Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,3,Mod(19,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.k (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: | \(2.69755461717\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 21x^{14} + 227x^{12} - 1488x^{10} + 24225x^{8} - 62832x^{6} + 64372x^{4} + 7986x^{2} + 14641 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 28.2 | ||
Root | \(-0.386583 - 0.532086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.28 |
Dual form | 99.3.k.b.46.2 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.625505 | + | 0.203239i | −0.312753 | + | 0.101619i | −0.461187 | − | 0.887303i | \(-0.652576\pi\) |
0.148435 | + | 0.988922i | \(0.452576\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.88612 | + | 2.09689i | −0.721529 | + | 0.524222i | ||||
\(5\) | 2.50346 | − | 7.70484i | 0.500691 | − | 1.54097i | −0.307205 | − | 0.951643i | \(-0.599394\pi\) |
0.807896 | − | 0.589325i | \(-0.200606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.40175 | − | 3.30573i | −0.343108 | − | 0.472247i | 0.602238 | − | 0.798316i | \(-0.294276\pi\) |
−0.945346 | + | 0.326069i | \(0.894276\pi\) | |||||||
\(8\) | 2.92545 | − | 4.02653i | 0.365681 | − | 0.503316i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 5.32822i | 0.532822i | ||||||||
\(11\) | 6.70179 | − | 8.72273i | 0.609254 | − | 0.792975i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.0643 | − | 4.56975i | 1.08187 | − | 0.351520i | 0.286768 | − | 0.958000i | \(-0.407419\pi\) |
0.795098 | + | 0.606481i | \(0.207419\pi\) | |||||||
\(14\) | 2.17416 | + | 1.57962i | 0.155297 | + | 0.112830i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.39806 | − | 10.4582i | 0.212379 | − | 0.653635i | ||||
\(17\) | −28.0003 | − | 9.09786i | −1.64708 | − | 0.535169i | −0.668975 | − | 0.743285i | \(-0.733267\pi\) |
−0.978104 | + | 0.208116i | \(0.933267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.52161 | + | 10.3526i | −0.395874 | + | 0.544874i | −0.959702 | − | 0.281018i | \(-0.909328\pi\) |
0.563828 | + | 0.825892i | \(0.309328\pi\) | |||||||
\(20\) | 8.93092 | + | 27.4865i | 0.446546 | + | 1.37433i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.41921 | + | 6.81818i | −0.109964 | + | 0.309917i | ||||
\(23\) | 12.6293 | 0.549101 | 0.274551 | − | 0.961573i | \(-0.411471\pi\) | ||||
0.274551 | + | 0.961573i | \(0.411471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −32.8719 | − | 23.8828i | −1.31488 | − | 0.955314i | ||||
\(26\) | −7.86851 | + | 5.71681i | −0.302635 | + | 0.219877i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.8635 | + | 4.50452i | 0.495124 | + | 0.160876i | ||||
\(29\) | 7.85901 | + | 10.8170i | 0.271000 | + | 0.373000i | 0.922727 | − | 0.385454i | \(-0.125955\pi\) |
−0.651727 | + | 0.758454i | \(0.725955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.9884 | + | 33.8187i | 0.354464 | + | 1.09093i | 0.956320 | + | 0.292322i | \(0.0944280\pi\) |
−0.601856 | + | 0.798604i | \(0.705572\pi\) | |||||||
\(32\) | 27.1405i | 0.848141i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 19.3634 | 0.569512 | ||||||||
\(35\) | −31.4828 | + | 10.2294i | −0.899509 | + | 0.292268i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.5329 | − | 10.5587i | 0.392780 | − | 0.285371i | −0.373814 | − | 0.927504i | \(-0.621950\pi\) |
0.766594 | + | 0.642132i | \(0.221950\pi\) | |||||||
\(38\) | 2.60075 | − | 8.00429i | 0.0684408 | − | 0.210639i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −23.7001 | − | 32.6203i | −0.592502 | − | 0.815509i | ||||
\(41\) | −9.51144 | + | 13.0914i | −0.231986 | + | 0.319302i | −0.909101 | − | 0.416576i | \(-0.863230\pi\) |
0.677115 | + | 0.735877i | \(0.263230\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 44.2415i | 1.02887i | 0.857529 | + | 0.514436i | \(0.171999\pi\) | ||||
−0.857529 | + | 0.514436i | \(0.828001\pi\) | |||||||
\(44\) | −1.05159 | + | 39.2277i | −0.0238998 | + | 0.891539i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.89971 | + | 2.56677i | −0.171733 | + | 0.0557994i | ||||
\(47\) | −7.76454 | − | 5.64127i | −0.165203 | − | 0.120027i | 0.502112 | − | 0.864803i | \(-0.332557\pi\) |
−0.667315 | + | 0.744776i | \(0.732557\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.98240 | − | 30.7227i | 0.203723 | − | 0.626994i | ||||
\(50\) | 25.4155 | + | 8.25799i | 0.508309 | + | 0.165160i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −31.0088 | + | 42.6800i | −0.596324 | + | 0.820769i | ||||
\(53\) | −17.8438 | − | 54.9177i | −0.336676 | − | 1.03618i | −0.965890 | − | 0.258951i | \(-0.916623\pi\) |
0.629214 | − | 0.777232i | \(-0.283377\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −50.4296 | − | 73.4732i | −0.916902 | − | 1.33588i | ||||
\(56\) | −20.3368 | −0.363157 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.11429 | − | 5.16883i | −0.122660 | − | 0.0891178i | ||||
\(59\) | 81.1105 | − | 58.9302i | 1.37475 | − | 0.998817i | 0.377405 | − | 0.926048i | \(-0.376817\pi\) |
0.997349 | − | 0.0727685i | \(-0.0231834\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 79.0445 | + | 25.6831i | 1.29581 | + | 0.421035i | 0.874123 | − | 0.485705i | \(-0.161437\pi\) |
0.421690 | + | 0.906740i | \(0.361437\pi\) | |||||||
\(62\) | −13.7466 | − | 18.9205i | −0.221719 | − | 0.305170i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.07624 | + | 24.8561i | 0.126191 | + | 0.388377i | ||||
\(65\) | − | 119.803i | − | 1.84312i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 87.5688 | 1.30700 | 0.653499 | − | 0.756928i | \(-0.273301\pi\) | ||||
0.653499 | + | 0.756928i | \(0.273301\pi\) | |||||||
\(68\) | 99.8895 | − | 32.4561i | 1.46896 | − | 0.477295i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 17.6136 | − | 12.7971i | 0.251624 | − | 0.182815i | ||||
\(71\) | −21.1594 | + | 65.1219i | −0.298019 | + | 0.917210i | 0.684171 | + | 0.729322i | \(0.260164\pi\) |
−0.982190 | + | 0.187888i | \(0.939836\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.2790 | − | 21.0298i | −0.209302 | − | 0.288079i | 0.691440 | − | 0.722434i | \(-0.256977\pi\) |
−0.900742 | + | 0.434355i | \(0.856977\pi\) | |||||||
\(74\) | −6.94443 | + | 9.55819i | −0.0938436 | + | 0.129165i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 45.6508i | − | 0.600668i | ||||||
\(77\) | −44.9310 | − | 1.20448i | −0.583520 | − | 0.0156426i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −62.3915 | + | 20.2722i | −0.789766 | + | 0.256611i | −0.676004 | − | 0.736898i | \(-0.736290\pi\) |
−0.113762 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(80\) | −72.0716 | − | 52.3631i | −0.900895 | − | 0.654538i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.28878 | − | 10.1218i | 0.0401070 | − | 0.123437i | ||||
\(83\) | 83.0198 | + | 26.9748i | 1.00024 | + | 0.324997i | 0.762961 | − | 0.646444i | \(-0.223745\pi\) |
0.237278 | + | 0.971442i | \(0.423745\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −140.195 | + | 192.962i | −1.64936 | + | 2.27014i | ||||
\(86\) | −8.99160 | − | 27.6733i | −0.104554 | − | 0.321783i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.5166 | − | 52.5028i | −0.176325 | − | 0.596623i | ||||
\(89\) | −29.3444 | −0.329713 | −0.164856 | − | 0.986318i | \(-0.552716\pi\) | ||||
−0.164856 | + | 0.986318i | \(0.552716\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −48.8852 | − | 35.5172i | −0.537200 | − | 0.390299i | ||||
\(92\) | −36.4497 | + | 26.4823i | −0.396193 | + | 0.287851i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00329 | + | 1.95059i | 0.0638647 | + | 0.0207509i | ||||
\(95\) | 60.9352 | + | 83.8701i | 0.641423 | + | 0.882843i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3670 | − | 34.9841i | −0.117186 | − | 0.360661i | 0.875211 | − | 0.483741i | \(-0.160723\pi\) |
−0.992397 | + | 0.123081i | \(0.960723\pi\) | |||||||
\(98\) | 21.2460i | 0.216796i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 144.952 | 1.44952 | ||||||||
\(101\) | −86.1862 | + | 28.0036i | −0.853329 | + | 0.277263i | −0.702840 | − | 0.711348i | \(-0.748085\pi\) |
−0.150489 | + | 0.988612i | \(0.548085\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 124.184 | − | 90.2248i | 1.20567 | − | 0.875969i | 0.210838 | − | 0.977521i | \(-0.432381\pi\) |
0.994830 | + | 0.101552i | \(0.0323809\pi\) | |||||||
\(104\) | 22.7440 | − | 69.9987i | 0.218692 | − | 0.673065i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.3228 | + | 30.7247i | 0.210593 | + | 0.289856i | ||||
\(107\) | −39.6735 | + | 54.6059i | −0.370780 | + | 0.510336i | −0.953113 | − | 0.302615i | \(-0.902140\pi\) |
0.582332 | + | 0.812951i | \(0.302140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 150.536i | 1.38106i | 0.723304 | + | 0.690530i | \(0.242623\pi\) | ||||
−0.723304 | + | 0.690530i | \(0.757377\pi\) | |||||||
