Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(11,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.15 | ||
Character | \(\chi\) | \(=\) | 60.11 |
Dual form | 60.4.e.a.11.16 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.622346 | − | 2.75911i | 0.220033 | − | 0.975492i | ||||
\(3\) | −1.95519 | − | 4.81427i | −0.376277 | − | 0.926507i | ||||
\(4\) | −7.22537 | − | 3.43424i | −0.903171 | − | 0.429280i | ||||
\(5\) | 5.00000i | 0.447214i | ||||||||
\(6\) | −14.4999 | + | 2.39845i | −0.986594 | + | 0.163194i | ||||
\(7\) | − | 20.3642i | − | 1.09957i | −0.835308 | − | 0.549783i | \(-0.814710\pi\) | ||
0.835308 | − | 0.549783i | \(-0.185290\pi\) | |||||||
\(8\) | −13.9721 | + | 17.7983i | −0.617487 | + | 0.786581i | ||||
\(9\) | −19.3544 | + | 18.8257i | −0.716831 | + | 0.697247i | ||||
\(10\) | 13.7955 | + | 3.11173i | 0.436254 | + | 0.0984016i | ||||
\(11\) | −15.2982 | −0.419327 | −0.209663 | − | 0.977774i | \(-0.567237\pi\) | ||||
−0.209663 | + | 0.977774i | \(0.567237\pi\) | |||||||
\(12\) | −2.40639 | + | 41.4995i | −0.0578889 | + | 0.998323i | ||||
\(13\) | 27.7054 | 0.591084 | 0.295542 | − | 0.955330i | \(-0.404500\pi\) | ||||
0.295542 | + | 0.955330i | \(0.404500\pi\) | |||||||
\(14\) | −56.1872 | − | 12.6736i | −1.07262 | − | 0.241940i | ||||
\(15\) | 24.0714 | − | 9.77596i | 0.414347 | − | 0.168276i | ||||
\(16\) | 40.4119 | + | 49.6274i | 0.631437 | + | 0.775428i | ||||
\(17\) | − | 92.5031i | − | 1.31972i | −0.751387 | − | 0.659861i | \(-0.770615\pi\) | ||
0.751387 | − | 0.659861i | \(-0.229385\pi\) | |||||||
\(18\) | 39.8969 | + | 65.1171i | 0.522433 | + | 0.852681i | ||||
\(19\) | − | 127.926i | − | 1.54465i | −0.635230 | − | 0.772323i | \(-0.719095\pi\) | ||
0.635230 | − | 0.772323i | \(-0.280905\pi\) | |||||||
\(20\) | 17.1712 | − | 36.1268i | 0.191980 | − | 0.403910i | ||||
\(21\) | −98.0390 | + | 39.8160i | −1.01876 | + | 0.413741i | ||||
\(22\) | −9.52081 | + | 42.2095i | −0.0922656 | + | 0.409050i | ||||
\(23\) | 51.1779 | 0.463971 | 0.231985 | − | 0.972719i | \(-0.425478\pi\) | ||||
0.231985 | + | 0.972719i | \(0.425478\pi\) | |||||||
\(24\) | 113.004 | + | 32.4666i | 0.961119 | + | 0.276134i | ||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | 17.2423 | − | 76.4421i | 0.130058 | − | 0.576598i | ||||
\(27\) | 128.474 | + | 56.3698i | 0.915731 | + | 0.401791i | ||||
\(28\) | −69.9358 | + | 147.139i | −0.472022 | + | 0.993096i | ||||
\(29\) | − | 99.2953i | − | 0.635816i | −0.948121 | − | 0.317908i | \(-0.897020\pi\) | ||
0.948121 | − | 0.317908i | \(-0.102980\pi\) | |||||||
\(30\) | −11.9922 | − | 72.4996i | −0.0729824 | − | 0.441218i | ||||
\(31\) | − | 25.8075i | − | 0.149521i | −0.997202 | − | 0.0747606i | \(-0.976181\pi\) | ||
0.997202 | − | 0.0747606i | \(-0.0238193\pi\) | |||||||
\(32\) | 162.078 | − | 80.6156i | 0.895360 | − | 0.445342i | ||||
\(33\) | 29.9110 | + | 73.6499i | 0.157783 | + | 0.388509i | ||||
\(34\) | −255.226 | − | 57.5690i | −1.28738 | − | 0.290382i | ||||
\(35\) | 101.821 | 0.491741 | ||||||||
\(36\) | 204.495 | − | 69.5545i | 0.946736 | − | 0.322012i | ||||
\(37\) | 356.629 | 1.58458 | 0.792290 | − | 0.610144i | \(-0.208888\pi\) | ||||
0.792290 | + | 0.610144i | \(0.208888\pi\) | |||||||
\(38\) | −352.962 | − | 79.6144i | −1.50679 | − | 0.339873i | ||||
\(39\) | −54.1693 | − | 133.381i | −0.222411 | − | 0.547643i | ||||
\(40\) | −88.9915 | − | 69.8607i | −0.351770 | − | 0.276149i | ||||
\(41\) | 292.895i | 1.11567i | 0.829952 | + | 0.557835i | \(0.188368\pi\) | ||||
−0.829952 | + | 0.557835i | \(0.811632\pi\) | |||||||
\(42\) | 48.8425 | + | 295.280i | 0.179442 | + | 1.08483i | ||||
\(43\) | 521.476i | 1.84940i | 0.380694 | + | 0.924701i | \(0.375685\pi\) | ||||
−0.380694 | + | 0.924701i | \(0.624315\pi\) | |||||||
\(44\) | 110.535 | + | 52.5379i | 0.378724 | + | 0.180009i | ||||
\(45\) | −94.1283 | − | 96.7722i | −0.311818 | − | 0.320577i | ||||
\(46\) | 31.8504 | − | 141.205i | 0.102089 | − | 0.452600i | ||||
\(47\) | −573.546 | −1.78001 | −0.890003 | − | 0.455955i | \(-0.849298\pi\) | ||||
−0.890003 | + | 0.455955i | \(0.849298\pi\) | |||||||
\(48\) | 159.907 | − | 291.585i | 0.480844 | − | 0.876806i | ||||
\(49\) | −71.7025 | −0.209045 | ||||||||
\(50\) | −15.5587 | + | 68.9777i | −0.0440065 | + | 0.195098i | ||||
\(51\) | −445.335 | + | 180.861i | −1.22273 | + | 0.496581i | ||||
\(52\) | −200.182 | − | 95.1470i | −0.533850 | − | 0.253741i | ||||
\(53\) | − | 305.765i | − | 0.792454i | −0.918153 | − | 0.396227i | \(-0.870319\pi\) | ||
0.918153 | − | 0.396227i | \(-0.129681\pi\) | |||||||
\(54\) | 235.485 | − | 319.391i | 0.593435 | − | 0.804882i | ||||
\(55\) | − | 76.4912i | − | 0.187529i | ||||||
\(56\) | 362.449 | + | 284.532i | 0.864898 | + | 0.678968i | ||||
\(57\) | −615.871 | + | 250.120i | −1.43113 | + | 0.581215i | ||||
\(58\) | −273.967 | − | 61.7961i | −0.620234 | − | 0.139900i | ||||
\(59\) | 295.688 | 0.652462 | 0.326231 | − | 0.945290i | \(-0.394221\pi\) | ||||
0.326231 | + | 0.945290i | \(0.394221\pi\) | |||||||
\(60\) | −207.498 | − | 12.0320i | −0.446464 | − | 0.0258887i | ||||
\(61\) | 326.449 | 0.685204 | 0.342602 | − | 0.939481i | \(-0.388692\pi\) | ||||
0.342602 | + | 0.939481i | \(0.388692\pi\) | |||||||
\(62\) | −71.2056 | − | 16.0612i | −0.145857 | − | 0.0328995i | ||||
\(63\) | 383.370 | + | 394.139i | 0.766669 | + | 0.788203i | ||||
\(64\) | −121.559 | − | 497.361i | −0.237419 | − | 0.971407i | ||||
\(65\) | 138.527i | 0.264341i | ||||||||
\(66\) | 221.823 | − | 36.6920i | 0.413705 | − | 0.0684314i | ||||
\(67\) | − | 299.605i | − | 0.546307i | −0.961971 | − | 0.273153i | \(-0.911933\pi\) | ||
0.961971 | − | 0.273153i | \(-0.0880666\pi\) | |||||||
\(68\) | −317.678 | + | 668.369i | −0.566531 | + | 1.19194i | ||||
\(69\) | −100.063 | − | 246.384i | −0.174581 | − | 0.429872i | ||||
\(70\) | 63.3681 | − | 280.936i | 0.108199 | − | 0.479689i | ||||
\(71\) | −653.840 | −1.09291 | −0.546454 | − | 0.837489i | \(-0.684023\pi\) | ||||
−0.546454 | + | 0.837489i | \(0.684023\pi\) | |||||||
\(72\) | −64.6418 | − | 607.511i | −0.105807 | − | 0.994387i | ||||
\(73\) | 504.190 | 0.808369 | 0.404184 | − | 0.914677i | \(-0.367555\pi\) | ||||
0.404184 | + | 0.914677i | \(0.367555\pi\) | |||||||
\(74\) | 221.947 | − | 983.979i | 0.348660 | − | 1.54575i | ||||
\(75\) | 48.8798 | + | 120.357i | 0.0752554 | + | 0.185301i | ||||
\(76\) | −439.330 | + | 924.314i | −0.663086 | + | 1.39508i | ||||
\(77\) | 311.537i | 0.461077i | ||||||||
\(78\) | −401.725 | + | 66.4498i | −0.583160 | + | 0.0964610i | ||||
\(79\) | 110.758i | 0.157738i | 0.996885 | + | 0.0788688i | \(0.0251308\pi\) | ||||
−0.996885 | + | 0.0788688i | \(0.974869\pi\) | |||||||
\(80\) | −248.137 | + | 202.060i | −0.346782 | + | 0.282387i | ||||
\(81\) | 20.1889 | − | 728.720i | 0.0276939 | − | 0.999616i | ||||
\(82\) | 808.129 | + | 182.282i | 1.08833 | + | 0.245484i | ||||
\(83\) | 1479.78 | 1.95695 | 0.978474 | − | 0.206371i | \(-0.0661655\pi\) | ||||
0.978474 | + | 0.206371i | \(0.0661655\pi\) | |||||||
\(84\) | 845.106 | + | 49.0044i | 1.09772 | + | 0.0636526i | ||||
\(85\) | 462.515 | 0.590198 | ||||||||
\(86\) | 1438.81 | + | 324.539i | 1.80408 | + | 0.406929i | ||||
\(87\) | −478.035 | + | 194.141i | −0.589089 | + | 0.239243i | ||||
\(88\) | 213.749 | − | 272.283i | 0.258929 | − | 0.329834i | ||||
\(89\) | 772.934i | 0.920572i | 0.887771 | + | 0.460286i | \(0.152253\pi\) | ||||
−0.887771 | + | 0.460286i | \(0.847747\pi\) | |||||||
\(90\) | −325.586 | + | 199.484i | −0.381330 | + | 0.233639i | ||||
\(91\) | − | 564.199i | − | 0.649935i | ||||||
\(92\) | −369.779 | − | 175.757i | −0.419045 | − | 0.199174i | ||||
\(93\) | −124.244 | + | 50.4585i | −0.138532 | + | 0.0562614i | ||||
\(94\) | −356.944 | + | 1582.48i | −0.391659 | + | 1.73638i | ||||
\(95\) | 639.631 | 0.690787 | ||||||||
\(96\) | −704.998 | − | 622.667i | −0.749516 | − | 0.661986i | ||||
\(97\) | −26.1154 | −0.0273362 | −0.0136681 | − | 0.999907i | \(-0.504351\pi\) | ||||
−0.0136681 | + | 0.999907i | \(0.504351\pi\) | |||||||
\(98\) | −44.6238 | + | 197.835i | −0.0459967 | + | 0.203922i | ||||
\(99\) | 296.089 | − | 288.000i | 0.300586 | − | 0.292374i | ||||
\(100\) | 180.634 | + | 85.8561i | 0.180634 | + | 0.0858561i | ||||
\(101\) | − | 196.046i | − | 0.193141i | −0.995326 | − | 0.0965706i | \(-0.969213\pi\) | ||
0.995326 | − | 0.0965706i | \(-0.0307874\pi\) | |||||||
\(102\) | 221.864 | + | 1341.29i | 0.215370 | + | 1.30203i | ||||
\(103\) | − | 685.393i | − | 0.655668i | −0.944735 | − | 0.327834i | \(-0.893681\pi\) | ||
0.944735 | − | 0.327834i | \(-0.106319\pi\) | |||||||
\(104\) | −387.103 | + | 493.108i | −0.364986 | + | 0.464935i | ||||
\(105\) | −199.080 | − | 490.195i | −0.185031 | − | 0.455601i | ||||
\(106\) | −843.639 | − | 190.292i | −0.773033 | − | 0.174366i | ||||
\(107\) | 503.806 | 0.455185 | 0.227593 | − | 0.973756i | \(-0.426915\pi\) | ||||
0.227593 | + | 0.973756i | \(0.426915\pi\) | |||||||
\(108\) | −734.681 | − | 848.502i | −0.654581 | − | 0.755992i | ||||
\(109\) | −928.609 | −0.816006 | −0.408003 | − | 0.912981i | \(-0.633775\pi\) | ||||
−0.408003 | + | 0.912981i | \(0.633775\pi\) | |||||||
\(110\) | −211.048 | − | 47.6040i | −0.182933 | − | 0.0412624i | ||||
\(111\) | −697.279 | − | 1716.91i | −0.596241 | − | 1.46813i | ||||
\(112\) | 1010.62 | − | 822.959i | 0.852634 | − | 0.694306i | ||||
\(113\) | − | 451.244i | − | 0.375659i | −0.982202 | − | 0.187830i | \(-0.939855\pi\) | ||
0.982202 | − | 0.187830i | \(-0.0601453\pi\) | |||||||
\(114\) | 306.824 | + | 1854.92i | 0.252076 | + | 1.52394i | ||||
\(115\) | 255.889i | 0.207494i | ||||||||
