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 | 191.16 | ||
Character | \(\chi\) | \(=\) | 1110.191 |
Dual form | 1110.2.u.e.401.16 |
$q$-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 | ||||
\(3\) | −1.64725 | + | 0.535321i | −0.951040 | + | 0.309068i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.707107 | − | 0.707107i | 0.316228 | − | 0.316228i | ||||
\(6\) | −1.54331 | − | 0.786252i | −0.630054 | − | 0.320986i | ||||
\(7\) | −2.53955 | −0.959861 | −0.479930 | − | 0.877307i | \(-0.659338\pi\) | ||||
−0.479930 | + | 0.877307i | \(0.659338\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 2.42686 | − | 1.76361i | 0.808954 | − | 0.587872i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.55248 | 0.468089 | 0.234045 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234045 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(12\) | −0.535321 | − | 1.64725i | −0.154534 | − | 0.475520i | ||||
\(13\) | −1.11554 | − | 1.11554i | −0.309396 | − | 0.309396i | 0.535279 | − | 0.844675i | \(-0.320206\pi\) |
−0.844675 | + | 0.535279i | \(0.820206\pi\) | |||||||
\(14\) | −1.79574 | − | 1.79574i | −0.479930 | − | 0.479930i | ||||
\(15\) | −0.786252 | + | 1.54331i | −0.203009 | + | 0.398481i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.84198 | − | 4.84198i | 1.17435 | − | 1.17435i | 0.193193 | − | 0.981161i | \(-0.438116\pi\) |
0.981161 | − | 0.193193i | \(-0.0618843\pi\) | |||||||
\(18\) | 2.96312 | + | 0.468987i | 0.698413 | + | 0.110541i | ||||
\(19\) | −2.49053 | − | 2.49053i | −0.571367 | − | 0.571367i | 0.361143 | − | 0.932510i | \(-0.382387\pi\) |
−0.932510 | + | 0.361143i | \(0.882387\pi\) | |||||||
\(20\) | 0.707107 | + | 0.707107i | 0.158114 | + | 0.158114i | ||||
\(21\) | 4.18328 | − | 1.35948i | 0.912866 | − | 0.296662i | ||||
\(22\) | 1.09777 | + | 1.09777i | 0.234045 | + | 0.234045i | ||||
\(23\) | 0.856269 | − | 0.856269i | 0.178544 | − | 0.178544i | −0.612177 | − | 0.790721i | \(-0.709706\pi\) |
0.790721 | + | 0.612177i | \(0.209706\pi\) | |||||||
\(24\) | 0.786252 | − | 1.54331i | 0.160493 | − | 0.315027i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | − | 1.57762i | − | 0.309396i | ||||||
\(27\) | −3.05355 | + | 4.20426i | −0.587656 | + | 0.809111i | ||||
\(28\) | − | 2.53955i | − | 0.479930i | ||||||
\(29\) | 5.19422 | + | 5.19422i | 0.964543 | + | 0.964543i | 0.999393 | − | 0.0348499i | \(-0.0110953\pi\) |
−0.0348499 | + | 0.999393i | \(0.511095\pi\) | |||||||
\(30\) | −1.64725 | + | 0.535321i | −0.300745 | + | 0.0977358i | ||||
\(31\) | 1.70231 | − | 1.70231i | 0.305743 | − | 0.305743i | −0.537513 | − | 0.843256i | \(-0.680636\pi\) |
0.843256 | + | 0.537513i | \(0.180636\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −2.55731 | + | 0.831073i | −0.445171 | + | 0.144671i | ||||
\(34\) | 6.84760 | 1.17435 | ||||||||
\(35\) | −1.79574 | + | 1.79574i | −0.303535 | + | 0.303535i | ||||
\(36\) | 1.76361 | + | 2.42686i | 0.293936 | + | 0.404477i | ||||
\(37\) | 3.85543 | + | 4.70486i | 0.633829 | + | 0.773474i | ||||
\(38\) | − | 3.52214i | − | 0.571367i | ||||||
\(39\) | 2.43475 | + | 1.24041i | 0.389873 | + | 0.198624i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | 10.4791 | 1.63657 | 0.818284 | − | 0.574815i | \(-0.194926\pi\) | ||||
0.818284 | + | 0.574815i | \(0.194926\pi\) | |||||||
\(42\) | 3.91932 | + | 1.99673i | 0.604764 | + | 0.308102i | ||||
\(43\) | −2.78010 | − | 2.78010i | −0.423961 | − | 0.423961i | 0.462604 | − | 0.886565i | \(-0.346915\pi\) |
−0.886565 | + | 0.462604i | \(0.846915\pi\) | |||||||
\(44\) | 1.55248i | 0.234045i | ||||||||
\(45\) | 0.468987 | − | 2.96312i | 0.0699125 | − | 0.441715i | ||||
\(46\) | 1.21095 | 0.178544 | ||||||||
\(47\) | − | 10.4277i | − | 1.52104i | −0.649317 | − | 0.760518i | \(-0.724945\pi\) | ||
0.649317 | − | 0.760518i | \(-0.275055\pi\) | |||||||
\(48\) | 1.64725 | − | 0.535321i | 0.237760 | − | 0.0772669i | ||||
\(49\) | −0.550669 | −0.0786670 | ||||||||
\(50\) | 0.707107 | − | 0.707107i | 0.100000 | − | 0.100000i | ||||
\(51\) | −5.38394 | + | 10.5680i | −0.753902 | + | 1.47981i | ||||
\(52\) | 1.11554 | − | 1.11554i | 0.154698 | − | 0.154698i | ||||
\(53\) | 5.16143i | 0.708978i | 0.935060 | + | 0.354489i | \(0.115345\pi\) | ||||
−0.935060 | + | 0.354489i | \(0.884655\pi\) | |||||||
\(54\) | −5.13205 | + | 0.813678i | −0.698383 | + | 0.110728i | ||||
\(55\) | 1.09777 | − | 1.09777i | 0.148023 | − | 0.148023i | ||||
\(56\) | 1.79574 | − | 1.79574i | 0.239965 | − | 0.239965i | ||||
\(57\) | 5.43576 | + | 2.76929i | 0.719984 | + | 0.366802i | ||||
\(58\) | 7.34574i | 0.964543i | ||||||||
\(59\) | 8.36584 | − | 8.36584i | 1.08914 | − | 1.08914i | 0.0935229 | − | 0.995617i | \(-0.470187\pi\) |
0.995617 | − | 0.0935229i | \(-0.0298128\pi\) | |||||||
\(60\) | −1.54331 | − | 0.786252i | −0.199241 | − | 0.101505i | ||||
\(61\) | 7.41355 | − | 7.41355i | 0.949208 | − | 0.949208i | −0.0495632 | − | 0.998771i | \(-0.515783\pi\) |
0.998771 | + | 0.0495632i | \(0.0157829\pi\) | |||||||
\(62\) | 2.40742 | 0.305743 | ||||||||
\(63\) | −6.16315 | + | 4.47879i | −0.776484 | + | 0.564275i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −1.57762 | −0.195679 | ||||||||
\(66\) | −2.39595 | − | 1.22064i | −0.294921 | − | 0.150250i | ||||
\(67\) | 1.98974i | 0.243085i | 0.992586 | + | 0.121543i | \(0.0387841\pi\) | ||||
−0.992586 | + | 0.121543i | \(0.961216\pi\) | |||||||
\(68\) | 4.84198 | + | 4.84198i | 0.587177 | + | 0.587177i | ||||
\(69\) | −0.952110 | + | 1.86887i | −0.114621 | + | 0.224985i | ||||
\(70\) | −2.53955 | −0.303535 | ||||||||
\(71\) | − | 3.37621i | − | 0.400682i | −0.979726 | − | 0.200341i | \(-0.935795\pi\) | ||
0.979726 | − | 0.200341i | \(-0.0642050\pi\) | |||||||
\(72\) | −0.468987 | + | 2.96312i | −0.0552707 | + | 0.349206i | ||||
\(73\) | − | 0.480190i | − | 0.0562020i | −0.999605 | − | 0.0281010i | \(-0.991054\pi\) | ||
0.999605 | − | 0.0281010i | \(-0.00894601\pi\) | |||||||
\(74\) | −0.600636 | + | 6.05304i | −0.0698225 | + | 0.703651i | ||||
\(75\) | 0.535321 | + | 1.64725i | 0.0618135 | + | 0.190208i | ||||
\(76\) | 2.49053 | − | 2.49053i | 0.285684 | − | 0.285684i | ||||
\(77\) | −3.94259 | −0.449300 | ||||||||
\(78\) | 0.844532 | + | 2.59873i | 0.0956244 | + | 0.294248i | ||||
\(79\) | 6.52251 | + | 6.52251i | 0.733840 | + | 0.733840i | 0.971378 | − | 0.237538i | \(-0.0763405\pi\) |
−0.237538 | + | 0.971378i | \(0.576341\pi\) | |||||||
\(80\) | −0.707107 | + | 0.707107i | −0.0790569 | + | 0.0790569i | ||||
\(81\) | 2.77933 | − | 8.56010i | 0.308814 | − | 0.951122i | ||||
\(82\) | 7.40987 | + | 7.40987i | 0.818284 | + | 0.818284i | ||||
\(83\) | 8.64749i | 0.949186i | 0.880205 | + | 0.474593i | \(0.157405\pi\) | ||||
−0.880205 | + | 0.474593i | \(0.842595\pi\) | |||||||
\(84\) | 1.35948 | + | 4.18328i | 0.148331 | + | 0.456433i | ||||
\(85\) | − | 6.84760i | − | 0.742726i | ||||||
\(86\) | − | 3.93165i | − | 0.423961i | ||||||
\(87\) | −11.3368 | − | 5.77560i | −1.21543 | − | 0.619210i | ||||
\(88\) | −1.09777 | + | 1.09777i | −0.117022 | + | 0.117022i | ||||
\(89\) | 10.5685 | + | 10.5685i | 1.12026 | + | 1.12026i | 0.991702 | + | 0.128557i | \(0.0410345\pi\) |
0.128557 | + | 0.991702i | \(0.458965\pi\) | |||||||
