Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(32,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.p (of order \(12\), degree \(4\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.5 | ||
Character | \(\chi\) | \(=\) | 225.32 |
Dual form | 225.4.p.b.218.5 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15214 | − | 0.576664i | −0.760896 | − | 0.203881i | −0.142550 | − | 0.989788i | \(-0.545530\pi\) |
−0.618346 | + | 0.785906i | \(0.712197\pi\) | |||||||
\(3\) | −4.75638 | − | 2.09209i | −0.915366 | − | 0.402623i | ||||
\(4\) | −2.62904 | − | 1.51788i | −0.328630 | − | 0.189735i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 9.02996 | + | 7.24530i | 0.614411 | + | 0.492980i | ||||
\(7\) | 3.70051 | − | 13.8105i | 0.199809 | − | 0.745696i | −0.791161 | − | 0.611608i | \(-0.790523\pi\) |
0.990969 | − | 0.134088i | \(-0.0428104\pi\) | |||||||
\(8\) | 17.3866 | + | 17.3866i | 0.768385 | + | 0.768385i | ||||
\(9\) | 18.2463 | + | 19.9016i | 0.675789 | + | 0.737095i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −35.0788 | + | 20.2528i | −0.961516 | + | 0.555131i | −0.896639 | − | 0.442762i | \(-0.853999\pi\) |
−0.0648764 | + | 0.997893i | \(0.520665\pi\) | |||||||
\(12\) | 9.32918 | + | 12.7198i | 0.224425 | + | 0.305991i | ||||
\(13\) | 14.4092 | + | 53.7760i | 0.307416 | + | 1.14729i | 0.930846 | + | 0.365412i | \(0.119072\pi\) |
−0.623431 | + | 0.781879i | \(0.714262\pi\) | |||||||
\(14\) | −15.9280 | + | 27.5881i | −0.304067 | + | 0.526660i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15.2491 | − | 26.4122i | −0.238267 | − | 0.412690i | ||||
\(17\) | −18.3703 | + | 18.3703i | −0.262086 | + | 0.262086i | −0.825901 | − | 0.563815i | \(-0.809333\pi\) |
0.563815 | + | 0.825901i | \(0.309333\pi\) | |||||||
\(18\) | −27.7921 | − | 53.3529i | −0.363925 | − | 0.698634i | ||||
\(19\) | − | 29.3394i | − | 0.354259i | −0.984188 | − | 0.177130i | \(-0.943319\pi\) | ||
0.984188 | − | 0.177130i | \(-0.0566812\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −46.4938 | + | 57.9461i | −0.483132 | + | 0.602137i | ||||
\(22\) | 87.1736 | − | 23.3581i | 0.844794 | − | 0.226362i | ||||
\(23\) | 176.622 | − | 47.3257i | 1.60123 | − | 0.429047i | 0.655814 | − | 0.754923i | \(-0.272326\pi\) |
0.945413 | + | 0.325875i | \(0.105659\pi\) | |||||||
\(24\) | −46.3228 | − | 119.071i | −0.393984 | − | 1.01272i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 124.043i | − | 0.935645i | ||||||
\(27\) | −45.1505 | − | 132.832i | −0.321823 | − | 0.946800i | ||||
\(28\) | −30.6914 | + | 30.6914i | −0.207148 | + | 0.207148i | ||||
\(29\) | 39.7429 | + | 68.8368i | 0.254486 | + | 0.440782i | 0.964756 | − | 0.263147i | \(-0.0847606\pi\) |
−0.710270 | + | 0.703929i | \(0.751427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 62.6702 | − | 108.548i | 0.363093 | − | 0.628896i | −0.625375 | − | 0.780324i | \(-0.715054\pi\) |
0.988468 | + | 0.151428i | \(0.0483873\pi\) | |||||||
\(32\) | −33.3242 | − | 124.368i | −0.184092 | − | 0.687041i | ||||
\(33\) | 209.219 | − | 22.9418i | 1.10365 | − | 0.121020i | ||||
\(34\) | 50.1290 | − | 28.9420i | 0.252854 | − | 0.145986i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17.7622 | − | 80.0177i | −0.0822323 | − | 0.370452i | ||||
\(37\) | −248.921 | − | 248.921i | −1.10601 | − | 1.10601i | −0.993670 | − | 0.112342i | \(-0.964165\pi\) |
−0.112342 | − | 0.993670i | \(-0.535835\pi\) | |||||||
\(38\) | −16.9190 | + | 63.1425i | −0.0722269 | + | 0.269554i | ||||
\(39\) | 43.9685 | − | 285.924i | 0.180528 | − | 1.17396i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 155.350 | + | 89.6914i | 0.591746 | + | 0.341645i | 0.765788 | − | 0.643093i | \(-0.222349\pi\) |
−0.174041 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(42\) | 133.477 | − | 97.8968i | 0.490378 | − | 0.359662i | ||||
\(43\) | −361.167 | − | 96.7744i | −1.28087 | − | 0.343208i | −0.446685 | − | 0.894691i | \(-0.647395\pi\) |
−0.834186 | + | 0.551483i | \(0.814062\pi\) | |||||||
\(44\) | 122.965 | 0.421311 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −407.406 | −1.30584 | ||||||||
\(47\) | 253.018 | + | 67.7961i | 0.785245 | + | 0.210406i | 0.629096 | − | 0.777328i | \(-0.283425\pi\) |
0.156149 | + | 0.987733i | \(0.450092\pi\) | |||||||
\(48\) | 17.2737 | + | 157.529i | 0.0519426 | + | 0.473694i | ||||
\(49\) | 120.011 | + | 69.2884i | 0.349886 | + | 0.202007i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 125.809 | − | 48.9438i | 0.345426 | − | 0.134383i | ||||
\(52\) | 43.7429 | − | 163.251i | 0.116655 | − | 0.435362i | ||||
\(53\) | 56.9787 | + | 56.9787i | 0.147672 | + | 0.147672i | 0.777077 | − | 0.629405i | \(-0.216701\pi\) |
−0.629405 | + | 0.777077i | \(0.716701\pi\) | |||||||
\(54\) | 20.5705 | + | 311.910i | 0.0518388 | + | 0.786030i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 304.456 | − | 175.778i | 0.726511 | − | 0.419451i | ||||
\(57\) | −61.3807 | + | 139.549i | −0.142633 | + | 0.324277i | ||||
\(58\) | −45.8366 | − | 171.065i | −0.103770 | − | 0.387274i | ||||
\(59\) | 213.746 | − | 370.219i | 0.471651 | − | 0.816923i | −0.527823 | − | 0.849354i | \(-0.676992\pi\) |
0.999474 | + | 0.0324311i | \(0.0103250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −400.668 | − | 693.978i | −0.840989 | − | 1.45664i | −0.889059 | − | 0.457792i | \(-0.848641\pi\) |
0.0480704 | − | 0.998844i | \(-0.484693\pi\) | |||||||
\(62\) | −197.471 | + | 197.471i | −0.404496 | + | 0.404496i | ||||
\(63\) | 342.371 | − | 178.344i | 0.684677 | − | 0.356655i | ||||
\(64\) | 530.858i | 1.03683i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −463.498 | − | 71.2751i | −0.864434 | − | 0.132930i | ||||
\(67\) | 576.627 | − | 154.507i | 1.05144 | − | 0.281732i | 0.308591 | − | 0.951195i | \(-0.400142\pi\) |
0.742845 | + | 0.669463i | \(0.233476\pi\) | |||||||
\(68\) | 76.1803 | − | 20.4124i | 0.135856 | − | 0.0364025i | ||||
\(69\) | −939.091 | − | 144.410i | −1.63845 | − | 0.251956i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 655.546i | 1.09576i | 0.836557 | + | 0.547880i | \(0.184565\pi\) | ||||
−0.836557 | + | 0.547880i | \(0.815435\pi\) | |||||||
\(72\) | −28.7792 | + | 663.260i | −0.0471064 | + | 1.08564i | ||||
\(73\) | 91.3719 | − | 91.3719i | 0.146497 | − | 0.146497i | −0.630054 | − | 0.776551i | \(-0.716967\pi\) |
0.776551 | + | 0.630054i | \(0.216967\pi\) | |||||||
\(74\) | 392.170 | + | 679.258i | 0.616065 | + | 1.06706i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −44.5337 | + | 77.1346i | −0.0672153 | + | 0.116420i | ||||
\(77\) | 149.891 | + | 559.401i | 0.221840 | + | 0.827918i | ||||
\(78\) | −259.509 | + | 589.994i | −0.376712 | + | 0.856458i | ||||
\(79\) | 529.437 | − | 305.671i | 0.754004 | − | 0.435325i | −0.0731347 | − | 0.997322i | \(-0.523300\pi\) |
0.827139 | + | 0.561998i | \(0.189967\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −63.1444 | + | 726.260i | −0.0866179 | + | 0.996242i | ||||
\(82\) | −282.613 | − | 282.613i | −0.380602 | − | 0.380602i | ||||
\(83\) | 55.3072 | − | 206.409i | 0.0731417 | − | 0.272968i | −0.919664 | − | 0.392707i | \(-0.871539\pi\) |
0.992806 | + | 0.119738i | \(0.0382055\pi\) | |||||||
\(84\) | 210.189 | − | 81.7708i | 0.273018 | − | 0.106213i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 721.475 | + | 416.544i | 0.904636 | + | 0.522292i | ||||
\(87\) | −45.0197 | − | 410.560i | −0.0554784 | − | 0.505938i | ||||
\(88\) | −962.027 | − | 257.774i | −1.16537 | − | 0.312259i | ||||
\(89\) | −451.962 | −0.538291 | −0.269146 | − | 0.963100i | \(-0.586741\pi\) | ||||
−0.269146 | + | 0.963100i | \(0.586741\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 795.994 | 0.916954 | ||||||||
\(92\) | −536.181 | − | 143.669i | −0.607617 | − | 0.162810i | ||||
\(93\) | −525.175 | + | 385.183i | −0.585571 | + | 0.429480i | ||||
\(94\) | −505.435 | − | 291.813i | −0.554592 | − | 0.320194i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −101.686 | + | 661.257i | −0.108107 | + | 0.703013i | ||||
\(97\) | −310.669 | + | 1159.43i | −0.325193 | + | 1.21364i | 0.588926 | + | 0.808187i | \(0.299551\pi\) |
−0.914118 | + | 0.405448i | \(0.867116\pi\) | |||||||
\(98\) | −218.324 | − | 218.324i | −0.225042 | − | 0.225042i | ||||
\(99\) | −1043.12 | − | 328.585i | −1.05897 | − | 0.333577i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 919.775 | − | 531.032i | 0.906149 | − | 0.523165i | 0.0269588 | − | 0.999637i | \(-0.491418\pi\) |
0.879190 | + | 0.476471i | \(0.158084\pi\) | |||||||
\(102\) | −298.982 | + | 32.7847i | −0.290231 | + | 0.0318252i | ||||
\(103\) | 22.8146 | + | 85.1453i | 0.0218251 | + | 0.0814526i | 0.975979 | − | 0.217863i | \(-0.0699085\pi\) |
−0.954154 | + | 0.299315i | \(0.903242\pi\) | |||||||
\(104\) | −684.452 | + | 1185.51i | −0.645347 | + | 1.11777i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −89.7685 | − | 155.484i | −0.0822555 | − | 0.142471i | ||||
\(107\) | 422.554 | − | 422.554i | 0.381774 | − | 0.381774i | −0.489967 | − | 0.871741i | \(-0.662991\pi\) |
0.871741 | + | 0.489967i | \(0.162991\pi\) | |||||||
\(108\) | −82.9208 | + | 417.755i | −0.0738801 | + | 0.372208i | ||||
\(109\) | − | 1529.73i | − | 1.34424i | −0.740444 | − | 0.672118i | \(-0.765385\pi\) | ||
0.740444 | − | 0.672118i | \(-0.234615\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 663.199 | + | 1704.73i | 0.567100 | + | 1.45771i | ||||
\(112\) | −421.194 | + | 112.859i | −0.355349 | + | 0.0952155i | ||||
\(113\) | 2041.91 | − | 547.128i | 1.69988 | − | 0.455482i | 0.726971 | − | 0.686668i | \(-0.240927\pi\) |
