Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(23,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), degree \(2\), not 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 147.4 | ||
Root | \(-2.21837 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.147 |
Dual form | 169.4.e.g.23.4 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.95042 | + | 2.28078i | 1.39668 | + | 0.806376i | 0.994044 | − | 0.108982i | \(-0.0347590\pi\) |
0.402641 | + | 0.915358i | \(0.368092\pi\) | |||||||
\(3\) | −4.34233 | + | 7.52113i | −0.835682 | + | 1.44744i | 0.0577926 | + | 0.998329i | \(0.481594\pi\) |
−0.893474 | + | 0.449114i | \(0.851740\pi\) | |||||||
\(4\) | 6.40388 | + | 11.0918i | 0.800485 | + | 1.38648i | ||||
\(5\) | 2.80776i | 0.251134i | 0.992085 | + | 0.125567i | \(0.0400750\pi\) | ||||
−0.992085 | + | 0.125567i | \(0.959925\pi\) | |||||||
\(6\) | −34.3081 | + | 19.8078i | −2.33437 | + | 1.34775i | ||||
\(7\) | −8.28055 | + | 4.78078i | −0.447108 | + | 0.258138i | −0.706608 | − | 0.707605i | \(-0.749775\pi\) |
0.259500 | + | 0.965743i | \(0.416442\pi\) | |||||||
\(8\) | 21.9309i | 0.969217i | ||||||||
\(9\) | −24.2116 | − | 41.9358i | −0.896728 | − | 1.55318i | ||||
\(10\) | −6.40388 | + | 11.0918i | −0.202509 | + | 0.350755i | ||||
\(11\) | 34.1416 | + | 19.7116i | 0.935825 | + | 0.540299i | 0.888649 | − | 0.458588i | \(-0.151645\pi\) |
0.0471757 | + | 0.998887i | \(0.484978\pi\) | |||||||
\(12\) | −111.231 | −2.67580 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −43.6155 | −0.832624 | ||||||||
\(15\) | −21.1176 | − | 12.1922i | −0.363502 | − | 0.209868i | ||||
\(16\) | 1.21165 | − | 2.09863i | 0.0189320 | − | 0.0327911i | ||||
\(17\) | 1.00758 | + | 1.74518i | 0.0143749 | + | 0.0248981i | 0.873123 | − | 0.487499i | \(-0.162091\pi\) |
−0.858748 | + | 0.512397i | \(0.828758\pi\) | |||||||
\(18\) | − | 220.885i | − | 2.89240i | ||||||
\(19\) | −52.1280 | + | 30.0961i | −0.629420 | + | 0.363396i | −0.780528 | − | 0.625121i | \(-0.785049\pi\) |
0.151107 | + | 0.988517i | \(0.451716\pi\) | |||||||
\(20\) | −31.1433 | + | 17.9806i | −0.348193 | + | 0.201029i | ||||
\(21\) | − | 83.0388i | − | 0.862884i | ||||||
\(22\) | 89.9157 | + | 155.739i | 0.871368 | + | 1.50925i | ||||
\(23\) | 2.23438 | − | 3.87006i | 0.0202565 | − | 0.0350853i | −0.855719 | − | 0.517440i | \(-0.826885\pi\) |
0.875976 | + | 0.482355i | \(0.160218\pi\) | |||||||
\(24\) | −164.945 | − | 95.2311i | −1.40289 | − | 0.809957i | ||||
\(25\) | 117.116 | 0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 186.054 | 1.32615 | ||||||||
\(28\) | −106.055 | − | 61.2311i | −0.715806 | − | 0.413271i | ||||
\(29\) | −70.3466 | + | 121.844i | −0.450449 | + | 0.780201i | −0.998414 | − | 0.0563003i | \(-0.982070\pi\) |
0.547964 | + | 0.836502i | \(0.315403\pi\) | |||||||
\(30\) | −55.6155 | − | 96.3289i | −0.338465 | − | 0.586239i | ||||
\(31\) | 136.155i | 0.788845i | 0.918929 | + | 0.394423i | \(0.129055\pi\) | ||||
−0.918929 | + | 0.394423i | \(0.870945\pi\) | |||||||
\(32\) | 161.515 | − | 93.2505i | 0.892250 | − | 0.515141i | ||||
\(33\) | −296.508 | + | 171.189i | −1.56410 | + | 0.903035i | ||||
\(34\) | 9.19224i | 0.0463663i | ||||||||
\(35\) | −13.4233 | − | 23.2498i | −0.0648272 | − | 0.112284i | ||||
\(36\) | 310.097 | − | 537.104i | 1.43563 | − | 2.48659i | ||||
\(37\) | −160.828 | − | 92.8542i | −0.714594 | − | 0.412571i | 0.0981657 | − | 0.995170i | \(-0.468702\pi\) |
−0.812760 | + | 0.582599i | \(0.802036\pi\) | |||||||
\(38\) | −274.570 | −1.17214 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −61.5767 | −0.243403 | ||||||||
\(41\) | −268.668 | − | 155.116i | −1.02339 | − | 0.590853i | −0.108304 | − | 0.994118i | \(-0.534542\pi\) |
−0.915083 | + | 0.403265i | \(0.867875\pi\) | |||||||
\(42\) | 189.393 | − | 328.038i | 0.695809 | − | 1.20518i | ||||
\(43\) | 213.735 | + | 370.200i | 0.758008 | + | 1.31291i | 0.943865 | + | 0.330331i | \(0.107160\pi\) |
−0.185857 | + | 0.982577i | \(0.559506\pi\) | |||||||
\(44\) | 504.924i | 1.73000i | ||||||||
\(45\) | 117.746 | − | 67.9806i | 0.390056 | − | 0.225199i | ||||
\(46\) | 17.6535 | − | 10.1922i | 0.0565840 | − | 0.0326688i | ||||
\(47\) | 258.617i | 0.802622i | 0.915942 | + | 0.401311i | \(0.131445\pi\) | ||||
−0.915942 | + | 0.401311i | \(0.868555\pi\) | |||||||
\(48\) | 10.5227 | + | 18.2259i | 0.0316422 | + | 0.0548059i | ||||
\(49\) | −125.788 | + | 217.872i | −0.366730 | + | 0.635195i | ||||
\(50\) | 462.659 | + | 267.116i | 1.30860 | + | 0.755519i | ||||
\(51\) | −17.5009 | −0.0480514 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 612.656 | 1.58783 | 0.793913 | − | 0.608031i | \(-0.208040\pi\) | ||||
0.793913 | + | 0.608031i | \(0.208040\pi\) | |||||||
\(54\) | 734.991 | + | 424.348i | 1.85222 | + | 1.06938i | ||||
\(55\) | −55.3457 | + | 95.8615i | −0.135687 | + | 0.235017i | ||||
\(56\) | −104.847 | − | 181.600i | −0.250191 | − | 0.433344i | ||||
\(57\) | − | 522.749i | − | 1.21473i | ||||||
\(58\) | −555.797 | + | 320.890i | −1.25827 | + | 0.726463i | ||||
\(59\) | 448.502 | − | 258.943i | 0.989661 | − | 0.571381i | 0.0844878 | − | 0.996425i | \(-0.473075\pi\) |
0.905173 | + | 0.425044i | \(0.139741\pi\) | |||||||
\(60\) | − | 312.311i | − | 0.671985i | ||||||
\(61\) | 80.6553 | + | 139.699i | 0.169293 | + | 0.293223i | 0.938171 | − | 0.346171i | \(-0.112518\pi\) |
−0.768879 | + | 0.639395i | \(0.779185\pi\) | |||||||
\(62\) | −310.540 | + | 537.871i | −0.636106 | + | 1.10177i | ||||
\(63\) | 400.971 | + | 231.501i | 0.801867 | + | 0.462958i | ||||
\(64\) | 831.348 | 1.62373 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1561.77 | −2.91274 | ||||||||
\(67\) | 43.2135 | + | 24.9493i | 0.0787966 | + | 0.0454933i | 0.538881 | − | 0.842382i | \(-0.318847\pi\) |
−0.460084 | + | 0.887875i | \(0.652181\pi\) | |||||||
\(68\) | −12.9048 | + | 22.3518i | −0.0230138 | + | 0.0398611i | ||||
\(69\) | 19.4048 | + | 33.6101i | 0.0338560 | + | 0.0586403i | ||||
\(70\) | − | 122.462i | − | 0.209100i | ||||||
\(71\) | 242.455 | − | 139.982i | 0.405269 | − | 0.233982i | −0.283486 | − | 0.958976i | \(-0.591491\pi\) |
0.688755 | + | 0.724994i | \(0.258158\pi\) | |||||||
\(72\) | 919.689 | − | 530.982i | 1.50537 | − | 0.869123i | ||||
\(73\) | − | 467.732i | − | 0.749916i | −0.927042 | − | 0.374958i | \(-0.877657\pi\) | ||
0.927042 | − | 0.374958i | \(-0.122343\pi\) | |||||||
\(74\) | −423.559 | − | 733.626i | −0.665375 | − | 1.15246i | ||||
\(75\) | −508.558 | + | 880.849i | −0.782977 | + | 1.35616i | ||||
\(76\) | −667.643 | − | 385.464i | −1.00768 | − | 0.581786i | ||||
\(77\) | −376.948 | −0.557886 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37.5379 | 0.0534600 | 0.0267300 | − | 0.999643i | \(-0.491491\pi\) | ||||
0.0267300 | + | 0.999643i | \(0.491491\pi\) | |||||||
\(80\) | 5.89247 | + | 3.40202i | 0.00823497 | + | 0.00475446i | ||||
\(81\) | −154.193 | + | 267.070i | −0.211513 | + | 0.366352i | ||||
\(82\) | −707.568 | − | 1225.54i | −0.952900 | − | 1.65047i | ||||
\(83\) | − | 76.1553i | − | 0.100712i | −0.998731 | − | 0.0503562i | \(-0.983964\pi\) | ||
0.998731 | − | 0.0503562i | \(-0.0160357\pi\) | |||||||
\(84\) | 921.054 | − | 531.771i | 1.19637 | − | 0.690726i | ||||
\(85\) | −4.90004 | + | 2.82904i | −0.00625275 | + | 0.00361003i | ||||
\(86\) | 1949.93i | 2.44496i | ||||||||
\(87\) | −610.936 | − | 1058.17i | −0.752865 | − | 1.30400i | ||||
\(88\) | −432.294 | + | 748.754i | −0.523666 | + | 0.907017i | ||||
\(89\) | 175.635 | + | 101.403i | 0.209183 | + | 0.120772i | 0.600932 | − | 0.799300i | \(-0.294796\pi\) |
−0.391749 | + | 0.920072i | \(0.628130\pi\) | |||||||
\(90\) | 620.194 | 0.726380 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 57.2348 | 0.0648602 | ||||||||
\(93\) | −1024.04 | − | 591.231i | −1.14181 | − | 0.659224i | ||||
\(94\) | −589.848 | + | 1021.65i | −0.647215 | + | 1.12101i | ||||
\(95\) | −84.5028 | − | 146.363i | −0.0912611 | − | 0.158069i | ||||
\(96\) | 1619.70i | 1.72198i | ||||||||
\(97\) | −1017.03 | + | 587.184i | −1.06458 | + | 0.614634i | −0.926695 | − | 0.375814i | \(-0.877363\pi\) |
−0.137883 | + | 0.990449i | \(0.544030\pi\) | |||||||
\(98\) | −993.834 | + | 573.790i | −1.02441 | + | 0.591445i | ||||
\(99\) | − | 1909.01i | − | 1.93800i | ||||||
\(100\) | 750.000 | + | 1299.04i | 0.750000 | + | 1.29904i | ||||
\(101\) | 485.348 | − | 840.648i | 0.478158 | − | 0.828194i | −0.521528 | − | 0.853234i | \(-0.674638\pi\) |
0.999686 | + | 0.0250397i | \(0.00797123\pi\) | |||||||
\(102\) | −69.1360 | − | 39.9157i | −0.0671126 | − | 0.0387475i | ||||
\(103\) | 1899.70 | 1.81731 | 0.908654 | − | 0.417550i | \(-0.137111\pi\) | ||||
0.908654 | + | 0.417550i | \(0.137111\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 233.153 | 0.216699 | ||||||||
\(106\) | 2420.25 | + | 1397.33i | 2.21769 | + | 1.28039i | ||||
\(107\) | 953.247 | − | 1651.07i | 0.861251 | − | 1.49173i | −0.00947163 | − | 0.999955i | \(-0.503015\pi\) |
0.870722 | − | 0.491775i | \(-0.163652\pi\) | |||||||
\(108\) | 1191.47 | + | 2063.68i | 1.06157 | + | 1.83868i | ||||
\(109\) | − | 896.004i | − | 0.787354i | −0.919249 | − | 0.393677i | \(-0.871203\pi\) | ||
0.919249 | − | 0.393677i | \(-0.128797\pi\) | |||||||
\(110\) | −437.277 | + | 252.462i | −0.379025 | + | 0.218830i | ||||
\(111\) | 1396.74 | − | 806.407i | 1.19435 | − | 0.689556i | ||||
\(112\) | 23.1704i | 0.0195482i | ||||||||
\(113\) | 167.441 | + | 290.017i | 0.139394 | + | 0.241438i | 0.927267 | − | 0.374400i | \(-0.122151\pi\) |