\(90\) | 2.42686 | − | 1.76361i | 0.255814 | − | 0.185901i | ||||
\(91\) | 2.83298 | + | 2.83298i | 0.296977 | + | 0.296977i | ||||
\(92\) | 0.856269 | + | 0.856269i | 0.0892722 | + | 0.0892722i | ||||
\(93\) | −1.89284 | + | 3.71540i | −0.196279 | + | 0.385269i | ||||
\(94\) | 7.37349 | − | 7.37349i | 0.760518 | − | 0.760518i | ||||
\(95\) | −3.52214 | −0.361364 | ||||||||
\(96\) | 1.54331 | + | 0.786252i | 0.157513 | + | 0.0802465i | ||||
\(97\) | −5.01332 | − | 5.01332i | −0.509026 | − | 0.509026i | 0.405202 | − | 0.914227i | \(-0.367201\pi\) |
−0.914227 | + | 0.405202i | \(0.867201\pi\) | |||||||
\(98\) | −0.389382 | − | 0.389382i | −0.0393335 | − | 0.0393335i | ||||
\(99\) | 3.76765 | − | 2.73797i | 0.378663 | − | 0.275176i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −3.12753 | −0.311201 | −0.155600 | − | 0.987820i | \(-0.549731\pi\) | ||||
−0.155600 | + | 0.987820i | \(0.549731\pi\) | |||||||
\(102\) | −11.2797 | + | 3.66566i | −1.11686 | + | 0.362955i | ||||
\(103\) | −9.44888 | + | 9.44888i | −0.931026 | + | 0.931026i | −0.997770 | − | 0.0667446i | \(-0.978739\pi\) |
0.0667446 | + | 0.997770i | \(0.478739\pi\) | |||||||
\(104\) | 1.57762 | 0.154698 | ||||||||
\(105\) | 1.99673 | − | 3.91932i | 0.194861 | − | 0.382486i | ||||
\(106\) | −3.64969 | + | 3.64969i | −0.354489 | + | 0.354489i | ||||
\(107\) | − | 1.92564i | − | 0.186159i | −0.995659 | − | 0.0930794i | \(-0.970329\pi\) | ||
0.995659 | − | 0.0930794i | \(-0.0296710\pi\) | |||||||
\(108\) | −4.20426 | − | 3.05355i | −0.404556 | − | 0.293828i | ||||
\(109\) | −1.77468 | − | 1.77468i | −0.169983 | − | 0.169983i | 0.616989 | − | 0.786972i | \(-0.288352\pi\) |
−0.786972 | + | 0.616989i | \(0.788352\pi\) | |||||||
\(110\) | 1.55248 | 0.148023 | ||||||||
\(111\) | −8.86946 | − | 5.68618i | −0.841852 | − | 0.539708i | ||||
\(112\) | 2.53955 | 0.239965 | ||||||||
\(113\) | −11.3932 | − | 11.3932i | −1.07178 | − | 1.07178i | −0.997216 | − | 0.0745674i | \(-0.976242\pi\) |
−0.0745674 | − | 0.997216i | \(-0.523758\pi\) | |||||||
\(114\) | 1.88548 | + | 5.80185i | 0.176591 | + | 0.543393i | ||||
\(115\) | − | 1.21095i | − | 0.112921i | ||||||
\(116\) | −5.19422 | + | 5.19422i | −0.482271 | + | 0.482271i | ||||
\(117\) | −4.67466 | − | 0.739883i | −0.432173 | − | 0.0684022i | ||||
\(118\) | 11.8311 | 1.08914 | ||||||||
\(119\) | −12.2965 | + | 12.2965i | −1.12722 | + | 1.12722i | ||||
\(120\) | −0.535321 | − | 1.64725i | −0.0488679 | − | 0.150373i | ||||
\(121\) | −8.58982 | −0.780893 | ||||||||
\(122\) | 10.4843 | 0.949208 | ||||||||
\(123\) | −17.2618 | + | 5.60971i | −1.55644 | + | 0.505810i | ||||
\(124\) | 1.70231 | + | 1.70231i | 0.152872 | + | 0.152872i | ||||
\(125\) | −0.707107 | − | 0.707107i | −0.0632456 | − | 0.0632456i | ||||
\(126\) | −7.52499 | − | 1.19102i | −0.670379 | − | 0.106104i | ||||
\(127\) | 14.3170 | 1.27043 | 0.635215 | − | 0.772336i | \(-0.280912\pi\) | ||||
0.635215 | + | 0.772336i | \(0.280912\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 6.06776 | + | 3.09127i | 0.534236 | + | 0.272171i | ||||
\(130\) | −1.11554 | − | 1.11554i | −0.0978397 | − | 0.0978397i | ||||
\(131\) | 0.642612 | + | 0.642612i | 0.0561453 | + | 0.0561453i | 0.734622 | − | 0.678477i | \(-0.237360\pi\) |
−0.678477 | + | 0.734622i | \(0.737360\pi\) | |||||||
\(132\) | −0.831073 | − | 2.55731i | −0.0723356 | − | 0.222586i | ||||
\(133\) | 6.32484 | + | 6.32484i | 0.548433 | + | 0.548433i | ||||
\(134\) | −1.40696 | + | 1.40696i | −0.121543 | + | 0.121543i | ||||
\(135\) | 0.813678 | + | 5.13205i | 0.0700303 | + | 0.441696i | ||||
\(136\) | 6.84760i | 0.587177i | ||||||||
\(137\) | − | 22.7686i | − | 1.94525i | −0.232373 | − | 0.972627i | \(-0.574649\pi\) | ||
0.232373 | − | 0.972627i | \(-0.425351\pi\) | |||||||
\(138\) | −1.99473 | + | 0.648245i | −0.169803 | + | 0.0551823i | ||||
\(139\) | − | 6.95397i | − | 0.589828i | −0.955524 | − | 0.294914i | \(-0.904709\pi\) | ||
0.955524 | − | 0.294914i | \(-0.0952910\pi\) | |||||||
\(140\) | −1.79574 | − | 1.79574i | −0.151767 | − | 0.151767i | ||||
\(141\) | 5.58216 | + | 17.1770i | 0.470103 | + | 1.44657i | ||||
\(142\) | 2.38734 | − | 2.38734i | 0.200341 | − | 0.200341i | ||||
\(143\) | −1.73185 | − | 1.73185i | −0.144825 | − | 0.144825i | ||||
\(144\) | −2.42686 | + | 1.76361i | −0.202239 | + | 0.146968i | ||||
\(145\) | 7.34574 | 0.610030 | ||||||||
\(146\) | 0.339546 | − | 0.339546i | 0.0281010 | − | 0.0281010i | ||||
\(147\) | 0.907089 | − | 0.294785i | 0.0748154 | − | 0.0243134i | ||||
\(148\) | −4.70486 | + | 3.85543i | −0.386737 | + | 0.316914i | ||||
\(149\) | − | 15.3710i | − | 1.25924i | −0.776904 | − | 0.629619i | \(-0.783211\pi\) | ||
0.776904 | − | 0.629619i | \(-0.216789\pi\) | |||||||
\(150\) | −0.786252 | + | 1.54331i | −0.0641972 | + | 0.126011i | ||||
\(151\) | 8.84452i | 0.719756i | 0.932999 | + | 0.359878i | \(0.117182\pi\) | ||||
−0.932999 | + | 0.359878i | \(0.882818\pi\) | |||||||
\(152\) | 3.52214 | 0.285684 | ||||||||
\(153\) | 3.21144 | − | 20.2902i | 0.259629 | − | 1.64037i | ||||
\(154\) | −2.78784 | − | 2.78784i | −0.224650 | − | 0.224650i | ||||
\(155\) | − | 2.40742i | − | 0.193369i | ||||||
\(156\) | −1.24041 | + | 2.43475i | −0.0993119 | + | 0.194936i | ||||
\(157\) | 4.17933 | 0.333547 | 0.166774 | − | 0.985995i | \(-0.446665\pi\) | ||||
0.166774 | + | 0.985995i | \(0.446665\pi\) | |||||||
\(158\) | 9.22422i | 0.733840i | ||||||||
\(159\) | −2.76302 | − | 8.50217i | −0.219122 | − | 0.674266i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.17454 | + | 2.17454i | −0.171378 | + | 0.171378i | ||||
\(162\) | 8.01819 | − | 4.08763i | 0.629968 | − | 0.321154i | ||||
\(163\) | 1.54752 | − | 1.54752i | 0.121211 | − | 0.121211i | −0.643899 | − | 0.765110i | \(-0.722684\pi\) |
0.765110 | + | 0.643899i | \(0.222684\pi\) | |||||||
\(164\) | 10.4791i | 0.818284i | ||||||||
\(165\) | −1.22064 | + | 2.39595i | −0.0950265 | + | 0.186525i | ||||
\(166\) | −6.11470 | + | 6.11470i | −0.474593 | + | 0.474593i | ||||
\(167\) | 13.7766 | − | 13.7766i | 1.06607 | − | 1.06607i | 0.0684095 | − | 0.997657i | \(-0.478208\pi\) |
0.997657 | − | 0.0684095i | \(-0.0217924\pi\) | |||||||
\(168\) | −1.99673 | + | 3.91932i | −0.154051 | + | 0.302382i | ||||
\(169\) | − | 10.5111i | − | 0.808548i | ||||||
\(170\) | 4.84198 | − | 4.84198i | 0.371363 | − | 0.371363i | ||||
\(171\) | −10.4365 | − | 1.65184i | −0.798101 | − | 0.126319i | ||||
\(172\) | 2.78010 | − | 2.78010i | 0.211980 | − | 0.211980i | ||||
\(173\) | −22.4262 | −1.70503 | −0.852517 | − | 0.522699i | \(-0.824925\pi\) | ||||
−0.852517 | + | 0.522699i | \(0.824925\pi\) | |||||||
\(174\) | −3.93233 | − | 12.1003i | −0.298109 | − | 0.917319i | ||||
\(175\) | 2.53955i | 0.191972i | ||||||||
\(176\) | −1.55248 | −0.117022 | ||||||||
\(177\) | −9.30222 | + | 18.2590i | −0.699198 | + | 1.37243i | ||||
\(178\) | 14.9461i | 1.12026i | ||||||||
\(179\) | −5.77543 | − | 5.77543i | −0.431676 | − | 0.431676i | 0.457522 | − | 0.889198i | \(-0.348737\pi\) |
−0.889198 | + | 0.457522i | \(0.848737\pi\) | |||||||
\(180\) | 2.96312 | + | 0.468987i | 0.220858 | + | 0.0349563i | ||||
\(181\) | 13.1382 | 0.976553 | 0.488276 | − | 0.872689i | \(-0.337626\pi\) | ||||
