Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,4,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(1.23904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-6}, \sqrt{-17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 46x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.4 | ||
Root | \(-1.67362i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.4.c.b.20.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.12311i | 1.45774i | 0.684653 | + | 0.728869i | \(0.259954\pi\) | ||||
−0.684653 | + | 0.728869i | \(0.740046\pi\) | |||||||
\(3\) | 5.04975 | − | 1.22474i | 0.971825 | − | 0.235702i | ||||
\(4\) | −9.00000 | −1.12500 | ||||||||
\(5\) | −10.0995 | −0.903327 | −0.451664 | − | 0.892188i | \(-0.649169\pi\) | ||||
−0.451664 | + | 0.892188i | \(0.649169\pi\) | |||||||
\(6\) | 5.04975 | + | 20.8207i | 0.343592 | + | 1.41667i | ||||
\(7\) | 7.00000 | − | 17.1464i | 0.377964 | − | 0.925820i | ||||
\(8\) | − | 4.12311i | − | 0.182217i | ||||||
\(9\) | 24.0000 | − | 12.3693i | 0.888889 | − | 0.458123i | ||||
\(10\) | − | 41.6413i | − | 1.31681i | ||||||
\(11\) | − | 32.9848i | − | 0.904119i | −0.891988 | − | 0.452059i | \(-0.850690\pi\) | ||
0.891988 | − | 0.452059i | \(-0.149310\pi\) | |||||||
\(12\) | −45.4478 | + | 11.0227i | −1.09330 | + | 0.265165i | ||||
\(13\) | 56.3383i | 1.20196i | 0.799266 | + | 0.600978i | \(0.205222\pi\) | ||||
−0.799266 | + | 0.600978i | \(0.794778\pi\) | |||||||
\(14\) | 70.6965 | + | 28.8617i | 1.34960 | + | 0.550973i | ||||
\(15\) | −51.0000 | + | 12.3693i | −0.877876 | + | 0.212916i | ||||
\(16\) | −55.0000 | −0.859375 | ||||||||
\(17\) | −60.5970 | −0.864526 | −0.432263 | − | 0.901748i | \(-0.642285\pi\) | ||||
−0.432263 | + | 0.901748i | \(0.642285\pi\) | |||||||
\(18\) | 51.0000 | + | 98.9545i | 0.667823 | + | 1.29577i | ||||
\(19\) | − | 36.7423i | − | 0.443646i | −0.975087 | − | 0.221823i | \(-0.928799\pi\) | ||
0.975087 | − | 0.221823i | \(-0.0712007\pi\) | |||||||
\(20\) | 90.8955 | 1.01624 | ||||||||
\(21\) | 14.3483 | − | 95.1584i | 0.149098 | − | 0.988822i | ||||
\(22\) | 136.000 | 1.31797 | ||||||||
\(23\) | 90.7083i | 0.822348i | 0.911557 | + | 0.411174i | \(0.134881\pi\) | ||||
−0.911557 | + | 0.411174i | \(0.865119\pi\) | |||||||
\(24\) | −5.04975 | − | 20.8207i | −0.0429490 | − | 0.177083i | ||||
\(25\) | −23.0000 | −0.184000 | ||||||||
\(26\) | −232.289 | −1.75214 | ||||||||
\(27\) | 106.045 | − | 91.8559i | 0.755864 | − | 0.654729i | ||||
\(28\) | −63.0000 | + | 154.318i | −0.425210 | + | 1.04155i | ||||
\(29\) | − | 57.7235i | − | 0.369620i | −0.982774 | − | 0.184810i | \(-0.940833\pi\) | ||
0.982774 | − | 0.184810i | \(-0.0591670\pi\) | |||||||
\(30\) | −51.0000 | − | 210.278i | −0.310376 | − | 1.27971i | ||||
\(31\) | 254.747i | 1.47593i | 0.674838 | + | 0.737966i | \(0.264214\pi\) | ||||
−0.674838 | + | 0.737966i | \(0.735786\pi\) | |||||||
\(32\) | − | 259.756i | − | 1.43496i | ||||||
\(33\) | −40.3980 | − | 166.565i | −0.213103 | − | 0.878645i | ||||
\(34\) | − | 249.848i | − | 1.26025i | ||||||
\(35\) | −70.6965 | + | 173.170i | −0.341426 | + | 0.836318i | ||||
\(36\) | −216.000 | + | 111.324i | −1.00000 | + | 0.515388i | ||||
\(37\) | 230.000 | 1.02194 | 0.510970 | − | 0.859599i | \(-0.329286\pi\) | ||||
0.510970 | + | 0.859599i | \(0.329286\pi\) | |||||||
\(38\) | 151.493 | 0.646719 | ||||||||
\(39\) | 69.0000 | + | 284.494i | 0.283304 | + | 1.16809i | ||||
\(40\) | 41.6413i | 0.164602i | ||||||||
\(41\) | 141.393 | 0.538583 | 0.269291 | − | 0.963059i | \(-0.413211\pi\) | ||||
0.269291 | + | 0.963059i | \(0.413211\pi\) | |||||||
\(42\) | 392.348 | + | 59.1594i | 1.44144 | + | 0.217345i | ||||
\(43\) | 44.0000 | 0.156045 | 0.0780225 | − | 0.996952i | \(-0.475139\pi\) | ||||
0.0780225 | + | 0.996952i | \(0.475139\pi\) | |||||||
\(44\) | 296.864i | 1.01713i | ||||||||
\(45\) | −242.388 | + | 124.924i | −0.802957 | + | 0.413835i | ||||
\(46\) | −374.000 | −1.19877 | ||||||||
\(47\) | 343.383 | 1.06569 | 0.532847 | − | 0.846212i | \(-0.321122\pi\) | ||||
0.532847 | + | 0.846212i | \(0.321122\pi\) | |||||||
\(48\) | −277.736 | + | 67.3610i | −0.835162 | + | 0.202557i | ||||
\(49\) | −245.000 | − | 240.050i | −0.714286 | − | 0.699854i | ||||
\(50\) | − | 94.8314i | − | 0.268224i | ||||||
\(51\) | −306.000 | + | 74.2159i | −0.840168 | + | 0.203771i | ||||
\(52\) | − | 507.044i | − | 1.35220i | ||||||
\(53\) | − | 206.155i | − | 0.534294i | −0.963656 | − | 0.267147i | \(-0.913919\pi\) | ||
0.963656 | − | 0.267147i | \(-0.0860810\pi\) | |||||||
\(54\) | 378.731 | + | 437.234i | 0.954423 | + | 1.10185i | ||||
\(55\) | 333.131i | 0.816715i | ||||||||
\(56\) | −70.6965 | − | 28.8617i | −0.168700 | − | 0.0688716i | ||||
\(57\) | −45.0000 | − | 185.540i | −0.104568 | − | 0.431146i | ||||
\(58\) | 238.000 | 0.538809 | ||||||||
\(59\) | −131.294 | −0.289711 | −0.144856 | − | 0.989453i | \(-0.546272\pi\) | ||||
−0.144856 | + | 0.989453i | \(0.546272\pi\) | |||||||
\(60\) | 459.000 | − | 111.324i | 0.987611 | − | 0.239531i | ||||
\(61\) | − | 71.0352i | − | 0.149100i | −0.997217 | − | 0.0745502i | \(-0.976248\pi\) | ||
0.997217 | − | 0.0745502i | \(-0.0237521\pi\) | |||||||
\(62\) | −1050.35 | −2.15152 | ||||||||
\(63\) | −44.0896 | − | 498.099i | −0.0881709 | − | 0.996105i | ||||
\(64\) | 631.000 | 1.23242 | ||||||||
\(65\) | − | 568.989i | − | 1.08576i | ||||||
\(66\) | 686.766 | − | 166.565i | 1.28083 | − | 0.310648i | ||||
\(67\) | −64.0000 | −0.116699 | −0.0583496 | − | 0.998296i | \(-0.518584\pi\) | ||||
−0.0583496 | + | 0.998296i | \(0.518584\pi\) | |||||||
\(68\) | 545.373 | 0.972592 | ||||||||
\(69\) | 111.095 | + | 458.055i | 0.193829 | + | 0.799178i | ||||
\(70\) | −714.000 | − | 291.489i | −1.21913 | − | 0.497709i | ||||
\(71\) | 461.788i | 0.771889i | 0.922522 | + | 0.385945i | \(0.126124\pi\) | ||||
−0.922522 | + | 0.385945i | \(0.873876\pi\) | |||||||
\(72\) | −51.0000 | − | 98.9545i | −0.0834779 | − | 0.161971i | ||||
\(73\) | − | 88.1816i | − | 0.141382i | −0.997498 | − | 0.0706910i | \(-0.977480\pi\) | ||
0.997498 | − | 0.0706910i | \(-0.0225204\pi\) | |||||||
\(74\) | 948.314i | 1.48972i | ||||||||
\(75\) | −116.144 | + | 28.1691i | −0.178816 | + | 0.0433692i | ||||
\(76\) | 330.681i | 0.499102i | ||||||||
\(77\) | −565.572 | − | 230.894i | −0.837051 | − | 0.341725i | ||||
\(78\) | −1173.00 | + | 284.494i | −1.70277 | + | 0.412982i | ||||
\(79\) | −442.000 | −0.629480 | −0.314740 | − | 0.949178i | \(-0.601917\pi\) | ||||
−0.314740 | + | 0.949178i | \(0.601917\pi\) | |||||||
\(80\) | 555.473 | 0.776297 | ||||||||
\(81\) | 423.000 | − | 593.727i | 0.580247 | − | 0.814441i | ||||
\(82\) | 582.979i | 0.785112i | ||||||||
\(83\) | 494.876 | 0.654454 | 0.327227 | − | 0.944946i | \(-0.393886\pi\) | ||||
0.327227 | + | 0.944946i | \(0.393886\pi\) | |||||||
\(84\) | −129.134 | + | 856.426i | −0.167735 | + | 1.11243i | ||||
\(85\) | 612.000 | 0.780950 | ||||||||
\(86\) | 181.417i | 0.227473i | ||||||||
\(87\) | −70.6965 | − | 291.489i | −0.0871203 | − | 0.359206i | ||||
\(88\) | −136.000 | −0.164746 | ||||||||
\(89\) | 484.776 | 0.577373 | 0.288686 | − | 0.957424i | \(-0.406782\pi\) | ||||
0.288686 | + | 0.957424i | \(0.406782\pi\) | |||||||
\(90\) | −515.075 | − | 999.392i | −0.603263 | − | 1.17050i | ||||
\(91\) | 966.000 | + | 394.368i | 1.11279 | + | 0.454297i | ||||
\(92\) | − | 816.375i | − | 0.925141i | ||||||
\(93\) | 312.000 | + | 1286.41i | 0.347881 | + | 1.43435i | ||||
\(94\) | 1415.81i | 1.55350i | ||||||||
\(95\) | 371.080i | 0.400757i | ||||||||
\(96\) | −318.134 | − | 1311.70i | −0.338224 | − | 1.39453i | ||||
\(97\) | − | 1092.47i | − | 1.14354i | −0.820413 | − | 0.571772i | \(-0.806256\pi\) | ||
0.820413 | − | 0.571772i | \(-0.193744\pi\) | |||||||
\(98\) | 989.751 | − | 1010.16i | 1.02020 | − | 1.04124i | ||||
\(99\) | −408.000 | − | 791.636i | −0.414197 | − | 0.803661i | ||||
\(100\) | 207.000 | 0.207000 | ||||||||
\(101\) | −1262.44 | −1.24374 | −0.621868 | − | 0.783122i | \(-0.713626\pi\) | ||||
−0.621868 | + | 0.783122i | \(0.713626\pi\) | |||||||
\(102\) | −306.000 | − | 1261.67i | −0.297044 | − | 1.22474i | ||||
\(103\) | 48.9898i | 0.0468651i | 0.999725 | + | 0.0234326i | \(0.00745950\pi\) | ||||
−0.999725 | + | 0.0234326i | \(0.992541\pi\) | |||||||
\(104\) | 232.289 | 0.219017 | ||||||||
\(105\) | −144.910 | + | 961.053i | −0.134684 | + | 0.893230i | ||||
\(106\) | 850.000 | 0.778861 | ||||||||
\(107\) | − | 1467.83i | − | 1.32617i | −0.748545 | − | 0.663084i | \(-0.769247\pi\) | ||
0.748545 | − | 0.663084i | \(-0.230753\pi\) | |||||||
\(108\) | −954.403 | + | 826.703i | −0.850347 | + | 0.736570i | ||||
\(109\) | −1870.00 | −1.64324 | −0.821622 | − | 0.570033i | \(-0.806930\pi\) | ||||
−0.821622 | + | 0.570033i | \(0.806930\pi\) | |||||||
\(110\) | −1373.53 | −1.19056 | ||||||||
\(111\) | 1161.44 | − | 281.691i | 0.993147 | − | 0.240873i | ||||
\(112\) | −385.000 | + | 943.054i | −0.324813 | + | 0.795627i | ||||