−0.787873 | + | 0.615837i | \(0.788818\pi\) | |||||||
\(114\) | 1192.27 | − | 2065.08i | 0.979532 | − | 1.69660i | ||||
\(115\) | 10.8662 | + | 6.27361i | 0.00881112 | + | 0.00508710i | ||||
\(116\) | −1801.96 | −1.44231 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2362.36 | 1.84299 | ||||||||
\(119\) | −16.6866 | − | 9.63401i | −0.0128543 | − | 0.00742141i | ||||
\(120\) | 267.386 | − | 463.127i | 0.203408 | − | 0.352312i | ||||
\(121\) | 111.598 | + | 193.293i | 0.0838452 | + | 0.145224i | ||||
\(122\) | 735.827i | 0.546054i | ||||||||
\(123\) | 2333.29 | − | 1347.13i | 1.71045 | − | 0.987530i | ||||
\(124\) | −1510.21 | + | 871.922i | −1.09372 | + | 0.631459i | ||||
\(125\) | 679.806i | 0.486430i | ||||||||
\(126\) | 1056.00 | + | 1829.05i | 0.746637 | + | 1.29321i | ||||
\(127\) | 310.447 | − | 537.709i | 0.216911 | − | 0.375701i | −0.736951 | − | 0.675946i | \(-0.763735\pi\) |
0.953862 | + | 0.300245i | \(0.0970686\pi\) | |||||||
\(128\) | 1992.06 | + | 1150.11i | 1.37558 | + | 0.794193i | ||||
\(129\) | −3712.44 | −2.53381 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1331.70 | −0.888180 | −0.444090 | − | 0.895982i | \(-0.646473\pi\) | ||||
−0.444090 | + | 0.895982i | \(0.646473\pi\) | |||||||
\(132\) | −3797.60 | − | 2192.55i | −2.50408 | − | 1.44573i | ||||
\(133\) | 287.766 | − | 498.425i | 0.187612 | − | 0.324954i | ||||
\(134\) | 113.808 | + | 197.121i | 0.0733694 | + | 0.127079i | ||||
\(135\) | 522.396i | 0.333042i | ||||||||
\(136\) | −38.2732 | + | 22.0971i | −0.0241316 | + | 0.0139324i | ||||
\(137\) | −538.681 | + | 311.008i | −0.335932 | + | 0.193950i | −0.658471 | − | 0.752606i | \(-0.728797\pi\) |
0.322540 | + | 0.946556i | \(0.395463\pi\) | |||||||
\(138\) | 177.032i | 0.109203i | ||||||||
\(139\) | −165.290 | − | 286.291i | −0.100861 | − | 0.174697i | 0.811178 | − | 0.584799i | \(-0.198827\pi\) |
−0.912040 | + | 0.410102i | \(0.865493\pi\) | |||||||
\(140\) | 171.922 | − | 297.778i | 0.103786 | − | 0.179763i | ||||
\(141\) | −1945.10 | − | 1123.00i | −1.16175 | − | 0.670736i | ||||
\(142\) | 1277.07 | 0.754711 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −117.344 | −0.0679073 | ||||||||
\(145\) | −342.109 | − | 197.517i | −0.195935 | − | 0.113123i | ||||
\(146\) | 1066.79 | − | 1847.74i | 0.604715 | − | 1.04740i | ||||
\(147\) | −1092.43 | − | 1892.14i | −0.612939 | − | 1.06164i | ||||
\(148\) | − | 2378.51i | − | 1.32103i | ||||||
\(149\) | −1567.97 | + | 905.269i | −0.862102 | + | 0.497735i | −0.864716 | − | 0.502262i | \(-0.832501\pi\) |
0.00261337 | + | 0.999997i | \(0.499168\pi\) | |||||||
\(150\) | −4018.04 | + | 2319.82i | −2.18714 | + | 1.26275i | ||||
\(151\) | 423.239i | 0.228097i | 0.993475 | + | 0.114049i | \(0.0363819\pi\) | ||||
−0.993475 | + | 0.114049i | \(0.963618\pi\) | |||||||
\(152\) | −660.034 | − | 1143.21i | −0.352209 | − | 0.610045i | ||||
\(153\) | 48.7902 | − | 84.5071i | 0.0257808 | − | 0.0446536i | ||||
\(154\) | −1489.10 | − | 859.734i | −0.779190 | − | 0.449866i | ||||
\(155\) | −382.292 | −0.198106 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1322.17 | 0.672105 | 0.336052 | − | 0.941843i | \(-0.390908\pi\) | ||||
0.336052 | + | 0.941843i | \(0.390908\pi\) | |||||||
\(158\) | 148.290 | + | 85.6155i | 0.0746668 | + | 0.0431089i | ||||
\(159\) | −2660.35 | + | 4607.87i | −1.32692 | + | 2.29829i | ||||
\(160\) | 261.825 | + | 453.495i | 0.129369 | + | 0.224074i | ||||
\(161\) | 42.7283i | 0.0209159i | ||||||||
\(162\) | −1218.26 | + | 703.360i | −0.590835 | + | 0.341119i | ||||
\(163\) | 3123.23 | − | 1803.20i | 1.50080 | − | 0.866486i | 0.500798 | − | 0.865564i | \(-0.333040\pi\) |
1.00000 | 0.000922205i | \(-0.000293547\pi\) | ||||||||
\(164\) | − | 3973.37i | − | 1.89188i | ||||||
\(165\) | −480.658 | − | 832.524i | −0.226783 | − | 0.392800i | ||||
\(166\) | 173.693 | − | 300.845i | 0.0812121 | − | 0.140663i | ||||
\(167\) | −2957.85 | − | 1707.72i | −1.37057 | − | 0.791300i | −0.379571 | − | 0.925162i | \(-0.623929\pi\) |
−0.991000 | + | 0.133863i | \(0.957262\pi\) | |||||||
\(168\) | 1821.11 | 0.836321 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −25.8096 | −0.0116442 | ||||||||
\(171\) | 2524.21 | + | 1457.35i | 1.12884 | + | 0.651734i | ||||
\(172\) | −2737.47 | + | 4741.44i | −1.21355 | + | 2.10193i | ||||
\(173\) | 1171.11 | + | 2028.43i | 0.514671 | + | 0.891436i | 0.999855 | + | 0.0170243i | \(0.00541926\pi\) |
−0.485184 | + | 0.874412i | \(0.661247\pi\) | |||||||
\(174\) | − | 5573.63i | − | 2.42837i | ||||||
\(175\) | −969.788 | + | 559.908i | −0.418909 | + | 0.241857i | ||||
\(176\) | 82.7350 | − | 47.7671i | 0.0354340 | − | 0.0204578i | ||||
\(177\) | 4497.66i | 1.90997i | ||||||||
\(178\) | 462.555 | + | 801.169i | 0.194775 | + | 0.337360i | ||||
\(179\) | −333.446 | + | 577.545i | −0.139234 | + | 0.241160i | −0.927207 | − | 0.374550i | \(-0.877797\pi\) |
0.787973 | + | 0.615710i | \(0.211131\pi\) | |||||||
\(180\) | 1508.06 | + | 870.679i | 0.624468 | + | 0.360537i | ||||
\(181\) | 701.037 | 0.287888 | 0.143944 | − | 0.989586i | \(-0.454022\pi\) | ||||
0.143944 | + | 0.989586i | \(0.454022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1400.93 | −0.565899 | ||||||||
\(184\) | 84.8737 | + | 49.0019i | 0.0340053 | + | 0.0196330i | ||||
\(185\) | 260.713 | − | 451.567i | 0.103611 | − | 0.179459i | ||||
\(186\) | −2696.93 | − | 4671.22i | −1.06316 | − | 1.84146i | ||||
\(187\) | 79.4440i | 0.0310670i | ||||||||
\(188\) | −2868.55 | + | 1656.16i | −1.11282 | + | 0.642487i | ||||
\(189\) | −1540.63 | + | 889.482i | −0.592933 | + | 0.342330i | ||||
\(190\) | − | 770.928i | − | 0.294363i | ||||||
\(191\) | −650.440 | − | 1126.59i | −0.246409 | − | 0.426793i | 0.716118 | − | 0.697980i | \(-0.245917\pi\) |
−0.962527 | + | 0.271186i | \(0.912584\pi\) | |||||||
\(192\) | −3609.98 | + | 6252.68i | −1.35692 | + | 2.35025i | ||||
\(193\) | −449.756 | − | 259.667i | −0.167742 | − | 0.0968457i | 0.413779 | − | 0.910377i | \(-0.364209\pi\) |
−0.581521 | + | 0.813532i | \(0.697542\pi\) | |||||||
\(194\) | −5356.94 | −1.98251 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3222.14 | −1.17425 | ||||||||
\(197\) | −2702.91 | − | 1560.52i | −0.977534 | − | 0.564379i | −0.0760091 | − | 0.997107i | \(-0.524218\pi\) |
−0.901525 | + | 0.432728i | \(0.857551\pi\) | |||||||
\(198\) | 4354.01 | − | 7541.38i | 1.56276 | − | 2.70678i | ||||
\(199\) | 618.529 | + | 1071.32i | 0.220333 | + | 0.381629i | 0.954909 | − | 0.296898i | \(-0.0959521\pi\) |
−0.734576 | + | 0.678527i | \(0.762619\pi\) | |||||||
\(200\) | 2568.47i | 0.908090i | ||||||||
\(201\) | −375.295 | + | 216.677i | −0.131698 | + | 0.0760358i | ||||
\(202\) | 3834.66 | − | 2213.94i | 1.33567 | − | 0.771151i | ||||
\(203\) | − | 1345.25i | − | 0.465112i | ||||||
\(204\) | −112.074 | − | 194.118i | −0.0384644 | − | 0.0666223i | ||||
\(205\) | 435.528 | − | 754.356i | 0.148383 | − | 0.257007i | ||||
\(206\) | 7504.60 | + | 4332.78i | 2.53821 | + | 1.46543i | ||||
\(207\) | −216.392 | −0.0726584 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2372.98 | −0.785369 | ||||||||
\(210\) | 921.054 | + | 531.771i | 0.302661 | + | 0.174741i | ||||
\(211\) | 1265.83 | − | 2192.49i | 0.413003 | − | 0.715342i | −0.582214 | − | 0.813036i | \(-0.697813\pi\) |
0.995217 | + | 0.0976940i | \(0.0311466\pi\) | |||||||
\(212\) | 3923.38 | + | 6795.49i | 1.27103 | + | 2.20149i | ||||
\(213\) | 2431.38i | 0.782139i | ||||||||
\(214\) | 7531.45 | − | 4348.28i | 2.40579 | − | 1.38898i | ||||
\(215\) | −1039.44 | + | 600.118i | −0.329716 | + | 0.190362i | ||||
\(216\) | 4080.33i | 1.28533i | ||||||||
\(217\) | −650.928 | − | 1127.44i | −0.203631 | − | 0.352699i | ||||
\(218\) | 2043.58 | − | 3539.59i | 0.634904 | − | 1.09969i | ||||
\(219\) | 3517.88 | + | 2031.05i | 1.08546 | + | 0.626691i | ||||
\(220\) | −1417.71 | −0.434463 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7356.93 | 2.22417 | ||||||||
\(223\) | 1035.36 | + | 597.766i | 0.310910 | + | 0.179504i | 0.647333 | − | 0.762207i | \(-0.275884\pi\) |
−0.336424 | + | 0.941711i | \(0.609217\pi\) | |||||||
\(224\) | −891.619 | + | 1544.33i | −0.265955 | + | 0.460647i | ||||
\(225\) | −2835.58 | − | 4911.37i | −0.840173 | − | 1.45522i | ||||
\(226\) | 1527.58i | 0.449617i | ||||||||
\(227\) | −752.742 | + | 434.596i | −0.220094 | + | 0.127071i | −0.605994 | − | 0.795469i | \(-0.707224\pi\) |
0.385900 | + | 0.922541i | \(0.373891\pi\) | |||||||
\(228\) | 5798.25 | − | 3347.62i | 1.68420 | − | 0.972376i | ||||
\(229\) | − | 4684.64i | − | 1.35183i | −0.736978 | − | 0.675916i | \(-0.763748\pi\) | ||
0.736978 | − | 0.675916i | \(-0.236252\pi\) | |||||||
\(230\) | 28.6174 | + | 49.5668i | 0.00820424 | + | 0.0142102i | ||||
\(231\) | 1636.83 | − | 2835.08i | 0.466215 | − | 0.807508i | ||||
\(232\) | −2672.14 | − | 1542.76i | −0.756184 | − | 0.436583i | ||||
\(233\) | 4868.99 | 1.36900 | 0.684502 | − | 0.729011i | \(-0.260020\pi\) | ||||
0.684502 | + | 0.729011i | \(0.260020\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −726.137 | −0.201566 | ||||||||
\(236\) | 5744.31 | + | 3316.48i | 1.58442 | + | 0.914764i | ||||
\(237\) | −163.002 | + | 282.328i | −0.0446756 | + | 0.0773803i | ||||
\(238\) | −43.9460 | − | 76.1167i | −0.0119689 | − | 0.0207307i | ||||
\(239\) | 4807.53i | 1.30114i | 0.759444 | + | 0.650572i | \(0.225471\pi\) | ||||
−0.759444 | + | 0.650572i | \(0.774529\pi\) | |||||||
\(240\) | −51.1740 | + | 29.5454i | −0.0137636 | + | 0.00794643i | ||||
