Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(7,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.g (of order \(10\), 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: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 13.5 | ||
Character | \(\chi\) | \(=\) | 33.13 |
Dual form | 33.5.g.a.28.5 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.743344 | + | 0.241527i | 0.185836 | + | 0.0603818i | 0.400457 | − | 0.916316i | \(-0.368851\pi\) |
−0.214621 | + | 0.976697i | \(0.568851\pi\) | |||||||
\(3\) | −4.20378 | + | 3.05422i | −0.467086 | + | 0.339358i | ||||
\(4\) | −12.4500 | − | 9.04549i | −0.778128 | − | 0.565343i | ||||
\(5\) | −9.71709 | − | 29.9061i | −0.388684 | − | 1.19625i | −0.933773 | − | 0.357867i | \(-0.883504\pi\) |
0.545089 | − | 0.838378i | \(-0.316496\pi\) | |||||||
\(6\) | −3.86253 | + | 1.25501i | −0.107293 | + | 0.0348614i | ||||
\(7\) | 16.8776 | − | 23.2301i | 0.344441 | − | 0.474083i | −0.601291 | − | 0.799030i | \(-0.705347\pi\) |
0.945732 | + | 0.324947i | \(0.105347\pi\) | |||||||
\(8\) | −14.4205 | − | 19.8482i | −0.225321 | − | 0.310128i | ||||
\(9\) | 8.34346 | − | 25.6785i | 0.103006 | − | 0.317019i | ||||
\(10\) | − | 24.5775i | − | 0.245775i | ||||||
\(11\) | −24.4924 | + | 118.495i | −0.202416 | + | 0.979300i | ||||
\(12\) | 79.9641 | 0.555306 | ||||||||
\(13\) | −294.943 | − | 95.8329i | −1.74523 | − | 0.567058i | −0.749720 | − | 0.661755i | \(-0.769812\pi\) |
−0.995506 | + | 0.0946966i | \(0.969812\pi\) | |||||||
\(14\) | 18.1566 | − | 13.1915i | 0.0926356 | − | 0.0673037i | ||||
\(15\) | 132.188 | + | 96.0405i | 0.587504 | + | 0.426847i | ||||
\(16\) | 70.1624 | + | 215.938i | 0.274072 | + | 0.843506i | ||||
\(17\) | 397.531 | − | 129.166i | 1.37554 | − | 0.446940i | 0.474340 | − | 0.880342i | \(-0.342687\pi\) |
0.901201 | + | 0.433402i | \(0.142687\pi\) | |||||||
\(18\) | 12.4041 | − | 17.0728i | 0.0382843 | − | 0.0526939i | ||||
\(19\) | −144.131 | − | 198.379i | −0.399255 | − | 0.549527i | 0.561302 | − | 0.827611i | \(-0.310301\pi\) |
−0.960557 | + | 0.278084i | \(0.910301\pi\) | |||||||
\(20\) | −149.537 | + | 460.229i | −0.373843 | + | 1.15057i | ||||
\(21\) | 149.202i | 0.338327i | ||||||||
\(22\) | −46.8261 | + | 82.1672i | −0.0967481 | + | 0.169767i | ||||
\(23\) | 529.873 | 1.00165 | 0.500825 | − | 0.865548i | \(-0.333030\pi\) | ||||
0.500825 | + | 0.865548i | \(0.333030\pi\) | |||||||
\(24\) | 121.241 | + | 39.3937i | 0.210488 | + | 0.0683919i | ||||
\(25\) | −294.319 | + | 213.836i | −0.470911 | + | 0.342137i | ||||
\(26\) | −196.098 | − | 142.474i | −0.290086 | − | 0.210760i | ||||
\(27\) | 43.3539 | + | 133.430i | 0.0594703 | + | 0.183031i | ||||
\(28\) | −420.255 | + | 136.549i | −0.536039 | + | 0.174170i | ||||
\(29\) | 164.437 | − | 226.329i | 0.195526 | − | 0.269119i | −0.699985 | − | 0.714157i | \(-0.746810\pi\) |
0.895511 | + | 0.445039i | \(0.146810\pi\) | |||||||
\(30\) | 75.0651 | + | 103.318i | 0.0834057 | + | 0.114798i | ||||
\(31\) | 443.155 | − | 1363.89i | 0.461140 | − | 1.41924i | −0.402634 | − | 0.915361i | \(-0.631905\pi\) |
0.863773 | − | 0.503881i | \(-0.168095\pi\) | |||||||
\(32\) | 570.001i | 0.556641i | ||||||||
\(33\) | −258.950 | − | 572.933i | −0.237787 | − | 0.526109i | ||||
\(34\) | 326.700 | 0.282612 | ||||||||
\(35\) | −858.723 | − | 279.016i | −0.700998 | − | 0.227768i | ||||
\(36\) | −336.151 | + | 244.228i | −0.259376 | + | 0.188448i | ||||
\(37\) | −1466.49 | − | 1065.47i | −1.07122 | − | 0.778284i | −0.0950852 | − | 0.995469i | \(-0.530312\pi\) |
−0.976130 | + | 0.217185i | \(0.930312\pi\) | |||||||
\(38\) | −59.2249 | − | 182.276i | −0.0410145 | − | 0.126230i | ||||
\(39\) | 1532.57 | − | 497.962i | 1.00761 | − | 0.327391i | ||||
\(40\) | −453.456 | + | 624.129i | −0.283410 | + | 0.390080i | ||||
\(41\) | −289.849 | − | 398.943i | −0.172427 | − | 0.237325i | 0.714054 | − | 0.700091i | \(-0.246857\pi\) |
−0.886481 | + | 0.462766i | \(0.846857\pi\) | |||||||
\(42\) | −36.0363 | + | 110.908i | −0.0204288 | + | 0.0628733i | ||||
\(43\) | 287.561i | 0.155522i | 0.996972 | + | 0.0777612i | \(0.0247772\pi\) | ||||
−0.996972 | + | 0.0777612i | \(0.975223\pi\) | |||||||
\(44\) | 1376.78 | − | 1253.73i | 0.711146 | − | 0.647586i | ||||
\(45\) | −849.020 | −0.419269 | ||||||||
\(46\) | 393.878 | + | 127.979i | 0.186143 | + | 0.0604815i | ||||
\(47\) | −369.914 | + | 268.759i | −0.167458 | + | 0.121665i | −0.668358 | − | 0.743840i | \(-0.733002\pi\) |
0.500900 | + | 0.865505i | \(0.333002\pi\) | |||||||
\(48\) | −954.468 | − | 693.462i | −0.414266 | − | 0.300982i | ||||
\(49\) | 487.168 | + | 1499.35i | 0.202902 | + | 0.624469i | ||||
\(50\) | −270.428 | + | 87.8673i | −0.108171 | + | 0.0351469i | ||||
\(51\) | −1276.63 | + | 1757.13i | −0.490823 | + | 0.675560i | ||||
\(52\) | 2805.20 | + | 3861.03i | 1.03743 | + | 1.42790i | ||||
\(53\) | −343.249 | + | 1056.41i | −0.122196 | + | 0.376081i | −0.993380 | − | 0.114876i | \(-0.963353\pi\) |
0.871184 | + | 0.490957i | \(0.163353\pi\) | |||||||
\(54\) | 109.655i | 0.0376047i | ||||||||
\(55\) | 3781.73 | − | 418.957i | 1.25016 | − | 0.138498i | ||||
\(56\) | −704.458 | −0.224636 | ||||||||
\(57\) | 1211.79 | + | 393.734i | 0.372973 | + | 0.121186i | ||||
\(58\) | 176.898 | − | 128.524i | 0.0525857 | − | 0.0382057i | ||||
\(59\) | −295.213 | − | 214.485i | −0.0848068 | − | 0.0616158i | 0.544574 | − | 0.838713i | \(-0.316691\pi\) |
−0.629381 | + | 0.777097i | \(0.716691\pi\) | |||||||
\(60\) | −777.019 | − | 2391.42i | −0.215839 | − | 0.664283i | ||||
\(61\) | 445.037 | − | 144.601i | 0.119602 | − | 0.0388609i | −0.248605 | − | 0.968605i | \(-0.579972\pi\) |
0.368206 | + | 0.929744i | \(0.379972\pi\) | |||||||
\(62\) | 658.834 | − | 906.807i | 0.171393 | − | 0.235902i | ||||
\(63\) | −455.696 | − | 627.212i | −0.114814 | − | 0.158028i | ||||
\(64\) | 984.927 | − | 3031.29i | 0.240461 | − | 0.740062i | ||||
\(65\) | 9751.83i | 2.30813i | ||||||||
\(66\) | −54.1105 | − | 488.430i | −0.0124221 | − | 0.112128i | ||||
\(67\) | 5310.66 | 1.18304 | 0.591519 | − | 0.806291i | \(-0.298528\pi\) | ||||
0.591519 | + | 0.806291i | \(0.298528\pi\) | |||||||
\(68\) | −6117.65 | − | 1987.74i | −1.32302 | − | 0.429876i | ||||
\(69\) | −2227.47 | + | 1618.35i | −0.467857 | + | 0.339918i | ||||
\(70\) | −570.937 | − | 414.810i | −0.116518 | − | 0.0846551i | ||||
\(71\) | −2939.26 | − | 9046.10i | −0.583070 | − | 1.79450i | −0.606887 | − | 0.794788i | \(-0.707582\pi\) |
0.0238169 | − | 0.999716i | \(-0.492418\pi\) | |||||||
\(72\) | −629.989 | + | 204.696i | −0.121526 | + | 0.0394861i | ||||
\(73\) | −2514.99 | + | 3461.59i | −0.471944 | + | 0.649576i | −0.976932 | − | 0.213551i | \(-0.931497\pi\) |
0.504988 | + | 0.863127i | \(0.331497\pi\) | |||||||
\(74\) | −832.770 | − | 1146.21i | −0.152076 | − | 0.209315i | ||||
\(75\) | 584.151 | − | 1797.83i | 0.103849 | − | 0.319615i | ||||
\(76\) | 3773.56i | 0.653318i | ||||||||
\(77\) | 2339.28 | + | 2568.88i | 0.394549 | + | 0.433273i | ||||
\(78\) | 1259.50 | 0.207018 | ||||||||
\(79\) | −6201.43 | − | 2014.97i | −0.993659 | − | 0.322859i | −0.233330 | − | 0.972398i | \(-0.574962\pi\) |
−0.760329 | + | 0.649538i | \(0.774962\pi\) | |||||||
\(80\) | 5776.08 | − | 4196.57i | 0.902513 | − | 0.655714i | ||||
\(81\) | −589.773 | − | 428.495i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −119.102 | − | 366.559i | −0.0177130 | − | 0.0545150i | ||||
\(83\) | 5637.54 | − | 1831.75i | 0.818340 | − | 0.265895i | 0.130214 | − | 0.991486i | \(-0.458434\pi\) |
0.688126 | + | 0.725591i | \(0.258434\pi\) | |||||||
\(84\) | 1349.60 | − | 1857.57i | 0.191271 | − | 0.263261i | ||||
\(85\) | −7725.69 | − | 10633.5i | −1.06930 | − | 1.47177i | ||||
\(86\) | −69.4538 | + | 213.757i | −0.00939072 | + | 0.0289017i | ||||
\(87\) | 1453.66i | 0.192055i | ||||||||
\(88\) | 2705.11 | − | 1222.64i | 0.349316 | − | 0.157882i | ||||
\(89\) | 5361.08 | 0.676819 | 0.338410 | − | 0.940999i | \(-0.390111\pi\) | ||||
0.338410 | + | 0.940999i | \(0.390111\pi\) | |||||||
\(90\) | −631.114 | − | 205.061i | −0.0779153 | − | 0.0253162i | ||||
\(91\) | −7204.15 | + | 5234.12i | −0.869961 | + | 0.632064i | ||||
\(92\) | −6596.94 | − | 4792.96i | −0.779412 | − | 0.566276i | ||||
\(93\) | 2302.70 | + | 7086.99i | 0.266239 | + | 0.819400i | ||||
\(94\) | −339.886 | + | 110.436i | −0.0384661 | + | 0.0124984i | ||||
\(95\) | −4532.22 | + | 6238.07i | −0.502185 | + | 0.691198i | ||||
\(96\) | −1740.91 | − | 2396.16i | −0.188901 | − | 0.260000i | ||||
\(97\) | 1247.89 | − | 3840.60i | 0.132627 | − | 0.408183i | −0.862587 | − | 0.505910i | \(-0.831157\pi\) |
0.995213 | + | 0.0977262i | \(0.0311570\pi\) | |||||||
\(98\) | 1232.20i | 0.128300i | ||||||||
\(99\) | 2838.43 | + | 1617.59i | 0.289606 | + | 0.165043i | ||||
\(100\) | 5598.54 | 0.559854 | ||||||||
\(101\) | −285.671 | − | 92.8202i | −0.0280042 | − | 0.00909912i | 0.294981 | − | 0.955503i | \(-0.404687\pi\) |
−0.322986 | + | 0.946404i | \(0.604687\pi\) | |||||||
\(102\) | −1373.37 | + | 997.813i | −0.132004 | + | 0.0959067i | ||||
\(103\) | −584.919 | − | 424.969i | −0.0551342 | − | 0.0400574i | 0.559877 | − | 0.828576i | \(-0.310848\pi\) |
−0.615011 | + | 0.788519i | \(0.710848\pi\) | |||||||
\(104\) | 2351.13 | + | 7236.04i | 0.217375 | + | 0.669013i | ||||
\(105\) | 4462.05 | − | 1449.81i | 0.404722 | − | 0.131502i | ||||
\(106\) | −510.304 | + | 702.374i | −0.0454169 | + | 0.0625110i | ||||
\(107\) | 11494.7 | + | 15821.1i | 1.00399 | + | 1.38188i | 0.922844 | + | 0.385173i | \(0.125858\pi\) |
0.0811472 | + | 0.996702i | \(0.474142\pi\) | |||||||
\(108\) | 667.177 | − | 2053.36i | 0.0571997 | − | 0.176043i | ||||
\(109\) | 12001.4i | 1.01013i | 0.863081 | + | 0.505065i | \(0.168532\pi\) | ||||
−0.863081 | + | 0.505065i | \(0.831468\pi\) | |||||||
\(110\) | 2912.32 | + | 601.961i | 0.240687 | + | 0.0497489i | ||||
\(111\) | 9418.99 | 0.764467 | ||||||||
\(112\) | 6200.42 | + | 2014.64i | 0.494293 | + | 0.160606i | ||||
\(113\) | −4543.16 | + | 3300.80i | −0.355796 | + | 0.258501i | −0.751297 | − | 0.659965i | \(-0.770571\pi\) |
0.395500 | + | 0.918466i | \(0.370571\pi\) | |||||||
