 0.0713922 | − | 0.997448i | \(-0.477256\pi\) | ||||
0.0713922 | + | 0.997448i | \(0.477256\pi\) | |||||||
\(104\) | 144.028 | 0.135799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 78.1265 | 0.0715879 | ||||||||
\(107\) | 851.519 | 0.769341 | 0.384670 | − | 0.923054i | \(-0.374315\pi\) | ||||
0.384670 | + | 0.923054i | \(0.374315\pi\) | |||||||
\(108\) | −214.338 | −0.190970 | ||||||||
\(109\) | 1361.88 | 1.19674 | 0.598369 | − | 0.801221i | \(-0.295816\pi\) | ||||
0.598369 | + | 0.801221i | \(0.295816\pi\) | |||||||
\(110\) | 186.042 | 0.161258 | ||||||||
\(111\) | 208.581 | 0.178357 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1048.55 | 0.872917 | 0.436459 | − | 0.899724i | \(-0.356233\pi\) | ||||
0.436459 | + | 0.899724i | \(0.356233\pi\) | |||||||
\(114\) | 37.6201 | 0.0309074 | ||||||||
\(115\) | 1725.83 | 1.39943 | ||||||||
\(116\) | 485.313 | 0.388450 | ||||||||
\(117\) | −327.842 | −0.259051 | ||||||||
\(118\) | −209.503 | −0.163444 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −147.495 | −0.112203 | ||||||||
\(121\) | 2306.48 | 1.73289 | ||||||||
\(122\) | 83.9817 | 0.0623225 | ||||||||
\(123\) | −924.346 | −0.677605 | ||||||||
\(124\) | −9.28286 | −0.00672279 | ||||||||
\(125\) | −1186.02 | −0.848647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 488.408 | 0.341254 | 0.170627 | − | 0.985336i | \(-0.445421\pi\) | ||||
0.170627 | + | 0.985336i | \(0.445421\pi\) | |||||||
\(128\) | −498.326 | −0.344111 | ||||||||
\(129\) | 523.328 | 0.357182 | ||||||||
\(130\) | −112.365 | −0.0758083 | ||||||||
\(131\) | 1854.23 | 1.23668 | 0.618338 | − | 0.785912i | \(-0.287806\pi\) | ||||
0.618338 | + | 0.785912i | \(0.287806\pi\) | |||||||
\(132\) | −1436.34 | −0.947102 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −241.014 | −0.155377 | ||||||||
\(135\) | 335.734 | 0.214040 | ||||||||
\(136\) | −192.737 | −0.121522 | ||||||||
\(137\) | −511.115 | −0.318741 | −0.159370 | − | 0.987219i | \(-0.550946\pi\) | ||||
−0.159370 | + | 0.987219i | \(0.550946\pi\) | |||||||
\(138\) | 103.292 | 0.0637156 | ||||||||
\(139\) | −2266.10 | −1.38279 | −0.691397 | − | 0.722475i | \(-0.743005\pi\) | ||||
−0.691397 | + | 0.722475i | \(0.743005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1168.09 | −0.697663 | ||||||||
\(142\) | −24.4276 | −0.0144360 | ||||||||
\(143\) | −2196.96 | −1.28475 | ||||||||
\(144\) | 562.742 | 0.325661 | ||||||||
\(145\) | −760.183 | −0.435378 | ||||||||
\(146\) | −176.189 | −0.0998735 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −551.936 | −0.306546 | ||||||||
\(149\) | 1507.90 | 0.829074 | 0.414537 | − | 0.910033i | \(-0.363944\pi\) | ||||
0.414537 | + | 0.910033i | \(0.363944\pi\) | |||||||
\(150\) | 22.0432 | 0.0119988 | ||||||||
\(151\) | 1591.83 | 0.857887 | 0.428943 | − | 0.903331i | \(-0.358886\pi\) | ||||
0.428943 | + | 0.903331i | \(0.358886\pi\) | |||||||
\(152\) | −199.869 | −0.106655 | ||||||||
\(153\) | 438.715 | 0.231817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.5404 | 0.00753494 | ||||||||
\(156\) | 867.520 | 0.445239 | ||||||||
\(157\) | −1164.16 | −0.591784 | −0.295892 | − | 0.955221i | \(-0.595617\pi\) | ||||
−0.295892 | + | 0.955221i | \(0.595617\pi\) | |||||||
\(158\) | −120.782 | −0.0608160 | ||||||||
\(159\) | 944.805 | 0.471245 | ||||||||
\(160\) | 586.195 | 0.289642 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 20.0938 | 0.00974519 | ||||||||
\(163\) | −1155.88 | −0.555432 | −0.277716 | − | 0.960663i | \(-0.589577\pi\) | ||||
−0.277716 | + | 0.960663i | \(0.589577\pi\) | |||||||
\(164\) | 2445.96 | 1.16462 | ||||||||
\(165\) | 2249.85 | 1.06152 | ||||||||
\(166\) | −150.254 | −0.0702529 | ||||||||
\(167\) | 2890.61 | 1.33941 | 0.669707 | − | 0.742626i | \(-0.266420\pi\) | ||||
0.669707 | + | 0.742626i | \(0.266420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −870.082 | −0.396032 | ||||||||
\(170\) | 150.366 | 0.0678385 | ||||||||
\(171\) | 454.950 | 0.203455 | ||||||||
\(172\) | −1384.81 | −0.613898 | ||||||||
\(173\) | −1894.94 | −0.832770 | −0.416385 | − | 0.909188i | \(-0.636703\pi\) | ||||
−0.416385 | + | 0.909188i | \(0.636703\pi\) | |||||||
\(174\) | −45.4972 | −0.0198226 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3771.09 | 1.61509 | ||||||||
\(177\) | −2533.58 | −1.07591 | ||||||||
\(178\) | −54.0967 | −0.0227793 | ||||||||
\(179\) | −4288.49 | −1.79071 | −0.895355 | − | 0.445354i | \(-0.853078\pi\) | ||||
−0.895355 | + | 0.445354i | \(0.853078\pi\) | |||||||
\(180\) | −888.405 | −0.367876 | ||||||||
\(181\) | −383.732 | −0.157583 | −0.0787917 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787917 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1015.61 | 0.410253 | ||||||||
\(184\) | −548.769 | −0.219868 | ||||||||
\(185\) | 864.539 | 0.343579 | ||||||||
\(186\) | 0.870251 | 0.000343064 0 | ||||||||
\(187\) | 2939.95 | 1.14968 | ||||||||
\(188\) | 3090.93 | 1.19909 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 155.930 | 0.0595388 | ||||||||
\(191\) | 385.311 | 0.145969 | 0.0729845 | − | 0.997333i | \(-0.476748\pi\) | ||||
0.0729845 | + | 0.997333i | \(0.476748\pi\) | |||||||
\(192\) | −1465.56 | −0.550873 | ||||||||
\(193\) | 630.224 | 0.235049 | 0.117525 | − | 0.993070i | \(-0.462504\pi\) | ||||
0.117525 | + | 0.993070i | \(0.462504\pi\) | |||||||
\(194\) | 194.064 | 0.0718194 | ||||||||
\(195\) | −1358.86 | −0.499026 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1250.23 | −0.452158 | −0.226079 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226079 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(198\) | 134.654 | 0.0483307 | ||||||||
\(199\) | 1092.24 | 0.389081 | 0.194541 | − | 0.980894i | \(-0.437678\pi\) | ||||
0.194541 | + | 0.980894i | \(0.437678\pi\) | |||||||
\(200\) | −117.112 | −0.0414052 | ||||||||
\(201\) | −2914.65 | −1.02280 | ||||||||
\(202\) | 77.3105 | 0.0269285 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1160.91 | −0.398430 | ||||||||
\(205\) | −3831.29 | −1.30531 | ||||||||
\(206\) | 37.0267 | 0.0125232 | ||||||||
\(207\) | 1249.13 | 0.419423 | ||||||||
\(208\) | −2277.66 | −0.759265 | ||||||||
\(209\) | 3048.75 | 1.00902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3620.05 | −1.18111 | −0.590556 | − | 0.806997i | \(-0.701091\pi\) | ||||
−0.590556 | + | 0.806997i | \(0.701091\pi\) | |||||||
\(212\) | −2500.10 | −0.809941 | ||||||||
