Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(323,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("552.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.j (of order \(2\), degree \(1\), 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: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.4 | ||
Character | \(\chi\) | \(=\) | 552.323 |
Dual form | 552.2.j.d.323.3 |
$q$-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 \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.40766 | + | 0.136034i | −0.995363 | + | 0.0961907i | ||||
\(3\) | −1.50629 | + | 0.855045i | −0.869655 | + | 0.493660i | ||||
\(4\) | 1.96299 | − | 0.382978i | 0.981495 | − | 0.191489i | ||||
\(5\) | −2.98020 | −1.33279 | −0.666393 | − | 0.745601i | \(-0.732163\pi\) | ||||
−0.666393 | + | 0.745601i | \(0.732163\pi\) | |||||||
\(6\) | 2.00402 | − | 1.40851i | 0.818137 | − | 0.575024i | ||||
\(7\) | 1.36209i | 0.514823i | 0.966302 | + | 0.257411i | \(0.0828695\pi\) | ||||
−0.966302 | + | 0.257411i | \(0.917130\pi\) | |||||||
\(8\) | −2.71112 | + | 0.806135i | −0.958524 | + | 0.285012i | ||||
\(9\) | 1.53780 | − | 2.57588i | 0.512599 | − | 0.858628i | ||||
\(10\) | 4.19509 | − | 0.405409i | 1.32661 | − | 0.128202i | ||||
\(11\) | − | 5.80186i | − | 1.74933i | −0.484732 | − | 0.874663i | \(-0.661083\pi\) | ||
0.484732 | − | 0.874663i | \(-0.338917\pi\) | |||||||
\(12\) | −2.62936 | + | 2.25532i | −0.759031 | + | 0.651054i | ||||
\(13\) | − | 0.852288i | − | 0.236382i | −0.992991 | − | 0.118191i | \(-0.962290\pi\) | ||
0.992991 | − | 0.118191i | \(-0.0377095\pi\) | |||||||
\(14\) | −0.185291 | − | 1.91736i | −0.0495211 | − | 0.512435i | ||||
\(15\) | 4.48903 | − | 2.54820i | 1.15906 | − | 0.657943i | ||||
\(16\) | 3.70666 | − | 1.50357i | 0.926664 | − | 0.375891i | ||||
\(17\) | 5.38365i | 1.30573i | 0.757476 | + | 0.652863i | \(0.226432\pi\) | ||||
−0.757476 | + | 0.652863i | \(0.773568\pi\) | |||||||
\(18\) | −1.81428 | + | 3.83515i | −0.427630 | + | 0.903954i | ||||
\(19\) | −1.59177 | −0.365177 | −0.182589 | − | 0.983189i | \(-0.558448\pi\) | ||||
−0.182589 | + | 0.983189i | \(0.558448\pi\) | |||||||
\(20\) | −5.85010 | + | 1.14135i | −1.30812 | + | 0.255214i | ||||
\(21\) | −1.16465 | − | 2.05170i | −0.254147 | − | 0.447718i | ||||
\(22\) | 0.789250 | + | 8.16702i | 0.168269 | + | 1.74121i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 3.39443 | − | 3.53240i | 0.692886 | − | 0.721047i | ||||
\(25\) | 3.88159 | 0.776317 | ||||||||
\(26\) | 0.115940 | + | 1.19973i | 0.0227377 | + | 0.235286i | ||||
\(27\) | −0.113867 | + | 5.19490i | −0.0219136 | + | 0.999760i | ||||
\(28\) | 0.521652 | + | 2.67377i | 0.0985830 | + | 0.505296i | ||||
\(29\) | 4.01876 | 0.746266 | 0.373133 | − | 0.927778i | \(-0.378284\pi\) | ||||
0.373133 | + | 0.927778i | \(0.378284\pi\) | |||||||
\(30\) | −5.97237 | + | 4.19765i | −1.09040 | + | 0.766383i | ||||
\(31\) | − | 1.32088i | − | 0.237237i | −0.992940 | − | 0.118618i | \(-0.962153\pi\) | ||
0.992940 | − | 0.118618i | \(-0.0378465\pi\) | |||||||
\(32\) | −5.01316 | + | 2.62073i | −0.886210 | + | 0.463285i | ||||
\(33\) | 4.96085 | + | 8.73926i | 0.863572 | + | 1.52131i | ||||
\(34\) | −0.732360 | − | 7.57832i | −0.125599 | − | 1.29967i | ||||
\(35\) | − | 4.05931i | − | 0.686148i | ||||||
\(36\) | 2.03217 | − | 5.64538i | 0.338695 | − | 0.940896i | ||||
\(37\) | 0.210483i | 0.0346032i | 0.999850 | + | 0.0173016i | \(0.00550754\pi\) | ||||
−0.999850 | + | 0.0173016i | \(0.994492\pi\) | |||||||
\(38\) | 2.24067 | − | 0.216535i | 0.363484 | − | 0.0351266i | ||||
\(39\) | 0.728744 | + | 1.28379i | 0.116692 | + | 0.205571i | ||||
\(40\) | 8.07966 | − | 2.40244i | 1.27751 | − | 0.379860i | ||||
\(41\) | 10.6401i | 1.66171i | 0.556490 | + | 0.830854i | \(0.312148\pi\) | ||||
−0.556490 | + | 0.830854i | \(0.687852\pi\) | |||||||
\(42\) | 1.91853 | + | 2.72966i | 0.296035 | + | 0.421195i | ||||
\(43\) | 3.80028 | 0.579538 | 0.289769 | − | 0.957097i | \(-0.406422\pi\) | ||||
0.289769 | + | 0.957097i | \(0.406422\pi\) | |||||||
\(44\) | −2.22199 | − | 11.3890i | −0.334977 | − | 1.71695i | ||||
\(45\) | −4.58294 | + | 7.67665i | −0.683185 | + | 1.14437i | ||||
\(46\) | −1.40766 | + | 0.136034i | −0.207548 | + | 0.0200571i | ||||
\(47\) | 3.46377 | 0.505242 | 0.252621 | − | 0.967565i | \(-0.418707\pi\) | ||||
0.252621 | + | 0.967565i | \(0.418707\pi\) | |||||||
\(48\) | −4.29767 | + | 5.43416i | −0.620315 | + | 0.784353i | ||||
\(49\) | 5.14470 | 0.734958 | ||||||||
\(50\) | −5.46394 | + | 0.528028i | −0.772717 | + | 0.0746745i | ||||
\(51\) | −4.60326 | − | 8.10931i | −0.644585 | − | 1.13553i | ||||
\(52\) | −0.326408 | − | 1.67303i | −0.0452646 | − | 0.232008i | ||||
\(53\) | 12.5912 | 1.72954 | 0.864771 | − | 0.502167i | \(-0.167464\pi\) | ||||
0.864771 | + | 0.502167i | \(0.167464\pi\) | |||||||
\(54\) | −0.546399 | − | 7.32813i | −0.0743555 | − | 0.997232i | ||||
\(55\) | 17.2907i | 2.33148i | ||||||||
\(56\) | −1.09803 | − | 3.69279i | −0.146731 | − | 0.493470i | ||||
\(57\) | 2.39766 | − | 1.36104i | 0.317578 | − | 0.180274i | ||||
\(58\) | −5.65704 | + | 0.546689i | −0.742805 | + | 0.0717838i | ||||
\(59\) | 4.46664i | 0.581506i | 0.956798 | + | 0.290753i | \(0.0939059\pi\) | ||||
−0.956798 | + | 0.290753i | \(0.906094\pi\) | |||||||
\(60\) | 7.83602 | − | 6.72130i | 1.01163 | − | 0.867716i | ||||
\(61\) | 14.3544i | 1.83790i | 0.394376 | + | 0.918949i | \(0.370961\pi\) | ||||
−0.394376 | + | 0.918949i | \(0.629039\pi\) | |||||||
\(62\) | 0.179685 | + | 1.85934i | 0.0228200 | + | 0.236137i | ||||
\(63\) | 3.50859 | + | 2.09462i | 0.442041 | + | 0.263898i | ||||
\(64\) | 6.70029 | − | 4.37105i | 0.837536 | − | 0.546381i | ||||
\(65\) | 2.53999i | 0.315047i | ||||||||
\(66\) | −8.17200 | − | 11.6270i | −1.00590 | − | 1.43119i | ||||
\(67\) | −9.77174 | −1.19381 | −0.596904 | − | 0.802313i | \(-0.703603\pi\) | ||||
−0.596904 | + | 0.802313i | \(0.703603\pi\) | |||||||
\(68\) | 2.06182 | + | 10.5680i | 0.250032 | + | 1.28156i | ||||
\(69\) | −1.50629 | + | 0.855045i | −0.181336 | + | 0.102935i | ||||
\(70\) | 0.552204 | + | 5.71411i | 0.0660010 | + | 0.682966i | ||||
\(71\) | 3.27263 | 0.388390 | 0.194195 | − | 0.980963i | \(-0.437791\pi\) | ||||
0.194195 | + | 0.980963i | \(0.437791\pi\) | |||||||
\(72\) | −2.09263 | + | 8.22319i | −0.246619 | + | 0.969112i | ||||
\(73\) | 2.83293 | 0.331569 | 0.165785 | − | 0.986162i | \(-0.446984\pi\) | ||||
0.165785 | + | 0.986162i | \(0.446984\pi\) | |||||||
\(74\) | −0.0286329 | − | 0.296288i | −0.00332850 | − | 0.0344427i | ||||
\(75\) | −5.84678 | + | 3.31893i | −0.675128 | + | 0.383237i | ||||
\(76\) | −3.12463 | + | 0.609614i | −0.358420 | + | 0.0699275i | ||||
\(77\) | 7.90267 | 0.900592 | ||||||||
\(78\) | −1.20046 | − | 1.70800i | −0.135925 | − | 0.193393i | ||||
\(79\) | − | 4.99823i | − | 0.562345i | −0.959657 | − | 0.281173i | \(-0.909277\pi\) | ||
0.959657 | − | 0.281173i | \(-0.0907233\pi\) | |||||||
\(80\) | −11.0466 | + | 4.48092i | −1.23504 | + | 0.500983i | ||||
\(81\) | −4.27036 | − | 7.92237i | −0.474484 | − | 0.880264i | ||||
\(82\) | −1.44742 | − | 14.9776i | −0.159841 | − | 1.65400i | ||||
\(83\) | 3.09167i | 0.339355i | 0.985500 | + | 0.169678i | \(0.0542726\pi\) | ||||
−0.985500 | + | 0.169678i | \(0.945727\pi\) | |||||||
\(84\) | −3.07195 | − | 3.58143i | −0.335178 | − | 0.390766i | ||||
\(85\) | − | 16.0443i | − | 1.74025i | ||||||
\(86\) | −5.34949 | + | 0.516968i | −0.576850 | + | 0.0557461i | ||||
\(87\) | −6.05341 | + | 3.43622i | −0.648994 | + | 0.368402i | ||||
\(88\) | 4.67708 | + | 15.7295i | 0.498579 | + | 1.67677i | ||||
\(89\) | − | 13.7100i | − | 1.45326i | −0.687028 | − | 0.726631i | \(-0.741085\pi\) | ||
0.687028 | − | 0.726631i | \(-0.258915\pi\) | |||||||
\(90\) | 5.40692 | − | 11.4295i | 0.569939 | − | 1.20478i | ||||
\(91\) | 1.16089 | 0.121695 | ||||||||
\(92\) | 1.96299 | − | 0.382978i | 0.204656 | − | 0.0399283i | ||||
\(93\) | 1.12941 | + | 1.98962i | 0.117114 | + | 0.206314i | ||||
\(94\) | −4.87579 | + | 0.471191i | −0.502900 | + | 0.0485996i | ||||
\(95\) | 4.74379 | 0.486703 | ||||||||
\(96\) | 5.31041 | − | 8.23405i | 0.541991 | − | 0.840384i | ||||
\(97\) | 10.4354 | 1.05955 | 0.529775 | − | 0.848138i | \(-0.322276\pi\) | ||||
0.529775 | + | 0.848138i | \(0.322276\pi\) | |||||||
\(98\) | −7.24197 | + | 0.699855i | −0.731550 | + | 0.0706961i | ||||
\(99\) | −14.9449 | − | 8.92208i | −1.50202 | − | 0.896703i | ||||
\(100\) | 7.61951 | − | 1.48656i | 0.761951 | − | 0.148656i | ||||
\(101\) | 18.8027 | 1.87094 | 0.935468 | − | 0.353412i | \(-0.114979\pi\) | ||||
0.935468 | + | 0.353412i | \(0.114979\pi\) | |||||||
\(102\) | 7.58295 | + | 10.7889i | 0.750823 | + | 1.06826i | ||||
\(103\) | − | 13.5117i | − | 1.33134i | −0.746245 | − | 0.665672i | \(-0.768145\pi\) | ||
0.746245 | − | 0.665672i | \(-0.231855\pi\) | |||||||
\(104\) | 0.687059 | + | 2.31065i | 0.0673717 | + | 0.226578i | ||||
\(105\) | 3.47089 | + | 6.11448i | 0.338724 | + | 0.596712i | ||||
\(106\) | −17.7241 | + | 1.71284i | −1.72152 | + | 0.166366i | ||||
\(107\) | 1.99588i | 0.192949i | 0.995335 | + | 0.0964746i | \(0.0307566\pi\) | ||||
−0.995335 | + | 0.0964746i | \(0.969243\pi\) | |||||||
\(108\) | 1.76602 | + | 10.2412i | 0.169935 | + | 0.985455i | ||||
\(109\) | 9.17024i | 0.878350i | 0.898402 | + | 0.439175i | \(0.144729\pi\) | ||||
−0.898402 | + | 0.439175i | \(0.855271\pi\) | |||||||
\(110\) | −2.35212 | − | 24.3393i | −0.224266 | − | 2.32066i | ||||
\(111\) | −0.179972 | − | 0.317048i | −0.0170822 | − | 0.0300928i | ||||
\(112\) | 2.04800 | + | 5.04881i | 0.193517 | + | 0.477067i | ||||
\(113\) | 5.05032i | 0.475094i | 0.971376 | + | 0.237547i | \(0.0763434\pi\) | ||||
