Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 191.14 | ||
Character | \(\chi\) | \(=\) | 1110.191 |
Dual form | 1110.2.u.e.401.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.55689 | + | 0.759006i | −0.898871 | + | 0.438212i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | −1.63759 | − | 0.564190i | −0.668542 | − | 0.230330i | ||||
\(7\) | 1.92521 | 0.727659 | 0.363830 | − | 0.931466i | \(-0.381469\pi\) | ||||
0.363830 | + | 0.931466i | \(0.381469\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 1.84782 | − | 2.36338i | 0.615940 | − | 0.787793i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −5.18734 | −1.56404 | −0.782021 | − | 0.623252i | \(-0.785811\pi\) | ||||
−0.782021 | + | 0.623252i | \(0.785811\pi\) | |||||||
\(12\) | −0.759006 | − | 1.55689i | −0.219106 | − | 0.449436i | ||||
\(13\) | −3.96677 | − | 3.96677i | −1.10018 | − | 1.10018i | −0.994388 | − | 0.105797i | \(-0.966261\pi\) |
−0.105797 | − | 0.994388i | \(-0.533739\pi\) | |||||||
\(14\) | 1.36133 | + | 1.36133i | 0.363830 | + | 0.363830i | ||||
\(15\) | −0.564190 | + | 1.63759i | −0.145673 | + | 0.422823i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.83800 | + | 3.83800i | −0.930851 | + | 0.930851i | −0.997759 | − | 0.0669078i | \(-0.978687\pi\) |
0.0669078 | + | 0.997759i | \(0.478687\pi\) | |||||||
\(18\) | 2.97777 | − | 0.364556i | 0.701867 | − | 0.0859267i | ||||
\(19\) | 0.0989804 | + | 0.0989804i | 0.0227077 | + | 0.0227077i | 0.718369 | − | 0.695662i | \(-0.244889\pi\) |
−0.695662 | + | 0.718369i | \(0.744889\pi\) | |||||||
\(20\) | 0.707107 | + | 0.707107i | 0.158114 | + | 0.158114i | ||||
\(21\) | −2.99733 | + | 1.46124i | −0.654072 | + | 0.318869i | ||||
\(22\) | −3.66800 | − | 3.66800i | −0.782021 | − | 0.782021i | ||||
\(23\) | −1.07572 | + | 1.07572i | −0.224304 | + | 0.224304i | −0.810308 | − | 0.586004i | \(-0.800700\pi\) |
0.586004 | + | 0.810308i | \(0.300700\pi\) | |||||||
\(24\) | 0.564190 | − | 1.63759i | 0.115165 | − | 0.334271i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | − | 5.60986i | − | 1.10018i | ||||||
\(27\) | −1.08303 | + | 5.08203i | −0.208430 | + | 0.978037i | ||||
\(28\) | 1.92521i | 0.363830i | ||||||||
\(29\) | −1.77763 | − | 1.77763i | −0.330098 | − | 0.330098i | 0.522526 | − | 0.852624i | \(-0.324990\pi\) |
−0.852624 | + | 0.522526i | \(0.824990\pi\) | |||||||
\(30\) | −1.55689 | + | 0.759006i | −0.284248 | + | 0.138575i | ||||
\(31\) | −4.45832 | + | 4.45832i | −0.800738 | + | 0.800738i | −0.983211 | − | 0.182472i | \(-0.941590\pi\) |
0.182472 | + | 0.983211i | \(0.441590\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 8.07612 | − | 3.93722i | 1.40587 | − | 0.685382i | ||||
\(34\) | −5.42775 | −0.930851 | ||||||||
\(35\) | 1.36133 | − | 1.36133i | 0.230106 | − | 0.230106i | ||||
\(36\) | 2.36338 | + | 1.84782i | 0.393897 | + | 0.307970i | ||||
\(37\) | −5.86944 | − | 1.59678i | −0.964930 | − | 0.262508i | ||||
\(38\) | 0.139979i | 0.0227077i | ||||||||
\(39\) | 9.18664 | + | 3.16503i | 1.47104 | + | 0.506810i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −12.4094 | −1.93803 | −0.969014 | − | 0.247005i | \(-0.920554\pi\) | ||||
−0.969014 | + | 0.247005i | \(0.920554\pi\) | |||||||
\(42\) | −3.15269 | − | 1.08618i | −0.486471 | − | 0.167601i | ||||
\(43\) | 7.21797 | + | 7.21797i | 1.10073 | + | 1.10073i | 0.994323 | + | 0.106408i | \(0.0339349\pi\) |
0.106408 | + | 0.994323i | \(0.466065\pi\) | |||||||
\(44\) | − | 5.18734i | − | 0.782021i | ||||||
\(45\) | −0.364556 | − | 2.97777i | −0.0543448 | − | 0.443899i | ||||
\(46\) | −1.52130 | −0.224304 | ||||||||
\(47\) | − | 3.47762i | − | 0.507263i | −0.967301 | − | 0.253632i | \(-0.918375\pi\) | ||
0.967301 | − | 0.253632i | \(-0.0816251\pi\) | |||||||
\(48\) | 1.55689 | − | 0.759006i | 0.224718 | − | 0.109553i | ||||
\(49\) | −3.29358 | −0.470512 | ||||||||
\(50\) | 0.707107 | − | 0.707107i | 0.100000 | − | 0.100000i | ||||
\(51\) | 3.06228 | − | 8.88841i | 0.428805 | − | 1.24463i | ||||
\(52\) | 3.96677 | − | 3.96677i | 0.550092 | − | 0.550092i | ||||
\(53\) | 3.95819i | 0.543699i | 0.962340 | + | 0.271849i | \(0.0876352\pi\) | ||||
−0.962340 | + | 0.271849i | \(0.912365\pi\) | |||||||
\(54\) | −4.35936 | + | 2.82772i | −0.593234 | + | 0.384804i | ||||
\(55\) | −3.66800 | + | 3.66800i | −0.494593 | + | 0.494593i | ||||
\(56\) | −1.36133 | + | 1.36133i | −0.181915 | + | 0.181915i | ||||
\(57\) | −0.229228 | − | 0.0789750i | −0.0303620 | − | 0.0104605i | ||||
\(58\) | − | 2.51395i | − | 0.330098i | ||||||
\(59\) | 7.83820 | − | 7.83820i | 1.02045 | − | 1.02045i | 0.0206604 | − | 0.999787i | \(-0.493423\pi\) |
0.999787 | − | 0.0206604i | \(-0.00657688\pi\) | |||||||
\(60\) | −1.63759 | − | 0.564190i | −0.211412 | − | 0.0728366i | ||||
\(61\) | 9.10908 | − | 9.10908i | 1.16630 | − | 1.16630i | 0.183228 | − | 0.983070i | \(-0.441345\pi\) |
0.983070 | − | 0.183228i | \(-0.0586547\pi\) | |||||||
\(62\) | −6.30502 | −0.800738 | ||||||||
\(63\) | 3.55743 | − | 4.54999i | 0.448194 | − | 0.573245i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −5.60986 | −0.695818 | ||||||||
\(66\) | 8.49472 | + | 2.92664i | 1.04563 | + | 0.360245i | ||||
\(67\) | − | 9.29823i | − | 1.13596i | −0.823043 | − | 0.567980i | \(-0.807725\pi\) | ||
0.823043 | − | 0.567980i | \(-0.192275\pi\) | |||||||
\(68\) | −3.83800 | − | 3.83800i | −0.465426 | − | 0.465426i | ||||
\(69\) | 0.858304 | − | 2.49127i | 0.103328 | − | 0.299913i | ||||
\(70\) | 1.92521 | 0.230106 | ||||||||
\(71\) | − | 1.23955i | − | 0.147107i | −0.997291 | − | 0.0735537i | \(-0.976566\pi\) | ||
0.997291 | − | 0.0735537i | \(-0.0234340\pi\) | |||||||
\(72\) | 0.364556 | + | 2.97777i | 0.0429633 | + | 0.350933i | ||||
\(73\) | 6.92368i | 0.810355i | 0.914238 | + | 0.405178i | \(0.132790\pi\) | ||||
−0.914238 | + | 0.405178i | \(0.867210\pi\) | |||||||
\(74\) | −3.02123 | − | 5.27941i | −0.351211 | − | 0.613719i | ||||
\(75\) | 0.759006 | + | 1.55689i | 0.0876425 | + | 0.179774i | ||||
\(76\) | −0.0989804 | + | 0.0989804i | −0.0113538 | + | 0.0113538i | ||||
\(77\) | −9.98669 | −1.13809 | ||||||||
\(78\) | 4.25792 | + | 8.73394i | 0.482114 | + | 0.988925i | ||||
\(79\) | −0.761048 | − | 0.761048i | −0.0856246 | − | 0.0856246i | 0.662997 | − | 0.748622i | \(-0.269284\pi\) |
−0.748622 | + | 0.662997i | \(0.769284\pi\) | |||||||
\(80\) | −0.707107 | + | 0.707107i | −0.0790569 | + | 0.0790569i | ||||
\(81\) | −2.17113 | − | 8.73420i | −0.241236 | − | 0.970466i | ||||
\(82\) | −8.77480 | − | 8.77480i | −0.969014 | − | 0.969014i | ||||
\(83\) | − | 9.18336i | − | 1.00800i | −0.863702 | − | 0.504002i | \(-0.831860\pi\) | ||
0.863702 | − | 0.504002i | \(-0.168140\pi\) | |||||||
\(84\) | −1.46124 | − | 2.99733i | −0.159435 | − | 0.327036i | ||||
\(85\) | 5.42775i | 0.588722i | ||||||||
\(86\) | 10.2078i | 1.10073i | ||||||||
\(87\) | 4.11681 | + | 1.41835i | 0.441369 | + | 0.152063i | ||||
\(88\) | 3.66800 | − | 3.66800i | 0.391010 | − | 0.391010i | ||||
\(89\) | −5.54999 | − | 5.54999i | −0.588297 | − | 0.588297i | 0.348873 | − | 0.937170i | \(-0.386565\pi\) |
−0.937170 | + | 0.348873i | \(0.886565\pi\) | |||||||
\(90\) | 1.84782 | − | 2.36338i | 0.194777 | − | 0.249122i | ||||
\(91\) | −7.63685 | − | 7.63685i | −0.800559 | − | 0.800559i | ||||
\(92\) | −1.07572 | − | 1.07572i | −0.112152 | − | 0.112152i | ||||
\(93\) | 3.55723 | − | 10.3250i | 0.368867 | − | 1.07065i | ||||
\(94\) | 2.45905 | − | 2.45905i | 0.253632 | − | 0.253632i | ||||
\(95\) | 0.139979 | 0.0143616 | ||||||||
\(96\) | 1.63759 | + | 0.564190i | 0.167135 | + | 0.0575824i | ||||
\(97\) | 3.84448 | + | 3.84448i | 0.390347 | + | 0.390347i | 0.874811 | − | 0.484464i | \(-0.160985\pi\) |
−0.484464 | + | 0.874811i | \(0.660985\pi\) | |||||||
\(98\) | −2.32892 | − | 2.32892i | −0.235256 | − | 0.235256i | ||||
\(99\) | −9.58527 | + | 12.2597i | −0.963356 | + | 1.23214i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.35861 | 0.334194 | 0.167097 | − | 0.985940i | \(-0.446561\pi\) | ||||
0.167097 | + | 0.985940i | \(0.446561\pi\) | |||||||
\(102\) | 8.45041 | − | 4.11969i | 0.836716 | − | 0.407911i | ||||
\(103\) | −10.7788 | + | 10.7788i | −1.06207 | + | 1.06207i | −0.0641240 | + | 0.997942i | \(0.520425\pi\) |
−0.997942 | + | 0.0641240i | \(0.979575\pi\) | |||||||
\(104\) | 5.60986 | 0.550092 | ||||||||
\(105\) | −1.08618 | + | 3.15269i | −0.106000 | + | 0.307671i | ||||
\(106\) | −2.79886 | + | 2.79886i | −0.271849 | + | 0.271849i | ||||
\(107\) | 11.3682i | 1.09901i | 0.835492 | + | 0.549503i | \(0.185183\pi\) | ||||
−0.835492 | + | 0.549503i | \(0.814817\pi\) | |||||||
\(108\) | −5.08203 | − | 1.08303i | −0.489019 | − | 0.104215i | ||||
\(109\) | −11.3249 | − | 11.3249i | −1.08473 | − | 1.08473i | −0.996061 | − | 0.0886661i | \(-0.971740\pi\) |
−0.0886661 | − | 0.996061i | \(-0.528260\pi\) | |||||||
\(110\) | −5.18734 | −0.494593 | ||||||||
\(111\) | 10.3500 | − | 1.96893i | 0.982382 | − | 0.186883i | ||||
\(112\) | −1.92521 | −0.181915 | ||||||||
\(113\) | 14.1216 | + | 14.1216i | 1.32844 | + | 1.32844i | 0.906728 | + | 0.421716i | \(0.138572\pi\) |
0.421716 | + | 0.906728i | \(0.361428\pi\) | |||||||
\(114\) | −0.106245 | − | 0.217933i | −0.00995078 | − | 0.0204113i | ||||
\(115\) | 1.52130i | 0.141862i | ||||||||
\(116\) | 1.77763 | − | 1.77763i | 0.165049 | − | 0.165049i | ||||
\(117\) | −16.7049 | + | 2.04511i | −1.54437 | + | 0.189070i | ||||
\(118\) | 11.0849 | 1.02045 | ||||||||
\(119\) | −7.38893 | + | 7.38893i | −0.677343 | + | 0.677343i | ||||
\(120\) | −0.759006 | − | 1.55689i | −0.0692875 | − | 0.142124i | ||||