\(213\) | −295.409 | −0.0950287 | ||||||||
\(214\) | 211.238 | 0.0674763 | ||||||||
\(215\) | 2169.13 | 0.688061 | ||||||||
\(216\) | −106.755 | −0.0336285 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 337.844 | 0.104962 | ||||||||
\(219\) | −2130.70 | −0.657442 | ||||||||
\(220\) | −5953.45 | −1.82446 | ||||||||
\(221\) | −1775.67 | −0.540473 | ||||||||
\(222\) | 51.7430 | 0.0156431 | ||||||||
\(223\) | 183.844 | 0.0552069 | 0.0276034 | − | 0.999619i | \(-0.491212\pi\) | ||||
0.0276034 | + | 0.999619i | \(0.491212\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 266.574 | 0.0789850 | ||||||||
\(226\) | 260.117 | 0.0765607 | ||||||||
\(227\) | −2279.52 | −0.666506 | −0.333253 | − | 0.942837i | \(-0.608146\pi\) | ||||
−0.333253 | + | 0.942837i | \(0.608146\pi\) | |||||||
\(228\) | −1203.87 | −0.349684 | ||||||||
\(229\) | −5412.67 | −1.56192 | −0.780960 | − | 0.624582i | \(-0.785270\pi\) | ||||
−0.780960 | + | 0.624582i | \(0.785270\pi\) | |||||||
\(230\) | 428.130 | 0.122739 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 241.719 | 0.0684035 | ||||||||
\(233\) | 1138.37 | 0.320073 | 0.160036 | − | 0.987111i | \(-0.448839\pi\) | ||||
0.160036 | + | 0.987111i | \(0.448839\pi\) | |||||||
\(234\) | −81.3284 | −0.0227205 | ||||||||
\(235\) | −4841.56 | −1.34395 | ||||||||
\(236\) | 6704.24 | 1.84919 | ||||||||
\(237\) | −1460.65 | −0.400336 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6226.36 | −1.68515 | −0.842573 | − | 0.538583i | \(-0.818960\pi\) | ||||
−0.842573 | + | 0.538583i | \(0.818960\pi\) | |||||||
\(240\) | 2332.49 | 0.627340 | ||||||||
\(241\) | 3196.20 | 0.854295 | 0.427147 | − | 0.904182i | \(-0.359519\pi\) | ||||
0.427147 | + | 0.904182i | \(0.359519\pi\) | |||||||
\(242\) | 572.173 | 0.151986 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2687.47 | −0.705113 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −229.304 | −0.0594305 | ||||||||
\(247\) | −1841.38 | −0.474349 | ||||||||
\(248\) | −4.62349 | −0.00118384 | ||||||||
\(249\) | −1817.06 | −0.462457 | ||||||||
\(250\) | −294.218 | −0.0744320 | ||||||||
\(251\) | −239.608 | −0.0602546 | −0.0301273 | − | 0.999546i | \(-0.509591\pi\) | ||||
−0.0301273 | + | 0.999546i | \(0.509591\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8370.78 | 2.08010 | ||||||||
\(254\) | 121.160 | 0.0299302 | ||||||||
\(255\) | 1818.42 | 0.446563 | ||||||||
\(256\) | 3784.54 | 0.923960 | ||||||||
\(257\) | −699.117 | −0.169688 | −0.0848439 | − | 0.996394i | \(-0.527039\pi\) | ||||
−0.0848439 | + | 0.996394i | \(0.527039\pi\) | |||||||
\(258\) | 129.823 | 0.0313272 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3595.76 | 0.857690 | ||||||||
\(261\) | −550.210 | −0.130487 | ||||||||
\(262\) | 459.982 | 0.108465 | ||||||||
\(263\) | −919.040 | −0.215477 | −0.107738 | − | 0.994179i | \(-0.534361\pi\) | ||||
−0.107738 | + | 0.994179i | \(0.534361\pi\) | |||||||
\(264\) | −715.394 | −0.166778 | ||||||||
\(265\) | 3916.09 | 0.907787 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −654.206 | −0.149950 | ||||||||
\(268\) | 7712.61 | 1.75792 | ||||||||
\(269\) | 2779.17 | 0.629923 | 0.314961 | − | 0.949104i | \(-0.398008\pi\) | ||||
0.314961 | + | 0.949104i | \(0.398008\pi\) | |||||||
\(270\) | 83.2863 | 0.0187727 | ||||||||
\(271\) | −2226.98 | −0.499186 | −0.249593 | − | 0.968351i | \(-0.580297\pi\) | ||||
−0.249593 | + | 0.968351i | \(0.580297\pi\) | |||||||
\(272\) | 3047.94 | 0.679443 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −126.793 | −0.0279557 | ||||||||
\(275\) | 1786.39 | 0.391721 | ||||||||
\(276\) | −3305.39 | −0.720874 | ||||||||
\(277\) | 7307.69 | 1.58511 | 0.792557 | − | 0.609797i | \(-0.208749\pi\) | ||||
0.792557 | + | 0.609797i | \(0.208749\pi\) | |||||||
\(278\) | −562.157 | −0.121280 | ||||||||
\(279\) | 10.5242 | 0.00225830 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2730.61 | 0.579696 | 0.289848 | − | 0.957073i | \(-0.406395\pi\) | ||||
0.289848 | + | 0.957073i | \(0.406395\pi\) | |||||||
\(282\) | −289.769 | −0.0611897 | ||||||||
\(283\) | 1769.85 | 0.371755 | 0.185878 | − | 0.982573i | \(-0.440487\pi\) | ||||
0.185878 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(284\) | 781.698 | 0.163328 | ||||||||
\(285\) | 1885.71 | 0.391928 | ||||||||
\(286\) | −545.004 | −0.112681 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 424.280 | 0.0868088 | ||||||||
\(289\) | −2536.81 | −0.516347 | ||||||||
\(290\) | −188.580 | −0.0381855 | ||||||||
\(291\) | 2346.86 | 0.472768 | ||||||||
\(292\) | 5638.17 | 1.12996 | ||||||||
\(293\) | −8228.81 | −1.64072 | −0.820362 | − | 0.571844i | \(-0.806228\pi\) | ||||
−0.820362 | + | 0.571844i | \(0.806228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10501.4 | −2.07258 | ||||||||
\(296\) | −274.901 | −0.0539807 | ||||||||
\(297\) | 1628.41 | 0.318148 | ||||||||
\(298\) | 374.068 | 0.0727153 | ||||||||
\(299\) | −5055.78 | −0.977870 | ||||||||
\(300\) | −705.397 | −0.135754 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 394.887 | 0.0752424 | ||||||||
\(303\) | 934.937 | 0.177263 | ||||||||
\(304\) | 3160.73 | 0.596317 | ||||||||
\(305\) | 4209.58 | 0.790295 | ||||||||
\(306\) | 108.833 | 0.0203319 | ||||||||
\(307\) | −6019.62 | −1.11908 | −0.559541 | − | 0.828803i | \(-0.689023\pi\) | ||||
−0.559541 | + | 0.828803i | \(0.689023\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 447.773 | 0.0824366 | ||||||||
\(310\) | 3.60707 | 0.000660865 0 | ||||||||
\(311\) | −1193.71 | −0.217650 | −0.108825 | − | 0.994061i | \(-0.534709\pi\) | ||||
−0.108825 | + | 0.994061i | \(0.534709\pi\) | |||||||
\(312\) | 432.083 | 0.0784035 | ||||||||
\(313\) | 8846.04 | 1.59747 | 0.798734 | − | 0.601684i | \(-0.205503\pi\) | ||||
0.798734 | + | 0.601684i | \(0.205503\pi\) | |||||||
\(314\) | −288.795 | −0.0519034 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3865.11 | 0.688068 | ||||||||
\(317\) | 6081.43 | 1.07750 | 0.538750 | − | 0.842466i | \(-0.318897\pi\) | ||||
0.538750 | + | 0.842466i | \(0.318897\pi\) | |||||||
\(318\) | 234.380 | 0.0413313 | ||||||||
\(319\) | −3687.11 | −0.647143 | ||||||||
\(320\) | −6074.55 | −1.06118 | ||||||||
\(321\) | 2554.56 | 0.444179 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2464.12 | 0.424480 | ||||||||
\(324\) | −643.015 | −0.110256 | ||||||||
\(325\) | −1078.94 | −0.184151 | ||||||||