−0.971376 | + | 0.237547i | \(0.923657\pi\) | |||||||
\(114\) | −3.18994 | + | 2.24203i | −0.298765 | + | 0.209986i | ||||
\(115\) | −2.98020 | −0.277905 | ||||||||
\(116\) | 7.88879 | − | 1.53910i | 0.732456 | − | 0.142902i | ||||
\(117\) | −2.19539 | − | 1.31065i | −0.202964 | − | 0.121169i | ||||
\(118\) | −0.607615 | − | 6.28749i | −0.0559355 | − | 0.578810i | ||||
\(119\) | −7.33302 | −0.672217 | ||||||||
\(120\) | −10.1161 | + | 10.5272i | −0.923468 | + | 0.961001i | ||||
\(121\) | −22.6615 | −2.06014 | ||||||||
\(122\) | −1.95269 | − | 20.2061i | −0.176789 | − | 1.82938i | ||||
\(123\) | −9.09778 | − | 16.0271i | −0.820319 | − | 1.44511i | ||||
\(124\) | −0.505868 | − | 2.59287i | −0.0454283 | − | 0.232847i | ||||
\(125\) | 3.33310 | 0.298121 | ||||||||
\(126\) | −5.22383 | − | 2.47122i | −0.465376 | − | 0.220154i | ||||
\(127\) | − | 13.2467i | − | 1.17545i | −0.809059 | − | 0.587727i | \(-0.800023\pi\) | ||
0.809059 | − | 0.587727i | \(-0.199977\pi\) | |||||||
\(128\) | −8.83709 | + | 7.06440i | −0.781096 | + | 0.624411i | ||||
\(129\) | −5.72431 | + | 3.24941i | −0.503998 | + | 0.286095i | ||||
\(130\) | −0.345525 | − | 3.57543i | −0.0303045 | − | 0.313586i | ||||
\(131\) | − | 13.8089i | − | 1.20649i | −0.797555 | − | 0.603246i | \(-0.793874\pi\) | ||
0.797555 | − | 0.603246i | \(-0.206126\pi\) | |||||||
\(132\) | 13.0850 | + | 15.2552i | 1.13891 | + | 1.32779i | ||||
\(133\) | − | 2.16814i | − | 0.188002i | ||||||
\(134\) | 13.7552 | − | 1.32929i | 1.18827 | − | 0.114833i | ||||
\(135\) | 0.339345 | − | 15.4818i | 0.0292062 | − | 1.33247i | ||||
\(136\) | −4.33995 | − | 14.5957i | −0.372147 | − | 1.25157i | ||||
\(137\) | − | 12.7826i | − | 1.09209i | −0.837755 | − | 0.546046i | \(-0.816133\pi\) | ||
0.837755 | − | 0.546046i | \(-0.183867\pi\) | |||||||
\(138\) | 2.00402 | − | 1.40851i | 0.170593 | − | 0.119901i | ||||
\(139\) | 1.50160 | 0.127364 | 0.0636821 | − | 0.997970i | \(-0.479716\pi\) | ||||
0.0636821 | + | 0.997970i | \(0.479716\pi\) | |||||||
\(140\) | −1.55463 | − | 7.96838i | −0.131390 | − | 0.673451i | ||||
\(141\) | −5.21743 | + | 2.96168i | −0.439387 | + | 0.249418i | ||||
\(142\) | −4.60674 | + | 0.445190i | −0.386589 | + | 0.0373595i | ||||
\(143\) | −4.94485 | −0.413509 | ||||||||
\(144\) | 1.82707 | − | 11.8601i | 0.152256 | − | 0.988341i | ||||
\(145\) | −11.9767 | −0.994612 | ||||||||
\(146\) | −3.98779 | + | 0.385375i | −0.330032 | + | 0.0318939i | ||||
\(147\) | −7.74940 | + | 4.39895i | −0.639159 | + | 0.362819i | ||||
\(148\) | 0.0806104 | + | 0.413176i | 0.00662614 | + | 0.0339628i | ||||
\(149\) | −20.4255 | −1.67332 | −0.836661 | − | 0.547721i | \(-0.815495\pi\) | ||||
−0.836661 | + | 0.547721i | \(0.815495\pi\) | |||||||
\(150\) | 7.77877 | − | 5.46727i | 0.635134 | − | 0.446401i | ||||
\(151\) | 15.9023i | 1.29411i | 0.762443 | + | 0.647055i | \(0.224000\pi\) | ||||
−0.762443 | + | 0.647055i | \(0.776000\pi\) | |||||||
\(152\) | 4.31547 | − | 1.28318i | 0.350031 | − | 0.104080i | ||||
\(153\) | 13.8676 | + | 8.27896i | 1.12113 | + | 0.669314i | ||||
\(154\) | −11.1242 | + | 1.07503i | −0.896416 | + | 0.0866286i | ||||
\(155\) | 3.93648i | 0.316186i | ||||||||
\(156\) | 1.92218 | + | 2.24097i | 0.153898 | + | 0.179421i | ||||
\(157\) | 8.89088i | 0.709569i | 0.934948 | + | 0.354785i | \(0.115446\pi\) | ||||
−0.934948 | + | 0.354785i | \(0.884554\pi\) | |||||||
\(158\) | 0.679930 | + | 7.03579i | 0.0540923 | + | 0.559738i | ||||
\(159\) | −18.9660 | + | 10.7661i | −1.50410 | + | 0.853806i | ||||
\(160\) | 14.9402 | − | 7.81031i | 1.18113 | − | 0.617459i | ||||
\(161\) | 1.36209i | 0.107348i | ||||||||
\(162\) | 7.08891 | + | 10.5711i | 0.556957 | + | 0.830541i | ||||
\(163\) | 5.85236 | 0.458392 | 0.229196 | − | 0.973380i | \(-0.426390\pi\) | ||||
0.229196 | + | 0.973380i | \(0.426390\pi\) | |||||||
\(164\) | 4.07494 | + | 20.8865i | 0.318199 | + | 1.63096i | ||||
\(165\) | −14.7843 | − | 26.0447i | −1.15096 | − | 2.02758i | ||||
\(166\) | −0.420573 | − | 4.35201i | −0.0326428 | − | 0.337782i | ||||
\(167\) | 5.01615 | 0.388161 | 0.194081 | − | 0.980986i | \(-0.437828\pi\) | ||||
0.194081 | + | 0.980986i | \(0.437828\pi\) | |||||||
\(168\) | 4.81145 | + | 4.62353i | 0.371211 | + | 0.356713i | ||||
\(169\) | 12.2736 | 0.944124 | ||||||||
\(170\) | 2.18258 | + | 22.5849i | 0.167396 | + | 1.73218i | ||||
\(171\) | −2.44782 | + | 4.10022i | −0.187190 | + | 0.313552i | ||||
\(172\) | 7.45992 | − | 1.45543i | 0.568813 | − | 0.110975i | ||||
\(173\) | −9.08009 | −0.690346 | −0.345173 | − | 0.938539i | \(-0.612180\pi\) | ||||
−0.345173 | + | 0.938539i | \(0.612180\pi\) | |||||||
\(174\) | 8.05367 | − | 5.66049i | 0.610547 | − | 0.429121i | ||||
\(175\) | 5.28708i | 0.399666i | ||||||||
\(176\) | −8.72347 | − | 21.5055i | −0.657556 | − | 1.62104i | ||||
\(177\) | −3.81917 | − | 6.72803i | −0.287067 | − | 0.505710i | ||||
\(178\) | 1.86503 | + | 19.2990i | 0.139790 | + | 1.44652i | ||||
\(179\) | 18.9179i | 1.41399i | 0.707217 | + | 0.706996i | \(0.249950\pi\) | ||||
−0.707217 | + | 0.706996i | \(0.750050\pi\) | |||||||
\(180\) | −6.05627 | + | 16.8243i | −0.451408 | + | 1.25401i | ||||
\(181\) | 13.2998i | 0.988565i | 0.869301 | + | 0.494283i | \(0.164569\pi\) | ||||
−0.869301 | + | 0.494283i | \(0.835431\pi\) | |||||||
\(182\) | −1.63414 | + | 0.157921i | −0.121131 | + | 0.0117059i | ||||
\(183\) | −12.2737 | − | 21.6219i | −0.907297 | − | 1.59834i | ||||
\(184\) | −2.71112 | + | 0.806135i | −0.199866 | + | 0.0594291i | ||||
\(185\) | − | 0.627281i | − | 0.0461186i | ||||||
\(186\) | −1.86048 | − | 2.64706i | −0.136417 | − | 0.194092i | ||||
\(187\) | 31.2351 | 2.28414 | ||||||||
\(188\) | 6.79934 | − | 1.32655i | 0.495893 | − | 0.0967485i | ||||
\(189\) | −7.07594 | − | 0.155097i | −0.514699 | − | 0.0112816i | ||||
\(190\) | −6.67763 | + | 0.645318i | −0.484446 | + | 0.0468163i | ||||
\(191\) | 14.6288 | 1.05850 | 0.529250 | − | 0.848466i | \(-0.322473\pi\) | ||||
0.529250 | + | 0.848466i | \(0.322473\pi\) | |||||||
\(192\) | −6.35511 | + | 12.3131i | −0.458641 | + | 0.888622i | ||||
\(193\) | 8.05377 | 0.579723 | 0.289861 | − | 0.957069i | \(-0.406391\pi\) | ||||
0.289861 | + | 0.957069i | \(0.406391\pi\) | |||||||
\(194\) | −14.6894 | + | 1.41957i | −1.05464 | + | 0.101919i | ||||
\(195\) | −2.17180 | − | 3.82595i | −0.155526 | − | 0.273982i | ||||
\(196\) | 10.0990 | − | 1.97031i | 0.721357 | − | 0.140736i | ||||
\(197\) | −5.98939 | −0.426726 | −0.213363 | − | 0.976973i | \(-0.568442\pi\) | ||||
−0.213363 | + | 0.976973i | \(0.568442\pi\) | |||||||
\(198\) | 22.2510 | + | 10.5262i | 1.58131 | + | 0.748064i | ||||
\(199\) | − | 20.8081i | − | 1.47504i | −0.675323 | − | 0.737522i | \(-0.735996\pi\) | ||
0.675323 | − | 0.737522i | \(-0.264004\pi\) | |||||||
\(200\) | −10.5234 | + | 3.12908i | −0.744119 | + | 0.221260i | ||||
\(201\) | 14.7190 | − | 8.35528i | 1.03820 | − | 0.589336i | ||||
\(202\) | −26.4677 | + | 2.55780i | −1.86226 | + | 0.179967i | ||||
\(203\) | 5.47393i | 0.384195i | ||||||||
\(204\) | −12.1418 | − | 14.1555i | −0.850099 | − | 0.991086i | ||||
\(205\) | − | 31.7097i | − | 2.21470i | ||||||
\(206\) | 1.83805 | + | 19.0198i | 0.128063 | + | 1.32517i | ||||
\(207\) | 1.53780 | − | 2.57588i | 0.106884 | − | 0.179036i | ||||
\(208\) | −1.28147 | − | 3.15914i | −0.0888540 | − | 0.219047i | ||||
\(209\) | 9.23523i | 0.638814i | ||||||||
\(210\) | −5.71759 | − | 8.13492i | −0.394552 | − | 0.561363i | ||||
\(211\) | 15.6498 | 1.07737 | 0.538687 | − | 0.842506i | \(-0.318920\pi\) | ||||
0.538687 | + | 0.842506i | \(0.318920\pi\) | |||||||
\(212\) | 24.7165 | − | 4.82218i | 1.69754 | − | 0.331188i | ||||
\(213\) | −4.92952 | + | 2.79825i | −0.337765 | + | 0.191733i | ||||
\(214\) | −0.271508 | − | 2.80951i | −0.0185599 | − | 0.192054i | ||||
\(215\) | −11.3256 | −0.772399 | ||||||||
\(216\) | −3.87909 | − | 14.1758i | −0.263939 | − | 0.964539i | ||||
\(217\) | 1.79916 | 0.122135 | ||||||||
\(218\) | −1.24747 | − | 12.9085i | −0.0844890 | − | 0.874277i | ||||
\(219\) | −4.26720 | + | 2.42228i | −0.288351 | + | 0.163683i | ||||
\(220\) | 6.62196 | + | 33.9414i | 0.446452 | + | 2.28833i | ||||
\(221\) | 4.58842 | 0.308650 | ||||||||
\(222\) | 0.296468 | + | 0.421812i | 0.0198977 | + | 0.0283101i | ||||
\(223\) | 21.4944i | 1.43937i | 0.694298 | + | 0.719687i | \(0.255715\pi\) | ||||
−0.694298 | + | 0.719687i | \(0.744285\pi\) | |||||||
\(224\) | −3.56968 | − | 6.82839i | −0.238509 | − | 0.456241i | ||||
\(225\) | 5.96909 | − | 9.99852i | 0.397939 | − | 0.666568i | ||||
\(226\) | −0.687016 | − | 7.10911i | −0.0456996 | − | 0.472891i | ||||
\(227\) | − | 0.878929i | − | 0.0583366i | −0.999575 | − | 0.0291683i | \(-0.990714\pi\) | ||
0.999575 | − | 0.0291683i | \(-0.00928587\pi\) | |||||||
\(228\) | 4.18534 | − | 3.58995i | 0.277181 | − | 0.237750i | ||||
\(229\) | − | 17.2682i | − | 1.14111i | −0.821259 | − | 0.570556i | \(-0.806728\pi\) | ||
0.821259 | − | 0.570556i | \(-0.193272\pi\) | |||||||
\(230\) | 4.19509 | − | 0.405409i | 0.276616 | − | 0.0267319i | ||||
\(231\) | −11.9037 | + | 6.75713i | −0.783204 | + | 0.444587i | ||||
\(232\) | −10.8953 | + | 3.23967i | −0.715314 | + | 0.212695i | ||||
\(233\) | 12.7832i | 0.837454i | 0.908112 | + | 0.418727i | \(0.137524\pi\) | ||||
−0.908112 | + | 0.418727i | \(0.862476\pi\) | |||||||
\(234\) | 3.26865 | + | 1.54629i | 0.213678 | + | 0.101084i | ||||
\(235\) | −10.3227 | −0.673380 | ||||||||
\(236\) | 1.71063 | + | 8.76796i | 0.111352 | + | 0.570745i | ||||
\(237\) | 4.27371 | + | 7.52877i | 0.277607 | + | 0.489046i | ||||
\(238\) | 10.3224 | − | 0.997542i | 0.669100 | − | 0.0646610i | ||||