\(110\) | 46.4766 | + | 35.7086i | 0.422515 | + | 0.324624i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −42.7331 | + | 13.8848i | −0.381546 | + | 0.123972i | ||||
\(113\) | 118.763 | + | 86.2867i | 1.05100 | + | 0.763599i | 0.972403 | − | 0.233307i | \(-0.0749547\pi\) |
0.0786011 | + | 0.996906i | \(0.474955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.6170 | − | 97.3070i | 0.274930 | − | 0.846148i | ||||
\(116\) | −45.3641 | − | 14.7397i | −0.391070 | − | 0.127066i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −38.7581 | + | 53.3459i | −0.328458 | + | 0.452084i | ||||
\(119\) | 37.1748 | + | 114.412i | 0.312394 | + | 0.961449i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −31.1719 | − | 116.916i | −0.257619 | − | 0.966247i | ||||
\(122\) | −54.6626 | −0.448054 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −102.628 | − | 74.5634i | −0.827643 | − | 0.601318i | ||||
\(125\) | −102.454 | + | 74.4369i | −0.819629 | + | 0.595496i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 61.3816 | + | 19.9441i | 0.483320 | + | 0.157040i | 0.540535 | − | 0.841322i | \(-0.318222\pi\) |
−0.0572147 | + | 0.998362i | \(0.518222\pi\) | |||||||
\(128\) | −73.9146 | − | 101.735i | −0.577458 | − | 0.794803i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 24.3486 | + | 74.9374i | 0.187297 | + | 0.576442i | ||||
\(131\) | 222.809i | 1.70083i | 0.526110 | + | 0.850416i | \(0.323650\pi\) | ||||
−0.526110 | + | 0.850416i | \(0.676350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 52.2879 | 0.393142 | ||||||||
\(134\) | −54.7747 | + | 17.7974i | −0.408767 | + | 0.132816i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −118.546 | + | 86.1289i | −0.871664 | + | 0.633301i | ||||
\(137\) | −15.7350 | + | 48.4274i | −0.114854 | + | 0.353485i | −0.991917 | − | 0.126892i | \(-0.959500\pi\) |
0.877062 | + | 0.480376i | \(0.159500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −78.0268 | − | 107.395i | −0.561344 | − | 0.772623i | 0.430153 | − | 0.902756i | \(-0.358460\pi\) |
−0.991497 | + | 0.130133i | \(0.958460\pi\) | |||||||
\(140\) | 69.4132 | − | 95.5391i | 0.495809 | − | 0.682422i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 45.0345i | − | 0.317144i | ||||||
\(143\) | 54.3950 | − | 153.304i | 0.380385 | − | 1.07206i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 103.018 | − | 33.4726i | 0.710469 | − | 0.230845i | ||||
\(146\) | 13.8312 | + | 10.0489i | 0.0947341 | + | 0.0688283i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.8030 | + | 60.9475i | −0.133804 | + | 0.411808i | ||||
\(149\) | −250.465 | − | 81.3809i | −1.68097 | − | 0.546181i | −0.695872 | − | 0.718166i | \(-0.744982\pi\) |
−0.985100 | + | 0.171985i | \(0.944982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −29.6709 | + | 40.8385i | −0.196496 | + | 0.270453i | −0.895883 | − | 0.444289i | \(-0.853456\pi\) |
0.699387 | + | 0.714743i | \(0.253456\pi\) | |||||||
\(152\) | 19.6810 | + | 60.5720i | 0.129480 | + | 0.398500i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 28.3494 | − | 8.37832i | 0.184087 | − | 0.0544047i | ||||
\(155\) | 288.077 | 1.85856 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.3706 | − | 17.7063i | −0.155227 | − | 0.112779i | 0.507461 | − | 0.861675i | \(-0.330584\pi\) |
−0.662688 | + | 0.748896i | \(0.730584\pi\) | |||||||
\(158\) | 34.9061 | − | 25.3608i | 0.220925 | − | 0.160511i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 209.113 | + | 67.9451i | 1.30696 | + | 0.424657i | ||||
\(161\) | −30.3325 | − | 41.7491i | −0.188401 | − | 0.259311i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31.7613 | + | 97.7512i | 0.194855 | + | 0.599701i | 0.999978 | + | 0.00659367i | \(0.00209884\pi\) |
−0.805124 | + | 0.593107i | \(0.797901\pi\) | |||||||
\(164\) | − | 57.7276i | − | 0.351998i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −57.4117 | −0.345853 | ||||||||
\(167\) | 126.936 | − | 41.2441i | 0.760098 | − | 0.246971i | 0.0967772 | − | 0.995306i | \(-0.469147\pi\) |
0.663321 | + | 0.748335i | \(0.269147\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 40.1968 | − | 29.2047i | 0.237851 | − | 0.172809i | ||||
\(170\) | 48.4754 | − | 149.192i | 0.285150 | − | 0.877600i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −92.7695 | − | 127.686i | −0.539358 | − | 0.742362i | ||||
\(173\) | 144.968 | − | 199.531i | 0.837963 | − | 1.15336i | −0.148426 | − | 0.988924i | \(-0.547421\pi\) |
0.986388 | − | 0.164433i | \(-0.0525794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 166.026i | 0.948722i | ||||||||
\(176\) | −68.4505 | − | 99.7288i | −0.388924 | − | 0.566641i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.3551 | − | 5.96393i | 0.103119 | − | 0.0335052i | ||||
\(179\) | −53.5634 | − | 38.9161i | −0.299237 | − | 0.217408i | 0.428028 | − | 0.903766i | \(-0.359209\pi\) |
−0.727264 | + | 0.686357i | \(0.759209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 48.9480 | − | 150.646i | 0.270431 | − | 0.832301i | −0.719961 | − | 0.694014i | \(-0.755840\pi\) |
0.990392 | − | 0.138287i | \(-0.0441595\pi\) | |||||||
\(182\) | 37.7964 | + | 12.2808i | 0.207673 | + | 0.0674770i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 36.9464 | − | 50.8524i | 0.200796 | − | 0.276372i | ||||
\(185\) | −44.9711 | − | 138.407i | −0.243087 | − | 0.748144i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −267.011 | + | 183.267i | −1.42786 | + | 0.980039i | ||||
\(188\) | 34.2385 | 0.182120 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −55.1609 | − | 40.0768i | −0.290321 | − | 0.210930i | ||||
\(191\) | −120.402 | + | 87.4774i | −0.630378 | + | 0.457997i | −0.856531 | − | 0.516095i | \(-0.827385\pi\) |
0.226153 | + | 0.974092i | \(0.427385\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −204.065 | − | 66.3048i | −1.05733 | − | 0.343548i | −0.271790 | − | 0.962357i | \(-0.587616\pi\) |
−0.785542 | + | 0.618809i | \(0.787616\pi\) | |||||||
\(194\) | 14.2202 | + | 19.5725i | 0.0733003 | + | 0.100889i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 35.6116 | + | 109.601i | 0.181692 | + | 0.559190i | ||||
\(197\) | − | 54.8802i | − | 0.278580i | −0.990252 | − | 0.139290i | \(-0.955518\pi\) | ||
0.990252 | − | 0.139290i | \(-0.0444820\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −58.1547 | −0.292235 | −0.146117 | − | 0.989267i | \(-0.546678\pi\) | ||||
−0.146117 | + | 0.989267i | \(0.546678\pi\) | |||||||
\(200\) | −192.330 | + | 62.4918i | −0.961650 | + | 0.312459i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 48.2185 | − | 35.0328i | 0.238705 | − | 0.173430i | ||||
\(203\) | 16.8827 | − | 51.9595i | 0.0831659 | − | 0.255958i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 77.0555 | + | 106.058i | 0.375880 | + | 0.517355i | ||||
\(206\) | −59.3404 | + | 81.6750i | −0.288060 | + | 0.396481i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 162.615i | − | 0.781801i | ||||||
\(209\) | 39.8947 | + | 134.990i | 0.190884 | + | 0.645885i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 215.270 | − | 69.9454i | 1.02024 | − | 0.331495i | 0.249313 | − | 0.968423i | \(-0.419795\pi\) |
0.770923 | + | 0.636928i | \(0.219795\pi\) | |||||||
\(212\) | 166.656 | + | 121.082i | 0.786112 | + | 0.571144i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.7179 | − | 42.2195i | 0.0641025 | − | 0.197287i | ||||
\(215\) | 340.874 | + | 110.757i | 1.58546 | + | 0.515148i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 85.4042 | − | 117.549i | 0.393568 | − | 0.541700i | ||||
\(218\) | −30.5947 | − | 94.1607i | −0.140343 | − | 0.431930i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 299.611 | + | 106.307i | 1.36187 | + | 0.483215i | ||||
\(221\) | −435.379 | −1.97004 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 66.7089 | + | 48.4669i | 0.299143 | + | 0.217340i | 0.727224 | − | 0.686400i | \(-0.240810\pi\) |
−0.428081 | + | 0.903740i | \(0.640810\pi\) | |||||||
\(224\) | 89.7192 | − | 65.1848i | 0.400532 | − | 0.291004i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −91.8240 | − | 29.8354i | −0.406301 | − | 0.132015i | ||||
\(227\) | −103.962 | − | 143.092i | −0.457984 | − | 0.630361i | 0.516105 | − | 0.856525i | \(-0.327381\pi\) |
−0.974089 | + | 0.226164i | \(0.927381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.902758 | − | 2.77840i | −0.00394217 | − | 0.0121328i | 0.949066 | − | 0.315077i | \(-0.102030\pi\) |
−0.953008 | + | 0.302944i | \(0.902030\pi\) | |||||||
\(230\) | 67.2918i | 0.292573i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 66.5461 | 0.286837 | ||||||||
\(233\) | 280.090 | − | 91.0066i | 1.20210 | − | 0.390586i | 0.361568 | − | 0.932346i | \(-0.382242\pi\) |
0.840533 | + | 0.541760i | \(0.182242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −62.9033 | + | 45.7019i | −0.267674 | + | 0.194476i | ||||