\(326\) | −286.741 | −0.0487151 | ||||||||
\(327\) | 4085.64 | 0.690936 | ||||||||
\(328\) | 1218.25 | 0.205082 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 558.125 | 0.0931023 | ||||||||
\(331\) | 3053.30 | 0.507022 | 0.253511 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253511 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(332\) | 4808.23 | 0.794837 | ||||||||
\(333\) | 625.742 | 0.102974 | ||||||||
\(334\) | 717.079 | 0.117475 | ||||||||
\(335\) | −12080.8 | −1.97029 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3865.80 | 0.624877 | 0.312438 | − | 0.949938i | \(-0.398854\pi\) | ||||
0.312438 | + | 0.949938i | \(0.398854\pi\) | |||||||
\(338\) | −215.843 | −0.0347346 | ||||||||
\(339\) | 3145.66 | 0.503979 | ||||||||
\(340\) | −4811.81 | −0.767521 | ||||||||
\(341\) | 70.5255 | 0.0111999 | ||||||||
\(342\) | 112.860 | 0.0178444 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −689.726 | −0.108103 | ||||||||
\(345\) | 5177.49 | 0.807961 | ||||||||
\(346\) | −470.080 | −0.0730395 | ||||||||
\(347\) | −99.5931 | −0.0154076 | −0.00770380 | − | 0.999970i | \(-0.502452\pi\) | ||||
−0.00770380 | + | 0.999970i | \(0.502452\pi\) | |||||||
\(348\) | 1455.94 | 0.224272 | ||||||||
\(349\) | 3607.34 | 0.553285 | 0.276643 | − | 0.960973i | \(-0.410778\pi\) | ||||
0.276643 | + | 0.960973i | \(0.410778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −983.526 | −0.149563 | ||||||||
\(352\) | 2843.22 | 0.430523 | ||||||||
\(353\) | −7130.73 | −1.07516 | −0.537579 | − | 0.843214i | \(-0.680661\pi\) | ||||
−0.537579 | + | 0.843214i | \(0.680661\pi\) | |||||||
\(354\) | −628.510 | −0.0943642 | ||||||||
\(355\) | −1224.43 | −0.183060 | ||||||||
\(356\) | 1731.13 | 0.257724 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1063.85 | −0.157057 | ||||||||
\(359\) | −6500.29 | −0.955632 | −0.477816 | − | 0.878460i | \(-0.658572\pi\) | ||||
−0.477816 | + | 0.878460i | \(0.658572\pi\) | |||||||
\(360\) | −442.485 | −0.0647806 | ||||||||
\(361\) | −4303.70 | −0.627453 | ||||||||
\(362\) | −95.1932 | −0.0138211 | ||||||||
\(363\) | 6919.44 | 1.00049 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8831.49 | −1.26647 | ||||||||
\(366\) | 251.945 | 0.0359819 | ||||||||
\(367\) | −824.886 | −0.117326 | −0.0586631 | − | 0.998278i | \(-0.518684\pi\) | ||||
−0.0586631 | + | 0.998278i | \(0.518684\pi\) | |||||||
\(368\) | 8678.25 | 1.22931 | ||||||||
\(369\) | −2773.04 | −0.391216 | ||||||||
\(370\) | 214.468 | 0.0301342 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −27.8486 | −0.00388140 | ||||||||
\(373\) | 1333.85 | 0.185159 | 0.0925793 | − | 0.995705i | \(-0.470489\pi\) | ||||
0.0925793 | + | 0.995705i | \(0.470489\pi\) | |||||||
\(374\) | 729.320 | 0.100835 | ||||||||
\(375\) | −3558.06 | −0.489967 | ||||||||
\(376\) | 1539.49 | 0.211152 | ||||||||
\(377\) | 2226.94 | 0.304226 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1338.29 | −0.181380 | −0.0906902 | − | 0.995879i | \(-0.528907\pi\) | ||||
−0.0906902 | + | 0.995879i | \(0.528907\pi\) | |||||||
\(380\) | −4989.87 | −0.673618 | ||||||||
\(381\) | 1465.22 | 0.197023 | ||||||||
\(382\) | 95.5847 | 0.0128025 | ||||||||
\(383\) | −353.376 | −0.0471453 | −0.0235727 | − | 0.999722i | \(-0.507504\pi\) | ||||
−0.0235727 | + | 0.999722i | \(0.507504\pi\) | |||||||
\(384\) | −1494.98 | −0.198673 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 156.341 | 0.0206154 | ||||||||
\(387\) | 1569.98 | 0.206219 | ||||||||
\(388\) | −6210.16 | −0.812560 | ||||||||
\(389\) | 11737.2 | 1.52982 | 0.764908 | − | 0.644139i | \(-0.222784\pi\) | ||||
0.764908 | + | 0.644139i | \(0.222784\pi\) | |||||||
\(390\) | −337.096 | −0.0437679 | ||||||||
\(391\) | 6765.59 | 0.875066 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5562.68 | 0.713996 | ||||||||
\(394\) | −310.147 | −0.0396573 | ||||||||
\(395\) | −6054.21 | −0.771191 | ||||||||
\(396\) | −4309.03 | −0.546810 | ||||||||
\(397\) | −13281.4 | −1.67903 | −0.839516 | − | 0.543335i | \(-0.817161\pi\) | ||||
−0.839516 | + | 0.543335i | \(0.817161\pi\) | |||||||
\(398\) | 270.955 | 0.0341250 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1852.01 | 0.231501 | ||||||||
\(401\) | −7482.36 | −0.931798 | −0.465899 | − | 0.884838i | \(-0.654269\pi\) | ||||
−0.465899 | + | 0.884838i | \(0.654269\pi\) | |||||||
\(402\) | −723.043 | −0.0897067 | ||||||||
\(403\) | −42.5959 | −0.00526514 | ||||||||
\(404\) | −2473.99 | −0.304667 | ||||||||
\(405\) | 1007.20 | 0.123576 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4193.27 | 0.510694 | ||||||||
\(408\) | −578.210 | −0.0701609 | ||||||||
\(409\) | 13796.6 | 1.66797 | 0.833983 | − | 0.551791i | \(-0.186055\pi\) | ||||
0.833983 | + | 0.551791i | \(0.186055\pi\) | |||||||
\(410\) | −950.436 | −0.114485 | ||||||||
\(411\) | −1533.35 | −0.184025 | ||||||||
\(412\) | −1184.88 | −0.141686 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 309.875 | 0.0367862 | ||||||||
\(415\) | −7531.49 | −0.890859 | ||||||||
\(416\) | −1717.24 | −0.202391 | ||||||||
\(417\) | −6798.31 | −0.798357 | ||||||||
\(418\) | 756.308 | 0.0884982 | ||||||||
\(419\) | −9497.56 | −1.10737 | −0.553683 | − | 0.832728i | \(-0.686778\pi\) | ||||
−0.553683 | + | 0.832728i | \(0.686778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 624.367 | 0.0722797 | 0.0361399 | − | 0.999347i | \(-0.488494\pi\) | ||||
0.0361399 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(422\) | −898.032 | −0.103591 | ||||||||
\(423\) | −3504.26 | −0.402796 | ||||||||
\(424\) | −1245.22 | −0.142625 | ||||||||
\(425\) | 1443.83 | 0.164791 | ||||||||
\(426\) | −73.2827 | −0.00833465 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6759.75 | −0.763423 | ||||||||
\(429\) | −6590.88 | −0.741750 | ||||||||
\(430\) | 538.099 | 0.0603475 | ||||||||
\(431\) | −13397.3 | −1.49727 | −0.748636 | − | 0.662981i | \(-0.769291\pi\) | ||||
−0.748636 | + | 0.662981i | \(0.769291\pi\) | |||||||
\(432\) | 1688.22 | 0.188020 | ||||||||
\(433\) | 14057.3 | 1.56016 | 0.780079 | − | 0.625681i | \(-0.215179\pi\) | ||||
0.780079 | + | 0.625681i | \(0.215179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2280.55 | −0.251365 | ||||||||
\(436\) | −10811.2 | −1.18753 | ||||||||
\(437\) | 7015.95 | 0.768006 | ||||||||
\(438\) | −528.568 | −0.0576620 | ||||||||
\(439\) | 16368.8 | 1.77960 | 0.889798 | − | 0.456356i | \(-0.150845\pi\) | ||||
