Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 497.3 | ||
Root | \(-3.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.f.683.3 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.292893 | + | 1.70711i | 0.169102 | + | 0.985599i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.52773 | − | 1.63280i | −0.683220 | − | 0.730213i | ||||
\(6\) | 1.41421 | + | 1.00000i | 0.577350 | + | 0.408248i | ||||
\(7\) | −1.33991 | − | 1.33991i | −0.506439 | − | 0.506439i | 0.406992 | − | 0.913432i | \(-0.366578\pi\) |
−0.913432 | + | 0.406992i | \(0.866578\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | −2.23483 | − | 0.0743018i | −0.706716 | − | 0.0234963i | ||||
\(11\) | 1.30913i | 0.394719i | 0.980331 | + | 0.197360i | \(0.0632366\pi\) | ||||
−0.980331 | + | 0.197360i | \(0.936763\pi\) | |||||||
\(12\) | 1.70711 | − | 0.292893i | 0.492799 | − | 0.0845510i | ||||
\(13\) | −1.74632 | + | 1.74632i | −0.484341 | + | 0.484341i | −0.906515 | − | 0.422174i | \(-0.861267\pi\) |
0.422174 | + | 0.906515i | \(0.361267\pi\) | |||||||
\(14\) | −1.89492 | −0.506439 | ||||||||
\(15\) | 2.33991 | − | 3.08623i | 0.604163 | − | 0.796861i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.36459 | + | 5.36459i | −1.30110 | + | 1.30110i | −0.373456 | + | 0.927648i | \(0.621827\pi\) |
−0.927648 | + | 0.373456i | \(0.878173\pi\) | |||||||
\(18\) | −1.29289 | + | 2.70711i | −0.304738 | + | 0.638071i | ||||
\(19\) | 4.34772i | 0.997435i | 0.866765 | + | 0.498718i | \(0.166196\pi\) | ||||
−0.866765 | + | 0.498718i | \(0.833804\pi\) | |||||||
\(20\) | −1.63280 | + | 1.52773i | −0.365106 | + | 0.341610i | ||||
\(21\) | 1.89492 | − | 2.67982i | 0.413506 | − | 0.584785i | ||||
\(22\) | 0.925698 | + | 0.925698i | 0.197360 | + | 0.197360i | ||||
\(23\) | 4.75413 | + | 4.75413i | 0.991304 | + | 0.991304i | 0.999963 | − | 0.00865885i | \(-0.00275623\pi\) |
−0.00865885 | + | 0.999963i | \(0.502756\pi\) | |||||||
\(24\) | 1.00000 | − | 1.41421i | 0.204124 | − | 0.288675i | ||||
\(25\) | −0.332104 | + | 4.98896i | −0.0664208 | + | 0.997792i | ||||
\(26\) | 2.46967i | 0.484341i | ||||||||
\(27\) | −2.53553 | − | 4.53553i | −0.487964 | − | 0.872864i | ||||
\(28\) | −1.33991 | + | 1.33991i | −0.253220 | + | 0.253220i | ||||
\(29\) | −5.50825 | −1.02286 | −0.511428 | − | 0.859326i | \(-0.670883\pi\) | ||||
−0.511428 | + | 0.859326i | \(0.670883\pi\) | |||||||
\(30\) | −0.527726 | − | 3.83686i | −0.0963492 | − | 0.700512i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −2.23483 | + | 0.383437i | −0.389035 | + | 0.0667478i | ||||
\(34\) | 7.58667i | 1.30110i | ||||||||
\(35\) | −0.140796 | + | 4.23483i | −0.0237989 | + | 0.715817i | ||||
\(36\) | 1.00000 | + | 2.82843i | 0.166667 | + | 0.471405i | ||||
\(37\) | −2.00000 | − | 2.00000i | −0.328798 | − | 0.328798i | 0.523331 | − | 0.852129i | \(-0.324689\pi\) |
−0.852129 | + | 0.523331i | \(0.824689\pi\) | |||||||
\(38\) | 3.07430 | + | 3.07430i | 0.498718 | + | 0.498718i | ||||
\(39\) | −3.49264 | − | 2.46967i | −0.559269 | − | 0.395463i | ||||
\(40\) | −0.0743018 | + | 2.23483i | −0.0117481 | + | 0.353358i | ||||
\(41\) | − | 2.81281i | − | 0.439287i | −0.975580 | − | 0.219644i | \(-0.929511\pi\) | ||
0.975580 | − | 0.219644i | \(-0.0704895\pi\) | |||||||
\(42\) | −0.555010 | − | 3.23483i | −0.0856398 | − | 0.499146i | ||||
\(43\) | 3.50044 | − | 3.50044i | 0.533813 | − | 0.533813i | −0.387892 | − | 0.921705i | \(-0.626797\pi\) |
0.921705 | + | 0.387892i | \(0.126797\pi\) | |||||||
\(44\) | 1.30913 | 0.197360 | ||||||||
\(45\) | 5.95387 | + | 3.09054i | 0.887550 | + | 0.460711i | ||||
\(46\) | 6.72335 | 0.991304 | ||||||||
\(47\) | −3.66790 | + | 3.66790i | −0.535018 | + | 0.535018i | −0.922061 | − | 0.387044i | \(-0.873496\pi\) |
0.387044 | + | 0.922061i | \(0.373496\pi\) | |||||||
\(48\) | −0.292893 | − | 1.70711i | −0.0422755 | − | 0.246400i | ||||
\(49\) | − | 3.40927i | − | 0.487039i | ||||||
\(50\) | 3.29289 | + | 3.76256i | 0.465685 | + | 0.532106i | ||||
\(51\) | −10.7292 | − | 7.58667i | −1.50239 | − | 1.06235i | ||||
\(52\) | 1.74632 | + | 1.74632i | 0.242171 | + | 0.242171i | ||||
\(53\) | −6.45082 | − | 6.45082i | −0.886088 | − | 0.886088i | 0.108057 | − | 0.994145i | \(-0.465537\pi\) |
−0.994145 | + | 0.108057i | \(0.965537\pi\) | |||||||
\(54\) | −5.00000 | − | 1.41421i | −0.680414 | − | 0.192450i | ||||
\(55\) | 2.13756 | − | 2.00000i | 0.288229 | − | 0.269680i | ||||
\(56\) | 1.89492i | 0.253220i | ||||||||
\(57\) | −7.42202 | + | 1.27342i | −0.983071 | + | 0.168668i | ||||
\(58\) | −3.89492 | + | 3.89492i | −0.511428 | + | 0.511428i | ||||
\(59\) | −11.3765 | −1.48110 | −0.740548 | − | 0.672003i | \(-0.765434\pi\) | ||||
−0.740548 | + | 0.672003i | \(0.765434\pi\) | |||||||
\(60\) | −3.08623 | − | 2.33991i | −0.398431 | − | 0.302081i | ||||
\(61\) | 12.5481 | 1.60662 | 0.803309 | − | 0.595562i | \(-0.203071\pi\) | ||||
0.803309 | + | 0.595562i | \(0.203071\pi\) | |||||||
\(62\) | 0.707107 | − | 0.707107i | 0.0898027 | − | 0.0898027i | ||||
\(63\) | 5.12975 | + | 2.44993i | 0.646288 | + | 0.308662i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 5.51929 | + | 0.183501i | 0.684584 | + | 0.0227605i | ||||
\(66\) | −1.30913 | + | 1.85140i | −0.161143 | + | 0.227891i | ||||
\(67\) | 5.52512 | + | 5.52512i | 0.675001 | + | 0.675001i | 0.958865 | − | 0.283864i | \(-0.0916164\pi\) |
−0.283864 | + | 0.958865i | \(0.591616\pi\) | |||||||
\(68\) | 5.36459 | + | 5.36459i | 0.650552 | + | 0.650552i | ||||
\(69\) | −6.72335 | + | 9.50825i | −0.809396 | + | 1.14466i | ||||
\(70\) | 2.89492 | + | 3.09404i | 0.346009 | + | 0.369808i | ||||
\(71\) | − | 10.3477i | − | 1.22805i | −0.789287 | − | 0.614024i | \(-0.789550\pi\) | ||
0.789287 | − | 0.614024i | \(-0.210450\pi\) | |||||||
\(72\) | 2.70711 | + | 1.29289i | 0.319036 | + | 0.152369i | ||||
\(73\) | −1.87025 | + | 1.87025i | −0.218896 | + | 0.218896i | −0.808033 | − | 0.589137i | \(-0.799468\pi\) |
0.589137 | + | 0.808033i | \(0.299468\pi\) | |||||||
\(74\) | −2.82843 | −0.328798 | ||||||||
\(75\) | −8.61396 | + | 0.894295i | −0.994654 | + | 0.103264i | ||||
\(76\) | 4.34772 | 0.498718 | ||||||||
\(77\) | 1.75413 | − | 1.75413i | 0.199901 | − | 0.199901i | ||||
\(78\) | −4.21598 | + | 0.723349i | −0.477366 | + | 0.0819031i | ||||
\(79\) | − | 4.64493i | − | 0.522595i | −0.965258 | − | 0.261298i | \(-0.915850\pi\) | ||
0.965258 | − | 0.261298i | \(-0.0841504\pi\) | |||||||
\(80\) | 1.52773 | + | 1.63280i | 0.170805 | + | 0.182553i | ||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | −1.98896 | − | 1.98896i | −0.219644 | − | 0.219644i | ||||
\(83\) | −11.2871 | − | 11.2871i | −1.23891 | − | 1.23891i | −0.960445 | − | 0.278470i | \(-0.910173\pi\) |
−0.278470 | − | 0.960445i | \(-0.589827\pi\) | |||||||
\(84\) | −2.67982 | − | 1.89492i | −0.292393 | − | 0.206753i | ||||
\(85\) | 16.9549 | + | 0.563703i | 1.83902 | + | 0.0611422i | ||||
\(86\) | − | 4.95037i | − | 0.533813i | ||||||
\(87\) | −1.61333 | − | 9.40317i | −0.172967 | − | 1.00813i | ||||
\(88\) | 0.925698 | − | 0.925698i | 0.0986798 | − | 0.0986798i | ||||
\(89\) | −7.16053 | −0.759015 | −0.379507 | − | 0.925189i | \(-0.623907\pi\) | ||||
−0.379507 | + | 0.925189i | \(0.623907\pi\) | |||||||
\(90\) | 6.39536 | − | 2.02468i | 0.674131 | − | 0.213420i | ||||
\(91\) | 4.67982 | 0.490579 | ||||||||
\(92\) | 4.75413 | − | 4.75413i | 0.495652 | − | 0.495652i | ||||
\(93\) | 0.292893 | + | 1.70711i | 0.0303716 | + | 0.177019i | ||||
\(94\) | 5.18719i | 0.535018i | ||||||||
\(95\) | 7.09898 | − | 6.64213i | 0.728340 | − | 0.681468i | ||||
\(96\) | −1.41421 | − | 1.00000i | −0.144338 | − | 0.102062i | ||||
\(97\) | −1.49632 | − | 1.49632i | −0.151929 | − | 0.151929i | 0.627050 | − | 0.778979i | \(-0.284262\pi\) |
−0.778979 | + | 0.627050i | \(0.784262\pi\) | |||||||
\(98\) | −2.41072 | − | 2.41072i | −0.243519 | − | 0.243519i | ||||
\(99\) | −1.30913 | − | 3.70279i | −0.131573 | − | 0.372145i | ||||
\(100\) | 4.98896 | + | 0.332104i | 0.498896 | + | 0.0332104i | ||||
\(101\) | 13.4647i | 1.33979i | 0.742456 | + | 0.669895i | \(0.233661\pi\) | ||||
−0.742456 | + | 0.669895i | \(0.766339\pi\) | |||||||
\(102\) | −12.9513 | + | 2.22208i | −1.28237 | + | 0.220019i | ||||
\(103\) | −10.4032 | + | 10.4032i | −1.02506 | + | 1.02506i | −0.0253770 | + | 0.999678i | \(0.508079\pi\) |
−0.999678 | + | 0.0253770i | \(0.991921\pi\) | |||||||
\(104\) | 2.46967 | 0.242171 | ||||||||
\(105\) | −7.27055 | + | 1.00000i | −0.709533 | + | 0.0975900i | ||||
\(106\) | −9.12283 | −0.886088 | ||||||||
\(107\) | −8.11871 | + | 8.11871i | −0.784866 | + | 0.784866i | −0.980647 | − | 0.195782i | \(-0.937276\pi\) |
0.195782 | + | 0.980647i | \(0.437276\pi\) | |||||||
\(108\) | −4.53553 | + | 2.53553i | −0.436432 | + | 0.243982i | ||||
\(109\) | 0.305448i | 0.0292566i | 0.999893 | + | 0.0146283i | \(0.00465650\pi\) | ||||
−0.999893 | + | 0.0146283i | \(0.995344\pi\) | |||||||
\(110\) | 0.0972711 | − | 2.92570i | 0.00927443 | − | 0.278954i | ||||
\(111\) | 2.82843 | − | 4.00000i | 0.268462 | − | 0.379663i | ||||
\(112\) | 1.33991 | + | 1.33991i | 0.126610 | + | 0.126610i | ||||
\(113\) | 1.51148 | + | 1.51148i | 0.142189 | + | 0.142189i | 0.774618 | − | 0.632429i | \(-0.217942\pi\) |
−0.632429 | + | 0.774618i | \(0.717942\pi\) | |||||||
\(114\) | −4.34772 | + | 6.14860i | −0.407201 | + | 0.575869i | ||||
\(115\) | 0.499557 | − | 15.0256i | 0.0465839 | − | 1.40114i | ||||
\(116\) | 5.50825i | 0.511428i | ||||||||
\(117\) | 3.19301 | − | 6.68565i | 0.295194 | − | 0.618089i | ||||
\(118\) | −8.04441 | + | 8.04441i | −0.740548 | + | 0.740548i | ||||
\(119\) | 14.3761 | 1.31786 | ||||||||
\(120\) | −3.83686 | + | 0.527726i | −0.350256 | + | 0.0481746i | ||||
\(121\) | 9.28617 | 0.844197 | ||||||||