0.972910 | + | 0.231186i | \(0.0742607\pi\) | |||||||
\(114\) | 212.573 | − | 264.934i | 0.174643 | − | 0.217661i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 241.300i | − | 0.193139i | ||||||
\(117\) | −807.311 | + | 1267.98i | −0.637914 | + | 1.00192i | ||||
\(118\) | −673.504 | + | 673.504i | −0.525433 | + | 0.525433i | ||||
\(119\) | 185.723 | + | 321.683i | 0.143069 | + | 0.247803i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 154.850 | − | 268.209i | 0.116341 | − | 0.201509i | ||||
\(122\) | 462.102 | + | 1724.59i | 0.342924 | + | 1.27981i | ||||
\(123\) | −551.261 | − | 751.613i | −0.404110 | − | 0.550981i | ||||
\(124\) | −329.525 | + | 190.251i | −0.238647 | + | 0.137783i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −839.674 | + | 186.389i | −0.593684 | + | 0.131785i | ||||
\(127\) | 212.243 | + | 212.243i | 0.148296 | + | 0.148296i | 0.777356 | − | 0.629061i | \(-0.216560\pi\) |
−0.629061 | + | 0.777356i | \(0.716560\pi\) | |||||||
\(128\) | 39.5332 | − | 147.540i | 0.0272990 | − | 0.101881i | ||||
\(129\) | 1515.39 | + | 1215.89i | 1.03428 | + | 0.829869i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 285.089 | + | 164.596i | 0.190140 | + | 0.109777i | 0.592048 | − | 0.805903i | \(-0.298320\pi\) |
−0.401908 | + | 0.915680i | \(0.631653\pi\) | |||||||
\(132\) | −584.868 | − | 257.254i | −0.385654 | − | 0.169629i | ||||
\(133\) | −405.192 | − | 108.571i | −0.264170 | − | 0.0707840i | ||||
\(134\) | −1330.08 | −0.857474 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −638.793 | −0.402765 | ||||||||
\(137\) | 1269.01 | + | 340.030i | 0.791378 | + | 0.212049i | 0.631795 | − | 0.775136i | \(-0.282318\pi\) |
0.159583 | + | 0.987185i | \(0.448985\pi\) | |||||||
\(138\) | 1937.78 | + | 852.330i | 1.19532 | + | 0.525762i | ||||
\(139\) | 1886.00 | + | 1088.88i | 1.15085 | + | 0.664446i | 0.949095 | − | 0.314989i | \(-0.102001\pi\) |
0.201759 | + | 0.979435i | \(0.435334\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1061.62 | − | 851.801i | −0.634072 | − | 0.508756i | ||||
\(142\) | 378.029 | − | 1410.83i | 0.223405 | − | 0.833759i | ||||
\(143\) | −1594.57 | − | 1594.57i | −0.932482 | − | 0.932482i | ||||
\(144\) | 247.404 | − | 785.405i | 0.143174 | − | 0.454517i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −249.336 | + | 143.954i | −0.141337 | + | 0.0816009i | ||||
\(147\) | −425.861 | − | 580.636i | −0.238941 | − | 0.325783i | ||||
\(148\) | 276.593 | + | 1032.26i | 0.153620 | + | 0.573318i | ||||
\(149\) | −238.236 | + | 412.637i | −0.130987 | + | 0.226876i | −0.924057 | − | 0.382254i | \(-0.875148\pi\) |
0.793070 | + | 0.609130i | \(0.208481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −999.275 | − | 1730.80i | −0.538542 | − | 0.932783i | −0.998983 | − | 0.0450920i | \(-0.985642\pi\) |
0.460441 | − | 0.887691i | \(-0.347691\pi\) | |||||||
\(152\) | 510.112 | − | 510.112i | 0.272207 | − | 0.272207i | ||||
\(153\) | −700.789 | − | 30.4076i | −0.370297 | − | 0.0160674i | ||||
\(154\) | − | 1290.35i | − | 0.675189i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −549.594 | + | 684.969i | −0.282069 | + | 0.351547i | ||||
\(157\) | 1403.25 | − | 375.998i | 0.713320 | − | 0.191133i | 0.116131 | − | 0.993234i | \(-0.462951\pi\) |
0.597189 | + | 0.802101i | \(0.296284\pi\) | |||||||
\(158\) | −1315.69 | + | 352.538i | −0.662473 | + | 0.177509i | ||||
\(159\) | −151.808 | − | 390.217i | −0.0757178 | − | 0.194630i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 2614.36i | − | 1.27976i | ||||||
\(162\) | 554.704 | − | 1526.60i | 0.269022 | − | 0.740377i | ||||
\(163\) | 1588.23 | − | 1588.23i | 0.763188 | − | 0.763188i | −0.213710 | − | 0.976897i | \(-0.568555\pi\) |
0.976897 | + | 0.213710i | \(0.0685547\pi\) | |||||||
\(164\) | −272.281 | − | 471.605i | −0.129644 | − | 0.224550i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −238.058 | + | 412.328i | −0.111306 | + | 0.192788i | ||||
\(167\) | −500.820 | − | 1869.08i | −0.232063 | − | 0.866072i | −0.979451 | − | 0.201684i | \(-0.935359\pi\) |
0.747387 | − | 0.664389i | \(-0.231308\pi\) | |||||||
\(168\) | −1815.85 | + | 199.116i | −0.833904 | + | 0.0914413i | ||||
\(169\) | −781.573 | + | 451.241i | −0.355746 | + | 0.205390i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 583.900 | − | 535.336i | 0.261123 | − | 0.239405i | ||||
\(172\) | 802.631 | + | 802.631i | 0.355814 | + | 0.355814i | ||||
\(173\) | 93.5626 | − | 349.180i | 0.0411181 | − | 0.153455i | −0.942315 | − | 0.334729i | \(-0.891355\pi\) |
0.983433 | + | 0.181274i | \(0.0580220\pi\) | |||||||
\(174\) | −139.866 | + | 909.543i | −0.0609382 | + | 0.396278i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1069.84 | + | 617.672i | 0.458194 | + | 0.264539i | ||||
\(177\) | −1791.19 | + | 1313.73i | −0.760645 | + | 0.557886i | ||||
\(178\) | 972.686 | + | 260.630i | 0.409583 | + | 0.109748i | ||||
\(179\) | 1522.98 | 0.635937 | 0.317969 | − | 0.948101i | \(-0.396999\pi\) | ||||
0.317969 | + | 0.948101i | \(0.396999\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2025.51 | 0.831797 | 0.415898 | − | 0.909411i | \(-0.363467\pi\) | ||||
0.415898 | + | 0.909411i | \(0.363467\pi\) | |||||||
\(182\) | −1713.09 | − | 459.021i | −0.697707 | − | 0.186950i | ||||
\(183\) | 453.866 | + | 4139.06i | 0.183337 | + | 1.67196i | ||||
\(184\) | 3893.68 | + | 2248.02i | 1.56003 | + | 0.900685i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1352.37 | − | 526.119i | 0.533122 | − | 0.207403i | ||||
\(187\) | 272.360 | − | 1016.46i | 0.106508 | − | 0.397491i | ||||
\(188\) | −562.290 | − | 562.290i | −0.218134 | − | 0.218134i | ||||
\(189\) | −2001.56 | + | 132.003i | −0.770328 | + | 0.0508032i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1086.41 | + | 627.242i | −0.411572 | + | 0.237621i | −0.691465 | − | 0.722410i | \(-0.743034\pi\) |
0.279893 | + | 0.960031i | \(0.409701\pi\) | |||||||
\(192\) | 1110.60 | − | 2524.96i | 0.417453 | − | 0.949081i | ||||
\(193\) | −751.094 | − | 2803.12i | −0.280129 | − | 1.04546i | −0.952326 | − | 0.305084i | \(-0.901316\pi\) |
0.672196 | − | 0.740373i | \(-0.265351\pi\) | |||||||
\(194\) | 1337.21 | − | 2316.11i | 0.494876 | − | 0.857150i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −210.343 | − | 364.324i | −0.0766555 | − | 0.132771i | ||||
\(197\) | 1576.77 | − | 1576.77i | 0.570255 | − | 0.570255i | −0.361945 | − | 0.932200i | \(-0.617887\pi\) |
0.932200 | + | 0.361945i | \(0.117887\pi\) | |||||||
\(198\) | 2055.46 | + | 1308.69i | 0.737753 | + | 0.469721i | ||||
\(199\) | − | 3635.06i | − | 1.29489i | −0.762113 | − | 0.647444i | \(-0.775838\pi\) | ||
0.762113 | − | 0.647444i | \(-0.224162\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3065.90 | − | 471.464i | −1.07588 | − | 0.165445i | ||||
\(202\) | −2285.71 | + | 612.454i | −0.796149 | + | 0.213327i | ||||
\(203\) | 1097.74 | − | 294.138i | 0.379538 | − | 0.101697i | ||||
\(204\) | −405.047 | − | 62.2867i | −0.139015 | − | 0.0213772i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 196.401i | − | 0.0664267i | ||||||
\(207\) | 4164.55 | + | 2651.53i | 1.39834 | + | 0.890310i | ||||
\(208\) | 1200.61 | − | 1200.61i | 0.400228 | − | 0.400228i | ||||
\(209\) | 594.205 | + | 1029.19i | 0.196660 | + | 0.340626i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −870.723 | + | 1508.14i | −0.284090 | + | 0.492059i | −0.972388 | − | 0.233369i | \(-0.925025\pi\) |
0.688298 | + | 0.725428i | \(0.258358\pi\) | |||||||
\(212\) | −63.3126 | − | 236.286i | −0.0205110 | − | 0.0765481i | ||||
\(213\) | 1371.46 | − | 3118.02i | 0.441178 | − | 1.00302i | ||||
\(214\) | −1153.07 | + | 665.724i | −0.368327 | + | 0.212654i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1524.49 | − | 3094.51i | 0.480223 | − | 0.974790i | ||||
\(217\) | −1267.19 | − | 1267.19i | −0.396416 | − | 0.396416i | ||||
\(218\) | −882.142 | + | 3292.20i | −0.274065 | + | 1.02282i | ||||
\(219\) | −625.758 | + | 243.441i | −0.193081 | + | 0.0751152i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1252.58 | − | 723.180i | −0.381258 | − | 0.220119i | ||||
\(222\) | −444.239 | − | 4051.26i | −0.134303 | − | 1.22479i | ||||
\(223\) | 5027.28 | + | 1347.06i | 1.50965 | + | 0.404509i | 0.916318 | − | 0.400451i | \(-0.131146\pi\) |
0.593329 | + | 0.804960i | \(0.297813\pi\) | |||||||
\(224\) | −1840.89 | −0.549107 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4709.98 | −1.38630 | ||||||||
\(227\) | −2255.67 | − | 604.406i | −0.659534 | − | 0.176722i | −0.0864984 | − | 0.996252i | \(-0.527568\pi\) |
−0.573036 | + | 0.819530i | \(0.694234\pi\) | |||||||
\(228\) | 373.192 | − | 273.713i | 0.108400 | − | 0.0795047i | ||||
\(229\) | −2860.05 | − | 1651.25i | −0.825316 | − | 0.476496i | 0.0269303 | − | 0.999637i | \(-0.491427\pi\) |
−0.852246 | + | 0.523141i | \(0.824760\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 457.379 | − | 2974.31i | 0.130274 | − | 0.847166i | ||||
\(232\) | −505.842 | + | 1887.83i | −0.143147 | + | 0.534233i | ||||
\(233\) | 1380.71 | + | 1380.71i | 0.388213 | + | 0.388213i | 0.874049 | − | 0.485837i | \(-0.161485\pi\) |
−0.485837 | + | 0.874049i | \(0.661485\pi\) | |||||||
\(234\) | 2468.64 | − | 2263.32i | 0.689659 | − | 0.632299i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1123.90 | + | 648.882i | −0.309997 | + | 0.178977i | ||||
\(237\) | −3157.70 | + | 346.255i | −0.865461 | + | 0.0949017i | ||||
\(238\) | −214.200 | − | 799.406i | −0.0583384 | − | 0.217722i | ||||
\(239\) | 2043.12 | − | 3538.78i | 0.552963 | − | 0.957761i | −0.445095 | − | 0.895483i | \(-0.646830\pi\) |