\(239\) | 29.7037 | 1.92137 | 0.960687 | − | 0.277635i | \(-0.0895506\pi\) | ||||
0.960687 | + | 0.277635i | \(0.0895506\pi\) | |||||||
\(240\) | 12.8079 | − | 16.1949i | 0.826747 | − | 1.04537i | ||||
\(241\) | 9.93016 | 0.639658 | 0.319829 | − | 0.947475i | \(-0.396375\pi\) | ||||
0.319829 | + | 0.947475i | \(0.396375\pi\) | |||||||
\(242\) | 31.8996 | − | 3.08274i | 2.05059 | − | 0.198166i | ||||
\(243\) | 13.2064 | + | 8.28202i | 0.847189 | + | 0.531292i | ||||
\(244\) | 5.49744 | + | 28.1776i | 0.351938 | + | 1.80389i | ||||
\(245\) | −15.3322 | −0.979541 | ||||||||
\(246\) | 14.9868 | + | 21.3230i | 0.955522 | + | 1.35950i | ||||
\(247\) | 1.35665i | 0.0863214i | ||||||||
\(248\) | 1.06481 | + | 3.58105i | 0.0676153 | + | 0.227397i | ||||
\(249\) | −2.64352 | − | 4.65694i | −0.167526 | − | 0.295122i | ||||
\(250\) | −4.69185 | + | 0.453415i | −0.296739 | + | 0.0286765i | ||||
\(251\) | − | 3.64528i | − | 0.230088i | −0.993360 | − | 0.115044i | \(-0.963299\pi\) | ||
0.993360 | − | 0.115044i | \(-0.0367009\pi\) | |||||||
\(252\) | 7.68953 | + | 2.76801i | 0.484395 | + | 0.174368i | ||||
\(253\) | − | 5.80186i | − | 0.364760i | ||||||
\(254\) | 1.80200 | + | 18.6468i | 0.113068 | + | 1.17000i | ||||
\(255\) | 13.7186 | + | 24.1674i | 0.859094 | + | 1.51342i | ||||
\(256\) | 11.4786 | − | 11.1464i | 0.717411 | − | 0.696650i | ||||
\(257\) | − | 6.26550i | − | 0.390831i | −0.980721 | − | 0.195416i | \(-0.937394\pi\) | ||
0.980721 | − | 0.195416i | \(-0.0626055\pi\) | |||||||
\(258\) | 7.61583 | − | 5.35276i | 0.474141 | − | 0.333248i | ||||
\(259\) | −0.286697 | −0.0178145 | ||||||||
\(260\) | 0.972760 | + | 4.98597i | 0.0603280 | + | 0.309217i | ||||
\(261\) | 6.18004 | − | 10.3519i | 0.382535 | − | 0.640765i | ||||
\(262\) | 1.87849 | + | 19.4382i | 0.116053 | + | 1.20090i | ||||
\(263\) | 6.89077 | 0.424903 | 0.212452 | − | 0.977172i | \(-0.431855\pi\) | ||||
0.212452 | + | 0.977172i | \(0.431855\pi\) | |||||||
\(264\) | −20.4944 | − | 19.6940i | −1.26135 | − | 1.21208i | ||||
\(265\) | −37.5244 | −2.30511 | ||||||||
\(266\) | 0.294941 | + | 3.05199i | 0.0180840 | + | 0.187130i | ||||
\(267\) | 11.7227 | + | 20.6512i | 0.717418 | + | 1.26384i | ||||
\(268\) | −19.1818 | + | 3.74237i | −1.17172 | + | 0.228601i | ||||
\(269\) | 9.20381 | 0.561166 | 0.280583 | − | 0.959830i | \(-0.409472\pi\) | ||||
0.280583 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(270\) | 1.62838 | + | 21.8393i | 0.0991000 | + | 1.32910i | ||||
\(271\) | − | 5.65011i | − | 0.343220i | −0.985165 | − | 0.171610i | \(-0.945103\pi\) | ||
0.985165 | − | 0.171610i | \(-0.0548969\pi\) | |||||||
\(272\) | 8.09466 | + | 19.9553i | 0.490811 | + | 1.20997i | ||||
\(273\) | −1.74864 | + | 0.992617i | −0.105833 | + | 0.0600759i | ||||
\(274\) | 1.73887 | + | 17.9935i | 0.105049 | + | 1.08703i | ||||
\(275\) | − | 22.5204i | − | 1.35803i | ||||||
\(276\) | −2.62936 | + | 2.25532i | −0.158269 | + | 0.135754i | ||||
\(277\) | 20.0093i | 1.20224i | 0.799158 | + | 0.601121i | \(0.205279\pi\) | ||||
−0.799158 | + | 0.601121i | \(0.794721\pi\) | |||||||
\(278\) | −2.11374 | + | 0.204269i | −0.126774 | + | 0.0122512i | ||||
\(279\) | −3.40243 | − | 2.03124i | −0.203698 | − | 0.121607i | ||||
\(280\) | 3.27235 | + | 11.0052i | 0.195560 | + | 0.657689i | ||||
\(281\) | 17.2312i | 1.02793i | 0.857812 | + | 0.513963i | \(0.171823\pi\) | ||||
−0.857812 | + | 0.513963i | \(0.828177\pi\) | |||||||
\(282\) | 6.94145 | − | 4.87877i | 0.413357 | − | 0.290526i | ||||
\(283\) | 12.7408 | 0.757363 | 0.378682 | − | 0.925527i | \(-0.376378\pi\) | ||||
0.378682 | + | 0.925527i | \(0.376378\pi\) | |||||||
\(284\) | 6.42415 | − | 1.25335i | 0.381203 | − | 0.0743725i | ||||
\(285\) | −7.14551 | + | 4.05616i | −0.423264 | + | 0.240266i | ||||
\(286\) | 6.96065 | − | 0.672668i | 0.411592 | − | 0.0397757i | ||||
\(287\) | −14.4928 | −0.855485 | ||||||||
\(288\) | −0.958512 | + | 16.9435i | −0.0564809 | + | 0.998404i | ||||
\(289\) | −11.9836 | −0.704920 | ||||||||
\(290\) | 16.8591 | − | 1.62924i | 0.990000 | − | 0.0956724i | ||||
\(291\) | −15.7186 | + | 8.92270i | −0.921443 | + | 0.523058i | ||||
\(292\) | 5.56101 | − | 1.08495i | 0.325433 | − | 0.0634919i | ||||
\(293\) | −29.5288 | −1.72509 | −0.862544 | − | 0.505982i | \(-0.831130\pi\) | ||||
−0.862544 | + | 0.505982i | \(0.831130\pi\) | |||||||
\(294\) | 10.3101 | − | 7.24639i | 0.601296 | − | 0.422618i | ||||
\(295\) | − | 13.3115i | − | 0.775023i | ||||||
\(296\) | −0.169678 | − | 0.570644i | −0.00986232 | − | 0.0331680i | ||||
\(297\) | 30.1401 | + | 0.660638i | 1.74891 | + | 0.0383341i | ||||
\(298\) | 28.7521 | − | 2.77856i | 1.66556 | − | 0.160958i | ||||
\(299\) | − | 0.852288i | − | 0.0492891i | ||||||
\(300\) | −10.2061 | + | 8.75421i | −0.589249 | + | 0.505425i | ||||
\(301\) | 5.17634i | 0.298359i | ||||||||
\(302\) | −2.16325 | − | 22.3850i | −0.124481 | − | 1.28811i | ||||
\(303\) | −28.3222 | + | 16.0771i | −1.62707 | + | 0.923607i | ||||
\(304\) | −5.90015 | + | 2.39333i | −0.338397 | + | 0.137267i | ||||
\(305\) | − | 42.7791i | − | 2.44952i | ||||||
\(306\) | −20.6471 | − | 9.76745i | −1.18032 | − | 0.558368i | ||||
\(307\) | −24.3810 | −1.39149 | −0.695747 | − | 0.718287i | \(-0.744927\pi\) | ||||
−0.695747 | + | 0.718287i | \(0.744927\pi\) | |||||||
\(308\) | 15.5128 | − | 3.02655i | 0.883927 | − | 0.172454i | ||||
\(309\) | 11.5531 | + | 20.3524i | 0.657231 | + | 1.15781i | ||||
\(310\) | −0.535496 | − | 5.54121i | −0.0304141 | − | 0.314720i | ||||
\(311\) | 2.85460 | 0.161870 | 0.0809348 | − | 0.996719i | \(-0.474209\pi\) | ||||
0.0809348 | + | 0.996719i | \(0.474209\pi\) | |||||||
\(312\) | −3.01062 | − | 2.89303i | −0.170443 | − | 0.163786i | ||||
\(313\) | 8.10335 | 0.458029 | 0.229014 | − | 0.973423i | \(-0.426450\pi\) | ||||
0.229014 | + | 0.973423i | \(0.426450\pi\) | |||||||
\(314\) | −1.20946 | − | 12.5153i | −0.0682539 | − | 0.706279i | ||||
\(315\) | −10.4563 | − | 6.24239i | −0.589146 | − | 0.351719i | ||||
\(316\) | −1.91422 | − | 9.81148i | −0.107683 | − | 0.551939i | ||||
\(317\) | 22.9292 | 1.28783 | 0.643916 | − | 0.765096i | \(-0.277309\pi\) | ||||
0.643916 | + | 0.765096i | \(0.277309\pi\) | |||||||
\(318\) | 25.2331 | − | 17.7350i | 1.41500 | − | 0.994527i | ||||
\(319\) | − | 23.3163i | − | 1.30546i | ||||||
\(320\) | −19.9682 | + | 13.0266i | −1.11626 | + | 0.728209i | ||||
\(321\) | −1.70657 | − | 3.00637i | −0.0952513 | − | 0.167799i | ||||
\(322\) | −0.185291 | − | 1.91736i | −0.0103259 | − | 0.106850i | ||||
\(323\) | − | 8.56953i | − | 0.476822i | ||||||
\(324\) | −11.4168 | − | 13.9161i | −0.634265 | − | 0.773116i | ||||
\(325\) | − | 3.30823i | − | 0.183507i | ||||||
\(326\) | −8.23811 | + | 0.796121i | −0.456267 | + | 0.0440930i | ||||
\(327\) | −7.84096 | − | 13.8130i | −0.433606 | − | 0.763861i | ||||
\(328\) | −8.57738 | − | 28.8466i | −0.473607 | − | 1.59279i | ||||
\(329\) | 4.71797i | 0.260110i | ||||||||
\(330\) | 24.3542 | + | 34.6508i | 1.34065 | + | 1.90747i | ||||
\(331\) | 0.553549 | 0.0304258 | 0.0152129 | − | 0.999884i | \(-0.495157\pi\) | ||||
0.0152129 | + | 0.999884i | \(0.495157\pi\) | |||||||
\(332\) | 1.18404 | + | 6.06892i | 0.0649829 | + | 0.333075i | ||||
\(333\) | 0.542180 | + | 0.323680i | 0.0297113 | + | 0.0177376i | ||||
\(334\) | −7.06101 | + | 0.682367i | −0.386361 | + | 0.0373375i | ||||
\(335\) | 29.1217 | 1.59109 | ||||||||
\(336\) | −7.40182 | − | 5.85382i | −0.403803 | − | 0.319352i | ||||
\(337\) | −19.3916 | −1.05633 | −0.528165 | − | 0.849142i | \(-0.677120\pi\) | ||||
−0.528165 | + | 0.849142i | \(0.677120\pi\) | |||||||
\(338\) | −17.2770 | + | 1.66963i | −0.939746 | + | 0.0908159i | ||||
\(339\) | −4.31825 | − | 7.60723i | −0.234535 | − | 0.413168i | ||||
\(340\) | −6.14463 | − | 31.4949i | −0.333240 | − | 1.70805i | ||||
\(341\) | −7.66355 | −0.415004 | ||||||||
\(342\) | 2.88792 | − | 6.10468i | 0.156161 | − | 0.330103i | ||||
\(343\) | 16.5422i | 0.893195i | ||||||||
\(344\) | −10.3030 | + | 3.06354i | −0.555501 | + | 0.165175i | ||||
\(345\) | 4.48903 | − | 2.54820i | 0.241681 | − | 0.137191i | ||||
\(346\) | 12.7816 | − | 1.23520i | 0.687145 | − | 0.0664049i | ||||
\(347\) | 11.2938i | 0.606284i | 0.952945 | + | 0.303142i | \(0.0980356\pi\) | ||||
−0.952945 | + | 0.303142i | \(0.901964\pi\) | |||||||
\(348\) | −10.5668 | + | 9.06360i | −0.566439 | + | 0.485860i | ||||
\(349\) | − | 19.0039i | − | 1.01725i | −0.860987 | − | 0.508627i | \(-0.830153\pi\) | ||
0.860987 | − | 0.508627i | \(-0.169847\pi\) | |||||||
\(350\) | −0.719223 | − | 7.44239i | −0.0384441 | − | 0.397812i | ||||
\(351\) | 4.42755 | + | 0.0970471i | 0.236325 | + | 0.00517999i | ||||
\(352\) | 15.2051 | + | 29.0856i | 0.810436 | + | 1.55027i | ||||
\(353\) | 16.0338i | 0.853390i | 0.904395 | + | 0.426695i | \(0.140322\pi\) | ||||
−0.904395 | + | 0.426695i | \(0.859678\pi\) | |||||||
\(354\) | 6.29132 | + | 8.95122i | 0.334380 | + | 0.475752i | ||||
\(355\) | −9.75310 | −0.517641 | ||||||||
\(356\) | −5.25065 | − | 26.9127i | −0.278284 | − | 1.42637i | ||||
\(357\) | 11.0456 | − | 6.27006i | 0.584597 | − | 0.331847i | ||||
\(358\) | −2.57349 | − | 26.6299i | −0.136013 | − | 1.40744i | ||||
\(359\) | −30.6919 | −1.61986 | −0.809928 | − | 0.586530i | \(-0.800494\pi\) | ||||
−0.809928 | + | 0.586530i | \(0.800494\pi\) | |||||||
\(360\) | 6.23646 | − | 24.5067i | 0.328691 | − | 1.29162i | ||||
\(361\) | −16.4663 | −0.866646 | ||||||||
\(362\) | −1.80922 | − | 18.7215i | −0.0950907 | − | 0.983981i | ||||
\(363\) | 34.1348 | − | 19.3766i | 1.79161 | − | 1.01701i | ||||
\(364\) | 2.27882 | − | 0.444598i | 0.119443 | − | 0.0233033i | ||||
\(365\) | −8.44269 | −0.441911 | ||||||||
