Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.14 | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.f.191.14 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.392697 | + | 1.68695i | 0.226724 | + | 0.973959i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 1.47053 | + | 0.915172i | 0.600341 | + | 0.373618i | ||||
\(7\) | −0.873718 | −0.330234 | −0.165117 | − | 0.986274i | \(-0.552800\pi\) | ||||
−0.165117 | + | 0.986274i | \(0.552800\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.69158 | + | 1.32492i | −0.897193 | + | 0.441640i | ||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.24582 | 0.978653 | 0.489326 | − | 0.872101i | \(-0.337243\pi\) | ||||
0.489326 | + | 0.872101i | \(0.337243\pi\) | |||||||
\(12\) | 1.68695 | − | 0.392697i | 0.486980 | − | 0.113362i | ||||
\(13\) | 2.80064 | − | 2.80064i | 0.776758 | − | 0.776758i | −0.202520 | − | 0.979278i | \(-0.564913\pi\) |
0.979278 | + | 0.202520i | \(0.0649131\pi\) | |||||||
\(14\) | −0.617812 | + | 0.617812i | −0.165117 | + | 0.165117i | ||||
\(15\) | 0.915172 | − | 1.47053i | 0.236297 | − | 0.379689i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.67922 | + | 2.67922i | 0.649807 | + | 0.649807i | 0.952946 | − | 0.303139i | \(-0.0980347\pi\) |
−0.303139 | + | 0.952946i | \(0.598035\pi\) | |||||||
\(18\) | −0.966374 | + | 2.84009i | −0.227777 | + | 0.669416i | ||||
\(19\) | 2.24528 | − | 2.24528i | 0.515103 | − | 0.515103i | −0.400982 | − | 0.916086i | \(-0.631331\pi\) |
0.916086 | + | 0.400982i | \(0.131331\pi\) | |||||||
\(20\) | −0.707107 | + | 0.707107i | −0.158114 | + | 0.158114i | ||||
\(21\) | −0.343107 | − | 1.47392i | −0.0748720 | − | 0.321635i | ||||
\(22\) | 2.29514 | − | 2.29514i | 0.489326 | − | 0.489326i | ||||
\(23\) | 3.93841 | + | 3.93841i | 0.821215 | + | 0.821215i | 0.986282 | − | 0.165067i | \(-0.0527842\pi\) |
−0.165067 | + | 0.986282i | \(0.552784\pi\) | |||||||
\(24\) | 0.915172 | − | 1.47053i | 0.186809 | − | 0.300171i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | − | 3.96070i | − | 0.776758i | ||||||
\(27\) | −3.29204 | − | 4.02026i | −0.633554 | − | 0.773699i | ||||
\(28\) | 0.873718i | 0.165117i | ||||||||
\(29\) | 0.0117303 | − | 0.0117303i | 0.00217826 | − | 0.00217826i | −0.706017 | − | 0.708195i | \(-0.749510\pi\) |
0.708195 | + | 0.706017i | \(0.249510\pi\) | |||||||
\(30\) | −0.392697 | − | 1.68695i | −0.0716964 | − | 0.307993i | ||||
\(31\) | 5.20171 | + | 5.20171i | 0.934254 | + | 0.934254i | 0.997968 | − | 0.0637143i | \(-0.0202946\pi\) |
−0.0637143 | + | 0.997968i | \(0.520295\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 1.27463 | + | 5.47553i | 0.221884 | + | 0.953168i | ||||
\(34\) | 3.78900 | 0.649807 | ||||||||
\(35\) | 0.617812 | + | 0.617812i | 0.104429 | + | 0.104429i | ||||
\(36\) | 1.32492 | + | 2.69158i | 0.220820 | + | 0.448596i | ||||
\(37\) | −2.06314 | − | 5.72219i | −0.339179 | − | 0.940722i | ||||
\(38\) | − | 3.17531i | − | 0.515103i | ||||||
\(39\) | 5.82434 | + | 3.62473i | 0.932640 | + | 0.580421i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 12.1119 | 1.89157 | 0.945783 | − | 0.324799i | \(-0.105297\pi\) | ||||
0.945783 | + | 0.324799i | \(0.105297\pi\) | |||||||
\(42\) | −1.28483 | − | 0.799603i | −0.198253 | − | 0.123381i | ||||
\(43\) | 8.06425 | − | 8.06425i | 1.22979 | − | 1.22979i | 0.265743 | − | 0.964044i | \(-0.414383\pi\) |
0.964044 | − | 0.265743i | \(-0.0856174\pi\) | |||||||
\(44\) | − | 3.24582i | − | 0.489326i | ||||||
\(45\) | 2.84009 | + | 0.966374i | 0.423376 | + | 0.144059i | ||||
\(46\) | 5.56975 | 0.821215 | ||||||||
\(47\) | 3.06944i | 0.447724i | 0.974621 | + | 0.223862i | \(0.0718666\pi\) | ||||
−0.974621 | + | 0.223862i | \(0.928133\pi\) | |||||||
\(48\) | −0.392697 | − | 1.68695i | −0.0566810 | − | 0.243490i | ||||
\(49\) | −6.23662 | −0.890945 | ||||||||
\(50\) | 0.707107 | + | 0.707107i | 0.100000 | + | 0.100000i | ||||
\(51\) | −3.46758 | + | 5.57183i | −0.485559 | + | 0.780213i | ||||
\(52\) | −2.80064 | − | 2.80064i | −0.388379 | − | 0.388379i | ||||
\(53\) | 9.17714i | 1.26058i | 0.776361 | + | 0.630289i | \(0.217063\pi\) | ||||
−0.776361 | + | 0.630289i | \(0.782937\pi\) | |||||||
\(54\) | −5.17058 | − | 0.514925i | −0.703626 | − | 0.0700724i | ||||
\(55\) | −2.29514 | − | 2.29514i | −0.309477 | − | 0.309477i | ||||
\(56\) | 0.617812 | + | 0.617812i | 0.0825586 | + | 0.0825586i | ||||
\(57\) | 4.66939 | + | 2.90596i | 0.618476 | + | 0.384903i | ||||
\(58\) | − | 0.0165891i | − | 0.00217826i | ||||||
\(59\) | −7.96028 | − | 7.96028i | −1.03634 | − | 1.03634i | −0.999314 | − | 0.0370254i | \(-0.988212\pi\) |
−0.0370254 | − | 0.999314i | \(-0.511788\pi\) | |||||||
\(60\) | −1.47053 | − | 0.915172i | −0.189845 | − | 0.118148i | ||||
\(61\) | −6.64635 | − | 6.64635i | −0.850978 | − | 0.850978i | 0.139276 | − | 0.990254i | \(-0.455522\pi\) |
−0.990254 | + | 0.139276i | \(0.955522\pi\) | |||||||
\(62\) | 7.35632 | 0.934254 | ||||||||
\(63\) | 2.35168 | − | 1.15761i | 0.296284 | − | 0.145845i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −3.96070 | −0.491265 | ||||||||
\(66\) | 4.77308 | + | 2.97049i | 0.587526 | + | 0.365642i | ||||
\(67\) | 7.74070i | 0.945677i | 0.881149 | + | 0.472838i | \(0.156771\pi\) | ||||
−0.881149 | + | 0.472838i | \(0.843229\pi\) | |||||||
\(68\) | 2.67922 | − | 2.67922i | 0.324904 | − | 0.324904i | ||||
\(69\) | −5.09728 | + | 8.19049i | −0.613641 | + | 0.986019i | ||||
\(70\) | 0.873718 | 0.104429 | ||||||||
\(71\) | − | 0.580983i | − | 0.0689500i | −0.999406 | − | 0.0344750i | \(-0.989024\pi\) | ||
0.999406 | − | 0.0344750i | \(-0.0109759\pi\) | |||||||
\(72\) | 2.84009 | + | 0.966374i | 0.334708 | + | 0.113888i | ||||
\(73\) | 11.0501i | 1.29332i | 0.762780 | + | 0.646658i | \(0.223834\pi\) | ||||
−0.762780 | + | 0.646658i | \(0.776166\pi\) | |||||||
\(74\) | −5.50506 | − | 2.58734i | −0.639950 | − | 0.300772i | ||||
\(75\) | −1.68695 | + | 0.392697i | −0.194792 | + | 0.0453448i | ||||
\(76\) | −2.24528 | − | 2.24528i | −0.257552 | − | 0.257552i | ||||
\(77\) | −2.83593 | −0.323185 | ||||||||
\(78\) | 6.68150 | − | 1.55536i | 0.756531 | − | 0.176110i | ||||
\(79\) | 0.763562 | − | 0.763562i | 0.0859075 | − | 0.0859075i | −0.662847 | − | 0.748755i | \(-0.730652\pi\) |
0.748755 | + | 0.662847i | \(0.230652\pi\) | |||||||
\(80\) | 0.707107 | + | 0.707107i | 0.0790569 | + | 0.0790569i | ||||
\(81\) | 5.48918 | − | 7.13224i | 0.609909 | − | 0.792471i | ||||
\(82\) | 8.56443 | − | 8.56443i | 0.945783 | − | 0.945783i | ||||
\(83\) | 6.26833i | 0.688039i | 0.938963 | + | 0.344019i | \(0.111789\pi\) | ||||
−0.938963 | + | 0.344019i | \(0.888211\pi\) | |||||||
\(84\) | −1.47392 | + | 0.343107i | −0.160817 | + | 0.0374360i | ||||
\(85\) | − | 3.78900i | − | 0.410974i | ||||||
\(86\) | − | 11.4046i | − | 1.22979i | ||||||
\(87\) | 0.0243948 | + | 0.0151819i | 0.00261540 | + | 0.00162767i | ||||
\(88\) | −2.29514 | − | 2.29514i | −0.244663 | − | 0.244663i | ||||
\(89\) | −6.49421 | + | 6.49421i | −0.688385 | + | 0.688385i | −0.961875 | − | 0.273490i | \(-0.911822\pi\) |
0.273490 | + | 0.961875i | \(0.411822\pi\) | |||||||
\(90\) | 2.69158 | − | 1.32492i | 0.283717 | − | 0.139659i | ||||
\(91\) | −2.44697 | + | 2.44697i | −0.256512 | + | 0.256512i | ||||
\(92\) | 3.93841 | − | 3.93841i | 0.410607 | − | 0.410607i | ||||
\(93\) | −6.73230 | + | 10.8177i | −0.698107 | + | 1.12174i | ||||
\(94\) | 2.17042 | + | 2.17042i | 0.223862 | + | 0.223862i | ||||
\(95\) | −3.17531 | −0.325780 | ||||||||
\(96\) | −1.47053 | − | 0.915172i | −0.150085 | − | 0.0934044i | ||||
\(97\) | 7.15350 | − | 7.15350i | 0.726328 | − | 0.726328i | −0.243558 | − | 0.969886i | \(-0.578315\pi\) |
0.969886 | + | 0.243558i | \(0.0783147\pi\) | |||||||
\(98\) | −4.40995 | + | 4.40995i | −0.445473 | + | 0.445473i | ||||
\(99\) | −8.73639 | + | 4.30045i | −0.878040 | + | 0.432212i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.86993 | −0.982095 | −0.491048 | − | 0.871133i | \(-0.663386\pi\) | ||||
−0.491048 | + | 0.871133i | \(0.663386\pi\) | |||||||
\(102\) | 1.48793 | + | 6.39183i | 0.147327 | + | 0.632886i | ||||
\(103\) | −4.80415 | − | 4.80415i | −0.473367 | − | 0.473367i | 0.429636 | − | 0.903002i | \(-0.358642\pi\) |
−0.903002 | + | 0.429636i | \(0.858642\pi\) | |||||||
\(104\) | −3.96070 | −0.388379 | ||||||||
\(105\) | −0.799603 | + | 1.28483i | −0.0780332 | + | 0.125386i | ||||
\(106\) | 6.48922 | + | 6.48922i | 0.630289 | + | 0.630289i | ||||
\(107\) | − | 14.7208i | − | 1.42312i | −0.702628 | − | 0.711558i | \(-0.747990\pi\) | ||
0.702628 | − | 0.711558i | \(-0.252010\pi\) | |||||||
\(108\) | −4.02026 | + | 3.29204i | −0.386849 | + | 0.316777i | ||||
\(109\) | 12.8578 | − | 12.8578i | 1.23155 | − | 1.23155i | 0.268184 | − | 0.963368i | \(-0.413577\pi\) |
0.963368 | − | 0.268184i | \(-0.0864235\pi\) | |||||||
\(110\) | −3.24582 | −0.309477 | ||||||||
\(111\) | 8.84284 | − | 5.72750i | 0.839325 | − | 0.543630i | ||||
\(112\) | 0.873718 | 0.0825586 | ||||||||
\(113\) | −3.10020 | + | 3.10020i | −0.291643 | + | 0.291643i | −0.837729 | − | 0.546086i | \(-0.816117\pi\) |
0.546086 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(114\) | 5.35658 | − | 1.24694i | 0.501690 | − | 0.116786i | ||||
\(115\) | − | 5.56975i | − | 0.519382i | ||||||
\(116\) | −0.0117303 | − | 0.0117303i | −0.00108913 | − | 0.00108913i | ||||
\(117\) | −3.82752 | + | 11.2488i | −0.353854 | + | 1.03995i | ||||
\(118\) | −11.2575 | −1.03634 | ||||||||
\(119\) | −2.34089 | − | 2.34089i | −0.214589 | − | 0.214589i | ||||
\(120\) | −1.68695 | + | 0.392697i | −0.153996 | + | 0.0358482i | ||||