0.998059 | − | 0.0622776i | \(-0.0198364\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2368.28 | + | 4101.99i | 0.633007 | + | 1.09640i | 0.986934 | + | 0.161127i | \(0.0515128\pi\) |
−0.353927 | + | 0.935273i | \(0.615154\pi\) | |||||||
\(242\) | −487.926 | + | 487.926i | −0.129608 | + | 0.129608i | ||||
\(243\) | 1819.74 | − | 3322.27i | 0.480397 | − | 0.877051i | ||||
\(244\) | 2432.66i | 0.638259i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 752.963 | + | 1935.47i | 0.195151 | + | 0.501630i | ||||
\(247\) | 1577.76 | − | 422.759i | 0.406438 | − | 0.108905i | ||||
\(248\) | 2976.89 | − | 797.656i | 0.762229 | − | 0.204239i | ||||
\(249\) | −694.890 | + | 866.054i | −0.176855 | + | 0.220417i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3435.06i | 0.863822i | 0.901916 | + | 0.431911i | \(0.142161\pi\) | ||||
−0.901916 | + | 0.431911i | \(0.857839\pi\) | |||||||
\(252\) | −1170.81 | − | 50.8021i | −0.292676 | − | 0.0126993i | ||||
\(253\) | −5237.22 | + | 5237.22i | −1.30143 | + | 1.30143i | ||||
\(254\) | −334.384 | − | 579.170i | −0.0826028 | − | 0.143072i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1953.27 | − | 3383.17i | 0.476873 | − | 0.825968i | ||||
\(257\) | 614.874 | + | 2294.74i | 0.149240 | + | 0.556973i | 0.999530 | + | 0.0306577i | \(0.00976017\pi\) |
−0.850289 | + | 0.526315i | \(0.823573\pi\) | |||||||
\(258\) | −2560.16 | − | 3490.63i | −0.617786 | − | 0.842315i | ||||
\(259\) | −4358.86 | + | 2516.59i | −1.04574 | + | 0.603758i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −644.798 | + | 2046.96i | −0.152919 | + | 0.485456i | ||||
\(262\) | −518.634 | − | 518.634i | −0.122295 | − | 0.122295i | ||||
\(263\) | −1733.57 | + | 6469.78i | −0.406451 | + | 1.51690i | 0.394913 | + | 0.918718i | \(0.370775\pi\) |
−0.801364 | + | 0.598177i | \(0.795892\pi\) | |||||||
\(264\) | 4036.48 | + | 3238.72i | 0.941015 | + | 0.755036i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 809.420 | + | 467.319i | 0.186574 | + | 0.107719i | ||||
\(267\) | 2149.70 | + | 945.546i | 0.492733 | + | 0.216728i | ||||
\(268\) | −1750.50 | − | 469.045i | −0.398988 | − | 0.106909i | ||||
\(269\) | −3363.52 | −0.762370 | −0.381185 | − | 0.924499i | \(-0.624484\pi\) | ||||
−0.381185 | + | 0.924499i | \(0.624484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6582.75 | 1.47555 | 0.737775 | − | 0.675047i | \(-0.235877\pi\) | ||||
0.737775 | + | 0.675047i | \(0.235877\pi\) | |||||||
\(272\) | 765.330 | + | 205.070i | 0.170606 | + | 0.0457139i | ||||
\(273\) | −3786.05 | − | 1665.29i | −0.839348 | − | 0.369187i | ||||
\(274\) | −2535.00 | − | 1463.58i | −0.558923 | − | 0.322695i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2249.71 | + | 1805.09i | 0.490640 | + | 0.393672i | ||||
\(277\) | −297.389 | + | 1109.87i | −0.0645067 | + | 0.240742i | −0.990650 | − | 0.136430i | \(-0.956437\pi\) |
0.926143 | + | 0.377173i | \(0.123104\pi\) | |||||||
\(278\) | −3431.02 | − | 3431.02i | −0.740212 | − | 0.740212i | ||||
\(279\) | 3303.77 | − | 733.364i | 0.708931 | − | 0.157367i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5577.86 | + | 3220.38i | −1.18415 | + | 0.683672i | −0.956972 | − | 0.290180i | \(-0.906285\pi\) |
−0.227183 | + | 0.973852i | \(0.572951\pi\) | |||||||
\(282\) | 1793.54 | + | 2445.39i | 0.378737 | + | 0.516386i | ||||
\(283\) | 1473.52 | + | 5499.24i | 0.309511 | + | 1.15511i | 0.928992 | + | 0.370099i | \(0.120676\pi\) |
−0.619482 | + | 0.785011i | \(0.712657\pi\) | |||||||
\(284\) | 995.038 | − | 1723.46i | 0.207904 | − | 0.360100i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2512.21 | + | 4351.27i | 0.519406 | + | 0.899637i | ||||
\(287\) | 1813.56 | − | 1813.56i | 0.372999 | − | 0.372999i | ||||
\(288\) | 1867.07 | − | 2932.45i | 0.382007 | − | 0.599988i | ||||
\(289\) | 4238.06i | 0.862622i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3903.30 | − | 4864.76i | 0.786308 | − | 0.979990i | ||||
\(292\) | −378.912 | + | 101.529i | −0.0759388 | + | 0.0203477i | ||||
\(293\) | 988.051 | − | 264.747i | 0.197005 | − | 0.0527874i | −0.158967 | − | 0.987284i | \(-0.550816\pi\) |
0.355972 | + | 0.934496i | \(0.384150\pi\) | |||||||
\(294\) | 581.679 | + | 1495.19i | 0.115388 | + | 0.296603i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 8655.78i | − | 1.69969i | ||||||
\(297\) | 4274.05 | + | 3745.18i | 0.835036 | + | 0.731709i | ||||
\(298\) | 750.669 | − | 750.669i | 0.145923 | − | 0.145923i | ||||
\(299\) | 5089.97 | + | 8816.09i | 0.984484 | + | 1.70518i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2673.00 | + | 4629.77i | −0.511858 | + | 0.886564i | ||||
\(302\) | 1152.49 | + | 4301.16i | 0.219598 | + | 0.819549i | ||||
\(303\) | −5485.77 | + | 601.539i | −1.04010 | + | 0.114051i | ||||
\(304\) | −774.917 | + | 447.399i | −0.146199 | + | 0.0844082i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1490.66 | + | 469.561i | 0.278482 | + | 0.0877222i | ||||
\(307\) | −337.059 | − | 337.059i | −0.0626611 | − | 0.0626611i | 0.675082 | − | 0.737743i | \(-0.264108\pi\) |
−0.737743 | + | 0.675082i | \(0.764108\pi\) | |||||||
\(308\) | 455.033 | − | 1698.21i | 0.0841815 | − | 0.314170i | ||||
\(309\) | 69.6167 | − | 452.714i | 0.0128167 | − | 0.0833462i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4362.60 | − | 2518.75i | −0.795434 | − | 0.459244i | 0.0464378 | − | 0.998921i | \(-0.485213\pi\) |
−0.841872 | + | 0.539677i | \(0.818546\pi\) | |||||||
\(312\) | 5735.70 | − | 4206.78i | 1.04077 | − | 0.763340i | ||||
\(313\) | −4562.05 | − | 1222.40i | −0.823842 | − | 0.220748i | −0.177816 | − | 0.984064i | \(-0.556903\pi\) |
−0.646025 | + | 0.763316i | \(0.723570\pi\) | |||||||
\(314\) | −3236.80 | −0.581731 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1855.88 | −0.330385 | ||||||||
\(317\) | −9568.96 | − | 2563.99i | −1.69541 | − | 0.454285i | −0.723636 | − | 0.690182i | \(-0.757530\pi\) |
−0.971778 | + | 0.235897i | \(0.924197\pi\) | |||||||
\(318\) | 101.687 | + | 927.343i | 0.0179319 | + | 0.163531i | ||||
\(319\) | −2788.27 | − | 1609.81i | −0.489384 | − | 0.282546i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2893.85 | + | 1125.81i | −0.503175 | + | 0.195752i | ||||
\(322\) | −1507.61 | + | 5626.47i | −0.260918 | + | 0.973761i | ||||
\(323\) | 538.975 | + | 538.975i | 0.0928463 | + | 0.0928463i | ||||
\(324\) | 1268.38 | − | 1813.52i | 0.217487 | − | 0.310961i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4333.96 | + | 2502.21i | −0.736306 | + | 0.425107i | ||||
\(327\) | −3200.34 | + | 7275.99i | −0.541221 | + | 1.23047i | ||||
\(328\) | 1141.58 | + | 4260.43i | 0.192174 | + | 0.717204i | ||||
\(329\) | 1872.59 | − | 3243.43i | 0.313797 | − | 0.543513i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2314.33 | − | 4008.54i | −0.384312 | − | 0.665648i | 0.607362 | − | 0.794426i | \(-0.292228\pi\) |
−0.991673 | + | 0.128778i | \(0.958895\pi\) | |||||||
\(332\) | −458.710 | + | 458.710i | −0.0758282 | + | 0.0758282i | ||||
\(333\) | 412.028 | − | 9495.82i | 0.0678048 | − | 1.56267i | ||||
\(334\) | 4311.33i | 0.706304i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2239.47 | + | 344.378i | 0.363610 | + | 0.0559147i | ||||
\(337\) | −908.869 | + | 243.531i | −0.146912 | + | 0.0393649i | −0.331525 | − | 0.943446i | \(-0.607563\pi\) |
0.184614 | + | 0.982811i | \(0.440897\pi\) | |||||||
\(338\) | 1942.27 | − | 520.429i | 0.312561 | − | 0.0837503i | ||||
\(339\) | −10856.7 | − | 1669.51i | −1.73940 | − | 0.267479i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5076.98i | 0.806258i | ||||||||
\(342\) | −1565.34 | + | 815.403i | −0.247497 | + | 0.128924i | ||||
\(343\) | 4868.73 | − | 4868.73i | 0.766433 | − | 0.766433i | ||||
\(344\) | −4596.88 | − | 7962.02i | −0.720485 | − | 1.24792i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −402.719 | + | 697.531i | −0.0625732 | + | 0.108380i | ||||
\(347\) | −155.452 | − | 580.155i | −0.0240493 | − | 0.0897532i | 0.952858 | − | 0.303416i | \(-0.0981272\pi\) |
−0.976907 | + | 0.213663i | \(0.931461\pi\) | |||||||
\(348\) | −504.821 | + | 1147.71i | −0.0777622 | + | 0.176793i | ||||
\(349\) | 8983.64 | − | 5186.71i | 1.37789 | − | 0.795525i | 0.385984 | − | 0.922505i | \(-0.373862\pi\) |
0.991905 | + | 0.126980i | \(0.0405285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6492.61 | − | 4342.02i | 0.987321 | − | 0.660285i | ||||
\(352\) | 3687.77 | + | 3687.77i | 0.558405 | + | 0.558405i | ||||
\(353\) | −2450.37 | + | 9144.89i | −0.369461 | + | 1.37885i | 0.491810 | + | 0.870702i | \(0.336335\pi\) |
−0.861271 | + | 0.508145i | \(0.830331\pi\) | |||||||
\(354\) | 4612.47 | − | 1794.41i | 0.692515 | − | 0.269412i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1188.23 | + | 686.024i | 0.176899 | + | 0.102133i | ||||
\(357\) | −210.382 | − | 1918.59i | −0.0311894 | − | 0.284434i | ||||
\(358\) | −3277.66 | − | 878.247i | −0.483882 | − | 0.129656i | ||||
\(359\) | 6712.05 | 0.986765 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5998.20 | 0.874500 | ||||||||
\(362\) | −4359.19 | − | 1168.04i | −0.632911 | − | 0.169588i | ||||
\(363\) | −1297.64 | + | 951.742i | −0.187627 | + | 0.137613i | ||||
\(364\) | −2092.70 | − | 1208.22i | −0.301339 | − | 0.173978i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1410.06 | − | 9169.56i | 0.201380 | − | 1.30956i | ||||
\(367\) | 829.995 | − | 3097.58i | 0.118053 | − | 0.440579i | −0.881444 | − | 0.472288i | \(-0.843428\pi\) |
0.999497 | + | 0.0317089i | \(0.0100950\pi\) | |||||||