\(113\) | 1673.98i | 1.39358i | 0.717274 | + | 0.696791i | \(0.245390\pi\) | ||||
−0.717274 | + | 0.696791i | \(0.754610\pi\) | |||||||
\(114\) | 765.000 | − | 185.540i | 0.628498 | − | 0.152433i | ||||
\(115\) | − | 916.109i | − | 0.742849i | ||||||
\(116\) | 519.511i | 0.415823i | ||||||||
\(117\) | 696.866 | + | 1352.12i | 0.550643 | + | 1.06840i | ||||
\(118\) | − | 541.337i | − | 0.422323i | ||||||
\(119\) | −424.179 | + | 1039.02i | −0.326760 | + | 0.800395i | ||||
\(120\) | 51.0000 | + | 210.278i | 0.0387970 | + | 0.159964i | ||||
\(121\) | 243.000 | 0.182569 | ||||||||
\(122\) | 292.886 | 0.217349 | ||||||||
\(123\) | 714.000 | − | 173.170i | 0.523408 | − | 0.126945i | ||||
\(124\) | − | 2292.72i | − | 1.66042i | ||||||
\(125\) | 1494.73 | 1.06954 | ||||||||
\(126\) | 2053.72 | − | 181.786i | 1.45206 | − | 0.128530i | ||||
\(127\) | −1048.00 | −0.732244 | −0.366122 | − | 0.930567i | \(-0.619315\pi\) | ||||
−0.366122 | + | 0.930567i | \(0.619315\pi\) | |||||||
\(128\) | 523.634i | 0.361587i | ||||||||
\(129\) | 222.189 | − | 53.8888i | 0.151649 | − | 0.0367802i | ||||
\(130\) | 2346.00 | 1.58275 | ||||||||
\(131\) | −2555.17 | −1.70417 | −0.852086 | − | 0.523401i | \(-0.824663\pi\) | ||||
−0.852086 | + | 0.523401i | \(0.824663\pi\) | |||||||
\(132\) | 363.582 | + | 1499.09i | 0.239741 | + | 0.988476i | ||||
\(133\) | −630.000 | − | 257.196i | −0.410736 | − | 0.167682i | ||||
\(134\) | − | 263.879i | − | 0.170117i | ||||||
\(135\) | −1071.00 | + | 927.699i | −0.682793 | + | 0.591434i | ||||
\(136\) | 249.848i | 0.157532i | ||||||||
\(137\) | 1006.04i | 0.627384i | 0.949525 | + | 0.313692i | \(0.101566\pi\) | ||||
−0.949525 | + | 0.313692i | \(0.898434\pi\) | |||||||
\(138\) | −1888.61 | + | 458.055i | −1.16499 | + | 0.282552i | ||||
\(139\) | 1393.76i | 0.850483i | 0.905080 | + | 0.425242i | \(0.139811\pi\) | ||||
−0.905080 | + | 0.425242i | \(0.860189\pi\) | |||||||
\(140\) | 636.269 | − | 1558.53i | 0.384104 | − | 0.940858i | ||||
\(141\) | 1734.00 | − | 420.557i | 1.03567 | − | 0.251186i | ||||
\(142\) | −1904.00 | −1.12521 | ||||||||
\(143\) | 1858.31 | 1.08671 | ||||||||
\(144\) | −1320.00 | + | 680.312i | −0.763889 | + | 0.393699i | ||||
\(145\) | 582.979i | 0.333888i | ||||||||
\(146\) | 363.582 | 0.206098 | ||||||||
\(147\) | −1531.19 | − | 912.131i | −0.859118 | − | 0.511777i | ||||
\(148\) | −2070.00 | −1.14968 | ||||||||
\(149\) | − | 255.633i | − | 0.140552i | −0.997528 | − | 0.0702760i | \(-0.977612\pi\) | ||
0.997528 | − | 0.0702760i | \(-0.0223880\pi\) | |||||||
\(150\) | −116.144 | − | 478.875i | −0.0632210 | − | 0.260667i | ||||
\(151\) | 1448.00 | 0.780375 | 0.390187 | − | 0.920735i | \(-0.372410\pi\) | ||||
0.390187 | + | 0.920735i | \(0.372410\pi\) | |||||||
\(152\) | −151.493 | −0.0808399 | ||||||||
\(153\) | −1454.33 | + | 749.544i | −0.768467 | + | 0.396059i | ||||
\(154\) | 952.000 | − | 2331.91i | 0.498145 | − | 1.22020i | ||||
\(155\) | − | 2572.82i | − | 1.33325i | ||||||
\(156\) | −621.000 | − | 2560.45i | −0.318717 | − | 1.31410i | ||||
\(157\) | − | 3397.44i | − | 1.72704i | −0.504314 | − | 0.863520i | \(-0.668255\pi\) | ||
0.504314 | − | 0.863520i | \(-0.331745\pi\) | |||||||
\(158\) | − | 1822.41i | − | 0.917616i | ||||||
\(159\) | −252.488 | − | 1041.03i | −0.125934 | − | 0.519241i | ||||
\(160\) | 2623.40i | 1.29624i | ||||||||
\(161\) | 1555.32 | + | 634.958i | 0.761346 | + | 0.310818i | ||||
\(162\) | 2448.00 | + | 1744.07i | 1.18724 | + | 0.845848i | ||||
\(163\) | 3128.00 | 1.50309 | 0.751546 | − | 0.659681i | \(-0.229309\pi\) | ||||
0.751546 | + | 0.659681i | \(0.229309\pi\) | |||||||
\(164\) | −1272.54 | −0.605905 | ||||||||
\(165\) | 408.000 | + | 1682.23i | 0.192502 | + | 0.793704i | ||||
\(166\) | 2040.42i | 0.954022i | ||||||||
\(167\) | −706.965 | −0.327585 | −0.163792 | − | 0.986495i | \(-0.552373\pi\) | ||||
−0.163792 | + | 0.986495i | \(0.552373\pi\) | |||||||
\(168\) | −392.348 | − | 59.1594i | −0.180181 | − | 0.0271681i | ||||
\(169\) | −977.000 | −0.444697 | ||||||||
\(170\) | 2523.34i | 1.13842i | ||||||||
\(171\) | −454.478 | − | 881.816i | −0.203244 | − | 0.394352i | ||||
\(172\) | −396.000 | −0.175551 | ||||||||
\(173\) | 2252.19 | 0.989773 | 0.494887 | − | 0.868957i | \(-0.335210\pi\) | ||||
0.494887 | + | 0.868957i | \(0.335210\pi\) | |||||||
\(174\) | 1201.84 | − | 291.489i | 0.523628 | − | 0.126999i | ||||
\(175\) | −161.000 | + | 394.368i | −0.0695455 | + | 0.170351i | ||||
\(176\) | 1814.17i | 0.776977i | ||||||||
\(177\) | −663.000 | + | 160.801i | −0.281549 | + | 0.0682856i | ||||
\(178\) | 1998.78i | 0.841658i | ||||||||
\(179\) | − | 3496.39i | − | 1.45996i | −0.683469 | − | 0.729980i | \(-0.739529\pi\) | ||
0.683469 | − | 0.729980i | \(-0.260471\pi\) | |||||||
\(180\) | 2181.49 | − | 1124.32i | 0.903327 | − | 0.465564i | ||||
\(181\) | − | 183.712i | − | 0.0754430i | −0.999288 | − | 0.0377215i | \(-0.987990\pi\) | ||
0.999288 | − | 0.0377215i | \(-0.0120100\pi\) | |||||||
\(182\) | −1626.02 | + | 3982.92i | −0.662245 | + | 1.62216i | ||||
\(183\) | −87.0000 | − | 358.710i | −0.0351433 | − | 0.144900i | ||||
\(184\) | 374.000 | 0.149846 | ||||||||
\(185\) | −2322.89 | −0.923146 | ||||||||
\(186\) | −5304.00 | + | 1286.41i | −2.09090 | + | 0.507119i | ||||
\(187\) | 1998.78i | 0.781634i | ||||||||
\(188\) | −3090.45 | −1.19890 | ||||||||
\(189\) | −832.686 | − | 2461.28i | −0.320471 | − | 0.947258i | ||||
\(190\) | −1530.00 | −0.584199 | ||||||||
\(191\) | 263.879i | 0.0999665i | 0.998750 | + | 0.0499832i | \(0.0159168\pi\) | ||||
−0.998750 | + | 0.0499832i | \(0.984083\pi\) | |||||||
\(192\) | 3186.39 | − | 772.814i | 1.19770 | − | 0.290485i | ||||
\(193\) | −652.000 | −0.243171 | −0.121585 | − | 0.992581i | \(-0.538798\pi\) | ||||
−0.121585 | + | 0.992581i | \(0.538798\pi\) | |||||||
\(194\) | 4504.38 | 1.66699 | ||||||||
\(195\) | −696.866 | − | 2873.25i | −0.255916 | − | 1.05517i | ||||
\(196\) | 2205.00 | + | 2160.45i | 0.803571 | + | 0.787336i | ||||
\(197\) | 2020.32i | 0.730670i | 0.930876 | + | 0.365335i | \(0.119046\pi\) | ||||
−0.930876 | + | 0.365335i | \(0.880954\pi\) | |||||||
\(198\) | 3264.00 | − | 1682.23i | 1.17153 | − | 0.603791i | ||||
\(199\) | 4849.99i | 1.72767i | 0.503773 | + | 0.863836i | \(0.331945\pi\) | ||||
−0.503773 | + | 0.863836i | \(0.668055\pi\) | |||||||
\(200\) | 94.8314i | 0.0335280i | ||||||||
\(201\) | −323.184 | + | 78.3837i | −0.113411 | + | 0.0275063i | ||||
\(202\) | − | 5205.17i | − | 1.81304i | ||||||
\(203\) | −989.751 | − | 404.064i | −0.342202 | − | 0.139703i | ||||
\(204\) | 2754.00 | − | 667.943i | 0.945189 | − | 0.229242i | ||||
\(205\) | −1428.00 | −0.486516 | ||||||||
\(206\) | −201.990 | −0.0683171 | ||||||||
\(207\) | 1122.00 | + | 2177.00i | 0.376736 | + | 0.730976i | ||||
\(208\) | − | 3098.60i | − | 1.03293i | ||||||
\(209\) | −1211.94 | −0.401109 | ||||||||
\(210\) | −3962.52 | − | 597.481i | −1.30210 | − | 0.196334i | ||||
\(211\) | −2224.00 | −0.725623 | −0.362812 | − | 0.931863i | \(-0.618183\pi\) | ||||
−0.362812 | + | 0.931863i | \(0.618183\pi\) | |||||||
\(212\) | 1855.40i | 0.601081i | ||||||||
\(213\) | 565.572 | + | 2331.91i | 0.181936 | + | 0.750141i | ||||
\(214\) | 6052.00 | 1.93321 | ||||||||
\(215\) | −444.378 | −0.140960 | ||||||||
\(216\) | −378.731 | − | 437.234i | −0.119303 | − | 0.137731i | ||||
\(217\) | 4368.00 | + | 1783.23i | 1.36645 | + | 0.557850i | ||||
\(218\) | − | 7710.21i | − | 2.39542i | ||||||
\(219\) | −108.000 | − | 445.295i | −0.0333240 | − | 0.137399i | ||||
\(220\) | − | 2998.18i | − | 0.918804i | ||||||
\(221\) | − | 3413.93i | − | 1.03912i | ||||||
\(222\) | 1161.44 | + | 4788.75i | 0.351130 | + | 1.44775i | ||||
\(223\) | − | 1915.50i | − | 0.575208i | −0.957749 | − | 0.287604i | \(-0.907141\pi\) | ||
0.957749 | − | 0.287604i | \(-0.0928587\pi\) | |||||||
\(224\) | −4453.88 | − | 1818.29i | −1.32852 | − | 0.542364i | ||||
\(225\) | −552.000 | + | 284.494i | −0.163556 | + | 0.0842946i | ||||
\(226\) | −6902.00 | −2.03148 | ||||||||
\(227\) | 5948.61 | 1.73931 | 0.869654 | − | 0.493661i | \(-0.164342\pi\) | ||||
0.869654 | + | 0.493661i | \(0.164342\pi\) | |||||||
\(228\) | 405.000 | + | 1669.86i | 0.117639 | + | 0.485040i | ||||
\(229\) | − | 3706.08i | − | 1.06945i | −0.845025 | − | 0.534726i | \(-0.820415\pi\) | ||
0.845025 | − | 0.534726i | \(-0.179585\pi\) | |||||||
\(230\) | 3777.21 | 1.08288 | ||||||||
\(231\) | −3138.79 | − | 473.275i | −0.894013 | − | 0.134802i | ||||
\(232\) | −238.000 | −0.0673511 | ||||||||
\(233\) | 956.561i | 0.268954i | 0.990917 | + | 0.134477i | \(0.0429355\pi\) | ||||
−0.990917 | + | 0.134477i | \(0.957065\pi\) | |||||||
\(234\) | −5574.93 | + | 2873.25i | −1.55745 | + | 0.802694i | ||||
\(235\) | −3468.00 | −0.962670 | ||||||||
\(236\) | 1181.64 | 0.325925 | ||||||||
\(237\) | −2231.99 | + | 541.337i | −0.611744 | + | 0.148370i | ||||
\(238\) | −4284.00 | − | 1748.94i | −1.16677 | − | 0.476331i | ||||
\(239\) | 4791.05i | 1.29668i | 0.761350 | + | 0.648341i | \(0.224537\pi\) | ||||