\(121\) | −0.464630 | −0.0422391 | ||||||||
\(122\) | −9.39935 | −0.850978 | ||||||||
\(123\) | 4.75632 | + | 20.4322i | 0.428863 | + | 1.84231i | ||||
\(124\) | 5.20171 | − | 5.20171i | 0.467127 | − | 0.467127i | ||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0.844338 | − | 2.48144i | 0.0752196 | − | 0.221064i | ||||
\(127\) | −0.948940 | −0.0842048 | −0.0421024 | − | 0.999113i | \(-0.513406\pi\) | ||||
−0.0421024 | + | 0.999113i | \(0.513406\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 16.7708 | + | 10.4372i | 1.47658 | + | 0.918940i | ||||
\(130\) | −2.80064 | + | 2.80064i | −0.245632 | + | 0.245632i | ||||
\(131\) | 11.7356 | − | 11.7356i | 1.02535 | − | 1.02535i | 0.0256765 | − | 0.999670i | \(-0.491826\pi\) |
0.999670 | − | 0.0256765i | \(-0.00817399\pi\) | |||||||
\(132\) | 5.47553 | − | 1.27463i | 0.476584 | − | 0.110942i | ||||
\(133\) | −1.96174 | + | 1.96174i | −0.170105 | + | 0.170105i | ||||
\(134\) | 5.47350 | + | 5.47350i | 0.472838 | + | 0.472838i | ||||
\(135\) | −0.514925 | + | 5.17058i | −0.0443177 | + | 0.445012i | ||||
\(136\) | − | 3.78900i | − | 0.324904i | ||||||
\(137\) | 21.3281i | 1.82218i | 0.412209 | + | 0.911089i | \(0.364757\pi\) | ||||
−0.412209 | + | 0.911089i | \(0.635243\pi\) | |||||||
\(138\) | 2.18723 | + | 9.39587i | 0.186189 | + | 0.799830i | ||||
\(139\) | 14.6182i | 1.23990i | 0.784641 | + | 0.619951i | \(0.212847\pi\) | ||||
−0.784641 | + | 0.619951i | \(0.787153\pi\) | |||||||
\(140\) | 0.617812 | − | 0.617812i | 0.0522146 | − | 0.0522146i | ||||
\(141\) | −5.17799 | + | 1.20536i | −0.436065 | + | 0.101510i | ||||
\(142\) | −0.410817 | − | 0.410817i | −0.0344750 | − | 0.0344750i | ||||
\(143\) | 9.09039 | − | 9.09039i | 0.760176 | − | 0.760176i | ||||
\(144\) | 2.69158 | − | 1.32492i | 0.224298 | − | 0.110410i | ||||
\(145\) | −0.0165891 | −0.00137765 | ||||||||
\(146\) | 7.81360 | + | 7.81360i | 0.646658 | + | 0.646658i | ||||
\(147\) | −2.44910 | − | 10.5208i | −0.201999 | − | 0.867744i | ||||
\(148\) | −5.72219 | + | 2.06314i | −0.470361 | + | 0.169589i | ||||
\(149\) | − | 4.27966i | − | 0.350604i | −0.984515 | − | 0.175302i | \(-0.943910\pi\) | ||
0.984515 | − | 0.175302i | \(-0.0560902\pi\) | |||||||
\(150\) | −0.915172 | + | 1.47053i | −0.0747235 | + | 0.120068i | ||||
\(151\) | − | 16.2675i | − | 1.32383i | −0.749577 | − | 0.661917i | \(-0.769743\pi\) | ||
0.749577 | − | 0.661917i | \(-0.230257\pi\) | |||||||
\(152\) | −3.17531 | −0.257552 | ||||||||
\(153\) | −10.7611 | − | 3.66159i | −0.869983 | − | 0.296022i | ||||
\(154\) | −2.00531 | + | 2.00531i | −0.161592 | + | 0.161592i | ||||
\(155\) | − | 7.35632i | − | 0.590874i | ||||||
\(156\) | 3.62473 | − | 5.82434i | 0.290210 | − | 0.466320i | ||||
\(157\) | −18.4593 | −1.47321 | −0.736607 | − | 0.676321i | \(-0.763573\pi\) | ||||
−0.736607 | + | 0.676321i | \(0.763573\pi\) | |||||||
\(158\) | − | 1.07984i | − | 0.0859075i | ||||||
\(159\) | −15.4813 | + | 3.60384i | −1.22775 | + | 0.285803i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.44106 | − | 3.44106i | −0.271193 | − | 0.271193i | ||||
\(162\) | −1.16182 | − | 8.92469i | −0.0912812 | − | 0.701190i | ||||
\(163\) | −7.65805 | − | 7.65805i | −0.599825 | − | 0.599825i | 0.340441 | − | 0.940266i | \(-0.389424\pi\) |
−0.940266 | + | 0.340441i | \(0.889424\pi\) | |||||||
\(164\) | − | 12.1119i | − | 0.945783i | ||||||
\(165\) | 2.97049 | − | 4.77308i | 0.231252 | − | 0.371584i | ||||
\(166\) | 4.43238 | + | 4.43238i | 0.344019 | + | 0.344019i | ||||
\(167\) | −12.4791 | − | 12.4791i | −0.965665 | − | 0.965665i | 0.0337648 | − | 0.999430i | \(-0.489250\pi\) |
−0.999430 | + | 0.0337648i | \(0.989250\pi\) | |||||||
\(168\) | −0.799603 | + | 1.28483i | −0.0616907 | + | 0.0991267i | ||||
\(169\) | − | 2.68718i | − | 0.206706i | ||||||
\(170\) | −2.67922 | − | 2.67922i | −0.205487 | − | 0.205487i | ||||
\(171\) | −3.06854 | + | 9.01817i | −0.234657 | + | 0.689637i | ||||
\(172\) | −8.06425 | − | 8.06425i | −0.614894 | − | 0.614894i | ||||
\(173\) | 9.17456 | 0.697529 | 0.348765 | − | 0.937210i | \(-0.386601\pi\) | ||||
0.348765 | + | 0.937210i | \(0.386601\pi\) | |||||||
\(174\) | 0.0279850 | − | 0.00651450i | 0.00212153 | − | 0.000493863i | ||||
\(175\) | − | 0.873718i | − | 0.0660469i | ||||||
\(176\) | −3.24582 | −0.244663 | ||||||||
\(177\) | 10.3026 | − | 16.5545i | 0.774389 | − | 1.24432i | ||||
\(178\) | 9.18420i | 0.688385i | ||||||||
\(179\) | −10.0110 | + | 10.0110i | −0.748257 | + | 0.748257i | −0.974152 | − | 0.225895i | \(-0.927470\pi\) |
0.225895 | + | 0.974152i | \(0.427470\pi\) | |||||||
\(180\) | 0.966374 | − | 2.84009i | 0.0720293 | − | 0.211688i | ||||
\(181\) | −22.6754 | −1.68545 | −0.842724 | − | 0.538346i | \(-0.819049\pi\) | ||||
−0.842724 | + | 0.538346i | \(0.819049\pi\) | |||||||
\(182\) | 3.46054i | 0.256512i | ||||||||
\(183\) | 8.60203 | − | 13.8220i | 0.635880 | − | 1.02175i | ||||
\(184\) | − | 5.56975i | − | 0.410607i | ||||||
\(185\) | −2.58734 | + | 5.50506i | −0.190225 | + | 0.404740i | ||||
\(186\) | 2.88881 | + | 12.4097i | 0.211818 | + | 0.909925i | ||||
\(187\) | 8.69629 | + | 8.69629i | 0.635936 | + | 0.635936i | ||||
\(188\) | 3.06944 | 0.223862 | ||||||||
\(189\) | 2.87632 | + | 3.51257i | 0.209221 | + | 0.255502i | ||||
\(190\) | −2.24528 | + | 2.24528i | −0.162890 | + | 0.162890i | ||||
\(191\) | 6.59688 | + | 6.59688i | 0.477333 | + | 0.477333i | 0.904278 | − | 0.426945i | \(-0.140410\pi\) |
−0.426945 | + | 0.904278i | \(0.640410\pi\) | |||||||
\(192\) | −1.68695 | + | 0.392697i | −0.121745 | + | 0.0283405i | ||||
\(193\) | −0.721641 | + | 0.721641i | −0.0519448 | + | 0.0519448i | −0.732602 | − | 0.680657i | \(-0.761694\pi\) |
0.680657 | + | 0.732602i | \(0.261694\pi\) | |||||||
\(194\) | − | 10.1166i | − | 0.726328i | ||||||
\(195\) | −1.55536 | − | 6.68150i | −0.111381 | − | 0.478472i | ||||
\(196\) | 6.23662i | 0.445473i | ||||||||
\(197\) | 14.8081i | 1.05504i | 0.849544 | + | 0.527518i | \(0.176877\pi\) | ||||
−0.849544 | + | 0.527518i | \(0.823123\pi\) | |||||||
\(198\) | −3.13668 | + | 9.21844i | −0.222914 | + | 0.655126i | ||||
\(199\) | −15.3316 | − | 15.3316i | −1.08683 | − | 1.08683i | −0.995853 | − | 0.0909720i | \(-0.971003\pi\) |
−0.0909720 | − | 0.995853i | \(-0.528997\pi\) | |||||||
\(200\) | 0.707107 | − | 0.707107i | 0.0500000 | − | 0.0500000i | ||||
\(201\) | −13.0581 | + | 3.03975i | −0.921050 | + | 0.214408i | ||||
\(202\) | −6.97910 | + | 6.97910i | −0.491048 | + | 0.491048i | ||||
\(203\) | −0.0102490 | + | 0.0102490i | −0.000719336 | + | 0.000719336i | ||||
\(204\) | 5.57183 | + | 3.46758i | 0.390106 | + | 0.242779i | ||||
\(205\) | −8.56443 | − | 8.56443i | −0.598166 | − | 0.598166i | ||||
\(206\) | −6.79409 | −0.473367 | ||||||||
\(207\) | −15.8186 | − | 5.38246i | −1.09947 | − | 0.374107i | ||||
\(208\) | −2.80064 | + | 2.80064i | −0.194190 | + | 0.194190i | ||||
\(209\) | 7.28779 | − | 7.28779i | 0.504107 | − | 0.504107i | ||||
\(210\) | 0.343107 | + | 1.47392i | 0.0236766 | + | 0.101710i | ||||
\(211\) | −14.8756 | −1.02408 | −0.512039 | − | 0.858962i | \(-0.671109\pi\) | ||||
−0.512039 | + | 0.858962i | \(0.671109\pi\) | |||||||
\(212\) | 9.17714 | 0.630289 | ||||||||
\(213\) | 0.980088 | − | 0.228151i | 0.0671545 | − | 0.0156326i | ||||
\(214\) | −10.4092 | − | 10.4092i | −0.711558 | − | 0.711558i | ||||
\(215\) | −11.4046 | −0.777786 | ||||||||
\(216\) | −0.514925 | + | 5.17058i | −0.0350362 | + | 0.351813i | ||||
\(217\) | −4.54482 | − | 4.54482i | −0.308523 | − | 0.308523i | ||||
\(218\) | − | 18.1836i | − | 1.23155i | ||||||
\(219\) | −18.6409 | + | 4.33935i | −1.25964 | + | 0.293226i | ||||
\(220\) | −2.29514 | + | 2.29514i | −0.154739 | + | 0.154739i | ||||
\(221\) | 15.0071 | 1.00949 | ||||||||
\(222\) | 2.20288 | − | 10.3028i | 0.147847 | − | 0.691478i | ||||
\(223\) | 6.18301 | 0.414045 | 0.207022 | − | 0.978336i | \(-0.433623\pi\) | ||||
0.207022 | + | 0.978336i | \(0.433623\pi\) | |||||||
\(224\) | 0.617812 | − | 0.617812i | 0.0412793 | − | 0.0412793i | ||||
\(225\) | −1.32492 | − | 2.69158i | −0.0883279 | − | 0.179439i | ||||
\(226\) | 4.38435i | 0.291643i | ||||||||
\(227\) | 16.9434 | + | 16.9434i | 1.12457 | + | 1.12457i | 0.991045 | + | 0.133527i | \(0.0426304\pi\) |
0.133527 | + | 0.991045i | \(0.457370\pi\) | |||||||
\(228\) | 2.90596 | − | 4.66939i | 0.192452 | − | 0.309238i | ||||
\(229\) | 7.05363 | 0.466117 | 0.233058 | − | 0.972463i | \(-0.425127\pi\) | ||||
0.233058 | + | 0.972463i | \(0.425127\pi\) | |||||||
\(230\) | −3.93841 | − | 3.93841i | −0.259691 | − | 0.259691i | ||||
\(231\) | −1.11366 | − | 4.78407i | −0.0732737 | − | 0.314769i | ||||
\(232\) | −0.0165891 | −0.00108913 | ||||||||
\(233\) | 4.46090 | 0.292243 | 0.146122 | − | 0.989267i | \(-0.453321\pi\) | ||||
0.146122 | + | 0.989267i | \(0.453321\pi\) | |||||||
\(234\) | 5.24761 | + | 10.6605i | 0.343047 | + | 0.696902i | ||||
\(235\) | 2.17042 | − | 2.17042i | 0.141583 | − | 0.141583i | ||||
\(236\) | −7.96028 | + | 7.96028i | −0.518170 | + | 0.518170i | ||||
\(237\) | 1.58794 | + | 0.988240i | 0.103148 | + | 0.0641931i | ||||
\(238\) | −3.31051 | −0.214589 | ||||||||
\(239\) | −17.0743 | − | 17.0743i | −1.10444 | − | 1.10444i | −0.993868 | − | 0.110576i | \(-0.964730\pi\) |
−0.110576 | − | 0.993868i | \(-0.535270\pi\) | |||||||
\(240\) | −0.915172 | + | 1.47053i | −0.0590741 | + | 0.0949223i | ||||
\(241\) | −3.79899 | + | 3.79899i | −0.244715 | + | 0.244715i | −0.818797 | − | 0.574083i | \(-0.805359\pi\) |
0.574083 | + | 0.818797i | \(0.305359\pi\) | |||||||
\(242\) | −0.328543 | + | 0.328543i | −0.0211195 | + | 0.0211195i | ||||