\(368\) | −3943.29 | − | 3943.29i | −0.558582 | − | 0.558582i | ||||
\(369\) | 1049.57 | + | 4728.25i | 0.148071 | + | 0.667053i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 997.753 | − | 576.053i | 0.139625 | − | 0.0806123i | ||||
\(372\) | 1965.37 | − | 215.511i | 0.273924 | − | 0.0300369i | ||||
\(373\) | −793.369 | − | 2960.89i | −0.110132 | − | 0.411017i | 0.888745 | − | 0.458402i | \(-0.151578\pi\) |
−0.998877 | + | 0.0473850i | \(0.984911\pi\) | |||||||
\(374\) | −1172.31 | + | 2030.50i | −0.162082 | + | 0.280735i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3220.38 | + | 5577.86i | 0.441698 | + | 0.765043i | ||||
\(377\) | −3129.10 | + | 3129.10i | −0.427472 | + | 0.427472i | ||||
\(378\) | 4383.75 | + | 870.138i | 0.596497 | + | 0.118400i | ||||
\(379\) | 8477.84i | 1.14902i | 0.818499 | + | 0.574509i | \(0.194807\pi\) | ||||
−0.818499 | + | 0.574509i | \(0.805193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −565.477 | − | 1453.54i | −0.0760374 | − | 0.195452i | ||||
\(382\) | 2699.82 | − | 723.415i | 0.361610 | − | 0.0968930i | ||||
\(383\) | −6497.52 | + | 1741.00i | −0.866860 | + | 0.232275i | −0.664730 | − | 0.747084i | \(-0.731453\pi\) |
−0.202131 | + | 0.979359i | \(0.564787\pi\) | |||||||
\(384\) | −496.702 | + | 619.049i | −0.0660084 | + | 0.0822675i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6465.84i | 0.852597i | ||||||||
\(387\) | −4664.00 | − | 8953.56i | −0.612621 | − | 1.17606i | ||||
\(388\) | 2576.64 | − | 2576.64i | 0.337137 | − | 0.337137i | ||||
\(389\) | −2078.63 | − | 3600.30i | −0.270928 | − | 0.469260i | 0.698172 | − | 0.715930i | \(-0.253997\pi\) |
−0.969100 | + | 0.246670i | \(0.920664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2375.21 | + | 4113.99i | −0.307211 | + | 0.532106i | ||||
\(392\) | 881.892 | + | 3291.27i | 0.113628 | + | 0.424066i | ||||
\(393\) | −1011.64 | − | 1379.31i | −0.129849 | − | 0.177041i | ||||
\(394\) | −4302.70 | + | 2484.16i | −0.550169 | + | 0.317640i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2243.66 | + | 2447.20i | 0.284717 | + | 0.310546i | ||||
\(397\) | −2587.31 | − | 2587.31i | −0.327087 | − | 0.327087i | 0.524391 | − | 0.851478i | \(-0.324293\pi\) |
−0.851478 | + | 0.524391i | \(0.824293\pi\) | |||||||
\(398\) | −2096.21 | + | 7823.16i | −0.264004 | + | 0.985276i | ||||
\(399\) | 1700.11 | + | 1364.10i | 0.213313 | + | 0.171154i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8012.98 | + | 4626.29i | 0.997878 | + | 0.576125i | 0.907620 | − | 0.419794i | \(-0.137898\pi\) |
0.0902579 | + | 0.995918i | \(0.471231\pi\) | |||||||
\(402\) | 6326.37 | + | 2782.65i | 0.784902 | + | 0.345239i | ||||
\(403\) | 6740.30 | + | 1806.06i | 0.833147 | + | 0.223241i | ||||
\(404\) | −3224.17 | −0.397051 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2532.10 | −0.309523 | ||||||||
\(407\) | 13773.2 | + | 3690.53i | 1.67743 | + | 0.449466i | ||||
\(408\) | 3038.34 | + | 1336.41i | 0.368678 | + | 0.162163i | ||||
\(409\) | −6326.24 | − | 3652.45i | −0.764822 | − | 0.441570i | 0.0662023 | − | 0.997806i | \(-0.478912\pi\) |
−0.831024 | + | 0.556236i | \(0.812245\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5324.52 | − | 4272.19i | −0.639024 | − | 0.512729i | ||||
\(412\) | 69.2596 | − | 258.480i | 0.00828198 | − | 0.0309088i | ||||
\(413\) | −4321.94 | − | 4321.94i | −0.514936 | − | 0.514936i | ||||
\(414\) | −7433.65 | − | 8108.01i | −0.882474 | − | 0.962529i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6207.82 | − | 3584.08i | 0.731642 | − | 0.422414i | ||||
\(417\) | −6692.50 | − | 9124.84i | −0.785931 | − | 1.07157i | ||||
\(418\) | −685.313 | − | 2557.62i | −0.0801908 | − | 0.299276i | ||||
\(419\) | 2581.15 | − | 4470.68i | 0.300948 | − | 0.521257i | −0.675403 | − | 0.737449i | \(-0.736030\pi\) |
0.976351 | + | 0.216192i | \(0.0693636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 946.112 | + | 1638.71i | 0.109527 | + | 0.189705i | 0.915579 | − | 0.402139i | \(-0.131733\pi\) |
−0.806052 | + | 0.591845i | \(0.798400\pi\) | |||||||
\(422\) | 2743.61 | − | 2743.61i | 0.316485 | − | 0.316485i | ||||
\(423\) | 3267.40 | + | 6272.49i | 0.375571 | + | 0.720990i | ||||
\(424\) | 1981.33i | 0.226938i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4749.63 | + | 5919.55i | −0.540188 | + | 0.673247i | ||||
\(427\) | −11066.8 | + | 2965.35i | −1.25424 | + | 0.336074i | ||||
\(428\) | −1752.30 | + | 469.527i | −0.197899 | + | 0.0530268i | ||||
\(429\) | 4248.40 | + | 10920.4i | 0.478123 | + | 1.22900i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12717.6i | − | 1.42132i | −0.703538 | − | 0.710658i | \(-0.748397\pi\) | ||
0.703538 | − | 0.710658i | \(-0.251603\pi\) | |||||||
\(432\) | −2819.89 | + | 3218.09i | −0.314055 | + | 0.358404i | ||||
\(433\) | 4103.64 | − | 4103.64i | 0.455447 | − | 0.455447i | −0.441711 | − | 0.897158i | \(-0.645628\pi\) |
0.897158 | + | 0.441711i | \(0.145628\pi\) | |||||||
\(434\) | 1996.42 | + | 3457.90i | 0.220810 | + | 0.382453i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2321.95 | + | 4021.73i | −0.255048 | + | 0.441757i | ||||
\(437\) | −1388.51 | − | 5181.98i | −0.151994 | − | 0.567249i | ||||
\(438\) | 1487.10 | − | 163.067i | 0.162229 | − | 0.0177892i | ||||
\(439\) | 7178.99 | − | 4144.79i | 0.780488 | − | 0.450615i | −0.0561151 | − | 0.998424i | \(-0.517871\pi\) |
0.836603 | + | 0.547809i | \(0.184538\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 810.811 | + | 3652.67i | 0.0875511 | + | 0.394414i | ||||
\(442\) | 2278.70 | + | 2278.70i | 0.245219 | + | 0.245219i | ||||
\(443\) | 1535.41 | − | 5730.24i | 0.164672 | − | 0.614565i | −0.833410 | − | 0.552656i | \(-0.813614\pi\) |
0.998082 | − | 0.0619089i | \(-0.0197188\pi\) | |||||||
\(444\) | 843.997 | − | 5488.47i | 0.0902125 | − | 0.586647i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10042.6 | − | 5798.10i | −1.06621 | − | 0.615578i | ||||
\(447\) | 1996.41 | − | 1464.25i | 0.211246 | − | 0.154936i | ||||
\(448\) | 7331.41 | + | 1964.45i | 0.773162 | + | 0.207168i | ||||
\(449\) | −3855.25 | −0.405213 | −0.202606 | − | 0.979260i | \(-0.564941\pi\) | ||||
−0.202606 | + | 0.979260i | \(0.564941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7266.00 | −0.758631 | ||||||||
\(452\) | −6198.73 | − | 1660.95i | −0.645053 | − | 0.172841i | ||||
\(453\) | 1131.95 | + | 10322.9i | 0.117403 | + | 1.07067i | ||||
\(454\) | 4505.98 | + | 2601.53i | 0.465807 | + | 0.268934i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3493.48 | + | 1359.08i | −0.358766 | + | 0.139572i | ||||
\(457\) | 463.264 | − | 1728.92i | 0.0474192 | − | 0.176971i | −0.938155 | − | 0.346216i | \(-0.887466\pi\) |
0.985574 | + | 0.169245i | \(0.0541330\pi\) | |||||||
\(458\) | 5203.01 | + | 5203.01i | 0.530831 | + | 0.530831i | ||||
\(459\) | 3269.60 | + | 1610.74i | 0.332488 | + | 0.163798i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10218.4 | + | 5899.62i | −1.03237 | + | 0.596036i | −0.917661 | − | 0.397363i | \(-0.869925\pi\) |
−0.114704 | + | 0.993400i | \(0.536592\pi\) | |||||||
\(462\) | −2699.52 | + | 6137.38i | −0.271847 | + | 0.618045i | ||||
\(463\) | 640.951 | + | 2392.06i | 0.0643359 | + | 0.240105i | 0.990604 | − | 0.136760i | \(-0.0436689\pi\) |
−0.926268 | + | 0.376865i | \(0.877002\pi\) | |||||||
\(464\) | 1212.09 | − | 2099.39i | 0.121271 | − | 0.210047i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2175.28 | − | 3767.69i | −0.216240 | − | 0.374539i | ||||
\(467\) | 11085.9 | − | 11085.9i | 1.09849 | − | 1.09849i | 0.103901 | − | 0.994588i | \(-0.466868\pi\) |
0.994588 | − | 0.103901i | \(-0.0331324\pi\) | |||||||
\(468\) | 4047.09 | − | 2108.17i | 0.399737 | − | 0.208227i | ||||
\(469\) | − | 8535.26i | − | 0.840344i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7460.99 | − | 1147.33i | −0.729903 | − | 0.112242i | ||||
\(472\) | 10153.2 | − | 2720.53i | 0.990120 | − | 0.265302i | ||||
\(473\) | 14629.3 | − | 3919.90i | 1.42210 | − | 0.381051i | ||||
\(474\) | 6995.47 | + | 1075.74i | 0.677875 | + | 0.104241i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1127.62i | − | 0.108581i | ||||||
\(477\) | −94.3142 | + | 2173.61i | −0.00905314 | + | 0.208644i | ||||
\(478\) | −6437.76 | + | 6437.76i | −0.616017 | + | 0.616017i | ||||
\(479\) | 4528.18 | + | 7843.03i | 0.431937 | + | 0.748136i | 0.997040 | − | 0.0768839i | \(-0.0244971\pi\) |
−0.565103 | + | 0.825020i | \(0.691164\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9799.23 | − | 16972.8i | 0.928912 | − | 1.60892i | ||||
\(482\) | −2731.41 | − | 10193.8i | −0.258117 | − | 0.963305i | ||||
\(483\) | −5469.49 | + | 12434.9i | −0.515259 | + | 1.17144i | ||||
\(484\) | −814.217 | + | 470.088i | −0.0764666 | + | 0.0441480i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5832.17 | + | 6100.60i | −0.544347 | + | 0.569401i | ||||
\(487\) | 2327.30 | + | 2327.30i | 0.216551 | + | 0.216551i | 0.807043 | − | 0.590492i | \(-0.201066\pi\) |
−0.590492 | + | 0.807043i | \(0.701066\pi\) | |||||||
\(488\) | 5099.65 | − | 19032.1i | 0.473053 | − | 1.76546i | ||||
\(489\) | −10876.9 | + | 4231.50i | −1.00587 | + | 0.391319i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2623.22 | − | 1514.51i | −0.241108 | − | 0.139204i | 0.374578 | − | 0.927195i | \(-0.377788\pi\) |
−0.615686 | + | 0.787992i | \(0.711121\pi\) | |||||||
\(492\) | 308.433 | + | 2812.77i | 0.0282626 | + | 0.257743i | ||||
\(493\) | −1994.64 | − | 534.463i | −0.182220 | − | 0.0488256i | ||||
\(494\) | −3639.34 | −0.331461 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3822.65 | −0.346052 | ||||||||