\(236\) | −110.524 | + | 340.159i | −0.468323 | + | 1.44135i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −46.5061 | − | 64.0102i | −0.195404 | − | 0.268950i | ||||
\(239\) | −201.543 | + | 277.400i | −0.843275 | + | 1.16067i | 0.142029 | + | 0.989862i | \(0.454637\pi\) |
−0.985305 | + | 0.170806i | \(0.945363\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 43.2741i | − | 0.179561i | −0.995962 | − | 0.0897804i | \(-0.971383\pi\) | ||
0.995962 | − | 0.0897804i | \(-0.0286165\pi\) | |||||||
\(242\) | 43.2600 | + | 66.7961i | 0.178760 | + | 0.276017i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −281.986 | + | 91.6230i | −1.15568 | + | 0.375504i | ||||
\(245\) | −211.723 | − | 153.826i | −0.864175 | − | 0.627860i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −58.4770 | + | 179.974i | −0.236749 | + | 0.728638i | ||||
\(248\) | 168.318 | + | 54.6898i | 0.678702 | + | 0.220524i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 48.9568 | − | 67.3833i | 0.195827 | − | 0.269533i | ||||
\(251\) | 36.1563 | + | 111.278i | 0.144049 | + | 0.443337i | 0.996887 | − | 0.0788375i | \(-0.0251208\pi\) |
−0.852838 | + | 0.522175i | \(0.825121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 84.6391 | − | 110.162i | 0.334542 | − | 0.435423i | ||||
\(254\) | −42.4479 | −0.167118 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.6650 | − | 12.8344i | −0.0690040 | − | 0.0501344i | ||||
\(257\) | 22.8578 | − | 16.6072i | 0.0889409 | − | 0.0646193i | −0.542426 | − | 0.840104i | \(-0.682494\pi\) |
0.631367 | + | 0.775484i | \(0.282494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −69.8087 | − | 22.6822i | −0.269531 | − | 0.0875761i | ||||
\(260\) | 251.214 | + | 345.766i | 0.966206 | + | 1.32987i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −45.2835 | − | 139.368i | −0.172838 | − | 0.531940i | ||||
\(263\) | − | 247.683i | − | 0.941759i | −0.882198 | − | 0.470879i | \(-0.843937\pi\) | ||
0.882198 | − | 0.470879i | \(-0.156063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −467.804 | −1.76530 | ||||||||
\(266\) | −32.7064 | + | 10.6269i | −0.122956 | + | 0.0399509i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −252.734 | + | 183.622i | −0.943037 | + | 0.685156i | ||||
\(269\) | −85.7617 | + | 263.947i | −0.318817 | + | 0.981217i | 0.655338 | + | 0.755336i | \(0.272526\pi\) |
−0.974155 | + | 0.225882i | \(0.927474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 232.311 | + | 319.749i | 0.857238 | + | 1.17989i | 0.982221 | + | 0.187727i | \(0.0601122\pi\) |
−0.124984 | + | 0.992159i | \(0.539888\pi\) | |||||||
\(272\) | −190.294 | + | 261.917i | −0.699610 | + | 0.962930i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 33.4896i | − | 0.122225i | ||||||
\(275\) | −428.624 | + | 126.675i | −1.55863 | + | 0.460636i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 199.908 | − | 64.9542i | 0.721691 | − | 0.234492i | 0.0749347 | − | 0.997188i | \(-0.476125\pi\) |
0.646756 | + | 0.762697i | \(0.276125\pi\) | |||||||
\(278\) | 70.6329 | + | 51.3178i | 0.254075 | + | 0.184596i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −50.9123 | + | 156.692i | −0.181830 | + | 0.559614i | ||||
\(281\) | 24.8709 | + | 8.08106i | 0.0885087 | + | 0.0287582i | 0.352937 | − | 0.935647i | \(-0.385183\pi\) |
−0.264428 | + | 0.964405i | \(0.585183\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 173.462 | − | 238.750i | 0.612941 | − | 0.843641i | −0.383874 | − | 0.923385i | \(-0.625410\pi\) |
0.996815 | + | 0.0797445i | \(0.0254105\pi\) | |||||||
\(284\) | −75.4848 | − | 232.318i | −0.265791 | − | 0.818022i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.86699 | + | 106.948i | −0.0100244 | + | 0.373943i | ||||
\(287\) | 66.1206 | 0.230385 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 467.442 | + | 339.617i | 1.61745 | + | 1.17514i | ||||
\(290\) | −57.6354 | + | 41.8745i | −0.198743 | + | 0.144395i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 88.1941 | + | 28.6560i | 0.302035 | + | 0.0981370i | ||||
\(293\) | −36.5499 | − | 50.3066i | −0.124744 | − | 0.171695i | 0.742078 | − | 0.670314i | \(-0.233841\pi\) |
−0.866821 | + | 0.498619i | \(0.833841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −250.992 | − | 772.473i | −0.850819 | − | 2.61855i | ||||
\(296\) | − | 89.4060i | − | 0.302047i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 173.207 | 0.581231 | ||||||||
\(299\) | 177.622 | − | 57.7129i | 0.594054 | − | 0.193020i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 146.251 | − | 106.257i | 0.485882 | − | 0.353014i | ||||
\(302\) | 10.2593 | − | 31.5749i | 0.0339713 | − | 0.104553i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 82.7103 | + | 113.841i | 0.272073 | + | 0.374477i | ||||
\(305\) | 395.769 | − | 544.729i | 1.29760 | − | 1.78600i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 119.712i | 0.389941i | 0.980809 | + | 0.194970i | \(0.0624610\pi\) | ||||
−0.980809 | + | 0.194970i | \(0.937539\pi\) | |||||||
\(308\) | 132.202 | − | 90.7390i | 0.429227 | − | 0.294607i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −180.194 | + | 58.5484i | −0.581270 | + | 0.188866i | ||||
\(311\) | −253.352 | − | 184.071i | −0.814638 | − | 0.591869i | 0.100534 | − | 0.994934i | \(-0.467945\pi\) |
−0.915172 | + | 0.403065i | \(0.867945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −121.315 | + | 373.369i | −0.387588 | + | 1.19287i | 0.546998 | + | 0.837134i | \(0.315770\pi\) |
−0.934586 | + | 0.355738i | \(0.884230\pi\) | |||||||
\(314\) | 18.8426 | + | 6.12232i | 0.0600082 | + | 0.0194978i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 137.561 | − | 189.336i | 0.435319 | − | 0.599165i | ||||
\(317\) | 10.9585 | + | 33.7267i | 0.0345693 | + | 0.106393i | 0.966852 | − | 0.255337i | \(-0.0821863\pi\) |
−0.932283 | + | 0.361730i | \(0.882186\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 147.023 | + | 3.94131i | 0.460888 | + | 0.0123552i | ||||
\(320\) | 211.731 | 0.661659 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 27.4582 | + | 19.9495i | 0.0852739 | + | 0.0619551i | ||||
\(323\) | 304.794 | − | 221.446i | 0.943635 | − | 0.685591i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −571.458 | − | 185.678i | −1.75833 | − | 0.571317i | ||||
\(326\) | −39.7337 | − | 54.6887i | −0.121882 | − | 0.167757i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.8876 | + | 76.5962i | 0.0758768 | + | 0.233525i | ||||
\(329\) | 39.2164i | 0.119199i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −437.250 | −1.32100 | −0.660498 | − | 0.750828i | \(-0.729655\pi\) | ||||
−0.660498 | + | 0.750828i | \(0.729655\pi\) | |||||||
\(332\) | −296.168 | + | 96.2308i | −0.892072 | + | 0.289852i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −71.0169 | + | 51.5968i | −0.212625 | + | 0.154481i | ||||
\(335\) | 219.225 | − | 674.704i | 0.654402 | − | 2.01404i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 96.3092 | + | 132.558i | 0.285784 | + | 0.393348i | 0.927639 | − | 0.373478i | \(-0.121835\pi\) |
−0.641855 | + | 0.766826i | \(0.721835\pi\) | |||||||
\(338\) | −19.2078 | + | 26.4372i | −0.0568277 | + | 0.0782166i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 850.885i | − | 2.50260i | ||||||
\(341\) | 368.633 | + | 130.798i | 1.08104 | + | 0.383571i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −315.956 | + | 102.660i | −0.921154 | + | 0.299301i | ||||
\(344\) | 178.140 | + | 129.426i | 0.517849 | + | 0.376239i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −50.1255 | + | 154.271i | −0.144871 | + | 0.445868i | ||||
\(347\) | −475.145 | − | 154.384i | −1.36929 | − | 0.444910i | −0.470158 | − | 0.882582i | \(-0.655803\pi\) |
−0.899135 | + | 0.437672i | \(0.855803\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 172.838 | − | 237.892i | 0.495239 | − | 0.681638i | −0.486104 | − | 0.873901i | \(-0.661583\pi\) |
0.981344 | + | 0.192263i | \(0.0615825\pi\) | |||||||
\(350\) | −33.7430 | − | 103.850i | −0.0964086 | − | 0.296715i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 236.739 | + | 181.890i | 0.672555 | + | 0.516733i | ||||
\(353\) | 36.8161 | 0.104295 | 0.0521474 | − | 0.998639i | \(-0.483393\pi\) | ||||
0.0521474 | + | 0.998639i | \(0.483393\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 448.782 | + | 326.059i | 1.26418 | + | 0.918477i | ||||
\(356\) | 84.6915 | − | 61.5320i | 0.237897 | − | 0.172843i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 41.4134 | + | 13.4560i | 0.115680 | + | 0.0375867i | ||||
\(359\) | −219.070 | − | 301.524i | −0.610224 | − | 0.839901i | 0.386372 | − | 0.922343i | \(-0.373728\pi\) |
−0.996596 | + | 0.0824421i | \(0.973728\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 60.9533 | + | 187.595i | 0.168846 | + | 0.519654i | ||||
\(362\) | 104.178i | 0.287785i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 215.564 | 0.592209 | ||||||||