0.488276 | + | 0.872689i | \(0.337626\pi\) | |||||||
\(182\) | 4.00644i | 0.296977i | ||||||||
\(183\) | −8.24334 | + | 16.1806i | −0.609365 | + | 1.19610i | ||||
\(184\) | 1.21095i | 0.0892722i | ||||||||
\(185\) | 6.05304 | + | 0.600636i | 0.445028 | + | 0.0441596i | ||||
\(186\) | −3.96563 | + | 1.28874i | −0.290774 | + | 0.0944954i | ||||
\(187\) | 7.51706 | − | 7.51706i | 0.549702 | − | 0.549702i | ||||
\(188\) | 10.4277 | 0.760518 | ||||||||
\(189\) | 7.75465 | − | 10.6770i | 0.564068 | − | 0.776634i | ||||
\(190\) | −2.49053 | − | 2.49053i | −0.180682 | − | 0.180682i | ||||
\(191\) | −6.53325 | + | 6.53325i | −0.472729 | + | 0.472729i | −0.902797 | − | 0.430068i | \(-0.858490\pi\) |
0.430068 | + | 0.902797i | \(0.358490\pi\) | |||||||
\(192\) | 0.535321 | + | 1.64725i | 0.0386335 | + | 0.118880i | ||||
\(193\) | 1.18075 | + | 1.18075i | 0.0849921 | + | 0.0849921i | 0.748325 | − | 0.663333i | \(-0.230859\pi\) |
−0.663333 | + | 0.748325i | \(0.730859\pi\) | |||||||
\(194\) | − | 7.08991i | − | 0.509026i | ||||||
\(195\) | 2.59873 | − | 0.844532i | 0.186099 | − | 0.0604782i | ||||
\(196\) | − | 0.550669i | − | 0.0393335i | ||||||
\(197\) | − | 3.07165i | − | 0.218846i | −0.993995 | − | 0.109423i | \(-0.965100\pi\) | ||
0.993995 | − | 0.109423i | \(-0.0349003\pi\) | |||||||
\(198\) | 4.60016 | + | 0.728091i | 0.326919 | + | 0.0517432i | ||||
\(199\) | −1.93640 | + | 1.93640i | −0.137268 | + | 0.137268i | −0.772402 | − | 0.635134i | \(-0.780945\pi\) |
0.635134 | + | 0.772402i | \(0.280945\pi\) | |||||||
\(200\) | 0.707107 | + | 0.707107i | 0.0500000 | + | 0.0500000i | ||||
\(201\) | −1.06515 | − | 3.27760i | −0.0751298 | − | 0.231184i | ||||
\(202\) | −2.21150 | − | 2.21150i | −0.155600 | − | 0.155600i | ||||
\(203\) | −13.1910 | − | 13.1910i | −0.925827 | − | 0.925827i | ||||
\(204\) | −10.5680 | − | 5.38394i | −0.739906 | − | 0.376951i | ||||
\(205\) | 7.40987 | − | 7.40987i | 0.517528 | − | 0.517528i | ||||
\(206\) | −13.3627 | −0.931026 | ||||||||
\(207\) | 0.567919 | − | 3.58817i | 0.0394731 | − | 0.249395i | ||||
\(208\) | 1.11554 | + | 1.11554i | 0.0773490 | + | 0.0773490i | ||||
\(209\) | −3.86649 | − | 3.86649i | −0.267451 | − | 0.267451i | ||||
\(210\) | 4.18328 | − | 1.35948i | 0.288674 | − | 0.0938128i | ||||
\(211\) | −24.0332 | −1.65451 | −0.827257 | − | 0.561824i | \(-0.810100\pi\) | ||||
−0.827257 | + | 0.561824i | \(0.810100\pi\) | |||||||
\(212\) | −5.16143 | −0.354489 | ||||||||
\(213\) | 1.80736 | + | 5.56146i | 0.123838 | + | 0.381065i | ||||
\(214\) | 1.36163 | − | 1.36163i | 0.0930794 | − | 0.0930794i | ||||
\(215\) | −3.93165 | −0.268136 | ||||||||
\(216\) | −0.813678 | − | 5.13205i | −0.0553638 | − | 0.349192i | ||||
\(217\) | −4.32310 | + | 4.32310i | −0.293471 | + | 0.293471i | ||||
\(218\) | − | 2.50977i | − | 0.169983i | ||||||
\(219\) | 0.257056 | + | 0.790993i | 0.0173702 | + | 0.0534504i | ||||
\(220\) | 1.09777 | + | 1.09777i | 0.0740114 | + | 0.0740114i | ||||
\(221\) | −10.8029 | −0.726681 | ||||||||
\(222\) | −2.25092 | − | 10.2924i | −0.151072 | − | 0.690780i | ||||
\(223\) | −19.6653 | −1.31688 | −0.658442 | − | 0.752631i | \(-0.728784\pi\) | ||||
−0.658442 | + | 0.752631i | \(0.728784\pi\) | |||||||
\(224\) | 1.79574 | + | 1.79574i | 0.119983 | + | 0.119983i | ||||
\(225\) | −1.76361 | − | 2.42686i | −0.117574 | − | 0.161791i | ||||
\(226\) | − | 16.1124i | − | 1.07178i | ||||||
\(227\) | 2.56107 | − | 2.56107i | 0.169984 | − | 0.169984i | −0.616988 | − | 0.786972i | \(-0.711647\pi\) |
0.786972 | + | 0.616988i | \(0.211647\pi\) | |||||||
\(228\) | −2.76929 | + | 5.43576i | −0.183401 | + | 0.359992i | ||||
\(229\) | 13.0356 | 0.861418 | 0.430709 | − | 0.902491i | \(-0.358264\pi\) | ||||
0.430709 | + | 0.902491i | \(0.358264\pi\) | |||||||
\(230\) | 0.856269 | − | 0.856269i | 0.0564607 | − | 0.0564607i | ||||
\(231\) | 6.49444 | − | 2.11055i | 0.427303 | − | 0.138864i | ||||
\(232\) | −7.34574 | −0.482271 | ||||||||
\(233\) | −20.4916 | −1.34245 | −0.671223 | − | 0.741255i | \(-0.734231\pi\) | ||||
−0.671223 | + | 0.741255i | \(0.734231\pi\) | |||||||
\(234\) | −2.78231 | − | 3.82866i | −0.181885 | − | 0.250287i | ||||
\(235\) | −7.37349 | − | 7.37349i | −0.480994 | − | 0.480994i | ||||
\(236\) | 8.36584 | + | 8.36584i | 0.544570 | + | 0.544570i | ||||
\(237\) | −14.2358 | − | 7.25257i | −0.924717 | − | 0.471105i | ||||
\(238\) | −17.3898 | −1.12722 | ||||||||
\(239\) | −16.0579 | + | 16.0579i | −1.03870 | + | 1.03870i | −0.0394798 | + | 0.999220i | \(0.512570\pi\) |
−0.999220 | + | 0.0394798i | \(0.987430\pi\) | |||||||
\(240\) | 0.786252 | − | 1.54331i | 0.0507524 | − | 0.0996203i | ||||
\(241\) | −8.01194 | − | 8.01194i | −0.516095 | − | 0.516095i | 0.400293 | − | 0.916387i | \(-0.368908\pi\) |
−0.916387 | + | 0.400293i | \(0.868908\pi\) | |||||||
\(242\) | −6.07392 | − | 6.07392i | −0.390446 | − | 0.390446i | ||||
\(243\) | 0.00415661 | + | 15.5885i | 0.000266647 | + | 1.00000i | ||||
\(244\) | 7.41355 | + | 7.41355i | 0.474604 | + | 0.474604i | ||||
\(245\) | −0.389382 | + | 0.389382i | −0.0248767 | + | 0.0248767i | ||||
\(246\) | −16.1726 | − | 8.23925i | −1.03113 | − | 0.525315i | ||||
\(247\) | 5.55660i | 0.353558i | ||||||||
\(248\) | 2.40742i | 0.152872i | ||||||||
\(249\) | −4.62918 | − | 14.2446i | −0.293363 | − | 0.902714i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 5.39840 | + | 5.39840i | 0.340744 | + | 0.340744i | 0.856647 | − | 0.515903i | \(-0.172543\pi\) |
−0.515903 | + | 0.856647i | \(0.672543\pi\) | |||||||
\(252\) | −4.47879 | − | 6.16315i | −0.282137 | − | 0.388242i | ||||
\(253\) | 1.32934 | − | 1.32934i | 0.0835747 | − | 0.0835747i | ||||
\(254\) | 10.1237 | + | 10.1237i | 0.635215 | + | 0.635215i | ||||
\(255\) | 3.66566 | + | 11.2797i | 0.229553 | + | 0.706363i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.9474 | + | 12.9474i | −0.807636 | + | 0.807636i | −0.984276 | − | 0.176640i | \(-0.943477\pi\) |
0.176640 | + | 0.984276i | \(0.443477\pi\) | |||||||
\(258\) | 2.10470 | + | 6.47641i | 0.131033 | + | 0.403204i | ||||
\(259\) | −9.79107 | − | 11.9482i | −0.608387 | − | 0.742427i | ||||
\(260\) | − | 1.57762i | − | 0.0978397i | ||||||
\(261\) | 21.7663 | + | 3.44506i | 1.34730 | + | 0.213244i | ||||
\(262\) | 0.908791i | 0.0561453i | ||||||||
\(263\) | 7.40115 | 0.456375 | 0.228187 | − | 0.973617i | \(-0.426720\pi\) | ||||
0.228187 | + | 0.973617i | \(0.426720\pi\) | |||||||
\(264\) | 1.22064 | − | 2.39595i | 0.0751250 | − | 0.147461i | ||||
\(265\) | 3.64969 | + | 3.64969i | 0.224198 | + | 0.224198i | ||||
\(266\) | 8.94467i | 0.548433i | ||||||||
\(267\) | −23.0665 | − | 11.7514i | −1.41165 | − | 0.719175i | ||||
\(268\) | −1.98974 | −0.121543 | ||||||||
\(269\) | 22.3915i | 1.36523i | 0.730776 | + | 0.682617i | \(0.239158\pi\) | ||||
−0.730776 | + | 0.682617i | \(0.760842\pi\) | |||||||
\(270\) | −3.05355 | + | 4.20426i | −0.185833 | + | 0.255863i | ||||
\(271\) | 18.4875 | 1.12304 | 0.561518 | − | 0.827465i | \(-0.310218\pi\) | ||||
0.561518 | + | 0.827465i | \(0.310218\pi\) | |||||||
\(272\) | −4.84198 | + | 4.84198i | −0.293588 | + | 0.293588i | ||||
\(273\) | −6.18319 | − | 3.15008i | −0.374223 | − | 0.190651i | ||||