0.889798 | + | 0.456356i | \(0.150845\pi\) | |||||||
\(440\) | −2965.22 | −0.321275 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −440.494 | −0.0474031 | ||||||||
\(443\) | −1178.71 | −0.126416 | −0.0632078 | − | 0.998000i | \(-0.520133\pi\) | ||||
−0.0632078 | + | 0.998000i | \(0.520133\pi\) | |||||||
\(444\) | −1655.81 | −0.176985 | ||||||||
\(445\) | −2711.60 | −0.288858 | ||||||||
\(446\) | 45.6067 | 0.00484201 | ||||||||
\(447\) | 4523.70 | 0.478666 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12400.9 | −1.30342 | −0.651709 | − | 0.758469i | \(-0.725948\pi\) | ||||
−0.651709 | + | 0.758469i | \(0.725948\pi\) | |||||||
\(450\) | 66.1296 | 0.00692751 | ||||||||
\(451\) | −18582.9 | −1.94021 | ||||||||
\(452\) | −8323.90 | −0.866202 | ||||||||
\(453\) | 4775.48 | 0.495301 | ||||||||
\(454\) | −565.484 | −0.0584570 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −599.606 | −0.0615771 | ||||||||
\(457\) | 9925.58 | 1.01597 | 0.507986 | − | 0.861365i | \(-0.330390\pi\) | ||||
0.507986 | + | 0.861365i | \(0.330390\pi\) | |||||||
\(458\) | −1342.73 | −0.136991 | ||||||||
\(459\) | 1316.15 | 0.133840 | ||||||||
\(460\) | −13700.4 | −1.38866 | ||||||||
\(461\) | 16010.3 | 1.61751 | 0.808755 | − | 0.588146i | \(-0.200142\pi\) | ||||
0.808755 | + | 0.588146i | \(0.200142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17372.4 | 1.74377 | 0.871883 | − | 0.489714i | \(-0.162899\pi\) | ||||
0.871883 | + | 0.489714i | \(0.162899\pi\) | |||||||
\(464\) | −3822.54 | −0.382451 | ||||||||
\(465\) | 43.6213 | 0.00435030 | ||||||||
\(466\) | 282.397 | 0.0280725 | ||||||||
\(467\) | −2108.06 | −0.208886 | −0.104443 | − | 0.994531i | \(-0.533306\pi\) | ||||
−0.104443 | + | 0.994531i | \(0.533306\pi\) | |||||||
\(468\) | 2602.56 | 0.257059 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1201.05 | −0.117873 | ||||||||
\(471\) | −3492.48 | −0.341667 | ||||||||
\(472\) | 3339.16 | 0.325630 | ||||||||
\(473\) | 10520.9 | 1.02273 | ||||||||
\(474\) | −362.347 | −0.0351121 | ||||||||
\(475\) | 1497.26 | 0.144629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2834.41 | 0.272073 | ||||||||
\(478\) | −1544.59 | −0.147798 | ||||||||
\(479\) | 2450.04 | 0.233706 | 0.116853 | − | 0.993149i | \(-0.462719\pi\) | ||||
0.116853 | + | 0.993149i | \(0.462719\pi\) | |||||||
\(480\) | 1758.58 | 0.167225 | ||||||||
\(481\) | −2532.65 | −0.240081 | ||||||||
\(482\) | 792.887 | 0.0749274 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18309.9 | −1.71956 | ||||||||
\(485\) | 9727.44 | 0.910722 | ||||||||
\(486\) | 60.2815 | 0.00562639 | ||||||||
\(487\) | 645.236 | 0.0600379 | 0.0300189 | − | 0.999549i | \(-0.490443\pi\) | ||||
0.0300189 | + | 0.999549i | \(0.490443\pi\) | |||||||
\(488\) | −1338.54 | −0.124166 | ||||||||
\(489\) | −3467.64 | −0.320679 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11766.1 | 1.08146 | 0.540731 | − | 0.841196i | \(-0.318148\pi\) | ||||
0.540731 | + | 0.841196i | \(0.318148\pi\) | |||||||
\(492\) | 7337.88 | 0.672393 | ||||||||
\(493\) | −2980.07 | −0.272242 | ||||||||
\(494\) | −456.794 | −0.0416035 | ||||||||
\(495\) | 6749.55 | 0.612868 | ||||||||
\(496\) | 73.1159 | 0.00661896 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −450.763 | −0.0405606 | ||||||||
\(499\) | −44.0209 | −0.00394919 | −0.00197459 | − | 0.999998i | \(-0.500629\pi\) | ||||
−0.00197459 | + | 0.999998i | \(0.500629\pi\) | |||||||
\(500\) | 9415.17 | 0.842119 | ||||||||
\(501\) | 8671.83 | 0.773311 | ||||||||
\(502\) | −59.4399 | −0.00528473 | ||||||||
\(503\) | −8290.27 | −0.734880 | −0.367440 | − | 0.930047i | \(-0.619766\pi\) | ||||
−0.367440 | + | 0.930047i | \(0.619766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3875.19 | 0.341473 | ||||||||
\(506\) | 2076.56 | 0.182439 | ||||||||
\(507\) | −2610.24 | −0.228649 | ||||||||
\(508\) | −3877.21 | −0.338629 | ||||||||
\(509\) | −6915.04 | −0.602168 | −0.301084 | − | 0.953598i | \(-0.597349\pi\) | ||||
−0.301084 | + | 0.953598i | \(0.597349\pi\) | |||||||
\(510\) | 451.098 | 0.0391666 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4925.45 | 0.425148 | ||||||||
\(513\) | 1364.85 | 0.117465 | ||||||||
\(514\) | −173.431 | −0.0148827 | ||||||||
\(515\) | 1855.96 | 0.158803 | ||||||||
\(516\) | −4154.42 | −0.354434 | ||||||||
\(517\) | −23483.0 | −1.99764 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5684.81 | −0.480800 | ||||||||
\(520\) | 1790.93 | 0.151033 | ||||||||
\(521\) | −13399.3 | −1.12674 | −0.563371 | − | 0.826204i | \(-0.690496\pi\) | ||||
−0.563371 | + | 0.826204i | \(0.690496\pi\) | |||||||
\(522\) | −136.492 | −0.0114446 | ||||||||
\(523\) | 9936.99 | 0.830811 | 0.415406 | − | 0.909636i | \(-0.363640\pi\) | ||||
0.415406 | + | 0.909636i | \(0.363640\pi\) | |||||||
\(524\) | −14719.7 | −1.22716 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −227.988 | −0.0188988 | ||||||||
\(527\) | 57.0014 | 0.00471161 | ||||||||
\(528\) | 11313.3 | 0.932475 | ||||||||
\(529\) | 7096.33 | 0.583244 | ||||||||
\(530\) | 971.472 | 0.0796190 | ||||||||
\(531\) | −7600.74 | −0.621175 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11223.7 | 0.912104 | ||||||||
\(534\) | −162.290 | −0.0131516 | ||||||||
\(535\) | 10588.3 | 0.855649 | ||||||||
\(536\) | 3841.40 | 0.309558 | ||||||||
\(537\) | −12865.5 | −1.03387 | ||||||||
\(538\) | 689.435 | 0.0552484 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2665.21 | −0.212394 | ||||||||
\(541\) | 9286.17 | 0.737973 | 0.368987 | − | 0.929435i | \(-0.379705\pi\) | ||||
0.368987 | + | 0.929435i | \(0.379705\pi\) | |||||||
\(542\) | −552.452 | −0.0437820 | ||||||||
\(543\) | −1151.20 | −0.0909809 | ||||||||
\(544\) | 2298.00 | 0.181114 | ||||||||
\(545\) | 16934.4 | 1.33099 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16821.6 | −1.31488 | −0.657438 | − | 0.753508i | \(-0.728360\pi\) | ||||
−0.657438 | + | 0.753508i | \(0.728360\pi\) | |||||||
\(548\) | 4057.47 | 0.316289 | ||||||||
\(549\) | 3046.84 | 0.236860 | ||||||||
\(550\) | 443.153 | 0.0343566 | ||||||||
\(551\) | −3090.35 | −0.238935 | ||||||||
\(552\) | −1646.31 | −0.126941 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1812.83 | 0.139025 | ||||||||
\(555\) | 2593.62 | 0.198366 | ||||||||
\(556\) | 17989.4 | 1.37216 | ||||||||
\(557\) | 1805.94 | 0.137379 | 0.0686897 | − | 0.997638i | \(-0.478118\pi\) | ||||
