Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.10 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.a.487.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.91070 | + | 1.16157i | 0.854490 | + | 0.519468i | ||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | 2.90687 | − | 2.90687i | 1.09869 | − | 1.09869i | 0.104130 | − | 0.994564i | \(-0.466794\pi\) |
0.994564 | − | 0.104130i | \(-0.0332058\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.91070 | − | 1.16157i | −0.604216 | − | 0.367319i | ||||
\(11\) | 2.74715i | 0.828297i | 0.910209 | + | 0.414149i | \(0.135921\pi\) | ||||
−0.910209 | + | 0.414149i | \(0.864079\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 5.21529 | 1.44646 | 0.723231 | − | 0.690606i | \(-0.242656\pi\) | ||||
0.723231 | + | 0.690606i | \(0.242656\pi\) | |||||||
\(14\) | −2.90687 | + | 2.90687i | −0.776894 | + | 0.776894i | ||||
\(15\) | 2.17242 | − | 0.529716i | 0.560916 | − | 0.136772i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 4.16103i | − | 1.00920i | −0.863354 | − | 0.504599i | \(-0.831640\pi\) | ||
0.863354 | − | 0.504599i | \(-0.168360\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.87829 | − | 1.87829i | −0.430909 | − | 0.430909i | 0.458029 | − | 0.888937i | \(-0.348556\pi\) |
−0.888937 | + | 0.458029i | \(0.848556\pi\) | |||||||
\(20\) | 1.91070 | + | 1.16157i | 0.427245 | + | 0.259734i | ||||
\(21\) | − | 4.11094i | − | 0.897080i | ||||||
\(22\) | − | 2.74715i | − | 0.585695i | ||||||
\(23\) | −0.941868 | −0.196393 | −0.0981965 | − | 0.995167i | \(-0.531307\pi\) | ||||
−0.0981965 | + | 0.995167i | \(0.531307\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | 2.30153 | + | 4.43880i | 0.460306 | + | 0.887760i | ||||
\(26\) | −5.21529 | −1.02280 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 2.90687 | − | 2.90687i | 0.549347 | − | 0.549347i | ||||
\(29\) | −4.28806 | + | 4.28806i | −0.796273 | + | 0.796273i | −0.982506 | − | 0.186233i | \(-0.940372\pi\) |
0.186233 | + | 0.982506i | \(0.440372\pi\) | |||||||
\(30\) | −2.17242 | + | 0.529716i | −0.396627 | + | 0.0967125i | ||||
\(31\) | 5.51242 | + | 5.51242i | 0.990060 | + | 0.990060i | 0.999951 | − | 0.00989083i | \(-0.00314840\pi\) |
−0.00989083 | + | 0.999951i | \(0.503148\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.94253 | + | 1.94253i | 0.338151 | + | 0.338151i | ||||
\(34\) | 4.16103i | 0.713611i | ||||||||
\(35\) | 8.93067 | − | 2.17763i | 1.50956 | − | 0.368086i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −2.77109 | − | 5.41489i | −0.455565 | − | 0.890202i | ||||
\(38\) | 1.87829 | + | 1.87829i | 0.304699 | + | 0.304699i | ||||
\(39\) | 3.68777 | − | 3.68777i | 0.590516 | − | 0.590516i | ||||
\(40\) | −1.91070 | − | 1.16157i | −0.302108 | − | 0.183660i | ||||
\(41\) | − | 7.59421i | − | 1.18602i | −0.805196 | − | 0.593008i | \(-0.797940\pi\) | ||
0.805196 | − | 0.593008i | \(-0.202060\pi\) | |||||||
\(42\) | 4.11094i | 0.634331i | ||||||||
\(43\) | −6.23482 | −0.950802 | −0.475401 | − | 0.879769i | \(-0.657697\pi\) | ||||
−0.475401 | + | 0.879769i | \(0.657697\pi\) | |||||||
\(44\) | 2.74715i | 0.414149i | ||||||||
\(45\) | 1.16157 | − | 1.91070i | 0.173156 | − | 0.284830i | ||||
\(46\) | 0.941868 | 0.138871 | ||||||||
\(47\) | −6.04950 | + | 6.04950i | −0.882410 | + | 0.882410i | −0.993779 | − | 0.111369i | \(-0.964477\pi\) |
0.111369 | + | 0.993779i | \(0.464477\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | − | 9.89979i | − | 1.41426i | ||||||
\(50\) | −2.30153 | − | 4.43880i | −0.325485 | − | 0.627741i | ||||
\(51\) | −2.94229 | − | 2.94229i | −0.412004 | − | 0.412004i | ||||
\(52\) | 5.21529 | 0.723231 | ||||||||
\(53\) | 8.31822 | + | 8.31822i | 1.14259 | + | 1.14259i | 0.987974 | + | 0.154621i | \(0.0494156\pi\) |
0.154621 | + | 0.987974i | \(0.450584\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | −3.19100 | + | 5.24898i | −0.430274 | + | 0.707772i | ||||
\(56\) | −2.90687 | + | 2.90687i | −0.388447 | + | 0.388447i | ||||
\(57\) | −2.65630 | −0.351836 | ||||||||
\(58\) | 4.28806 | − | 4.28806i | 0.563050 | − | 0.563050i | ||||
\(59\) | 1.92935 | + | 1.92935i | 0.251180 | + | 0.251180i | 0.821454 | − | 0.570274i | \(-0.193163\pi\) |
−0.570274 | + | 0.821454i | \(0.693163\pi\) | |||||||
\(60\) | 2.17242 | − | 0.529716i | 0.280458 | − | 0.0683860i | ||||
\(61\) | −8.68618 | − | 8.68618i | −1.11215 | − | 1.11215i | −0.992859 | − | 0.119292i | \(-0.961937\pi\) |
−0.119292 | − | 0.992859i | \(-0.538063\pi\) | |||||||
\(62\) | −5.51242 | − | 5.51242i | −0.700078 | − | 0.700078i | ||||
\(63\) | −2.90687 | − | 2.90687i | −0.366231 | − | 0.366231i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.96485 | + | 6.05791i | 1.23599 | + | 0.751391i | ||||
\(66\) | −1.94253 | − | 1.94253i | −0.239109 | − | 0.239109i | ||||
\(67\) | 5.51165 | + | 5.51165i | 0.673355 | + | 0.673355i | 0.958488 | − | 0.285133i | \(-0.0920377\pi\) |
−0.285133 | + | 0.958488i | \(0.592038\pi\) | |||||||
\(68\) | − | 4.16103i | − | 0.504599i | ||||||
\(69\) | −0.666001 | + | 0.666001i | −0.0801771 | + | 0.0801771i | ||||
\(70\) | −8.93067 | + | 2.17763i | −1.06742 | + | 0.260276i | ||||
\(71\) | −8.51973 | −1.01111 | −0.505553 | − | 0.862796i | \(-0.668711\pi\) | ||||
−0.505553 | + | 0.862796i | \(0.668711\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −2.98121 | + | 2.98121i | −0.348924 | + | 0.348924i | −0.859709 | − | 0.510785i | \(-0.829355\pi\) |
0.510785 | + | 0.859709i | \(0.329355\pi\) | |||||||
\(74\) | 2.77109 | + | 5.41489i | 0.322133 | + | 0.629468i | ||||
\(75\) | 4.76613 | + | 1.51128i | 0.550346 | + | 0.174508i | ||||
\(76\) | −1.87829 | − | 1.87829i | −0.215454 | − | 0.215454i | ||||
\(77\) | 7.98561 | + | 7.98561i | 0.910045 | + | 0.910045i | ||||
\(78\) | −3.68777 | + | 3.68777i | −0.417558 | + | 0.417558i | ||||
\(79\) | 1.46581 | + | 1.46581i | 0.164916 | + | 0.164916i | 0.784741 | − | 0.619824i | \(-0.212796\pi\) |
−0.619824 | + | 0.784741i | \(0.712796\pi\) | |||||||
\(80\) | 1.91070 | + | 1.16157i | 0.213622 | + | 0.129867i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 7.59421i | 0.838640i | ||||||||
\(83\) | 7.26193 | + | 7.26193i | 0.797101 | + | 0.797101i | 0.982637 | − | 0.185536i | \(-0.0594023\pi\) |
−0.185536 | + | 0.982637i | \(0.559402\pi\) | |||||||
\(84\) | − | 4.11094i | − | 0.448540i | ||||||
\(85\) | 4.83331 | − | 7.95047i | 0.524246 | − | 0.862350i | ||||
\(86\) | 6.23482 | 0.672318 | ||||||||
\(87\) | 6.06423i | 0.650154i | ||||||||
\(88\) | − | 2.74715i | − | 0.292847i | ||||||
\(89\) | −1.62770 | + | 1.62770i | −0.172535 | + | 0.172535i | −0.788092 | − | 0.615557i | \(-0.788931\pi\) |
0.615557 | + | 0.788092i | \(0.288931\pi\) | |||||||
\(90\) | −1.16157 | + | 1.91070i | −0.122440 | + | 0.201405i | ||||
\(91\) | 15.1602 | − | 15.1602i | 1.58922 | − | 1.58922i | ||||
\(92\) | −0.941868 | −0.0981965 | ||||||||
\(93\) | 7.79574 | 0.808381 | ||||||||
\(94\) | 6.04950 | − | 6.04950i | 0.623958 | − | 0.623958i | ||||
\(95\) | −1.40708 | − | 5.77059i | −0.144364 | − | 0.592051i | ||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | − | 10.0910i | − | 1.02459i | −0.858810 | − | 0.512294i | \(-0.828796\pi\) | ||
0.858810 | − | 0.512294i | \(-0.171204\pi\) | |||||||
\(98\) | 9.89979i | 1.00003i | ||||||||
\(99\) | 2.74715 | 0.276099 | ||||||||
\(100\) | 2.30153 | + | 4.43880i | 0.230153 | + | 0.443880i | ||||
\(101\) | − | 9.40183i | − | 0.935517i | −0.883856 | − | 0.467759i | \(-0.845062\pi\) | ||
0.883856 | − | 0.467759i | \(-0.154938\pi\) | |||||||
\(102\) | 2.94229 | + | 2.94229i | 0.291330 | + | 0.291330i | ||||
\(103\) | 7.77490i | 0.766084i | 0.923731 | + | 0.383042i | \(0.125123\pi\) | ||||
−0.923731 | + | 0.383042i | \(0.874877\pi\) | |||||||
\(104\) | −5.21529 | −0.511402 | ||||||||
\(105\) | 4.77512 | − | 7.85475i | 0.466004 | − | 0.766546i | ||||
\(106\) | −8.31822 | − | 8.31822i | −0.807937 | − | 0.807937i | ||||
\(107\) | 5.67037 | − | 5.67037i | 0.548176 | − | 0.548176i | −0.377737 | − | 0.925913i | \(-0.623298\pi\) |
0.925913 | + | 0.377737i | \(0.123298\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | −5.58777 | − | 5.58777i | −0.535211 | − | 0.535211i | 0.386908 | − | 0.922118i | \(-0.373543\pi\) |
−0.922118 | + | 0.386908i | \(0.873543\pi\) | |||||||
\(110\) | 3.19100 | − | 5.24898i | 0.304250 | − | 0.500470i | ||||
\(111\) | −5.78837 | − | 1.86945i | −0.549407 | − | 0.177440i | ||||
\(112\) | 2.90687 | − | 2.90687i | 0.274673 | − | 0.274673i | ||||
\(113\) | − | 14.2804i | − | 1.34339i | −0.740829 | − | 0.671694i | \(-0.765567\pi\) | ||
0.740829 | − | 0.671694i | \(-0.234433\pi\) | |||||||
\(114\) | 2.65630 | 0.248785 | ||||||||
\(115\) | −1.79963 | − | 1.09404i | −0.167816 | − | 0.102020i | ||||
\(116\) | −4.28806 | + | 4.28806i | −0.398136 | + | 0.398136i | ||||
\(117\) | − | 5.21529i | − | 0.482154i | ||||||
\(118\) | −1.92935 | − | 1.92935i | −0.177611 | − | 0.177611i | ||||
\(119\) | −12.0956 | − | 12.0956i | −1.10880 | − | 1.10880i | ||||
\(120\) | −2.17242 | + | 0.529716i | −0.198314 | + | 0.0483562i | ||||
\(121\) | 3.45316 | 0.313923 | ||||||||
\(122\) | 8.68618 | + | 8.68618i | 0.786410 | + | 0.786410i | ||||
\(123\) | −5.36992 | − | 5.36992i | −0.484189 | − | 0.484189i | ||||