\(365\) | −200.281 | + | 65.0754i | −0.548716 | + | 0.178289i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 172.545 | − | 125.361i | 0.470150 | − | 0.341584i | −0.327350 | − | 0.944903i | \(-0.606156\pi\) |
0.797500 | + | 0.603319i | \(0.206156\pi\) | |||||||
\(368\) | 42.9152 | − | 132.079i | 0.116617 | − | 0.358912i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 56.2593 | + | 77.4342i | 0.152052 | + | 0.209282i | ||||
\(371\) | −138.687 | + | 190.886i | −0.373818 | + | 0.514517i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 32.7478i | − | 0.0877957i | −0.999036 | − | 0.0438978i | \(-0.986022\pi\) | ||
0.999036 | − | 0.0438978i | \(-0.0139776\pi\) | |||||||
\(374\) | 129.770 | − | 168.902i | 0.346977 | − | 0.451609i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −45.4295 | + | 14.7609i | −0.120823 | + | 0.0392578i | ||||
\(377\) | 159.962 | + | 116.219i | 0.424303 | + | 0.308274i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 167.782 | − | 516.378i | 0.442695 | − | 1.36248i | −0.442296 | − | 0.896869i | \(-0.645836\pi\) |
0.884992 | − | 0.465607i | \(-0.154164\pi\) | |||||||
\(380\) | −351.732 | − | 114.285i | −0.925611 | − | 0.300749i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 57.5334 | − | 79.1880i | 0.150611 | − | 0.207298i | ||||
\(383\) | 184.991 | + | 569.343i | 0.483005 | + | 1.48654i | 0.834850 | + | 0.550477i | \(0.185554\pi\) |
−0.351845 | + | 0.936058i | \(0.614446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −121.763 | + | 343.171i | −0.316268 | + | 0.891354i | ||||
\(386\) | 141.119 | 0.365594 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 106.164 | + | 77.1328i | 0.273619 | + | 0.198796i | ||||
\(389\) | −178.494 | + | 129.684i | −0.458854 | + | 0.333377i | −0.793082 | − | 0.609115i | \(-0.791525\pi\) |
0.334228 | + | 0.942492i | \(0.391525\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −353.625 | − | 114.900i | −0.904413 | − | 0.293862i | ||||
\(392\) | −94.5028 | − | 130.072i | −0.241079 | − | 0.331816i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.1538 | + | 34.3278i | 0.0283091 | + | 0.0871265i | ||||
\(395\) | 531.468i | 1.34549i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −734.263 | −1.84953 | −0.924764 | − | 0.380541i | \(-0.875738\pi\) | ||||
−0.924764 | + | 0.380541i | \(0.875738\pi\) | |||||||
\(398\) | 36.3760 | − | 11.8193i | 0.0913971 | − | 0.0296967i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −361.471 | + | 262.624i | −0.903678 | + | 0.656561i | ||||
\(401\) | −28.1108 | + | 86.5163i | −0.0701019 | + | 0.215751i | −0.979970 | − | 0.199147i | \(-0.936183\pi\) |
0.909868 | + | 0.414898i | \(0.136183\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 309.087 | + | 425.421i | 0.766964 | + | 1.05564i | ||||
\(404\) | 190.023 | − | 261.544i | 0.470354 | − | 0.647387i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35.9322i | 0.0885029i | ||||||||
\(407\) | 5.29522 | − | 197.529i | 0.0130104 | − | 0.485328i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 165.356 | − | 53.7274i | 0.404293 | − | 0.131363i | −0.0998094 | − | 0.995007i | \(-0.531823\pi\) |
0.504103 | + | 0.863644i | \(0.331823\pi\) | |||||||
\(410\) | −69.7537 | − | 50.6790i | −0.170131 | − | 0.123607i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −169.218 | + | 520.799i | −0.410723 | + | 1.26407i | ||||
\(413\) | −389.615 | − | 126.593i | −0.943377 | − | 0.306522i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 415.673 | − | 572.125i | 1.00162 | − | 1.37861i | ||||
\(416\) | 124.025 | + | 381.711i | 0.298138 | + | 0.917575i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −52.3895 | − | 76.3287i | −0.125334 | − | 0.182605i | ||||
\(419\) | 374.418 | 0.893599 | 0.446800 | − | 0.894634i | \(-0.352564\pi\) | ||||
0.446800 | + | 0.894634i | \(0.352564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0922850 | + | 0.0670490i | 0.000219204 | + | 0.000159261i | 0.587895 | − | 0.808937i | \(-0.299957\pi\) |
−0.587676 | + | 0.809097i | \(0.699957\pi\) | |||||||
\(422\) | −120.437 | + | 87.5024i | −0.285395 | + | 0.207352i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −273.329 | − | 88.8100i | −0.644644 | − | 0.209458i | ||||
\(425\) | 703.142 | + | 967.792i | 1.65445 | + | 2.27716i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −104.944 | − | 322.984i | −0.245770 | − | 0.756404i | ||||
\(428\) | − | 240.790i | − | 0.562593i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −235.729 | −0.548206 | ||||||||
\(431\) | −252.091 | + | 81.9092i | −0.584897 | + | 0.190045i | −0.586493 | − | 0.809954i | \(-0.699492\pi\) |
0.00159618 | + | 0.999999i | \(0.499492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 145.782 | − | 105.917i | 0.336679 | − | 0.244612i | −0.406580 | − | 0.913615i | \(-0.633279\pi\) |
0.743259 | + | 0.669003i | \(0.233279\pi\) | |||||||
\(434\) | −29.5303 | + | 90.8848i | −0.0680421 | + | 0.209412i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −315.656 | − | 434.463i | −0.723982 | − | 0.996475i | ||||
\(437\) | −94.9928 | + | 130.746i | −0.217375 | + | 0.299191i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 410.931i | 0.936062i | 0.883712 | + | 0.468031i | \(0.155037\pi\) | ||||
−0.883712 | + | 0.468031i | \(0.844963\pi\) | |||||||
\(440\) | −443.371 | − | 11.8856i | −1.00766 | − | 0.0270128i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 272.332 | − | 88.4860i | 0.616135 | − | 0.200195i | ||||
\(443\) | −17.7973 | − | 12.9305i | −0.0401744 | − | 0.0291884i | 0.567517 | − | 0.823362i | \(-0.307904\pi\) |
−0.607691 | + | 0.794173i | \(0.707904\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −73.4625 | + | 226.094i | −0.165084 | + | 0.508077i | ||||
\(446\) | −51.5771 | − | 16.7584i | −0.115644 | − | 0.0375749i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 62.7704 | − | 86.3961i | 0.140113 | − | 0.192848i | ||||
\(449\) | 44.5645 | + | 137.155i | 0.0992528 | + | 0.305469i | 0.988339 | − | 0.152272i | \(-0.0486589\pi\) |
−0.889086 | + | 0.457740i | \(0.848659\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 50.4487 | + | 170.701i | 0.111860 | + | 0.378495i | ||||
\(452\) | −523.699 | −1.15863 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 94.1109 | + | 68.3756i | 0.207293 | + | 0.150607i | ||||
\(455\) | −396.037 | + | 287.737i | −0.870410 | + | 0.632390i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 699.008 | + | 227.122i | 1.52956 | + | 0.496984i | 0.948473 | − | 0.316859i | \(-0.102628\pi\) |
0.581086 | + | 0.813842i | \(0.302628\pi\) | |||||||
\(458\) | 1.12936 | + | 1.55443i | 0.00246585 | + | 0.00339395i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 112.792 | + | 347.137i | 0.245199 | + | 0.754645i | ||||
\(461\) | 128.454i | 0.278643i | 0.990247 | + | 0.139321i | \(0.0444921\pi\) | ||||
−0.990247 | + | 0.139321i | \(0.955508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.10283 | 0.0153409 | 0.00767044 | − | 0.999971i | \(-0.497558\pi\) | ||||
0.00767044 | + | 0.999971i | \(0.497558\pi\) | |||||||
\(464\) | 139.831 | − | 45.4340i | 0.301361 | − | 0.0979180i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −156.701 | + | 113.850i | −0.336269 | + | 0.244314i | ||||
\(467\) | −88.2695 | + | 271.666i | −0.189014 | + | 0.581725i | −0.999994 | − | 0.00334813i | \(-0.998934\pi\) |
0.810980 | + | 0.585073i | \(0.198934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −210.319 | − | 289.479i | −0.448441 | − | 0.617225i | ||||
\(470\) | 30.0579 | − | 41.3712i | 0.0639530 | − | 0.0880238i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 498.991i | − | 1.05718i | ||||||
\(473\) | 385.907 | + | 296.498i | 0.815871 | + | 0.626845i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 494.499 | − | 160.673i | 1.04105 | − | 0.338258i | ||||
\(476\) | −347.201 | − | 252.256i | −0.729413 | − | 0.529950i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 69.6876 | − | 214.476i | 0.145790 | − | 0.448695i | ||||
\(479\) | 373.411 | + | 121.329i | 0.779564 | + | 0.253296i | 0.671654 | − | 0.740865i | \(-0.265584\pi\) |
0.107910 | + | 0.994161i | \(0.465584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 156.143 | − | 214.912i | 0.324622 | − | 0.446803i | ||||
\(482\) | 8.79499 | + | 27.0682i | 0.0182469 | + | 0.0561581i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 335.125 | + | 272.069i | 0.692407 | + | 0.562126i | ||||
\(485\) | −298.004 | −0.614440 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −417.281 | − | 303.173i | −0.856841 | − | 0.622531i | 0.0701830 | − | 0.997534i | \(-0.477642\pi\) |
−0.927024 | + | 0.375003i | \(0.877642\pi\) | |||||||
\(488\) | 334.654 | − | 243.141i | 0.685767 | − | 0.498239i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 163.697 | + | 53.1884i | 0.334076 | + | 0.108548i | ||||