\(121\) | 15.9085 | 1.44623 | ||||||||
\(122\) | 12.8822 | 1.16630 | ||||||||
\(123\) | 19.3201 | − | 9.41884i | 1.74204 | − | 0.849268i | ||||
\(124\) | −4.45832 | − | 4.45832i | −0.400369 | − | 0.400369i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | 5.73281 | − | 0.701845i | 0.510720 | − | 0.0625253i | ||||
\(127\) | 6.10120 | 0.541394 | 0.270697 | − | 0.962665i | \(-0.412746\pi\) | ||||
0.270697 | + | 0.962665i | \(0.412746\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −16.7161 | − | 5.75911i | −1.47177 | − | 0.507061i | ||||
\(130\) | −3.96677 | − | 3.96677i | −0.347909 | − | 0.347909i | ||||
\(131\) | 5.14147 | + | 5.14147i | 0.449212 | + | 0.449212i | 0.895093 | − | 0.445880i | \(-0.147109\pi\) |
−0.445880 | + | 0.895093i | \(0.647109\pi\) | |||||||
\(132\) | 3.93722 | + | 8.07612i | 0.342691 | + | 0.702936i | ||||
\(133\) | 0.190558 | + | 0.190558i | 0.0165234 | + | 0.0165234i | ||||
\(134\) | 6.57484 | − | 6.57484i | 0.567980 | − | 0.567980i | ||||
\(135\) | 2.82772 | + | 4.35936i | 0.243371 | + | 0.375194i | ||||
\(136\) | − | 5.42775i | − | 0.465426i | ||||||
\(137\) | 2.67319i | 0.228386i | 0.993459 | + | 0.114193i | \(0.0364282\pi\) | ||||
−0.993459 | + | 0.114193i | \(0.963572\pi\) | |||||||
\(138\) | 2.36850 | − | 1.15468i | 0.201620 | − | 0.0982928i | ||||
\(139\) | 10.8710i | 0.922067i | 0.887383 | + | 0.461034i | \(0.152521\pi\) | ||||
−0.887383 | + | 0.461034i | \(0.847479\pi\) | |||||||
\(140\) | 1.36133 | + | 1.36133i | 0.115053 | + | 0.115053i | ||||
\(141\) | 2.63954 | + | 5.41428i | 0.222289 | + | 0.455964i | ||||
\(142\) | 0.876494 | − | 0.876494i | 0.0735537 | − | 0.0735537i | ||||
\(143\) | 20.5770 | + | 20.5770i | 1.72073 | + | 1.72073i | ||||
\(144\) | −1.84782 | + | 2.36338i | −0.153985 | + | 0.196948i | ||||
\(145\) | −2.51395 | −0.208772 | ||||||||
\(146\) | −4.89578 | + | 4.89578i | −0.405178 | + | 0.405178i | ||||
\(147\) | 5.12775 | − | 2.49985i | 0.422930 | − | 0.206184i | ||||
\(148\) | 1.59678 | − | 5.86944i | 0.131254 | − | 0.482465i | ||||
\(149\) | − | 9.44249i | − | 0.773559i | −0.922172 | − | 0.386779i | \(-0.873587\pi\) | ||
0.922172 | − | 0.386779i | \(-0.126413\pi\) | |||||||
\(150\) | −0.564190 | + | 1.63759i | −0.0460659 | + | 0.133708i | ||||
\(151\) | 12.4031i | 1.00935i | 0.863310 | + | 0.504673i | \(0.168387\pi\) | ||||
−0.863310 | + | 0.504673i | \(0.831613\pi\) | |||||||
\(152\) | −0.139979 | −0.0113538 | ||||||||
\(153\) | 1.97872 | + | 16.1626i | 0.159970 | + | 1.30667i | ||||
\(154\) | −7.06166 | − | 7.06166i | −0.569045 | − | 0.569045i | ||||
\(155\) | 6.30502i | 0.506431i | ||||||||
\(156\) | −3.16503 | + | 9.18664i | −0.253405 | + | 0.735519i | ||||
\(157\) | 7.28854 | 0.581689 | 0.290844 | − | 0.956770i | \(-0.406064\pi\) | ||||
0.290844 | + | 0.956770i | \(0.406064\pi\) | |||||||
\(158\) | − | 1.07628i | − | 0.0856246i | ||||||
\(159\) | −3.00429 | − | 6.16247i | −0.238256 | − | 0.488715i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.07099 | + | 2.07099i | −0.163217 | + | 0.163217i | ||||
\(162\) | 4.64079 | − | 7.71123i | 0.364615 | − | 0.605851i | ||||
\(163\) | 14.2334 | − | 14.2334i | 1.11484 | − | 1.11484i | 0.122356 | − | 0.992486i | \(-0.460955\pi\) |
0.992486 | − | 0.122356i | \(-0.0390450\pi\) | |||||||
\(164\) | − | 12.4094i | − | 0.969014i | ||||||
\(165\) | 2.92664 | − | 8.49472i | 0.227839 | − | 0.661313i | ||||
\(166\) | 6.49361 | − | 6.49361i | 0.504002 | − | 0.504002i | ||||
\(167\) | −12.7580 | + | 12.7580i | −0.987247 | + | 0.987247i | −0.999920 | − | 0.0126725i | \(-0.995966\pi\) |
0.0126725 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(168\) | 1.08618 | − | 3.15269i | 0.0838007 | − | 0.243235i | ||||
\(169\) | 18.4706i | 1.42081i | ||||||||
\(170\) | −3.83800 | + | 3.83800i | −0.294361 | + | 0.294361i | ||||
\(171\) | 0.416826 | − | 0.0510303i | 0.0318755 | − | 0.00390239i | ||||
\(172\) | −7.21797 | + | 7.21797i | −0.550365 | + | 0.550365i | ||||
\(173\) | −4.28631 | −0.325882 | −0.162941 | − | 0.986636i | \(-0.552098\pi\) | ||||
−0.162941 | + | 0.986636i | \(0.552098\pi\) | |||||||
\(174\) | 1.90810 | + | 3.91395i | 0.144653 | + | 0.296716i | ||||
\(175\) | − | 1.92521i | − | 0.145532i | ||||||
\(176\) | 5.18734 | 0.391010 | ||||||||
\(177\) | −6.25398 | + | 18.1525i | −0.470078 | + | 1.36442i | ||||
\(178\) | − | 7.84887i | − | 0.588297i | ||||||
\(179\) | 6.48181 | + | 6.48181i | 0.484473 | + | 0.484473i | 0.906557 | − | 0.422084i | \(-0.138701\pi\) |
−0.422084 | + | 0.906557i | \(0.638701\pi\) | |||||||
\(180\) | 2.97777 | − | 0.364556i | 0.221950 | − | 0.0271724i | ||||
\(181\) | −13.5004 | −1.00347 | −0.501737 | − | 0.865020i | \(-0.667305\pi\) | ||||
−0.501737 | + | 0.865020i | \(0.667305\pi\) | |||||||
\(182\) | − | 10.8001i | − | 0.800559i | ||||||
\(183\) | −7.26800 | + | 21.0957i | −0.537266 | + | 1.55944i | ||||
\(184\) | − | 1.52130i | − | 0.112152i | ||||||
\(185\) | −5.27941 | + | 3.02123i | −0.388150 | + | 0.222125i | ||||
\(186\) | 9.81623 | − | 4.78555i | 0.719761 | − | 0.350894i | ||||
\(187\) | 19.9090 | − | 19.9090i | 1.45589 | − | 1.45589i | ||||
\(188\) | 3.47762 | 0.253632 | ||||||||
\(189\) | −2.08506 | + | 9.78395i | −0.151666 | + | 0.711678i | ||||
\(190\) | 0.0989804 | + | 0.0989804i | 0.00718079 | + | 0.00718079i | ||||
\(191\) | −9.94316 | + | 9.94316i | −0.719462 | + | 0.719462i | −0.968495 | − | 0.249033i | \(-0.919887\pi\) |
0.249033 | + | 0.968495i | \(0.419887\pi\) | |||||||
\(192\) | 0.759006 | + | 1.55689i | 0.0547765 | + | 0.112359i | ||||
\(193\) | −14.9338 | − | 14.9338i | −1.07496 | − | 1.07496i | −0.996953 | − | 0.0780070i | \(-0.975144\pi\) |
−0.0780070 | − | 0.996953i | \(-0.524856\pi\) | |||||||
\(194\) | 5.43691i | 0.390347i | ||||||||
\(195\) | 8.73394 | − | 4.25792i | 0.625451 | − | 0.304916i | ||||
\(196\) | − | 3.29358i | − | 0.235256i | ||||||
\(197\) | 10.0071i | 0.712980i | 0.934299 | + | 0.356490i | \(0.116027\pi\) | ||||
−0.934299 | + | 0.356490i | \(0.883973\pi\) | |||||||
\(198\) | −15.4467 | + | 1.89108i | −1.09775 | + | 0.134393i | ||||
\(199\) | −12.2484 | + | 12.2484i | −0.868264 | + | 0.868264i | −0.992280 | − | 0.124016i | \(-0.960423\pi\) |
0.124016 | + | 0.992280i | \(0.460423\pi\) | |||||||
\(200\) | 0.707107 | + | 0.707107i | 0.0500000 | + | 0.0500000i | ||||
\(201\) | 7.05741 | + | 14.4763i | 0.497791 | + | 1.02108i | ||||
\(202\) | 2.37490 | + | 2.37490i | 0.167097 | + | 0.167097i | ||||
\(203\) | −3.42231 | − | 3.42231i | −0.240199 | − | 0.240199i | ||||
\(204\) | 8.88841 | + | 3.06228i | 0.622313 | + | 0.214403i | ||||
\(205\) | −8.77480 | + | 8.77480i | −0.612858 | + | 0.612858i | ||||
\(206\) | −15.2435 | −1.06207 | ||||||||
\(207\) | 0.554600 | + | 4.53009i | 0.0385474 | + | 0.314863i | ||||
\(208\) | 3.96677 | + | 3.96677i | 0.275046 | + | 0.275046i | ||||
\(209\) | −0.513445 | − | 0.513445i | −0.0355157 | − | 0.0355157i | ||||
\(210\) | −2.99733 | + | 1.46124i | −0.206836 | + | 0.100835i | ||||
\(211\) | −22.1119 | −1.52225 | −0.761124 | − | 0.648606i | \(-0.775352\pi\) | ||||
−0.761124 | + | 0.648606i | \(0.775352\pi\) | |||||||
\(212\) | −3.95819 | −0.271849 | ||||||||
\(213\) | 0.940826 | + | 1.92984i | 0.0644643 | + | 0.132231i | ||||
\(214\) | −8.03854 | + | 8.03854i | −0.549503 | + | 0.549503i | ||||
\(215\) | 10.2078 | 0.696163 | ||||||||
\(216\) | −2.82772 | − | 4.35936i | −0.192402 | − | 0.296617i | ||||
\(217\) | −8.58319 | + | 8.58319i | −0.582665 | + | 0.582665i | ||||
\(218\) | − | 16.0158i | − | 1.08473i | ||||||
\(219\) | −5.25511 | − | 10.7794i | −0.355108 | − | 0.728405i | ||||
\(220\) | −3.66800 | − | 3.66800i | −0.247297 | − | 0.247297i | ||||
\(221\) | 30.4489 | 2.04822 | ||||||||
\(222\) | 8.71083 | + | 5.92634i | 0.584633 | + | 0.397750i | ||||
\(223\) | 15.3186 | 1.02581 | 0.512904 | − | 0.858446i | \(-0.328570\pi\) | ||||
0.512904 | + | 0.858446i | \(0.328570\pi\) | |||||||
\(224\) | −1.36133 | − | 1.36133i | −0.0909574 | − | 0.0909574i | ||||
\(225\) | −2.36338 | − | 1.84782i | −0.157559 | − | 0.123188i | ||||
\(226\) | 19.9709i | 1.32844i | ||||||||
\(227\) | 13.6849 | − | 13.6849i | 0.908298 | − | 0.908298i | −0.0878367 | − | 0.996135i | \(-0.527995\pi\) |
0.996135 | + | 0.0878367i | \(0.0279954\pi\) | |||||||
\(228\) | 0.0789750 | − | 0.229228i | 0.00523024 | − | 0.0151810i | ||||
\(229\) | −11.4150 | −0.754322 | −0.377161 | − | 0.926148i | \(-0.623100\pi\) | ||||
−0.377161 | + | 0.926148i | \(0.623100\pi\) | |||||||
\(230\) | −1.07572 | + | 1.07572i | −0.0709311 | + | 0.0709311i | ||||
\(231\) | 15.5482 | − | 7.57996i | 1.02300 | − | 0.498725i | ||||
\(232\) | 2.51395 | 0.165049 | ||||||||
\(233\) | 15.1403 | 0.991875 | 0.495937 | − | 0.868358i | \(-0.334825\pi\) | ||||
0.495937 | + | 0.868358i | \(0.334825\pi\) | |||||||
\(234\) | −13.2582 | − | 10.3660i | −0.866718 | − | 0.677648i | ||||
\(235\) | −2.45905 | − | 2.45905i | −0.160411 | − | 0.160411i | ||||
\(236\) | 7.83820 | + | 7.83820i | 0.510223 | + | 0.510223i | ||||
\(237\) | 1.76251 | + | 0.607229i | 0.114487 | + | 0.0394437i | ||||
\(238\) | −10.4495 | −0.677343 | ||||||||
\(239\) | 5.80735 | − | 5.80735i | 0.375647 | − | 0.375647i | −0.493882 | − | 0.869529i | \(-0.664423\pi\) |
0.869529 | + | 0.493882i | \(0.164423\pi\) | |||||||
\(240\) | 0.564190 | − | 1.63759i | 0.0364183 | − | 0.105706i | ||||
\(241\) | −18.6269 | − | 18.6269i | −1.19987 | − | 1.19987i | −0.974206 | − | 0.225659i | \(-0.927547\pi\) |
−0.225659 | − | 0.974206i | \(-0.572453\pi\) | |||||||
\(242\) | 11.2490 | + | 11.2490i | 0.723113 | + | 0.723113i | ||||
\(243\) | 10.0095 | + | 11.9503i | 0.642111 | + | 0.766612i | ||||