−0.761350 | + | 0.648341i | \(0.775463\pi\) | |||||||
\(240\) | 2805.00 | − | 680.312i | 0.754425 | − | 0.182975i | ||||
\(241\) | 3786.91i | 1.01218i | 0.862479 | + | 0.506092i | \(0.168910\pi\) | ||||
−0.862479 | + | 0.506092i | \(0.831090\pi\) | |||||||
\(242\) | 1001.91i | 0.266138i | ||||||||
\(243\) | 1408.88 | − | 3516.24i | 0.371933 | − | 0.928260i | ||||
\(244\) | 639.317i | 0.167738i | ||||||||
\(245\) | 2474.38 | + | 2424.39i | 0.645234 | + | 0.632197i | ||||
\(246\) | 714.000 | + | 2943.90i | 0.185053 | + | 0.762992i | ||||
\(247\) | 2070.00 | 0.533243 | ||||||||
\(248\) | 1050.35 | 0.268940 | ||||||||
\(249\) | 2499.00 | − | 606.097i | 0.636015 | − | 0.154256i | ||||
\(250\) | 6162.92i | 1.55911i | ||||||||
\(251\) | −4029.70 | −1.01336 | −0.506678 | − | 0.862135i | \(-0.669127\pi\) | ||||
−0.506678 | + | 0.862135i | \(0.669127\pi\) | |||||||
\(252\) | 396.806 | + | 4482.90i | 0.0991923 | + | 1.12062i | ||||
\(253\) | 2992.00 | 0.743500 | ||||||||
\(254\) | − | 4321.01i | − | 1.06742i | ||||||
\(255\) | 3090.45 | − | 749.544i | 0.758947 | − | 0.184072i | ||||
\(256\) | 2889.00 | 0.705322 | ||||||||
\(257\) | 201.990 | 0.0490264 | 0.0245132 | − | 0.999700i | \(-0.492196\pi\) | ||||
0.0245132 | + | 0.999700i | \(0.492196\pi\) | |||||||
\(258\) | 222.189 | + | 916.109i | 0.0536159 | + | 0.221064i | ||||
\(259\) | 1610.00 | − | 3943.68i | 0.386257 | − | 0.946132i | ||||
\(260\) | 5120.90i | 1.22148i | ||||||||
\(261\) | −714.000 | − | 1385.36i | −0.169331 | − | 0.328551i | ||||
\(262\) | − | 10535.3i | − | 2.48424i | ||||||
\(263\) | 8279.20i | 1.94113i | 0.240840 | + | 0.970565i | \(0.422577\pi\) | ||||
−0.240840 | + | 0.970565i | \(0.577423\pi\) | |||||||
\(264\) | −686.766 | + | 166.565i | −0.160104 | + | 0.0388310i | ||||
\(265\) | 2082.07i | 0.482643i | ||||||||
\(266\) | 1060.45 | − | 2597.56i | 0.244437 | − | 0.598746i | ||||
\(267\) | 2448.00 | − | 593.727i | 0.561105 | − | 0.136088i | ||||
\(268\) | 576.000 | 0.131287 | ||||||||
\(269\) | −5787.02 | −1.31168 | −0.655838 | − | 0.754902i | \(-0.727684\pi\) | ||||
−0.655838 | + | 0.754902i | \(0.727684\pi\) | |||||||
\(270\) | −3825.00 | − | 4415.85i | −0.862156 | − | 0.995333i | ||||
\(271\) | − | 1219.85i | − | 0.273433i | −0.990610 | − | 0.136717i | \(-0.956345\pi\) | ||
0.990610 | − | 0.136717i | \(-0.0436549\pi\) | |||||||
\(272\) | 3332.84 | 0.742952 | ||||||||
\(273\) | 5361.06 | + | 808.356i | 1.18852 | + | 0.179209i | ||||
\(274\) | −4148.00 | −0.914561 | ||||||||
\(275\) | 758.651i | 0.166358i | ||||||||
\(276\) | −999.851 | − | 4122.49i | −0.218058 | − | 0.899075i | ||||
\(277\) | −3214.00 | −0.697150 | −0.348575 | − | 0.937281i | \(-0.613334\pi\) | ||||
−0.348575 | + | 0.937281i | \(0.613334\pi\) | |||||||
\(278\) | −5746.62 | −1.23978 | ||||||||
\(279\) | 3151.05 | + | 6113.93i | 0.676158 | + | 1.31194i | ||||
\(280\) | 714.000 | + | 291.489i | 0.152392 | + | 0.0622136i | ||||
\(281\) | − | 9235.76i | − | 1.96071i | −0.197245 | − | 0.980354i | \(-0.563200\pi\) | ||
0.197245 | − | 0.980354i | \(-0.436800\pi\) | |||||||
\(282\) | 1734.00 | + | 7149.47i | 0.366164 | + | 1.50973i | ||||
\(283\) | 2981.03i | 0.626162i | 0.949726 | + | 0.313081i | \(0.101361\pi\) | ||||
−0.949726 | + | 0.313081i | \(0.898639\pi\) | |||||||
\(284\) | − | 4156.09i | − | 0.868375i | ||||||
\(285\) | 454.478 | + | 1873.86i | 0.0944594 | + | 0.389466i | ||||
\(286\) | 7662.00i | 1.58414i | ||||||||
\(287\) | 989.751 | − | 2424.39i | 0.203565 | − | 0.498631i | ||||
\(288\) | −3213.00 | − | 6234.14i | −0.657388 | − | 1.27552i | ||||
\(289\) | −1241.00 | −0.252595 | ||||||||
\(290\) | −2403.68 | −0.486721 | ||||||||
\(291\) | −1338.00 | − | 5516.72i | −0.269536 | − | 1.11133i | ||||
\(292\) | 793.635i | 0.159055i | ||||||||
\(293\) | −5160.85 | −1.02901 | −0.514505 | − | 0.857487i | \(-0.672024\pi\) | ||||
−0.514505 | + | 0.857487i | \(0.672024\pi\) | |||||||
\(294\) | 3760.81 | − | 6313.26i | 0.746037 | − | 1.25237i | ||||
\(295\) | 1326.00 | 0.261704 | ||||||||
\(296\) | − | 948.314i | − | 0.186215i | ||||||
\(297\) | −3029.85 | − | 3497.87i | −0.591952 | − | 0.683391i | ||||
\(298\) | 1054.00 | 0.204888 | ||||||||
\(299\) | −5110.35 | −0.988425 | ||||||||
\(300\) | 1045.30 | − | 253.522i | 0.201168 | − | 0.0487904i | ||||
\(301\) | 308.000 | − | 754.443i | 0.0589795 | − | 0.144470i | ||||
\(302\) | 5970.26i | 1.13758i | ||||||||
\(303\) | −6375.00 | + | 1546.16i | −1.20869 | + | 0.293151i | ||||
\(304\) | 2020.83i | 0.381258i | ||||||||
\(305\) | 717.420i | 0.134686i | ||||||||
\(306\) | −3090.45 | − | 5996.35i | −0.577350 | − | 1.12022i | ||||
\(307\) | 1873.86i | 0.348361i | 0.984714 | + | 0.174180i | \(0.0557276\pi\) | ||||
−0.984714 | + | 0.174180i | \(0.944272\pi\) | |||||||
\(308\) | 5090.15 | + | 2078.05i | 0.941683 | + | 0.384440i | ||||
\(309\) | 60.0000 | + | 247.386i | 0.0110462 | + | 0.0455447i | ||||
\(310\) | 10608.0 | 1.94353 | ||||||||
\(311\) | 8564.38 | 1.56155 | 0.780774 | − | 0.624814i | \(-0.214825\pi\) | ||||
0.780774 | + | 0.624814i | \(0.214825\pi\) | |||||||
\(312\) | 1173.00 | − | 284.494i | 0.212846 | − | 0.0516228i | ||||
\(313\) | − | 533.989i | − | 0.0964308i | −0.998837 | − | 0.0482154i | \(-0.984647\pi\) | ||
0.998837 | − | 0.0482154i | \(-0.0153534\pi\) | |||||||
\(314\) | 14008.0 | 2.51757 | ||||||||
\(315\) | 445.283 | + | 5030.56i | 0.0796472 | + | 0.899809i | ||||
\(316\) | 3978.00 | 0.708165 | ||||||||
\(317\) | − | 5104.40i | − | 0.904391i | −0.891919 | − | 0.452195i | \(-0.850641\pi\) | ||
0.891919 | − | 0.452195i | \(-0.149359\pi\) | |||||||
\(318\) | 4292.29 | − | 1041.03i | 0.756917 | − | 0.183579i | ||||
\(319\) | −1904.00 | −0.334180 | ||||||||
\(320\) | −6372.79 | −1.11328 | ||||||||
\(321\) | −1797.71 | − | 7412.16i | −0.312581 | − | 1.28880i | ||||
\(322\) | −2618.00 | + | 6412.76i | −0.453091 | + | 1.10984i | ||||
\(323\) | 2226.48i | 0.383543i | ||||||||
\(324\) | −3807.00 | + | 5343.54i | −0.652778 | + | 0.916246i | ||||
\(325\) | − | 1295.78i | − | 0.221160i | ||||||
\(326\) | 12897.1i | 2.19111i | ||||||||
\(327\) | −9443.04 | + | 2290.27i | −1.59695 | + | 0.387316i | ||||
\(328\) | − | 582.979i | − | 0.0981390i | ||||||
\(329\) | 2403.68 | − | 5887.79i | 0.402794 | − | 0.986640i | ||||
\(330\) | −6936.00 | + | 1682.23i | −1.15701 | + | 0.280617i | ||||
\(331\) | 3632.00 | 0.603120 | 0.301560 | − | 0.953447i | \(-0.402493\pi\) | ||||
0.301560 | + | 0.953447i | \(0.402493\pi\) | |||||||
\(332\) | −4453.88 | −0.736261 | ||||||||
\(333\) | 5520.00 | − | 2844.94i | 0.908391 | − | 0.468174i | ||||
\(334\) | − | 2914.89i | − | 0.477532i | ||||||
\(335\) | 646.368 | 0.105418 | ||||||||
\(336\) | −789.155 | + | 5233.71i | −0.128131 | + | 0.849769i | ||||
\(337\) | −6256.00 | −1.01123 | −0.505617 | − | 0.862758i | \(-0.668735\pi\) | ||||
−0.505617 | + | 0.862758i | \(0.668735\pi\) | |||||||
\(338\) | − | 4028.27i | − | 0.648252i | ||||||
\(339\) | 2050.20 | + | 8453.19i | 0.328471 | + | 1.35432i | ||||
\(340\) | −5508.00 | −0.878568 | ||||||||
\(341\) | 8402.79 | 1.33442 | ||||||||
\(342\) | 3635.82 | − | 1873.86i | 0.574862 | − | 0.296277i | ||||
\(343\) | −5831.00 | + | 2520.52i | −0.917914 | + | 0.396780i | ||||
\(344\) | − | 181.417i | − | 0.0284341i | ||||||
\(345\) | −1122.00 | − | 4626.12i | −0.175091 | − | 0.721919i | ||||
\(346\) | 9286.02i | 1.44283i | ||||||||
\(347\) | − | 1072.01i | − | 0.165845i | −0.996556 | − | 0.0829227i | \(-0.973575\pi\) | ||
0.996556 | − | 0.0829227i | \(-0.0264255\pi\) | |||||||
\(348\) | 636.269 | + | 2623.40i | 0.0980103 | + | 0.404107i | ||||
\(349\) | − | 6287.84i | − | 0.964414i | −0.876057 | − | 0.482207i | \(-0.839835\pi\) | ||
0.876057 | − | 0.482207i | \(-0.160165\pi\) | |||||||
\(350\) | −1626.02 | − | 663.820i | −0.248327 | − | 0.101379i | ||||
\(351\) | 5175.00 | + | 5974.38i | 0.786955 | + | 0.908515i | ||||
\(352\) | −8568.00 | −1.29737 | ||||||||
\(353\) | −5292.14 | −0.797938 | −0.398969 | − | 0.916964i | \(-0.630632\pi\) | ||||
−0.398969 | + | 0.916964i | \(0.630632\pi\) | |||||||
\(354\) | −663.000 | − | 2733.62i | −0.0995425 | − | 0.410424i | ||||
\(355\) | − | 4663.83i | − | 0.697268i | ||||||
\(356\) | −4362.99 | −0.649544 | ||||||||
\(357\) | −869.462 | + | 5766.32i | −0.128899 | + | 0.854863i | ||||
\(358\) | 14416.0 | 2.12824 | ||||||||
\(359\) | 3207.78i | 0.471588i | 0.971803 | + | 0.235794i | \(0.0757690\pi\) | ||||
−0.971803 | + | 0.235794i | \(0.924231\pi\) | |||||||
\(360\) | 515.075 | + | 999.392i | 0.0754078 | + | 0.146313i | ||||
\(361\) | 5509.00 | 0.803178 | ||||||||
\(362\) | 757.463 | 0.109976 | ||||||||
\(363\) | 1227.09 | − | 297.613i | 0.177426 | − | 0.0430320i | ||||
\(364\) | −8694.00 | − | 3549.31i | −1.25189 | − | 0.511084i | ||||
\(365\) | 890.591i | 0.127714i | ||||||||
\(366\) | 1479.00 | − | 358.710i | 0.211226 | − | 0.0512297i | ||||
\(367\) | − | 9381.55i | − | 1.33437i | −0.744893 | − | 0.667184i | \(-0.767500\pi\) | ||
0.744893 | − | 0.667184i | \(-0.232500\pi\) | |||||||