\(491\) | −181.495 | − | 249.807i | −0.369644 | − | 0.508771i | 0.583160 | − | 0.812357i | \(-0.301816\pi\) |
−0.952804 | + | 0.303586i | \(0.901816\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −121.643 | − | 374.380i | −0.246741 | − | 0.759392i | ||||
\(494\) | − | 124.459i | − | 0.251942i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 391.021 | 0.788348 | ||||||||
\(497\) | 266.095 | − | 86.4595i | 0.535402 | − | 0.173963i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −469.197 | + | 340.892i | −0.940275 | + | 0.683149i | −0.948487 | − | 0.316817i | \(-0.897386\pi\) |
0.00821221 | + | 0.999966i | \(0.497386\pi\) | |||||||
\(500\) | 139.607 | − | 429.668i | 0.279215 | − | 0.859335i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −45.2319 | − | 62.2564i | −0.0901034 | − | 0.124017i | ||||
\(503\) | −458.978 | + | 631.728i | −0.912480 | + | 1.25592i | 0.0538322 | + | 0.998550i | \(0.482856\pi\) |
−0.966313 | + | 0.257371i | \(0.917144\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 734.157i | 1.45378i | ||||||||
\(506\) | −30.5530 | + | 86.1089i | −0.0603814 | + | 0.170176i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −218.975 | + | 71.1493i | −0.431053 | + | 0.140058i | ||||
\(509\) | 547.788 | + | 397.992i | 1.07621 | + | 0.781909i | 0.977017 | − | 0.213160i | \(-0.0683756\pi\) |
0.0991877 | + | 0.995069i | \(0.468376\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.8223 | + | 101.017i | −0.0642315 | + | 0.197684i | ||||
\(512\) | 492.044 | + | 159.875i | 0.961023 | + | 0.312255i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.9225 | + | 15.0335i | −0.0212499 | + | 0.0292480i | ||||
\(515\) | −384.279 | − | 1182.69i | −0.746174 | − | 2.29649i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −101.244 | + | 29.9213i | −0.195829 | + | 0.0578750i | ||||
\(518\) | 48.2756 | 0.0931961 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −482.391 | − | 350.477i | −0.927675 | − | 0.673995i | ||||
\(521\) | 538.428 | − | 391.191i | 1.03345 | − | 0.750846i | 0.0644546 | − | 0.997921i | \(-0.479469\pi\) |
0.968997 | + | 0.247074i | \(0.0794692\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −856.820 | − | 278.398i | −1.63828 | − | 0.532309i | −0.662127 | − | 0.749392i | \(-0.730346\pi\) |
−0.976153 | + | 0.217083i | \(0.930346\pi\) | |||||||
\(524\) | −467.205 | − | 643.053i | −0.891613 | − | 1.22720i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 50.3387 | + | 154.927i | 0.0957010 | + | 0.294537i | ||||
\(527\) | − | 1046.91i | − | 1.98654i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −369.500 | −0.698488 | ||||||||
\(530\) | 292.614 | − | 95.0759i | 0.552101 | − | 0.179389i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −150.909 | + | 109.642i | −0.283664 | + | 0.206094i | ||||
\(533\) | −73.9469 | + | 227.585i | −0.138737 | + | 0.426989i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 321.409 | + | 442.382i | 0.600765 | + | 0.826882i | ||||
\(536\) | 256.178 | − | 352.598i | 0.477944 | − | 0.657833i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 182.531i | − | 0.339276i | ||||||
\(539\) | −201.086 | − | 292.971i | −0.373072 | − | 0.543545i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 370.362 | − | 120.338i | 0.684587 | − | 0.222436i | 0.0539846 | − | 0.998542i | \(-0.482808\pi\) |
0.630603 | + | 0.776106i | \(0.282808\pi\) | |||||||
\(542\) | −210.297 | − | 152.790i | −0.388003 | − | 0.281900i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 246.921 | − | 759.944i | 0.453898 | − | 1.39696i | ||||
\(545\) | 1159.85 | + | 376.859i | 2.12817 | + | 0.691485i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −414.894 | + | 571.053i | −0.758490 | + | 1.04397i | 0.238848 | + | 0.971057i | \(0.423230\pi\) |
−0.997338 | + | 0.0729151i | \(0.976770\pi\) | |||||||
\(548\) | −56.1337 | − | 172.762i | −0.102434 | − | 0.315259i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 242.361 | − | 166.349i | 0.440657 | − | 0.302453i | ||||
\(551\) | −171.097 | −0.310520 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 216.863 | + | 157.561i | 0.392158 | + | 0.284920i | ||||
\(554\) | −111.842 | + | 81.2583i | −0.201882 | + | 0.146676i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 450.389 | + | 146.340i | 0.810052 | + | 0.263202i | ||||
\(557\) | −97.3073 | − | 133.932i | −0.174699 | − | 0.240452i | 0.712684 | − | 0.701485i | \(-0.247479\pi\) |
−0.887383 | + | 0.461032i | \(0.847479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 202.173 | + | 622.224i | 0.361669 | + | 1.11310i | ||||
\(560\) | 364.012i | 0.650022i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.1993 | −0.0306037 | ||||||||
\(563\) | −345.683 | + | 112.319i | −0.614002 | + | 0.199501i | −0.599475 | − | 0.800393i | \(-0.704624\pi\) |
−0.0145265 | + | 0.999894i | \(0.504624\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 962.145 | − | 699.039i | 1.70291 | − | 1.23724i | ||||
\(566\) | −59.9782 | + | 184.594i | −0.105968 | + | 0.326138i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 200.315 | + | 275.709i | 0.352667 | + | 0.485404i | ||||
\(569\) | 136.330 | − | 187.642i | 0.239596 | − | 0.329775i | −0.672238 | − | 0.740335i | \(-0.734667\pi\) |
0.911834 | + | 0.410560i | \(0.134667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 306.665i | 0.537067i | 0.963270 | + | 0.268533i | \(0.0865390\pi\) | ||||
−0.963270 | + | 0.268533i | \(0.913461\pi\) | |||||||
\(572\) | 164.471 | + | 556.514i | 0.287537 | + | 0.972927i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −41.3588 | + | 13.4383i | −0.0720536 | + | 0.0234116i | ||||
\(575\) | −415.150 | − | 301.624i | −0.722000 | − | 0.524564i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.3161 | − | 80.9927i | 0.0456085 | − | 0.140369i | −0.925659 | − | 0.378359i | \(-0.876489\pi\) |
0.971268 | + | 0.237990i | \(0.0764886\pi\) | |||||||
\(578\) | −361.411 | − | 117.430i | −0.625279 | − | 0.203165i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −227.134 | + | 312.623i | −0.391610 | + | 0.539005i | ||||
\(581\) | −110.222 | − | 339.228i | −0.189711 | − | 0.583869i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −598.618 | − | 212.400i | −1.02679 | − | 0.364323i | ||||
\(584\) | −129.375 | −0.221532 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.0864 | + | 24.0387i | 0.0564614 | + | 0.0410216i | ||||
\(587\) | 497.688 | − | 361.591i | 0.847849 | − | 0.615999i | −0.0767029 | − | 0.997054i | \(-0.524439\pi\) |
0.924552 | + | 0.381055i | \(0.124439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −432.762 | − | 140.613i | −0.734740 | − | 0.238732i | ||||
\(590\) | 313.993 | + | 432.174i | 0.532192 | + | 0.732499i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −61.0414 | − | 187.866i | −0.103110 | − | 0.317341i | ||||
\(593\) | − | 74.4809i | − | 0.125600i | −0.998026 | − | 0.0628001i | \(-0.979997\pi\) | ||
0.998026 | − | 0.0628001i | \(-0.0200030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 974.595 | 1.63798 | ||||||||
\(596\) | 893.517 | − | 290.321i | 1.49919 | − | 0.487116i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −99.3740 | + | 72.1994i | −0.166177 | + | 0.120735i | ||||
\(599\) | −229.210 | + | 705.436i | −0.382654 | + | 1.17769i | 0.555513 | + | 0.831508i | \(0.312522\pi\) |
−0.938168 | + | 0.346181i | \(0.887478\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −659.404 | − | 907.591i | −1.09718 | − | 1.51014i | −0.839073 | − | 0.544018i | \(-0.816902\pi\) |
−0.258104 | − | 0.966117i | \(-0.583098\pi\) | |||||||
\(602\) | −69.8848 | + | 96.1882i | −0.116088 | + | 0.159781i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 180.081i | − | 0.298147i | ||||||
\(605\) | −978.856 | − | 52.5188i | −1.61794 | − | 0.0868080i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.5343 | − | 3.42282i | 0.0173548 | − | 0.00563891i | −0.300327 | − | 0.953836i | \(-0.597096\pi\) |
0.317682 | + | 0.948197i | \(0.397096\pi\) | |||||||
\(608\) | −280.975 | − | 204.140i | −0.462130 | − | 0.335757i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −136.845 | + | 421.167i | −0.224337 | + | 0.690437i | ||||
\(611\) | −134.982 | − | 43.8582i | −0.220919 | − | 0.0717811i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −439.604 | + | 605.064i | −0.717136 | + | 0.987053i | 0.282478 | + | 0.959274i | \(0.408844\pi\) |
−0.999614 | + | 0.0277794i | \(0.991156\pi\) | |||||||
\(614\) | −24.3301 | − | 74.8803i | −0.0396255 | − | 0.121955i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −136.293 | + | 177.392i | −0.221255 | + | 0.287975i | ||||
\(617\) | 771.423 | 1.25028 | 0.625140 | − | 0.780513i | \(-0.285042\pi\) | ||||
0.625140 | + | 0.780513i | \(0.285042\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −141.847 | − | 103.058i | −0.229156 | − | 0.166491i | 0.467283 | − | 0.884108i | \(-0.345233\pi\) |