\(116\) | −341.004 | + | 717.445i | −0.272944 | + | 0.574251i | ||||
\(117\) | −536.222 | + | 521.572i | −0.423707 | + | 0.412131i | ||||
\(118\) | 184.020 | − | 815.835i | 0.143563 | − | 0.636472i | ||||
\(119\) | −1883.75 | −1.45112 | ||||||||
\(120\) | −162.333 | + | 565.020i | −0.123491 | + | 0.429826i | ||||
\(121\) | −1096.96 | −0.824165 | ||||||||
\(122\) | 203.164 | − | 900.708i | 0.150767 | − | 0.668412i | ||||
\(123\) | 1410.08 | − | 572.666i | 1.03368 | − | 0.419801i | ||||
\(124\) | −88.6291 | + | 186.468i | −0.0641865 | + | 0.135043i | ||||
\(125\) | − | 125.000i | − | 0.0894427i | ||||||
\(126\) | 1326.06 | − | 812.470i | 0.937578 | − | 0.574449i | ||||
\(127\) | − | 1069.78i | − | 0.747463i | −0.927537 | − | 0.373732i | \(-0.878078\pi\) | ||
0.927537 | − | 0.373732i | \(-0.121922\pi\) | |||||||
\(128\) | −1447.92 | + | 25.8634i | −0.999841 | + | 0.0178595i | ||||
\(129\) | 2510.53 | − | 1019.59i | 1.71348 | − | 0.695888i | ||||
\(130\) | 382.211 | + | 86.2117i | 0.257862 | + | 0.0581636i | ||||
\(131\) | −728.141 | −0.485633 | −0.242817 | − | 0.970072i | \(-0.578071\pi\) | ||||
−0.242817 | + | 0.970072i | \(0.578071\pi\) | |||||||
\(132\) | 36.8136 | − | 634.870i | 0.0242743 | − | 0.418623i | ||||
\(133\) | −2605.12 | −1.69844 | ||||||||
\(134\) | −826.642 | − | 186.458i | −0.532918 | − | 0.120205i | ||||
\(135\) | −281.849 | + | 642.368i | −0.179687 | + | 0.409527i | ||||
\(136\) | 1646.40 | + | 1292.47i | 1.03807 | + | 0.814912i | ||||
\(137\) | − | 1335.43i | − | 0.832801i | −0.909181 | − | 0.416400i | \(-0.863291\pi\) | ||
0.909181 | − | 0.416400i | \(-0.136709\pi\) | |||||||
\(138\) | −742.075 | + | 122.747i | −0.457751 | + | 0.0757170i | ||||
\(139\) | 2006.84i | 1.22459i | 0.790629 | + | 0.612296i | \(0.209754\pi\) | ||||
−0.790629 | + | 0.612296i | \(0.790246\pi\) | |||||||
\(140\) | −735.696 | − | 349.679i | −0.444126 | − | 0.211095i | ||||
\(141\) | 1121.39 | + | 2761.21i | 0.669775 | + | 1.64919i | ||||
\(142\) | −406.915 | + | 1804.01i | −0.240476 | + | 1.06612i | ||||
\(143\) | −423.843 | −0.247857 | ||||||||
\(144\) | −1716.42 | − | 199.728i | −0.993298 | − | 0.115584i | ||||
\(145\) | 496.477 | 0.284346 | ||||||||
\(146\) | 313.781 | − | 1391.11i | 0.177868 | − | 0.788558i | ||||
\(147\) | 140.192 | + | 345.195i | 0.0786588 | + | 0.193682i | ||||
\(148\) | −2576.78 | − | 1224.75i | −1.43115 | − | 0.680230i | ||||
\(149\) | 2021.25i | 1.11132i | 0.831409 | + | 0.555661i | \(0.187535\pi\) | ||||
−0.831409 | + | 0.555661i | \(0.812465\pi\) | |||||||
\(150\) | 362.498 | − | 59.9611i | 0.197319 | − | 0.0326387i | ||||
\(151\) | 264.606i | 0.142605i | 0.997455 | + | 0.0713024i | \(0.0227155\pi\) | ||||
−0.997455 | + | 0.0713024i | \(0.977284\pi\) | |||||||
\(152\) | 2276.87 | + | 1787.40i | 1.21499 | + | 0.953799i | ||||
\(153\) | 1741.43 | + | 1790.35i | 0.920172 | + | 0.946019i | ||||
\(154\) | 859.565 | + | 193.884i | 0.449777 | + | 0.101452i | ||||
\(155\) | 129.037 | 0.0668679 | ||||||||
\(156\) | −66.6701 | + | 1149.76i | −0.0342172 | + | 0.590092i | ||||
\(157\) | 2339.73 | 1.18937 | 0.594684 | − | 0.803960i | \(-0.297277\pi\) | ||||
0.594684 | + | 0.803960i | \(0.297277\pi\) | |||||||
\(158\) | 305.594 | + | 68.9299i | 0.153872 | + | 0.0347074i | ||||
\(159\) | −1472.04 | + | 597.830i | −0.734215 | + | 0.298182i | ||||
\(160\) | 403.078 | + | 810.388i | 0.199163 | + | 0.400417i | ||||
\(161\) | − | 1042.20i | − | 0.510166i | ||||||
\(162\) | −1998.05 | − | 509.220i | −0.969025 | − | 0.246964i | ||||
\(163\) | 1541.95i | 0.740948i | 0.928843 | + | 0.370474i | \(0.120805\pi\) | ||||
−0.928843 | + | 0.370474i | \(0.879195\pi\) | |||||||
\(164\) | 1005.87 | − | 2116.27i | 0.478935 | − | 1.00764i | ||||
\(165\) | −368.250 | + | 149.555i | −0.173747 | + | 0.0705627i | ||||
\(166\) | 920.934 | − | 4082.87i | 0.430592 | − | 1.90899i | ||||
\(167\) | −151.105 | −0.0700173 | −0.0350086 | − | 0.999387i | \(-0.511146\pi\) | ||||
−0.0350086 | + | 0.999387i | \(0.511146\pi\) | |||||||
\(168\) | 661.157 | − | 2301.24i | 0.303627 | − | 1.05681i | ||||
\(169\) | −1429.41 | −0.650620 | ||||||||
\(170\) | 287.845 | − | 1276.13i | 0.129863 | − | 0.575734i | ||||
\(171\) | 2408.29 | + | 2475.94i | 1.07700 | + | 1.10725i | ||||
\(172\) | 1790.87 | − | 3767.85i | 0.793912 | − | 1.67033i | ||||
\(173\) | − | 4436.11i | − | 1.94954i | −0.223206 | − | 0.974771i | \(-0.571652\pi\) | ||
0.223206 | − | 0.974771i | \(-0.428348\pi\) | |||||||
\(174\) | 238.154 | + | 1439.77i | 0.103761 | + | 0.627293i | ||||
\(175\) | 509.106i | 0.219913i | ||||||||
\(176\) | −618.232 | − | 759.211i | −0.264778 | − | 0.325157i | ||||
\(177\) | −578.127 | − | 1423.52i | −0.245507 | − | 0.604511i | ||||
\(178\) | 2132.61 | + | 481.033i | 0.898011 | + | 0.202556i | ||||
\(179\) | 2609.23 | 1.08951 | 0.544757 | − | 0.838594i | \(-0.316622\pi\) | ||||
0.544757 | + | 0.838594i | \(0.316622\pi\) | |||||||
\(180\) | 347.773 | + | 1022.47i | 0.144008 | + | 0.423393i | ||||
\(181\) | −1528.41 | −0.627657 | −0.313828 | − | 0.949480i | \(-0.601612\pi\) | ||||
−0.313828 | + | 0.949480i | \(0.601612\pi\) | |||||||
\(182\) | −1556.69 | − | 351.127i | −0.634007 | − | 0.143007i | ||||
\(183\) | −638.270 | − | 1571.61i | −0.257827 | − | 0.634847i | ||||
\(184\) | −715.064 | + | 910.879i | −0.286496 | + | 0.364951i | ||||
\(185\) | 1783.15i | 0.708646i | ||||||||
\(186\) | 61.8978 | + | 374.206i | 0.0244009 | + | 0.147517i | ||||
\(187\) | 1415.13i | 0.553395i | ||||||||
\(188\) | 4144.08 | + | 1969.70i | 1.60765 | + | 0.764122i | ||||
\(189\) | 1147.93 | − | 2616.27i | 0.441796 | − | 1.00691i | ||||
\(190\) | 398.072 | − | 1764.81i | 0.151996 | − | 0.673857i | ||||
\(191\) | −832.060 | −0.315213 | −0.157607 | − | 0.987502i | \(-0.550378\pi\) | ||||
−0.157607 | + | 0.987502i | \(0.550378\pi\) | |||||||
\(192\) | −2156.76 | + | 1557.65i | −0.810680 | + | 0.585489i | ||||
\(193\) | 659.353 | 0.245913 | 0.122957 | − | 0.992412i | \(-0.460762\pi\) | ||||
0.122957 | + | 0.992412i | \(0.460762\pi\) | |||||||
\(194\) | −16.2528 | + | 72.0552i | −0.00601487 | + | 0.0266663i | ||||
\(195\) | 666.906 | − | 270.847i | 0.244913 | − | 0.0994653i | ||||
\(196\) | 518.077 | + | 246.244i | 0.188803 | + | 0.0897390i | ||||
\(197\) | 963.336i | 0.348400i | 0.984710 | + | 0.174200i | \(0.0557340\pi\) | ||||
−0.984710 | + | 0.174200i | \(0.944266\pi\) | |||||||
\(198\) | −610.352 | − | 996.177i | −0.219070 | − | 0.357552i | ||||
\(199\) | 870.488i | 0.310087i | 0.987908 | + | 0.155043i | \(0.0495517\pi\) | ||||
−0.987908 | + | 0.155043i | \(0.950448\pi\) | |||||||
\(200\) | 349.303 | − | 444.957i | 0.123497 | − | 0.157316i | ||||
\(201\) | −1442.38 | + | 585.785i | −0.506157 | + | 0.205563i | ||||
\(202\) | −540.911 | − | 122.008i | −0.188408 | − | 0.0424974i | ||||
\(203\) | −2022.07 | −0.699122 | ||||||||
\(204\) | 3838.83 | + | 222.599i | 1.31751 | + | 0.0763973i | ||||
\(205\) | −1464.47 | −0.498943 | ||||||||
\(206\) | −1891.08 | − | 426.552i | −0.639599 | − | 0.144268i | ||||
\(207\) | −990.519 | + | 963.457i | −0.332589 | + | 0.323502i | ||||
\(208\) | 1119.63 | + | 1374.94i | 0.373232 | + | 0.458342i | ||||
\(209\) | 1957.05i | 0.647711i | ||||||||
\(210\) | −1476.40 | + | 244.213i | −0.485149 | + | 0.0802489i | ||||
\(211\) | − | 102.524i | − | 0.0334503i | −0.999860 | − | 0.0167252i | \(-0.994676\pi\) | ||
0.999860 | − | 0.0167252i | \(-0.00532404\pi\) | |||||||
\(212\) | −1050.07 | + | 2209.27i | −0.340185 | + | 0.715722i | ||||
\(213\) | 1278.38 | + | 3147.76i | 0.411236 | + | 1.01259i | ||||
\(214\) | 313.542 | − | 1390.06i | 0.100156 | − | 0.444030i | ||||
\(215\) | −2607.38 | −0.827078 | ||||||||
\(216\) | −2798.34 | + | 1499.00i | −0.881494 | + | 0.472196i | ||||
\(217\) | −525.549 | −0.164408 | ||||||||
\(218\) | −577.917 | + | 2562.14i | −0.179548 | + | 0.796008i | ||||
\(219\) | −985.788 | − | 2427.31i | −0.304171 | − | 0.748960i | ||||
\(220\) | −262.689 | + | 552.677i | −0.0805024 | + | 0.169370i | ||||
\(221\) | − | 2562.83i | − | 0.780067i | ||||||
\(222\) | −5171.09 | + | 855.356i | −1.56334 | + | 0.258593i | ||||
\(223\) | − | 1477.75i | − | 0.443756i | −0.975074 | − | 0.221878i | \(-0.928781\pi\) | ||
0.975074 | − | 0.221878i | \(-0.0712187\pi\) | |||||||
\(224\) | −1641.67 | − | 3300.59i | −0.489683 | − | 0.984508i | ||||
\(225\) | 483.861 | − | 470.642i | 0.143366 | − | 0.139449i | ||||
\(226\) | −1245.03 | − | 280.830i | −0.366453 | − | 0.0826573i | ||||
\(227\) | −817.892 | −0.239143 | −0.119571 | − | 0.992826i | \(-0.538152\pi\) | ||||
−0.119571 | + | 0.992826i | \(0.538152\pi\) | |||||||
\(228\) | 5308.87 | + | 307.841i | 1.54206 | + | 0.0894178i | ||||
\(229\) | 1154.61 | 0.333182 | 0.166591 | − | 0.986026i | \(-0.446724\pi\) | ||||
0.166591 | + | 0.986026i | \(0.446724\pi\) | |||||||
\(230\) | 706.027 | + | 159.252i | 0.202409 | + | 0.0456555i | ||||
\(231\) | 1499.82 | − | 609.115i | 0.427191 | − | 0.173493i | ||||
\(232\) | 1767.29 | + | 1387.37i | 0.500121 | + | 0.392608i | ||||
\(233\) | 3871.61i | 1.08857i | 0.838899 | + | 0.544287i | \(0.183200\pi\) | ||||
−0.838899 | + | 0.544287i | \(0.816800\pi\) | |||||||
\(234\) | 1105.36 | + | 1804.09i | 0.308801 | + | 0.504005i | ||||
\(235\) | − | 2867.73i | − | 0.796043i | ||||||
\(236\) | −2136.45 | − | 1015.46i | −0.589285 | − | 0.280089i | ||||
\(237\) | 533.220 | − | 216.554i | 0.146145 | − | 0.0593530i | ||||
\(238\) | −1172.35 | + | 5197.49i | −0.319294 | + | 1.41556i | ||||
\(239\) | 4418.94 | 1.19597 | 0.597987 | − | 0.801506i | \(-0.295968\pi\) | ||||
0.597987 | + | 0.801506i | \(0.295968\pi\) | |||||||
\(240\) | 1457.93 | + | 799.533i | 0.392120 | + | 0.215040i | ||||
