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 | 20.1 | ||
Root | \(6.57260i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.4.c.b.20.3 |
$q$-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 | \(-0.740046\pi\) | ||
0.684653 | − | 0.728869i | \(-0.259954\pi\) | |||||||
\(3\) | −5.04975 | − | 1.22474i | −0.971825 | − | 0.235702i | ||||
\(4\) | −9.00000 | −1.12500 | ||||||||
\(5\) | 10.0995 | 0.903327 | 0.451664 | − | 0.892188i | \(-0.350831\pi\) | ||||
0.451664 | + | 0.892188i | \(0.350831\pi\) | |||||||
\(6\) | −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 | \(0.149310\pi\) | ||||
−0.891988 | + | 0.452059i | \(0.850690\pi\) | |||||||
\(12\) | 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 | \(-0.357715\pi\) | ||||
0.432263 | + | 0.901748i | \(0.357715\pi\) | |||||||
\(18\) | 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 | ||||||||
\(21\) | −56.3483 | + | 78.0120i | −0.585533 | + | 0.810648i | ||||
\(22\) | 136.000 | 1.31797 | ||||||||
\(23\) | − | 90.7083i | − | 0.822348i | −0.911557 | − | 0.411174i | \(-0.865119\pi\) | ||
0.911557 | − | 0.411174i | \(-0.134881\pi\) | |||||||
\(24\) | 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 | \(0.0591670\pi\) | ||||
−0.982774 | + | 0.184810i | \(0.940833\pi\) | |||||||
\(30\) | −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 | \(-0.586789\pi\) | ||||
−0.269291 | + | 0.963059i | \(0.586789\pi\) | |||||||
\(42\) | 321.652 | + | 232.330i | 1.18171 | + | 0.853554i | ||||
\(43\) | 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 | \(-0.678878\pi\) | ||||
−0.532847 | + | 0.846212i | \(0.678878\pi\) | |||||||
\(48\) | 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 | \(0.0860810\pi\) | ||||
−0.963656 | + | 0.267147i | \(0.913919\pi\) | |||||||
\(54\) | −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 | \(-0.453728\pi\) | ||||
0.144856 | + | 0.989453i | \(0.453728\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 380.090 | − | 324.929i | 0.760108 | − | 0.649797i | ||||
\(64\) | 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 | \(-0.873876\pi\) | ||
0.922522 | − | 0.385945i | \(-0.126124\pi\) | |||||||
\(72\) | −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 | \(-0.606114\pi\) | ||||
−0.327227 | + | 0.944946i | \(0.606114\pi\) | |||||||
\(84\) | 507.134 | − | 702.108i | 0.658725 | − | 0.911979i | ||||
\(85\) | 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 | \(-0.593218\pi\) | ||||
−0.288686 | + | 0.957424i | \(0.593218\pi\) | |||||||
\(90\) | 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 | \(-0.286374\pi\) | ||||
0.621868 | + | 0.783122i | \(0.286374\pi\) | |||||||
\(102\) | −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 | ||||||||
\(105\) | −569.090 | + | 787.883i | −0.528928 | + | 0.732281i | ||||
\(106\) | 850.000 | 0.778861 | ||||||||
\(107\) | 1467.83i | 1.32617i | 0.748545 | + | 0.663084i | \(0.230753\pi\) | ||||
−0.748545 | + | 0.663084i | \(0.769247\pi\) | |||||||
\(108\) | 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 | \(-0.754610\pi\) | ||
0.717274 | − | 0.696791i | \(-0.245390\pi\) | |||||||
\(114\) | 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 | ||||||||
\(126\) | −1339.72 | − | 1567.15i | −0.947234 | − | 1.10804i | ||||
\(127\) | −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 | \(-0.175337\pi\) | ||||
0.852086 | + | 0.523401i | \(0.175337\pi\) | |||||||
\(132\) | −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 | \(-0.898434\pi\) | ||