\(241\) | −5088.73 | + | 2937.98i | −1.36014 | + | 0.785278i | −0.989642 | − | 0.143555i | \(-0.954147\pi\) |
−0.370499 | + | 0.928833i | \(0.620813\pi\) | |||||||
\(242\) | 1018.12i | 0.270443i | ||||||||
\(243\) | 1172.61 | + | 2031.03i | 0.309561 | + | 0.536175i | ||||
\(244\) | −1033.01 | + | 1789.23i | −0.271033 | + | 0.469442i | ||||
\(245\) | −611.733 | − | 353.184i | −0.159519 | − | 0.0920984i | ||||
\(246\) | 12290.0 | 3.18528 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2986.00 | −0.764562 | ||||||||
\(249\) | 572.774 | + | 330.691i | 0.145775 | + | 0.0841635i | ||||
\(250\) | −1550.49 | + | 2685.52i | −0.392245 | + | 0.679389i | ||||
\(251\) | 2903.13 | + | 5028.38i | 0.730057 | + | 1.26450i | 0.956858 | + | 0.290554i | \(0.0938397\pi\) |
−0.226802 | + | 0.973941i | \(0.572827\pi\) | |||||||
\(252\) | 5930.02i | 1.48237i | ||||||||
\(253\) | 152.570 | − | 88.0866i | 0.0379131 | − | 0.0218891i | ||||
\(254\) | 2452.79 | − | 1416.12i | 0.605912 | − | 0.349823i | ||||
\(255\) | − | 49.1385i | − | 0.0120673i | ||||||
\(256\) | 1920.92 | + | 3327.12i | 0.468974 | + | 0.812286i | ||||
\(257\) | −597.930 | + | 1035.65i | −0.145128 | + | 0.251369i | −0.929421 | − | 0.369022i | \(-0.879693\pi\) |
0.784293 | + | 0.620391i | \(0.213026\pi\) | |||||||
\(258\) | −14665.7 | − | 8467.24i | −3.53894 | − | 2.04321i | ||||
\(259\) | 1775.66 | 0.426001 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6812.83 | 1.61572 | ||||||||
\(262\) | −5260.79 | − | 3037.32i | −1.24051 | − | 0.716207i | ||||
\(263\) | −117.092 | + | 202.810i | −0.0274533 | + | 0.0475505i | −0.879426 | − | 0.476036i | \(-0.842073\pi\) |
0.851972 | + | 0.523587i | \(0.175406\pi\) | |||||||
\(264\) | −3754.32 | − | 6502.68i | −0.875237 | − | 1.51595i | ||||
\(265\) | 1720.19i | 0.398757i | ||||||||
\(266\) | 2273.59 | − | 1312.66i | 0.524071 | − | 0.302572i | ||||
\(267\) | −1525.33 | + | 880.650i | −0.349621 | + | 0.201854i | ||||
\(268\) | 639.091i | 0.145667i | ||||||||
\(269\) | 1334.13 | + | 2310.79i | 0.302393 | + | 0.523760i | 0.976677 | − | 0.214712i | \(-0.0688813\pi\) |
−0.674285 | + | 0.738471i | \(0.735548\pi\) | |||||||
\(270\) | −1191.47 | + | 2063.68i | −0.268557 | + | 0.465155i | ||||
\(271\) | 4937.45 | + | 2850.64i | 1.10675 | + | 0.638982i | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
0.168763 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(272\) | 4.88331 | 0.00108858 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2837.35 | −0.625587 | ||||||||
\(275\) | 3998.54 | + | 2308.56i | 0.876804 | + | 0.506223i | ||||
\(276\) | −248.532 | + | 430.471i | −0.0542025 | + | 0.0938815i | ||||
\(277\) | −3576.24 | − | 6194.24i | −0.775725 | − | 1.34359i | −0.934386 | − | 0.356261i | \(-0.884051\pi\) |
0.158662 | − | 0.987333i | \(-0.449282\pi\) | |||||||
\(278\) | − | 1507.96i | − | 0.325329i | ||||||
\(279\) | 5709.78 | − | 3296.54i | 1.22522 | − | 0.707380i | ||||
\(280\) | 509.889 | − | 294.384i | 0.108827 | − | 0.0628316i | ||||
\(281\) | 6132.87i | 1.30198i | 0.759086 | + | 0.650990i | \(0.225646\pi\) | ||||
−0.759086 | + | 0.650990i | \(0.774354\pi\) | |||||||
\(282\) | −5122.63 | − | 8872.66i | −1.08173 | − | 1.87361i | ||||
\(283\) | 1688.58 | − | 2924.70i | 0.354683 | − | 0.614330i | −0.632380 | − | 0.774658i | \(-0.717922\pi\) |
0.987064 | + | 0.160328i | \(0.0512553\pi\) | |||||||
\(284\) | 3105.31 | + | 1792.85i | 0.648824 | + | 0.374599i | ||||
\(285\) | 1467.76 | 0.305061 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2966.29 | 0.610086 | ||||||||
\(288\) | −7821.07 | − | 4515.49i | −1.60021 | − | 0.923882i | ||||
\(289\) | 2454.47 | − | 4251.27i | 0.499587 | − | 0.865310i | ||||
\(290\) | −900.982 | − | 1560.55i | −0.182440 | − | 0.315995i | ||||
\(291\) | − | 10199.0i | − | 2.05455i | ||||||
\(292\) | 5188.01 | − | 2995.30i | 1.03974 | − | 0.600297i | ||||
\(293\) | 4074.45 | − | 2352.38i | 0.812395 | − | 0.469037i | −0.0353917 | − | 0.999374i | \(-0.511268\pi\) |
0.847787 | + | 0.530337i | \(0.177935\pi\) | |||||||
\(294\) | − | 9966.34i | − | 1.97704i | ||||||
\(295\) | 727.050 | + | 1259.29i | 0.143493 | + | 0.248537i | ||||
\(296\) | 2036.37 | − | 3527.10i | 0.399871 | − | 0.692596i | ||||
\(297\) | 6352.18 | + | 3667.43i | 1.24105 | + | 0.716518i | ||||
\(298\) | −8258.86 | −1.60545 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −13027.0 | −2.50704 | ||||||||
\(301\) | −3539.69 | − | 2043.64i | −0.677822 | − | 0.391341i | ||||
\(302\) | −965.312 | + | 1671.97i | −0.183932 | + | 0.318580i | ||||
\(303\) | 4215.09 | + | 7300.74i | 0.799176 | + | 1.38421i | ||||
\(304\) | 145.863i | 0.0275192i | ||||||||
\(305\) | −392.242 | + | 226.461i | −0.0736384 | + | 0.0425151i | ||||
\(306\) | 385.484 | − | 222.559i | 0.0720152 | − | 0.0415780i | ||||
\(307\) | − | 5130.49i | − | 0.953787i | −0.878961 | − | 0.476894i | \(-0.841763\pi\) | ||
0.878961 | − | 0.476894i | \(-0.158237\pi\) | |||||||
\(308\) | −2413.93 | − | 4181.05i | −0.446579 | − | 0.773498i | ||||
\(309\) | −8249.11 | + | 14287.9i | −1.51869 | + | 2.63045i | ||||
\(310\) | −1510.21 | − | 871.922i | −0.276692 | − | 0.159748i | ||||
\(311\) | −7948.94 | −1.44933 | −0.724667 | − | 0.689099i | \(-0.758006\pi\) | ||||
−0.724667 | + | 0.689099i | \(0.758006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8521.87 | −1.53893 | −0.769465 | − | 0.638689i | \(-0.779477\pi\) | ||||
−0.769465 | + | 0.638689i | \(0.779477\pi\) | |||||||
\(314\) | 5223.12 | + | 3015.57i | 0.938718 | + | 0.541969i | ||||
\(315\) | −650.000 | + | 1125.83i | −0.116265 | + | 0.201376i | ||||
\(316\) | 240.388 | + | 416.365i | 0.0427940 | + | 0.0741213i | ||||
\(317\) | − | 6662.46i | − | 1.18044i | −0.807241 | − | 0.590222i | \(-0.799040\pi\) | ||
0.807241 | − | 0.590222i | \(-0.200960\pi\) | |||||||
\(318\) | −21019.0 | + | 12135.3i | −3.70657 | + | 2.13999i | ||||
\(319\) | −4803.49 | + | 2773.29i | −0.843083 | + | 0.486754i | ||||
\(320\) | 2334.23i | 0.407773i | ||||||||
\(321\) | 8278.62 | + | 14339.0i | 1.43946 | + | 2.49322i | ||||
\(322\) | −97.4536 | + | 168.795i | −0.0168661 | + | 0.0292129i | ||||
\(323\) | −105.046 | − | 60.6483i | −0.0180957 | − | 0.0104476i | ||||
\(324\) | −3949.74 | −0.677253 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16450.8 | 2.79486 | ||||||||
\(327\) | 6738.96 | + | 3890.74i | 1.13965 | + | 0.657977i | ||||
\(328\) | 3401.82 | − | 5892.12i | 0.572665 | − | 0.991884i | ||||
\(329\) | −1236.39 | − | 2141.49i | −0.207187 | − | 0.358858i | ||||
\(330\) | − | 4385.09i | − | 0.731489i | ||||||
\(331\) | −3387.69 | + | 1955.89i | −0.562551 | + | 0.324789i | −0.754169 | − | 0.656681i | \(-0.771960\pi\) |
0.191618 | + | 0.981470i | \(0.438627\pi\) | |||||||
\(332\) | 844.703 | − | 487.689i | 0.139636 | − | 0.0806188i | ||||
\(333\) | 8992.61i | 1.47986i | ||||||||
\(334\) | −7789.84 | − | 13492.4i | −1.27617 | − | 2.21039i | ||||
\(335\) | −70.0519 | + | 121.333i | −0.0114249 | + | 0.0197885i | ||||
\(336\) | −174.268 | − | 100.614i | −0.0282949 | − | 0.0163361i | ||||
\(337\) | 627.211 | 0.101384 | 0.0506919 | − | 0.998714i | \(-0.483857\pi\) | ||||
0.0506919 | + | 0.998714i | \(0.483857\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2908.34 | −0.465957 | ||||||||
\(340\) | −62.7586 | − | 36.2337i | −0.0100105 | − | 0.00577955i | ||||
\(341\) | −2683.84 | + | 4648.56i | −0.426212 | + | 0.738221i | ||||
\(342\) | 6647.79 | + | 11514.3i | 1.05109 | + | 1.82053i | ||||
\(343\) | − | 5685.08i | − | 0.894943i | ||||||
\(344\) | −8118.82 | + | 4687.40i | −1.27249 | + | 0.734674i | ||||
\(345\) | −94.3693 | + | 54.4841i | −0.0147266 | + | 0.00850240i | ||||
\(346\) | 10684.2i | 1.66007i | ||||||||
\(347\) | 1911.51 | + | 3310.83i | 0.295721 | + | 0.512204i | 0.975152 | − | 0.221535i | \(-0.0711068\pi\) |
−0.679431 | + | 0.733739i | \(0.737773\pi\) | |||||||
\(348\) | 7824.72 | − | 13552.8i | 1.20531 | − | 2.08767i | ||||
\(349\) | 2953.72 | + | 1705.33i | 0.453035 | + | 0.261560i | 0.709111 | − | 0.705097i | \(-0.249096\pi\) |
−0.256076 | + | 0.966657i | \(0.582430\pi\) | |||||||
\(350\) | −5108.10 | −0.780112 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7352.48 | 1.11332 | ||||||||
\(353\) | 4839.03 | + | 2793.82i | 0.729620 | + | 0.421246i | 0.818283 | − | 0.574815i | \(-0.194926\pi\) |
−0.0886632 | + | 0.996062i | \(0.528259\pi\) | |||||||
\(354\) | −10258.2 | + | 17767.6i | −1.54015 | + | 2.66763i | ||||
\(355\) | 393.035 | + | 680.757i | 0.0587609 | + | 0.101777i | ||||
\(356\) | 2597.49i | 0.386704i | ||||||||
\(357\) | 144.917 | − | 83.6680i | 0.0214841 | − | 0.0124039i | ||||
\(358\) | −2634.50 | + | 1521.03i | −0.388932 | + | 0.224550i | ||||
\(359\) | − | 2230.14i | − | 0.327861i | −0.986472 | − | 0.163931i | \(-0.947583\pi\) | ||
0.986472 | − | 0.163931i | \(-0.0524173\pi\) | |||||||
\(360\) | 1490.87 | + | 2582.27i | 0.218266 | + | 0.378049i | ||||
\(361\) | −1617.95 | + | 2802.37i | −0.235887 | + | 0.408568i | ||||
\(362\) | 2769.39 | + | 1598.91i | 0.402088 | + | 0.232146i | ||||
\(363\) | −1938.38 | −0.280272 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1313.28 | 0.188330 | ||||||||
\(366\) | −5534.25 | − | 3195.20i | −0.790382 | − | 0.456327i | ||||
\(367\) | 4349.57 | − | 7533.68i | 0.618653 | − | 1.07154i | −0.371078 | − | 0.928602i | \(-0.621012\pi\) |
0.989732 | − | 0.142938i | \(-0.0456548\pi\) | |||||||
\(368\) | −5.41455 | − | 9.37828i | −0.000766992 | − | 0.00132847i | ||||