\(497\) | 9053.40 | + | 2425.85i | 0.817104 | + | 0.218942i | ||||
\(498\) | 1994.92 | − | 1463.15i | 0.179507 | − | 0.131657i | ||||
\(499\) | −171.019 | − | 98.7379i | −0.0153424 | − | 0.00885795i | 0.492309 | − | 0.870420i | \(-0.336153\pi\) |
−0.507652 | + | 0.861562i | \(0.669486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1528.21 | + | 9937.84i | −0.136278 | + | 0.886207i | ||||
\(502\) | 1980.88 | − | 7392.73i | 0.176117 | − | 0.657279i | ||||
\(503\) | −4650.74 | − | 4650.74i | −0.412259 | − | 0.412259i | 0.470266 | − | 0.882525i | \(-0.344158\pi\) |
−0.882525 | + | 0.470266i | \(0.844158\pi\) | |||||||
\(504\) | 9053.45 | + | 2851.85i | 0.800144 | + | 0.252047i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14291.3 | − | 8251.10i | 1.25559 | − | 0.724914i | ||||
\(507\) | 4661.50 | − | 511.154i | 0.408332 | − | 0.0447754i | ||||
\(508\) | −235.837 | − | 880.155i | −0.0205976 | − | 0.0768712i | ||||
\(509\) | −7091.29 | + | 12282.5i | −0.617517 | + | 1.06957i | 0.372420 | + | 0.928064i | \(0.378528\pi\) |
−0.989937 | + | 0.141506i | \(0.954805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −923.767 | − | 1600.01i | −0.0799708 | − | 0.138513i | ||||
\(512\) | −7018.72 | + | 7018.72i | −0.605833 | + | 0.605833i | ||||
\(513\) | −3897.22 | + | 1324.69i | −0.335413 | + | 0.114009i | ||||
\(514\) | − | 5293.18i | − | 0.454226i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2138.44 | − | 5496.80i | −0.182441 | − | 0.468959i | ||||
\(517\) | −10248.6 | + | 2746.12i | −0.871828 | + | 0.233606i | ||||
\(518\) | 10832.1 | − | 2902.45i | 0.918794 | − | 0.246190i | ||||
\(519\) | −1175.54 | + | 1465.09i | −0.0994226 | + | 0.123912i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5590.04i | 0.470065i | 0.971987 | + | 0.235033i | \(0.0755197\pi\) | ||||
−0.971987 | + | 0.235033i | \(0.924480\pi\) | |||||||
\(522\) | 2568.11 | − | 4033.52i | 0.215331 | − | 0.338204i | ||||
\(523\) | −7113.75 | + | 7113.75i | −0.594766 | + | 0.594766i | −0.938915 | − | 0.344149i | \(-0.888167\pi\) |
0.344149 | + | 0.938915i | \(0.388167\pi\) | |||||||
\(524\) | −499.673 | − | 865.459i | −0.0416571 | − | 0.0721522i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7461.77 | − | 12924.2i | 0.618534 | − | 1.07133i | ||||
\(527\) | 842.789 | + | 3145.33i | 0.0696631 | + | 0.259986i | ||||
\(528\) | −3796.34 | − | 5176.08i | −0.312906 | − | 0.426629i | ||||
\(529\) | 18418.6 | − | 10634.0i | 1.51382 | − | 0.874004i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11268.0 | − | 2501.25i | 0.920886 | − | 0.204416i | ||||
\(532\) | 900.468 | + | 900.468i | 0.0733839 | + | 0.0733839i | ||||
\(533\) | −2584.77 | + | 9646.49i | −0.210054 | + | 0.783932i | ||||
\(534\) | −4081.20 | − | 3274.60i | −0.330732 | − | 0.265367i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12711.9 | + | 7339.23i | 1.02439 | + | 0.591430i | ||||
\(537\) | −7243.86 | − | 3186.21i | −0.582115 | − | 0.256043i | ||||
\(538\) | 7238.77 | + | 1939.62i | 0.580084 | + | 0.155433i | ||||
\(539\) | −5613.13 | −0.448562 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1631.46 | −0.129652 | −0.0648261 | − | 0.997897i | \(-0.520649\pi\) | ||||
−0.0648261 | + | 0.997897i | \(0.520649\pi\) | |||||||
\(542\) | −14167.0 | − | 3796.04i | −1.12274 | − | 0.300837i | ||||
\(543\) | −9634.11 | − | 4237.56i | −0.761398 | − | 0.334901i | ||||
\(544\) | 2896.85 | + | 1672.50i | 0.228311 | + | 0.131816i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7187.79 | + | 5767.22i | 0.563387 | + | 0.452040i | ||||
\(547\) | 4021.44 | − | 15008.2i | 0.314341 | − | 1.17314i | −0.610260 | − | 0.792201i | \(-0.708935\pi\) |
0.924601 | − | 0.380936i | \(-0.124398\pi\) | |||||||
\(548\) | −2820.15 | − | 2820.15i | −0.219838 | − | 0.219838i | ||||
\(549\) | 6500.53 | − | 20636.5i | 0.505348 | − | 1.60427i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2019.63 | − | 1166.03i | 0.156151 | − | 0.0901538i | ||||
\(552\) | −13816.8 | − | 18838.4i | −1.06536 | − | 1.45256i | ||||
\(553\) | −2262.27 | − | 8442.92i | −0.173963 | − | 0.649239i | ||||
\(554\) | 1280.04 | − | 2217.10i | 0.0981658 | − | 0.170028i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3305.59 | − | 5725.45i | −0.252137 | − | 0.436714i | ||||
\(557\) | 1370.40 | − | 1370.40i | 0.104247 | − | 0.104247i | −0.653059 | − | 0.757307i | \(-0.726515\pi\) |
0.757307 | + | 0.653059i | \(0.226515\pi\) | |||||||
\(558\) | −7533.08 | − | 326.864i | −0.571507 | − | 0.0247979i | ||||
\(559\) | − | 20816.6i | − | 1.57504i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3421.97 | + | 4264.87i | −0.257533 | + | 0.320968i | ||||
\(562\) | 13861.4 | − | 3714.16i | 1.04041 | − | 0.278776i | ||||
\(563\) | −716.566 | + | 192.003i | −0.0536406 | + | 0.0143730i | −0.285540 | − | 0.958367i | \(-0.592173\pi\) |
0.231899 | + | 0.972740i | \(0.425506\pi\) | |||||||
\(564\) | 1498.10 | + | 3850.82i | 0.111847 | + | 0.287498i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 12684.9i | − | 0.942022i | ||||||
\(567\) | 9796.34 | + | 3559.59i | 0.725586 | + | 0.263648i | ||||
\(568\) | −11397.7 | + | 11397.7i | −0.841965 | + | 0.841965i | ||||
\(569\) | 1596.11 | + | 2764.54i | 0.117596 | + | 0.203683i | 0.918815 | − | 0.394689i | \(-0.129148\pi\) |
−0.801218 | + | 0.598372i | \(0.795814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5375.08 | − | 9309.91i | 0.393941 | − | 0.682325i | −0.599025 | − | 0.800730i | \(-0.704445\pi\) |
0.992965 | + | 0.118405i | \(0.0377783\pi\) | |||||||
\(572\) | 1771.83 | + | 6612.57i | 0.129517 | + | 0.483366i | ||||
\(573\) | 6479.65 | − | 710.522i | 0.472410 | − | 0.0518019i | ||||
\(574\) | −4948.84 | + | 2857.21i | −0.359861 | + | 0.207766i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10564.9 | + | 9686.21i | −0.764244 | + | 0.700680i | ||||
\(577\) | −6620.53 | − | 6620.53i | −0.477671 | − | 0.477671i | 0.426715 | − | 0.904386i | \(-0.359671\pi\) |
−0.904386 | + | 0.426715i | \(0.859671\pi\) | |||||||
\(578\) | 2443.94 | − | 9120.90i | 0.175873 | − | 0.656366i | ||||
\(579\) | −2291.90 | + | 14904.1i | −0.164504 | + | 1.06976i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2645.95 | − | 1527.64i | −0.188937 | − | 0.109083i | ||||
\(582\) | −11205.8 | + | 8218.74i | −0.798100 | + | 0.585357i | ||||
\(583\) | −3152.72 | − | 844.769i | −0.223966 | − | 0.0600116i | ||||
\(584\) | 3177.28 | 0.225132 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2279.09 | −0.160663 | ||||||||
\(587\) | 9951.28 | + | 2666.44i | 0.699716 | + | 0.187488i | 0.591103 | − | 0.806596i | \(-0.298693\pi\) |
0.108613 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(588\) | 238.270 | + | 2172.92i | 0.0167111 | + | 0.152398i | ||||
\(589\) | −3184.73 | − | 1838.71i | −0.222792 | − | 0.128629i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10798.5 | + | 4200.97i | −0.751590 | + | 0.292394i | ||||
\(592\) | −2778.73 | + | 10370.4i | −0.192914 | + | 0.719966i | ||||
\(593\) | 670.349 | + | 670.349i | 0.0464215 | + | 0.0464215i | 0.729936 | − | 0.683515i | \(-0.239550\pi\) |
−0.683515 | + | 0.729936i | \(0.739550\pi\) | |||||||
\(594\) | −7038.64 | − | 10524.8i | −0.486194 | − | 0.727003i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1252.66 | − | 723.226i | 0.0860925 | − | 0.0497055i | ||||
\(597\) | −7604.89 | + | 17289.7i | −0.521352 | + | 1.18530i | ||||
\(598\) | −5870.41 | − | 21908.7i | −0.401436 | − | 1.49818i | ||||
\(599\) | 273.430 | − | 473.594i | 0.0186511 | − | 0.0323047i | −0.856549 | − | 0.516065i | \(-0.827396\pi\) |
0.875200 | + | 0.483761i | \(0.160729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −536.667 | − | 929.535i | −0.0364245 | − | 0.0630890i | 0.847238 | − | 0.531213i | \(-0.178264\pi\) |
−0.883663 | + | 0.468124i | \(0.844930\pi\) | |||||||
\(602\) | 8422.50 | − | 8422.50i | 0.570225 | − | 0.570225i | ||||
\(603\) | 13596.3 | + | 8656.61i | 0.918213 | + | 0.584617i | ||||
\(604\) | 6067.11i | 0.408721i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12153.0 | + | 1868.85i | 0.814658 | + | 0.125275i | ||||
\(607\) | −9826.68 | + | 2633.05i | −0.657089 | + | 0.176066i | −0.571932 | − | 0.820301i | \(-0.693806\pi\) |
−0.0851568 | + | 0.996368i | \(0.527139\pi\) | |||||||
\(608\) | −3648.87 | + | 977.713i | −0.243390 | + | 0.0652163i | ||||
\(609\) | −5836.63 | − | 897.536i | −0.388361 | − | 0.0597209i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14583.2i | 0.965586i | ||||||||
\(612\) | 1796.25 | + | 1143.65i | 0.118642 | + | 0.0755384i | ||||
\(613\) | 10740.6 | − | 10740.6i | 0.707681 | − | 0.707681i | −0.258366 | − | 0.966047i | \(-0.583184\pi\) |
0.966047 | + | 0.258366i | \(0.0831840\pi\) | |||||||
\(614\) | 531.028 | + | 919.767i | 0.0349031 | + | 0.0604540i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7119.97 | + | 12332.2i | −0.465701 | + | 0.806618i | ||||
\(617\) | 5191.49 | + | 19374.9i | 0.338738 | + | 1.26419i | 0.899759 | + | 0.436387i | \(0.143742\pi\) |
−0.561021 | + | 0.827802i | \(0.689591\pi\) | |||||||
\(618\) | −410.888 | + | 934.157i | −0.0267449 | + | 0.0608047i | ||||
\(619\) | −21899.4 | + | 12643.6i | −1.42199 | + | 0.820987i | −0.996469 | − | 0.0839615i | \(-0.973243\pi\) |
−0.425522 | + | 0.904948i | \(0.639909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14261.0 | − | 21324.3i | −0.921533 | − | 1.37796i | ||||
\(622\) | 7936.44 | + | 7936.44i | 0.511611 | + | 0.511611i | ||||
\(623\) | −1672.49 | + | 6241.82i | −0.107555 | + | 0.401401i | ||||