\(243\) | 14.1873 | + | 6.45914i | 0.910116 | + | 0.414354i | ||||
\(244\) | −6.64635 | + | 6.64635i | −0.425489 | + | 0.425489i | ||||
\(245\) | 4.40995 | + | 4.40995i | 0.281742 | + | 0.281742i | ||||
\(246\) | 17.8110 | + | 11.0845i | 1.13559 | + | 0.706722i | ||||
\(247\) | − | 12.5765i | − | 0.800221i | ||||||
\(248\) | − | 7.35632i | − | 0.467127i | ||||||
\(249\) | −10.5743 | + | 2.46156i | −0.670122 | + | 0.155995i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −2.59871 | + | 2.59871i | −0.164029 | + | 0.164029i | −0.784349 | − | 0.620320i | \(-0.787003\pi\) |
0.620320 | + | 0.784349i | \(0.287003\pi\) | |||||||
\(252\) | −1.15761 | − | 2.35168i | −0.0729223 | − | 0.148142i | ||||
\(253\) | 12.7834 | + | 12.7834i | 0.803684 | + | 0.803684i | ||||
\(254\) | −0.671002 | + | 0.671002i | −0.0421024 | + | 0.0421024i | ||||
\(255\) | 6.39183 | − | 1.48793i | 0.400272 | − | 0.0931777i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.1036 | + | 13.1036i | 0.817381 | + | 0.817381i | 0.985728 | − | 0.168346i | \(-0.0538427\pi\) |
−0.168346 | + | 0.985728i | \(0.553843\pi\) | |||||||
\(258\) | 19.2389 | − | 4.47855i | 1.19776 | − | 0.278822i | ||||
\(259\) | 1.80260 | + | 4.99958i | 0.112008 | + | 0.310659i | ||||
\(260\) | 3.96070i | 0.245632i | ||||||||
\(261\) | −0.0160313 | + | 0.0471146i | −0.000992312 | + | 0.00291632i | ||||
\(262\) | − | 16.5967i | − | 1.02535i | ||||||
\(263\) | 3.79960 | 0.234293 | 0.117147 | − | 0.993115i | \(-0.462625\pi\) | ||||
0.117147 | + | 0.993115i | \(0.462625\pi\) | |||||||
\(264\) | 2.97049 | − | 4.77308i | 0.182821 | − | 0.293763i | ||||
\(265\) | 6.48922 | − | 6.48922i | 0.398630 | − | 0.398630i | ||||
\(266\) | 2.77433i | 0.170105i | ||||||||
\(267\) | −13.5056 | − | 8.40513i | −0.826532 | − | 0.514385i | ||||
\(268\) | 7.74070 | 0.472838 | ||||||||
\(269\) | − | 12.5379i | − | 0.764450i | −0.924069 | − | 0.382225i | \(-0.875158\pi\) | ||
0.924069 | − | 0.382225i | \(-0.124842\pi\) | |||||||
\(270\) | 3.29204 | + | 4.02026i | 0.200347 | + | 0.244665i | ||||
\(271\) | −16.9560 | −1.03000 | −0.515001 | − | 0.857189i | \(-0.672209\pi\) | ||||
−0.515001 | + | 0.857189i | \(0.672209\pi\) | |||||||
\(272\) | −2.67922 | − | 2.67922i | −0.162452 | − | 0.162452i | ||||
\(273\) | −5.08883 | − | 3.16699i | −0.307990 | − | 0.191675i | ||||
\(274\) | 15.0812 | + | 15.0812i | 0.911089 | + | 0.911089i | ||||
\(275\) | 3.24582i | 0.195731i | ||||||||
\(276\) | 8.19049 | + | 5.09728i | 0.493009 | + | 0.306820i | ||||
\(277\) | 13.7206 | + | 13.7206i | 0.824392 | + | 0.824392i | 0.986735 | − | 0.162342i | \(-0.0519048\pi\) |
−0.162342 | + | 0.986735i | \(0.551905\pi\) | |||||||
\(278\) | 10.3366 | + | 10.3366i | 0.619951 | + | 0.619951i | ||||
\(279\) | −20.8926 | − | 7.10896i | −1.25081 | − | 0.425602i | ||||
\(280\) | − | 0.873718i | − | 0.0522146i | ||||||
\(281\) | 16.4710 | + | 16.4710i | 0.982575 | + | 0.982575i | 0.999851 | − | 0.0172753i | \(-0.00549917\pi\) |
−0.0172753 | + | 0.999851i | \(0.505499\pi\) | |||||||
\(282\) | −2.80907 | + | 4.51371i | −0.167278 | + | 0.268788i | ||||
\(283\) | −0.457464 | − | 0.457464i | −0.0271934 | − | 0.0271934i | 0.693379 | − | 0.720573i | \(-0.256121\pi\) |
−0.720573 | + | 0.693379i | \(0.756121\pi\) | |||||||
\(284\) | −0.580983 | −0.0344750 | ||||||||
\(285\) | −1.24694 | − | 5.35658i | −0.0738621 | − | 0.317296i | ||||
\(286\) | − | 12.8557i | − | 0.760176i | ||||||
\(287\) | −10.5824 | −0.624660 | ||||||||
\(288\) | 0.966374 | − | 2.84009i | 0.0569441 | − | 0.167354i | ||||
\(289\) | − | 2.64352i | − | 0.155501i | ||||||
\(290\) | −0.0117303 | + | 0.0117303i | −0.000688826 | + | 0.000688826i | ||||
\(291\) | 14.8767 | + | 9.25842i | 0.872090 | + | 0.542738i | ||||
\(292\) | 11.0501 | 0.646658 | ||||||||
\(293\) | 6.48865i | 0.379071i | 0.981874 | + | 0.189536i | \(0.0606983\pi\) | ||||
−0.981874 | + | 0.189536i | \(0.939302\pi\) | |||||||
\(294\) | −9.17113 | − | 5.70758i | −0.534871 | − | 0.332873i | ||||
\(295\) | 11.2575i | 0.655439i | ||||||||
\(296\) | −2.58734 | + | 5.50506i | −0.150386 | + | 0.319975i | ||||
\(297\) | −10.6854 | − | 13.0490i | −0.620029 | − | 0.757182i | ||||
\(298\) | −3.02618 | − | 3.02618i | −0.175302 | − | 0.175302i | ||||
\(299\) | 22.0601 | 1.27577 | ||||||||
\(300\) | 0.392697 | + | 1.68695i | 0.0226724 | + | 0.0973959i | ||||
\(301\) | −7.04588 | + | 7.04588i | −0.406118 | + | 0.406118i | ||||
\(302\) | −11.5029 | − | 11.5029i | −0.661917 | − | 0.661917i | ||||
\(303\) | −3.87590 | − | 16.6501i | −0.222664 | − | 0.956520i | ||||
\(304\) | −2.24528 | + | 2.24528i | −0.128776 | + | 0.128776i | ||||
\(305\) | 9.39935i | 0.538205i | ||||||||
\(306\) | −10.1984 | + | 5.02011i | −0.583002 | + | 0.286981i | ||||
\(307\) | − | 4.82152i | − | 0.275178i | −0.990489 | − | 0.137589i | \(-0.956065\pi\) | ||
0.990489 | − | 0.137589i | \(-0.0439354\pi\) | |||||||
\(308\) | 2.83593i | 0.161592i | ||||||||
\(309\) | 6.21776 | − | 9.99091i | 0.353716 | − | 0.568363i | ||||
\(310\) | −5.20171 | − | 5.20171i | −0.295437 | − | 0.295437i | ||||
\(311\) | −6.45365 | + | 6.45365i | −0.365953 | + | 0.365953i | −0.865999 | − | 0.500046i | \(-0.833316\pi\) |
0.500046 | + | 0.865999i | \(0.333316\pi\) | |||||||
\(312\) | −1.55536 | − | 6.68150i | −0.0880548 | − | 0.378265i | ||||
\(313\) | −23.6394 | + | 23.6394i | −1.33618 | + | 1.33618i | −0.436449 | + | 0.899729i | \(0.643764\pi\) |
−0.899729 | + | 0.436449i | \(0.856236\pi\) | |||||||
\(314\) | −13.0527 | + | 13.0527i | −0.736607 | + | 0.736607i | ||||
\(315\) | −2.48144 | − | 0.844338i | −0.139813 | − | 0.0475731i | ||||
\(316\) | −0.763562 | − | 0.763562i | −0.0429537 | − | 0.0429537i | ||||
\(317\) | −2.73418 | −0.153567 | −0.0767834 | − | 0.997048i | \(-0.524465\pi\) | ||||
−0.0767834 | + | 0.997048i | \(0.524465\pi\) | |||||||
\(318\) | −8.39867 | + | 13.4953i | −0.470974 | + | 0.756777i | ||||
\(319\) | 0.0380744 | − | 0.0380744i | 0.00213176 | − | 0.00213176i | ||||
\(320\) | 0.707107 | − | 0.707107i | 0.0395285 | − | 0.0395285i | ||||
\(321\) | 24.8332 | − | 5.78083i | 1.38606 | − | 0.322654i | ||||
\(322\) | −4.86639 | −0.271193 | ||||||||
\(323\) | 12.0312 | 0.669436 | ||||||||
\(324\) | −7.13224 | − | 5.48918i | −0.396236 | − | 0.304955i | ||||
\(325\) | 2.80064 | + | 2.80064i | 0.155352 | + | 0.155352i | ||||
\(326\) | −10.8301 | −0.599825 | ||||||||
\(327\) | 26.7396 | + | 16.6412i | 1.47870 | + | 0.920259i | ||||
\(328\) | −8.56443 | − | 8.56443i | −0.472891 | − | 0.472891i | ||||
\(329\) | − | 2.68183i | − | 0.147854i | ||||||
\(330\) | −1.27463 | − | 5.47553i | −0.0701659 | − | 0.301418i | ||||
\(331\) | −15.9221 | + | 15.9221i | −0.875158 | + | 0.875158i | −0.993029 | − | 0.117871i | \(-0.962393\pi\) |
0.117871 | + | 0.993029i | \(0.462393\pi\) | |||||||
\(332\) | 6.26833 | 0.344019 | ||||||||
\(333\) | 13.1345 | + | 12.6682i | 0.719769 | + | 0.694214i | ||||
\(334\) | −17.6482 | −0.965665 | ||||||||
\(335\) | 5.47350 | − | 5.47350i | 0.299049 | − | 0.299049i | ||||
\(336\) | 0.343107 | + | 1.47392i | 0.0187180 | + | 0.0804087i | ||||
\(337\) | − | 6.36440i | − | 0.346691i | −0.984861 | − | 0.173346i | \(-0.944542\pi\) | ||
0.984861 | − | 0.173346i | \(-0.0554577\pi\) | |||||||
\(338\) | −1.90012 | − | 1.90012i | −0.103353 | − | 0.103353i | ||||
\(339\) | −6.44732 | − | 4.01244i | −0.350170 | − | 0.217926i | ||||
\(340\) | −3.78900 | −0.205487 | ||||||||
\(341\) | 16.8838 | + | 16.8838i | 0.914310 | + | 0.914310i | ||||
\(342\) | 4.20703 | + | 8.54659i | 0.227490 | + | 0.462147i | ||||
\(343\) | 11.5651 | 0.624455 | ||||||||
\(344\) | −11.4046 | −0.614894 | ||||||||
\(345\) | 9.39587 | − | 2.18723i | 0.505857 | − | 0.117756i | ||||
\(346\) | 6.48740 | − | 6.48740i | 0.348765 | − | 0.348765i | ||||
\(347\) | −11.1501 | + | 11.1501i | −0.598571 | + | 0.598571i | −0.939932 | − | 0.341361i | \(-0.889112\pi\) |
0.341361 | + | 0.939932i | \(0.389112\pi\) | |||||||
\(348\) | 0.0151819 | − | 0.0243948i | 0.000813836 | − | 0.00130770i | ||||
\(349\) | −5.32513 | −0.285048 | −0.142524 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142524 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(350\) | −0.617812 | − | 0.617812i | −0.0330234 | − | 0.0330234i | ||||
\(351\) | −20.4791 | − | 2.03946i | −1.09309 | − | 0.108859i | ||||
\(352\) | −2.29514 | + | 2.29514i | −0.122332 | + | 0.122332i | ||||
\(353\) | 1.76426 | − | 1.76426i | 0.0939022 | − | 0.0939022i | −0.658595 | − | 0.752497i | \(-0.728849\pi\) |
0.752497 | + | 0.658595i | \(0.228849\pi\) | |||||||
\(354\) | −4.42080 | − | 18.9909i | −0.234963 | − | 1.00935i | ||||
\(355\) | −0.410817 | + | 0.410817i | −0.0218039 | + | 0.0218039i | ||||
\(356\) | 6.49421 | + | 6.49421i | 0.344192 | + | 0.344192i | ||||
\(357\) | 3.02969 | − | 4.86821i | 0.160348 | − | 0.257653i | ||||
\(358\) | 14.1577i | 0.748257i | ||||||||
\(359\) | − | 31.2814i | − | 1.65097i | −0.564426 | − | 0.825483i | \(-0.690903\pi\) | ||
0.564426 | − | 0.825483i | \(-0.309097\pi\) | |||||||
\(360\) | −1.32492 | − | 2.69158i | −0.0698293 | − | 0.141859i | ||||
\(361\) | 8.91741i | 0.469337i | ||||||||
\(362\) | −16.0339 | + | 16.0339i | −0.842724 | + | 0.842724i | ||||
\(363\) | −0.182459 | − | 0.783806i | −0.00957661 | − | 0.0411391i | ||||
\(364\) | 2.44697 | + | 2.44697i | 0.128256 | + | 0.128256i | ||||
\(365\) | 7.81360 | − | 7.81360i | 0.408983 | − | 0.408983i | ||||
\(366\) | −3.69110 | − | 15.8562i | −0.192937 | − | 0.828817i | ||||
\(367\) | 9.81757 | 0.512473 | 0.256237 | − | 0.966614i | \(-0.417517\pi\) | ||||
0.256237 | + | 0.966614i | \(0.417517\pi\) | |||||||
