Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), degree \(2\), 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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 66x^{6} + 59x^{5} + 3770x^{4} + 721x^{3} + 29779x^{2} + 1374x + 209764 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.3 | ||
Root | \(-1.44566 - 2.50395i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.163 |
Dual form | 378.4.g.e.109.3 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 1.18685 | − | 2.05569i | 0.106155 | − | 0.183866i | −0.808054 | − | 0.589108i | \(-0.799479\pi\) |
0.914210 | + | 0.405242i | \(0.132813\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.15909 | + | 16.0969i | 0.494544 | + | 0.869152i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.37371 | − | 4.11138i | −0.0750632 | − | 0.130013i | ||||
\(11\) | 19.5527 | + | 33.8662i | 0.535942 | + | 0.928278i | 0.999117 | + | 0.0420115i | \(0.0133766\pi\) |
−0.463176 | + | 0.886267i | \(0.653290\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −24.4393 | −0.521403 | −0.260702 | − | 0.965419i | \(-0.583954\pi\) | ||||
−0.260702 | + | 0.965419i | \(0.583954\pi\) | |||||||
\(14\) | 37.0398 | + | 0.232922i | 0.707093 | + | 0.00444650i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −23.8709 | − | 41.3456i | −0.340561 | − | 0.589869i | 0.643976 | − | 0.765046i | \(-0.277284\pi\) |
−0.984537 | + | 0.175177i | \(0.943950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −59.8352 | + | 103.638i | −0.722481 | + | 1.25137i | 0.237521 | + | 0.971382i | \(0.423665\pi\) |
−0.960002 | + | 0.279992i | \(0.909668\pi\) | |||||||
\(20\) | −9.49483 | −0.106155 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 78.2108 | 0.757936 | ||||||||
\(23\) | −76.6464 | + | 132.755i | −0.694864 | + | 1.20354i | 0.275362 | + | 0.961341i | \(0.411202\pi\) |
−0.970226 | + | 0.242200i | \(0.922131\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 59.6828 | + | 103.374i | 0.477462 | + | 0.826989i | ||||
\(26\) | −24.4393 | + | 42.3301i | −0.184344 | + | 0.319293i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 37.4432 | − | 63.9219i | 0.252718 | − | 0.431432i | ||||
\(29\) | 215.634 | 1.38076 | 0.690382 | − | 0.723445i | \(-0.257443\pi\) | ||||
0.690382 | + | 0.723445i | \(0.257443\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.6485 | + | 51.3527i | 0.171775 | + | 0.297523i | 0.939041 | − | 0.343806i | \(-0.111716\pi\) |
−0.767265 | + | 0.641330i | \(0.778383\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −95.4835 | −0.481626 | ||||||||
\(35\) | 43.9608 | + | 0.276444i | 0.212307 | + | 0.00133507i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 104.999 | − | 181.863i | 0.466532 | − | 0.808057i | −0.532737 | − | 0.846281i | \(-0.678837\pi\) |
0.999269 | + | 0.0382238i | \(0.0121700\pi\) | |||||||
\(38\) | 119.670 | + | 207.275i | 0.510871 | + | 0.884855i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.49483 | + | 16.4455i | −0.0375316 | + | 0.0650066i | ||||
\(41\) | 415.622 | 1.58315 | 0.791577 | − | 0.611070i | \(-0.209261\pi\) | ||||
0.791577 | + | 0.611070i | \(0.209261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −452.341 | −1.60422 | −0.802109 | − | 0.597178i | \(-0.796289\pi\) | ||||
−0.802109 | + | 0.597178i | \(0.796289\pi\) | |||||||
\(44\) | 78.2108 | − | 135.465i | 0.267971 | − | 0.464139i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 153.293 | + | 265.511i | 0.491343 | + | 0.851032i | ||||
\(47\) | 114.366 | − | 198.087i | 0.354935 | − | 0.614766i | −0.632172 | − | 0.774828i | \(-0.717836\pi\) |
0.987107 | + | 0.160063i | \(0.0511697\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −175.222 | + | 294.866i | −0.510852 | + | 0.859669i | ||||
\(50\) | 238.731 | 0.675233 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 48.8786 | + | 84.6602i | 0.130351 | + | 0.225774i | ||||
\(53\) | 220.936 | + | 382.673i | 0.572603 | + | 0.991777i | 0.996298 | + | 0.0859723i | \(0.0273996\pi\) |
−0.423695 | + | 0.905805i | \(0.639267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 92.8247 | 0.227572 | ||||||||
\(56\) | −73.2727 | − | 128.775i | −0.174848 | − | 0.307292i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 215.634 | − | 373.488i | 0.488174 | − | 0.845542i | ||||
\(59\) | 362.528 | + | 627.916i | 0.799951 | + | 1.38556i | 0.919648 | + | 0.392745i | \(0.128474\pi\) |
−0.119697 | + | 0.992810i | \(0.538192\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 170.880 | − | 295.973i | 0.358671 | − | 0.621237i | −0.629068 | − | 0.777351i | \(-0.716563\pi\) |
0.987739 | + | 0.156113i | \(0.0498965\pi\) | |||||||
\(62\) | 118.594 | 0.242927 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −29.0059 | + | 50.2396i | −0.0553497 | + | 0.0958686i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −125.678 | − | 217.681i | −0.229165 | − | 0.396925i | 0.728396 | − | 0.685156i | \(-0.240266\pi\) |
−0.957561 | + | 0.288231i | \(0.906933\pi\) | |||||||
\(68\) | −95.4835 | + | 165.382i | −0.170280 | + | 0.294934i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 44.4396 | − | 75.8659i | 0.0758793 | − | 0.129539i | ||||
\(71\) | 209.119 | 0.349547 | 0.174773 | − | 0.984609i | \(-0.444081\pi\) | ||||
0.174773 | + | 0.984609i | \(0.444081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60.9267 | − | 105.528i | −0.0976841 | − | 0.169194i | 0.813042 | − | 0.582206i | \(-0.197810\pi\) |
−0.910726 | + | 0.413012i | \(0.864477\pi\) | |||||||
\(74\) | −209.997 | − | 363.726i | −0.329888 | − | 0.571382i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 478.682 | 0.722481 | ||||||||
\(77\) | −366.058 | + | 624.922i | −0.541768 | + | 0.924889i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −399.598 | + | 692.123i | −0.569092 | + | 0.985696i | 0.427565 | + | 0.903985i | \(0.359372\pi\) |
−0.996656 | + | 0.0817107i | \(0.973962\pi\) | |||||||
\(80\) | 18.9897 | + | 32.8910i | 0.0265388 | + | 0.0459666i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 415.622 | − | 719.879i | 0.559729 | − | 0.969479i | ||||
\(83\) | 116.801 | 0.154465 | 0.0772324 | − | 0.997013i | \(-0.475392\pi\) | ||||
0.0772324 | + | 0.997013i | \(0.475392\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −113.325 | −0.144609 | ||||||||
\(86\) | −452.341 | + | 783.477i | −0.567176 | + | 0.982378i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −156.422 | − | 270.930i | −0.189484 | − | 0.328196i | ||||
\(89\) | 183.244 | − | 317.387i | 0.218245 | − | 0.378011i | −0.736027 | − | 0.676952i | \(-0.763300\pi\) |
0.954271 | + | 0.298942i | \(0.0966336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −223.842 | − | 393.398i | −0.257857 | − | 0.453179i | ||||
\(92\) | 613.171 | 0.694864 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −228.731 | − | 396.174i | −0.250977 | − | 0.434705i | ||||
\(95\) | 142.031 | + | 246.005i | 0.153391 | + | 0.265680i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1045.65 | −1.09454 | −0.547268 | − | 0.836957i | \(-0.684332\pi\) | ||||
−0.547268 | + | 0.836957i | \(0.684332\pi\) | |||||||
\(98\) | 335.501 | + | 598.360i | 0.345824 | + | 0.616770i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 238.731 | − | 413.494i | 0.238731 | − | 0.413494i | ||||
\(101\) | −581.936 | − | 1007.94i | −0.573314 | − | 0.993010i | −0.996223 | − | 0.0868370i | \(-0.972324\pi\) |
0.422908 | − | 0.906173i | \(-0.361009\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −79.1611 | + | 137.111i | −0.0757279 | + | 0.131165i | −0.901403 | − | 0.432982i | \(-0.857461\pi\) |
0.825675 | + | 0.564147i | \(0.190795\pi\) | |||||||
\(104\) | 195.514 | 0.184344 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 883.746 | 0.809783 | ||||||||
\(107\) | −79.6283 | + | 137.920i | −0.0719436 | + | 0.124610i | −0.899753 | − | 0.436399i | \(-0.856253\pi\) |
0.827809 | + | 0.561009i | \(0.189587\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0923 | + | 31.3368i | 0.0158984 | + | 0.0275369i | 0.873865 | − | 0.486168i | \(-0.161606\pi\) |
−0.857967 | + | 0.513705i | \(0.828272\pi\) | |||||||
\(110\) | 92.8247 | − | 160.777i | 0.0804590 | − | 0.139359i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −296.318 | − | 1.86337i | −0.249995 | − | 0.00157207i | ||||
\(113\) | 211.787 | 0.176312 | 0.0881561 | − | 0.996107i | \(-0.471903\pi\) | ||||
0.0881561 | + | 0.996107i | \(0.471903\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 181.936 | + | 315.123i | 0.147527 | + | 0.255525i | ||||