\(624\) | −8222.36 | + | 3198.78i | −0.527497 | + | 0.205214i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9113.26 | + | 5261.54i | 0.581852 | + | 0.335932i | ||||
\(627\) | −673.099 | − | 6138.36i | −0.0428724 | − | 0.390977i | ||||
\(628\) | −4259.91 | − | 1141.44i | −0.270683 | − | 0.0725293i | ||||
\(629\) | 9145.54 | 0.579740 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12431.8 | −0.784313 | −0.392156 | − | 0.919899i | \(-0.628271\pi\) | ||||
−0.392156 | + | 0.919899i | \(0.628271\pi\) | |||||||
\(632\) | 14519.7 | + | 3890.53i | 0.913862 | + | 0.244869i | ||||
\(633\) | 7296.65 | − | 5351.64i | 0.458161 | − | 0.336033i | ||||
\(634\) | 19115.2 | + | 11036.1i | 1.19741 | + | 0.691327i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −193.193 | + | 1256.32i | −0.0120450 | + | 0.0783277i | ||||
\(637\) | −1996.79 | + | 7452.11i | −0.124200 | + | 0.463521i | ||||
\(638\) | 5072.43 | + | 5072.43i | 0.314764 | + | 0.314764i | ||||
\(639\) | −13046.4 | + | 11961.3i | −0.807679 | + | 0.740503i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19099.7 | − | 11027.2i | 1.17690 | − | 0.679484i | 0.221605 | − | 0.975136i | \(-0.428870\pi\) |
0.955296 | + | 0.295652i | \(0.0955370\pi\) | |||||||
\(642\) | 6877.18 | − | 754.113i | 0.422774 | − | 0.0463590i | ||||
\(643\) | −1494.46 | − | 5577.39i | −0.0916572 | − | 0.342069i | 0.904834 | − | 0.425764i | \(-0.139995\pi\) |
−0.996491 | + | 0.0836947i | \(0.973328\pi\) | |||||||
\(644\) | −3968.28 | + | 6873.27i | −0.242814 | + | 0.420566i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −849.141 | − | 1470.76i | −0.0517167 | − | 0.0895760i | ||||
\(647\) | −19898.4 | + | 19898.4i | −1.20910 | + | 1.20910i | −0.237779 | + | 0.971319i | \(0.576419\pi\) |
−0.971319 | + | 0.237779i | \(0.923581\pi\) | |||||||
\(648\) | −13725.0 | + | 11529.3i | −0.832053 | + | 0.698941i | ||||
\(649\) | 17315.8i | 1.04731i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3376.15 | + | 8678.30i | 0.203259 | + | 0.522472i | ||||
\(652\) | −6586.25 | + | 1764.78i | −0.395610 | + | 0.106003i | ||||
\(653\) | −5622.98 | + | 1506.67i | −0.336974 | + | 0.0902920i | −0.423338 | − | 0.905972i | \(-0.639142\pi\) |
0.0863641 | + | 0.996264i | \(0.472475\pi\) | |||||||
\(654\) | 11083.4 | − | 13813.4i | 0.662682 | − | 0.825914i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 5470.84i | − | 0.325610i | ||||||
\(657\) | 3485.64 | + | 151.244i | 0.206983 | + | 0.00898109i | ||||
\(658\) | −5900.45 | + | 5900.45i | −0.349579 | + | 0.349579i | ||||
\(659\) | 10262.3 | + | 17774.8i | 0.606618 | + | 1.05069i | 0.991794 | + | 0.127849i | \(0.0408074\pi\) |
−0.385176 | + | 0.922843i | \(0.625859\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13997.3 | + | 24244.1i | −0.823652 | + | 1.42661i | 0.0792938 | + | 0.996851i | \(0.474733\pi\) |
−0.902945 | + | 0.429755i | \(0.858600\pi\) | |||||||
\(662\) | 2669.18 | + | 9961.53i | 0.156708 | + | 0.584843i | ||||
\(663\) | 4444.81 | + | 6060.24i | 0.260365 | + | 0.354993i | ||||
\(664\) | 4550.35 | − | 2627.15i | 0.265946 | − | 0.153544i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6362.64 | + | 20198.7i | −0.370191 | + | 1.17520i | ||||
\(667\) | 10277.2 | + | 10277.2i | 0.596605 | + | 0.596605i | ||||
\(668\) | −1520.37 | + | 5674.08i | −0.0880610 | + | 0.328648i | ||||
\(669\) | −21093.5 | − | 16924.6i | −1.21902 | − | 0.978093i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28110.0 | + | 16229.3i | 1.61725 | + | 0.933719i | ||||
\(672\) | 8755.99 | + | 3851.32i | 0.502633 | + | 0.221083i | ||||
\(673\) | −20519.6 | − | 5498.22i | −1.17530 | − | 0.314919i | −0.382236 | − | 0.924065i | \(-0.624846\pi\) |
−0.793059 | + | 0.609145i | \(0.791513\pi\) | |||||||
\(674\) | 2096.45 | 0.119810 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2739.72 | 0.155878 | ||||||||
\(677\) | −4854.11 | − | 1300.65i | −0.275567 | − | 0.0738379i | 0.118389 | − | 0.992967i | \(-0.462227\pi\) |
−0.393956 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(678\) | 22402.4 | + | 9853.70i | 1.26897 | + | 0.558155i | ||||
\(679\) | 14862.7 | + | 8580.98i | 0.840027 | + | 0.484990i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9464.37 | + | 7593.86i | 0.532563 | + | 0.427309i | ||||
\(682\) | 2927.71 | − | 10926.4i | 0.164381 | − | 0.613478i | ||||
\(683\) | −1391.88 | − | 1391.88i | −0.0779778 | − | 0.0779778i | 0.667042 | − | 0.745020i | \(-0.267560\pi\) |
−0.745020 | + | 0.667042i | \(0.767560\pi\) | |||||||
\(684\) | −2347.67 | + | 521.132i | −0.131236 | + | 0.0291315i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13285.8 | + | 7670.56i | −0.739438 | + | 0.426915i | ||||
\(687\) | 10148.9 | + | 13837.5i | 0.563617 | + | 0.768460i | ||||
\(688\) | 2951.44 | + | 11014.9i | 0.163550 | + | 0.610378i | ||||
\(689\) | −2243.06 | + | 3885.10i | −0.124026 | + | 0.214819i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1846.79 | + | 3198.73i | 0.101672 | + | 0.176100i | 0.912373 | − | 0.409359i | \(-0.134248\pi\) |
−0.810702 | + | 0.585459i | \(0.800914\pi\) | |||||||
\(692\) | −775.993 | + | 775.993i | −0.0426284 | + | 0.0426284i | ||||
\(693\) | −8398.00 | + | 13190.1i | −0.460337 | + | 0.723015i | ||||
\(694\) | 1338.22i | 0.0731961i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6355.49 | − | 7920.96i | 0.346127 | − | 0.431384i | ||||
\(697\) | −4501.49 | + | 1206.17i | −0.244629 | + | 0.0655480i | ||||
\(698\) | −22325.0 | + | 5981.98i | −1.21062 | + | 0.324386i | ||||
\(699\) | −3678.62 | − | 9455.78i | −0.199053 | − | 0.511660i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25198.2i | 1.35766i | 0.734294 | + | 0.678831i | \(0.237513\pi\) | ||||
−0.734294 | + | 0.678831i | \(0.762487\pi\) | |||||||
\(702\) | −16476.9 | + | 5600.59i | −0.885869 | + | 0.301112i | ||||
\(703\) | −7303.21 | + | 7303.21i | −0.391815 | + | 0.391815i | ||||
\(704\) | −10751.4 | − | 18621.9i | −0.575578 | − | 0.996931i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10547.1 | − | 18268.0i | 0.562243 | − | 0.973834i | ||||
\(707\) | −3930.18 | − | 14667.6i | −0.209066 | − | 0.780244i | ||||
\(708\) | 6703.20 | − | 735.035i | 0.355821 | − | 0.0390174i | ||||
\(709\) | −215.222 | + | 124.258i | −0.0114003 | + | 0.00658198i | −0.505689 | − | 0.862716i | \(-0.668762\pi\) |
0.494289 | + | 0.869298i | \(0.335428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15743.6 | + | 4959.26i | 0.830423 | + | 0.261585i | ||||
\(712\) | −7858.07 | − | 7858.07i | −0.413615 | − | 0.413615i | ||||
\(713\) | 5931.82 | − | 22137.8i | 0.311568 | − | 1.16279i | ||||
\(714\) | −653.612 | + | 4250.40i | −0.0342589 | + | 0.222783i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4003.97 | − | 2311.70i | −0.208988 | − | 0.120659i | ||||
\(717\) | −17121.3 | + | 12557.4i | −0.891780 | + | 0.654066i | ||||
\(718\) | −14445.3 | − | 3870.60i | −0.750825 | − | 0.201183i | ||||
\(719\) | −5173.80 | −0.268359 | −0.134180 | − | 0.990957i | \(-0.542840\pi\) | ||||
−0.134180 | + | 0.990957i | \(0.542840\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1260.32 | 0.0650997 | ||||||||
\(722\) | −12909.0 | − | 3458.94i | −0.665404 | − | 0.178294i | ||||
\(723\) | −2682.73 | − | 24465.3i | −0.137997 | − | 1.25847i | ||||
\(724\) | −5325.16 | − | 3074.48i | −0.273354 | − | 0.157821i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3341.55 | − | 1299.98i | 0.170822 | − | 0.0664554i | ||||
\(727\) | 5344.55 | − | 19946.1i | 0.272653 | − | 1.01755i | −0.684745 | − | 0.728782i | \(-0.740087\pi\) |
0.957398 | − | 0.288771i | \(-0.0932468\pi\) | |||||||
\(728\) | 13839.6 | + | 13839.6i | 0.704573 | + | 0.704573i | ||||
\(729\) | −15605.9 | + | 11994.9i | −0.792860 | + | 0.609404i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8412.53 | − | 4856.98i | 0.425648 | − | 0.245748i | ||||
\(732\) | 5089.35 | − | 11570.7i | 0.256978 | − | 0.584241i | ||||
\(733\) | 5458.69 | + | 20372.1i | 0.275063 | + | 1.02655i | 0.955799 | + | 0.294021i | \(0.0949934\pi\) |
−0.680736 | + | 0.732529i | \(0.738340\pi\) | |||||||
\(734\) | −3572.53 | + | 6187.80i | −0.179652 | + | 0.311166i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11771.6 | − | 20389.0i | −0.589546 | − | 1.02112i | ||||
\(737\) | −17098.2 | + | 17098.2i | −0.854575 | + | 0.854575i | ||||
\(738\) | 467.797 | − | 10781.1i | 0.0233331 | − | 0.537747i | ||||
\(739\) | − | 3372.43i | − | 0.167871i | −0.996471 | − | 0.0839356i | \(-0.973251\pi\) | ||
0.996471 | − | 0.0839356i | \(-0.0267490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8388.86 | − | 1290.01i | −0.415887 | − | 0.0639537i | ||||
\(742\) | −2479.49 | + | 664.378i | −0.122675 | + | 0.0328707i | ||||
\(743\) | 19508.9 | − | 5227.39i | 0.963273 | − | 0.258108i | 0.257288 | − | 0.966335i | \(-0.417171\pi\) |
0.705985 | + | 0.708227i | \(0.250504\pi\) | |||||||
\(744\) | −15828.0 | − | 2433.98i | −0.779950 | − | 0.119938i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6829.76i | 0.335195i | ||||||||
\(747\) | 5117.02 | − | 2665.51i | 0.250632 | − | 0.130557i | ||||
\(748\) | −2258.91 | + | 2258.91i | −0.110420 | + | 0.110420i | ||||
\(749\) | −4272.01 | − | 7399.34i | −0.208406 | − | 0.360970i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3536.97 | + | 6126.21i | −0.171859 | + | 0.297668i | −0.939070 | − | 0.343727i | \(-0.888311\pi\) |
0.767211 | + | 0.641395i | \(0.221644\pi\) | |||||||
\(752\) | −2067.65 | − | 7716.59i | −0.100265 | − | 0.374195i | ||||
\(753\) | 7186.47 | − | 16338.5i | 0.347795 | − | 0.790713i | ||||