\(274\) | 16.0998 | − | 16.0998i | 0.972627 | − | 0.972627i | ||||
\(275\) | − | 1.55248i | − | 0.0936178i | ||||||
\(276\) | −1.86887 | − | 0.952110i | −0.112493 | − | 0.0573103i | ||||
\(277\) | 7.72665 | − | 7.72665i | 0.464249 | − | 0.464249i | −0.435796 | − | 0.900045i | \(-0.643533\pi\) |
0.900045 | + | 0.435796i | \(0.143533\pi\) | |||||||
\(278\) | 4.91720 | − | 4.91720i | 0.294914 | − | 0.294914i | ||||
\(279\) | 1.12905 | − | 7.13348i | 0.0675946 | − | 0.427070i | ||||
\(280\) | − | 2.53955i | − | 0.151767i | ||||||
\(281\) | −3.95236 | + | 3.95236i | −0.235778 | + | 0.235778i | −0.815099 | − | 0.579321i | \(-0.803318\pi\) |
0.579321 | + | 0.815099i | \(0.303318\pi\) | |||||||
\(282\) | −8.19880 | + | 16.0932i | −0.488231 | + | 0.958334i | ||||
\(283\) | 4.17375 | − | 4.17375i | 0.248104 | − | 0.248104i | −0.572088 | − | 0.820192i | \(-0.693867\pi\) |
0.820192 | + | 0.572088i | \(0.193867\pi\) | |||||||
\(284\) | 3.37621 | 0.200341 | ||||||||
\(285\) | 5.80185 | − | 1.88548i | 0.343672 | − | 0.111686i | ||||
\(286\) | − | 2.44921i | − | 0.144825i | ||||||
\(287\) | −26.6123 | −1.57088 | ||||||||
\(288\) | −2.96312 | − | 0.468987i | −0.174603 | − | 0.0276353i | ||||
\(289\) | − | 29.8896i | − | 1.75821i | ||||||
\(290\) | 5.19422 | + | 5.19422i | 0.305015 | + | 0.305015i | ||||
\(291\) | 10.9419 | + | 5.57445i | 0.641427 | + | 0.326780i | ||||
\(292\) | 0.480190 | 0.0281010 | ||||||||
\(293\) | 15.2274i | 0.889593i | 0.895632 | + | 0.444796i | \(0.146724\pi\) | ||||
−0.895632 | + | 0.444796i | \(0.853276\pi\) | |||||||
\(294\) | 0.849853 | + | 0.432965i | 0.0495644 | + | 0.0252510i | ||||
\(295\) | − | 11.8311i | − | 0.688833i | ||||||
\(296\) | −6.05304 | − | 0.600636i | −0.351826 | − | 0.0349113i | ||||
\(297\) | −4.74056 | + | 6.52702i | −0.275075 | + | 0.378736i | ||||
\(298\) | 10.8689 | − | 10.8689i | 0.629619 | − | 0.629619i | ||||
\(299\) | −1.91041 | −0.110482 | ||||||||
\(300\) | −1.64725 | + | 0.535321i | −0.0951040 | + | 0.0309068i | ||||
\(301\) | 7.06021 | + | 7.06021i | 0.406944 | + | 0.406944i | ||||
\(302\) | −6.25402 | + | 6.25402i | −0.359878 | + | 0.359878i | ||||
\(303\) | 5.15182 | − | 1.67423i | 0.295964 | − | 0.0961821i | ||||
\(304\) | 2.49053 | + | 2.49053i | 0.142842 | + | 0.142842i | ||||
\(305\) | − | 10.4843i | − | 0.600332i | ||||||
\(306\) | 16.6182 | − | 12.0765i | 0.949998 | − | 0.690369i | ||||
\(307\) | 22.5433i | 1.28661i | 0.765609 | + | 0.643306i | \(0.222438\pi\) | ||||
−0.765609 | + | 0.643306i | \(0.777562\pi\) | |||||||
\(308\) | − | 3.94259i | − | 0.224650i | ||||||
\(309\) | 10.5065 | − | 20.6228i | 0.597693 | − | 1.17319i | ||||
\(310\) | 1.70231 | − | 1.70231i | 0.0966845 | − | 0.0966845i | ||||
\(311\) | 6.11792 | + | 6.11792i | 0.346915 | + | 0.346915i | 0.858959 | − | 0.512044i | \(-0.171112\pi\) |
−0.512044 | + | 0.858959i | \(0.671112\pi\) | |||||||
\(312\) | −2.59873 | + | 0.844532i | −0.147124 | + | 0.0478122i | ||||
\(313\) | 3.26673 | + | 3.26673i | 0.184646 | + | 0.184646i | 0.793377 | − | 0.608731i | \(-0.208321\pi\) |
−0.608731 | + | 0.793377i | \(0.708321\pi\) | |||||||
\(314\) | 2.95524 | + | 2.95524i | 0.166774 | + | 0.166774i | ||||
\(315\) | −1.19102 | + | 7.52499i | −0.0671063 | + | 0.423985i | ||||
\(316\) | −6.52251 | + | 6.52251i | −0.366920 | + | 0.366920i | ||||
\(317\) | 30.0184 | 1.68600 | 0.843001 | − | 0.537912i | \(-0.180787\pi\) | ||||
0.843001 | + | 0.537912i | \(0.180787\pi\) | |||||||
\(318\) | 4.05819 | − | 7.96570i | 0.227572 | − | 0.446694i | ||||
\(319\) | 8.06390 | + | 8.06390i | 0.451492 | + | 0.451492i | ||||
\(320\) | −0.707107 | − | 0.707107i | −0.0395285 | − | 0.0395285i | ||||
\(321\) | 1.03084 | + | 3.17201i | 0.0575357 | + | 0.177044i | ||||
\(322\) | −3.07526 | −0.171378 | ||||||||
\(323\) | −24.1182 | −1.34197 | ||||||||
\(324\) | 8.56010 | + | 2.77933i | 0.475561 | + | 0.154407i | ||||
\(325\) | −1.11554 | + | 1.11554i | −0.0618792 | + | 0.0618792i | ||||
\(326\) | 2.18852 | 0.121211 | ||||||||
\(327\) | 3.87336 | + | 1.97331i | 0.214197 | + | 0.109124i | ||||
\(328\) | −7.40987 | + | 7.40987i | −0.409142 | + | 0.409142i | ||||
\(329\) | 26.4817i | 1.45998i | ||||||||
\(330\) | −2.55731 | + | 0.831073i | −0.140776 | + | 0.0457490i | ||||
\(331\) | 9.21805 | + | 9.21805i | 0.506670 | + | 0.506670i | 0.913503 | − | 0.406833i | \(-0.133367\pi\) |
−0.406833 | + | 0.913503i | \(0.633367\pi\) | |||||||
\(332\) | −8.64749 | −0.474593 | ||||||||
\(333\) | 17.6541 | + | 4.61855i | 0.967441 | + | 0.253095i | ||||
\(334\) | 19.4831 | 1.06607 | ||||||||
\(335\) | 1.40696 | + | 1.40696i | 0.0768704 | + | 0.0768704i | ||||
\(336\) | −4.18328 | + | 1.35948i | −0.228217 | + | 0.0741655i | ||||
\(337\) | 22.7367i | 1.23855i | 0.785175 | + | 0.619275i | \(0.212573\pi\) | ||||
−0.785175 | + | 0.619275i | \(0.787427\pi\) | |||||||
\(338\) | 7.43249 | − | 7.43249i | 0.404274 | − | 0.404274i | ||||
\(339\) | 24.8665 | + | 12.6684i | 1.35056 | + | 0.688055i | ||||
\(340\) | 6.84760 | 0.371363 | ||||||||
\(341\) | 2.64279 | − | 2.64279i | 0.143115 | − | 0.143115i | ||||
\(342\) | −6.21171 | − | 8.54776i | −0.335891 | − | 0.462210i | ||||
\(343\) | 19.1753 | 1.03537 | ||||||||
\(344\) | 3.93165 | 0.211980 | ||||||||
\(345\) | 0.648245 | + | 1.99473i | 0.0349003 | + | 0.107393i | ||||
\(346\) | −15.8577 | − | 15.8577i | −0.852517 | − | 0.852517i | ||||
\(347\) | 12.8734 | + | 12.8734i | 0.691078 | + | 0.691078i | 0.962469 | − | 0.271391i | \(-0.0874837\pi\) |
−0.271391 | + | 0.962469i | \(0.587484\pi\) | |||||||
\(348\) | 5.77560 | − | 11.3368i | 0.309605 | − | 0.607714i | ||||
\(349\) | −17.1933 | −0.920336 | −0.460168 | − | 0.887832i | \(-0.652211\pi\) | ||||
−0.460168 | + | 0.887832i | \(0.652211\pi\) | |||||||
\(350\) | −1.79574 | + | 1.79574i | −0.0959861 | + | 0.0959861i | ||||
\(351\) | 8.09641 | − | 1.28367i | 0.432154 | − | 0.0685174i | ||||
\(352\) | −1.09777 | − | 1.09777i | −0.0585111 | − | 0.0585111i | ||||
\(353\) | 13.6457 | + | 13.6457i | 0.726286 | + | 0.726286i | 0.969878 | − | 0.243592i | \(-0.0783257\pi\) |
−0.243592 | + | 0.969878i | \(0.578326\pi\) | |||||||
\(354\) | −19.4888 | + | 6.33343i | −1.03582 | + | 0.336618i | ||||
\(355\) | −2.38734 | − | 2.38734i | −0.126707 | − | 0.126707i | ||||
\(356\) | −10.5685 | + | 10.5685i | −0.560130 | + | 0.560130i | ||||
\(357\) | 13.6728 | − | 26.8379i | 0.723642 | − | 1.42041i | ||||
\(358\) | − | 8.16769i | − | 0.431676i | ||||||
\(359\) | − | 32.6347i | − | 1.72239i | −0.508272 | − | 0.861197i | \(-0.669716\pi\) | ||
0.508272 | − | 0.861197i | \(-0.330284\pi\) | |||||||
\(360\) | 1.76361 | + | 2.42686i | 0.0929507 | + | 0.127907i | ||||
\(361\) | − | 6.59450i | − | 0.347079i | ||||||
\(362\) | 9.29009 | + | 9.29009i | 0.488276 | + | 0.488276i | ||||
\(363\) | 14.1496 | − | 4.59831i | 0.742660 | − | 0.241349i | ||||
\(364\) | −2.83298 | + | 2.83298i | −0.148489 | + | 0.148489i | ||||
\(365\) | −0.339546 | − | 0.339546i | −0.0177726 | − | 0.0177726i | ||||
\(366\) | −17.2703 | + | 5.61249i | −0.902735 | + | 0.293369i | ||||
\(367\) | −12.0728 | −0.630194 | −0.315097 | − | 0.949060i | \(-0.602037\pi\) | ||||
−0.315097 | + | 0.949060i | \(0.602037\pi\) | |||||||