−0.696438 | + | 0.717617i | \(0.745233\pi\) | |||||||
\(620\) | −831.424 | + | 604.065i | −1.34101 | + | 0.974298i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 195.884 | + | 63.6465i | 0.314925 | + | 0.102325i | ||||
\(623\) | 70.4781 | + | 97.0048i | 0.113127 | + | 0.155706i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.13803 | + | 9.65786i | 0.00502085 | + | 0.0154526i | ||||
\(626\) | − | 258.200i | − | 0.412460i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 107.465 | 0.171122 | ||||||||
\(629\) | −502.987 | + | 163.430i | −0.799661 | + | 0.259826i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −214.772 | + | 156.041i | −0.340367 | + | 0.247291i | −0.744817 | − | 0.667269i | \(-0.767463\pi\) |
0.404450 | + | 0.914560i | \(0.367463\pi\) | |||||||
\(632\) | −100.896 | + | 310.527i | −0.159646 | + | 0.491340i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.7092 | − | 18.8690i | −0.0216233 | − | 0.0297619i | ||||
\(635\) | 307.332 | − | 423.007i | 0.483988 | − | 0.666152i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 477.709i | − | 0.749935i | ||||||
\(638\) | −92.7648 | + | 27.4155i | −0.145399 | + | 0.0429711i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −968.892 | + | 314.812i | −1.51389 | + | 0.491894i | ||||
\(641\) | 925.226 | + | 672.216i | 1.44341 | + | 1.04870i | 0.987316 | + | 0.158768i | \(0.0507522\pi\) |
0.456095 | + | 0.889931i | \(0.349248\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 174.074 | − | 535.744i | 0.270721 | − | 0.833195i | −0.719599 | − | 0.694390i | \(-0.755674\pi\) |
0.990320 | − | 0.138804i | \(-0.0443259\pi\) | |||||||
\(644\) | 175.086 | + | 56.8890i | 0.271873 | + | 0.0883370i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −145.644 | + | 200.462i | −0.225455 | + | 0.310312i | ||||
\(647\) | 17.5246 | + | 53.9352i | 0.0270859 | + | 0.0833620i | 0.963686 | − | 0.267039i | \(-0.0860453\pi\) |
−0.936600 | + | 0.350401i | \(0.886045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.5536 | − | 1102.44i | 0.0455371 | − | 1.69868i | ||||
\(650\) | 395.187 | 0.607980 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −296.640 | − | 215.522i | −0.454969 | − | 0.330555i | ||||
\(653\) | −616.756 | + | 448.100i | −0.944496 | + | 0.686217i | −0.949499 | − | 0.313771i | \(-0.898408\pi\) |
0.00500247 | + | 0.999987i | \(0.498408\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1716.71 | + | 557.793i | 2.62093 | + | 0.851592i | ||||
\(656\) | 104.591 | + | 143.957i | 0.159438 | + | 0.219447i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.97030 | − | 24.5301i | −0.0121129 | − | 0.0372797i | ||||
\(659\) | 1137.55i | 1.72617i | 0.505056 | + | 0.863086i | \(0.331472\pi\) | ||||
−0.505056 | + | 0.863086i | \(0.668528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 814.127 | 1.23166 | 0.615829 | − | 0.787879i | \(-0.288821\pi\) | ||||
0.615829 | + | 0.787879i | \(0.288821\pi\) | |||||||
\(662\) | 273.502 | − | 88.8661i | 0.413145 | − | 0.134239i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 351.485 | − | 255.369i | 0.529345 | − | 0.384591i | ||||
\(665\) | 130.901 | − | 402.870i | 0.196843 | − | 0.605820i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 99.2540 | + | 136.611i | 0.148807 | + | 0.204815i | ||||
\(668\) | −279.869 | + | 385.207i | −0.418965 | + | 0.576656i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 466.586i | 0.696397i | ||||||||
\(671\) | 753.767 | − | 517.361i | 1.12335 | − | 0.771030i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −301.768 | + | 98.0504i | −0.448393 | + | 0.145692i | −0.524504 | − | 0.851408i | \(-0.675749\pi\) |
0.0761119 | + | 0.997099i | \(0.475749\pi\) | |||||||
\(674\) | −87.1829 | − | 63.3421i | −0.129352 | − | 0.0939794i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −54.7737 | + | 168.576i | −0.0810262 | + | 0.249373i | ||||
\(677\) | −467.770 | − | 151.988i | −0.690946 | − | 0.224502i | −0.0575647 | − | 0.998342i | \(-0.518334\pi\) |
−0.633381 | + | 0.773840i | \(0.718334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −88.3471 | + | 121.599i | −0.130114 | + | 0.179086i | ||||
\(680\) | 366.835 | + | 1129.00i | 0.539463 | + | 1.66030i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −257.165 | − | 6.89392i | −0.377075 | − | 0.0101084i | ||||
\(683\) | −1267.89 | −1.85635 | −0.928176 | − | 0.372142i | \(-0.878624\pi\) | ||||
−0.928176 | + | 0.372142i | \(0.878624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 333.734 | + | 242.472i | 0.487203 | + | 0.353973i | ||||
\(686\) | 176.767 | − | 128.429i | 0.257678 | − | 0.187214i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 462.685 | + | 150.335i | 0.672507 | + | 0.218511i | ||||
\(689\) | −501.921 | − | 690.835i | −0.728477 | − | 1.00266i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −71.8167 | − | 221.029i | −0.103932 | − | 0.319868i | 0.885547 | − | 0.464550i | \(-0.153784\pi\) |
−0.989478 | + | 0.144682i | \(0.953784\pi\) | |||||||
\(692\) | 879.850i | 1.27146i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 328.582 | 0.473461 | ||||||||
\(695\) | −1022.80 | + | 332.326i | −1.47165 | + | 0.478167i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 385.427 | − | 280.029i | 0.552980 | − | 0.401763i | ||||
\(698\) | −59.7625 | + | 183.930i | −0.0856196 | + | 0.263510i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −348.138 | − | 479.171i | −0.497341 | − | 0.684531i | ||||
\(701\) | −260.786 | + | 358.941i | −0.372020 | + | 0.512041i | −0.953448 | − | 0.301556i | \(-0.902494\pi\) |
0.581429 | + | 0.813597i | \(0.302494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 229.872i | 0.326987i | ||||||||
\(704\) | 270.938 | + | 96.1337i | 0.384856 | + | 0.136554i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.0286 | + | 7.48246i | −0.0326185 | + | 0.0105984i | ||||
\(707\) | 299.570 | + | 217.650i | 0.423720 | + | 0.307851i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −126.852 | + | 390.411i | −0.178917 | + | 0.550650i | −0.999791 | − | 0.0204599i | \(-0.993487\pi\) |
0.820874 | + | 0.571110i | \(0.193487\pi\) | |||||||
\(710\) | −346.984 | − | 112.742i | −0.488709 | − | 0.158791i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −85.8456 | + | 118.156i | −0.120570 | + | 0.165950i | ||||
\(713\) | 138.776 | + | 427.108i | 0.194636 | + | 0.599029i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1045.01 | − | 802.896i | −1.46155 | − | 1.12293i | ||||
\(716\) | 236.193 | 0.329878 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 198.311 | + | 144.081i | 0.276199 | + | 0.200671i | ||||
\(719\) | −187.845 | + | 136.477i | −0.261259 | + | 0.189815i | −0.710702 | − | 0.703493i | \(-0.751622\pi\) |
0.449443 | + | 0.893309i | \(0.351622\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −596.517 | − | 193.820i | −0.827347 | − | 0.268821i | ||||
\(722\) | −76.2532 | − | 104.954i | −0.105614 | − | 0.145365i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 174.619 | + | 537.422i | 0.241186 | + | 0.742295i | ||||
\(725\) | − | 543.271i | − | 0.749339i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −523.474 | −0.720047 | −0.360024 | − | 0.932943i | \(-0.617231\pi\) | ||||
−0.360024 | + | 0.932943i | \(0.617231\pi\) | |||||||
\(728\) | −286.022 | + | 92.9342i | −0.392888 | + | 0.127657i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 112.051 | − | 81.4100i | 0.153495 | − | 0.111521i | ||||
\(731\) | 402.504 | − | 1238.78i | 0.550620 | − | 1.69464i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 186.056 | + | 256.084i | 0.253828 | + | 0.349365i | 0.916847 | − | 0.399238i | \(-0.130725\pi\) |
−0.663019 | + | 0.748602i | \(0.730725\pi\) | |||||||
\(734\) | −82.4495 | + | 113.482i | −0.112329 | + | 0.154608i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 342.766i | 0.465715i | ||||||||
\(737\) | 586.868 | − | 763.839i | 0.796293 | − | 1.03642i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −671.840 | + | 218.294i | −0.909120 | + | 0.295391i | −0.725996 | − | 0.687699i | \(-0.758621\pi\) |
−0.183124 | + | 0.983090i | \(0.558621\pi\) | |||||||
\(740\) | 420.015 | + | 305.159i | 0.567588 | + | 0.412377i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 47.9538 | − | 147.586i | 0.0646277 | − | 0.198904i | ||||
\(743\) | −306.573 | − | 99.6115i | −0.412615 | − | 0.134067i | 0.0953515 | − | 0.995444i | \(-0.469602\pi\) |
−0.507966 | + | 0.861377i | \(0.669602\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1254.05 | + | 1726.06i | −1.68329 | + | 2.31686i | ||||
\(746\) | 6.65563 | + | 20.4839i | 0.00892175 | + | 0.0274583i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 386.333 | − | 1088.82i | 0.516489 | − | 1.45565i | ||||