\(368\) | − | 4988.96i | − | 0.706705i | ||||||
\(369\) | 3393.43 | − | 1748.94i | 0.478740 | − | 0.246737i | ||||
\(370\) | − | 9577.50i | − | 1.34570i | ||||||
\(371\) | −3534.83 | − | 1443.09i | −0.494661 | − | 0.201944i | ||||
\(372\) | −2808.00 | − | 11577.7i | −0.391366 | − | 1.61364i | ||||
\(373\) | 4598.00 | 0.638272 | 0.319136 | − | 0.947709i | \(-0.396607\pi\) | ||||
0.319136 | + | 0.947709i | \(0.396607\pi\) | |||||||
\(374\) | −8241.20 | −1.13942 | ||||||||
\(375\) | 7548.00 | − | 1830.66i | 1.03941 | − | 0.252093i | ||||
\(376\) | − | 1415.81i | − | 0.194188i | ||||||
\(377\) | 3252.04 | 0.444267 | ||||||||
\(378\) | 10148.1 | − | 3433.25i | 1.38085 | − | 0.467163i | ||||
\(379\) | 5252.00 | 0.711813 | 0.355906 | − | 0.934522i | \(-0.384172\pi\) | ||||
0.355906 | + | 0.934522i | \(0.384172\pi\) | |||||||
\(380\) | − | 3339.72i | − | 0.450852i | ||||||
\(381\) | −5292.14 | + | 1283.53i | −0.711613 | + | 0.172592i | ||||
\(382\) | −1088.00 | −0.145725 | ||||||||
\(383\) | −1918.91 | −0.256009 | −0.128005 | − | 0.991774i | \(-0.540857\pi\) | ||||
−0.128005 | + | 0.991774i | \(0.540857\pi\) | |||||||
\(384\) | 641.319 | + | 2644.22i | 0.0852270 | + | 0.351400i | ||||
\(385\) | 5712.00 | + | 2331.91i | 0.756131 | + | 0.308689i | ||||
\(386\) | − | 2688.26i | − | 0.354479i | ||||||
\(387\) | 1056.00 | − | 544.250i | 0.138707 | − | 0.0714878i | ||||
\(388\) | 9832.25i | 1.28649i | ||||||||
\(389\) | 7067.00i | 0.921109i | 0.887632 | + | 0.460554i | \(0.152349\pi\) | ||||
−0.887632 | + | 0.460554i | \(0.847651\pi\) | |||||||
\(390\) | 11846.7 | − | 2873.25i | 1.53816 | − | 0.373058i | ||||
\(391\) | − | 5496.65i | − | 0.710941i | ||||||
\(392\) | −989.751 | + | 1010.16i | −0.127526 | + | 0.130155i | ||||
\(393\) | −12903.0 | + | 3129.44i | −1.65616 | + | 0.401677i | ||||
\(394\) | −8330.00 | −1.06513 | ||||||||
\(395\) | 4463.98 | 0.568626 | ||||||||
\(396\) | 3672.00 | + | 7124.73i | 0.465972 | + | 0.904119i | ||||
\(397\) | 13337.5i | 1.68612i | 0.537822 | + | 0.843059i | \(0.319247\pi\) | ||||
−0.537822 | + | 0.843059i | \(0.680753\pi\) | |||||||
\(398\) | −19997.0 | −2.51849 | ||||||||
\(399\) | −3496.34 | − | 527.189i | −0.438687 | − | 0.0661465i | ||||
\(400\) | 1265.00 | 0.158125 | ||||||||
\(401\) | 13251.7i | 1.65027i | 0.564939 | + | 0.825133i | \(0.308900\pi\) | ||||
−0.564939 | + | 0.825133i | \(0.691100\pi\) | |||||||
\(402\) | −323.184 | − | 1332.52i | −0.0400969 | − | 0.165324i | ||||
\(403\) | −14352.0 | −1.77401 | ||||||||
\(404\) | 11361.9 | 1.39920 | ||||||||
\(405\) | −4272.09 | + | 5996.35i | −0.524153 | + | 0.735706i | ||||
\(406\) | 1666.00 | − | 4080.85i | 0.203651 | − | 0.498840i | ||||
\(407\) | − | 7586.51i | − | 0.923955i | ||||||
\(408\) | 306.000 | + | 1261.67i | 0.0371305 | + | 0.153093i | ||||
\(409\) | − | 7461.15i | − | 0.902029i | −0.892517 | − | 0.451015i | \(-0.851062\pi\) | ||
0.892517 | − | 0.451015i | \(-0.148938\pi\) | |||||||
\(410\) | − | 5887.79i | − | 0.709213i | ||||||
\(411\) | 1232.14 | + | 5080.24i | 0.147876 | + | 0.609708i | ||||
\(412\) | − | 440.908i | − | 0.0527233i | ||||||
\(413\) | −919.055 | + | 2251.22i | −0.109501 | + | 0.268221i | ||||
\(414\) | −8976.00 | + | 4626.12i | −1.06557 | + | 0.549183i | ||||
\(415\) | −4998.00 | −0.591186 | ||||||||
\(416\) | 14634.2 | 1.72476 | ||||||||
\(417\) | 1707.00 | + | 7038.14i | 0.200461 | + | 0.826521i | ||||
\(418\) | − | 4996.96i | − | 0.584711i | ||||||
\(419\) | 9261.25 | 1.07981 | 0.539906 | − | 0.841725i | \(-0.318460\pi\) | ||||
0.539906 | + | 0.841725i | \(0.318460\pi\) | |||||||
\(420\) | 1304.19 | − | 8649.48i | 0.151519 | − | 1.00488i | ||||
\(421\) | −2854.00 | −0.330393 | −0.165196 | − | 0.986261i | \(-0.552826\pi\) | ||||
−0.165196 | + | 0.986261i | \(0.552826\pi\) | |||||||
\(422\) | − | 9169.79i | − | 1.05777i | ||||||
\(423\) | 8241.20 | − | 4247.42i | 0.947283 | − | 0.488218i | ||||
\(424\) | −850.000 | −0.0973577 | ||||||||
\(425\) | 1393.73 | 0.159073 | ||||||||
\(426\) | −9614.73 | + | 2331.91i | −1.09351 | + | 0.265215i | ||||
\(427\) | −1218.00 | − | 497.246i | −0.138040 | − | 0.0563547i | ||||
\(428\) | 13210.4i | 1.49194i | ||||||||
\(429\) | 9384.00 | − | 2275.95i | 1.05609 | − | 0.256140i | ||||
\(430\) | − | 1832.22i | − | 0.205482i | ||||||
\(431\) | − | 11289.1i | − | 1.26166i | −0.775921 | − | 0.630830i | \(-0.782715\pi\) | ||
0.775921 | − | 0.630830i | \(-0.217285\pi\) | |||||||
\(432\) | −5832.46 | + | 5052.07i | −0.649571 | + | 0.562657i | ||||
\(433\) | 13036.2i | 1.44683i | 0.690411 | + | 0.723417i | \(0.257430\pi\) | ||||
−0.690411 | + | 0.723417i | \(0.742570\pi\) | |||||||
\(434\) | −7352.44 | + | 18009.7i | −0.813199 | + | 1.99192i | ||||
\(435\) | 714.000 | + | 2943.90i | 0.0786981 | + | 0.324481i | ||||
\(436\) | 16830.0 | 1.84865 | ||||||||
\(437\) | 3332.84 | 0.364831 | ||||||||
\(438\) | 1836.00 | − | 445.295i | 0.200291 | − | 0.0485777i | ||||
\(439\) | − | 3003.07i | − | 0.326490i | −0.986586 | − | 0.163245i | \(-0.947804\pi\) | ||
0.986586 | − | 0.163245i | \(-0.0521960\pi\) | |||||||
\(440\) | 1373.53 | 0.148820 | ||||||||
\(441\) | −8849.25 | − | 2730.72i | −0.955540 | − | 0.294862i | ||||
\(442\) | 14076.0 | 1.51477 | ||||||||
\(443\) | 6844.36i | 0.734052i | 0.930211 | + | 0.367026i | \(0.119624\pi\) | ||||
−0.930211 | + | 0.367026i | \(0.880376\pi\) | |||||||
\(444\) | −10453.0 | + | 2535.22i | −1.11729 | + | 0.270983i | ||||
\(445\) | −4896.00 | −0.521557 | ||||||||
\(446\) | 7897.81 | 0.838503 | ||||||||
\(447\) | −313.085 | − | 1290.88i | −0.0331284 | − | 0.136592i | ||||
\(448\) | 4417.00 | − | 10819.4i | 0.465812 | − | 1.14100i | ||||
\(449\) | − | 2655.28i | − | 0.279088i | −0.990216 | − | 0.139544i | \(-0.955436\pi\) | ||
0.990216 | − | 0.139544i | \(-0.0445636\pi\) | |||||||
\(450\) | −1173.00 | − | 2275.95i | −0.122879 | − | 0.238421i | ||||
\(451\) | − | 4663.83i | − | 0.486943i | ||||||
\(452\) | − | 15065.8i | − | 1.56778i | ||||||
\(453\) | 7312.04 | − | 1773.43i | 0.758388 | − | 0.183936i | ||||
\(454\) | 24526.7i | 2.53546i | ||||||||
\(455\) | −9756.12 | − | 3982.92i | −1.00522 | − | 0.410378i | ||||
\(456\) | −765.000 | + | 185.540i | −0.0785623 | + | 0.0190542i | ||||
\(457\) | 1196.00 | 0.122421 | 0.0612106 | − | 0.998125i | \(-0.480504\pi\) | ||||
0.0612106 | + | 0.998125i | \(0.480504\pi\) | |||||||
\(458\) | 15280.6 | 1.55898 | ||||||||
\(459\) | −6426.00 | + | 5566.19i | −0.653464 | + | 0.566030i | ||||
\(460\) | 8244.98i | 0.835705i | ||||||||
\(461\) | −5443.63 | −0.549968 | −0.274984 | − | 0.961449i | \(-0.588673\pi\) | ||||
−0.274984 | + | 0.961449i | \(0.588673\pi\) | |||||||
\(462\) | 1951.36 | − | 12941.5i | 0.196506 | − | 1.30324i | ||||
\(463\) | 926.000 | 0.0929479 | 0.0464739 | − | 0.998920i | \(-0.485202\pi\) | ||||
0.0464739 | + | 0.998920i | \(0.485202\pi\) | |||||||
\(464\) | 3174.79i | 0.317642i | ||||||||
\(465\) | −3151.05 | − | 12992.1i | −0.314250 | − | 1.29569i | ||||
\(466\) | −3944.00 | −0.392065 | ||||||||
\(467\) | −7786.72 | −0.771577 | −0.385788 | − | 0.922587i | \(-0.626071\pi\) | ||||
−0.385788 | + | 0.922587i | \(0.626071\pi\) | |||||||
\(468\) | −6271.79 | − | 12169.1i | −0.619474 | − | 1.20196i | ||||
\(469\) | −448.000 | + | 1097.37i | −0.0441081 | + | 0.108042i | ||||
\(470\) | − | 14298.9i | − | 1.40332i | ||||||
\(471\) | −4161.00 | − | 17156.2i | −0.407067 | − | 1.67838i | ||||
\(472\) | 541.337i | 0.0527904i | ||||||||
\(473\) | − | 1451.33i | − | 0.141083i | ||||||
\(474\) | −2231.99 | − | 9202.73i | −0.216284 | − | 0.891763i | ||||
\(475\) | 845.074i | 0.0816308i | ||||||||
\(476\) | 3817.61 | − | 9351.20i | 0.367605 | − | 0.900445i | ||||
\(477\) | −2550.00 | − | 4947.73i | −0.244772 | − | 0.474928i | ||||
\(478\) | −19754.0 | −1.89022 | ||||||||
\(479\) | −12503.2 | −1.19266 | −0.596331 | − | 0.802739i | \(-0.703375\pi\) | ||||
−0.596331 | + | 0.802739i | \(0.703375\pi\) | |||||||
\(480\) | 3213.00 | + | 13247.5i | 0.305526 | + | 1.25972i | ||||
\(481\) | 12957.8i | 1.22833i | ||||||||
\(482\) | −15613.8 | −1.47550 | ||||||||
\(483\) | 8631.66 | + | 1301.51i | 0.813156 | + | 0.122610i | ||||
\(484\) | −2187.00 | −0.205391 | ||||||||
\(485\) | 11033.4i | 1.03299i | ||||||||
\(486\) | 14497.8 | + | 5808.96i | 1.35316 | + | 0.542181i | ||||
\(487\) | 13712.0 | 1.27587 | 0.637936 | − | 0.770089i | \(-0.279788\pi\) | ||||
0.637936 | + | 0.770089i | \(0.279788\pi\) | |||||||
\(488\) | −292.886 | −0.0271687 | ||||||||
\(489\) | 15795.6 | − | 3831.00i | 1.46074 | − | 0.354282i | ||||
\(490\) | −9996.00 | + | 10202.1i | −0.921578 | + | 0.940582i | ||||
\(491\) | − | 5772.35i | − | 0.530555i | −0.964172 | − | 0.265277i | \(-0.914536\pi\) | ||
0.964172 | − | 0.265277i | \(-0.0854635\pi\) | |||||||
\(492\) | −6426.00 | + | 1558.53i | −0.588834 | + | 0.142813i | ||||
\(493\) | 3497.87i | 0.319546i | ||||||||
\(494\) | 8534.83i | 0.777328i | ||||||||
\(495\) | 4120.60 | + | 7995.13i | 0.374156 | + | 0.725969i | ||||