\(122\) | 8.87284 | − | 8.87284i | 0.803309 | − | 0.803309i | ||||
\(123\) | 4.80177 | − | 0.823854i | 0.432961 | − | 0.0742844i | ||||
\(124\) | − | 1.00000i | − | 0.0898027i | ||||||
\(125\) | 8.65336 | − | 7.07950i | 0.773980 | − | 0.633210i | ||||
\(126\) | 5.35965 | − | 1.89492i | 0.477475 | − | 0.168813i | ||||
\(127\) | −2.40811 | − | 2.40811i | −0.213685 | − | 0.213685i | 0.592146 | − | 0.805831i | \(-0.298281\pi\) |
−0.805831 | + | 0.592146i | \(0.798281\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 7.00089 | + | 4.95037i | 0.616394 | + | 0.435856i | ||||
\(130\) | 4.03248 | − | 3.77297i | 0.353672 | − | 0.330912i | ||||
\(131\) | 8.82321i | 0.770888i | 0.922731 | + | 0.385444i | \(0.125952\pi\) | ||||
−0.922731 | + | 0.385444i | \(0.874048\pi\) | |||||||
\(132\) | 0.383437 | + | 2.23483i | 0.0333739 | + | 0.194517i | ||||
\(133\) | 5.82556 | − | 5.82556i | 0.505140 | − | 0.505140i | ||||
\(134\) | 7.81370 | 0.675001 | ||||||||
\(135\) | −3.53204 | + | 11.0691i | −0.303990 | + | 0.952675i | ||||
\(136\) | 7.58667 | 0.650552 | ||||||||
\(137\) | −12.2546 | + | 12.2546i | −1.04698 | + | 1.04698i | −0.0481377 | + | 0.998841i | \(0.515329\pi\) |
−0.998841 | + | 0.0481377i | \(0.984671\pi\) | |||||||
\(138\) | 1.96922 | + | 11.4775i | 0.167631 | + | 0.977027i | ||||
\(139\) | − | 10.0563i | − | 0.852968i | −0.904495 | − | 0.426484i | \(-0.859752\pi\) | ||
0.904495 | − | 0.426484i | \(-0.140248\pi\) | |||||||
\(140\) | 4.23483 | + | 0.140796i | 0.357909 | + | 0.0118994i | ||||
\(141\) | −7.33579 | − | 5.18719i | −0.617785 | − | 0.436840i | ||||
\(142\) | −7.31694 | − | 7.31694i | −0.614024 | − | 0.614024i | ||||
\(143\) | −2.28617 | − | 2.28617i | −0.191179 | − | 0.191179i | ||||
\(144\) | 2.82843 | − | 1.00000i | 0.235702 | − | 0.0833333i | ||||
\(145\) | 8.41510 | + | 8.99390i | 0.698836 | + | 0.746903i | ||||
\(146\) | 2.64493i | 0.218896i | ||||||||
\(147\) | 5.81999 | − | 0.998553i | 0.480025 | − | 0.0823593i | ||||
\(148\) | −2.00000 | + | 2.00000i | −0.164399 | + | 0.164399i | ||||
\(149\) | 18.7711 | 1.53779 | 0.768893 | − | 0.639378i | \(-0.220808\pi\) | ||||
0.768893 | + | 0.639378i | \(0.220808\pi\) | |||||||
\(150\) | −5.45862 | + | 6.72335i | −0.445695 | + | 0.548959i | ||||
\(151\) | 4.51902 | 0.367752 | 0.183876 | − | 0.982949i | \(-0.441135\pi\) | ||||
0.183876 | + | 0.982949i | \(0.441135\pi\) | |||||||
\(152\) | 3.07430 | − | 3.07430i | 0.249359 | − | 0.249359i | ||||
\(153\) | 9.80876 | − | 20.5379i | 0.792991 | − | 1.66039i | ||||
\(154\) | − | 2.48071i | − | 0.199901i | ||||||
\(155\) | −1.52773 | − | 1.63280i | −0.122710 | − | 0.131150i | ||||
\(156\) | −2.46967 | + | 3.49264i | −0.197732 | + | 0.279635i | ||||
\(157\) | 11.5063 | + | 11.5063i | 0.918300 | + | 0.918300i | 0.996906 | − | 0.0786055i | \(-0.0250467\pi\) |
−0.0786055 | + | 0.996906i | \(0.525047\pi\) | |||||||
\(158\) | −3.28446 | − | 3.28446i | −0.261298 | − | 0.261298i | ||||
\(159\) | 9.12283 | − | 12.9016i | 0.723488 | − | 1.02317i | ||||
\(160\) | 2.23483 | + | 0.0743018i | 0.176679 | + | 0.00587407i | ||||
\(161\) | − | 12.7402i | − | 1.00407i | ||||||
\(162\) | 0.949747 | − | 8.94975i | 0.0746192 | − | 0.703159i | ||||
\(163\) | −0.105079 | + | 0.105079i | −0.00823039 | + | 0.00823039i | −0.711210 | − | 0.702980i | \(-0.751852\pi\) |
0.702980 | + | 0.711210i | \(0.251852\pi\) | |||||||
\(164\) | −2.81281 | −0.219644 | ||||||||
\(165\) | 4.04029 | + | 3.06326i | 0.314536 | + | 0.238474i | ||||
\(166\) | −15.9623 | −1.23891 | ||||||||
\(167\) | 0.887114 | − | 0.887114i | 0.0686469 | − | 0.0686469i | −0.671950 | − | 0.740597i | \(-0.734543\pi\) |
0.740597 | + | 0.671950i | \(0.234543\pi\) | |||||||
\(168\) | −3.23483 | + | 0.555010i | −0.249573 | + | 0.0428199i | ||||
\(169\) | 6.90075i | 0.530827i | ||||||||
\(170\) | 12.3876 | − | 11.5904i | 0.950082 | − | 0.888940i | ||||
\(171\) | −4.34772 | − | 12.2972i | −0.332478 | − | 0.940391i | ||||
\(172\) | −3.50044 | − | 3.50044i | −0.266906 | − | 0.266906i | ||||
\(173\) | 16.8692 | + | 16.8692i | 1.28254 | + | 1.28254i | 0.939219 | + | 0.343319i | \(0.111551\pi\) |
0.343319 | + | 0.939219i | \(0.388449\pi\) | |||||||
\(174\) | −7.78984 | − | 5.50825i | −0.590546 | − | 0.417579i | ||||
\(175\) | 7.12975 | − | 6.23977i | 0.538959 | − | 0.471683i | ||||
\(176\) | − | 1.30913i | − | 0.0986798i | ||||||
\(177\) | −3.33210 | − | 19.4209i | −0.250456 | − | 1.45977i | ||||
\(178\) | −5.06326 | + | 5.06326i | −0.379507 | + | 0.379507i | ||||
\(179\) | 12.3622 | 0.923992 | 0.461996 | − | 0.886882i | \(-0.347133\pi\) | ||||
0.461996 | + | 0.886882i | \(0.347133\pi\) | |||||||
\(180\) | 3.09054 | − | 5.95387i | 0.230356 | − | 0.443775i | ||||
\(181\) | 0.00582690 | 0.000433110 | 0.000216555 | − | 1.00000i | \(-0.499931\pi\) | ||||
0.000216555 | 1.00000i | \(0.499931\pi\) | ||||||||
\(182\) | 3.30913 | − | 3.30913i | 0.245289 | − | 0.245289i | ||||
\(183\) | 3.67525 | + | 21.4209i | 0.271682 | + | 1.58348i | ||||
\(184\) | − | 6.72335i | − | 0.495652i | ||||||
\(185\) | −0.210157 | + | 6.32106i | −0.0154511 | + | 0.464734i | ||||
\(186\) | 1.41421 | + | 1.00000i | 0.103695 | + | 0.0733236i | ||||
\(187\) | −7.02297 | − | 7.02297i | −0.513570 | − | 0.513570i | ||||
\(188\) | 3.66790 | + | 3.66790i | 0.267509 | + | 0.267509i | ||||
\(189\) | −2.67982 | + | 9.47461i | −0.194928 | + | 0.689176i | ||||
\(190\) | 0.323043 | − | 9.71643i | 0.0234360 | − | 0.704904i | ||||
\(191\) | 4.58453i | 0.331725i | 0.986149 | + | 0.165863i | \(0.0530408\pi\) | ||||
−0.986149 | + | 0.165863i | \(0.946959\pi\) | |||||||
\(192\) | −1.70711 | + | 0.292893i | −0.123200 | + | 0.0211377i | ||||
\(193\) | −16.9513 | + | 16.9513i | −1.22018 | + | 1.22018i | −0.252610 | + | 0.967568i | \(0.581289\pi\) |
−0.967568 | + | 0.252610i | \(0.918711\pi\) | |||||||
\(194\) | −2.11612 | −0.151929 | ||||||||
\(195\) | 1.30331 | + | 9.47577i | 0.0933318 | + | 0.678574i | ||||
\(196\) | −3.40927 | −0.243519 | ||||||||
\(197\) | 10.6096 | − | 10.6096i | 0.755906 | − | 0.755906i | −0.219669 | − | 0.975575i | \(-0.570498\pi\) |
0.975575 | + | 0.219669i | \(0.0704977\pi\) | |||||||
\(198\) | −3.54397 | − | 1.69257i | −0.251859 | − | 0.120286i | ||||
\(199\) | − | 4.67866i | − | 0.331662i | −0.986154 | − | 0.165831i | \(-0.946969\pi\) | ||
0.986154 | − | 0.165831i | \(-0.0530306\pi\) | |||||||
\(200\) | 3.76256 | − | 3.29289i | 0.266053 | − | 0.232843i | ||||
\(201\) | −7.81370 | + | 11.0502i | −0.551136 | + | 0.779424i | ||||
\(202\) | 9.52100 | + | 9.52100i | 0.669895 | + | 0.669895i | ||||
\(203\) | 7.38057 | + | 7.38057i | 0.518014 | + | 0.518014i | ||||
\(204\) | −7.58667 | + | 10.7292i | −0.531173 | + | 0.751193i | ||||
\(205\) | −4.59277 | + | 4.29721i | −0.320773 | + | 0.300130i | ||||
\(206\) | 14.7123i | 1.02506i | ||||||||
\(207\) | −18.2008 | − | 8.69257i | −1.26504 | − | 0.604175i | ||||
\(208\) | 1.74632 | − | 1.74632i | 0.121085 | − | 0.121085i | ||||
\(209\) | −5.69175 | −0.393707 | ||||||||
\(210\) | −4.43395 | + | 5.84816i | −0.305972 | + | 0.403562i | ||||
\(211\) | −11.3551 | −0.781715 | −0.390858 | − | 0.920451i | \(-0.627822\pi\) | ||||
−0.390858 | + | 0.920451i | \(0.627822\pi\) | |||||||
\(212\) | −6.45082 | + | 6.45082i | −0.443044 | + | 0.443044i | ||||
\(213\) | 17.6647 | − | 3.03078i | 1.21036 | − | 0.207665i | ||||
\(214\) | 11.4816i | 0.784866i | ||||||||
\(215\) | −11.0633 | − | 0.367822i | −0.754508 | − | 0.0250852i | ||||
\(216\) | −1.41421 | + | 5.00000i | −0.0962250 | + | 0.340207i | ||||
\(217\) | −1.33991 | − | 1.33991i | −0.0909591 | − | 0.0909591i | ||||
\(218\) | 0.215984 | + | 0.215984i | 0.0146283 | + | 0.0146283i | ||||
\(219\) | −3.74049 | − | 2.64493i | −0.252759 | − | 0.178728i | ||||
\(220\) | −2.00000 | − | 2.13756i | −0.134840 | − | 0.144114i | ||||
\(221\) | − | 18.7365i | − | 1.26036i | ||||||
\(222\) | −0.828427 | − | 4.82843i | −0.0556004 | − | 0.324063i | ||||
\(223\) | 11.0613 | − | 11.0613i | 0.740718 | − | 0.740718i | −0.231998 | − | 0.972716i | \(-0.574526\pi\) |
0.972716 | + | 0.231998i | \(0.0745263\pi\) | |||||||
\(224\) | 1.89492 | 0.126610 | ||||||||
\(225\) | −4.04963 | − | 14.4430i | −0.269975 | − | 0.962867i | ||||
\(226\) | 2.13756 | 0.142189 | ||||||||
\(227\) | −10.1647 | + | 10.1647i | −0.674652 | + | 0.674652i | −0.958785 | − | 0.284133i | \(-0.908294\pi\) |
0.284133 | + | 0.958785i | \(0.408294\pi\) | |||||||
\(228\) | 1.27342 | + | 7.42202i | 0.0843341 | + | 0.491535i | ||||
\(229\) | − | 13.4188i | − | 0.886738i | −0.896339 | − | 0.443369i | \(-0.853783\pi\) | ||
0.896339 | − | 0.443369i | \(-0.146217\pi\) | |||||||
\(230\) | −10.2714 | − | 10.9779i | −0.677278 | − | 0.723862i | ||||
\(231\) | 3.50825 | + | 2.48071i | 0.230826 | + | 0.163219i | ||||
\(232\) | 3.89492 | + | 3.89492i | 0.255714 | + | 0.255714i | ||||
\(233\) | 9.55096 | + | 9.55096i | 0.625704 | + | 0.625704i | 0.946984 | − | 0.321280i | \(-0.104113\pi\) |
−0.321280 | + | 0.946984i | \(0.604113\pi\) | |||||||
\(234\) | −2.46967 | − | 6.98527i | −0.161447 | − | 0.456641i | ||||
\(235\) | 11.5925 | + | 0.385417i | 0.756211 | + | 0.0251419i | ||||
\(236\) | 11.3765i | 0.740548i | ||||||||
\(237\) | 7.92939 | − | 1.36047i | 0.515069 | − | 0.0883719i | ||||
\(238\) | 10.1655 | − | 10.1655i | 0.658930 | − | 0.658930i | ||||
\(239\) | −28.4935 | −1.84309 | −0.921546 | − | 0.388268i | \(-0.873073\pi\) | ||||
−0.921546 | + | 0.388268i | \(0.873073\pi\) | |||||||
\(240\) | −2.33991 | + | 3.08623i | −0.151041 | + | 0.199215i | ||||
\(241\) | −10.4697 | −0.674410 | −0.337205 | − | 0.941431i | \(-0.609482\pi\) | ||||
−0.337205 | + | 0.941431i | \(0.609482\pi\) | |||||||
\(242\) | 6.56631 | − | 6.56631i | 0.422098 | − | 0.422098i | ||||
\(243\) | 11.7071 | + | 10.2929i | 0.751011 | + | 0.660289i | ||||