\(124\) | 5.51242 | + | 5.51242i | 0.495030 | + | 0.495030i | ||||
\(125\) | −0.758434 | + | 11.1546i | −0.0678364 | + | 0.997696i | ||||
\(126\) | 2.90687 | + | 2.90687i | 0.258965 | + | 0.258965i | ||||
\(127\) | 8.01885 | − | 8.01885i | 0.711558 | − | 0.711558i | −0.255303 | − | 0.966861i | \(-0.582175\pi\) |
0.966861 | + | 0.255303i | \(0.0821752\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.40869 | + | 4.40869i | −0.388163 | + | 0.388163i | ||||
\(130\) | −9.96485 | − | 6.05791i | −0.873975 | − | 0.531314i | ||||
\(131\) | 6.63665 | + | 6.63665i | 0.579847 | + | 0.579847i | 0.934861 | − | 0.355014i | \(-0.115524\pi\) |
−0.355014 | + | 0.934861i | \(0.615524\pi\) | |||||||
\(132\) | 1.94253 | + | 1.94253i | 0.169075 | + | 0.169075i | ||||
\(133\) | −10.9199 | −0.946874 | ||||||||
\(134\) | −5.51165 | − | 5.51165i | −0.476134 | − | 0.476134i | ||||
\(135\) | −0.529716 | − | 2.17242i | −0.0455907 | − | 0.186972i | ||||
\(136\) | 4.16103i | 0.356806i | ||||||||
\(137\) | 7.91811 | − | 7.91811i | 0.676490 | − | 0.676490i | −0.282714 | − | 0.959204i | \(-0.591235\pi\) |
0.959204 | + | 0.282714i | \(0.0912348\pi\) | |||||||
\(138\) | 0.666001 | − | 0.666001i | 0.0566938 | − | 0.0566938i | ||||
\(139\) | 13.0683 | 1.10844 | 0.554221 | − | 0.832369i | \(-0.313016\pi\) | ||||
0.554221 | + | 0.832369i | \(0.313016\pi\) | |||||||
\(140\) | 8.93067 | − | 2.17763i | 0.754779 | − | 0.184043i | ||||
\(141\) | 8.55529i | 0.720485i | ||||||||
\(142\) | 8.51973 | 0.714960 | ||||||||
\(143\) | 14.3272i | 1.19810i | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −13.1741 | + | 3.21232i | −1.09405 | + | 0.266769i | ||||
\(146\) | 2.98121 | − | 2.98121i | 0.246727 | − | 0.246727i | ||||
\(147\) | −7.00021 | − | 7.00021i | −0.577368 | − | 0.577368i | ||||
\(148\) | −2.77109 | − | 5.41489i | −0.227783 | − | 0.445101i | ||||
\(149\) | − | 6.80855i | − | 0.557778i | −0.960323 | − | 0.278889i | \(-0.910034\pi\) | ||
0.960323 | − | 0.278889i | \(-0.0899661\pi\) | |||||||
\(150\) | −4.76613 | − | 1.51128i | −0.389153 | − | 0.123395i | ||||
\(151\) | − | 17.8917i | − | 1.45600i | −0.685575 | − | 0.728002i | \(-0.740449\pi\) | ||
0.685575 | − | 0.728002i | \(-0.259551\pi\) | |||||||
\(152\) | 1.87829 | + | 1.87829i | 0.152349 | + | 0.152349i | ||||
\(153\) | −4.16103 | −0.336399 | ||||||||
\(154\) | −7.98561 | − | 7.98561i | −0.643499 | − | 0.643499i | ||||
\(155\) | 4.12953 | + | 16.9356i | 0.331692 | + | 1.36030i | ||||
\(156\) | 3.68777 | − | 3.68777i | 0.295258 | − | 0.295258i | ||||
\(157\) | 3.05662 | − | 3.05662i | 0.243945 | − | 0.243945i | −0.574535 | − | 0.818480i | \(-0.694817\pi\) |
0.818480 | + | 0.574535i | \(0.194817\pi\) | |||||||
\(158\) | −1.46581 | − | 1.46581i | −0.116613 | − | 0.116613i | ||||
\(159\) | 11.7637 | 0.932925 | ||||||||
\(160\) | −1.91070 | − | 1.16157i | −0.151054 | − | 0.0918298i | ||||
\(161\) | −2.73789 | + | 2.73789i | −0.215776 | + | 0.215776i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 19.5350i | 1.53010i | 0.643971 | + | 0.765050i | \(0.277286\pi\) | ||||
−0.643971 | + | 0.765050i | \(0.722714\pi\) | |||||||
\(164\) | − | 7.59421i | − | 0.593008i | ||||||
\(165\) | 1.45521 | + | 5.96796i | 0.113288 | + | 0.464605i | ||||
\(166\) | −7.26193 | − | 7.26193i | −0.563635 | − | 0.563635i | ||||
\(167\) | 7.60664i | 0.588620i | 0.955710 | + | 0.294310i | \(0.0950898\pi\) | ||||
−0.955710 | + | 0.294310i | \(0.904910\pi\) | |||||||
\(168\) | 4.11094i | 0.317166i | ||||||||
\(169\) | 14.1993 | 1.09225 | ||||||||
\(170\) | −4.83331 | + | 7.95047i | −0.370698 | + | 0.609773i | ||||
\(171\) | −1.87829 | + | 1.87829i | −0.143636 | + | 0.143636i | ||||
\(172\) | −6.23482 | −0.475401 | ||||||||
\(173\) | −17.6561 | + | 17.6561i | −1.34237 | + | 1.34237i | −0.448675 | + | 0.893695i | \(0.648104\pi\) |
−0.893695 | + | 0.448675i | \(0.851896\pi\) | |||||||
\(174\) | − | 6.06423i | − | 0.459728i | ||||||
\(175\) | 19.5933 | + | 6.21277i | 1.48111 | + | 0.469642i | ||||
\(176\) | 2.74715i | 0.207074i | ||||||||
\(177\) | 2.72851 | 0.205087 | ||||||||
\(178\) | 1.62770 | − | 1.62770i | 0.122001 | − | 0.122001i | ||||
\(179\) | −5.23093 | + | 5.23093i | −0.390978 | + | 0.390978i | −0.875036 | − | 0.484058i | \(-0.839162\pi\) |
0.484058 | + | 0.875036i | \(0.339162\pi\) | |||||||
\(180\) | 1.16157 | − | 1.91070i | 0.0865780 | − | 0.142415i | ||||
\(181\) | 6.81886 | 0.506842 | 0.253421 | − | 0.967356i | \(-0.418444\pi\) | ||||
0.253421 | + | 0.967356i | \(0.418444\pi\) | |||||||
\(182\) | −15.1602 | + | 15.1602i | −1.12375 | + | 1.12375i | ||||
\(183\) | −12.2841 | −0.908068 | ||||||||
\(184\) | 0.941868 | 0.0694354 | ||||||||
\(185\) | 0.995030 | − | 13.5650i | 0.0731560 | − | 0.997321i | ||||
\(186\) | −7.79574 | −0.571612 | ||||||||
\(187\) | 11.4310 | 0.835916 | ||||||||
\(188\) | −6.04950 | + | 6.04950i | −0.441205 | + | 0.441205i | ||||
\(189\) | −4.11094 | −0.299027 | ||||||||
\(190\) | 1.40708 | + | 5.77059i | 0.102081 | + | 0.418643i | ||||
\(191\) | −7.19163 | + | 7.19163i | −0.520368 | + | 0.520368i | −0.917683 | − | 0.397315i | \(-0.869942\pi\) |
0.397315 | + | 0.917683i | \(0.369942\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −16.3418 | −1.17631 | −0.588154 | − | 0.808749i | \(-0.700145\pi\) | ||||
−0.588154 | + | 0.808749i | \(0.700145\pi\) | |||||||
\(194\) | 10.0910i | 0.724493i | ||||||||
\(195\) | 11.3298 | − | 2.76262i | 0.811344 | − | 0.197836i | ||||
\(196\) | − | 9.89979i | − | 0.707128i | ||||||
\(197\) | −11.4834 | + | 11.4834i | −0.818161 | + | 0.818161i | −0.985841 | − | 0.167680i | \(-0.946372\pi\) |
0.167680 | + | 0.985841i | \(0.446372\pi\) | |||||||
\(198\) | −2.74715 | −0.195232 | ||||||||
\(199\) | −12.9349 | + | 12.9349i | −0.916929 | + | 0.916929i | −0.996805 | − | 0.0798762i | \(-0.974548\pi\) |
0.0798762 | + | 0.996805i | \(0.474548\pi\) | |||||||
\(200\) | −2.30153 | − | 4.43880i | −0.162743 | − | 0.313871i | ||||
\(201\) | 7.79465 | 0.549792 | ||||||||
\(202\) | 9.40183i | 0.661511i | ||||||||
\(203\) | 24.9297i | 1.74972i | ||||||||
\(204\) | −2.94229 | − | 2.94229i | −0.206002 | − | 0.206002i | ||||
\(205\) | 8.82118 | − | 14.5102i | 0.616098 | − | 1.01344i | ||||
\(206\) | − | 7.77490i | − | 0.541703i | ||||||
\(207\) | 0.941868i | 0.0654644i | ||||||||
\(208\) | 5.21529 | 0.361616 | ||||||||
\(209\) | 5.15994 | − | 5.15994i | 0.356921 | − | 0.356921i | ||||
\(210\) | −4.77512 | + | 7.85475i | −0.329515 | + | 0.542030i | ||||
\(211\) | −23.4609 | −1.61512 | −0.807558 | − | 0.589788i | \(-0.799211\pi\) | ||||
−0.807558 | + | 0.589788i | \(0.799211\pi\) | |||||||
\(212\) | 8.31822 | + | 8.31822i | 0.571297 | + | 0.571297i | ||||
\(213\) | −6.02436 | + | 6.02436i | −0.412782 | + | 0.412782i | ||||
\(214\) | −5.67037 | + | 5.67037i | −0.387619 | + | 0.387619i | ||||
\(215\) | −11.9129 | − | 7.24216i | −0.812450 | − | 0.493911i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | 32.0478 | 2.17555 | ||||||||
\(218\) | 5.58777 | + | 5.58777i | 0.378451 | + | 0.378451i | ||||
\(219\) | 4.21607i | 0.284895i | ||||||||
\(220\) | −3.19100 | + | 5.24898i | −0.215137 | + | 0.353886i | ||||
\(221\) | − | 21.7010i | − | 1.45977i | ||||||
\(222\) | 5.78837 | + | 1.86945i | 0.388490 | + | 0.125469i | ||||
\(223\) | −2.83314 | − | 2.83314i | −0.189721 | − | 0.189721i | 0.605854 | − | 0.795576i | \(-0.292831\pi\) |
−0.795576 | + | 0.605854i | \(0.792831\pi\) | |||||||
\(224\) | −2.90687 | + | 2.90687i | −0.194223 | + | 0.194223i | ||||
\(225\) | 4.43880 | − | 2.30153i | 0.295920 | − | 0.153435i | ||||
\(226\) | 14.2804i | 0.949919i | ||||||||
\(227\) | − | 7.49379i | − | 0.497380i | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||
0.968583 | − | 0.248690i | \(-0.0800001\pi\) | |||||||
\(228\) | −2.65630 | −0.175918 | ||||||||
\(229\) | 24.0930i | 1.59211i | 0.605224 | + | 0.796055i | \(0.293083\pi\) | ||||
−0.605224 | + | 0.796055i | \(0.706917\pi\) | |||||||
\(230\) | 1.79963 | + | 1.09404i | 0.118664 | + | 0.0721390i | ||||
\(231\) | 11.2934 | 0.743049 | ||||||||
\(232\) | 4.28806 | − | 4.28806i | 0.281525 | − | 0.281525i | ||||
\(233\) | 7.78522 | − | 7.78522i | 0.510027 | − | 0.510027i | −0.404508 | − | 0.914535i | \(-0.632557\pi\) |
0.914535 | + | 0.404508i | \(0.132557\pi\) | |||||||
\(234\) | 5.21529i | 0.340934i | ||||||||
\(235\) | −18.5857 | + | 4.53187i | −1.21239 | + | 0.295627i | ||||
\(236\) | 1.92935 | + | 1.92935i | 0.125590 | + | 0.125590i | ||||
\(237\) | 2.07297 | 0.134654 | ||||||||
\(238\) | 12.0956 | + | 12.0956i | 0.784040 | + | 0.784040i | ||||
\(239\) | −1.88427 | − | 1.88427i | −0.121884 | − | 0.121884i | 0.643534 | − | 0.765418i | \(-0.277468\pi\) |
−0.765418 | + | 0.643534i | \(0.777468\pi\) | |||||||
\(240\) | 2.17242 | − | 0.529716i | 0.140229 | − | 0.0341930i | ||||
\(241\) | −18.1268 | + | 18.1268i | −1.16765 | + | 1.16765i | −0.184888 | + | 0.982760i | \(0.559192\pi\) |
−0.982760 | + | 0.184888i | \(0.940808\pi\) | |||||||
\(242\) | −3.45316 | −0.221977 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −8.68618 | − | 8.68618i | −0.556076 | − | 0.556076i | ||||
\(245\) | 11.4993 | − | 18.9155i | 0.734661 | − | 1.20847i | ||||
\(246\) | 5.36992 | + | 5.36992i | 0.342373 | + | 0.342373i | ||||
\(247\) | −9.79582 | − | 9.79582i | −0.623293 | − | 0.623293i | ||||