0.949525 | − | 0.313692i | \(-0.101566\pi\) | |||||||
\(138\) | 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 | ||||||||
\(147\) | 943.189 | + | 1512.26i | 0.529204 | + | 0.848495i | ||||
\(148\) | −2070.00 | −1.14968 | ||||||||
\(149\) | 255.633i | 0.140552i | 0.997528 | + | 0.0702760i | \(0.0223880\pi\) | ||||
−0.997528 | + | 0.0702760i | \(0.977612\pi\) | |||||||
\(150\) | 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 | \(-0.447627\pi\) | ||||
0.163792 | + | 0.986495i | \(0.447627\pi\) | |||||||
\(168\) | −321.652 | − | 232.330i | −0.147714 | − | 0.106694i | ||||
\(169\) | −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 | \(-0.664790\pi\) | ||||
−0.494887 | + | 0.868957i | \(0.664790\pi\) | |||||||
\(174\) | −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 | \(0.260471\pi\) | ||||
−0.683469 | + | 0.729980i | \(0.739529\pi\) | |||||||
\(180\) | −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 | ||||||||
\(189\) | −2317.31 | + | 1175.30i | −0.891851 | + | 0.452330i | ||||
\(190\) | −1530.00 | −0.584199 | ||||||||
\(191\) | − | 263.879i | − | 0.0999665i | −0.998750 | − | 0.0499832i | \(-0.984083\pi\) | ||
0.998750 | − | 0.0499832i | \(-0.0159168\pi\) | |||||||
\(192\) | −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 | \(-0.880954\pi\) | ||
0.930876 | − | 0.365335i | \(-0.119046\pi\) | |||||||
\(198\) | 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 | ||||||||
\(210\) | 3248.52 | + | 2346.42i | 1.06747 | + | 0.771039i | ||||
\(211\) | −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 | \(-0.835658\pi\) | ||||
−0.869654 | + | 0.493661i | \(0.835658\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | −2573.21 | − | 1858.64i | −0.732922 | − | 0.529392i | ||||
\(232\) | −238.000 | −0.0673511 | ||||||||
\(233\) | − | 956.561i | − | 0.268954i | −0.990917 | − | 0.134477i | \(-0.957065\pi\) | ||
0.990917 | − | 0.134477i | \(-0.0429355\pi\) | |||||||
\(234\) | 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 | \(-0.775463\pi\) | ||
0.761350 | − | 0.648341i | \(-0.224537\pi\) | |||||||
\(240\) | 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 | \(-0.330873\pi\) | ||||
0.506678 | + | 0.862135i | \(0.330873\pi\) | |||||||
\(252\) | −3420.81 | + | 2924.36i | −0.855121 | + | 0.731022i | ||||
\(253\) | 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 | \(-0.507804\pi\) | ||||
−0.0245132 | + | 0.999700i | \(0.507804\pi\) | |||||||
\(258\) | −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 | \(-0.577423\pi\) | ||
0.240840 | − | 0.970565i | \(-0.422577\pi\) | |||||||
\(264\) | 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 | \(-0.272316\pi\) | ||||
0.655838 | + | 0.754902i | \(0.272316\pi\) | |||||||
\(270\) | −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 | ||||||||
\(273\) | −4395.06 | − | 3174.56i | −0.974363 | − | 0.703785i | ||||
\(274\) | −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 | \(0.436800\pi\) | ||||
−0.197245 | + | 0.980354i | \(0.563200\pi\) | |||||||
\(282\) | 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 | \(-0.327976\pi\) | ||||
0.514505 | + | 0.857487i | \(0.327976\pi\) | |||||||
\(294\) | 6235.19 | − | 3888.87i | 1.23688 | − | 0.771440i | ||||
\(295\) | 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 | \(-0.785175\pi\) | ||||
−0.780774 | + | 0.624814i | \(0.785175\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | 3838.72 | − | 3281.62i | 0.686626 | − | 0.586979i | ||||
\(316\) | 3978.00 | 0.708165 | ||||||||