\(754\) | 8538.70 | − | 4929.82i | 0.412415 | − | 0.238108i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5462.55 | + | 2691.08i | 0.262792 | + | 0.129462i | ||||
\(757\) | −6425.25 | − | 6425.25i | −0.308494 | − | 0.308494i | 0.535831 | − | 0.844325i | \(-0.319998\pi\) |
−0.844325 | + | 0.535831i | \(0.819998\pi\) | |||||||
\(758\) | 4888.87 | − | 18245.5i | 0.234263 | − | 0.874283i | ||||
\(759\) | 35866.9 | − | 13953.5i | 1.71527 | − | 0.667297i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11481.3 | − | 6628.75i | −0.546909 | − | 0.315758i | 0.200965 | − | 0.979598i | \(-0.435592\pi\) |
−0.747875 | + | 0.663840i | \(0.768926\pi\) | |||||||
\(762\) | 378.781 | + | 3454.31i | 0.0180076 | + | 0.164221i | ||||
\(763\) | −21126.3 | − | 5660.79i | −1.00239 | − | 0.268590i | ||||
\(764\) | 3808.30 | 0.180340 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14987.5 | 0.706947 | ||||||||
\(767\) | 22988.8 | + | 6159.84i | 1.08224 | + | 0.289986i | ||||
\(768\) | −16368.4 | + | 12005.2i | −0.769067 | + | 0.564063i | ||||
\(769\) | −19228.5 | − | 11101.6i | −0.901686 | − | 0.520589i | −0.0239392 | − | 0.999713i | \(-0.507621\pi\) |
−0.877747 | + | 0.479125i | \(0.840954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1876.23 | − | 12201.0i | 0.0876406 | − | 0.569922i | ||||
\(772\) | −2280.14 | + | 8509.60i | −0.106301 | + | 0.396719i | ||||
\(773\) | 13738.9 | + | 13738.9i | 0.639265 | + | 0.639265i | 0.950374 | − | 0.311109i | \(-0.100700\pi\) |
−0.311109 | + | 0.950374i | \(0.600700\pi\) | |||||||
\(774\) | 4874.38 | + | 21958.9i | 0.226364 | + | 1.01976i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25560.0 | + | 14757.1i | −1.18241 | + | 0.682666i | ||||
\(777\) | 25997.3 | − | 2850.72i | 1.20032 | − | 0.131620i | ||||
\(778\) | 2397.34 | + | 8947.01i | 0.110474 | + | 0.412296i | ||||
\(779\) | 2631.49 | − | 4557.88i | 0.121031 | − | 0.209632i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13276.6 | − | 22995.8i | −0.608290 | − | 1.05359i | ||||
\(782\) | 7484.18 | − | 7484.18i | 0.342243 | − | 0.342243i | ||||
\(783\) | 7349.34 | − | 8387.16i | 0.335433 | − | 0.382801i | ||||
\(784\) | − | 4226.33i | − | 0.192526i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1381.79 | + | 3551.85i | 0.0627059 | + | 0.161183i | ||||
\(787\) | 35866.4 | − | 9610.38i | 1.62452 | − | 0.435290i | 0.672197 | − | 0.740372i | \(-0.265351\pi\) |
0.952326 | + | 0.305082i | \(0.0986839\pi\) | |||||||
\(788\) | −6538.74 | + | 1752.05i | −0.295600 | + | 0.0792059i | ||||
\(789\) | 21780.9 | − | 27145.9i | 0.982788 | − | 1.22487i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 30224.4i | − | 1.35860i | ||||||
\(792\) | −12423.3 | − | 23849.3i | −0.557378 | − | 1.07001i | ||||
\(793\) | 31546.0 | − | 31546.0i | 1.41265 | − | 1.41265i | ||||
\(794\) | 4076.25 | + | 7060.27i | 0.182192 | + | 0.315566i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5517.58 | + | 9556.74i | −0.245685 | + | 0.425540i | ||||
\(797\) | −4570.50 | − | 17057.3i | −0.203131 | − | 0.758096i | −0.990011 | − | 0.140990i | \(-0.954972\pi\) |
0.786880 | − | 0.617106i | \(-0.211695\pi\) | |||||||
\(798\) | −2872.23 | − | 3916.13i | −0.127414 | − | 0.173721i | ||||
\(799\) | −5893.46 | + | 3402.59i | −0.260946 | + | 0.150657i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8246.64 | − | 8994.75i | −0.363771 | − | 0.396772i | ||||
\(802\) | −14577.2 | − | 14577.2i | −0.641820 | − | 0.641820i | ||||
\(803\) | −1354.69 | + | 5055.75i | −0.0595340 | + | 0.222184i | ||||
\(804\) | 7344.76 | + | 5893.16i | 0.322176 | + | 0.258502i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13464.6 | − | 7773.77i | −0.588423 | − | 0.339726i | ||||
\(807\) | 15998.2 | + | 7036.80i | 0.697848 | + | 0.306948i | ||||
\(808\) | 25224.5 | + | 6758.90i | 1.09826 | + | 0.294279i | ||||
\(809\) | 32490.3 | 1.41199 | 0.705993 | − | 0.708219i | \(-0.250501\pi\) | ||||
0.705993 | + | 0.708219i | \(0.250501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13686.9 | 0.592616 | 0.296308 | − | 0.955092i | \(-0.404244\pi\) | ||||
0.296308 | + | 0.955092i | \(0.404244\pi\) | |||||||
\(812\) | −3332.47 | − | 892.932i | −0.144023 | − | 0.0385908i | ||||
\(813\) | −31310.1 | − | 13771.7i | −1.35067 | − | 0.594090i | ||||
\(814\) | −27513.7 | − | 15885.1i | −1.18471 | − | 0.683994i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3211.18 | − | 2576.53i | −0.137762 | − | 0.110535i | ||||
\(817\) | −2839.30 | + | 10596.4i | −0.121585 | + | 0.453760i | ||||
\(818\) | 11508.7 | + | 11508.7i | 0.491922 | + | 0.491922i | ||||
\(819\) | 14523.9 | + | 15841.5i | 0.619668 | + | 0.675882i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28854.2 | − | 16659.0i | 1.22658 | − | 0.708164i | 0.260264 | − | 0.965537i | \(-0.416190\pi\) |
0.966312 | + | 0.257373i | \(0.0828570\pi\) | |||||||
\(822\) | 8995.48 | + | 12264.8i | 0.381695 | + | 0.520419i | ||||
\(823\) | 2308.70 | + | 8616.20i | 0.0977842 | + | 0.364936i | 0.997427 | − | 0.0716914i | \(-0.0228397\pi\) |
−0.899643 | + | 0.436627i | \(0.856173\pi\) | |||||||
\(824\) | −1083.72 | + | 1877.05i | −0.0458168 | + | 0.0793570i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6809.11 | + | 11793.7i | 0.286827 | + | 0.496799i | ||||
\(827\) | −1754.96 | + | 1754.96i | −0.0737919 | + | 0.0737919i | −0.743039 | − | 0.669248i | \(-0.766617\pi\) |
0.669248 | + | 0.743039i | \(0.266617\pi\) | |||||||
\(828\) | −6924.08 | − | 13292.3i | −0.290614 | − | 0.557897i | ||||
\(829\) | 5248.56i | 0.219891i | 0.993938 | + | 0.109946i | \(0.0350677\pi\) | ||||
−0.993938 | + | 0.109946i | \(0.964932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3736.44 | − | 4656.80i | 0.155976 | − | 0.194395i | ||||
\(832\) | −28547.4 | + | 7649.26i | −1.18955 | + | 0.318738i | ||||
\(833\) | −3477.49 | + | 931.791i | −0.144643 | + | 0.0387571i | ||||
\(834\) | 9141.23 | + | 23497.3i | 0.379538 | + | 0.975592i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 3607.72i | − | 0.149253i | ||||||
\(837\) | −17248.3 | − | 3423.63i | −0.712290 | − | 0.141384i | ||||
\(838\) | −8133.06 | + | 8133.06i | −0.335265 | + | 0.335265i | ||||
\(839\) | −23083.9 | − | 39982.5i | −0.949876 | − | 1.64523i | −0.745682 | − | 0.666302i | \(-0.767876\pi\) |
−0.204194 | − | 0.978930i | \(-0.565457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9035.50 | − | 15649.9i | 0.370474 | − | 0.641680i | ||||
\(842\) | −1091.18 | − | 4072.33i | −0.0446609 | − | 0.166677i | ||||
\(843\) | 33267.8 | − | 3647.96i | 1.35920 | − | 0.149042i | ||||
\(844\) | 4578.34 | − | 2643.30i | 0.186721 | − | 0.107804i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3414.79 | − | 15383.5i | −0.138774 | − | 0.625170i | ||||
\(847\) | −3131.07 | − | 3131.07i | −0.127019 | − | 0.127019i | ||||
\(848\) | 636.058 | − | 2373.80i | 0.0257575 | − | 0.0961281i | ||||
\(849\) | 4496.31 | − | 29239.2i | 0.181758 | − | 1.18196i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55745.4 | − | 32184.6i | −2.24551 | − | 1.29644i | ||||
\(852\) | −8338.41 | + | 6115.71i | −0.335292 | + | 0.245916i | ||||
\(853\) | 8397.50 | + | 2250.10i | 0.337075 | + | 0.0903189i | 0.423386 | − | 0.905949i | \(-0.360841\pi\) |
−0.0863114 | + | 0.996268i | \(0.527508\pi\) | |||||||
\(854\) | 25527.4 | 1.02287 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14693.5 | 0.586699 | ||||||||
\(857\) | −9796.17 | − | 2624.87i | −0.390467 | − | 0.104625i | 0.0582434 | − | 0.998302i | \(-0.481450\pi\) |
−0.448711 | + | 0.893677i | \(0.648117\pi\) | |||||||
\(858\) | −2845.76 | − | 25952.1i | −0.113232 | − | 1.03262i | ||||
\(859\) | −9807.59 | − | 5662.41i | −0.389558 | − | 0.224912i | 0.292410 | − | 0.956293i | \(-0.405543\pi\) |
−0.681969 | + | 0.731381i | \(0.738876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12420.1 | + | 4831.84i | −0.491609 | + | 0.191253i | ||||
\(862\) | −7333.80 | + | 27370.1i | −0.289780 | + | 1.08147i | ||||
\(863\) | 9646.02 | + | 9646.02i | 0.380480 | + | 0.380480i | 0.871275 | − | 0.490795i | \(-0.163294\pi\) |
−0.490795 | + | 0.871275i | \(0.663294\pi\) | |||||||
\(864\) | −15015.4 | + | 10041.8i | −0.591245 | + | 0.395404i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11198.0 | + | 6465.19i | −0.439405 | + | 0.253691i | ||||
\(867\) | 8866.41 | − | 20157.8i | 0.347312 | − | 0.789615i | ||||
\(868\) | 1408.05 | + | 5254.92i | 0.0550604 | + | 0.205488i | ||||
\(869\) | −12381.4 | + | 21445.2i | −0.483324 | + | 0.837143i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16617.5 | + | 28782.4i | 0.646456 | + | 1.11969i | ||||
\(872\) | 26596.8 | − | 26596.8i | 1.03289 | − | 1.03289i | ||||
\(873\) | −28743.1 | + | 14972.6i | −1.11433 | + | 0.580464i | ||||
\(874\) | 11953.1i | 0.462606i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2014.66 | + | 309.807i | 0.0777043 | + | 0.0119491i | ||||
\(877\) | 46975.5 | − | 12587.0i | 1.80872 | − | 0.484646i | 0.813439 | − | 0.581651i | \(-0.197593\pi\) |
0.995284 | + | 0.0970048i | \(0.0309262\pi\) | |||||||
\(878\) | −17840.3 | + | 4780.30i | −0.685742 | + | 0.183744i | ||||
\(879\) | −5253.42 | − | 807.853i | −0.201585 | − | 0.0309991i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26406.8i | 1.00984i | 0.863166 | + | 0.504920i | \(0.168478\pi\) | ||||
−0.863166 | + | 0.504920i | \(0.831522\pi\) | |||||||
\(882\) | 361.382 | − | 8328.61i | 0.0137963 | − | 0.317958i | ||||
\(883\) | −1035.61 | + | 1035.61i | −0.0394689 | + | 0.0394689i | −0.726566 | − | 0.687097i | \(-0.758885\pi\) |
0.687097 | + | 0.726566i | \(0.258885\pi\) | |||||||