\(248\) | −5.51242 | − | 5.51242i | −0.350039 | − | 0.350039i | ||||
\(249\) | 10.2699 | 0.650830 | ||||||||
\(250\) | 0.758434 | − | 11.1546i | 0.0479676 | − | 0.705478i | ||||
\(251\) | −10.2960 | − | 10.2960i | −0.649879 | − | 0.649879i | 0.303085 | − | 0.952964i | \(-0.401983\pi\) |
−0.952964 | + | 0.303085i | \(0.901983\pi\) | |||||||
\(252\) | −2.90687 | − | 2.90687i | −0.183116 | − | 0.183116i | ||||
\(253\) | − | 2.58745i | − | 0.162672i | ||||||
\(254\) | −8.01885 | + | 8.01885i | −0.503148 | + | 0.503148i | ||||
\(255\) | −2.20417 | − | 9.03950i | −0.138030 | − | 0.566076i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 2.69763i | − | 0.168274i | −0.996454 | − | 0.0841369i | \(-0.973187\pi\) | ||
0.996454 | − | 0.0841369i | \(-0.0268133\pi\) | |||||||
\(258\) | 4.40869 | − | 4.40869i | 0.274473 | − | 0.274473i | ||||
\(259\) | −23.7956 | − | 7.68517i | −1.47859 | − | 0.477533i | ||||
\(260\) | 9.96485 | + | 6.05791i | 0.617994 | + | 0.375695i | ||||
\(261\) | 4.28806 | + | 4.28806i | 0.265424 | + | 0.265424i | ||||
\(262\) | −6.63665 | − | 6.63665i | −0.410014 | − | 0.410014i | ||||
\(263\) | −15.0006 | + | 15.0006i | −0.924974 | + | 0.924974i | −0.997376 | − | 0.0724014i | \(-0.976934\pi\) |
0.0724014 | + | 0.997376i | \(0.476934\pi\) | |||||||
\(264\) | −1.94253 | − | 1.94253i | −0.119554 | − | 0.119554i | ||||
\(265\) | 6.23144 | + | 25.5557i | 0.382794 | + | 1.56988i | ||||
\(266\) | 10.9199 | 0.669541 | ||||||||
\(267\) | 2.30191i | 0.140875i | ||||||||
\(268\) | 5.51165 | + | 5.51165i | 0.336678 | + | 0.336678i | ||||
\(269\) | 3.86256i | 0.235505i | 0.993043 | + | 0.117752i | \(0.0375689\pi\) | ||||
−0.993043 | + | 0.117752i | \(0.962431\pi\) | |||||||
\(270\) | 0.529716 | + | 2.17242i | 0.0322375 | + | 0.132209i | ||||
\(271\) | −11.2551 | −0.683697 | −0.341848 | − | 0.939755i | \(-0.611053\pi\) | ||||
−0.341848 | + | 0.939755i | \(0.611053\pi\) | |||||||
\(272\) | − | 4.16103i | − | 0.252300i | ||||||
\(273\) | − | 21.4397i | − | 1.29759i | ||||||
\(274\) | −7.91811 | + | 7.91811i | −0.478351 | + | 0.478351i | ||||
\(275\) | −12.1941 | + | 6.32265i | −0.735330 | + | 0.381270i | ||||
\(276\) | −0.666001 | + | 0.666001i | −0.0400886 | + | 0.0400886i | ||||
\(277\) | 16.2009 | 0.973420 | 0.486710 | − | 0.873564i | \(-0.338197\pi\) | ||||
0.486710 | + | 0.873564i | \(0.338197\pi\) | |||||||
\(278\) | −13.0683 | −0.783787 | ||||||||
\(279\) | 5.51242 | − | 5.51242i | 0.330020 | − | 0.330020i | ||||
\(280\) | −8.93067 | + | 2.17763i | −0.533710 | + | 0.130138i | ||||
\(281\) | −7.78699 | + | 7.78699i | −0.464533 | + | 0.464533i | −0.900138 | − | 0.435605i | \(-0.856534\pi\) |
0.435605 | + | 0.900138i | \(0.356534\pi\) | |||||||
\(282\) | − | 8.55529i | − | 0.509460i | ||||||
\(283\) | 21.1035i | 1.25447i | 0.778829 | + | 0.627237i | \(0.215814\pi\) | ||||
−0.778829 | + | 0.627237i | \(0.784186\pi\) | |||||||
\(284\) | −8.51973 | −0.505553 | ||||||||
\(285\) | −5.07539 | − | 3.08547i | −0.300640 | − | 0.182767i | ||||
\(286\) | − | 14.3272i | − | 0.847185i | ||||||
\(287\) | −22.0754 | − | 22.0754i | −1.30307 | − | 1.30307i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −0.314185 | −0.0184815 | ||||||||
\(290\) | 13.1741 | − | 3.21232i | 0.773607 | − | 0.188634i | ||||
\(291\) | −7.13543 | − | 7.13543i | −0.418286 | − | 0.418286i | ||||
\(292\) | −2.98121 | + | 2.98121i | −0.174462 | + | 0.174462i | ||||
\(293\) | −2.76877 | − | 2.76877i | −0.161753 | − | 0.161753i | 0.621590 | − | 0.783343i | \(-0.286487\pi\) |
−0.783343 | + | 0.621590i | \(0.786487\pi\) | |||||||
\(294\) | 7.00021 | + | 7.00021i | 0.408261 | + | 0.408261i | ||||
\(295\) | 1.44534 | + | 5.92747i | 0.0841507 | + | 0.345110i | ||||
\(296\) | 2.77109 | + | 5.41489i | 0.161067 | + | 0.314734i | ||||
\(297\) | 1.94253 | − | 1.94253i | 0.112717 | − | 0.112717i | ||||
\(298\) | 6.80855i | 0.394408i | ||||||||
\(299\) | −4.91212 | −0.284075 | ||||||||
\(300\) | 4.76613 | + | 1.51128i | 0.275173 | + | 0.0872538i | ||||
\(301\) | −18.1238 | + | 18.1238i | −1.04464 | + | 1.04464i | ||||
\(302\) | 17.8917i | 1.02955i | ||||||||
\(303\) | −6.64810 | − | 6.64810i | −0.381923 | − | 0.381923i | ||||
\(304\) | −1.87829 | − | 1.87829i | −0.107727 | − | 0.107727i | ||||
\(305\) | −6.50709 | − | 26.6862i | −0.372595 | − | 1.52805i | ||||
\(306\) | 4.16103 | 0.237870 | ||||||||
\(307\) | 6.12720 | + | 6.12720i | 0.349698 | + | 0.349698i | 0.859997 | − | 0.510299i | \(-0.170465\pi\) |
−0.510299 | + | 0.859997i | \(0.670465\pi\) | |||||||
\(308\) | 7.98561 | + | 7.98561i | 0.455023 | + | 0.455023i | ||||
\(309\) | 5.49768 | + | 5.49768i | 0.312752 | + | 0.312752i | ||||
\(310\) | −4.12953 | − | 16.9356i | −0.234542 | − | 0.961878i | ||||
\(311\) | −1.06423 | − | 1.06423i | −0.0603471 | − | 0.0603471i | 0.676289 | − | 0.736636i | \(-0.263587\pi\) |
−0.736636 | + | 0.676289i | \(0.763587\pi\) | |||||||
\(312\) | −3.68777 | + | 3.68777i | −0.208779 | + | 0.208779i | ||||
\(313\) | −7.63668 | −0.431650 | −0.215825 | − | 0.976432i | \(-0.569244\pi\) | ||||
−0.215825 | + | 0.976432i | \(0.569244\pi\) | |||||||
\(314\) | −3.05662 | + | 3.05662i | −0.172495 | + | 0.172495i | ||||
\(315\) | −2.17763 | − | 8.93067i | −0.122695 | − | 0.503186i | ||||
\(316\) | 1.46581 | + | 1.46581i | 0.0824581 | + | 0.0824581i | ||||
\(317\) | 19.5287 | + | 19.5287i | 1.09684 | + | 1.09684i | 0.994778 | + | 0.102064i | \(0.0325445\pi\) |
0.102064 | + | 0.994778i | \(0.467455\pi\) | |||||||
\(318\) | −11.7637 | −0.659677 | ||||||||
\(319\) | −11.7800 | − | 11.7800i | −0.659551 | − | 0.659551i | ||||
\(320\) | 1.91070 | + | 1.16157i | 0.106811 | + | 0.0649335i | ||||
\(321\) | − | 8.01912i | − | 0.447584i | ||||||
\(322\) | 2.73789 | − | 2.73789i | 0.152577 | − | 0.152577i | ||||
\(323\) | −7.81562 | + | 7.81562i | −0.434872 | + | 0.434872i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 12.0032 | + | 23.1497i | 0.665815 | + | 1.28411i | ||||
\(326\) | − | 19.5350i | − | 1.08194i | ||||||
\(327\) | −7.90229 | −0.436998 | ||||||||
\(328\) | 7.59421i | 0.419320i | ||||||||
\(329\) | 35.1702i | 1.93900i | ||||||||
\(330\) | −1.45521 | − | 5.96796i | −0.0801067 | − | 0.328526i | ||||
\(331\) | −10.6002 | + | 10.6002i | −0.582640 | + | 0.582640i | −0.935628 | − | 0.352988i | \(-0.885166\pi\) |
0.352988 | + | 0.935628i | \(0.385166\pi\) | |||||||
\(332\) | 7.26193 | + | 7.26193i | 0.398550 | + | 0.398550i | ||||
\(333\) | −5.41489 | + | 2.77109i | −0.296734 | + | 0.151855i | ||||
\(334\) | − | 7.60664i | − | 0.416217i | ||||||
\(335\) | 4.12895 | + | 16.9332i | 0.225589 | + | 0.925162i | ||||
\(336\) | − | 4.11094i | − | 0.224270i | ||||||
\(337\) | −14.7087 | − | 14.7087i | −0.801235 | − | 0.801235i | 0.182054 | − | 0.983289i | \(-0.441725\pi\) |
−0.983289 | + | 0.182054i | \(0.941725\pi\) | |||||||
\(338\) | −14.1993 | −0.772340 | ||||||||
\(339\) | −10.0978 | − | 10.0978i | −0.548436 | − | 0.548436i | ||||
\(340\) | 4.83331 | − | 7.95047i | 0.262123 | − | 0.431175i | ||||
\(341\) | −15.1435 | + | 15.1435i | −0.820064 | + | 0.820064i | ||||
\(342\) | 1.87829 | − | 1.87829i | 0.101566 | − | 0.101566i | ||||
\(343\) | −8.42932 | − | 8.42932i | −0.455140 | − | 0.455140i | ||||
\(344\) | 6.23482 | 0.336159 | ||||||||
\(345\) | −2.04613 | + | 0.498923i | −0.110160 | + | 0.0268611i | ||||
\(346\) | 17.6561 | − | 17.6561i | 0.949199 | − | 0.949199i | ||||
\(347\) | −5.20503 | −0.279421 | −0.139710 | − | 0.990192i | \(-0.544617\pi\) | ||||
−0.139710 | + | 0.990192i | \(0.544617\pi\) | |||||||
\(348\) | 6.06423i | 0.325077i | ||||||||
\(349\) | − | 8.31963i | − | 0.445339i | −0.974894 | − | 0.222670i | \(-0.928523\pi\) | ||
0.974894 | − | 0.222670i | \(-0.0714771\pi\) | |||||||
\(350\) | −19.5933 | − | 6.21277i | −1.04730 | − | 0.332087i | ||||
\(351\) | −3.68777 | − | 3.68777i | −0.196839 | − | 0.196839i | ||||
\(352\) | − | 2.74715i | − | 0.146424i | ||||||
\(353\) | − | 32.6034i | − | 1.73530i | −0.497173 | − | 0.867651i | \(-0.665629\pi\) | ||
0.497173 | − | 0.867651i | \(-0.334371\pi\) | |||||||
\(354\) | −2.72851 | −0.145019 | ||||||||
\(355\) | −16.2786 | − | 9.89623i | −0.863980 | − | 0.525237i | ||||
\(356\) | −1.62770 | + | 1.62770i | −0.0862677 | + | 0.0862677i | ||||
\(357\) | −17.1057 | −0.905331 | ||||||||
\(358\) | 5.23093 | − | 5.23093i | 0.276463 | − | 0.276463i | ||||
\(359\) | − | 17.3163i | − | 0.913921i | −0.889487 | − | 0.456960i | \(-0.848938\pi\) | ||
0.889487 | − | 0.456960i | \(-0.151062\pi\) | |||||||
\(360\) | −1.16157 | + | 1.91070i | −0.0612199 | + | 0.100703i | ||||
\(361\) | − | 11.9441i | − | 0.628635i | ||||||
\(362\) | −6.81886 | −0.358391 | ||||||||
\(363\) | 2.44175 | − | 2.44175i | 0.128159 | − | 0.128159i | ||||
\(364\) | 15.1602 | − | 15.1602i | 0.794610 | − | 0.794610i | ||||
\(365\) | −9.15906 | + | 2.23332i | −0.479407 | + | 0.116897i | ||||
\(366\) | 12.2841 | 0.642101 | ||||||||
\(367\) | −19.8485 | + | 19.8485i | −1.03608 | + | 1.03608i | −0.0367606 | + | 0.999324i | \(0.511704\pi\) |
−0.999324 | + | 0.0367606i | \(0.988296\pi\) | |||||||
\(368\) | −0.941868 | −0.0490983 | ||||||||
\(369\) | −7.59421 | −0.395339 | ||||||||
\(370\) | −0.995030 | + | 13.5650i | −0.0517291 | + | 0.705212i | ||||
\(371\) | 48.3600 | 2.51072 | ||||||||