\(366\) | 20.2184 | + | 28.7666i | 1.05684 | + | 1.50365i | ||||
\(367\) | 12.7262i | 0.664304i | 0.943226 | + | 0.332152i | \(0.107775\pi\) | ||||
−0.943226 | + | 0.332152i | \(0.892225\pi\) | |||||||
\(368\) | 3.70666 | − | 1.50357i | 0.193223 | − | 0.0783788i | ||||
\(369\) | 27.4077 | + | 16.3624i | 1.42679 | + | 0.851790i | ||||
\(370\) | 0.0853316 | + | 0.882996i | 0.00443618 | + | 0.0459048i | ||||
\(371\) | 17.1504i | 0.890407i | ||||||||
\(372\) | 2.97900 | + | 3.47307i | 0.154454 | + | 0.180070i | ||||
\(373\) | − | 0.102701i | − | 0.00531768i | −0.999996 | − | 0.00265884i | \(-0.999154\pi\) | ||
0.999996 | − | 0.00265884i | \(-0.000846336\pi\) | |||||||
\(374\) | −43.9683 | + | 4.24904i | −2.27355 | + | 0.219713i | ||||
\(375\) | −5.02060 | + | 2.84995i | −0.259263 | + | 0.147171i | ||||
\(376\) | −9.39067 | + | 2.79227i | −0.484287 | + | 0.144000i | ||||
\(377\) | − | 3.42514i | − | 0.176404i | ||||||
\(378\) | 9.98159 | − | 0.744247i | 0.513397 | − | 0.0382799i | ||||
\(379\) | 22.9132 | 1.17697 | 0.588485 | − | 0.808508i | \(-0.299724\pi\) | ||||
0.588485 | + | 0.808508i | \(0.299724\pi\) | |||||||
\(380\) | 9.31202 | − | 1.81677i | 0.477696 | − | 0.0931984i | ||||
\(381\) | 11.3265 | + | 19.9533i | 0.580275 | + | 1.02224i | ||||
\(382\) | −20.5923 | + | 1.99001i | −1.05359 | + | 0.101818i | ||||
\(383\) | −28.1640 | −1.43911 | −0.719556 | − | 0.694435i | \(-0.755654\pi\) | ||||
−0.719556 | + | 0.694435i | \(0.755654\pi\) | |||||||
\(384\) | 7.27081 | − | 18.1971i | 0.371037 | − | 0.928618i | ||||
\(385\) | −23.5515 | −1.20030 | ||||||||
\(386\) | −11.3369 | + | 1.09559i | −0.577035 | + | 0.0557639i | ||||
\(387\) | 5.84406 | − | 9.78909i | 0.297070 | − | 0.497607i | ||||
\(388\) | 20.4845 | − | 3.99652i | 1.03994 | − | 0.202892i | ||||
\(389\) | 5.41823 | 0.274715 | 0.137358 | − | 0.990522i | \(-0.456139\pi\) | ||||
0.137358 | + | 0.990522i | \(0.456139\pi\) | |||||||
\(390\) | 3.57761 | + | 5.09018i | 0.181159 | + | 0.257751i | ||||
\(391\) | 5.38365i | 0.272263i | ||||||||
\(392\) | −13.9479 | + | 4.14733i | −0.704475 | + | 0.209472i | ||||
\(393\) | 11.8073 | + | 20.8002i | 0.595597 | + | 1.04923i | ||||
\(394\) | 8.43100 | − | 0.814761i | 0.424748 | − | 0.0410471i | ||||
\(395\) | 14.8957i | 0.749485i | ||||||||
\(396\) | −32.7537 | − | 11.7904i | −1.64593 | − | 0.592488i | ||||
\(397\) | − | 22.1875i | − | 1.11356i | −0.830660 | − | 0.556780i | \(-0.812037\pi\) | ||
0.830660 | − | 0.556780i | \(-0.187963\pi\) | |||||||
\(398\) | 2.83061 | + | 29.2906i | 0.141885 | + | 1.46820i | ||||
\(399\) | 1.85386 | + | 3.26584i | 0.0928089 | + | 0.163496i | ||||
\(400\) | 14.3877 | − | 5.83622i | 0.719385 | − | 0.291811i | ||||
\(401\) | 25.6622i | 1.28151i | 0.767745 | + | 0.640755i | \(0.221379\pi\) | ||||
−0.767745 | + | 0.640755i | \(0.778621\pi\) | |||||||
\(402\) | −19.5827 | + | 13.7636i | −0.976698 | + | 0.686468i | ||||
\(403\) | −1.12577 | −0.0560785 | ||||||||
\(404\) | 36.9094 | − | 7.20102i | 1.83631 | − | 0.358264i | ||||
\(405\) | 12.7265 | + | 23.6103i | 0.632386 | + | 1.17320i | ||||
\(406\) | −0.744641 | − | 7.70541i | −0.0369559 | − | 0.382413i | ||||
\(407\) | 1.22119 | 0.0605322 | ||||||||
\(408\) | 19.0172 | + | 18.2744i | 0.941490 | + | 0.904719i | ||||
\(409\) | −30.4116 | −1.50376 | −0.751880 | − | 0.659300i | \(-0.770853\pi\) | ||||
−0.751880 | + | 0.659300i | \(0.770853\pi\) | |||||||
\(410\) | 4.31360 | + | 44.6363i | 0.213034 | + | 2.20443i | ||||
\(411\) | 10.9297 | + | 19.2543i | 0.539122 | + | 0.949742i | ||||
\(412\) | −5.17468 | − | 26.5232i | −0.254938 | − | 1.30671i | ||||
\(413\) | −6.08397 | −0.299373 | ||||||||
\(414\) | −1.81428 | + | 3.83515i | −0.0891670 | + | 0.188487i | ||||
\(415\) | − | 9.21380i | − | 0.452288i | ||||||
\(416\) | 2.23362 | + | 4.27265i | 0.109512 | + | 0.209484i | ||||
\(417\) | −2.26184 | + | 1.28394i | −0.110763 | + | 0.0628746i | ||||
\(418\) | −1.25631 | − | 13.0000i | −0.0614479 | − | 0.635852i | ||||
\(419\) | − | 16.8895i | − | 0.825105i | −0.910934 | − | 0.412552i | \(-0.864637\pi\) | ||
0.910934 | − | 0.412552i | \(-0.135363\pi\) | |||||||
\(420\) | 9.15503 | + | 10.6734i | 0.446720 | + | 0.520808i | ||||
\(421\) | 21.1951i | 1.03298i | 0.856292 | + | 0.516492i | \(0.172762\pi\) | ||||
−0.856292 | + | 0.516492i | \(0.827238\pi\) | |||||||
\(422\) | −22.0295 | + | 2.12890i | −1.07238 | + | 0.103633i | ||||
\(423\) | 5.32657 | − | 8.92227i | 0.258987 | − | 0.433815i | ||||
\(424\) | −34.1363 | + | 10.1503i | −1.65781 | + | 0.492940i | ||||
\(425\) | 20.8971i | 1.01366i | ||||||||
\(426\) | 6.55841 | − | 4.60955i | 0.317756 | − | 0.223334i | ||||
\(427\) | −19.5521 | −0.946192 | ||||||||
\(428\) | 0.764379 | + | 3.91789i | 0.0369477 | + | 0.189379i | ||||
\(429\) | 7.44836 | − | 4.22807i | 0.359610 | − | 0.204133i | ||||
\(430\) | 15.9425 | − | 1.54067i | 0.768818 | − | 0.0742976i | ||||
\(431\) | 22.2205 | 1.07033 | 0.535163 | − | 0.844749i | \(-0.320250\pi\) | ||||
0.535163 | + | 0.844749i | \(0.320250\pi\) | |||||||
\(432\) | 7.38881 | + | 19.4269i | 0.355494 | + | 0.934678i | ||||
\(433\) | −0.426510 | −0.0204967 | −0.0102484 | − | 0.999947i | \(-0.503262\pi\) | ||||
−0.0102484 | + | 0.999947i | \(0.503262\pi\) | |||||||
\(434\) | −2.53260 | + | 0.244747i | −0.121569 | + | 0.0117482i | ||||
\(435\) | 18.0404 | − | 10.2406i | 0.864969 | − | 0.491001i | ||||
\(436\) | 3.51200 | + | 18.0011i | 0.168194 | + | 0.862095i | ||||
\(437\) | −1.59177 | −0.0761447 | ||||||||
\(438\) | 5.67724 | − | 3.99022i | 0.271269 | − | 0.190660i | ||||
\(439\) | − | 4.91908i | − | 0.234775i | −0.993086 | − | 0.117387i | \(-0.962548\pi\) | ||
0.993086 | − | 0.117387i | \(-0.0374519\pi\) | |||||||
\(440\) | −13.9386 | − | 46.8770i | −0.664498 | − | 2.23478i | ||||
\(441\) | 7.91151 | − | 13.2522i | 0.376739 | − | 0.631055i | ||||
\(442\) | −6.45891 | + | 0.624181i | −0.307219 | + | 0.0296893i | ||||
\(443\) | − | 39.8938i | − | 1.89541i | −0.319143 | − | 0.947707i | \(-0.603395\pi\) | ||
0.319143 | − | 0.947707i | \(-0.396605\pi\) | |||||||
\(444\) | −0.474706 | − | 0.553436i | −0.0225286 | − | 0.0262649i | ||||
\(445\) | 40.8587i | 1.93689i | ||||||||
\(446\) | −2.92398 | − | 30.2568i | −0.138454 | − | 1.43270i | ||||
\(447\) | 30.7666 | − | 17.4647i | 1.45521 | − | 0.826053i | ||||
\(448\) | 5.95378 | + | 9.12642i | 0.281290 | + | 0.431183i | ||||
\(449\) | − | 18.8142i | − | 0.887899i | −0.896052 | − | 0.443950i | \(-0.853577\pi\) | ||
0.896052 | − | 0.443950i | \(-0.146423\pi\) | |||||||
\(450\) | −7.04229 | + | 14.8865i | −0.331977 | + | 0.701755i | ||||
\(451\) | 61.7325 | 2.90687 | ||||||||
\(452\) | 1.93416 | + | 9.91372i | 0.0909754 | + | 0.466302i | ||||
\(453\) | −13.5972 | − | 23.9534i | −0.638851 | − | 1.12543i | ||||
\(454\) | 0.119564 | + | 1.23723i | 0.00561143 | + | 0.0580660i | ||||
\(455\) | −3.45970 | −0.162193 | ||||||||
\(456\) | −5.40316 | + | 5.62277i | −0.253026 | + | 0.263310i | ||||
\(457\) | 6.47683 | 0.302973 | 0.151487 | − | 0.988459i | \(-0.451594\pi\) | ||||
0.151487 | + | 0.988459i | \(0.451594\pi\) | |||||||
\(458\) | 2.34906 | + | 24.3076i | 0.109764 | + | 1.13582i | ||||
\(459\) | −27.9675 | − | 0.613017i | −1.30541 | − | 0.0286132i | ||||
\(460\) | −5.85010 | + | 1.14135i | −0.272762 | + | 0.0532158i | ||||
\(461\) | 38.5365 | 1.79482 | 0.897412 | − | 0.441194i | \(-0.145445\pi\) | ||||
0.897412 | + | 0.441194i | \(0.145445\pi\) | |||||||
\(462\) | 15.8371 | − | 11.1310i | 0.736808 | − | 0.517862i | ||||
\(463\) | 31.4845i | 1.46321i | 0.681730 | + | 0.731604i | \(0.261228\pi\) | ||||
−0.681730 | + | 0.731604i | \(0.738772\pi\) | |||||||
\(464\) | 14.8962 | − | 6.04247i | 0.691537 | − | 0.280515i | ||||
\(465\) | −3.36587 | − | 5.92947i | −0.156088 | − | 0.274973i | ||||
\(466\) | −1.73895 | − | 17.9943i | −0.0805553 | − | 0.833571i | ||||
\(467\) | 28.5861i | 1.32281i | 0.750030 | + | 0.661404i | \(0.230039\pi\) | ||||
−0.750030 | + | 0.661404i | \(0.769961\pi\) | |||||||
\(468\) | −4.81149 | − | 1.73199i | −0.222411 | − | 0.0800615i | ||||
\(469\) | − | 13.3100i | − | 0.614599i | ||||||
\(470\) | 14.5308 | − | 1.40424i | 0.670257 | − | 0.0647729i | ||||
\(471\) | −7.60210 | − | 13.3922i | −0.350286 | − | 0.617080i | ||||
\(472\) | −3.60071 | − | 12.1096i | −0.165736 | − | 0.557388i | ||||
\(473\) | − | 22.0487i | − | 1.01380i | ||||||
\(474\) | −7.04009 | − | 10.0165i | −0.323362 | − | 0.460075i | ||||
\(475\) | −6.17860 | −0.283493 | ||||||||
\(476\) | −14.3946 | + | 2.80839i | −0.659778 | + | 0.128722i | ||||
\(477\) | 19.3628 | − | 32.4336i | 0.886561 | − | 1.48503i | ||||
\(478\) | −41.8126 | + | 4.04072i | −1.91246 | + | 0.184818i | ||||
\(479\) | −17.8359 | −0.814943 | −0.407471 | − | 0.913218i | \(-0.633589\pi\) | ||||
−0.407471 | + | 0.913218i | \(0.633589\pi\) | |||||||
\(480\) | −15.8261 | + | 24.5391i | −0.722358 | + | 1.12005i | ||||
\(481\) | 0.179392 | 0.00817957 | ||||||||
\(482\) | −13.9783 | + | 1.35084i | −0.636692 | + | 0.0615291i | ||||
\(483\) | −1.16465 | − | 2.05170i | −0.0529934 | − | 0.0933557i | ||||
\(484\) | −44.4844 | + | 8.67888i | −2.02202 | + | 0.394495i | ||||
\(485\) | −31.0995 | −1.41215 | ||||||||
\(486\) | −19.7167 | − | 9.86171i | −0.894366 | − | 0.447336i | ||||
\(487\) | − | 4.21929i | − | 0.191194i | −0.995420 | − | 0.0955972i | \(-0.969524\pi\) | ||
0.995420 | − | 0.0955972i | \(-0.0304761\pi\) | |||||||
\(488\) | −11.5716 | − | 38.9166i | −0.523823 | − | 1.76167i | ||||
\(489\) | −8.81533 | + | 5.00403i | −0.398643 | + | 0.226290i | ||||
\(490\) | 21.5825 | − | 2.08571i | 0.974999 | − | 0.0942227i | ||||
\(491\) | − | 19.7601i | − | 0.891763i | −0.895092 | − | 0.445881i | \(-0.852890\pi\) | ||