\(244\) | − | 12.5481i | − | 0.803309i | ||||||
\(245\) | −5.56668 | + | 5.20844i | −0.355642 | + | 0.332755i | ||||
\(246\) | 2.81281 | − | 3.97792i | 0.179338 | − | 0.253623i | ||||
\(247\) | −7.59250 | − | 7.59250i | −0.483099 | − | 0.483099i | ||||
\(248\) | −0.707107 | − | 0.707107i | −0.0449013 | − | 0.0449013i | ||||
\(249\) | 15.9623 | − | 22.5741i | 1.01157 | − | 1.43058i | ||||
\(250\) | 1.11289 | − | 11.1248i | 0.0703851 | − | 0.703595i | ||||
\(251\) | − | 27.8155i | − | 1.75570i | −0.478938 | − | 0.877848i | \(-0.658978\pi\) | ||
0.478938 | − | 0.877848i | \(-0.341022\pi\) | |||||||
\(252\) | 2.44993 | − | 5.12975i | 0.154331 | − | 0.323144i | ||||
\(253\) | −6.22379 | + | 6.22379i | −0.391286 | + | 0.391286i | ||||
\(254\) | −3.40559 | −0.213685 | ||||||||
\(255\) | 4.00369 | + | 29.1090i | 0.250721 | + | 1.82288i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.61162 | + | 4.61162i | −0.287665 | + | 0.287665i | −0.836156 | − | 0.548491i | \(-0.815202\pi\) |
0.548491 | + | 0.836156i | \(0.315202\pi\) | |||||||
\(258\) | 8.45082 | − | 1.44993i | 0.526125 | − | 0.0902688i | ||||
\(259\) | 5.35965i | 0.333032i | ||||||||
\(260\) | 0.183501 | − | 5.51929i | 0.0113802 | − | 0.342292i | ||||
\(261\) | 15.5797 | − | 5.50825i | 0.964358 | − | 0.340952i | ||||
\(262\) | 6.23895 | + | 6.23895i | 0.385444 | + | 0.385444i | ||||
\(263\) | 1.18350 | + | 1.18350i | 0.0729778 | + | 0.0729778i | 0.742654 | − | 0.669676i | \(-0.233567\pi\) |
−0.669676 | + | 0.742654i | \(0.733567\pi\) | |||||||
\(264\) | 1.85140 | + | 1.30913i | 0.113946 | + | 0.0805717i | ||||
\(265\) | −0.677843 | + | 20.3880i | −0.0416396 | + | 1.25243i | ||||
\(266\) | − | 8.23859i | − | 0.505140i | ||||||
\(267\) | −2.09727 | − | 12.2238i | −0.128351 | − | 0.748084i | ||||
\(268\) | 5.52512 | − | 5.52512i | 0.337500 | − | 0.337500i | ||||
\(269\) | 1.84316 | 0.112379 | 0.0561896 | − | 0.998420i | \(-0.482105\pi\) | ||||
0.0561896 | + | 0.998420i | \(0.482105\pi\) | |||||||
\(270\) | 5.32950 | + | 10.3246i | 0.324343 | + | 0.628332i | ||||
\(271\) | −15.8832 | −0.964838 | −0.482419 | − | 0.875941i | \(-0.660242\pi\) | ||||
−0.482419 | + | 0.875941i | \(0.660242\pi\) | |||||||
\(272\) | 5.36459 | − | 5.36459i | 0.325276 | − | 0.325276i | ||||
\(273\) | 1.37069 | + | 7.98896i | 0.0829578 | + | 0.483514i | ||||
\(274\) | 17.3306i | 1.04698i | ||||||||
\(275\) | −6.53122 | − | 0.434769i | −0.393847 | − | 0.0262176i | ||||
\(276\) | 9.50825 | + | 6.72335i | 0.572329 | + | 0.404698i | ||||
\(277\) | −1.16916 | − | 1.16916i | −0.0702480 | − | 0.0702480i | 0.671110 | − | 0.741358i | \(-0.265818\pi\) |
−0.741358 | + | 0.671110i | \(0.765818\pi\) | |||||||
\(278\) | −7.11091 | − | 7.11091i | −0.426484 | − | 0.426484i | ||||
\(279\) | −2.82843 | + | 1.00000i | −0.169334 | + | 0.0598684i | ||||
\(280\) | 3.09404 | − | 2.89492i | 0.184904 | − | 0.173005i | ||||
\(281\) | − | 5.69059i | − | 0.339472i | −0.985490 | − | 0.169736i | \(-0.945708\pi\) | ||
0.985490 | − | 0.169736i | \(-0.0542915\pi\) | |||||||
\(282\) | −8.85508 | + | 1.51929i | −0.527313 | + | 0.0904725i | ||||
\(283\) | −0.590360 | + | 0.590360i | −0.0350933 | + | 0.0350933i | −0.724436 | − | 0.689342i | \(-0.757900\pi\) |
0.689342 | + | 0.724436i | \(0.257900\pi\) | |||||||
\(284\) | −10.3477 | −0.614024 | ||||||||
\(285\) | 13.4181 | + | 10.1733i | 0.794817 | + | 0.602613i | ||||
\(286\) | −3.23313 | −0.191179 | ||||||||
\(287\) | −3.76892 | + | 3.76892i | −0.222472 | + | 0.222472i | ||||
\(288\) | 1.29289 | − | 2.70711i | 0.0761845 | − | 0.159518i | ||||
\(289\) | − | 40.5576i | − | 2.38574i | ||||||
\(290\) | 12.3100 | + | 0.409273i | 0.722869 | + | 0.0240333i | ||||
\(291\) | 2.11612 | − | 2.99265i | 0.124049 | − | 0.175432i | ||||
\(292\) | 1.87025 | + | 1.87025i | 0.109448 | + | 0.109448i | ||||
\(293\) | −5.10139 | − | 5.10139i | −0.298026 | − | 0.298026i | 0.542214 | − | 0.840240i | \(-0.317586\pi\) |
−0.840240 | + | 0.542214i | \(0.817586\pi\) | |||||||
\(294\) | 3.40927 | − | 4.82144i | 0.198833 | − | 0.281192i | ||||
\(295\) | 17.3802 | + | 18.5756i | 1.01191 | + | 1.08152i | ||||
\(296\) | 2.82843i | 0.164399i | ||||||||
\(297\) | 5.93763 | − | 3.31936i | 0.344536 | − | 0.192609i | ||||
\(298\) | 13.2731 | − | 13.2731i | 0.768893 | − | 0.768893i | ||||
\(299\) | −16.6044 | −0.960259 | ||||||||
\(300\) | 0.894295 | + | 8.61396i | 0.0516321 | + | 0.497327i | ||||
\(301\) | −9.38057 | −0.540687 | ||||||||
\(302\) | 3.19543 | − | 3.19543i | 0.183876 | − | 0.183876i | ||||
\(303\) | −22.9857 | + | 3.94373i | −1.32050 | + | 0.226561i | ||||
\(304\) | − | 4.34772i | − | 0.249359i | ||||||
\(305\) | −19.1700 | − | 20.4886i | −1.09767 | − | 1.17317i | ||||
\(306\) | −7.58667 | − | 21.4584i | −0.433701 | − | 1.22669i | ||||
\(307\) | 6.63514 | + | 6.63514i | 0.378687 | + | 0.378687i | 0.870628 | − | 0.491941i | \(-0.163712\pi\) |
−0.491941 | + | 0.870628i | \(0.663712\pi\) | |||||||
\(308\) | −1.75413 | − | 1.75413i | −0.0999506 | − | 0.0999506i | ||||
\(309\) | −20.8063 | − | 14.7123i | −1.18363 | − | 0.836954i | ||||
\(310\) | −2.23483 | − | 0.0743018i | −0.126930 | − | 0.00422006i | ||||
\(311\) | 23.4363i | 1.32895i | 0.747311 | + | 0.664474i | \(0.231345\pi\) | ||||
−0.747311 | + | 0.664474i | \(0.768655\pi\) | |||||||
\(312\) | 0.723349 | + | 4.21598i | 0.0409515 | + | 0.238683i | ||||
\(313\) | −6.44060 | + | 6.44060i | −0.364044 | + | 0.364044i | −0.865299 | − | 0.501255i | \(-0.832872\pi\) |
0.501255 | + | 0.865299i | \(0.332872\pi\) | |||||||
\(314\) | 16.2723 | 0.918300 | ||||||||
\(315\) | −3.83660 | − | 12.1187i | −0.216168 | − | 0.682812i | ||||
\(316\) | −4.64493 | −0.261298 | ||||||||
\(317\) | −18.9985 | + | 18.9985i | −1.06706 | + | 1.06706i | −0.0694770 | + | 0.997584i | \(0.522133\pi\) |
−0.997584 | + | 0.0694770i | \(0.977867\pi\) | |||||||
\(318\) | −2.67202 | − | 15.5737i | −0.149839 | − | 0.873327i | ||||
\(319\) | − | 7.21104i | − | 0.403741i | ||||||
\(320\) | 1.63280 | − | 1.52773i | 0.0912766 | − | 0.0854025i | ||||
\(321\) | −16.2374 | − | 11.4816i | −0.906285 | − | 0.640840i | ||||
\(322\) | −9.00869 | − | 9.00869i | −0.502035 | − | 0.502035i | ||||
\(323\) | −23.3237 | − | 23.3237i | −1.29777 | − | 1.29777i | ||||
\(324\) | −5.65685 | − | 7.00000i | −0.314270 | − | 0.388889i | ||||
\(325\) | −8.13235 | − | 9.29227i | −0.451101 | − | 0.515442i | ||||
\(326\) | 0.148604i | 0.00823039i | ||||||||
\(327\) | −0.521432 | + | 0.0894635i | −0.0288352 | + | 0.00494735i | ||||
\(328\) | −1.98896 | + | 1.98896i | −0.109822 | + | 0.109822i | ||||
\(329\) | 9.82931 | 0.541908 | ||||||||
\(330\) | 5.02297 | − | 0.690865i | 0.276505 | − | 0.0380309i | ||||
\(331\) | 4.04810 | 0.222504 | 0.111252 | − | 0.993792i | \(-0.464514\pi\) | ||||
0.111252 | + | 0.993792i | \(0.464514\pi\) | |||||||
\(332\) | −11.2871 | + | 11.2871i | −0.619457 | + | 0.619457i | ||||
\(333\) | 7.65685 | + | 3.65685i | 0.419593 | + | 0.200394i | ||||
\(334\) | − | 1.25457i | − | 0.0686469i | ||||||
\(335\) | 0.580572 | − | 17.4623i | 0.0317200 | − | 0.954068i | ||||
\(336\) | −1.89492 | + | 2.67982i | −0.103376 | + | 0.146196i | ||||
\(337\) | 6.07018 | + | 6.07018i | 0.330664 | + | 0.330664i | 0.852839 | − | 0.522175i | \(-0.174879\pi\) |
−0.522175 | + | 0.852839i | \(0.674879\pi\) | |||||||
\(338\) | 4.87957 | + | 4.87957i | 0.265413 | + | 0.265413i | ||||
\(339\) | −2.13756 | + | 3.02297i | −0.116096 | + | 0.164185i | ||||
\(340\) | 0.563703 | − | 16.9549i | 0.0305711 | − | 0.919511i | ||||
\(341\) | 1.30913i | 0.0708936i | ||||||||
\(342\) | −11.7697 | − | 5.62114i | −0.636435 | − | 0.303956i | ||||
\(343\) | −13.9475 | + | 13.9475i | −0.753095 | + | 0.753095i | ||||
\(344\) | −4.95037 | −0.266906 | ||||||||
\(345\) | 25.7966 | − | 3.54809i | 1.38884 | − | 0.191023i | ||||
\(346\) | 23.8566 | 1.28254 | ||||||||
\(347\) | 17.7567 | − | 17.7567i | 0.953231 | − | 0.953231i | −0.0457236 | − | 0.998954i | \(-0.514559\pi\) |
0.998954 | + | 0.0457236i | \(0.0145593\pi\) | |||||||
\(348\) | −9.40317 | + | 1.61333i | −0.504063 | + | 0.0864835i | ||||
\(349\) | − | 12.4731i | − | 0.667669i | −0.942632 | − | 0.333834i | \(-0.891657\pi\) | ||
0.942632 | − | 0.333834i | \(-0.108343\pi\) | |||||||
\(350\) | 0.629311 | − | 9.45368i | 0.0336381 | − | 0.505321i | ||||
\(351\) | 12.3483 | + | 3.49264i | 0.659105 | + | 0.186423i | ||||
\(352\) | −0.925698 | − | 0.925698i | −0.0493399 | − | 0.0493399i | ||||
\(353\) | 2.56282 | + | 2.56282i | 0.136405 | + | 0.136405i | 0.772012 | − | 0.635607i | \(-0.219250\pi\) |
−0.635607 | + | 0.772012i | \(0.719250\pi\) | |||||||
\(354\) | −16.0888 | − | 11.3765i | −0.855111 | − | 0.604655i | ||||
\(355\) | −16.8958 | + | 15.8085i | −0.896736 | + | 0.839027i | ||||
\(356\) | 7.16053i | 0.379507i | ||||||||
\(357\) | 4.21068 | + | 24.5416i | 0.222853 | + | 1.29888i | ||||
\(358\) | 8.74138 | − | 8.74138i | 0.461996 | − | 0.461996i | ||||
\(359\) | −3.97334 | −0.209705 | −0.104853 | − | 0.994488i | \(-0.533437\pi\) | ||||
−0.104853 | + | 0.994488i | \(0.533437\pi\) | |||||||
\(360\) | −2.02468 | − | 6.39536i | −0.106710 | − | 0.337065i | ||||
\(361\) | 0.0973369 | 0.00512300 | ||||||||
\(362\) | 0.00412024 | − | 0.00412024i | 0.000216555 | − | 0.000216555i | ||||
\(363\) | 2.71985 | + | 15.8525i | 0.142755 | + | 0.832039i | ||||
\(364\) | − | 4.67982i | − | 0.245289i | ||||||
\(365\) | 5.91097 | + | 0.196523i | 0.309394 | + | 0.0102865i | ||||
\(366\) | 17.7457 | + | 12.5481i | 0.927581 | + | 0.655899i | ||||
\(367\) | 17.9779 | + | 17.9779i | 0.938440 | + | 0.938440i | 0.998212 | − | 0.0597724i | \(-0.0190375\pi\) |
−0.0597724 | + | 0.998212i | \(0.519037\pi\) | |||||||
\(368\) | −4.75413 | − | 4.75413i | −0.247826 | − | 0.247826i | ||||