\(317\) | 5104.40i | 0.904391i | 0.891919 | + | 0.452195i | \(0.149359\pi\) | ||||
−0.891919 | + | 0.452195i | \(0.850641\pi\) | |||||||
\(318\) | −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 | ||||||||
\(336\) | 3099.15 | − | 4290.66i | 0.503193 | − | 0.696651i | ||||
\(337\) | −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 | \(0.0264255\pi\) | ||||
−0.996556 | + | 0.0829227i | \(0.973575\pi\) | |||||||
\(348\) | −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 | \(-0.369368\pi\) | ||||
0.398969 | + | 0.916964i | \(0.369368\pi\) | |||||||
\(354\) | −663.000 | + | 2733.62i | −0.0995425 | + | 0.410424i | ||||
\(355\) | − | 4663.83i | − | 0.697268i | ||||||
\(356\) | 4362.99 | 0.649544 | ||||||||
\(357\) | −3414.54 | + | 4727.30i | −0.506209 | + | 0.700826i | ||||
\(358\) | 14416.0 | 2.12824 | ||||||||
\(359\) | − | 3207.78i | − | 0.471588i | −0.971803 | − | 0.235794i | \(-0.924231\pi\) | ||
0.971803 | − | 0.235794i | \(-0.0757690\pi\) | |||||||
\(360\) | −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 | ||||||||
\(378\) | 4845.88 | + | 9554.53i | 0.659379 | + | 1.30008i | ||||
\(379\) | 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 | \(-0.459143\pi\) | ||||
0.128005 | + | 0.991774i | \(0.459143\pi\) | |||||||
\(384\) | −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 | \(-0.847651\pi\) | ||
0.887632 | − | 0.460554i | \(-0.152349\pi\) | |||||||
\(390\) | −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 | ||||||||
\(399\) | 2866.34 | + | 2070.37i | 0.359641 | + | 0.259769i | ||||
\(400\) | 1265.00 | 0.158125 | ||||||||
\(401\) | − | 13251.7i | − | 1.65027i | −0.564939 | − | 0.825133i | \(-0.691100\pi\) | ||
0.564939 | − | 0.825133i | \(-0.308900\pi\) | |||||||
\(402\) | 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 | \(-0.681540\pi\) | ||||
−0.539906 | + | 0.841725i | \(0.681540\pi\) | |||||||
\(420\) | 5121.81 | − | 7090.94i | 0.595044 | − | 0.823816i | ||||
\(421\) | −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 | \(0.217285\pi\) | ||||
−0.775921 | + | 0.630830i | \(0.782715\pi\) | |||||||
\(432\) | 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 | ||||||||
\(441\) | −2910.75 | − | 8791.68i | −0.314301 | − | 0.949323i | ||||
\(442\) | 14076.0 | 1.51477 | ||||||||
\(443\) | − | 6844.36i | − | 0.734052i | −0.930211 | − | 0.367026i | \(-0.880376\pi\) | ||
0.930211 | − | 0.367026i | \(-0.119624\pi\) | |||||||
\(444\) | 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 | \(0.0445636\pi\) | ||||
−0.990216 | + | 0.139544i | \(0.955436\pi\) | |||||||
\(450\) | −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 | \(-0.411327\pi\) | ||||
0.274984 | + | 0.961449i | \(0.411327\pi\) | |||||||
\(462\) | −7663.36 | + | 10609.6i | −0.771714 | + | 1.06841i | ||||
\(463\) | 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 | \(-0.373929\pi\) | ||||
0.385788 | + | 0.922587i | \(0.373929\pi\) | |||||||
\(468\) | 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 | \(-0.296625\pi\) | ||||
0.596331 | + | 0.802739i | \(0.296625\pi\) | |||||||
\(480\) | 3213.00 | − | 13247.5i | 0.305526 | − | 1.25972i | ||||
\(481\) | 12957.8i | 1.22833i | ||||||||
\(482\) | 15613.8 | 1.47550 | ||||||||
\(483\) | 7076.34 | + | 5111.26i | 0.666635 | + | 0.481512i | ||||
\(484\) | −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 | \(0.0854635\pi\) | ||||
−0.964172 | + | 0.265277i | \(0.914536\pi\) | |||||||
\(492\) | −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 | \(-0.523960\pi\) | ||||