\(114\) | 805.678 | + | 585.359i | 0.0619943 | + | 0.0450415i | ||||
\(115\) | −5148.83 | − | 15846.5i | −0.389325 | − | 1.19822i | ||||
\(116\) | −4094.51 | + | 1330.39i | −0.304289 | + | 0.0988694i | ||||
\(117\) | −4921.69 | + | 6774.13i | −0.359536 | + | 0.494859i | ||||
\(118\) | −167.641 | − | 230.738i | −0.0120397 | − | 0.0165712i | ||||
\(119\) | 3708.86 | − | 11414.7i | 0.261906 | − | 0.806065i | ||||
\(120\) | − | 4008.65i | − | 0.278379i | ||||||
\(121\) | −13441.2 | − | 5804.46i | −0.918055 | − | 0.396452i | ||||
\(122\) | 365.741 | 0.0245728 | ||||||||
\(123\) | 2436.92 | + | 791.804i | 0.161076 | + | 0.0523368i | ||||
\(124\) | −17854.4 | + | 12972.0i | −1.16118 | + | 0.843650i | ||||
\(125\) | −6644.88 | − | 4827.78i | −0.425272 | − | 0.308978i | ||||
\(126\) | −187.250 | − | 576.297i | −0.0117946 | − | 0.0362999i | ||||
\(127\) | 19597.2 | − | 6367.52i | 1.21503 | − | 0.394787i | 0.369760 | − | 0.929127i | \(-0.379440\pi\) |
0.845270 | + | 0.534340i | \(0.179440\pi\) | |||||||
\(128\) | 6824.89 | − | 9393.65i | 0.416558 | − | 0.573343i | ||||
\(129\) | −878.275 | − | 1208.84i | −0.0527778 | − | 0.0726424i | ||||
\(130\) | −2355.33 | + | 7248.97i | −0.139369 | + | 0.428933i | ||||
\(131\) | − | 756.713i | − | 0.0440949i | −0.999757 | − | 0.0220475i | \(-0.992982\pi\) | ||
0.999757 | − | 0.0220475i | \(-0.00701849\pi\) | |||||||
\(132\) | −1958.51 | + | 9475.37i | −0.112403 | + | 0.543811i | ||||
\(133\) | −7040.95 | −0.398041 | ||||||||
\(134\) | 3947.65 | + | 1282.67i | 0.219851 | + | 0.0714340i | ||||
\(135\) | 3569.09 | − | 2593.09i | 0.195835 | − | 0.142282i | ||||
\(136\) | −8296.31 | − | 6027.62i | −0.448546 | − | 0.325888i | ||||
\(137\) | −886.946 | − | 2729.74i | −0.0472559 | − | 0.145439i | 0.924644 | − | 0.380832i | \(-0.124362\pi\) |
−0.971900 | + | 0.235393i | \(0.924362\pi\) | |||||||
\(138\) | −2046.65 | + | 664.997i | −0.107470 | + | 0.0349190i | ||||
\(139\) | 5616.88 | − | 7730.97i | 0.290714 | − | 0.400133i | −0.638532 | − | 0.769595i | \(-0.720458\pi\) |
0.929246 | + | 0.369462i | \(0.120458\pi\) | |||||||
\(140\) | 8167.30 | + | 11241.3i | 0.416699 | + | 0.573537i | ||||
\(141\) | 734.189 | − | 2259.60i | 0.0369292 | − | 0.113656i | ||||
\(142\) | − | 7434.28i | − | 0.368691i | ||||||
\(143\) | 18579.6 | − | 32602.2i | 0.908582 | − | 1.59432i | ||||
\(144\) | 6130.35 | 0.295638 | ||||||||
\(145\) | −8366.47 | − | 2718.43i | −0.397930 | − | 0.129295i | ||||
\(146\) | −2705.57 | + | 1965.71i | −0.126927 | + | 0.0922177i | ||||
\(147\) | −6627.29 | − | 4815.01i | −0.306691 | − | 0.222824i | ||||
\(148\) | 8620.22 | + | 26530.3i | 0.393545 | + | 1.21121i | ||||
\(149\) | −37496.0 | + | 12183.2i | −1.68893 | + | 0.548767i | −0.986611 | − | 0.163093i | \(-0.947853\pi\) |
−0.702321 | + | 0.711860i | \(0.747853\pi\) | |||||||
\(150\) | 868.451 | − | 1195.32i | 0.0385978 | − | 0.0531254i | ||||
\(151\) | −5861.14 | − | 8067.16i | −0.257056 | − | 0.353807i | 0.660911 | − | 0.750465i | \(-0.270170\pi\) |
−0.917967 | + | 0.396657i | \(0.870170\pi\) | |||||||
\(152\) | −1859.02 | + | 5721.47i | −0.0804630 | + | 0.247640i | ||||
\(153\) | − | 11285.7i | − | 0.482110i | ||||||
\(154\) | 1118.44 | + | 2474.56i | 0.0471595 | + | 0.104341i | ||||
\(155\) | −45094.9 | −1.87700 | ||||||||
\(156\) | −23584.9 | − | 7663.19i | −0.969135 | − | 0.314891i | ||||
\(157\) | 33352.5 | − | 24232.0i | 1.35310 | − | 0.983084i | 0.354248 | − | 0.935151i | \(-0.384737\pi\) |
0.998851 | − | 0.0479324i | \(-0.0152632\pi\) | |||||||
\(158\) | −4123.13 | − | 2995.63i | −0.165163 | − | 0.119998i | ||||
\(159\) | −1783.57 | − | 5489.28i | −0.0705500 | − | 0.217131i | ||||
\(160\) | 17046.5 | − | 5538.75i | 0.665880 | − | 0.216357i | ||||
\(161\) | 8943.00 | − | 12309.0i | 0.345010 | − | 0.474865i | ||||
\(162\) | −334.911 | − | 460.966i | −0.0127614 | − | 0.0175646i | ||||
\(163\) | −4897.70 | + | 15073.6i | −0.184339 | + | 0.567337i | −0.999936 | − | 0.0112827i | \(-0.996409\pi\) |
0.815597 | + | 0.578620i | \(0.196409\pi\) | |||||||
\(164\) | 7588.69i | 0.282149i | ||||||||
\(165\) | −14618.0 | + | 13311.4i | −0.536931 | + | 0.488942i | ||||
\(166\) | 4633.05 | 0.168132 | ||||||||
\(167\) | 26766.0 | + | 8696.81i | 0.959734 | + | 0.311836i | 0.746665 | − | 0.665201i | \(-0.231654\pi\) |
0.213069 | + | 0.977037i | \(0.431654\pi\) | |||||||
\(168\) | 2961.39 | − | 2151.57i | 0.104924 | − | 0.0762320i | ||||
\(169\) | 54701.2 | + | 39742.8i | 1.91524 | + | 1.39151i | ||||
\(170\) | −3174.57 | − | 9770.32i | −0.109847 | − | 0.338073i | ||||
\(171\) | −6296.63 | + | 2045.90i | −0.215336 | + | 0.0699668i | ||||
\(172\) | 2601.13 | − | 3580.15i | 0.0879235 | − | 0.121016i | ||||
\(173\) | 19454.8 | + | 26777.3i | 0.650032 | + | 0.894692i | 0.999101 | − | 0.0424048i | \(-0.0135019\pi\) |
−0.349068 | + | 0.937097i | \(0.613502\pi\) | |||||||
\(174\) | −351.099 | + | 1080.57i | −0.0115966 | + | 0.0356907i | ||||
\(175\) | 10446.1i | 0.341097i | ||||||||
\(176\) | −27306.0 | + | 3025.08i | −0.881522 | + | 0.0976590i | ||||
\(177\) | 1896.09 | 0.0605219 | ||||||||
\(178\) | 3985.13 | + | 1294.85i | 0.125777 | + | 0.0408676i | ||||
\(179\) | 39493.1 | − | 28693.4i | 1.23258 | − | 0.895521i | 0.235499 | − | 0.971875i | \(-0.424328\pi\) |
0.997081 | + | 0.0763532i | \(0.0243276\pi\) | |||||||
\(180\) | 10570.3 | + | 7679.80i | 0.326245 | + | 0.237031i | ||||
\(181\) | −2129.02 | − | 6552.45i | −0.0649864 | − | 0.200008i | 0.913291 | − | 0.407308i | \(-0.133532\pi\) |
−0.978277 | + | 0.207300i | \(0.933532\pi\) | |||||||
\(182\) | −6619.34 | + | 2150.75i | −0.199835 | + | 0.0649304i | ||||
\(183\) | −1429.19 | + | 1967.12i | −0.0426765 | + | 0.0587391i | ||||
\(184\) | −7641.05 | − | 10517.0i | −0.225693 | − | 0.310639i | ||||
\(185\) | −17614.0 | + | 54210.4i | −0.514654 | + | 1.58394i | ||||
\(186\) | 5824.24i | 0.168350i | ||||||||
\(187\) | 5569.04 | + | 50269.1i | 0.159257 | + | 1.43753i | ||||
\(188\) | 7036.50 | 0.199086 | ||||||||
\(189\) | 3831.29 | + | 1244.86i | 0.107256 | + | 0.0348495i | ||||
\(190\) | −4875.66 | + | 3542.38i | −0.135060 | + | 0.0981268i | ||||
\(191\) | −11240.2 | − | 8166.49i | −0.308111 | − | 0.223856i | 0.422974 | − | 0.906142i | \(-0.360986\pi\) |
−0.731086 | + | 0.682286i | \(0.760986\pi\) | |||||||
\(192\) | 5117.83 | + | 15751.1i | 0.138830 | + | 0.427275i | ||||
\(193\) | −45283.3 | + | 14713.4i | −1.21569 | + | 0.395002i | −0.845511 | − | 0.533958i | \(-0.820704\pi\) |
−0.370180 | + | 0.928960i | \(0.620704\pi\) | |||||||
\(194\) | 1855.22 | − | 2553.49i | 0.0492937 | − | 0.0678469i | ||||
\(195\) | −29784.2 | − | 40994.5i | −0.783281 | − | 1.07809i | ||||
\(196\) | 7497.08 | − | 23073.7i | 0.195155 | − | 0.600626i | ||||
\(197\) | − | 50314.5i | − | 1.29646i | −0.761443 | − | 0.648232i | \(-0.775509\pi\) | ||
0.761443 | − | 0.648232i | \(-0.224491\pi\) | |||||||
\(198\) | 1719.24 | + | 1887.98i | 0.0438537 | + | 0.0481579i | ||||
\(199\) | 12094.2 | 0.305401 | 0.152700 | − | 0.988273i | \(-0.451203\pi\) | ||||
0.152700 | + | 0.988273i | \(0.451203\pi\) | |||||||
\(200\) | 8488.48 | + | 2758.08i | 0.212212 | + | 0.0689519i | ||||
\(201\) | −22324.8 | + | 16219.9i | −0.552581 | + | 0.401474i | ||||
\(202\) | −189.933 | − | 137.995i | −0.00465477 | − | 0.00338189i | ||||
\(203\) | −2482.32 | − | 7639.78i | −0.0602372 | − | 0.185391i | ||||
\(204\) | 31788.2 | − | 10328.6i | 0.763846 | − | 0.248189i | ||||
\(205\) | −9114.36 | + | 12544.8i | −0.216879 | + | 0.298509i | ||||
\(206\) | −332.155 | − | 457.172i | −0.00782719 | − | 0.0107732i | ||||
\(207\) | 4420.97 | − | 13606.4i | 0.103176 | − | 0.317542i | ||||
\(208\) | − | 70413.2i | − | 1.62752i | ||||||
\(209\) | 27037.1 | − | 12220.0i | 0.618967 | − | 0.279757i | ||||
\(210\) | 3667.01 | 0.0831522 | ||||||||
\(211\) | 9760.75 | + | 3171.46i | 0.219239 | + | 0.0712351i | 0.416577 | − | 0.909100i | \(-0.363230\pi\) |
−0.197338 | + | 0.980336i | \(0.563230\pi\) | |||||||
\(212\) | 13829.2 | − | 10047.5i | 0.307699 | − | 0.223556i | ||||
\(213\) | 39984.8 | + | 29050.6i | 0.881323 | + | 0.640319i | ||||
\(214\) | 4723.29 | + | 14536.8i | 0.103138 | + | 0.317425i | ||||
\(215\) | 8599.83 | − | 2794.26i | 0.186043 | − | 0.0604490i | ||||
\(216\) | 2023.14 | − | 2784.62i | 0.0433630 | − | 0.0596841i | ||||
\(217\) | −24203.9 | − | 33313.8i | −0.514003 | − | 0.707464i | ||||
\(218\) | −2898.66 | + | 8921.14i | −0.0609935 | + | 0.187719i | ||||
\(219\) | − | 22233.1i | − | 0.463566i | ||||||
\(220\) | −50872.4 | − | 28991.6i | −1.05108 | − | 0.598999i | ||||
\(221\) | −129627. | −2.65407 | ||||||||
\(222\) | 7001.56 | + | 2274.94i | 0.142065 | + | 0.0461599i | ||||
\(223\) | −24376.6 | + | 17710.7i | −0.490189 | + | 0.356143i | −0.805257 | − | 0.592926i | \(-0.797973\pi\) |
0.315068 | + | 0.949069i | \(0.397973\pi\) | |||||||
\(224\) | 13241.2 | + | 9620.26i | 0.263894 | + | 0.191730i | ||||
\(225\) | 3035.34 | + | 9341.82i | 0.0599573 | + | 0.184530i | ||||
\(226\) | −4174.37 | + | 1356.33i | −0.0817286 | + | 0.0265552i | ||||
\(227\) | −21102.5 | + | 29045.0i | −0.409526 | + | 0.563664i | −0.963103 | − | 0.269134i | \(-0.913263\pi\) |
0.553577 | + | 0.832798i | \(0.313263\pi\) | |||||||
\(228\) | −11525.3 | − | 15863.2i | −0.221709 | − | 0.305156i | ||||
\(229\) | 8252.28 | − | 25397.9i | 0.157363 | − | 0.484314i | −0.841029 | − | 0.540989i | \(-0.818050\pi\) |
0.998393 | + | 0.0566752i | \(0.0180500\pi\) | |||||||
\(230\) | − | 13023.0i | − | 0.246181i | ||||||
\(231\) | −17679.7 | − | 3654.31i | −0.331323 | − | 0.0684828i | ||||
\(232\) | −6863.48 | −0.127517 | ||||||||
\(233\) | 48394.7 | + | 15724.4i | 0.891428 | + | 0.289643i | 0.718694 | − | 0.695326i | \(-0.244740\pi\) |
0.172734 | + | 0.984969i | \(0.444740\pi\) | |||||||
\(234\) | −5294.65 | + | 3846.79i | −0.0966953 | + | 0.0702533i | ||||
\(235\) | 11632.0 | + | 8451.16i | 0.210630 | + | 0.153031i | ||||
\(236\) | 1735.29 | + | 5340.68i | 0.0311565 | + | 0.0958899i | ||||
\(237\) | 32223.6 | − | 10470.1i | 0.573689 | − | 0.186403i | ||||
\(238\) | 5513.91 | − | 7589.25i | 0.0973433 | − | 0.133982i | ||||
\(239\) | 32633.6 | + | 44916.3i | 0.571306 | + | 0.786335i | 0.992709 | − | 0.120538i | \(-0.0384621\pi\) |