\(369\) | 2.81281 | + | 7.95583i | 0.146429 | + | 0.414164i | ||||
\(370\) | 4.32106 | + | 4.61827i | 0.224641 | + | 0.240092i | ||||
\(371\) | 17.2871i | 0.897499i | ||||||||
\(372\) | 1.70711 | − | 0.292893i | 0.0885094 | − | 0.0151858i | ||||
\(373\) | −17.2008 | + | 17.2008i | −0.890625 | + | 0.890625i | −0.994582 | − | 0.103957i | \(-0.966850\pi\) |
0.103957 | + | 0.994582i | \(0.466850\pi\) | |||||||
\(374\) | −9.93198 | −0.513570 | ||||||||
\(375\) | 14.6200 | + | 12.6987i | 0.754972 | + | 0.655757i | ||||
\(376\) | 5.18719 | 0.267509 | ||||||||
\(377\) | 9.61916 | − | 9.61916i | 0.495412 | − | 0.495412i | ||||
\(378\) | 4.80464 | + | 8.59448i | 0.247124 | + | 0.442052i | ||||
\(379\) | − | 14.4899i | − | 0.744294i | −0.928174 | − | 0.372147i | \(-0.878622\pi\) | ||
0.928174 | − | 0.372147i | \(-0.121378\pi\) | |||||||
\(380\) | −6.64213 | − | 7.09898i | −0.340734 | − | 0.364170i | ||||
\(381\) | 3.40559 | − | 4.81623i | 0.174473 | − | 0.246743i | ||||
\(382\) | 3.24175 | + | 3.24175i | 0.165863 | + | 0.165863i | ||||
\(383\) | 24.7567 | + | 24.7567i | 1.26501 | + | 1.26501i | 0.948634 | + | 0.316375i | \(0.102466\pi\) |
0.316375 | + | 0.948634i | \(0.397534\pi\) | |||||||
\(384\) | −1.00000 | + | 1.41421i | −0.0510310 | + | 0.0721688i | ||||
\(385\) | −5.54397 | − | 0.184321i | −0.282547 | − | 0.00939387i | ||||
\(386\) | 23.9727i | 1.22018i | ||||||||
\(387\) | −6.40031 | + | 13.4012i | −0.325346 | + | 0.681221i | ||||
\(388\) | −1.49632 | + | 1.49632i | −0.0759643 | + | 0.0759643i | ||||
\(389\) | 33.0438 | 1.67539 | 0.837693 | − | 0.546142i | \(-0.183904\pi\) | ||||
0.837693 | + | 0.546142i | \(0.183904\pi\) | |||||||
\(390\) | 7.62196 | + | 5.77880i | 0.385953 | + | 0.292621i | ||||
\(391\) | −51.0078 | −2.57958 | ||||||||
\(392\) | −2.41072 | + | 2.41072i | −0.121760 | + | 0.121760i | ||||
\(393\) | −15.0622 | + | 2.58426i | −0.759786 | + | 0.130359i | ||||
\(394\) | − | 15.0043i | − | 0.755906i | ||||||
\(395\) | −7.58426 | + | 7.09618i | −0.381605 | + | 0.357047i | ||||
\(396\) | −3.70279 | + | 1.30913i | −0.186072 | + | 0.0657865i | ||||
\(397\) | 6.05133 | + | 6.05133i | 0.303708 | + | 0.303708i | 0.842463 | − | 0.538755i | \(-0.181105\pi\) |
−0.538755 | + | 0.842463i | \(0.681105\pi\) | |||||||
\(398\) | −3.30831 | − | 3.30831i | −0.165831 | − | 0.165831i | ||||
\(399\) | 11.6511 | + | 8.23859i | 0.583286 | + | 0.412445i | ||||
\(400\) | 0.332104 | − | 4.98896i | 0.0166052 | − | 0.249448i | ||||
\(401\) | − | 25.3585i | − | 1.26634i | −0.774012 | − | 0.633171i | \(-0.781753\pi\) | ||
0.774012 | − | 0.633171i | \(-0.218247\pi\) | |||||||
\(402\) | 2.28858 | + | 13.3388i | 0.114144 | + | 0.665280i | ||||
\(403\) | −1.74632 | + | 1.74632i | −0.0869903 | + | 0.0869903i | ||||
\(404\) | 13.4647 | 0.669895 | ||||||||
\(405\) | −19.9306 | − | 2.78751i | −0.990361 | − | 0.138512i | ||||
\(406\) | 10.4377 | 0.518014 | ||||||||
\(407\) | 2.61827 | − | 2.61827i | 0.129783 | − | 0.129783i | ||||
\(408\) | 2.22208 | + | 12.9513i | 0.110010 | + | 0.641183i | ||||
\(409\) | 10.0337i | 0.496136i | 0.968743 | + | 0.248068i | \(0.0797957\pi\) | ||||
−0.968743 | + | 0.248068i | \(0.920204\pi\) | |||||||
\(410\) | −0.208997 | + | 6.28617i | −0.0103216 | + | 0.310452i | ||||
\(411\) | −24.5091 | − | 17.3306i | −1.20895 | − | 0.854854i | ||||
\(412\) | 10.4032 | + | 10.4032i | 0.512528 | + | 0.512528i | ||||
\(413\) | 15.2435 | + | 15.2435i | 0.750085 | + | 0.750085i | ||||
\(414\) | −19.0165 | + | 6.72335i | −0.934610 | + | 0.330435i | ||||
\(415\) | −1.18603 | + | 35.6731i | −0.0582198 | + | 1.75112i | ||||
\(416\) | − | 2.46967i | − | 0.121085i | ||||||
\(417\) | 17.1672 | − | 2.94543i | 0.840684 | − | 0.144238i | ||||
\(418\) | −4.02468 | + | 4.02468i | −0.196853 | + | 0.196853i | ||||
\(419\) | 26.8198 | 1.31023 | 0.655116 | − | 0.755528i | \(-0.272620\pi\) | ||||
0.655116 | + | 0.755528i | \(0.272620\pi\) | |||||||
\(420\) | 1.00000 | + | 7.27055i | 0.0487950 | + | 0.354767i | ||||
\(421\) | 18.6954 | 0.911160 | 0.455580 | − | 0.890195i | \(-0.349432\pi\) | ||||
0.455580 | + | 0.890195i | \(0.349432\pi\) | |||||||
\(422\) | −8.02925 | + | 8.02925i | −0.390858 | + | 0.390858i | ||||
\(423\) | 6.70648 | − | 14.0423i | 0.326080 | − | 0.682759i | ||||
\(424\) | 9.12283i | 0.443044i | ||||||||
\(425\) | −24.9821 | − | 28.5453i | −1.21181 | − | 1.38465i | ||||
\(426\) | 10.3477 | − | 14.6339i | 0.501349 | − | 0.709014i | ||||
\(427\) | −16.8133 | − | 16.8133i | −0.813654 | − | 0.813654i | ||||
\(428\) | 8.11871 | + | 8.11871i | 0.392433 | + | 0.392433i | ||||
\(429\) | 3.23313 | − | 4.57233i | 0.156097 | − | 0.220754i | ||||
\(430\) | −8.08300 | + | 7.56282i | −0.389797 | + | 0.364711i | ||||
\(431\) | − | 17.2267i | − | 0.829779i | −0.909872 | − | 0.414889i | \(-0.863820\pi\) | ||
0.909872 | − | 0.414889i | \(-0.136180\pi\) | |||||||
\(432\) | 2.53553 | + | 4.53553i | 0.121991 | + | 0.218216i | ||||
\(433\) | −9.70944 | + | 9.70944i | −0.466606 | + | 0.466606i | −0.900813 | − | 0.434207i | \(-0.857029\pi\) |
0.434207 | + | 0.900813i | \(0.357029\pi\) | |||||||
\(434\) | −1.89492 | −0.0909591 | ||||||||
\(435\) | −12.8888 | + | 16.9997i | −0.617972 | + | 0.815074i | ||||
\(436\) | 0.305448 | 0.0146283 | ||||||||
\(437\) | −20.6696 | + | 20.6696i | −0.988761 | + | 0.988761i | ||||
\(438\) | −4.51517 | + | 0.774681i | −0.215743 | + | 0.0370157i | ||||
\(439\) | 26.9329i | 1.28544i | 0.766103 | + | 0.642718i | \(0.222193\pi\) | ||||
−0.766103 | + | 0.642718i | \(0.777807\pi\) | |||||||
\(440\) | −2.92570 | − | 0.0972711i | −0.139477 | − | 0.00463722i | ||||
\(441\) | 3.40927 | + | 9.64288i | 0.162346 | + | 0.459185i | ||||
\(442\) | −13.2487 | − | 13.2487i | −0.630178 | − | 0.630178i | ||||
\(443\) | −23.3635 | − | 23.3635i | −1.11003 | − | 1.11003i | −0.993145 | − | 0.116888i | \(-0.962708\pi\) |
−0.116888 | − | 0.993145i | \(-0.537292\pi\) | |||||||
\(444\) | −4.00000 | − | 2.82843i | −0.189832 | − | 0.134231i | ||||
\(445\) | 10.9393 | + | 11.6918i | 0.518574 | + | 0.554242i | ||||
\(446\) | − | 15.6430i | − | 0.740718i | ||||||
\(447\) | 5.49792 | + | 32.0442i | 0.260043 | + | 1.51564i | ||||
\(448\) | 1.33991 | − | 1.33991i | 0.0633049 | − | 0.0633049i | ||||
\(449\) | 26.7530 | 1.26255 | 0.631277 | − | 0.775558i | \(-0.282531\pi\) | ||||
0.631277 | + | 0.775558i | \(0.282531\pi\) | |||||||
\(450\) | −13.0763 | − | 7.34923i | −0.616421 | − | 0.346446i | ||||
\(451\) | 3.68235 | 0.173395 | ||||||||
\(452\) | 1.51148 | − | 1.51148i | 0.0710943 | − | 0.0710943i | ||||
\(453\) | 1.32359 | + | 7.71445i | 0.0621877 | + | 0.362456i | ||||
\(454\) | 14.3750i | 0.674652i | ||||||||
\(455\) | −7.14949 | − | 7.64124i | −0.335173 | − | 0.358227i | ||||
\(456\) | 6.14860 | + | 4.34772i | 0.287935 | + | 0.203601i | ||||
\(457\) | 25.1188 | + | 25.1188i | 1.17501 | + | 1.17501i | 0.981000 | + | 0.194007i | \(0.0621484\pi\) |
0.194007 | + | 0.981000i | \(0.437852\pi\) | |||||||
\(458\) | −9.48852 | − | 9.48852i | −0.443369 | − | 0.443369i | ||||
\(459\) | 37.9334 | + | 10.7292i | 1.77058 | + | 0.500795i | ||||
\(460\) | −15.0256 | − | 0.499557i | −0.700570 | − | 0.0232920i | ||||
\(461\) | 5.36953i | 0.250084i | 0.992151 | + | 0.125042i | \(0.0399065\pi\) | ||||
−0.992151 | + | 0.125042i | \(0.960093\pi\) | |||||||
\(462\) | 4.23483 | − | 0.726583i | 0.197022 | − | 0.0338037i | ||||
\(463\) | −4.97423 | + | 4.97423i | −0.231172 | + | 0.231172i | −0.813182 | − | 0.582010i | \(-0.802267\pi\) |
0.582010 | + | 0.813182i | \(0.302267\pi\) | |||||||
\(464\) | 5.50825 | 0.255714 | ||||||||
\(465\) | 2.33991 | − | 3.08623i | 0.108511 | − | 0.143120i | ||||
\(466\) | 13.5071 | 0.625704 | ||||||||
\(467\) | −15.3051 | + | 15.3051i | −0.708235 | + | 0.708235i | −0.966164 | − | 0.257929i | \(-0.916960\pi\) |
0.257929 | + | 0.966164i | \(0.416960\pi\) | |||||||
\(468\) | −6.68565 | − | 3.19301i | −0.309044 | − | 0.147597i | ||||
\(469\) | − | 14.8063i | − | 0.683693i | ||||||
\(470\) | 8.46967 | − | 7.92460i | 0.390677 | − | 0.365535i | ||||
\(471\) | −16.2723 | + | 23.0125i | −0.749789 | + | 1.06036i | ||||
\(472\) | 8.04441 | + | 8.04441i | 0.370274 | + | 0.370274i | ||||
\(473\) | 4.58255 | + | 4.58255i | 0.210706 | + | 0.210706i | ||||
\(474\) | 4.64493 | − | 6.56892i | 0.213349 | − | 0.301720i | ||||
\(475\) | −21.6906 | − | 1.44390i | −0.995233 | − | 0.0662505i | ||||
\(476\) | − | 14.3761i | − | 0.658930i | ||||||
\(477\) | 24.6965 | + | 11.7948i | 1.13077 | + | 0.540049i | ||||
\(478\) | −20.1480 | + | 20.1480i | −0.921546 | + | 0.921546i | ||||
\(479\) | −16.3832 | −0.748569 | −0.374284 | − | 0.927314i | \(-0.622112\pi\) | ||||
−0.374284 | + | 0.927314i | \(0.622112\pi\) | |||||||
\(480\) | 0.527726 | + | 3.83686i | 0.0240873 | + | 0.175128i | ||||
\(481\) | 6.98527 | 0.318501 | ||||||||
\(482\) | −7.40317 | + | 7.40317i | −0.337205 | + | 0.337205i | ||||
\(483\) | 21.7489 | − | 3.73152i | 0.989610 | − | 0.169790i | ||||
\(484\) | − | 9.28617i | − | 0.422098i | ||||||
\(485\) | −0.157232 | + | 4.72918i | −0.00713952 | + | 0.214741i | ||||
\(486\) | 15.5563 | − | 1.00000i | 0.705650 | − | 0.0453609i | ||||
\(487\) | −7.85481 | − | 7.85481i | −0.355935 | − | 0.355935i | 0.506377 | − | 0.862312i | \(-0.330984\pi\) |
−0.862312 | + | 0.506377i | \(0.830984\pi\) | |||||||
\(488\) | −8.87284 | − | 8.87284i | −0.401655 | − | 0.401655i | ||||
\(489\) | −0.210157 | − | 0.148604i | −0.00950364 | − | 0.00672009i | ||||
\(490\) | −0.253315 | + | 7.61916i | −0.0114436 | + | 0.344198i | ||||
\(491\) | 34.0475i | 1.53654i | 0.640126 | + | 0.768270i | \(0.278882\pi\) | ||||
−0.640126 | + | 0.768270i | \(0.721118\pi\) | |||||||
\(492\) | −0.823854 | − | 4.80177i | −0.0371422 | − | 0.216481i | ||||