\(368\) | −0.856269 | + | 0.856269i | −0.0446361 | + | 0.0446361i | ||||
\(369\) | 25.4314 | − | 18.4812i | 1.32391 | − | 0.962091i | ||||
\(370\) | 3.85543 | + | 4.70486i | 0.200434 | + | 0.244594i | ||||
\(371\) | − | 13.1077i | − | 0.680520i | ||||||
\(372\) | −3.71540 | − | 1.89284i | −0.192635 | − | 0.0981393i | ||||
\(373\) | 26.6336i | 1.37904i | 0.724268 | + | 0.689518i | \(0.242178\pi\) | ||||
−0.724268 | + | 0.689518i | \(0.757822\pi\) | |||||||
\(374\) | 10.6307 | 0.549702 | ||||||||
\(375\) | 1.54331 | + | 0.786252i | 0.0796962 | + | 0.0406019i | ||||
\(376\) | 7.37349 | + | 7.37349i | 0.380259 | + | 0.380259i | ||||
\(377\) | − | 11.5888i | − | 0.596852i | ||||||
\(378\) | 13.0331 | − | 2.06638i | 0.670351 | − | 0.106283i | ||||
\(379\) | 20.7514 | 1.06593 | 0.532963 | − | 0.846139i | \(-0.321078\pi\) | ||||
0.532963 | + | 0.846139i | \(0.321078\pi\) | |||||||
\(380\) | − | 3.52214i | − | 0.180682i | ||||||
\(381\) | −23.5837 | + | 7.66420i | −1.20823 | + | 0.392649i | ||||
\(382\) | −9.23941 | −0.472729 | ||||||||
\(383\) | 15.8691 | − | 15.8691i | 0.810874 | − | 0.810874i | −0.173891 | − | 0.984765i | \(-0.555634\pi\) |
0.984765 | + | 0.173891i | \(0.0556340\pi\) | |||||||
\(384\) | −0.786252 | + | 1.54331i | −0.0401233 | + | 0.0787567i | ||||
\(385\) | −2.78784 | + | 2.78784i | −0.142081 | + | 0.142081i | ||||
\(386\) | 1.66983i | 0.0849921i | ||||||||
\(387\) | −11.6499 | − | 1.84390i | −0.592200 | − | 0.0937305i | ||||
\(388\) | 5.01332 | − | 5.01332i | 0.254513 | − | 0.254513i | ||||
\(389\) | −8.71629 | + | 8.71629i | −0.441934 | + | 0.441934i | −0.892661 | − | 0.450728i | \(-0.851164\pi\) |
0.450728 | + | 0.892661i | \(0.351164\pi\) | |||||||
\(390\) | 2.43475 | + | 1.24041i | 0.123289 | + | 0.0628104i | ||||
\(391\) | − | 8.29208i | − | 0.419348i | ||||||
\(392\) | 0.389382 | − | 0.389382i | 0.0196667 | − | 0.0196667i | ||||
\(393\) | −1.40255 | − | 0.714539i | −0.0707491 | − | 0.0360437i | ||||
\(394\) | 2.17198 | − | 2.17198i | 0.109423 | − | 0.109423i | ||||
\(395\) | 9.22422 | 0.464121 | ||||||||
\(396\) | 2.73797 | + | 3.76765i | 0.137588 | + | 0.189331i | ||||
\(397\) | − | 0.0949796i | − | 0.00476689i | −0.999997 | − | 0.00238345i | \(-0.999241\pi\) | ||
0.999997 | − | 0.00238345i | \(-0.000758675\pi\) | |||||||
\(398\) | −2.73848 | −0.137268 | ||||||||
\(399\) | −13.8044 | − | 7.03277i | −0.691085 | − | 0.352079i | ||||
\(400\) | 1.00000i | 0.0500000i | ||||||||
\(401\) | 3.89325 | + | 3.89325i | 0.194420 | + | 0.194420i | 0.797603 | − | 0.603183i | \(-0.206101\pi\) |
−0.603183 | + | 0.797603i | \(0.706101\pi\) | |||||||
\(402\) | 1.56444 | − | 3.07079i | 0.0780270 | − | 0.153157i | ||||
\(403\) | −3.79799 | −0.189192 | ||||||||
\(404\) | − | 3.12753i | − | 0.155600i | ||||||
\(405\) | −4.08763 | − | 8.01819i | −0.203116 | − | 0.398427i | ||||
\(406\) | − | 18.6549i | − | 0.925827i | ||||||
\(407\) | 5.98546 | + | 7.30417i | 0.296688 | + | 0.362054i | ||||
\(408\) | −3.66566 | − | 11.2797i | −0.181477 | − | 0.558429i | ||||
\(409\) | 22.8071 | − | 22.8071i | 1.12774 | − | 1.12774i | 0.137192 | − | 0.990544i | \(-0.456192\pi\) |
0.990544 | − | 0.137192i | \(-0.0438078\pi\) | |||||||
\(410\) | 10.4791 | 0.517528 | ||||||||
\(411\) | 12.1885 | + | 37.5056i | 0.601215 | + | 1.85001i | ||||
\(412\) | −9.44888 | − | 9.44888i | −0.465513 | − | 0.465513i | ||||
\(413\) | −21.2455 | + | 21.2455i | −1.04542 | + | 1.04542i | ||||
\(414\) | 2.93880 | − | 2.13564i | 0.144434 | − | 0.104961i | ||||
\(415\) | 6.11470 | + | 6.11470i | 0.300159 | + | 0.300159i | ||||
\(416\) | 1.57762i | 0.0773490i | ||||||||
\(417\) | 3.72260 | + | 11.4549i | 0.182297 | + | 0.560950i | ||||
\(418\) | − | 5.46804i | − | 0.267451i | ||||||
\(419\) | − | 19.4604i | − | 0.950701i | −0.879797 | − | 0.475350i | \(-0.842321\pi\) | ||
0.879797 | − | 0.475350i | \(-0.157679\pi\) | |||||||
\(420\) | 3.91932 | + | 1.99673i | 0.191243 | + | 0.0974304i | ||||
\(421\) | −14.1201 | + | 14.1201i | −0.688171 | + | 0.688171i | −0.961827 | − | 0.273657i | \(-0.911767\pi\) |
0.273657 | + | 0.961827i | \(0.411767\pi\) | |||||||
\(422\) | −16.9940 | − | 16.9940i | −0.827257 | − | 0.827257i | ||||
\(423\) | −18.3904 | − | 25.3066i | −0.894174 | − | 1.23045i | ||||
\(424\) | −3.64969 | − | 3.64969i | −0.177244 | − | 0.177244i | ||||
\(425\) | −4.84198 | − | 4.84198i | −0.234871 | − | 0.234871i | ||||
\(426\) | −2.65455 | + | 5.21054i | −0.128613 | + | 0.252451i | ||||
\(427\) | −18.8271 | + | 18.8271i | −0.911107 | + | 0.911107i | ||||
\(428\) | 1.92564 | 0.0930794 | ||||||||
\(429\) | 3.77989 | + | 1.92570i | 0.182495 | + | 0.0929736i | ||||
\(430\) | −2.78010 | − | 2.78010i | −0.134068 | − | 0.134068i | ||||
\(431\) | 23.2957 | + | 23.2957i | 1.12211 | + | 1.12211i | 0.991423 | + | 0.130692i | \(0.0417198\pi\) |
0.130692 | + | 0.991423i | \(0.458280\pi\) | |||||||
\(432\) | 3.05355 | − | 4.20426i | 0.146914 | − | 0.202278i | ||||
\(433\) | −6.51982 | −0.313323 | −0.156661 | − | 0.987652i | \(-0.550073\pi\) | ||||
−0.156661 | + | 0.987652i | \(0.550073\pi\) | |||||||
\(434\) | −6.11378 | −0.293471 | ||||||||
\(435\) | −12.1003 | + | 3.93233i | −0.580163 | + | 0.188541i | ||||
\(436\) | 1.77468 | − | 1.77468i | 0.0849916 | − | 0.0849916i | ||||
\(437\) | −4.26513 | −0.204029 | ||||||||
\(438\) | −0.377551 | + | 0.741083i | −0.0180401 | + | 0.0354103i | ||||
\(439\) | −7.97830 | + | 7.97830i | −0.380783 | + | 0.380783i | −0.871384 | − | 0.490601i | \(-0.836777\pi\) |
0.490601 | + | 0.871384i | \(0.336777\pi\) | |||||||
\(440\) | 1.55248i | 0.0740114i | ||||||||
\(441\) | −1.33640 | + | 0.971168i | −0.0636380 | + | 0.0462461i | ||||
\(442\) | −7.63880 | − | 7.63880i | −0.363341 | − | 0.363341i | ||||
\(443\) | −0.170503 | −0.00810085 | −0.00405043 | − | 0.999992i | \(-0.501289\pi\) | ||||
−0.00405043 | + | 0.999992i | \(0.501289\pi\) | |||||||
\(444\) | 5.68618 | − | 8.86946i | 0.269854 | − | 0.420926i | ||||
\(445\) | 14.9461 | 0.708514 | ||||||||
\(446\) | −13.9055 | − | 13.9055i | −0.658442 | − | 0.658442i | ||||
\(447\) | 8.22839 | + | 25.3198i | 0.389190 | + | 1.19759i | ||||
\(448\) | 2.53955i | 0.119983i | ||||||||
\(449\) | −25.9266 | + | 25.9266i | −1.22355 | + | 1.22355i | −0.257189 | + | 0.966361i | \(0.582796\pi\) |
−0.966361 | + | 0.257189i | \(0.917204\pi\) | |||||||
\(450\) | 0.468987 | − | 2.96312i | 0.0221083 | − | 0.139683i | ||||
\(451\) | 16.2686 | 0.766059 | ||||||||
\(452\) | 11.3932 | − | 11.3932i | 0.535892 | − | 0.535892i | ||||
\(453\) | −4.73465 | − | 14.5691i | −0.222453 | − | 0.684517i | ||||
\(454\) | 3.62190 | 0.169984 | ||||||||
\(455\) | 4.00644 | 0.187825 | ||||||||
\(456\) | −5.80185 | + | 1.88548i | −0.271697 | + | 0.0882956i | ||||
\(457\) | −1.83261 | − | 1.83261i | −0.0857259 | − | 0.0857259i | 0.662944 | − | 0.748669i | \(-0.269307\pi\) |
−0.748669 | + | 0.662944i | \(0.769307\pi\) | |||||||
\(458\) | 9.21757 | + | 9.21757i | 0.430709 | + | 0.430709i | ||||
\(459\) | 5.57174 | + | 35.1422i | 0.260067 | + | 1.64030i | ||||
\(460\) | 1.21095 | 0.0564607 | ||||||||
\(461\) | 11.4366 | − | 11.4366i | 0.532656 | − | 0.532656i | −0.388706 | − | 0.921362i | \(-0.627078\pi\) |
0.921362 | + | 0.388706i | \(0.127078\pi\) | |||||||