\(244\) | 9.10908 | + | 9.10908i | 0.583149 | + | 0.583149i | ||||
\(245\) | −2.32892 | + | 2.32892i | −0.148789 | + | 0.148789i | ||||
\(246\) | 20.3215 | + | 7.00128i | 1.29565 | + | 0.446385i | ||||
\(247\) | − | 0.785265i | − | 0.0499652i | ||||||
\(248\) | − | 6.30502i | − | 0.400369i | ||||||
\(249\) | 6.97022 | + | 14.2975i | 0.441720 | + | 0.906067i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −8.68049 | − | 8.68049i | −0.547908 | − | 0.547908i | 0.377927 | − | 0.925835i | \(-0.376637\pi\) |
−0.925835 | + | 0.377927i | \(0.876637\pi\) | |||||||
\(252\) | 4.54999 | + | 3.55743i | 0.286622 | + | 0.224097i | ||||
\(253\) | 5.58015 | − | 5.58015i | 0.350821 | − | 0.350821i | ||||
\(254\) | 4.31420 | + | 4.31420i | 0.270697 | + | 0.270697i | ||||
\(255\) | −4.11969 | − | 8.45041i | −0.257985 | − | 0.529185i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −6.47192 | + | 6.47192i | −0.403707 | + | 0.403707i | −0.879537 | − | 0.475830i | \(-0.842148\pi\) |
0.475830 | + | 0.879537i | \(0.342148\pi\) | |||||||
\(258\) | −7.74775 | − | 15.8924i | −0.482354 | − | 0.989415i | ||||
\(259\) | −11.2999 | − | 3.07412i | −0.702140 | − | 0.191017i | ||||
\(260\) | − | 5.60986i | − | 0.347909i | ||||||
\(261\) | −7.48596 | + | 0.916476i | −0.463369 | + | 0.0567284i | ||||
\(262\) | 7.27114i | 0.449212i | ||||||||
\(263\) | 21.9588 | 1.35404 | 0.677019 | − | 0.735966i | \(-0.263272\pi\) | ||||
0.677019 | + | 0.735966i | \(0.263272\pi\) | |||||||
\(264\) | −2.92664 | + | 8.49472i | −0.180122 | + | 0.522814i | ||||
\(265\) | 2.79886 | + | 2.79886i | 0.171933 | + | 0.171933i | ||||
\(266\) | 0.269489i | 0.0165234i | ||||||||
\(267\) | 12.8532 | + | 4.42825i | 0.786603 | + | 0.271005i | ||||
\(268\) | 9.29823 | 0.567980 | ||||||||
\(269\) | − | 0.470491i | − | 0.0286863i | −0.999897 | − | 0.0143432i | \(-0.995434\pi\) | ||
0.999897 | − | 0.0143432i | \(-0.00456573\pi\) | |||||||
\(270\) | −1.08303 | + | 5.08203i | −0.0659114 | + | 0.309283i | ||||
\(271\) | 1.85985 | 0.112978 | 0.0564891 | − | 0.998403i | \(-0.482009\pi\) | ||||
0.0564891 | + | 0.998403i | \(0.482009\pi\) | |||||||
\(272\) | 3.83800 | − | 3.83800i | 0.232713 | − | 0.232713i | ||||
\(273\) | 17.6862 | + | 6.09333i | 1.07042 | + | 0.368785i | ||||
\(274\) | −1.89023 | + | 1.89023i | −0.114193 | + | 0.114193i | ||||
\(275\) | 5.18734i | 0.312808i | ||||||||
\(276\) | 2.49127 | + | 0.858304i | 0.149957 | + | 0.0516638i | ||||
\(277\) | −20.9504 | + | 20.9504i | −1.25879 | + | 1.25879i | −0.307118 | + | 0.951672i | \(0.599365\pi\) |
−0.951672 | + | 0.307118i | \(0.900635\pi\) | |||||||
\(278\) | −7.68697 | + | 7.68697i | −0.461034 | + | 0.461034i | ||||
\(279\) | 2.29853 | + | 18.7749i | 0.137610 | + | 1.12402i | ||||
\(280\) | 1.92521i | 0.115053i | ||||||||
\(281\) | 16.4406 | − | 16.4406i | 0.980762 | − | 0.980762i | −0.0190566 | − | 0.999818i | \(-0.506066\pi\) |
0.999818 | + | 0.0190566i | \(0.00606628\pi\) | |||||||
\(282\) | −1.96204 | + | 5.69490i | −0.116838 | + | 0.339127i | ||||
\(283\) | 3.56217 | − | 3.56217i | 0.211749 | − | 0.211749i | −0.593261 | − | 0.805010i | \(-0.702160\pi\) |
0.805010 | + | 0.593261i | \(0.202160\pi\) | |||||||
\(284\) | 1.23955 | 0.0735537 | ||||||||
\(285\) | −0.217933 | + | 0.106245i | −0.0129092 | + | 0.00629342i | ||||
\(286\) | 29.1003i | 1.72073i | ||||||||
\(287\) | −23.8907 | −1.41022 | ||||||||
\(288\) | −2.97777 | + | 0.364556i | −0.175467 | + | 0.0214817i | ||||
\(289\) | − | 12.4605i | − | 0.732968i | ||||||
\(290\) | −1.77763 | − | 1.77763i | −0.104386 | − | 0.104386i | ||||
\(291\) | −8.90341 | − | 3.06745i | −0.521927 | − | 0.179817i | ||||
\(292\) | −6.92368 | −0.405178 | ||||||||
\(293\) | 22.5243i | 1.31588i | 0.753069 | + | 0.657942i | \(0.228573\pi\) | ||||
−0.753069 | + | 0.657942i | \(0.771427\pi\) | |||||||
\(294\) | 5.39353 | + | 1.85821i | 0.314557 | + | 0.108373i | ||||
\(295\) | − | 11.0849i | − | 0.645387i | ||||||
\(296\) | 5.27941 | − | 3.02123i | 0.306860 | − | 0.175605i | ||||
\(297\) | 5.61807 | − | 26.3622i | 0.325993 | − | 1.52969i | ||||
\(298\) | 6.67685 | − | 6.67685i | 0.386779 | − | 0.386779i | ||||
\(299\) | 8.53430 | 0.493552 | ||||||||
\(300\) | −1.55689 | + | 0.759006i | −0.0898871 | + | 0.0438212i | ||||
\(301\) | 13.8961 | + | 13.8961i | 0.800957 | + | 0.800957i | ||||
\(302\) | −8.77029 | + | 8.77029i | −0.504673 | + | 0.504673i | ||||
\(303\) | −5.22899 | + | 2.54921i | −0.300398 | + | 0.146448i | ||||
\(304\) | −0.0989804 | − | 0.0989804i | −0.00567691 | − | 0.00567691i | ||||
\(305\) | − | 12.8822i | − | 0.737632i | ||||||
\(306\) | −10.0295 | + | 12.8278i | −0.573348 | + | 0.733318i | ||||
\(307\) | − | 11.0158i | − | 0.628707i | −0.949306 | − | 0.314353i | \(-0.898212\pi\) | ||
0.949306 | − | 0.314353i | \(-0.101788\pi\) | |||||||
\(308\) | − | 9.98669i | − | 0.569045i | ||||||
\(309\) | 8.60024 | − | 24.9626i | 0.489250 | − | 1.42007i | ||||
\(310\) | −4.45832 | + | 4.45832i | −0.253216 | + | 0.253216i | ||||
\(311\) | −18.1688 | − | 18.1688i | −1.03026 | − | 1.03026i | −0.999528 | − | 0.0307306i | \(-0.990217\pi\) |
−0.0307306 | − | 0.999528i | \(-0.509783\pi\) | |||||||
\(312\) | −8.73394 | + | 4.25792i | −0.494462 | + | 0.241057i | ||||
\(313\) | 3.51658 | + | 3.51658i | 0.198769 | + | 0.198769i | 0.799472 | − | 0.600703i | \(-0.205113\pi\) |
−0.600703 | + | 0.799472i | \(0.705113\pi\) | |||||||
\(314\) | 5.15378 | + | 5.15378i | 0.290844 | + | 0.290844i | ||||
\(315\) | −0.701845 | − | 5.73281i | −0.0395445 | − | 0.323007i | ||||
\(316\) | 0.761048 | − | 0.761048i | 0.0428123 | − | 0.0428123i | ||||
\(317\) | −11.6758 | −0.655777 | −0.327889 | − | 0.944716i | \(-0.606337\pi\) | ||||
−0.327889 | + | 0.944716i | \(0.606337\pi\) | |||||||
\(318\) | 2.23317 | − | 6.48187i | 0.125230 | − | 0.363485i | ||||
\(319\) | 9.22118 | + | 9.22118i | 0.516287 | + | 0.516287i | ||||
\(320\) | −0.707107 | − | 0.707107i | −0.0395285 | − | 0.0395285i | ||||
\(321\) | −8.62854 | − | 17.6991i | −0.481598 | − | 0.987865i | ||||
\(322\) | −2.92882 | −0.163217 | ||||||||
\(323\) | −0.759773 | −0.0422749 | ||||||||
\(324\) | 8.73420 | − | 2.17113i | 0.485233 | − | 0.120618i | ||||
\(325\) | −3.96677 | + | 3.96677i | −0.220037 | + | 0.220037i | ||||
\(326\) | 20.1290 | 1.11484 | ||||||||
\(327\) | 26.2273 | + | 9.03596i | 1.45037 | + | 0.499690i | ||||
\(328\) | 8.77480 | − | 8.77480i | 0.484507 | − | 0.484507i | ||||
\(329\) | − | 6.69513i | − | 0.369115i | ||||||
\(330\) | 8.07612 | − | 3.93722i | 0.444576 | − | 0.216737i | ||||
\(331\) | −0.607386 | − | 0.607386i | −0.0333850 | − | 0.0333850i | 0.690217 | − | 0.723602i | \(-0.257515\pi\) |
−0.723602 | + | 0.690217i | \(0.757515\pi\) | |||||||
\(332\) | 9.18336 | 0.504002 | ||||||||
\(333\) | −14.6195 | + | 10.9212i | −0.801141 | + | 0.598476i | ||||
\(334\) | −18.0426 | −0.987247 | ||||||||
\(335\) | −6.57484 | − | 6.57484i | −0.359222 | − | 0.359222i | ||||
\(336\) | 2.99733 | − | 1.46124i | 0.163518 | − | 0.0797173i | ||||
\(337\) | 1.97402i | 0.107532i | 0.998554 | + | 0.0537659i | \(0.0171225\pi\) | ||||
−0.998554 | + | 0.0537659i | \(0.982878\pi\) | |||||||
\(338\) | −13.0607 | + | 13.0607i | −0.710406 | + | 0.710406i | ||||
\(339\) | −32.7041 | − | 11.2674i | −1.77624 | − | 0.611960i | ||||
\(340\) | −5.42775 | −0.294361 | ||||||||
\(341\) | 23.1268 | − | 23.1268i | 1.25239 | − | 1.25239i | ||||
\(342\) | 0.330824 | + | 0.258657i | 0.0178889 | + | 0.0139866i | ||||
\(343\) | −19.8173 | −1.07003 | ||||||||
\(344\) | −10.2078 | −0.550365 | ||||||||
\(345\) | −1.15468 | − | 2.36850i | −0.0621658 | − | 0.127516i | ||||
\(346\) | −3.03088 | − | 3.03088i | −0.162941 | − | 0.162941i | ||||
\(347\) | −2.87749 | − | 2.87749i | −0.154472 | − | 0.154472i | 0.625640 | − | 0.780112i | \(-0.284838\pi\) |
−0.780112 | + | 0.625640i | \(0.784838\pi\) | |||||||
\(348\) | −1.41835 | + | 4.11681i | −0.0760313 | + | 0.220684i | ||||
\(349\) | 5.35928 | 0.286876 | 0.143438 | − | 0.989659i | \(-0.454184\pi\) | ||||
0.143438 | + | 0.989659i | \(0.454184\pi\) | |||||||
\(350\) | 1.36133 | − | 1.36133i | 0.0727659 | − | 0.0727659i | ||||
\(351\) | 24.4554 | − | 15.8631i | 1.30533 | − | 0.846710i | ||||
\(352\) | 3.66800 | + | 3.66800i | 0.195505 | + | 0.195505i | ||||
\(353\) | 8.81237 | + | 8.81237i | 0.469035 | + | 0.469035i | 0.901602 | − | 0.432567i | \(-0.142392\pi\) |
−0.432567 | + | 0.901602i | \(0.642392\pi\) | |||||||
\(354\) | −17.2580 | + | 8.41350i | −0.917251 | + | 0.447172i | ||||
\(355\) | −0.876494 | − | 0.876494i | −0.0465195 | − | 0.0465195i | ||||
\(356\) | 5.54999 | − | 5.54999i | 0.294149 | − | 0.294149i | ||||
\(357\) | 5.89552 | − | 17.1120i | 0.312024 | − | 0.905664i | ||||
\(358\) | 9.16666i | 0.484473i | ||||||||
\(359\) | − | 10.4710i | − | 0.552637i | −0.961066 | − | 0.276319i | \(-0.910886\pi\) | ||
0.961066 | − | 0.276319i | \(-0.0891145\pi\) | |||||||
\(360\) | 2.36338 | + | 1.84782i | 0.124561 | + | 0.0973886i | ||||
\(361\) | − | 18.9804i | − | 0.998969i | ||||||
\(362\) | −9.54619 | − | 9.54619i | −0.501737 | − | 0.501737i | ||||
\(363\) | −24.7678 | + | 12.0746i | −1.29997 | + | 0.633754i | ||||
\(364\) | 7.63685 | − | 7.63685i | 0.400280 | − | 0.400280i | ||||
\(365\) | 4.89578 | + | 4.89578i | 0.256257 | + | 0.256257i | ||||
\(366\) | −20.0562 | + | 9.77766i | −1.04835 | + | 0.511086i | ||||
\(367\) | −15.6683 | −0.817877 | −0.408938 | − | 0.912562i | \(-0.634101\pi\) | ||||
−0.408938 | + | 0.912562i | \(0.634101\pi\) | |||||||
\(368\) | 1.07572 | − | 1.07572i | 0.0560760 | − | 0.0560760i | ||||