\(241\) | 1310.51 | 0.350279 | 0.175139 | − | 0.984544i | \(-0.443962\pi\) | ||||
0.175139 | + | 0.984544i | \(0.443962\pi\) | |||||||
\(242\) | −682.691 | + | 3026.64i | −0.181343 | + | 0.803967i | ||||
\(243\) | −3547.73 | + | 1327.59i | −0.936572 | + | 0.350474i | ||||
\(244\) | −2358.71 | − | 1121.10i | −0.618857 | − | 0.294145i | ||||
\(245\) | − | 358.512i | − | 0.0934878i | ||||||
\(246\) | −702.492 | − | 4246.95i | −0.182070 | − | 1.10071i | ||||
\(247\) | − | 3544.24i | − | 0.913015i | ||||||
\(248\) | 459.329 | + | 360.585i | 0.117610 | + | 0.0923274i | ||||
\(249\) | −2893.25 | − | 7124.05i | −0.736354 | − | 1.81313i | ||||
\(250\) | −344.889 | − | 77.7933i | −0.0872507 | − | 0.0196803i | ||||
\(251\) | 5925.09 | 1.48999 | 0.744997 | − | 0.667068i | \(-0.232451\pi\) | ||||
0.744997 | + | 0.667068i | \(0.232451\pi\) | |||||||
\(252\) | −1416.42 | − | 4164.38i | −0.354073 | − | 1.04100i | ||||
\(253\) | −782.932 | −0.194555 | ||||||||
\(254\) | −2951.65 | − | 665.775i | −0.729145 | − | 0.164466i | ||||
\(255\) | −904.307 | − | 2226.67i | −0.222078 | − | 0.546823i | ||||
\(256\) | −829.750 | + | 4011.08i | −0.202576 | + | 0.979267i | ||||
\(257\) | 4401.57i | 1.06834i | 0.845378 | + | 0.534168i | \(0.179375\pi\) | ||||
−0.845378 | + | 0.534168i | \(0.820625\pi\) | |||||||
\(258\) | −1250.73 | − | 7561.35i | −0.301811 | − | 1.82461i | ||||
\(259\) | − | 7262.49i | − | 1.74235i | ||||||
\(260\) | 475.735 | − | 1000.91i | 0.113476 | − | 0.238745i | ||||
\(261\) | 1869.30 | + | 1921.81i | 0.443321 | + | 0.455773i | ||||
\(262\) | −453.156 | + | 2009.02i | −0.106855 | + | 0.473732i | ||||
\(263\) | −4384.53 | −1.02799 | −0.513996 | − | 0.857793i | \(-0.671835\pi\) | ||||
−0.513996 | + | 0.857793i | \(0.671835\pi\) | |||||||
\(264\) | −1728.76 | − | 496.682i | −0.403023 | − | 0.115790i | ||||
\(265\) | 1528.83 | 0.354396 | ||||||||
\(266\) | −1621.29 | + | 7187.81i | −0.373712 | + | 1.65682i | ||||
\(267\) | 3721.12 | − | 1511.24i | 0.852916 | − | 0.346390i | ||||
\(268\) | −1028.92 | + | 2164.75i | −0.234519 | + | 0.493408i | ||||
\(269\) | 3387.40i | 0.767783i | 0.923378 | + | 0.383892i | \(0.125416\pi\) | ||||
−0.923378 | + | 0.383892i | \(0.874584\pi\) | |||||||
\(270\) | 1596.96 | + | 1177.43i | 0.359954 | + | 0.265392i | ||||
\(271\) | 4088.66i | 0.916489i | 0.888826 | + | 0.458244i | \(0.151522\pi\) | ||||
−0.888826 | + | 0.458244i | \(0.848478\pi\) | |||||||
\(272\) | 4590.68 | − | 3738.23i | 1.02335 | − | 0.833321i | ||||
\(273\) | −2716.21 | + | 1103.12i | −0.602170 | + | 0.244556i | ||||
\(274\) | −3684.60 | − | 831.102i | −0.812391 | − | 0.183243i | ||||
\(275\) | 382.456 | 0.0838653 | ||||||||
\(276\) | −123.154 | + | 2123.86i | −0.0268587 | + | 0.463193i | ||||
\(277\) | −3485.20 | −0.755977 | −0.377988 | − | 0.925810i | \(-0.623384\pi\) | ||||
−0.377988 | + | 0.925810i | \(0.623384\pi\) | |||||||
\(278\) | 5537.10 | + | 1248.95i | 1.19458 | + | 0.269450i | ||||
\(279\) | 485.842 | + | 499.489i | 0.104253 | + | 0.107181i | ||||
\(280\) | −1422.66 | + | 1812.24i | −0.303644 | + | 0.386794i | ||||
\(281\) | − | 4399.79i | − | 0.934056i | −0.884243 | − | 0.467028i | \(-0.845325\pi\) | ||
0.884243 | − | 0.467028i | \(-0.154675\pi\) | |||||||
\(282\) | 8316.37 | − | 1375.62i | 1.75614 | − | 0.290485i | ||||
\(283\) | 505.577i | 0.106196i | 0.998589 | + | 0.0530980i | \(0.0169096\pi\) | ||||
−0.998589 | + | 0.0530980i | \(0.983090\pi\) | |||||||
\(284\) | 4724.23 | + | 2245.44i | 0.987083 | + | 0.469164i | ||||
\(285\) | −1250.60 | − | 3079.36i | −0.259927 | − | 0.640019i | ||||
\(286\) | −263.777 | + | 1169.43i | −0.0545367 | + | 0.241783i | ||||
\(287\) | 5964.58 | 1.22675 | ||||||||
\(288\) | −1619.28 | + | 4611.49i | −0.331309 | + | 0.943522i | ||||
\(289\) | −3643.82 | −0.741668 | ||||||||
\(290\) | 308.980 | − | 1369.83i | 0.0625654 | − | 0.277377i | ||||
\(291\) | 51.0606 | + | 125.727i | 0.0102860 | + | 0.0253272i | ||||
\(292\) | −3642.96 | − | 1731.51i | −0.730096 | − | 0.347017i | ||||
\(293\) | − | 6365.91i | − | 1.26928i | −0.772806 | − | 0.634642i | \(-0.781147\pi\) | ||
0.772806 | − | 0.634642i | \(-0.218853\pi\) | |||||||
\(294\) | 1039.68 | − | 171.974i | 0.206243 | − | 0.0341148i | ||||
\(295\) | 1478.44i | 0.291790i | ||||||||
\(296\) | −4982.87 | + | 6347.39i | −0.978458 | + | 1.24640i | ||||
\(297\) | −1965.42 | − | 862.358i | −0.383991 | − | 0.168482i | ||||
\(298\) | 5576.84 | + | 1257.92i | 1.08409 | + | 0.244527i | ||||
\(299\) | 1417.90 | 0.274245 | ||||||||
\(300\) | 60.1599 | − | 1037.49i | 0.0115778 | − | 0.199665i | ||||
\(301\) | 10619.5 | 2.03354 | ||||||||
\(302\) | 730.077 | + | 164.677i | 0.139110 | + | 0.0313777i | ||||
\(303\) | −943.817 | + | 383.307i | −0.178947 | + | 0.0726746i | ||||
\(304\) | 6348.64 | − | 5169.74i | 1.19776 | − | 0.975346i | ||||
\(305\) | 1632.24i | 0.306433i | ||||||||
\(306\) | 6023.53 | − | 3690.58i | 1.12530 | − | 0.689466i | ||||
\(307\) | 7389.54i | 1.37376i | 0.726772 | + | 0.686879i | \(0.241020\pi\) | ||||
−0.726772 | + | 0.686879i | \(0.758980\pi\) | |||||||
\(308\) | 1069.89 | − | 2250.97i | 0.197931 | − | 0.416432i | ||||
\(309\) | −3299.67 | + | 1340.08i | −0.607481 | + | 0.246713i | ||||
\(310\) | 80.3059 | − | 356.028i | 0.0147131 | − | 0.0652291i | ||||
\(311\) | 1630.49 | 0.297288 | 0.148644 | − | 0.988891i | \(-0.452509\pi\) | ||||
0.148644 | + | 0.988891i | \(0.452509\pi\) | |||||||
\(312\) | 3130.82 | + | 899.498i | 0.568102 | + | 0.163218i | ||||
\(313\) | 5922.15 | 1.06946 | 0.534728 | − | 0.845024i | \(-0.320414\pi\) | ||||
0.534728 | + | 0.845024i | \(0.320414\pi\) | |||||||
\(314\) | 1456.12 | − | 6455.57i | 0.261700 | − | 1.16022i | ||||
\(315\) | −1970.69 | + | 1916.85i | −0.352495 | + | 0.342865i | ||||
\(316\) | 380.370 | − | 800.269i | 0.0677136 | − | 0.142464i | ||||
\(317\) | − | 7808.36i | − | 1.38347i | −0.722149 | − | 0.691737i | \(-0.756846\pi\) | ||
0.722149 | − | 0.691737i | \(-0.243154\pi\) | |||||||
\(318\) | 733.361 | + | 4433.57i | 0.129323 | + | 0.781831i | ||||
\(319\) | 1519.04i | 0.266615i | ||||||||
\(320\) | 2486.80 | − | 607.794i | 0.434427 | − | 0.106177i | ||||
\(321\) | −985.039 | − | 2425.46i | −0.171276 | − | 0.421732i | ||||
\(322\) | −2875.54 | − | 648.609i | −0.497663 | − | 0.112253i | ||||
\(323\) | −11833.6 | −2.03850 | ||||||||
\(324\) | −2648.48 | + | 5195.94i | −0.454128 | + | 0.890936i | ||||
\(325\) | −692.634 | −0.118217 | ||||||||
\(326\) | 4254.40 | + | 959.624i | 0.722789 | + | 0.163033i | ||||
\(327\) | 1815.61 | + | 4470.58i | 0.307044 | + | 0.756035i | ||||
\(328\) | −5213.03 | − | 4092.37i | −0.877565 | − | 0.688912i | ||||
\(329\) | 11679.8i | 1.95723i | ||||||||
\(330\) | 183.460 | + | 1109.12i | 0.0306035 | + | 0.185015i | ||||
\(331\) | 1569.05i | 0.260552i | 0.991478 | + | 0.130276i | \(0.0415863\pi\) | ||||
−0.991478 | + | 0.130276i | \(0.958414\pi\) | |||||||
\(332\) | −10691.9 | − | 5081.92i | −1.76746 | − | 0.840079i | ||||
\(333\) | −6902.36 | + | 6713.78i | −1.13588 | + | 1.10484i | ||||
\(334\) | −94.0399 | + | 416.916i | −0.0154061 | + | 0.0683013i | ||||
\(335\) | 1498.02 | 0.244316 | ||||||||
\(336\) | −5937.91 | − | 3256.38i | −0.964106 | − | 0.528720i | ||||
\(337\) | 6488.72 | 1.04885 | 0.524426 | − | 0.851456i | \(-0.324280\pi\) | ||||
0.524426 | + | 0.851456i | \(0.324280\pi\) | |||||||
\(338\) | −889.590 | + | 3943.91i | −0.143158 | + | 0.634675i | ||||
\(339\) | −2172.41 | + | 882.269i | −0.348051 | + | 0.141352i | ||||
\(340\) | −3341.84 | − | 1588.39i | −0.533050 | − | 0.253360i | ||||
\(341\) | 394.809i | 0.0626982i | ||||||||
\(342\) | 8330.18 | − | 5103.86i | 1.31709 | − | 0.806974i | ||||
\(343\) | − | 5524.77i | − | 0.869707i | ||||||
\(344\) | −9281.38 | − | 7286.13i | −1.45470 | − | 1.14198i | ||||
\(345\) | 1231.92 | − | 500.313i | 0.192245 | − | 0.0780752i | ||||
\(346\) | −12239.7 | − | 2760.79i | −1.90176 | − | 0.428963i | ||||
\(347\) | 595.599 | 0.0921425 | 0.0460712 | − | 0.998938i | \(-0.485330\pi\) | ||||
0.0460712 | + | 0.998938i | \(0.485330\pi\) | |||||||
\(348\) | 4120.71 | + | 238.944i | 0.634750 | + | 0.0368067i | ||||
\(349\) | 9358.18 | 1.43534 | 0.717668 | − | 0.696386i | \(-0.245210\pi\) | ||||
0.717668 | + | 0.696386i | \(0.245210\pi\) | |||||||
\(350\) | 1404.68 | + | 316.840i | 0.214524 | + | 0.0483881i | ||||
\(351\) | 3559.41 | + | 1561.75i | 0.541274 | + | 0.237492i | ||||
\(352\) | −2479.50 | + | 1233.28i | −0.375449 | + | 0.186744i | ||||
\(353\) | − | 573.683i | − | 0.0864988i | −0.999064 | − | 0.0432494i | \(-0.986229\pi\) | ||
0.999064 | − | 0.0432494i | \(-0.0137710\pi\) | |||||||
\(354\) | −4287.45 | + | 709.191i | −0.643715 | + | 0.106478i | ||||
\(355\) | − | 3269.20i | − | 0.488763i | ||||||
\(356\) | 2654.44 | − | 5584.74i | 0.395183 | − | 0.831434i | ||||
\(357\) | 3683.10 | + | 9068.91i | 0.546024 | + | 1.34448i | ||||
\(358\) | 1623.84 | − | 7199.15i | 0.239729 | − | 1.06281i | ||||
\(359\) | −8718.72 | −1.28177 | −0.640886 | − | 0.767636i | \(-0.721433\pi\) | ||||
−0.640886 | + | 0.767636i | \(0.721433\pi\) | |||||||
\(360\) | 3037.55 | − | 323.209i | 0.444703 | − | 0.0473184i | ||||
\(361\) | −9506.11 | −1.38593 | ||||||||
\(362\) | −951.201 | + | 4217.05i | −0.138105 | + | 0.612274i | ||||
\(363\) | 2144.78 | + | 5281.08i | 0.310114 | + | 0.763595i | ||||
\(364\) | −1937.60 | + | 4076.55i | −0.279005 | + | 0.587003i | ||||
\(365\) | 2520.95i | 0.361514i | ||||||||
\(366\) | −4733.48 | + | 782.969i | −0.676019 | + | 0.111821i | ||||
\(367\) | 3926.75i | 0.558515i | 0.960216 | + | 0.279257i | \(0.0900882\pi\) | ||||
−0.960216 | + | 0.279257i | \(0.909912\pi\) | |||||||