\(116\) | −431.267 | − | 746.977i | −0.345191 | − | 0.597888i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1450.11 | 1.13130 | ||||||||
\(119\) | 446.901 | − | 762.935i | 0.344263 | − | 0.587716i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −99.1152 | + | 171.673i | −0.0744667 | + | 0.128980i | ||||
\(122\) | −341.760 | − | 591.946i | −0.253619 | − | 0.439281i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 118.594 | − | 205.411i | 0.0858876 | − | 0.148762i | ||||
\(125\) | 580.052 | 0.415051 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −818.436 | −0.571846 | −0.285923 | − | 0.958253i | \(-0.592300\pi\) | ||||
−0.285923 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 58.0117 | + | 100.479i | 0.0391382 | + | 0.0677893i | ||||
\(131\) | −174.364 | + | 302.007i | −0.116292 | + | 0.201424i | −0.918295 | − | 0.395896i | \(-0.870434\pi\) |
0.802004 | + | 0.597319i | \(0.203767\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2216.28 | − | 13.9369i | −1.44493 | − | 0.00908635i | ||||
\(134\) | −502.713 | −0.324088 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 190.967 | + | 330.764i | 0.120406 | + | 0.208550i | ||||
\(137\) | −904.288 | − | 1566.27i | −0.563931 | − | 0.976757i | −0.997148 | − | 0.0754677i | \(-0.975955\pi\) |
0.433217 | − | 0.901290i | \(-0.357378\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1673.29 | 1.02106 | 0.510528 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510528 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(140\) | −86.9639 | − | 152.838i | −0.0524985 | − | 0.0922652i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 209.119 | − | 362.204i | 0.123583 | − | 0.214053i | ||||
\(143\) | −477.854 | − | 827.667i | −0.279442 | − | 0.484007i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 255.925 | − | 443.276i | 0.146575 | − | 0.253876i | ||||
\(146\) | −243.707 | −0.138146 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −839.989 | −0.466532 | ||||||||
\(149\) | −1605.66 | + | 2781.09i | −0.882824 | + | 1.52910i | −0.0346375 | + | 0.999400i | \(0.511028\pi\) |
−0.848187 | + | 0.529697i | \(0.822306\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1423.80 | + | 2466.09i | 0.767331 | + | 1.32906i | 0.939005 | + | 0.343902i | \(0.111749\pi\) |
−0.171675 | + | 0.985154i | \(0.554918\pi\) | |||||||
\(152\) | 478.682 | − | 829.101i | 0.255436 | − | 0.442428i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 716.339 | + | 1258.95i | 0.374833 | + | 0.658762i | ||||
\(155\) | 140.754 | 0.0729394 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −206.423 | − | 357.536i | −0.104932 | − | 0.181748i | 0.808778 | − | 0.588114i | \(-0.200129\pi\) |
−0.913711 | + | 0.406366i | \(0.866796\pi\) | |||||||
\(158\) | 799.195 | + | 1384.25i | 0.402409 | + | 0.696992i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 75.9586 | 0.0375316 | ||||||||
\(161\) | −2838.97 | − | 17.8526i | −1.38970 | − | 0.00873903i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1027.57 | + | 1779.80i | −0.493774 | + | 0.855241i | −0.999974 | − | 0.00717453i | \(-0.997716\pi\) |
0.506200 | + | 0.862416i | \(0.331050\pi\) | |||||||
\(164\) | −831.244 | − | 1439.76i | −0.395788 | − | 0.685525i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 116.801 | − | 202.305i | 0.0546116 | − | 0.0945900i | ||||
\(167\) | −3780.59 | −1.75180 | −0.875900 | − | 0.482493i | \(-0.839732\pi\) | ||||
−0.875900 | + | 0.482493i | \(0.839732\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1599.72 | −0.728139 | ||||||||
\(170\) | −113.325 | + | 196.284i | −0.0511272 | + | 0.0885549i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 904.682 | + | 1566.95i | 0.401054 | + | 0.694646i | ||||
\(173\) | 1775.75 | − | 3075.68i | 0.780390 | − | 1.35168i | −0.151325 | − | 0.988484i | \(-0.548354\pi\) |
0.931715 | − | 0.363191i | \(-0.118313\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1117.36 | + | 1907.52i | −0.482653 | + | 0.823970i | ||||
\(176\) | −625.686 | −0.267971 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −366.487 | − | 634.774i | −0.154322 | − | 0.267294i | ||||
\(179\) | −1974.70 | − | 3420.28i | −0.824558 | − | 1.42818i | −0.902257 | − | 0.431200i | \(-0.858090\pi\) |
0.0776984 | − | 0.996977i | \(-0.475243\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2448.62 | −1.00555 | −0.502774 | − | 0.864418i | \(-0.667687\pi\) | ||||
−0.502774 | + | 0.864418i | \(0.667687\pi\) | |||||||
\(182\) | −905.226 | − | 5.69245i | −0.368680 | − | 0.00231842i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 613.171 | − | 1062.04i | 0.245672 | − | 0.425516i | ||||
\(185\) | −249.236 | − | 431.689i | −0.0990497 | − | 0.171559i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 933.479 | − | 1616.83i | 0.365041 | − | 0.632270i | ||||
\(188\) | −914.925 | −0.354935 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 568.125 | 0.216927 | ||||||||
\(191\) | 381.726 | − | 661.169i | 0.144611 | − | 0.250474i | −0.784617 | − | 0.619981i | \(-0.787140\pi\) |
0.929228 | + | 0.369507i | \(0.120474\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1365.76 | + | 2365.57i | 0.509376 | + | 0.882266i | 0.999941 | + | 0.0108609i | \(0.00345719\pi\) |
−0.490565 | + | 0.871405i | \(0.663209\pi\) | |||||||
\(194\) | −1045.65 | + | 1811.12i | −0.386977 | + | 0.670264i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1371.89 | + | 17.2547i | 0.499960 | + | 0.00628817i | ||||
\(197\) | 3476.58 | 1.25734 | 0.628671 | − | 0.777671i | \(-0.283599\pi\) | ||||
0.628671 | + | 0.777671i | \(0.283599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1627.72 | − | 2819.30i | −0.579831 | − | 1.00430i | −0.995498 | − | 0.0947796i | \(-0.969785\pi\) |
0.415668 | − | 0.909517i | \(-0.363548\pi\) | |||||||
\(200\) | −477.462 | − | 826.989i | −0.168808 | − | 0.292385i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2327.74 | −0.810789 | ||||||||
\(203\) | 1975.01 | + | 3471.04i | 0.682849 | + | 1.20009i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 493.282 | − | 854.390i | 0.168060 | − | 0.291089i | ||||
\(206\) | 158.322 | + | 274.222i | 0.0535477 | + | 0.0927473i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 195.514 | − | 338.641i | 0.0651754 | − | 0.112887i | ||||
\(209\) | −4679.76 | −1.54883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1596.29 | 0.520822 | 0.260411 | − | 0.965498i | \(-0.416142\pi\) | ||||
0.260411 | + | 0.965498i | \(0.416142\pi\) | |||||||
\(212\) | 883.746 | − | 1530.69i | 0.286301 | − | 0.495889i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 159.257 | + | 275.841i | 0.0508718 | + | 0.0881125i | ||||
\(215\) | −536.862 | + | 929.873i | −0.170296 | + | 0.294962i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −555.068 | + | 947.594i | −0.173643 | + | 0.296437i | ||||
\(218\) | 72.3693 | 0.0224838 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −185.649 | − | 321.554i | −0.0568931 | − | 0.0985417i | ||||
\(221\) | 583.387 | + | 1010.46i | 0.177570 | + | 0.307559i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5869.21 | 1.76247 | 0.881236 | − | 0.472677i | \(-0.156712\pi\) | ||||
0.881236 | + | 0.472677i | \(0.156712\pi\) | |||||||
\(224\) | −299.546 | + | 511.375i | −0.0893493 | + | 0.152534i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 211.787 | − | 366.827i | 0.0623358 | − | 0.107969i | ||||
\(227\) | −2979.05 | − | 5159.86i | −0.871041 | − | 1.50869i | −0.860922 | − | 0.508738i | \(-0.830112\pi\) |
−0.0101189 | − | 0.999949i | \(-0.503221\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −319.983 | + | 554.227i | −0.0923366 | + | 0.159932i | −0.908494 | − | 0.417898i | \(-0.862767\pi\) |
0.816157 | + | 0.577830i | \(0.196100\pi\) | |||||||
\(230\) | 727.744 | 0.208635 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1725.07 | −0.488174 | ||||||||
\(233\) | −20.5054 | + | 35.5163i | −0.00576545 | + | 0.00998606i | −0.868894 | − | 0.494999i | \(-0.835169\pi\) |
0.863128 | + | 0.504985i | \(0.168502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −271.470 | − | 470.201i | −0.0753565 | − | 0.130521i | ||||
\(236\) | 1450.11 | − | 2511.67i | 0.399975 | − | 0.692778i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −874.541 | − | 1536.99i | −0.238185 | − | 0.418606i | ||||
\(239\) | 2995.72 | 0.810783 | 0.405391 | − | 0.914143i | \(-0.367135\pi\) | ||||