\(496\) | − | 14011.1i | − | 1.26838i | ||||||
\(497\) | 7918.01 | + | 3232.51i | 0.714631 | + | 0.291747i | ||||
\(498\) | 2499.00 | + | 10303.6i | 0.224865 | + | 0.927143i | ||||
\(499\) | 15476.0 | 1.38838 | 0.694189 | − | 0.719792i | \(-0.255763\pi\) | ||||
0.694189 | + | 0.719792i | \(0.255763\pi\) | |||||||
\(500\) | −13452.5 | −1.20323 | ||||||||
\(501\) | −3570.00 | + | 865.852i | −0.318355 | + | 0.0772124i | ||||
\(502\) | − | 16614.9i | − | 1.47721i | ||||||
\(503\) | 1696.72 | 0.150403 | 0.0752017 | − | 0.997168i | \(-0.476040\pi\) | ||||
0.0752017 | + | 0.997168i | \(0.476040\pi\) | |||||||
\(504\) | −2053.72 | + | 181.786i | −0.181508 | + | 0.0160663i | ||||
\(505\) | 12750.0 | 1.12350 | ||||||||
\(506\) | 12336.3i | 1.08383i | ||||||||
\(507\) | −4933.61 | + | 1196.58i | −0.432168 | + | 0.104816i | ||||
\(508\) | 9432.00 | 0.823774 | ||||||||
\(509\) | 4231.69 | 0.368500 | 0.184250 | − | 0.982879i | \(-0.441014\pi\) | ||||
0.184250 | + | 0.982879i | \(0.441014\pi\) | |||||||
\(510\) | 3090.45 | + | 12742.2i | 0.268328 | + | 1.10635i | ||||
\(511\) | −1512.00 | − | 617.271i | −0.130894 | − | 0.0534373i | ||||
\(512\) | 16100.7i | 1.38976i | ||||||||
\(513\) | −3375.00 | − | 3896.33i | −0.290468 | − | 0.335336i | ||||
\(514\) | 832.827i | 0.0714677i | ||||||||
\(515\) | − | 494.773i | − | 0.0423345i | ||||||
\(516\) | −1999.70 | + | 484.999i | −0.170605 | + | 0.0413777i | ||||
\(517\) | − | 11326.4i | − | 0.963513i | ||||||
\(518\) | 16260.2 | + | 6638.20i | 1.37921 | + | 0.563061i | ||||
\(519\) | 11373.0 | − | 2758.36i | 0.961887 | − | 0.233292i | ||||
\(520\) | −2346.00 | −0.197844 | ||||||||
\(521\) | −19572.8 | −1.64588 | −0.822938 | − | 0.568131i | \(-0.807667\pi\) | ||||
−0.822938 | + | 0.568131i | \(0.807667\pi\) | |||||||
\(522\) | 5712.00 | − | 2943.90i | 0.478941 | − | 0.246841i | ||||
\(523\) | − | 8369.91i | − | 0.699791i | −0.936789 | − | 0.349895i | \(-0.886217\pi\) | ||
0.936789 | − | 0.349895i | \(-0.113783\pi\) | |||||||
\(524\) | 22996.6 | 1.91719 | ||||||||
\(525\) | −330.010 | + | 2188.64i | −0.0274339 | + | 0.181943i | ||||
\(526\) | −34136.0 | −2.82966 | ||||||||
\(527\) | − | 15436.9i | − | 1.27598i | ||||||
\(528\) | 2221.89 | + | 9161.09i | 0.183135 | + | 0.755086i | ||||
\(529\) | 3939.00 | 0.323745 | ||||||||
\(530\) | −8584.58 | −0.703567 | ||||||||
\(531\) | −3151.05 | + | 1624.01i | −0.257521 | + | 0.132723i | ||||
\(532\) | 5670.00 | + | 2314.77i | 0.462078 | + | 0.188643i | ||||
\(533\) | 7965.84i | 0.647352i | ||||||||
\(534\) | 2448.00 | + | 10093.4i | 0.198381 | + | 0.817945i | ||||
\(535\) | 14824.3i | 1.19796i | ||||||||
\(536\) | 263.879i | 0.0212646i | ||||||||
\(537\) | −4282.19 | − | 17655.9i | −0.344116 | − | 1.41883i | ||||
\(538\) | − | 23860.5i | − | 1.91208i | ||||||
\(539\) | −7918.01 | + | 8081.29i | −0.632751 | + | 0.645799i | ||||
\(540\) | 9639.00 | − | 8349.29i | 0.768142 | − | 0.665363i | ||||
\(541\) | −16150.0 | −1.28344 | −0.641722 | − | 0.766938i | \(-0.721780\pi\) | ||||
−0.641722 | + | 0.766938i | \(0.721780\pi\) | |||||||
\(542\) | 5029.55 | 0.398594 | ||||||||
\(543\) | −225.000 | − | 927.699i | −0.0177821 | − | 0.0733174i | ||||
\(544\) | 15740.4i | 1.24056i | ||||||||
\(545\) | 18886.1 | 1.48439 | ||||||||
\(546\) | −3332.94 | + | 22104.2i | −0.261239 | + | 1.73255i | ||||
\(547\) | −18352.0 | −1.43451 | −0.717253 | − | 0.696813i | \(-0.754601\pi\) | ||||
−0.717253 | + | 0.696813i | \(0.754601\pi\) | |||||||
\(548\) | − | 9054.34i | − | 0.705807i | ||||||
\(549\) | −878.657 | − | 1704.84i | −0.0683063 | − | 0.132534i | ||||
\(550\) | −3128.00 | −0.242506 | ||||||||
\(551\) | −2120.90 | −0.163980 | ||||||||
\(552\) | 1888.61 | − | 458.055i | 0.145624 | − | 0.0353190i | ||||
\(553\) | −3094.00 | + | 7578.72i | −0.237921 | + | 0.582785i | ||||
\(554\) | − | 13251.7i | − | 1.01626i | ||||||
\(555\) | −11730.0 | + | 2844.94i | −0.897137 | + | 0.217588i | ||||
\(556\) | − | 12543.8i | − | 0.956793i | ||||||
\(557\) | − | 3323.22i | − | 0.252800i | −0.991979 | − | 0.126400i | \(-0.959658\pi\) | ||
0.991979 | − | 0.126400i | \(-0.0403423\pi\) | |||||||
\(558\) | −25208.4 | + | 12992.1i | −1.91246 | + | 0.985662i | ||||
\(559\) | 2478.88i | 0.187559i | ||||||||
\(560\) | 3888.31 | − | 9524.37i | 0.293413 | − | 0.718711i | ||||
\(561\) | 2448.00 | + | 10093.4i | 0.184233 | + | 0.759612i | ||||
\(562\) | 38080.0 | 2.85820 | ||||||||
\(563\) | 14290.8 | 1.06978 | 0.534889 | − | 0.844922i | \(-0.320353\pi\) | ||||
0.534889 | + | 0.844922i | \(0.320353\pi\) | |||||||
\(564\) | −15606.0 | + | 3785.01i | −1.16513 | + | 0.282585i | ||||
\(565\) | − | 16906.4i | − | 1.25886i | ||||||
\(566\) | −12291.1 | −0.912780 | ||||||||
\(567\) | −7219.30 | − | 11409.0i | −0.534713 | − | 0.845034i | ||||
\(568\) | 1904.00 | 0.140652 | ||||||||
\(569\) | − | 14801.9i | − | 1.09056i | −0.838253 | − | 0.545281i | \(-0.816423\pi\) | ||
0.838253 | − | 0.545281i | \(-0.183577\pi\) | |||||||
\(570\) | −7726.12 | + | 1873.86i | −0.567740 | + | 0.137697i | ||||
\(571\) | 4136.00 | 0.303128 | 0.151564 | − | 0.988447i | \(-0.451569\pi\) | ||||
0.151564 | + | 0.988447i | \(0.451569\pi\) | |||||||
\(572\) | −16724.8 | −1.22255 | ||||||||
\(573\) | 323.184 | + | 1332.52i | 0.0235623 | + | 0.0971500i | ||||
\(574\) | 9996.00 | + | 4080.85i | 0.726873 | + | 0.296745i | ||||
\(575\) | − | 2086.29i | − | 0.151312i | ||||||
\(576\) | 15144.0 | − | 7805.04i | 1.09549 | − | 0.564601i | ||||
\(577\) | 19458.7i | 1.40395i | 0.712202 | + | 0.701974i | \(0.247698\pi\) | ||||
−0.712202 | + | 0.701974i | \(0.752302\pi\) | |||||||
\(578\) | − | 5116.77i | − | 0.368218i | ||||||
\(579\) | −3292.44 | + | 798.534i | −0.236320 | + | 0.0573159i | ||||
\(580\) | − | 5246.81i | − | 0.375624i | ||||||
\(581\) | 3464.13 | − | 8485.35i | 0.247360 | − | 0.605907i | ||||
\(582\) | 22746.0 | − | 5516.72i | 1.62002 | − | 0.392913i | ||||
\(583\) | −6800.00 | −0.483066 | ||||||||
\(584\) | −363.582 | −0.0257622 | ||||||||
\(585\) | −7038.00 | − | 13655.7i | −0.497411 | − | 0.965119i | ||||
\(586\) | − | 21278.7i | − | 1.50003i | ||||||
\(587\) | 18310.4 | 1.28748 | 0.643740 | − | 0.765244i | \(-0.277382\pi\) | ||||
0.643740 | + | 0.765244i | \(0.277382\pi\) | |||||||
\(588\) | 13780.7 | + | 8209.18i | 0.966508 | + | 0.575749i | ||||
\(589\) | 9360.00 | 0.654791 | ||||||||
\(590\) | 5467.24i | 0.381496i | ||||||||
\(591\) | 2474.38 | + | 10202.1i | 0.172221 | + | 0.710083i | ||||
\(592\) | −12650.0 | −0.878229 | ||||||||
\(593\) | −7998.81 | −0.553915 | −0.276958 | − | 0.960882i | \(-0.589326\pi\) | ||||
−0.276958 | + | 0.960882i | \(0.589326\pi\) | |||||||
\(594\) | 14422.1 | − | 12492.4i | 0.996205 | − | 0.862911i | ||||
\(595\) | 4284.00 | − | 10493.6i | 0.295171 | − | 0.723019i | ||||
\(596\) | 2300.69i | 0.158121i | ||||||||
\(597\) | 5940.00 | + | 24491.2i | 0.407216 | + | 1.67900i | ||||
\(598\) | − | 21070.5i | − | 1.44086i | ||||||
\(599\) | 12435.3i | 0.848234i | 0.905607 | + | 0.424117i | \(0.139415\pi\) | ||||
−0.905607 | + | 0.424117i | \(0.860585\pi\) | |||||||
\(600\) | 116.144 | + | 478.875i | 0.00790262 | + | 0.0325833i | ||||
\(601\) | 18557.3i | 1.25952i | 0.776791 | + | 0.629758i | \(0.216846\pi\) | ||||
−0.776791 | + | 0.629758i | \(0.783154\pi\) | |||||||
\(602\) | 3110.65 | + | 1269.92i | 0.210599 | + | 0.0859766i | ||||
\(603\) | −1536.00 | + | 791.636i | −0.103733 | + | 0.0534626i | ||||
\(604\) | −13032.0 | −0.877921 | ||||||||
\(605\) | −2454.18 | −0.164920 | ||||||||
\(606\) | −6375.00 | − | 26284.8i | −0.427338 | − | 1.76196i | ||||
\(607\) | 1592.17i | 0.106465i | 0.998582 | + | 0.0532324i | \(0.0169524\pi\) | ||||
−0.998582 | + | 0.0532324i | \(0.983048\pi\) | |||||||
\(608\) | −9544.03 | −0.636614 | ||||||||
\(609\) | −5492.88 | − | 828.232i | −0.365489 | − | 0.0551094i | ||||
\(610\) | −2958.00 | −0.196338 | ||||||||
\(611\) | 19345.6i | 1.28092i | ||||||||
\(612\) | 13089.0 | − | 6745.89i | 0.864526 | − | 0.445566i | ||||
\(613\) | −1786.00 | −0.117677 | −0.0588384 | − | 0.998268i | \(-0.518740\pi\) | ||||
−0.0588384 | + | 0.998268i | \(0.518740\pi\) | |||||||
\(614\) | −7726.12 | −0.507819 | ||||||||
\(615\) | −7211.05 | + | 1748.94i | −0.472809 | + | 0.114673i | ||||
\(616\) | −952.000 | + | 2331.91i | −0.0622681 | + | 0.152525i | ||||
\(617\) | 8254.46i | 0.538593i | 0.963057 | + | 0.269297i | \(0.0867912\pi\) | ||||
−0.963057 | + | 0.269297i | \(0.913209\pi\) | |||||||
\(618\) | −1020.00 | + | 247.386i | −0.0663923 | + | 0.0161025i | ||||
\(619\) | − | 8301.32i | − | 0.539028i | −0.962996 | − | 0.269514i | \(-0.913137\pi\) | ||
0.962996 | − | 0.269514i | \(-0.0868630\pi\) | |||||||
\(620\) | 23155.4i | 1.49991i | ||||||||
\(621\) | 8332.09 | + | 9619.15i | 0.538414 | + | 0.621583i | ||||
\(622\) | 35311.8i | 2.27633i | ||||||||
\(623\) | 3393.43 | − | 8312.18i | 0.218226 | − | 0.534543i | ||||
\(624\) | −3795.00 | − | 15647.2i | −0.243464 | − | 1.00383i | ||||
\(625\) | −12221.0 | −0.782144 | ||||||||