\(372\) | 7.79574 | 0.404190 | ||||||||
\(373\) | 19.3419 | − | 19.3419i | 1.00149 | − | 1.00149i | 0.00148728 | − | 0.999999i | \(-0.499527\pi\) |
0.999999 | − | 0.00148728i | \(-0.000473415\pi\) | |||||||
\(374\) | −11.4310 | −0.591082 | ||||||||
\(375\) | 7.35119 | + | 8.42378i | 0.379614 | + | 0.435002i | ||||
\(376\) | 6.04950 | − | 6.04950i | 0.311979 | − | 0.311979i | ||||
\(377\) | −22.3635 | + | 22.3635i | −1.15178 | + | 1.15178i | ||||
\(378\) | 4.11094 | 0.211444 | ||||||||
\(379\) | 3.56273i | 0.183005i | 0.995805 | + | 0.0915027i | \(0.0291670\pi\) | ||||
−0.995805 | + | 0.0915027i | \(0.970833\pi\) | |||||||
\(380\) | −1.40708 | − | 5.77059i | −0.0721819 | − | 0.296025i | ||||
\(381\) | − | 11.3404i | − | 0.580985i | ||||||
\(382\) | 7.19163 | − | 7.19163i | 0.367956 | − | 0.367956i | ||||
\(383\) | −17.5102 | −0.894730 | −0.447365 | − | 0.894351i | \(-0.647638\pi\) | ||||
−0.447365 | + | 0.894351i | \(0.647638\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 5.98228 | + | 24.5339i | 0.304885 | + | 1.25036i | ||||
\(386\) | 16.3418 | 0.831776 | ||||||||
\(387\) | 6.23482i | 0.316934i | ||||||||
\(388\) | − | 10.0910i | − | 0.512294i | ||||||
\(389\) | 5.52680 | + | 5.52680i | 0.280220 | + | 0.280220i | 0.833197 | − | 0.552977i | \(-0.186508\pi\) |
−0.552977 | + | 0.833197i | \(0.686508\pi\) | |||||||
\(390\) | −11.3298 | + | 2.76262i | −0.573707 | + | 0.139891i | ||||
\(391\) | 3.91914i | 0.198200i | ||||||||
\(392\) | 9.89979i | 0.500015i | ||||||||
\(393\) | 9.38564 | 0.473443 | ||||||||
\(394\) | 11.4834 | − | 11.4834i | 0.578527 | − | 0.578527i | ||||
\(395\) | 1.09808 | + | 4.50335i | 0.0552505 | + | 0.226588i | ||||
\(396\) | 2.74715 | 0.138050 | ||||||||
\(397\) | 7.17123 | + | 7.17123i | 0.359913 | + | 0.359913i | 0.863781 | − | 0.503867i | \(-0.168090\pi\) |
−0.503867 | + | 0.863781i | \(0.668090\pi\) | |||||||
\(398\) | 12.9349 | − | 12.9349i | 0.648366 | − | 0.648366i | ||||
\(399\) | −7.72152 | + | 7.72152i | −0.386560 | + | 0.386560i | ||||
\(400\) | 2.30153 | + | 4.43880i | 0.115076 | + | 0.221940i | ||||
\(401\) | 12.3057 | + | 12.3057i | 0.614518 | + | 0.614518i | 0.944120 | − | 0.329602i | \(-0.106914\pi\) |
−0.329602 | + | 0.944120i | \(0.606914\pi\) | |||||||
\(402\) | −7.79465 | −0.388762 | ||||||||
\(403\) | 28.7489 | + | 28.7489i | 1.43208 | + | 1.43208i | ||||
\(404\) | − | 9.40183i | − | 0.467759i | ||||||
\(405\) | −1.91070 | − | 1.16157i | −0.0949433 | − | 0.0577187i | ||||
\(406\) | − | 24.9297i | − | 1.23724i | ||||||
\(407\) | 14.8755 | − | 7.61262i | 0.737352 | − | 0.377343i | ||||
\(408\) | 2.94229 | + | 2.94229i | 0.145665 | + | 0.145665i | ||||
\(409\) | −20.8384 | + | 20.8384i | −1.03039 | + | 1.03039i | −0.0308695 | + | 0.999523i | \(0.509828\pi\) |
−0.999523 | + | 0.0308695i | \(0.990172\pi\) | |||||||
\(410\) | −8.82118 | + | 14.5102i | −0.435647 | + | 0.716610i | ||||
\(411\) | − | 11.1979i | − | 0.552352i | ||||||
\(412\) | 7.77490i | 0.383042i | ||||||||
\(413\) | 11.2167 | 0.551939 | ||||||||
\(414\) | − | 0.941868i | − | 0.0462903i | ||||||
\(415\) | 5.44014 | + | 22.3106i | 0.267046 | + | 1.09518i | ||||
\(416\) | −5.21529 | −0.255701 | ||||||||
\(417\) | 9.24072 | − | 9.24072i | 0.452520 | − | 0.452520i | ||||
\(418\) | −5.15994 | + | 5.15994i | −0.252381 | + | 0.252381i | ||||
\(419\) | − | 36.4587i | − | 1.78113i | −0.454860 | − | 0.890563i | \(-0.650311\pi\) | ||
0.454860 | − | 0.890563i | \(-0.349689\pi\) | |||||||
\(420\) | 4.77512 | − | 7.85475i | 0.233002 | − | 0.383273i | ||||
\(421\) | 15.1883 | + | 15.1883i | 0.740231 | + | 0.740231i | 0.972622 | − | 0.232392i | \(-0.0746551\pi\) |
−0.232392 | + | 0.972622i | \(0.574655\pi\) | |||||||
\(422\) | 23.4609 | 1.14206 | ||||||||
\(423\) | 6.04950 | + | 6.04950i | 0.294137 | + | 0.294137i | ||||
\(424\) | −8.31822 | − | 8.31822i | −0.403968 | − | 0.403968i | ||||
\(425\) | 18.4700 | − | 9.57674i | 0.895926 | − | 0.464540i | ||||
\(426\) | 6.02436 | − | 6.02436i | 0.291881 | − | 0.291881i | ||||
\(427\) | −50.4992 | −2.44383 | ||||||||
\(428\) | 5.67037 | − | 5.67037i | 0.274088 | − | 0.274088i | ||||
\(429\) | 10.1309 | + | 10.1309i | 0.489123 | + | 0.489123i | ||||
\(430\) | 11.9129 | + | 7.24216i | 0.574489 | + | 0.349248i | ||||
\(431\) | −6.39166 | − | 6.39166i | −0.307875 | − | 0.307875i | 0.536210 | − | 0.844085i | \(-0.319856\pi\) |
−0.844085 | + | 0.536210i | \(0.819856\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 15.4619 | + | 15.4619i | 0.743053 | + | 0.743053i | 0.973164 | − | 0.230111i | \(-0.0739089\pi\) |
−0.230111 | + | 0.973164i | \(0.573909\pi\) | |||||||
\(434\) | −32.0478 | −1.53834 | ||||||||
\(435\) | −7.04401 | + | 11.5869i | −0.337734 | + | 0.555550i | ||||
\(436\) | −5.58777 | − | 5.58777i | −0.267605 | − | 0.267605i | ||||
\(437\) | 1.76910 | + | 1.76910i | 0.0846275 | + | 0.0846275i | ||||
\(438\) | − | 4.21607i | − | 0.201451i | ||||||
\(439\) | 15.6685 | − | 15.6685i | 0.747816 | − | 0.747816i | −0.226253 | − | 0.974069i | \(-0.572648\pi\) |
0.974069 | + | 0.226253i | \(0.0726476\pi\) | |||||||
\(440\) | 3.19100 | − | 5.24898i | 0.152125 | − | 0.250235i | ||||
\(441\) | −9.89979 | −0.471419 | ||||||||
\(442\) | 21.7010i | 1.03221i | ||||||||
\(443\) | 27.2120 | − | 27.2120i | 1.29288 | − | 1.29288i | 0.359887 | − | 0.932996i | \(-0.382815\pi\) |
0.932996 | − | 0.359887i | \(-0.117185\pi\) | |||||||
\(444\) | −5.78837 | − | 1.86945i | −0.274704 | − | 0.0887200i | ||||
\(445\) | −5.00071 | + | 1.21936i | −0.237056 | + | 0.0578031i | ||||
\(446\) | 2.83314 | + | 2.83314i | 0.134153 | + | 0.134153i | ||||
\(447\) | −4.81437 | − | 4.81437i | −0.227712 | − | 0.227712i | ||||
\(448\) | 2.90687 | − | 2.90687i | 0.137337 | − | 0.137337i | ||||
\(449\) | −18.9735 | − | 18.9735i | −0.895416 | − | 0.895416i | 0.0996105 | − | 0.995027i | \(-0.468240\pi\) |
−0.995027 | + | 0.0996105i | \(0.968240\pi\) | |||||||
\(450\) | −4.43880 | + | 2.30153i | −0.209247 | + | 0.108495i | ||||
\(451\) | 20.8624 | 0.982374 | ||||||||
\(452\) | − | 14.2804i | − | 0.671694i | ||||||
\(453\) | −12.6513 | − | 12.6513i | −0.594411 | − | 0.594411i | ||||
\(454\) | 7.49379i | 0.351701i | ||||||||
\(455\) | 46.5761 | − | 11.3570i | 2.18352 | − | 0.532423i | ||||
\(456\) | 2.65630 | 0.124393 | ||||||||
\(457\) | 9.71477i | 0.454438i | 0.973844 | + | 0.227219i | \(0.0729632\pi\) | ||||
−0.973844 | + | 0.227219i | \(0.927037\pi\) | |||||||
\(458\) | − | 24.0930i | − | 1.12579i | ||||||
\(459\) | −2.94229 | + | 2.94229i | −0.137335 | + | 0.137335i | ||||
\(460\) | −1.79963 | − | 1.09404i | −0.0839080 | − | 0.0510100i | ||||
\(461\) | 17.2735 | − | 17.2735i | 0.804507 | − | 0.804507i | −0.179290 | − | 0.983796i | \(-0.557380\pi\) |
0.983796 | + | 0.179290i | \(0.0573799\pi\) | |||||||
\(462\) | −11.2934 | −0.525415 | ||||||||
\(463\) | 16.3891 | 0.761664 | 0.380832 | − | 0.924644i | \(-0.375638\pi\) | ||||
0.380832 | + | 0.924644i | \(0.375638\pi\) | |||||||
\(464\) | −4.28806 | + | 4.28806i | −0.199068 | + | 0.199068i | ||||
\(465\) | 14.8953 | + | 9.05527i | 0.690753 | + | 0.419928i | ||||
\(466\) | −7.78522 | + | 7.78522i | −0.360643 | + | 0.360643i | ||||
\(467\) | − | 1.29508i | − | 0.0599293i | −0.999551 | − | 0.0299647i | \(-0.990461\pi\) | ||
0.999551 | − | 0.0299647i | \(-0.00953947\pi\) | |||||||
\(468\) | − | 5.21529i | − | 0.241077i | ||||||
\(469\) | 32.0433 | 1.47962 | ||||||||
\(470\) | 18.5857 | − | 4.53187i | 0.857293 | − | 0.209040i | ||||
\(471\) | − | 4.32271i | − | 0.199180i | ||||||
\(472\) | −1.92935 | − | 1.92935i | −0.0888054 | − | 0.0888054i | ||||
\(473\) | − | 17.1280i | − | 0.787547i | ||||||
\(474\) | −2.07297 | −0.0952144 | ||||||||
\(475\) | 4.01441 | − | 12.6603i | 0.184194 | − | 0.580894i | ||||
\(476\) | −12.0956 | − | 12.0956i | −0.554400 | − | 0.554400i | ||||
\(477\) | 8.31822 | − | 8.31822i | 0.380865 | − | 0.380865i | ||||
\(478\) | 1.88427 | + | 1.88427i | 0.0861847 | + | 0.0861847i | ||||
\(479\) | 27.0885 | + | 27.0885i | 1.23770 | + | 1.23770i | 0.960937 | + | 0.276766i | \(0.0892628\pi\) |
0.276766 | + | 0.960937i | \(0.410737\pi\) | |||||||
\(480\) | −2.17242 | + | 0.529716i | −0.0991569 | + | 0.0241781i | ||||
\(481\) | −14.4521 | − | 28.2402i | −0.658958 | − | 1.28764i | ||||
\(482\) | 18.1268 | − | 18.1268i | 0.825652 | − | 0.825652i | ||||
\(483\) | 3.87196i | 0.176180i | ||||||||
\(484\) | 3.45316 | 0.156962 | ||||||||
\(485\) | 11.7214 | − | 19.2809i | 0.532241 | − | 0.875500i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | 27.5508i | 1.24844i | 0.781247 | + | 0.624222i | \(0.214584\pi\) | ||||
−0.781247 | + | 0.624222i | \(0.785416\pi\) | |||||||
\(488\) | 8.68618 | + | 8.68618i | 0.393205 | + | 0.393205i | ||||
\(489\) | 13.8133 | + | 13.8133i | 0.624661 | + | 0.624661i | ||||
\(490\) | −11.4993 | + | 18.9155i | −0.519484 | + | 0.854515i | ||||
\(491\) | −24.9010 | −1.12376 | −0.561882 | − | 0.827217i | \(-0.689923\pi\) | ||||
−0.561882 | + | 0.827217i | \(0.689923\pi\) | |||||||
\(492\) | −5.36992 | − | 5.36992i | −0.242095 | − | 0.242095i | ||||
\(493\) | 17.8428 | + | 17.8428i | 0.803597 | + | 0.803597i | ||||
\(494\) | 9.79582 | + | 9.79582i | 0.440735 | + | 0.440735i | ||||
\(495\) | 5.24898 | + | 3.19100i | 0.235924 | + | 0.143425i | ||||