\(368\) | −3.93841 | − | 3.93841i | −0.205304 | − | 0.205304i | ||||
\(369\) | −32.6002 | + | 16.0473i | −1.69710 | + | 0.835390i | ||||
\(370\) | 2.06314 | + | 5.72219i | 0.107258 | + | 0.297482i | ||||
\(371\) | − | 8.01823i | − | 0.416286i | ||||||
\(372\) | 10.8177 | + | 6.73230i | 0.560871 | + | 0.349054i | ||||
\(373\) | − | 22.1399i | − | 1.14636i | −0.819429 | − | 0.573181i | \(-0.805709\pi\) | ||
0.819429 | − | 0.573181i | \(-0.194291\pi\) | |||||||
\(374\) | 12.2984 | 0.635936 | ||||||||
\(375\) | 1.47053 | + | 0.915172i | 0.0759379 | + | 0.0472593i | ||||
\(376\) | 2.17042 | − | 2.17042i | 0.111931 | − | 0.111931i | ||||
\(377\) | − | 0.0657046i | − | 0.00338396i | ||||||
\(378\) | 4.51762 | + | 0.449899i | 0.232362 | + | 0.0231403i | ||||
\(379\) | −5.96113 | −0.306203 | −0.153101 | − | 0.988211i | \(-0.548926\pi\) | ||||
−0.153101 | + | 0.988211i | \(0.548926\pi\) | |||||||
\(380\) | 3.17531i | 0.162890i | ||||||||
\(381\) | −0.372646 | − | 1.60081i | −0.0190912 | − | 0.0820121i | ||||
\(382\) | 9.32939 | 0.477333 | ||||||||
\(383\) | 9.16947 | + | 9.16947i | 0.468538 | + | 0.468538i | 0.901441 | − | 0.432903i | \(-0.142511\pi\) |
−0.432903 | + | 0.901441i | \(0.642511\pi\) | |||||||
\(384\) | −0.915172 | + | 1.47053i | −0.0467022 | + | 0.0750427i | ||||
\(385\) | 2.00531 | + | 2.00531i | 0.102200 | + | 0.102200i | ||||
\(386\) | 1.02055i | 0.0519448i | ||||||||
\(387\) | −11.0211 | + | 32.3900i | −0.560233 | + | 1.64648i | ||||
\(388\) | −7.15350 | − | 7.15350i | −0.363164 | − | 0.363164i | ||||
\(389\) | −6.40269 | − | 6.40269i | −0.324629 | − | 0.324629i | 0.525911 | − | 0.850540i | \(-0.323725\pi\) |
−0.850540 | + | 0.525911i | \(0.823725\pi\) | |||||||
\(390\) | −5.82434 | − | 3.62473i | −0.294927 | − | 0.183545i | ||||
\(391\) | 21.1038i | 1.06726i | ||||||||
\(392\) | 4.40995 | + | 4.40995i | 0.222736 | + | 0.222736i | ||||
\(393\) | 24.4059 | + | 15.1888i | 1.23112 | + | 0.766175i | ||||
\(394\) | 10.4709 | + | 10.4709i | 0.527518 | + | 0.527518i | ||||
\(395\) | −1.07984 | −0.0543327 | ||||||||
\(396\) | 4.30045 | + | 8.73639i | 0.216106 | + | 0.439020i | ||||
\(397\) | − | 2.29166i | − | 0.115015i | −0.998345 | − | 0.0575075i | \(-0.981685\pi\) | ||
0.998345 | − | 0.0575075i | \(-0.0183153\pi\) | |||||||
\(398\) | −21.6821 | −1.08683 | ||||||||
\(399\) | −4.07973 | − | 2.53899i | −0.204242 | − | 0.127108i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −17.9575 | + | 17.9575i | −0.896756 | + | 0.896756i | −0.995148 | − | 0.0983914i | \(-0.968630\pi\) |
0.0983914 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(402\) | −7.08407 | + | 11.3829i | −0.353321 | + | 0.567729i | ||||
\(403\) | 29.1362 | 1.45138 | ||||||||
\(404\) | 9.86993i | 0.491048i | ||||||||
\(405\) | −8.92469 | + | 1.16182i | −0.443472 | + | 0.0577313i | ||||
\(406\) | 0.0144942i | 0.000719336i | ||||||||
\(407\) | −6.69660 | − | 18.5732i | −0.331938 | − | 0.920640i | ||||
\(408\) | 6.39183 | − | 1.48793i | 0.316443 | − | 0.0736634i | ||||
\(409\) | 2.75786 | + | 2.75786i | 0.136367 | + | 0.136367i | 0.771995 | − | 0.635628i | \(-0.219259\pi\) |
−0.635628 | + | 0.771995i | \(0.719259\pi\) | |||||||
\(410\) | −12.1119 | −0.598166 | ||||||||
\(411\) | −35.9793 | + | 8.37547i | −1.77473 | + | 0.413131i | ||||
\(412\) | −4.80415 | + | 4.80415i | −0.236683 | + | 0.236683i | ||||
\(413\) | 6.95504 | + | 6.95504i | 0.342235 | + | 0.342235i | ||||
\(414\) | −14.9914 | + | 7.37947i | −0.736788 | + | 0.362681i | ||||
\(415\) | 4.43238 | − | 4.43238i | 0.217577 | − | 0.217577i | ||||
\(416\) | 3.96070i | 0.194190i | ||||||||
\(417\) | −24.6602 | + | 5.74054i | −1.20761 | + | 0.281115i | ||||
\(418\) | − | 10.3065i | − | 0.504107i | ||||||
\(419\) | − | 9.86970i | − | 0.482166i | −0.970504 | − | 0.241083i | \(-0.922497\pi\) | ||
0.970504 | − | 0.241083i | \(-0.0775027\pi\) | |||||||
\(420\) | 1.28483 | + | 0.799603i | 0.0626932 | + | 0.0390166i | ||||
\(421\) | −5.59923 | − | 5.59923i | −0.272890 | − | 0.272890i | 0.557373 | − | 0.830262i | \(-0.311809\pi\) |
−0.830262 | + | 0.557373i | \(0.811809\pi\) | |||||||
\(422\) | −10.5186 | + | 10.5186i | −0.512039 | + | 0.512039i | ||||
\(423\) | −4.06676 | − | 8.26165i | −0.197733 | − | 0.401695i | ||||
\(424\) | 6.48922 | − | 6.48922i | 0.315144 | − | 0.315144i | ||||
\(425\) | −2.67922 | + | 2.67922i | −0.129961 | + | 0.129961i | ||||
\(426\) | 0.531700 | − | 0.854354i | 0.0257609 | − | 0.0413936i | ||||
\(427\) | 5.80703 | + | 5.80703i | 0.281022 | + | 0.281022i | ||||
\(428\) | −14.7208 | −0.711558 | ||||||||
\(429\) | 18.9048 | + | 11.7652i | 0.912731 | + | 0.568030i | ||||
\(430\) | −8.06425 | + | 8.06425i | −0.388893 | + | 0.388893i | ||||
\(431\) | −16.1018 | + | 16.1018i | −0.775598 | + | 0.775598i | −0.979079 | − | 0.203481i | \(-0.934774\pi\) |
0.203481 | + | 0.979079i | \(0.434774\pi\) | |||||||
\(432\) | 3.29204 | + | 4.02026i | 0.158388 | + | 0.193425i | ||||
\(433\) | 32.3378 | 1.55405 | 0.777027 | − | 0.629468i | \(-0.216727\pi\) | ||||
0.777027 | + | 0.629468i | \(0.216727\pi\) | |||||||
\(434\) | −6.42735 | −0.308523 | ||||||||
\(435\) | −0.00651450 | − | 0.0279850i | −0.000312347 | − | 0.00134178i | ||||
\(436\) | −12.8578 | − | 12.8578i | −0.615776 | − | 0.615776i | ||||
\(437\) | 17.6857 | 0.846021 | ||||||||
\(438\) | −10.1128 | + | 16.2495i | −0.483206 | + | 0.776432i | ||||
\(439\) | 18.7980 | + | 18.7980i | 0.897177 | + | 0.897177i | 0.995186 | − | 0.0980082i | \(-0.0312472\pi\) |
−0.0980082 | + | 0.995186i | \(0.531247\pi\) | |||||||
\(440\) | 3.24582i | 0.154739i | ||||||||
\(441\) | 16.7863 | − | 8.26301i | 0.799349 | − | 0.393477i | ||||
\(442\) | 10.6116 | − | 10.6116i | 0.504743 | − | 0.504743i | ||||
\(443\) | −14.1166 | −0.670698 | −0.335349 | − | 0.942094i | \(-0.608854\pi\) | ||||
−0.335349 | + | 0.942094i | \(0.608854\pi\) | |||||||
\(444\) | −5.72750 | − | 8.84284i | −0.271815 | − | 0.419662i | ||||
\(445\) | 9.18420 | 0.435373 | ||||||||
\(446\) | 4.37205 | − | 4.37205i | 0.207022 | − | 0.207022i | ||||
\(447\) | 7.21957 | − | 1.68061i | 0.341474 | − | 0.0794903i | ||||
\(448\) | − | 0.873718i | − | 0.0412793i | ||||||
\(449\) | 6.93149 | + | 6.93149i | 0.327117 | + | 0.327117i | 0.851489 | − | 0.524372i | \(-0.175700\pi\) |
−0.524372 | + | 0.851489i | \(0.675700\pi\) | |||||||
\(450\) | −2.84009 | − | 0.966374i | −0.133883 | − | 0.0455553i | ||||
\(451\) | 39.3132 | 1.85119 | ||||||||
\(452\) | 3.10020 | + | 3.10020i | 0.145821 | + | 0.145821i | ||||
\(453\) | 27.4425 | − | 6.38822i | 1.28936 | − | 0.300145i | ||||
\(454\) | 23.9616 | 1.12457 | ||||||||
\(455\) | 3.46054 | 0.162233 | ||||||||
\(456\) | −1.24694 | − | 5.35658i | −0.0583931 | − | 0.250845i | ||||
\(457\) | 14.8024 | − | 14.8024i | 0.692425 | − | 0.692425i | −0.270340 | − | 0.962765i | \(-0.587136\pi\) |
0.962765 | + | 0.270340i | \(0.0871361\pi\) | |||||||
\(458\) | 4.98767 | − | 4.98767i | 0.233058 | − | 0.233058i | ||||
\(459\) | 1.95105 | − | 19.5913i | 0.0910671 | − | 0.914443i | ||||
\(460\) | −5.56975 | −0.259691 | ||||||||
\(461\) | −5.43289 | − | 5.43289i | −0.253035 | − | 0.253035i | 0.569179 | − | 0.822214i | \(-0.307261\pi\) |
−0.822214 | + | 0.569179i | \(0.807261\pi\) | |||||||
\(462\) | −4.17033 | − | 2.59537i | −0.194021 | − | 0.120747i | ||||
\(463\) | −1.14209 | + | 1.14209i | −0.0530773 | + | 0.0530773i | −0.733147 | − | 0.680070i | \(-0.761949\pi\) |
0.680070 | + | 0.733147i | \(0.261949\pi\) | |||||||
\(464\) | −0.0117303 | + | 0.0117303i | −0.000544565 | + | 0.000544565i | ||||
\(465\) | 12.4097 | − | 2.88881i | 0.575487 | − | 0.133965i | ||||
\(466\) | 3.15433 | − | 3.15433i | 0.146122 | − | 0.146122i | ||||
\(467\) | 8.44172 | + | 8.44172i | 0.390636 | + | 0.390636i | 0.874914 | − | 0.484278i | \(-0.160918\pi\) |
−0.484278 | + | 0.874914i | \(0.660918\pi\) | |||||||
\(468\) | 11.2488 | + | 3.82752i | 0.519974 | + | 0.176927i | ||||
\(469\) | − | 6.76319i | − | 0.312295i | ||||||
\(470\) | − | 3.06944i | − | 0.141583i | ||||||
\(471\) | −7.24893 | − | 31.1399i | −0.334013 | − | 1.43485i | ||||
\(472\) | 11.2575i | 0.518170i | ||||||||
\(473\) | 26.1751 | − | 26.1751i | 1.20353 | − | 1.20353i | ||||
\(474\) | 1.82163 | − | 0.424050i | 0.0836704 | − | 0.0194773i | ||||
\(475\) | 2.24528 | + | 2.24528i | 0.103021 | + | 0.103021i | ||||
\(476\) | −2.34089 | + | 2.34089i | −0.107294 | + | 0.107294i | ||||
\(477\) | −12.1590 | − | 24.7010i | −0.556721 | − | 1.13098i | ||||
\(478\) | −24.1467 | −1.10444 | ||||||||
\(479\) | −9.71035 | − | 9.71035i | −0.443677 | − | 0.443677i | 0.449569 | − | 0.893246i | \(-0.351578\pi\) |
−0.893246 | + | 0.449569i | \(0.851578\pi\) | |||||||
\(480\) | 0.392697 | + | 1.68695i | 0.0179241 | + | 0.0769982i | ||||
\(481\) | −21.8039 | − | 10.2477i | −0.994173 | − | 0.467254i | ||||
\(482\) | 5.37258i | 0.244715i | ||||||||
\(483\) | 4.45359 | − | 7.15618i | 0.202645 | − | 0.325617i | ||||
\(484\) | 0.464630i | 0.0211195i | ||||||||
\(485\) | −10.1166 | −0.459370 | ||||||||
\(486\) | 14.5992 | − | 5.46463i | 0.662235 | − | 0.247881i | ||||
\(487\) | −3.87550 | + | 3.87550i | −0.175616 | + | 0.175616i | −0.789442 | − | 0.613826i | \(-0.789630\pi\) |
0.613826 | + | 0.789442i | \(0.289630\pi\) | |||||||
\(488\) | 9.39935i | 0.425489i | ||||||||
\(489\) | 9.91143 | − | 15.9260i | 0.448210 | − | 0.720199i | ||||
\(490\) | 6.23662 | 0.281742 | ||||||||
\(491\) | − | 37.5934i | − | 1.69657i | −0.529541 | − | 0.848284i | \(-0.677636\pi\) | ||
0.529541 | − | 0.848284i | \(-0.322364\pi\) | |||||||
\(492\) | 20.4322 | − | 4.75632i | 0.921154 | − | 0.214432i | ||||
\(493\) | 0.0628561 | 0.00283090 | ||||||||