0.0686897 | + | 0.997638i | \(0.478118\pi\) | |||||||
\(558\) | 2.61075 | 0.000198068 0 | ||||||||
\(559\) | −6354.40 | −0.480792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8819.86 | 0.663770 | ||||||||
\(562\) | 677.388 | 0.0508432 | ||||||||
\(563\) | −12214.9 | −0.914381 | −0.457190 | − | 0.889369i | \(-0.651144\pi\) | ||||
−0.457190 | + | 0.889369i | \(0.651144\pi\) | |||||||
\(564\) | 9272.80 | 0.692296 | ||||||||
\(565\) | 13038.3 | 0.970845 | ||||||||
\(566\) | 439.050 | 0.0326054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 389.338 | 0.0287610 | ||||||||
\(569\) | 4283.77 | 0.315615 | 0.157808 | − | 0.987470i | \(-0.449557\pi\) | ||||
0.157808 | + | 0.987470i | \(0.449557\pi\) | |||||||
\(570\) | 467.791 | 0.0343747 | ||||||||
\(571\) | 6359.94 | 0.466121 | 0.233060 | − | 0.972462i | \(-0.425126\pi\) | ||||
0.233060 | + | 0.972462i | \(0.425126\pi\) | |||||||
\(572\) | 17440.5 | 1.27487 | ||||||||
\(573\) | 1155.93 | 0.0842753 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4110.95 | 0.298153 | ||||||||
\(576\) | −4396.68 | −0.318047 | ||||||||
\(577\) | −14468.7 | −1.04392 | −0.521959 | − | 0.852971i | \(-0.674799\pi\) | ||||
−0.521959 | + | 0.852971i | \(0.674799\pi\) | |||||||
\(578\) | −629.313 | −0.0452871 | ||||||||
\(579\) | 1890.67 | 0.135706 | ||||||||
\(580\) | 6034.68 | 0.432028 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 582.191 | 0.0414649 | ||||||||
\(583\) | 18994.2 | 1.34933 | ||||||||
\(584\) | 2808.19 | 0.198979 | ||||||||
\(585\) | −4076.59 | −0.288113 | ||||||||
\(586\) | −2041.34 | −0.143903 | ||||||||
\(587\) | 11132.6 | 0.782777 | 0.391388 | − | 0.920226i | \(-0.371995\pi\) | ||||
0.391388 | + | 0.920226i | \(0.371995\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.1108 | 0.00413517 | ||||||||
\(590\) | −2605.09 | −0.181779 | ||||||||
\(591\) | −3750.69 | −0.261054 | ||||||||
\(592\) | 4347.29 | 0.301812 | ||||||||
\(593\) | 19775.6 | 1.36946 | 0.684728 | − | 0.728799i | \(-0.259921\pi\) | ||||
0.684728 | + | 0.728799i | \(0.259921\pi\) | |||||||
\(594\) | 403.963 | 0.0279037 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11970.4 | −0.822696 | ||||||||
\(597\) | 3276.73 | 0.224636 | ||||||||
\(598\) | −1254.20 | −0.0857657 | ||||||||
\(599\) | −23891.0 | −1.62965 | −0.814825 | − | 0.579707i | \(-0.803167\pi\) | ||||
−0.814825 | + | 0.579707i | \(0.803167\pi\) | |||||||
\(600\) | −351.335 | −0.0239053 | ||||||||
\(601\) | −19395.5 | −1.31641 | −0.658204 | − | 0.752840i | \(-0.728683\pi\) | ||||
−0.658204 | + | 0.752840i | \(0.728683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8743.95 | −0.590516 | ||||||||
\(604\) | −12636.6 | −0.851288 | ||||||||
\(605\) | 28680.2 | 1.92730 | ||||||||
\(606\) | 231.932 | 0.0155472 | ||||||||
\(607\) | −14596.7 | −0.976051 | −0.488025 | − | 0.872829i | \(-0.662283\pi\) | ||||
−0.488025 | + | 0.872829i | \(0.662283\pi\) | |||||||
\(608\) | 2383.04 | 0.158956 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1044.28 | 0.0693142 | ||||||||
\(611\) | 14183.2 | 0.939104 | ||||||||
\(612\) | −3482.72 | −0.230034 | ||||||||
\(613\) | 1979.80 | 0.130446 | 0.0652229 | − | 0.997871i | \(-0.479224\pi\) | ||||
0.0652229 | + | 0.997871i | \(0.479224\pi\) | |||||||
\(614\) | −1493.30 | −0.0981509 | ||||||||
\(615\) | −11493.9 | −0.753622 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16262.4 | 1.06110 | 0.530551 | − | 0.847653i | \(-0.321985\pi\) | ||||
0.530551 | + | 0.847653i | \(0.321985\pi\) | |||||||
\(618\) | 111.080 | 0.00723024 | ||||||||
\(619\) | 12021.0 | 0.780555 | 0.390278 | − | 0.920697i | \(-0.372379\pi\) | ||||
0.390278 | + | 0.920697i | \(0.372379\pi\) | |||||||
\(620\) | −115.429 | −0.00747698 | ||||||||
\(621\) | 3747.39 | 0.242154 | ||||||||
\(622\) | −296.127 | −0.0190894 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6832.97 | −0.438362 | ||||||||
\(625\) | −18450.1 | −1.18081 | ||||||||
\(626\) | 2194.45 | 0.140109 | ||||||||
\(627\) | 9146.24 | 0.582561 | ||||||||
\(628\) | 9241.64 | 0.587232 | ||||||||
\(629\) | 3389.16 | 0.214841 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25347.6 | 1.59916 | 0.799582 | − | 0.600557i | \(-0.205055\pi\) | ||||
0.799582 | + | 0.600557i | \(0.205055\pi\) | |||||||
\(632\) | 1925.08 | 0.121164 | ||||||||
\(633\) | −10860.1 | −0.681915 | ||||||||
\(634\) | 1508.63 | 0.0945039 | ||||||||
\(635\) | 6073.16 | 0.379537 | ||||||||
\(636\) | −7500.29 | −0.467620 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −914.669 | −0.0567588 | ||||||||
\(639\) | −886.228 | −0.0548648 | ||||||||
\(640\) | −6196.49 | −0.382715 | ||||||||
\(641\) | −5111.60 | −0.314971 | −0.157485 | − | 0.987521i | \(-0.550339\pi\) | ||||
−0.157485 | + | 0.987521i | \(0.550339\pi\) | |||||||
\(642\) | 633.714 | 0.0389575 | ||||||||
\(643\) | 10931.3 | 0.670435 | 0.335217 | − | 0.942141i | \(-0.391190\pi\) | ||||
0.335217 | + | 0.942141i | \(0.391190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6507.38 | 0.397252 | ||||||||
\(646\) | 611.278 | 0.0372297 | ||||||||
\(647\) | 18406.1 | 1.11842 | 0.559211 | − | 0.829025i | \(-0.311104\pi\) | ||||
0.559211 | + | 0.829025i | \(0.311104\pi\) | |||||||
\(648\) | −320.265 | −0.0194154 | ||||||||
\(649\) | −50934.7 | −3.08068 | ||||||||
\(650\) | −267.655 | −0.0161512 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9175.91 | 0.551160 | ||||||||
\(653\) | 19921.4 | 1.19385 | 0.596926 | − | 0.802296i | \(-0.296389\pi\) | ||||
0.596926 | + | 0.802296i | \(0.296389\pi\) | |||||||
\(654\) | 1013.53 | 0.0605997 | ||||||||
\(655\) | 23056.6 | 1.37541 | ||||||||
\(656\) | −19265.5 | −1.14663 | ||||||||
\(657\) | −6392.11 | −0.379574 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18858.8 | −1.11477 | −0.557385 | − | 0.830254i | \(-0.688195\pi\) | ||||
−0.557385 | + | 0.830254i | \(0.688195\pi\) | |||||||
\(660\) | −17860.3 | −1.05335 | ||||||||
\(661\) | −25832.1 | −1.52005 | −0.760023 | − | 0.649896i | \(-0.774812\pi\) | ||||
−0.760023 | + | 0.649896i | \(0.774812\pi\) | |||||||
\(662\) | 757.437 | 0.0444692 | ||||||||
\(663\) | −5327.01 | −0.312042 | ||||||||
\(664\) | 2394.82 | 0.139965 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 155.229 | 0.00903153 | ||||||||
\(667\) | −8485.00 | −0.492564 | ||||||||
\(668\) | −22947.0 | −1.32911 | ||||||||
\(669\) | 551.533 | 0.0318737 | ||||||||