\(884\) | 2195.40 | + | 3802.54i | 0.0835285 | + | 0.144676i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6608.85 | + | 11446.9i | −0.250597 | + | 0.434046i | ||||
\(887\) | −6392.19 | − | 23856.0i | −0.241972 | − | 0.903050i | −0.974881 | − | 0.222724i | \(-0.928505\pi\) |
0.732910 | − | 0.680326i | \(-0.238162\pi\) | |||||||
\(888\) | −18108.7 | + | 41170.2i | −0.684333 | + | 1.55583i | ||||
\(889\) | 3716.59 | − | 2145.77i | 0.140214 | − | 0.0809526i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12493.8 | − | 26755.2i | −0.469760 | − | 1.00599i | ||||
\(892\) | −11172.3 | − | 11172.3i | −0.419367 | − | 0.419367i | ||||
\(893\) | 1989.10 | − | 7423.41i | 0.0745382 | − | 0.278180i | ||||
\(894\) | −5140.94 | + | 2000.00i | −0.192325 | + | 0.0748211i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1891.30 | − | 1091.95i | −0.0705179 | − | 0.0407135i | ||||
\(897\) | −5765.78 | − | 52581.4i | −0.214620 | − | 1.95724i | ||||
\(898\) | 8297.03 | + | 2223.18i | 0.308325 | + | 0.0826154i | ||||
\(899\) | 9962.79 | 0.369608 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2093.43 | −0.0774055 | ||||||||
\(902\) | 15637.4 | + | 4190.04i | 0.577239 | + | 0.154671i | ||||
\(903\) | 22399.7 | − | 16428.8i | 0.825489 | − | 0.605445i | ||||
\(904\) | 45014.4 | + | 25989.1i | 1.65615 | + | 0.956177i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3516.73 | − | 22869.1i | 0.128957 | − | 0.838603i | ||||
\(907\) | −6722.31 | + | 25088.0i | −0.246098 | + | 0.918450i | 0.726731 | + | 0.686923i | \(0.241039\pi\) |
−0.972828 | + | 0.231527i | \(0.925628\pi\) | |||||||
\(908\) | 5012.84 | + | 5012.84i | 0.183213 | + | 0.183213i | ||||
\(909\) | 27350.9 | + | 8615.58i | 0.997988 | + | 0.314368i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3490.35 | + | 2015.15i | −0.126938 | + | 0.0732877i | −0.562124 | − | 0.827053i | \(-0.690016\pi\) |
0.435186 | + | 0.900340i | \(0.356682\pi\) | |||||||
\(912\) | 4621.80 | − | 506.801i | 0.167810 | − | 0.0184012i | ||||
\(913\) | 2240.25 | + | 8360.73i | 0.0812065 | + | 0.303067i | ||||
\(914\) | −1994.02 | + | 3453.74i | −0.0721622 | + | 0.124989i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5012.79 | + | 8682.41i | 0.180816 | + | 0.313182i | ||||
\(917\) | 3328.12 | − | 3328.12i | 0.119852 | − | 0.119852i | ||||
\(918\) | −6107.78 | − | 5352.01i | −0.219593 | − | 0.192421i | ||||
\(919\) | − | 33304.4i | − | 1.19544i | −0.801704 | − | 0.597722i | \(-0.796073\pi\) | ||
0.801704 | − | 0.597722i | \(-0.203927\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 898.022 | + | 2308.34i | 0.0321290 | + | 0.0825866i | ||||
\(922\) | 25393.6 | − | 6804.20i | 0.907044 | − | 0.243042i | ||||
\(923\) | −35252.6 | + | 9445.91i | −1.25715 | + | 0.336854i | ||||
\(924\) | −5717.11 | + | 7125.34i | −0.203549 | + | 0.253687i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 5517.66i | − | 0.195812i | ||||||
\(927\) | −1278.24 | + | 2007.63i | −0.0452891 | + | 0.0711320i | ||||
\(928\) | 7236.67 | − | 7236.67i | 0.255986 | − | 0.255986i | ||||
\(929\) | −6.85930 | − | 11.8807i | −0.000242246 | − | 0.000419582i | 0.865904 | − | 0.500210i | \(-0.166744\pi\) |
−0.866147 | + | 0.499790i | \(0.833410\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2032.88 | − | 3521.05i | 0.0715628 | − | 0.123950i | ||||
\(932\) | −1534.20 | − | 5725.71i | −0.0539210 | − | 0.201236i | ||||
\(933\) | 15480.7 | + | 21107.1i | 0.543211 | + | 0.740637i | ||||
\(934\) | −30251.2 | + | 17465.6i | −1.05980 | + | 0.611874i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −36082.2 | + | 8009.44i | −1.26002 | + | 0.279697i | ||||
\(937\) | −5283.80 | − | 5283.80i | −0.184220 | − | 0.184220i | 0.608972 | − | 0.793192i | \(-0.291582\pi\) |
−0.793192 | + | 0.608972i | \(0.791582\pi\) | |||||||
\(938\) | −4921.97 | + | 18369.1i | −0.171331 | + | 0.639415i | ||||
\(939\) | 19141.5 | + | 15358.4i | 0.665239 | + | 0.533763i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23901.0 | + | 13799.2i | 0.828002 | + | 0.478047i | 0.853168 | − | 0.521636i | \(-0.174678\pi\) |
−0.0251660 | + | 0.999683i | \(0.508011\pi\) | |||||||
\(942\) | 15395.5 | + | 6771.69i | 0.532496 | + | 0.234218i | ||||
\(943\) | 31682.9 | + | 8489.42i | 1.09410 | + | 0.293164i | ||||
\(944\) | −13037.7 | −0.449515 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33744.7 | −1.15976 | ||||||||
\(947\) | −8508.47 | − | 2279.84i | −0.291962 | − | 0.0782310i | 0.109865 | − | 0.993946i | \(-0.464958\pi\) |
−0.401827 | + | 0.915716i | \(0.631625\pi\) | |||||||
\(948\) | 8827.29 | + | 3882.68i | 0.302423 | + | 0.133021i | ||||
\(949\) | 6230.21 | + | 3597.01i | 0.213110 | + | 0.123039i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40149.5 | + | 32214.5i | 1.36902 | + | 1.09845i | ||||
\(952\) | −2363.86 | + | 8822.04i | −0.0804760 | + | 0.300340i | ||||
\(953\) | −28229.0 | − | 28229.0i | −0.959524 | − | 0.959524i | 0.0396877 | − | 0.999212i | \(-0.487364\pi\) |
−0.999212 | + | 0.0396877i | \(0.987364\pi\) | |||||||
\(954\) | 1456.42 | − | 4623.53i | 0.0494271 | − | 0.156910i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10742.9 | + | 6202.41i | −0.363441 | + | 0.209833i | ||||
\(957\) | 9894.22 | + | 13490.2i | 0.334206 | + | 0.455670i | ||||
\(958\) | −5222.47 | − | 19490.5i | −0.176128 | − | 0.657318i | ||||
\(959\) | 9391.95 | − | 16267.3i | 0.316248 | − | 0.547758i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7040.40 | + | 12194.3i | 0.236327 | + | 0.409330i | ||||
\(962\) | −30876.9 | + | 30876.9i | −1.03483 | + | 1.03483i | ||||
\(963\) | 16119.5 | + | 699.435i | 0.539403 | + | 0.0234050i | ||||
\(964\) | − | 14379.1i | − | 0.480414i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 18941.9 | − | 23607.6i | 0.630895 | − | 0.786296i | ||||
\(967\) | −45973.1 | + | 12318.4i | −1.52885 | + | 0.409653i | −0.922642 | − | 0.385657i | \(-0.873975\pi\) |
−0.606203 | + | 0.795310i | \(0.707308\pi\) | |||||||
\(968\) | 7355.54 | − | 1970.91i | 0.244232 | − | 0.0654417i | ||||
\(969\) | −1435.98 | − | 3691.15i | −0.0476062 | − | 0.122370i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 12138.7i | − | 0.401183i | −0.979675 | − | 0.200591i | \(-0.935714\pi\) | ||
0.979675 | − | 0.200591i | \(-0.0642863\pi\) | |||||||
\(972\) | −9826.97 | + | 5972.23i | −0.324280 | + | 0.197078i | ||||
\(973\) | 22017.2 | − | 22017.2i | 0.725425 | − | 0.725425i | ||||
\(974\) | −3666.61 | − | 6350.75i | −0.120622 | − | 0.208923i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12219.6 | + | 21165.0i | −0.400759 | + | 0.694135i | ||||
\(977\) | 1341.59 | + | 5006.88i | 0.0439317 | + | 0.163955i | 0.984407 | − | 0.175908i | \(-0.0562860\pi\) |
−0.940475 | + | 0.339863i | \(0.889619\pi\) | |||||||
\(978\) | 25848.8 | − | 2834.44i | 0.845147 | − | 0.0926741i | ||||
\(979\) | 15854.3 | − | 9153.49i | 0.517575 | − | 0.298822i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30444.1 | − | 27912.0i | 0.990830 | − | 0.908421i | ||||
\(982\) | 4772.16 | + | 4772.16i | 0.155077 | + | 0.155077i | ||||
\(983\) | 3555.00 | − | 13267.4i | 0.115348 | − | 0.430484i | −0.883965 | − | 0.467553i | \(-0.845136\pi\) |
0.999313 | + | 0.0370695i | \(0.0118023\pi\) | |||||||
\(984\) | 3483.42 | − | 22652.5i | 0.112853 | − | 0.733877i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3984.55 | + | 2300.48i | 0.128696 | + | 0.0743024i | ||||
\(987\) | −15692.3 | + | 11509.3i | −0.506070 | + | 0.371171i | ||||
\(988\) | −4789.68 | − | 1283.39i | −0.154231 | − | 0.0413260i | ||||
\(989\) | −68369.9 | −2.19822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10353.2 | 0.331868 | 0.165934 | − | 0.986137i | \(-0.446936\pi\) | ||||
0.165934 | + | 0.986137i | \(0.446936\pi\) | |||||||
\(992\) | −15588.3 | − | 4176.87i | −0.498920 | − | 0.133685i | ||||
\(993\) | 2621.61 | + | 23907.9i | 0.0837808 | + | 0.764044i | ||||
\(994\) | −18085.3 | − | 10441.5i | −0.577093 | − | 0.333185i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3141.46 | − | 1222.13i | 0.0999407 | − | 0.0388803i | ||||
\(997\) | −3347.43 | + | 12492.8i | −0.106333 | + | 0.396841i | −0.998493 | − | 0.0548790i | \(-0.982523\pi\) |
0.892160 | + | 0.451720i | \(0.149189\pi\) | |||||||
\(998\) | 311.118 | + | 311.118i | 0.00986802 | + | 0.00986802i | ||||
\(999\) | −21825.9 | + | 44303.8i | −0.691232 | + | 1.40311i |
(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 | 225.4.p.b.32.5 | 64 | ||
5.2 | odd | 4 | 45.4.l.a.23.12 | yes | 64 | ||
5.3 | odd | 4 | inner | 225.4.p.b.68.5 | 64 | ||
5.4 | even | 2 | 45.4.l.a.32.12 | yes | 64 | ||
9.2 | odd | 6 | inner | 225.4.p.b.182.5 | 64 | ||
15.2 | even | 4 | 135.4.m.a.98.5 | 64 | |||
15.14 | odd | 2 | 135.4.m.a.17.5 | 64 | |||
45.2 | even | 12 | 45.4.l.a.38.12 | yes | 64 | ||
45.7 | odd | 12 | 135.4.m.a.8.5 | 64 | |||
45.29 | odd | 6 | 45.4.l.a.2.12 | ✓ | 64 | ||
45.34 | even | 6 | 135.4.m.a.62.5 | 64 | |||
45.38 | even | 12 | inner | 225.4.p.b.218.5 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.l.a.2.12 | ✓ | 64 | 45.29 | odd | 6 | ||
45.4.l.a.23.12 | yes | 64 | 5.2 | odd | 4 | ||
45.4.l.a.32.12 | yes | 64 | 5.4 | even | 2 | ||
45.4.l.a.38.12 | yes | 64 | 45.2 | even | 12 | ||
135.4.m.a.8.5 | 64 | 45.7 | odd | 12 | |||
135.4.m.a.17.5 | 64 | 15.14 | odd | 2 | |||
135.4.m.a.62.5 | 64 | 45.34 | even | 6 | |||
135.4.m.a.98.5 | 64 | 15.2 | even | 4 | |||
225.4.p.b.32.5 | 64 | 1.1 | even | 1 | trivial | ||
225.4.p.b.68.5 | 64 | 5.3 | odd | 4 | inner | ||
225.4.p.b.182.5 | 64 | 9.2 | odd | 6 | inner | ||
225.4.p.b.218.5 | 64 | 45.38 | even | 12 | inner |