\(496\) | 5.51242 | + | 5.51242i | 0.247515 | + | 0.247515i | ||||
\(497\) | −24.7657 | + | 24.7657i | −1.11090 | + | 1.11090i | ||||
\(498\) | −10.2699 | −0.460206 | ||||||||
\(499\) | −9.41283 | + | 9.41283i | −0.421376 | + | 0.421376i | −0.885677 | − | 0.464301i | \(-0.846305\pi\) |
0.464301 | + | 0.885677i | \(0.346305\pi\) | |||||||
\(500\) | −0.758434 | + | 11.1546i | −0.0339182 | + | 0.498848i | ||||
\(501\) | 5.37871 | + | 5.37871i | 0.240303 | + | 0.240303i | ||||
\(502\) | 10.2960 | + | 10.2960i | 0.459534 | + | 0.459534i | ||||
\(503\) | −32.7145 | −1.45867 | −0.729334 | − | 0.684158i | \(-0.760170\pi\) | ||||
−0.729334 | + | 0.684158i | \(0.760170\pi\) | |||||||
\(504\) | 2.90687 | + | 2.90687i | 0.129482 | + | 0.129482i | ||||
\(505\) | 10.9208 | − | 17.9641i | 0.485971 | − | 0.799390i | ||||
\(506\) | 2.58745i | 0.115026i | ||||||||
\(507\) | 10.0404 | − | 10.0404i | 0.445910 | − | 0.445910i | ||||
\(508\) | 8.01885 | − | 8.01885i | 0.355779 | − | 0.355779i | ||||
\(509\) | 13.1690 | 0.583707 | 0.291854 | − | 0.956463i | \(-0.405728\pi\) | ||||
0.291854 | + | 0.956463i | \(0.405728\pi\) | |||||||
\(510\) | 2.20417 | + | 9.03950i | 0.0976021 | + | 0.400276i | ||||
\(511\) | 17.3320i | 0.766722i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.65630i | 0.117279i | ||||||||
\(514\) | 2.69763i | 0.118988i | ||||||||
\(515\) | −9.03106 | + | 14.8555i | −0.397956 | + | 0.654611i | ||||
\(516\) | −4.40869 | + | 4.40869i | −0.194082 | + | 0.194082i | ||||
\(517\) | −16.6189 | − | 16.6189i | −0.730898 | − | 0.730898i | ||||
\(518\) | 23.7956 | + | 7.68517i | 1.04552 | + | 0.337667i | ||||
\(519\) | 24.9695i | 1.09604i | ||||||||
\(520\) | −9.96485 | − | 6.05791i | −0.436988 | − | 0.265657i | ||||
\(521\) | 30.7232i | 1.34601i | 0.739639 | + | 0.673004i | \(0.234996\pi\) | ||||
−0.739639 | + | 0.673004i | \(0.765004\pi\) | |||||||
\(522\) | −4.28806 | − | 4.28806i | −0.187683 | − | 0.187683i | ||||
\(523\) | 17.6544 | 0.771972 | 0.385986 | − | 0.922505i | \(-0.373861\pi\) | ||||
0.385986 | + | 0.922505i | \(0.373861\pi\) | |||||||
\(524\) | 6.63665 | + | 6.63665i | 0.289924 | + | 0.289924i | ||||
\(525\) | 18.2476 | − | 9.46144i | 0.796392 | − | 0.412931i | ||||
\(526\) | 15.0006 | − | 15.0006i | 0.654055 | − | 0.654055i | ||||
\(527\) | 22.9374 | − | 22.9374i | 0.999167 | − | 0.999167i | ||||
\(528\) | 1.94253 | + | 1.94253i | 0.0845377 | + | 0.0845377i | ||||
\(529\) | −22.1129 | −0.961430 | ||||||||
\(530\) | −6.23144 | − | 25.5557i | −0.270676 | − | 1.11007i | ||||
\(531\) | 1.92935 | − | 1.92935i | 0.0837266 | − | 0.0837266i | ||||
\(532\) | −10.9199 | −0.473437 | ||||||||
\(533\) | − | 39.6060i | − | 1.71553i | ||||||
\(534\) | − | 2.30191i | − | 0.0996134i | ||||||
\(535\) | 17.4209 | − | 4.24786i | 0.753170 | − | 0.183651i | ||||
\(536\) | −5.51165 | − | 5.51165i | −0.238067 | − | 0.238067i | ||||
\(537\) | 7.39765i | 0.319232i | ||||||||
\(538\) | − | 3.86256i | − | 0.166527i | ||||||
\(539\) | 27.1962 | 1.17142 | ||||||||
\(540\) | −0.529716 | − | 2.17242i | −0.0227953 | − | 0.0934860i | ||||
\(541\) | −24.2940 | + | 24.2940i | −1.04448 | + | 1.04448i | −0.0455156 | + | 0.998964i | \(0.514493\pi\) |
−0.998964 | + | 0.0455156i | \(0.985507\pi\) | |||||||
\(542\) | 11.2551 | 0.483447 | ||||||||
\(543\) | 4.82166 | − | 4.82166i | 0.206917 | − | 0.206917i | ||||
\(544\) | 4.16103i | 0.178403i | ||||||||
\(545\) | −4.18597 | − | 17.1671i | −0.179307 | − | 0.735357i | ||||
\(546\) | 21.4397i | 0.917536i | ||||||||
\(547\) | −22.8223 | −0.975811 | −0.487906 | − | 0.872896i | \(-0.662239\pi\) | ||||
−0.487906 | + | 0.872896i | \(0.662239\pi\) | |||||||
\(548\) | 7.91811 | − | 7.91811i | 0.338245 | − | 0.338245i | ||||
\(549\) | −8.68618 | + | 8.68618i | −0.370717 | + | 0.370717i | ||||
\(550\) | 12.1941 | − | 6.32265i | 0.519957 | − | 0.269599i | ||||
\(551\) | 16.1084 | 0.686242 | ||||||||
\(552\) | 0.666001 | − | 0.666001i | 0.0283469 | − | 0.0283469i | ||||
\(553\) | 8.52183 | 0.362385 | ||||||||
\(554\) | −16.2009 | −0.688312 | ||||||||
\(555\) | −8.88833 | − | 10.2955i | −0.377289 | − | 0.437020i | ||||
\(556\) | 13.0683 | 0.554221 | ||||||||
\(557\) | 22.2337 | 0.942073 | 0.471036 | − | 0.882114i | \(-0.343880\pi\) | ||||
0.471036 | + | 0.882114i | \(0.343880\pi\) | |||||||
\(558\) | −5.51242 | + | 5.51242i | −0.233359 | + | 0.233359i | ||||
\(559\) | −32.5164 | −1.37530 | ||||||||
\(560\) | 8.93067 | − | 2.17763i | 0.377390 | − | 0.0920216i | ||||
\(561\) | 8.08293 | − | 8.08293i | 0.341261 | − | 0.341261i | ||||
\(562\) | 7.78699 | − | 7.78699i | 0.328474 | − | 0.328474i | ||||
\(563\) | −25.9596 | −1.09407 | −0.547034 | − | 0.837110i | \(-0.684243\pi\) | ||||
−0.547034 | + | 0.837110i | \(0.684243\pi\) | |||||||
\(564\) | 8.55529i | 0.360243i | ||||||||
\(565\) | 16.5876 | − | 27.2855i | 0.697847 | − | 1.14791i | ||||
\(566\) | − | 21.1035i | − | 0.887046i | ||||||
\(567\) | −2.90687 | + | 2.90687i | −0.122077 | + | 0.122077i | ||||
\(568\) | 8.51973 | 0.357480 | ||||||||
\(569\) | 4.18660 | − | 4.18660i | 0.175512 | − | 0.175512i | −0.613884 | − | 0.789396i | \(-0.710394\pi\) |
0.789396 | + | 0.613884i | \(0.210394\pi\) | |||||||
\(570\) | 5.07539 | + | 3.08547i | 0.212585 | + | 0.129236i | ||||
\(571\) | −24.7600 | −1.03617 | −0.518087 | − | 0.855328i | \(-0.673356\pi\) | ||||
−0.518087 | + | 0.855328i | \(0.673356\pi\) | |||||||
\(572\) | 14.3272i | 0.599050i | ||||||||
\(573\) | 10.1705i | 0.424879i | ||||||||
\(574\) | 22.0754 | + | 22.0754i | 0.921409 | + | 0.921409i | ||||
\(575\) | −2.16774 | − | 4.18077i | −0.0904009 | − | 0.174350i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 34.1071i | − | 1.41990i | −0.704254 | − | 0.709948i | \(-0.748718\pi\) | ||
0.704254 | − | 0.709948i | \(-0.251282\pi\) | |||||||
\(578\) | 0.314185 | 0.0130684 | ||||||||
\(579\) | −11.5554 | + | 11.5554i | −0.480226 | + | 0.480226i | ||||
\(580\) | −13.1741 | + | 3.21232i | −0.547023 | + | 0.133384i | ||||
\(581\) | 42.2190 | 1.75154 | ||||||||
\(582\) | 7.13543 | + | 7.13543i | 0.295773 | + | 0.295773i | ||||
\(583\) | −22.8514 | + | 22.8514i | −0.946408 | + | 0.946408i | ||||
\(584\) | 2.98121 | − | 2.98121i | 0.123363 | − | 0.123363i | ||||
\(585\) | 6.05791 | − | 9.96485i | 0.250464 | − | 0.411996i | ||||
\(586\) | 2.76877 | + | 2.76877i | 0.114377 | + | 0.114377i | ||||
\(587\) | −46.3514 | −1.91313 | −0.956564 | − | 0.291522i | \(-0.905838\pi\) | ||||
−0.956564 | + | 0.291522i | \(0.905838\pi\) | |||||||
\(588\) | −7.00021 | − | 7.00021i | −0.288684 | − | 0.288684i | ||||
\(589\) | − | 20.7078i | − | 0.853251i | ||||||
\(590\) | −1.44534 | − | 5.92747i | −0.0595035 | − | 0.244030i | ||||
\(591\) | 16.2400i | 0.668026i | ||||||||
\(592\) | −2.77109 | − | 5.41489i | −0.113891 | − | 0.222551i | ||||
\(593\) | −16.9988 | − | 16.9988i | −0.698058 | − | 0.698058i | 0.265934 | − | 0.963991i | \(-0.414320\pi\) |
−0.963991 | + | 0.265934i | \(0.914320\pi\) | |||||||
\(594\) | −1.94253 | + | 1.94253i | −0.0797030 | + | 0.0797030i | ||||
\(595\) | −9.06118 | − | 37.1608i | −0.371472 | − | 1.52344i | ||||
\(596\) | − | 6.80855i | − | 0.278889i | ||||||
\(597\) | 18.2927i | 0.748669i | ||||||||
\(598\) | 4.91212 | 0.200871 | ||||||||
\(599\) | − | 12.7894i | − | 0.522561i | −0.965263 | − | 0.261281i | \(-0.915855\pi\) | ||
0.965263 | − | 0.261281i | \(-0.0841448\pi\) | |||||||
\(600\) | −4.76613 | − | 1.51128i | −0.194577 | − | 0.0616977i | ||||
\(601\) | 17.7183 | 0.722744 | 0.361372 | − | 0.932422i | \(-0.382308\pi\) | ||||
0.361372 | + | 0.932422i | \(0.382308\pi\) | |||||||
\(602\) | 18.1238 | − | 18.1238i | 0.738672 | − | 0.738672i | ||||
\(603\) | 5.51165 | − | 5.51165i | 0.224452 | − | 0.224452i | ||||
\(604\) | − | 17.8917i | − | 0.728002i | ||||||
\(605\) | 6.59794 | + | 4.01107i | 0.268244 | + | 0.163073i | ||||
\(606\) | 6.64810 | + | 6.64810i | 0.270061 | + | 0.270061i | ||||
\(607\) | 33.5114 | 1.36018 | 0.680092 | − | 0.733127i | \(-0.261940\pi\) | ||||
0.680092 | + | 0.733127i | \(0.261940\pi\) | |||||||
\(608\) | 1.87829 | + | 1.87829i | 0.0761746 | + | 0.0761746i | ||||
\(609\) | 17.6279 | + | 17.6279i | 0.714320 | + | 0.714320i | ||||
\(610\) | 6.50709 | + | 26.6862i | 0.263464 | + | 1.08049i | ||||
\(611\) | −31.5499 | + | 31.5499i | −1.27637 | + | 1.27637i | ||||
\(612\) | −4.16103 | −0.168200 | ||||||||
\(613\) | −1.15839 | + | 1.15839i | −0.0467871 | + | 0.0467871i | −0.730113 | − | 0.683326i | \(-0.760533\pi\) |
0.683326 | + | 0.730113i | \(0.260533\pi\) | |||||||
\(614\) | −6.12720 | − | 6.12720i | −0.247274 | − | 0.247274i | ||||
\(615\) | −4.02278 | − | 16.4978i | −0.162214 | − | 0.665256i | ||||
\(616\) | −7.98561 | − | 7.98561i | −0.321750 | − | 0.321750i | ||||
\(617\) | 15.5057 | + | 15.5057i | 0.624237 | + | 0.624237i | 0.946612 | − | 0.322375i | \(-0.104481\pi\) |
−0.322375 | + | 0.946612i | \(0.604481\pi\) | |||||||
\(618\) | −5.49768 | − | 5.49768i | −0.221149 | − | 0.221149i | ||||
\(619\) | 23.4133 | 0.941060 | 0.470530 | − | 0.882384i | \(-0.344063\pi\) | ||||
0.470530 | + | 0.882384i | \(0.344063\pi\) | |||||||
\(620\) | 4.12953 | + | 16.9356i | 0.165846 | + | 0.680151i | ||||
\(621\) | 0.666001 | + | 0.666001i | 0.0267257 | + | 0.0267257i | ||||