\(369\) | 15022.4i | 2.11934i | ||||||||
\(370\) | 2059.85 | − | 1189.25i | 0.289423 | − | 0.167098i | ||||
\(371\) | −5073.13 | + | 2928.97i | −0.709929 | + | 0.409878i | ||||
\(372\) | − | 15144.7i | − | 2.11080i | ||||||
\(373\) | −5482.09 | − | 9495.26i | −0.760997 | − | 1.31809i | −0.942337 | − | 0.334665i | \(-0.891377\pi\) |
0.181340 | − | 0.983420i | \(-0.441956\pi\) | |||||||
\(374\) | −181.194 | + | 313.837i | −0.0250517 | + | 0.0433908i | ||||
\(375\) | −5112.91 | − | 2951.94i | −0.704079 | − | 0.406500i | ||||
\(376\) | −5671.70 | −0.777914 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −8114.84 | −1.10419 | ||||||||
\(379\) | −12046.5 | − | 6955.06i | −1.63269 | − | 0.942631i | −0.983260 | − | 0.182206i | \(-0.941676\pi\) |
−0.649425 | − | 0.760426i | \(-0.724990\pi\) | |||||||
\(380\) | 1082.29 | − | 1874.58i | 0.146106 | − | 0.253064i | ||||
\(381\) | 2696.12 | + | 4669.82i | 0.362537 | + | 0.627932i | ||||
\(382\) | − | 5934.03i | − | 0.794794i | ||||||
\(383\) | −428.469 | + | 247.377i | −0.0571638 | + | 0.0330035i | −0.528310 | − | 0.849052i | \(-0.677174\pi\) |
0.471146 | + | 0.882055i | \(0.343841\pi\) | |||||||
\(384\) | −17300.3 | + | 9988.35i | −2.29910 | + | 1.32738i | ||||
\(385\) | − | 1058.38i | − | 0.140104i | ||||||
\(386\) | −1184.48 | − | 2051.59i | −0.156188 | − | 0.270526i | ||||
\(387\) | 10349.8 | − | 17926.3i | 1.35945 | − | 2.35464i | ||||
\(388\) | −13025.9 | − | 7520.52i | −1.70436 | − | 0.984011i | ||||
\(389\) | 4140.47 | 0.539666 | 0.269833 | − | 0.962907i | \(-0.413032\pi\) | ||||
0.269833 | + | 0.962907i | \(0.413032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00524 | 0.00116474 | ||||||||
\(392\) | −4778.12 | − | 2758.65i | −0.615641 | − | 0.355441i | ||||
\(393\) | 5782.70 | − | 10015.9i | 0.742236 | − | 1.28559i | ||||
\(394\) | −7118.41 | − | 12329.5i | −0.910204 | − | 1.57652i | ||||
\(395\) | 105.398i | 0.0134256i | ||||||||
\(396\) | 21174.4 | − | 12225.0i | 2.68700 | − | 1.55134i | ||||
\(397\) | 1629.68 | − | 940.896i | 0.206023 | − | 0.118948i | −0.393439 | − | 0.919351i | \(-0.628715\pi\) |
0.599462 | + | 0.800403i | \(0.295381\pi\) | |||||||
\(398\) | 5642.90i | 0.710686i | ||||||||
\(399\) | 2499.15 | + | 4328.65i | 0.313568 | + | 0.543116i | ||||
\(400\) | 141.904 | − | 245.784i | 0.0177380 | − | 0.0307231i | ||||
\(401\) | 365.259 | + | 210.883i | 0.0454867 | + | 0.0262618i | 0.522571 | − | 0.852596i | \(-0.324973\pi\) |
−0.477084 | + | 0.878858i | \(0.658306\pi\) | |||||||
\(402\) | −1976.76 | −0.245254 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12432.5 | 1.53103 | ||||||||
\(405\) | −749.871 | − | 432.938i | −0.0920034 | − | 0.0531182i | ||||
\(406\) | 3068.20 | − | 5314.28i | 0.375055 | − | 0.649615i | ||||
\(407\) | −3660.62 | − | 6340.37i | −0.445823 | − | 0.772188i | ||||
\(408\) | − | 383.811i | − | 0.0465722i | ||||||
\(409\) | 2208.55 | − | 1275.11i | 0.267007 | − | 0.154157i | −0.360520 | − | 0.932752i | \(-0.617401\pi\) |
0.627527 | + | 0.778595i | \(0.284067\pi\) | |||||||
\(410\) | 3441.04 | − | 1986.68i | 0.414489 | − | 0.239306i | ||||
\(411\) | − | 5401.99i | − | 0.648322i | ||||||
\(412\) | 12165.4 | + | 21071.2i | 1.45473 | + | 2.51966i | ||||
\(413\) | −2475.89 | + | 4288.37i | −0.294990 | + | 0.510937i | ||||
\(414\) | −854.839 | − | 493.542i | −0.101481 | − | 0.0585900i | ||||
\(415\) | 213.826 | 0.0252923 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2870.98 | 0.337152 | ||||||||
\(418\) | −9374.25 | − | 5412.23i | −1.09691 | − | 0.633303i | ||||
\(419\) | −6192.41 | + | 10725.6i | −0.722002 | + | 1.25054i | 0.238194 | + | 0.971218i | \(0.423445\pi\) |
−0.960196 | + | 0.279327i | \(0.909889\pi\) | |||||||
\(420\) | 1493.09 | + | 2586.10i | 0.173465 | + | 0.300450i | ||||
\(421\) | 10463.0i | 1.21124i | 0.795752 | + | 0.605622i | \(0.207076\pi\) | ||||
−0.795752 | + | 0.605622i | \(0.792924\pi\) | |||||||
\(422\) | 10001.2 | − | 5774.17i | 1.15367 | − | 0.666071i | ||||
\(423\) | 10845.3 | − | 6261.55i | 1.24661 | − | 0.719733i | ||||
\(424\) | 13436.1i | 1.53895i | ||||||||
\(425\) | 118.004 | + | 204.389i | 0.0134683 | + | 0.0233278i | ||||
\(426\) | −5545.44 | + | 9604.99i | −0.630698 | + | 1.09240i | ||||
\(427\) | −1335.74 | − | 771.190i | −0.151384 | − | 0.0874016i | ||||
\(428\) | 24417.9 | 2.75767 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5474.94 | −0.614012 | ||||||||
\(431\) | 3431.53 | + | 1981.19i | 0.383506 | + | 0.221417i | 0.679342 | − | 0.733821i | \(-0.262265\pi\) |
−0.295837 | + | 0.955238i | \(0.595598\pi\) | |||||||
\(432\) | 225.432 | − | 390.459i | 0.0251067 | − | 0.0434860i | ||||
\(433\) | −4197.07 | − | 7269.54i | −0.465816 | − | 0.806817i | 0.533422 | − | 0.845849i | \(-0.320906\pi\) |
−0.999238 | + | 0.0390321i | \(0.987573\pi\) | |||||||
\(434\) | − | 5938.48i | − | 0.656812i | ||||||
\(435\) | 2971.10 | − | 1715.36i | 0.327479 | − | 0.189070i | ||||
\(436\) | 9938.34 | − | 5737.90i | 1.09165 | − | 0.630265i | ||||
\(437\) | 268.984i | 0.0294446i | ||||||||
\(438\) | 9264.72 | + | 16047.0i | 1.01070 | + | 1.75058i | ||||
\(439\) | 5087.26 | − | 8811.39i | 0.553079 | − | 0.957960i | −0.444972 | − | 0.895545i | \(-0.646786\pi\) |
0.998050 | − | 0.0624156i | \(-0.0198804\pi\) | |||||||
\(440\) | −2102.33 | − | 1213.78i | −0.227783 | − | 0.131510i | ||||
\(441\) | 12182.2 | 1.31543 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5880.74 | −0.630705 | −0.315353 | − | 0.948975i | \(-0.602123\pi\) | ||||
−0.315353 | + | 0.948975i | \(0.602123\pi\) | |||||||
\(444\) | 17889.1 | + | 10328.3i | 1.91211 | + | 1.10396i | ||||
\(445\) | −284.716 | + | 493.142i | −0.0303299 | + | 0.0525330i | ||||
\(446\) | 2726.74 | + | 4722.85i | 0.289495 | + | 0.501420i | ||||
\(447\) | − | 15723.9i | − | 1.66379i | ||||||
\(448\) | −6884.01 | + | 3974.49i | −0.725980 | + | 0.419145i | ||||
\(449\) | −9236.05 | + | 5332.43i | −0.970771 | + | 0.560475i | −0.899471 | − | 0.436980i | \(-0.856048\pi\) |
−0.0712996 | + | 0.997455i | \(0.522715\pi\) | |||||||
\(450\) | − | 25869.3i | − | 2.70998i | ||||||
\(451\) | −6115.16 | − | 10591.8i | −0.638474 | − | 1.10587i | ||||
\(452\) | −2144.55 | + | 3714.47i | −0.223166 | + | 0.386535i | ||||
\(453\) | −3183.23 | − | 1837.84i | −0.330158 | − | 0.190617i | ||||
\(454\) | −3964.87 | −0.409869 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11464.3 | 1.17734 | ||||||||
\(457\) | 12842.2 | + | 7414.43i | 1.31451 | + | 0.758933i | 0.982840 | − | 0.184462i | \(-0.0590544\pi\) |
0.331671 | + | 0.943395i | \(0.392388\pi\) | |||||||
\(458\) | 10684.6 | − | 18506.3i | 1.09009 | − | 1.88808i | ||||
\(459\) | 187.464 | + | 324.697i | 0.0190633 | + | 0.0330186i | ||||
\(460\) | 160.702i | 0.0162886i | ||||||||
\(461\) | −8410.58 | + | 4855.85i | −0.849717 | + | 0.490585i | −0.860555 | − | 0.509357i | \(-0.829883\pi\) |
0.0108381 | + | 0.999941i | \(0.496550\pi\) | |||||||
\(462\) | 12932.3 | − | 7466.49i | 1.30231 | − | 0.751889i | ||||
\(463\) | − | 11353.5i | − | 1.13962i | −0.821777 | − | 0.569809i | \(-0.807017\pi\) | ||
0.821777 | − | 0.569809i | \(-0.192983\pi\) | |||||||
\(464\) | 170.470 | + | 295.263i | 0.0170558 | + | 0.0295415i | ||||
\(465\) | 1660.04 | − | 2875.27i | 0.165554 | − | 0.286747i | ||||
\(466\) | 19234.6 | + | 11105.1i | 1.91207 | + | 1.10393i | ||||
\(467\) | −6451.31 | −0.639252 | −0.319626 | − | 0.947544i | \(-0.603557\pi\) | ||||
−0.319626 | + | 0.947544i | \(0.603557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −477.109 | −0.0469741 | ||||||||
\(470\) | −2868.55 | − | 1656.16i | −0.281524 | − | 0.162538i | ||||
\(471\) | −5741.29 | + | 9944.20i | −0.561666 | + | 0.972833i | ||||
\(472\) | 5678.84 | + | 9836.04i | 0.553792 | + | 0.959196i | ||||
\(473\) | 16852.3i | 1.63820i | ||||||||
\(474\) | −1287.85 | + | 743.542i | −0.124795 | + | 0.0720506i | ||||
\(475\) | −6105.05 | + | 3524.75i | −0.589724 | + | 0.340477i | ||||
\(476\) | − | 246.780i | − | 0.0237629i | ||||||
\(477\) | −14833.4 | − | 25692.2i | −1.42385 | − | 2.46618i | ||||
\(478\) | −10964.9 | + | 18991.8i | −1.04921 | + | 1.81729i | ||||
\(479\) | −8284.79 | − | 4783.23i | −0.790275 | − | 0.456266i | 0.0497842 | − | 0.998760i | \(-0.484147\pi\) |
−0.840059 | + | 0.542494i | \(0.817480\pi\) | |||||||
\(480\) | −4547.73 | −0.432447 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −26803.5 | −2.53292 | ||||||||
\(483\) | −321.365 | − | 185.540i | −0.0302746 | − | 0.0174790i | ||||
\(484\) | −1429.32 | + | 2475.66i | −0.134234 | + | 0.232500i | ||||
\(485\) | −1648.67 | − | 2855.59i | −0.154356 | − | 0.267352i | ||||
\(486\) | 10697.9i | 0.998489i | ||||||||
\(487\) | 4258.35 | − | 2458.56i | 0.396230 | − | 0.228764i | −0.288626 | − | 0.957442i | \(-0.593198\pi\) |
0.684856 | + | 0.728678i | \(0.259865\pi\) | |||||||
\(488\) | −3063.72 | + | 1768.84i | −0.284197 | + | 0.164081i | ||||
\(489\) | 31320.3i | 2.89643i | ||||||||
\(490\) | −1611.07 | − | 2790.45i | −0.148532 | − | 0.257265i | ||||
\(491\) | 1475.41 | − | 2555.49i | 0.135610 | − | 0.234883i | −0.790220 | − | 0.612823i | \(-0.790034\pi\) |
0.925830 | + | 0.377940i | \(0.123367\pi\) | |||||||
\(492\) | 29884.2 | + | 17253.7i | 2.73838 | + | 1.58101i | ||||
\(493\) | −283.519 | −0.0259007 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5360.04 | 0.486699 | ||||||||
\(496\) | 285.740 | + | 164.972i | 0.0258671 | + | 0.0149344i | ||||
\(497\) | −1338.44 | + | 2318.25i | −0.120799 | + | 0.209231i | ||||