0.405391 | + | 0.914143i | \(0.367135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 332.680 | + | 576.218i | 0.0889203 | + | 0.154014i | 0.907055 | − | 0.421012i | \(-0.138325\pi\) |
−0.818135 | + | 0.575027i | \(0.804992\pi\) | |||||||
\(242\) | 198.230 | + | 343.345i | 0.0526559 | + | 0.0912027i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1367.04 | −0.358671 | ||||||||
\(245\) | 398.191 | + | 710.166i | 0.103835 | + | 0.185187i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1462.33 | − | 2532.83i | 0.376704 | − | 0.652470i | ||||
\(248\) | −237.188 | − | 410.822i | −0.0607317 | − | 0.105190i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 580.052 | − | 1004.68i | 0.146743 | − | 0.254166i | ||||
\(251\) | −611.679 | −0.153820 | −0.0769100 | − | 0.997038i | \(-0.524505\pi\) | ||||
−0.0769100 | + | 0.997038i | \(0.524505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5994.57 | −1.48963 | ||||||||
\(254\) | −818.436 | + | 1417.57i | −0.202178 | + | 0.350183i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1049.17 | + | 1817.21i | −0.254651 | + | 0.441069i | −0.964801 | − | 0.262982i | \(-0.915294\pi\) |
0.710149 | + | 0.704051i | \(0.248627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3889.13 | + | 24.4565i | 0.933045 | + | 0.00586738i | ||||
\(260\) | 232.047 | 0.0553497 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 348.728 | + | 604.014i | 0.0822308 | + | 0.142428i | ||||
\(263\) | 2070.93 | + | 3586.95i | 0.485547 | + | 0.840992i | 0.999862 | − | 0.0166096i | \(-0.00528725\pi\) |
−0.514315 | + | 0.857601i | \(0.671954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1048.88 | 0.243140 | ||||||||
\(266\) | −2240.42 | + | 3824.78i | −0.516425 | + | 0.881625i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −502.713 | + | 870.725i | −0.114582 | + | 0.198463i | ||||
\(269\) | −1941.13 | − | 3362.14i | −0.439974 | − | 0.762058i | 0.557713 | − | 0.830034i | \(-0.311679\pi\) |
−0.997687 | + | 0.0679765i | \(0.978346\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 698.842 | − | 1210.43i | 0.156648 | − | 0.271322i | −0.777010 | − | 0.629488i | \(-0.783264\pi\) |
0.933658 | + | 0.358166i | \(0.116598\pi\) | |||||||
\(272\) | 763.868 | 0.170280 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3617.15 | −0.797519 | ||||||||
\(275\) | −2333.92 | + | 4042.46i | −0.511784 | + | 0.886435i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3305.04 | − | 5724.50i | −0.716898 | − | 1.24170i | −0.962223 | − | 0.272262i | \(-0.912228\pi\) |
0.245325 | − | 0.969441i | \(-0.421105\pi\) | |||||||
\(278\) | 1673.29 | − | 2898.23i | 0.360998 | − | 0.625267i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −351.686 | − | 2.21155i | −0.0750617 | − | 0.000472020i | ||||
\(281\) | 7076.82 | 1.50238 | 0.751188 | − | 0.660088i | \(-0.229481\pi\) | ||||
0.751188 | + | 0.660088i | \(0.229481\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 937.326 | + | 1623.50i | 0.196884 | + | 0.341013i | 0.947517 | − | 0.319707i | \(-0.103584\pi\) |
−0.750632 | + | 0.660720i | \(0.770251\pi\) | |||||||
\(284\) | −418.238 | − | 724.409i | −0.0873867 | − | 0.151358i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1911.42 | −0.395190 | ||||||||
\(287\) | 3806.72 | + | 6690.24i | 0.782939 | + | 1.37600i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1316.86 | − | 2280.87i | 0.268037 | − | 0.464253i | ||||
\(290\) | −511.851 | − | 886.551i | −0.103645 | − | 0.179518i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −243.707 | + | 422.113i | −0.0488420 | + | 0.0845969i | ||||
\(293\) | 6964.76 | 1.38869 | 0.694344 | − | 0.719643i | \(-0.255694\pi\) | ||||
0.694344 | + | 0.719643i | \(0.255694\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1721.07 | 0.339676 | ||||||||
\(296\) | −839.989 | + | 1454.90i | −0.164944 | + | 0.285691i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3211.32 | + | 5562.17i | 0.624251 | + | 1.08123i | ||||
\(299\) | 1873.18 | − | 3244.45i | 0.362305 | − | 0.627530i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4143.03 | − | 7281.30i | −0.793356 | − | 1.39431i | ||||
\(302\) | 5695.19 | 1.08517 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −957.364 | − | 1658.20i | −0.180620 | − | 0.312844i | ||||
\(305\) | −405.619 | − | 702.553i | −0.0761498 | − | 0.131895i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5750.23 | 1.06900 | 0.534500 | − | 0.845169i | \(-0.320500\pi\) | ||||
0.534500 | + | 0.845169i | \(0.320500\pi\) | |||||||
\(308\) | 2896.91 | + | 18.2170i | 0.535931 | + | 0.00337016i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 140.754 | − | 243.793i | 0.0257880 | − | 0.0446661i | ||||
\(311\) | −2392.17 | − | 4143.35i | −0.436165 | − | 0.755460i | 0.561225 | − | 0.827663i | \(-0.310330\pi\) |
−0.997390 | + | 0.0722036i | \(0.976997\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4449.28 | − | 7706.39i | 0.803477 | − | 1.39166i | −0.113837 | − | 0.993499i | \(-0.536314\pi\) |
0.917314 | − | 0.398164i | \(-0.130353\pi\) | |||||||
\(314\) | −825.693 | −0.148397 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3196.78 | 0.569092 | ||||||||
\(317\) | −2036.68 | + | 3527.63i | −0.360856 | + | 0.625021i | −0.988102 | − | 0.153800i | \(-0.950849\pi\) |
0.627246 | + | 0.778821i | \(0.284182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4216.22 | + | 7302.70i | 0.740009 | + | 1.28173i | ||||
\(320\) | 75.9586 | − | 131.564i | 0.0132694 | − | 0.0229833i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2869.89 | + | 4899.38i | −0.496685 | + | 0.847925i | ||||
\(323\) | 5713.27 | 0.984195 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1458.60 | − | 2526.38i | −0.248950 | − | 0.431194i | ||||
\(326\) | 2055.13 | + | 3559.59i | 0.349151 | + | 0.604747i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3324.98 | −0.559729 | ||||||||
\(329\) | 4236.08 | + | 26.6383i | 0.709856 | + | 0.00446387i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1613.95 | + | 2795.44i | −0.268008 | + | 0.464203i | −0.968347 | − | 0.249607i | \(-0.919699\pi\) |
0.700340 | + | 0.713810i | \(0.253032\pi\) | |||||||
\(332\) | −233.602 | − | 404.611i | −0.0386162 | − | 0.0668853i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3780.59 | + | 6548.17i | −0.619355 | + | 1.07275i | ||||
\(335\) | −596.647 | −0.0973083 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9639.76 | 1.55819 | 0.779097 | − | 0.626904i | \(-0.215678\pi\) | ||||
0.779097 | + | 0.626904i | \(0.215678\pi\) | |||||||
\(338\) | −1599.72 | + | 2770.80i | −0.257436 | + | 0.445892i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 226.650 | + | 392.569i | 0.0361524 | + | 0.0626177i | ||||
\(341\) | −1159.42 | + | 2008.17i | −0.184123 | + | 0.318910i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6351.32 | − | 119.832i | −0.999822 | − | 0.0188639i | ||||
\(344\) | 3618.73 | 0.567176 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3551.49 | − | 6151.37i | −0.551819 | − | 0.955779i | ||||
\(347\) | 832.775 | + | 1442.41i | 0.128835 | + | 0.223149i | 0.923225 | − | 0.384259i | \(-0.125543\pi\) |
−0.794391 | + | 0.607407i | \(0.792210\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4441.18 | 0.681177 | 0.340589 | − | 0.940212i | \(-0.389374\pi\) | ||||
0.340589 | + | 0.940212i | \(0.389374\pi\) | |||||||
\(350\) | 2186.56 | + | 3842.84i | 0.333933 | + | 0.586881i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −625.686 | + | 1083.72i | −0.0947420 | + | 0.164098i | ||||
\(353\) | 4399.42 | + | 7620.02i | 0.663336 | + | 1.14893i | 0.979734 | + | 0.200305i | \(0.0641933\pi\) |
−0.316397 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 248.193 | − | 429.883i | 0.0371063 | − | 0.0642700i | ||||
\(356\) | −1465.95 | −0.218245 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7898.79 | −1.16610 | ||||||||
\(359\) | 2769.49 | − | 4796.89i | 0.407153 | − | 0.705210i | −0.587417 | − | 0.809285i | \(-0.699855\pi\) |
0.994569 | + | 0.104075i | \(0.0331883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3731.01 | − | 6462.30i | −0.543958 | − | 0.942163i | ||||
\(362\) | −2448.62 | + | 4241.13i | −0.355515 | + | 0.615770i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −915.086 | + | 1562.21i | −0.131768 | + | 0.224950i | ||||
\(365\) | −289.244 | −0.0414788 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5721.93 | + | 9910.68i | 0.813848 | + | 1.40963i | 0.910152 | + | 0.414275i | \(0.135965\pi\) |