\(369\) | −22.9304 | + | 29.3282i | −1.19371 | + | 1.52677i | ||||
\(370\) | −5.86944 | − | 1.59678i | −0.305138 | − | 0.0830124i | ||||
\(371\) | 7.62032i | 0.395627i | ||||||||
\(372\) | 10.3250 | + | 3.55723i | 0.535327 | + | 0.184434i | ||||
\(373\) | − | 4.20515i | − | 0.217735i | −0.994056 | − | 0.108867i | \(-0.965278\pi\) | ||
0.994056 | − | 0.108867i | \(-0.0347224\pi\) | |||||||
\(374\) | 28.1556 | 1.45589 | ||||||||
\(375\) | 1.63759 | + | 0.564190i | 0.0845646 | + | 0.0291346i | ||||
\(376\) | 2.45905 | + | 2.45905i | 0.126816 | + | 0.126816i | ||||
\(377\) | 14.1029i | 0.726337i | ||||||||
\(378\) | −8.39266 | + | 5.44394i | −0.431672 | + | 0.280006i | ||||
\(379\) | 10.8211 | 0.555842 | 0.277921 | − | 0.960604i | \(-0.410355\pi\) | ||||
0.277921 | + | 0.960604i | \(0.410355\pi\) | |||||||
\(380\) | 0.139979i | 0.00718079i | ||||||||
\(381\) | −9.49890 | + | 4.63084i | −0.486643 | + | 0.237245i | ||||
\(382\) | −14.0617 | −0.719462 | ||||||||
\(383\) | −3.27972 | + | 3.27972i | −0.167586 | + | 0.167586i | −0.785917 | − | 0.618332i | \(-0.787809\pi\) |
0.618332 | + | 0.785917i | \(0.287809\pi\) | |||||||
\(384\) | −0.564190 | + | 1.63759i | −0.0287912 | + | 0.0835677i | ||||
\(385\) | −7.06166 | + | 7.06166i | −0.359895 | + | 0.359895i | ||||
\(386\) | − | 21.1196i | − | 1.07496i | ||||||
\(387\) | 30.3963 | − | 3.72130i | 1.54513 | − | 0.189164i | ||||
\(388\) | −3.84448 | + | 3.84448i | −0.195174 | + | 0.195174i | ||||
\(389\) | 17.5886 | − | 17.5886i | 0.891778 | − | 0.891778i | −0.102912 | − | 0.994690i | \(-0.532816\pi\) |
0.994690 | + | 0.102912i | \(0.0328162\pi\) | |||||||
\(390\) | 9.18664 | + | 3.16503i | 0.465183 | + | 0.160267i | ||||
\(391\) | − | 8.25726i | − | 0.417587i | ||||||
\(392\) | 2.32892 | − | 2.32892i | 0.117628 | − | 0.117628i | ||||
\(393\) | −11.9071 | − | 4.10230i | −0.600634 | − | 0.206934i | ||||
\(394\) | −7.07612 | + | 7.07612i | −0.356490 | + | 0.356490i | ||||
\(395\) | −1.07628 | −0.0541537 | ||||||||
\(396\) | −12.2597 | − | 9.58527i | −0.616071 | − | 0.481678i | ||||
\(397\) | − | 29.2824i | − | 1.46964i | −0.678262 | − | 0.734820i | \(-0.737266\pi\) | ||
0.678262 | − | 0.734820i | \(-0.262734\pi\) | |||||||
\(398\) | −17.3218 | −0.868264 | ||||||||
\(399\) | −0.441312 | − | 0.152043i | −0.0220932 | − | 0.00761167i | ||||
\(400\) | 1.00000i | 0.0500000i | ||||||||
\(401\) | −19.3076 | − | 19.3076i | −0.964177 | − | 0.964177i | 0.0352035 | − | 0.999380i | \(-0.488792\pi\) |
−0.999380 | + | 0.0352035i | \(0.988792\pi\) | |||||||
\(402\) | −5.24597 | + | 15.2267i | −0.261645 | + | 0.759436i | ||||
\(403\) | 35.3703 | 1.76192 | ||||||||
\(404\) | 3.35861i | 0.167097i | ||||||||
\(405\) | −7.71123 | − | 4.64079i | −0.383174 | − | 0.230603i | ||||
\(406\) | − | 4.83987i | − | 0.240199i | ||||||
\(407\) | 30.4468 | + | 8.28302i | 1.50919 | + | 0.410574i | ||||
\(408\) | 4.11969 | + | 8.45041i | 0.203955 | + | 0.418358i | ||||
\(409\) | 6.57668 | − | 6.57668i | 0.325196 | − | 0.325196i | −0.525560 | − | 0.850756i | \(-0.676144\pi\) |
0.850756 | + | 0.525560i | \(0.176144\pi\) | |||||||
\(410\) | −12.4094 | −0.612858 | ||||||||
\(411\) | −2.02897 | − | 4.16186i | −0.100082 | − | 0.205290i | ||||
\(412\) | −10.7788 | − | 10.7788i | −0.531033 | − | 0.531033i | ||||
\(413\) | 15.0901 | − | 15.0901i | 0.742538 | − | 0.742538i | ||||
\(414\) | −2.81109 | + | 3.59542i | −0.138158 | + | 0.176705i | ||||
\(415\) | −6.49361 | − | 6.49361i | −0.318759 | − | 0.318759i | ||||
\(416\) | 5.60986i | 0.275046i | ||||||||
\(417\) | −8.25116 | − | 16.9250i | −0.404061 | − | 0.828820i | ||||
\(418\) | − | 0.726121i | − | 0.0355157i | ||||||
\(419\) | 26.3846i | 1.28897i | 0.764617 | + | 0.644485i | \(0.222928\pi\) | ||||
−0.764617 | + | 0.644485i | \(0.777072\pi\) | |||||||
\(420\) | −3.15269 | − | 1.08618i | −0.153836 | − | 0.0530002i | ||||
\(421\) | −21.6083 | + | 21.6083i | −1.05312 | + | 1.05312i | −0.0546159 | + | 0.998507i | \(0.517393\pi\) |
−0.998507 | + | 0.0546159i | \(0.982607\pi\) | |||||||
\(422\) | −15.6355 | − | 15.6355i | −0.761124 | − | 0.761124i | ||||
\(423\) | −8.21894 | − | 6.42601i | −0.399618 | − | 0.312444i | ||||
\(424\) | −2.79886 | − | 2.79886i | −0.135925 | − | 0.135925i | ||||
\(425\) | 3.83800 | + | 3.83800i | 0.186170 | + | 0.186170i | ||||
\(426\) | −0.699341 | + | 2.02987i | −0.0338832 | + | 0.0983475i | ||||
\(427\) | 17.5369 | − | 17.5369i | 0.848668 | − | 0.848668i | ||||
\(428\) | −11.3682 | −0.549503 | ||||||||
\(429\) | −47.6542 | − | 16.4181i | −2.30077 | − | 0.792672i | ||||
\(430\) | 7.21797 | + | 7.21797i | 0.348082 | + | 0.348082i | ||||
\(431\) | 16.8691 | + | 16.8691i | 0.812557 | + | 0.812557i | 0.985017 | − | 0.172460i | \(-0.0551715\pi\) |
−0.172460 | + | 0.985017i | \(0.555172\pi\) | |||||||
\(432\) | 1.08303 | − | 5.08203i | 0.0521075 | − | 0.244509i | ||||
\(433\) | −20.9643 | −1.00748 | −0.503740 | − | 0.863855i | \(-0.668043\pi\) | ||||
−0.503740 | + | 0.863855i | \(0.668043\pi\) | |||||||
\(434\) | −12.1385 | −0.582665 | ||||||||
\(435\) | 3.91395 | − | 1.90810i | 0.187659 | − | 0.0914866i | ||||
\(436\) | 11.3249 | − | 11.3249i | 0.542364 | − | 0.542364i | ||||
\(437\) | −0.212951 | −0.0101868 | ||||||||
\(438\) | 3.90627 | − | 11.3381i | 0.186649 | − | 0.541756i | ||||
\(439\) | −1.59624 | + | 1.59624i | −0.0761842 | + | 0.0761842i | −0.744172 | − | 0.667988i | \(-0.767156\pi\) |
0.667988 | + | 0.744172i | \(0.267156\pi\) | |||||||
\(440\) | − | 5.18734i | − | 0.247297i | ||||||
\(441\) | −6.08595 | + | 7.78399i | −0.289807 | + | 0.370666i | ||||
\(442\) | 21.5306 | + | 21.5306i | 1.02411 | + | 1.02411i | ||||
\(443\) | 26.6898 | 1.26807 | 0.634035 | − | 0.773304i | \(-0.281397\pi\) | ||||
0.634035 | + | 0.773304i | \(0.281397\pi\) | |||||||
\(444\) | 1.96893 | + | 10.3500i | 0.0934414 | + | 0.491191i | ||||
\(445\) | −7.84887 | −0.372072 | ||||||||
\(446\) | 10.8319 | + | 10.8319i | 0.512904 | + | 0.512904i | ||||
\(447\) | 7.16691 | + | 14.7009i | 0.338983 | + | 0.695330i | ||||
\(448\) | − | 1.92521i | − | 0.0909574i | ||||||
\(449\) | 9.86107 | − | 9.86107i | 0.465372 | − | 0.465372i | −0.435039 | − | 0.900412i | \(-0.643265\pi\) |
0.900412 | + | 0.435039i | \(0.143265\pi\) | |||||||
\(450\) | −0.364556 | − | 2.97777i | −0.0171853 | − | 0.140373i | ||||
\(451\) | 64.3720 | 3.03116 | ||||||||
\(452\) | −14.1216 | + | 14.1216i | −0.664222 | + | 0.664222i | ||||
\(453\) | −9.41400 | − | 19.3102i | −0.442308 | − | 0.907273i | ||||
\(454\) | 19.3534 | 0.908298 | ||||||||
\(455\) | −10.8001 | −0.506318 | ||||||||
\(456\) | 0.217933 | − | 0.106245i | 0.0102056 | − | 0.00497539i | ||||
\(457\) | 6.55173 | + | 6.55173i | 0.306477 | + | 0.306477i | 0.843541 | − | 0.537064i | \(-0.180467\pi\) |
−0.537064 | + | 0.843541i | \(0.680467\pi\) | |||||||
\(458\) | −8.07160 | − | 8.07160i | −0.377161 | − | 0.377161i | ||||
\(459\) | −15.3481 | − | 23.6615i | −0.716390 | − | 1.10442i | ||||
\(460\) | −1.52130 | −0.0709311 | ||||||||
\(461\) | −14.2328 | + | 14.2328i | −0.662887 | + | 0.662887i | −0.956060 | − | 0.293172i | \(-0.905289\pi\) |
0.293172 | + | 0.956060i | \(0.405289\pi\) | |||||||
\(462\) | 16.3541 | + | 5.63439i | 0.760860 | + | 0.262136i | ||||
\(463\) | −3.29627 | − | 3.29627i | −0.153191 | − | 0.153191i | 0.626351 | − | 0.779541i | \(-0.284548\pi\) |
−0.779541 | + | 0.626351i | \(0.784548\pi\) | |||||||
\(464\) | 1.77763 | + | 1.77763i | 0.0825245 | + | 0.0825245i | ||||
\(465\) | −4.78555 | − | 9.81623i | −0.221925 | − | 0.455217i | ||||
\(466\) | 10.7058 | + | 10.7058i | 0.495937 | + | 0.495937i | ||||
\(467\) | −8.25546 | + | 8.25546i | −0.382017 | + | 0.382017i | −0.871828 | − | 0.489811i | \(-0.837066\pi\) |
0.489811 | + | 0.871828i | \(0.337066\pi\) | |||||||
\(468\) | −2.04511 | − | 16.7049i | −0.0945352 | − | 0.772183i | ||||
\(469\) | − | 17.9010i | − | 0.826591i | ||||||
\(470\) | − | 3.47762i | − | 0.160411i | ||||||
\(471\) | −11.3475 | + | 5.53205i | −0.522863 | + | 0.254903i | ||||
\(472\) | 11.0849i | 0.510223i | ||||||||
\(473\) | −37.4421 | − | 37.4421i | −1.72159 | − | 1.72159i | ||||
\(474\) | 0.816906 | + | 1.67566i | 0.0375218 | + | 0.0769655i | ||||
\(475\) | 0.0989804 | − | 0.0989804i | 0.00454153 | − | 0.00454153i | ||||
\(476\) | −7.38893 | − | 7.38893i | −0.338671 | − | 0.338671i | ||||
\(477\) | 9.35470 | + | 7.31401i | 0.428322 | + | 0.334886i | ||||
\(478\) | 8.21284 | 0.375647 | ||||||||
\(479\) | −15.7716 | + | 15.7716i | −0.720622 | + | 0.720622i | −0.968732 | − | 0.248110i | \(-0.920190\pi\) |
0.248110 | + | 0.968732i | \(0.420190\pi\) | |||||||
\(480\) | 1.55689 | − | 0.759006i | 0.0710620 | − | 0.0346437i | ||||
\(481\) | 16.9487 | + | 29.6168i | 0.772793 | + | 1.35041i | ||||
\(482\) | − | 26.3424i | − | 1.19987i | ||||||
\(483\) | 1.65241 | − | 4.79620i | 0.0751873 | − | 0.218235i | ||||
\(484\) | 15.9085i | 0.723113i | ||||||||
\(485\) | 5.43691 | 0.246877 | ||||||||
\(486\) | −1.37234 | + | 15.5279i | −0.0622506 | + | 0.704361i | ||||
\(487\) | 12.9849 | + | 12.9849i | 0.588400 | + | 0.588400i | 0.937198 | − | 0.348798i | \(-0.113410\pi\) |
−0.348798 | + | 0.937198i | \(0.613410\pi\) | |||||||
\(488\) | 12.8822i | 0.583149i | ||||||||
\(489\) | −11.3566 | + | 32.9630i | −0.513562 | + | 1.49064i | ||||
\(490\) | −3.29358 | −0.148789 | ||||||||
\(491\) | 30.8895i | 1.39402i | 0.717059 | + | 0.697012i | \(0.245488\pi\) | ||||
−0.717059 | + | 0.697012i | \(0.754512\pi\) | |||||||
\(492\) | 9.41884 | + | 19.3201i | 0.424634 | + | 0.871019i | ||||
\(493\) | 13.6451 | 0.614544 | ||||||||
\(494\) | 0.555266 | − | 0.555266i | 0.0249826 | − | 0.0249826i | ||||