\(626\) | 2201.69 | 0.140571 | ||||||||
\(627\) | −6120.00 | + | 1484.32i | −0.389807 | + | 0.0945422i | ||||
\(628\) | 30577.0i | 1.94292i | ||||||||
\(629\) | −13937.3 | −0.883493 | ||||||||
\(630\) | −20741.5 | + | 1835.95i | −1.31169 | + | 0.116105i | ||||
\(631\) | −13102.0 | −0.826596 | −0.413298 | − | 0.910596i | \(-0.635623\pi\) | ||||
−0.413298 | + | 0.910596i | \(0.635623\pi\) | |||||||
\(632\) | 1822.41i | 0.114702i | ||||||||
\(633\) | −11230.6 | + | 2723.83i | −0.705179 | + | 0.171031i | ||||
\(634\) | 21046.0 | 1.31837 | ||||||||
\(635\) | 10584.3 | 0.661456 | ||||||||
\(636\) | 2272.39 | + | 9369.30i | 0.141676 | + | 0.584146i | ||||
\(637\) | 13524.0 | − | 13802.9i | 0.841194 | − | 0.858540i | ||||
\(638\) | − | 7850.39i | − | 0.487147i | ||||||
\(639\) | 5712.00 | + | 11082.9i | 0.353620 | + | 0.686124i | ||||
\(640\) | − | 5288.45i | − | 0.326632i | ||||||
\(641\) | 9837.73i | 0.606189i | 0.952961 | + | 0.303094i | \(0.0980197\pi\) | ||||
−0.952961 | + | 0.303094i | \(0.901980\pi\) | |||||||
\(642\) | 30561.1 | − | 7412.16i | 1.87874 | − | 0.455661i | ||||
\(643\) | 9624.05i | 0.590257i | 0.955458 | + | 0.295129i | \(0.0953625\pi\) | ||||
−0.955458 | + | 0.295129i | \(0.904638\pi\) | |||||||
\(644\) | −13997.9 | − | 5714.62i | −0.856514 | − | 0.349670i | ||||
\(645\) | −2244.00 | + | 544.250i | −0.136988 | + | 0.0332245i | ||||
\(646\) | −9180.00 | −0.559106 | ||||||||
\(647\) | −7695.82 | −0.467626 | −0.233813 | − | 0.972282i | \(-0.575120\pi\) | ||||
−0.233813 | + | 0.972282i | \(0.575120\pi\) | |||||||
\(648\) | −2448.00 | − | 1744.07i | −0.148405 | − | 0.105731i | ||||
\(649\) | 4330.70i | 0.261933i | ||||||||
\(650\) | 5342.64 | 0.322393 | ||||||||
\(651\) | 24241.3 | + | 3655.18i | 1.45944 | + | 0.220058i | ||||
\(652\) | −28152.0 | −1.69098 | ||||||||
\(653\) | − | 28309.2i | − | 1.69652i | −0.529582 | − | 0.848259i | \(-0.677651\pi\) | ||
0.529582 | − | 0.848259i | \(-0.322349\pi\) | |||||||
\(654\) | −9443.04 | − | 38934.6i | −0.564605 | − | 2.32793i | ||||
\(655\) | 25806.0 | 1.53943 | ||||||||
\(656\) | −7776.62 | −0.462844 | ||||||||
\(657\) | −1090.75 | − | 2116.36i | −0.0647703 | − | 0.125673i | ||||
\(658\) | 24276.0 | + | 9910.64i | 1.43826 | + | 0.587168i | ||||
\(659\) | 22973.9i | 1.35802i | 0.734127 | + | 0.679012i | \(0.237592\pi\) | ||||
−0.734127 | + | 0.679012i | \(0.762408\pi\) | |||||||
\(660\) | −3672.00 | − | 15140.0i | −0.216564 | − | 0.892917i | ||||
\(661\) | − | 10804.7i | − | 0.635785i | −0.948127 | − | 0.317893i | \(-0.897025\pi\) | ||
0.948127 | − | 0.317893i | \(-0.102975\pi\) | |||||||
\(662\) | 14975.1i | 0.879191i | ||||||||
\(663\) | −4181.20 | − | 17239.5i | −0.244923 | − | 1.00984i | ||||
\(664\) | − | 2040.42i | − | 0.119253i | ||||||
\(665\) | 6362.69 | + | 2597.56i | 0.371029 | + | 0.151472i | ||||
\(666\) | 11730.0 | + | 22759.5i | 0.682475 | + | 1.32420i | ||||
\(667\) | 5236.00 | 0.303956 | ||||||||
\(668\) | 6362.69 | 0.368533 | ||||||||
\(669\) | −2346.00 | − | 9672.81i | −0.135578 | − | 0.559002i | ||||
\(670\) | 2665.04i | 0.153671i | ||||||||
\(671\) | −2343.09 | −0.134804 | ||||||||
\(672\) | −24717.9 | − | 3727.04i | −1.41892 | − | 0.213949i | ||||
\(673\) | 26882.0 | 1.53971 | 0.769855 | − | 0.638219i | \(-0.220328\pi\) | ||||
0.769855 | + | 0.638219i | \(0.220328\pi\) | |||||||
\(674\) | − | 25794.1i | − | 1.47411i | ||||||
\(675\) | −2439.03 | + | 2112.68i | −0.139079 | + | 0.120470i | ||||
\(676\) | 8793.00 | 0.500284 | ||||||||
\(677\) | 20491.9 | 1.16332 | 0.581660 | − | 0.813432i | \(-0.302403\pi\) | ||||
0.581660 | + | 0.813432i | \(0.302403\pi\) | |||||||
\(678\) | −34853.4 | + | 8453.19i | −1.97424 | + | 0.478824i | ||||
\(679\) | −18732.0 | − | 7647.31i | −1.05872 | − | 0.432219i | ||||
\(680\) | − | 2523.34i | − | 0.142302i | ||||||
\(681\) | 30039.0 | − | 7285.53i | 1.69030 | − | 0.409959i | ||||
\(682\) | 34645.6i | 1.94523i | ||||||||
\(683\) | − | 725.667i | − | 0.0406543i | −0.999793 | − | 0.0203271i | \(-0.993529\pi\) | ||
0.999793 | − | 0.0203271i | \(-0.00647077\pi\) | |||||||
\(684\) | 4090.30 | + | 7936.35i | 0.228650 | + | 0.443646i | ||||
\(685\) | − | 10160.5i | − | 0.566733i | ||||||
\(686\) | −10392.4 | − | 24041.8i | −0.578401 | − | 1.33808i | ||||
\(687\) | −4539.00 | − | 18714.8i | −0.252072 | − | 1.03932i | ||||
\(688\) | −2420.00 | −0.134101 | ||||||||
\(689\) | 11614.4 | 0.642198 | ||||||||
\(690\) | 19074.0 | − | 4626.12i | 1.05237 | − | 0.255237i | ||||
\(691\) | 11760.0i | 0.647426i | 0.946155 | + | 0.323713i | \(0.104931\pi\) | ||||
−0.946155 | + | 0.323713i | \(0.895069\pi\) | |||||||
\(692\) | −20269.7 | −1.11350 | ||||||||
\(693\) | −16429.7 | + | 1454.29i | −0.900597 | + | 0.0797170i | ||||
\(694\) | 4420.00 | 0.241759 | ||||||||
\(695\) | − | 14076.3i | − | 0.768265i | ||||||
\(696\) | −1201.84 | + | 291.489i | −0.0654535 | + | 0.0158748i | ||||
\(697\) | −8568.00 | −0.465619 | ||||||||
\(698\) | 25925.4 | 1.40586 | ||||||||
\(699\) | 1171.54 | + | 4830.39i | 0.0633931 | + | 0.261377i | ||||
\(700\) | 1449.00 | − | 3549.31i | 0.0782386 | − | 0.191645i | ||||
\(701\) | − | 21877.2i | − | 1.17873i | −0.807867 | − | 0.589365i | \(-0.799378\pi\) | ||
0.807867 | − | 0.589365i | \(-0.200622\pi\) | |||||||
\(702\) | −24633.0 | + | 21337.1i | −1.32438 | + | 1.14717i | ||||
\(703\) | − | 8450.74i | − | 0.453379i | ||||||
\(704\) | − | 20813.4i | − | 1.11426i | ||||||
\(705\) | −17512.5 | + | 4247.42i | −0.935547 | + | 0.226903i | ||||
\(706\) | − | 21820.1i | − | 1.16318i | ||||||
\(707\) | −8837.07 | + | 21646.3i | −0.470088 | + | 1.15148i | ||||
\(708\) | 5967.00 | − | 1447.21i | 0.316742 | − | 0.0768213i | ||||
\(709\) | −24382.0 | −1.29152 | −0.645758 | − | 0.763542i | \(-0.723459\pi\) | ||||
−0.645758 | + | 0.763542i | \(0.723459\pi\) | |||||||
\(710\) | 19229.5 | 1.01643 | ||||||||
\(711\) | −10608.0 | + | 5467.24i | −0.559537 | + | 0.288379i | ||||
\(712\) | − | 1998.78i | − | 0.105207i | ||||||
\(713\) | −23107.7 | −1.21373 | ||||||||
\(714\) | −23775.1 | − | 3584.89i | −1.24617 | − | 0.187901i | ||||
\(715\) | −18768.0 | −0.981655 | ||||||||
\(716\) | 31467.5i | 1.64245i | ||||||||
\(717\) | 5867.81 | + | 24193.6i | 0.305631 | + | 1.26015i | ||||
\(718\) | −13226.0 | −0.687451 | ||||||||
\(719\) | 11089.3 | 0.575187 | 0.287594 | − | 0.957753i | \(-0.407145\pi\) | ||||
0.287594 | + | 0.957753i | \(0.407145\pi\) | |||||||
\(720\) | 13331.3 | − | 6870.82i | 0.690042 | − | 0.355639i | ||||
\(721\) | 840.000 | + | 342.929i | 0.0433887 | + | 0.0177134i | ||||
\(722\) | 22714.2i | 1.17082i | ||||||||
\(723\) | 4638.00 | + | 19123.0i | 0.238574 | + | 0.983666i | ||||
\(724\) | 1653.41i | 0.0848734i | ||||||||
\(725\) | 1327.64i | 0.0680101i | ||||||||
\(726\) | 1227.09 | + | 5059.42i | 0.0627294 | + | 0.258640i | ||||
\(727\) | − | 5927.77i | − | 0.302405i | −0.988503 | − | 0.151203i | \(-0.951685\pi\) | ||
0.988503 | − | 0.151203i | \(-0.0483146\pi\) | |||||||
\(728\) | 1626.02 | − | 3982.92i | 0.0827807 | − | 0.202770i | ||||
\(729\) | 2808.00 | − | 19481.7i | 0.142661 | − | 0.989772i | ||||
\(730\) | −3672.00 | −0.186174 | ||||||||
\(731\) | −2666.27 | −0.134905 | ||||||||
\(732\) | 783.000 | + | 3228.39i | 0.0395362 | + | 0.163012i | ||||
\(733\) | − | 22532.9i | − | 1.13543i | −0.823225 | − | 0.567715i | \(-0.807828\pi\) | ||
0.823225 | − | 0.567715i | \(-0.192172\pi\) | |||||||
\(734\) | 38681.1 | 1.94516 | ||||||||
\(735\) | 15464.3 | + | 9212.07i | 0.776065 | + | 0.462302i | ||||
\(736\) | 23562.0 | 1.18004 | ||||||||
\(737\) | 2111.03i | 0.105510i | ||||||||
\(738\) | 7211.05 | + | 13991.5i | 0.359678 | + | 0.697878i | ||||
\(739\) | −9220.00 | −0.458949 | −0.229474 | − | 0.973315i | \(-0.573701\pi\) | ||||
−0.229474 | + | 0.973315i | \(0.573701\pi\) | |||||||
\(740\) | 20906.0 | 1.03854 | ||||||||
\(741\) | 10453.0 | − | 2535.22i | 0.518219 | − | 0.125687i | ||||
\(742\) | 5950.00 | − | 14574.5i | 0.294382 | − | 0.721085i | ||||
\(743\) | − | 14950.4i | − | 0.738191i | −0.929391 | − | 0.369096i | \(-0.879667\pi\) | ||
0.929391 | − | 0.369096i | \(-0.120333\pi\) | |||||||
\(744\) | 5304.00 | − | 1286.41i | 0.261363 | − | 0.0633898i | ||||
\(745\) | 2581.76i | 0.126964i | ||||||||
\(746\) | 18958.0i | 0.930433i | ||||||||
\(747\) | 11877.0 | − | 6121.27i | 0.581737 | − | 0.299820i | ||||
\(748\) | − | 17989.1i | − | 0.879338i | ||||||
\(749\) | −25168.0 | − | 10274.8i | −1.22779 | − | 0.501245i | ||||
\(750\) | 7548.00 | + | 31121.2i | 0.367485 | + | 1.51518i | ||||
\(751\) | 26648.0 | 1.29481 | 0.647403 | − | 0.762148i | \(-0.275855\pi\) | ||||
0.647403 | + | 0.762148i | \(0.275855\pi\) | |||||||
\(752\) | −18886.1 | −0.915830 | ||||||||
\(753\) | −20349.0 | + | 4935.36i | −0.984806 | + | 0.238850i | ||||
\(754\) | 13408.5i | 0.647625i | ||||||||
\(755\) | −14624.1 | −0.704934 | ||||||||
\(756\) | 7494.18 | + | 22151.5i | 0.360530 | + | 1.06567i | ||||
\(757\) | −3274.00 | −0.157194 | −0.0785968 | − | 0.996906i | \(-0.525044\pi\) | ||||