−0.0963034 | + | 0.995352i | \(0.530702\pi\) | |||||||
\(368\) | −1226.34 | − | 2124.09i | −0.173716 | − | 0.300885i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −996.944 | −0.140077 | ||||||||
\(371\) | −4136.29 | + | 7061.34i | −0.578828 | + | 0.988157i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6187.63 | + | 10717.3i | −0.858936 | + | 1.48772i | 0.0140082 | + | 0.999902i | \(0.495541\pi\) |
−0.872945 | + | 0.487819i | \(0.837792\pi\) | |||||||
\(374\) | −1866.96 | − | 3233.67i | −0.258123 | − | 0.447083i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −914.925 | + | 1584.70i | −0.125488 | + | 0.217352i | ||||
\(377\) | −5269.93 | −0.719935 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 621.352 | 0.0842129 | 0.0421064 | − | 0.999113i | \(-0.486593\pi\) | ||||
0.0421064 | + | 0.999113i | \(0.486593\pi\) | |||||||
\(380\) | 568.125 | − | 984.021i | 0.0766953 | − | 0.132840i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −763.452 | − | 1322.34i | −0.102256 | − | 0.177112i | ||||
\(383\) | 4673.97 | − | 8095.56i | 0.623574 | − | 1.08006i | −0.365241 | − | 0.930913i | \(-0.619013\pi\) |
0.988815 | − | 0.149149i | \(-0.0476533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 850.189 | + | 1494.19i | 0.112545 | + | 0.197795i | ||||
\(386\) | 5463.04 | 0.720367 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2091.31 | + | 3622.25i | 0.273634 | + | 0.473948i | ||||
\(389\) | 575.571 | + | 996.918i | 0.0750195 | + | 0.129938i | 0.901095 | − | 0.433622i | \(-0.142765\pi\) |
−0.826075 | + | 0.563560i | \(0.809431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7318.46 | 0.946575 | ||||||||
\(392\) | 1401.78 | − | 2358.93i | 0.180613 | − | 0.303939i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3476.58 | − | 6021.62i | 0.444538 | − | 0.769962i | ||||
\(395\) | 948.527 | + | 1642.90i | 0.120824 | + | 0.209274i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2714.27 | − | 4701.26i | 0.343137 | − | 0.594331i | −0.641876 | − | 0.766808i | \(-0.721844\pi\) |
0.985014 | + | 0.172477i | \(0.0551771\pi\) | |||||||
\(398\) | −6510.90 | −0.820004 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1909.85 | −0.238731 | ||||||||
\(401\) | −2182.88 | + | 3780.87i | −0.271841 | + | 0.470842i | −0.969333 | − | 0.245750i | \(-0.920966\pi\) |
0.697493 | + | 0.716592i | \(0.254299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −724.589 | − | 1255.02i | −0.0895641 | − | 0.155130i | ||||
\(404\) | −2327.74 | + | 4031.77i | −0.286657 | + | 0.496505i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7987.02 | + | 50.2258i | 0.976328 | + | 0.00613956i | ||||
\(407\) | 8212.03 | 1.00014 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1654.33 | − | 2865.38i | −0.200003 | − | 0.346415i | 0.748526 | − | 0.663105i | \(-0.230762\pi\) |
−0.948529 | + | 0.316690i | \(0.897428\pi\) | |||||||
\(410\) | −986.565 | − | 1708.78i | −0.118837 | − | 0.205831i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 633.288 | 0.0757279 | ||||||||
\(413\) | −6787.10 | + | 11586.7i | −0.808648 | + | 1.38050i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 138.626 | − | 240.107i | 0.0163973 | − | 0.0284009i | ||||
\(416\) | −391.029 | − | 677.282i | −0.0460860 | − | 0.0798232i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4679.76 | + | 8105.58i | −0.547594 | + | 0.948461i | ||||
\(419\) | −3249.72 | −0.378900 | −0.189450 | − | 0.981890i | \(-0.560670\pi\) | ||||
−0.189450 | + | 0.981890i | \(0.560670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2932.21 | −0.339447 | −0.169724 | − | 0.985492i | \(-0.554287\pi\) | ||||
−0.169724 | + | 0.985492i | \(0.554287\pi\) | |||||||
\(422\) | 1596.29 | − | 2764.86i | 0.184138 | − | 0.318937i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1767.49 | − | 3061.39i | −0.202446 | − | 0.350646i | ||||
\(425\) | 2849.36 | − | 4935.23i | 0.325210 | − | 0.563280i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6329.36 | + | 39.8017i | 0.717329 | + | 0.00451087i | ||||
\(428\) | 637.027 | 0.0719436 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1073.72 | + | 1859.75i | 0.120418 | + | 0.208569i | ||||
\(431\) | 3981.70 | + | 6896.50i | 0.444992 | + | 0.770749i | 0.998052 | − | 0.0623926i | \(-0.0198731\pi\) |
−0.553059 | + | 0.833142i | \(0.686540\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7441.66 | −0.825920 | −0.412960 | − | 0.910749i | \(-0.635505\pi\) | ||||
−0.412960 | + | 0.910749i | \(0.635505\pi\) | |||||||
\(434\) | 1086.21 | + | 1909.00i | 0.120138 | + | 0.211140i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 72.3693 | − | 125.347i | 0.00794922 | − | 0.0137685i | ||||
\(437\) | −9172.31 | − | 15886.9i | −1.00405 | − | 1.73907i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2822.84 | + | 4889.30i | −0.306895 | + | 0.531557i | −0.977681 | − | 0.210093i | \(-0.932623\pi\) |
0.670787 | + | 0.741650i | \(0.265957\pi\) | |||||||
\(440\) | −742.597 | −0.0804590 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2333.55 | 0.251121 | ||||||||
\(443\) | −6952.30 | + | 12041.7i | −0.745630 | + | 1.29147i | 0.204270 | + | 0.978915i | \(0.434518\pi\) |
−0.949900 | + | 0.312554i | \(0.898816\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −434.966 | − | 753.384i | −0.0463357 | − | 0.0802558i | ||||
\(446\) | 5869.21 | − | 10165.8i | 0.623128 | − | 1.07929i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 586.182 | + | 1030.20i | 0.0618180 | + | 0.108644i | ||||
\(449\) | 15582.7 | 1.63784 | 0.818921 | − | 0.573906i | \(-0.194573\pi\) | ||||
0.818921 | + | 0.573906i | \(0.194573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8126.53 | + | 14075.6i | 0.848477 | + | 1.46961i | ||||
\(452\) | −423.575 | − | 733.653i | −0.0440781 | − | 0.0763454i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11916.2 | −1.23184 | ||||||||
\(455\) | −1074.37 | − | 6.75610i | −0.110697 | − | 0.000696111i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4679.71 | + | 8105.49i | −0.479010 | + | 0.829670i | −0.999710 | − | 0.0240700i | \(-0.992338\pi\) |
0.520700 | + | 0.853740i | \(0.325671\pi\) | |||||||
\(458\) | 639.966 | + | 1108.45i | 0.0652918 | + | 0.113089i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 727.744 | − | 1260.49i | 0.0737636 | − | 0.127762i | ||||
\(461\) | −1558.11 | −0.157415 | −0.0787074 | − | 0.996898i | \(-0.525079\pi\) | ||||
−0.0787074 | + | 0.996898i | \(0.525079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12753.6 | 1.28015 | 0.640074 | − | 0.768313i | \(-0.278904\pi\) | ||||
0.640074 | + | 0.768313i | \(0.278904\pi\) | |||||||
\(464\) | −1725.07 | + | 2987.91i | −0.172595 | + | 0.298944i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 41.0107 | + | 71.0326i | 0.00407679 | + | 0.00706121i | ||||
\(467\) | 5556.71 | − | 9624.51i | 0.550608 | − | 0.953681i | −0.447623 | − | 0.894223i | \(-0.647729\pi\) |
0.998231 | − | 0.0594586i | \(-0.0189374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2352.90 | − | 4016.80i | 0.231656 | − | 0.395476i | ||||
\(470\) | −1085.88 | −0.106570 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2900.22 | − | 5023.33i | −0.282825 | − | 0.489868i | ||||
\(473\) | −8844.48 | − | 15319.1i | −0.859767 | − | 1.48916i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14284.5 | −1.37983 | ||||||||
\(476\) | −3536.69 | − | 22.2402i | −0.340554 | − | 0.00214155i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2995.72 | − | 5188.74i | 0.286655 | − | 0.496501i | ||||
\(479\) | −9495.17 | − | 16446.1i | −0.905731 | − | 1.56877i | −0.819933 | − | 0.572460i | \(-0.805989\pi\) |
−0.0857987 | − | 0.996312i | \(-0.527344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2566.09 | + | 4444.61i | −0.243251 | + | 0.421323i | ||||
\(482\) | 1330.72 | 0.125752 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 792.922 | 0.0744667 | ||||||||
\(485\) | −1241.04 | + | 2149.54i | −0.116191 | + | 0.201249i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2474.13 | − | 4285.31i | −0.230212 | − | 0.398739i | 0.727658 | − | 0.685940i | \(-0.240609\pi\) |
−0.957870 | + | 0.287201i | \(0.907275\pi\) | |||||||
\(488\) | −1367.04 | + | 2367.78i | −0.126810 | + | 0.219641i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1628.23 | + | 20.4789i | 0.150114 | + | 0.00188804i | ||||