\(368\) | 2068.20 | + | 2539.82i | 0.292968 | + | 0.359776i | ||||
\(369\) | −5513.94 | − | 5668.81i | −0.777897 | − | 0.799747i | ||||
\(370\) | 4919.90 | + | 1109.73i | 0.691279 | + | 0.155925i | ||||
\(371\) | −6226.68 | −0.871356 | ||||||||
\(372\) | 1071.00 | + | 62.1029i | 0.149270 | + | 0.00865561i | ||||
\(373\) | 5278.89 | 0.732789 | 0.366395 | − | 0.930460i | \(-0.380592\pi\) | ||||
0.366395 | + | 0.930460i | \(0.380592\pi\) | |||||||
\(374\) | 3904.51 | + | 880.704i | 0.539833 | + | 0.121765i | ||||
\(375\) | −601.784 | + | 244.399i | −0.0828693 | + | 0.0336552i | ||||
\(376\) | 8013.66 | − | 10208.1i | 1.09913 | − | 1.40012i | ||||
\(377\) | − | 2751.01i | − | 0.375821i | ||||||
\(378\) | −6504.16 | − | 4795.48i | −0.885020 | − | 0.652521i | ||||
\(379\) | 1153.98i | 0.156401i | 0.996938 | + | 0.0782003i | \(0.0249174\pi\) | ||||
−0.996938 | + | 0.0782003i | \(0.975083\pi\) | |||||||
\(380\) | −4621.57 | − | 2196.65i | −0.623899 | − | 0.296541i | ||||
\(381\) | −5150.23 | + | 2091.63i | −0.692530 | + | 0.281253i | ||||
\(382\) | −517.830 | + | 2295.75i | −0.0693573 | + | 0.307488i | ||||
\(383\) | 6431.26 | 0.858021 | 0.429010 | − | 0.903300i | \(-0.358862\pi\) | ||||
0.429010 | + | 0.903300i | \(0.358862\pi\) | |||||||
\(384\) | 2955.48 | + | 6920.13i | 0.392764 | + | 0.919639i | ||||
\(385\) | −1557.69 | −0.206200 | ||||||||
\(386\) | 410.346 | − | 1819.23i | 0.0541089 | − | 0.239886i | ||||
\(387\) | −9817.13 | − | 10092.9i | −1.28949 | − | 1.32571i | ||||
\(388\) | 188.693 | + | 89.6866i | 0.0246893 | + | 0.0117349i | ||||
\(389\) | − | 9956.93i | − | 1.29778i | −0.760882 | − | 0.648890i | \(-0.775233\pi\) | ||
0.760882 | − | 0.648890i | \(-0.224767\pi\) | |||||||
\(390\) | −332.249 | − | 2008.63i | −0.0431387 | − | 0.260797i | ||||
\(391\) | − | 4734.11i | − | 0.612313i | ||||||
\(392\) | 1001.84 | − | 1276.18i | 0.129083 | − | 0.164431i | ||||
\(393\) | 1423.66 | + | 3505.47i | 0.182733 | + | 0.449943i | ||||
\(394\) | 2657.95 | + | 599.529i | 0.339862 | + | 0.0766595i | ||||
\(395\) | −553.791 | −0.0705424 | ||||||||
\(396\) | −3128.41 | + | 1064.06i | −0.396992 | + | 0.135028i | ||||
\(397\) | −11143.6 | −1.40877 | −0.704386 | − | 0.709817i | \(-0.748777\pi\) | ||||
−0.704386 | + | 0.709817i | \(0.748777\pi\) | |||||||
\(398\) | 2401.77 | + | 541.745i | 0.302487 | + | 0.0682292i | ||||
\(399\) | 5093.51 | + | 12541.8i | 0.639084 | + | 1.57362i | ||||
\(400\) | −1010.30 | − | 1240.68i | −0.126287 | − | 0.155086i | ||||
\(401\) | 4045.81i | 0.503836i | 0.967749 | + | 0.251918i | \(0.0810613\pi\) | ||||
−0.967749 | + | 0.251918i | \(0.918939\pi\) | |||||||
\(402\) | 718.585 | + | 4344.24i | 0.0891537 | + | 0.538983i | ||||
\(403\) | − | 715.005i | − | 0.0883795i | ||||||
\(404\) | −673.268 | + | 1416.50i | −0.0829117 | + | 0.174440i | ||||
\(405\) | 3643.60 | + | 100.944i | 0.447042 | + | 0.0123851i | ||||
\(406\) | −1258.43 | + | 5579.12i | −0.153830 | + | 0.681988i | ||||
\(407\) | −5455.80 | −0.664457 | ||||||||
\(408\) | 3003.26 | − | 10453.2i | 0.364420 | − | 1.26841i | ||||
\(409\) | 12909.8 | 1.56076 | 0.780379 | − | 0.625307i | \(-0.215026\pi\) | ||||
0.780379 | + | 0.625307i | \(0.215026\pi\) | |||||||
\(410\) | −911.410 | + | 4040.64i | −0.109784 | + | 0.486715i | ||||
\(411\) | −6429.14 | + | 2611.03i | −0.771596 | + | 0.313364i | ||||
\(412\) | −2353.81 | + | 4952.22i | −0.281465 | + | 0.592180i | ||||
\(413\) | − | 6021.46i | − | 0.717425i | ||||||
\(414\) | 2041.84 | + | 3332.56i | 0.242393 | + | 0.395619i | ||||
\(415\) | 7398.89i | 0.875174i | ||||||||
\(416\) | 4490.42 | − | 2233.48i | 0.529233 | − | 0.263234i | ||||
\(417\) | 9661.49 | − | 3923.76i | 1.13459 | − | 0.460786i | ||||
\(418\) | 5399.70 | + | 1217.96i | 0.631838 | + | 0.142518i | ||||
\(419\) | −425.462 | −0.0496067 | −0.0248033 | − | 0.999692i | \(-0.507896\pi\) | ||||
−0.0248033 | + | 0.999692i | \(0.507896\pi\) | |||||||
\(420\) | −245.022 | + | 4225.53i | −0.0284663 | + | 0.490916i | ||||
\(421\) | −6347.87 | −0.734860 | −0.367430 | − | 0.930051i | \(-0.619762\pi\) | ||||
−0.367430 | + | 0.930051i | \(0.619762\pi\) | |||||||
\(422\) | −282.874 | − | 63.8053i | −0.0326306 | − | 0.00736017i | ||||
\(423\) | 11100.7 | − | 10797.4i | 1.27596 | − | 1.24110i | ||||
\(424\) | 5442.10 | + | 4272.19i | 0.623329 | + | 0.489330i | ||||
\(425\) | 2312.58i | 0.263945i | ||||||||
\(426\) | 9480.62 | − | 1568.20i | 1.07826 | − | 0.178356i | ||||
\(427\) | − | 6647.88i | − | 0.753427i | ||||||
\(428\) | −3640.19 | − | 1730.19i | −0.411110 | − | 0.195402i | ||||
\(429\) | 828.696 | + | 2040.50i | 0.0932629 | + | 0.229641i | ||||
\(430\) | −1622.69 | + | 7194.04i | −0.181984 | + | 0.806808i | ||||
\(431\) | 14572.3 | 1.62859 | 0.814295 | − | 0.580452i | \(-0.197124\pi\) | ||||
0.814295 | + | 0.580452i | \(0.197124\pi\) | |||||||
\(432\) | 2394.38 | + | 8653.81i | 0.266666 | + | 0.963789i | ||||
\(433\) | −8416.25 | −0.934086 | −0.467043 | − | 0.884235i | \(-0.654681\pi\) | ||||
−0.467043 | + | 0.884235i | \(0.654681\pi\) | |||||||
\(434\) | −327.074 | + | 1450.05i | −0.0361752 | + | 0.160379i | ||||
\(435\) | −970.707 | − | 2390.17i | −0.106993 | − | 0.263448i | ||||
\(436\) | 6709.55 | + | 3189.07i | 0.736993 | + | 0.350295i | ||||
\(437\) | − | 6546.99i | − | 0.716670i | ||||||
\(438\) | −7310.71 | + | 1209.27i | −0.797532 | + | 0.131921i | ||||
\(439\) | 10822.6i | 1.17661i | 0.808638 | + | 0.588306i | \(0.200205\pi\) | ||||
−0.808638 | + | 0.588306i | \(0.799795\pi\) | |||||||
\(440\) | 1361.41 | + | 1068.75i | 0.147506 | + | 0.115796i | ||||
\(441\) | 1387.76 | − | 1349.85i | 0.149850 | − | 0.145756i | ||||
\(442\) | −7071.13 | − | 1594.97i | −0.760949 | − | 0.171640i | ||||
\(443\) | 11962.9 | 1.28301 | 0.641507 | − | 0.767117i | \(-0.278309\pi\) | ||||
0.641507 | + | 0.767117i | \(0.278309\pi\) | |||||||
\(444\) | −858.191 | + | 14799.9i | −0.0917296 | + | 1.58192i | ||||
\(445\) | −3864.67 | −0.411692 | ||||||||
\(446\) | −4077.28 | − | 919.674i | −0.432881 | − | 0.0976408i | ||||
\(447\) | 9730.84 | − | 3951.93i | 1.02965 | − | 0.418165i | ||||
\(448\) | −10128.4 | + | 2475.45i | −1.06813 | + | 0.261058i | ||||
\(449\) | − | 3582.84i | − | 0.376581i | −0.982113 | − | 0.188291i | \(-0.939705\pi\) | ||
0.982113 | − | 0.188291i | \(-0.0602947\pi\) | |||||||
\(450\) | −997.422 | − | 1627.93i | −0.104487 | − | 0.170536i | ||||
\(451\) | − | 4480.77i | − | 0.467830i | ||||||
\(452\) | −1549.68 | + | 3260.41i | −0.161263 | + | 0.339285i | ||||
\(453\) | 1273.89 | − | 517.356i | 0.132124 | − | 0.0536589i | ||||
\(454\) | −509.012 | + | 2256.65i | −0.0526192 | + | 0.233282i | ||||
\(455\) | 2820.99 | 0.290660 | ||||||||
\(456\) | 4153.33 | − | 14456.2i | 0.426529 | − | 1.48459i | ||||
\(457\) | −9998.12 | −1.02340 | −0.511699 | − | 0.859165i | \(-0.670984\pi\) | ||||
−0.511699 | + | 0.859165i | \(0.670984\pi\) | |||||||
\(458\) | 718.566 | − | 3185.69i | 0.0733109 | − | 0.325016i | ||||
\(459\) | 5214.38 | − | 11884.2i | 0.530253 | − | 1.20851i | ||||
\(460\) | 878.787 | − | 1848.90i | 0.0890731 | − | 0.187403i | ||||
\(461\) | 9035.94i | 0.912897i | 0.889750 | + | 0.456449i | \(0.150879\pi\) | ||||
−0.889750 | + | 0.456449i | \(0.849121\pi\) | |||||||
\(462\) | −747.205 | − | 4517.26i | −0.0752448 | − | 0.454896i | ||||
\(463\) | − | 2608.87i | − | 0.261867i | −0.991391 | − | 0.130933i | \(-0.958203\pi\) | ||
0.991391 | − | 0.130933i | \(-0.0417974\pi\) | |||||||
\(464\) | 4927.76 | − | 4012.72i | 0.493030 | − | 0.401478i | ||||
\(465\) | −252.293 | − | 621.221i | −0.0251608 | − | 0.0619536i | ||||
\(466\) | 10682.2 | + | 2409.49i | 1.06190 | + | 0.239522i | ||||
\(467\) | −9712.48 | −0.962398 | −0.481199 | − | 0.876611i | \(-0.659799\pi\) | ||||
−0.481199 | + | 0.876611i | \(0.659799\pi\) | |||||||
\(468\) | 5665.61 | − | 1927.03i | 0.559600 | − | 0.190336i | ||||
\(469\) | −6101.22 | −0.600700 | ||||||||
\(470\) | −7912.38 | − | 1784.72i | −0.776534 | − | 0.175155i | ||||
\(471\) | −4574.62 | − | 11264.1i | −0.447531 | − | 1.10196i | ||||
\(472\) | −4131.39 | + | 5262.74i | −0.402887 | + | 0.513214i | ||||
\(473\) | − | 7977.66i | − | 0.775504i | ||||||
\(474\) | −265.647 | − | 1605.98i | −0.0257417 | − | 0.155623i | ||||
\(475\) | 3198.15i | 0.308929i | ||||||||
\(476\) | 13610.8 | + | 6469.27i | 1.31061 | + | 0.622938i | ||||
\(477\) | 5756.23 | + | 5917.91i | 0.552536 | + | 0.568056i | ||||
\(478\) | 2750.11 | − | 12192.3i | 0.263153 | − | 1.16666i | ||||
\(479\) | 3430.18 | 0.327200 | 0.163600 | − | 0.986527i | \(-0.447689\pi\) | ||||
0.163600 | + | 0.986527i | \(0.447689\pi\) | |||||||
\(480\) | 3113.33 | − | 3524.99i | 0.296049 | − | 0.335194i | ||||
\(481\) | 9880.55 | 0.936620 | ||||||||
\(482\) | 815.589 | − | 3615.83i | 0.0770727 | − | 0.341694i | ||||
\(483\) | −5017.43 | + | 2037.70i | −0.472673 | + | 0.191964i | ||||
\(484\) | 7925.97 | + | 3767.24i | 0.744362 | + | 0.353798i | ||||
\(485\) | − | 130.577i | − | 0.0122251i | ||||||
\(486\) | 1455.06 | + | 10614.8i | 0.135808 | + | 0.990735i | ||||
\(487\) | − | 7275.39i | − | 0.676960i | −0.940974 | − | 0.338480i | \(-0.890087\pi\) | ||
0.940974 | − | 0.338480i | \(-0.109913\pi\) | |||||||
\(488\) | −4561.19 | + | 5810.23i | −0.423105 | + | 0.538969i | ||||
\(489\) | 7423.35 | − | 3014.80i | 0.686494 | − | 0.278802i | ||||
\(490\) | −989.175 | − | 223.119i | −0.0911966 | − | 0.0205704i | ||||
\(491\) | −17601.4 | −1.61780 | −0.808902 | − | 0.587944i | \(-0.799938\pi\) | ||||
−0.808902 | + | 0.587944i | \(0.799938\pi\) | |||||||
\(492\) | −12155.0 | − | 704.820i | −1.11380 | − | 0.0645849i | ||||