\(494\) | −8.89290 | − | 8.89290i | −0.400111 | − | 0.400111i | ||||
\(495\) | 9.21844 | + | 3.13668i | 0.414338 | + | 0.140983i | ||||
\(496\) | −5.20171 | − | 5.20171i | −0.233563 | − | 0.233563i | ||||
\(497\) | 0.507616i | 0.0227697i | ||||||||
\(498\) | −5.73660 | + | 9.21777i | −0.257063 | + | 0.413058i | ||||
\(499\) | −13.8728 | − | 13.8728i | −0.621031 | − | 0.621031i | 0.324764 | − | 0.945795i | \(-0.394715\pi\) |
−0.945795 | + | 0.324764i | \(0.894715\pi\) | |||||||
\(500\) | −0.707107 | − | 0.707107i | −0.0316228 | − | 0.0316228i | ||||
\(501\) | 16.1511 | − | 25.9522i | 0.721579 | − | 1.15946i | ||||
\(502\) | 3.67514i | 0.164029i | ||||||||
\(503\) | 11.0121 | + | 11.0121i | 0.491005 | + | 0.491005i | 0.908623 | − | 0.417618i | \(-0.137135\pi\) |
−0.417618 | + | 0.908623i | \(0.637135\pi\) | |||||||
\(504\) | −2.48144 | − | 0.844338i | −0.110532 | − | 0.0376098i | ||||
\(505\) | 6.97910 | + | 6.97910i | 0.310566 | + | 0.310566i | ||||
\(506\) | 18.0784 | 0.803684 | ||||||||
\(507\) | 4.53313 | − | 1.05525i | 0.201323 | − | 0.0468652i | ||||
\(508\) | 0.948940i | 0.0421024i | ||||||||
\(509\) | 8.43066 | 0.373683 | 0.186841 | − | 0.982390i | \(-0.440175\pi\) | ||||
0.186841 | + | 0.982390i | \(0.440175\pi\) | |||||||
\(510\) | 3.46758 | − | 5.57183i | 0.153547 | − | 0.246725i | ||||
\(511\) | − | 9.65467i | − | 0.427098i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −16.4182 | − | 1.63505i | −0.724880 | − | 0.0721890i | ||||
\(514\) | 18.5313 | 0.817381 | ||||||||
\(515\) | 6.79409i | 0.299383i | ||||||||
\(516\) | 10.4372 | − | 16.7708i | 0.459470 | − | 0.738292i | ||||
\(517\) | 9.96287i | 0.438167i | ||||||||
\(518\) | 4.80987 | + | 2.26060i | 0.211334 | + | 0.0993251i | ||||
\(519\) | 3.60283 | + | 15.4770i | 0.158147 | + | 0.679365i | ||||
\(520\) | 2.80064 | + | 2.80064i | 0.122816 | + | 0.122816i | ||||
\(521\) | −10.1891 | −0.446392 | −0.223196 | − | 0.974774i | \(-0.571649\pi\) | ||||
−0.223196 | + | 0.974774i | \(0.571649\pi\) | |||||||
\(522\) | 0.0219792 | + | 0.0446509i | 0.000962005 | + | 0.00195432i | ||||
\(523\) | 21.5024 | − | 21.5024i | 0.940233 | − | 0.940233i | −0.0580790 | − | 0.998312i | \(-0.518498\pi\) |
0.998312 | + | 0.0580790i | \(0.0184975\pi\) | |||||||
\(524\) | −11.7356 | − | 11.7356i | −0.512673 | − | 0.512673i | ||||
\(525\) | 1.47392 | − | 0.343107i | 0.0643269 | − | 0.0149744i | ||||
\(526\) | 2.68672 | − | 2.68672i | 0.117147 | − | 0.117147i | ||||
\(527\) | 27.8731i | 1.21417i | ||||||||
\(528\) | −1.27463 | − | 5.47553i | −0.0554710 | − | 0.238292i | ||||
\(529\) | 8.02212i | 0.348788i | ||||||||
\(530\) | − | 9.17714i | − | 0.398630i | ||||||
\(531\) | 31.9724 | + | 10.8790i | 1.38748 | + | 0.472108i | ||||
\(532\) | 1.96174 | + | 1.96174i | 0.0850524 | + | 0.0850524i | ||||
\(533\) | 33.9212 | − | 33.9212i | 1.46929 | − | 1.46929i | ||||
\(534\) | −15.4933 | + | 3.60661i | −0.670459 | + | 0.156073i | ||||
\(535\) | −10.4092 | + | 10.4092i | −0.450029 | + | 0.450029i | ||||
\(536\) | 5.47350 | − | 5.47350i | 0.236419 | − | 0.236419i | ||||
\(537\) | −20.8193 | − | 12.9567i | −0.898420 | − | 0.559124i | ||||
\(538\) | −8.86564 | − | 8.86564i | −0.382225 | − | 0.382225i | ||||
\(539\) | −20.2430 | −0.871926 | ||||||||
\(540\) | 5.17058 | + | 0.514925i | 0.222506 | + | 0.0221588i | ||||
\(541\) | −14.4179 | + | 14.4179i | −0.619875 | + | 0.619875i | −0.945499 | − | 0.325625i | \(-0.894425\pi\) |
0.325625 | + | 0.945499i | \(0.394425\pi\) | |||||||
\(542\) | −11.9897 | + | 11.9897i | −0.515001 | + | 0.515001i | ||||
\(543\) | −8.90456 | − | 38.2522i | −0.382131 | − | 1.64156i | ||||
\(544\) | −3.78900 | −0.162452 | ||||||||
\(545\) | −18.1836 | −0.778902 | ||||||||
\(546\) | −5.83774 | + | 1.35894i | −0.249832 | + | 0.0581574i | ||||
\(547\) | −16.2982 | − | 16.2982i | −0.696862 | − | 0.696862i | 0.266870 | − | 0.963732i | \(-0.414010\pi\) |
−0.963732 | + | 0.266870i | \(0.914010\pi\) | |||||||
\(548\) | 21.3281 | 0.911089 | ||||||||
\(549\) | 26.6950 | + | 9.08329i | 1.13932 | + | 0.387665i | ||||
\(550\) | 2.29514 | + | 2.29514i | 0.0978653 | + | 0.0978653i | ||||
\(551\) | − | 0.0526756i | − | 0.00224406i | ||||||
\(552\) | 9.39587 | − | 2.18723i | 0.399915 | − | 0.0930945i | ||||
\(553\) | −0.667138 | + | 0.667138i | −0.0283696 | + | 0.0283696i | ||||
\(554\) | 19.4039 | 0.824392 | ||||||||
\(555\) | −10.3028 | − | 2.20288i | −0.437329 | − | 0.0935069i | ||||
\(556\) | 14.6182 | 0.619951 | ||||||||
\(557\) | 13.8613 | − | 13.8613i | 0.587322 | − | 0.587322i | −0.349583 | − | 0.936905i | \(-0.613677\pi\) |
0.936905 | + | 0.349583i | \(0.113677\pi\) | |||||||
\(558\) | −19.8001 | + | 9.74653i | −0.838206 | + | 0.412603i | ||||
\(559\) | − | 45.1702i | − | 1.91049i | ||||||
\(560\) | −0.617812 | − | 0.617812i | −0.0261073 | − | 0.0261073i | ||||
\(561\) | −11.2552 | + | 18.0852i | −0.475193 | + | 0.763557i | ||||
\(562\) | 23.2935 | 0.982575 | ||||||||
\(563\) | −9.05310 | − | 9.05310i | −0.381543 | − | 0.381543i | 0.490115 | − | 0.871658i | \(-0.336955\pi\) |
−0.871658 | + | 0.490115i | \(0.836955\pi\) | |||||||
\(564\) | 1.20536 | + | 5.17799i | 0.0507549 | + | 0.218033i | ||||
\(565\) | 4.38435 | 0.184451 | ||||||||
\(566\) | −0.646951 | −0.0271934 | ||||||||
\(567\) | −4.79600 | + | 6.23157i | −0.201413 | + | 0.261701i | ||||
\(568\) | −0.410817 | + | 0.410817i | −0.0172375 | + | 0.0172375i | ||||
\(569\) | −22.3048 | + | 22.3048i | −0.935066 | + | 0.935066i | −0.998017 | − | 0.0629509i | \(-0.979949\pi\) |
0.0629509 | + | 0.998017i | \(0.479949\pi\) | |||||||
\(570\) | −4.66939 | − | 2.90596i | −0.195579 | − | 0.121717i | ||||
\(571\) | −15.8222 | −0.662138 | −0.331069 | − | 0.943607i | \(-0.607409\pi\) | ||||
−0.331069 | + | 0.943607i | \(0.607409\pi\) | |||||||
\(572\) | −9.09039 | − | 9.09039i | −0.380088 | − | 0.380088i | ||||
\(573\) | −8.53800 | + | 13.7192i | −0.356680 | + | 0.573126i | ||||
\(574\) | −7.48290 | + | 7.48290i | −0.312330 | + | 0.312330i | ||||
\(575\) | −3.93841 | + | 3.93841i | −0.164243 | + | 0.164243i | ||||
\(576\) | −1.32492 | − | 2.69158i | −0.0552049 | − | 0.112149i | ||||
\(577\) | −16.3027 | + | 16.3027i | −0.678689 | + | 0.678689i | −0.959704 | − | 0.281014i | \(-0.909329\pi\) |
0.281014 | + | 0.959704i | \(0.409329\pi\) | |||||||
\(578\) | −1.86925 | − | 1.86925i | −0.0777505 | − | 0.0777505i | ||||
\(579\) | −1.50076 | − | 0.933983i | −0.0623693 | − | 0.0388150i | ||||
\(580\) | 0.0165891i | 0.000688826i | ||||||||
\(581\) | − | 5.47675i | − | 0.227214i | ||||||
\(582\) | 17.0661 | − | 3.97275i | 0.707414 | − | 0.164676i | ||||
\(583\) | 29.7874i | 1.23367i | ||||||||
\(584\) | 7.81360 | − | 7.81360i | 0.323329 | − | 0.323329i | ||||
\(585\) | 10.6605 | − | 5.24761i | 0.440759 | − | 0.216962i | ||||
\(586\) | 4.58817 | + | 4.58817i | 0.189536 | + | 0.189536i | ||||
\(587\) | −12.6200 | + | 12.6200i | −0.520882 | + | 0.520882i | −0.917838 | − | 0.396956i | \(-0.870067\pi\) |
0.396956 | + | 0.917838i | \(0.370067\pi\) | |||||||
\(588\) | −10.5208 | + | 2.44910i | −0.433872 | + | 0.100999i | ||||
\(589\) | 23.3586 | 0.962474 | ||||||||
\(590\) | 7.96028 | + | 7.96028i | 0.327719 | + | 0.327719i | ||||
\(591\) | −24.9805 | + | 5.81512i | −1.02756 | + | 0.239202i | ||||
\(592\) | 2.06314 | + | 5.72219i | 0.0847946 | + | 0.235180i | ||||
\(593\) | − | 21.6189i | − | 0.887782i | −0.896081 | − | 0.443891i | \(-0.853598\pi\) | ||
0.896081 | − | 0.443891i | \(-0.146402\pi\) | |||||||
\(594\) | −16.7828 | − | 1.67136i | −0.688606 | − | 0.0685765i | ||||
\(595\) | 3.31051i | 0.135718i | ||||||||
\(596\) | −4.27966 | −0.175302 | ||||||||
\(597\) | 19.8429 | − | 31.8842i | 0.812114 | − | 1.30493i | ||||
\(598\) | 15.5989 | − | 15.5989i | 0.637885 | − | 0.637885i | ||||
\(599\) | 0.728152i | 0.0297515i | 0.999889 | + | 0.0148757i | \(0.00473527\pi\) | ||||
−0.999889 | + | 0.0148757i | \(0.995265\pi\) | |||||||
\(600\) | 1.47053 | + | 0.915172i | 0.0600341 | + | 0.0373618i | ||||
\(601\) | 39.4004 | 1.60718 | 0.803588 | − | 0.595186i | \(-0.202921\pi\) | ||||
0.803588 | + | 0.595186i | \(0.202921\pi\) | |||||||
\(602\) | 9.96438i | 0.406118i | ||||||||
\(603\) | −10.2558 | − | 20.8347i | −0.417648 | − | 0.848454i | ||||
\(604\) | −16.2675 | −0.661917 | ||||||||
\(605\) | 0.328543 | + | 0.328543i | 0.0133572 | + | 0.0133572i | ||||
\(606\) | −14.5140 | − | 9.03269i | −0.589592 | − | 0.366928i | ||||
\(607\) | 18.6181 | + | 18.6181i | 0.755684 | + | 0.755684i | 0.975534 | − | 0.219850i | \(-0.0705567\pi\) |
−0.219850 | + | 0.975534i | \(0.570557\pi\) | |||||||
\(608\) | 3.17531i | 0.128776i | ||||||||
\(609\) | −0.0213142 | − | 0.0132647i | −0.000863694 | − | 0.000537513i | ||||
\(610\) | 6.64635 | + | 6.64635i | 0.269103 | + | 0.269103i | ||||
\(611\) | 8.59641 | + | 8.59641i | 0.347774 | + | 0.347774i | ||||
\(612\) | −3.66159 | + | 10.7611i | −0.148011 | + | 0.434991i | ||||
\(613\) | − | 34.7946i | − | 1.40534i | −0.711516 | − | 0.702670i | \(-0.751991\pi\) | ||
0.711516 | − | 0.702670i | \(-0.248009\pi\) | |||||||
\(614\) | −3.40933 | − | 3.40933i | −0.137589 | − | 0.137589i | ||||
\(615\) | 11.0845 | − | 17.8110i | 0.446970 | − | 0.718207i | ||||
\(616\) | 2.00531 | + | 2.00531i | 0.0807962 | + | 0.0807962i | ||||
\(617\) | −9.78568 | −0.393957 | −0.196978 | − | 0.980408i | \(-0.563113\pi\) | ||||
−0.196978 | + | 0.980408i | \(0.563113\pi\) | |||||||
\(618\) | −2.66802 | − | 11.4613i | −0.107324 | − | 0.461040i | ||||
\(619\) | − | 36.0295i | − | 1.44815i | −0.689723 | − | 0.724074i | \(-0.742268\pi\) | ||
0.689723 | − | 0.724074i | \(-0.257732\pi\) | |||||||
\(620\) | −7.35632 | −0.295437 | ||||||||