\(491\) | 9178.86 | 0.843658 | 0.421829 | − | 0.906675i | \(-0.361388\pi\) | ||||
0.421829 | + | 0.906675i | \(0.361388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5147.36 | − | 8915.49i | −0.470234 | − | 0.814469i | ||||
\(494\) | −2924.66 | − | 5065.66i | −0.266370 | − | 0.461366i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −948.752 | −0.0858876 | ||||||||
\(497\) | 1915.34 | + | 3366.17i | 0.172866 | + | 0.303810i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8374.31 | − | 14504.7i | 0.751274 | − | 1.30125i | −0.195931 | − | 0.980618i | \(-0.562773\pi\) |
0.947205 | − | 0.320627i | \(-0.103894\pi\) | |||||||
\(500\) | −1160.10 | − | 2009.36i | −0.103763 | − | 0.179723i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −611.679 | + | 1059.46i | −0.0543836 | + | 0.0941952i | ||||
\(503\) | −10162.0 | −0.900794 | −0.450397 | − | 0.892828i | \(-0.648718\pi\) | ||||
−0.450397 | + | 0.892828i | \(0.648718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2762.69 | −0.243442 | ||||||||
\(506\) | −5994.57 | + | 10382.9i | −0.526663 | + | 0.912206i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1636.87 | + | 2835.14i | 0.142961 | + | 0.247617i | ||||
\(509\) | 2831.68 | − | 4904.62i | 0.246586 | − | 0.427099i | −0.715991 | − | 0.698110i | \(-0.754025\pi\) |
0.962576 | + | 0.271011i | \(0.0873580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1140.65 | − | 1947.28i | 0.0987461 | − | 0.168576i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2098.34 | + | 3634.43i | 0.180066 | + | 0.311883i | ||||
\(515\) | 187.905 | + | 325.461i | 0.0160778 | + | 0.0278476i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8944.62 | 0.760898 | ||||||||
\(518\) | 3931.49 | − | 6711.71i | 0.333474 | − | 0.569297i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 232.047 | − | 401.917i | 0.0195691 | − | 0.0338947i | ||||
\(521\) | 839.858 | + | 1454.68i | 0.0706235 | + | 0.122324i | 0.899175 | − | 0.437590i | \(-0.144168\pi\) |
−0.828551 | + | 0.559913i | \(0.810834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3522.27 | − | 6100.76i | 0.294490 | − | 0.510072i | −0.680376 | − | 0.732863i | \(-0.738184\pi\) |
0.974866 | + | 0.222791i | \(0.0715169\pi\) | |||||||
\(524\) | 1394.91 | 0.116292 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8283.70 | 0.686667 | ||||||||
\(527\) | 1415.47 | − | 2451.67i | 0.117000 | − | 0.202650i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5665.85 | − | 9813.53i | −0.465673 | − | 0.806570i | ||||
\(530\) | 1048.88 | − | 1816.71i | 0.0859628 | − | 0.148892i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4384.29 | + | 7705.31i | 0.357299 | + | 0.627946i | ||||
\(533\) | −10157.5 | −0.825461 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 189.014 | + | 327.382i | 0.0152744 | + | 0.0264560i | ||||
\(536\) | 1005.43 | + | 1741.45i | 0.0810220 | + | 0.140334i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7764.54 | −0.622217 | ||||||||
\(539\) | −13412.1 | − | 168.688i | −1.07180 | − | 0.0134804i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −884.613 | + | 1532.20i | −0.0703004 | + | 0.121764i | −0.899033 | − | 0.437881i | \(-0.855729\pi\) |
0.828733 | + | 0.559645i | \(0.189062\pi\) | |||||||
\(542\) | −1397.68 | − | 2420.86i | −0.110767 | − | 0.191854i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 763.868 | − | 1323.06i | 0.0602032 | − | 0.104275i | ||||
\(545\) | 85.8917 | 0.00675082 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5279.46 | 0.412676 | 0.206338 | − | 0.978481i | \(-0.433845\pi\) | ||||
0.206338 | + | 0.978481i | \(0.433845\pi\) | |||||||
\(548\) | −3617.15 | + | 6265.09i | −0.281966 | + | 0.488379i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4667.83 | + | 8084.92i | 0.361886 | + | 0.626804i | ||||
\(551\) | −12902.5 | + | 22347.8i | −0.997576 | + | 1.72785i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14801.0 | − | 93.0750i | −1.13816 | − | 0.00715724i | ||||
\(554\) | −13220.2 | −1.01385 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3346.59 | − | 5796.46i | −0.255264 | − | 0.442131i | ||||
\(557\) | −10662.5 | − | 18468.1i | −0.811107 | − | 1.40488i | −0.912090 | − | 0.409990i | \(-0.865532\pi\) |
0.100984 | − | 0.994888i | \(-0.467801\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11054.9 | 0.836444 | ||||||||
\(560\) | −355.517 | + | 606.927i | −0.0268274 | + | 0.0457988i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7076.82 | − | 12257.4i | 0.531170 | − | 0.920014i | ||||
\(563\) | −12490.1 | − | 21633.4i | −0.934979 | − | 1.61943i | −0.774671 | − | 0.632364i | \(-0.782085\pi\) |
−0.160308 | − | 0.987067i | \(-0.551249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 251.361 | − | 435.369i | 0.0187165 | − | 0.0324179i | ||||
\(566\) | 3749.30 | 0.278436 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1672.95 | −0.123583 | ||||||||
\(569\) | −8527.32 | + | 14769.7i | −0.628267 | + | 1.08819i | 0.359633 | + | 0.933094i | \(0.382902\pi\) |
−0.987899 | + | 0.155096i | \(0.950431\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7455.68 | − | 12913.6i | −0.546429 | − | 0.946442i | −0.998516 | − | 0.0544681i | \(-0.982654\pi\) |
0.452087 | − | 0.891974i | \(-0.350680\pi\) | |||||||
\(572\) | −1911.42 | + | 3310.67i | −0.139721 | + | 0.242004i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15394.6 | + | 96.8075i | 1.11944 | + | 0.00703949i | ||||
\(575\) | −18297.9 | −1.32709 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11224.7 | − | 19441.7i | −0.809860 | − | 1.40272i | −0.912960 | − | 0.408048i | \(-0.866210\pi\) |
0.103100 | − | 0.994671i | \(-0.467124\pi\) | |||||||
\(578\) | −2633.73 | − | 4561.75i | −0.189530 | − | 0.328276i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2047.40 | −0.146575 | ||||||||
\(581\) | 1069.79 | + | 1880.14i | 0.0763897 | + | 0.134254i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8639.80 | + | 14964.6i | −0.613763 | + | 1.06307i | ||||
\(584\) | 487.414 | + | 844.226i | 0.0345365 | + | 0.0598190i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6964.76 | − | 12063.3i | 0.490976 | − | 0.850395i | ||||
\(587\) | 7613.92 | 0.535367 | 0.267683 | − | 0.963507i | \(-0.413742\pi\) | ||||
0.267683 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7096.10 | −0.496417 | ||||||||
\(590\) | 1721.07 | − | 2980.98i | 0.120094 | − | 0.208008i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1679.98 | + | 2909.81i | 0.116633 | + | 0.202014i | ||||
\(593\) | 6920.65 | − | 11986.9i | 0.479253 | − | 0.830090i | −0.520464 | − | 0.853884i | \(-0.674241\pi\) |
0.999717 | + | 0.0237934i | \(0.00757438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1037.95 | − | 1824.18i | −0.0715158 | − | 0.125688i | ||||
\(596\) | 12845.3 | 0.882824 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3746.37 | − | 6488.90i | −0.256188 | − | 0.443731i | ||||
\(599\) | −3038.99 | − | 5263.69i | −0.207295 | − | 0.359046i | 0.743566 | − | 0.668662i | \(-0.233133\pi\) |
−0.950862 | + | 0.309616i | \(0.899799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5719.48 | −0.388190 | −0.194095 | − | 0.980983i | \(-0.562177\pi\) | ||||
−0.194095 | + | 0.980983i | \(0.562177\pi\) | |||||||
\(602\) | −16754.6 | − | 105.360i | −1.13433 | − | 0.00713315i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5695.19 | − | 9864.35i | 0.383665 | − | 0.664528i | ||||
\(605\) | 235.270 | + | 407.500i | 0.0158101 | + | 0.0273839i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14768.8 | + | 25580.3i | −0.987558 | + | 1.71050i | −0.357592 | + | 0.933878i | \(0.616402\pi\) |
−0.629966 | + | 0.776623i | \(0.716931\pi\) | |||||||
\(608\) | −3829.45 | −0.255436 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1622.48 | −0.107692 | ||||||||
\(611\) | −2795.02 | + | 4841.11i | −0.185064 | + | 0.320541i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10569.8 | − | 18307.5i | −0.696429 | − | 1.20625i | −0.969697 | − | 0.244312i | \(-0.921438\pi\) |
0.273267 | − | 0.961938i | \(-0.411896\pi\) | |||||||
\(614\) | 5750.23 | − | 9959.69i | 0.377949 | − | 0.654626i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2928.46 | − | 4999.38i | 0.191544 | − | 0.326998i | ||||
\(617\) | 6754.03 | 0.440692 | 0.220346 | − | 0.975422i | \(-0.429281\pi\) | ||||
0.220346 | + | 0.975422i | \(0.429281\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13387.6 | + | 23188.0i | 0.869292 | + | 1.50566i | 0.862721 | + | 0.505680i | \(0.168758\pi\) |