\(493\) | −9185.12 | −0.839102 | ||||||||
\(494\) | −9778.95 | − | 2205.75i | −0.890639 | − | 0.200893i | ||||
\(495\) | 1440.00 | + | 1480.44i | 0.130754 | + | 0.134426i | ||||
\(496\) | 1280.76 | − | 1042.93i | 0.115943 | − | 0.0944131i | ||||
\(497\) | 13314.9i | 1.20172i | ||||||||
\(498\) | −21456.6 | + | 3549.16i | −1.93071 | + | 0.319361i | ||||
\(499\) | − | 17324.8i | − | 1.55424i | −0.629355 | − | 0.777118i | \(-0.716681\pi\) | ||
0.629355 | − | 0.777118i | \(-0.283319\pi\) | |||||||
\(500\) | −429.280 | + | 903.171i | −0.0383960 | + | 0.0807821i | ||||
\(501\) | 295.440 | + | 727.462i | 0.0263459 | + | 0.0648715i | ||||
\(502\) | 3687.46 | − | 16348.0i | 0.327847 | − | 1.45348i | ||||
\(503\) | 17802.1 | 1.57805 | 0.789023 | − | 0.614364i | \(-0.210587\pi\) | ||||
0.789023 | + | 0.614364i | \(0.210587\pi\) | |||||||
\(504\) | −12371.5 | + | 1316.38i | −1.09339 | + | 0.116342i | ||||
\(505\) | 980.228 | 0.0863754 | ||||||||
\(506\) | −487.255 | + | 2160.19i | −0.0428085 | + | 0.189787i | ||||
\(507\) | 2794.78 | + | 6881.58i | 0.244813 | + | 0.602804i | ||||
\(508\) | −3673.89 | + | 7729.57i | −0.320871 | + | 0.675087i | ||||
\(509\) | 14138.0i | 1.23115i | 0.788078 | + | 0.615576i | \(0.211076\pi\) | ||||
−0.788078 | + | 0.615576i | \(0.788924\pi\) | |||||||
\(510\) | −6706.43 | + | 1109.32i | −0.582286 | + | 0.0963165i | ||||
\(511\) | − | 10267.4i | − | 0.888855i | ||||||
\(512\) | 10550.6 | + | 4785.65i | 0.910694 | + | 0.413082i | ||||
\(513\) | 7211.17 | − | 16435.1i | 0.620625 | − | 1.41448i | ||||
\(514\) | 12144.4 | + | 2739.30i | 1.04215 | + | 0.235069i | ||||
\(515\) | 3426.97 | 0.293224 | ||||||||
\(516\) | −21641.0 | − | 1254.88i | −1.84630 | − | 0.107060i | ||||
\(517\) | 8774.25 | 0.746404 | ||||||||
\(518\) | −20038.0 | − | 4519.78i | −1.69965 | − | 0.383374i | ||||
\(519\) | −21356.6 | + | 8673.44i | −1.80627 | + | 0.733568i | ||||
\(520\) | −2465.54 | − | 1935.52i | −0.207925 | − | 0.163227i | ||||
\(521\) | 3032.05i | 0.254965i | 0.991841 | + | 0.127482i | \(0.0406896\pi\) | ||||
−0.991841 | + | 0.127482i | \(0.959310\pi\) | |||||||
\(522\) | 6465.82 | − | 3961.57i | 0.542148 | − | 0.332171i | ||||
\(523\) | 12845.0i | 1.07394i | 0.843601 | + | 0.536971i | \(0.180432\pi\) | ||||
−0.843601 | + | 0.536971i | \(0.819568\pi\) | |||||||
\(524\) | 5261.09 | + | 2500.61i | 0.438610 | + | 0.208473i | ||||
\(525\) | 2450.98 | − | 995.401i | 0.203751 | − | 0.0827483i | ||||
\(526\) | −2728.70 | + | 12097.4i | −0.226192 | + | 1.00280i | ||||
\(527\) | −2387.27 | −0.197326 | ||||||||
\(528\) | −2446.29 | + | 4460.74i | −0.201631 | + | 0.367668i | ||||
\(529\) | −9547.82 | −0.784731 | ||||||||
\(530\) | 951.459 | − | 4218.20i | 0.0779788 | − | 0.345711i | ||||
\(531\) | −5722.87 | + | 5566.52i | −0.467705 | + | 0.454927i | ||||
\(532\) | 18823.0 | + | 8946.62i | 1.53398 | + | 0.729107i | ||||
\(533\) | 8114.76i | 0.659454i | ||||||||
\(534\) | −1853.84 | − | 11207.5i | −0.150231 | − | 0.908231i | ||||
\(535\) | 2519.03i | 0.203565i | ||||||||
\(536\) | 5332.45 | + | 4186.12i | 0.429714 | + | 0.337337i | ||||
\(537\) | −5101.55 | − | 12561.5i | −0.409959 | − | 1.00944i | ||||
\(538\) | 9346.22 | + | 2108.14i | 0.748967 | + | 0.168937i | ||||
\(539\) | 1096.92 | 0.0876582 | ||||||||
\(540\) | 4242.51 | − | 3673.41i | 0.338090 | − | 0.292738i | ||||
\(541\) | −11333.2 | −0.900654 | −0.450327 | − | 0.892864i | \(-0.648693\pi\) | ||||
−0.450327 | + | 0.892864i | \(0.648693\pi\) | |||||||
\(542\) | 11281.1 | + | 2544.56i | 0.894028 | + | 0.201657i | ||||
\(543\) | 2988.34 | + | 7358.18i | 0.236173 | + | 0.581528i | ||||
\(544\) | −7457.19 | − | 14992.7i | −0.587728 | − | 1.18163i | ||||
\(545\) | − | 4643.05i | − | 0.364929i | ||||||
\(546\) | 1353.20 | + | 8180.83i | 0.106065 | + | 0.641222i | ||||
\(547\) | 7995.82i | 0.625003i | 0.949917 | + | 0.312501i | \(0.101167\pi\) | ||||
−0.949917 | + | 0.312501i | \(0.898833\pi\) | |||||||
\(548\) | −4586.20 | + | 9648.99i | −0.357505 | + | 0.752162i | ||||
\(549\) | −6318.23 | + | 6145.61i | −0.491176 | + | 0.477757i | ||||
\(550\) | 238.020 | − | 1055.24i | 0.0184531 | − | 0.0818100i | ||||
\(551\) | −12702.5 | −0.982111 | ||||||||
\(552\) | 5783.31 | + | 1661.57i | 0.445931 | + | 0.128118i | ||||
\(553\) | 2255.51 | 0.173443 | ||||||||
\(554\) | −2169.00 | + | 9616.06i | −0.166340 | + | 0.737450i | ||||
\(555\) | 8584.55 | − | 3486.40i | 0.656566 | − | 0.266647i | ||||
\(556\) | 6891.99 | − | 14500.2i | 0.525693 | − | 1.10602i | ||||
\(557\) | 6218.87i | 0.473074i | 0.971623 | + | 0.236537i | \(0.0760124\pi\) | ||||
−0.971623 | + | 0.236537i | \(0.923988\pi\) | |||||||
\(558\) | 1680.51 | − | 1029.64i | 0.127494 | − | 0.0781147i | ||||
\(559\) | 14447.7i | 1.09315i | ||||||||
\(560\) | 4114.79 | + | 5053.12i | 0.310503 | + | 0.381309i | ||||
\(561\) | 6812.84 | − | 2766.86i | 0.512724 | − | 0.208230i | ||||
\(562\) | −12139.5 | − | 2738.20i | −0.911164 | − | 0.205523i | ||||
\(563\) | −7704.32 | −0.576729 | −0.288364 | − | 0.957521i | \(-0.593111\pi\) | ||||
−0.288364 | + | 0.957521i | \(0.593111\pi\) | |||||||
\(564\) | 1380.18 | − | 23801.9i | 0.103043 | − | 1.77702i | ||||
\(565\) | 2256.22 | 0.168000 | ||||||||
\(566\) | 1394.94 | + | 314.644i | 0.103593 | + | 0.0233666i | ||||
\(567\) | −14839.8 | − | 411.131i | −1.09914 | − | 0.0304513i | ||||
\(568\) | 9135.54 | − | 11637.2i | 0.674857 | − | 0.859661i | ||||
\(569\) | 4897.62i | 0.360841i | 0.983590 | + | 0.180421i | \(0.0577459\pi\) | ||||
−0.983590 | + | 0.180421i | \(0.942254\pi\) | |||||||
\(570\) | −9274.59 | + | 1534.12i | −0.681526 | + | 0.112732i | ||||
\(571\) | 7425.55i | 0.544220i | 0.962266 | + | 0.272110i | \(0.0877215\pi\) | ||||
−0.962266 | + | 0.272110i | \(0.912279\pi\) | |||||||
\(572\) | 3062.43 | + | 1455.58i | 0.223857 | + | 0.106400i | ||||
\(573\) | 1626.84 | + | 4005.76i | 0.118608 | + | 0.292047i | ||||
\(574\) | 3712.03 | − | 16456.9i | 0.269926 | − | 1.19669i | ||||
\(575\) | −1279.45 | −0.0927941 | ||||||||
\(576\) | 11715.8 | + | 7337.71i | 0.847500 | + | 0.530795i | ||||
\(577\) | −13212.1 | −0.953254 | −0.476627 | − | 0.879106i | \(-0.658141\pi\) | ||||
−0.476627 | + | 0.879106i | \(0.658141\pi\) | |||||||
\(578\) | −2267.72 | + | 10053.7i | −0.163191 | + | 0.723492i | ||||
\(579\) | −1289.16 | − | 3174.30i | −0.0925315 | − | 0.227840i | ||||
\(580\) | −3587.23 | − | 1705.02i | −0.256813 | − | 0.122064i | ||||
\(581\) | − | 30134.5i | − | 2.15179i | ||||||
\(582\) | 378.671 | − | 62.6363i | 0.0269698 | − | 0.00446110i | ||||
\(583\) | 4677.67i | 0.332297i | ||||||||
\(584\) | −7044.61 | + | 8973.72i | −0.499157 | + | 0.635848i | ||||
\(585\) | −2607.86 | − | 2681.11i | −0.184311 | − | 0.189488i | ||||
\(586\) | −17564.2 | − | 3961.80i | −1.23818 | − | 0.279284i | ||||
\(587\) | 7041.44 | 0.495113 | 0.247557 | − | 0.968873i | \(-0.420372\pi\) | ||||
0.247557 | + | 0.968873i | \(0.420372\pi\) | |||||||
\(588\) | 172.544 | − | 2975.62i | 0.0121014 | − | 0.208694i | ||||
\(589\) | −3301.45 | −0.230957 | ||||||||
\(590\) | 4079.18 | + | 920.101i | 0.284639 | + | 0.0642033i | ||||
\(591\) | 4637.76 | − | 1883.51i | 0.322795 | − | 0.131095i | ||||
\(592\) | 14412.1 | + | 17698.6i | 1.00056 | + | 1.22873i | ||||
\(593\) | 18675.4i | 1.29326i | 0.762802 | + | 0.646632i | \(0.223823\pi\) | ||||
−0.762802 | + | 0.646632i | \(0.776177\pi\) | |||||||
\(594\) | −3602.51 | + | 4886.12i | −0.248843 | + | 0.337508i | ||||
\(595\) | − | 9418.77i | − | 0.648962i | ||||||
\(596\) | 6941.46 | − | 14604.3i | 0.477069 | − | 1.00371i | ||||
\(597\) | 4190.77 | − | 1701.97i | 0.287298 | − | 0.116679i | ||||
\(598\) | 882.426 | − | 3912.15i | 0.0603430 | − | 0.267524i | ||||
\(599\) | 8073.52 | 0.550709 | 0.275355 | − | 0.961343i | \(-0.411205\pi\) | ||||
0.275355 | + | 0.961343i | \(0.411205\pi\) | |||||||
\(600\) | −2825.10 | − | 811.664i | −0.192224 | − | 0.0552268i | ||||
\(601\) | 8290.31 | 0.562677 | 0.281338 | − | 0.959609i | \(-0.409222\pi\) | ||||
0.281338 | + | 0.959609i | \(0.409222\pi\) | |||||||
\(602\) | 6608.98 | − | 29300.2i | 0.447445 | − | 1.98370i | ||||
\(603\) | 5640.26 | + | 5798.68i | 0.380910 | + | 0.391610i | ||||
\(604\) | 908.722 | − | 1911.88i | 0.0612175 | − | 0.128797i | ||||
\(605\) | − | 5484.82i | − | 0.368578i | ||||||
\(606\) | 470.205 | + | 2842.64i | 0.0315194 | + | 0.190552i | ||||
\(607\) | 15779.1i | 1.05511i | 0.849521 | + | 0.527556i | \(0.176891\pi\) | ||||
−0.849521 | + | 0.527556i | \(0.823109\pi\) | |||||||
\(608\) | −10312.8 | − | 20734.0i | −0.687896 | − | 1.38302i | ||||
\(609\) | 3953.54 | + | 9734.82i | 0.263064 | + | 0.647742i | ||||
\(610\) | 4503.54 | + | 1015.82i | 0.298923 | + | 0.0674252i | ||||
\(611\) | −15890.3 | −1.05213 | ||||||||
\(612\) | −6434.00 | − | 18916.4i | −0.424966 | − | 1.24943i | ||||
\(613\) | 27380.0 | 1.80403 | 0.902014 | − | 0.431708i | \(-0.142089\pi\) | ||||
0.902014 | + | 0.431708i | \(0.142089\pi\) | |||||||
\(614\) | 20388.6 | + | 4598.86i | 1.34009 | + | 0.302272i | ||||
\(615\) | 2863.33 | + | 7050.38i | 0.187741 | + | 0.462274i | ||||
\(616\) | −5544.83 | − | 4352.84i | −0.362675 | − | 0.284709i | ||||
\(617\) | − | 212.657i | − | 0.0138756i | −0.999976 | − | 0.00693782i | \(-0.997792\pi\) | ||
0.999976 | − | 0.00693782i | \(-0.00220839\pi\) | |||||||
\(618\) | 1643.88 | + | 9938.14i | 0.107001 | + | 0.646878i | ||||
\(619\) | − | 19326.6i | − | 1.25493i | −0.778645 | − | 0.627465i | \(-0.784092\pi\) | ||
0.778645 | − | 0.627465i | \(-0.215908\pi\) | |||||||
\(620\) | −932.342 | − | 443.145i | −0.0603932 | − | 0.0287051i | ||||
\(621\) | 6575.00 | + | 2884.88i | 0.424872 | + | 0.186419i | ||||