−0.0752017 | + | 0.997168i | \(0.523960\pi\) | |||||||
\(504\) | 1339.72 | + | 1567.15i | 0.118404 | + | 0.138505i | ||||
\(505\) | 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 | \(-0.558986\pi\) | ||||
−0.184250 | + | 0.982879i | \(0.558986\pi\) | |||||||
\(510\) | −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 | \(-0.192333\pi\) | ||||
0.822938 | + | 0.568131i | \(0.192333\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | 1296.01 | − | 1794.28i | 0.107738 | − | 0.149159i | ||||
\(526\) | −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 | ||||||||
\(546\) | −13089.1 | + | 18121.3i | −1.02593 | + | 1.42037i | ||||
\(547\) | −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 | \(0.0403423\pi\) | ||||
−0.991979 | + | 0.126400i | \(0.959658\pi\) | |||||||
\(558\) | 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 | \(-0.679647\pi\) | ||||
−0.534889 | + | 0.844922i | \(0.679647\pi\) | |||||||
\(564\) | −15606.0 | − | 3785.01i | −1.16513 | − | 0.282585i | ||||
\(565\) | − | 16906.4i | − | 1.25886i | ||||||
\(566\) | 12291.1 | 0.912780 | ||||||||
\(567\) | 13141.3 | − | 3096.85i | 0.973338 | − | 0.229375i | ||||
\(568\) | 1904.00 | 0.140652 | ||||||||
\(569\) | 14801.9i | 1.09056i | 0.838253 | + | 0.545281i | \(0.183577\pi\) | ||||
−0.838253 | + | 0.545281i | \(0.816423\pi\) | |||||||
\(570\) | 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 | \(-0.722618\pi\) | ||||
−0.643740 | + | 0.765244i | \(0.722618\pi\) | |||||||
\(588\) | −8488.70 | − | 13610.3i | −0.595354 | − | 0.954557i | ||||
\(589\) | 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 | \(-0.410674\pi\) | ||||
0.276958 | + | 0.960882i | \(0.410674\pi\) | |||||||
\(594\) | −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 | \(-0.860585\pi\) | ||
0.905607 | − | 0.424117i | \(-0.139415\pi\) | |||||||
\(600\) | −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 | ||||||||
\(609\) | −4503.12 | − | 3252.62i | −0.299632 | − | 0.216425i | ||||
\(610\) | −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 | \(-0.913209\pi\) | ||
0.963057 | − | 0.269297i | \(-0.0867912\pi\) | |||||||
\(618\) | −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 | ||||||||
\(630\) | −13530.5 | − | 15827.4i | −0.855662 | − | 1.00092i | ||||
\(631\) | −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 | \(-0.901980\pi\) | ||
0.952961 | − | 0.303094i | \(-0.0980197\pi\) | |||||||
\(642\) | −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 | \(-0.424880\pi\) | ||||
0.233813 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(648\) | −2448.00 | + | 1744.07i | −0.148405 | + | 0.105731i | ||||
\(649\) | 4330.70i | 0.261933i | ||||||||
\(650\) | −5342.64 | −0.322393 | ||||||||
\(651\) | −19873.3 | − | 14354.5i | −1.19646 | − | 0.864208i | ||||
\(652\) | −28152.0 | −1.69098 | ||||||||
\(653\) | 28309.2i | 1.69652i | 0.529582 | + | 0.848259i | \(0.322349\pi\) | ||||
−0.529582 | + | 0.848259i | \(0.677651\pi\) | |||||||
\(654\) | 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 | \(-0.762408\pi\) | ||
0.734127 | − | 0.679012i | \(-0.237592\pi\) | |||||||
\(660\) | −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 | ||||||||
\(672\) | −20264.1 | − | 14636.8i | −1.16325 | − | 0.840217i | ||||
\(673\) | 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 | \(-0.697597\pi\) | ||||
−0.581660 | + | 0.813432i | \(0.697597\pi\) | |||||||
\(678\) | 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 | \(0.00647077\pi\) | ||||