0.00657132 | + | 0.999978i | \(0.497908\pi\) | |||||||
\(620\) | −281.507 | − | 487.585i | −0.0182349 | − | 0.0315837i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9568.66 | −0.616830 | ||||||||
\(623\) | 6787.30 | + | 42.6814i | 0.436481 | + | 0.00274478i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6771.91 | + | 11729.3i | −0.433402 | + | 0.750675i | ||||
\(626\) | −8898.57 | − | 15412.8i | −0.568144 | − | 0.984055i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −825.693 | + | 1430.14i | −0.0524662 | + | 0.0908741i | ||||
\(629\) | −10025.6 | −0.635530 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17990.3 | 1.13500 | 0.567499 | − | 0.823374i | \(-0.307911\pi\) | ||||
0.567499 | + | 0.823374i | \(0.307911\pi\) | |||||||
\(632\) | 3196.78 | − | 5536.99i | 0.201204 | − | 0.348496i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4073.36 | + | 7055.27i | 0.255164 | + | 0.441957i | ||||
\(635\) | −971.363 | + | 1682.45i | −0.0607045 | + | 0.105143i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4282.31 | − | 7206.33i | 0.266360 | − | 0.448234i | ||||
\(638\) | 16864.9 | 1.04653 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −151.917 | − | 263.128i | −0.00938290 | − | 0.0162517i | ||||
\(641\) | 4678.17 | + | 8102.83i | 0.288263 | + | 0.499287i | 0.973395 | − | 0.229132i | \(-0.0735888\pi\) |
−0.685132 | + | 0.728419i | \(0.740256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14794.8 | 0.907388 | 0.453694 | − | 0.891158i | \(-0.350106\pi\) | ||||
0.453694 | + | 0.891158i | \(0.350106\pi\) | |||||||
\(644\) | 5616.09 | + | 9870.17i | 0.343641 | + | 0.603943i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5713.27 | − | 9895.68i | 0.347966 | − | 0.602694i | ||||
\(647\) | 13672.9 | + | 23682.2i | 0.830816 | + | 1.43902i | 0.897392 | + | 0.441234i | \(0.145459\pi\) |
−0.0665758 | + | 0.997781i | \(0.521207\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14176.8 | + | 24554.9i | −0.857454 | + | 1.48515i | ||||
\(650\) | −5834.42 | −0.352069 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8220.52 | 0.493774 | ||||||||
\(653\) | 3351.78 | − | 5805.46i | 0.200866 | − | 0.347910i | −0.747942 | − | 0.663764i | \(-0.768958\pi\) |
0.948808 | + | 0.315854i | \(0.102291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 413.889 | + | 716.876i | 0.0246900 | + | 0.0427644i | ||||
\(656\) | −3324.98 | + | 5759.03i | −0.197894 | + | 0.342763i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4282.22 | − | 7310.47i | 0.253706 | − | 0.433118i | ||||
\(659\) | 13321.2 | 0.787433 | 0.393717 | − | 0.919232i | \(-0.371189\pi\) | ||||
0.393717 | + | 0.919232i | \(0.371189\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9509.03 | + | 16470.1i | 0.559544 | + | 0.969158i | 0.997534 | + | 0.0701787i | \(0.0223570\pi\) |
−0.437991 | + | 0.898980i | \(0.644310\pi\) | |||||||
\(662\) | 3227.89 | + | 5590.88i | 0.189510 | + | 0.328241i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −934.409 | −0.0546116 | ||||||||
\(665\) | −2659.05 | + | 4539.45i | −0.155058 | + | 0.264710i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16527.5 | + | 28626.5i | −0.959444 | + | 1.66181i | ||||
\(668\) | 7561.17 | + | 13096.3i | 0.437950 | + | 0.758552i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −596.647 | + | 1033.42i | −0.0344037 | + | 0.0595890i | ||||
\(671\) | 13364.7 | 0.768908 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12786.8 | −0.732386 | −0.366193 | − | 0.930539i | \(-0.619339\pi\) | ||||
−0.366193 | + | 0.930539i | \(0.619339\pi\) | |||||||
\(674\) | 9639.76 | − | 16696.6i | 0.550905 | − | 0.954195i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3199.44 | + | 5541.60i | 0.182035 | + | 0.315293i | ||||
\(677\) | 4555.10 | − | 7889.67i | 0.258592 | − | 0.447895i | −0.707273 | − | 0.706941i | \(-0.750075\pi\) |
0.965865 | + | 0.259046i | \(0.0834081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9577.23 | − | 16831.8i | −0.541297 | − | 0.951319i | ||||
\(680\) | 906.599 | 0.0511272 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2318.83 | + | 4016.34i | 0.130195 | + | 0.225504i | ||||
\(683\) | −10067.1 | − | 17436.7i | −0.563993 | − | 0.976864i | −0.997143 | − | 0.0755422i | \(-0.975931\pi\) |
0.433150 | − | 0.901322i | \(-0.357402\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4293.03 | −0.239457 | ||||||||
\(686\) | −6558.87 | + | 10881.0i | −0.365042 | + | 0.605594i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3618.73 | − | 6267.82i | 0.200527 | − | 0.347323i | ||||
\(689\) | −5399.53 | − | 9352.26i | −0.298557 | − | 0.517116i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15688.3 | − | 27173.0i | 0.863693 | − | 1.49596i | −0.00464517 | − | 0.999989i | \(-0.501479\pi\) |
0.868339 | − | 0.495972i | \(-0.165188\pi\) | |||||||
\(692\) | −14206.0 | −0.780390 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3331.10 | 0.182200 | ||||||||
\(695\) | 1985.95 | − | 3439.77i | 0.108391 | − | 0.187738i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9921.26 | − | 17184.1i | −0.539160 | − | 0.933852i | ||||
\(698\) | 4441.18 | − | 7692.35i | 0.240833 | − | 0.417134i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8842.55 | + | 55.6057i | 0.477453 | + | 0.00300242i | ||||
\(701\) | 22364.5 | 1.20498 | 0.602492 | − | 0.798125i | \(-0.294174\pi\) | ||||
0.602492 | + | 0.798125i | \(0.294174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12565.2 | + | 21763.6i | 0.674121 | + | 1.16761i | ||||
\(704\) | 1251.37 | + | 2167.44i | 0.0669927 | + | 0.116035i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17597.7 | 0.938099 | ||||||||
\(707\) | 10894.8 | − | 18599.2i | 0.579547 | − | 0.989385i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5772.08 | + | 9997.54i | −0.305748 | + | 0.529571i | −0.977428 | − | 0.211271i | \(-0.932240\pi\) |
0.671680 | + | 0.740842i | \(0.265573\pi\) | |||||||
\(710\) | −496.387 | − | 859.767i | −0.0262381 | − | 0.0454457i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1465.95 | + | 2539.10i | −0.0771611 | + | 0.133647i | ||||
\(713\) | −9089.81 | −0.477442 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2268.57 | −0.118657 | ||||||||
\(716\) | −7898.79 | + | 13681.1i | −0.412279 | + | 0.714088i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5538.97 | − | 9593.78i | −0.287901 | − | 0.498658i | ||||
\(719\) | 940.338 | − | 1628.71i | 0.0487742 | − | 0.0844795i | −0.840608 | − | 0.541645i | \(-0.817802\pi\) |
0.889382 | + | 0.457165i | \(0.151135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2932.11 | − | 18.4383i | −0.151453 | − | 0.000952399i | ||||
\(722\) | −14924.0 | −0.769273 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4897.23 | + | 8482.26i | 0.251387 | + | 0.435415i | ||||
\(725\) | 12869.6 | + | 22290.8i | 0.659262 | + | 1.14188i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2783.27 | −0.141988 | −0.0709942 | − | 0.997477i | \(-0.522617\pi\) | ||||
−0.0709942 | + | 0.997477i | \(0.522617\pi\) | |||||||
\(728\) | 1790.73 | + | 3147.18i | 0.0911662 | + | 0.160223i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −289.244 | + | 500.986i | −0.0146650 | + | 0.0254004i | ||||
\(731\) | 10797.8 | + | 18702.3i | 0.546334 | + | 0.946278i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14210.9 | + | 24614.0i | −0.716088 | + | 1.24030i | 0.246451 | + | 0.969155i | \(0.420736\pi\) |
−0.962539 | + | 0.271145i | \(0.912598\pi\) | |||||||
\(734\) | 22887.7 | 1.15096 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4905.37 | −0.245672 | ||||||||
\(737\) | 4914.70 | − | 8512.51i | 0.245638 | − | 0.425458i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3402.66 | − | 5893.58i | −0.169376 | − | 0.293368i | 0.768825 | − | 0.639460i | \(-0.220842\pi\) |
−0.938201 | + | 0.346092i | \(0.887509\pi\) | |||||||
\(740\) | −996.944 | + | 1726.76i | −0.0495249 | + | 0.0857796i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8094.31 | + | 14225.6i | 0.400473 | + | 0.703825i | ||||
\(743\) | −4302.19 | −0.212426 | −0.106213 | − | 0.994343i | \(-0.533872\pi\) | ||||
−0.106213 | + | 0.994343i | \(0.533872\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3811.37 | + | 6601.48i | 0.187433 | + | 0.324644i | ||||
\(746\) | 12375.3 | + | 21434.6i | 0.607360 | + | 1.05198i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7467.83 | −0.365041 | ||||||||