\(493\) | 29.5495 | − | 29.5495i | 1.33084 | − | 1.33084i | ||||
\(494\) | −10.7374 | −0.483099 | ||||||||
\(495\) | −4.04594 | + | 7.79442i | −0.181851 | + | 0.350333i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −13.8650 | + | 13.8650i | −0.621932 | + | 0.621932i | ||||
\(498\) | −4.67525 | − | 27.2494i | −0.209503 | − | 1.22107i | ||||
\(499\) | 0.442369i | 0.0198031i | 0.999951 | + | 0.00990157i | \(0.00315182\pi\) | ||||
−0.999951 | + | 0.00990157i | \(0.996848\pi\) | |||||||
\(500\) | −7.07950 | − | 8.65336i | −0.316605 | − | 0.386990i | ||||
\(501\) | 1.77423 | + | 1.25457i | 0.0792666 | + | 0.0560500i | ||||
\(502\) | −19.6685 | − | 19.6685i | −0.877848 | − | 0.877848i | ||||
\(503\) | −0.431356 | − | 0.431356i | −0.0192332 | − | 0.0192332i | 0.697425 | − | 0.716658i | \(-0.254329\pi\) |
−0.716658 | + | 0.697425i | \(0.754329\pi\) | |||||||
\(504\) | −1.89492 | − | 5.35965i | −0.0844065 | − | 0.238738i | ||||
\(505\) | 21.9853 | − | 20.5704i | 0.978332 | − | 0.915372i | ||||
\(506\) | 8.80177i | 0.391286i | ||||||||
\(507\) | −11.7803 | + | 2.02118i | −0.523182 | + | 0.0897639i | ||||
\(508\) | −2.40811 | + | 2.40811i | −0.106843 | + | 0.106843i | ||||
\(509\) | −11.4584 | −0.507882 | −0.253941 | − | 0.967220i | \(-0.581727\pi\) | ||||
−0.253941 | + | 0.967220i | \(0.581727\pi\) | |||||||
\(510\) | 23.4142 | + | 17.7521i | 1.03680 | + | 0.786078i | ||||
\(511\) | 5.01193 | 0.221715 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 19.7192 | − | 11.0238i | 0.870625 | − | 0.486712i | ||||
\(514\) | 6.52182i | 0.287665i | ||||||||
\(515\) | 32.8796 | + | 1.09315i | 1.44885 | + | 0.0481700i | ||||
\(516\) | 4.95037 | − | 7.00089i | 0.217928 | − | 0.308197i | ||||
\(517\) | −4.80177 | − | 4.80177i | −0.211182 | − | 0.211182i | ||||
\(518\) | 3.78984 | + | 3.78984i | 0.166516 | + | 0.166516i | ||||
\(519\) | −23.8566 | + | 33.7383i | −1.04719 | + | 1.48095i | ||||
\(520\) | −3.77297 | − | 4.03248i | −0.165456 | − | 0.176836i | ||||
\(521\) | 28.0633i | 1.22948i | 0.788731 | + | 0.614738i | \(0.210738\pi\) | ||||
−0.788731 | + | 0.614738i | \(0.789262\pi\) | |||||||
\(522\) | 7.12158 | − | 14.9114i | 0.311703 | − | 0.652655i | ||||
\(523\) | 17.9033 | − | 17.9033i | 0.782858 | − | 0.782858i | −0.197454 | − | 0.980312i | \(-0.563267\pi\) |
0.980312 | + | 0.197454i | \(0.0632672\pi\) | |||||||
\(524\) | 8.82321 | 0.385444 | ||||||||
\(525\) | 12.7402 | + | 10.3437i | 0.556029 | + | 0.451435i | ||||
\(526\) | 1.67372 | 0.0729778 | ||||||||
\(527\) | −5.36459 | + | 5.36459i | −0.233685 | + | 0.233685i | ||||
\(528\) | 2.23483 | − | 0.383437i | 0.0972586 | − | 0.0166869i | ||||
\(529\) | 22.2034i | 0.965366i | ||||||||
\(530\) | 13.9372 | + | 14.8958i | 0.605393 | + | 0.647033i | ||||
\(531\) | 32.1776 | − | 11.3765i | 1.39639 | − | 0.493699i | ||||
\(532\) | −5.82556 | − | 5.82556i | −0.252570 | − | 0.252570i | ||||
\(533\) | 4.91206 | + | 4.91206i | 0.212765 | + | 0.212765i | ||||
\(534\) | −10.1265 | − | 7.16053i | −0.438217 | − | 0.309866i | ||||
\(535\) | 25.6594 | + | 0.853103i | 1.10935 | + | 0.0368829i | ||||
\(536\) | − | 7.81370i | − | 0.337500i | ||||||
\(537\) | 3.62080 | + | 21.1036i | 0.156249 | + | 0.910685i | ||||
\(538\) | 1.30331 | − | 1.30331i | 0.0561896 | − | 0.0561896i | ||||
\(539\) | 4.46320 | 0.192244 | ||||||||
\(540\) | 11.0691 | + | 3.53204i | 0.476338 | + | 0.151995i | ||||
\(541\) | −15.0757 | −0.648156 | −0.324078 | − | 0.946030i | \(-0.605054\pi\) | ||||
−0.324078 | + | 0.946030i | \(0.605054\pi\) | |||||||
\(542\) | −11.2311 | + | 11.2311i | −0.482419 | + | 0.482419i | ||||
\(543\) | 0.00170666 | + | 0.00994714i | 7.32397e−5 | + | 0.000426873i | ||||
\(544\) | − | 7.58667i | − | 0.325276i | ||||||
\(545\) | 0.498736 | − | 0.466640i | 0.0213635 | − | 0.0199887i | ||||
\(546\) | 6.61827 | + | 4.67982i | 0.283236 | + | 0.200278i | ||||
\(547\) | 11.0600 | + | 11.0600i | 0.472893 | + | 0.472893i | 0.902849 | − | 0.429957i | \(-0.141471\pi\) |
−0.429957 | + | 0.902849i | \(0.641471\pi\) | |||||||
\(548\) | 12.2546 | + | 12.2546i | 0.523489 | + | 0.523489i | ||||
\(549\) | −35.4914 | + | 12.5481i | −1.51473 | + | 0.535539i | ||||
\(550\) | −4.92570 | + | 4.31084i | −0.210032 | + | 0.183815i | ||||
\(551\) | − | 23.9483i | − | 1.02023i | ||||||
\(552\) | 11.4775 | − | 1.96922i | 0.488514 | − | 0.0838157i | ||||
\(553\) | −6.22379 | + | 6.22379i | −0.264663 | + | 0.264663i | ||||
\(554\) | −1.65344 | −0.0702480 | ||||||||
\(555\) | −10.8523 | + | 1.49264i | −0.460654 | + | 0.0633589i | ||||
\(556\) | −10.0563 | −0.426484 | ||||||||
\(557\) | 9.15272 | − | 9.15272i | 0.387813 | − | 0.387813i | −0.486093 | − | 0.873907i | \(-0.661579\pi\) |
0.873907 | + | 0.486093i | \(0.161579\pi\) | |||||||
\(558\) | −1.29289 | + | 2.70711i | −0.0547325 | + | 0.114601i | ||||
\(559\) | 12.2258i | 0.517095i | ||||||||
\(560\) | 0.140796 | − | 4.23483i | 0.00594972 | − | 0.178954i | ||||
\(561\) | 9.93198 | − | 14.0459i | 0.419328 | − | 0.593020i | ||||
\(562\) | −4.02386 | − | 4.02386i | −0.169736 | − | 0.169736i | ||||
\(563\) | −23.0321 | − | 23.0321i | −0.970688 | − | 0.970688i | 0.0288945 | − | 0.999582i | \(-0.490801\pi\) |
−0.999582 | + | 0.0288945i | \(0.990801\pi\) | |||||||
\(564\) | −5.18719 | + | 7.33579i | −0.218420 | + | 0.308893i | ||||
\(565\) | 0.158825 | − | 4.77709i | 0.00668181 | − | 0.200974i | ||||
\(566\) | 0.834895i | 0.0350933i | ||||||||
\(567\) | −16.9591 | − | 1.79970i | −0.712214 | − | 0.0755802i | ||||
\(568\) | −7.31694 | + | 7.31694i | −0.307012 | + | 0.307012i | ||||
\(569\) | −19.7684 | −0.828733 | −0.414367 | − | 0.910110i | \(-0.635997\pi\) | ||||
−0.414367 | + | 0.910110i | \(0.635997\pi\) | |||||||
\(570\) | 16.6816 | − | 2.29441i | 0.698715 | − | 0.0961021i | ||||
\(571\) | 28.0308 | 1.17305 | 0.586527 | − | 0.809930i | \(-0.300495\pi\) | ||||
0.586527 | + | 0.809930i | \(0.300495\pi\) | |||||||
\(572\) | −2.28617 | + | 2.28617i | −0.0955894 | + | 0.0955894i | ||||
\(573\) | −7.82629 | + | 1.34278i | −0.326948 | + | 0.0560954i | ||||
\(574\) | 5.33006i | 0.222472i | ||||||||
\(575\) | −25.2970 | + | 22.1393i | −1.05496 | + | 0.923271i | ||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | −28.9740 | − | 28.9740i | −1.20620 | − | 1.20620i | −0.972248 | − | 0.233954i | \(-0.924834\pi\) |
−0.233954 | − | 0.972248i | \(-0.575166\pi\) | |||||||
\(578\) | −28.6786 | − | 28.6786i | −1.19287 | − | 1.19287i | ||||
\(579\) | −33.9025 | − | 23.9727i | −1.40894 | − | 0.996272i | ||||
\(580\) | 8.99390 | − | 8.41510i | 0.373451 | − | 0.349418i | ||||
\(581\) | 30.2473i | 1.25487i | ||||||||
\(582\) | −0.619797 | − | 3.61244i | −0.0256914 | − | 0.149741i | ||||
\(583\) | 8.44499 | − | 8.44499i | 0.349756 | − | 0.349756i | ||||
\(584\) | 2.64493 | 0.109448 | ||||||||
\(585\) | −15.7944 | + | 5.00027i | −0.653019 | + | 0.206736i | ||||
\(586\) | −7.21446 | −0.298026 | ||||||||
\(587\) | −15.8009 | + | 15.8009i | −0.652172 | + | 0.652172i | −0.953516 | − | 0.301343i | \(-0.902565\pi\) |
0.301343 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(588\) | −0.998553 | − | 5.81999i | −0.0411796 | − | 0.240012i | ||||
\(589\) | 4.34772i | 0.179145i | ||||||||
\(590\) | 25.4246 | + | 0.845296i | 1.04671 | + | 0.0348003i | ||||
\(591\) | 21.2193 | + | 15.0043i | 0.872845 | + | 0.617194i | ||||
\(592\) | 2.00000 | + | 2.00000i | 0.0821995 | + | 0.0821995i | ||||
\(593\) | 14.7665 | + | 14.7665i | 0.606387 | + | 0.606387i | 0.942000 | − | 0.335613i | \(-0.108943\pi\) |
−0.335613 | + | 0.942000i | \(0.608943\pi\) | |||||||
\(594\) | 1.85140 | − | 6.54567i | 0.0759637 | − | 0.268572i | ||||
\(595\) | −21.9628 | − | 23.4734i | −0.900388 | − | 0.962317i | ||||
\(596\) | − | 18.7711i | − | 0.768893i | ||||||
\(597\) | 7.98698 | − | 1.37035i | 0.326885 | − | 0.0560846i | ||||
\(598\) | −11.7411 | + | 11.7411i | −0.480129 | + | 0.480129i | ||||
\(599\) | 41.7822 | 1.70718 | 0.853588 | − | 0.520949i | \(-0.174422\pi\) | ||||
0.853588 | + | 0.520949i | \(0.174422\pi\) | |||||||
\(600\) | 6.72335 | + | 5.45862i | 0.274480 | + | 0.222847i | ||||
\(601\) | −6.41153 | −0.261532 | −0.130766 | − | 0.991413i | \(-0.541744\pi\) | ||||
−0.130766 | + | 0.991413i | \(0.541744\pi\) | |||||||
\(602\) | −6.63306 | + | 6.63306i | −0.270344 | + | 0.270344i | ||||
\(603\) | −21.1525 | − | 10.1023i | −0.861397 | − | 0.411397i | ||||
\(604\) | − | 4.51902i | − | 0.183876i | ||||||
\(605\) | −14.1867 | − | 15.1625i | −0.576772 | − | 0.616443i | ||||
\(606\) | −13.4647 | + | 19.0420i | −0.546967 | + | 0.773528i | ||||
\(607\) | −22.7744 | − | 22.7744i | −0.924385 | − | 0.924385i | 0.0729509 | − | 0.997336i | \(-0.476758\pi\) |
−0.997336 | + | 0.0729509i | \(0.976758\pi\) | |||||||
\(608\) | −3.07430 | − | 3.07430i | −0.124679 | − | 0.124679i | ||||
\(609\) | −10.4377 | + | 14.7611i | −0.422957 | + | 0.598152i | ||||
\(610\) | −28.0429 | − | 0.932346i | −1.13542 | − | 0.0377496i | ||||
\(611\) | − | 12.8106i | − | 0.518262i | ||||||
\(612\) | −20.5379 | − | 9.80876i | −0.830197 | − | 0.396496i | ||||
\(613\) | 31.6523 | − | 31.6523i | 1.27842 | − | 1.27842i | 0.336872 | − | 0.941550i | \(-0.390631\pi\) |
0.941550 | − | 0.336872i | \(-0.109369\pi\) | |||||||
\(614\) | 9.38350 | 0.378687 | ||||||||
\(615\) | −8.68098 | − | 6.58173i | −0.350051 | − | 0.265401i | ||||
\(616\) | −2.48071 | −0.0999506 | ||||||||
\(617\) | 25.0215 | − | 25.0215i | 1.00733 | − | 1.00733i | 0.00735502 | − | 0.999973i | \(-0.497659\pi\) |
0.999973 | − | 0.00735502i | \(-0.00234120\pi\) | |||||||
\(618\) | −25.1155 | + | 4.30913i | −1.01029 | + | 0.173339i | ||||
\(619\) | − | 13.5269i | − | 0.543692i | −0.962341 | − | 0.271846i | \(-0.912366\pi\) | ||
0.962341 | − | 0.271846i | \(-0.0876341\pi\) | |||||||
\(620\) | −1.63280 | + | 1.52773i | −0.0655750 | + | 0.0613550i | ||||