−0.421403 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(240\) | −11464.1 | + | 35282.9i | −0.199030 | + | 0.612550i | ||||
\(241\) | − | 108102.i | − | 1.86123i | −0.365998 | − | 0.930616i | \(-0.619272\pi\) | ||
0.365998 | − | 0.930616i | \(-0.380728\pi\) | |||||||
\(242\) | −8589.54 | − | 7561.14i | −0.146669 | − | 0.129109i | ||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | −6848.73 | − | 2225.29i | −0.115035 | − | 0.0373772i | ||||
\(245\) | 40105.9 | − | 29138.6i | 0.668153 | − | 0.485442i | ||||
\(246\) | 1620.23 | + | 1177.17i | 0.0267736 | + | 0.0194521i | ||||
\(247\) | 23499.2 | + | 72323.1i | 0.385176 | + | 1.18545i | ||||
\(248\) | −33461.3 | + | 10872.2i | −0.544050 | + | 0.176773i | ||||
\(249\) | −18104.4 | + | 24918.6i | −0.292002 | + | 0.401906i | ||||
\(250\) | −3773.39 | − | 5193.62i | −0.0603742 | − | 0.0830980i | ||||
\(251\) | 11178.4 | − | 34403.5i | 0.177432 | − | 0.546078i | −0.822305 | − | 0.569048i | \(-0.807312\pi\) |
0.999736 | + | 0.0229694i | \(0.00731203\pi\) | |||||||
\(252\) | 11930.8i | 0.187875i | ||||||||
\(253\) | −12977.8 | + | 62787.4i | −0.202750 | + | 0.980916i | ||||
\(254\) | 16105.4 | 0.249634 | ||||||||
\(255\) | 64954.2 | + | 21104.9i | 0.998911 | + | 0.324566i | ||||
\(256\) | −33915.1 | + | 24640.8i | −0.517503 | + | 0.375988i | ||||
\(257\) | 70741.8 | + | 51396.9i | 1.07105 | + | 0.778163i | 0.976101 | − | 0.217319i | \(-0.0697311\pi\) |
0.0949493 | + | 0.995482i | \(0.469731\pi\) | |||||||
\(258\) | −360.892 | − | 1110.71i | −0.00542174 | − | 0.0166864i | ||||
\(259\) | −49501.9 | + | 16084.1i | −0.737942 | + | 0.239772i | ||||
\(260\) | 88210.1 | − | 121411.i | 1.30488 | − | 1.79602i | ||||
\(261\) | −4439.81 | − | 6110.88i | −0.0651754 | − | 0.0897062i | ||||
\(262\) | 182.767 | − | 562.498i | 0.00266253 | − | 0.00819443i | ||||
\(263\) | 108577.i | 1.56973i | 0.619667 | + | 0.784865i | \(0.287268\pi\) | ||||
−0.619667 | + | 0.784865i | \(0.712732\pi\) | |||||||
\(264\) | −7637.46 | + | 13401.7i | −0.109582 | + | 0.192288i | ||||
\(265\) | 34928.6 | 0.497381 | ||||||||
\(266\) | −5233.85 | − | 1700.58i | −0.0739704 | − | 0.0240344i | ||||
\(267\) | −22536.8 | + | 16373.9i | −0.316133 | + | 0.229684i | ||||
\(268\) | −66118.0 | − | 48037.5i | −0.920556 | − | 0.668823i | ||||
\(269\) | −18841.0 | − | 57986.8i | −0.260376 | − | 0.801354i | −0.992723 | − | 0.120422i | \(-0.961575\pi\) |
0.732347 | − | 0.680931i | \(-0.238425\pi\) | |||||||
\(270\) | 3279.36 | − | 1065.53i | 0.0449844 | − | 0.0146163i | ||||
\(271\) | −54823.2 | + | 75457.6i | −0.746493 | + | 1.02746i | 0.251726 | + | 0.967799i | \(0.419002\pi\) |
−0.998219 | + | 0.0596605i | \(0.980998\pi\) | |||||||
\(272\) | 55783.5 | + | 76779.3i | 0.753994 | + | 1.03778i | ||||
\(273\) | 14298.5 | − | 44006.1i | 0.191851 | − | 0.590456i | ||||
\(274\) | − | 2243.36i | − | 0.0298812i | ||||||
\(275\) | −18129.9 | − | 40112.8i | −0.239734 | − | 0.530417i | ||||
\(276\) | 42370.8 | 0.556223 | ||||||||
\(277\) | 40067.3 | + | 13018.7i | 0.522193 | + | 0.169671i | 0.558240 | − | 0.829679i | \(-0.311477\pi\) |
−0.0360475 | + | 0.999350i | \(0.511477\pi\) | |||||||
\(278\) | 6042.51 | − | 4390.14i | 0.0781858 | − | 0.0568053i | ||||
\(279\) | −31325.3 | − | 22759.1i | −0.402426 | − | 0.292380i | ||||
\(280\) | 6845.29 | + | 21067.6i | 0.0873123 | + | 0.268720i | ||||
\(281\) | −80859.4 | + | 26272.8i | −1.02404 | + | 0.332731i | −0.772432 | − | 0.635097i | \(-0.780960\pi\) |
−0.251610 | + | 0.967829i | \(0.580960\pi\) | |||||||
\(282\) | 1091.51 | − | 1502.33i | 0.0137255 | − | 0.0188916i | ||||
\(283\) | −9337.45 | − | 12851.9i | −0.116588 | − | 0.160470i | 0.746734 | − | 0.665123i | \(-0.231621\pi\) |
−0.863323 | + | 0.504652i | \(0.831621\pi\) | |||||||
\(284\) | −45232.5 | + | 139211.i | −0.560808 | + | 1.72599i | ||||
\(285\) | − | 40065.8i | − | 0.493270i | ||||||
\(286\) | 21685.4 | − | 19747.2i | 0.265115 | − | 0.241420i | ||||
\(287\) | −14159.4 | −0.171903 | ||||||||
\(288\) | 14636.8 | + | 4755.78i | 0.176466 | + | 0.0573372i | ||||
\(289\) | 73777.4 | − | 53602.4i | 0.883339 | − | 0.641783i | ||||
\(290\) | −5562.59 | − | 4041.46i | −0.0661426 | − | 0.0480554i | ||||
\(291\) | 6484.20 | + | 19956.3i | 0.0765721 | + | 0.235665i | ||||
\(292\) | 62623.5 | − | 20347.6i | 0.734466 | − | 0.238642i | ||||
\(293\) | 54235.4 | − | 74648.6i | 0.631753 | − | 0.869533i | −0.366389 | − | 0.930462i | \(-0.619406\pi\) |
0.998142 | + | 0.0609283i | \(0.0194061\pi\) | |||||||
\(294\) | −3763.40 | − | 5179.88i | −0.0435398 | − | 0.0599274i | ||||
\(295\) | −3545.79 | + | 10912.8i | −0.0407446 | + | 0.125399i | ||||
\(296\) | 44471.9i | 0.507577i | ||||||||
\(297\) | −16872.6 | + | 1869.22i | −0.191280 | + | 0.0211908i | ||||
\(298\) | −30815.0 | −0.347000 | ||||||||
\(299\) | −156282. | − | 50779.3i | −1.74811 | − | 0.567994i | ||||
\(300\) | −23535.0 | + | 17099.2i | −0.261500 | + | 0.189991i | ||||
\(301\) | 6680.06 | + | 4853.35i | 0.0737305 | + | 0.0535683i | ||||
\(302\) | −2408.40 | − | 7412.30i | −0.0264068 | − | 0.0812717i | ||||
\(303\) | 1484.39 | − | 482.308i | 0.0161682 | − | 0.00525338i | ||||
\(304\) | 32724.9 | − | 45042.0i | 0.354105 | − | 0.487383i | ||||
\(305\) | −8648.94 | − | 11904.2i | −0.0929744 | − | 0.127968i | ||||
\(306\) | 2725.80 | − | 8389.16i | 0.0291106 | − | 0.0895934i | ||||
\(307\) | 28341.3i | 0.300707i | 0.988632 | + | 0.150354i | \(0.0480412\pi\) | ||||
−0.988632 | + | 0.150354i | \(0.951959\pi\) | |||||||
\(308\) | −5887.37 | − | 53142.6i | −0.0620612 | − | 0.560197i | ||||
\(309\) | 3756.82 | 0.0393462 | ||||||||
\(310\) | −33521.0 | − | 10891.6i | −0.348814 | − | 0.113337i | ||||
\(311\) | 98842.4 | − | 71813.2i | 1.02193 | − | 0.742478i | 0.0552546 | − | 0.998472i | \(-0.482403\pi\) |
0.966678 | + | 0.255995i | \(0.0824030\pi\) | |||||||
\(312\) | −31984.1 | − | 23237.8i | −0.328568 | − | 0.238719i | ||||
\(313\) | −26528.3 | − | 81645.8i | −0.270783 | − | 0.833384i | −0.990304 | − | 0.138914i | \(-0.955639\pi\) |
0.719522 | − | 0.694470i | \(-0.244361\pi\) | |||||||
\(314\) | 30645.1 | − | 9957.20i | 0.310815 | − | 0.100990i | ||||
\(315\) | −14329.4 | + | 19722.8i | −0.144414 | + | 0.198768i | ||||
\(316\) | 58981.7 | + | 81181.3i | 0.590668 | + | 0.812984i | ||||
\(317\) | −1321.53 | + | 4067.25i | −0.0131510 | + | 0.0404746i | −0.957417 | − | 0.288710i | \(-0.906774\pi\) |
0.944266 | + | 0.329184i | \(0.106774\pi\) | |||||||
\(318\) | − | 4511.21i | − | 0.0446106i | ||||||
\(319\) | 22791.4 | + | 25028.4i | 0.223970 | + | 0.245953i | ||||
\(320\) | −100225. | −0.978759 | ||||||||
\(321\) | −96642.3 | − | 31401.0i | −0.937901 | − | 0.304743i | ||||
\(322\) | 9620.68 | − | 6989.84i | 0.0927885 | − | 0.0674148i | ||||
\(323\) | −82920.3 | − | 60245.1i | −0.794796 | − | 0.577453i | ||||
\(324\) | 3466.76 | + | 10669.6i | 0.0330243 | + | 0.101638i | ||||
\(325\) | 107300. | − | 34863.9i | 1.01586 | − | 0.330072i | ||||
\(326\) | −7281.36 | + | 10021.9i | −0.0685137 | + | 0.0943010i | ||||
\(327\) | −36654.8 | − | 50451.0i | −0.342796 | − | 0.471818i | ||||
\(328\) | −3738.51 | + | 11505.9i | −0.0347497 | + | 0.106948i | ||||
\(329\) | 13129.1i | 0.121295i | ||||||||
\(330\) | −14081.2 | + | 6364.35i | −0.129304 | + | 0.0584422i | ||||
\(331\) | 64827.7 | 0.591704 | 0.295852 | − | 0.955234i | \(-0.404396\pi\) | ||||
0.295852 | + | 0.955234i | \(0.404396\pi\) | |||||||
\(332\) | −86756.7 | − | 28189.0i | −0.787095 | − | 0.255743i | ||||
\(333\) | −39595.3 | + | 28767.7i | −0.357072 | + | 0.259428i | ||||
\(334\) | 17795.9 | + | 12929.4i | 0.159524 | + | 0.115901i | ||||
\(335\) | −51604.2 | − | 158821.i | −0.459828 | − | 1.41520i | ||||
\(336\) | −32218.3 | + | 10468.4i | −0.285380 | + | 0.0927257i | ||||
\(337\) | 45452.8 | − | 62560.5i | 0.400222 | − | 0.550859i | −0.560578 | − | 0.828102i | \(-0.689421\pi\) |
0.960800 | + | 0.277243i | \(0.0894208\pi\) | |||||||
\(338\) | 31062.9 | + | 42754.4i | 0.271900 | + | 0.374238i | ||||
\(339\) | 9017.06 | − | 27751.7i | 0.0784631 | − | 0.241485i | ||||
\(340\) | 202270.i | 1.74974i | ||||||||
\(341\) | 150761. | + | 85916.7i | 1.29652 | + | 0.738872i | ||||
\(342\) | −5174.71 | −0.0442419 | ||||||||
\(343\) | 108620. | + | 35292.8i | 0.923256 | + | 0.299984i | ||||
\(344\) | 5707.55 | − | 4146.78i | 0.0482318 | − | 0.0350424i | ||||
\(345\) | 70043.1 | + | 50889.3i | 0.588474 | + | 0.427551i | ||||
\(346\) | 7994.19 | + | 24603.6i | 0.0667763 | + | 0.205516i | ||||
\(347\) | −124930. | + | 40592.2i | −1.03755 | + | 0.337119i | −0.777769 | − | 0.628550i | \(-0.783649\pi\) |
−0.259776 | + | 0.965669i | \(0.583649\pi\) | |||||||
\(348\) | 13149.1 | − | 18098.2i | 0.108577 | − | 0.149443i | ||||
\(349\) | −71975.4 | − | 99065.6i | −0.590926 | − | 0.813340i | 0.403914 | − | 0.914797i | \(-0.367650\pi\) |
−0.994840 | + | 0.101457i | \(0.967650\pi\) | |||||||
\(350\) | −2523.02 | + | 7765.04i | −0.0205960 | + | 0.0633881i | ||||
\(351\) | − | 43508.9i | − | 0.353154i | ||||||
\(352\) | −67542.4 | − | 13960.7i | −0.545119 | − | 0.112673i | ||||
\(353\) | 203580. | 1.63375 | 0.816877 | − | 0.576812i | \(-0.195703\pi\) | ||||
0.816877 | + | 0.576812i | \(0.195703\pi\) | |||||||
\(354\) | 1409.45 | + | 457.958i | 0.0112472 | + | 0.00365442i | ||||
\(355\) | −241973. | + | 175804.i | −1.92004 | + | 1.39499i | ||||
\(356\) | −66745.7 | − | 48493.6i | −0.526652 | − | 0.382635i | ||||
\(357\) | 19271.8 | + | 59312.4i | 0.151212 | + | 0.465382i | ||||
\(358\) | 36287.2 | − | 11790.4i | 0.283131 | − | 0.0919948i | ||||
\(359\) | −100730. | + | 138642.i | −0.781570 | + | 1.07574i | 0.213537 | + | 0.976935i | \(0.431502\pi\) |
−0.995107 | + | 0.0988039i | \(0.968498\pi\) | |||||||
\(360\) | 12243.3 | + | 16851.5i | 0.0944700 | + | 0.130027i | ||||
\(361\) | 21690.8 | − | 66757.5i | 0.166442 | − | 0.512254i | ||||
\(362\) | − | 5384.94i | − | 0.0410926i | ||||||
\(363\) | 74232.1 | − | 16651.9i | 0.563350 | − | 0.126372i | ||||
\(364\) | 137037. | 1.03427 | ||||||||
\(365\) | 127961. | + | 41577.1i | 0.960489 | + | 0.312082i | ||||
\(366\) | −1537.49 | + | 1117.05i | −0.0114776 | + | 0.00833897i | ||||