\(498\) | 1508.47 | + | 2612.74i | 0.135735 | + | 0.235100i | ||||
\(499\) | 13430.1i | 1.20484i | 0.798180 | + | 0.602418i | \(0.205796\pi\) | ||||
−0.798180 | + | 0.602418i | \(0.794204\pi\) | |||||||
\(500\) | −7540.30 | + | 4353.40i | −0.674425 | + | 0.389380i | ||||
\(501\) | 25687.9 | − | 14830.9i | 2.29072 | − | 1.32255i | ||||
\(502\) | 26485.6i | 2.35480i | ||||||||
\(503\) | −660.143 | − | 1143.40i | −0.0585175 | − | 0.101355i | 0.835283 | − | 0.549821i | \(-0.185304\pi\) |
−0.893800 | + | 0.448466i | \(0.851971\pi\) | |||||||
\(504\) | −5077.02 | + | 8793.65i | −0.448707 | + | 0.777183i | ||||
\(505\) | 2360.34 | + | 1362.74i | 0.207988 | + | 0.120082i | ||||
\(506\) | 803.623 | 0.0706036 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7952.25 | 0.694536 | ||||||||
\(509\) | −18114.2 | − | 10458.2i | −1.57740 | − | 0.910713i | −0.995221 | − | 0.0976524i | \(-0.968867\pi\) |
−0.582180 | − | 0.813060i | \(-0.697800\pi\) | |||||||
\(510\) | 112.074 | − | 194.118i | 0.00973082 | − | 0.0168543i | ||||
\(511\) | 2236.12 | + | 3873.08i | 0.193582 | + | 0.335293i | ||||
\(512\) | − | 877.105i | − | 0.0757089i | ||||||
\(513\) | −9698.62 | + | 5599.50i | −0.834707 | + | 0.481918i | ||||
\(514\) | −4724.15 | + | 2727.49i | −0.405396 | + | 0.234055i | ||||
\(515\) | 5333.90i | 0.456388i | ||||||||
\(516\) | −23774.0 | − | 41177.8i | −2.02828 | − | 3.51308i | ||||
\(517\) | −5097.77 | + | 8829.60i | −0.433655 | + | 0.751113i | ||||
\(518\) | 7014.60 | + | 4049.88i | 0.594988 | + | 0.343517i | ||||
\(519\) | −20341.4 | −1.72040 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10104.2 | −0.849661 | −0.424831 | − | 0.905273i | \(-0.639666\pi\) | ||||
−0.424831 | + | 0.905273i | \(0.639666\pi\) | |||||||
\(522\) | 26913.5 | + | 15538.5i | 2.25665 | + | 1.30288i | ||||
\(523\) | −3565.61 | + | 6175.82i | −0.298113 | + | 0.516347i | −0.975704 | − | 0.219092i | \(-0.929691\pi\) |
0.677591 | + | 0.735439i | \(0.263024\pi\) | |||||||
\(524\) | −8528.08 | − | 14771.1i | −0.710975 | − | 1.23144i | ||||
\(525\) | − | 9725.21i | − | 0.808463i | ||||||
\(526\) | −925.127 | + | 534.122i | −0.0766871 | + | 0.0442753i | ||||
\(527\) | −237.615 | + | 137.187i | −0.0196407 | + | 0.0113396i | ||||
\(528\) | 829.682i | 0.0683849i | ||||||||
\(529\) | 6073.52 | + | 10519.6i | 0.499179 | + | 0.864604i | ||||
\(530\) | −3923.38 | + | 6795.49i | −0.321548 | + | 0.556938i | ||||
\(531\) | −21717.9 | − | 12538.9i | −1.77491 | − | 1.02475i | ||||
\(532\) | 7371.27 | 0.600724 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8034.26 | −0.651080 | ||||||||
\(535\) | 4635.82 | + | 2676.49i | 0.374624 | + | 0.216289i | ||||
\(536\) | −547.161 | + | 947.710i | −0.0440928 | + | 0.0763710i | ||||
\(537\) | −2895.86 | − | 5015.78i | −0.232711 | − | 0.403067i | ||||
\(538\) | 12171.5i | 0.975369i | ||||||||
\(539\) | −8589.22 | + | 4958.99i | −0.686390 | + | 0.396287i | ||||
\(540\) | −5794.33 | + | 3345.36i | −0.461756 | + | 0.266595i | ||||
\(541\) | − | 16831.7i | − | 1.33762i | −0.743435 | − | 0.668809i | \(-0.766805\pi\) | ||
0.743435 | − | 0.668809i | \(-0.233195\pi\) | |||||||
\(542\) | 13003.3 | + | 22522.5i | 1.03052 | + | 1.78491i | ||||
\(543\) | −3044.13 | + | 5272.59i | −0.240582 | + | 0.416701i | ||||
\(544\) | 325.477 | + | 187.914i | 0.0256520 | + | 0.0148102i | ||||
\(545\) | 2515.77 | 0.197731 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9560.55 | −0.747312 | −0.373656 | − | 0.927567i | \(-0.621896\pi\) | ||||
−0.373656 | + | 0.927567i | \(0.621896\pi\) | |||||||
\(548\) | −6899.30 | − | 3983.31i | −0.537816 | − | 0.310508i | ||||
\(549\) | 3905.59 | − | 6764.69i | 0.303619 | − | 0.525883i | ||||
\(550\) | 10530.6 | + | 18239.6i | 0.816412 | + | 1.41407i | ||||
\(551\) | − | 8468.64i | − | 0.654766i | ||||||
\(552\) | −737.099 | + | 425.564i | −0.0568352 | + | 0.0328138i | ||||
\(553\) | −310.834 | + | 179.460i | −0.0239024 | + | 0.0138000i | ||||
\(554\) | − | 32626.5i | − | 2.50210i | ||||||
\(555\) | 2264.20 | + | 3921.71i | 0.173171 | + | 0.299941i | ||||
\(556\) | 2117.00 | − | 3666.75i | 0.161476 | − | 0.279685i | ||||
\(557\) | −19769.5 | − | 11414.0i | −1.50388 | − | 0.868267i | −0.999990 | − | 0.00450060i | \(-0.998567\pi\) |
−0.503893 | − | 0.863766i | \(-0.668099\pi\) | |||||||
\(558\) | 30074.7 | 2.28166 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −65.0571 | −0.00490922 | ||||||||
\(561\) | −597.509 | − | 344.972i | −0.0449677 | − | 0.0259621i | ||||
\(562\) | −13987.7 | + | 24227.4i | −1.04989 | + | 1.81846i | ||||
\(563\) | 10814.9 | + | 18731.9i | 0.809578 | + | 1.40223i | 0.913157 | + | 0.407609i | \(0.133637\pi\) |
−0.103579 | + | 0.994621i | \(0.533029\pi\) | |||||||
\(564\) | − | 28766.3i | − | 2.14766i | ||||||
\(565\) | −814.299 | + | 470.136i | −0.0606333 | + | 0.0350066i | ||||
\(566\) | 13341.2 | − | 7702.53i | 0.990761 | − | 0.572016i | ||||
\(567\) | − | 2948.65i | − | 0.218398i | ||||||
\(568\) | 3069.92 | + | 5317.25i | 0.226780 | + | 0.392794i | ||||
\(569\) | −5294.93 | + | 9171.09i | −0.390114 | + | 0.675698i | −0.992464 | − | 0.122534i | \(-0.960898\pi\) |
0.602350 | + | 0.798232i | \(0.294231\pi\) | |||||||
\(570\) | 5798.25 | + | 3347.62i | 0.426074 | + | 0.245994i | ||||
\(571\) | 1757.27 | 0.128791 | 0.0643954 | − | 0.997924i | \(-0.479488\pi\) | ||||
0.0643954 | + | 0.997924i | \(0.479488\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11297.7 | 0.823679 | ||||||||
\(574\) | 11718.1 | + | 6765.45i | 0.852097 | + | 0.491959i | ||||
\(575\) | 261.683 | − | 453.247i | 0.0189790 | − | 0.0328726i | ||||
\(576\) | −20128.3 | − | 34863.2i | −1.45604 | − | 2.52193i | ||||
\(577\) | − | 13580.6i | − | 0.979840i | −0.871767 | − | 0.489920i | \(-0.837026\pi\) | ||
0.871767 | − | 0.489920i | \(-0.162974\pi\) | |||||||
\(578\) | 19392.4 | − | 11196.2i | 1.39553 | − | 0.805710i | ||||
\(579\) | 3905.98 | − | 2255.12i | 0.280357 | − | 0.161864i | ||||
\(580\) | − | 5059.49i | − | 0.362214i | ||||||
\(581\) | 364.081 | + | 630.607i | 0.0259977 | + | 0.0450293i | ||||
\(582\) | 23261.6 | − | 40290.3i | 1.65674 | − | 2.86956i | ||||
\(583\) | 20917.0 | + | 12076.5i | 1.48593 | + | 0.857900i | ||||
\(584\) | 10257.8 | 0.726831 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21461.0 | 1.51288 | ||||||||
\(587\) | 829.068 | + | 478.663i | 0.0582952 | + | 0.0336568i | 0.528864 | − | 0.848706i | \(-0.322618\pi\) |
−0.470569 | + | 0.882363i | \(0.655951\pi\) | |||||||
\(588\) | 13991.6 | − | 24234.1i | 0.981297 | − | 1.69966i | ||||
\(589\) | −4097.75 | − | 7097.50i | −0.286663 | − | 0.496515i | ||||
\(590\) | 6632.95i | 0.462838i | ||||||||
\(591\) | 23473.8 | − | 13552.6i | 1.63381 | − | 0.943283i | ||||
\(592\) | −389.734 | + | 225.013i | −0.0270573 | + | 0.0156216i | ||||
\(593\) | − | 6729.49i | − | 0.466015i | −0.972475 | − | 0.233007i | \(-0.925143\pi\) | ||
0.972475 | − | 0.233007i | \(-0.0748567\pi\) | |||||||
\(594\) | 16729.2 | + | 28975.8i | 1.15557 | + | 2.00150i | ||||
\(595\) | 27.0500 | − | 46.8520i | 0.00186377 | − | 0.00322814i | ||||
\(596\) | −20082.2 | − | 11594.5i | −1.38020 | − | 0.796859i | ||||
\(597\) | −10743.4 | −0.736514 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2281.52 | 0.155626 | 0.0778132 | − | 0.996968i | \(-0.475206\pi\) | ||||
0.0778132 | + | 0.996968i | \(0.475206\pi\) | |||||||
\(600\) | −19317.8 | − | 11153.1i | −1.31441 | − | 0.758874i | ||||
\(601\) | −3200.71 | + | 5543.79i | −0.217237 | + | 0.376266i | −0.953962 | − | 0.299926i | \(-0.903038\pi\) |
0.736725 | + | 0.676192i | \(0.236371\pi\) | |||||||
\(602\) | −9322.18 | − | 16146.5i | −0.631136 | − | 1.09316i | ||||
\(603\) | − | 2416.26i | − | 0.163180i | ||||||
\(604\) | −4694.50 | + | 2710.37i | −0.316252 | + | 0.182588i | ||||
\(605\) | −542.722 | + | 313.341i | −0.0364707 | + | 0.0210564i | ||||
\(606\) | 38454.7i | 2.57775i | ||||||||
\(607\) | −1389.62 | − | 2406.89i | −0.0929207 | − | 0.160943i | 0.815818 | − | 0.578308i | \(-0.196287\pi\) |
−0.908739 | + | 0.417365i | \(0.862954\pi\) | |||||||
\(608\) | −5612.95 | + | 9721.92i | −0.374400 | + | 0.648480i | ||||
\(609\) | 10117.8 | + | 5841.50i | 0.673223 | + | 0.388685i | ||||
\(610\) | −2066.03 | −0.137133 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1249.79 | 0.0825485 | ||||||||
\(613\) | −19590.2 | − | 11310.4i | −1.29077 | − | 0.745226i | −0.311979 | − | 0.950089i | \(-0.600992\pi\) |
−0.978791 | + | 0.204863i | \(0.934325\pi\) | |||||||
\(614\) | 11701.5 | − | 20267.6i | 0.769111 | − | 1.33214i | ||||
\(615\) | 3782.41 | + | 6551.33i | 0.248002 | + | 0.429553i | ||||
\(616\) | − | 8266.80i | − | 0.540712i | ||||||
\(617\) | 19030.1 | − | 10987.0i | 1.24169 | − | 0.716889i | 0.272250 | − | 0.962226i | \(-0.412232\pi\) |
0.969438 | + | 0.245337i | \(0.0788988\pi\) | |||||||
\(618\) | −65174.9 | + | 37628.7i | −4.24226 | + | 2.44927i | ||||
\(619\) | − | 7145.19i | − | 0.463957i | −0.972721 | − | 0.231979i | \(-0.925480\pi\) | ||
0.972721 | − | 0.231979i | \(-0.0745199\pi\) | |||||||
\(620\) | −2448.15 | − | 4240.32i | −0.158581 | − | 0.274670i | ||||
\(621\) | 415.715 | − | 720.040i | 0.0268632 | − | 0.0465285i | ||||
\(622\) | −31401.7 | − | 18129.8i | −2.02426 | − | 1.16871i | ||||
\(623\) | −1939.14 | −0.124703 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12730.8 | 0.814773 | ||||||||
\(626\) | −33665.0 | − | 19436.5i | −2.14940 | − | 1.24096i | ||||
\(627\) | 10304.2 | − | 17847.5i | 0.656319 | − | 1.13678i | ||||