\(622\) | 1014.73 | − | 4498.70i | 0.0654131 | − | 0.290002i | ||||
\(623\) | 15740.2 | 1.01223 | ||||||||
\(624\) | 4430.27 | − | 8078.47i | 0.284219 | − | 0.518266i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 3685.63 | − | 16339.8i | 0.235315 | − | 1.04325i | ||||
\(627\) | 9421.75 | − | 3826.40i | 0.600109 | − | 0.243719i | ||||
\(628\) | −16905.4 | − | 8035.20i | −1.07420 | − | 0.510572i | ||||
\(629\) | − | 32989.3i | − | 2.09121i | ||||||
\(630\) | 4062.35 | + | 6630.30i | 0.256901 | + | 0.419298i | ||||
\(631\) | 13797.7i | 0.870486i | 0.900313 | + | 0.435243i | \(0.143338\pi\) | ||||
−0.900313 | + | 0.435243i | \(0.856662\pi\) | |||||||
\(632\) | −1971.31 | − | 1547.53i | −0.124073 | − | 0.0974009i | ||||
\(633\) | −493.577 | + | 200.454i | −0.0309920 | + | 0.0125866i | ||||
\(634\) | −21544.1 | − | 4859.51i | −1.34957 | − | 0.304410i | ||||
\(635\) | 5348.91 | 0.334276 | ||||||||
\(636\) | 12689.1 | + | 735.792i | 0.791125 | + | 0.0458743i | ||||
\(637\) | −1986.54 | −0.123563 | ||||||||
\(638\) | 4191.21 | + | 945.372i | 0.260081 | + | 0.0586640i | ||||
\(639\) | 12654.7 | − | 12309.0i | 0.783431 | − | 0.762027i | ||||
\(640\) | −129.317 | − | 7239.62i | −0.00798702 | − | 0.447142i | ||||
\(641\) | 25984.0i | 1.60110i | 0.599264 | + | 0.800552i | \(0.295460\pi\) | ||||
−0.599264 | + | 0.800552i | \(0.704540\pi\) | |||||||
\(642\) | −7305.15 | + | 1208.35i | −0.449083 | + | 0.0742833i | ||||
\(643\) | 29221.5i | 1.79220i | 0.443853 | + | 0.896099i | \(0.353611\pi\) | ||||
−0.443853 | + | 0.896099i | \(0.646389\pi\) | |||||||
\(644\) | −3579.16 | + | 7530.27i | −0.219004 | + | 0.460768i | ||||
\(645\) | 5097.93 | + | 12552.6i | 0.311210 | + | 0.766294i | ||||
\(646\) | −7364.58 | + | 32650.1i | −0.448538 | + | 1.98855i | ||||
\(647\) | 3210.39 | 0.195075 | 0.0975375 | − | 0.995232i | \(-0.468903\pi\) | ||||
0.0975375 | + | 0.995232i | \(0.468903\pi\) | |||||||
\(648\) | 12687.9 | + | 10541.1i | 0.769179 | + | 0.639034i | ||||
\(649\) | −4523.50 | −0.273595 | ||||||||
\(650\) | −431.058 | + | 1911.05i | −0.0260115 | + | 0.115320i | ||||
\(651\) | 1027.55 | + | 2530.14i | 0.0618631 | + | 0.152326i | ||||
\(652\) | 5295.42 | − | 11141.1i | 0.318074 | − | 0.669203i | ||||
\(653\) | − | 1248.39i | − | 0.0748136i | −0.999300 | − | 0.0374068i | \(-0.988090\pi\) | ||
0.999300 | − | 0.0374068i | \(-0.0119097\pi\) | |||||||
\(654\) | 13464.8 | − | 2227.22i | 0.805067 | − | 0.133167i | ||||
\(655\) | − | 3640.70i | − | 0.217182i | ||||||
\(656\) | −14535.6 | + | 11836.4i | −0.865121 | + | 0.704475i | ||||
\(657\) | −9758.31 | + | 9491.70i | −0.579464 | + | 0.563633i | ||||
\(658\) | 32225.9 | + | 7268.90i | 1.90927 | + | 0.430655i | ||||
\(659\) | −9138.61 | −0.540197 | −0.270098 | − | 0.962833i | \(-0.587056\pi\) | ||||
−0.270098 | + | 0.962833i | \(0.587056\pi\) | |||||||
\(660\) | 3174.35 | + | 184.068i | 0.187214 | + | 0.0108558i | ||||
\(661\) | 4756.08 | 0.279864 | 0.139932 | − | 0.990161i | \(-0.455312\pi\) | ||||
0.139932 | + | 0.990161i | \(0.455312\pi\) | |||||||
\(662\) | 4329.18 | + | 976.492i | 0.254166 | + | 0.0573299i | ||||
\(663\) | −12338.2 | + | 5010.83i | −0.722737 | + | 0.293521i | ||||
\(664\) | −20675.6 | + | 26337.5i | −1.20839 | + | 1.53930i | ||||
\(665\) | − | 13025.6i | − | 0.759566i | ||||||
\(666\) | 14228.4 | + | 23222.7i | 0.827837 | + | 1.35114i | ||||
\(667\) | − | 5081.72i | − | 0.295000i | ||||||
\(668\) | 1091.79 | + | 518.933i | 0.0632376 | + | 0.0300570i | ||||
\(669\) | −7114.30 | + | 2889.29i | −0.411143 | + | 0.166975i | ||||
\(670\) | 932.289 | − | 4133.21i | 0.0537574 | − | 0.238328i | ||||
\(671\) | −4994.09 | −0.287324 | ||||||||
\(672\) | −12680.1 | + | 14356.8i | −0.727897 | + | 0.824143i | ||||
\(673\) | −23520.9 | −1.34720 | −0.673598 | − | 0.739098i | \(-0.735252\pi\) | ||||
−0.673598 | + | 0.739098i | \(0.735252\pi\) | |||||||
\(674\) | 4038.23 | − | 17903.1i | 0.230782 | − | 1.02315i | ||||
\(675\) | −3211.84 | − | 1409.24i | −0.183146 | − | 0.0803583i | ||||
\(676\) | 10328.0 | + | 4908.95i | 0.587621 | + | 0.279299i | ||||
\(677\) | 3924.98i | 0.222820i | 0.993775 | + | 0.111410i | \(0.0355367\pi\) | ||||
−0.993775 | + | 0.111410i | \(0.964463\pi\) | |||||||
\(678\) | 1082.28 | + | 6543.00i | 0.0613051 | + | 0.370623i | ||||
\(679\) | 531.820i | 0.0300580i | ||||||||
\(680\) | −6462.33 | + | 8231.98i | −0.364440 | + | 0.464239i | ||||
\(681\) | 1599.14 | + | 3937.56i | 0.0899840 | + | 0.221568i | ||||
\(682\) | 1089.32 | + | 245.708i | 0.0611616 | + | 0.0137957i | ||||
\(683\) | −2097.25 | −0.117495 | −0.0587473 | − | 0.998273i | \(-0.518711\pi\) | ||||
−0.0587473 | + | 0.998273i | \(0.518711\pi\) | |||||||
\(684\) | −8897.84 | − | 26160.3i | −0.497394 | − | 1.46237i | ||||
\(685\) | 6677.16 | 0.372440 | ||||||||
\(686\) | −15243.4 | − | 3438.32i | −0.848393 | − | 0.191364i | ||||
\(687\) | −2257.48 | − | 5558.60i | −0.125369 | − | 0.308695i | ||||
\(688\) | −25879.5 | + | 21073.8i | −1.43408 | + | 1.16778i | ||||
\(689\) | − | 8471.34i | − | 0.468407i | ||||||
\(690\) | −613.737 | − | 3710.37i | −0.0338617 | − | 0.204712i | ||||
\(691\) | − | 595.762i | − | 0.0327987i | −0.999866 | − | 0.0163993i | \(-0.994780\pi\) | ||
0.999866 | − | 0.0163993i | \(-0.00522030\pi\) | |||||||
\(692\) | −15234.7 | + | 32052.5i | −0.836901 | + | 1.76077i | ||||
\(693\) | −5864.89 | − | 6029.63i | −0.321485 | − | 0.330515i | ||||
\(694\) | 370.669 | − | 1643.32i | 0.0202744 | − | 0.0898843i | ||||
\(695\) | −10034.2 | −0.547654 | ||||||||
\(696\) | 3223.78 | − | 11220.8i | 0.175570 | − | 0.611095i | ||||
\(697\) | 27093.7 | 1.47238 | ||||||||
\(698\) | 5824.03 | − | 25820.3i | 0.315821 | − | 1.40016i | ||||
\(699\) | 18639.0 | − | 7569.75i | 1.00857 | − | 0.409606i | ||||
\(700\) | 1748.39 | − | 3678.48i | 0.0944044 | − | 0.198619i | ||||
\(701\) | − | 9077.51i | − | 0.489091i | −0.969638 | − | 0.244545i | \(-0.921361\pi\) | ||
0.969638 | − | 0.244545i | \(-0.0786387\pi\) | |||||||
\(702\) | 6524.21 | − | 8848.85i | 0.350770 | − | 0.475752i | ||||
\(703\) | − | 45622.2i | − | 2.44762i | ||||||
\(704\) | 1859.64 | + | 7608.74i | 0.0995563 | + | 0.407337i | ||||
\(705\) | −13806.0 | + | 5606.96i | −0.737539 | + | 0.299533i | ||||
\(706\) | −1582.85 | − | 357.030i | −0.0843789 | − | 0.0190326i | ||||
\(707\) | −3992.32 | −0.212371 | ||||||||
\(708\) | −711.542 | + | 12270.9i | −0.0377703 | + | 0.651368i | ||||
\(709\) | −8539.10 | −0.452317 | −0.226158 | − | 0.974091i | \(-0.572617\pi\) | ||||
−0.226158 | + | 0.974091i | \(0.572617\pi\) | |||||||
\(710\) | −9020.07 | − | 2034.57i | −0.476785 | − | 0.107544i | ||||
\(711\) | −2085.10 | − | 2143.66i | −0.109982 | − | 0.113071i | ||||
\(712\) | −13756.9 | − | 10799.5i | −0.724104 | − | 0.568441i | ||||
\(713\) | − | 1320.77i | − | 0.0693734i | ||||||
\(714\) | 27314.3 | − | 4518.08i | 1.43167 | − | 0.236814i | ||||
\(715\) | − | 2119.22i | − | 0.110845i | ||||||
\(716\) | −18852.6 | − | 8960.73i | −0.984018 | − | 0.467707i | ||||
\(717\) | −8639.89 | − | 21274.0i | −0.450017 | − | 1.10808i | ||||
\(718\) | −5426.06 | + | 24055.9i | −0.282032 | + | 1.25036i | ||||
\(719\) | −17913.1 | −0.929130 | −0.464565 | − | 0.885539i | \(-0.653789\pi\) | ||||
−0.464565 | + | 0.885539i | \(0.653789\pi\) | |||||||
\(720\) | 998.642 | − | 8582.09i | 0.0516905 | − | 0.444216i | ||||
\(721\) | −13957.5 | −0.720950 | ||||||||
\(722\) | −5916.09 | + | 26228.4i | −0.304950 | + | 1.35197i | ||||
\(723\) | −2562.29 | − | 6309.13i | −0.131802 | − | 0.324536i | ||||
\(724\) | 11043.3 | + | 5248.93i | 0.566881 | + | 0.269441i | ||||
\(725\) | 2482.38i | 0.127163i | ||||||||
\(726\) | 15905.9 | − | 2631.01i | 0.813116 | − | 0.134498i | ||||
\(727\) | − | 32276.8i | − | 1.64660i | −0.567605 | − | 0.823301i | \(-0.692130\pi\) | ||
0.567605 | − | 0.823301i | \(-0.307870\pi\) | |||||||
\(728\) | 10041.8 | + | 7883.06i | 0.511227 | + | 0.401327i | ||||
\(729\) | 13327.9 | + | 14484.0i | 0.677127 | + | 0.735866i | ||||
\(730\) | 6955.57 | + | 1568.90i | 0.352654 | + | 0.0795448i | ||||
\(731\) | 48238.1 | 2.44070 | ||||||||
\(732\) | −785.564 | + | 13547.5i | −0.0396657 | + | 0.684055i | ||||
\(733\) | 12015.9 | 0.605481 | 0.302740 | − | 0.953073i | \(-0.402099\pi\) | ||||
0.302740 | + | 0.953073i | \(0.402099\pi\) | |||||||
\(734\) | 10834.3 | + | 2443.80i | 0.544827 | + | 0.122891i | ||||
\(735\) | −1725.98 | + | 700.961i | −0.0866171 | + | 0.0351773i | ||||
\(736\) | 8294.78 | − | 4125.73i | 0.415421 | − | 0.206626i | ||||
\(737\) | 4583.42i | 0.229081i | ||||||||
\(738\) | −19072.5 | + | 11685.6i | −0.951310 | + | 0.582862i | ||||
\(739\) | − | 18920.3i | − | 0.941804i | −0.882185 | − | 0.470902i | \(-0.843928\pi\) | ||
0.882185 | − | 0.470902i | \(-0.156072\pi\) | |||||||
\(740\) | 6123.76 | − | 12883.9i | 0.304208 | − | 0.640029i | ||||
\(741\) | −17062.9 | + | 6929.68i | −0.845915 | + | 0.343547i | ||||
\(742\) | −3875.15 | + | 17180.1i | −0.191727 | + | 0.850001i | ||||
\(743\) | −32431.7 | −1.60135 | −0.800676 | − | 0.599097i | \(-0.795526\pi\) | ||||
−0.800676 | + | 0.599097i | \(0.795526\pi\) | |||||||
\(744\) | 837.880 | − | 2916.35i | 0.0412878 | − | 0.143708i | ||||
\(745\) | −10106.2 | −0.496999 | ||||||||
\(746\) | 3285.30 | − | 14565.0i | 0.161238 | − | 0.714831i | ||||
\(747\) | −28640.3 | + | 27857.8i | −1.40280 | + | 1.36448i | ||||
\(748\) | 4859.92 | − | 10224.9i | 0.237562 | − | 0.499810i | ||||
\(749\) | − | 10259.6i | − | 0.500506i | ||||||
\(750\) | 299.806 | + | 1812.49i | 0.0145965 | + | 0.0882437i | ||||
\(751\) | − | 23544.8i | − | 1.14402i | −0.820245 | − | 0.572012i | \(-0.806163\pi\) | ||