\(367\) | 53128.3 | + | 38600.0i | 0.394452 | + | 0.286586i | 0.767277 | − | 0.641315i | \(-0.221611\pi\) |
−0.372826 | + | 0.927901i | \(0.621611\pi\) | |||||||
\(368\) | 37177.1 | + | 114419.i | 0.274524 | + | 0.844898i | ||||
\(369\) | −12662.6 | + | 4114.33i | −0.0929974 | + | 0.0302167i | ||||
\(370\) | −26186.6 | + | 36042.8i | −0.191283 | + | 0.263278i | ||||
\(371\) | 18747.3 | + | 25803.4i | 0.136204 | + | 0.187469i | ||||
\(372\) | 35436.5 | − | 109062.i | 0.256074 | − | 0.788114i | ||||
\(373\) | 20440.8i | 0.146920i | 0.997298 | + | 0.0734600i | \(0.0234041\pi\) | ||||
−0.997298 | + | 0.0734600i | \(0.976596\pi\) | |||||||
\(374\) | −8001.65 | + | 38712.3i | −0.0572053 | + | 0.276762i | ||||
\(375\) | 42678.7 | 0.303493 | ||||||||
\(376\) | 10668.7 | + | 3466.48i | 0.0754635 | + | 0.0245196i | ||||
\(377\) | −70189.4 | + | 50995.6i | −0.493843 | + | 0.358798i | ||||
\(378\) | 2547.30 | + | 1850.72i | 0.0178277 | + | 0.0129526i | ||||
\(379\) | −33288.2 | − | 102451.i | −0.231746 | − | 0.713240i | −0.997536 | − | 0.0701501i | \(-0.977652\pi\) |
0.765791 | − | 0.643090i | \(-0.222348\pi\) | |||||||
\(380\) | 112853. | − | 36668.1i | 0.781528 | − | 0.253934i | ||||
\(381\) | −62934.5 | + | 86621.9i | −0.433550 | + | 0.596730i | ||||
\(382\) | −6382.91 | − | 8785.33i | −0.0437414 | − | 0.0602048i | ||||
\(383\) | 41910.9 | − | 128988.i | 0.285713 | − | 0.879333i | −0.700472 | − | 0.713680i | \(-0.747027\pi\) |
0.986184 | − | 0.165653i | \(-0.0529730\pi\) | |||||||
\(384\) | 60333.5i | 0.409163i | ||||||||
\(385\) | 54094.2 | − | 94920.8i | 0.364947 | − | 0.640383i | ||||
\(386\) | −37214.8 | −0.249770 | ||||||||
\(387\) | 7384.14 | + | 2399.25i | 0.0493035 | + | 0.0160197i | ||||
\(388\) | −50276.3 | + | 36527.9i | −0.333964 | + | 0.242639i | ||||
\(389\) | −143271. | − | 104092.i | −0.946801 | − | 0.687891i | 0.00324734 | − | 0.999995i | \(-0.498966\pi\) |
−0.950048 | + | 0.312104i | \(0.898966\pi\) | |||||||
\(390\) | −12238.7 | − | 37666.7i | −0.0804646 | − | 0.247645i | ||||
\(391\) | 210641. | − | 68441.4i | 1.37781 | − | 0.447678i | ||||
\(392\) | 22734.1 | − | 31290.8i | 0.147947 | − | 0.203631i | ||||
\(393\) | 2311.17 | + | 3181.05i | 0.0149640 | + | 0.0205961i | ||||
\(394\) | 12152.3 | − | 37401.0i | 0.0782828 | − | 0.240930i | ||||
\(395\) | 205040.i | 1.31415i | ||||||||
\(396\) | −20706.7 | − | 45814.1i | −0.132045 | − | 0.292152i | ||||
\(397\) | −133408. | −0.846448 | −0.423224 | − | 0.906025i | \(-0.639102\pi\) | ||||
−0.423224 | + | 0.906025i | \(0.639102\pi\) | |||||||
\(398\) | 8990.13 | + | 2921.07i | 0.0567545 | + | 0.0184406i | ||||
\(399\) | 29598.6 | − | 21504.6i | 0.185919 | − | 0.135078i | ||||
\(400\) | −66825.3 | − | 48551.4i | −0.417658 | − | 0.303446i | ||||
\(401\) | 31102.9 | + | 95724.8i | 0.193425 | + | 0.595300i | 0.999991 | + | 0.00415669i | \(0.00132312\pi\) |
−0.806567 | + | 0.591143i | \(0.798677\pi\) | |||||||
\(402\) | −20512.6 | + | 6664.95i | −0.126931 | + | 0.0412425i | ||||
\(403\) | −261411. | + | 359802.i | −1.60959 | + | 2.21541i | ||||
\(404\) | 2717.01 | + | 3739.65i | 0.0166467 | + | 0.0229123i | ||||
\(405\) | −7083.76 | + | 21801.6i | −0.0431871 | + | 0.132916i | ||||
\(406\) | − | 6278.54i | − | 0.0380896i | ||||||
\(407\) | 162171. | − | 147677.i | 0.979004 | − | 0.891504i | ||||
\(408\) | 53285.5 | 0.320102 | ||||||||
\(409\) | −254914. | − | 82826.6i | −1.52387 | − | 0.495134i | −0.576995 | − | 0.816747i | \(-0.695775\pi\) |
−0.946871 | + | 0.321613i | \(0.895775\pi\) | |||||||
\(410\) | −9805.02 | + | 7123.77i | −0.0583285 | + | 0.0423782i | ||||
\(411\) | 12065.8 | + | 8766.28i | 0.0714284 | + | 0.0518958i | ||||
\(412\) | 3438.22 | + | 10581.8i | 0.0202553 | + | 0.0623395i | ||||
\(413\) | −9964.98 | + | 3237.82i | −0.0584220 | + | 0.0189824i | ||||
\(414\) | 6572.61 | − | 9046.42i | 0.0383475 | − | 0.0527808i | ||||
\(415\) | −109561. | − | 150798.i | −0.636151 | − | 0.875586i | ||||
\(416\) | 54624.8 | − | 168118.i | 0.315648 | − | 0.971465i | ||||
\(417\) | 49654.4i | 0.285552i | ||||||||
\(418\) | 23049.3 | − | 2553.51i | 0.131919 | − | 0.0146145i | ||||
\(419\) | 72104.0 | 0.410706 | 0.205353 | − | 0.978688i | \(-0.434166\pi\) | ||||
0.205353 | + | 0.978688i | \(0.434166\pi\) | |||||||
\(420\) | −68667.0 | − | 22311.3i | −0.389269 | − | 0.126481i | ||||
\(421\) | 223279. | − | 162222.i | 1.25975 | − | 0.915261i | 0.261003 | − | 0.965338i | \(-0.415947\pi\) |
0.998745 | + | 0.0500775i | \(0.0159468\pi\) | |||||||
\(422\) | 6489.60 | + | 4714.97i | 0.0364412 | + | 0.0264761i | ||||
\(423\) | 3814.96 | + | 11741.2i | 0.0213211 | + | 0.0656195i | ||||
\(424\) | 25917.7 | − | 8421.16i | 0.144166 | − | 0.0468425i | ||||
\(425\) | −89380.9 | + | 123022.i | −0.494842 | + | 0.681092i | ||||
\(426\) | 22705.9 | + | 31252.0i | 0.125118 | + | 0.172210i | ||||
\(427\) | 4152.08 | − | 12778.8i | 0.0227724 | − | 0.0700864i | ||||
\(428\) | − | 300949.i | − | 1.64288i | ||||||
\(429\) | 21469.9 | + | 193799.i | 0.116658 | + | 1.05302i | ||||
\(430\) | 7067.53 | 0.0382235 | ||||||||
\(431\) | 57809.8 | + | 18783.5i | 0.311205 | + | 0.101117i | 0.460456 | − | 0.887683i | \(-0.347686\pi\) |
−0.149250 | + | 0.988799i | \(0.547686\pi\) | |||||||
\(432\) | −25770.6 | + | 18723.5i | −0.138089 | + | 0.100327i | ||||
\(433\) | −171586. | − | 124665.i | −0.915181 | − | 0.664918i | 0.0271389 | − | 0.999632i | \(-0.491360\pi\) |
−0.942320 | + | 0.334714i | \(0.891360\pi\) | |||||||
\(434\) | −9945.63 | − | 30609.5i | −0.0528023 | − | 0.162509i | ||||
\(435\) | 43473.5 | − | 14125.4i | 0.229745 | − | 0.0746486i | ||||
\(436\) | 108558. | − | 149418.i | 0.571070 | − | 0.786011i | ||||
\(437\) | −76371.1 | − | 105116.i | −0.399913 | − | 0.550434i | ||||
\(438\) | 5369.89 | − | 16526.8i | 0.0279909 | − | 0.0861473i | ||||
\(439\) | 98152.6i | 0.509299i | 0.967033 | + | 0.254649i | \(0.0819601\pi\) | ||||
−0.967033 | + | 0.254649i | \(0.918040\pi\) | |||||||
\(440\) | −62850.1 | − | 69018.8i | −0.324639 | − | 0.356502i | ||||
\(441\) | 42565.8 | 0.218868 | ||||||||
\(442\) | −96357.8 | − | 31308.6i | −0.493222 | − | 0.160258i | ||||
\(443\) | −171631. | + | 124697.i | −0.874556 | + | 0.635402i | −0.931806 | − | 0.362958i | \(-0.881767\pi\) |
0.0572497 | + | 0.998360i | \(0.481767\pi\) | |||||||
\(444\) | −117267. | − | 85199.4i | −0.594853 | − | 0.432186i | ||||
\(445\) | −52094.1 | − | 160329.i | −0.263069 | − | 0.809642i | ||||
\(446\) | −22397.8 | + | 7277.50i | −0.112599 | + | 0.0365858i | ||||
\(447\) | 120415. | − | 165736.i | 0.602648 | − | 0.829474i | ||||
\(448\) | −53793.9 | − | 74041.0i | −0.268026 | − | 0.368906i | ||||
\(449\) | −24825.1 | + | 76403.6i | −0.123140 | + | 0.378984i | −0.993558 | − | 0.113329i | \(-0.963849\pi\) |
0.870418 | + | 0.492313i | \(0.163849\pi\) | |||||||
\(450\) | 7677.30i | 0.0379126i | ||||||||
\(451\) | 54372.0 | − | 24574.7i | 0.267314 | − | 0.120819i | ||||
\(452\) | 86420.0 | 0.422997 | ||||||||
\(453\) | 49277.8 | + | 16011.3i | 0.240135 | + | 0.0780245i | ||||
\(454\) | −22701.6 | + | 16493.7i | −0.110140 | + | 0.0800212i | ||||
\(455\) | 226536. | + | 164588.i | 1.09424 | + | 0.795014i | ||||
\(456\) | −9659.74 | − | 29729.6i | −0.0464553 | − | 0.142975i | ||||
\(457\) | −313153. | + | 101750.i | −1.49942 | + | 0.487192i | −0.939849 | − | 0.341589i | \(-0.889035\pi\) |
−0.559573 | + | 0.828781i | \(0.689035\pi\) | |||||||
\(458\) | 12268.6 | − | 16886.2i | 0.0584875 | − | 0.0805011i | ||||
\(459\) | 34469.0 | + | 47442.6i | 0.163608 | + | 0.225187i | ||||
\(460\) | −79235.8 | + | 243863.i | −0.374460 | + | 1.15247i | ||||
\(461\) | 398720.i | 1.87614i | 0.346439 | + | 0.938072i | \(0.387391\pi\) | ||||
−0.346439 | + | 0.938072i | \(0.612609\pi\) | |||||||
\(462\) | −12259.5 | − | 6986.55i | −0.0574367 | − | 0.0327325i | ||||
\(463\) | −96682.3 | −0.451009 | −0.225504 | − | 0.974242i | \(-0.572403\pi\) | ||||
−0.225504 | + | 0.974242i | \(0.572403\pi\) | |||||||
\(464\) | 60410.2 | + | 19628.5i | 0.280591 | + | 0.0911696i | ||||
\(465\) | 189569. | − | 137730.i | 0.876720 | − | 0.636975i | ||||
\(466\) | 32176.1 | + | 23377.3i | 0.148170 | + | 0.107652i | ||||
\(467\) | −25684.0 | − | 79047.4i | −0.117769 | − | 0.362455i | 0.874746 | − | 0.484582i | \(-0.161028\pi\) |
−0.992514 | + | 0.122128i | \(0.961028\pi\) | |||||||
\(468\) | 122551. | − | 39819.1i | 0.559531 | − | 0.181803i | ||||
\(469\) | 89631.4 | − | 123367.i | 0.407488 | − | 0.560859i | ||||
\(470\) | 6605.41 | + | 9091.57i | 0.0299023 | + | 0.0411569i | ||||
\(471\) | −66196.6 | + | 203732.i | −0.298396 | + | 0.918370i | ||||
\(472\) | 8952.41i | 0.0401842i | ||||||||
\(473\) | −34074.6 | − | 7043.05i | −0.152303 | − | 0.0314803i | ||||
\(474\) | 26482.0 | 0.117868 | ||||||||
\(475\) | 84841.0 | + | 27566.5i | 0.376027 | + | 0.122178i | ||||
\(476\) | −149427. | + | 108565.i | −0.659500 | + | 0.479155i | ||||
\(477\) | 24263.2 | + | 17628.3i | 0.106638 | + | 0.0774770i | ||||
\(478\) | 13409.5 | + | 41270.1i | 0.0586889 | + | 0.180626i | ||||
\(479\) | 319650. | − | 103861.i | 1.39317 | − | 0.452668i | 0.486193 | − | 0.873851i | \(-0.338385\pi\) |
0.906975 | + | 0.421184i | \(0.138385\pi\) | |||||||
\(480\) | −54743.2 | + | 75347.5i | −0.237601 | + | 0.327029i | ||||
\(481\) | 330425. | + | 454792.i | 1.42818 | + | 1.96572i | ||||
\(482\) | 26109.6 | − | 80357.2i | 0.112385 | − | 0.345884i | ||||
\(483\) | 79058.1i | 0.338885i | ||||||||
\(484\) | 114840. | + | 193848.i | 0.490233 | + | 0.827507i | ||||
\(485\) | −126983. | −0.539837 | ||||||||
\(486\) | 2815.78 | + | 914.904i | 0.0119214 | + | 0.00387349i | ||||
\(487\) | 55907.8 | − | 40619.4i | 0.235730 | − | 0.171268i | −0.463649 | − | 0.886019i | \(-0.653460\pi\) |
0.699379 | + | 0.714751i | \(0.253460\pi\) | |||||||
\(488\) | −9287.75 | − | 6747.95i | −0.0390006 | − | 0.0283356i | ||||
\(489\) | −25449.2 | − | 78324.6i | −0.106428 | − | 0.327552i | ||||
\(490\) | 36850.3 | − | 11973.4i | 0.153479 | − | 0.0498683i | ||||
\(491\) | 62573.8 | − | 86125.4i | 0.259555 | − | 0.357247i | −0.659274 | − | 0.751903i | \(-0.729136\pi\) |