\(628\) | 8467.00 | + | 14665.3i | 0.538010 | + | 0.931861i | ||||
\(629\) | − | 374.231i | − | 0.0237227i | ||||||
\(630\) | −5135.55 | + | 2965.01i | −0.324770 | + | 0.187506i | ||||
\(631\) | 16353.4 | − | 9441.62i | 1.03172 | − | 0.595666i | 0.114245 | − | 0.993453i | \(-0.463555\pi\) |
0.917478 | + | 0.397787i | \(0.130222\pi\) | |||||||
\(632\) | 823.239i | 0.0518144i | ||||||||
\(633\) | 10993.3 | + | 19041.0i | 0.690278 | + | 1.19560i | ||||
\(634\) | 15195.6 | − | 26319.5i | 0.951882 | − | 1.64871i | ||||
\(635\) | 1509.76 | + | 871.661i | 0.0943512 | + | 0.0544737i | ||||
\(636\) | −68146.4 | −4.24871 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25301.1 | −1.57003 | ||||||||
\(639\) | −11740.5 | − | 6778.37i | −0.726833 | − | 0.419637i | ||||
\(640\) | −3229.25 | + | 5593.22i | −0.199449 | + | 0.345456i | ||||
\(641\) | −1815.54 | − | 3144.61i | −0.111871 | − | 0.193767i | 0.804653 | − | 0.593745i | \(-0.202351\pi\) |
−0.916525 | + | 0.399978i | \(0.869018\pi\) | |||||||
\(642\) | 75526.7i | 4.64299i | ||||||||
\(643\) | −9328.78 | + | 5385.98i | −0.572148 | + | 0.330330i | −0.758007 | − | 0.652247i | \(-0.773827\pi\) |
0.185859 | + | 0.982576i | \(0.440493\pi\) | |||||||
\(644\) | −473.935 | + | 273.627i | −0.0289995 | + | 0.0167429i | ||||
\(645\) | − | 10423.6i | − | 0.636327i | ||||||
\(646\) | −276.651 | − | 479.173i | −0.0168493 | − | 0.0291839i | ||||
\(647\) | 7574.14 | − | 13118.8i | 0.460232 | − | 0.797146i | −0.538740 | − | 0.842472i | \(-0.681099\pi\) |
0.998972 | + | 0.0453265i | \(0.0144328\pi\) | |||||||
\(648\) | −5857.09 | − | 3381.59i | −0.355074 | − | 0.205002i | ||||
\(649\) | 20416.7 | 1.23487 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11306.2 | 0.680682 | ||||||||
\(652\) | 40001.6 | + | 23094.9i | 2.40273 | + | 1.38722i | ||||
\(653\) | −3679.45 | + | 6372.99i | −0.220502 | + | 0.381921i | −0.954961 | − | 0.296733i | \(-0.904103\pi\) |
0.734458 | + | 0.678654i | \(0.237436\pi\) | |||||||
\(654\) | 17747.8 | + | 30740.1i | 1.06115 | + | 1.83797i | ||||
\(655\) | − | 3739.11i | − | 0.223052i | ||||||
\(656\) | −651.061 | + | 375.890i | −0.0387495 | + | 0.0223720i | ||||
\(657\) | −19614.7 | + | 11324.6i | −1.16475 | + | 0.672471i | ||||
\(658\) | − | 11279.7i | − | 0.668282i | ||||||
\(659\) | −14166.6 | − | 24537.3i | −0.837411 | − | 1.45044i | −0.892052 | − | 0.451932i | \(-0.850735\pi\) |
0.0546414 | − | 0.998506i | \(-0.482598\pi\) | |||||||
\(660\) | 6156.16 | − | 10662.8i | 0.363073 | − | 0.628860i | ||||
\(661\) | 961.014 | + | 554.842i | 0.0565493 | + | 0.0326488i | 0.528008 | − | 0.849239i | \(-0.322939\pi\) |
−0.471459 | + | 0.881888i | \(0.656272\pi\) | |||||||
\(662\) | −17843.8 | −1.04761 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1670.15 | 0.0976121 | ||||||||
\(665\) | 1399.46 | + | 807.978i | 0.0816071 | + | 0.0471159i | ||||
\(666\) | −20510.1 | + | 35524.6i | −1.19332 | + | 2.06689i | ||||
\(667\) | 314.362 | + | 544.491i | 0.0182491 | + | 0.0316083i | ||||
\(668\) | − | 43744.1i | − | 2.53369i | ||||||
\(669\) | −8991.75 | + | 5191.39i | −0.519643 | + | 0.300016i | ||||
\(670\) | −553.469 | + | 319.545i | −0.0319140 | + | 0.0184255i | ||||
\(671\) | 6359.39i | 0.365874i | ||||||||
\(672\) | −7743.41 | − | 13412.0i | −0.444507 | − | 0.769908i | ||||
\(673\) | 10489.5 | − | 18168.4i | 0.600806 | − | 1.04063i | −0.391893 | − | 0.920011i | \(-0.628180\pi\) |
0.992699 | − | 0.120616i | \(-0.0384868\pi\) | |||||||
\(674\) | 2477.75 | + | 1430.53i | 0.141601 | + | 0.0817535i | ||||
\(675\) | 21790.0 | 1.24251 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30941.9 | 1.75656 | 0.878282 | − | 0.478142i | \(-0.158690\pi\) | ||||
0.878282 | + | 0.478142i | \(0.158690\pi\) | |||||||
\(678\) | −11489.2 | − | 6633.27i | −0.650795 | − | 0.375736i | ||||
\(679\) | 5614.39 | − | 9724.41i | 0.317320 | − | 0.549615i | ||||
\(680\) | −62.0433 | − | 107.462i | −0.00349890 | − | 0.00606027i | ||||
\(681\) | − | 7548.64i | − | 0.424764i | ||||||
\(682\) | −21204.6 | + | 12242.5i | −1.19057 | + | 0.687375i | ||||
\(683\) | −4699.24 | + | 2713.11i | −0.263267 | + | 0.151997i | −0.625824 | − | 0.779964i | \(-0.715237\pi\) |
0.362557 | + | 0.931962i | \(0.381904\pi\) | |||||||
\(684\) | 37330.9i | 2.08682i | ||||||||
\(685\) | −873.236 | − | 1512.49i | −0.0487075 | − | 0.0843638i | ||||
\(686\) | 12966.4 | − | 22458.4i | 0.721660 | − | 1.24995i | ||||
\(687\) | 35233.8 | + | 20342.2i | 1.95670 | + | 1.12970i | ||||
\(688\) | 1035.89 | 0.0574023 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −497.065 | −0.0274245 | ||||||||
\(691\) | 29265.3 | + | 16896.3i | 1.61115 | + | 0.930199i | 0.989104 | + | 0.147219i | \(0.0470324\pi\) |
0.622048 | + | 0.782979i | \(0.286301\pi\) | |||||||
\(692\) | −14999.3 | + | 25979.6i | −0.823973 | + | 1.42716i | ||||
\(693\) | 9126.53 | + | 15807.6i | 0.500272 | + | 0.866496i | ||||
\(694\) | 17438.9i | 0.953849i | ||||||||
\(695\) | 803.838 | − | 464.096i | 0.0438724 | − | 0.0253297i | ||||
\(696\) | 23206.6 | − | 13398.4i | 1.26386 | − | 0.729689i | ||||
\(697\) | − | 625.164i | − | 0.0339738i | ||||||
\(698\) | 7778.97 | + | 13473.6i | 0.421831 | + | 0.730633i | ||||
\(699\) | −21142.8 | + | 36620.3i | −1.14405 | + | 1.98156i | ||||
\(700\) | −12420.8 | − | 7171.16i | −0.670661 | − | 0.387206i | ||||
\(701\) | −6905.96 | −0.372089 | −0.186045 | − | 0.982541i | \(-0.559567\pi\) | ||||
−0.186045 | + | 0.982541i | \(0.559567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11178.2 | 0.599707 | ||||||||
\(704\) | 28383.5 | + | 16387.2i | 1.51952 | + | 0.877297i | ||||
\(705\) | 3153.12 | − | 5461.37i | 0.168445 | − | 0.291755i | ||||
\(706\) | 12744.1 | + | 22073.5i | 0.679366 | + | 1.17670i | ||||
\(707\) | 9281.37i | 0.493723i | ||||||||
\(708\) | −49887.3 | + | 28802.5i | −2.64814 | + | 1.52890i | ||||
\(709\) | 1738.22 | − | 1003.56i | 0.0920739 | − | 0.0531589i | −0.453256 | − | 0.891380i | \(-0.649738\pi\) |
0.545330 | + | 0.838221i | \(0.316404\pi\) | |||||||
\(710\) | 3585.70i | 0.189534i | ||||||||
\(711\) | −908.854 | − | 1574.18i | −0.0479391 | − | 0.0830329i | ||||
\(712\) | −2223.85 | + | 3851.83i | −0.117054 | + | 0.202744i | ||||
\(713\) | 526.929 | + | 304.222i | 0.0276769 | + | 0.0159793i | ||||
\(714\) | 763.312 | 0.0400088 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8541.38 | −0.445819 | ||||||||
\(717\) | −36158.1 | − | 20875.9i | −1.88333 | − | 1.08734i | ||||
\(718\) | 5086.44 | − | 8809.98i | 0.264379 | − | 0.457918i | ||||
\(719\) | −6393.72 | − | 11074.3i | −0.331635 | − | 0.574409i | 0.651198 | − | 0.758908i | \(-0.274267\pi\) |
−0.982833 | + | 0.184499i | \(0.940934\pi\) | |||||||
\(720\) | − | 329.474i | − | 0.0170538i | ||||||
\(721\) | −15730.5 | + | 9082.03i | −0.812532 | + | 0.469116i | ||||
\(722\) | −12783.1 | + | 7380.35i | −0.658919 | + | 0.380427i | ||||
\(723\) | − | 51030.7i | − | 2.62497i | ||||||
\(724\) | 4489.36 | + | 7775.80i | 0.230450 | + | 0.399151i | ||||
\(725\) | −8238.74 | + | 14269.9i | −0.422040 | + | 0.730995i | ||||
\(726\) | −7657.42 | − | 4421.01i | −0.391451 | − | 0.226004i | ||||
\(727\) | 6090.70 | 0.310717 | 0.155359 | − | 0.987858i | \(-0.450347\pi\) | ||||
0.155359 | + | 0.987858i | \(0.450347\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28693.9 | −1.45780 | ||||||||
\(730\) | 5188.01 | + | 2995.30i | 0.263037 | + | 0.151864i | ||||
\(731\) | −430.710 | + | 746.011i | −0.0217926 | + | 0.0377459i | ||||
\(732\) | −8971.37 | − | 15538.9i | −0.452994 | − | 0.784608i | ||||
\(733\) | − | 38846.5i | − | 1.95747i | −0.205117 | − | 0.978737i | \(-0.565757\pi\) | ||
0.205117 | − | 0.978737i | \(-0.434243\pi\) | |||||||
\(734\) | 34365.3 | − | 19840.8i | 1.72813 | − | 0.997735i | ||||
\(735\) | 5312.69 | − | 3067.28i | 0.266614 | − | 0.153930i | ||||
\(736\) | − | 833.427i | − | 0.0417399i | ||||||
\(737\) | 983.585 | + | 1703.62i | 0.0491599 | + | 0.0851474i | ||||
\(738\) | −34262.8 | + | 59344.8i | −1.70898 | + | 2.96005i | ||||
\(739\) | 12520.6 | + | 7228.77i | 0.623245 | + | 0.359830i | 0.778131 | − | 0.628102i | \(-0.216168\pi\) |
−0.154887 | + | 0.987932i | \(0.549501\pi\) | |||||||
\(740\) | 6678.29 | 0.331755 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26721.3 | −1.32206 | ||||||||
\(743\) | 1106.61 | + | 638.901i | 0.0546400 | + | 0.0315464i | 0.527071 | − | 0.849821i | \(-0.323290\pi\) |
−0.472431 | + | 0.881368i | \(0.656623\pi\) | |||||||
\(744\) | 12966.2 | − | 22458.1i | 0.638931 | − | 1.10666i | ||||
\(745\) | −2541.78 | − | 4402.49i | −0.124998 | − | 0.216503i | ||||
\(746\) | − | 50013.7i | − | 2.45460i | ||||||
\(747\) | −3193.63 | + | 1843.84i | −0.156424 | + | 0.0903116i | ||||
\(748\) | −881.181 | + | 508.750i | −0.0430738 | + | 0.0248687i | ||||
\(749\) | 18229.0i | 0.889285i | ||||||||
\(750\) | −13465.4 | − | 23322.8i | −0.655584 | − | 1.13551i | ||||
\(751\) | −6503.93 | + | 11265.1i | −0.316021 | + | 0.547364i | −0.979654 | − | 0.200694i | \(-0.935680\pi\) |
0.663633 | + | 0.748058i | \(0.269014\pi\) | |||||||
\(752\) | 542.743 | + | 313.353i | 0.0263189 | + | 0.0151952i | ||||
\(753\) | −50425.5 | −2.44038 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1188.35 | −0.0572829 | ||||||||
\(756\) | −19732.0 | − | 11392.3i | −0.949268 | − | 0.548060i | ||||
\(757\) | 5361.61 | − | 9286.57i | 0.257425 | − | 0.445874i | −0.708126 | − | 0.706086i | \(-0.750459\pi\) |
0.965551 | + | 0.260212i | \(0.0837926\pi\) | |||||||
\(758\) | −31725.9 | − | 54950.8i | −1.52023 | − | 2.63312i | ||||