\(622\) | 1.06423 | + | 1.06423i | 0.0426719 | + | 0.0426719i | ||||
\(623\) | 9.46300i | 0.379127i | ||||||||
\(624\) | 3.68777 | − | 3.68777i | 0.147629 | − | 0.147629i | ||||
\(625\) | −14.4059 | + | 20.4321i | −0.576237 | + | 0.817283i | ||||
\(626\) | 7.63668 | 0.305223 | ||||||||
\(627\) | − | 7.29726i | − | 0.291424i | ||||||
\(628\) | 3.05662 | − | 3.05662i | 0.121972 | − | 0.121972i | ||||
\(629\) | −22.5315 | + | 11.5306i | −0.898391 | + | 0.459756i | ||||
\(630\) | 2.17763 | + | 8.93067i | 0.0867588 | + | 0.355806i | ||||
\(631\) | −29.2036 | − | 29.2036i | −1.16258 | − | 1.16258i | −0.983910 | − | 0.178667i | \(-0.942821\pi\) |
−0.178667 | − | 0.983910i | \(-0.557179\pi\) | |||||||
\(632\) | −1.46581 | − | 1.46581i | −0.0583067 | − | 0.0583067i | ||||
\(633\) | −16.5894 | + | 16.5894i | −0.659368 | + | 0.659368i | ||||
\(634\) | −19.5287 | − | 19.5287i | −0.775584 | − | 0.775584i | ||||
\(635\) | 24.6360 | − | 6.00718i | 0.977651 | − | 0.238388i | ||||
\(636\) | 11.7637 | 0.466462 | ||||||||
\(637\) | − | 51.6303i | − | 2.04567i | ||||||
\(638\) | 11.7800 | + | 11.7800i | 0.466373 | + | 0.466373i | ||||
\(639\) | 8.51973i | 0.337035i | ||||||||
\(640\) | −1.91070 | − | 1.16157i | −0.0755269 | − | 0.0459149i | ||||
\(641\) | −27.5707 | −1.08898 | −0.544488 | − | 0.838769i | \(-0.683276\pi\) | ||||
−0.544488 | + | 0.838769i | \(0.683276\pi\) | |||||||
\(642\) | 8.01912i | 0.316489i | ||||||||
\(643\) | − | 18.0002i | − | 0.709858i | −0.934893 | − | 0.354929i | \(-0.884505\pi\) | ||
0.934893 | − | 0.354929i | \(-0.115495\pi\) | |||||||
\(644\) | −2.73789 | + | 2.73789i | −0.107888 | + | 0.107888i | ||||
\(645\) | −13.5446 | + | 3.30269i | −0.533320 | + | 0.130043i | ||||
\(646\) | 7.81562 | − | 7.81562i | 0.307501 | − | 0.307501i | ||||
\(647\) | 26.1609 | 1.02849 | 0.514245 | − | 0.857643i | \(-0.328072\pi\) | ||||
0.514245 | + | 0.857643i | \(0.328072\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.30021 | + | 5.30021i | −0.208052 | + | 0.208052i | ||||
\(650\) | −12.0032 | − | 23.1497i | −0.470802 | − | 0.908004i | ||||
\(651\) | 22.6612 | − | 22.6612i | 0.888163 | − | 0.888163i | ||||
\(652\) | 19.5350i | 0.765050i | ||||||||
\(653\) | − | 27.1758i | − | 1.06347i | −0.846911 | − | 0.531735i | \(-0.821540\pi\) | ||
0.846911 | − | 0.531735i | \(-0.178460\pi\) | |||||||
\(654\) | 7.90229 | 0.309004 | ||||||||
\(655\) | 4.97173 | + | 20.3895i | 0.194261 | + | 0.796685i | ||||
\(656\) | − | 7.59421i | − | 0.296504i | ||||||
\(657\) | 2.98121 | + | 2.98121i | 0.116308 | + | 0.116308i | ||||
\(658\) | − | 35.1702i | − | 1.37108i | ||||||
\(659\) | 11.2236 | 0.437210 | 0.218605 | − | 0.975813i | \(-0.429849\pi\) | ||||
0.218605 | + | 0.975813i | \(0.429849\pi\) | |||||||
\(660\) | 1.45521 | + | 5.96796i | 0.0566440 | + | 0.232303i | ||||
\(661\) | −1.74533 | − | 1.74533i | −0.0678853 | − | 0.0678853i | 0.672349 | − | 0.740234i | \(-0.265285\pi\) |
−0.740234 | + | 0.672349i | \(0.765285\pi\) | |||||||
\(662\) | 10.6002 | − | 10.6002i | 0.411988 | − | 0.411988i | ||||
\(663\) | −15.3449 | − | 15.3449i | −0.595948 | − | 0.595948i | ||||
\(664\) | −7.26193 | − | 7.26193i | −0.281818 | − | 0.281818i | ||||
\(665\) | −20.8646 | − | 12.6842i | −0.809094 | − | 0.491871i | ||||
\(666\) | 5.41489 | − | 2.77109i | 0.209823 | − | 0.107378i | ||||
\(667\) | 4.03879 | − | 4.03879i | 0.156382 | − | 0.156382i | ||||
\(668\) | 7.60664i | 0.294310i | ||||||||
\(669\) | −4.00667 | −0.154907 | ||||||||
\(670\) | −4.12895 | − | 16.9332i | −0.159515 | − | 0.654188i | ||||
\(671\) | 23.8623 | − | 23.8623i | 0.921192 | − | 0.921192i | ||||
\(672\) | 4.11094i | 0.158583i | ||||||||
\(673\) | 21.3478 | + | 21.3478i | 0.822898 | + | 0.822898i | 0.986523 | − | 0.163624i | \(-0.0523185\pi\) |
−0.163624 | + | 0.986523i | \(0.552318\pi\) | |||||||
\(674\) | 14.7087 | + | 14.7087i | 0.566558 | + | 0.566558i | ||||
\(675\) | 1.51128 | − | 4.76613i | 0.0581692 | − | 0.183449i | ||||
\(676\) | 14.1993 | 0.546127 | ||||||||
\(677\) | −29.6755 | − | 29.6755i | −1.14052 | − | 1.14052i | −0.988355 | − | 0.152168i | \(-0.951375\pi\) |
−0.152168 | − | 0.988355i | \(-0.548625\pi\) | |||||||
\(678\) | 10.0978 | + | 10.0978i | 0.387803 | + | 0.387803i | ||||
\(679\) | −29.3333 | − | 29.3333i | −1.12571 | − | 1.12571i | ||||
\(680\) | −4.83331 | + | 7.95047i | −0.185349 | + | 0.304887i | ||||
\(681\) | −5.29891 | − | 5.29891i | −0.203055 | − | 0.203055i | ||||
\(682\) | 15.1435 | − | 15.1435i | 0.579873 | − | 0.579873i | ||||
\(683\) | −3.99926 | −0.153027 | −0.0765137 | − | 0.997069i | \(-0.524379\pi\) | ||||
−0.0765137 | + | 0.997069i | \(0.524379\pi\) | |||||||
\(684\) | −1.87829 | + | 1.87829i | −0.0718181 | + | 0.0718181i | ||||
\(685\) | 24.3265 | − | 5.93171i | 0.929469 | − | 0.226639i | ||||
\(686\) | 8.42932 | + | 8.42932i | 0.321833 | + | 0.321833i | ||||
\(687\) | 17.0363 | + | 17.0363i | 0.649976 | + | 0.649976i | ||||
\(688\) | −6.23482 | −0.237700 | ||||||||
\(689\) | 43.3819 | + | 43.3819i | 1.65272 | + | 1.65272i | ||||
\(690\) | 2.04613 | − | 0.498923i | 0.0778949 | − | 0.0189937i | ||||
\(691\) | 20.3772i | 0.775184i | 0.921831 | + | 0.387592i | \(0.126693\pi\) | ||||
−0.921831 | + | 0.387592i | \(0.873307\pi\) | |||||||
\(692\) | −17.6561 | + | 17.6561i | −0.671185 | + | 0.671185i | ||||
\(693\) | 7.98561 | − | 7.98561i | 0.303348 | − | 0.303348i | ||||
\(694\) | 5.20503 | 0.197580 | ||||||||
\(695\) | 24.9697 | + | 15.1797i | 0.947153 | + | 0.575801i | ||||
\(696\) | − | 6.06423i | − | 0.229864i | ||||||
\(697\) | −31.5998 | −1.19693 | ||||||||
\(698\) | 8.31963i | 0.314902i | ||||||||
\(699\) | − | 11.0100i | − | 0.416435i | ||||||
\(700\) | 19.5933 | + | 6.21277i | 0.740556 | + | 0.234821i | ||||
\(701\) | −5.28962 | + | 5.28962i | −0.199786 | + | 0.199786i | −0.799908 | − | 0.600122i | \(-0.795119\pi\) |
0.600122 | + | 0.799908i | \(0.295119\pi\) | |||||||
\(702\) | 3.68777 | + | 3.68777i | 0.139186 | + | 0.139186i | ||||
\(703\) | −4.96581 | + | 15.3756i | −0.187289 | + | 0.579903i | ||||
\(704\) | 2.74715i | 0.103537i | ||||||||
\(705\) | −9.93753 | + | 16.3466i | −0.374269 | + | 0.615647i | ||||
\(706\) | 32.6034i | 1.22704i | ||||||||
\(707\) | −27.3299 | − | 27.3299i | −1.02785 | − | 1.02785i | ||||
\(708\) | 2.72851 | 0.102544 | ||||||||
\(709\) | −17.3563 | − | 17.3563i | −0.651828 | − | 0.651828i | 0.301605 | − | 0.953433i | \(-0.402478\pi\) |
−0.953433 | + | 0.301605i | \(0.902478\pi\) | |||||||
\(710\) | 16.2786 | + | 9.89623i | 0.610926 | + | 0.371399i | ||||
\(711\) | 1.46581 | − | 1.46581i | 0.0549721 | − | 0.0549721i | ||||
\(712\) | 1.62770 | − | 1.62770i | 0.0610005 | − | 0.0610005i | ||||
\(713\) | −5.19197 | − | 5.19197i | −0.194441 | − | 0.194441i | ||||
\(714\) | 17.1057 | 0.640166 | ||||||||
\(715\) | −16.6420 | + | 27.3750i | −0.622375 | + | 1.02377i | ||||
\(716\) | −5.23093 | + | 5.23093i | −0.195489 | + | 0.195489i | ||||
\(717\) | −2.66477 | −0.0995175 | ||||||||
\(718\) | 17.3163i | 0.646240i | ||||||||
\(719\) | 10.6066i | 0.395558i | 0.980247 | + | 0.197779i | \(0.0633729\pi\) | ||||
−0.980247 | + | 0.197779i | \(0.936627\pi\) | |||||||
\(720\) | 1.16157 | − | 1.91070i | 0.0432890 | − | 0.0712075i | ||||
\(721\) | 22.6006 | + | 22.6006i | 0.841691 | + | 0.841691i | ||||
\(722\) | 11.9441i | 0.444512i | ||||||||
\(723\) | 25.6351i | 0.953381i | ||||||||
\(724\) | 6.81886 | 0.253421 | ||||||||
\(725\) | −28.9029 | − | 9.16475i | −1.07343 | − | 0.340370i | ||||
\(726\) | −2.44175 | + | 2.44175i | −0.0906219 | + | 0.0906219i | ||||
\(727\) | 41.4047 | 1.53561 | 0.767807 | − | 0.640681i | \(-0.221348\pi\) | ||||
0.767807 | + | 0.640681i | \(0.221348\pi\) | |||||||
\(728\) | −15.1602 | + | 15.1602i | −0.561874 | + | 0.561874i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 9.15906 | − | 2.23332i | 0.338992 | − | 0.0826588i | ||||
\(731\) | 25.9433i | 0.959548i | ||||||||
\(732\) | −12.2841 | −0.454034 | ||||||||
\(733\) | 33.6863 | − | 33.6863i | 1.24423 | − | 1.24423i | 0.286005 | − | 0.958228i | \(-0.407673\pi\) |
0.958228 | − | 0.286005i | \(-0.0923272\pi\) | |||||||
\(734\) | 19.8485 | − | 19.8485i | 0.732622 | − | 0.732622i | ||||
\(735\) | −5.24408 | − | 21.5065i | −0.193431 | − | 0.793279i | ||||
\(736\) | 0.941868 | 0.0347177 | ||||||||
\(737\) | −15.1413 | + | 15.1413i | −0.557738 | + | 0.557738i | ||||
\(738\) | 7.59421 | 0.279547 | ||||||||
\(739\) | 30.7911 | 1.13267 | 0.566335 | − | 0.824175i | \(-0.308361\pi\) | ||||
0.566335 | + | 0.824175i | \(0.308361\pi\) | |||||||
\(740\) | 0.995030 | − | 13.5650i | 0.0365780 | − | 0.498660i | ||||
\(741\) | −13.8534 | −0.508917 | ||||||||
\(742\) | −48.3600 | −1.77535 | ||||||||
\(743\) | 21.8367 | − | 21.8367i | 0.801110 | − | 0.801110i | −0.182159 | − | 0.983269i | \(-0.558309\pi\) |
0.983269 | + | 0.182159i | \(0.0583086\pi\) | |||||||
\(744\) | −7.79574 | −0.285806 | ||||||||
\(745\) | 7.90857 | − | 13.0091i | 0.289748 | − | 0.476615i | ||||
\(746\) | −19.3419 | + | 19.3419i | −0.708158 | + | 0.708158i | ||||
\(747\) | 7.26193 | − | 7.26193i | 0.265700 | − | 0.265700i | ||||
\(748\) | 11.4310 | 0.417958 | ||||||||
\(749\) | − | 32.9661i | − | 1.20455i | ||||||
\(750\) | −7.35119 | − | 8.42378i | −0.268427 | − | 0.307593i | ||||