\(670\) | −2996.92 | −0.172807 | ||||||||
\(671\) | 20417.7 | 1.17469 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16275.0 | −0.932178 | −0.466089 | − | 0.884738i | \(-0.654337\pi\) | ||||
−0.466089 | + | 0.884738i | \(0.654337\pi\) | |||||||
\(674\) | 958.996 | 0.0548059 | ||||||||
\(675\) | 799.723 | 0.0456020 | ||||||||
\(676\) | 6907.11 | 0.392985 | ||||||||
\(677\) | 26271.8 | 1.49144 | 0.745720 | − | 0.666259i | \(-0.232105\pi\) | ||||
0.745720 | + | 0.666259i | \(0.232105\pi\) | |||||||
\(678\) | 780.350 | 0.0442023 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2396.60 | −0.135155 | ||||||||
\(681\) | −6838.55 | −0.384808 | ||||||||
\(682\) | 17.4954 | 0.000982306 0 | ||||||||
\(683\) | −8072.29 | −0.452237 | −0.226118 | − | 0.974100i | \(-0.572604\pi\) | ||||
−0.226118 | + | 0.974100i | \(0.572604\pi\) | |||||||
\(684\) | −3611.60 | −0.201890 | ||||||||
\(685\) | −6355.51 | −0.354499 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16238.0 | −0.901774 | ||||||||
\(688\) | 10907.3 | 0.604417 | ||||||||
\(689\) | −11472.1 | −0.634328 | ||||||||
\(690\) | 1284.39 | 0.0708636 | ||||||||
\(691\) | 24485.3 | 1.34799 | 0.673997 | − | 0.738734i | \(-0.264576\pi\) | ||||
0.673997 | + | 0.738734i | \(0.264576\pi\) | |||||||
\(692\) | 15042.9 | 0.826364 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −24.7062 | −0.00135135 | ||||||||
\(695\) | −28178.1 | −1.53792 | ||||||||
\(696\) | 725.156 | 0.0394928 | ||||||||
\(697\) | −15019.4 | −0.816214 | ||||||||
\(698\) | 894.880 | 0.0485268 | ||||||||
\(699\) | 3415.10 | 0.184794 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 778.448 | 0.0419423 | 0.0209712 | − | 0.999780i | \(-0.493324\pi\) | ||||
0.0209712 | + | 0.999780i | \(0.493324\pi\) | |||||||
\(702\) | −243.985 | −0.0131177 | ||||||||
\(703\) | 3514.58 | 0.188556 | ||||||||
\(704\) | −29463.4 | −1.57733 | ||||||||
\(705\) | −14524.7 | −0.775930 | ||||||||
\(706\) | −1768.93 | −0.0942985 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20112.7 | 1.06763 | ||||||||
\(709\) | −24172.0 | −1.28039 | −0.640197 | − | 0.768211i | \(-0.721147\pi\) | ||||
−0.640197 | + | 0.768211i | \(0.721147\pi\) | |||||||
\(710\) | −303.747 | −0.0160555 | ||||||||
\(711\) | −4381.96 | −0.231134 | ||||||||
\(712\) | 862.218 | 0.0453834 | ||||||||
\(713\) | 162.297 | 0.00852466 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27318.3 | −1.42888 | ||||||||
\(716\) | 34044.0 | 1.77693 | ||||||||
\(717\) | −18679.1 | −0.972919 | ||||||||
\(718\) | −1612.54 | −0.0838153 | ||||||||
\(719\) | 81.8835 | 0.00424720 | 0.00212360 | − | 0.999998i | \(-0.499324\pi\) | ||||
0.00212360 | + | 0.999998i | \(0.499324\pi\) | |||||||
\(720\) | 6997.47 | 0.362195 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1067.63 | −0.0550318 | ||||||||
\(723\) | 9588.59 | 0.493227 | ||||||||
\(724\) | 3046.24 | 0.156371 | ||||||||
\(725\) | −1810.76 | −0.0927588 | ||||||||
\(726\) | 1716.52 | 0.0877493 | ||||||||
\(727\) | 32542.9 | 1.66018 | 0.830088 | − | 0.557632i | \(-0.188290\pi\) | ||||
0.830088 | + | 0.557632i | \(0.188290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −2190.85 | −0.111078 | ||||||||
\(731\) | 8503.40 | 0.430246 | ||||||||
\(732\) | −8062.41 | −0.407097 | ||||||||
\(733\) | 5068.94 | 0.255424 | 0.127712 | − | 0.991811i | \(-0.459237\pi\) | ||||
0.127712 | + | 0.991811i | \(0.459237\pi\) | |||||||
\(734\) | −204.631 | −0.0102903 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6542.98 | 0.327687 | ||||||||
\(737\) | −58595.6 | −2.92863 | ||||||||
\(738\) | −687.913 | −0.0343122 | ||||||||
\(739\) | −38428.5 | −1.91287 | −0.956437 | − | 0.291939i | \(-0.905700\pi\) | ||||
−0.956437 | + | 0.291939i | \(0.905700\pi\) | |||||||
\(740\) | −6863.11 | −0.340936 | ||||||||
\(741\) | −5524.14 | −0.273865 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21592.9 | 1.06617 | 0.533086 | − | 0.846061i | \(-0.321032\pi\) | ||||
0.533086 | + | 0.846061i | \(0.321032\pi\) | |||||||
\(744\) | −13.8705 | −0.000683489 0 | ||||||||
\(745\) | 18750.1 | 0.922083 | ||||||||
\(746\) | 330.891 | 0.0162396 | ||||||||
\(747\) | −5451.19 | −0.267000 | ||||||||
\(748\) | −23338.7 | −1.14084 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −882.655 | −0.0429733 | ||||||||
\(751\) | 8112.60 | 0.394185 | 0.197093 | − | 0.980385i | \(-0.436850\pi\) | ||||
0.197093 | + | 0.980385i | \(0.436850\pi\) | |||||||
\(752\) | −24345.6 | −1.18057 | ||||||||
\(753\) | −718.823 | −0.0347880 | ||||||||
\(754\) | 552.441 | 0.0266826 | ||||||||
\(755\) | 19793.7 | 0.954129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3108.01 | 0.149224 | 0.0746120 | − | 0.997213i | \(-0.476228\pi\) | ||||
0.0746120 | + | 0.997213i | \(0.476228\pi\) | |||||||
\(758\) | −331.992 | −0.0159083 | ||||||||
\(759\) | 25112.3 | 1.20095 | ||||||||
\(760\) | −2485.29 | −0.118620 | ||||||||
\(761\) | 7211.93 | 0.343538 | 0.171769 | − | 0.985137i | \(-0.445052\pi\) | ||||
0.171769 | + | 0.985137i | \(0.445052\pi\) | |||||||
\(762\) | 363.481 | 0.0172802 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3058.77 | −0.144846 | ||||||||
\(765\) | 5455.25 | 0.257823 | ||||||||
\(766\) | −87.6626 | −0.00413496 | ||||||||
\(767\) | 30763.5 | 1.44825 | ||||||||
\(768\) | 11353.6 | 0.533448 | ||||||||
\(769\) | 7533.07 | 0.353250 | 0.176625 | − | 0.984278i | \(-0.443482\pi\) | ||||
0.176625 | + | 0.984278i | \(0.443482\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2097.35 | −0.0979693 | ||||||||
\(772\) | −5003.00 | −0.233241 | ||||||||
\(773\) | 24832.6 | 1.15546 | 0.577728 | − | 0.816229i | \(-0.303940\pi\) | ||||
0.577728 | + | 0.816229i | \(0.303940\pi\) | |||||||
\(774\) | 389.469 | 0.0180868 | ||||||||
\(775\) | 34.6355 | 0.00160535 | ||||||||
\(776\) | −3093.08 | −0.143086 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2911.66 | 0.134175 | ||||||||
\(779\) | −15575.2 | −0.716355 | ||||||||
\(780\) | 10787.3 | 0.495188 | ||||||||
\(781\) | −5938.86 | −0.272099 | ||||||||
\(782\) | 1678.35 | 0.0767491 | ||||||||
\(783\) | −1650.63 | −0.0753368 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14475.9 | −0.658173 | ||||||||
\(786\) | 1379.95 | 0.0626222 | ||||||||
\(787\) | −36313.1 | −1.64476 | −0.822378 | − | 0.568941i | \(-0.807353\pi\) | ||||
−0.822378 | + | 0.568941i | \(0.807353\pi\) | |||||||
\(788\) | 9924.89 | 0.448680 | ||||||||