\(749\) | 275.798 | 0.368222 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1067.26 | − | 775.408i | −1.42112 | − | 1.03250i | −0.991586 | − | 0.129448i | \(-0.958679\pi\) |
−0.429530 | − | 0.903053i | \(-0.641321\pi\) | |||||||
\(752\) | −85.3817 | + | 62.0334i | −0.113539 | + | 0.0824913i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −123.677 | − | 40.1852i | −0.164028 | − | 0.0532961i | ||||
\(755\) | 240.374 | + | 330.847i | 0.318376 | + | 0.438208i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 281.697 | + | 866.976i | 0.372123 | + | 1.14528i | 0.945399 | + | 0.325915i | \(0.105672\pi\) |
−0.573275 | + | 0.819363i | \(0.694328\pi\) | |||||||
\(758\) | 357.097i | 0.471104i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 515.968 | 0.678905 | ||||||||
\(761\) | 166.965 | − | 54.2501i | 0.219402 | − | 0.0712879i | −0.197254 | − | 0.980352i | \(-0.563202\pi\) |
0.416655 | + | 0.909065i | \(0.363202\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 497.630 | − | 361.549i | 0.652201 | − | 0.473852i | ||||
\(764\) | 164.065 | − | 504.940i | 0.214745 | − | 0.660916i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −231.425 | − | 318.530i | −0.302122 | − | 0.415835i | ||||
\(767\) | 871.462 | − | 1199.46i | 1.13620 | − | 1.56384i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 692.657i | 0.900725i | 0.892846 | + | 0.450362i | \(0.148705\pi\) | ||||
−0.892846 | + | 0.450362i | \(0.851295\pi\) | |||||||
\(770\) | 6.41775 | − | 239.402i | 0.00833473 | − | 0.310912i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 727.989 | − | 236.538i | 0.942991 | − | 0.306396i | ||||
\(773\) | −339.099 | − | 246.370i | −0.438679 | − | 0.318719i | 0.346431 | − | 0.938076i | \(-0.387394\pi\) |
−0.785110 | + | 0.619357i | \(0.787394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 446.479 | − | 1374.12i | 0.576101 | − | 1.77306i | ||||
\(776\) | −174.118 | − | 56.5744i | −0.224379 | − | 0.0729051i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 85.2923 | − | 117.395i | 0.109630 | − | 0.150893i | ||||
\(779\) | −63.9885 | − | 196.936i | −0.0821418 | − | 0.252806i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 426.235 | + | 621.001i | 0.545755 | + | 0.795136i | ||||
\(782\) | 244.547 | 0.312720 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −287.382 | − | 208.795i | −0.366558 | − | 0.266320i | ||||
\(785\) | −197.435 | + | 143.445i | −0.251510 | + | 0.182732i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 936.899 | + | 304.417i | 1.19047 | + | 0.386807i | 0.836246 | − | 0.548355i | \(-0.184746\pi\) |
0.354222 | + | 0.935161i | \(0.384746\pi\) | |||||||
\(788\) | 115.078 | + | 158.391i | 0.146038 | + | 0.201003i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −108.015 | − | 332.436i | −0.136728 | − | 0.420805i | ||||
\(791\) | − | 599.839i | − | 0.758330i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1229.07 | 1.54990 | ||||||||
\(794\) | 459.285 | − | 149.231i | 0.578445 | − | 0.187948i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 167.841 | − | 121.944i | 0.210856 | − | 0.153196i | ||||
\(797\) | 231.830 | − | 713.499i | 0.290878 | − | 0.895230i | −0.693697 | − | 0.720267i | \(-0.744019\pi\) |
0.984575 | − | 0.174963i | \(-0.0559807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 166.086 | + | 228.598i | 0.207868 | + | 0.286105i | ||||
\(800\) | 648.193 | − | 892.161i | 0.810241 | − | 1.11520i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 59.8296i | − | 0.0746005i | ||||||
\(803\) | −285.834 | − | 7.66245i | −0.355957 | − | 0.00954228i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −397.607 | + | 129.190i | −0.493921 | + | 0.160485i | ||||
\(806\) | −279.797 | − | 203.285i | −0.347143 | − | 0.252214i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −139.376 | + | 428.954i | −0.172495 | + | 0.530884i | ||||
\(809\) | −694.235 | − | 225.571i | −0.858140 | − | 0.278827i | −0.153288 | − | 0.988181i | \(-0.548986\pi\) |
−0.704851 | + | 0.709355i | \(0.748986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0885 | + | 19.3911i | −0.0173717 | + | 0.0239101i | −0.817615 | − | 0.575766i | \(-0.804704\pi\) |
0.800243 | + | 0.599676i | \(0.204704\pi\) | |||||||
\(812\) | 60.2279 | + | 185.362i | 0.0741723 | + | 0.228279i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 36.8333 | + | 124.631i | 0.0452498 | + | 0.153110i | ||||
\(815\) | 832.671 | 1.02168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −458.015 | − | 332.767i | −0.560606 | − | 0.407304i | ||||
\(818\) | −92.5115 | + | 67.2135i | −0.113095 | + | 0.0821681i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −444.782 | − | 144.519i | −0.542418 | − | 0.176242i | ||||
\(821\) | −1.54301 | − | 2.12377i | −0.00187943 | − | 0.00258681i | 0.808076 | − | 0.589078i | \(-0.200509\pi\) |
−0.809956 | + | 0.586491i | \(0.800509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.4352 | + | 32.1162i | 0.0126795 | + | 0.0390233i | 0.957196 | − | 0.289440i | \(-0.0934692\pi\) |
−0.944517 | + | 0.328464i | \(0.893469\pi\) | |||||||
\(824\) | − | 763.978i | − | 0.927157i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 269.435 | 0.326192 | ||||||||
\(827\) | 1132.85 | − | 368.086i | 1.36984 | − | 0.445086i | 0.470521 | − | 0.882389i | \(-0.344066\pi\) |
0.899314 | + | 0.437303i | \(0.144066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −380.631 | + | 276.544i | −0.459144 | + | 0.333588i | −0.793195 | − | 0.608967i | \(-0.791584\pi\) |
0.334051 | + | 0.942555i | \(0.391584\pi\) | |||||||
\(830\) | −143.728 | + | 442.348i | −0.173166 | + | 0.532949i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 227.173 | + | 312.676i | 0.273044 | + | 0.375813i | ||||
\(833\) | −559.022 | + | 769.427i | −0.671094 | + | 0.923682i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1081.28i | − | 1.29494i | ||||||
\(836\) | −398.199 | − | 305.942i | −0.476315 | − | 0.365960i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −234.200 | + | 76.0963i | −0.279475 | + | 0.0908071i | ||||
\(839\) | −439.290 | − | 319.163i | −0.523588 | − | 0.380409i | 0.294366 | − | 0.955693i | \(-0.404892\pi\) |
−0.817954 | + | 0.575284i | \(0.804892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 204.640 | − | 629.817i | 0.243329 | − | 0.748890i | ||||
\(842\) | −0.0713517 | − | 0.0231836i | −8.47408e−5 | − | 2.75339e-5i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −474.626 | + | 653.267i | −0.562353 | + | 0.774013i | ||||
\(845\) | −124.387 | − | 382.823i | −0.147203 | − | 0.453044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −311.625 | + | 383.849i | −0.367916 | + | 0.453186i | ||||
\(848\) | −634.973 | −0.748789 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −636.512 | − | 462.453i | −0.748838 | − | 0.544062i | ||||
\(851\) | 183.540 | − | 133.350i | 0.215676 | − | 0.156698i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 411.114 | + | 133.579i | 0.481962 | + | 0.156599i | 0.539914 | − | 0.841720i | \(-0.318457\pi\) |
−0.0579514 | + | 0.998319i | \(0.518457\pi\) | |||||||
\(854\) | 131.286 | + | 180.700i | 0.153731 | + | 0.211592i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 103.810 | + | 319.493i | 0.121273 | + | 0.373240i | ||||
\(857\) | 267.129i | 0.311703i | 0.987781 | + | 0.155851i | \(0.0498121\pi\) | ||||
−0.987781 | + | 0.155851i | \(0.950188\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 537.909 | 0.626203 | 0.313102 | − | 0.949720i | \(-0.398632\pi\) | ||||
0.313102 | + | 0.949720i | \(0.398632\pi\) | |||||||
\(860\) | −1216.05 | + | 395.118i | −1.41401 | + | 0.459439i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 141.037 | − | 102.469i | 0.163616 | − | 0.118874i | ||||
\(863\) | −351.588 | + | 1082.08i | −0.407402 | + | 1.25386i | 0.511470 | + | 0.859301i | \(0.329101\pi\) |
−0.918872 | + | 0.394555i | \(0.870899\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1174.43 | − | 1616.47i | −1.35773 | − | 1.86875i | ||||
\(866\) | −69.6610 | + | 95.8802i | −0.0804400 | + | 0.110716i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 518.343i | 0.597169i | ||||||||
\(869\) | −241.306 | + | 680.084i | −0.277682 | + | 0.782606i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1231.59 | − | 400.168i | 1.41400 | − | 0.459435i | ||||
\(872\) | 606.136 | + | 440.384i | 0.695110 | + | 0.505027i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32.8457 | − | 101.089i | 0.0375809 | − | 0.115662i | ||||
\(875\) | 492.137 | + | 159.905i | 0.562442 | + | 0.182748i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −399.155 | + | 549.389i | −0.455136 | + | 0.626442i | −0.973491 | − | 0.228724i | \(-0.926545\pi\) |
0.518355 | + | 0.855166i | \(0.326545\pi\) | |||||||
\(878\) | −83.5172 | − | 257.040i | −0.0951222 | − | 0.292756i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −939.758 | + | 277.734i | −1.06791 | + | 0.315607i | ||||