0.918829 | + | 0.394656i | \(0.129136\pi\) | |||||||
\(492\) | −23177.5 | − | 31901.1i | −0.0957496 | − | 0.131788i | ||||
\(493\) | 36135.1 | − | 111212.i | 0.148674 | − | 0.457572i | ||||
\(494\) | 59436.6i | 0.243557i | ||||||||
\(495\) | 20794.5 | − | 100605.i | 0.0848669 | − | 0.410590i | ||||
\(496\) | 325608. | 1.32352 | ||||||||
\(497\) | −259749. | − | 84397.6i | −1.05158 | − | 0.341678i | ||||
\(498\) | −19476.3 | + | 14150.4i | −0.0785323 | + | 0.0570570i | ||||
\(499\) | 4425.98 | + | 3215.66i | 0.0177750 | + | 0.0129143i | 0.596637 | − | 0.802511i | \(-0.296503\pi\) |
−0.578862 | + | 0.815425i | \(0.696503\pi\) | |||||||
\(500\) | 39059.3 | + | 120212.i | 0.156237 | + | 0.480849i | ||||
\(501\) | −139080. | + | 45189.9i | −0.554103 | + | 0.180039i | ||||
\(502\) | 16618.7 | − | 22873.7i | 0.0659464 | − | 0.0907674i | ||||
\(503\) | 67445.6 | + | 92830.9i | 0.266574 | + | 0.366907i | 0.921229 | − | 0.389020i | \(-0.127186\pi\) |
−0.654655 | + | 0.755927i | \(0.727186\pi\) | |||||||
\(504\) | −5877.62 | + | 18089.5i | −0.0231388 | + | 0.0712138i | ||||
\(505\) | 9445.26i | 0.0370366i | ||||||||
\(506\) | −24811.9 | + | 43538.2i | −0.0969078 | + | 0.170047i | ||||
\(507\) | −351335. | −1.36680 | ||||||||
\(508\) | −301584. | − | 97990.5i | −1.16864 | − | 0.379714i | ||||
\(509\) | 162877. | − | 118337.i | 0.628674 | − | 0.456758i | −0.227267 | − | 0.973833i | \(-0.572979\pi\) |
0.855940 | + | 0.517074i | \(0.172979\pi\) | |||||||
\(510\) | 43185.9 | + | 31376.4i | 0.166036 | + | 0.120632i | ||||
\(511\) | 37965.8 | + | 116847.i | 0.145396 | + | 0.447481i | ||||
\(512\) | −207848. | + | 67534.1i | −0.792879 | + | 0.257622i | ||||
\(513\) | 20221.0 | − | 27831.8i | 0.0768366 | − | 0.105756i | ||||
\(514\) | 40171.7 | + | 55291.7i | 0.152053 | + | 0.209283i | ||||
\(515\) | −7025.45 | + | 21622.1i | −0.0264887 | + | 0.0815237i | ||||
\(516\) | 22994.6i | 0.0863626i | ||||||||
\(517\) | −22786.5 | − | 50415.6i | −0.0852505 | − | 0.188618i | ||||
\(518\) | −40681.7 | −0.151614 | ||||||||
\(519\) | −163567. | − | 53146.2i | −0.607242 | − | 0.197305i | ||||
\(520\) | 193556. | − | 140627.i | 0.715813 | − | 0.520069i | ||||
\(521\) | −165041. | − | 119909.i | −0.608017 | − | 0.441750i | 0.240699 | − | 0.970600i | \(-0.422623\pi\) |
−0.848715 | + | 0.528850i | \(0.822623\pi\) | |||||||
\(522\) | −1824.37 | − | 5614.82i | −0.00669531 | − | 0.0206061i | ||||
\(523\) | −219991. | + | 71479.4i | −0.804270 | + | 0.261323i | −0.682169 | − | 0.731195i | \(-0.738963\pi\) |
−0.122101 | + | 0.992518i | \(0.538963\pi\) | |||||||
\(524\) | −6844.84 | + | 9421.11i | −0.0249288 | + | 0.0343115i | ||||
\(525\) | −31904.7 | − | 43913.0i | −0.115754 | − | 0.159322i | ||||
\(526\) | −26224.2 | + | 80709.8i | −0.0947831 | + | 0.291712i | ||||
\(527\) | − | 599430.i | − | 2.15833i | ||||||
\(528\) | 105549. | − | 96115.4i | 0.378605 | − | 0.344767i | ||||
\(529\) | 924.458 | 0.00330351 | ||||||||
\(530\) | 25964.0 | + | 8436.20i | 0.0924313 | + | 0.0300328i | ||||
\(531\) | −7970.74 | + | 5791.08i | −0.0282689 | + | 0.0205386i | ||||
\(532\) | 87660.1 | + | 63688.8i | 0.309727 | + | 0.225030i | ||||
\(533\) | 47257.2 | + | 145443.i | 0.166346 | + | 0.511962i | ||||
\(534\) | −20707.4 | + | 6728.23i | −0.0726176 | + | 0.0235949i | ||||
\(535\) | 361453. | − | 497497.i | 1.26283 | − | 1.73813i | ||||
\(536\) | −76582.6 | − | 105407.i | −0.266563 | − | 0.366893i | ||||
\(537\) | −78384.0 | + | 241241.i | −0.271819 | + | 0.836571i | ||||
\(538\) | − | 47654.7i | − | 0.164642i | ||||||
\(539\) | −189598. | + | 21004.5i | −0.652613 | + | 0.0722994i | ||||
\(540\) | −67891.1 | −0.232823 | ||||||||
\(541\) | 383084. | + | 124472.i | 1.30888 | + | 0.425280i | 0.878662 | − | 0.477445i | \(-0.158437\pi\) |
0.430217 | + | 0.902725i | \(0.358437\pi\) | |||||||
\(542\) | −58977.6 | + | 42849.7i | −0.200765 | + | 0.145864i | ||||
\(543\) | 28962.6 | + | 21042.5i | 0.0982285 | + | 0.0713672i | ||||
\(544\) | 73624.6 | + | 226593.i | 0.248785 | + | 0.765683i | ||||
\(545\) | 358914. | − | 116618.i | 1.20836 | − | 0.392621i | ||||
\(546\) | 21257.4 | − | 29258.2i | 0.0713056 | − | 0.0981438i | ||||
\(547\) | −56143.2 | − | 77274.5i | −0.187639 | − | 0.258263i | 0.704825 | − | 0.709381i | \(-0.251025\pi\) |
−0.892464 | + | 0.451118i | \(0.851025\pi\) | |||||||
\(548\) | −13649.3 | + | 42008.3i | −0.0454516 | + | 0.139886i | ||||
\(549\) | − | 12634.4i | − | 0.0419188i | ||||||
\(550\) | −3788.44 | − | 34196.5i | −0.0125238 | − | 0.113046i | ||||
\(551\) | −68599.4 | −0.225953 | ||||||||
\(552\) | 64242.5 | + | 20873.7i | 0.210836 | + | 0.0685047i | ||||
\(553\) | −151473. | + | 110052.i | −0.495319 | + | 0.359871i | ||||
\(554\) | 26639.5 | + | 19354.7i | 0.0867972 | + | 0.0630619i | ||||
\(555\) | −91525.2 | − | 281686.i | −0.297136 | − | 0.914490i | ||||
\(556\) | −139861. | + | 45443.5i | −0.452425 | + | 0.147002i | ||||
\(557\) | −268703. | + | 369838.i | −0.866088 | + | 1.19207i | 0.113996 | + | 0.993481i | \(0.463635\pi\) |
−0.980083 | + | 0.198586i | \(0.936365\pi\) | |||||||
\(558\) | −17788.5 | − | 24483.8i | −0.0571309 | − | 0.0786340i | ||||
\(559\) | 27557.8 | − | 84814.1i | 0.0881903 | − | 0.271422i | ||||
\(560\) | − | 205007.i | − | 0.653721i | ||||||
\(561\) | −176944. | − | 194311.i | −0.562225 | − | 0.617407i | ||||
\(562\) | −66451.9 | −0.210395 | ||||||||
\(563\) | 325812. | + | 105863.i | 1.02790 | + | 0.333984i | 0.773959 | − | 0.633236i | \(-0.218274\pi\) |
0.253939 | + | 0.967220i | \(0.418274\pi\) | |||||||
\(564\) | −29579.9 | + | 21491.0i | −0.0929904 | + | 0.0675615i | ||||
\(565\) | 142861. | + | 103794.i | 0.447523 | + | 0.325145i | ||||
\(566\) | −3836.86 | − | 11808.6i | −0.0119769 | − | 0.0368610i | ||||
\(567\) | −19908.0 | + | 6468.49i | −0.0619242 | + | 0.0201204i | ||||
\(568\) | −137163. | + | 188788.i | −0.425147 | + | 0.585165i | ||||
\(569\) | −302690. | − | 416617.i | −0.934918 | − | 1.28680i | −0.957910 | − | 0.287068i | \(-0.907319\pi\) |
0.0229927 | − | 0.999736i | \(-0.492681\pi\) | |||||||
\(570\) | 9676.99 | − | 29782.7i | 0.0297845 | − | 0.0916673i | ||||
\(571\) | − | 374190.i | − | 1.14768i | −0.818969 | − | 0.573838i | \(-0.805454\pi\) | ||
0.818969 | − | 0.573838i | \(-0.194546\pi\) | |||||||
\(572\) | −526220. | + | 237837.i | −1.60833 | + | 0.726922i | ||||
\(573\) | 72193.6 | 0.219882 | ||||||||
\(574\) | −10525.3 | − | 3419.89i | −0.0319457 | − | 0.0103798i | ||||
\(575\) | −155952. | + | 113306.i | −0.471688 | + | 0.342702i | ||||
\(576\) | −69621.5 | − | 50583.0i | −0.209845 | − | 0.152461i | ||||
\(577\) | 26557.4 | + | 81735.2i | 0.0797689 | + | 0.245503i | 0.982986 | − | 0.183681i | \(-0.0588012\pi\) |
−0.903217 | + | 0.429184i | \(0.858801\pi\) | |||||||
\(578\) | 67788.4 | − | 22025.8i | 0.202908 | − | 0.0659289i | ||||
\(579\) | 145423. | − | 200157.i | 0.433786 | − | 0.597055i | ||||
\(580\) | 79573.4 | + | 109523.i | 0.236544 | + | 0.325575i | ||||
\(581\) | 52596.7 | − | 161876.i | 0.155814 | − | 0.479546i | ||||
\(582\) | 16400.5i | 0.0484186i | ||||||||
\(583\) | −116773. | − | 66547.4i | −0.343562 | − | 0.195792i | ||||
\(584\) | 104974. | 0.307790 | ||||||||
\(585\) | 250413. | + | 81364.0i | 0.731719 | + | 0.237750i | ||||
\(586\) | 58345.2 | − | 42390.3i | 0.169906 | − | 0.123444i | ||||
\(587\) | −8573.10 | − | 6228.72i | −0.0248806 | − | 0.0180768i | 0.575275 | − | 0.817960i | \(-0.304895\pi\) |
−0.600156 | + | 0.799883i | \(0.704895\pi\) | |||||||
\(588\) | 38956.0 | + | 119894.i | 0.112673 | + | 0.346772i | ||||
\(589\) | −334440. | + | 108666.i | −0.964024 | + | 0.313230i | ||||
\(590\) | −5271.49 | + | 7255.59i | −0.0151436 | + | 0.0208434i | ||||
\(591\) | 153672. | + | 211511.i | 0.439965 | + | 0.605560i | ||||
\(592\) | 127182. | − | 391427.i | 0.362897 | − | 1.11688i | ||||
\(593\) | − | 170532.i | − | 0.484949i | −0.970158 | − | 0.242474i | \(-0.922041\pi\) | ||
0.970158 | − | 0.242474i | \(-0.0779590\pi\) | |||||||
\(594\) | −12993.6 | − | 2685.72i | −0.0368262 | − | 0.00761180i | ||||
\(595\) | −377408. | −1.06605 | ||||||||
\(596\) | 577029. | + | 187488.i | 1.62445 | + | 0.527815i | ||||
\(597\) | −50841.2 | + | 36938.3i | −0.142648 | + | 0.103640i | ||||
\(598\) | −103907. | − | 75492.9i | −0.290565 | − | 0.211108i | ||||
\(599\) | −6611.99 | − | 20349.6i | −0.0184280 | − | 0.0567156i | 0.941420 | − | 0.337237i | \(-0.109492\pi\) |
−0.959848 | + | 0.280522i | \(0.909492\pi\) | |||||||
\(600\) | −44107.5 | + | 14331.4i | −0.122521 | + | 0.0398094i | ||||
\(601\) | −108789. | + | 149736.i | −0.301188 | + | 0.414550i | −0.932608 | − | 0.360891i | \(-0.882472\pi\) |
0.631420 | + | 0.775441i | \(0.282472\pi\) | |||||||
\(602\) | 3793.37 | + | 5221.12i | 0.0104672 | + | 0.0144069i | ||||
\(603\) | 44309.3 | − | 136370.i | 0.121860 | − | 0.375046i | ||||
\(604\) | 153453.i | 0.420632i | ||||||||
\(605\) | −42979.1 | + | 458378.i | −0.117421 | + | 1.25231i | ||||
\(606\) | 1219.90 | 0.00332185 | ||||||||
\(607\) | 640205. | + | 208015.i | 1.73757 | + | 0.564570i | 0.994508 | − | 0.104657i | \(-0.0333745\pi\) |
0.743058 | + | 0.669227i | \(0.233374\pi\) | |||||||
\(608\) | 113076. | − | 82154.7i | 0.305889 | − | 0.222242i | ||||
\(609\) | 33768.7 | + | 24534.4i | 0.0910499 | + | 0.0661517i | ||||
\(610\) | −3553.94 | − | 10937.9i | −0.00955104 | − | 0.0293951i | ||||
\(611\) | 134860. | − | 43818.6i | 0.361243 | − | 0.117375i | ||||
\(612\) | −102085. | + | 140508.i | −0.272557 | + | 0.375143i | ||||
\(613\) | 54637.2 | + | 75201.7i | 0.145401 | + | 0.200128i | 0.875505 | − | 0.483208i | \(-0.160529\pi\) |
−0.730104 | + | 0.683336i | \(0.760529\pi\) | |||||||
\(614\) | −6845.21 | + | 21067.4i | −0.0181572 | + | 0.0558822i | ||||
\(615\) | − | 80572.9i | − | 0.213029i | ||||||
\(616\) | 17253.9 | − | 83475.0i | 0.0454700 | − | 0.219986i | ||||
\(617\) | 614426. | 1.61398 | 0.806992 | − | 0.590562i | \(-0.201094\pi\) | ||||
0.806992 | + | 0.590562i | \(0.201094\pi\) | |||||||
\(618\) | 2792.61 | + | 907.373i | 0.00731195 | + | 0.00237580i | ||||
\(619\) | 77585.4 | − | 56369.1i | 0.202488 | − | 0.147116i | −0.481921 | − | 0.876215i | \(-0.660061\pi\) |