\(789\) | −2757.12 | −0.124406 | ||||||||
\(790\) | −1501.88 | −0.0676386 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2146.18 | −0.0962895 | ||||||||
\(793\) | −12331.9 | −0.552229 | ||||||||
\(794\) | −3294.75 | −0.147262 | ||||||||
\(795\) | 11748.3 | 0.524111 | ||||||||
\(796\) | −8670.74 | −0.386088 | ||||||||
\(797\) | −31665.7 | −1.40735 | −0.703675 | − | 0.710522i | \(-0.748459\pi\) | ||||
−0.703675 | + | 0.710522i | \(0.748459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18979.9 | −0.840375 | ||||||||
\(800\) | 1396.32 | 0.0617094 | ||||||||
\(801\) | −1962.62 | −0.0865738 | ||||||||
\(802\) | −1856.16 | −0.0817249 | ||||||||
\(803\) | −42835.4 | −1.88247 | ||||||||
\(804\) | 23137.8 | 1.01494 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.5668 | −0.000461788 0 | ||||||||
\(807\) | 8337.52 | 0.363686 | ||||||||
\(808\) | −1232.21 | −0.0536498 | ||||||||
\(809\) | 12384.6 | 0.538219 | 0.269110 | − | 0.963110i | \(-0.413271\pi\) | ||||
0.269110 | + | 0.963110i | \(0.413271\pi\) | |||||||
\(810\) | 249.859 | 0.0108384 | ||||||||
\(811\) | −16742.4 | −0.724914 | −0.362457 | − | 0.932000i | \(-0.618062\pi\) | ||||
−0.362457 | + | 0.932000i | \(0.618062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6680.94 | −0.288205 | ||||||||
\(814\) | 1040.23 | 0.0447913 | ||||||||
\(815\) | −14372.9 | −0.617744 | ||||||||
\(816\) | 9143.82 | 0.392277 | ||||||||
\(817\) | 8818.07 | 0.377607 | ||||||||
\(818\) | 3422.55 | 0.146292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30414.6 | 1.29527 | ||||||||
\(821\) | 26456.3 | 1.12464 | 0.562322 | − | 0.826918i | \(-0.309908\pi\) | ||||
0.562322 | + | 0.826918i | \(0.309908\pi\) | |||||||
\(822\) | −380.380 | −0.0161402 | ||||||||
\(823\) | 23098.5 | 0.978328 | 0.489164 | − | 0.872192i | \(-0.337302\pi\) | ||||
0.489164 | + | 0.872192i | \(0.337302\pi\) | |||||||
\(824\) | −590.148 | −0.0249500 | ||||||||
\(825\) | 5359.17 | 0.226160 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20647.6 | 0.868183 | 0.434092 | − | 0.900869i | \(-0.357069\pi\) | ||||
0.434092 | + | 0.900869i | \(0.357069\pi\) | |||||||
\(828\) | −9916.18 | −0.416197 | ||||||||
\(829\) | 23368.5 | 0.979037 | 0.489519 | − | 0.871993i | \(-0.337173\pi\) | ||||
0.489519 | + | 0.871993i | \(0.337173\pi\) | |||||||
\(830\) | −1868.35 | −0.0781343 | ||||||||
\(831\) | 21923.1 | 0.915166 | ||||||||
\(832\) | 17795.3 | 0.741514 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1686.47 | −0.0700212 | ||||||||
\(835\) | 35943.6 | 1.48968 | ||||||||
\(836\) | −24202.3 | −1.00126 | ||||||||
\(837\) | 31.5725 | 0.00130383 | ||||||||
\(838\) | −2356.08 | −0.0971234 | ||||||||
\(839\) | −16735.5 | −0.688645 | −0.344322 | − | 0.938851i | \(-0.611891\pi\) | ||||
−0.344322 | + | 0.938851i | \(0.611891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20651.6 | −0.846758 | ||||||||
\(842\) | 154.888 | 0.00633941 | ||||||||
\(843\) | 8191.84 | 0.334688 | ||||||||
\(844\) | 28737.6 | 1.17203 | ||||||||
\(845\) | −10819.1 | −0.440460 | ||||||||
\(846\) | −869.307 | −0.0353279 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19691.9 | 0.797432 | ||||||||
\(849\) | 5309.55 | 0.214633 | ||||||||
\(850\) | 358.174 | 0.0144532 | ||||||||
\(851\) | 9649.80 | 0.388708 | ||||||||
\(852\) | 2345.09 | 0.0942977 | ||||||||
\(853\) | 10294.5 | 0.413219 | 0.206609 | − | 0.978424i | \(-0.433757\pi\) | ||||
0.206609 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5657.12 | 0.226280 | ||||||||
\(856\) | −3366.81 | −0.134434 | ||||||||
\(857\) | 32788.6 | 1.30693 | 0.653463 | − | 0.756958i | \(-0.273315\pi\) | ||||
0.653463 | + | 0.756958i | \(0.273315\pi\) | |||||||
\(858\) | −1635.01 | −0.0650565 | ||||||||
\(859\) | 4909.76 | 0.195016 | 0.0975081 | − | 0.995235i | \(-0.468913\pi\) | ||||
0.0975081 | + | 0.995235i | \(0.468913\pi\) | |||||||
\(860\) | −17219.5 | −0.682768 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3323.49 | −0.131321 | ||||||||
\(863\) | 17795.0 | 0.701909 | 0.350954 | − | 0.936393i | \(-0.385857\pi\) | ||||
0.350954 | + | 0.936393i | \(0.385857\pi\) | |||||||
\(864\) | 1272.84 | 0.0501191 | ||||||||
\(865\) | −23562.8 | −0.926195 | ||||||||
\(866\) | 3487.21 | 0.136836 | ||||||||
\(867\) | −7610.44 | −0.298113 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29364.7 | −1.14629 | ||||||||
\(870\) | −565.740 | −0.0220464 | ||||||||
\(871\) | 35390.5 | 1.37677 | ||||||||
\(872\) | −5384.71 | −0.209116 | ||||||||
\(873\) | 7040.59 | 0.272953 | ||||||||
\(874\) | 1740.46 | 0.0673592 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16914.5 | 0.652384 | ||||||||
\(877\) | 34672.2 | 1.33500 | 0.667501 | − | 0.744609i | \(-0.267364\pi\) | ||||
0.667501 | + | 0.744609i | \(0.267364\pi\) | |||||||
\(878\) | 4060.65 | 0.156082 | ||||||||
\(879\) | −24686.4 | −0.947273 | ||||||||
\(880\) | 46892.0 | 1.79628 | ||||||||
\(881\) | −40848.2 | −1.56210 | −0.781051 | − | 0.624467i | \(-0.785316\pi\) | ||||
−0.781051 | + | 0.624467i | \(0.785316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30035.1 | 1.14469 | 0.572345 | − | 0.820013i | \(-0.306034\pi\) | ||||
0.572345 | + | 0.820013i | \(0.306034\pi\) | |||||||
\(884\) | 14096.1 | 0.536315 | ||||||||
\(885\) | −31504.1 | −1.19661 | ||||||||
\(886\) | −292.404 | −0.0110875 | ||||||||
\(887\) | −33210.7 | −1.25717 | −0.628583 | − | 0.777742i | \(-0.716365\pi\) | ||||
−0.628583 | + | 0.777742i | \(0.716365\pi\) | |||||||
\(888\) | −824.703 | −0.0311658 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −672.671 | −0.0253348 | ||||||||
\(891\) | 4885.23 | 0.183683 | ||||||||
\(892\) | −1459.44 | −0.0547822 | ||||||||
\(893\) | −19682.2 | −0.737559 | ||||||||
\(894\) | 1122.20 | 0.0419822 | ||||||||
\(895\) | −53325.7 | −1.99160 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15167.3 | −0.564573 | ||||||||
\(898\) | −3076.32 | −0.114318 | ||||||||
\(899\) | −71.4878 | −0.00265211 | ||||||||
\(900\) | −2116.19 | −0.0783774 | ||||||||
\(901\) | 15351.9 | 0.567641 | ||||||||
\(902\) | −4609.90 | −0.170169 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4145.86 | −0.152532 | ||||||||
\(905\) | −4771.56 | −0.175262 | ||||||||
\(906\) | 1184.66 | 0.0434412 | ||||||||
\(907\) | 2497.83 | 0.0914433 | 0.0457217 | − | 0.998954i | \(-0.485441\pi\) | ||||
0.0457217 | + | 0.998954i | \(0.485441\pi\) | |||||||