\(621\) | 9.50825 | − | 33.6167i | 0.381553 | − | 1.34899i | ||||
\(622\) | 16.5719 | + | 16.5719i | 0.664474 | + | 0.664474i | ||||
\(623\) | 9.59448 | + | 9.59448i | 0.384395 | + | 0.384395i | ||||
\(624\) | 3.49264 | + | 2.46967i | 0.139817 | + | 0.0988658i | ||||
\(625\) | −24.7794 | − | 3.31371i | −0.991177 | − | 0.132548i | ||||
\(626\) | 9.10838i | 0.364044i | ||||||||
\(627\) | −1.66708 | − | 9.71643i | −0.0665766 | − | 0.388037i | ||||
\(628\) | 11.5063 | − | 11.5063i | 0.459150 | − | 0.459150i | ||||
\(629\) | 21.4584 | 0.855600 | ||||||||
\(630\) | −11.2821 | − | 5.85634i | −0.449490 | − | 0.233322i | ||||
\(631\) | −7.61854 | −0.303289 | −0.151645 | − | 0.988435i | \(-0.548457\pi\) | ||||
−0.151645 | + | 0.988435i | \(0.548457\pi\) | |||||||
\(632\) | −3.28446 | + | 3.28446i | −0.130649 | + | 0.130649i | ||||
\(633\) | −3.32582 | − | 19.3843i | −0.132190 | − | 0.770458i | ||||
\(634\) | 26.8679i | 1.06706i | ||||||||
\(635\) | −0.253041 | + | 7.61092i | −0.0100416 | + | 0.302030i | ||||
\(636\) | −12.9016 | − | 9.12283i | −0.511583 | − | 0.361744i | ||||
\(637\) | 5.95367 | + | 5.95367i | 0.235893 | + | 0.235893i | ||||
\(638\) | −5.09898 | − | 5.09898i | −0.201870 | − | 0.201870i | ||||
\(639\) | 10.3477 | + | 29.2678i | 0.409349 | + | 1.15782i | ||||
\(640\) | 0.0743018 | − | 2.23483i | 0.00293704 | − | 0.0883395i | ||||
\(641\) | 27.0147i | 1.06702i | 0.845795 | + | 0.533509i | \(0.179127\pi\) | ||||
−0.845795 | + | 0.533509i | \(0.820873\pi\) | |||||||
\(642\) | −19.6003 | + | 3.36288i | −0.773562 | + | 0.132722i | ||||
\(643\) | −22.7661 | + | 22.7661i | −0.897805 | + | 0.897805i | −0.995242 | − | 0.0974363i | \(-0.968936\pi\) |
0.0974363 | + | 0.995242i | \(0.468936\pi\) | |||||||
\(644\) | −12.7402 | −0.502035 | ||||||||
\(645\) | −2.61244 | − | 18.9939i | −0.102865 | − | 0.747884i | ||||
\(646\) | −32.9847 | −1.29777 | ||||||||
\(647\) | 1.65399 | − | 1.65399i | 0.0650250 | − | 0.0650250i | −0.673846 | − | 0.738871i | \(-0.735359\pi\) |
0.738871 | + | 0.673846i | \(0.235359\pi\) | |||||||
\(648\) | −8.94975 | − | 0.949747i | −0.351579 | − | 0.0373096i | ||||
\(649\) | − | 14.8934i | − | 0.584617i | ||||||
\(650\) | −12.3211 | − | 0.820187i | −0.483272 | − | 0.0321704i | ||||
\(651\) | 1.89492 | − | 2.67982i | 0.0742678 | − | 0.105031i | ||||
\(652\) | 0.105079 | + | 0.105079i | 0.00411520 | + | 0.00411520i | ||||
\(653\) | −21.6841 | − | 21.6841i | −0.848565 | − | 0.848565i | 0.141389 | − | 0.989954i | \(-0.454843\pi\) |
−0.989954 | + | 0.141389i | \(0.954843\pi\) | |||||||
\(654\) | −0.305448 | + | 0.431968i | −0.0119439 | + | 0.0168913i | ||||
\(655\) | 14.4066 | − | 13.4795i | 0.562912 | − | 0.526686i | ||||
\(656\) | 2.81281i | 0.109822i | ||||||||
\(657\) | 3.41961 | − | 7.16010i | 0.133412 | − | 0.279342i | ||||
\(658\) | 6.95037 | − | 6.95037i | 0.270954 | − | 0.270954i | ||||
\(659\) | −16.5520 | −0.644776 | −0.322388 | − | 0.946608i | \(-0.604486\pi\) | ||||
−0.322388 | + | 0.946608i | \(0.604486\pi\) | |||||||
\(660\) | 3.06326 | − | 4.04029i | 0.119237 | − | 0.157268i | ||||
\(661\) | −37.1356 | −1.44441 | −0.722205 | − | 0.691679i | \(-0.756871\pi\) | ||||
−0.722205 | + | 0.691679i | \(0.756871\pi\) | |||||||
\(662\) | 2.86244 | − | 2.86244i | 0.111252 | − | 0.111252i | ||||
\(663\) | 31.9853 | − | 5.48781i | 1.24221 | − | 0.213129i | ||||
\(664\) | 15.9623i | 0.619457i | ||||||||
\(665\) | −18.4119 | − | 0.612142i | −0.713982 | − | 0.0237378i | ||||
\(666\) | 8.00000 | − | 2.82843i | 0.309994 | − | 0.109599i | ||||
\(667\) | −26.1869 | − | 26.1869i | −1.01396 | − | 1.01396i | ||||
\(668\) | −0.887114 | − | 0.887114i | −0.0343235 | − | 0.0343235i | ||||
\(669\) | 22.1226 | + | 15.6430i | 0.855308 | + | 0.604794i | ||||
\(670\) | −11.9372 | − | 12.7582i | −0.461174 | − | 0.492894i | ||||
\(671\) | 16.4271i | 0.634163i | ||||||||
\(672\) | 0.555010 | + | 3.23483i | 0.0214100 | + | 0.124786i | ||||
\(673\) | −18.2328 | + | 18.2328i | −0.702821 | + | 0.702821i | −0.965015 | − | 0.262194i | \(-0.915554\pi\) |
0.262194 | + | 0.965015i | \(0.415554\pi\) | |||||||
\(674\) | 8.58453 | 0.330664 | ||||||||
\(675\) | 23.4697 | − | 11.1434i | 0.903347 | − | 0.428910i | ||||
\(676\) | 6.90075 | 0.265413 | ||||||||
\(677\) | −25.1358 | + | 25.1358i | −0.966048 | + | 0.966048i | −0.999442 | − | 0.0333940i | \(-0.989368\pi\) |
0.0333940 | + | 0.999442i | \(0.489368\pi\) | |||||||
\(678\) | 0.626077 | + | 3.64905i | 0.0240444 | + | 0.140141i | ||||
\(679\) | 4.00988i | 0.153885i | ||||||||
\(680\) | −11.5904 | − | 12.3876i | −0.444470 | − | 0.475041i | ||||
\(681\) | −20.3293 | − | 14.3750i | −0.779021 | − | 0.550851i | ||||
\(682\) | 0.925698 | + | 0.925698i | 0.0354468 | + | 0.0354468i | ||||
\(683\) | −13.0152 | − | 13.0152i | −0.498011 | − | 0.498011i | 0.412807 | − | 0.910818i | \(-0.364548\pi\) |
−0.910818 | + | 0.412807i | \(0.864548\pi\) | |||||||
\(684\) | −12.2972 | + | 4.34772i | −0.470195 | + | 0.166239i | ||||
\(685\) | 38.7309 | + | 1.28769i | 1.47983 | + | 0.0492002i | ||||
\(686\) | 19.7248i | 0.753095i | ||||||||
\(687\) | 22.9073 | − | 3.93027i | 0.873968 | − | 0.149949i | ||||
\(688\) | −3.50044 | + | 3.50044i | −0.133453 | + | 0.133453i | ||||
\(689\) | 22.5304 | 0.858338 | ||||||||
\(690\) | 15.7320 | − | 20.7498i | 0.598909 | − | 0.789931i | ||||
\(691\) | −43.9053 | −1.67024 | −0.835119 | − | 0.550070i | \(-0.814601\pi\) | ||||
−0.835119 | + | 0.550070i | \(0.814601\pi\) | |||||||
\(692\) | 16.8692 | − | 16.8692i | 0.641269 | − | 0.641269i | ||||
\(693\) | −3.20729 | + | 6.71554i | −0.121835 | + | 0.255102i | ||||
\(694\) | − | 25.1118i | − | 0.953231i | ||||||
\(695\) | −16.4200 | + | 15.3633i | −0.622848 | + | 0.582764i | ||||
\(696\) | −5.50825 | + | 7.78984i | −0.208790 | + | 0.295273i | ||||
\(697\) | 15.0896 | + | 15.0896i | 0.571558 | + | 0.571558i | ||||
\(698\) | −8.81980 | − | 8.81980i | −0.333834 | − | 0.333834i | ||||
\(699\) | −13.5071 | + | 19.1019i | −0.510885 | + | 0.722501i | ||||
\(700\) | −6.23977 | − | 7.12975i | −0.235841 | − | 0.269479i | ||||
\(701\) | 4.67181i | 0.176452i | 0.996100 | + | 0.0882259i | \(0.0281197\pi\) | ||||
−0.996100 | + | 0.0882259i | \(0.971880\pi\) | |||||||
\(702\) | 11.2013 | − | 6.26192i | 0.422764 | − | 0.236341i | ||||
\(703\) | 8.69544 | − | 8.69544i | 0.327955 | − | 0.327955i | ||||
\(704\) | −1.30913 | −0.0493399 | ||||||||
\(705\) | 2.73742 | + | 19.9025i | 0.103097 | + | 0.749572i | ||||
\(706\) | 3.62437 | 0.136405 | ||||||||
\(707\) | 18.0415 | − | 18.0415i | 0.678522 | − | 0.678522i | ||||
\(708\) | −19.4209 | + | 3.33210i | −0.729883 | + | 0.125228i | ||||
\(709\) | − | 34.5708i | − | 1.29833i | −0.760646 | − | 0.649167i | \(-0.775118\pi\) | ||
0.760646 | − | 0.649167i | \(-0.224882\pi\) | |||||||
\(710\) | −0.768854 | + | 23.1254i | −0.0288546 | + | 0.867882i | ||||
\(711\) | 4.64493 | + | 13.1378i | 0.174198 | + | 0.492707i | ||||
\(712\) | 5.06326 | + | 5.06326i | 0.189754 | + | 0.189754i | ||||
\(713\) | 4.75413 | + | 4.75413i | 0.178043 | + | 0.178043i | ||||
\(714\) | 20.3309 | + | 14.3761i | 0.760866 | + | 0.538014i | ||||
\(715\) | −0.240227 | + | 7.22550i | −0.00898398 | + | 0.270218i | ||||
\(716\) | − | 12.3622i | − | 0.461996i | ||||||
\(717\) | −8.34556 | − | 48.6415i | −0.311671 | − | 1.81655i | ||||
\(718\) | −2.80958 | + | 2.80958i | −0.104853 | + | 0.104853i | ||||
\(719\) | 35.9553 | 1.34091 | 0.670453 | − | 0.741952i | \(-0.266100\pi\) | ||||
0.670453 | + | 0.741952i | \(0.266100\pi\) | |||||||
\(720\) | −5.95387 | − | 3.09054i | −0.221888 | − | 0.115178i | ||||
\(721\) | 27.8787 | 1.03826 | ||||||||
\(722\) | 0.0688276 | − | 0.0688276i | 0.00256150 | − | 0.00256150i | ||||
\(723\) | −3.06649 | − | 17.8728i | −0.114044 | − | 0.664698i | ||||
\(724\) | − | 0.00582690i | − | 0.000216555i | ||||||
\(725\) | 1.82931 | − | 27.4804i | 0.0679390 | − | 1.02060i | ||||
\(726\) | 13.1326 | + | 9.28617i | 0.487397 | + | 0.344642i | ||||
\(727\) | 9.01238 | + | 9.01238i | 0.334251 | + | 0.334251i | 0.854198 | − | 0.519948i | \(-0.174049\pi\) |
−0.519948 | + | 0.854198i | \(0.674049\pi\) | |||||||
\(728\) | −3.30913 | − | 3.30913i | −0.122645 | − | 0.122645i | ||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | 4.31865 | − | 4.04072i | 0.159840 | − | 0.149554i | ||||
\(731\) | 37.5569i | 1.38909i | ||||||||
\(732\) | 21.4209 | − | 3.67525i | 0.791740 | − | 0.135841i | ||||
\(733\) | −13.6035 | + | 13.6035i | −0.502458 | + | 0.502458i | −0.912201 | − | 0.409743i | \(-0.865618\pi\) |
0.409743 | + | 0.912201i | \(0.365618\pi\) | |||||||
\(734\) | 25.4246 | 0.938440 | ||||||||
\(735\) | −10.5218 | − | 7.97740i | −0.388102 | − | 0.294251i | ||||
\(736\) | −6.72335 | −0.247826 | ||||||||
\(737\) | −7.23313 | + | 7.23313i | −0.266436 | + | 0.266436i | ||||
\(738\) | 7.61458 | + | 3.63667i | 0.280297 | + | 0.133868i | ||||
\(739\) | − | 7.56118i | − | 0.278142i | −0.990282 | − | 0.139071i | \(-0.955588\pi\) | ||
0.990282 | − | 0.139071i | \(-0.0444117\pi\) | |||||||
\(740\) | 6.32106 | + | 0.210157i | 0.232367 | + | 0.00772553i | ||||
\(741\) | 10.7374 | − | 15.1850i | 0.394449 | − | 0.557835i | ||||
\(742\) | 12.2238 | + | 12.2238i | 0.448750 | + | 0.448750i | ||||
\(743\) | 5.94778 | + | 5.94778i | 0.218203 | + | 0.218203i | 0.807741 | − | 0.589538i | \(-0.200690\pi\) |
−0.589538 | + | 0.807741i | \(0.700690\pi\) | |||||||
\(744\) | 1.00000 | − | 1.41421i | 0.0366618 | − | 0.0518476i | ||||
\(745\) | −28.6770 | − | 30.6495i | −1.05065 | − | 1.12291i | ||||
\(746\) | 24.3256i | 0.890625i | ||||||||
\(747\) | 43.2117 | + | 20.6376i | 1.58103 | + | 0.755089i | ||||
\(748\) | −7.02297 | + | 7.02297i | −0.256785 | + | 0.256785i | ||||
\(749\) | 21.7567 | 0.794973 | ||||||||