−0.0785968 | + | 0.996906i | \(0.525044\pi\) | |||||||
\(758\) | 21654.6i | 1.03764i | ||||||||
\(759\) | 15108.9 | − | 3664.44i | 0.722552 | − | 0.175245i | ||||
\(760\) | 1530.00 | 0.0730249 | ||||||||
\(761\) | −36701.6 | −1.74827 | −0.874134 | − | 0.485685i | \(-0.838570\pi\) | ||||
−0.874134 | + | 0.485685i | \(0.838570\pi\) | |||||||
\(762\) | −5292.14 | − | 21820.1i | −0.251593 | − | 1.03735i | ||||
\(763\) | −13090.0 | + | 32063.8i | −0.621088 | + | 1.52135i | ||||
\(764\) | − | 2374.91i | − | 0.112462i | ||||||
\(765\) | 14688.0 | − | 7570.02i | 0.694177 | − | 0.357771i | ||||
\(766\) | − | 7911.85i | − | 0.373194i | ||||||
\(767\) | − | 7396.85i | − | 0.348220i | ||||||
\(768\) | 14588.7 | − | 3538.29i | 0.685450 | − | 0.166246i | ||||
\(769\) | − | 20570.8i | − | 0.964633i | −0.875997 | − | 0.482316i | \(-0.839796\pi\) | ||
0.875997 | − | 0.482316i | \(-0.160204\pi\) | |||||||
\(770\) | −9614.73 | + | 23551.2i | −0.449988 | + | 1.10224i | ||||
\(771\) | 1020.00 | − | 247.386i | 0.0476451 | − | 0.0115556i | ||||
\(772\) | 5868.00 | 0.273567 | ||||||||
\(773\) | 26450.6 | 1.23074 | 0.615370 | − | 0.788238i | \(-0.289007\pi\) | ||||
0.615370 | + | 0.788238i | \(0.289007\pi\) | |||||||
\(774\) | 2244.00 | + | 4354.00i | 0.104210 | + | 0.202198i | ||||
\(775\) | − | 5859.18i | − | 0.271572i | ||||||
\(776\) | −4504.38 | −0.208373 | ||||||||
\(777\) | 3300.10 | − | 21886.4i | 0.152369 | − | 1.01052i | ||||
\(778\) | −29138.0 | −1.34274 | ||||||||
\(779\) | − | 5195.11i | − | 0.238940i | ||||||
\(780\) | 6271.79 | + | 25859.3i | 0.287905 | + | 1.18706i | ||||
\(781\) | 15232.0 | 0.697879 | ||||||||
\(782\) | 22663.3 | 1.03637 | ||||||||
\(783\) | −5302.24 | − | 6121.27i | −0.242001 | − | 0.279383i | ||||
\(784\) | 13475.0 | + | 13202.7i | 0.613839 | + | 0.601437i | ||||
\(785\) | 34312.5i | 1.56008i | ||||||||
\(786\) | −12903.0 | − | 53200.4i | −0.585540 | − | 2.41424i | ||||
\(787\) | 24071.1i | 1.09027i | 0.838348 | + | 0.545136i | \(0.183522\pi\) | ||||
−0.838348 | + | 0.545136i | \(0.816478\pi\) | |||||||
\(788\) | − | 18182.9i | − | 0.822004i | ||||||
\(789\) | 10139.9 | + | 41807.9i | 0.457529 | + | 1.88644i | ||||
\(790\) | 18405.5i | 0.828908i | ||||||||
\(791\) | 28702.8 | + | 11717.9i | 1.29021 | + | 0.526725i | ||||
\(792\) | −3264.00 | + | 1682.23i | −0.146441 | + | 0.0754739i | ||||
\(793\) | 4002.00 | 0.179212 | ||||||||
\(794\) | −54991.8 | −2.45792 | ||||||||
\(795\) | 2550.00 | + | 10513.9i | 0.113760 | + | 0.469044i | ||||
\(796\) | − | 43649.9i | − | 1.94363i | ||||||
\(797\) | −24673.1 | −1.09657 | −0.548285 | − | 0.836292i | \(-0.684719\pi\) | ||||
−0.548285 | + | 0.836292i | \(0.684719\pi\) | |||||||
\(798\) | 2173.66 | − | 14415.8i | 0.0964243 | − | 0.639491i | ||||
\(799\) | −20808.0 | −0.921319 | ||||||||
\(800\) | 5974.38i | 0.264033i | ||||||||
\(801\) | 11634.6 | − | 5996.35i | 0.513220 | − | 0.264508i | ||||
\(802\) | −54638.0 | −2.40565 | ||||||||
\(803\) | −2908.66 | −0.127826 | ||||||||
\(804\) | 2908.66 | − | 705.453i | 0.127588 | − | 0.0309445i | ||||
\(805\) | −15708.0 | − | 6412.76i | −0.687744 | − | 0.280770i | ||||
\(806\) | − | 59174.8i | − | 2.58603i | ||||||
\(807\) | −29223.0 | + | 7087.62i | −1.27472 | + | 0.309165i | ||||
\(808\) | 5205.17i | 0.226630i | ||||||||
\(809\) | − | 44884.1i | − | 1.95061i | −0.220867 | − | 0.975304i | \(-0.570889\pi\) | ||
0.220867 | − | 0.975304i | \(-0.429111\pi\) | |||||||
\(810\) | −24723.6 | − | 17614.3i | −1.07247 | − | 0.764077i | ||||
\(811\) | − | 30430.0i | − | 1.31756i | −0.752335 | − | 0.658781i | \(-0.771073\pi\) | ||
0.752335 | − | 0.658781i | \(-0.228927\pi\) | |||||||
\(812\) | 8907.76 | + | 3636.58i | 0.384977 | + | 0.157166i | ||||
\(813\) | −1494.00 | − | 6159.92i | −0.0644488 | − | 0.265729i | ||||
\(814\) | 31280.0 | 1.34688 | ||||||||
\(815\) | −31591.3 | −1.35778 | ||||||||
\(816\) | 16830.0 | − | 4081.87i | 0.722019 | − | 0.175115i | ||||
\(817\) | − | 1616.66i | − | 0.0692287i | ||||||
\(818\) | 30763.1 | 1.31492 | ||||||||
\(819\) | 28062.1 | − | 2483.93i | 1.19727 | − | 0.105978i | ||||
\(820\) | 12852.0 | 0.547331 | ||||||||
\(821\) | 18446.8i | 0.784162i | 0.919931 | + | 0.392081i | \(0.128245\pi\) | ||||
−0.919931 | + | 0.392081i | \(0.871755\pi\) | |||||||
\(822\) | −20946.4 | + | 5080.24i | −0.888794 | + | 0.215564i | ||||
\(823\) | 35006.0 | 1.48266 | 0.741332 | − | 0.671138i | \(-0.234194\pi\) | ||||
0.741332 | + | 0.671138i | \(0.234194\pi\) | |||||||
\(824\) | 201.990 | 0.00853963 | ||||||||
\(825\) | 929.154 | + | 3831.00i | 0.0392109 | + | 0.161671i | ||||
\(826\) | −9282.00 | − | 3789.36i | −0.390995 | − | 0.159623i | ||||
\(827\) | 1500.81i | 0.0631056i | 0.999502 | + | 0.0315528i | \(0.0100452\pi\) | ||||
−0.999502 | + | 0.0315528i | \(0.989955\pi\) | |||||||
\(828\) | −10098.0 | − | 19593.0i | −0.423828 | − | 0.822348i | ||||
\(829\) | − | 34089.5i | − | 1.42820i | −0.700043 | − | 0.714101i | \(-0.746836\pi\) | ||
0.700043 | − | 0.714101i | \(-0.253164\pi\) | |||||||
\(830\) | − | 20607.3i | − | 0.861794i | ||||||
\(831\) | −16229.9 | + | 3936.33i | −0.677508 | + | 0.164320i | ||||
\(832\) | 35549.4i | 1.48132i | ||||||||
\(833\) | 14846.3 | + | 14546.3i | 0.617518 | + | 0.605042i | ||||
\(834\) | −29019.0 | + | 7038.14i | −1.20485 | + | 0.292219i | ||||
\(835\) | 7140.00 | 0.295916 | ||||||||
\(836\) | 10907.5 | 0.451247 | ||||||||
\(837\) | 23400.0 | + | 27014.6i | 0.966335 | + | 1.11560i | ||||
\(838\) | 38185.1i | 1.57408i | ||||||||
\(839\) | −989.751 | −0.0407271 | −0.0203635 | − | 0.999793i | \(-0.506482\pi\) | ||||
−0.0203635 | + | 0.999793i | \(0.506482\pi\) | |||||||
\(840\) | 3962.52 | + | 597.481i | 0.162762 | + | 0.0245417i | ||||
\(841\) | 21057.0 | 0.863381 | ||||||||
\(842\) | − | 11767.3i | − | 0.481626i | ||||||
\(843\) | −11311.4 | − | 46638.3i | −0.462143 | − | 1.90547i | ||||
\(844\) | 20016.0 | 0.816326 | ||||||||
\(845\) | 9867.22 | 0.401707 | ||||||||
\(846\) | 17512.5 | + | 33979.3i | 0.711695 | + | 1.38089i | ||||
\(847\) | 1701.00 | − | 4166.58i | 0.0690048 | − | 0.169027i | ||||
\(848\) | 11338.5i | 0.459159i | ||||||||
\(849\) | 3651.00 | + | 15053.5i | 0.147588 | + | 0.608520i | ||||
\(850\) | 5746.50i | 0.231886i | ||||||||
\(851\) | 20862.9i | 0.840390i | ||||||||
\(852\) | −5090.15 | − | 20987.2i | −0.204678 | − | 0.843909i | ||||
\(853\) | 21592.3i | 0.866711i | 0.901223 | + | 0.433356i | \(0.142671\pi\) | ||||
−0.901223 | + | 0.433356i | \(0.857329\pi\) | |||||||
\(854\) | 2050.20 | − | 5021.94i | 0.0821503 | − | 0.201226i | ||||
\(855\) | 4590.00 | + | 8905.91i | 0.183596 | + | 0.356229i | ||||
\(856\) | −6052.00 | −0.241651 | ||||||||
\(857\) | 46881.9 | 1.86868 | 0.934338 | − | 0.356388i | \(-0.115992\pi\) | ||||
0.934338 | + | 0.356388i | \(0.115992\pi\) | |||||||
\(858\) | 9384.00 | + | 38691.2i | 0.373385 | + | 1.53951i | ||||
\(859\) | 35593.5i | 1.41378i | 0.707324 | + | 0.706889i | \(0.249902\pi\) | ||||
−0.707324 | + | 0.706889i | \(0.750098\pi\) | |||||||
\(860\) | 3999.40 | 0.158580 | ||||||||
\(861\) | 2028.75 | − | 13454.7i | 0.0803014 | − | 0.532563i | ||||
\(862\) | 46546.0 | 1.83917 | ||||||||
\(863\) | 3727.29i | 0.147020i | 0.997294 | + | 0.0735100i | \(0.0234201\pi\) | ||||
−0.997294 | + | 0.0735100i | \(0.976580\pi\) | |||||||
\(864\) | −23860.1 | − | 27545.7i | −0.939510 | − | 1.08464i | ||||
\(865\) | −22746.0 | −0.894089 | ||||||||
\(866\) | −53749.6 | −2.10910 | ||||||||
\(867\) | −6266.74 | + | 1519.91i | −0.245478 | + | 0.0595372i | ||||
\(868\) | −39312.0 | − | 16049.1i | −1.53725 | − | 0.627581i | ||||
\(869\) | 14579.3i | 0.569124i | ||||||||
\(870\) | −12138.0 | + | 2943.90i | −0.473008 | + | 0.114721i | ||||
\(871\) | − | 3605.65i | − | 0.140267i | ||||||
\(872\) | 7710.21i | 0.299427i | ||||||||
\(873\) | −13513.1 | − | 26219.3i | −0.523884 | − | 1.01648i | ||||
\(874\) | 13741.6i | 0.531828i | ||||||||
\(875\) | 10463.1 | − | 25629.2i | 0.404248 | − | 0.990201i | ||||
\(876\) | 972.000 | + | 4007.66i | 0.0374895 | + | 0.154573i | ||||
\(877\) | −30430.0 | −1.17166 | −0.585831 | − | 0.810433i | \(-0.699232\pi\) | ||||
−0.585831 | + | 0.810433i | \(0.699232\pi\) | |||||||
\(878\) | 12382.0 | 0.475936 | ||||||||
\(879\) | −26061.0 | + | 6320.72i | −1.00002 | + | 0.242540i | ||||
\(880\) | − | 18322.2i | − | 0.701864i | ||||||
\(881\) | 36479.4 | 1.39503 | 0.697516 | − | 0.716570i | \(-0.254289\pi\) | ||||
0.697516 | + | 0.716570i | \(0.254289\pi\) | |||||||
\(882\) | 11259.0 | − | 36486.4i | 0.429832 | − | 1.39293i | ||||
\(883\) | 21632.0 | 0.824433 | 0.412217 | − | 0.911086i | \(-0.364755\pi\) | ||||
0.412217 | + | 0.911086i | \(0.364755\pi\) | |||||||
\(884\) | 30725.4i | 1.16901i | ||||||||
\(885\) | 6695.97 | − | 1624.01i | 0.254331 | − | 0.0616842i | ||||
\(886\) | −28220.0 | −1.07006 | ||||||||
\(887\) | 3171.24 | 0.120045 | 0.0600225 | − | 0.998197i | \(-0.480883\pi\) | ||||
0.0600225 | + | 0.998197i | \(0.480883\pi\) | |||||||