\(462\) | 6.08465 | + | 3.09987i | 0.283083 | + | 0.144219i | ||||
\(463\) | −14.6615 | − | 14.6615i | −0.681376 | − | 0.681376i | 0.278934 | − | 0.960310i | \(-0.410019\pi\) |
−0.960310 | + | 0.278934i | \(0.910019\pi\) | |||||||
\(464\) | −5.19422 | − | 5.19422i | −0.241136 | − | 0.241136i | ||||
\(465\) | 1.28874 | + | 3.96563i | 0.0597641 | + | 0.183902i | ||||
\(466\) | −14.4897 | − | 14.4897i | −0.671223 | − | 0.671223i | ||||
\(467\) | 7.91991 | − | 7.91991i | 0.366490 | − | 0.366490i | −0.499706 | − | 0.866195i | \(-0.666558\pi\) |
0.866195 | + | 0.499706i | \(0.166558\pi\) | |||||||
\(468\) | 0.739883 | − | 4.67466i | 0.0342011 | − | 0.216086i | ||||
\(469\) | − | 5.05305i | − | 0.233328i | ||||||
\(470\) | − | 10.4277i | − | 0.480994i | ||||||
\(471\) | −6.88441 | + | 2.23729i | −0.317217 | + | 0.103089i | ||||
\(472\) | 11.8311i | 0.544570i | ||||||||
\(473\) | −4.31603 | − | 4.31603i | −0.198451 | − | 0.198451i | ||||
\(474\) | −4.93792 | − | 15.1946i | −0.226806 | − | 0.697911i | ||||
\(475\) | −2.49053 | + | 2.49053i | −0.114273 | + | 0.114273i | ||||
\(476\) | −12.2965 | − | 12.2965i | −0.563608 | − | 0.563608i | ||||
\(477\) | 9.10278 | + | 12.5261i | 0.416788 | + | 0.573530i | ||||
\(478\) | −22.7093 | −1.03870 | ||||||||
\(479\) | −18.6437 | + | 18.6437i | −0.851853 | + | 0.851853i | −0.990361 | − | 0.138509i | \(-0.955769\pi\) |
0.138509 | + | 0.990361i | \(0.455769\pi\) | |||||||
\(480\) | 1.64725 | − | 0.535321i | 0.0751863 | − | 0.0244339i | ||||
\(481\) | 0.947574 | − | 9.54937i | 0.0432057 | − | 0.435414i | ||||
\(482\) | − | 11.3306i | − | 0.516095i | ||||||
\(483\) | 2.41793 | − | 4.74609i | 0.110020 | − | 0.215954i | ||||
\(484\) | − | 8.58982i | − | 0.390446i | ||||||
\(485\) | −7.08991 | −0.321936 | ||||||||
\(486\) | −11.0198 | + | 11.0256i | −0.499867 | + | 0.500133i | ||||
\(487\) | 8.90792 | + | 8.90792i | 0.403657 | + | 0.403657i | 0.879519 | − | 0.475863i | \(-0.157864\pi\) |
−0.475863 | + | 0.879519i | \(0.657864\pi\) | |||||||
\(488\) | 10.4843i | 0.474604i | ||||||||
\(489\) | −1.72073 | + | 3.37757i | −0.0778142 | + | 0.152739i | ||||
\(490\) | −0.550669 | −0.0248767 | ||||||||
\(491\) | − | 0.432806i | − | 0.0195322i | −0.999952 | − | 0.00976612i | \(-0.996891\pi\) | ||
0.999952 | − | 0.00976612i | \(-0.00310870\pi\) | |||||||
\(492\) | −5.60971 | − | 17.2618i | −0.252905 | − | 0.778220i | ||||
\(493\) | 50.3007 | 2.26543 | ||||||||
\(494\) | −3.92911 | + | 3.92911i | −0.176779 | + | 0.176779i | ||||
\(495\) | 0.728091 | − | 4.60016i | 0.0327253 | − | 0.206762i | ||||
\(496\) | −1.70231 | + | 1.70231i | −0.0764358 | + | 0.0764358i | ||||
\(497\) | 8.57406i | 0.384599i | ||||||||
\(498\) | 6.79911 | − | 13.3458i | 0.304675 | − | 0.598038i | ||||
\(499\) | −19.8374 | + | 19.8374i | −0.888044 | + | 0.888044i | −0.994335 | − | 0.106291i | \(-0.966102\pi\) |
0.106291 | + | 0.994335i | \(0.466102\pi\) | |||||||
\(500\) | 0.707107 | − | 0.707107i | 0.0316228 | − | 0.0316228i | ||||
\(501\) | −15.3186 | + | 30.0684i | −0.684385 | + | 1.34336i | ||||
\(502\) | 7.63449i | 0.340744i | ||||||||
\(503\) | 20.0416 | − | 20.0416i | 0.893611 | − | 0.893611i | −0.101250 | − | 0.994861i | \(-0.532284\pi\) |
0.994861 | + | 0.101250i | \(0.0322841\pi\) | |||||||
\(504\) | 1.19102 | − | 7.52499i | 0.0530522 | − | 0.335190i | ||||
\(505\) | −2.21150 | + | 2.21150i | −0.0984104 | + | 0.0984104i | ||||
\(506\) | 1.87997 | 0.0835747 | ||||||||
\(507\) | 5.62683 | + | 17.3144i | 0.249896 | + | 0.768962i | ||||
\(508\) | 14.3170i | 0.635215i | ||||||||
\(509\) | 3.66498 | 0.162447 | 0.0812237 | − | 0.996696i | \(-0.474117\pi\) | ||||
0.0812237 | + | 0.996696i | \(0.474117\pi\) | |||||||
\(510\) | −5.38394 | + | 10.5680i | −0.238405 | + | 0.467958i | ||||
\(511\) | 1.21947i | 0.0539461i | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 18.0758 | − | 2.86589i | 0.798067 | − | 0.126532i | ||||
\(514\) | −18.3104 | −0.807636 | ||||||||
\(515\) | 13.3627i | 0.588832i | ||||||||
\(516\) | −3.09127 | + | 6.06776i | −0.136086 | + | 0.267118i | ||||
\(517\) | − | 16.1887i | − | 0.711980i | ||||||
\(518\) | 1.52535 | − | 15.3720i | 0.0670199 | − | 0.675407i | ||||
\(519\) | 36.9416 | − | 12.0052i | 1.62156 | − | 0.526971i | ||||
\(520\) | 1.11554 | − | 1.11554i | 0.0489198 | − | 0.0489198i | ||||
\(521\) | 3.46852 | 0.151959 | 0.0759793 | − | 0.997109i | \(-0.475792\pi\) | ||||
0.0759793 | + | 0.997109i | \(0.475792\pi\) | |||||||
\(522\) | 12.9551 | + | 17.8271i | 0.567027 | + | 0.780271i | ||||
\(523\) | 13.9403 | + | 13.9403i | 0.609567 | + | 0.609567i | 0.942833 | − | 0.333266i | \(-0.108151\pi\) |
−0.333266 | + | 0.942833i | \(0.608151\pi\) | |||||||
\(524\) | −0.642612 | + | 0.642612i | −0.0280726 | + | 0.0280726i | ||||
\(525\) | −1.35948 | − | 4.18328i | −0.0593324 | − | 0.182573i | ||||
\(526\) | 5.23341 | + | 5.23341i | 0.228187 | + | 0.228187i | ||||
\(527\) | − | 16.4851i | − | 0.718101i | ||||||
\(528\) | 2.55731 | − | 0.831073i | 0.111293 | − | 0.0361678i | ||||
\(529\) | 21.5336i | 0.936244i | ||||||||
\(530\) | 5.16143i | 0.224198i | ||||||||
\(531\) | 5.54863 | − | 35.0569i | 0.240790 | − | 1.52134i | ||||
\(532\) | −6.32484 | + | 6.32484i | −0.274217 | + | 0.274217i | ||||
\(533\) | −11.6899 | − | 11.6899i | −0.506348 | − | 0.506348i | ||||
\(534\) | −8.00097 | − | 24.6200i | −0.346236 | − | 1.06541i | ||||
\(535\) | −1.36163 | − | 1.36163i | −0.0588686 | − | 0.0588686i | ||||
\(536\) | −1.40696 | − | 1.40696i | −0.0607713 | − | 0.0607713i | ||||
\(537\) | 12.6053 | + | 6.42187i | 0.543958 | + | 0.277124i | ||||
\(538\) | −15.8332 | + | 15.8332i | −0.682617 | + | 0.682617i | ||||
\(539\) | −0.854900 | −0.0368231 | ||||||||
\(540\) | −5.13205 | + | 0.813678i | −0.220848 | + | 0.0350151i | ||||
\(541\) | −5.11347 | − | 5.11347i | −0.219845 | − | 0.219845i | 0.588588 | − | 0.808433i | \(-0.299684\pi\) |
−0.808433 | + | 0.588588i | \(0.799684\pi\) | |||||||
\(542\) | 13.0726 | + | 13.0726i | 0.561518 | + | 0.561518i | ||||
\(543\) | −21.6419 | + | 7.03314i | −0.928741 | + | 0.301821i | ||||
\(544\) | −6.84760 | −0.293588 | ||||||||
\(545\) | −2.50977 | −0.107507 | ||||||||
\(546\) | −2.14473 | − | 6.59961i | −0.0917861 | − | 0.282437i | ||||
\(547\) | −17.1654 | + | 17.1654i | −0.733939 | + | 0.733939i | −0.971398 | − | 0.237459i | \(-0.923686\pi\) |
0.237459 | + | 0.971398i | \(0.423686\pi\) | |||||||
\(548\) | 22.7686 | 0.972627 | ||||||||
\(549\) | 4.91702 | − | 31.0663i | 0.209853 | − | 1.32588i | ||||
\(550\) | 1.09777 | − | 1.09777i | 0.0468089 | − | 0.0468089i | ||||
\(551\) | − | 25.8728i | − | 1.10222i | ||||||
\(552\) | −0.648245 | − | 1.99473i | −0.0275911 | − | 0.0849014i | ||||
\(553\) | −16.5643 | − | 16.5643i | −0.704384 | − | 0.704384i | ||||
\(554\) | 10.9271 | 0.464249 | ||||||||
\(555\) | −10.2924 | + | 2.25092i | −0.436888 | + | 0.0955462i | ||||
\(556\) | 6.95397 | 0.294914 | ||||||||
\(557\) | 21.7065 | + | 21.7065i | 0.919733 | + | 0.919733i | 0.997010 | − | 0.0772768i | \(-0.0246225\pi\) |
−0.0772768 | + | 0.997010i | \(0.524623\pi\) | |||||||
\(558\) | 5.84249 | − | 4.24577i | 0.247332 | − | 0.179738i | ||||
\(559\) | 6.20264i | 0.262344i | ||||||||