0.684408 | + | 0.729099i | \(0.260061\pi\) | |||||||
\(620\) | 561434. | + | 407905.i | 1.46055 | + | 1.06115i | ||||
\(621\) | 22972.1 | + | 70700.7i | 0.0595685 | + | 0.183333i | ||||
\(622\) | 90818.7 | − | 29508.8i | 0.234744 | − | 0.0762730i | ||||
\(623\) | 90482.4 | − | 124538.i | 0.233125 | − | 0.320868i | ||||
\(624\) | 215057. | + | 296001.i | 0.552313 | + | 0.760194i | ||||
\(625\) | −150074. | + | 461880.i | −0.384189 | + | 1.18241i | ||||
\(626\) | − | 67098.3i | − | 0.171223i | ||||||
\(627\) | −76335.1 | + | 133948.i | −0.194173 | + | 0.340722i | ||||
\(628\) | −634431. | −1.60866 | ||||||||
\(629\) | −720599. | − | 234137.i | −1.82135 | − | 0.591791i | ||||
\(630\) | −15415.3 | + | 11199.9i | −0.0388392 | + | 0.0282184i | ||||
\(631\) | 340719. | + | 247547.i | 0.855732 | + | 0.621726i | 0.926720 | − | 0.375752i | \(-0.122615\pi\) |
−0.0709886 | + | 0.997477i | \(0.522615\pi\) | |||||||
\(632\) | 49434.5 | + | 152144.i | 0.123765 | + | 0.380908i | ||||
\(633\) | −50718.3 | + | 16479.4i | −0.126578 | + | 0.0411276i | ||||
\(634\) | −1964.70 | + | 2704.18i | −0.00488785 | + | 0.00672755i | ||||
\(635\) | −380856. | − | 524203.i | −0.944525 | − | 1.30003i | ||||
\(636\) | −27447.6 | + | 84475.1i | −0.0678563 | + | 0.208840i | ||||
\(637\) | − | 488910.i | − | 1.20490i | ||||||
\(638\) | 10896.8 | + | 24109.5i | 0.0267707 | + | 0.0592306i | ||||
\(639\) | −256814. | −0.628951 | ||||||||
\(640\) | −347246. | − | 112827.i | −0.847768 | − | 0.275457i | ||||
\(641\) | −223509. | + | 162389.i | −0.543974 | + | 0.395220i | −0.825559 | − | 0.564316i | \(-0.809140\pi\) |
0.281585 | + | 0.959536i | \(0.409140\pi\) | |||||||
\(642\) | −64254.3 | − | 46683.5i | −0.155895 | − | 0.113264i | ||||
\(643\) | 90308.2 | + | 277940.i | 0.218427 | + | 0.672248i | 0.998893 | + | 0.0470496i | \(0.0149819\pi\) |
−0.780466 | + | 0.625198i | \(0.785018\pi\) | |||||||
\(644\) | −222682. | + | 72353.6i | −0.536924 | + | 0.174457i | ||||
\(645\) | −27617.5 | + | 38012.2i | −0.0663842 | + | 0.0913700i | ||||
\(646\) | −47087.5 | − | 64810.4i | −0.112834 | − | 0.155303i | ||||
\(647\) | −115020. | + | 353996.i | −0.274768 | + | 0.845648i | 0.714513 | + | 0.699622i | \(0.246648\pi\) |
−0.989281 | + | 0.146026i | \(0.953352\pi\) | |||||||
\(648\) | 17885.0i | 0.0425932i | ||||||||
\(649\) | 32645.9 | − | 29728.1i | 0.0775066 | − | 0.0705793i | ||||
\(650\) | 88181.4 | 0.208713 | ||||||||
\(651\) | 203495. | + | 66119.6i | 0.480167 | + | 0.156016i | ||||
\(652\) | 197325. | − | 143365.i | 0.464179 | − | 0.337246i | ||||
\(653\) | 473453. | + | 343984.i | 1.11033 | + | 0.806699i | 0.982715 | − | 0.185125i | \(-0.0592691\pi\) |
0.127611 | + | 0.991824i | \(0.459269\pi\) | |||||||
\(654\) | −15061.9 | − | 46355.6i | −0.0352146 | − | 0.108379i | ||||
\(655\) | −22630.4 | + | 7353.05i | −0.0527483 | + | 0.0171390i | ||||
\(656\) | 65810.3 | − | 90580.1i | 0.152928 | − | 0.210487i | ||||
\(657\) | 67904.8 | + | 93462.9i | 0.157315 | + | 0.216525i | ||||
\(658\) | −3171.04 | + | 9759.47i | −0.00732404 | + | 0.0225411i | ||||
\(659\) | 68585.7i | 0.157929i | 0.996877 | + | 0.0789647i | \(0.0251614\pi\) | ||||
−0.996877 | + | 0.0789647i | \(0.974839\pi\) | |||||||
\(660\) | 302403. | − | 33501.5i | 0.694221 | − | 0.0769089i | ||||
\(661\) | −197426. | −0.451857 | −0.225928 | − | 0.974144i | \(-0.572542\pi\) | ||||
−0.225928 | + | 0.974144i | \(0.572542\pi\) | |||||||
\(662\) | 48189.3 | + | 15657.6i | 0.109960 | + | 0.0357282i | ||||
\(663\) | 544925. | − | 395911.i | 1.23968 | − | 0.900680i | ||||
\(664\) | −117653. | − | 85480.1i | −0.266850 | − | 0.193878i | ||||
\(665\) | 68417.5 | + | 210568.i | 0.154712 | + | 0.476155i | ||||
\(666\) | −36381.2 | + | 11821.0i | −0.0820216 | + | 0.0266504i | ||||
\(667\) | 87131.0 | − | 119925.i | 0.195849 | − | 0.269563i | ||||
\(668\) | −254571. | − | 350387.i | −0.570501 | − | 0.785228i | ||||
\(669\) | 48381.6 | − | 148903.i | 0.108101 | − | 0.332699i | ||||
\(670\) | − | 130523.i | − | 0.290761i | ||||||
\(671\) | 6234.56 | + | 56276.5i | 0.0138472 | + | 0.124992i | ||||
\(672\) | −85045.3 | −0.188327 | ||||||||
\(673\) | −126138. | − | 40984.7i | −0.278494 | − | 0.0904880i | 0.166440 | − | 0.986052i | \(-0.446773\pi\) |
−0.444934 | + | 0.895564i | \(0.646773\pi\) | |||||||
\(674\) | 48897.2 | − | 35525.9i | 0.107638 | − | 0.0782033i | ||||
\(675\) | −41291.9 | − | 30000.3i | −0.0906269 | − | 0.0658443i | ||||
\(676\) | −321540. | − | 989599.i | −0.703626 | − | 2.16554i | ||||
\(677\) | −116862. | + | 37970.7i | −0.254974 | + | 0.0828460i | −0.433715 | − | 0.901050i | \(-0.642798\pi\) |
0.178741 | + | 0.983896i | \(0.442798\pi\) | |||||||
\(678\) | 13405.6 | − | 18451.2i | 0.0291626 | − | 0.0401388i | ||||
\(679\) | −68156.0 | − | 93808.6i | −0.147831 | − | 0.203471i | ||||
\(680\) | −99646.9 | + | 306682.i | −0.215499 | + | 0.663239i | ||||
\(681\) | − | 186550.i | − | 0.402256i | ||||||
\(682\) | 91315.9 | + | 100279.i | 0.196326 | + | 0.215595i | ||||
\(683\) | 320565. | 0.687187 | 0.343593 | − | 0.939119i | \(-0.388356\pi\) | ||||
0.343593 | + | 0.939119i | \(0.388356\pi\) | |||||||
\(684\) | 96899.6 | + | 31484.6i | 0.207114 | + | 0.0672954i | ||||
\(685\) | −73017.4 | + | 53050.3i | −0.155613 | + | 0.113059i | ||||
\(686\) | 72218.0 | + | 52469.4i | 0.153461 | + | 0.111496i | ||||
\(687\) | 42880.1 | + | 131971.i | 0.0908537 | + | 0.279619i | ||||
\(688\) | −62095.2 | + | 20176.0i | −0.131184 | + | 0.0426243i | ||||
\(689\) | 202478. | − | 278687.i | 0.426520 | − | 0.587054i | ||||
\(690\) | 39775.0 | + | 54745.6i | 0.0835433 | + | 0.114988i | ||||
\(691\) | −103330. | + | 318018.i | −0.216407 | + | 0.666032i | 0.782644 | + | 0.622470i | \(0.213871\pi\) |
−0.999051 | + | 0.0435621i | \(0.986129\pi\) | |||||||
\(692\) | − | 509356.i | − | 1.06368i | ||||||
\(693\) | 85482.7 | − | 38635.9i | 0.177997 | − | 0.0804497i | ||||
\(694\) | −102670. | −0.213169 | ||||||||
\(695\) | −285783. | − | 92856.5i | −0.591653 | − | 0.192240i | ||||
\(696\) | 28852.5 | − | 20962.6i | 0.0595615 | − | 0.0432740i | ||||
\(697\) | −166754. | − | 121154.i | −0.343250 | − | 0.249386i | ||||
\(698\) | −29575.4 | − | 91023.9i | −0.0607044 | − | 0.186829i | ||||
\(699\) | −251466. | + | 81706.4i | −0.514666 | + | 0.167225i | ||||
\(700\) | 94490.0 | − | 130054.i | 0.192837 | − | 0.265417i | ||||
\(701\) | −75545.2 | − | 103979.i | −0.153734 | − | 0.211597i | 0.725202 | − | 0.688536i | \(-0.241746\pi\) |
−0.878936 | + | 0.476939i | \(0.841746\pi\) | |||||||
\(702\) | 10508.6 | − | 32342.1i | 0.0213240 | − | 0.0656287i | ||||
\(703\) | 444489.i | 0.899395i | ||||||||
\(704\) | 335071. | + | 190953.i | 0.676069 | + | 0.385284i | ||||
\(705\) | −74710.1 | −0.150315 | ||||||||
\(706\) | 151330. | + | 49170.2i | 0.303610 | + | 0.0986490i | ||||
\(707\) | −6977.67 | + | 5069.57i | −0.0139596 | + | 0.0101422i | ||||
\(708\) | −23606.4 | − | 17151.1i | −0.0470938 | − | 0.0342156i | ||||
\(709\) | −104746. | − | 322376.i | −0.208375 | − | 0.641312i | −0.999558 | − | 0.0297327i | \(-0.990534\pi\) |
0.791183 | − | 0.611580i | \(-0.209466\pi\) | |||||||
\(710\) | −222330. | + | 72239.5i | −0.441044 | + | 0.143304i | ||||
\(711\) | −103483. | + | 142432.i | −0.204705 | + | 0.281752i | ||||
\(712\) | −77309.7 | − | 106408.i | −0.152501 | − | 0.209900i | ||||
\(713\) | 234816. | − | 722689.i | 0.461901 | − | 1.42158i | ||||
\(714\) | 48744.2i | 0.0956152i | ||||||||
\(715\) | −1.15555e6 | − | 238845.i | −2.26035 | − | 0.467202i | ||||
\(716\) | −751237. | −1.46538 | ||||||||
\(717\) | −274368. | − | 89147.7i | −0.533698 | − | 0.173409i | ||||
\(718\) | −108363. | + | 78730.0i | −0.210199 | + | 0.152718i | ||||
\(719\) | 44414.8 | + | 32269.2i | 0.0859151 | + | 0.0624210i | 0.629914 | − | 0.776665i | \(-0.283090\pi\) |
−0.543999 | + | 0.839086i | \(0.683090\pi\) | |||||||
\(720\) | −59569.2 | − | 183335.i | −0.114910 | − | 0.353656i | ||||
\(721\) | −19744.1 | + | 6415.24i | −0.0379810 | + | 0.0123408i | ||||
\(722\) | 32247.5 | − | 44384.9i | 0.0618617 | − | 0.0851453i | ||||
\(723\) | 330168. | + | 454437.i | 0.631624 | + | 0.869356i | ||||
\(724\) | −32763.7 | + | 100836.i | −0.0625052 | + | 0.192371i | ||||
\(725\) | 101775.i | 0.193628i | ||||||||
\(726\) | 59201.9 | + | 5550.97i | 0.112321 | + | 0.0105316i | ||||
\(727\) | 87856.0 | 0.166227 | 0.0831137 | − | 0.996540i | \(-0.473514\pi\) | ||||
0.0831137 | + | 0.996540i | \(0.473514\pi\) | |||||||
\(728\) | 207775. | + | 67510.3i | 0.392041 | + | 0.127382i | ||||
\(729\) | −15923.9 | + | 11569.4i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 85077.2 | + | 61812.2i | 0.159649 | + | 0.115992i | ||||
\(731\) | 37143.0 | + | 114314.i | 0.0695092 | + | 0.213927i | ||||
\(732\) | 35587.0 | − | 11562.9i | 0.0664155 | − | 0.0215797i | ||||
\(733\) | 92401.6 | − | 127180.i | 0.171977 | − | 0.236707i | −0.714324 | − | 0.699815i | \(-0.753266\pi\) |
0.886302 | + | 0.463108i | \(0.153266\pi\) | |||||||
\(734\) | 30169.7 | + | 41525.0i | 0.0559988 | + | 0.0770757i | ||||
\(735\) | −79600.3 | + | 244985.i | −0.147347 | + | 0.453486i | ||||
\(736\) | 302028.i | 0.557560i | ||||||||
\(737\) | −130071. | + | 629288.i | −0.239466 | + | 1.15855i | ||||
\(738\) | −10406.4 | −0.0191068 | ||||||||
\(739\) | 86255.3 | + | 28026.0i | 0.157942 | + | 0.0513184i | 0.386921 | − | 0.922113i | \(-0.373539\pi\) |
−0.228979 | + | 0.973431i | \(0.573539\pi\) | |||||||
\(740\) | 709656. | − | 515595.i | 1.29594 | − | 0.941554i | ||||
\(741\) | −319676. | − | 232258.i | −0.582202 | − | 0.422994i | ||||
\(742\) | 7703.46 | + | 23708.8i | 0.0139919 | + | 0.0430628i | ||||
\(743\) | 287546. | − | 93429.2i | 0.520870 | − | 0.169241i | −0.0367703 | − | 0.999324i | \(-0.511707\pi\) |
0.557640 | + | 0.830083i | \(0.311707\pi\) | |||||||
\(744\) | 107457. | − | 147903.i | 0.194129 | − | 0.267196i | ||||
\(745\) | 728704. | + | 1.00297e6i | 1.31292 | + | 1.80708i | ||||
\(746\) | −4937.01 | + | 15194.6i | −0.00887129 | + | 0.0273030i | ||||
\(747\) | − | 160047.i | − | 0.286818i | ||||||
\(748\) | 385374. | − | 676228.i | 0.688778 | − | 1.20862i | ||||
\(749\) | 561528. | 1.00094 | ||||||||