0.895092 | − | 0.445881i | \(-0.147110\pi\) | |||||||
\(492\) | −23.9969 | − | 27.9767i | −1.08186 | − | 1.26129i | ||||
\(493\) | 21.6356i | 0.974419i | ||||||||
\(494\) | −0.184550 | − | 1.90969i | −0.00830331 | − | 0.0859211i | ||||
\(495\) | 44.5388 | + | 26.5896i | 2.00187 | + | 1.19511i | ||||
\(496\) | −1.98603 | − | 4.89604i | −0.0891753 | − | 0.219839i | ||||
\(497\) | 4.45763i | 0.199952i | ||||||||
\(498\) | 4.35467 | + | 6.19577i | 0.195137 | + | 0.277639i | ||||
\(499\) | −13.1506 | −0.588701 | −0.294351 | − | 0.955697i | \(-0.595103\pi\) | ||||
−0.294351 | + | 0.955697i | \(0.595103\pi\) | |||||||
\(500\) | 6.54283 | − | 1.27650i | 0.292604 | − | 0.0570870i | ||||
\(501\) | −7.55575 | + | 4.28903i | −0.337566 | + | 0.191620i | ||||
\(502\) | 0.495883 | + | 5.13130i | 0.0221323 | + | 0.229021i | ||||
\(503\) | −40.6941 | −1.81446 | −0.907230 | − | 0.420634i | \(-0.861808\pi\) | ||||
−0.907230 | + | 0.420634i | \(0.861808\pi\) | |||||||
\(504\) | −11.2007 | − | 2.85036i | −0.498921 | − | 0.126965i | ||||
\(505\) | −56.0357 | −2.49356 | ||||||||
\(506\) | 0.789250 | + | 8.16702i | 0.0350865 | + | 0.363068i | ||||
\(507\) | −18.4876 | + | 10.4945i | −0.821062 | + | 0.466076i | ||||
\(508\) | −5.07320 | − | 26.0031i | −0.225087 | − | 1.15370i | ||||
\(509\) | −6.52138 | −0.289055 | −0.144528 | − | 0.989501i | \(-0.546166\pi\) | ||||
−0.144528 | + | 0.989501i | \(0.546166\pi\) | |||||||
\(510\) | −22.5987 | − | 32.1531i | −1.00069 | − | 1.42376i | ||||
\(511\) | 3.85871i | 0.170699i | ||||||||
\(512\) | −14.6416 | + | 17.2518i | −0.647074 | + | 0.762428i | ||||
\(513\) | 0.181250 | − | 8.26910i | 0.00800236 | − | 0.365090i | ||||
\(514\) | 0.852322 | + | 8.81966i | 0.0375943 | + | 0.389019i | ||||
\(515\) | 40.2674i | 1.77440i | ||||||||
\(516\) | −9.99231 | + | 8.57085i | −0.439887 | + | 0.377311i | ||||
\(517\) | − | 20.0963i | − | 0.883834i | ||||||
\(518\) | 0.403571 | − | 0.0390006i | 0.0177319 | − | 0.00171359i | ||||
\(519\) | 13.6772 | − | 7.76388i | 0.600363 | − | 0.340797i | ||||
\(520\) | −2.04757 | − | 6.88620i | −0.0897920 | − | 0.301980i | ||||
\(521\) | − | 9.55394i | − | 0.418566i | −0.977855 | − | 0.209283i | \(-0.932887\pi\) | ||
0.977855 | − | 0.209283i | \(-0.0671129\pi\) | |||||||
\(522\) | −7.29117 | + | 15.4126i | −0.319126 | + | 0.674590i | ||||
\(523\) | 18.5211 | 0.809871 | 0.404935 | − | 0.914345i | \(-0.367294\pi\) | ||||
0.404935 | + | 0.914345i | \(0.367294\pi\) | |||||||
\(524\) | −5.28852 | − | 27.1068i | −0.231030 | − | 1.18417i | ||||
\(525\) | −4.52069 | − | 7.96386i | −0.197299 | − | 0.347571i | ||||
\(526\) | −9.69983 | + | 0.937380i | −0.422933 | + | 0.0408717i | ||||
\(527\) | 7.11114 | 0.309766 | ||||||||
\(528\) | 31.5282 | + | 24.9345i | 1.37209 | + | 1.08513i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 52.8215 | − | 5.10460i | 2.29442 | − | 0.221730i | ||||
\(531\) | 11.5055 | + | 6.86878i | 0.499298 | + | 0.298080i | ||||
\(532\) | −0.830351 | − | 4.25604i | −0.0360003 | − | 0.184523i | ||||
\(533\) | 9.06845 | 0.392798 | ||||||||
\(534\) | −19.3108 | − | 27.4752i | −0.835660 | − | 1.18897i | ||||
\(535\) | − | 5.94812i | − | 0.257160i | ||||||
\(536\) | 26.4923 | − | 7.87735i | 1.14429 | − | 0.340250i | ||||
\(537\) | −16.1757 | − | 28.4958i | −0.698032 | − | 1.22969i | ||||
\(538\) | −12.9558 | + | 1.25203i | −0.558564 | + | 0.0539790i | ||||
\(539\) | − | 29.8488i | − | 1.28568i | ||||||
\(540\) | −5.26308 | − | 30.5207i | −0.226487 | − | 1.31340i | ||||
\(541\) | 6.54485i | 0.281385i | 0.990053 | + | 0.140693i | \(0.0449329\pi\) | ||||
−0.990053 | + | 0.140693i | \(0.955067\pi\) | |||||||
\(542\) | 0.768608 | + | 7.95341i | 0.0330145 | + | 0.341628i | ||||
\(543\) | −11.3719 | − | 20.0333i | −0.488015 | − | 0.859711i | ||||
\(544\) | −14.1091 | − | 26.9891i | −0.604923 | − | 1.15715i | ||||
\(545\) | − | 27.3291i | − | 1.17065i | ||||||
\(546\) | 2.32645 | − | 1.63514i | 0.0995630 | − | 0.0699774i | ||||
\(547\) | 22.1440 | 0.946808 | 0.473404 | − | 0.880845i | \(-0.343025\pi\) | ||||
0.473404 | + | 0.880845i | \(0.343025\pi\) | |||||||
\(548\) | −4.89546 | − | 25.0921i | −0.209124 | − | 1.07188i | ||||
\(549\) | 36.9754 | + | 22.0742i | 1.57807 | + | 0.942105i | ||||
\(550\) | 3.06354 | + | 31.7010i | 0.130630 | + | 1.35173i | ||||
\(551\) | −6.39695 | −0.272519 | ||||||||
\(552\) | 3.39443 | − | 3.53240i | 0.144477 | − | 0.150349i | ||||
\(553\) | 6.80806 | 0.289508 | ||||||||
\(554\) | −2.72195 | − | 28.1662i | −0.115644 | − | 1.19667i | ||||
\(555\) | 0.536353 | + | 0.944865i | 0.0227669 | + | 0.0401073i | ||||
\(556\) | 2.94763 | − | 0.575081i | 0.125007 | − | 0.0243889i | ||||
\(557\) | −13.7714 | −0.583514 | −0.291757 | − | 0.956492i | \(-0.594240\pi\) | ||||
−0.291757 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(558\) | 5.06577 | + | 2.39645i | 0.214451 | + | 0.101450i | ||||
\(559\) | − | 3.23893i | − | 0.136992i | ||||||
\(560\) | −6.10343 | − | 15.0465i | −0.257917 | − | 0.635829i | ||||
\(561\) | −47.0491 | + | 26.7074i | −1.98641 | + | 1.12759i | ||||
\(562\) | −2.34403 | − | 24.2556i | −0.0988768 | − | 1.02316i | ||||
\(563\) | 43.5521i | 1.83550i | 0.397155 | + | 0.917752i | \(0.369998\pi\) | ||||
−0.397155 | + | 0.917752i | \(0.630002\pi\) | |||||||
\(564\) | −9.10749 | + | 7.81190i | −0.383495 | + | 0.328940i | ||||
\(565\) | − | 15.0510i | − | 0.633198i | ||||||
\(566\) | −17.9347 | + | 1.73319i | −0.753851 | + | 0.0728513i | ||||
\(567\) | 10.7910 | − | 5.81663i | 0.453180 | − | 0.244275i | ||||
\(568\) | −8.87249 | + | 2.63819i | −0.372281 | + | 0.110696i | ||||
\(569\) | − | 36.7256i | − | 1.53962i | −0.638274 | − | 0.769809i | \(-0.720351\pi\) | ||
0.638274 | − | 0.769809i | \(-0.279649\pi\) | |||||||
\(570\) | 9.50665 | − | 6.68171i | 0.398190 | − | 0.279866i | ||||
\(571\) | −6.35399 | −0.265906 | −0.132953 | − | 0.991122i | \(-0.542446\pi\) | ||||
−0.132953 | + | 0.991122i | \(0.542446\pi\) | |||||||
\(572\) | −9.70669 | + | 1.89377i | −0.405857 | + | 0.0791826i | ||||
\(573\) | −22.0351 | + | 12.5082i | −0.920530 | + | 0.522540i | ||||
\(574\) | 20.4009 | − | 1.97152i | 0.851518 | − | 0.0822897i | ||||
\(575\) | 3.88159 | 0.161873 | ||||||||
\(576\) | −0.955635 | − | 23.9810i | −0.0398181 | − | 0.999207i | ||||
\(577\) | 36.0375 | 1.50026 | 0.750130 | − | 0.661290i | \(-0.229991\pi\) | ||||
0.750130 | + | 0.661290i | \(0.229991\pi\) | |||||||
\(578\) | 16.8688 | − | 1.63018i | 0.701651 | − | 0.0678067i | ||||
\(579\) | −12.1313 | + | 6.88633i | −0.504159 | + | 0.286186i | ||||
\(580\) | −23.5102 | + | 4.58682i | −0.976207 | + | 0.190458i | ||||
\(581\) | −4.21114 | −0.174708 | ||||||||
\(582\) | 20.9126 | − | 14.6984i | 0.866857 | − | 0.609267i | ||||
\(583\) | − | 73.0526i | − | 3.02553i | ||||||
\(584\) | −7.68039 | + | 2.28372i | −0.317817 | + | 0.0945012i | ||||
\(585\) | 6.54271 | + | 3.90598i | 0.270508 | + | 0.161493i | ||||
\(586\) | 41.5663 | − | 4.01692i | 1.71709 | − | 0.165937i | ||||
\(587\) | 0.173544i | 0.00716291i | 0.999994 | + | 0.00358146i | \(0.00114002\pi\) | ||||
−0.999994 | + | 0.00358146i | \(0.998860\pi\) | |||||||
\(588\) | −13.5273 | + | 11.6029i | −0.557856 | + | 0.478497i | ||||
\(589\) | 2.10254i | 0.0866335i | ||||||||
\(590\) | 1.81081 | + | 18.7380i | 0.0745500 | + | 0.771429i | ||||
\(591\) | 9.02174 | − | 5.12120i | 0.371105 | − | 0.210658i | ||||
\(592\) | 0.316475 | + | 0.780188i | 0.0130070 | + | 0.0320655i | ||||
\(593\) | − | 26.2045i | − | 1.07609i | −0.842917 | − | 0.538044i | \(-0.819163\pi\) | ||
0.842917 | − | 0.538044i | \(-0.180837\pi\) | |||||||
\(594\) | −42.5167 | + | 3.17013i | −1.74448 | + | 0.130072i | ||||
\(595\) | 21.8539 | 0.895921 | ||||||||
\(596\) | −40.0950 | + | 7.82253i | −1.64236 | + | 0.320423i | ||||
\(597\) | 17.7918 | + | 31.3429i | 0.728171 | + | 1.28278i | ||||
\(598\) | 0.115940 | + | 1.19973i | 0.00474115 | + | 0.0490605i | ||||
\(599\) | 10.2797 | 0.420016 | 0.210008 | − | 0.977700i | \(-0.432651\pi\) | ||||
0.210008 | + | 0.977700i | \(0.432651\pi\) | |||||||
\(600\) | 13.1758 | − | 13.7113i | 0.537899 | − | 0.559761i | ||||
\(601\) | −14.5446 | −0.593287 | −0.296644 | − | 0.954988i | \(-0.595867\pi\) | ||||
−0.296644 | + | 0.954988i | \(0.595867\pi\) | |||||||
\(602\) | −0.704159 | − | 7.28650i | −0.0286994 | − | 0.296976i | ||||
\(603\) | −15.0270 | + | 25.1709i | −0.611945 | + | 1.02504i | ||||
\(604\) | 6.09023 | + | 31.2160i | 0.247808 | + | 1.27016i | ||||
\(605\) | 67.5359 | 2.74572 | ||||||||
\(606\) | 37.6809 | − | 26.4838i | 1.53068 | − | 1.07583i | ||||
\(607\) | 37.4693i | 1.52083i | 0.649436 | + | 0.760417i | \(0.275005\pi\) | ||||
−0.649436 | + | 0.760417i | \(0.724995\pi\) | |||||||
\(608\) | 7.97980 | − | 4.17161i | 0.323624 | − | 0.169181i | ||||
\(609\) | −4.68045 | − | 8.24531i | −0.189662 | − | 0.334117i | ||||
\(610\) | 5.81942 | + | 60.2182i | 0.235621 | + | 2.43817i | ||||
\(611\) | − | 2.95213i | − | 0.119430i | ||||||
\(612\) | 30.3927 | + | 10.9405i | 1.22855 | + | 0.442243i | ||||
\(613\) | − | 35.8106i | − | 1.44638i | −0.690651 | − | 0.723188i | \(-0.742676\pi\) | ||
0.690651 | − | 0.723188i | \(-0.257324\pi\) | |||||||
\(614\) | 34.3200 | − | 3.31664i | 1.38504 | − | 0.133849i | ||||
\(615\) | 27.1132 | + | 47.7639i | 1.09331 | + | 1.92603i | ||||
\(616\) | −21.4250 | + | 6.37062i | −0.863239 | + | 0.256680i | ||||
\(617\) | − | 17.1786i | − | 0.691583i | −0.938311 | − | 0.345791i | \(-0.887610\pi\) | ||
0.938311 | − | 0.345791i | \(-0.112390\pi\) | |||||||
\(618\) | −19.0314 | − | 27.0776i | −0.765554 | − | 1.08922i | ||||
\(619\) | −30.4234 | −1.22282 | −0.611410 | − | 0.791314i | \(-0.709398\pi\) | ||||