0.820245 | − | 0.572012i | \(-0.193837\pi\) | |||||||
\(752\) | −23178.1 | − | 28463.6i | −1.12396 | − | 1.38027i | ||||
\(753\) | −11584.7 | − | 28525.0i | −0.560650 | − | 1.38049i | ||||
\(754\) | −7590.35 | − | 1712.08i | −0.366610 | − | 0.0826928i | ||||
\(755\) | −1323.03 | −0.0637748 | ||||||||
\(756\) | −17279.1 | + | 14961.2i | −0.831263 | + | 0.719755i | ||||
\(757\) | 11963.2 | 0.574388 | 0.287194 | − | 0.957872i | \(-0.407278\pi\) | ||||
0.287194 | + | 0.957872i | \(0.407278\pi\) | |||||||
\(758\) | 3183.95 | + | 718.173i | 0.152568 | + | 0.0344132i | ||||
\(759\) | 1530.78 | + | 3769.25i | 0.0732067 | + | 0.180257i | ||||
\(760\) | −8937.01 | + | 11384.3i | −0.426552 | + | 0.543360i | ||||
\(761\) | 2168.96i | 0.103318i | 0.998665 | + | 0.0516588i | \(0.0164508\pi\) | ||||
−0.998665 | + | 0.0516588i | \(0.983549\pi\) | |||||||
\(762\) | 2565.82 | + | 15511.8i | 0.121981 | + | 0.737443i | ||||
\(763\) | 18910.4i | 0.897252i | ||||||||
\(764\) | 6011.94 | + | 2857.50i | 0.284692 | + | 0.135315i | ||||
\(765\) | −8951.73 | + | 8707.16i | −0.423072 | + | 0.411514i | ||||
\(766\) | 4002.47 | − | 17744.5i | 0.188793 | − | 0.836993i | ||||
\(767\) | 8192.14 | 0.385660 | ||||||||
\(768\) | 20932.7 | − | 3847.78i | 0.983522 | − | 0.180788i | ||||
\(769\) | 6990.21 | 0.327794 | 0.163897 | − | 0.986477i | \(-0.447594\pi\) | ||||
0.163897 | + | 0.986477i | \(0.447594\pi\) | |||||||
\(770\) | −969.420 | + | 4297.83i | −0.0453707 | + | 0.201147i | ||||
\(771\) | 21190.4 | − | 8605.92i | 0.989821 | − | 0.401990i | ||||
\(772\) | −4764.07 | − | 2264.38i | −0.222102 | − | 0.105566i | ||||
\(773\) | 15944.4i | 0.741887i | 0.928655 | + | 0.370944i | \(0.120966\pi\) | ||||
−0.928655 | + | 0.370944i | \(0.879034\pi\) | |||||||
\(774\) | −33957.0 | + | 20805.3i | −1.57695 | + | 0.966188i | ||||
\(775\) | 645.186i | 0.0299042i | ||||||||
\(776\) | 364.888 | − | 464.809i | 0.0168798 | − | 0.0215022i | ||||
\(777\) | −34963.6 | + | 14199.6i | −1.61430 | + | 0.655607i | ||||
\(778\) | −27472.3 | − | 6196.66i | −1.26597 | − | 0.285554i | ||||
\(779\) | 37468.9 | 1.72332 | ||||||||
\(780\) | −5748.80 | − | 333.350i | −0.263897 | − | 0.0153024i | ||||
\(781\) | 10002.6 | 0.458286 | ||||||||
\(782\) | −13061.9 | − | 2946.26i | −0.597306 | − | 0.134729i | ||||
\(783\) | 5597.25 | − | 12756.8i | 0.255466 | − | 0.582237i | ||||
\(784\) | −2897.64 | − | 3558.40i | −0.131999 | − | 0.162099i | ||||
\(785\) | 11698.6i | 0.531901i | ||||||||
\(786\) | 10558.0 | − | 1746.41i | 0.479123 | − | 0.0792522i | ||||
\(787\) | − | 13904.9i | − | 0.629803i | −0.949124 | − | 0.314901i | \(-0.898029\pi\) | ||
0.949124 | − | 0.314901i | \(-0.101971\pi\) | |||||||
\(788\) | 3308.33 | − | 6960.46i | 0.149561 | − | 0.314665i | ||||
\(789\) | 8572.61 | + | 21108.3i | 0.386810 | + | 0.952442i | ||||
\(790\) | −344.650 | + | 1527.97i | −0.0155216 | + | 0.0688136i | ||||
\(791\) | −9189.25 | −0.413062 | ||||||||
\(792\) | 988.906 | + | 9293.85i | 0.0443677 | + | 0.416973i | ||||
\(793\) | 9044.38 | 0.405013 | ||||||||
\(794\) | −6935.19 | + | 30746.5i | −0.309976 | + | 1.37425i | ||||
\(795\) | −2989.15 | − | 7360.18i | −0.133351 | − | 0.328351i | ||||
\(796\) | 2989.47 | − | 6289.60i | 0.133114 | − | 0.280061i | ||||
\(797\) | − | 6202.60i | − | 0.275668i | −0.990455 | − | 0.137834i | \(-0.955986\pi\) | ||
0.990455 | − | 0.137834i | \(-0.0440140\pi\) | |||||||
\(798\) | 37774.0 | − | 6248.24i | 1.67567 | − | 0.277174i | ||||
\(799\) | 53054.8i | 2.34911i | ||||||||
\(800\) | −4051.94 | + | 2015.39i | −0.179072 | + | 0.0890684i | ||||
\(801\) | −14551.0 | − | 14959.7i | −0.641866 | − | 0.659894i | ||||
\(802\) | 11162.8 | + | 2517.90i | 0.491488 | + | 0.110860i | ||||
\(803\) | −7713.22 | −0.338971 | ||||||||
\(804\) | 12433.4 | + | 720.967i | 0.545390 | + | 0.0316251i | ||||
\(805\) | 5210.99 | 0.228153 | ||||||||
\(806\) | −1972.78 | − | 444.981i | −0.0862135 | − | 0.0194464i | ||||
\(807\) | 16307.9 | − | 6623.03i | 0.711357 | − | 0.288899i | ||||
\(808\) | 3489.28 | + | 2739.18i | 0.151921 | + | 0.119262i | ||||
\(809\) | − | 16847.6i | − | 0.732175i | −0.930580 | − | 0.366088i | \(-0.880697\pi\) | ||
0.930580 | − | 0.366088i | \(-0.119303\pi\) | |||||||
\(810\) | 2546.10 | − | 9990.27i | 0.110445 | − | 0.433361i | ||||
\(811\) | 33782.0i | 1.46270i | 0.682004 | + | 0.731348i | \(0.261109\pi\) | ||||
−0.682004 | + | 0.731348i | \(0.738891\pi\) | |||||||
\(812\) | 14610.2 | + | 6944.30i | 0.631427 | + | 0.300119i | ||||
\(813\) | 19683.9 | − | 7994.12i | 0.849133 | − | 0.344854i | ||||
\(814\) | −3395.40 | + | 15053.2i | −0.146202 | + | 0.648173i | ||||
\(815\) | −7709.73 | −0.331362 | ||||||||
\(816\) | −26972.5 | − | 14791.8i | −1.15714 | − | 0.634581i | ||||
\(817\) | 66710.4 | 2.85667 | ||||||||
\(818\) | 8034.39 | − | 35619.6i | 0.343418 | − | 1.52251i | ||||
\(819\) | 10621.4 | + | 10919.8i | 0.453165 | + | 0.465894i | ||||
\(820\) | 10581.4 | + | 5029.36i | 0.450631 | + | 0.214186i | ||||
\(821\) | 26588.7i | 1.13027i | 0.824998 | + | 0.565135i | \(0.191176\pi\) | ||||
−0.824998 | + | 0.565135i | \(0.808824\pi\) | |||||||
\(822\) | 3202.96 | + | 19363.7i | 0.135908 | + | 0.821636i | ||||
\(823\) | − | 33619.7i | − | 1.42395i | −0.702205 | − | 0.711975i | \(-0.747801\pi\) | ||
0.702205 | − | 0.711975i | \(-0.252199\pi\) | |||||||
\(824\) | 12198.8 | + | 9576.41i | 0.515736 | + | 0.404867i | ||||
\(825\) | −747.775 | − | 1841.25i | −0.0315566 | − | 0.0777018i | ||||
\(826\) | −16613.9 | − | 3747.43i | −0.699843 | − | 0.157857i | ||||
\(827\) | 27338.2 | 1.14951 | 0.574753 | − | 0.818327i | \(-0.305098\pi\) | ||||
0.574753 | + | 0.818327i | \(0.305098\pi\) | |||||||
\(828\) | 10465.6 | − | 3559.65i | 0.439258 | − | 0.149404i | ||||
\(829\) | 18514.6 | 0.775680 | 0.387840 | − | 0.921727i | \(-0.373221\pi\) | ||||
0.387840 | + | 0.921727i | \(0.373221\pi\) | |||||||
\(830\) | 20414.3 | + | 4604.67i | 0.853725 | + | 0.192567i | ||||
\(831\) | 6814.24 | + | 16778.7i | 0.284457 | + | 0.700418i | ||||
\(832\) | −3367.83 | − | 13779.6i | −0.140335 | − | 0.574183i | ||||
\(833\) | 6632.70i | 0.275882i | ||||||||
\(834\) | −4813.30 | − | 29099.0i | −0.199845 | − | 1.20817i | ||||
\(835\) | − | 755.527i | − | 0.0313127i | ||||||
\(836\) | 6720.97 | − | 14140.4i | 0.278050 | − | 0.584994i | ||||
\(837\) | 1454.76 | − | 3315.57i | 0.0600763 | − | 0.136921i | ||||
\(838\) | −264.785 | + | 1173.90i | −0.0109151 | + | 0.0483909i | ||||
\(839\) | −42265.2 | −1.73916 | −0.869580 | − | 0.493792i | \(-0.835610\pi\) | ||||
−0.869580 | + | 0.493792i | \(0.835610\pi\) | |||||||
\(840\) | 11506.2 | + | 3305.79i | 0.472622 | + | 0.135786i | ||||
\(841\) | 14529.4 | 0.595737 | ||||||||
\(842\) | −3950.57 | + | 17514.5i | −0.161693 | + | 0.716851i | ||||
\(843\) | −21181.8 | + | 8602.44i | −0.865409 | + | 0.351464i | ||||
\(844\) | −352.091 | + | 740.772i | −0.0143596 | + | 0.0302114i | ||||
\(845\) | − | 7147.06i | − | 0.290966i | ||||||
\(846\) | −22882.7 | − | 37347.7i | −0.929933 | − | 1.51778i | ||||
\(847\) | 22338.8i | 0.906224i | ||||||||
\(848\) | 15174.3 | − | 12356.6i | 0.614491 | − | 0.500385i | ||||
\(849\) | 2433.99 | − | 988.501i | 0.0983913 | − | 0.0399591i | ||||
\(850\) | 6380.65 | + | 1439.22i | 0.257476 | + | 0.0580764i | ||||
\(851\) | 18251.5 | 0.735199 | ||||||||
\(852\) | 1573.40 | − | 27134.0i | 0.0632672 | − | 1.09108i | ||||
\(853\) | −39949.7 | −1.60358 | −0.801789 | − | 0.597607i | \(-0.796118\pi\) | ||||
−0.801789 | + | 0.597607i | \(0.796118\pi\) | |||||||
\(854\) | −18342.2 | − | 4137.28i | −0.734963 | − | 0.165779i | ||||
\(855\) | −12379.7 | + | 12041.5i | −0.495177 | + | 0.481649i | ||||
\(856\) | −7039.25 | + | 8966.89i | −0.281071 | + | 0.358040i | ||||
\(857\) | − | 35527.4i | − | 1.41609i | −0.706165 | − | 0.708047i | \(-0.749576\pi\) | ||
0.706165 | − | 0.708047i | \(-0.250424\pi\) | |||||||
\(858\) | 6145.69 | − | 1016.57i | 0.244534 | − | 0.0404487i | ||||
\(859\) | 15149.2i | 0.601728i | 0.953667 | + | 0.300864i | \(0.0972750\pi\) | ||||
−0.953667 | + | 0.300864i | \(0.902725\pi\) | |||||||
\(860\) | 18839.3 | + | 8954.37i | 0.746993 | + | 0.355048i | ||||
\(861\) | −11661.9 | − | 28715.1i | −0.461599 | − | 1.13660i | ||||
\(862\) | 9069.01 | − | 40206.5i | 0.358343 | − | 1.58868i | ||||
\(863\) | 3598.72 | 0.141949 | 0.0709744 | − | 0.997478i | \(-0.477389\pi\) | ||||
0.0709744 | + | 0.997478i | \(0.477389\pi\) | |||||||
\(864\) | 25367.0 | − | 1220.69i | 0.998844 | − | 0.0480657i | ||||
\(865\) | 22180.5 | 0.871862 | ||||||||
\(866\) | −5237.82 | + | 23221.4i | −0.205529 | + | 0.911194i | ||||
\(867\) | 7124.36 | + | 17542.3i | 0.279073 | + | 0.687161i | ||||
\(868\) | 3797.29 | + | 1804.86i | 0.148489 | + | 0.0705773i | ||||
\(869\) | − | 1694.40i | − | 0.0661436i | ||||||
\(870\) | −7198.87 | + | 1190.77i | −0.280534 | + | 0.0464034i | ||||
\(871\) | − | 8300.66i | − | 0.322913i | ||||||
\(872\) | 12974.7 | − | 16527.7i | 0.503873 | − | 0.641855i | ||||
\(873\) | 505.449 | − | 491.640i | 0.0195955 | − | 0.0190601i | ||||
\(874\) | −18063.9 | − | 4074.50i | −0.699107 | − | 0.157691i | ||||
\(875\) | −2545.53 | −0.0983482 | ||||||||
\(876\) | −1213.28 | + | 20923.6i | −0.0467956 | + | 0.807013i | ||||
\(877\) | −47342.6 | −1.82286 | −0.911428 | − | 0.411459i | \(-0.865019\pi\) | ||||
−0.911428 | + | 0.411459i | \(0.865019\pi\) | |||||||
\(878\) | 29860.6 | + | 6735.38i | 1.14778 | + | 0.258893i | ||||
\(879\) | −30647.2 | + | 12446.6i | −1.17600 | + | 0.477603i | ||||
\(880\) | 3796.06 | − | 3091.16i | 0.145415 | − | 0.118412i | ||||
\(881\) | 5694.16i | 0.217754i | 0.994055 | + | 0.108877i | \(0.0347254\pi\) | ||||