\(751\) | − | 4.98993i | − | 0.182085i | −0.995847 | − | 0.0910426i | \(-0.970980\pi\) | ||
0.995847 | − | 0.0910426i | \(-0.0290199\pi\) | |||||||
\(752\) | −6.04950 | + | 6.04950i | −0.220603 | + | 0.220603i | ||||
\(753\) | −14.5608 | −0.530624 | ||||||||
\(754\) | 22.3635 | − | 22.3635i | 0.814430 | − | 0.814430i | ||||
\(755\) | 20.7824 | − | 34.1856i | 0.756348 | − | 1.24414i | ||||
\(756\) | −4.11094 | −0.149513 | ||||||||
\(757\) | 5.34349i | 0.194213i | 0.995274 | + | 0.0971063i | \(0.0309587\pi\) | ||||
−0.995274 | + | 0.0971063i | \(0.969041\pi\) | |||||||
\(758\) | − | 3.56273i | − | 0.129404i | ||||||
\(759\) | −1.82961 | − | 1.82961i | −0.0664105 | − | 0.0664105i | ||||
\(760\) | 1.40708 | + | 5.77059i | 0.0510403 | + | 0.209321i | ||||
\(761\) | 29.9342i | 1.08511i | 0.840019 | + | 0.542557i | \(0.182544\pi\) | ||||
−0.840019 | + | 0.542557i | \(0.817456\pi\) | |||||||
\(762\) | 11.3404i | 0.410818i | ||||||||
\(763\) | −32.4858 | −1.17607 | ||||||||
\(764\) | −7.19163 | + | 7.19163i | −0.260184 | + | 0.260184i | ||||
\(765\) | −7.95047 | − | 4.83331i | −0.287450 | − | 0.174749i | ||||
\(766\) | 17.5102 | 0.632670 | ||||||||
\(767\) | 10.0621 | + | 10.0621i | 0.363322 | + | 0.363322i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | 17.9570 | − | 17.9570i | 0.647546 | − | 0.647546i | −0.304853 | − | 0.952399i | \(-0.598607\pi\) |
0.952399 | + | 0.304853i | \(0.0986074\pi\) | |||||||
\(770\) | −5.98228 | − | 24.5339i | −0.215586 | − | 0.884141i | ||||
\(771\) | −1.90752 | − | 1.90752i | −0.0686975 | − | 0.0686975i | ||||
\(772\) | −16.3418 | −0.588154 | ||||||||
\(773\) | 20.5041 | + | 20.5041i | 0.737483 | + | 0.737483i | 0.972090 | − | 0.234607i | \(-0.0753804\pi\) |
−0.234607 | + | 0.972090i | \(0.575380\pi\) | |||||||
\(774\) | − | 6.23482i | − | 0.224106i | ||||||
\(775\) | −11.7815 | + | 37.1556i | −0.423206 | + | 1.33467i | ||||
\(776\) | 10.0910i | 0.362247i | ||||||||
\(777\) | −22.2603 | + | 11.3918i | −0.798583 | + | 0.408678i | ||||
\(778\) | −5.52680 | − | 5.52680i | −0.198145 | − | 0.198145i | ||||
\(779\) | −14.2641 | + | 14.2641i | −0.511065 | + | 0.511065i | ||||
\(780\) | 11.3298 | − | 2.76262i | 0.405672 | − | 0.0989178i | ||||
\(781\) | − | 23.4050i | − | 0.837496i | ||||||
\(782\) | − | 3.91914i | − | 0.140148i | ||||||
\(783\) | 6.06423 | 0.216718 | ||||||||
\(784\) | − | 9.89979i | − | 0.353564i | ||||||
\(785\) | 9.39073 | − | 2.28981i | 0.335170 | − | 0.0817268i | ||||
\(786\) | −9.38564 | −0.334775 | ||||||||
\(787\) | 0.00644958 | − | 0.00644958i | 0.000229903 | − | 0.000229903i | −0.706992 | − | 0.707222i | \(-0.749948\pi\) |
0.707222 | + | 0.706992i | \(0.249948\pi\) | |||||||
\(788\) | −11.4834 | + | 11.4834i | −0.409080 | + | 0.409080i | ||||
\(789\) | 21.2140i | 0.755238i | ||||||||
\(790\) | −1.09808 | − | 4.50335i | −0.0390680 | − | 0.160222i | ||||
\(791\) | −41.5113 | − | 41.5113i | −1.47597 | − | 1.47597i | ||||
\(792\) | −2.74715 | −0.0976158 | ||||||||
\(793\) | −45.3010 | − | 45.3010i | −1.60869 | − | 1.60869i | ||||
\(794\) | −7.17123 | − | 7.17123i | −0.254497 | − | 0.254497i | ||||
\(795\) | 22.4769 | + | 13.6644i | 0.797175 | + | 0.484625i | ||||
\(796\) | −12.9349 | + | 12.9349i | −0.458464 | + | 0.458464i | ||||
\(797\) | −16.8684 | −0.597510 | −0.298755 | − | 0.954330i | \(-0.596571\pi\) | ||||
−0.298755 | + | 0.954330i | \(0.596571\pi\) | |||||||
\(798\) | 7.72152 | − | 7.72152i | 0.273339 | − | 0.273339i | ||||
\(799\) | 25.1722 | + | 25.1722i | 0.890527 | + | 0.890527i | ||||
\(800\) | −2.30153 | − | 4.43880i | −0.0813714 | − | 0.156935i | ||||
\(801\) | 1.62770 | + | 1.62770i | 0.0575118 | + | 0.0575118i | ||||
\(802\) | −12.3057 | − | 12.3057i | −0.434530 | − | 0.434530i | ||||
\(803\) | −8.18983 | − | 8.18983i | −0.289013 | − | 0.289013i | ||||
\(804\) | 7.79465 | 0.274896 | ||||||||
\(805\) | −8.41151 | + | 2.05104i | −0.296467 | + | 0.0722896i | ||||
\(806\) | −28.7489 | − | 28.7489i | −1.01264 | − | 1.01264i | ||||
\(807\) | 2.73124 | + | 2.73124i | 0.0961444 | + | 0.0961444i | ||||
\(808\) | 9.40183i | 0.330755i | ||||||||
\(809\) | −32.7152 | + | 32.7152i | −1.15020 | + | 1.15020i | −0.163692 | + | 0.986511i | \(0.552340\pi\) |
−0.986511 | + | 0.163692i | \(0.947660\pi\) | |||||||
\(810\) | 1.91070 | + | 1.16157i | 0.0671351 | + | 0.0408133i | ||||
\(811\) | −32.0761 | −1.12634 | −0.563172 | − | 0.826339i | \(-0.690419\pi\) | ||||
−0.563172 | + | 0.826339i | \(0.690419\pi\) | |||||||
\(812\) | 24.9297i | 0.874860i | ||||||||
\(813\) | −7.95854 | + | 7.95854i | −0.279118 | + | 0.279118i | ||||
\(814\) | −14.8755 | + | 7.61262i | −0.521387 | + | 0.266822i | ||||
\(815\) | −22.6912 | + | 37.3255i | −0.794838 | + | 1.30745i | ||||
\(816\) | −2.94229 | − | 2.94229i | −0.103001 | − | 0.103001i | ||||
\(817\) | 11.7108 | + | 11.7108i | 0.409709 | + | 0.409709i | ||||
\(818\) | 20.8384 | − | 20.8384i | 0.728598 | − | 0.728598i | ||||
\(819\) | −15.1602 | − | 15.1602i | −0.529740 | − | 0.529740i | ||||
\(820\) | 8.82118 | − | 14.5102i | 0.308049 | − | 0.506720i | ||||
\(821\) | 46.5821 | 1.62573 | 0.812863 | − | 0.582455i | \(-0.197908\pi\) | ||||
0.812863 | + | 0.582455i | \(0.197908\pi\) | |||||||
\(822\) | 11.1979i | 0.390572i | ||||||||
\(823\) | 14.9085 | + | 14.9085i | 0.519678 | + | 0.519678i | 0.917474 | − | 0.397796i | \(-0.130225\pi\) |
−0.397796 | + | 0.917474i | \(0.630225\pi\) | |||||||
\(824\) | − | 7.77490i | − | 0.270851i | ||||||
\(825\) | −4.15171 | + | 13.0933i | −0.144544 | + | 0.455850i | ||||
\(826\) | −11.2167 | −0.390280 | ||||||||
\(827\) | − | 32.9874i | − | 1.14708i | −0.819176 | − | 0.573542i | \(-0.805569\pi\) | ||
0.819176 | − | 0.573542i | \(-0.194431\pi\) | |||||||
\(828\) | 0.941868i | 0.0327322i | ||||||||
\(829\) | 26.5468 | − | 26.5468i | 0.922009 | − | 0.922009i | −0.0751625 | − | 0.997171i | \(-0.523948\pi\) |
0.997171 | + | 0.0751625i | \(0.0239475\pi\) | |||||||
\(830\) | −5.44014 | − | 22.3106i | −0.188830 | − | 0.774411i | ||||
\(831\) | 11.4558 | − | 11.4558i | 0.397397 | − | 0.397397i | ||||
\(832\) | 5.21529 | 0.180808 | ||||||||
\(833\) | −41.1933 | −1.42726 | ||||||||
\(834\) | −9.24072 | + | 9.24072i | −0.319980 | + | 0.319980i | ||||
\(835\) | −8.83562 | + | 14.5340i | −0.305769 | + | 0.502970i | ||||
\(836\) | 5.15994 | − | 5.15994i | 0.178460 | − | 0.178460i | ||||
\(837\) | − | 7.79574i | − | 0.269460i | ||||||
\(838\) | 36.4587i | 1.25945i | ||||||||
\(839\) | −28.9665 | −1.00004 | −0.500018 | − | 0.866015i | \(-0.666673\pi\) | ||||
−0.500018 | + | 0.866015i | \(0.666673\pi\) | |||||||
\(840\) | −4.77512 | + | 7.85475i | −0.164757 | + | 0.271015i | ||||
\(841\) | − | 7.77493i | − | 0.268101i | ||||||
\(842\) | −15.1883 | − | 15.1883i | −0.523422 | − | 0.523422i | ||||
\(843\) | 11.0125i | 0.379289i | ||||||||
\(844\) | −23.4609 | −0.807558 | ||||||||
\(845\) | 27.1305 | + | 16.4934i | 0.933319 | + | 0.567391i | ||||
\(846\) | −6.04950 | − | 6.04950i | −0.207986 | − | 0.207986i | ||||
\(847\) | 10.0379 | − | 10.0379i | 0.344906 | − | 0.344906i | ||||
\(848\) | 8.31822 | + | 8.31822i | 0.285649 | + | 0.285649i | ||||
\(849\) | 14.9224 | + | 14.9224i | 0.512136 | + | 0.512136i | ||||
\(850\) | −18.4700 | + | 9.57674i | −0.633516 | + | 0.328479i | ||||
\(851\) | 2.61001 | + | 5.10011i | 0.0894698 | + | 0.174830i | ||||
\(852\) | −6.02436 | + | 6.02436i | −0.206391 | + | 0.206391i | ||||
\(853\) | 46.9335i | 1.60697i | 0.595323 | + | 0.803487i | \(0.297024\pi\) | ||||
−0.595323 | + | 0.803487i | \(0.702976\pi\) | |||||||
\(854\) | 50.4992 | 1.72805 | ||||||||
\(855\) | −5.77059 | + | 1.40708i | −0.197350 | + | 0.0481213i | ||||
\(856\) | −5.67037 | + | 5.67037i | −0.193809 | + | 0.193809i | ||||
\(857\) | 20.5633i | 0.702429i | 0.936295 | + | 0.351214i | \(0.114231\pi\) | ||||
−0.936295 | + | 0.351214i | \(0.885769\pi\) | |||||||
\(858\) | −10.1309 | − | 10.1309i | −0.345862 | − | 0.345862i | ||||
\(859\) | 35.4390 | + | 35.4390i | 1.20916 | + | 1.20916i | 0.971299 | + | 0.237863i | \(0.0764469\pi\) |
0.237863 | + | 0.971299i | \(0.423553\pi\) | |||||||
\(860\) | −11.9129 | − | 7.24216i | −0.406225 | − | 0.246956i | ||||
\(861\) | −31.2193 | −1.06395 | ||||||||
\(862\) | 6.39166 | + | 6.39166i | 0.217701 | + | 0.217701i | ||||
\(863\) | −36.0727 | − | 36.0727i | −1.22793 | − | 1.22793i | −0.964746 | − | 0.263181i | \(-0.915228\pi\) |
−0.263181 | − | 0.964746i | \(-0.584772\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | −54.2443 | + | 13.2268i | −1.84436 | + | 0.449723i | ||||
\(866\) | −15.4619 | − | 15.4619i | −0.525418 | − | 0.525418i | ||||
\(867\) | −0.222162 | + | 0.222162i | −0.00754503 | + | 0.00754503i | ||||
\(868\) | 32.0478 | 1.08777 | ||||||||
\(869\) | −4.02680 | + | 4.02680i | −0.136600 | + | 0.136600i | ||||
\(870\) | 7.04401 | − | 11.5869i | 0.238814 | − | 0.392833i | ||||
\(871\) | 28.7449 | + | 28.7449i | 0.973983 | + | 0.973983i | ||||
\(872\) | 5.58777 | + | 5.58777i | 0.189226 | + | 0.189226i | ||||
\(873\) | −10.0910 | −0.341529 | ||||||||
\(874\) | −1.76910 | − | 1.76910i | −0.0598407 | − | 0.0598407i | ||||
\(875\) | 30.2203 | + | 34.6296i | 1.02163 | + | 1.17069i | ||||
\(876\) | 4.21607i | 0.142448i | ||||||||
\(877\) | 11.9117 | − | 11.9117i | 0.402229 | − | 0.402229i | −0.476789 | − | 0.879018i | \(-0.658199\pi\) |