\(495\) | 1.89108 | + | 15.4467i | 0.0849975 | + | 0.694277i | ||||
\(496\) | 4.45832 | − | 4.45832i | 0.200185 | − | 0.200185i | ||||
\(497\) | − | 2.38639i | − | 0.107044i | ||||||
\(498\) | −5.18116 | + | 15.0385i | −0.232173 | + | 0.673893i | ||||
\(499\) | 20.2463 | − | 20.2463i | 0.906350 | − | 0.906350i | −0.0896254 | − | 0.995976i | \(-0.528567\pi\) |
0.995976 | + | 0.0896254i | \(0.0285670\pi\) | |||||||
\(500\) | 0.707107 | − | 0.707107i | 0.0316228 | − | 0.0316228i | ||||
\(501\) | 10.1795 | − | 29.5463i | 0.454784 | − | 1.32003i | ||||
\(502\) | − | 12.2761i | − | 0.547908i | ||||||
\(503\) | −19.1000 | + | 19.1000i | −0.851627 | + | 0.851627i | −0.990333 | − | 0.138707i | \(-0.955705\pi\) |
0.138707 | + | 0.990333i | \(0.455705\pi\) | |||||||
\(504\) | 0.701845 | + | 5.73281i | 0.0312627 | + | 0.255360i | ||||
\(505\) | 2.37490 | − | 2.37490i | 0.105681 | − | 0.105681i | ||||
\(506\) | 7.89152 | 0.350821 | ||||||||
\(507\) | −14.0193 | − | 28.7566i | −0.622617 | − | 1.27713i | ||||
\(508\) | 6.10120i | 0.270697i | ||||||||
\(509\) | −30.8742 | −1.36848 | −0.684238 | − | 0.729259i | \(-0.739865\pi\) | ||||
−0.684238 | + | 0.729259i | \(0.739865\pi\) | |||||||
\(510\) | 3.06228 | − | 8.88841i | 0.135600 | − | 0.393585i | ||||
\(511\) | 13.3295i | 0.589662i | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −0.610220 | + | 0.395822i | −0.0269419 | + | 0.0174760i | ||||
\(514\) | −9.15268 | −0.403707 | ||||||||
\(515\) | 15.2435i | 0.671709i | ||||||||
\(516\) | 5.75911 | − | 16.7161i | 0.253531 | − | 0.735884i | ||||
\(517\) | 18.0396i | 0.793381i | ||||||||
\(518\) | −5.81649 | − | 10.1639i | −0.255562 | − | 0.446578i | ||||
\(519\) | 6.67332 | − | 3.25333i | 0.292926 | − | 0.142806i | ||||
\(520\) | 3.96677 | − | 3.96677i | 0.173954 | − | 0.173954i | ||||
\(521\) | 19.1245 | 0.837858 | 0.418929 | − | 0.908019i | \(-0.362406\pi\) | ||||
0.418929 | + | 0.908019i | \(0.362406\pi\) | |||||||
\(522\) | −5.94142 | − | 4.64533i | −0.260049 | − | 0.203321i | ||||
\(523\) | −5.56709 | − | 5.56709i | −0.243432 | − | 0.243432i | 0.574836 | − | 0.818268i | \(-0.305066\pi\) |
−0.818268 | + | 0.574836i | \(0.805066\pi\) | |||||||
\(524\) | −5.14147 | + | 5.14147i | −0.224606 | + | 0.224606i | ||||
\(525\) | 1.46124 | + | 2.99733i | 0.0637738 | + | 0.130814i | ||||
\(526\) | 15.5272 | + | 15.5272i | 0.677019 | + | 0.677019i | ||||
\(527\) | − | 34.2221i | − | 1.49074i | ||||||
\(528\) | −8.07612 | + | 3.93722i | −0.351468 | + | 0.171346i | ||||
\(529\) | 20.6856i | 0.899375i | ||||||||
\(530\) | 3.95819i | 0.171933i | ||||||||
\(531\) | −4.04106 | − | 33.0082i | −0.175367 | − | 1.43244i | ||||
\(532\) | −0.190558 | + | 0.190558i | −0.00826172 | + | 0.00826172i | ||||
\(533\) | 49.2254 | + | 49.2254i | 2.13219 | + | 2.13219i | ||||
\(534\) | 5.95734 | + | 12.2198i | 0.257799 | + | 0.528804i | ||||
\(535\) | 8.03854 | + | 8.03854i | 0.347536 | + | 0.347536i | ||||
\(536\) | 6.57484 | + | 6.57484i | 0.283990 | + | 0.283990i | ||||
\(537\) | −15.0112 | − | 5.17174i | −0.647781 | − | 0.223177i | ||||
\(538\) | 0.332687 | − | 0.332687i | 0.0143432 | − | 0.0143432i | ||||
\(539\) | 17.0849 | 0.735901 | ||||||||
\(540\) | −4.35936 | + | 2.82772i | −0.187597 | + | 0.121686i | ||||
\(541\) | −4.99094 | − | 4.99094i | −0.214577 | − | 0.214577i | 0.591631 | − | 0.806209i | \(-0.298484\pi\) |
−0.806209 | + | 0.591631i | \(0.798484\pi\) | |||||||
\(542\) | 1.31512 | + | 1.31512i | 0.0564891 | + | 0.0564891i | ||||
\(543\) | 21.0186 | − | 10.2469i | 0.901994 | − | 0.439735i | ||||
\(544\) | 5.42775 | 0.232713 | ||||||||
\(545\) | −16.0158 | −0.686042 | ||||||||
\(546\) | 8.19737 | + | 16.8146i | 0.350815 | + | 0.719600i | ||||
\(547\) | −24.8167 | + | 24.8167i | −1.06108 | + | 1.06108i | −0.0630758 | + | 0.998009i | \(0.520091\pi\) |
−0.998009 | + | 0.0630758i | \(0.979909\pi\) | |||||||
\(548\) | −2.67319 | −0.114193 | ||||||||
\(549\) | −4.69628 | − | 38.3602i | −0.200432 | − | 1.63717i | ||||
\(550\) | −3.66800 | + | 3.66800i | −0.156404 | + | 0.156404i | ||||
\(551\) | − | 0.351901i | − | 0.0149915i | ||||||
\(552\) | 1.15468 | + | 2.36850i | 0.0491464 | + | 0.100810i | ||||
\(553\) | −1.46517 | − | 1.46517i | −0.0623055 | − | 0.0623055i | ||||
\(554\) | −29.6284 | −1.25879 | ||||||||
\(555\) | 5.92634 | − | 8.71083i | 0.251559 | − | 0.369754i | ||||
\(556\) | −10.8710 | −0.461034 | ||||||||
\(557\) | 4.85816 | + | 4.85816i | 0.205847 | + | 0.205847i | 0.802500 | − | 0.596653i | \(-0.203503\pi\) |
−0.596653 | + | 0.802500i | \(0.703503\pi\) | |||||||
\(558\) | −11.6505 | + | 14.9012i | −0.493207 | + | 0.630816i | ||||
\(559\) | − | 57.2641i | − | 2.42201i | ||||||
\(560\) | −1.36133 | + | 1.36133i | −0.0575265 | + | 0.0575265i | ||||
\(561\) | −15.8851 | + | 46.1072i | −0.670669 | + | 1.94665i | ||||
\(562\) | 23.2505 | 0.980762 | ||||||||
\(563\) | −18.9481 | + | 18.9481i | −0.798568 | + | 0.798568i | −0.982870 | − | 0.184302i | \(-0.940998\pi\) |
0.184302 | + | 0.982870i | \(0.440998\pi\) | |||||||
\(564\) | −5.41428 | + | 2.63954i | −0.227982 | + | 0.111144i | ||||
\(565\) | 19.9709 | 0.840182 | ||||||||
\(566\) | 5.03767 | 0.211749 | ||||||||
\(567\) | −4.17986 | − | 16.8151i | −0.175538 | − | 0.706169i | ||||
\(568\) | 0.876494 | + | 0.876494i | 0.0367769 | + | 0.0367769i | ||||
\(569\) | 8.68225 | + | 8.68225i | 0.363979 | + | 0.363979i | 0.865276 | − | 0.501297i | \(-0.167143\pi\) |
−0.501297 | + | 0.865276i | \(0.667143\pi\) | |||||||
\(570\) | −0.229228 | − | 0.0789750i | −0.00960132 | − | 0.00330790i | ||||
\(571\) | −1.59002 | −0.0665404 | −0.0332702 | − | 0.999446i | \(-0.510592\pi\) | ||||
−0.0332702 | + | 0.999446i | \(0.510592\pi\) | |||||||
\(572\) | −20.5770 | + | 20.5770i | −0.860367 | + | 0.860367i | ||||
\(573\) | 7.93350 | − | 23.0273i | 0.331427 | − | 0.961980i | ||||
\(574\) | −16.8933 | − | 16.8933i | −0.705112 | − | 0.705112i | ||||
\(575\) | 1.07572 | + | 1.07572i | 0.0448608 | + | 0.0448608i | ||||
\(576\) | −2.36338 | − | 1.84782i | −0.0984741 | − | 0.0769925i | ||||
\(577\) | −1.81221 | − | 1.81221i | −0.0754435 | − | 0.0754435i | 0.668378 | − | 0.743822i | \(-0.266989\pi\) |
−0.743822 | + | 0.668378i | \(0.766989\pi\) | |||||||
\(578\) | 8.81088 | − | 8.81088i | 0.366484 | − | 0.366484i | ||||
\(579\) | 34.5852 | + | 11.9155i | 1.43731 | + | 0.495190i | ||||
\(580\) | − | 2.51395i | − | 0.104386i | ||||||
\(581\) | − | 17.6798i | − | 0.733484i | ||||||
\(582\) | −4.12665 | − | 8.46468i | −0.171055 | − | 0.350872i | ||||
\(583\) | − | 20.5325i | − | 0.850367i | ||||||
\(584\) | −4.89578 | − | 4.89578i | −0.202589 | − | 0.202589i | ||||
\(585\) | −10.3660 | + | 13.2582i | −0.428582 | + | 0.548161i | ||||
\(586\) | −15.9271 | + | 15.9271i | −0.657942 | + | 0.657942i | ||||
\(587\) | −26.2589 | − | 26.2589i | −1.08382 | − | 1.08382i | −0.996150 | − | 0.0876694i | \(-0.972058\pi\) |
−0.0876694 | − | 0.996150i | \(-0.527942\pi\) | |||||||
\(588\) | 2.49985 | + | 5.12775i | 0.103092 | + | 0.211465i | ||||
\(589\) | −0.882573 | −0.0363658 | ||||||||
\(590\) | 7.83820 | − | 7.83820i | 0.322694 | − | 0.322694i | ||||
\(591\) | −7.59549 | − | 15.5800i | −0.312437 | − | 0.640877i | ||||
\(592\) | 5.86944 | + | 1.59678i | 0.241232 | + | 0.0656271i | ||||
\(593\) | − | 44.3173i | − | 1.81989i | −0.414727 | − | 0.909946i | \(-0.636123\pi\) | ||
0.414727 | − | 0.909946i | \(-0.363877\pi\) | |||||||
\(594\) | 22.6135 | − | 14.6683i | 0.927842 | − | 0.601849i | ||||
\(595\) | 10.4495i | 0.428389i | ||||||||
\(596\) | 9.44249 | 0.386779 | ||||||||
\(597\) | 9.77279 | − | 28.3660i | 0.399974 | − | 1.16094i | ||||
\(598\) | 6.03466 | + | 6.03466i | 0.246776 | + | 0.246776i | ||||
\(599\) | 9.25641i | 0.378207i | 0.981957 | + | 0.189103i | \(0.0605581\pi\) | ||||
−0.981957 | + | 0.189103i | \(0.939442\pi\) | |||||||
\(600\) | −1.63759 | − | 0.564190i | −0.0668542 | − | 0.0230330i | ||||
\(601\) | −1.16650 | −0.0475826 | −0.0237913 | − | 0.999717i | \(-0.507574\pi\) | ||||
−0.0237913 | + | 0.999717i | \(0.507574\pi\) | |||||||
\(602\) | 19.6520i | 0.800957i | ||||||||
\(603\) | −21.9752 | − | 17.1814i | −0.894901 | − | 0.699682i | ||||
\(604\) | −12.4031 | −0.504673 | ||||||||
\(605\) | 11.2490 | − | 11.2490i | 0.457337 | − | 0.457337i | ||||
\(606\) | −5.50001 | − | 1.89489i | −0.223423 | − | 0.0769748i | ||||
\(607\) | 15.4706 | − | 15.4706i | 0.627934 | − | 0.627934i | −0.319614 | − | 0.947548i | \(-0.603553\pi\) |
0.947548 | + | 0.319614i | \(0.103553\pi\) | |||||||
\(608\) | − | 0.139979i | − | 0.00567691i | ||||||
\(609\) | 7.92571 | + | 2.73061i | 0.321166 | + | 0.110650i | ||||
\(610\) | 9.10908 | − | 9.10908i | 0.368816 | − | 0.368816i | ||||
\(611\) | −13.7949 | + | 13.7949i | −0.558083 | + | 0.558083i | ||||
\(612\) | −16.1626 | + | 1.97872i | −0.653333 | + | 0.0799850i | ||||
\(613\) | − | 2.39296i | − | 0.0966506i | −0.998832 | − | 0.0483253i | \(-0.984612\pi\) | ||
0.998832 | − | 0.0483253i | \(-0.0153884\pi\) | |||||||
\(614\) | 7.78937 | − | 7.78937i | 0.314353 | − | 0.314353i | ||||
\(615\) | 7.00128 | − | 20.3215i | 0.282319 | − | 0.819443i | ||||
\(616\) | 7.06166 | − | 7.06166i | 0.284522 | − | 0.284522i | ||||
\(617\) | 8.86781 | 0.357005 | 0.178502 | − | 0.983939i | \(-0.442875\pi\) | ||||
0.178502 | + | 0.983939i | \(0.442875\pi\) | |||||||
\(618\) | 23.7325 | − | 11.5699i | 0.954661 | − | 0.465410i | ||||
\(619\) | − | 17.1208i | − | 0.688141i | −0.938944 | − | 0.344071i | \(-0.888194\pi\) | ||
0.938944 | − | 0.344071i | \(-0.111806\pi\) | |||||||
\(620\) | −6.30502 | −0.253216 | ||||||||