\(750\) | 19.3172 | − | 1.35857i | 0.705364 | − | 0.0496079i | ||||
\(751\) | −16.5568 | −0.604168 | −0.302084 | − | 0.953281i | \(-0.597682\pi\) | ||||
−0.302084 | + | 0.953281i | \(0.597682\pi\) | |||||||
\(752\) | 3.66790 | − | 3.66790i | 0.133754 | − | 0.133754i | ||||
\(753\) | 47.4840 | − | 8.14696i | 1.73041 | − | 0.296892i | ||||
\(754\) | − | 13.6035i | − | 0.495412i | ||||||
\(755\) | −6.90382 | − | 7.37868i | −0.251256 | − | 0.268537i | ||||
\(756\) | 9.47461 | + | 2.67982i | 0.344588 | + | 0.0974642i | ||||
\(757\) | −34.3170 | − | 34.3170i | −1.24727 | − | 1.24727i | −0.956919 | − | 0.290353i | \(-0.906227\pi\) |
−0.290353 | − | 0.956919i | \(-0.593773\pi\) | |||||||
\(758\) | −10.2459 | − | 10.2459i | −0.372147 | − | 0.372147i | ||||
\(759\) | −12.4476 | − | 8.80177i | −0.451819 | − | 0.319484i | ||||
\(760\) | −9.71643 | − | 0.323043i | −0.352452 | − | 0.0117180i | ||||
\(761\) | 3.62624i | 0.131451i | 0.997838 | + | 0.0657255i | \(0.0209362\pi\) | ||||
−0.997838 | + | 0.0657255i | \(0.979064\pi\) | |||||||
\(762\) | −0.997473 | − | 5.81370i | −0.0361346 | − | 0.210608i | ||||
\(763\) | 0.409273 | − | 0.409273i | 0.0148167 | − | 0.0148167i | ||||
\(764\) | 4.58453 | 0.165863 | ||||||||
\(765\) | −48.5195 | + | 15.3606i | −1.75423 | + | 0.555362i | ||||
\(766\) | 35.0113 | 1.26501 | ||||||||
\(767\) | 19.8670 | − | 19.8670i | 0.717356 | − | 0.717356i | ||||
\(768\) | 0.292893 | + | 1.70711i | 0.0105689 | + | 0.0615999i | ||||
\(769\) | 1.52093i | 0.0548462i | 0.999624 | + | 0.0274231i | \(0.00873015\pi\) | ||||
−0.999624 | + | 0.0274231i | \(0.991270\pi\) | |||||||
\(770\) | −4.05051 | + | 3.78984i | −0.145970 | + | 0.136576i | ||||
\(771\) | −9.22325 | − | 6.52182i | −0.332167 | − | 0.234878i | ||||
\(772\) | 16.9513 | + | 16.9513i | 0.610089 | + | 0.610089i | ||||
\(773\) | −8.91707 | − | 8.91707i | −0.320725 | − | 0.320725i | 0.528320 | − | 0.849045i | \(-0.322822\pi\) |
−0.849045 | + | 0.528320i | \(0.822822\pi\) | |||||||
\(774\) | 4.95037 | + | 14.0018i | 0.177938 | + | 0.503283i | ||||
\(775\) | −0.332104 | + | 4.98896i | −0.0119295 | + | 0.179209i | ||||
\(776\) | 2.11612i | 0.0759643i | ||||||||
\(777\) | −9.14949 | + | 1.56980i | −0.328236 | + | 0.0563164i | ||||
\(778\) | 23.3655 | − | 23.3655i | 0.837693 | − | 0.837693i | ||||
\(779\) | 12.2293 | 0.438161 | ||||||||
\(780\) | 9.47577 | − | 1.30331i | 0.339287 | − | 0.0466659i | ||||
\(781\) | 13.5466 | 0.484734 | ||||||||
\(782\) | −36.0680 | + | 36.0680i | −1.28979 | + | 1.28979i | ||||
\(783\) | 13.9664 | + | 24.9829i | 0.499117 | + | 0.892814i | ||||
\(784\) | 3.40927i | 0.121760i | ||||||||
\(785\) | 1.20906 | − | 36.3659i | 0.0431533 | − | 1.29796i | ||||
\(786\) | −8.82321 | + | 12.4779i | −0.314714 | + | 0.445072i | ||||
\(787\) | 27.2682 | + | 27.2682i | 0.972006 | + | 0.972006i | 0.999619 | − | 0.0276123i | \(-0.00879037\pi\) |
−0.0276123 | + | 0.999619i | \(0.508790\pi\) | |||||||
\(788\) | −10.6096 | − | 10.6096i | −0.377953 | − | 0.377953i | ||||
\(789\) | −1.67372 | + | 2.36700i | −0.0595861 | + | 0.0842675i | ||||
\(790\) | −0.345126 | + | 10.3806i | −0.0122790 | + | 0.369326i | ||||
\(791\) | − | 4.05051i | − | 0.144020i | ||||||
\(792\) | −1.69257 | + | 3.54397i | −0.0601429 | + | 0.125929i | ||||
\(793\) | −21.9130 | + | 21.9130i | −0.778152 | + | 0.778152i | ||||
\(794\) | 8.55788 | 0.303708 | ||||||||
\(795\) | −35.0030 | + | 4.81436i | −1.24143 | + | 0.170748i | ||||
\(796\) | −4.67866 | −0.165831 | ||||||||
\(797\) | −23.5030 | + | 23.5030i | −0.832520 | + | 0.832520i | −0.987861 | − | 0.155341i | \(-0.950352\pi\) |
0.155341 | + | 0.987861i | \(0.450352\pi\) | |||||||
\(798\) | 14.0641 | − | 2.41303i | 0.497865 | − | 0.0854202i | ||||
\(799\) | − | 39.3535i | − | 1.39223i | ||||||
\(800\) | −3.29289 | − | 3.76256i | −0.116421 | − | 0.133027i | ||||
\(801\) | 20.2530 | − | 7.16053i | 0.715606 | − | 0.253005i | ||||
\(802\) | −17.9312 | − | 17.9312i | −0.633171 | − | 0.633171i | ||||
\(803\) | −2.44840 | − | 2.44840i | −0.0864023 | − | 0.0864023i | ||||
\(804\) | 11.0502 | + | 7.81370i | 0.389712 | + | 0.275568i | ||||
\(805\) | −20.8023 | + | 19.4636i | −0.733184 | + | 0.686001i | ||||
\(806\) | 2.46967i | 0.0869903i | ||||||||
\(807\) | 0.539848 | + | 3.14646i | 0.0190035 | + | 0.110761i | ||||
\(808\) | 9.52100 | − | 9.52100i | 0.334948 | − | 0.334948i | ||||
\(809\) | −29.9087 | −1.05154 | −0.525768 | − | 0.850628i | \(-0.676222\pi\) | ||||
−0.525768 | + | 0.850628i | \(0.676222\pi\) | |||||||
\(810\) | −16.0641 | + | 12.1220i | −0.564437 | + | 0.425924i | ||||
\(811\) | −1.40533 | −0.0493479 | −0.0246739 | − | 0.999696i | \(-0.507855\pi\) | ||||
−0.0246739 | + | 0.999696i | \(0.507855\pi\) | |||||||
\(812\) | 7.38057 | − | 7.38057i | 0.259007 | − | 0.259007i | ||||
\(813\) | −4.65209 | − | 27.1144i | −0.163156 | − | 0.950943i | ||||
\(814\) | − | 3.70279i | − | 0.129783i | ||||||
\(815\) | 0.332104 | + | 0.0110415i | 0.0116331 | + | 0.000386767i | ||||
\(816\) | 10.7292 | + | 7.58667i | 0.375596 | + | 0.265587i | ||||
\(817\) | 15.2189 | + | 15.2189i | 0.532443 | + | 0.532443i | ||||
\(818\) | 7.09492 | + | 7.09492i | 0.248068 | + | 0.248068i | ||||
\(819\) | −13.2365 | + | 4.67982i | −0.462522 | + | 0.163526i | ||||
\(820\) | 4.29721 | + | 4.59277i | 0.150065 | + | 0.160387i | ||||
\(821\) | − | 16.9090i | − | 0.590128i | −0.955477 | − | 0.295064i | \(-0.904659\pi\) | ||
0.955477 | − | 0.295064i | \(-0.0953411\pi\) | |||||||
\(822\) | −29.5851 | + | 5.07601i | −1.03190 | + | 0.177046i | ||||
\(823\) | −19.2227 | + | 19.2227i | −0.670061 | + | 0.670061i | −0.957730 | − | 0.287669i | \(-0.907120\pi\) |
0.287669 | + | 0.957730i | \(0.407120\pi\) | |||||||
\(824\) | 14.7123 | 0.512528 | ||||||||
\(825\) | −1.17075 | − | 11.2768i | −0.0407604 | − | 0.392609i | ||||
\(826\) | 21.5576 | 0.750085 | ||||||||
\(827\) | 22.7919 | − | 22.7919i | 0.792552 | − | 0.792552i | −0.189357 | − | 0.981908i | \(-0.560640\pi\) |
0.981908 | + | 0.189357i | \(0.0606403\pi\) | |||||||
\(828\) | −8.69257 | + | 18.2008i | −0.302088 | + | 0.632522i | ||||
\(829\) | − | 35.3312i | − | 1.22710i | −0.789655 | − | 0.613551i | \(-0.789740\pi\) | ||
0.789655 | − | 0.613551i | \(-0.210260\pi\) | |||||||
\(830\) | 24.3860 | + | 26.0633i | 0.846451 | + | 0.904671i | ||||
\(831\) | 1.65344 | − | 2.33832i | 0.0573572 | − | 0.0811154i | ||||
\(832\) | −1.74632 | − | 1.74632i | −0.0605427 | − | 0.0605427i | ||||
\(833\) | 18.2893 | + | 18.2893i | 0.633688 | + | 0.633688i | ||||
\(834\) | 10.0563 | − | 14.2218i | 0.348223 | − | 0.492461i | ||||
\(835\) | −2.80375 | − | 0.0932167i | −0.0970278 | − | 0.00322590i | ||||
\(836\) | 5.69175i | 0.196853i | ||||||||
\(837\) | −2.53553 | − | 4.53553i | −0.0876409 | − | 0.156771i | ||||
\(838\) | 18.9645 | − | 18.9645i | 0.655116 | − | 0.655116i | ||||
\(839\) | 9.14241 | 0.315631 | 0.157816 | − | 0.987469i | \(-0.449555\pi\) | ||||
0.157816 | + | 0.987469i | \(0.449555\pi\) | |||||||
\(840\) | 5.84816 | + | 4.43395i | 0.201781 | + | 0.152986i | ||||
\(841\) | 1.34083 | 0.0462354 | ||||||||
\(842\) | 13.2197 | − | 13.2197i | 0.455580 | − | 0.455580i | ||||
\(843\) | 9.71445 | − | 1.66674i | 0.334583 | − | 0.0574054i | ||||
\(844\) | 11.3551i | 0.390858i | ||||||||
\(845\) | 11.2676 | − | 10.5425i | 0.387616 | − | 0.362671i | ||||
\(846\) | −5.18719 | − | 14.6716i | −0.178339 | − | 0.504419i | ||||
\(847\) | −12.4426 | − | 12.4426i | −0.427534 | − | 0.427534i | ||||
\(848\) | 6.45082 | + | 6.45082i | 0.221522 | + | 0.221522i | ||||
\(849\) | −1.18072 | − | 0.834895i | −0.0405222 | − | 0.0286535i | ||||
\(850\) | −37.8496 | − | 2.51957i | −1.29823 | − | 0.0864204i | ||||
\(851\) | − | 19.0165i | − | 0.651877i | ||||||
\(852\) | −3.03078 | − | 17.6647i | −0.103833 | − | 0.605181i | ||||
\(853\) | 0.613783 | − | 0.613783i | 0.0210155 | − | 0.0210155i | −0.696521 | − | 0.717536i | \(-0.745270\pi\) |
0.717536 | + | 0.696521i | \(0.245270\pi\) | |||||||
\(854\) | −23.7776 | −0.813654 | ||||||||
\(855\) | −13.4368 | + | 25.8857i | −0.459529 | + | 0.885274i | ||||
\(856\) | 11.4816 | 0.392433 | ||||||||
\(857\) | −12.3462 | + | 12.3462i | −0.421737 | + | 0.421737i | −0.885802 | − | 0.464064i | \(-0.846391\pi\) |
0.464064 | + | 0.885802i | \(0.346391\pi\) | |||||||
\(858\) | −0.946961 | − | 5.51929i | −0.0323287 | − | 0.188426i | ||||
\(859\) | 31.5163i | 1.07532i | 0.843161 | + | 0.537662i | \(0.180692\pi\) | ||||
−0.843161 | + | 0.537662i | \(0.819308\pi\) | |||||||
\(860\) | −0.367822 | + | 11.0633i | −0.0125426 | + | 0.377254i | ||||
\(861\) | −7.53784 | − | 5.33006i | −0.256889 | − | 0.181648i | ||||
\(862\) | −12.1811 | − | 12.1811i | −0.414889 | − | 0.414889i | ||||
\(863\) | −8.10553 | − | 8.10553i | −0.275916 | − | 0.275916i | 0.555561 | − | 0.831476i | \(-0.312504\pi\) |
−0.831476 | + | 0.555561i | \(0.812504\pi\) | |||||||
\(864\) | 5.00000 | + | 1.41421i | 0.170103 | + | 0.0481125i | ||||
\(865\) | 1.77259 | − | 53.3155i | 0.0602698 | − | 1.81278i | ||||
\(866\) | 13.7312i | 0.466606i | ||||||||
\(867\) | 69.2362 | − | 11.8790i | 2.35138 | − | 0.403434i | ||||
\(868\) | −1.33991 | + | 1.33991i | −0.0454796 | + | 0.0454796i | ||||
\(869\) | 6.08084 | 0.206278 | ||||||||
\(870\) | 2.90685 | + | 21.1344i | 0.0985514 | + | 0.716523i | ||||
\(871\) | −19.2972 | −0.653862 | ||||||||
\(872\) | 0.215984 | − | 0.215984i | 0.00731415 | − | 0.00731415i | ||||
\(873\) | 5.72856 | + | 2.73592i | 0.193882 | + | 0.0925968i | ||||
\(874\) | 29.2312i | 0.988761i | ||||||||
\(875\) | −21.0806 | − | 2.10883i | −0.712656 | − | 0.0712915i | ||||
\(876\) | −2.64493 | + | 3.74049i | −0.0893638 | + | 0.126379i | ||||
\(877\) | 32.5143 | + | 32.5143i | 1.09793 | + | 1.09793i | 0.994653 | + | 0.103278i | \(0.0329332\pi\) |