\(621\) | 2.86800 | − | 28.7988i | 0.115089 | − | 1.15566i | ||||
\(622\) | 9.12683i | 0.365953i | ||||||||
\(623\) | 5.67411 | − | 5.67411i | 0.227328 | − | 0.227328i | ||||
\(624\) | −5.82434 | − | 3.62473i | −0.233160 | − | 0.145105i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 33.4312i | 1.33618i | ||||||||
\(627\) | 15.1560 | + | 9.43222i | 0.605273 | + | 0.376687i | ||||
\(628\) | 18.4593i | 0.736607i | ||||||||
\(629\) | 9.80340 | − | 20.8586i | 0.390887 | − | 0.831689i | ||||
\(630\) | −2.35168 | + | 1.15761i | −0.0936932 | + | 0.0461201i | ||||
\(631\) | −0.797835 | − | 0.797835i | −0.0317613 | − | 0.0317613i | 0.691048 | − | 0.722809i | \(-0.257149\pi\) |
−0.722809 | + | 0.691048i | \(0.757149\pi\) | |||||||
\(632\) | −1.07984 | −0.0429537 | ||||||||
\(633\) | −5.84160 | − | 25.0943i | −0.232183 | − | 0.997409i | ||||
\(634\) | −1.93336 | + | 1.93336i | −0.0767834 | + | 0.0767834i | ||||
\(635\) | 0.671002 | + | 0.671002i | 0.0266279 | + | 0.0266279i | ||||
\(636\) | 3.60384 | + | 15.4813i | 0.142902 | + | 0.613875i | ||||
\(637\) | −17.4665 | + | 17.4665i | −0.692049 | + | 0.692049i | ||||
\(638\) | − | 0.0538454i | − | 0.00213176i | ||||||
\(639\) | 0.769756 | + | 1.56376i | 0.0304511 | + | 0.0618615i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | 0.310559i | 0.0122663i | 0.999981 | + | 0.00613317i | \(0.00195226\pi\) | ||||
−0.999981 | + | 0.00613317i | \(0.998048\pi\) | |||||||
\(642\) | 13.4721 | − | 21.6474i | 0.531701 | − | 0.854355i | ||||
\(643\) | 24.4682 | + | 24.4682i | 0.964931 | + | 0.964931i | 0.999406 | − | 0.0344744i | \(-0.0109757\pi\) |
−0.0344744 | + | 0.999406i | \(0.510976\pi\) | |||||||
\(644\) | −3.44106 | + | 3.44106i | −0.135597 | + | 0.135597i | ||||
\(645\) | −4.47855 | − | 19.2389i | −0.176343 | − | 0.757531i | ||||
\(646\) | 8.50737 | − | 8.50737i | 0.334718 | − | 0.334718i | ||||
\(647\) | −4.14891 | + | 4.14891i | −0.163111 | + | 0.163111i | −0.783943 | − | 0.620833i | \(-0.786795\pi\) |
0.620833 | + | 0.783943i | \(0.286795\pi\) | |||||||
\(648\) | −8.92469 | + | 1.16182i | −0.350595 | + | 0.0456406i | ||||
\(649\) | −25.8377 | − | 25.8377i | −1.01422 | − | 1.01422i | ||||
\(650\) | 3.96070 | 0.155352 | ||||||||
\(651\) | 5.88213 | − | 9.45161i | 0.230539 | − | 0.370438i | ||||
\(652\) | −7.65805 | + | 7.65805i | −0.299912 | + | 0.299912i | ||||
\(653\) | 6.38197 | − | 6.38197i | 0.249746 | − | 0.249746i | −0.571120 | − | 0.820866i | \(-0.693491\pi\) |
0.820866 | + | 0.571120i | \(0.193491\pi\) | |||||||
\(654\) | 30.6748 | − | 7.14067i | 1.19948 | − | 0.279222i | ||||
\(655\) | −16.5967 | −0.648486 | ||||||||
\(656\) | −12.1119 | −0.472891 | ||||||||
\(657\) | −14.6405 | − | 29.7422i | −0.571180 | − | 1.16035i | ||||
\(658\) | −1.89634 | − | 1.89634i | −0.0739270 | − | 0.0739270i | ||||
\(659\) | 40.6095 | 1.58192 | 0.790960 | − | 0.611867i | \(-0.209581\pi\) | ||||
0.790960 | + | 0.611867i | \(0.209581\pi\) | |||||||
\(660\) | −4.77308 | − | 2.97049i | −0.185792 | − | 0.115626i | ||||
\(661\) | 18.2484 | + | 18.2484i | 0.709782 | + | 0.709782i | 0.966489 | − | 0.256707i | \(-0.0826375\pi\) |
−0.256707 | + | 0.966489i | \(0.582637\pi\) | |||||||
\(662\) | 22.5172i | 0.875158i | ||||||||
\(663\) | 5.89324 | + | 25.3162i | 0.228875 | + | 0.983198i | ||||
\(664\) | 4.43238 | − | 4.43238i | 0.172010 | − | 0.172010i | ||||
\(665\) | 2.77433 | 0.107584 | ||||||||
\(666\) | 18.2453 | − | 0.329742i | 0.706991 | − | 0.0127772i | ||||
\(667\) | 0.0923973 | 0.00357764 | ||||||||
\(668\) | −12.4791 | + | 12.4791i | −0.482833 | + | 0.482833i | ||||
\(669\) | 2.42805 | + | 10.4304i | 0.0938738 | + | 0.403263i | ||||
\(670\) | − | 7.74070i | − | 0.299049i | ||||||
\(671\) | −21.5729 | − | 21.5729i | −0.832811 | − | 0.832811i | ||||
\(672\) | 1.28483 | + | 0.799603i | 0.0495633 | + | 0.0308453i | ||||
\(673\) | 43.2033 | 1.66536 | 0.832682 | − | 0.553752i | \(-0.186804\pi\) | ||||
0.832682 | + | 0.553752i | \(0.186804\pi\) | |||||||
\(674\) | −4.50031 | − | 4.50031i | −0.173346 | − | 0.173346i | ||||
\(675\) | 4.02026 | − | 3.29204i | 0.154740 | − | 0.126711i | ||||
\(676\) | −2.68718 | −0.103353 | ||||||||
\(677\) | −20.8361 | −0.800797 | −0.400399 | − | 0.916341i | \(-0.631128\pi\) | ||||
−0.400399 | + | 0.916341i | \(0.631128\pi\) | |||||||
\(678\) | −7.39616 | + | 1.72172i | −0.284048 | + | 0.0661223i | ||||
\(679\) | −6.25014 | + | 6.25014i | −0.239859 | + | 0.239859i | ||||
\(680\) | −2.67922 | + | 2.67922i | −0.102744 | + | 0.102744i | ||||
\(681\) | −21.9290 | + | 35.2362i | −0.840320 | + | 1.35025i | ||||
\(682\) | 23.8773 | 0.914310 | ||||||||
\(683\) | −28.5744 | − | 28.5744i | −1.09337 | − | 1.09337i | −0.995166 | − | 0.0982022i | \(-0.968691\pi\) |
−0.0982022 | − | 0.995166i | \(-0.531309\pi\) | |||||||
\(684\) | 9.01817 | + | 3.06854i | 0.344818 | + | 0.117328i | ||||
\(685\) | 15.0812 | − | 15.0812i | 0.576223 | − | 0.576223i | ||||
\(686\) | 8.17774 | − | 8.17774i | 0.312228 | − | 0.312228i | ||||
\(687\) | 2.76994 | + | 11.8991i | 0.105680 | + | 0.453979i | ||||
\(688\) | −8.06425 | + | 8.06425i | −0.307447 | + | 0.307447i | ||||
\(689\) | 25.7019 | + | 25.7019i | 0.979164 | + | 0.979164i | ||||
\(690\) | 5.09728 | − | 8.19049i | 0.194050 | − | 0.311807i | ||||
\(691\) | 34.9094i | 1.32802i | 0.747725 | + | 0.664008i | \(0.231146\pi\) | ||||
−0.747725 | + | 0.664008i | \(0.768854\pi\) | |||||||
\(692\) | − | 9.17456i | − | 0.348765i | ||||||
\(693\) | 7.63314 | − | 3.75738i | 0.289959 | − | 0.142731i | ||||
\(694\) | 15.7687i | 0.598571i | ||||||||
\(695\) | 10.3366 | − | 10.3366i | 0.392091 | − | 0.392091i | ||||
\(696\) | −0.00651450 | − | 0.0279850i | −0.000246932 | − | 0.00106077i | ||||
\(697\) | 32.4506 | + | 32.4506i | 1.22915 | + | 1.22915i | ||||
\(698\) | −3.76544 | + | 3.76544i | −0.142524 | + | 0.142524i | ||||
\(699\) | 1.75178 | + | 7.52530i | 0.0662585 | + | 0.284633i | ||||
\(700\) | −0.873718 | −0.0330234 | ||||||||
\(701\) | −5.73772 | − | 5.73772i | −0.216711 | − | 0.216711i | 0.590400 | − | 0.807111i | \(-0.298970\pi\) |
−0.807111 | + | 0.590400i | \(0.798970\pi\) | |||||||
\(702\) | −15.9230 | + | 13.0388i | −0.600977 | + | 0.492118i | ||||
\(703\) | −17.4803 | − | 8.21559i | −0.659281 | − | 0.309857i | ||||
\(704\) | 3.24582i | 0.122332i | ||||||||
\(705\) | 4.51371 | + | 2.80907i | 0.169996 | + | 0.105796i | ||||
\(706\) | − | 2.49504i | − | 0.0939022i | ||||||
\(707\) | 8.62354 | 0.324322 | ||||||||
\(708\) | −16.5545 | − | 10.3026i | −0.622158 | − | 0.387195i | ||||
\(709\) | −18.6081 | + | 18.6081i | −0.698842 | + | 0.698842i | −0.964161 | − | 0.265319i | \(-0.914523\pi\) |
0.265319 | + | 0.964161i | \(0.414523\pi\) | |||||||
\(710\) | 0.580983i | 0.0218039i | ||||||||
\(711\) | −1.04353 | + | 3.06685i | −0.0391354 | + | 0.115016i | ||||
\(712\) | 9.18420 | 0.344192 | ||||||||
\(713\) | 40.9729i | 1.53445i | ||||||||
\(714\) | −1.30003 | − | 5.58466i | −0.0486524 | − | 0.209001i | ||||
\(715\) | −12.8557 | −0.480778 | ||||||||
\(716\) | 10.0110 | + | 10.0110i | 0.374129 | + | 0.374129i | ||||
\(717\) | 22.0984 | − | 35.5084i | 0.825279 | − | 1.32609i | ||||
\(718\) | −22.1193 | − | 22.1193i | −0.825483 | − | 0.825483i | ||||
\(719\) | 18.6694i | 0.696252i | 0.937448 | + | 0.348126i | \(0.113182\pi\) | ||||
−0.937448 | + | 0.348126i | \(0.886818\pi\) | |||||||
\(720\) | −2.84009 | − | 0.966374i | −0.105844 | − | 0.0360146i | ||||
\(721\) | 4.19747 | + | 4.19747i | 0.156322 | + | 0.156322i | ||||
\(722\) | 6.30556 | + | 6.30556i | 0.234669 | + | 0.234669i | ||||
\(723\) | −7.90055 | − | 4.91684i | −0.293825 | − | 0.182859i | ||||
\(724\) | 22.6754i | 0.842724i | ||||||||
\(725\) | 0.0117303 | + | 0.0117303i | 0.000435652 | + | 0.000435652i | ||||
\(726\) | −0.683252 | − | 0.425216i | −0.0253579 | − | 0.0157813i | ||||
\(727\) | 20.9335 | + | 20.9335i | 0.776381 | + | 0.776381i | 0.979213 | − | 0.202833i | \(-0.0650147\pi\) |
−0.202833 | + | 0.979213i | \(0.565015\pi\) | |||||||
\(728\) | 3.46054 | 0.128256 | ||||||||
\(729\) | −5.32492 | + | 26.4697i | −0.197219 | + | 0.980359i | ||||
\(730\) | − | 11.0501i | − | 0.408983i | ||||||
\(731\) | 43.2119 | 1.59825 | ||||||||
\(732\) | −13.8220 | − | 8.60203i | −0.510877 | − | 0.317940i | ||||
\(733\) | 45.5805i | 1.68355i | 0.539825 | + | 0.841777i | \(0.318490\pi\) | ||||
−0.539825 | + | 0.841777i | \(0.681510\pi\) | |||||||
\(734\) | 6.94207 | − | 6.94207i | 0.256237 | − | 0.256237i | ||||
\(735\) | −5.70758 | + | 9.17113i | −0.210527 | + | 0.338282i | ||||
\(736\) | −5.56975 | −0.205304 | ||||||||
\(737\) | 25.1249i | 0.925489i | ||||||||
\(738\) | −11.7047 | + | 34.3990i | −0.430854 | + | 1.26624i | ||||
\(739\) | − | 30.7839i | − | 1.13240i | −0.824267 | − | 0.566202i | \(-0.808412\pi\) | ||
0.824267 | − | 0.566202i | \(-0.191588\pi\) | |||||||
\(740\) | 5.50506 | + | 2.58734i | 0.202370 | + | 0.0951124i | ||||
\(741\) | 21.2158 | − | 4.93874i | 0.779383 | − | 0.181429i | ||||
\(742\) | −5.66975 | − | 5.66975i | −0.208143 | − | 0.208143i | ||||
\(743\) | −5.50584 | −0.201990 | −0.100995 | − | 0.994887i | \(-0.532203\pi\) | ||||
−0.100995 | + | 0.994887i | \(0.532203\pi\) | |||||||
\(744\) | 12.4097 | − | 2.88881i | 0.454963 | − | 0.105909i | ||||
\(745\) | −3.02618 | + | 3.02618i | −0.110871 | + | 0.110871i | ||||
\(746\) | −15.6553 | − | 15.6553i | −0.573181 | − | 0.573181i | ||||
\(747\) | −8.30503 | − | 16.8717i | −0.303865 | − | 0.617303i | ||||
\(748\) | 8.69629 | − | 8.69629i | 0.317968 | − | 0.317968i | ||||
\(749\) | 12.8618i | 0.469962i | ||||||||
\(750\) | 1.68695 | − | 0.392697i | 0.0615986 | − | 0.0143393i | ||||