−0.611410 | + | 0.791314i | \(0.709398\pi\) | |||||||
\(620\) | 1.50759 | + | 7.72727i | 0.0605462 | + | 0.310335i | ||||
\(621\) | −0.113867 | + | 5.19490i | −0.00456931 | + | 0.208464i | ||||
\(622\) | −4.01830 | + | 0.388323i | −0.161119 | + | 0.0155703i | ||||
\(623\) | 18.6743 | 0.748172 | ||||||||
\(624\) | 4.63146 | + | 3.66285i | 0.185407 | + | 0.146631i | ||||
\(625\) | −29.3412 | −1.17365 | ||||||||
\(626\) | −11.4067 | + | 1.10233i | −0.455905 | + | 0.0440581i | ||||
\(627\) | −7.89653 | − | 13.9109i | −0.315357 | − | 0.555548i | ||||
\(628\) | 3.40502 | + | 17.4527i | 0.135875 | + | 0.696439i | ||||
\(629\) | −1.13317 | −0.0451823 | ||||||||
\(630\) | 15.5681 | + | 7.36472i | 0.620246 | + | 0.293418i | ||||
\(631\) | 34.7687i | 1.38412i | 0.721839 | + | 0.692061i | \(0.243297\pi\) | ||||
−0.721839 | + | 0.692061i | \(0.756703\pi\) | |||||||
\(632\) | 4.02925 | + | 13.5508i | 0.160275 | + | 0.539021i | ||||
\(633\) | −23.5730 | + | 13.3813i | −0.936944 | + | 0.531857i | ||||
\(634\) | −32.2764 | + | 3.11915i | −1.28186 | + | 0.123877i | ||||
\(635\) | 39.4778i | 1.56663i | ||||||||
\(636\) | −33.1069 | + | 28.3973i | −1.31278 | + | 1.12603i | ||||
\(637\) | − | 4.38477i | − | 0.173731i | ||||||
\(638\) | 3.17181 | + | 32.8213i | 0.125573 | + | 1.29941i | ||||
\(639\) | 5.03265 | − | 8.42993i | 0.199088 | − | 0.333483i | ||||
\(640\) | 26.3363 | − | 21.0533i | 1.04103 | − | 0.832206i | ||||
\(641\) | 12.0542i | 0.476112i | 0.971251 | + | 0.238056i | \(0.0765102\pi\) | ||||
−0.971251 | + | 0.238056i | \(0.923490\pi\) | |||||||
\(642\) | 2.81123 | + | 3.99978i | 0.110950 | + | 0.157859i | ||||
\(643\) | −11.6786 | −0.460561 | −0.230280 | − | 0.973124i | \(-0.573964\pi\) | ||||
−0.230280 | + | 0.973124i | \(0.573964\pi\) | |||||||
\(644\) | 0.521652 | + | 2.67377i | 0.0205560 | + | 0.105361i | ||||
\(645\) | 17.0596 | − | 9.68389i | 0.671721 | − | 0.381303i | ||||
\(646\) | 1.16575 | + | 12.0630i | 0.0458658 | + | 0.474610i | ||||
\(647\) | −23.7356 | −0.933142 | −0.466571 | − | 0.884484i | \(-0.654511\pi\) | ||||
−0.466571 | + | 0.884484i | \(0.654511\pi\) | |||||||
\(648\) | 17.9639 | + | 18.0360i | 0.705690 | + | 0.708520i | ||||
\(649\) | 25.9148 | 1.01724 | ||||||||
\(650\) | 0.450032 | + | 4.65685i | 0.0176517 | + | 0.182657i | ||||
\(651\) | −2.71005 | + | 1.53836i | −0.106215 | + | 0.0602932i | ||||
\(652\) | 11.4881 | − | 2.24133i | 0.449909 | − | 0.0877772i | ||||
\(653\) | −19.7060 | −0.771157 | −0.385578 | − | 0.922675i | \(-0.625998\pi\) | ||||
−0.385578 | + | 0.922675i | \(0.625998\pi\) | |||||||
\(654\) | 12.9164 | + | 18.3773i | 0.505072 | + | 0.718610i | ||||
\(655\) | 41.1534i | 1.60799i | ||||||||
\(656\) | 15.9981 | + | 39.4393i | 0.624622 | + | 1.53984i | ||||
\(657\) | 4.35647 | − | 7.29730i | 0.169962 | − | 0.284695i | ||||
\(658\) | −0.641805 | − | 6.64128i | −0.0250202 | − | 0.258904i | ||||
\(659\) | − | 22.9550i | − | 0.894198i | −0.894484 | − | 0.447099i | \(-0.852457\pi\) | ||
0.894484 | − | 0.447099i | \(-0.147543\pi\) | |||||||
\(660\) | −38.9960 | − | 45.4634i | −1.51792 | − | 1.76966i | ||||
\(661\) | − | 25.4471i | − | 0.989777i | −0.868956 | − | 0.494889i | \(-0.835209\pi\) | ||
0.868956 | − | 0.494889i | \(-0.164791\pi\) | |||||||
\(662\) | −0.779206 | + | 0.0753015i | −0.0302847 | + | 0.00292668i | ||||
\(663\) | −6.91147 | + | 3.92330i | −0.268419 | + | 0.152368i | ||||
\(664\) | −2.49231 | − | 8.38188i | −0.0967203 | − | 0.325280i | ||||
\(665\) | 6.46149i | 0.250566i | ||||||||
\(666\) | −0.807234 | − | 0.381875i | −0.0312797 | − | 0.0147974i | ||||
\(667\) | 4.01876 | 0.155607 | ||||||||
\(668\) | 9.84664 | − | 1.92108i | 0.380978 | − | 0.0743287i | ||||
\(669\) | −18.3787 | − | 32.3768i | −0.710562 | − | 1.25176i | ||||
\(670\) | −40.9934 | + | 3.96155i | −1.58371 | + | 0.153048i | ||||
\(671\) | 83.2824 | 3.21508 | ||||||||
\(672\) | 11.2155 | + | 7.23327i | 0.432649 | + | 0.279029i | ||||
\(673\) | 15.0164 | 0.578838 | 0.289419 | − | 0.957202i | \(-0.406538\pi\) | ||||
0.289419 | + | 0.957202i | \(0.406538\pi\) | |||||||
\(674\) | 27.2967 | − | 2.63792i | 1.05143 | − | 0.101609i | ||||
\(675\) | −0.441983 | + | 20.1645i | −0.0170119 | + | 0.776131i | ||||
\(676\) | 24.0930 | − | 4.70053i | 0.926652 | − | 0.180789i | ||||
\(677\) | −4.56679 | −0.175516 | −0.0877581 | − | 0.996142i | \(-0.527970\pi\) | ||||
−0.0877581 | + | 0.996142i | \(0.527970\pi\) | |||||||
\(678\) | 7.11345 | + | 10.1209i | 0.273190 | + | 0.388692i | ||||
\(679\) | 14.2139i | 0.545480i | ||||||||
\(680\) | 12.9339 | + | 43.4980i | 0.495993 | + | 1.66807i | ||||
\(681\) | 0.751523 | + | 1.32392i | 0.0287984 | + | 0.0507327i | ||||
\(682\) | 10.7876 | − | 1.04250i | 0.413080 | − | 0.0399196i | ||||
\(683\) | 24.9270i | 0.953804i | 0.878956 | + | 0.476902i | \(0.158240\pi\) | ||||
−0.878956 | + | 0.476902i | \(0.841760\pi\) | |||||||
\(684\) | −3.23475 | + | 8.98615i | −0.123684 | + | 0.343594i | ||||
\(685\) | 38.0947i | 1.45552i | ||||||||
\(686\) | −2.25031 | − | 23.2857i | −0.0859171 | − | 0.889054i | ||||
\(687\) | 14.7650 | + | 26.0108i | 0.563322 | + | 0.992374i | ||||
\(688\) | 14.0863 | − | 5.71397i | 0.537037 | − | 0.217843i | ||||
\(689\) | − | 10.7314i | − | 0.408833i | ||||||
\(690\) | −5.97237 | + | 4.19765i | −0.227364 | + | 0.159802i | ||||
\(691\) | 33.0419 | 1.25697 | 0.628486 | − | 0.777821i | \(-0.283675\pi\) | ||||
0.628486 | + | 0.777821i | \(0.283675\pi\) | |||||||
\(692\) | −17.8241 | + | 3.47748i | −0.677571 | + | 0.132194i | ||||
\(693\) | 12.1527 | − | 20.3564i | 0.461643 | − | 0.773274i | ||||
\(694\) | −1.53634 | − | 15.8978i | −0.0583188 | − | 0.603472i | ||||
\(695\) | −4.47507 | −0.169749 | ||||||||
\(696\) | 13.6414 | − | 14.1959i | 0.517077 | − | 0.538093i | ||||
\(697\) | −57.2827 | −2.16974 | ||||||||
\(698\) | 2.58518 | + | 26.7509i | 0.0978503 | + | 1.01254i | ||||
\(699\) | −10.9302 | − | 19.2551i | −0.413418 | − | 0.728296i | ||||
\(700\) | 2.02484 | + | 10.3785i | 0.0765317 | + | 0.392270i | ||||
\(701\) | −4.39569 | −0.166023 | −0.0830114 | − | 0.996549i | \(-0.526454\pi\) | ||||
−0.0830114 | + | 0.996549i | \(0.526454\pi\) | |||||||
\(702\) | −6.24567 | + | 0.465690i | −0.235728 | + | 0.0175763i | ||||
\(703\) | − | 0.335041i | − | 0.0126363i | ||||||
\(704\) | −25.3602 | − | 38.8741i | −0.955799 | − | 1.46512i | ||||
\(705\) | 15.5490 | − | 8.82639i | 0.585608 | − | 0.332421i | ||||
\(706\) | −2.18114 | − | 22.5700i | −0.0820882 | − | 0.849433i | ||||
\(707\) | 25.6110i | 0.963200i | ||||||||
\(708\) | −10.0737 | − | 11.7444i | −0.378592 | − | 0.441381i | ||||
\(709\) | 6.77578i | 0.254470i | 0.991873 | + | 0.127235i | \(0.0406102\pi\) | ||||
−0.991873 | + | 0.127235i | \(0.959390\pi\) | |||||||
\(710\) | 13.7290 | − | 1.32675i | 0.515240 | − | 0.0497922i | ||||
\(711\) | −12.8749 | − | 7.68627i | −0.482845 | − | 0.288258i | ||||
\(712\) | 11.0521 | + | 37.1695i | 0.414197 | + | 1.39299i | ||||
\(713\) | − | 1.32088i | − | 0.0494673i | ||||||
\(714\) | −14.6955 | + | 10.3287i | −0.549966 | + | 0.386541i | ||||
\(715\) | 14.7366 | 0.551119 | ||||||||
\(716\) | 7.24516 | + | 37.1357i | 0.270764 | + | 1.38783i | ||||
\(717\) | −44.7423 | + | 25.3980i | −1.67093 | + | 0.948506i | ||||
\(718\) | 43.2036 | − | 4.17514i | 1.61234 | − | 0.155815i | ||||
\(719\) | −30.9094 | −1.15273 | −0.576363 | − | 0.817194i | \(-0.695529\pi\) | ||||
−0.576363 | + | 0.817194i | \(0.695529\pi\) | |||||||
\(720\) | −5.44504 | + | 35.3454i | −0.202925 | + | 1.31725i | ||||
\(721\) | 18.4041 | 0.685406 | ||||||||
\(722\) | 23.1788 | − | 2.23997i | 0.862627 | − | 0.0833632i | ||||
\(723\) | −14.9577 | + | 8.49073i | −0.556282 | + | 0.315774i | ||||
\(724\) | 5.09353 | + | 26.1073i | 0.189300 | + | 0.970272i | ||||
\(725\) | 15.5992 | 0.579339 | ||||||||
\(726\) | −45.4141 | + | 31.9191i | −1.68548 | + | 1.18463i | ||||
\(727\) | − | 12.8729i | − | 0.477429i | −0.971090 | − | 0.238714i | \(-0.923274\pi\) | ||
0.971090 | − | 0.238714i | \(-0.0767260\pi\) | |||||||
\(728\) | −3.14732 | + | 0.935838i | −0.116647 | + | 0.0346845i | ||||
\(729\) | −26.9741 | − | 1.18305i | −0.999040 | − | 0.0438167i | ||||
\(730\) | 11.8844 | − | 1.14849i | 0.439861 | − | 0.0425077i | ||||
\(731\) | 20.4594i | 0.756717i | ||||||||
\(732\) | −32.3738 | − | 37.7430i | −1.19657 | − | 1.39502i | ||||
\(733\) | 16.9056i | 0.624424i | 0.950012 | + | 0.312212i | \(0.101070\pi\) | ||||
−0.950012 | + | 0.312212i | \(0.898930\pi\) | |||||||
\(734\) | −1.73120 | − | 17.9142i | −0.0638999 | − | 0.661224i | ||||
\(735\) | 23.0947 | − | 13.1098i | 0.851862 | − | 0.483560i | ||||
\(736\) | −5.01316 | + | 2.62073i | −0.184787 | + | 0.0966015i | ||||
\(737\) | 56.6942i | 2.08836i | ||||||||
\(738\) | −40.8065 | − | 19.3042i | −1.50211 | − | 0.710596i | ||||
\(739\) | 41.2310 | 1.51671 | 0.758353 | − | 0.651844i | \(-0.226004\pi\) | ||||
0.758353 | + | 0.651844i | \(0.226004\pi\) | |||||||
\(740\) | −0.240235 | − | 1.23135i | −0.00883122 | − | 0.0452652i | ||||
\(741\) | −1.15999 | − | 2.04350i | −0.0426134 | − | 0.0750698i | ||||
\(742\) | −2.33305 | − | 24.1419i | −0.0856488 | − | 0.886278i | ||||
\(743\) | −31.9621 | −1.17258 | −0.586289 | − | 0.810102i | \(-0.699412\pi\) | ||||
−0.586289 | + | 0.810102i | \(0.699412\pi\) | |||||||
\(744\) | −4.66587 | − | 4.48364i | −0.171059 | − | 0.164378i | ||||
\(745\) | 60.8720 | 2.23018 | ||||||||
\(746\) | 0.0139709 | + | 0.144568i | 0.000511511 | + | 0.00529302i | ||||
\(747\) | 7.96379 | + | 4.75437i | 0.291380 | + | 0.173953i | ||||
\(748\) | 61.3142 | − | 11.9624i | 2.24187 | − | 0.437388i | ||||
\(749\) | −2.71857 | −0.0993346 | ||||||||
\(750\) | 6.67958 | − | 4.69472i | 0.243904 | − | 0.171427i | ||||