\(621\) | −4.30182 | − | 6.63191i | −0.172626 | − | 0.266129i | ||||
\(622\) | − | 25.6946i | − | 1.03026i | ||||||
\(623\) | −10.6849 | − | 10.6849i | −0.428080 | − | 0.428080i | ||||
\(624\) | −9.18664 | − | 3.16503i | −0.367760 | − | 0.126703i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 4.97320i | 0.198769i | ||||||||
\(627\) | 1.18909 | + | 0.409670i | 0.0474875 | + | 0.0163606i | ||||
\(628\) | 7.28854i | 0.290844i | ||||||||
\(629\) | 28.6553 | − | 16.3985i | 1.14256 | − | 0.653850i | ||||
\(630\) | 3.55743 | − | 4.54999i | 0.141731 | − | 0.181276i | ||||
\(631\) | −22.6451 | + | 22.6451i | −0.901487 | + | 0.901487i | −0.995565 | − | 0.0940780i | \(-0.970010\pi\) |
0.0940780 | + | 0.995565i | \(0.470010\pi\) | |||||||
\(632\) | 1.07628 | 0.0428123 | ||||||||
\(633\) | 34.4259 | − | 16.7831i | 1.36831 | − | 0.667068i | ||||
\(634\) | −8.25603 | − | 8.25603i | −0.327889 | − | 0.327889i | ||||
\(635\) | 4.31420 | − | 4.31420i | 0.171204 | − | 0.171204i | ||||
\(636\) | 6.16247 | − | 3.00429i | 0.244358 | − | 0.119128i | ||||
\(637\) | 13.0649 | + | 13.0649i | 0.517650 | + | 0.517650i | ||||
\(638\) | 13.0407i | 0.516287i | ||||||||
\(639\) | −2.92953 | − | 2.29046i | −0.115890 | − | 0.0906094i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | − | 12.4293i | − | 0.490929i | −0.969406 | − | 0.245465i | \(-0.921059\pi\) | ||
0.969406 | − | 0.245465i | \(-0.0789405\pi\) | |||||||
\(642\) | 6.41383 | − | 18.6164i | 0.253134 | − | 0.734732i | ||||
\(643\) | −10.0677 | + | 10.0677i | −0.397030 | + | 0.397030i | −0.877184 | − | 0.480154i | \(-0.840581\pi\) |
0.480154 | + | 0.877184i | \(0.340581\pi\) | |||||||
\(644\) | −2.07099 | − | 2.07099i | −0.0816084 | − | 0.0816084i | ||||
\(645\) | −15.8924 | + | 7.74775i | −0.625761 | + | 0.305067i | ||||
\(646\) | −0.537241 | − | 0.537241i | −0.0211375 | − | 0.0211375i | ||||
\(647\) | −23.6939 | − | 23.6939i | −0.931504 | − | 0.931504i | 0.0662961 | − | 0.997800i | \(-0.478882\pi\) |
−0.997800 | + | 0.0662961i | \(0.978882\pi\) | |||||||
\(648\) | 7.71123 | + | 4.64079i | 0.302926 | + | 0.182308i | ||||
\(649\) | −40.6594 | + | 40.6594i | −1.59602 | + | 1.59602i | ||||
\(650\) | −5.60986 | −0.220037 | ||||||||
\(651\) | 6.84840 | − | 19.8778i | 0.268410 | − | 0.779072i | ||||
\(652\) | 14.2334 | + | 14.2334i | 0.557421 | + | 0.557421i | ||||
\(653\) | 16.2030 | + | 16.2030i | 0.634071 | + | 0.634071i | 0.949087 | − | 0.315016i | \(-0.102010\pi\) |
−0.315016 | + | 0.949087i | \(0.602010\pi\) | |||||||
\(654\) | 12.1561 | + | 24.9349i | 0.475341 | + | 0.975031i | ||||
\(655\) | 7.27114 | 0.284107 | ||||||||
\(656\) | 12.4094 | 0.484507 | ||||||||
\(657\) | 16.3633 | + | 12.7937i | 0.638392 | + | 0.499130i | ||||
\(658\) | 4.73417 | − | 4.73417i | 0.184557 | − | 0.184557i | ||||
\(659\) | 22.4489 | 0.874484 | 0.437242 | − | 0.899344i | \(-0.355955\pi\) | ||||
0.437242 | + | 0.899344i | \(0.355955\pi\) | |||||||
\(660\) | 8.49472 | + | 2.92664i | 0.330656 | + | 0.113919i | ||||
\(661\) | 20.3735 | − | 20.3735i | 0.792436 | − | 0.792436i | −0.189453 | − | 0.981890i | \(-0.560672\pi\) |
0.981890 | + | 0.189453i | \(0.0606716\pi\) | |||||||
\(662\) | − | 0.858974i | − | 0.0333850i | ||||||
\(663\) | −47.4057 | + | 23.1109i | −1.84108 | + | 0.897554i | ||||
\(664\) | 6.49361 | + | 6.49361i | 0.252001 | + | 0.252001i | ||||
\(665\) | 0.269489 | 0.0104503 | ||||||||
\(666\) | −18.0599 | − | 2.61509i | −0.699808 | − | 0.101333i | ||||
\(667\) | 3.82448 | 0.148085 | ||||||||
\(668\) | −12.7580 | − | 12.7580i | −0.493624 | − | 0.493624i | ||||
\(669\) | −23.8494 | + | 11.6269i | −0.922070 | + | 0.449522i | ||||
\(670\) | − | 9.29823i | − | 0.359222i | ||||||
\(671\) | −47.2519 | + | 47.2519i | −1.82414 | + | 1.82414i | ||||
\(672\) | 3.15269 | + | 1.08618i | 0.121618 | + | 0.0419004i | ||||
\(673\) | 27.9883 | 1.07887 | 0.539435 | − | 0.842027i | \(-0.318638\pi\) | ||||
0.539435 | + | 0.842027i | \(0.318638\pi\) | |||||||
\(674\) | −1.39584 | + | 1.39584i | −0.0537659 | + | 0.0537659i | ||||
\(675\) | 5.08203 | + | 1.08303i | 0.195607 | + | 0.0416860i | ||||
\(676\) | −18.4706 | −0.710406 | ||||||||
\(677\) | −36.3628 | −1.39754 | −0.698769 | − | 0.715348i | \(-0.746268\pi\) | ||||
−0.698769 | + | 0.715348i | \(0.746268\pi\) | |||||||
\(678\) | −15.1580 | − | 31.0925i | −0.582141 | − | 1.19410i | ||||
\(679\) | 7.40140 | + | 7.40140i | 0.284040 | + | 0.284040i | ||||
\(680\) | −3.83800 | − | 3.83800i | −0.147181 | − | 0.147181i | ||||
\(681\) | −10.9190 | + | 31.6928i | −0.418416 | + | 1.21447i | ||||
\(682\) | 32.7063 | 1.25239 | ||||||||
\(683\) | −31.9090 | + | 31.9090i | −1.22097 | + | 1.22097i | −0.253677 | + | 0.967289i | \(0.581640\pi\) |
−0.967289 | + | 0.253677i | \(0.918360\pi\) | |||||||
\(684\) | 0.0510303 | + | 0.416826i | 0.00195119 | + | 0.0159377i | ||||
\(685\) | 1.89023 | + | 1.89023i | 0.0722220 | + | 0.0722220i | ||||
\(686\) | −14.0129 | − | 14.0129i | −0.535016 | − | 0.535016i | ||||
\(687\) | 17.7719 | − | 8.66403i | 0.678039 | − | 0.330553i | ||||
\(688\) | −7.21797 | − | 7.21797i | −0.275183 | − | 0.275183i | ||||
\(689\) | 15.7012 | − | 15.7012i | 0.598169 | − | 0.598169i | ||||
\(690\) | 0.858304 | − | 2.49127i | 0.0326751 | − | 0.0948409i | ||||
\(691\) | − | 35.8528i | − | 1.36391i | −0.731396 | − | 0.681953i | \(-0.761131\pi\) | ||
0.731396 | − | 0.681953i | \(-0.238869\pi\) | |||||||
\(692\) | − | 4.28631i | − | 0.162941i | ||||||
\(693\) | −18.4536 | + | 23.6023i | −0.700994 | + | 0.896579i | ||||
\(694\) | − | 4.06939i | − | 0.154472i | ||||||
\(695\) | 7.68697 | + | 7.68697i | 0.291583 | + | 0.291583i | ||||
\(696\) | −3.91395 | + | 1.90810i | −0.148358 | + | 0.0723265i | ||||
\(697\) | 47.6274 | − | 47.6274i | 1.80402 | − | 1.80402i | ||||
\(698\) | 3.78958 | + | 3.78958i | 0.143438 | + | 0.143438i | ||||
\(699\) | −23.5718 | + | 11.4916i | −0.891568 | + | 0.434652i | ||||
\(700\) | 1.92521 | 0.0727659 | ||||||||
\(701\) | 8.81865 | − | 8.81865i | 0.333076 | − | 0.333076i | −0.520678 | − | 0.853753i | \(-0.674321\pi\) |
0.853753 | + | 0.520678i | \(0.174321\pi\) | |||||||
\(702\) | 28.5095 | + | 6.07567i | 1.07602 | + | 0.229312i | ||||
\(703\) | −0.422910 | − | 0.739009i | −0.0159503 | − | 0.0278722i | ||||
\(704\) | 5.18734i | 0.195505i | ||||||||
\(705\) | 5.69490 | + | 1.96204i | 0.214483 | + | 0.0738946i | ||||
\(706\) | 12.4626i | 0.469035i | ||||||||
\(707\) | 6.46601 | 0.243179 | ||||||||
\(708\) | −18.1525 | − | 6.25398i | −0.682212 | − | 0.235039i | ||||
\(709\) | 26.8621 | + | 26.8621i | 1.00883 | + | 1.00883i | 0.999961 | + | 0.00886777i | \(0.00282274\pi\) |
0.00886777 | + | 0.999961i | \(0.497177\pi\) | |||||||
\(710\) | − | 1.23955i | − | 0.0465195i | ||||||
\(711\) | −3.20492 | + | 0.392366i | −0.120194 | + | 0.0147149i | ||||
\(712\) | 7.84887 | 0.294149 | ||||||||
\(713\) | − | 9.59185i | − | 0.359218i | ||||||
\(714\) | 16.2688 | − | 7.93126i | 0.608844 | − | 0.296820i | ||||
\(715\) | 29.1003 | 1.08829 | ||||||||
\(716\) | −6.48181 | + | 6.48181i | −0.242237 | + | 0.242237i | ||||
\(717\) | −4.63360 | + | 13.4492i | −0.173045 | + | 0.502271i | ||||
\(718\) | 7.40410 | − | 7.40410i | 0.276319 | − | 0.276319i | ||||
\(719\) | − | 32.4752i | − | 1.21112i | −0.795799 | − | 0.605561i | \(-0.792949\pi\) | ||
0.795799 | − | 0.605561i | \(-0.207051\pi\) | |||||||
\(720\) | 0.364556 | + | 2.97777i | 0.0135862 | + | 0.110975i | ||||
\(721\) | −20.7514 | + | 20.7514i | −0.772822 | + | 0.772822i | ||||
\(722\) | 13.4212 | − | 13.4212i | 0.499484 | − | 0.499484i | ||||
\(723\) | 43.1380 | + | 14.8621i | 1.60432 | + | 0.552729i | ||||
\(724\) | − | 13.5004i | − | 0.501737i | ||||||
\(725\) | −1.77763 | + | 1.77763i | −0.0660196 | + | 0.0660196i | ||||
\(726\) | −26.0515 | − | 8.97541i | −0.966863 | − | 0.333109i | ||||
\(727\) | 15.5520 | − | 15.5520i | 0.576792 | − | 0.576792i | −0.357226 | − | 0.934018i | \(-0.616277\pi\) |
0.934018 | + | 0.357226i | \(0.116277\pi\) | |||||||
\(728\) | 10.8001 | 0.400280 | ||||||||
\(729\) | −24.6541 | − | 11.0080i | −0.913114 | − | 0.407705i | ||||
\(730\) | 6.92368i | 0.256257i | ||||||||
\(731\) | −55.4051 | −2.04923 | ||||||||
\(732\) | −21.0957 | − | 7.26800i | −0.779719 | − | 0.268633i | ||||
\(733\) | 20.2890i | 0.749390i | 0.927148 | + | 0.374695i | \(0.122253\pi\) | ||||
−0.927148 | + | 0.374695i | \(0.877747\pi\) | |||||||
\(734\) | −11.0791 | − | 11.0791i | −0.408938 | − | 0.408938i | ||||
\(735\) | 1.85821 | − | 5.39353i | 0.0685410 | − | 0.198943i | ||||
\(736\) | 1.52130 | 0.0560760 | ||||||||
\(737\) | 48.2331i | 1.77669i | ||||||||
\(738\) | −36.9524 | + | 4.52393i | −1.36024 | + | 0.166528i | ||||
\(739\) | − | 16.8745i | − | 0.620738i | −0.950616 | − | 0.310369i | \(-0.899547\pi\) | ||
0.950616 | − | 0.310369i | \(-0.100453\pi\) | |||||||
\(740\) | −3.02123 | − | 5.27941i | −0.111063 | − | 0.194075i | ||||
\(741\) | 0.596021 | + | 1.22257i | 0.0218954 | + | 0.0449123i | ||||
\(742\) | −5.38838 | + | 5.38838i | −0.197814 | + | 0.197814i | ||||
\(743\) | −19.1398 | −0.702172 | −0.351086 | − | 0.936343i | \(-0.614187\pi\) | ||||
−0.351086 | + | 0.936343i | \(0.614187\pi\) | |||||||
\(744\) | 4.78555 | + | 9.81623i | 0.175447 | + | 0.359880i | ||||
\(745\) | −6.67685 | − | 6.67685i | −0.244621 | − | 0.244621i | ||||
\(746\) | 2.97349 | − | 2.97349i | 0.108867 | − | 0.108867i | ||||
\(747\) | −21.7038 | − | 16.9692i | −0.794099 | − | 0.620870i | ||||
\(748\) | 19.9090 | + | 19.9090i | 0.727945 | + | 0.727945i | ||||
\(749\) | 21.8861i | 0.799702i | ||||||||
\(750\) | 0.759006 | + | 1.55689i | 0.0277150 | + | 0.0568496i | ||||