0.103278 | + | 0.994653i | \(0.467067\pi\) | |||||||
\(878\) | 19.0444 | + | 19.0444i | 0.642718 | + | 0.642718i | ||||
\(879\) | 7.21446 | − | 10.2028i | 0.243338 | − | 0.344131i | ||||
\(880\) | −2.13756 | + | 2.00000i | −0.0720572 | + | 0.0674200i | ||||
\(881\) | 45.3738i | 1.52868i | 0.644811 | + | 0.764342i | \(0.276936\pi\) | ||||
−0.644811 | + | 0.764342i | \(0.723064\pi\) | |||||||
\(882\) | 9.22927 | + | 4.40783i | 0.310766 | + | 0.148419i | ||||
\(883\) | 12.5798 | − | 12.5798i | 0.423342 | − | 0.423342i | −0.463010 | − | 0.886353i | \(-0.653231\pi\) |
0.886353 | + | 0.463010i | \(0.153231\pi\) | |||||||
\(884\) | −18.7365 | −0.630178 | ||||||||
\(885\) | −26.6200 | + | 35.1105i | −0.894823 | + | 1.18023i | ||||
\(886\) | −33.0410 | −1.11003 | ||||||||
\(887\) | 17.1081 | − | 17.1081i | 0.574435 | − | 0.574435i | −0.358930 | − | 0.933365i | \(-0.616858\pi\) |
0.933365 | + | 0.358930i | \(0.116858\pi\) | |||||||
\(888\) | −4.82843 | + | 0.828427i | −0.162031 | + | 0.0278002i | ||||
\(889\) | 6.45332i | 0.216437i | ||||||||
\(890\) | 16.0026 | + | 0.532040i | 0.536408 | + | 0.0178340i | ||||
\(891\) | 7.40559 | + | 9.16394i | 0.248096 | + | 0.307004i | ||||
\(892\) | −11.0613 | − | 11.0613i | −0.370359 | − | 0.370359i | ||||
\(893\) | −15.9470 | − | 15.9470i | −0.533645 | − | 0.533645i | ||||
\(894\) | 26.5463 | + | 18.7711i | 0.887841 | + | 0.627798i | ||||
\(895\) | −18.8860 | − | 20.1850i | −0.631290 | − | 0.674711i | ||||
\(896\) | − | 1.89492i | − | 0.0633049i | ||||||
\(897\) | −4.86332 | − | 28.3455i | −0.162382 | − | 0.946430i | ||||
\(898\) | 18.9172 | − | 18.9172i | 0.631277 | − | 0.631277i | ||||
\(899\) | −5.50825 | −0.183710 | ||||||||
\(900\) | −14.4430 | + | 4.04963i | −0.481434 | + | 0.134988i | ||||
\(901\) | 69.2120 | 2.30578 | ||||||||
\(902\) | 2.60382 | − | 2.60382i | 0.0866976 | − | 0.0866976i | ||||
\(903\) | −2.74751 | − | 16.0136i | −0.0914313 | − | 0.532900i | ||||
\(904\) | − | 2.13756i | − | 0.0710943i | ||||||
\(905\) | −0.00890191 | − | 0.00951419i | −0.000295909 | − | 0.000316262i | ||||
\(906\) | 6.39086 | + | 4.51902i | 0.212322 | + | 0.150134i | ||||
\(907\) | −24.5342 | − | 24.5342i | −0.814646 | − | 0.814646i | 0.170680 | − | 0.985326i | \(-0.445403\pi\) |
−0.985326 | + | 0.170680i | \(0.945403\pi\) | |||||||
\(908\) | 10.1647 | + | 10.1647i | 0.337326 | + | 0.337326i | ||||
\(909\) | −13.4647 | − | 38.0840i | −0.446597 | − | 1.26317i | ||||
\(910\) | −10.4586 | − | 0.347719i | −0.346700 | − | 0.0115268i | ||||
\(911\) | − | 17.4844i | − | 0.579284i | −0.957135 | − | 0.289642i | \(-0.906464\pi\) | ||
0.957135 | − | 0.289642i | \(-0.0935362\pi\) | |||||||
\(912\) | 7.42202 | − | 1.27342i | 0.245768 | − | 0.0421671i | ||||
\(913\) | 14.7763 | − | 14.7763i | 0.489023 | − | 0.489023i | ||||
\(914\) | 35.5233 | 1.17501 | ||||||||
\(915\) | 29.3614 | − | 38.7263i | 0.970659 | − | 1.28025i | ||||
\(916\) | −13.4188 | −0.443369 | ||||||||
\(917\) | 11.8223 | − | 11.8223i | 0.390408 | − | 0.390408i | ||||
\(918\) | 34.4096 | − | 19.2363i | 1.13569 | − | 0.634891i | ||||
\(919\) | 50.1999i | 1.65594i | 0.560772 | + | 0.827970i | \(0.310504\pi\) | ||||
−0.560772 | + | 0.827970i | \(0.689496\pi\) | |||||||
\(920\) | −10.9779 | + | 10.2714i | −0.361931 | + | 0.338639i | ||||
\(921\) | −9.38350 | + | 13.2703i | −0.309197 | + | 0.437270i | ||||
\(922\) | 3.79683 | + | 3.79683i | 0.125042 | + | 0.125042i | ||||
\(923\) | 18.0704 | + | 18.0704i | 0.594795 | + | 0.594795i | ||||
\(924\) | 2.48071 | − | 3.50825i | 0.0816093 | − | 0.115413i | ||||
\(925\) | 10.6421 | − | 9.31371i | 0.349911 | − | 0.306233i | ||||
\(926\) | 7.03462i | 0.231172i | ||||||||
\(927\) | 19.0214 | − | 39.8278i | 0.624746 | − | 1.30812i | ||||
\(928\) | 3.89492 | − | 3.89492i | 0.127857 | − | 0.127857i | ||||
\(929\) | 39.4235 | 1.29344 | 0.646721 | − | 0.762727i | \(-0.276140\pi\) | ||||
0.646721 | + | 0.762727i | \(0.276140\pi\) | |||||||
\(930\) | −0.527726 | − | 3.83686i | −0.0173048 | − | 0.125816i | ||||
\(931\) | 14.8226 | 0.485790 | ||||||||
\(932\) | 9.55096 | − | 9.55096i | 0.312852 | − | 0.312852i | ||||
\(933\) | −40.0082 | + | 6.86432i | −1.30981 | + | 0.224728i | ||||
\(934\) | 21.6447i | 0.708235i | ||||||||
\(935\) | −0.737964 | + | 22.1963i | −0.0241340 | + | 0.725897i | ||||
\(936\) | −6.98527 | + | 2.46967i | −0.228321 | + | 0.0807236i | ||||
\(937\) | 12.3259 | + | 12.3259i | 0.402670 | + | 0.402670i | 0.879173 | − | 0.476503i | \(-0.158096\pi\) |
−0.476503 | + | 0.879173i | \(0.658096\pi\) | |||||||
\(938\) | −10.4697 | − | 10.4697i | −0.341847 | − | 0.341847i | ||||
\(939\) | −12.8812 | − | 9.10838i | −0.420362 | − | 0.297241i | ||||
\(940\) | 0.385417 | − | 11.5925i | 0.0125709 | − | 0.378106i | ||||
\(941\) | 27.9228i | 0.910258i | 0.890425 | + | 0.455129i | \(0.150407\pi\) | ||||
−0.890425 | + | 0.455129i | \(0.849593\pi\) | |||||||
\(942\) | 4.76605 | + | 27.7786i | 0.155286 | + | 0.905075i | ||||
\(943\) | 13.3725 | − | 13.3725i | 0.435467 | − | 0.435467i | ||||
\(944\) | 11.3765 | 0.370274 | ||||||||
\(945\) | 19.5642 | − | 10.0990i | 0.636424 | − | 0.328520i | ||||
\(946\) | 6.48071 | 0.210706 | ||||||||
\(947\) | 25.8753 | − | 25.8753i | 0.840833 | − | 0.840833i | −0.148135 | − | 0.988967i | \(-0.547327\pi\) |
0.988967 | + | 0.148135i | \(0.0473269\pi\) | |||||||
\(948\) | −1.36047 | − | 7.92939i | −0.0441859 | − | 0.257534i | ||||
\(949\) | − | 6.53209i | − | 0.212040i | ||||||
\(950\) | −16.3586 | + | 14.3166i | −0.530742 | + | 0.464491i | ||||
\(951\) | −37.9969 | − | 26.8679i | −1.23214 | − | 0.871251i | ||||
\(952\) | −10.1655 | − | 10.1655i | −0.329465 | − | 0.329465i | ||||
\(953\) | −3.42614 | − | 3.42614i | −0.110984 | − | 0.110984i | 0.649434 | − | 0.760418i | \(-0.275006\pi\) |
−0.760418 | + | 0.649434i | \(0.775006\pi\) | |||||||
\(954\) | 25.8033 | − | 9.12283i | 0.835412 | − | 0.295363i | ||||
\(955\) | 7.48565 | − | 7.00391i | 0.242230 | − | 0.226641i | ||||
\(956\) | 28.4935i | 0.921546i | ||||||||
\(957\) | 12.3100 | − | 2.11207i | 0.397926 | − | 0.0682734i | ||||
\(958\) | −11.5847 | + | 11.5847i | −0.374284 | + | 0.374284i | ||||
\(959\) | 32.8401 | 1.06046 | ||||||||
\(960\) | 3.08623 | + | 2.33991i | 0.0996076 | + | 0.0755203i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 4.93933 | − | 4.93933i | 0.159250 | − | 0.159250i | ||||
\(963\) | 14.8445 | − | 31.0819i | 0.478357 | − | 1.00160i | ||||
\(964\) | 10.4697i | 0.337205i | ||||||||
\(965\) | 53.5750 | + | 1.78121i | 1.72464 | + | 0.0573393i | ||||
\(966\) | 12.7402 | − | 18.0174i | 0.409910 | − | 0.579700i | ||||
\(967\) | −22.5928 | − | 22.5928i | −0.726535 | − | 0.726535i | 0.243393 | − | 0.969928i | \(-0.421739\pi\) |
−0.969928 | + | 0.243393i | \(0.921739\pi\) | |||||||
\(968\) | −6.56631 | − | 6.56631i | −0.211049 | − | 0.211049i | ||||
\(969\) | 32.9847 | − | 46.6474i | 1.05962 | − | 1.49853i | ||||
\(970\) | 3.23285 | + | 3.45521i | 0.103801 | + | 0.110940i | ||||
\(971\) | − | 34.1559i | − | 1.09612i | −0.836440 | − | 0.548058i | \(-0.815367\pi\) | ||
0.836440 | − | 0.548058i | \(-0.184633\pi\) | |||||||
\(972\) | 10.2929 | − | 11.7071i | 0.330145 | − | 0.375506i | ||||
\(973\) | −13.4746 | + | 13.4746i | −0.431976 | + | 0.431976i | ||||
\(974\) | −11.1084 | −0.355935 | ||||||||
\(975\) | 13.4810 | − | 16.6044i | 0.431737 | − | 0.531767i | ||||
\(976\) | −12.5481 | −0.401655 | ||||||||
\(977\) | −15.3207 | + | 15.3207i | −0.490152 | + | 0.490152i | −0.908354 | − | 0.418202i | \(-0.862661\pi\) |
0.418202 | + | 0.908354i | \(0.362661\pi\) | |||||||
\(978\) | −0.253682 | + | 0.0435250i | −0.00811186 | + | 0.00139178i | ||||
\(979\) | − | 9.37410i | − | 0.299598i | ||||||
\(980\) | 5.20844 | + | 5.56668i | 0.166377 | + | 0.177821i | ||||
\(981\) | −0.305448 | − | 0.863936i | −0.00975219 | − | 0.0275834i | ||||
\(982\) | 24.0752 | + | 24.0752i | 0.768270 | + | 0.768270i | ||||
\(983\) | −18.1926 | − | 18.1926i | −0.580255 | − | 0.580255i | 0.354718 | − | 0.934973i | \(-0.384577\pi\) |
−0.934973 | + | 0.354718i | \(0.884577\pi\) | |||||||
\(984\) | −3.97792 | − | 2.81281i | −0.126811 | − | 0.0896692i | ||||
\(985\) | −33.5321 | − | 1.11485i | −1.06842 | − | 0.0355220i | ||||
\(986\) | − | 41.7893i | − | 1.33084i | ||||||
\(987\) | 2.87894 | + | 16.7797i | 0.0916376 | + | 0.534103i | ||||
\(988\) | −7.59250 | + | 7.59250i | −0.241550 | + | 0.241550i | ||||
\(989\) | 33.2831 | 1.05834 | ||||||||
\(990\) | 2.65057 | + | 8.37240i | 0.0842408 | + | 0.266092i | ||||
\(991\) | −35.8784 | −1.13972 | −0.569858 | − | 0.821743i | \(-0.693002\pi\) | ||||
−0.569858 | + | 0.821743i | \(0.693002\pi\) | |||||||
\(992\) | −0.707107 | + | 0.707107i | −0.0224507 | + | 0.0224507i | ||||
\(993\) | 1.18566 | + | 6.91054i | 0.0376258 | + | 0.219299i | ||||
\(994\) | 19.6081i | 0.621932i | ||||||||
\(995\) | −7.63934 | + | 7.14772i | −0.242184 | + | 0.226598i | ||||
\(996\) | −22.5741 | − | 15.9623i | −0.715288 | − | 0.505785i | ||||
\(997\) | −0.00824048 | − | 0.00824048i | −0.000260979 | − | 0.000260979i | 0.706976 | − | 0.707237i | \(-0.250059\pi\) |
−0.707237 | + | 0.706976i | \(0.750059\pi\) | |||||||
\(998\) | 0.312802 | + | 0.312802i | 0.00990157 | + | 0.00990157i | ||||
\(999\) | −4.00000 | + | 14.1421i | −0.126554 | + | 0.447437i |
(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 | 930.2.j.f.497.3 | yes | 8 | |
3.2 | odd | 2 | 930.2.j.c.497.2 | ✓ | 8 | ||
5.3 | odd | 4 | 930.2.j.c.683.2 | yes | 8 | ||
15.8 | even | 4 | inner | 930.2.j.f.683.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.c.497.2 | ✓ | 8 | 3.2 | odd | 2 | ||
930.2.j.c.683.2 | yes | 8 | 5.3 | odd | 4 | ||
930.2.j.f.497.3 | yes | 8 | 1.1 | even | 1 | trivial | |
930.2.j.f.683.3 | yes | 8 | 15.8 | even | 4 | inner |