0.879018 | + | 0.476789i | \(0.158199\pi\) | |||||||
\(878\) | −15.6685 | + | 15.6685i | −0.528785 | + | 0.528785i | ||||
\(879\) | −3.91564 | −0.132071 | ||||||||
\(880\) | −3.19100 | + | 5.24898i | −0.107569 | + | 0.176943i | ||||
\(881\) | 0.418792i | 0.0141095i | 0.999975 | + | 0.00705473i | \(0.00224561\pi\) | ||||
−0.999975 | + | 0.00705473i | \(0.997754\pi\) | |||||||
\(882\) | 9.89979 | 0.333343 | ||||||||
\(883\) | 26.3766i | 0.887643i | 0.896115 | + | 0.443821i | \(0.146378\pi\) | ||||
−0.896115 | + | 0.443821i | \(0.853622\pi\) | |||||||
\(884\) | − | 21.7010i | − | 0.729884i | ||||||
\(885\) | 5.21336 | + | 3.16934i | 0.175245 | + | 0.106536i | ||||
\(886\) | −27.2120 | + | 27.2120i | −0.914206 | + | 0.914206i | ||||
\(887\) | 22.4081 | + | 22.4081i | 0.752390 | + | 0.752390i | 0.974925 | − | 0.222535i | \(-0.0714332\pi\) |
−0.222535 | + | 0.974925i | \(0.571433\pi\) | |||||||
\(888\) | 5.78837 | + | 1.86945i | 0.194245 | + | 0.0627345i | ||||
\(889\) | − | 46.6195i | − | 1.56357i | ||||||
\(890\) | 5.00071 | − | 1.21936i | 0.167624 | − | 0.0408730i | ||||
\(891\) | − | 2.74715i | − | 0.0920330i | ||||||
\(892\) | −2.83314 | − | 2.83314i | −0.0948606 | − | 0.0948606i | ||||
\(893\) | 22.7254 | 0.760477 | ||||||||
\(894\) | 4.81437 | + | 4.81437i | 0.161017 | + | 0.161017i | ||||
\(895\) | −16.0708 | + | 3.91865i | −0.537187 | + | 0.130986i | ||||
\(896\) | −2.90687 | + | 2.90687i | −0.0971117 | + | 0.0971117i | ||||
\(897\) | −3.47339 | + | 3.47339i | −0.115973 | + | 0.115973i | ||||
\(898\) | 18.9735 | + | 18.9735i | 0.633155 | + | 0.633155i | ||||
\(899\) | −47.2752 | −1.57672 | ||||||||
\(900\) | 4.43880 | − | 2.30153i | 0.147960 | − | 0.0767176i | ||||
\(901\) | 34.6124 | − | 34.6124i | 1.15310 | − | 1.15310i | ||||
\(902\) | −20.8624 | −0.694644 | ||||||||
\(903\) | 25.6310i | 0.852945i | ||||||||
\(904\) | 14.2804i | 0.474959i | ||||||||
\(905\) | 13.0288 | + | 7.92055i | 0.433091 | + | 0.263288i | ||||
\(906\) | 12.6513 | + | 12.6513i | 0.420312 | + | 0.420312i | ||||
\(907\) | − | 23.3935i | − | 0.776769i | −0.921497 | − | 0.388384i | \(-0.873033\pi\) | ||
0.921497 | − | 0.388384i | \(-0.126967\pi\) | |||||||
\(908\) | − | 7.49379i | − | 0.248690i | ||||||
\(909\) | −9.40183 | −0.311839 | ||||||||
\(910\) | −46.5761 | + | 11.3570i | −1.54398 | + | 0.376480i | ||||
\(911\) | 26.3920 | − | 26.3920i | 0.874406 | − | 0.874406i | −0.118543 | − | 0.992949i | \(-0.537822\pi\) |
0.992949 | + | 0.118543i | \(0.0378223\pi\) | |||||||
\(912\) | −2.65630 | −0.0879589 | ||||||||
\(913\) | −19.9496 | + | 19.9496i | −0.660237 | + | 0.660237i | ||||
\(914\) | − | 9.71477i | − | 0.321336i | ||||||
\(915\) | −23.4712 | − | 14.2688i | −0.775935 | − | 0.471712i | ||||
\(916\) | 24.0930i | 0.796055i | ||||||||
\(917\) | 38.5838 | 1.27415 | ||||||||
\(918\) | 2.94229 | − | 2.94229i | 0.0971102 | − | 0.0971102i | ||||
\(919\) | −28.2985 | + | 28.2985i | −0.933482 | + | 0.933482i | −0.997922 | − | 0.0644393i | \(-0.979474\pi\) |
0.0644393 | + | 0.997922i | \(0.479474\pi\) | |||||||
\(920\) | 1.79963 | + | 1.09404i | 0.0593319 | + | 0.0360695i | ||||
\(921\) | 8.66517 | 0.285527 | ||||||||
\(922\) | −17.2735 | + | 17.2735i | −0.568872 | + | 0.568872i | ||||
\(923\) | −44.4329 | −1.46253 | ||||||||
\(924\) | 11.2934 | 0.371524 | ||||||||
\(925\) | 17.6579 | − | 24.7629i | 0.580587 | − | 0.814198i | ||||
\(926\) | −16.3891 | −0.538578 | ||||||||
\(927\) | 7.77490 | 0.255361 | ||||||||
\(928\) | 4.28806 | − | 4.28806i | 0.140762 | − | 0.140762i | ||||
\(929\) | 31.6997 | 1.04003 | 0.520016 | − | 0.854156i | \(-0.325926\pi\) | ||||
0.520016 | + | 0.854156i | \(0.325926\pi\) | |||||||
\(930\) | −14.8953 | − | 9.05527i | −0.488436 | − | 0.296934i | ||||
\(931\) | −18.5947 | + | 18.5947i | −0.609415 | + | 0.609415i | ||||
\(932\) | 7.78522 | − | 7.78522i | 0.255013 | − | 0.255013i | ||||
\(933\) | −1.50505 | −0.0492732 | ||||||||
\(934\) | 1.29508i | 0.0423764i | ||||||||
\(935\) | 21.8412 | + | 13.2778i | 0.714282 | + | 0.434232i | ||||
\(936\) | 5.21529i | 0.170467i | ||||||||
\(937\) | 30.6502 | − | 30.6502i | 1.00130 | − | 1.00130i | 0.00129830 | − | 0.999999i | \(-0.499587\pi\) |
0.999999 | − | 0.00129830i | \(-0.000413263\pi\) | |||||||
\(938\) | −32.0433 | −1.04625 | ||||||||
\(939\) | −5.39995 | + | 5.39995i | −0.176221 | + | 0.176221i | ||||
\(940\) | −18.5857 | + | 4.53187i | −0.606197 | + | 0.147813i | ||||
\(941\) | −7.87515 | −0.256722 | −0.128361 | − | 0.991727i | \(-0.540972\pi\) | ||||
−0.128361 | + | 0.991727i | \(0.540972\pi\) | |||||||
\(942\) | 4.32271i | 0.140841i | ||||||||
\(943\) | 7.15275i | 0.232925i | ||||||||
\(944\) | 1.92935 | + | 1.92935i | 0.0627949 | + | 0.0627949i | ||||
\(945\) | −7.85475 | − | 4.77512i | −0.255515 | − | 0.155335i | ||||
\(946\) | 17.1280i | 0.556880i | ||||||||
\(947\) | 7.99597i | 0.259834i | 0.991525 | + | 0.129917i | \(0.0414711\pi\) | ||||
−0.991525 | + | 0.129917i | \(0.958529\pi\) | |||||||
\(948\) | 2.07297 | 0.0673268 | ||||||||
\(949\) | −15.5479 | + | 15.5479i | −0.504706 | + | 0.504706i | ||||
\(950\) | −4.01441 | + | 12.6603i | −0.130245 | + | 0.410754i | ||||
\(951\) | 27.6178 | 0.895567 | ||||||||
\(952\) | 12.0956 | + | 12.0956i | 0.392020 | + | 0.392020i | ||||
\(953\) | 40.8082 | − | 40.8082i | 1.32191 | − | 1.32191i | 0.409677 | − | 0.912231i | \(-0.365641\pi\) |
0.912231 | − | 0.409677i | \(-0.134359\pi\) | |||||||
\(954\) | −8.31822 | + | 8.31822i | −0.269312 | + | 0.269312i | ||||
\(955\) | −22.0946 | + | 5.38748i | −0.714964 | + | 0.174335i | ||||
\(956\) | −1.88427 | − | 1.88427i | −0.0609418 | − | 0.0609418i | ||||
\(957\) | −16.6594 | −0.538521 | ||||||||
\(958\) | −27.0885 | − | 27.0885i | −0.875189 | − | 0.875189i | ||||
\(959\) | − | 46.0338i | − | 1.48651i | ||||||
\(960\) | 2.17242 | − | 0.529716i | 0.0701145 | − | 0.0170965i | ||||
\(961\) | 29.7736i | 0.960439i | ||||||||
\(962\) | 14.4521 | + | 28.2402i | 0.465953 | + | 0.910502i | ||||
\(963\) | −5.67037 | − | 5.67037i | −0.182725 | − | 0.182725i | ||||
\(964\) | −18.1268 | + | 18.1268i | −0.583824 | + | 0.583824i | ||||
\(965\) | −31.2242 | − | 18.9821i | −1.00514 | − | 0.611055i | ||||
\(966\) | − | 3.87196i | − | 0.124578i | ||||||
\(967\) | 35.2833i | 1.13463i | 0.823500 | + | 0.567317i | \(0.192018\pi\) | ||||
−0.823500 | + | 0.567317i | \(0.807982\pi\) | |||||||
\(968\) | −3.45316 | −0.110989 | ||||||||
\(969\) | 11.0529i | 0.355072i | ||||||||
\(970\) | −11.7214 | + | 19.2809i | −0.376351 | + | 0.619072i | ||||
\(971\) | −29.9340 | −0.960629 | −0.480314 | − | 0.877096i | \(-0.659477\pi\) | ||||
−0.480314 | + | 0.877096i | \(0.659477\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 37.9880 | − | 37.9880i | 1.21784 | − | 1.21784i | ||||
\(974\) | − | 27.5508i | − | 0.882783i | ||||||
\(975\) | 24.8568 | + | 7.88177i | 0.796054 | + | 0.252419i | ||||
\(976\) | −8.68618 | − | 8.68618i | −0.278038 | − | 0.278038i | ||||
\(977\) | −55.5148 | −1.77608 | −0.888038 | − | 0.459770i | \(-0.847932\pi\) | ||||
−0.888038 | + | 0.459770i | \(0.847932\pi\) | |||||||
\(978\) | −13.8133 | − | 13.8133i | −0.441702 | − | 0.441702i | ||||
\(979\) | −4.47153 | − | 4.47153i | −0.142911 | − | 0.142911i | ||||
\(980\) | 11.4993 | − | 18.9155i | 0.367330 | − | 0.604234i | ||||
\(981\) | −5.58777 | + | 5.58777i | −0.178404 | + | 0.178404i | ||||
\(982\) | 24.9010 | 0.794622 | ||||||||
\(983\) | 3.83723 | − | 3.83723i | 0.122388 | − | 0.122388i | −0.643260 | − | 0.765648i | \(-0.722418\pi\) |
0.765648 | + | 0.643260i | \(0.222418\pi\) | |||||||
\(984\) | 5.36992 | + | 5.36992i | 0.171187 | + | 0.171187i | ||||
\(985\) | −35.2801 | + | 8.60261i | −1.12412 | + | 0.274102i | ||||
\(986\) | −17.8428 | − | 17.8428i | −0.568229 | − | 0.568229i | ||||
\(987\) | 24.8691 | + | 24.8691i | 0.791593 | + | 0.791593i | ||||
\(988\) | −9.79582 | − | 9.79582i | −0.311647 | − | 0.311647i | ||||
\(989\) | 5.87238 | 0.186731 | ||||||||
\(990\) | −5.24898 | − | 3.19100i | −0.166823 | − | 0.101417i | ||||
\(991\) | 0.156434 | + | 0.156434i | 0.00496928 | + | 0.00496928i | 0.709587 | − | 0.704618i | \(-0.248882\pi\) |
−0.704618 | + | 0.709587i | \(0.748882\pi\) | |||||||
\(992\) | −5.51242 | − | 5.51242i | −0.175020 | − | 0.175020i | ||||
\(993\) | 14.9909i | 0.475723i | ||||||||
\(994\) | 24.7657 | − | 24.7657i | 0.785522 | − | 0.785522i | ||||
\(995\) | −39.7393 | + | 9.68992i | −1.25982 | + | 0.307191i | ||||
\(996\) | 10.2699 | 0.325415 | ||||||||
\(997\) | − | 3.25867i | − | 0.103203i | −0.998668 | − | 0.0516016i | \(-0.983567\pi\) | ||
0.998668 | − | 0.0516016i | \(-0.0164326\pi\) | |||||||
\(998\) | 9.41283 | − | 9.41283i | 0.297958 | − | 0.297958i | ||||
\(999\) | −1.86945 | + | 5.78837i | −0.0591467 | + | 0.183136i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.o.a.253.10 | yes | 36 | |
5.2 | odd | 4 | 1110.2.l.a.697.9 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.l.a.43.9 | ✓ | 36 | ||
185.117 | even | 4 | inner | 1110.2.o.a.487.10 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.9 | ✓ | 36 | 37.6 | odd | 4 | ||
1110.2.l.a.697.9 | yes | 36 | 5.2 | odd | 4 | ||
1110.2.o.a.253.10 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.487.10 | yes | 36 | 185.117 | even | 4 | inner |