\(881\) | 419.212 | 0.475837 | 0.237918 | − | 0.971285i | \(-0.423535\pi\) | ||||
0.237918 | + | 0.971285i | \(0.423535\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 292.750 | + | 212.695i | 0.331540 | + | 0.240878i | 0.741084 | − | 0.671413i | \(-0.234312\pi\) |
−0.409544 | + | 0.912290i | \(0.634312\pi\) | |||||||
\(884\) | 1256.56 | − | 912.941i | 1.42144 | − | 1.03274i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.7602 | + | 4.47097i | 0.0155308 | + | 0.00504625i | ||||
\(887\) | 24.9623 | + | 34.3576i | 0.0281424 | + | 0.0387346i | 0.822856 | − | 0.568249i | \(-0.192379\pi\) |
−0.794714 | + | 0.606984i | \(0.792379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −81.4937 | − | 250.812i | −0.0916690 | − | 0.282128i | ||||
\(890\) | − | 156.354i | − | 0.175678i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −294.159 | −0.329775 | ||||||||
\(893\) | 116.804 | − | 37.9518i | 0.130799 | − | 0.0424992i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −433.936 | + | 315.273i | −0.484844 | + | 0.352260i | ||||
\(896\) | −158.783 | + | 488.683i | −0.177213 | + | 0.545406i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55.7506 | − | 76.7342i | −0.0620831 | − | 0.0854501i | ||||
\(899\) | −279.460 | + | 384.643i | −0.310856 | + | 0.427857i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1700.06i | 1.88685i | ||||||||
\(902\) | −66.2491 | − | 96.5214i | −0.0734469 | − | 0.107008i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 694.872 | − | 225.778i | 0.768664 | − | 0.249754i | ||||
\(905\) | −1038.17 | − | 754.274i | −1.14715 | − | 0.833451i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.0536 | + | 58.6409i | −0.0210073 | + | 0.0646537i | −0.961011 | − | 0.276512i | \(-0.910822\pi\) |
0.940003 | + | 0.341165i | \(0.110822\pi\) | |||||||
\(908\) | 600.096 | + | 194.983i | 0.660898 | + | 0.214739i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 189.243 | − | 260.471i | 0.207960 | − | 0.286232i | ||||
\(911\) | 83.8172 | + | 257.963i | 0.0920057 | + | 0.283165i | 0.986462 | − | 0.163991i | \(-0.0524369\pi\) |
−0.894456 | + | 0.447156i | \(0.852437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 791.675 | − | 543.380i | 0.867114 | − | 0.595159i | ||||
\(914\) | −483.393 | −0.528877 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.43146 | + | 6.12581i | 0.00920465 | + | 0.00668757i | ||||
\(917\) | 736.546 | − | 535.132i | 0.803213 | − | 0.583568i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 119.898 | + | 38.9574i | 0.130466 | + | 0.0423910i | 0.373522 | − | 0.927621i | \(-0.378150\pi\) |
−0.243056 | + | 0.970012i | \(0.578150\pi\) | |||||||
\(920\) | −299.316 | − | 411.973i | −0.325343 | − | 0.447797i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26.1069 | − | 80.3488i | −0.0283155 | − | 0.0871462i | ||||
\(923\) | 1012.58i | 1.09706i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −729.895 | −0.789076 | ||||||||
\(926\) | −4.44286 | + | 1.44357i | −0.00479790 | + | 0.00155893i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −293.579 | + | 213.298i | −0.316357 | + | 0.229847i | ||||
\(929\) | −85.0652 | + | 261.804i | −0.0915664 | + | 0.281813i | −0.986344 | − | 0.164700i | \(-0.947334\pi\) |
0.894777 | + | 0.446513i | \(0.147334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 242.976 | + | 334.428i | 0.260984 | + | 0.359214i | ||||
\(932\) | −617.541 | + | 849.972i | −0.662597 | + | 0.911987i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 187.868i | − | 0.201144i | ||||||
\(935\) | 743.597 | + | 2516.08i | 0.795291 | + | 2.69099i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1469.07 | − | 477.330i | 1.56784 | − | 0.509424i | 0.608955 | − | 0.793204i | \(-0.291589\pi\) |
0.958889 | + | 0.283781i | \(0.0915888\pi\) | |||||||
\(938\) | 190.389 | + | 138.325i | 0.202973 | + | 0.147469i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 85.7145 | − | 263.802i | 0.0911857 | − | 0.280641i | ||||
\(941\) | 1018.35 | + | 330.882i | 1.08220 | + | 0.351628i | 0.795228 | − | 0.606310i | \(-0.207351\pi\) |
0.286973 | + | 0.957939i | \(0.407351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −120.123 | + | 165.335i | −0.127384 | + | 0.175329i | ||||
\(944\) | −340.683 | − | 1048.51i | −0.360893 | − | 1.11071i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −301.647 | − | 107.030i | −0.318865 | − | 0.113139i | ||||
\(947\) | −1480.48 | −1.56333 | −0.781667 | − | 0.623696i | \(-0.785630\pi\) | ||||
−0.781667 | + | 0.623696i | \(0.785630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −310.989 | − | 225.947i | −0.327702 | − | 0.238089i | ||||
\(950\) | −276.657 | + | 201.003i | −0.291218 | + | 0.211582i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 569.438 | + | 185.022i | 0.598149 | + | 0.194350i | ||||
\(953\) | −254.489 | − | 350.274i | −0.267040 | − | 0.367549i | 0.654348 | − | 0.756194i | \(-0.272943\pi\) |
−0.921388 | + | 0.388645i | \(0.872943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 372.578 | + | 1146.68i | 0.390134 | + | 1.20071i | ||||
\(956\) | − | 1223.22i | − | 1.27952i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −258.229 | −0.269550 | ||||||||
\(959\) | 197.880 | − | 64.2950i | 0.206339 | − | 0.0670437i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −245.497 | + | 178.364i | −0.255460 | + | 0.185602i | ||||
\(962\) | −53.9897 | + | 166.163i | −0.0561223 | + | 0.172727i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 90.7410 | + | 124.894i | 0.0941297 | + | 0.129558i | ||||
\(965\) | −1021.74 | + | 1406.30i | −1.05879 | + | 1.45730i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 211.542i | − | 0.218761i | −0.994000 | − | 0.109381i | \(-0.965113\pi\) | ||
0.994000 | − | 0.109381i | \(-0.0348867\pi\) | |||||||
\(968\) | −561.957 | − | 216.516i | −0.580534 | − | 0.223674i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 186.403 | − | 60.5659i | 0.192168 | − | 0.0624391i | ||||
\(971\) | 1125.89 | + | 818.004i | 1.15951 | + | 0.842434i | 0.989716 | − | 0.143045i | \(-0.0456894\pi\) |
0.169795 | + | 0.985479i | \(0.445689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −167.617 | + | 515.871i | −0.172268 | + | 0.530186i | ||||
\(974\) | 322.628 | + | 104.828i | 0.331240 | + | 0.107627i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 537.196 | − | 739.388i | 0.550406 | − | 0.757569i | ||||
\(977\) | −10.0534 | − | 30.9411i | −0.0102900 | − | 0.0316695i | 0.945780 | − | 0.324809i | \(-0.105300\pi\) |
−0.956070 | + | 0.293139i | \(0.905300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −196.660 | + | 255.964i | −0.200879 | + | 0.261454i | ||||
\(980\) | 933.613 | 0.952666 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 164.296 | + | 119.368i | 0.167308 | + | 0.121556i | ||||
\(983\) | −980.893 | + | 712.660i | −0.997856 | + | 0.724985i | −0.961627 | − | 0.274359i | \(-0.911534\pi\) |
−0.0362286 | + | 0.999344i | \(0.511534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −422.843 | − | 137.390i | −0.429283 | − | 0.139482i | ||||
\(986\) | 152.177 | + | 209.454i | 0.154338 | + | 0.212428i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −208.613 | − | 642.044i | −0.211147 | − | 0.649843i | ||||
\(989\) | 558.741i | 0.564955i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −106.677 | −0.107645 | −0.0538227 | − | 0.998551i | \(-0.517141\pi\) | ||||
−0.0538227 | + | 0.998551i | \(0.517141\pi\) | |||||||
\(992\) | −917.858 | + | 298.230i | −0.925260 | + | 0.300635i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −148.872 | + | 108.162i | −0.149770 | + | 0.108815i | ||||
\(995\) | −145.588 | + | 448.073i | −0.146319 | + | 0.450324i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −759.309 | − | 1045.10i | −0.761593 | − | 1.04824i | −0.997080 | − | 0.0763658i | \(-0.975668\pi\) |
0.235486 | − | 0.971878i | \(-0.424332\pi\) | |||||||
\(998\) | 224.203 | − | 308.588i | 0.224652 | − | 0.309207i | ||||
\(999\) | 0 | 0 |
(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 | 99.3.k.b.28.2 | ✓ | 16 | |
3.2 | odd | 2 | inner | 99.3.k.b.28.3 | yes | 16 | |
11.2 | odd | 10 | inner | 99.3.k.b.46.2 | yes | 16 | |
11.3 | even | 5 | 1089.3.c.l.604.10 | 16 | |||
11.8 | odd | 10 | 1089.3.c.l.604.8 | 16 | |||
33.2 | even | 10 | inner | 99.3.k.b.46.3 | yes | 16 | |
33.8 | even | 10 | 1089.3.c.l.604.9 | 16 | |||
33.14 | odd | 10 | 1089.3.c.l.604.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.k.b.28.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
99.3.k.b.28.3 | yes | 16 | 3.2 | odd | 2 | inner | |
99.3.k.b.46.2 | yes | 16 | 11.2 | odd | 10 | inner | |
99.3.k.b.46.3 | yes | 16 | 33.2 | even | 10 | inner | |
1089.3.c.l.604.7 | 16 | 33.14 | odd | 10 | |||
1089.3.c.l.604.8 | 16 | 11.8 | odd | 10 | |||
1089.3.c.l.604.9 | 16 | 33.8 | even | 10 | |||
1089.3.c.l.604.10 | 16 | 11.3 | even | 5 |