\(750\) | 31725.0 | + | 10308.1i | 0.0563999 | + | 0.0183254i | ||||
\(751\) | 399821. | − | 290487.i | 0.708901 | − | 0.515047i | −0.173918 | − | 0.984760i | \(-0.555643\pi\) |
0.882819 | + | 0.469713i | \(0.155643\pi\) | |||||||
\(752\) | −83989.1 | − | 61021.7i | −0.148521 | − | 0.107907i | ||||
\(753\) | 58084.5 | + | 178766.i | 0.102440 | + | 0.315278i | ||||
\(754\) | −64491.7 | + | 20954.6i | −0.113439 | + | 0.0368585i | ||||
\(755\) | −184304. | + | 253673.i | −0.323327 | + | 0.445021i | ||||
\(756\) | −36439.3 | − | 50154.4i | −0.0637568 | − | 0.0877538i | ||||
\(757\) | −108607. | + | 334257.i | −0.189524 | + | 0.583296i | −0.999997 | − | 0.00248051i | \(-0.999210\pi\) |
0.810473 | + | 0.585777i | \(0.199210\pi\) | |||||||
\(758\) | − | 84196.0i | − | 0.146539i | ||||||
\(759\) | −137211. | − | 303582.i | −0.238180 | − | 0.526977i | ||||
\(760\) | 189171. | 0.327512 | ||||||||
\(761\) | −458813. | − | 149077.i | −0.792257 | − | 0.257420i | −0.115192 | − | 0.993343i | \(-0.536748\pi\) |
−0.677065 | + | 0.735923i | \(0.736748\pi\) | |||||||
\(762\) | −67703.5 | + | 49189.5i | −0.116601 | + | 0.0847154i | ||||
\(763\) | 278792. | + | 202555.i | 0.478886 | + | 0.347931i | ||||
\(764\) | 66071.2 | + | 203346.i | 0.113195 | + | 0.348377i | ||||
\(765\) | −337512. | + | 109664.i | −0.576721 | + | 0.187388i | ||||
\(766\) | 62308.4 | − | 85760.2i | 0.106191 | − | 0.146160i | ||||
\(767\) | 66516.3 | + | 91551.8i | 0.113067 | + | 0.155624i | ||||
\(768\) | 67313.1 | − | 207168.i | 0.114124 | − | 0.351238i | ||||
\(769\) | 701862.i | 1.18686i | 0.804886 | + | 0.593430i | \(0.202226\pi\) | ||||
−0.804886 | + | 0.593430i | \(0.797774\pi\) | |||||||
\(770\) | 63136.6 | − | 57493.6i | 0.106488 | − | 0.0969702i | ||||
\(771\) | −454360. | −0.764349 | ||||||||
\(772\) | 696869. | + | 226427.i | 1.16928 | + | 0.379921i | ||||
\(773\) | −632317. | + | 459405.i | −1.05822 | + | 0.768842i | −0.973758 | − | 0.227585i | \(-0.926917\pi\) |
−0.0844615 | + | 0.996427i | \(0.526917\pi\) | |||||||
\(774\) | 4909.47 | + | 3566.94i | 0.00819508 | + | 0.00595407i | ||||
\(775\) | 161219. | + | 496182.i | 0.268419 | + | 0.826110i | ||||
\(776\) | −94224.0 | + | 30615.2i | −0.156472 | + | 0.0508410i | ||||
\(777\) | 158970. | − | 218804.i | 0.263314 | − | 0.362421i | ||||
\(778\) | −81358.4 | − | 111980.i | −0.134414 | − | 0.185004i | ||||
\(779\) | −37365.8 | + | 115000.i | −0.0615743 | + | 0.189506i | ||||
\(780\) | 779797.i | 1.28172i | ||||||||
\(781\) | 1.14391e6 | − | 126727.i | 1.87538 | − | 0.207763i | ||||
\(782\) | 173109. | 0.283079 | ||||||||
\(783\) | 37327.9 | + | 12128.6i | 0.0608850 | + | 0.0197827i | ||||
\(784\) | −289585. | + | 210396.i | −0.471134 | + | 0.342299i | ||||
\(785\) | −1.04878e6 | − | 761980.i | −1.70194 | − | 1.23653i | ||||
\(786\) | 949.684 | + | 2922.83i | 0.00153721 | + | 0.00473105i | ||||
\(787\) | 1.12996e6 | − | 367145.i | 1.82437 | − | 0.592772i | 0.824737 | − | 0.565516i | \(-0.191323\pi\) |
0.999628 | − | 0.0272562i | \(-0.00867700\pi\) | |||||||
\(788\) | −455119. | + | 626417.i | −0.732947 | + | 1.00881i | ||||
\(789\) | −331617. | − | 456432.i | −0.532700 | − | 0.733199i | ||||
\(790\) | −49522.8 | + | 152416.i | −0.0793508 | + | 0.244217i | ||||
\(791\) | 161248.i | 0.257715i | ||||||||
\(792\) | −8825.55 | − | 79664.1i | −0.0140699 | − | 0.127003i | ||||
\(793\) | −145118. | −0.230768 | ||||||||
\(794\) | −99168.0 | − | 32221.6i | −0.157301 | − | 0.0511101i | ||||
\(795\) | −146832. | + | 106680.i | −0.232320 | + | 0.168790i | ||||
\(796\) | −150573. | − | 109398.i | −0.237641 | − | 0.172656i | ||||
\(797\) | 181012. | + | 557098.i | 0.284965 | + | 0.877032i | 0.986409 | + | 0.164307i | \(0.0525389\pi\) |
−0.701444 | + | 0.712724i | \(0.747461\pi\) | |||||||
\(798\) | 27195.9 | − | 8836.48i | 0.0427068 | − | 0.0138763i | ||||
\(799\) | −112338. | + | 154620.i | −0.175968 | + | 0.242199i | ||||
\(800\) | −121886. | − | 167762.i | −0.190448 | − | 0.262129i | ||||
\(801\) | 44730.0 | − | 137665.i | 0.0697162 | − | 0.214564i | ||||
\(802\) | 78668.7i | 0.122307i | ||||||||
\(803\) | −348584. | − | 382797.i | −0.540600 | − | 0.593660i | ||||
\(804\) | 424662. | 0.656949 | ||||||||
\(805\) | −455014. | − | 147843.i | −0.702155 | − | 0.228144i | ||||
\(806\) | −281221. | + | 204319.i | −0.432889 | + | 0.314513i | ||||
\(807\) | 256308. | + | 186219.i | 0.393564 | + | 0.285941i | ||||
\(808\) | 2277.22 | + | 7008.56i | 0.00348805 | + | 0.0107351i | ||||
\(809\) | 1.04061e6 | − | 338116.i | 1.58998 | − | 0.516616i | 0.625379 | − | 0.780321i | \(-0.284945\pi\) |
0.964603 | + | 0.263705i | \(0.0849445\pi\) | |||||||
\(810\) | −10531.3 | + | 14495.2i | −0.0160514 | + | 0.0220929i | ||||
\(811\) | −182823. | − | 251634.i | −0.277964 | − | 0.382585i | 0.647094 | − | 0.762410i | \(-0.275984\pi\) |
−0.925058 | + | 0.379825i | \(0.875984\pi\) | |||||||
\(812\) | −38200.6 | + | 117569.i | −0.0579373 | + | 0.178313i | ||||
\(813\) | − | 484649.i | − | 0.733240i | ||||||
\(814\) | 156217. | − | 70605.9i | 0.235765 | − | 0.106559i | ||||
\(815\) | 498384. | 0.750324 | ||||||||
\(816\) | −469002. | − | 152388.i | −0.704360 | − | 0.228860i | ||||
\(817\) | 57046.1 | − | 41446.4i | 0.0854637 | − | 0.0620930i | ||||
\(818\) | −169484. | − | 123137.i | −0.253292 | − | 0.184028i | ||||
\(819\) | 74297.0 | + | 228663.i | 0.110765 | + | 0.340900i | ||||
\(820\) | 226948. | − | 73740.0i | 0.337520 | − | 0.109667i | ||||
\(821\) | −72613.1 | + | 99943.4i | −0.107728 | + | 0.148275i | −0.859477 | − | 0.511175i | \(-0.829211\pi\) |
0.751749 | + | 0.659449i | \(0.229211\pi\) | |||||||
\(822\) | 6851.71 | + | 9430.57i | 0.0101404 | + | 0.0139571i | ||||
\(823\) | 117740. | − | 362367.i | 0.173830 | − | 0.534994i | −0.825748 | − | 0.564039i | \(-0.809247\pi\) |
0.999578 | + | 0.0290451i | \(0.00924665\pi\) | |||||||
\(824\) | 17737.8i | 0.0261244i | ||||||||
\(825\) | 198727. | + | 113252.i | 0.291978 | + | 0.166395i | ||||
\(826\) | −8189.43 | −0.0120031 | ||||||||
\(827\) | 403873. | + | 131226.i | 0.590519 | + | 0.191871i | 0.589007 | − | 0.808128i | \(-0.299519\pi\) |
0.00151143 | + | 0.999999i | \(0.499519\pi\) | |||||||
\(828\) | −178117. | + | 129410.i | −0.259804 | + | 0.188759i | ||||
\(829\) | −224958. | − | 163442.i | −0.327335 | − | 0.237823i | 0.411964 | − | 0.911200i | \(-0.364843\pi\) |
−0.739299 | + | 0.673377i | \(0.764843\pi\) | |||||||
\(830\) | −45019.8 | − | 138557.i | −0.0653503 | − | 0.201127i | ||||
\(831\) | −208196. | + | 67646.9i | −0.301488 | + | 0.0979594i | ||||
\(832\) | −580995. | + | 799671.i | −0.839317 | + | 1.15522i | ||||
\(833\) | 387329. | + | 533113.i | 0.558201 | + | 0.768297i | ||||
\(834\) | −11992.9 | + | 36910.3i | −0.0172422 | + | 0.0530660i | ||||
\(835\) | − | 884976.i | − | 1.26928i | ||||||
\(836\) | −447149. | − | 92423.5i | −0.639794 | − | 0.132242i | ||||
\(837\) | 201196. | 0.287189 | ||||||||
\(838\) | 53598.1 | + | 17415.1i | 0.0763241 | + | 0.0247992i | ||||
\(839\) | −1.06899e6 | + | 776670.i | −1.51863 | + | 1.10335i | −0.556467 | + | 0.830870i | \(0.687843\pi\) |
−0.962162 | + | 0.272478i | \(0.912157\pi\) | |||||||
\(840\) | −93121.3 | − | 67656.6i | −0.131975 | − | 0.0958851i | ||||
\(841\) | 194377. | + | 598230.i | 0.274823 | + | 0.845817i | ||||
\(842\) | 205154. | − | 66658.6i | 0.289372 | − | 0.0940226i | ||||
\(843\) | 259672. | − | 357407.i | 0.365401 | − | 0.502931i | ||||
\(844\) | −92834.4 | − | 127776.i | −0.130324 | − | 0.179375i | ||||
\(845\) | 657016. | − | 2.02209e6i | 0.920158 | − | 2.83196i | ||||
\(846\) | 9649.19i | 0.0134819i | ||||||||
\(847\) | −361694. | + | 214276.i | −0.504168 | + | 0.298680i | ||||
\(848\) | −252202. | −0.350717 | ||||||||
\(849\) | 78505.1 | + | 25507.9i | 0.108914 | + | 0.0353882i | ||||
\(850\) | −96154.0 | + | 69860.0i | −0.133085 | + | 0.0966920i | ||||
\(851\) | −777056. | − | 564564.i | −1.07298 | − | 0.779568i | ||||
\(852\) | −235035. | − | 723363.i | −0.323782 | − | 0.996500i | ||||
\(853\) | −875522. | + | 284474.i | −1.20329 | + | 0.390971i | −0.840969 | − | 0.541083i | \(-0.818014\pi\) |
−0.362317 | + | 0.932055i | \(0.618014\pi\) | |||||||
\(854\) | 6172.85 | − | 8496.19i | 0.00846388 | − | 0.0116495i | ||||
\(855\) | 122370. | + | 168428.i | 0.167395 | + | 0.230399i | ||||
\(856\) | 148260. | − | 456297.i | 0.202337 | − | 0.622731i | ||||
\(857\) | − | 4741.96i | − | 0.00645649i | −0.999995 | − | 0.00322824i | \(-0.998972\pi\) | ||
0.999995 | − | 0.00322824i | \(-0.00102758\pi\) | |||||||
\(858\) | −30848.1 | + | 149245.i | −0.0419039 | + | 0.202733i | ||||
\(859\) | 816737. | 1.10687 | 0.553434 | − | 0.832893i | \(-0.313317\pi\) | ||||
0.553434 | + | 0.832893i | \(0.313317\pi\) | |||||||
\(860\) | −132344. | − | 43001.1i | −0.178940 | − | 0.0581410i | ||||
\(861\) | 59523.1 | − | 43246.1i | 0.0802933 | − | 0.0583365i | ||||
\(862\) | 38435.8 | + | 27925.3i | 0.0517275 | + | 0.0375823i | ||||
\(863\) | −260499. | − | 801735.i | −0.349772 | − | 1.07649i | −0.958979 | − | 0.283477i | \(-0.908512\pi\) |
0.609207 | − | 0.793011i | \(-0.291488\pi\) | |||||||
\(864\) | −76055.0 | + | 24711.8i | −0.101883 | + | 0.0331037i | ||||
\(865\) | 611760. | − | 842015.i | 0.817615 | − | 1.12535i | ||||
\(866\) | −97437.8 | − | 134112.i | −0.129925 | − | 0.178826i | ||||
\(867\) | −146430. | + | 450665.i | −0.194801 | + | 0.599536i | ||||
\(868\) | 633694.i | 0.841086i | ||||||||
\(869\) | 390651. | − | 685488.i | 0.517309 | − | 0.907738i | ||||
\(870\) | 35727.4 | 0.0472023 | ||||||||
\(871\) | −1.56634e6 | − | 508936.i | −2.06467 | − | 0.670852i | ||||
\(872\) | 238205. | − | 173066.i | 0.313269 | − | 0.227603i | ||||
\(873\) | −88209.2 | − | 64087.7i | −0.115740 | − | 0.0840904i | ||||
\(874\) | −31381.7 | − | 96582.9i | −0.0410822 | − | 0.126438i | ||||
\(875\) | −224300. | + | 72879.3i | −0.292963 | + | 0.0951893i | ||||
\(876\) | −201109. | + | 276803.i | −0.262074 | + | 0.360714i | ||||
\(877\) | −148432. | − | 204300.i | −0.192988 | − | 0.265625i | 0.701547 | − | 0.712623i | \(-0.252493\pi\) |
−0.894535 | + | 0.446998i | \(0.852493\pi\) | |||||||
\(878\) | −23706.5 | + | 72961.2i | −0.0307524 | + | 0.0946461i | ||||