\(751\) | − | 45.1238i | − | 1.64659i | −0.567613 | − | 0.823295i | \(-0.692133\pi\) | ||
0.567613 | − | 0.823295i | \(-0.307867\pi\) | |||||||
\(752\) | − | 3.06944i | − | 0.111931i | ||||||
\(753\) | −5.40440 | − | 3.36339i | −0.196947 | − | 0.122569i | ||||
\(754\) | −0.0464602 | − | 0.0464602i | −0.00169198 | − | 0.00169198i | ||||
\(755\) | −11.5029 | + | 11.5029i | −0.418633 | + | 0.418633i | ||||
\(756\) | 3.51257 | − | 2.87632i | 0.127751 | − | 0.104611i | ||||
\(757\) | 14.1289 | − | 14.1289i | 0.513524 | − | 0.513524i | −0.402080 | − | 0.915605i | \(-0.631713\pi\) |
0.915605 | + | 0.402080i | \(0.131713\pi\) | |||||||
\(758\) | −4.21515 | + | 4.21515i | −0.153101 | + | 0.153101i | ||||
\(759\) | −16.5449 | + | 26.5849i | −0.600541 | + | 0.964970i | ||||
\(760\) | 2.24528 | + | 2.24528i | 0.0814450 | + | 0.0814450i | ||||
\(761\) | −0.980959 | −0.0355597 | −0.0177799 | − | 0.999842i | \(-0.505660\pi\) | ||||
−0.0177799 | + | 0.999842i | \(0.505660\pi\) | |||||||
\(762\) | −1.39545 | − | 0.868444i | −0.0505517 | − | 0.0314604i | ||||
\(763\) | −11.2341 | + | 11.2341i | −0.406701 | + | 0.406701i | ||||
\(764\) | 6.59688 | − | 6.59688i | 0.238667 | − | 0.238667i | ||||
\(765\) | 5.02011 | + | 10.1984i | 0.181502 | + | 0.368723i | ||||
\(766\) | 12.9676 | 0.468538 | ||||||||
\(767\) | −44.5878 | −1.60997 | ||||||||
\(768\) | 0.392697 | + | 1.68695i | 0.0141702 | + | 0.0608724i | ||||
\(769\) | −5.20667 | − | 5.20667i | −0.187757 | − | 0.187757i | 0.606968 | − | 0.794726i | \(-0.292385\pi\) |
−0.794726 | + | 0.606968i | \(0.792385\pi\) | |||||||
\(770\) | 2.83593 | 0.102200 | ||||||||
\(771\) | −16.9594 | + | 27.2509i | −0.610776 | + | 0.981416i | ||||
\(772\) | 0.721641 | + | 0.721641i | 0.0259724 | + | 0.0259724i | ||||
\(773\) | 19.8914i | 0.715444i | 0.933828 | + | 0.357722i | \(0.116446\pi\) | ||||
−0.933828 | + | 0.357722i | \(0.883554\pi\) | |||||||
\(774\) | 15.1101 | + | 30.6963i | 0.543123 | + | 1.10336i | ||||
\(775\) | −5.20171 | + | 5.20171i | −0.186851 | + | 0.186851i | ||||
\(776\) | −10.1166 | −0.363164 | ||||||||
\(777\) | −7.72614 | + | 5.00422i | −0.277174 | + | 0.179525i | ||||
\(778\) | −9.05477 | −0.324629 | ||||||||
\(779\) | 27.1947 | − | 27.1947i | 0.974352 | − | 0.974352i | ||||
\(780\) | −6.68150 | + | 1.55536i | −0.239236 | + | 0.0556907i | ||||
\(781\) | − | 1.88577i | − | 0.0674781i | ||||||
\(782\) | 14.9226 | + | 14.9226i | 0.533631 | + | 0.533631i | ||||
\(783\) | −0.0857753 | − | 0.00854215i | −0.00306536 | − | 0.000305272i | ||||
\(784\) | 6.23662 | 0.222736 | ||||||||
\(785\) | 13.0527 | + | 13.0527i | 0.465871 | + | 0.465871i | ||||
\(786\) | 27.9977 | − | 6.51747i | 0.998646 | − | 0.232471i | ||||
\(787\) | −8.14992 | −0.290513 | −0.145257 | − | 0.989394i | \(-0.546401\pi\) | ||||
−0.145257 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(788\) | 14.8081 | 0.527518 | ||||||||
\(789\) | 1.49209 | + | 6.40972i | 0.0531199 | + | 0.228192i | ||||
\(790\) | −0.763562 | + | 0.763562i | −0.0271663 | + | 0.0271663i | ||||
\(791\) | 2.70870 | − | 2.70870i | 0.0963104 | − | 0.0963104i | ||||
\(792\) | 9.21844 | + | 3.13668i | 0.327563 | + | 0.111457i | ||||
\(793\) | −37.2281 | −1.32201 | ||||||||
\(794\) | −1.62045 | − | 1.62045i | −0.0575075 | − | 0.0575075i | ||||
\(795\) | 13.4953 | + | 8.39867i | 0.478628 | + | 0.297870i | ||||
\(796\) | −15.3316 | + | 15.3316i | −0.543413 | + | 0.543413i | ||||
\(797\) | 10.4496 | − | 10.4496i | 0.370146 | − | 0.370146i | −0.497385 | − | 0.867530i | \(-0.665706\pi\) |
0.867530 | + | 0.497385i | \(0.165706\pi\) | |||||||
\(798\) | −4.68014 | + | 1.08947i | −0.165675 | + | 0.0385668i | ||||
\(799\) | −8.22373 | + | 8.22373i | −0.290935 | + | 0.290935i | ||||
\(800\) | −0.707107 | − | 0.707107i | −0.0250000 | − | 0.0250000i | ||||
\(801\) | 8.87537 | − | 26.0840i | 0.313596 | − | 0.921632i | ||||
\(802\) | 25.3958i | 0.896756i | ||||||||
\(803\) | 35.8667i | 1.26571i | ||||||||
\(804\) | 3.03975 | + | 13.0581i | 0.107204 | + | 0.460525i | ||||
\(805\) | 4.86639i | 0.171518i | ||||||||
\(806\) | 20.6024 | − | 20.6024i | 0.725689 | − | 0.725689i | ||||
\(807\) | 21.1508 | − | 4.92360i | 0.744543 | − | 0.173319i | ||||
\(808\) | 6.97910 | + | 6.97910i | 0.245524 | + | 0.245524i | ||||
\(809\) | 13.8558 | − | 13.8558i | 0.487143 | − | 0.487143i | −0.420260 | − | 0.907404i | \(-0.638061\pi\) |
0.907404 | + | 0.420260i | \(0.138061\pi\) | |||||||
\(810\) | −5.48918 | + | 7.13224i | −0.192870 | + | 0.250601i | ||||
\(811\) | −8.21906 | −0.288610 | −0.144305 | − | 0.989533i | \(-0.546095\pi\) | ||||
−0.144305 | + | 0.989533i | \(0.546095\pi\) | |||||||
\(812\) | 0.0102490 | + | 0.0102490i | 0.000359668 | + | 0.000359668i | ||||
\(813\) | −6.65857 | − | 28.6038i | −0.233526 | − | 1.00318i | ||||
\(814\) | −17.8685 | − | 8.39804i | −0.626289 | − | 0.294351i | ||||
\(815\) | 10.8301i | 0.379362i | ||||||||
\(816\) | 3.46758 | − | 5.57183i | 0.121390 | − | 0.195053i | ||||
\(817\) | − | 36.2131i | − | 1.26693i | ||||||
\(818\) | 3.90020 | 0.136367 | ||||||||
\(819\) | 3.34417 | − | 9.82825i | 0.116855 | − | 0.343427i | ||||
\(820\) | −8.56443 | + | 8.56443i | −0.299083 | + | 0.299083i | ||||
\(821\) | − | 31.5158i | − | 1.09991i | −0.835194 | − | 0.549955i | \(-0.814645\pi\) | ||
0.835194 | − | 0.549955i | \(-0.185355\pi\) | |||||||
\(822\) | −19.5188 | + | 31.3635i | −0.680798 | + | 1.09393i | ||||
\(823\) | 2.89732 | 0.100994 | 0.0504971 | − | 0.998724i | \(-0.483919\pi\) | ||||
0.0504971 | + | 0.998724i | \(0.483919\pi\) | |||||||
\(824\) | 6.79409i | 0.236683i | ||||||||
\(825\) | −5.47553 | + | 1.27463i | −0.190634 | + | 0.0443768i | ||||
\(826\) | 9.83591 | 0.342235 | ||||||||
\(827\) | −19.0188 | − | 19.0188i | −0.661348 | − | 0.661348i | 0.294350 | − | 0.955698i | \(-0.404897\pi\) |
−0.955698 | + | 0.294350i | \(0.904897\pi\) | |||||||
\(828\) | −5.38246 | + | 15.8186i | −0.187053 | + | 0.549734i | ||||
\(829\) | 38.2891 | + | 38.2891i | 1.32984 | + | 1.32984i | 0.905509 | + | 0.424328i | \(0.139490\pi\) |
0.424328 | + | 0.905509i | \(0.360510\pi\) | |||||||
\(830\) | − | 6.26833i | − | 0.217577i | ||||||
\(831\) | −17.7579 | + | 28.5340i | −0.616015 | + | 0.989834i | ||||
\(832\) | 2.80064 | + | 2.80064i | 0.0970948 | + | 0.0970948i | ||||
\(833\) | −16.7093 | − | 16.7093i | −0.578943 | − | 0.578943i | ||||
\(834\) | −13.3782 | + | 21.4965i | −0.463249 | + | 0.744364i | ||||
\(835\) | 17.6482i | 0.610740i | ||||||||
\(836\) | −7.28779 | − | 7.28779i | −0.252054 | − | 0.252054i | ||||
\(837\) | 3.78795 | − | 38.0364i | 0.130931 | − | 1.31473i | ||||
\(838\) | −6.97893 | − | 6.97893i | −0.241083 | − | 0.241083i | ||||
\(839\) | −28.1427 | −0.971595 | −0.485797 | − | 0.874071i | \(-0.661471\pi\) | ||||
−0.485797 | + | 0.874071i | \(0.661471\pi\) | |||||||
\(840\) | 1.47392 | − | 0.343107i | 0.0508549 | − | 0.0118383i | ||||
\(841\) | 28.9997i | 0.999991i | ||||||||
\(842\) | −7.91851 | −0.272890 | ||||||||
\(843\) | −21.3175 | + | 34.2537i | −0.734215 | + | 1.17976i | ||||
\(844\) | 14.8756i | 0.512039i | ||||||||
\(845\) | −1.90012 | + | 1.90012i | −0.0653662 | + | 0.0653662i | ||||
\(846\) | −8.71750 | − | 2.96623i | −0.299714 | − | 0.101981i | ||||
\(847\) | 0.405955 | 0.0139488 | ||||||||
\(848\) | − | 9.17714i | − | 0.315144i | ||||||
\(849\) | 0.592072 | − | 0.951362i | 0.0203199 | − | 0.0326506i | ||||
\(850\) | 3.78900i | 0.129961i | ||||||||
\(851\) | 14.4108 | − | 30.6618i | 0.493996 | − | 1.05107i | ||||
\(852\) | −0.228151 | − | 0.980088i | −0.00781631 | − | 0.0335773i | ||||
\(853\) | 15.2906 | + | 15.2906i | 0.523541 | + | 0.523541i | 0.918639 | − | 0.395098i | \(-0.129289\pi\) |
−0.395098 | + | 0.918639i | \(0.629289\pi\) | |||||||
\(854\) | 8.21239 | 0.281022 | ||||||||
\(855\) | 8.54659 | − | 4.20703i | 0.292287 | − | 0.143877i | ||||
\(856\) | −10.4092 | + | 10.4092i | −0.355779 | + | 0.355779i | ||||
\(857\) | 11.5743 | + | 11.5743i | 0.395369 | + | 0.395369i | 0.876596 | − | 0.481227i | \(-0.159809\pi\) |
−0.481227 | + | 0.876596i | \(0.659809\pi\) | |||||||
\(858\) | 21.6870 | − | 5.04842i | 0.740381 | − | 0.172350i | ||||
\(859\) | 9.96139 | − | 9.96139i | 0.339878 | − | 0.339878i | −0.516443 | − | 0.856321i | \(-0.672744\pi\) |
0.856321 | + | 0.516443i | \(0.172744\pi\) | |||||||
\(860\) | 11.4046i | 0.388893i | ||||||||
\(861\) | −4.15568 | − | 17.8520i | −0.141625 | − | 0.608393i | ||||
\(862\) | 22.7714i | 0.775598i | ||||||||
\(863\) | − | 35.5287i | − | 1.20941i | −0.796450 | − | 0.604705i | \(-0.793291\pi\) | ||
0.796450 | − | 0.604705i | \(-0.206709\pi\) | |||||||
\(864\) | 5.17058 | + | 0.514925i | 0.175907 | + | 0.0175181i | ||||
\(865\) | −6.48740 | − | 6.48740i | −0.220578 | − | 0.220578i | ||||
\(866\) | 22.8662 | − | 22.8662i | 0.777027 | − | 0.777027i | ||||
\(867\) | 4.45947 | − | 1.03810i | 0.151452 | − | 0.0352558i | ||||
\(868\) | −4.54482 | + | 4.54482i | −0.154261 | + | 0.154261i | ||||
\(869\) | 2.47839 | − | 2.47839i | 0.0840736 | − | 0.0840736i | ||||
\(870\) | −0.0243948 | − | 0.0151819i | −0.000827061 | − | 0.000514715i | ||||
\(871\) | 21.6789 | + | 21.6789i | 0.734562 | + | 0.734562i | ||||
\(872\) | −18.1836 | −0.615776 | ||||||||
\(873\) | −9.77640 | + | 28.7320i | −0.330881 | + | 0.972431i | ||||
\(874\) | 12.5057 | − | 12.5057i | 0.423010 | − | 0.423010i | ||||
\(875\) | −0.617812 | + | 0.617812i | −0.0208859 | + | 0.0208859i | ||||
\(876\) | 4.33935 | + | 18.6409i | 0.146613 | + | 0.629819i | ||||
\(877\) | −20.3035 | −0.685599 | −0.342800 | − | 0.939409i | \(-0.611375\pi\) | ||||
−0.342800 | + | 0.939409i | \(0.611375\pi\) | |||||||