\(560\) | 1.79574 | − | 1.79574i | 0.0758837 | − | 0.0758837i | ||||
\(561\) | −8.35844 | + | 16.4065i | −0.352893 | + | 0.692684i | ||||
\(562\) | −5.58948 | −0.235778 | ||||||||
\(563\) | 17.3652 | − | 17.3652i | 0.731858 | − | 0.731858i | −0.239130 | − | 0.970988i | \(-0.576862\pi\) |
0.970988 | + | 0.239130i | \(0.0768622\pi\) | |||||||
\(564\) | −17.1770 | + | 5.58216i | −0.723283 | + | 0.235052i | ||||
\(565\) | −16.1124 | −0.677855 | ||||||||
\(566\) | 5.90258 | 0.248104 | ||||||||
\(567\) | −7.05825 | + | 21.7388i | −0.296419 | + | 0.912945i | ||||
\(568\) | 2.38734 | + | 2.38734i | 0.100171 | + | 0.100171i | ||||
\(569\) | −0.287563 | − | 0.287563i | −0.0120553 | − | 0.0120553i | 0.701053 | − | 0.713109i | \(-0.252713\pi\) |
−0.713109 | + | 0.701053i | \(0.752713\pi\) | |||||||
\(570\) | 5.43576 | + | 2.76929i | 0.227679 | + | 0.115993i | ||||
\(571\) | −27.3088 | −1.14284 | −0.571420 | − | 0.820658i | \(-0.693607\pi\) | ||||
−0.571420 | + | 0.820658i | \(0.693607\pi\) | |||||||
\(572\) | 1.73185 | − | 1.73185i | 0.0724125 | − | 0.0724125i | ||||
\(573\) | 7.26450 | − | 14.2593i | 0.303479 | − | 0.595690i | ||||
\(574\) | −18.8178 | − | 18.8178i | −0.785438 | − | 0.785438i | ||||
\(575\) | −0.856269 | − | 0.856269i | −0.0357089 | − | 0.0357089i | ||||
\(576\) | −1.76361 | − | 2.42686i | −0.0734839 | − | 0.101119i | ||||
\(577\) | −20.2984 | − | 20.2984i | −0.845034 | − | 0.845034i | 0.144475 | − | 0.989509i | \(-0.453851\pi\) |
−0.989509 | + | 0.144475i | \(0.953851\pi\) | |||||||
\(578\) | 21.1352 | − | 21.1352i | 0.879106 | − | 0.879106i | ||||
\(579\) | −2.57707 | − | 1.31291i | −0.107099 | − | 0.0545626i | ||||
\(580\) | 7.34574i | 0.305015i | ||||||||
\(581\) | − | 21.9608i | − | 0.911086i | ||||||
\(582\) | 3.79538 | + | 11.6788i | 0.157323 | + | 0.484104i | ||||
\(583\) | 8.01300i | 0.331865i | ||||||||
\(584\) | 0.339546 | + | 0.339546i | 0.0140505 | + | 0.0140505i | ||||
\(585\) | −3.82866 | + | 2.78231i | −0.158296 | + | 0.115034i | ||||
\(586\) | −10.7674 | + | 10.7674i | −0.444796 | + | 0.444796i | ||||
\(587\) | 14.6086 | + | 14.6086i | 0.602960 | + | 0.602960i | 0.941097 | − | 0.338137i | \(-0.109797\pi\) |
−0.338137 | + | 0.941097i | \(0.609797\pi\) | |||||||
\(588\) | 0.294785 | + | 0.907089i | 0.0121567 | + | 0.0374077i | ||||
\(589\) | −8.47930 | −0.349383 | ||||||||
\(590\) | 8.36584 | − | 8.36584i | 0.344416 | − | 0.344416i | ||||
\(591\) | 1.64432 | + | 5.05977i | 0.0676382 | + | 0.208131i | ||||
\(592\) | −3.85543 | − | 4.70486i | −0.158457 | − | 0.193368i | ||||
\(593\) | 30.9176i | 1.26963i | 0.772663 | + | 0.634817i | \(0.218924\pi\) | ||||
−0.772663 | + | 0.634817i | \(0.781076\pi\) | |||||||
\(594\) | −7.96738 | + | 1.26322i | −0.326906 | + | 0.0518304i | ||||
\(595\) | 17.3898i | 0.712914i | ||||||||
\(596\) | 15.3710 | 0.629619 | ||||||||
\(597\) | 2.15314 | − | 4.22633i | 0.0881221 | − | 0.172972i | ||||
\(598\) | −1.35086 | − | 1.35086i | −0.0552409 | − | 0.0552409i | ||||
\(599\) | − | 13.3000i | − | 0.543423i | −0.962379 | − | 0.271712i | \(-0.912410\pi\) | ||
0.962379 | − | 0.271712i | \(-0.0875897\pi\) | |||||||
\(600\) | −1.54331 | − | 0.786252i | −0.0630054 | − | 0.0320986i | ||||
\(601\) | −13.2105 | −0.538866 | −0.269433 | − | 0.963019i | \(-0.586836\pi\) | ||||
−0.269433 | + | 0.963019i | \(0.586836\pi\) | |||||||
\(602\) | 9.98464i | 0.406944i | ||||||||
\(603\) | 3.50913 | + | 4.82883i | 0.142903 | + | 0.196645i | ||||
\(604\) | −8.84452 | −0.359878 | ||||||||
\(605\) | −6.07392 | + | 6.07392i | −0.246940 | + | 0.246940i | ||||
\(606\) | 4.82675 | + | 2.45903i | 0.196073 | + | 0.0998912i | ||||
\(607\) | −1.58980 | + | 1.58980i | −0.0645280 | + | 0.0645280i | −0.738634 | − | 0.674106i | \(-0.764529\pi\) |
0.674106 | + | 0.738634i | \(0.264529\pi\) | |||||||
\(608\) | 3.52214i | 0.142842i | ||||||||
\(609\) | 28.7903 | + | 14.6675i | 1.16664 | + | 0.594355i | ||||
\(610\) | 7.41355 | − | 7.41355i | 0.300166 | − | 0.300166i | ||||
\(611\) | −11.6326 | + | 11.6326i | −0.470603 | + | 0.470603i | ||||
\(612\) | 20.2902 | + | 3.21144i | 0.820184 | + | 0.129815i | ||||
\(613\) | 35.8533i | 1.44810i | 0.689747 | + | 0.724051i | \(0.257722\pi\) | ||||
−0.689747 | + | 0.724051i | \(0.742278\pi\) | |||||||
\(614\) | −15.9405 | + | 15.9405i | −0.643306 | + | 0.643306i | ||||
\(615\) | −8.23925 | + | 16.1726i | −0.332239 | + | 0.652141i | ||||
\(616\) | 2.78784 | − | 2.78784i | 0.112325 | − | 0.112325i | ||||
\(617\) | 22.8071 | 0.918178 | 0.459089 | − | 0.888390i | \(-0.348176\pi\) | ||||
0.459089 | + | 0.888390i | \(0.348176\pi\) | |||||||
\(618\) | 22.0118 | − | 7.15335i | 0.885443 | − | 0.287750i | ||||
\(619\) | 33.8714i | 1.36141i | 0.732559 | + | 0.680704i | \(0.238326\pi\) | ||||
−0.732559 | + | 0.680704i | \(0.761674\pi\) | |||||||
\(620\) | 2.40742 | 0.0966845 | ||||||||
\(621\) | 0.985321 | + | 6.21464i | 0.0395396 | + | 0.249385i | ||||
\(622\) | 8.65204i | 0.346915i | ||||||||
\(623\) | −26.8393 | − | 26.8393i | −1.07529 | − | 1.07529i | ||||
\(624\) | −2.43475 | − | 1.24041i | −0.0974681 | − | 0.0496559i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 4.61985i | 0.184646i | ||||||||
\(627\) | 8.43889 | + | 4.29926i | 0.337017 | + | 0.171696i | ||||
\(628\) | 4.17933i | 0.166774i | ||||||||
\(629\) | 41.4488 | + | 4.11292i | 1.65267 | + | 0.163993i | ||||
\(630\) | −6.16315 | + | 4.47879i | −0.245546 | + | 0.178439i | ||||
\(631\) | −3.90804 | + | 3.90804i | −0.155576 | + | 0.155576i | −0.780603 | − | 0.625027i | \(-0.785088\pi\) |
0.625027 | + | 0.780603i | \(0.285088\pi\) | |||||||
\(632\) | −9.22422 | −0.366920 | ||||||||
\(633\) | 39.5887 | − | 12.8655i | 1.57351 | − | 0.511357i | ||||
\(634\) | 21.2262 | + | 21.2262i | 0.843001 | + | 0.843001i | ||||
\(635\) | 10.1237 | − | 10.1237i | 0.401745 | − | 0.401745i | ||||
\(636\) | 8.50217 | − | 2.76302i | 0.337133 | − | 0.109561i | ||||
\(637\) | 0.614295 | + | 0.614295i | 0.0243393 | + | 0.0243393i | ||||
\(638\) | 11.4041i | 0.451492i | ||||||||
\(639\) | −5.95433 | − | 8.19360i | −0.235550 | − | 0.324134i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | − | 29.9478i | − | 1.18287i | −0.806353 | − | 0.591434i | \(-0.798562\pi\) | ||
0.806353 | − | 0.591434i | \(-0.201438\pi\) | |||||||
\(642\) | −1.51404 | + | 2.97186i | −0.0597544 | + | 0.117290i | ||||
\(643\) | −16.6932 | + | 16.6932i | −0.658317 | + | 0.658317i | −0.954982 | − | 0.296664i | \(-0.904126\pi\) |
0.296664 | + | 0.954982i | \(0.404126\pi\) | |||||||
\(644\) | −2.17454 | − | 2.17454i | −0.0856889 | − | 0.0856889i | ||||
\(645\) | 6.47641 | − | 2.10470i | 0.255008 | − | 0.0828723i | ||||
\(646\) | −17.0542 | − | 17.0542i | −0.670987 | − | 0.670987i | ||||
\(647\) | 1.28867 | + | 1.28867i | 0.0506627 | + | 0.0506627i | 0.731984 | − | 0.681322i | \(-0.238594\pi\) |
−0.681322 | + | 0.731984i | \(0.738594\pi\) | |||||||
\(648\) | 4.08763 | + | 8.01819i | 0.160577 | + | 0.314984i | ||||
\(649\) | 12.9878 | − | 12.9878i | 0.509814 | − | 0.509814i | ||||
\(650\) | −1.57762 | −0.0618792 | ||||||||
\(651\) | 4.80698 | − | 9.43547i | 0.188400 | − | 0.369805i | ||||
\(652\) | 1.54752 | + | 1.54752i | 0.0606056 | + | 0.0606056i | ||||