\(888\) | −1161.44 | − | 4788.75i | −0.0438913 | − | 0.180968i | ||||
\(889\) | −7336.00 | + | 17969.5i | −0.276762 | + | 0.677926i | ||||
\(890\) | − | 20186.7i | − | 0.760293i | ||||||
\(891\) | −19584.0 | − | 13952.6i | −0.736351 | − | 0.524612i | ||||
\(892\) | 17239.5i | 0.647109i | ||||||||
\(893\) | − | 12616.7i | − | 0.472790i | ||||||
\(894\) | 5322.44 | − | 1290.88i | 0.199115 | − | 0.0482925i | ||||
\(895\) | 35311.8i | 1.31882i | ||||||||
\(896\) | 8978.46 | + | 3665.44i | 0.334765 | + | 0.136667i | ||||
\(897\) | −25806.0 | + | 6258.87i | −0.960577 | + | 0.232974i | ||||
\(898\) | 10948.0 | 0.406837 | ||||||||
\(899\) | 14704.9 | 0.545534 | ||||||||
\(900\) | 4968.00 | − | 2560.45i | 0.184000 | − | 0.0948314i | ||||
\(901\) | 12492.4i | 0.461911i | ||||||||
\(902\) | 19229.5 | 0.709835 | ||||||||
\(903\) | 631.324 | − | 4186.97i | 0.0232659 | − | 0.154301i | ||||
\(904\) | 6902.00 | 0.253935 | ||||||||
\(905\) | 1855.40i | 0.0681497i | ||||||||
\(906\) | 7312.04 | + | 30148.3i | 0.268131 | + | 1.10553i | ||||
\(907\) | 26900.0 | 0.984785 | 0.492392 | − | 0.870373i | \(-0.336123\pi\) | ||||
0.492392 | + | 0.870373i | \(0.336123\pi\) | |||||||
\(908\) | −53537.5 | −1.95672 | ||||||||
\(909\) | −30298.5 | + | 15615.5i | −1.10554 | + | 0.569784i | ||||
\(910\) | 16422.0 | − | 40225.5i | 0.598224 | − | 1.46534i | ||||
\(911\) | 25917.8i | 0.942587i | 0.881977 | + | 0.471293i | \(0.156213\pi\) | ||||
−0.881977 | + | 0.471293i | \(0.843787\pi\) | |||||||
\(912\) | 2475.00 | + | 10204.7i | 0.0898634 | + | 0.370516i | ||||
\(913\) | − | 16323.4i | − | 0.591704i | ||||||
\(914\) | 4931.23i | 0.178458i | ||||||||
\(915\) | 878.657 | + | 3622.80i | 0.0317459 | + | 0.130892i | ||||
\(916\) | 33354.7i | 1.20313i | ||||||||
\(917\) | −17886.2 | + | 43812.1i | −0.644117 | + | 1.57776i | ||||
\(918\) | −22950.0 | − | 26495.1i | −0.825123 | − | 0.952579i | ||||
\(919\) | −13126.0 | −0.471150 | −0.235575 | − | 0.971856i | \(-0.575697\pi\) | ||||
−0.235575 | + | 0.971856i | \(0.575697\pi\) | |||||||
\(920\) | −3777.21 | −0.135360 | ||||||||
\(921\) | 2295.00 | + | 9462.53i | 0.0821095 | + | 0.338546i | ||||
\(922\) | − | 22444.7i | − | 0.801709i | ||||||
\(923\) | −26016.3 | −0.927777 | ||||||||
\(924\) | 28249.1 | + | 4259.48i | 1.00576 | + | 0.151652i | ||||
\(925\) | −5290.00 | −0.188037 | ||||||||
\(926\) | 3818.00i | 0.135494i | ||||||||
\(927\) | 605.970 | + | 1175.76i | 0.0214700 | + | 0.0416579i | ||||
\(928\) | −14994.0 | −0.530390 | ||||||||
\(929\) | −41226.2 | −1.45596 | −0.727980 | − | 0.685598i | \(-0.759541\pi\) | ||||
−0.727980 | + | 0.685598i | \(0.759541\pi\) | |||||||
\(930\) | 53567.8 | − | 12992.1i | 1.88877 | − | 0.458094i | ||||
\(931\) | −8820.00 | + | 9001.87i | −0.310487 | + | 0.316890i | ||||
\(932\) | − | 8609.04i | − | 0.302574i | ||||||
\(933\) | 43248.0 | − | 10489.2i | 1.51755 | − | 0.368060i | ||||
\(934\) | − | 32105.5i | − | 1.12476i | ||||||
\(935\) | − | 20186.7i | − | 0.706071i | ||||||
\(936\) | 5574.93 | − | 2873.25i | 0.194682 | − | 0.100337i | ||||
\(937\) | − | 12580.6i | − | 0.438623i | −0.975655 | − | 0.219311i | \(-0.929619\pi\) | ||
0.975655 | − | 0.219311i | \(-0.0703811\pi\) | |||||||
\(938\) | −4524.58 | − | 1847.15i | −0.157498 | − | 0.0642981i | ||||
\(939\) | −654.000 | − | 2696.51i | −0.0227289 | − | 0.0937139i | ||||
\(940\) | 31212.0 | 1.08300 | ||||||||
\(941\) | 5383.04 | 0.186485 | 0.0932423 | − | 0.995643i | \(-0.470277\pi\) | ||||
0.0932423 | + | 0.995643i | \(0.470277\pi\) | |||||||
\(942\) | 70737.0 | − | 17156.2i | 2.44664 | − | 0.593398i | ||||
\(943\) | 12825.5i | 0.442902i | ||||||||
\(944\) | 7221.15 | 0.248971 | ||||||||
\(945\) | 8409.72 | + | 24857.7i | 0.289490 | + | 0.855684i | ||||
\(946\) | 5984.00 | 0.205662 | ||||||||
\(947\) | − | 51340.9i | − | 1.76173i | −0.473370 | − | 0.880863i | \(-0.656963\pi\) | ||
0.473370 | − | 0.880863i | \(-0.343037\pi\) | |||||||
\(948\) | 20087.9 | − | 4872.04i | 0.688212 | − | 0.166916i | ||||
\(949\) | 4968.00 | 0.169935 | ||||||||
\(950\) | −3484.33 | −0.118996 | ||||||||
\(951\) | −6251.59 | − | 25776.0i | −0.213167 | − | 0.878910i | ||||
\(952\) | 4284.00 | + | 1748.94i | 0.145846 | + | 0.0595413i | ||||
\(953\) | − | 32440.6i | − | 1.10268i | −0.834281 | − | 0.551340i | \(-0.814117\pi\) | ||
0.834281 | − | 0.551340i | \(-0.185883\pi\) | |||||||
\(954\) | 20400.0 | − | 10513.9i | 0.692321 | − | 0.356814i | ||||
\(955\) | − | 2665.04i | − | 0.0903024i | ||||||
\(956\) | − | 43119.4i | − | 1.45877i | ||||||
\(957\) | −9614.73 | + | 2331.91i | −0.324765 | + | 0.0787671i | ||||
\(958\) | − | 51552.0i | − | 1.73859i | ||||||
\(959\) | 17250.0 | + | 7042.26i | 0.580845 | + | 0.237129i | ||||
\(960\) | −32181.0 | + | 7805.04i | −1.08191 | + | 0.262403i | ||||
\(961\) | −35105.0 | −1.17838 | ||||||||
\(962\) | −53426.4 | −1.79058 | ||||||||
\(963\) | −18156.0 | − | 35227.8i | −0.607548 | − | 1.17882i | ||||
\(964\) | − | 34082.2i | − | 1.13871i | ||||||
\(965\) | 6584.88 | 0.219663 | ||||||||
\(966\) | −5366.25 | + | 35589.3i | −0.178733 | + | 1.18537i | ||||
\(967\) | 34232.0 | 1.13839 | 0.569197 | − | 0.822201i | \(-0.307254\pi\) | ||||
0.569197 | + | 0.822201i | \(0.307254\pi\) | |||||||
\(968\) | − | 1001.91i | − | 0.0332673i | ||||||
\(969\) | 2726.87 | + | 11243.2i | 0.0904020 | + | 0.372737i | ||||
\(970\) | −45492.0 | −1.50584 | ||||||||
\(971\) | 19784.9 | 0.653891 | 0.326946 | − | 0.945043i | \(-0.393981\pi\) | ||||
0.326946 | + | 0.945043i | \(0.393981\pi\) | |||||||
\(972\) | −12679.9 | + | 31646.2i | −0.418425 | + | 1.04429i | ||||
\(973\) | 23898.0 | + | 9756.32i | 0.787394 | + | 0.321452i | ||||
\(974\) | 56536.0i | 1.85989i | ||||||||
\(975\) | −1587.00 | − | 6543.37i | −0.0521279 | − | 0.214929i | ||||
\(976\) | 3906.94i | 0.128133i | ||||||||
\(977\) | 39796.2i | 1.30317i | 0.758577 | + | 0.651583i | \(0.225895\pi\) | ||||
−0.758577 | + | 0.651583i | \(0.774105\pi\) | |||||||
\(978\) | 15795.6 | + | 65127.0i | 0.516450 | + | 2.12938i | ||||
\(979\) | − | 15990.3i | − | 0.522013i | ||||||
\(980\) | −22269.4 | − | 21819.5i | −0.725888 | − | 0.711222i | ||||
\(981\) | −44880.0 | + | 23130.6i | −1.46066 | + | 0.752807i | ||||
\(982\) | 23800.0 | 0.773410 | ||||||||
\(983\) | −22683.5 | −0.736003 | −0.368001 | − | 0.929825i | \(-0.619958\pi\) | ||||
−0.368001 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(984\) | −714.000 | − | 2943.90i | −0.0231316 | − | 0.0953740i | ||||
\(985\) | − | 20404.2i | − | 0.660034i | ||||||
\(986\) | −14422.1 | −0.465814 | ||||||||
\(987\) | 4926.95 | − | 32675.8i | 0.158892 | − | 1.05378i | ||||
\(988\) | −18630.0 | −0.599898 | ||||||||
\(989\) | 3991.17i | 0.128323i | ||||||||
\(990\) | −32964.8 | + | 16989.7i | −1.05827 | + | 0.545421i | ||||
\(991\) | −50422.0 | −1.61625 | −0.808127 | − | 0.589008i | \(-0.799519\pi\) | ||||
−0.808127 | + | 0.589008i | \(0.799519\pi\) | |||||||
\(992\) | 66172.0 | 2.11790 | ||||||||
\(993\) | 18340.7 | − | 4448.27i | 0.586127 | − | 0.142157i | ||||
\(994\) | −13328.0 | + | 32646.8i | −0.425290 | + | 1.04174i | ||||
\(995\) | − | 48982.5i | − | 1.56065i | ||||||
\(996\) | −22491.0 | + | 5454.87i | −0.715517 | + | 0.173538i | ||||
\(997\) | 46121.4i | 1.46508i | 0.680726 | + | 0.732538i | \(0.261664\pi\) | ||||
−0.680726 | + | 0.732538i | \(0.738336\pi\) | |||||||
\(998\) | 63809.2i | 2.02389i | ||||||||
\(999\) | 24390.3 | − | 21126.8i | 0.772448 | − | 0.669093i |
(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 | 21.4.c.b.20.4 | yes | 4 | |
3.2 | odd | 2 | inner | 21.4.c.b.20.1 | ✓ | 4 | |
4.3 | odd | 2 | 336.4.k.b.209.2 | 4 | |||
7.2 | even | 3 | 147.4.g.c.80.3 | 8 | |||
7.3 | odd | 6 | 147.4.g.c.68.2 | 8 | |||
7.4 | even | 3 | 147.4.g.c.68.1 | 8 | |||
7.5 | odd | 6 | 147.4.g.c.80.4 | 8 | |||
7.6 | odd | 2 | inner | 21.4.c.b.20.3 | yes | 4 | |
12.11 | even | 2 | 336.4.k.b.209.4 | 4 | |||
21.2 | odd | 6 | 147.4.g.c.80.2 | 8 | |||
21.5 | even | 6 | 147.4.g.c.80.1 | 8 | |||
21.11 | odd | 6 | 147.4.g.c.68.4 | 8 | |||
21.17 | even | 6 | 147.4.g.c.68.3 | 8 | |||
21.20 | even | 2 | inner | 21.4.c.b.20.2 | yes | 4 | |
28.27 | even | 2 | 336.4.k.b.209.3 | 4 | |||
84.83 | odd | 2 | 336.4.k.b.209.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.c.b.20.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
21.4.c.b.20.2 | yes | 4 | 21.20 | even | 2 | inner | |
21.4.c.b.20.3 | yes | 4 | 7.6 | odd | 2 | inner | |
21.4.c.b.20.4 | yes | 4 | 1.1 | even | 1 | trivial | |
147.4.g.c.68.1 | 8 | 7.4 | even | 3 | |||
147.4.g.c.68.2 | 8 | 7.3 | odd | 6 | |||
147.4.g.c.68.3 | 8 | 21.17 | even | 6 | |||
147.4.g.c.68.4 | 8 | 21.11 | odd | 6 | |||
147.4.g.c.80.1 | 8 | 21.5 | even | 6 | |||
147.4.g.c.80.2 | 8 | 21.2 | odd | 6 | |||
147.4.g.c.80.3 | 8 | 7.2 | even | 3 | |||
147.4.g.c.80.4 | 8 | 7.5 | odd | 6 | |||
336.4.k.b.209.1 | 4 | 84.83 | odd | 2 | |||
336.4.k.b.209.2 | 4 | 4.3 | odd | 2 | |||
336.4.k.b.209.3 | 4 | 28.27 | even | 2 | |||
336.4.k.b.209.4 | 4 | 12.11 | even | 2 |