\(878\) | 26.5843 | 0.897177 | ||||||||
\(879\) | −10.9460 | + | 2.54808i | −0.369200 | + | 0.0859445i | ||||
\(880\) | 2.29514 | + | 2.29514i | 0.0773693 | + | 0.0773693i | ||||
\(881\) | −6.22716 | −0.209798 | −0.104899 | − | 0.994483i | \(-0.533452\pi\) | ||||
−0.104899 | + | 0.994483i | \(0.533452\pi\) | |||||||
\(882\) | 6.02690 | − | 17.7126i | 0.202936 | − | 0.596413i | ||||
\(883\) | −23.8218 | − | 23.8218i | −0.801669 | − | 0.801669i | 0.181687 | − | 0.983356i | \(-0.441844\pi\) |
−0.983356 | + | 0.181687i | \(0.941844\pi\) | |||||||
\(884\) | − | 15.0071i | − | 0.504743i | ||||||
\(885\) | −18.9909 | + | 4.42080i | −0.638371 | + | 0.148604i | ||||
\(886\) | −9.98191 | + | 9.98191i | −0.335349 | + | 0.335349i | ||||
\(887\) | −43.3246 | −1.45470 | −0.727350 | − | 0.686267i | \(-0.759248\pi\) | ||||
−0.727350 | + | 0.686267i | \(0.759248\pi\) | |||||||
\(888\) | −10.3028 | − | 2.20288i | −0.345739 | − | 0.0739237i | ||||
\(889\) | 0.829106 | 0.0278073 | ||||||||
\(890\) | 6.49421 | − | 6.49421i | 0.217686 | − | 0.217686i | ||||
\(891\) | 17.8169 | − | 23.1500i | 0.596889 | − | 0.775554i | ||||
\(892\) | − | 6.18301i | − | 0.207022i | ||||||
\(893\) | 6.89177 | + | 6.89177i | 0.230624 | + | 0.230624i | ||||
\(894\) | 3.91663 | − | 6.29338i | 0.130992 | − | 0.210482i | ||||
\(895\) | 14.1577 | 0.473239 | ||||||||
\(896\) | −0.617812 | − | 0.617812i | −0.0206396 | − | 0.0206396i | ||||
\(897\) | 8.66295 | + | 37.2143i | 0.289248 | + | 1.24255i | ||||
\(898\) | 9.80260 | 0.327117 | ||||||||
\(899\) | 0.122035 | 0.00407009 | ||||||||
\(900\) | −2.69158 | + | 1.32492i | −0.0897193 | + | 0.0441640i | ||||
\(901\) | −24.5876 | + | 24.5876i | −0.819132 | + | 0.819132i | ||||
\(902\) | 27.7986 | − | 27.7986i | 0.925593 | − | 0.925593i | ||||
\(903\) | −14.6529 | − | 9.11913i | −0.487619 | − | 0.303466i | ||||
\(904\) | 4.38435 | 0.145821 | ||||||||
\(905\) | 16.0339 | + | 16.0339i | 0.532985 | + | 0.532985i | ||||
\(906\) | 14.8876 | − | 23.9219i | 0.494608 | − | 0.794752i | ||||
\(907\) | −12.4807 | + | 12.4807i | −0.414413 | + | 0.414413i | −0.883273 | − | 0.468859i | \(-0.844665\pi\) |
0.468859 | + | 0.883273i | \(0.344665\pi\) | |||||||
\(908\) | 16.9434 | − | 16.9434i | 0.562286 | − | 0.562286i | ||||
\(909\) | 26.5657 | − | 13.0769i | 0.881128 | − | 0.433732i | ||||
\(910\) | 2.44697 | − | 2.44697i | 0.0811163 | − | 0.0811163i | ||||
\(911\) | −35.6884 | − | 35.6884i | −1.18241 | − | 1.18241i | −0.979118 | − | 0.203291i | \(-0.934836\pi\) |
−0.203291 | − | 0.979118i | \(-0.565164\pi\) | |||||||
\(912\) | −4.66939 | − | 2.90596i | −0.154619 | − | 0.0962258i | ||||
\(913\) | 20.3459i | 0.673351i | ||||||||
\(914\) | − | 20.9337i | − | 0.692425i | ||||||
\(915\) | −15.8562 | + | 3.69110i | −0.524190 | + | 0.122024i | ||||
\(916\) | − | 7.05363i | − | 0.233058i | ||||||
\(917\) | −10.2536 | + | 10.2536i | −0.338605 | + | 0.338605i | ||||
\(918\) | −12.4735 | − | 15.2327i | −0.411688 | − | 0.502755i | ||||
\(919\) | 10.4021 | + | 10.4021i | 0.343134 | + | 0.343134i | 0.857544 | − | 0.514411i | \(-0.171989\pi\) |
−0.514411 | + | 0.857544i | \(0.671989\pi\) | |||||||
\(920\) | −3.93841 | + | 3.93841i | −0.129845 | + | 0.129845i | ||||
\(921\) | 8.13364 | − | 1.89340i | 0.268013 | − | 0.0623895i | ||||
\(922\) | −7.68326 | −0.253035 | ||||||||
\(923\) | −1.62713 | − | 1.62713i | −0.0535575 | − | 0.0535575i | ||||
\(924\) | −4.78407 | + | 1.11366i | −0.157384 | + | 0.0366368i | ||||
\(925\) | 5.72219 | − | 2.06314i | 0.188144 | − | 0.0678357i | ||||
\(926\) | 1.61515i | 0.0530773i | ||||||||
\(927\) | 19.2958 | + | 6.56563i | 0.633758 | + | 0.215644i | ||||
\(928\) | 0.0165891i | 0.000544565i | ||||||||
\(929\) | 16.9964 | 0.557632 | 0.278816 | − | 0.960344i | \(-0.410058\pi\) | ||||
0.278816 | + | 0.960344i | \(0.410058\pi\) | |||||||
\(930\) | 6.73230 | − | 10.8177i | 0.220761 | − | 0.354726i | ||||
\(931\) | −14.0030 | + | 14.0030i | −0.458929 | + | 0.458929i | ||||
\(932\) | − | 4.46090i | − | 0.146122i | ||||||
\(933\) | −13.4213 | − | 8.35263i | −0.439393 | − | 0.273453i | ||||
\(934\) | 11.9384 | 0.390636 | ||||||||
\(935\) | − | 12.2984i | − | 0.402201i | ||||||
\(936\) | 10.6605 | − | 5.24761i | 0.348451 | − | 0.171524i | ||||
\(937\) | −18.6700 | −0.609923 | −0.304961 | − | 0.952365i | \(-0.598644\pi\) | ||||
−0.304961 | + | 0.952365i | \(0.598644\pi\) | |||||||
\(938\) | −4.78230 | − | 4.78230i | −0.156147 | − | 0.156147i | ||||
\(939\) | −49.1615 | − | 30.5953i | −1.60433 | − | 0.998439i | ||||
\(940\) | −2.17042 | − | 2.17042i | −0.0707914 | − | 0.0707914i | ||||
\(941\) | − | 16.2052i | − | 0.528275i | −0.964485 | − | 0.264137i | \(-0.914913\pi\) | ||
0.964485 | − | 0.264137i | \(-0.0850872\pi\) | |||||||
\(942\) | −27.1450 | − | 16.8935i | −0.884432 | − | 0.550419i | ||||
\(943\) | 47.7017 | + | 47.7017i | 1.55338 | + | 1.55338i | ||||
\(944\) | 7.96028 | + | 7.96028i | 0.259085 | + | 0.259085i | ||||
\(945\) | 0.449899 | − | 4.51762i | 0.0146352 | − | 0.146958i | ||||
\(946\) | − | 37.0172i | − | 1.20353i | ||||||
\(947\) | 30.9113 | + | 30.9113i | 1.00448 | + | 1.00448i | 0.999990 | + | 0.00449357i | \(0.00143035\pi\) |
0.00449357 | + | 0.999990i | \(0.498570\pi\) | |||||||
\(948\) | 0.988240 | − | 1.58794i | 0.0320965 | − | 0.0515738i | ||||
\(949\) | 30.9474 | + | 30.9474i | 1.00459 | + | 1.00459i | ||||
\(950\) | 3.17531 | 0.103021 | ||||||||
\(951\) | −1.07370 | − | 4.61241i | −0.0348172 | − | 0.149568i | ||||
\(952\) | 3.31051i | 0.107294i | ||||||||
\(953\) | −60.8196 | −1.97014 | −0.985070 | − | 0.172157i | \(-0.944926\pi\) | ||||
−0.985070 | + | 0.172157i | \(0.944926\pi\) | |||||||
\(954\) | −26.0639 | − | 8.86855i | −0.843851 | − | 0.287130i | ||||
\(955\) | − | 9.32939i | − | 0.301892i | ||||||
\(956\) | −17.0743 | + | 17.0743i | −0.552222 | + | 0.552222i | ||||
\(957\) | 0.0791812 | + | 0.0492778i | 0.00255957 | + | 0.00159292i | ||||
\(958\) | −13.7325 | −0.443677 | ||||||||
\(959\) | − | 18.6347i | − | 0.601746i | ||||||
\(960\) | 1.47053 | + | 0.915172i | 0.0474612 | + | 0.0295371i | ||||
\(961\) | 23.1155i | 0.745661i | ||||||||
\(962\) | −22.6639 | + | 8.17150i | −0.730713 | + | 0.263460i | ||||
\(963\) | 19.5039 | + | 39.6222i | 0.628504 | + | 1.27681i | ||||
\(964\) | 3.79899 | + | 3.79899i | 0.122357 | + | 0.122357i | ||||
\(965\) | 1.02055 | 0.0328528 | ||||||||
\(966\) | −1.91102 | − | 8.20934i | −0.0614860 | − | 0.264131i | ||||
\(967\) | −32.1280 | + | 32.1280i | −1.03317 | + | 1.03317i | −0.0337345 | + | 0.999431i | \(0.510740\pi\) |
−0.999431 | + | 0.0337345i | \(0.989260\pi\) | |||||||
\(968\) | 0.328543 | + | 0.328543i | 0.0105598 | + | 0.0105598i | ||||
\(969\) | 4.72463 | + | 20.2960i | 0.151777 | + | 0.652003i | ||||
\(970\) | −7.15350 | + | 7.15350i | −0.229685 | + | 0.229685i | ||||
\(971\) | 46.3264i | 1.48668i | 0.668911 | + | 0.743342i | \(0.266761\pi\) | ||||
−0.668911 | + | 0.743342i | \(0.733239\pi\) | |||||||
\(972\) | 6.45914 | − | 14.1873i | 0.207177 | − | 0.455058i | ||||
\(973\) | − | 12.7722i | − | 0.409458i | ||||||
\(974\) | 5.48079i | 0.175616i | ||||||||
\(975\) | −3.62473 | + | 5.82434i | −0.116084 | + | 0.186528i | ||||
\(976\) | 6.64635 | + | 6.64635i | 0.212744 | + | 0.212744i | ||||
\(977\) | 20.5956 | − | 20.5956i | 0.658912 | − | 0.658912i | −0.296211 | − | 0.955123i | \(-0.595723\pi\) |
0.955123 | + | 0.296211i | \(0.0957230\pi\) | |||||||
\(978\) | −4.25296 | − | 18.2698i | −0.135995 | − | 0.584205i | ||||
\(979\) | −21.0791 | + | 21.0791i | −0.673690 | + | 0.673690i | ||||
\(980\) | 4.40995 | − | 4.40995i | 0.140871 | − | 0.140871i | ||||
\(981\) | −17.5722 | + | 51.6432i | −0.561037 | + | 1.64884i | ||||
\(982\) | −26.5826 | − | 26.5826i | −0.848284 | − | 0.848284i | ||||
\(983\) | 5.10058 | 0.162683 | 0.0813416 | − | 0.996686i | \(-0.474080\pi\) | ||||
0.0813416 | + | 0.996686i | \(0.474080\pi\) | |||||||
\(984\) | 11.0845 | − | 17.8110i | 0.353361 | − | 0.567793i | ||||
\(985\) | 10.4709 | − | 10.4709i | 0.333632 | − | 0.333632i | ||||
\(986\) | 0.0444460 | − | 0.0444460i | 0.00141545 | − | 0.00141545i | ||||
\(987\) | 4.52410 | − | 1.05315i | 0.144004 | − | 0.0335220i | ||||
\(988\) | −12.5765 | −0.400111 | ||||||||
\(989\) | 63.5206 | 2.01984 | ||||||||
\(990\) | 8.73639 | − | 4.30045i | 0.277661 | − | 0.136677i | ||||
\(991\) | −37.2894 | − | 37.2894i | −1.18454 | − | 1.18454i | −0.978556 | − | 0.205980i | \(-0.933962\pi\) |
−0.205980 | − | 0.978556i | \(-0.566038\pi\) | |||||||
\(992\) | −7.35632 | −0.233563 | ||||||||
\(993\) | −33.1123 | − | 20.6072i | −1.05079 | − | 0.653949i | ||||
\(994\) | 0.358938 | + | 0.358938i | 0.0113848 | + | 0.0113848i | ||||
\(995\) | 21.6821i | 0.687369i | ||||||||
\(996\) | 2.46156 | + | 10.5743i | 0.0779974 | + | 0.335061i | ||||
\(997\) | −20.2213 | + | 20.2213i | −0.640416 | + | 0.640416i | −0.950658 | − | 0.310242i | \(-0.899590\pi\) |
0.310242 | + | 0.950658i | \(0.399590\pi\) | |||||||
\(998\) | −19.6191 | −0.621031 | ||||||||
\(999\) | −16.2127 | + | 27.1320i | −0.512947 | + | 0.858420i |
(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 | 1110.2.u.f.401.14 | yes | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.f.401.2 | yes | 40 | |
37.6 | odd | 4 | inner | 1110.2.u.f.191.2 | ✓ | 40 | |
111.80 | even | 4 | inner | 1110.2.u.f.191.14 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.f.191.2 | ✓ | 40 | 37.6 | odd | 4 | inner | |
1110.2.u.f.191.14 | yes | 40 | 111.80 | even | 4 | inner | |
1110.2.u.f.401.2 | yes | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.f.401.14 | yes | 40 | 1.1 | even | 1 | trivial |