\(751\) | 22.7550i | 0.830341i | 0.909744 | + | 0.415171i | \(0.136278\pi\) | ||||
−0.909744 | + | 0.415171i | \(0.863722\pi\) | |||||||
\(752\) | 12.8390 | − | 5.20800i | 0.468190 | − | 0.189916i | ||||
\(753\) | 3.11688 | + | 5.49084i | 0.113585 | + | 0.200097i | ||||
\(754\) | 0.465936 | + | 4.82142i | 0.0169684 | + | 0.175586i | ||||
\(755\) | − | 47.3920i | − | 1.72477i | ||||||
\(756\) | −13.9494 | + | 2.40548i | −0.507335 | + | 0.0874865i | ||||
\(757\) | 19.6164i | 0.712969i | 0.934301 | + | 0.356485i | \(0.116025\pi\) | ||||
−0.934301 | + | 0.356485i | \(0.883975\pi\) | |||||||
\(758\) | −32.2539 | + | 3.11697i | −1.17151 | + | 0.113214i | ||||
\(759\) | 4.96085 | + | 8.73926i | 0.180067 | + | 0.317215i | ||||
\(760\) | −12.8610 | + | 3.82414i | −0.466517 | + | 0.138716i | ||||
\(761\) | 2.64074i | 0.0957268i | 0.998854 | + | 0.0478634i | \(0.0152412\pi\) | ||||
−0.998854 | + | 0.0478634i | \(0.984759\pi\) | |||||||
\(762\) | −18.6582 | − | 26.5466i | −0.675914 | − | 0.961682i | ||||
\(763\) | −12.4907 | −0.452194 | ||||||||
\(764\) | 28.7161 | − | 5.60250i | 1.03891 | − | 0.202691i | ||||
\(765\) | −41.3284 | − | 24.6729i | −1.49423 | − | 0.892052i | ||||
\(766\) | 39.6452 | − | 3.83126i | 1.43244 | − | 0.138429i | ||||
\(767\) | 3.80686 | 0.137458 | ||||||||
\(768\) | −7.75937 | + | 26.6044i | −0.279992 | + | 0.960002i | ||||
\(769\) | 17.6328 | 0.635856 | 0.317928 | − | 0.948115i | \(-0.397013\pi\) | ||||
0.317928 | + | 0.948115i | \(0.397013\pi\) | |||||||
\(770\) | 33.1524 | − | 3.20381i | 1.19473 | − | 0.115457i | ||||
\(771\) | 5.35728 | + | 9.43763i | 0.192938 | + | 0.339888i | ||||
\(772\) | 15.8095 | − | 3.08442i | 0.568995 | − | 0.111011i | ||||
\(773\) | 10.4930 | 0.377407 | 0.188704 | − | 0.982034i | \(-0.439571\pi\) | ||||
0.188704 | + | 0.982034i | \(0.439571\pi\) | |||||||
\(774\) | −6.89478 | + | 14.5747i | −0.247828 | + | 0.523875i | ||||
\(775\) | − | 5.12710i | − | 0.184171i | ||||||
\(776\) | −28.2915 | + | 8.41231i | −1.01560 | + | 0.301984i | ||||
\(777\) | 0.431848 | − | 0.245139i | 0.0154925 | − | 0.00879431i | ||||
\(778\) | −7.62700 | + | 0.737064i | −0.273441 | + | 0.0264250i | ||||
\(779\) | − | 16.9366i | − | 0.606818i | ||||||
\(780\) | −5.72848 | − | 6.67854i | −0.205113 | − | 0.239130i | ||||
\(781\) | − | 18.9873i | − | 0.679421i | ||||||
\(782\) | −0.732360 | − | 7.57832i | −0.0261891 | − | 0.271000i | ||||
\(783\) | −0.457603 | + | 20.8771i | −0.0163534 | + | 0.746087i | ||||
\(784\) | 19.0696 | − | 7.73540i | 0.681059 | − | 0.276264i | ||||
\(785\) | − | 26.4966i | − | 0.945704i | ||||||
\(786\) | −19.4501 | − | 27.6733i | −0.693762 | − | 0.987075i | ||||
\(787\) | 30.6123 | 1.09121 | 0.545606 | − | 0.838042i | \(-0.316299\pi\) | ||||
0.545606 | + | 0.838042i | \(0.316299\pi\) | |||||||
\(788\) | −11.7571 | + | 2.29381i | −0.418830 | + | 0.0817135i | ||||
\(789\) | −10.3795 | + | 5.89192i | −0.369519 | + | 0.209758i | ||||
\(790\) | −2.02633 | − | 20.9681i | −0.0720935 | − | 0.746010i | ||||
\(791\) | −6.87900 | −0.244589 | ||||||||
\(792\) | 47.7098 | + | 12.1412i | 1.69529 | + | 0.431417i | ||||
\(793\) | 12.2341 | 0.434446 | ||||||||
\(794\) | 3.01826 | + | 31.2324i | 0.107114 | + | 1.10840i | ||||
\(795\) | 56.5225 | − | 32.0851i | 2.00465 | − | 1.13794i | ||||
\(796\) | −7.96904 | − | 40.8460i | −0.282455 | − | 1.44775i | ||||
\(797\) | 10.4447 | 0.369971 | 0.184985 | − | 0.982741i | \(-0.440776\pi\) | ||||
0.184985 | + | 0.982741i | \(0.440776\pi\) | |||||||
\(798\) | −3.05386 | − | 4.34499i | −0.108105 | − | 0.153811i | ||||
\(799\) | 18.6477i | 0.659708i | ||||||||
\(800\) | −19.4590 | + | 10.1726i | −0.687980 | + | 0.359656i | ||||
\(801\) | −35.3155 | − | 21.0833i | −1.24781 | − | 0.744940i | ||||
\(802\) | −3.49094 | − | 36.1236i | −0.123269 | − | 1.27557i | ||||
\(803\) | − | 16.4362i | − | 0.580022i | ||||||
\(804\) | 25.6934 | − | 22.0384i | 0.906137 | − | 0.777234i | ||||
\(805\) | − | 4.05931i | − | 0.143072i | ||||||
\(806\) | 1.58470 | − | 0.153143i | 0.0558185 | − | 0.00539423i | ||||
\(807\) | −13.8636 | + | 7.86967i | −0.488021 | + | 0.277026i | ||||
\(808\) | −50.9762 | + | 15.1575i | −1.79334 | + | 0.533239i | ||||
\(809\) | 48.5755i | 1.70782i | 0.520418 | + | 0.853911i | \(0.325776\pi\) | ||||
−0.520418 | + | 0.853911i | \(0.674224\pi\) | |||||||
\(810\) | −21.1264 | − | 31.5039i | −0.742305 | − | 1.10693i | ||||
\(811\) | 26.2605 | 0.922132 | 0.461066 | − | 0.887366i | \(-0.347467\pi\) | ||||
0.461066 | + | 0.887366i | \(0.347467\pi\) | |||||||
\(812\) | 2.09640 | + | 10.7453i | 0.0735691 | + | 0.377085i | ||||
\(813\) | 4.83110 | + | 8.51069i | 0.169434 | + | 0.298483i | ||||
\(814\) | −1.71902 | + | 0.166124i | −0.0602515 | + | 0.00582264i | ||||
\(815\) | −17.4412 | −0.610938 | ||||||||
\(816\) | −29.2556 | − | 23.1371i | −1.02415 | − | 0.809961i | ||||
\(817\) | −6.04918 | −0.211634 | ||||||||
\(818\) | 42.8091 | − | 4.13702i | 1.49679 | − | 0.144648i | ||||
\(819\) | 1.78522 | − | 2.99033i | 0.0623807 | − | 0.104491i | ||||
\(820\) | −12.1441 | − | 62.2458i | −0.424091 | − | 2.17372i | ||||
\(821\) | 1.69169 | 0.0590404 | 0.0295202 | − | 0.999564i | \(-0.490602\pi\) | ||||
0.0295202 | + | 0.999564i | \(0.490602\pi\) | |||||||
\(822\) | −18.0045 | − | 25.6166i | −0.627978 | − | 0.893480i | ||||
\(823\) | − | 11.4145i | − | 0.397883i | −0.980011 | − | 0.198942i | \(-0.936250\pi\) | ||
0.980011 | − | 0.198942i | \(-0.0637504\pi\) | |||||||
\(824\) | 10.8922 | + | 36.6317i | 0.379449 | + | 1.27612i | ||||
\(825\) | 19.2560 | + | 33.9222i | 0.670406 | + | 1.18102i | ||||
\(826\) | 8.56414 | − | 0.827628i | 0.297984 | − | 0.0287969i | ||||
\(827\) | − | 15.8926i | − | 0.552640i | −0.961066 | − | 0.276320i | \(-0.910885\pi\) | ||
0.961066 | − | 0.276320i | \(-0.0891150\pi\) | |||||||
\(828\) | 2.03217 | − | 5.64538i | 0.0706228 | − | 0.196190i | ||||
\(829\) | 35.6637i | 1.23865i | 0.785134 | + | 0.619326i | \(0.212594\pi\) | ||||
−0.785134 | + | 0.619326i | \(0.787406\pi\) | |||||||
\(830\) | 1.25339 | + | 12.9699i | 0.0435058 | + | 0.450190i | ||||
\(831\) | −17.1088 | − | 30.1397i | −0.593499 | − | 1.04553i | ||||
\(832\) | −3.72539 | − | 5.71058i | −0.129155 | − | 0.197979i | ||||
\(833\) | 27.6973i | 0.959653i | ||||||||
\(834\) | 3.00924 | − | 2.11503i | 0.104201 | − | 0.0732374i | ||||
\(835\) | −14.9491 | −0.517335 | ||||||||
\(836\) | 3.53689 | + | 18.1287i | 0.122326 | + | 0.626993i | ||||
\(837\) | 6.86184 | + | 0.150404i | 0.237180 | + | 0.00519872i | ||||
\(838\) | 2.29754 | + | 23.7746i | 0.0793674 | + | 0.821279i | ||||
\(839\) | −22.4175 | −0.773939 | −0.386969 | − | 0.922093i | \(-0.626478\pi\) | ||||
−0.386969 | + | 0.922093i | \(0.626478\pi\) | |||||||
\(840\) | −14.3391 | − | 13.7791i | −0.494745 | − | 0.475422i | ||||
\(841\) | −12.8495 | −0.443087 | ||||||||
\(842\) | −2.88325 | − | 29.8353i | −0.0993634 | − | 1.02819i | ||||
\(843\) | −14.7334 | − | 25.9551i | −0.507446 | − | 0.893940i | ||||
\(844\) | 30.7203 | − | 5.99352i | 1.05744 | − | 0.206306i | ||||
\(845\) | −36.5778 | −1.25831 | ||||||||
\(846\) | −6.28425 | + | 13.2841i | −0.216057 | + | 0.456716i | ||||
\(847\) | − | 30.8671i | − | 1.06061i | ||||||
\(848\) | 46.6714 | − | 18.9318i | 1.60270 | − | 0.650119i | ||||
\(849\) | −19.1913 | + | 10.8940i | −0.658645 | + | 0.373880i | ||||
\(850\) | −2.84272 | − | 29.4159i | −0.0975044 | − | 1.00896i | ||||
\(851\) | 0.210483i | 0.00721526i | ||||||||
\(852\) | −8.60493 | + | 7.38083i | −0.294800 | + | 0.252863i | ||||
\(853\) | − | 33.3784i | − | 1.14285i | −0.820653 | − | 0.571427i | \(-0.806390\pi\) | ||
0.820653 | − | 0.571427i | \(-0.193610\pi\) | |||||||
\(854\) | 27.5226 | − | 2.65975i | 0.941804 | − | 0.0910148i | ||||
\(855\) | 7.29499 | − | 12.2195i | 0.249484 | − | 0.417897i | ||||
\(856\) | −1.60895 | − | 5.41106i | −0.0549928 | − | 0.184946i | ||||
\(857\) | 28.8345i | 0.984966i | 0.870322 | + | 0.492483i | \(0.163911\pi\) | ||||
−0.870322 | + | 0.492483i | \(0.836089\pi\) | |||||||
\(858\) | −9.90957 | + | 6.96490i | −0.338307 | + | 0.237778i | ||||
\(859\) | −20.3286 | −0.693602 | −0.346801 | − | 0.937939i | \(-0.612732\pi\) | ||||
−0.346801 | + | 0.937939i | \(0.612732\pi\) | |||||||
\(860\) | −22.2320 | + | 4.33746i | −0.758106 | + | 0.147906i | ||||
\(861\) | 21.8304 | − | 12.3920i | 0.743977 | − | 0.422319i | ||||
\(862\) | −31.2789 | + | 3.02275i | −1.06536 | + | 0.102955i | ||||
\(863\) | −13.9426 | −0.474612 | −0.237306 | − | 0.971435i | \(-0.576264\pi\) | ||||
−0.237306 | + | 0.971435i | \(0.576264\pi\) | |||||||
\(864\) | −13.0436 | − | 26.3413i | −0.443753 | − | 0.896149i | ||||
\(865\) | 27.0605 | 0.920084 | ||||||||
\(866\) | 0.600379 | − | 0.0580199i | 0.0204017 | − | 0.00197160i | ||||
\(867\) | 18.0508 | − | 10.2465i | 0.613037 | − | 0.347991i | ||||
\(868\) | 3.53173 | − | 0.689039i | 0.119875 | − | 0.0233875i | ||||
\(869\) | −28.9990 | −0.983725 | ||||||||
\(870\) | −24.0015 | + | 16.8694i | −0.813729 | + | 0.571926i | ||||
\(871\) | 8.32834i | 0.282195i | ||||||||
\(872\) | −7.39245 | − | 24.8616i | −0.250340 | − | 0.841919i | ||||
\(873\) | 16.0475 | − | 26.8803i | 0.543124 | − | 0.909760i | ||||
\(874\) | 2.24067 | − | 0.216535i | 0.0757917 | − | 0.00732441i | ||||
\(875\) | 4.53999i | 0.153480i | ||||||||
\(876\) | −7.44879 | + | 6.38916i | −0.251671 | + | 0.215870i | ||||
\(877\) | − | 4.44841i | − | 0.150212i | −0.997176 | − | 0.0751061i | \(-0.976070\pi\) | ||
0.997176 | − | 0.0751061i | \(-0.0239295\pi\) | |||||||
\(878\) | 0.669163 | + | 6.92437i | 0.0225832 | + | 0.233686i | ||||
\(879\) | 44.4788 | − | 25.2484i | 1.50023 | − | 0.851608i | ||||
\(880\) | 25.9977 | + | 64.0906i | 0.876381 | + | 2.16049i | ||||