−0.999793 | + | 0.0203271i | \(0.993529\pi\) | |||||||
\(684\) | −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 | ||||||||
\(693\) | 10717.7 | + | 12537.2i | 0.587494 | + | 0.687228i | ||||
\(694\) | 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 | \(0.200622\pi\) | ||||
−0.807867 | + | 0.589365i | \(0.799378\pi\) | |||||||
\(702\) | −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 | ||||||||
\(714\) | 19491.1 | + | 14078.5i | 1.02162 | + | 0.737920i | ||||
\(715\) | −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 | \(-0.592855\pi\) | ||||
−0.287594 | + | 0.957753i | \(0.592855\pi\) | |||||||
\(720\) | −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 | ||||||||
\(735\) | 9525.75 | + | 15273.0i | 0.478044 | + | 0.766468i | ||||
\(736\) | 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 | \(0.120333\pi\) | ||||
−0.929391 | + | 0.369096i | \(0.879667\pi\) | |||||||
\(744\) | 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 | ||||||||
\(756\) | 20855.8 | − | 10577.7i | 1.00333 | − | 0.508871i | ||||
\(757\) | −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 | \(-0.161430\pi\) | ||||
0.874134 | + | 0.485685i | \(0.161430\pi\) | |||||||
\(762\) | 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 | \(-0.710993\pi\) | ||||
−0.615370 | + | 0.788238i | \(0.710993\pi\) | |||||||
\(774\) | 2244.00 | − | 4354.00i | 0.104210 | − | 0.202198i | ||||
\(775\) | − | 5859.18i | − | 0.271572i | ||||||
\(776\) | 4504.38 | 0.208373 | ||||||||
\(777\) | −12960.1 | + | 17942.8i | −0.598380 | + | 0.828434i | ||||
\(778\) | −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 | \(-0.315281\pi\) | ||||
0.548285 | + | 0.836292i | \(0.315281\pi\) | |||||||
\(798\) | 8536.34 | − | 11818.2i | 0.378676 | − | 0.524262i | ||||
\(799\) | −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 | \(0.429111\pi\) | ||||
−0.220867 | + | 0.975304i | \(0.570889\pi\) | |||||||
\(810\) | 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 | ||||||||
\(819\) | 18305.9 | + | 21413.6i | 0.781027 | + | 0.913616i | ||||
\(820\) | 12852.0 | 0.547331 | ||||||||
\(821\) | − | 18446.8i | − | 0.784162i | −0.919931 | − | 0.392081i | \(-0.871755\pi\) | ||
0.919931 | − | 0.392081i | \(-0.128245\pi\) | |||||||
\(822\) | 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 | \(-0.989955\pi\) | ||
0.999502 | − | 0.0315528i | \(-0.0100452\pi\) | |||||||
\(828\) | −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 | \(-0.493518\pi\) | ||||
0.0203635 | + | 0.999793i | \(0.493518\pi\) | |||||||
\(840\) | −3248.52 | − | 2346.42i | −0.133434 | − | 0.0963798i | ||||
\(841\) | 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 | \(-0.884008\pi\) | ||||
−0.934338 | + | 0.356388i | \(0.884008\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | 7967.25 | − | 11030.4i | 0.315358 | − | 0.436601i | ||||
\(862\) | 46546.0 | 1.83917 | ||||||||
\(863\) | − | 3727.29i | − | 0.147020i | −0.997294 | − | 0.0735100i | \(-0.976580\pi\) | ||
0.997294 | − | 0.0735100i | \(-0.0234201\pi\) | |||||||
\(864\) | 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 | \(-0.745711\pi\) | ||||
−0.697516 | + | 0.716570i | \(0.745711\pi\) | |||||||
\(882\) | −36249.0 | + | 12001.3i | −1.38386 | + | 0.458169i | ||||
\(883\) | 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 | \(-0.519117\pi\) | ||||
−0.0600225 | + | 0.998197i | \(0.519117\pi\) | |||||||
\(888\) | 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 | ||||||||