\(759\) | 1530.00i | 0.0731694i | ||||||||
\(760\) | 3209.87 | − | 1853.22i | 0.153203 | − | 0.0884518i | ||||
\(761\) | −11796.8 | + | 6810.90i | −0.561938 | + | 0.324435i | −0.753923 | − | 0.656963i | \(-0.771841\pi\) |
0.191985 | + | 0.981398i | \(0.438508\pi\) | |||||||
\(762\) | 24597.0i | 1.16936i | ||||||||
\(763\) | 4283.59 | + | 7419.40i | 0.203246 | + | 0.352032i | ||||
\(764\) | 8330.68 | − | 14429.2i | 0.394494 | − | 0.683284i | ||||
\(765\) | 237.276 | + | 136.991i | 0.0112140 | + | 0.00647443i | ||||
\(766\) | −2256.84 | −0.106453 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −33365.0 | −1.56765 | ||||||||
\(769\) | 7357.01 | + | 4247.57i | 0.344994 | + | 0.199183i | 0.662478 | − | 0.749081i | \(-0.269505\pi\) |
−0.317484 | + | 0.948264i | \(0.602838\pi\) | |||||||
\(770\) | 2413.93 | − | 4181.05i | 0.112977 | − | 0.195681i | ||||
\(771\) | −5192.82 | − | 8994.22i | −0.242561 | − | 0.420128i | ||||
\(772\) | − | 6651.50i | − | 0.310094i | ||||||
\(773\) | 29672.2 | − | 17131.3i | 1.38064 | − | 0.797113i | 0.388405 | − | 0.921489i | \(-0.373026\pi\) |
0.992235 | + | 0.124375i | \(0.0396927\pi\) | |||||||
\(774\) | 81771.9 | − | 47211.0i | 3.79745 | − | 2.19246i | ||||
\(775\) | 15946.0i | 0.739094i | ||||||||
\(776\) | −12877.5 | − | 22304.4i | −0.595714 | − | 1.03181i | ||||
\(777\) | −7710.50 | + | 13355.0i | −0.356001 | + | 0.616612i | ||||
\(778\) | 16356.6 | + | 9443.48i | 0.753743 | + | 0.435174i | ||||
\(779\) | 18673.5 | 0.858854 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11037.1 | 0.505681 | ||||||||
\(782\) | 35.5745 | + | 20.5389i | 0.00162678 | + | 0.000939221i | ||||
\(783\) | −13088.3 | + | 22669.5i | −0.597364 | + | 1.03467i | ||||
\(784\) | 304.822 | + | 527.967i | 0.0138858 | + | 0.0240510i | ||||
\(785\) | 3712.33i | 0.168788i | ||||||||
\(786\) | 45688.2 | − | 26378.1i | 2.07334 | − | 1.19704i | ||||
\(787\) | 10948.8 | − | 6321.29i | 0.495912 | − | 0.286315i | −0.231112 | − | 0.972927i | \(-0.574236\pi\) |
0.727024 | + | 0.686612i | \(0.240903\pi\) | |||||||
\(788\) | − | 39973.6i | − | 1.80711i | ||||||
\(789\) | −1016.91 | − | 1761.33i | −0.0458844 | − | 0.0794741i | ||||
\(790\) | −240.388 | + | 416.365i | −0.0108261 | + | 0.0187514i | ||||
\(791\) | −2773.01 | − | 1601.00i | −0.124648 | − | 0.0719658i | ||||
\(792\) | 41866.2 | 1.87834 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 8583.89 | 0.383666 | ||||||||
\(795\) | −12937.8 | − | 7469.65i | −0.577178 | − | 0.333234i | ||||
\(796\) | −7921.97 | + | 13721.3i | −0.352747 | + | 0.610976i | ||||
\(797\) | 9542.18 | + | 16527.5i | 0.424092 | + | 0.734549i | 0.996335 | − | 0.0855350i | \(-0.0272600\pi\) |
−0.572243 | + | 0.820084i | \(0.693927\pi\) | |||||||
\(798\) | 22800.0i | 1.01142i | ||||||||
\(799\) | −451.333 | + | 260.577i | −0.0199837 | + | 0.0115376i | ||||
\(800\) | 18916.0 | − | 10921.2i | 0.835978 | − | 0.482652i | ||||
\(801\) | − | 9820.53i | − | 0.433198i | ||||||
\(802\) | 961.952 | + | 1666.15i | 0.0423538 | + | 0.0733589i | ||||
\(803\) | 9219.77 | − | 15969.1i | 0.405179 | − | 0.701790i | ||||
\(804\) | −4806.69 | − | 2775.14i | −0.210844 | − | 0.121731i | ||||
\(805\) | −119.971 | −0.00525269 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23173.0 | −1.01082 | ||||||||
\(808\) | 18436.1 | + | 10644.1i | 0.802700 | + | 0.463439i | ||||
\(809\) | −5805.02 | + | 10054.6i | −0.252279 | + | 0.436960i | −0.964153 | − | 0.265347i | \(-0.914513\pi\) |
0.711874 | + | 0.702307i | \(0.247847\pi\) | |||||||
\(810\) | −1974.87 | − | 3420.57i | −0.0856665 | − | 0.148379i | ||||
\(811\) | 9613.36i | 0.416240i | 0.978103 | + | 0.208120i | \(0.0667345\pi\) | ||||
−0.978103 | + | 0.208120i | \(0.933266\pi\) | |||||||
\(812\) | 14921.3 | − | 8614.79i | 0.644869 | − | 0.372315i | ||||
\(813\) | −42880.1 | + | 24756.8i | −1.84978 | + | 1.06797i | ||||
\(814\) | − | 33396.2i | − | 1.43800i | ||||||
\(815\) | 5062.95 | + | 8769.29i | 0.217604 | + | 0.376901i | ||||
\(816\) | −21.2049 | + | 36.7280i | −0.000909707 | + | 0.00157566i | ||||
\(817\) | −22283.2 | − | 12865.2i | −0.954211 | − | 0.550914i | ||||
\(818\) | 11632.9 | 0.497233 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11156.3 | 0.475115 | ||||||||
\(821\) | 22933.6 | + | 13240.7i | 0.974895 | + | 0.562856i | 0.900725 | − | 0.434390i | \(-0.143036\pi\) |
0.0741699 | + | 0.997246i | \(0.476369\pi\) | |||||||
\(822\) | 12320.7 | − | 21340.1i | 0.522792 | − | 0.905502i | ||||
\(823\) | 6907.25 | + | 11963.7i | 0.292553 | + | 0.506718i | 0.974413 | − | 0.224766i | \(-0.0721617\pi\) |
−0.681859 | + | 0.731483i | \(0.738828\pi\) | |||||||
\(824\) | 41662.0i | 1.76136i | ||||||||
\(825\) | −34726.0 | + | 20049.0i | −1.46546 | + | 0.846082i | ||||
\(826\) | −19561.6 | + | 11293.9i | −0.824015 | + | 0.475746i | ||||
\(827\) | 44401.0i | 1.86696i | 0.358633 | + | 0.933479i | \(0.383243\pi\) | ||||
−0.358633 | + | 0.933479i | \(0.616757\pi\) | |||||||
\(828\) | −1385.75 | − | 2400.19i | −0.0581619 | − | 0.100739i | ||||
\(829\) | 12168.7 | − | 21076.8i | 0.509815 | − | 0.883025i | −0.490120 | − | 0.871655i | \(-0.663047\pi\) |
0.999935 | − | 0.0113707i | \(-0.00361948\pi\) | |||||||
\(830\) | 844.703 | + | 487.689i | 0.0353254 | + | 0.0203951i | ||||
\(831\) | 62116.9 | 2.59303 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −506.966 | −0.0210868 | ||||||||
\(834\) | 11341.6 | + | 6548.06i | 0.470895 | + | 0.271871i | ||||
\(835\) | 4794.86 | − | 8304.95i | 0.198722 | − | 0.344197i | ||||
\(836\) | −15196.3 | − | 26320.7i | −0.628677 | − | 1.08890i | ||||
\(837\) | 25332.2i | 1.04613i | ||||||||
\(838\) | −48925.2 | + | 28247.0i | −2.01682 | + | 1.16441i | ||||
\(839\) | 21373.6 | − | 12340.0i | 0.879497 | − | 0.507778i | 0.00900472 | − | 0.999959i | \(-0.497134\pi\) |
0.870493 | + | 0.492181i | \(0.163800\pi\) | |||||||
\(840\) | 5113.26i | 0.210029i | ||||||||
\(841\) | 2297.22 | + | 3978.90i | 0.0941907 | + | 0.163143i | ||||
\(842\) | −23863.7 | + | 41333.1i | −0.976719 | + | 1.69173i | ||||
\(843\) | −46126.2 | − | 26631.0i | −1.88454 | − | 1.08804i | ||||
\(844\) | 32425.0 | 1.32241 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 57124.8 | 2.32150 | ||||||||
\(847\) | −1848.18 | − | 1067.05i | −0.0749757 | − | 0.0432872i | ||||
\(848\) | 742.323 | − | 1285.74i | 0.0300607 | − | 0.0520666i | ||||
\(849\) | 14664.7 | + | 25400.0i | 0.592805 | + | 1.02677i | ||||
\(850\) | 1076.56i | 0.0434421i | ||||||||
\(851\) | −718.702 | + | 414.943i | −0.0289504 | + | 0.0167145i | ||||
\(852\) | −26968.5 | + | 15570.3i | −1.08442 | + | 0.626091i | ||||
\(853\) | 10151.7i | 0.407490i | 0.979024 | + | 0.203745i | \(0.0653113\pi\) | ||||
−0.979024 | + | 0.203745i | \(0.934689\pi\) | |||||||
\(854\) | −3517.82 | − | 6093.05i | −0.140957 | − | 0.244145i | ||||
\(855\) | −4091.90 | + | 7087.39i | −0.163673 | + | 0.283489i | ||||
\(856\) | 36209.4 | + | 20905.5i | 1.44581 | + | 0.834739i | ||||
\(857\) | −2028.92 | −0.0808713 | −0.0404357 | − | 0.999182i | \(-0.512875\pi\) | ||||
−0.0404357 | + | 0.999182i | \(0.512875\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6655.76 | 0.264367 | 0.132184 | − | 0.991225i | \(-0.457801\pi\) | ||||
0.132184 | + | 0.991225i | \(0.457801\pi\) | |||||||
\(860\) | −13312.8 | − | 7686.17i | −0.527865 | − | 0.304763i | ||||
\(861\) | −12880.6 | + | 22309.9i | −0.509837 | + | 0.883064i | ||||
\(862\) | 9037.32 | + | 15653.1i | 0.357091 | + | 0.618500i | ||||
\(863\) | 45690.8i | 1.80224i | 0.433568 | + | 0.901121i | \(0.357254\pi\) | ||||
−0.433568 | + | 0.901121i | \(0.642746\pi\) | |||||||
\(864\) | 30050.4 | − | 17349.6i | 1.18326 | − | 0.683155i | ||||
\(865\) | −5695.35 | + | 3288.21i | −0.223870 | + | 0.129251i | ||||
\(866\) | − | 38290.3i | − | 1.50249i | ||||||
\(867\) | 21316.2 | + | 36920.8i | 0.834991 | + | 1.44625i | ||||
\(868\) | 8336.93 | − | 14440.0i | 0.326007 | − | 0.564660i | ||||
\(869\) | 1281.60 | + | 739.934i | 0.0500292 | + | 0.0288844i | ||||
\(870\) | 15649.4 | 0.609846 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19650.1 | 0.763117 | ||||||||
\(873\) | 49248.1 | + | 28433.4i | 1.90927 | + | 1.10232i | ||||
\(874\) | −613.493 | + | 1062.60i | −0.0237434 | + | 0.0411248i | ||||
\(875\) | −3250.00 | − | 5629.17i | −0.125566 | − | 0.217486i | ||||
\(876\) | 52026.3i | 2.00663i | ||||||||
\(877\) | 26368.3 | − | 15223.8i | 1.01527 | − | 0.586168i | 0.102542 | − | 0.994729i | \(-0.467302\pi\) |
0.912731 | + | 0.408560i | \(0.133969\pi\) | |||||||
\(878\) | 40193.6 | − | 23205.8i | 1.54495 | − | 0.891979i | ||||
\(879\) | 40859.3i | 1.56786i | ||||||||
\(880\) | 134.119 | + | 232.300i | 0.00513766 | + | 0.00889869i | ||||
\(881\) | 16271.0 | − | 28182.2i | 0.622230 | − | 1.07773i | −0.366840 | − | 0.930284i | \(-0.619560\pi\) |
0.989070 | − | 0.147450i | \(-0.0471065\pi\) | |||||||
\(882\) | 48124.7 | + | 27784.8i | 1.83724 | + | 1.06073i | ||||
\(883\) | −27641.9 | −1.05348 | −0.526741 | − | 0.850026i | \(-0.676586\pi\) | ||||
−0.526741 | + | 0.850026i | \(0.676586\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12628.4 | −0.479658 | ||||||||
\(886\) | −23231.4 | − | 13412.7i | −0.880896 | − | 0.508586i | ||||
\(887\) | −20050.0 | + | 34727.5i | −0.758976 | + | 1.31458i | 0.184397 | + | 0.982852i | \(0.440967\pi\) |
−0.943373 | + | 0.331733i | \(0.892367\pi\) | |||||||
\(888\) | 17685.2 | + | 30631.7i | 0.668329 | + | 1.15758i | ||||
\(889\) | 5936.70i | 0.223971i | ||||||||