\(881\) | − | 8.99796i | − | 0.303149i | −0.988446 | − | 0.151575i | \(-0.951566\pi\) | ||
0.988446 | − | 0.151575i | \(-0.0484344\pi\) | |||||||
\(882\) | −9.33394 | + | 19.7307i | −0.314290 | + | 0.664368i | ||||
\(883\) | −10.7222 | −0.360832 | −0.180416 | − | 0.983590i | \(-0.557744\pi\) | ||||
−0.180416 | + | 0.983590i | \(0.557744\pi\) | |||||||
\(884\) | 9.00701 | − | 1.75726i | 0.302939 | − | 0.0591032i | ||||
\(885\) | 11.3819 | + | 20.0509i | 0.382598 | + | 0.674003i | ||||
\(886\) | 5.42692 | + | 56.1568i | 0.182321 | + | 1.88662i | ||||
\(887\) | 9.72570 | 0.326557 | 0.163278 | − | 0.986580i | \(-0.447793\pi\) | ||||
0.163278 | + | 0.986580i | \(0.447793\pi\) | |||||||
\(888\) | 0.743509 | + | 0.714471i | 0.0249505 | + | 0.0239761i | ||||
\(889\) | 18.0432 | 0.605151 | ||||||||
\(890\) | −5.55817 | − | 57.5149i | −0.186310 | − | 1.92790i | ||||
\(891\) | −45.9645 | + | 24.7760i | −1.53987 | + | 0.830028i | ||||
\(892\) | 8.23191 | + | 42.1934i | 0.275625 | + | 1.41274i | ||||
\(893\) | −5.51353 | −0.184503 | ||||||||
\(894\) | −40.9331 | + | 28.7696i | −1.36901 | + | 0.962200i | ||||
\(895\) | − | 56.3792i | − | 1.88455i | ||||||
\(896\) | −9.62237 | − | 12.0369i | −0.321461 | − | 0.402126i | ||||
\(897\) | 0.728744 | + | 1.28379i | 0.0243321 | + | 0.0428645i | ||||
\(898\) | 2.55938 | + | 26.4840i | 0.0854076 | + | 0.883782i | ||||
\(899\) | − | 5.30830i | − | 0.177042i | ||||||
\(900\) | 7.88805 | − | 21.9130i | 0.262935 | − | 0.730434i | ||||
\(901\) | 67.7868i | 2.25831i | ||||||||
\(902\) | −86.8981 | + | 8.39772i | −2.89339 | + | 0.279614i | ||||
\(903\) | −4.42600 | − | 7.79705i | −0.147288 | − | 0.259469i | ||||
\(904\) | −4.07124 | − | 13.6920i | −0.135407 | − | 0.455389i | ||||
\(905\) | − | 39.6360i | − | 1.31755i | ||||||
\(906\) | 22.3986 | + | 31.8685i | 0.744144 | + | 1.05876i | ||||
\(907\) | −28.4008 | −0.943033 | −0.471516 | − | 0.881857i | \(-0.656293\pi\) | ||||
−0.471516 | + | 0.881857i | \(0.656293\pi\) | |||||||
\(908\) | −0.336611 | − | 1.72533i | −0.0111708 | − | 0.0572570i | ||||
\(909\) | 28.9147 | − | 48.4335i | 0.959040 | − | 1.60644i | ||||
\(910\) | 4.87006 | − | 0.470637i | 0.161441 | − | 0.0156015i | ||||
\(911\) | 15.7823 | 0.522892 | 0.261446 | − | 0.965218i | \(-0.415801\pi\) | ||||
0.261446 | + | 0.965218i | \(0.415801\pi\) | |||||||
\(912\) | 6.84090 | − | 8.64993i | 0.226525 | − | 0.286428i | ||||
\(913\) | 17.9374 | 0.593643 | ||||||||
\(914\) | −9.11715 | + | 0.881070i | −0.301568 | + | 0.0291432i | ||||
\(915\) | 36.5780 | + | 64.4376i | 1.20923 | + | 2.13024i | ||||
\(916\) | −6.61333 | − | 33.8972i | −0.218511 | − | 1.12000i | ||||
\(917\) | 18.8090 | 0.621129 | ||||||||
\(918\) | 39.4520 | − | 2.94162i | 1.30211 | − | 0.0970880i | ||||
\(919\) | − | 9.07586i | − | 0.299385i | −0.988733 | − | 0.149692i | \(-0.952172\pi\) | ||
0.988733 | − | 0.149692i | \(-0.0478284\pi\) | |||||||
\(920\) | 8.07966 | − | 2.40244i | 0.266379 | − | 0.0792062i | ||||
\(921\) | 36.7247 | − | 20.8468i | 1.21012 | − | 0.686926i | ||||
\(922\) | −54.2461 | + | 5.24228i | −1.78650 | + | 0.172645i | ||||
\(923\) | − | 2.78923i | − | 0.0918085i | ||||||
\(924\) | −20.7790 | + | 17.8230i | −0.683577 | + | 0.586335i | ||||
\(925\) | 0.817008i | 0.0268630i | ||||||||
\(926\) | −4.28296 | − | 44.3193i | −0.140747 | − | 1.45642i | ||||
\(927\) | −34.8045 | − | 20.7782i | −1.14313 | − | 0.682445i | ||||
\(928\) | −20.1467 | + | 10.5321i | −0.661348 | + | 0.345734i | ||||
\(929\) | 9.96935i | 0.327084i | 0.986536 | + | 0.163542i | \(0.0522919\pi\) | ||||
−0.986536 | + | 0.163542i | \(0.947708\pi\) | |||||||
\(930\) | 5.54459 | + | 7.88878i | 0.181814 | + | 0.258683i | ||||
\(931\) | −8.18919 | −0.268390 | ||||||||
\(932\) | 4.89569 | + | 25.0933i | 0.160363 | + | 0.821957i | ||||
\(933\) | −4.29985 | + | 2.44081i | −0.140771 | + | 0.0799086i | ||||
\(934\) | −3.88869 | − | 40.2394i | −0.127242 | − | 1.31667i | ||||
\(935\) | −93.0869 | −3.04427 | ||||||||
\(936\) | 7.00853 | + | 1.78353i | 0.229081 | + | 0.0582964i | ||||
\(937\) | −8.42781 | −0.275324 | −0.137662 | − | 0.990479i | \(-0.543959\pi\) | ||||
−0.137662 | + | 0.990479i | \(0.543959\pi\) | |||||||
\(938\) | 1.81062 | + | 18.7359i | 0.0591187 | + | 0.611750i | ||||
\(939\) | −12.2060 | + | 6.92873i | −0.398327 | + | 0.226111i | ||||
\(940\) | −20.2634 | + | 3.95338i | −0.660919 | + | 0.128945i | ||||
\(941\) | 26.7191 | 0.871018 | 0.435509 | − | 0.900184i | \(-0.356568\pi\) | ||||
0.435509 | + | 0.900184i | \(0.356568\pi\) | |||||||
\(942\) | 12.5229 | + | 17.8175i | 0.408019 | + | 0.580525i | ||||
\(943\) | 10.6401i | 0.346490i | ||||||||
\(944\) | 6.71588 | + | 16.5563i | 0.218583 | + | 0.538861i | ||||
\(945\) | 21.0877 | + | 0.462219i | 0.685983 | + | 0.0150360i | ||||
\(946\) | 2.99938 | + | 31.0370i | 0.0975181 | + | 1.00910i | ||||
\(947\) | − | 37.2705i | − | 1.21113i | −0.795797 | − | 0.605564i | \(-0.792948\pi\) | ||
0.795797 | − | 0.605564i | \(-0.207052\pi\) | |||||||
\(948\) | 11.2726 | + | 13.1422i | 0.366117 | + | 0.426837i | ||||
\(949\) | − | 2.41447i | − | 0.0783770i | ||||||
\(950\) | 8.69734 | − | 0.840500i | 0.282179 | − | 0.0272694i | ||||
\(951\) | −34.5379 | + | 19.6055i | −1.11997 | + | 0.635751i | ||||
\(952\) | 19.8807 | − | 5.91141i | 0.644336 | − | 0.191590i | ||||
\(953\) | − | 28.9414i | − | 0.937505i | −0.883330 | − | 0.468753i | \(-0.844704\pi\) | ||
0.883330 | − | 0.468753i | \(-0.155296\pi\) | |||||||
\(954\) | −22.8441 | + | 48.2893i | −0.739604 | + | 1.56343i | ||||
\(955\) | −43.5966 | −1.41075 | ||||||||
\(956\) | 58.3081 | − | 11.3759i | 1.88582 | − | 0.367922i | ||||
\(957\) | 19.9365 | + | 35.1210i | 0.644455 | + | 1.13530i | ||||
\(958\) | 25.1068 | − | 2.42629i | 0.811164 | − | 0.0783899i | ||||
\(959\) | 17.4111 | 0.562233 | ||||||||
\(960\) | 18.9395 | − | 36.6955i | 0.611270 | − | 1.18434i | ||||
\(961\) | 29.2553 | 0.943719 | ||||||||
\(962\) | −0.252522 | + | 0.0244034i | −0.00814164 | + | 0.000786799i | ||||
\(963\) | 5.14116 | + | 3.06926i | 0.165672 | + | 0.0989055i | ||||
\(964\) | 19.4928 | − | 3.80304i | 0.627821 | − | 0.122488i | ||||
\(965\) | −24.0018 | −0.772646 | ||||||||
\(966\) | 1.91853 | + | 2.72966i | 0.0617276 | + | 0.0878253i | ||||
\(967\) | − | 8.93046i | − | 0.287184i | −0.989637 | − | 0.143592i | \(-0.954135\pi\) | ||
0.989637 | − | 0.143592i | \(-0.0458653\pi\) | |||||||
\(968\) | 61.4380 | − | 18.2683i | 1.97469 | − | 0.587164i | ||||
\(969\) | 7.32733 | + | 12.9082i | 0.235388 | + | 0.414670i | ||||
\(970\) | 43.7773 | − | 4.23059i | 1.40561 | − | 0.135836i | ||||
\(971\) | 35.2297i | 1.13058i | 0.824893 | + | 0.565288i | \(0.191235\pi\) | ||||
−0.824893 | + | 0.565288i | \(0.808765\pi\) | |||||||
\(972\) | 29.0958 | + | 11.1998i | 0.933248 | + | 0.359232i | ||||
\(973\) | 2.04532i | 0.0655700i | ||||||||
\(974\) | 0.573968 | + | 5.93931i | 0.0183911 | + | 0.190308i | ||||
\(975\) | 2.82868 | + | 4.98314i | 0.0905903 | + | 0.159588i | ||||
\(976\) | 21.5828 | + | 53.2070i | 0.690850 | + | 1.70311i | ||||
\(977\) | − | 32.5344i | − | 1.04087i | −0.853902 | − | 0.520434i | \(-0.825770\pi\) | ||
0.853902 | − | 0.520434i | \(-0.174230\pi\) | |||||||
\(978\) | 11.7282 | − | 8.24314i | 0.375027 | − | 0.263586i | ||||
\(979\) | −79.5437 | −2.54223 | ||||||||
\(980\) | −30.0970 | + | 5.87192i | −0.961414 | + | 0.187572i | ||||
\(981\) | 23.6215 | + | 14.1020i | 0.754176 | + | 0.450241i | ||||
\(982\) | 2.68805 | + | 27.8155i | 0.0857792 | + | 0.887627i | ||||
\(983\) | 27.1694 | 0.866570 | 0.433285 | − | 0.901257i | \(-0.357354\pi\) | ||||
0.433285 | + | 0.901257i | \(0.357354\pi\) | |||||||
\(984\) | 37.5851 | + | 36.1172i | 1.19817 | + | 1.15137i | ||||
\(985\) | 17.8496 | 0.568735 | ||||||||
\(986\) | −2.94318 | − | 30.4555i | −0.0937300 | − | 0.969900i | ||||
\(987\) | −4.03408 | − | 7.10662i | −0.128406 | − | 0.226206i | ||||
\(988\) | 0.519567 | + | 2.66308i | 0.0165296 | + | 0.0847240i | ||||
\(989\) | 3.80028 | 0.120842 | ||||||||
\(990\) | −66.3124 | − | 31.3702i | −2.10755 | − | 0.997009i | ||||
\(991\) | 40.3567i | 1.28197i | 0.767553 | + | 0.640986i | \(0.221474\pi\) | ||||
−0.767553 | + | 0.640986i | \(0.778526\pi\) | |||||||
\(992\) | 3.46167 | + | 6.62177i | 0.109908 | + | 0.210242i | ||||
\(993\) | −0.833803 | + | 0.473309i | −0.0264599 | + | 0.0150200i | ||||
\(994\) | −0.606390 | − | 6.27481i | −0.0192335 | − | 0.199025i | ||||
\(995\) | 62.0122i | 1.96592i | ||||||||
\(996\) | −6.97271 | − | 8.12912i | −0.220939 | − | 0.257581i | ||||
\(997\) | 40.2642i | 1.27518i | 0.770376 | + | 0.637589i | \(0.220068\pi\) | ||||
−0.770376 | + | 0.637589i | \(0.779932\pi\) | |||||||
\(998\) | 18.5115 | − | 1.78893i | 0.585971 | − | 0.0566276i | ||||
\(999\) | −1.09344 | − | 0.0239670i | −0.0345949 | − | 0.000758282i |
(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 | 552.2.j.d.323.4 | yes | 42 | |
3.2 | odd | 2 | 552.2.j.c.323.39 | ✓ | 42 | ||
4.3 | odd | 2 | 2208.2.j.d.47.35 | 42 | |||
8.3 | odd | 2 | 552.2.j.c.323.40 | yes | 42 | ||
8.5 | even | 2 | 2208.2.j.c.47.35 | 42 | |||
12.11 | even | 2 | 2208.2.j.c.47.36 | 42 | |||
24.5 | odd | 2 | 2208.2.j.d.47.36 | 42 | |||
24.11 | even | 2 | inner | 552.2.j.d.323.3 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.j.c.323.39 | ✓ | 42 | 3.2 | odd | 2 | ||
552.2.j.c.323.40 | yes | 42 | 8.3 | odd | 2 | ||
552.2.j.d.323.3 | yes | 42 | 24.11 | even | 2 | inner | |
552.2.j.d.323.4 | yes | 42 | 1.1 | even | 1 | trivial | |
2208.2.j.c.47.35 | 42 | 8.5 | even | 2 | |||
2208.2.j.c.47.36 | 42 | 12.11 | even | 2 | |||
2208.2.j.d.47.35 | 42 | 4.3 | odd | 2 | |||
2208.2.j.d.47.36 | 42 | 24.5 | odd | 2 |