\(751\) | − | 3.29443i | − | 0.120216i | −0.998192 | − | 0.0601078i | \(-0.980856\pi\) | ||
0.998192 | − | 0.0601078i | \(-0.0191444\pi\) | |||||||
\(752\) | 3.47762i | 0.126816i | ||||||||
\(753\) | 20.1031 | + | 6.92603i | 0.732599 | + | 0.252399i | ||||
\(754\) | −9.97227 | + | 9.97227i | −0.363169 | + | 0.363169i | ||||
\(755\) | 8.77029 | + | 8.77029i | 0.319183 | + | 0.319183i | ||||
\(756\) | −9.78395 | − | 2.08506i | −0.355839 | − | 0.0758330i | ||||
\(757\) | −26.1797 | − | 26.1797i | −0.951518 | − | 0.951518i | 0.0473602 | − | 0.998878i | \(-0.484919\pi\) |
−0.998878 | + | 0.0473602i | \(0.984919\pi\) | |||||||
\(758\) | 7.65167 | + | 7.65167i | 0.277921 | + | 0.277921i | ||||
\(759\) | −4.45231 | + | 12.9230i | −0.161609 | + | 0.469077i | ||||
\(760\) | −0.0989804 | + | 0.0989804i | −0.00359040 | + | 0.00359040i | ||||
\(761\) | −13.0239 | −0.472118 | −0.236059 | − | 0.971739i | \(-0.575856\pi\) | ||||
−0.236059 | + | 0.971739i | \(0.575856\pi\) | |||||||
\(762\) | −9.99124 | − | 3.44223i | −0.361944 | − | 0.124699i | ||||
\(763\) | −21.8027 | − | 21.8027i | −0.789312 | − | 0.789312i | ||||
\(764\) | −9.94316 | − | 9.94316i | −0.359731 | − | 0.359731i | ||||
\(765\) | 12.8278 | + | 10.0295i | 0.463791 | + | 0.362617i | ||||
\(766\) | −4.63822 | −0.167586 | ||||||||
\(767\) | −62.1847 | −2.24536 | ||||||||
\(768\) | −1.55689 | + | 0.759006i | −0.0561795 | + | 0.0273883i | ||||
\(769\) | −22.4249 | + | 22.4249i | −0.808662 | + | 0.808662i | −0.984431 | − | 0.175769i | \(-0.943759\pi\) |
0.175769 | + | 0.984431i | \(0.443759\pi\) | |||||||
\(770\) | −9.98669 | −0.359895 | ||||||||
\(771\) | 5.16385 | − | 14.9883i | 0.185971 | − | 0.539791i | ||||
\(772\) | 14.9338 | − | 14.9338i | 0.537480 | − | 0.537480i | ||||
\(773\) | − | 20.2597i | − | 0.728691i | −0.931264 | − | 0.364345i | \(-0.881293\pi\) | ||
0.931264 | − | 0.364345i | \(-0.118707\pi\) | |||||||
\(774\) | 24.1248 | + | 18.8621i | 0.867148 | + | 0.677984i | ||||
\(775\) | 4.45832 | + | 4.45832i | 0.160148 | + | 0.160148i | ||||
\(776\) | −5.43691 | −0.195174 | ||||||||
\(777\) | 19.9259 | − | 3.79060i | 0.714839 | − | 0.135987i | ||||
\(778\) | 24.8741 | 0.891778 | ||||||||
\(779\) | −1.22829 | − | 1.22829i | −0.0440081 | − | 0.0440081i | ||||
\(780\) | 4.25792 | + | 8.73394i | 0.152458 | + | 0.312725i | ||||
\(781\) | 6.42997i | 0.230082i | ||||||||
\(782\) | 5.83876 | − | 5.83876i | 0.208794 | − | 0.208794i | ||||
\(783\) | 10.9592 | − | 7.10875i | 0.391651 | − | 0.254046i | ||||
\(784\) | 3.29358 | 0.117628 | ||||||||
\(785\) | 5.15378 | − | 5.15378i | 0.183946 | − | 0.183946i | ||||
\(786\) | −5.51884 | − | 11.3204i | −0.196850 | − | 0.403784i | ||||
\(787\) | −51.8393 | −1.84787 | −0.923936 | − | 0.382546i | \(-0.875047\pi\) | ||||
−0.923936 | + | 0.382546i | \(0.875047\pi\) | |||||||
\(788\) | −10.0071 | −0.356490 | ||||||||
\(789\) | −34.1874 | + | 16.6669i | −1.21711 | + | 0.593356i | ||||
\(790\) | −0.761048 | − | 0.761048i | −0.0270769 | − | 0.0270769i | ||||
\(791\) | 27.1869 | + | 27.1869i | 0.966654 | + | 0.966654i | ||||
\(792\) | −1.89108 | − | 15.4467i | −0.0671964 | − | 0.548874i | ||||
\(793\) | −72.2673 | −2.56629 | ||||||||
\(794\) | 20.7058 | − | 20.7058i | 0.734820 | − | 0.734820i | ||||
\(795\) | −6.48187 | − | 2.23317i | −0.229888 | − | 0.0792023i | ||||
\(796\) | −12.2484 | − | 12.2484i | −0.434132 | − | 0.434132i | ||||
\(797\) | −15.4144 | − | 15.4144i | −0.546006 | − | 0.546006i | 0.379277 | − | 0.925283i | \(-0.376173\pi\) |
−0.925283 | + | 0.379277i | \(0.876173\pi\) | |||||||
\(798\) | −0.204544 | − | 0.419565i | −0.00724077 | − | 0.0148524i | ||||
\(799\) | 13.3471 | + | 13.3471i | 0.472187 | + | 0.472187i | ||||
\(800\) | −0.707107 | + | 0.707107i | −0.0250000 | + | 0.0250000i | ||||
\(801\) | −23.3721 | + | 2.86135i | −0.825812 | + | 0.101101i | ||||
\(802\) | − | 27.3051i | − | 0.964177i | ||||||
\(803\) | − | 35.9155i | − | 1.26743i | ||||||
\(804\) | −14.4763 | + | 7.05741i | −0.510541 | + | 0.248896i | ||||
\(805\) | 2.92882i | 0.103227i | ||||||||
\(806\) | 25.0106 | + | 25.0106i | 0.880960 | + | 0.880960i | ||||
\(807\) | 0.357105 | + | 0.732503i | 0.0125707 | + | 0.0257853i | ||||
\(808\) | −2.37490 | + | 2.37490i | −0.0835485 | + | 0.0835485i | ||||
\(809\) | 21.9588 | + | 21.9588i | 0.772032 | + | 0.772032i | 0.978461 | − | 0.206430i | \(-0.0661845\pi\) |
−0.206430 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(810\) | −2.17113 | − | 8.73420i | −0.0762856 | − | 0.306888i | ||||
\(811\) | 35.3528 | 1.24141 | 0.620703 | − | 0.784046i | \(-0.286847\pi\) | ||||
0.620703 | + | 0.784046i | \(0.286847\pi\) | |||||||
\(812\) | 3.42231 | − | 3.42231i | 0.120099 | − | 0.120099i | ||||
\(813\) | −2.89559 | + | 1.41164i | −0.101553 | + | 0.0495084i | ||||
\(814\) | 15.6721 | + | 27.3861i | 0.549308 | + | 0.959882i | ||||
\(815\) | − | 20.1290i | − | 0.705088i | ||||||
\(816\) | −3.06228 | + | 8.88841i | −0.107201 | + | 0.311157i | ||||
\(817\) | 1.42888i | 0.0499900i | ||||||||
\(818\) | 9.30083 | 0.325196 | ||||||||
\(819\) | −32.1603 | + | 3.93725i | −1.12377 | + | 0.137579i | ||||
\(820\) | −8.77480 | − | 8.77480i | −0.306429 | − | 0.306429i | ||||
\(821\) | − | 11.3942i | − | 0.397660i | −0.980034 | − | 0.198830i | \(-0.936286\pi\) | ||
0.980034 | − | 0.198830i | \(-0.0637141\pi\) | |||||||
\(822\) | 1.50819 | − | 4.37758i | 0.0526040 | − | 0.152686i | ||||
\(823\) | −24.7384 | −0.862327 | −0.431163 | − | 0.902274i | \(-0.641897\pi\) | ||||
−0.431163 | + | 0.902274i | \(0.641897\pi\) | |||||||
\(824\) | − | 15.2435i | − | 0.531033i | ||||||
\(825\) | −3.93722 | − | 8.07612i | −0.137076 | − | 0.281174i | ||||
\(826\) | 21.3407 | 0.742538 | ||||||||
\(827\) | −0.846501 | + | 0.846501i | −0.0294357 | + | 0.0294357i | −0.721671 | − | 0.692236i | \(-0.756626\pi\) |
0.692236 | + | 0.721671i | \(0.256626\pi\) | |||||||
\(828\) | −4.53009 | + | 0.554600i | −0.157431 | + | 0.0192737i | ||||
\(829\) | −12.4499 | + | 12.4499i | −0.432404 | + | 0.432404i | −0.889445 | − | 0.457041i | \(-0.848909\pi\) |
0.457041 | + | 0.889445i | \(0.348909\pi\) | |||||||
\(830\) | − | 9.18336i | − | 0.318759i | ||||||
\(831\) | 16.7160 | − | 48.5190i | 0.579873 | − | 1.68311i | ||||
\(832\) | −3.96677 | + | 3.96677i | −0.137523 | + | 0.137523i | ||||
\(833\) | 12.6408 | − | 12.6408i | 0.437977 | − | 0.437977i | ||||
\(834\) | 6.13332 | − | 17.8022i | 0.212379 | − | 0.616441i | ||||
\(835\) | 18.0426i | 0.624390i | ||||||||
\(836\) | 0.513445 | − | 0.513445i | 0.0177579 | − | 0.0177579i | ||||
\(837\) | −17.8288 | − | 27.4859i | −0.616254 | − | 0.950050i | ||||
\(838\) | −18.6567 | + | 18.6567i | −0.644485 | + | 0.644485i | ||||
\(839\) | −24.1404 | −0.833419 | −0.416709 | − | 0.909040i | \(-0.636817\pi\) | ||||
−0.416709 | + | 0.909040i | \(0.636817\pi\) | |||||||
\(840\) | −1.46124 | − | 2.99733i | −0.0504177 | − | 0.103418i | ||||
\(841\) | − | 22.6800i | − | 0.782071i | ||||||
\(842\) | −30.5587 | −1.05312 | ||||||||
\(843\) | −13.1177 | + | 38.0747i | −0.451797 | + | 1.31136i | ||||
\(844\) | − | 22.1119i | − | 0.761124i | ||||||
\(845\) | 13.0607 | + | 13.0607i | 0.449300 | + | 0.449300i | ||||
\(846\) | −1.26779 | − | 10.3555i | −0.0435874 | − | 0.356031i | ||||
\(847\) | 30.6271 | 1.05236 | ||||||||
\(848\) | − | 3.95819i | − | 0.135925i | ||||||
\(849\) | −2.84220 | + | 8.24962i | −0.0975442 | + | 0.283126i | ||||
\(850\) | 5.42775i | 0.186170i | ||||||||
\(851\) | 8.03159 | − | 4.59621i | 0.275319 | − | 0.157556i | ||||
\(852\) | −1.92984 | + | 0.940826i | −0.0661154 | + | 0.0322322i | ||||
\(853\) | 12.1090 | − | 12.1090i | 0.414603 | − | 0.414603i | −0.468735 | − | 0.883339i | \(-0.655290\pi\) |
0.883339 | + | 0.468735i | \(0.155290\pi\) | |||||||
\(854\) | 24.8009 | 0.848668 | ||||||||
\(855\) | 0.258657 | − | 0.330824i | 0.00884587 | − | 0.0113140i | ||||
\(856\) | −8.03854 | − | 8.03854i | −0.274751 | − | 0.274751i | ||||
\(857\) | 9.78821 | − | 9.78821i | 0.334359 | − | 0.334359i | −0.519880 | − | 0.854239i | \(-0.674023\pi\) |
0.854239 | + | 0.519880i | \(0.174023\pi\) | |||||||
\(858\) | −22.0873 | − | 45.3059i | −0.754047 | − | 1.54672i | ||||
\(859\) | 14.5905 | + | 14.5905i | 0.497821 | + | 0.497821i | 0.910759 | − | 0.412938i | \(-0.135498\pi\) |
−0.412938 | + | 0.910759i | \(0.635498\pi\) | |||||||
\(860\) | 10.2078i | 0.348082i | ||||||||
\(861\) | 37.1952 | − | 18.1332i | 1.26761 | − | 0.617978i | ||||
\(862\) | 23.8565i | 0.812557i | ||||||||
\(863\) | − | 12.6373i | − | 0.430178i | −0.976595 | − | 0.215089i | \(-0.930996\pi\) | ||
0.976595 | − | 0.215089i | \(-0.0690041\pi\) | |||||||
\(864\) | 4.35936 | − | 2.82772i | 0.148308 | − | 0.0962009i | ||||
\(865\) | −3.03088 | + | 3.03088i | −0.103053 | + | 0.103053i | ||||
\(866\) | −14.8240 | − | 14.8240i | −0.503740 | − | 0.503740i | ||||
\(867\) | 9.45757 | + | 19.3996i | 0.321196 | + | 0.658844i | ||||
\(868\) | −8.58319 | − | 8.58319i | −0.291332 | − | 0.291332i | ||||
\(869\) | 3.94781 | + | 3.94781i | 0.133920 | + | 0.133920i | ||||
\(870\) | 4.11681 | + | 1.41835i | 0.139573 | + | 0.0480864i | ||||
\(871\) | −36.8839 | + | 36.8839i | −1.24976 | + | 1.24976i | ||||
\(872\) | 16.0158 | 0.542364 | ||||||||
\(873\) | 16.1899 | − | 1.98206i | 0.547943 | − | 0.0670825i | ||||
\(874\) | −0.150579 | − | 0.150579i | −0.00509342 | − | 0.00509342i | ||||
\(875\) | −1.36133 | − | 1.36133i | −0.0460212 | − | 0.0460212i | ||||
\(876\) | 10.7794 | − | 5.25511i | 0.364203 | − | 0.177554i | ||||
\(877\) | −4.55805 | −0.153914 | −0.0769572 | − | 0.997034i | \(-0.524520\pi\) | ||||