\(749\) | −2949.42 | − | 18.5472i | −0.143884 | − | 0.000904805i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9151.88 | + | 15851.5i | −0.444683 | + | 0.770213i | −0.998030 | − | 0.0627375i | \(-0.980017\pi\) |
0.553347 | + | 0.832951i | \(0.313350\pi\) | |||||||
\(752\) | 1829.85 | + | 3169.39i | 0.0887338 | + | 0.153691i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5269.93 | + | 9127.79i | −0.254535 | + | 0.440868i | ||||
\(755\) | 6759.35 | 0.325825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4475.34 | 0.214873 | 0.107437 | − | 0.994212i | \(-0.465736\pi\) | ||||
0.107437 | + | 0.994212i | \(0.465736\pi\) | |||||||
\(758\) | 621.352 | − | 1076.21i | 0.0297738 | − | 0.0515696i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1136.25 | − | 1968.04i | −0.0542317 | − | 0.0939321i | ||||
\(761\) | −12248.0 | + | 21214.1i | −0.583428 | + | 1.01053i | 0.411641 | + | 0.911346i | \(0.364956\pi\) |
−0.995069 | + | 0.0991813i | \(0.968378\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −338.717 | + | 578.247i | −0.0160713 | + | 0.0274364i | ||||
\(764\) | −3053.81 | −0.144611 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9347.94 | − | 16191.1i | −0.440933 | − | 0.763719i | ||||
\(767\) | −8859.92 | − | 15345.8i | −0.417097 | − | 0.722433i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11671.0 | −0.547290 | −0.273645 | − | 0.961831i | \(-0.588229\pi\) | ||||
−0.273645 | + | 0.961831i | \(0.588229\pi\) | |||||||
\(770\) | 3438.21 | + | 21.6209i | 0.160915 | + | 0.00101190i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5463.04 | − | 9462.27i | 0.254688 | − | 0.441133i | ||||
\(773\) | 17808.5 | + | 30845.3i | 0.828627 | + | 1.43522i | 0.899115 | + | 0.437711i | \(0.144211\pi\) |
−0.0704885 | + | 0.997513i | \(0.522456\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3539.01 | + | 6129.75i | −0.164032 | + | 0.284112i | ||||
\(776\) | 8365.23 | 0.386977 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2302.28 | 0.106094 | ||||||||
\(779\) | −24868.8 | + | 43074.1i | −1.14380 | + | 1.98112i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4088.83 | + | 7082.07i | 0.187337 | + | 0.324477i | ||||
\(782\) | 7318.46 | − | 12676.0i | 0.334665 | − | 0.579656i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2684.01 | − | 4786.88i | −0.122267 | − | 0.218061i | ||||
\(785\) | −979.977 | −0.0445565 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21576.7 | − | 37372.0i | −0.977291 | − | 1.69272i | −0.672158 | − | 0.740408i | \(-0.734632\pi\) |
−0.305134 | − | 0.952310i | \(-0.598701\pi\) | |||||||
\(788\) | −6953.17 | − | 12043.2i | −0.314336 | − | 0.544445i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3794.11 | 0.170871 | ||||||||
\(791\) | 1939.78 | + | 3409.13i | 0.0871942 | + | 0.153242i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4176.19 | + | 7233.37i | −0.187012 | + | 0.323915i | ||||
\(794\) | −5428.54 | − | 9402.51i | −0.242635 | − | 0.420255i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6510.90 | + | 11277.2i | −0.289915 | + | 0.502148i | ||||
\(797\) | 15094.7 | 0.670866 | 0.335433 | − | 0.942064i | \(-0.391117\pi\) | ||||
0.335433 | + | 0.942064i | \(0.391117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10920.0 | −0.483508 | ||||||||
\(800\) | −1909.85 | + | 3307.95i | −0.0844042 | + | 0.146192i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4365.77 | + | 7561.73i | 0.192220 | + | 0.332935i | ||||
\(803\) | 2382.56 | − | 4126.72i | 0.104706 | − | 0.181356i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3406.14 | + | 5814.85i | −0.149131 | + | 0.254592i | ||||
\(806\) | −2898.35 | −0.126663 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4655.48 | + | 8063.54i | 0.202697 | + | 0.351082i | ||||
\(809\) | 16161.4 | + | 27992.3i | 0.702354 | + | 1.21651i | 0.967638 | + | 0.252342i | \(0.0812008\pi\) |
−0.265284 | + | 0.964170i | \(0.585466\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24077.3 | 1.04250 | 0.521251 | − | 0.853403i | \(-0.325465\pi\) | ||||
0.521251 | + | 0.853403i | \(0.325465\pi\) | |||||||
\(812\) | 8074.01 | − | 13783.7i | 0.348944 | − | 0.595706i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8212.03 | − | 14223.6i | 0.353601 | − | 0.612455i | ||||
\(815\) | 2439.14 | + | 4224.71i | 0.104833 | + | 0.181577i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27065.9 | − | 46879.6i | 1.15902 | − | 2.00748i | ||||
\(818\) | −6617.30 | −0.282847 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3946.26 | −0.168060 | ||||||||
\(821\) | 10389.9 | − | 17995.9i | 0.441669 | − | 0.764994i | −0.556144 | − | 0.831086i | \(-0.687720\pi\) |
0.997814 | + | 0.0660921i | \(0.0210531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7628.70 | + | 13213.3i | 0.323110 | + | 0.559644i | 0.981128 | − | 0.193359i | \(-0.0619382\pi\) |
−0.658018 | + | 0.753002i | \(0.728605\pi\) | |||||||
\(824\) | 633.288 | − | 1096.89i | 0.0267738 | − | 0.0463737i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13281.7 | + | 23342.3i | 0.559479 | + | 0.983273i | ||||
\(827\) | 27962.7 | 1.17577 | 0.587884 | − | 0.808945i | \(-0.299961\pi\) | ||||
0.587884 | + | 0.808945i | \(0.299961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7240.55 | + | 12541.0i | 0.303347 | + | 0.525413i | 0.976892 | − | 0.213734i | \(-0.0685625\pi\) |
−0.673545 | + | 0.739146i | \(0.735229\pi\) | |||||||
\(830\) | −277.251 | − | 480.214i | −0.0115946 | − | 0.0200825i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1564.11 | −0.0651754 | ||||||||
\(833\) | 16374.1 | + | 205.943i | 0.681068 | + | 0.00856602i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4487.00 | + | 7771.71i | −0.185963 | + | 0.322097i | ||||
\(836\) | 9359.52 | + | 16211.2i | 0.387208 | + | 0.670663i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3249.72 | + | 5628.67i | −0.133961 | + | 0.232028i | ||||
\(839\) | 33893.5 | 1.39468 | 0.697339 | − | 0.716742i | \(-0.254367\pi\) | ||||
0.697339 | + | 0.716742i | \(0.254367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22108.8 | 0.906508 | ||||||||
\(842\) | −2932.21 | + | 5078.74i | −0.120013 | + | 0.207868i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3192.59 | − | 5529.73i | −0.130206 | − | 0.225523i | ||||
\(845\) | −1898.63 | + | 3288.53i | −0.0772958 | + | 0.133880i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3671.21 | − | 23.0861i | −0.148930 | − | 0.000936538i | ||||
\(848\) | −7069.97 | −0.286301 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5698.72 | − | 9870.47i | −0.229958 | − | 0.398299i | ||||
\(851\) | 16095.5 | + | 27878.3i | 0.648353 | + | 1.12298i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5250.20 | 0.210743 | 0.105371 | − | 0.994433i | \(-0.466397\pi\) | ||||
0.105371 | + | 0.994433i | \(0.466397\pi\) | |||||||
\(854\) | 6398.30 | − | 10923.0i | 0.256376 | − | 0.437678i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 637.027 | − | 1103.36i | 0.0254359 | − | 0.0440563i | ||||
\(857\) | −23042.4 | − | 39910.5i | −0.918450 | − | 1.59080i | −0.801770 | − | 0.597633i | \(-0.796108\pi\) |
−0.116681 | − | 0.993169i | \(-0.537225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18043.8 | − | 31252.8i | 0.716703 | − | 1.24137i | −0.245597 | − | 0.969372i | \(-0.578984\pi\) |
0.962299 | − | 0.271993i | \(-0.0876828\pi\) | |||||||
\(860\) | 4294.90 | 0.170296 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15926.8 | 0.629314 | ||||||||
\(863\) | 22120.3 | − | 38313.6i | 0.872520 | − | 1.51125i | 0.0131396 | − | 0.999914i | \(-0.495817\pi\) |
0.859381 | − | 0.511336i | \(-0.170849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4215.10 | − | 7300.77i | −0.165685 | − | 0.286975i | ||||
\(866\) | −7441.66 | + | 12889.3i | −0.292007 | + | 0.505771i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4392.70 | + | 27.6231i | 0.171772 | + | 0.00108017i | ||||
\(869\) | −31252.8 | −1.22000 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3071.49 | + | 5319.98i | 0.119487 | + | 0.206958i | ||||
\(872\) | −144.739 | − | 250.695i | −0.00562095 | − | 0.00973577i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36689.2 | −1.41995 | ||||||||
\(875\) | 5312.75 | + | 9337.05i | 0.205261 | + | 0.360743i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 600.202 | − | 1039.58i | 0.0231099 | − | 0.0400275i | −0.854239 | − | 0.519880i | \(-0.825977\pi\) |