−0.994055 | + | 0.108877i | \(0.965275\pi\) | |||||||
\(882\) | −2860.71 | − | 4669.06i | −0.109212 | − | 0.178249i | ||||
\(883\) | − | 1161.20i | − | 0.0442555i | −0.999755 | − | 0.0221278i | \(-0.992956\pi\) | ||
0.999755 | − | 0.0221278i | \(-0.00704406\pi\) | |||||||
\(884\) | −8801.39 | + | 18517.4i | −0.334867 | + | 0.704534i | ||||
\(885\) | 7117.61 | − | 2890.63i | 0.270346 | − | 0.109794i | ||||
\(886\) | 7445.08 | − | 33007.0i | 0.282305 | − | 1.25157i | ||||
\(887\) | 1024.65 | 0.0387874 | 0.0193937 | − | 0.999812i | \(-0.493826\pi\) | ||||
0.0193937 | + | 0.999812i | \(0.493826\pi\) | |||||||
\(888\) | 40300.6 | + | 11578.5i | 1.52297 | + | 0.437556i | ||||
\(889\) | −21785.3 | −0.821885 | ||||||||
\(890\) | −2405.16 | + | 10663.1i | −0.0905857 | + | 0.401603i | ||||
\(891\) | −308.854 | + | 11148.1i | −0.0116128 | + | 0.419166i | ||||
\(892\) | −5074.96 | + | 10677.3i | −0.190496 | + | 0.400788i | ||||
\(893\) | 73371.5i | 2.74948i | ||||||||
\(894\) | −4847.85 | − | 29307.9i | −0.181361 | − | 1.09642i | ||||
\(895\) | 13046.1i | 0.487245i | ||||||||
\(896\) | 526.688 | + | 29485.9i | 0.0196377 | + | 1.09939i | ||||
\(897\) | −2772.27 | − | 6826.17i | −0.103192 | − | 0.254090i | ||||
\(898\) | −9885.46 | − | 2229.77i | −0.367352 | − | 0.0828601i | ||||
\(899\) | −2562.56 | −0.0950680 | ||||||||
\(900\) | −5112.37 | + | 1738.86i | −0.189347 | + | 0.0644023i | ||||
\(901\) | −28284.2 | −1.04582 | ||||||||
\(902\) | −12362.9 | − | 2788.59i | −0.456365 | − | 0.102938i | ||||
\(903\) | −20763.1 | − | 51125.0i | −0.765174 | − | 1.88409i | ||||
\(904\) | 8031.38 | + | 6304.85i | 0.295486 | + | 0.231965i | ||||
\(905\) | − | 7642.05i | − | 0.280697i | ||||||
\(906\) | −634.643 | − | 3836.76i | −0.0232722 | − | 0.140693i | ||||
\(907\) | 6399.77i | 0.234290i | 0.993115 | + | 0.117145i | \(0.0373742\pi\) | ||||
−0.993115 | + | 0.117145i | \(0.962626\pi\) | |||||||
\(908\) | 5909.58 | + | 2808.84i | 0.215987 | + | 0.102659i | ||||
\(909\) | 3690.69 | + | 3794.35i | 0.134667 | + | 0.138450i | ||||
\(910\) | 1755.64 | − | 7783.43i | 0.0639547 | − | 0.283537i | ||||
\(911\) | 36922.8 | 1.34282 | 0.671410 | − | 0.741086i | \(-0.265689\pi\) | ||||
0.671410 | + | 0.741086i | \(0.265689\pi\) | |||||||
\(912\) | −37301.4 | − | 20456.2i | −1.35436 | − | 0.742734i | ||||
\(913\) | −22638.0 | −0.820600 | ||||||||
\(914\) | −6222.30 | + | 27585.9i | −0.225181 | + | 0.998316i | ||||
\(915\) | 7858.06 | − | 3191.35i | 0.283912 | − | 0.115304i | ||||
\(916\) | −8342.47 | − | 3965.20i | −0.300920 | − | 0.143028i | ||||
\(917\) | 14828.0i | 0.533986i | ||||||||
\(918\) | −29544.6 | − | 21783.1i | −1.06222 | − | 0.783170i | ||||
\(919\) | 3415.26i | 0.122589i | 0.998120 | + | 0.0612944i | \(0.0195229\pi\) | ||||
−0.998120 | + | 0.0612944i | \(0.980477\pi\) | |||||||
\(920\) | −4554.40 | − | 3575.32i | −0.163211 | − | 0.128125i | ||||
\(921\) | 35575.3 | − | 14448.0i | 1.27280 | − | 0.516913i | ||||
\(922\) | 24931.2 | + | 5623.49i | 0.890525 | + | 0.200867i | ||||
\(923\) | −18114.9 | −0.646000 | ||||||||
\(924\) | −12928.6 | − | 749.681i | −0.460304 | − | 0.0266912i | ||||
\(925\) | −8915.73 | −0.316916 | ||||||||
\(926\) | −7198.15 | − | 1623.62i | −0.255449 | − | 0.0576192i | ||||
\(927\) | 12903.0 | + | 13265.4i | 0.457162 | + | 0.470003i | ||||
\(928\) | −8004.75 | − | 16093.5i | −0.283156 | − | 0.569285i | ||||
\(929\) | − | 25200.8i | − | 0.890001i | −0.895530 | − | 0.445001i | \(-0.853203\pi\) | ||
0.895530 | − | 0.445001i | \(-0.146797\pi\) | |||||||
\(930\) | −1871.03 | + | 309.489i | −0.0659715 | + | 0.0109124i | ||||
\(931\) | 9172.62i | 0.322901i | ||||||||
\(932\) | 13296.1 | − | 27973.8i | 0.467304 | − | 0.983169i | ||||
\(933\) | −3187.92 | − | 7849.62i | −0.111863 | − | 0.275440i | ||||
\(934\) | −6044.53 | + | 26797.8i | −0.211759 | + | 0.938812i | ||||
\(935\) | −7075.67 | −0.247486 | ||||||||
\(936\) | −1790.92 | − | 16831.3i | −0.0625408 | − | 0.587766i | ||||
\(937\) | −17484.4 | −0.609595 | −0.304797 | − | 0.952417i | \(-0.598589\pi\) | ||||
−0.304797 | + | 0.952417i | \(0.598589\pi\) | |||||||
\(938\) | −3797.07 | + | 16833.9i | −0.132174 | + | 0.585978i | ||||
\(939\) | −11578.9 | − | 28510.8i | −0.402411 | − | 0.990858i | ||||
\(940\) | −9848.48 | + | 20720.4i | −0.341726 | + | 0.718963i | ||||
\(941\) | − | 10865.5i | − | 0.376412i | −0.982130 | − | 0.188206i | \(-0.939733\pi\) | ||
0.982130 | − | 0.188206i | \(-0.0602672\pi\) | |||||||
\(942\) | −33925.9 | + | 5611.71i | −1.17342 | + | 0.194097i | ||||
\(943\) | 14989.7i | 0.517638i | ||||||||
\(944\) | 11949.3 | + | 14674.2i | 0.411989 | + | 0.505937i | ||||
\(945\) | 13081.3 | + | 5739.64i | 0.450302 | + | 0.197577i | ||||
\(946\) | −22011.2 | − | 4964.87i | −0.756498 | − | 0.170636i | ||||
\(947\) | −6102.06 | −0.209388 | −0.104694 | − | 0.994504i | \(-0.533386\pi\) | ||||
−0.104694 | + | 0.994504i | \(0.533386\pi\) | |||||||
\(948\) | −4596.41 | − | 266.528i | −0.157473 | − | 0.00913125i | ||||
\(949\) | 13968.8 | 0.477814 | ||||||||
\(950\) | 8824.06 | + | 1990.36i | 0.301358 | + | 0.0679745i | ||||
\(951\) | −37591.6 | + | 15266.9i | −1.28180 | + | 0.520570i | ||||
\(952\) | 26320.1 | − | 33527.6i | 0.896049 | − | 1.14143i | ||||
\(953\) | − | 11131.8i | − | 0.378377i | −0.981941 | − | 0.189189i | \(-0.939414\pi\) | ||
0.981941 | − | 0.189189i | \(-0.0605858\pi\) | |||||||
\(954\) | 19910.5 | − | 12199.1i | 0.675710 | − | 0.414004i | ||||
\(955\) | − | 4160.30i | − | 0.140968i | ||||||
\(956\) | −31928.5 | − | 15175.7i | −1.08017 | − | 0.513408i | ||||
\(957\) | 7313.09 | − | 2970.02i | 0.247021 | − | 0.100321i | ||||
\(958\) | 2134.76 | − | 9464.25i | 0.0719948 | − | 0.319182i | ||||
\(959\) | −27195.1 | −0.915719 | ||||||||
\(960\) | −7788.26 | − | 10783.8i | −0.261839 | − | 0.362547i | ||||
\(961\) | 29125.0 | 0.977643 | ||||||||
\(962\) | 6149.12 | − | 27261.5i | 0.206087 | − | 0.913666i | ||||
\(963\) | −9750.89 | + | 9484.49i | −0.326291 | + | 0.317376i | ||||
\(964\) | −9468.89 | − | 4500.60i | −0.316361 | − | 0.150368i | ||||
\(965\) | 3296.76i | 0.109976i | ||||||||
\(966\) | 2499.66 | + | 15111.8i | 0.0832558 | + | 0.503327i | ||||
\(967\) | 17597.4i | 0.585207i | 0.956234 | + | 0.292603i | \(0.0945215\pi\) | ||||
−0.956234 | + | 0.292603i | \(0.905478\pi\) | |||||||
\(968\) | 15326.9 | − | 19524.1i | 0.508911 | − | 0.648273i | ||||
\(969\) | 23136.9 | + | 56970.0i | 0.767043 | + | 1.88869i | ||||
\(970\) | −360.276 | − | 81.2641i | −0.0119255 | − | 0.00268993i | ||||
\(971\) | −742.846 | −0.0245510 | −0.0122755 | − | 0.999925i | \(-0.503908\pi\) | ||||
−0.0122755 | + | 0.999925i | \(0.503908\pi\) | |||||||
\(972\) | 30193.0 | + | 2591.42i | 0.996337 | + | 0.0855141i | ||||
\(973\) | 40867.8 | 1.34652 | ||||||||
\(974\) | −20073.6 | − | 4527.81i | −0.660369 | − | 0.148953i | ||||
\(975\) | 1354.23 | + | 3334.53i | 0.0444822 | + | 0.109529i | ||||
\(976\) | 13192.4 | + | 16200.8i | 0.432663 | + | 0.531326i | ||||
\(977\) | 41139.6i | 1.34716i | 0.739116 | + | 0.673578i | \(0.235244\pi\) | ||||
−0.739116 | + | 0.673578i | \(0.764756\pi\) | |||||||
\(978\) | −3698.27 | − | 22358.1i | −0.120918 | − | 0.731015i | ||||
\(979\) | − | 11824.5i | − | 0.386020i | ||||||
\(980\) | −1231.22 | + | 2590.38i | −0.0401325 | + | 0.0844355i | ||||
\(981\) | 17972.7 | − | 17481.7i | 0.584939 | − | 0.568958i | ||||
\(982\) | −10954.2 | + | 48564.3i | −0.355970 | + | 1.57816i | ||||
\(983\) | −23649.8 | −0.767356 | −0.383678 | − | 0.923467i | \(-0.625343\pi\) | ||||
−0.383678 | + | 0.923467i | \(0.625343\pi\) | |||||||
\(984\) | −9509.29 | + | 33098.3i | −0.308074 | + | 1.07229i | ||||
\(985\) | −4816.68 | −0.155809 | ||||||||
\(986\) | −5716.33 | + | 25342.8i | −0.184630 | + | 0.818537i | ||||
\(987\) | 56229.9 | − | 22836.3i | 1.81339 | − | 0.736462i | ||||
\(988\) | −12171.8 | + | 25608.5i | −0.391940 | + | 0.824609i | ||||
\(989\) | 26688.0i | 0.858068i | ||||||||
\(990\) | 4980.89 | − | 3051.76i | 0.159902 | − | 0.0979711i | ||||
\(991\) | − | 38069.9i | − | 1.22031i | −0.792280 | − | 0.610157i | \(-0.791106\pi\) | ||
0.792280 | − | 0.610157i | \(-0.208894\pi\) | |||||||
\(992\) | −2080.48 | − | 4182.81i | −0.0665881 | − | 0.133875i | ||||
\(993\) | 7553.83 | − | 3067.79i | 0.241403 | − | 0.0980397i | ||||
\(994\) | 36737.4 | + | 8286.51i | 1.17227 | + | 0.264419i | ||||
\(995\) | −4352.44 | −0.138675 | ||||||||
\(996\) | −3560.93 | + | 61410.0i | −0.113285 | + | 1.95367i | ||||
\(997\) | −2800.44 | −0.0889576 | −0.0444788 | − | 0.999010i | \(-0.514163\pi\) | ||||
−0.0444788 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(998\) | −47801.0 | − | 10782.0i | −1.51615 | − | 0.341983i | ||||
\(999\) | 45817.4 | + | 20103.1i | 1.45105 | + | 0.636671i |
(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 | 60.4.e.a.11.15 | yes | 24 | |
3.2 | odd | 2 | inner | 60.4.e.a.11.10 | yes | 24 | |
4.3 | odd | 2 | inner | 60.4.e.a.11.9 | ✓ | 24 | |
8.3 | odd | 2 | 960.4.h.d.191.9 | 24 | |||
8.5 | even | 2 | 960.4.h.d.191.16 | 24 | |||
12.11 | even | 2 | inner | 60.4.e.a.11.16 | yes | 24 | |
24.5 | odd | 2 | 960.4.h.d.191.10 | 24 | |||
24.11 | even | 2 | 960.4.h.d.191.15 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.e.a.11.9 | ✓ | 24 | 4.3 | odd | 2 | inner | |
60.4.e.a.11.10 | yes | 24 | 3.2 | odd | 2 | inner | |
60.4.e.a.11.15 | yes | 24 | 1.1 | even | 1 | trivial | |
60.4.e.a.11.16 | yes | 24 | 12.11 | even | 2 | inner | |
960.4.h.d.191.9 | 24 | 8.3 | odd | 2 | |||
960.4.h.d.191.10 | 24 | 24.5 | odd | 2 | |||
960.4.h.d.191.15 | 24 | 24.11 | even | 2 | |||
960.4.h.d.191.16 | 24 | 8.5 | even | 2 |