−0.0769572 | + | 0.997034i | \(0.524520\pi\) | |||||||
\(878\) | −2.25742 | −0.0761842 | ||||||||
\(879\) | −17.0961 | − | 35.0679i | −0.576637 | − | 1.18281i | ||||
\(880\) | 3.66800 | − | 3.66800i | 0.123648 | − | 0.123648i | ||||
\(881\) | −24.5294 | −0.826416 | −0.413208 | − | 0.910637i | \(-0.635592\pi\) | ||||
−0.413208 | + | 0.910637i | \(0.635592\pi\) | |||||||
\(882\) | −9.80753 | + | 1.20070i | −0.330237 | + | 0.0404295i | ||||
\(883\) | −30.6747 | + | 30.6747i | −1.03229 | + | 1.03229i | −0.0328243 | + | 0.999461i | \(0.510450\pi\) |
−0.999461 | + | 0.0328243i | \(0.989550\pi\) | |||||||
\(884\) | 30.4489i | 1.02411i | ||||||||
\(885\) | 8.41350 | + | 17.2580i | 0.282817 | + | 0.580120i | ||||
\(886\) | 18.8725 | + | 18.8725i | 0.634035 | + | 0.634035i | ||||
\(887\) | 54.5342 | 1.83108 | 0.915540 | − | 0.402227i | \(-0.131764\pi\) | ||||
0.915540 | + | 0.402227i | \(0.131764\pi\) | |||||||
\(888\) | −5.92634 | + | 8.71083i | −0.198875 | + | 0.292316i | ||||
\(889\) | 11.7461 | 0.393950 | ||||||||
\(890\) | −5.54999 | − | 5.54999i | −0.186036 | − | 0.186036i | ||||
\(891\) | 11.2624 | + | 45.3072i | 0.377303 | + | 1.51785i | ||||
\(892\) | 15.3186i | 0.512904i | ||||||||
\(893\) | 0.344216 | − | 0.344216i | 0.0115188 | − | 0.0115188i | ||||
\(894\) | −5.32736 | + | 15.4629i | −0.178173 | + | 0.517156i | ||||
\(895\) | 9.16666 | 0.306408 | ||||||||
\(896\) | 1.36133 | − | 1.36133i | 0.0454787 | − | 0.0454787i | ||||
\(897\) | −13.2870 | + | 6.47759i | −0.443639 | + | 0.216280i | ||||
\(898\) | 13.9457 | 0.465372 | ||||||||
\(899\) | 15.8505 | 0.528644 | ||||||||
\(900\) | 1.84782 | − | 2.36338i | 0.0615940 | − | 0.0787793i | ||||
\(901\) | −15.1915 | − | 15.1915i | −0.506103 | − | 0.506103i | ||||
\(902\) | 45.5178 | + | 45.5178i | 1.51558 | + | 1.51558i | ||||
\(903\) | −32.1819 | − | 11.0875i | −1.07095 | − | 0.368968i | ||||
\(904\) | −19.9709 | −0.664222 | ||||||||
\(905\) | −9.54619 | + | 9.54619i | −0.317326 | + | 0.317326i | ||||
\(906\) | 6.99768 | − | 20.3111i | 0.232482 | − | 0.674791i | ||||
\(907\) | 5.52271 | + | 5.52271i | 0.183379 | + | 0.183379i | 0.792826 | − | 0.609448i | \(-0.208609\pi\) |
−0.609448 | + | 0.792826i | \(0.708609\pi\) | |||||||
\(908\) | 13.6849 | + | 13.6849i | 0.454149 | + | 0.454149i | ||||
\(909\) | 6.20610 | − | 7.93767i | 0.205844 | − | 0.263276i | ||||
\(910\) | −7.63685 | − | 7.63685i | −0.253159 | − | 0.253159i | ||||
\(911\) | 3.48960 | − | 3.48960i | 0.115616 | − | 0.115616i | −0.646932 | − | 0.762548i | \(-0.723948\pi\) |
0.762548 | + | 0.646932i | \(0.223948\pi\) | |||||||
\(912\) | 0.229228 | + | 0.0789750i | 0.00759051 | + | 0.00261512i | ||||
\(913\) | 47.6372i | 1.57656i | ||||||||
\(914\) | 9.26555i | 0.306477i | ||||||||
\(915\) | 9.77766 | + | 20.0562i | 0.323239 | + | 0.663036i | ||||
\(916\) | − | 11.4150i | − | 0.377161i | ||||||
\(917\) | 9.89838 | + | 9.89838i | 0.326873 | + | 0.326873i | ||||
\(918\) | 5.87844 | − | 27.5840i | 0.194017 | − | 0.910407i | ||||
\(919\) | 23.9392 | − | 23.9392i | 0.789680 | − | 0.789680i | −0.191762 | − | 0.981442i | \(-0.561420\pi\) |
0.981442 | + | 0.191762i | \(0.0614201\pi\) | |||||||
\(920\) | −1.07572 | − | 1.07572i | −0.0354656 | − | 0.0354656i | ||||
\(921\) | 8.36109 | + | 17.1505i | 0.275507 | + | 0.565127i | ||||
\(922\) | −20.1282 | −0.662887 | ||||||||
\(923\) | −4.91701 | + | 4.91701i | −0.161845 | + | 0.161845i | ||||
\(924\) | 7.57996 | + | 15.5482i | 0.249362 | + | 0.511498i | ||||
\(925\) | −1.59678 | + | 5.86944i | −0.0525017 | + | 0.192986i | ||||
\(926\) | − | 4.66163i | − | 0.153191i | ||||||
\(927\) | 5.55711 | + | 45.3916i | 0.182520 | + | 1.49086i | ||||
\(928\) | 2.51395i | 0.0825245i | ||||||||
\(929\) | 39.0723 | 1.28192 | 0.640961 | − | 0.767574i | \(-0.278536\pi\) | ||||
0.640961 | + | 0.767574i | \(0.278536\pi\) | |||||||
\(930\) | 3.55723 | − | 10.3250i | 0.116646 | − | 0.338571i | ||||
\(931\) | −0.326000 | − | 0.326000i | −0.0106842 | − | 0.0106842i | ||||
\(932\) | 15.1403i | 0.495937i | ||||||||
\(933\) | 42.0771 | + | 14.4966i | 1.37754 | + | 0.474598i | ||||
\(934\) | −11.6750 | −0.382017 | ||||||||
\(935\) | − | 28.1556i | − | 0.920786i | ||||||
\(936\) | 10.3660 | − | 13.2582i | 0.338824 | − | 0.433359i | ||||
\(937\) | −5.26195 | −0.171900 | −0.0859502 | − | 0.996299i | \(-0.527393\pi\) | ||||
−0.0859502 | + | 0.996299i | \(0.527393\pi\) | |||||||
\(938\) | 12.6579 | − | 12.6579i | 0.413296 | − | 0.413296i | ||||
\(939\) | −8.14404 | − | 2.80583i | −0.265771 | − | 0.0915647i | ||||
\(940\) | 2.45905 | − | 2.45905i | 0.0802053 | − | 0.0802053i | ||||
\(941\) | − | 48.3770i | − | 1.57704i | −0.615007 | − | 0.788522i | \(-0.710847\pi\) | ||
0.615007 | − | 0.788522i | \(-0.289153\pi\) | |||||||
\(942\) | −11.9356 | − | 4.11212i | −0.388883 | − | 0.133980i | ||||
\(943\) | 13.3491 | − | 13.3491i | 0.434708 | − | 0.434708i | ||||
\(944\) | −7.83820 | + | 7.83820i | −0.255112 | + | 0.255112i | ||||
\(945\) | 5.44394 | + | 8.39266i | 0.177091 | + | 0.273013i | ||||
\(946\) | − | 52.9511i | − | 1.72159i | ||||||
\(947\) | 9.05959 | − | 9.05959i | 0.294397 | − | 0.294397i | −0.544417 | − | 0.838814i | \(-0.683249\pi\) |
0.838814 | + | 0.544417i | \(0.183249\pi\) | |||||||
\(948\) | −0.607229 | + | 1.76251i | −0.0197219 | + | 0.0572436i | ||||
\(949\) | 27.4647 | − | 27.4647i | 0.891540 | − | 0.891540i | ||||
\(950\) | 0.139979 | 0.00454153 | ||||||||
\(951\) | 18.1779 | − | 8.86199i | 0.589460 | − | 0.287370i | ||||
\(952\) | − | 10.4495i | − | 0.338671i | ||||||
\(953\) | 9.84569 | 0.318933 | 0.159467 | − | 0.987203i | \(-0.449023\pi\) | ||||
0.159467 | + | 0.987203i | \(0.449023\pi\) | |||||||
\(954\) | 1.44298 | + | 11.7866i | 0.0467182 | + | 0.381604i | ||||
\(955\) | 14.0617i | 0.455027i | ||||||||
\(956\) | 5.80735 | + | 5.80735i | 0.187823 | + | 0.187823i | ||||
\(957\) | −21.3553 | − | 7.35744i | −0.690319 | − | 0.237832i | ||||
\(958\) | −22.3044 | −0.720622 | ||||||||
\(959\) | 5.14644i | 0.166187i | ||||||||
\(960\) | 1.63759 | + | 0.564190i | 0.0528529 | + | 0.0182091i | ||||
\(961\) | − | 8.75329i | − | 0.282364i | ||||||
\(962\) | −8.95769 | + | 32.9267i | −0.288808 | + | 1.06160i | ||||
\(963\) | 26.8674 | + | 21.0064i | 0.865789 | + | 0.676922i | ||||
\(964\) | 18.6269 | − | 18.6269i | 0.599933 | − | 0.599933i | ||||
\(965\) | −21.1196 | −0.679864 | ||||||||
\(966\) | 4.55986 | − | 2.22299i | 0.146711 | − | 0.0715236i | ||||
\(967\) | 23.0717 | + | 23.0717i | 0.741937 | + | 0.741937i | 0.972951 | − | 0.231013i | \(-0.0742041\pi\) |
−0.231013 | + | 0.972951i | \(0.574204\pi\) | |||||||
\(968\) | −11.2490 | + | 11.2490i | −0.361557 | + | 0.361557i | ||||
\(969\) | 1.18288 | − | 0.576672i | 0.0379997 | − | 0.0185254i | ||||
\(970\) | 3.84448 | + | 3.84448i | 0.123439 | + | 0.123439i | ||||
\(971\) | − | 8.02634i | − | 0.257577i | −0.991672 | − | 0.128789i | \(-0.958891\pi\) | ||
0.991672 | − | 0.128789i | \(-0.0411089\pi\) | |||||||
\(972\) | −11.9503 | + | 10.0095i | −0.383306 | + | 0.321055i | ||||
\(973\) | 20.9289i | 0.670951i | ||||||||
\(974\) | 18.3634i | 0.588400i | ||||||||
\(975\) | 3.16503 | − | 9.18664i | 0.101362 | − | 0.294208i | ||||
\(976\) | −9.10908 | + | 9.10908i | −0.291575 | + | 0.291575i | ||||
\(977\) | −17.8008 | − | 17.8008i | −0.569499 | − | 0.569499i | 0.362489 | − | 0.931988i | \(-0.381927\pi\) |
−0.931988 | + | 0.362489i | \(0.881927\pi\) | |||||||
\(978\) | −31.3387 | + | 15.2780i | −1.00210 | + | 0.488538i | ||||
\(979\) | 28.7897 | + | 28.7897i | 0.920122 | + | 0.920122i | ||||
\(980\) | −2.32892 | − | 2.32892i | −0.0743945 | − | 0.0743945i | ||||
\(981\) | −47.6914 | + | 5.83866i | −1.52267 | + | 0.186414i | ||||
\(982\) | −21.8422 | + | 21.8422i | −0.697012 | + | 0.697012i | ||||
\(983\) | 49.9878 | 1.59436 | 0.797181 | − | 0.603740i | \(-0.206323\pi\) | ||||
0.797181 | + | 0.603740i | \(0.206323\pi\) | |||||||
\(984\) | −7.00128 | + | 20.3215i | −0.223193 | + | 0.647827i | ||||
\(985\) | 7.07612 | + | 7.07612i | 0.225464 | + | 0.225464i | ||||
\(986\) | 9.64854 | + | 9.64854i | 0.307272 | + | 0.307272i | ||||
\(987\) | 5.08165 | + | 10.4236i | 0.161751 | + | 0.331787i | ||||
\(988\) | 0.785265 | 0.0249826 | ||||||||
\(989\) | −15.5291 | −0.493796 | ||||||||
\(990\) | −9.58527 | + | 12.2597i | −0.304640 | + | 0.389637i | ||||
\(991\) | 7.00029 | − | 7.00029i | 0.222372 | − | 0.222372i | −0.587125 | − | 0.809496i | \(-0.699740\pi\) |
0.809496 | + | 0.587125i | \(0.199740\pi\) | |||||||
\(992\) | 6.30502 | 0.200185 | ||||||||
\(993\) | 1.40664 | + | 0.484624i | 0.0446385 | + | 0.0153791i | ||||
\(994\) | 1.68743 | − | 1.68743i | 0.0535221 | − | 0.0535221i | ||||
\(995\) | 17.3218i | 0.549138i | ||||||||
\(996\) | −14.2975 | + | 6.97022i | −0.453033 | + | 0.220860i | ||||
\(997\) | −4.54972 | − | 4.54972i | −0.144091 | − | 0.144091i | 0.631381 | − | 0.775473i | \(-0.282488\pi\) |
−0.775473 | + | 0.631381i | \(0.782488\pi\) | |||||||
\(998\) | 28.6326 | 0.906350 | ||||||||
\(999\) | 14.4717 | − | 28.0993i | 0.457863 | − | 0.889023i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.u.e.191.14 | yes | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.e.191.10 | ✓ | 40 | |
37.31 | odd | 4 | inner | 1110.2.u.e.401.10 | yes | 40 | |
111.68 | even | 4 | inner | 1110.2.u.e.401.14 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.e.191.10 | ✓ | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.e.191.14 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.e.401.10 | yes | 40 | 37.31 | odd | 4 | inner | |
1110.2.u.e.401.14 | yes | 40 | 111.68 | even | 4 | inner |