0.877349 | + | 0.479853i | \(0.159310\pi\) | |||||||
\(878\) | 5645.68 | + | 9778.60i | 0.217007 | + | 0.375868i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −742.597 | + | 1286.22i | −0.0284465 | + | 0.0492708i | ||||
\(881\) | −38060.7 | −1.45550 | −0.727751 | − | 0.685842i | \(-0.759434\pi\) | ||||
−0.727751 | + | 0.685842i | \(0.759434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47249.0 | −1.80074 | −0.900372 | − | 0.435121i | \(-0.856706\pi\) | ||||
−0.900372 | + | 0.435121i | \(0.856706\pi\) | |||||||
\(884\) | 2333.55 | − | 4041.82i | 0.0887848 | − | 0.153780i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13904.6 | + | 24083.5i | 0.527240 | + | 0.913206i | ||||
\(887\) | −1056.33 | + | 1829.62i | −0.0399867 | + | 0.0692590i | −0.885326 | − | 0.464971i | \(-0.846065\pi\) |
0.845339 | + | 0.534230i | \(0.179398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7496.12 | − | 13174.3i | −0.282803 | − | 0.497021i | ||||
\(890\) | −1739.87 | −0.0655286 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11738.4 | − | 20331.5i | −0.440618 | − | 0.763173i | ||||
\(893\) | 13686.2 | + | 23705.2i | 0.512868 | + | 0.888313i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9374.71 | −0.350125 | ||||||||
\(896\) | 2370.55 | + | 14.9070i | 0.0883866 | + | 0.000555812i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15582.7 | − | 26989.9i | 0.579065 | − | 1.00297i | ||||
\(899\) | 6393.21 | + | 11073.4i | 0.237181 | + | 0.410809i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10547.9 | − | 18269.5i | 0.390012 | − | 0.675521i | ||||
\(902\) | 32506.1 | 1.19993 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1694.30 | −0.0623358 | ||||||||
\(905\) | −2906.15 | + | 5033.60i | −0.106744 | + | 0.184887i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 434.958 | + | 753.369i | 0.0159234 | + | 0.0275802i | 0.873877 | − | 0.486147i | \(-0.161598\pi\) |
−0.857954 | + | 0.513727i | \(0.828265\pi\) | |||||||
\(908\) | −11916.2 | + | 20639.4i | −0.435520 | + | 0.754343i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1086.07 | + | 1854.11i | −0.0395637 | + | 0.0675419i | ||||
\(911\) | −36371.4 | −1.32276 | −0.661381 | − | 0.750050i | \(-0.730029\pi\) | ||||
−0.661381 | + | 0.750050i | \(0.730029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2283.78 | + | 3955.61i | 0.0827841 | + | 0.143386i | ||||
\(914\) | 9359.42 | + | 16211.0i | 0.338711 | + | 0.586665i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2559.86 | 0.0923366 | ||||||||
\(917\) | −6458.40 | − | 40.6132i | −0.232579 | − | 0.00146256i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 327.756 | − | 567.690i | 0.0117646 | − | 0.0203769i | −0.860083 | − | 0.510154i | \(-0.829588\pi\) |
0.871848 | + | 0.489777i | \(0.162922\pi\) | |||||||
\(920\) | −1455.49 | − | 2520.98i | −0.0521587 | − | 0.0903416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1558.11 | + | 2698.72i | −0.0556545 | + | 0.0963965i | ||||
\(923\) | −5110.72 | −0.182255 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25066.4 | 0.891005 | ||||||||
\(926\) | 12753.6 | − | 22089.8i | 0.452601 | − | 0.783927i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3450.14 | + | 5975.81i | 0.122043 | + | 0.211385i | ||||
\(929\) | 3797.48 | − | 6577.42i | 0.134113 | − | 0.232291i | −0.791145 | − | 0.611628i | \(-0.790515\pi\) |
0.925258 | + | 0.379338i | \(0.123848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20074.8 | − | 35803.0i | −0.706686 | − | 1.26036i | ||||
\(932\) | 164.043 | 0.00576545 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11113.4 | − | 19249.0i | −0.389339 | − | 0.674354i | ||||
\(935\) | −2215.81 | − | 3837.89i | −0.0775022 | − | 0.134238i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37468.6 | 1.30634 | 0.653172 | − | 0.757210i | \(-0.273438\pi\) | ||||
0.653172 | + | 0.757210i | \(0.273438\pi\) | |||||||
\(938\) | −4604.40 | − | 8092.14i | −0.160276 | − | 0.281682i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1085.88 | + | 1880.80i | −0.0376783 | + | 0.0652607i | ||||
\(941\) | 11501.0 | + | 19920.4i | 0.398430 | + | 0.690102i | 0.993532 | − | 0.113549i | \(-0.0362217\pi\) |
−0.595102 | + | 0.803650i | \(0.702888\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31855.9 | + | 55176.1i | −1.10008 | + | 1.90539i | ||||
\(944\) | −11600.9 | −0.399975 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35377.9 | −1.21589 | ||||||||
\(947\) | 17442.3 | − | 30211.0i | 0.598520 | − | 1.03667i | −0.394519 | − | 0.918888i | \(-0.629089\pi\) |
0.993040 | − | 0.117780i | \(-0.0375777\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1489.01 | + | 2579.04i | 0.0509328 | + | 0.0882182i | ||||
\(950\) | −14284.5 | + | 24741.5i | −0.487843 | + | 0.844970i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3575.21 | + | 6103.48i | −0.121715 | + | 0.207789i | ||||
\(953\) | −33867.3 | −1.15118 | −0.575588 | − | 0.817740i | \(-0.695227\pi\) | ||||
−0.575588 | + | 0.817740i | \(0.695227\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −906.106 | − | 1569.42i | −0.0307025 | − | 0.0531783i | ||||
\(956\) | −5991.44 | − | 10377.5i | −0.202696 | − | 0.351079i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −37980.7 | −1.28090 | ||||||||
\(959\) | 16929.7 | − | 28901.9i | 0.570062 | − | 0.973192i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13137.4 | − | 22754.7i | 0.440987 | − | 0.763811i | ||||
\(962\) | 5132.19 | + | 8889.21i | 0.172005 | + | 0.297921i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1330.72 | − | 2304.87i | 0.0444601 | − | 0.0770072i | ||||
\(965\) | 6483.83 | 0.216292 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5998.34 | 0.199476 | 0.0997382 | − | 0.995014i | \(-0.468199\pi\) | ||||
0.0997382 | + | 0.995014i | \(0.468199\pi\) | |||||||
\(968\) | 792.922 | − | 1373.38i | 0.0263280 | − | 0.0456014i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2482.07 | + | 4299.08i | 0.0821594 | + | 0.142304i | ||||
\(971\) | −1682.43 | + | 2914.05i | −0.0556042 | + | 0.0963093i | −0.892488 | − | 0.451072i | \(-0.851042\pi\) |
0.836883 | + | 0.547381i | \(0.184375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15325.8 | + | 26934.9i | 0.504958 | + | 0.887454i | ||||
\(974\) | −9896.50 | −0.325569 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2734.08 | + | 4735.57i | 0.0896679 | + | 0.155309i | ||||
\(977\) | 3294.28 | + | 5705.85i | 0.107874 | + | 0.186844i | 0.914909 | − | 0.403660i | \(-0.132262\pi\) |
−0.807035 | + | 0.590504i | \(0.798929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14331.6 | 0.467866 | ||||||||
\(980\) | 1663.70 | − | 2799.70i | 0.0542297 | − | 0.0912585i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9178.86 | − | 15898.2i | 0.298278 | − | 0.516633i | ||||
\(983\) | 6015.47 | + | 10419.1i | 0.195182 | + | 0.338065i | 0.946960 | − | 0.321351i | \(-0.104137\pi\) |
−0.751778 | + | 0.659416i | \(0.770804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4126.20 | − | 7146.78i | 0.133474 | − | 0.231183i | ||||
\(986\) | −20589.4 | −0.665011 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −11698.6 | −0.376704 | ||||||||
\(989\) | 34670.3 | − | 60050.7i | 1.11471 | − | 1.93074i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4081.69 | + | 7069.69i | 0.130837 | + | 0.226616i | 0.923999 | − | 0.382394i | \(-0.124900\pi\) |
−0.793163 | + | 0.609010i | \(0.791567\pi\) | |||||||
\(992\) | −948.752 | + | 1643.29i | −0.0303658 | + | 0.0525952i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7745.71 | + | 48.7083i | 0.247162 | + | 0.00155426i | ||||
\(995\) | −7727.48 | −0.246209 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17358.0 | − | 30064.9i | −0.551387 | − | 0.955031i | −0.998175 | − | 0.0603908i | \(-0.980765\pi\) |
0.446787 | − | 0.894640i | \(-0.352568\pi\) | |||||||
\(998\) | −16748.6 | − | 29009.5i | −0.531231 | − | 0.920119i | ||||
\(999\) | 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 | 378.4.g.e.163.3 | yes | 8 | |
3.2 | odd | 2 | 378.4.g.d.163.2 | yes | 8 | ||
7.4 | even | 3 | inner | 378.4.g.e.109.3 | yes | 8 | |
21.11 | odd | 6 | 378.4.g.d.109.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.g.d.109.2 | ✓ | 8 | 21.11 | odd | 6 | ||
378.4.g.d.163.2 | yes | 8 | 3.2 | odd | 2 | ||
378.4.g.e.109.3 | yes | 8 | 7.4 | even | 3 | inner | |
378.4.g.e.163.3 | yes | 8 | 1.1 | even | 1 | trivial |