\(903\) | −2479.32 | + | 3432.53i | −0.0913696 | + | 0.126498i | ||||
\(904\) | 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 | \(-0.843787\pi\) | ||
0.881977 | − | 0.471293i | \(-0.156213\pi\) | |||||||
\(912\) | 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 | ||||||||
\(924\) | 23158.9 | + | 16727.7i | 0.824538 | + | 0.595566i | ||||
\(925\) | −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 | \(-0.240459\pi\) | ||||
0.727980 | + | 0.685598i | \(0.240459\pi\) | |||||||
\(930\) | −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 | \(-0.529723\pi\) | ||||
−0.0932423 | + | 0.995643i | \(0.529723\pi\) | |||||||
\(942\) | 70737.0 | + | 17156.2i | 2.44664 | + | 0.593398i | ||||
\(943\) | 12825.5i | 0.442902i | ||||||||
\(944\) | −7221.15 | −0.248971 | ||||||||
\(945\) | −23403.7 | + | 11869.9i | −0.805633 | + | 0.408602i | ||||
\(946\) | 5984.00 | 0.205662 | ||||||||
\(947\) | 51340.9i | 1.76173i | 0.473370 | + | 0.880863i | \(0.343037\pi\) | ||||
−0.473370 | + | 0.880863i | \(0.656963\pi\) | |||||||
\(948\) | −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 | \(0.185883\pi\) | ||||
−0.834281 | + | 0.551340i | \(0.814117\pi\) | |||||||
\(954\) | 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 | ||||||||
\(966\) | 21074.3 | − | 29176.5i | 0.701918 | − | 0.971779i | ||||
\(967\) | 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 | \(-0.606019\pi\) | ||||
−0.326946 | + | 0.945043i | \(0.606019\pi\) | |||||||
\(972\) | 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 | \(-0.774105\pi\) | ||
0.758577 | − | 0.651583i | \(-0.225895\pi\) | |||||||
\(978\) | −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 | \(-0.380042\pi\) | ||||
0.368001 | + | 0.929825i | \(0.380042\pi\) | |||||||
\(984\) | −714.000 | + | 2943.90i | −0.0231316 | + | 0.0953740i | ||||
\(985\) | − | 20404.2i | − | 0.660034i | ||||||
\(986\) | 14422.1 | 0.465814 | ||||||||
\(987\) | 19349.0 | − | 26788.0i | 0.623999 | − | 0.863902i | ||||
\(988\) | −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.20.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 21.4.c.b.20.4 | yes | 4 | |
4.3 | odd | 2 | 336.4.k.b.209.4 | 4 | |||
7.2 | even | 3 | 147.4.g.c.80.2 | 8 | |||
7.3 | odd | 6 | 147.4.g.c.68.3 | 8 | |||
7.4 | even | 3 | 147.4.g.c.68.4 | 8 | |||
7.5 | odd | 6 | 147.4.g.c.80.1 | 8 | |||
7.6 | odd | 2 | inner | 21.4.c.b.20.2 | yes | 4 | |
12.11 | even | 2 | 336.4.k.b.209.2 | 4 | |||
21.2 | odd | 6 | 147.4.g.c.80.3 | 8 | |||
21.5 | even | 6 | 147.4.g.c.80.4 | 8 | |||
21.11 | odd | 6 | 147.4.g.c.68.1 | 8 | |||
21.17 | even | 6 | 147.4.g.c.68.2 | 8 | |||
21.20 | even | 2 | inner | 21.4.c.b.20.3 | yes | 4 | |
28.27 | even | 2 | 336.4.k.b.209.1 | 4 | |||
84.83 | odd | 2 | 336.4.k.b.209.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.c.b.20.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
21.4.c.b.20.2 | yes | 4 | 7.6 | odd | 2 | inner | |
21.4.c.b.20.3 | yes | 4 | 21.20 | even | 2 | inner | |
21.4.c.b.20.4 | yes | 4 | 3.2 | odd | 2 | inner | |
147.4.g.c.68.1 | 8 | 21.11 | odd | 6 | |||
147.4.g.c.68.2 | 8 | 21.17 | even | 6 | |||
147.4.g.c.68.3 | 8 | 7.3 | odd | 6 | |||
147.4.g.c.68.4 | 8 | 7.4 | even | 3 | |||
147.4.g.c.80.1 | 8 | 7.5 | odd | 6 | |||
147.4.g.c.80.2 | 8 | 7.2 | even | 3 | |||
147.4.g.c.80.3 | 8 | 21.2 | odd | 6 | |||
147.4.g.c.80.4 | 8 | 21.5 | even | 6 | |||
336.4.k.b.209.1 | 4 | 28.27 | even | 2 | |||
336.4.k.b.209.2 | 4 | 12.11 | even | 2 | |||
336.4.k.b.209.3 | 4 | 84.83 | odd | 2 | |||
336.4.k.b.209.4 | 4 | 4.3 | odd | 2 |