\(908\) | 18095.9 | 0.661379 | ||||||||
\(909\) | 2804.81 | 0.102343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1895.00 | −0.0689180 | −0.0344590 | − | 0.999406i | \(-0.510971\pi\) | ||||
−0.0344590 | + | 0.999406i | \(0.510971\pi\) | |||||||
\(912\) | 9482.19 | 0.344284 | ||||||||
\(913\) | −36530.0 | −1.32417 | ||||||||
\(914\) | 2462.26 | 0.0891075 | ||||||||
\(915\) | 12628.8 | 0.456277 | ||||||||
\(916\) | 42968.3 | 1.54990 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 326.499 | 0.0117386 | ||||||||
\(919\) | 6270.71 | 0.225083 | 0.112542 | − | 0.993647i | \(-0.464101\pi\) | ||||
0.112542 | + | 0.993647i | \(0.464101\pi\) | |||||||
\(920\) | −6823.73 | −0.244534 | ||||||||
\(921\) | −18058.9 | −0.646102 | ||||||||
\(922\) | 3971.69 | 0.141866 | ||||||||
\(923\) | 3586.95 | 0.127915 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2059.34 | 0.0732008 | ||||||||
\(926\) | 4309.61 | 0.152940 | ||||||||
\(927\) | 1343.32 | 0.0475948 | ||||||||
\(928\) | −2882.01 | −0.101947 | ||||||||
\(929\) | 31552.6 | 1.11432 | 0.557161 | − | 0.830404i | \(-0.311890\pi\) | ||||
0.557161 | + | 0.830404i | \(0.311890\pi\) | |||||||
\(930\) | 10.8212 | 0.000381550 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9036.89 | −0.317611 | ||||||||
\(933\) | −3581.14 | −0.125661 | ||||||||
\(934\) | −522.951 | −0.0183207 | ||||||||
\(935\) | 36557.2 | 1.27866 | ||||||||
\(936\) | 1296.25 | 0.0452663 | ||||||||
\(937\) | 22030.2 | 0.768084 | 0.384042 | − | 0.923316i | \(-0.374532\pi\) | ||||
0.384042 | + | 0.923316i | \(0.374532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26538.1 | 0.922299 | ||||||||
\(940\) | 38434.5 | 1.33361 | ||||||||
\(941\) | 32538.6 | 1.12724 | 0.563618 | − | 0.826036i | \(-0.309409\pi\) | ||||
0.563618 | + | 0.826036i | \(0.309409\pi\) | |||||||
\(942\) | −866.386 | −0.0299664 | ||||||||
\(943\) | −42764.1 | −1.47677 | ||||||||
\(944\) | −52805.6 | −1.82063 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2609.94 | 0.0897003 | ||||||||
\(947\) | −40711.0 | −1.39697 | −0.698485 | − | 0.715625i | \(-0.746142\pi\) | ||||
−0.698485 | + | 0.715625i | \(0.746142\pi\) | |||||||
\(948\) | 11595.3 | 0.397256 | ||||||||
\(949\) | 25871.7 | 0.884962 | ||||||||
\(950\) | 371.428 | 0.0126850 | ||||||||
\(951\) | 18244.3 | 0.622095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52516.4 | −1.78507 | −0.892536 | − | 0.450976i | \(-0.851076\pi\) | ||||
−0.892536 | + | 0.450976i | \(0.851076\pi\) | |||||||
\(954\) | 703.139 | 0.0238626 | ||||||||
\(955\) | 4791.18 | 0.162345 | ||||||||
\(956\) | 49427.7 | 1.67218 | ||||||||
\(957\) | −11061.3 | −0.373628 | ||||||||
\(958\) | 607.786 | 0.0204976 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −18223.7 | −0.612673 | ||||||||
\(961\) | −29789.6 | −0.999954 | ||||||||
\(962\) | −628.279 | −0.0210567 | ||||||||
\(963\) | 7663.67 | 0.256447 | ||||||||
\(964\) | −25372.9 | −0.847723 | ||||||||
\(965\) | 7836.58 | 0.261418 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14721.6 | 0.489570 | 0.244785 | − | 0.969577i | \(-0.421283\pi\) | ||||
0.244785 | + | 0.969577i | \(0.421283\pi\) | |||||||
\(968\) | −9119.56 | −0.302803 | ||||||||
\(969\) | 7392.35 | 0.245074 | ||||||||
\(970\) | 2413.10 | 0.0798764 | ||||||||
\(971\) | −13772.5 | −0.455181 | −0.227590 | − | 0.973757i | \(-0.573085\pi\) | ||||
−0.227590 | + | 0.973757i | \(0.573085\pi\) | |||||||
\(972\) | −1929.05 | −0.0636566 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 160.065 | 0.00526572 | ||||||||
\(975\) | −3236.83 | −0.106319 | ||||||||
\(976\) | 21167.7 | 0.694223 | ||||||||
\(977\) | 24782.1 | 0.811513 | 0.405757 | − | 0.913981i | \(-0.367008\pi\) | ||||
0.405757 | + | 0.913981i | \(0.367008\pi\) | |||||||
\(978\) | −860.224 | −0.0281257 | ||||||||
\(979\) | −13152.0 | −0.429358 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12256.9 | 0.398912 | ||||||||
\(982\) | 2918.84 | 0.0948514 | ||||||||
\(983\) | −42804.7 | −1.38887 | −0.694435 | − | 0.719556i | \(-0.744345\pi\) | ||||
−0.694435 | + | 0.719556i | \(0.744345\pi\) | |||||||
\(984\) | 3654.76 | 0.118404 | ||||||||
\(985\) | −15546.1 | −0.502883 | ||||||||
\(986\) | −739.271 | −0.0238775 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14617.7 | 0.470700 | ||||||||
\(989\) | 24211.3 | 0.778438 | ||||||||
\(990\) | 1674.37 | 0.0537526 | ||||||||
\(991\) | 449.862 | 0.0144201 | 0.00721006 | − | 0.999974i | \(-0.497705\pi\) | ||||
0.00721006 | + | 0.999974i | \(0.497705\pi\) | |||||||
\(992\) | 55.1259 | 0.00176436 | ||||||||
\(993\) | 9159.89 | 0.292729 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13581.6 | 0.432730 | ||||||||
\(996\) | 14424.7 | 0.458899 | ||||||||
\(997\) | 21473.7 | 0.682127 | 0.341063 | − | 0.940040i | \(-0.389213\pi\) | ||||
0.341063 | + | 0.940040i | \(0.389213\pi\) | |||||||
\(998\) | −10.9203 | −0.000346370 0 | ||||||||
\(999\) | 1877.22 | 0.0594522 |
(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 | 147.4.a.m.1.2 | 3 | ||
3.2 | odd | 2 | 441.4.a.t.1.2 | 3 | |||
4.3 | odd | 2 | 2352.4.a.cg.1.3 | 3 | |||
7.2 | even | 3 | 147.4.e.n.67.2 | 6 | |||
7.3 | odd | 6 | 21.4.e.b.16.2 | yes | 6 | ||
7.4 | even | 3 | 147.4.e.n.79.2 | 6 | |||
7.5 | odd | 6 | 21.4.e.b.4.2 | ✓ | 6 | ||
7.6 | odd | 2 | 147.4.a.l.1.2 | 3 | |||
21.2 | odd | 6 | 441.4.e.w.361.2 | 6 | |||
21.5 | even | 6 | 63.4.e.c.46.2 | 6 | |||
21.11 | odd | 6 | 441.4.e.w.226.2 | 6 | |||
21.17 | even | 6 | 63.4.e.c.37.2 | 6 | |||
21.20 | even | 2 | 441.4.a.s.1.2 | 3 | |||
28.3 | even | 6 | 336.4.q.k.289.3 | 6 | |||
28.19 | even | 6 | 336.4.q.k.193.3 | 6 | |||
28.27 | even | 2 | 2352.4.a.ci.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.2 | ✓ | 6 | 7.5 | odd | 6 | ||
21.4.e.b.16.2 | yes | 6 | 7.3 | odd | 6 | ||
63.4.e.c.37.2 | 6 | 21.17 | even | 6 | |||
63.4.e.c.46.2 | 6 | 21.5 | even | 6 | |||
147.4.a.l.1.2 | 3 | 7.6 | odd | 2 | |||
147.4.a.m.1.2 | 3 | 1.1 | even | 1 | trivial | ||
147.4.e.n.67.2 | 6 | 7.2 | even | 3 | |||
147.4.e.n.79.2 | 6 | 7.4 | even | 3 | |||
336.4.q.k.193.3 | 6 | 28.19 | even | 6 | |||
336.4.q.k.289.3 | 6 | 28.3 | even | 6 | |||
441.4.a.s.1.2 | 3 | 21.20 | even | 2 | |||
441.4.a.t.1.2 | 3 | 3.2 | odd | 2 | |||
441.4.e.w.226.2 | 6 | 21.11 | odd | 6 | |||
441.4.e.w.361.2 | 6 | 21.2 | odd | 6 | |||
2352.4.a.cg.1.3 | 3 | 4.3 | odd | 2 | |||
2352.4.a.ci.1.1 | 3 | 28.27 | even | 2 |