\(890\) | −2249.49 | + | 1298.75i | −0.0847226 | + | 0.0489146i | ||||
\(891\) | −10528.8 | + | 6078.80i | −0.395879 | + | 0.228561i | ||||
\(892\) | 15312.1i | 0.574761i | ||||||||
\(893\) | −7783.38 | − | 13481.2i | −0.291670 | − | 0.505186i | ||||
\(894\) | 35862.7 | − | 62116.0i | 1.34164 | − | 2.32379i | ||||
\(895\) | −1621.61 | − | 936.236i | −0.0605636 | − | 0.0349664i | ||||
\(896\) | −21993.8 | −0.820044 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −48648.4 | −1.80781 | ||||||||
\(899\) | −16589.7 | − | 9578.06i | −0.615458 | − | 0.355335i | ||||
\(900\) | 36317.5 | − | 62903.7i | 1.34509 | − | 2.32977i | ||||
\(901\) | 617.299 | + | 1069.19i | 0.0228249 | + | 0.0395338i | ||||
\(902\) | − | 55789.3i | − | 2.05940i | ||||||
\(903\) | 30741.0 | − | 17748.3i | 1.13289 | − | 0.654072i | ||||
\(904\) | −6360.32 | + | 3672.13i | −0.234006 | + | 0.135103i | ||||
\(905\) | 1968.35i | 0.0722984i | ||||||||
\(906\) | −8383.41 | − | 14520.5i | −0.307417 | − | 0.532462i | ||||
\(907\) | −18412.4 | + | 31891.3i | −0.674062 | + | 1.16751i | 0.302679 | + | 0.953092i | \(0.402119\pi\) |
−0.976742 | + | 0.214418i | \(0.931215\pi\) | |||||||
\(908\) | −9640.95 | − | 5566.20i | −0.352363 | − | 0.203437i | ||||
\(909\) | −47004.3 | −1.71511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34520.5 | 1.25545 | 0.627725 | − | 0.778435i | \(-0.283986\pi\) | ||||
0.627725 | + | 0.778435i | \(0.283986\pi\) | |||||||
\(912\) | −1097.06 | − | 633.387i | −0.0398325 | − | 0.0229973i | ||||
\(913\) | 1501.15 | − | 2600.06i | 0.0544148 | − | 0.0942491i | ||||
\(914\) | 33821.3 | + | 58580.2i | 1.22397 | + | 2.11998i | ||||
\(915\) | − | 3933.47i | − | 0.142117i | ||||||
\(916\) | 51961.3 | − | 29999.9i | 1.87429 | − | 1.08212i | ||||
\(917\) | 11027.2 | − | 6366.58i | 0.397112 | − | 0.229273i | ||||
\(918\) | 1710.25i | 0.0614888i | ||||||||
\(919\) | −11761.4 | − | 20371.3i | −0.422168 | − | 0.731216i | 0.573983 | − | 0.818867i | \(-0.305397\pi\) |
−0.996151 | + | 0.0876506i | \(0.972064\pi\) | |||||||
\(920\) | −137.586 | + | 238.305i | −0.00493051 | + | 0.00853989i | ||||
\(921\) | 38587.1 | + | 22278.3i | 1.38055 | + | 0.797062i | ||||
\(922\) | −44300.4 | −1.58238 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 41928.3 | 1.49279 | ||||||||
\(925\) | −18835.6 | − | 10874.8i | −0.669526 | − | 0.386551i | ||||
\(926\) | 25894.8 | − | 44851.2i | 0.918961 | − | 1.59169i | ||||
\(927\) | −45994.8 | − | 79665.3i | −1.62963 | − | 2.82260i | ||||
\(928\) | 26239.4i | 0.928180i | ||||||||
\(929\) | −21272.3 | + | 12281.6i | −0.751262 | + | 0.433741i | −0.826150 | − | 0.563451i | \(-0.809473\pi\) |
0.0748880 | + | 0.997192i | \(0.476140\pi\) | |||||||
\(930\) | 13115.7 | − | 7572.35i | 0.462452 | − | 0.266997i | ||||
\(931\) | − | 15143.0i | − | 0.533073i | ||||||
\(932\) | 31180.4 | + | 54006.1i | 1.09587 | + | 1.89810i | ||||
\(933\) | 34516.9 | − | 59785.0i | 1.21118 | − | 2.09783i | ||||
\(934\) | −25485.4 | − | 14714.0i | −0.892834 | − | 0.515478i | ||||
\(935\) | −223.060 | −0.00780197 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12115.6 | −0.422411 | −0.211206 | − | 0.977442i | \(-0.567739\pi\) | ||||
−0.211206 | + | 0.977442i | \(0.567739\pi\) | |||||||
\(938\) | −1884.78 | − | 1088.18i | −0.0656080 | − | 0.0378788i | ||||
\(939\) | 37004.8 | − | 64094.2i | 1.28605 | − | 2.22751i | ||||
\(940\) | −4650.09 | − | 8054.20i | −0.161350 | − | 0.279467i | ||||
\(941\) | 14898.3i | 0.516123i | 0.966128 | + | 0.258062i | \(0.0830837\pi\) | ||||
−0.966128 | + | 0.258062i | \(0.916916\pi\) | |||||||
\(942\) | −45361.0 | + | 26189.2i | −1.56894 | + | 0.905828i | ||||
\(943\) | −1200.61 | + | 693.174i | −0.0414606 | + | 0.0239373i | ||||
\(944\) | − | 1254.99i | − | 0.0432695i | ||||||
\(945\) | −2497.46 | − | 4325.72i | −0.0859707 | − | 0.148906i | ||||
\(946\) | −38436.3 | + | 66573.7i | −1.32101 | + | 2.28805i | ||||
\(947\) | 6438.31 | + | 3717.16i | 0.220926 | + | 0.127552i | 0.606379 | − | 0.795176i | \(-0.292621\pi\) |
−0.385453 | + | 0.922727i | \(0.625955\pi\) | |||||||
\(948\) | −4175.38 | −0.143049 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −32156.7 | −1.09821 | ||||||||
\(951\) | 50109.2 | + | 28930.6i | 1.70863 | + | 0.986476i | ||||
\(952\) | 211.282 | − | 365.951i | 0.00719295 | − | 0.0124586i | ||||
\(953\) | −11764.3 | − | 20376.3i | −0.399877 | − | 0.692607i | 0.593833 | − | 0.804588i | \(-0.297614\pi\) |
−0.993710 | + | 0.111981i | \(0.964280\pi\) | |||||||
\(954\) | − | 135327.i | − | 4.59263i | ||||||
\(955\) | 3163.21 | − | 1826.28i | 0.107182 | − | 0.0618818i | ||||
\(956\) | −53324.4 | + | 30786.9i | −1.80401 | + | 1.04155i | ||||
\(957\) | − | 48170.2i | − | 1.62709i | ||||||
\(958\) | −21818.9 | − | 37791.5i | −0.735844 | − | 1.27452i | ||||
\(959\) | 2973.72 | − | 5150.63i | 0.100132 | − | 0.173433i | ||||
\(960\) | −17556.0 | − | 10136.0i | −0.590228 | − | 0.340768i | ||||
\(961\) | 11252.7 | 0.377723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −92318.7 | −3.08923 | ||||||||
\(964\) | −65175.3 | − | 37629.0i | −2.17755 | − | 1.25721i | ||||
\(965\) | 729.083 | − | 1262.81i | 0.0243213 | − | 0.0421256i | ||||
\(966\) | −846.351 | − | 1465.92i | −0.0281893 | − | 0.0488254i | ||||
\(967\) | 23558.0i | 0.783427i | 0.920087 | + | 0.391713i | \(0.128118\pi\) | ||||
−0.920087 | + | 0.391713i | \(0.871882\pi\) | |||||||
\(968\) | −4239.09 | + | 2447.44i | −0.140754 | + | 0.0812642i | ||||
\(969\) | 912.289 | − | 526.710i | 0.0302445 | − | 0.0174617i | ||||
\(970\) | − | 15041.0i | − | 0.497875i | ||||||
\(971\) | 131.169 | + | 227.191i | 0.00433513 | + | 0.00750866i | 0.868185 | − | 0.496241i | \(-0.165287\pi\) |
−0.863850 | + | 0.503750i | \(0.831953\pi\) | |||||||
\(972\) | −15018.6 | + | 26012.9i | −0.495597 | + | 0.858400i | ||||
\(973\) | 2737.39 | + | 1580.43i | 0.0901918 | + | 0.0520722i | ||||
\(974\) | 22429.7 | 0.737878 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 390.903 | 0.0128202 | ||||||||
\(977\) | −28703.9 | − | 16572.2i | −0.939936 | − | 0.542673i | −0.0499960 | − | 0.998749i | \(-0.515921\pi\) |
−0.889940 | + | 0.456077i | \(0.849254\pi\) | |||||||
\(978\) | −71434.6 | + | 123728.i | −2.33561 | + | 4.04539i | ||||
\(979\) | 3997.64 | + | 6924.11i | 0.130506 | + | 0.226042i | ||||
\(980\) | − | 9047.00i | − | 0.294894i | ||||||
\(981\) | −37574.6 | + | 21693.7i | −1.22290 | + | 0.706042i | ||||
\(982\) | 11657.0 | − | 6730.17i | 0.378808 | − | 0.218705i | ||||
\(983\) | 4866.80i | 0.157911i | 0.996878 | + | 0.0789557i | \(0.0251586\pi\) | ||||
−0.996878 | + | 0.0789557i | \(0.974841\pi\) | |||||||
\(984\) | 29543.6 | + | 51171.1i | 0.957131 | + | 1.65780i | ||||
\(985\) | 4381.58 | − | 7589.12i | 0.141735 | − | 0.245492i | ||||
\(986\) | −1120.02 | − | 646.642i | −0.0361751 | − | 0.0208857i | ||||
\(987\) | 21475.3 | 0.692569 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1910.26 | 0.0614184 | ||||||||
\(990\) | 21174.4 | + | 12225.0i | 0.679764 | + | 0.392462i | ||||
\(991\) | −6266.97 | + | 10854.7i | −0.200885 | + | 0.347943i | −0.948814 | − | 0.315836i | \(-0.897715\pi\) |
0.747929 | + | 0.663779i | \(0.231048\pi\) | |||||||
\(992\) | 12696.5 | + | 21991.1i | 0.406367 | + | 0.703848i | ||||
\(993\) | − | 33972.4i | − | 1.08568i | ||||||
\(994\) | −10574.8 | + | 6105.37i | −0.337437 | + | 0.194819i | ||||
\(995\) | −3008.02 | + | 1736.68i | −0.0958399 | + | 0.0553332i | ||||
\(996\) | 8470.83i | 0.269487i | ||||||||
\(997\) | 1780.46 | + | 3083.84i | 0.0565574 | + | 0.0979602i | 0.892918 | − | 0.450220i | \(-0.148654\pi\) |
−0.836361 | + | 0.548180i | \(0.815321\pi\) | |||||||
\(998\) | −30631.0 | + | 53054.5i | −0.971552 | + | 1.68278i | ||||
\(999\) | −29922.7 | − | 17275.9i | −0.947660 | − | 0.547132i |
(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 | 169.4.e.g.147.4 | 8 | ||
13.2 | odd | 12 | 13.4.c.b.3.2 | ✓ | 4 | ||
13.3 | even | 3 | inner | 169.4.e.g.23.1 | 8 | ||
13.4 | even | 6 | 169.4.b.e.168.4 | 4 | |||
13.5 | odd | 4 | 13.4.c.b.9.2 | yes | 4 | ||
13.6 | odd | 12 | 169.4.a.f.1.1 | 2 | |||
13.7 | odd | 12 | 169.4.a.j.1.2 | 2 | |||
13.8 | odd | 4 | 169.4.c.f.22.1 | 4 | |||
13.9 | even | 3 | 169.4.b.e.168.1 | 4 | |||
13.10 | even | 6 | inner | 169.4.e.g.23.4 | 8 | ||
13.11 | odd | 12 | 169.4.c.f.146.1 | 4 | |||
13.12 | even | 2 | inner | 169.4.e.g.147.1 | 8 | ||
39.2 | even | 12 | 117.4.g.d.55.1 | 4 | |||
39.5 | even | 4 | 117.4.g.d.100.1 | 4 | |||
39.20 | even | 12 | 1521.4.a.l.1.1 | 2 | |||
39.32 | even | 12 | 1521.4.a.t.1.2 | 2 | |||
52.15 | even | 12 | 208.4.i.e.81.2 | 4 | |||
52.31 | even | 4 | 208.4.i.e.113.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.c.b.3.2 | ✓ | 4 | 13.2 | odd | 12 | ||
13.4.c.b.9.2 | yes | 4 | 13.5 | odd | 4 | ||
117.4.g.d.55.1 | 4 | 39.2 | even | 12 | |||
117.4.g.d.100.1 | 4 | 39.5 | even | 4 | |||
169.4.a.f.1.1 | 2 | 13.6 | odd | 12 | |||
169.4.a.j.1.2 | 2 | 13.7 | odd | 12 | |||
169.4.b.e.168.1 | 4 | 13.9 | even | 3 | |||
169.4.b.e.168.4 | 4 | 13.4 | even | 6 | |||
169.4.c.f.22.1 | 4 | 13.8 | odd | 4 | |||
169.4.c.f.146.1 | 4 | 13.11 | odd | 12 | |||
169.4.e.g.23.1 | 8 | 13.3 | even | 3 | inner | ||
169.4.e.g.23.4 | 8 | 13.10 | even | 6 | inner | ||
169.4.e.g.147.1 | 8 | 13.12 | even | 2 | inner | ||
169.4.e.g.147.4 | 8 | 1.1 | even | 1 | trivial | ||
208.4.i.e.81.2 | 4 | 52.15 | even | 12 | |||
208.4.i.e.113.2 | 4 | 52.31 | even | 4 | |||
1521.4.a.l.1.1 | 2 | 39.20 | even | 12 | |||
1521.4.a.t.1.2 | 2 | 39.32 | even | 12 |