\(879\) | 479453.i | 0.620537i | ||||||||
\(880\) | 355804. | + | 787222.i | 0.459457 | + | 1.01656i | ||||
\(881\) | 567478. | 0.731134 | 0.365567 | − | 0.930785i | \(-0.380875\pi\) | ||||
0.365567 | + | 0.930785i | \(0.380875\pi\) | |||||||
\(882\) | 31641.0 | + | 10280.8i | 0.0406737 | + | 0.0132157i | ||||
\(883\) | −324452. | + | 235728.i | −0.416130 | + | 0.302336i | −0.776079 | − | 0.630636i | \(-0.782794\pi\) |
0.359949 | + | 0.932972i | \(0.382794\pi\) | |||||||
\(884\) | 1.61387e6 | + | 1.17254e6i | 2.06521 | + | 1.50046i | ||||
\(885\) | −18424.5 | − | 56704.7i | −0.0235239 | − | 0.0723990i | ||||
\(886\) | −157698. | + | 51239.3i | −0.200891 | + | 0.0652734i | ||||
\(887\) | −241774. | + | 332773.i | −0.307299 | + | 0.422961i | −0.934537 | − | 0.355867i | \(-0.884186\pi\) |
0.627237 | + | 0.778828i | \(0.284186\pi\) | |||||||
\(888\) | −135827. | − | 186950.i | −0.172250 | − | 0.237082i | ||||
\(889\) | 182837. | − | 562713.i | 0.231345 | − | 0.712006i | ||||
\(890\) | − | 131762.i | − | 0.166345i | ||||||
\(891\) | 65219.6 | − | 59390.5i | 0.0821529 | − | 0.0748103i | ||||
\(892\) | 463692. | 0.582773 | ||||||||
\(893\) | 106632. | + | 34646.9i | 0.133717 | + | 0.0434472i | ||||
\(894\) | 129539. | − | 94115.8i | 0.162079 | − | 0.117757i | ||||
\(895\) | −1.24187e6 | − | 902269.i | −1.55035 | − | 1.12639i | ||||
\(896\) | −103027. | − | 317085.i | −0.128332 | − | 0.394966i | ||||
\(897\) | 812068. | − | 263857.i | 1.00927 | − | 0.327932i | ||||
\(898\) | −36907.1 | + | 50798.3i | −0.0457675 | + | 0.0629936i | ||||
\(899\) | −235817. | − | 324574.i | −0.291780 | − | 0.401600i | ||||
\(900\) | 46711.2 | − | 143762.i | 0.0576681 | − | 0.177484i | ||||
\(901\) | 464293.i | 0.571929i | ||||||||
\(902\) | 46352.5 | − | 5135.14i | 0.0569719 | − | 0.00631160i | ||||
\(903\) | −42904.7 | −0.0526173 | ||||||||
\(904\) | 131030. | + | 42574.1i | 0.160337 | + | 0.0520965i | ||||
\(905\) | −175271. | + | 127342.i | −0.213999 | + | 0.155479i | ||||
\(906\) | 32763.2 | + | 23803.9i | 0.0399144 | + | 0.0289995i | ||||
\(907\) | −253651. | − | 780656.i | −0.308334 | − | 0.948954i | −0.978412 | − | 0.206664i | \(-0.933739\pi\) |
0.670078 | − | 0.742291i | \(-0.266261\pi\) | |||||||
\(908\) | 525453. | − | 170730.i | 0.637327 | − | 0.207080i | ||||
\(909\) | −4766.97 | + | 6561.17i | −0.00576919 | + | 0.00794061i | ||||
\(910\) | 128642. | + | 177060.i | 0.155345 | + | 0.213815i | ||||
\(911\) | −486724. | + | 1.49798e6i | −0.586470 | + | 1.80497i | 0.00681336 | + | 0.999977i | \(0.497831\pi\) |
−0.593284 | + | 0.804993i | \(0.702169\pi\) | |||||||
\(912\) | 289296.i | 0.347818i | ||||||||
\(913\) | 78976.7 | + | 712886.i | 0.0947453 | + | 0.855221i | ||||
\(914\) | −257356. | −0.308064 | ||||||||
\(915\) | 72716.4 | + | 23627.0i | 0.0868541 | + | 0.0282206i | ||||
\(916\) | −332478. | + | 241559.i | −0.396252 | + | 0.287894i | ||||
\(917\) | −17578.5 | − | 12771.5i | −0.0209046 | − | 0.0151881i | ||||
\(918\) | 14163.7 | + | 43591.4i | 0.0168070 | + | 0.0517267i | ||||
\(919\) | 719997. | − | 233941.i | 0.852510 | − | 0.276997i | 0.150013 | − | 0.988684i | \(-0.452068\pi\) |
0.702497 | + | 0.711687i | \(0.252068\pi\) | |||||||
\(920\) | −240274. | + | 330709.i | −0.283878 | + | 0.390724i | ||||
\(921\) | −86560.8 | − | 119141.i | −0.102047 | − | 0.140456i | ||||
\(922\) | −96301.8 | + | 296386.i | −0.113285 | + | 0.348655i | ||||
\(923\) | 2.94976e6i | 3.46245i | ||||||||
\(924\) | 187058. | + | 205418.i | 0.219095 | + | 0.240600i | ||||
\(925\) | 659453. | 0.770727 | ||||||||
\(926\) | −71868.2 | − | 23351.4i | −0.0838137 | − | 0.0272327i | ||||
\(927\) | −15792.8 | + | 11474.2i | −0.0183781 | + | 0.0133525i | ||||
\(928\) | 129008. | + | 93729.5i | 0.149803 | + | 0.108838i | ||||
\(929\) | 165153. | + | 508288.i | 0.191361 | + | 0.588950i | 1.00000 | 0.000643743i | \(0.000204910\pi\) | |
−0.808638 | + | 0.588306i | \(0.799795\pi\) | |||||||
\(930\) | 174180. | − | 56594.7i | 0.201388 | − | 0.0654349i | ||||
\(931\) | 227224. | − | 312747.i | 0.262153 | − | 0.360822i | ||||
\(932\) | −460282. | − | 633524.i | −0.529898 | − | 0.729342i | ||||
\(933\) | −196178. | + | 603773.i | −0.225365 | + | 0.693602i | ||||
\(934\) | − | 64962.8i | − | 0.0744682i | ||||||
\(935\) | 1.44924e6 | − | 655018.i | 1.65774 | − | 0.749256i | ||||
\(936\) | 205427. | 0.234481 | ||||||||
\(937\) | −564428. | − | 183394.i | −0.642879 | − | 0.208884i | −0.0306074 | − | 0.999531i | \(-0.509744\pi\) |
−0.612272 | + | 0.790647i | \(0.709744\pi\) | |||||||
\(938\) | 96423.5 | − | 70055.7i | 0.109592 | − | 0.0796229i | ||||
\(939\) | 360884. | + | 262197.i | 0.409295 | + | 0.297370i | ||||
\(940\) | −68374.3 | − | 210435.i | −0.0773816 | − | 0.238156i | ||||
\(941\) | −560514. | + | 182122.i | −0.633005 | + | 0.205676i | −0.607906 | − | 0.794009i | \(-0.707990\pi\) |
−0.0250993 | + | 0.999685i | \(0.507990\pi\) | |||||||
\(942\) | −98413.7 | + | 135455.i | −0.110906 | + | 0.152649i | ||||
\(943\) | −153583. | − | 211389.i | −0.172711 | − | 0.237717i | ||||
\(944\) | 25602.4 | − | 78796.2i | 0.0287301 | − | 0.0884222i | ||||
\(945\) | − | 126675.i | − | 0.141850i | ||||||
\(946\) | −23628.1 | − | 13465.4i | −0.0264026 | − | 0.0150465i | ||||
\(947\) | −178526. | −0.199068 | −0.0995341 | − | 0.995034i | \(-0.531735\pi\) | ||||
−0.0995341 | + | 0.995034i | \(0.531735\pi\) | |||||||
\(948\) | −495892. | − | 161125.i | −0.551785 | − | 0.179286i | ||||
\(949\) | 1.07351e6 | − | 779953.i | 1.19200 | − | 0.866036i | ||||
\(950\) | 56408.0 | + | 40982.8i | 0.0625020 | + | 0.0454103i | ||||
\(951\) | −6866.87 | − | 21134.0i | −0.00759272 | − | 0.0233680i | ||||
\(952\) | −280044. | + | 90991.9i | −0.308996 | + | 0.100399i | ||||
\(953\) | 510482. | − | 702618.i | 0.562075 | − | 0.773630i | −0.429513 | − | 0.903060i | \(-0.641315\pi\) |
0.991588 | + | 0.129431i | \(0.0413149\pi\) | |||||||
\(954\) | 13778.2 | + | 18964.1i | 0.0151390 | + | 0.0208370i | ||||
\(955\) | −135006. | + | 415506.i | −0.148029 | + | 0.455586i | ||||
\(956\) | − | 854396.i | − | 0.934853i | ||||||
\(957\) | −172252. | − | 35603.7i | −0.188079 | − | 0.0388750i | ||||
\(958\) | 262695. | 0.286234 | ||||||||
\(959\) | −78381.6 | − | 25467.7i | −0.0852269 | − | 0.0276919i | ||||
\(960\) | 421323. | − | 306109.i | 0.457165 | − | 0.332150i | ||||
\(961\) | −916669. | − | 665999.i | −0.992581 | − | 0.721152i | ||||
\(962\) | 135775. | + | 417873.i | 0.146714 | + | 0.451538i | ||||
\(963\) | 502168. | − | 163164.i | 0.541497 | − | 0.175943i | ||||
\(964\) | −977837. | + | 1.34588e6i | −1.05223 | + | 1.44828i | ||||
\(965\) | 880044. | + | 1.21128e6i | 0.945039 | + | 1.30073i | ||||
\(966\) | −19094.7 | + | 58767.4i | −0.0204625 | + | 0.0629770i | ||||
\(967\) | 258949.i | 0.276925i | 0.990368 | + | 0.138462i | \(0.0442160\pi\) | ||||
−0.990368 | + | 0.138462i | \(0.955784\pi\) | |||||||
\(968\) | 78622.1 | + | 350487.i | 0.0839062 | + | 0.374043i | ||||
\(969\) | 532580. | 0.567202 | ||||||||
\(970\) | −94392.3 | − | 30669.9i | −0.100321 | − | 0.0325963i | ||||
\(971\) | 780921. | − | 567373.i | 0.828264 | − | 0.601769i | −0.0908035 | − | 0.995869i | \(-0.528944\pi\) |
0.919068 | + | 0.394100i | \(0.128944\pi\) | |||||||
\(972\) | −47160.7 | − | 34264.3i | −0.0499169 | − | 0.0362668i | ||||
\(973\) | −84791.3 | − | 260961.i | −0.0895624 | − | 0.275645i | ||||
\(974\) | 51369.4 | − | 16690.9i | 0.0541485 | − | 0.0175939i | ||||
\(975\) | −344583. | + | 474278.i | −0.362481 | + | 0.498912i | ||||
\(976\) | 62449.8 | + | 85954.7i | 0.0655588 | + | 0.0902340i | ||||
\(977\) | 337487. | − | 1.03868e6i | 0.353563 | − | 1.08816i | −0.603274 | − | 0.797534i | \(-0.706138\pi\) |
0.956838 | − | 0.290623i | \(-0.0938624\pi\) | |||||||
\(978\) | − | 64368.8i | − | 0.0672974i | ||||||
\(979\) | −131306. | + | 635263.i | −0.136999 | + | 0.662809i | ||||
\(980\) | −762894. | −0.794350 | ||||||||
\(981\) | 308177. | + | 100133.i | 0.320230 | + | 0.104049i | ||||
\(982\) | 67315.5 | − | 48907.6i | 0.0698059 | − | 0.0507170i | ||||
\(983\) | −279917. | − | 203371.i | −0.289682 | − | 0.210466i | 0.433447 | − | 0.901179i | \(-0.357297\pi\) |
−0.723129 | + | 0.690713i | \(0.757297\pi\) | |||||||
\(984\) | −19425.9 | − | 59786.6i | −0.0200627 | − | 0.0617467i | ||||
\(985\) | −1.50471e6 | + | 488910.i | −1.55089 | + | 0.503914i | ||||
\(986\) | 53721.6 | − | 73941.5i | 0.0552580 | − | 0.0760562i | ||||
\(987\) | −40099.3 | − | 55192.0i | −0.0411626 | − | 0.0566554i | ||||
\(988\) | 361631. | − | 1.11299e6i | 0.370469 | − | 1.14019i | ||||
\(989\) | 152371.i | 0.155779i | ||||||||
\(990\) | 39756.3 | − | 69761.6i | 0.0405635 | − | 0.0711780i | ||||
\(991\) | −1.42675e6 | −1.45278 | −0.726392 | − | 0.687281i | \(-0.758804\pi\) | ||||
−0.726392 | + | 0.687281i | \(0.758804\pi\) | |||||||
\(992\) | 777419. | + | 252599.i | 0.790009 | + | 0.256689i | ||||
\(993\) | −272521. | + | 197998.i | −0.276377 | + | 0.200799i | ||||
\(994\) | −172699. | − | 125473.i | −0.174790 | − | 0.126992i | ||||
\(995\) | −117520. | − | 361690.i | −0.118704 | − | 0.365334i | ||||
\(996\) | 450801. | − | 146474.i | 0.454429 | − | 0.147653i | ||||
\(997\) | −151253. | + | 208182.i | −0.152165 | + | 0.209437i | −0.878293 | − | 0.478122i | \(-0.841318\pi\) |
0.726129 | + | 0.687559i | \(0.241318\pi\) | |||||||
\(998\) | 2513.36 | + | 3459.34i | 0.00252344 | + | 0.00347322i | ||||
\(999\) | 78587.0 | − | 241866.i | 0.0787444 | − | 0.242350i |
(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 | 33.5.g.a.13.5 | ✓ | 32 | |
3.2 | odd | 2 | 99.5.k.c.46.4 | 32 | |||
11.4 | even | 5 | 363.5.c.e.241.20 | 32 | |||
11.6 | odd | 10 | inner | 33.5.g.a.28.5 | yes | 32 | |
11.7 | odd | 10 | 363.5.c.e.241.13 | 32 | |||
33.17 | even | 10 | 99.5.k.c.28.4 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.g.a.13.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
33.5.g.a.28.5 | yes | 32 | 11.6 | odd | 10 | inner | |
99.5.k.c.28.4 | 32 | 33.17 | even | 10 | |||
99.5.k.c.46.4 | 32 | 3.2 | odd | 2 | |||
363.5.c.e.241.13 | 32 | 11.7 | odd | 10 | |||
363.5.c.e.241.20 | 32 | 11.4 | even | 5 |