\(653\) | 8.09056 | + | 8.09056i | 0.316608 | + | 0.316608i | 0.847463 | − | 0.530855i | \(-0.178129\pi\) |
−0.530855 | + | 0.847463i | \(0.678129\pi\) | |||||||
\(654\) | 1.34353 | + | 4.13422i | 0.0525363 | + | 0.161661i | ||||
\(655\) | 0.908791 | 0.0355094 | ||||||||
\(656\) | −10.4791 | −0.409142 | ||||||||
\(657\) | −0.846870 | − | 1.16536i | −0.0330396 | − | 0.0454649i | ||||
\(658\) | −18.7254 | + | 18.7254i | −0.729991 | + | 0.729991i | ||||
\(659\) | 12.6087 | 0.491164 | 0.245582 | − | 0.969376i | \(-0.421021\pi\) | ||||
0.245582 | + | 0.969376i | \(0.421021\pi\) | |||||||
\(660\) | −2.39595 | − | 1.22064i | −0.0932623 | − | 0.0475133i | ||||
\(661\) | −2.03012 | + | 2.03012i | −0.0789624 | + | 0.0789624i | −0.745485 | − | 0.666523i | \(-0.767782\pi\) |
0.666523 | + | 0.745485i | \(0.267782\pi\) | |||||||
\(662\) | 13.0363i | 0.506670i | ||||||||
\(663\) | 17.7951 | − | 5.78301i | 0.691103 | − | 0.224594i | ||||
\(664\) | −6.11470 | − | 6.11470i | −0.237296 | − | 0.237296i | ||||
\(665\) | 8.94467 | 0.346860 | ||||||||
\(666\) | 9.21756 | + | 15.7492i | 0.357173 | + | 0.610268i | ||||
\(667\) | 8.89530 | 0.344427 | ||||||||
\(668\) | 13.7766 | + | 13.7766i | 0.533033 | + | 0.533033i | ||||
\(669\) | 32.3936 | − | 10.5272i | 1.25241 | − | 0.407007i | ||||
\(670\) | 1.98974i | 0.0768704i | ||||||||
\(671\) | 11.5094 | − | 11.5094i | 0.444314 | − | 0.444314i | ||||
\(672\) | −3.91932 | − | 1.99673i | −0.151191 | − | 0.0770255i | ||||
\(673\) | −40.7016 | −1.56893 | −0.784466 | − | 0.620172i | \(-0.787063\pi\) | ||||
−0.784466 | + | 0.620172i | \(0.787063\pi\) | |||||||
\(674\) | −16.0773 | + | 16.0773i | −0.619275 | + | 0.619275i | ||||
\(675\) | 4.20426 | + | 3.05355i | 0.161822 | + | 0.117531i | ||||
\(676\) | 10.5111 | 0.404274 | ||||||||
\(677\) | −33.5797 | −1.29057 | −0.645286 | − | 0.763941i | \(-0.723262\pi\) | ||||
−0.645286 | + | 0.763941i | \(0.723262\pi\) | |||||||
\(678\) | 8.62533 | + | 26.5412i | 0.331254 | + | 1.01931i | ||||
\(679\) | 12.7316 | + | 12.7316i | 0.488594 | + | 0.488594i | ||||
\(680\) | 4.84198 | + | 4.84198i | 0.185682 | + | 0.185682i | ||||
\(681\) | −2.84773 | + | 5.58972i | −0.109125 | + | 0.214198i | ||||
\(682\) | 3.73747 | 0.143115 | ||||||||
\(683\) | −18.5669 | + | 18.5669i | −0.710442 | + | 0.710442i | −0.966628 | − | 0.256186i | \(-0.917534\pi\) |
0.256186 | + | 0.966628i | \(0.417534\pi\) | |||||||
\(684\) | 1.65184 | − | 10.4365i | 0.0631597 | − | 0.399050i | ||||
\(685\) | −16.0998 | − | 16.0998i | −0.615143 | − | 0.615143i | ||||
\(686\) | 13.5590 | + | 13.5590i | 0.517685 | + | 0.517685i | ||||
\(687\) | −21.4729 | + | 6.97824i | −0.819243 | + | 0.266236i | ||||
\(688\) | 2.78010 | + | 2.78010i | 0.105990 | + | 0.105990i | ||||
\(689\) | 5.75781 | − | 5.75781i | 0.219355 | − | 0.219355i | ||||
\(690\) | −0.952110 | + | 1.86887i | −0.0362462 | + | 0.0711465i | ||||
\(691\) | − | 14.7237i | − | 0.560118i | −0.959983 | − | 0.280059i | \(-0.909646\pi\) | ||
0.959983 | − | 0.280059i | \(-0.0903540\pi\) | |||||||
\(692\) | − | 22.4262i | − | 0.852517i | ||||||
\(693\) | −9.56814 | + | 6.95322i | −0.363463 | + | 0.264131i | ||||
\(694\) | 18.2057i | 0.691078i | ||||||||
\(695\) | −4.91720 | − | 4.91720i | −0.186520 | − | 0.186520i | ||||
\(696\) | 12.1003 | − | 3.93233i | 0.458659 | − | 0.149054i | ||||
\(697\) | 50.7398 | − | 50.7398i | 1.92191 | − | 1.92191i | ||||
\(698\) | −12.1575 | − | 12.1575i | −0.460168 | − | 0.460168i | ||||
\(699\) | 33.7547 | − | 10.9696i | 1.27672 | − | 0.414907i | ||||
\(700\) | −2.53955 | −0.0959861 | ||||||||
\(701\) | −1.36351 | + | 1.36351i | −0.0514990 | + | 0.0514990i | −0.732387 | − | 0.680888i | \(-0.761594\pi\) |
0.680888 | + | 0.732387i | \(0.261594\pi\) | |||||||
\(702\) | 6.63272 | + | 4.81733i | 0.250336 | + | 0.181818i | ||||
\(703\) | 2.11553 | − | 21.3197i | 0.0797886 | − | 0.804086i | ||||
\(704\) | − | 1.55248i | − | 0.0585111i | ||||||
\(705\) | 16.0932 | + | 8.19880i | 0.606104 | + | 0.308785i | ||||
\(706\) | 19.2979i | 0.726286i | ||||||||
\(707\) | 7.94253 | 0.298710 | ||||||||
\(708\) | −18.2590 | − | 9.30222i | −0.686217 | − | 0.349599i | ||||
\(709\) | 5.92223 | + | 5.92223i | 0.222414 | + | 0.222414i | 0.809514 | − | 0.587100i | \(-0.199731\pi\) |
−0.587100 | + | 0.809514i | \(0.699731\pi\) | |||||||
\(710\) | − | 3.37621i | − | 0.126707i | ||||||
\(711\) | 27.3324 | + | 4.32604i | 1.02505 | + | 0.162239i | ||||
\(712\) | −14.9461 | −0.560130 | ||||||||
\(713\) | − | 2.91526i | − | 0.109177i | ||||||
\(714\) | 28.6454 | − | 9.30915i | 1.07203 | − | 0.348386i | ||||
\(715\) | −2.44921 | −0.0915953 | ||||||||
\(716\) | 5.77543 | − | 5.77543i | 0.215838 | − | 0.215838i | ||||
\(717\) | 17.8553 | − | 35.0475i | 0.666817 | − | 1.30887i | ||||
\(718\) | 23.0762 | − | 23.0762i | 0.861197 | − | 0.861197i | ||||
\(719\) | − | 30.0602i | − | 1.12106i | −0.828135 | − | 0.560529i | \(-0.810598\pi\) | ||
0.828135 | − | 0.560529i | \(-0.189402\pi\) | |||||||
\(720\) | −0.468987 | + | 2.96312i | −0.0174781 | + | 0.110429i | ||||
\(721\) | 23.9959 | − | 23.9959i | 0.893655 | − | 0.893655i | ||||
\(722\) | 4.66301 | − | 4.66301i | 0.173539 | − | 0.173539i | ||||
\(723\) | 17.4866 | + | 8.90871i | 0.650335 | + | 0.331318i | ||||
\(724\) | 13.1382i | 0.488276i | ||||||||
\(725\) | 5.19422 | − | 5.19422i | 0.192909 | − | 0.192909i | ||||
\(726\) | 13.2568 | + | 6.75377i | 0.492004 | + | 0.250656i | ||||
\(727\) | −0.0366111 | + | 0.0366111i | −0.00135783 | + | 0.00135783i | −0.707785 | − | 0.706428i | \(-0.750306\pi\) |
0.706428 | + | 0.707785i | \(0.250306\pi\) | |||||||
\(728\) | −4.00644 | −0.148489 | ||||||||
\(729\) | −8.35167 | − | 25.6759i | −0.309321 | − | 0.950958i | ||||
\(730\) | − | 0.480190i | − | 0.0177726i | ||||||
\(731\) | −26.9224 | −0.995760 | ||||||||
\(732\) | −16.1806 | − | 8.24334i | −0.598052 | − | 0.304683i | ||||
\(733\) | − | 23.8385i | − | 0.880494i | −0.897877 | − | 0.440247i | \(-0.854891\pi\) | ||
0.897877 | − | 0.440247i | \(-0.145109\pi\) | |||||||
\(734\) | −8.53674 | − | 8.53674i | −0.315097 | − | 0.315097i | ||||
\(735\) | 0.432965 | − | 0.849853i | 0.0159701 | − | 0.0313473i | ||||
\(736\) | −1.21095 | −0.0446361 | ||||||||
\(737\) | 3.08902i | 0.113786i | ||||||||
\(738\) | 31.0509 | + | 4.91459i | 1.14300 | + | 0.180908i | ||||
\(739\) | 38.4233i | 1.41343i | 0.707501 | + | 0.706713i | \(0.249823\pi\) | ||||
−0.707501 | + | 0.706713i | \(0.750177\pi\) | |||||||
\(740\) | −0.600636 | + | 6.05304i | −0.0220798 | + | 0.222514i | ||||
\(741\) | −2.97456 | − | 9.15310i | −0.109273 | − | 0.336248i | ||||
\(742\) | 9.26857 | − | 9.26857i | 0.340260 | − | 0.340260i | ||||
\(743\) | −22.9840 | −0.843202 | −0.421601 | − | 0.906782i | \(-0.638532\pi\) | ||||
−0.421601 | + | 0.906782i | \(0.638532\pi\) | |||||||
\(744\) | −1.28874 | − | 3.96563i | −0.0472477 | − | 0.145387i | ||||
\(745\) | −10.8689 | − | 10.8689i | −0.398206 | − | 0.398206i | ||||
\(746\) | −18.8328 | + | 18.8328i | −0.689518 | + | 0.689518i | ||||
\(747\) | 15.2508 | + | 20.9863i | 0.557999 | + | 0.767848i | ||||
\(748\) | 7.51706 | + | 7.51706i | 0.274851 | + | 0.274851i | ||||
\(749\) | 4.89027i | 0.178687i | ||||||||
\(750\) | 0.535321 | + | 1.64725i | 0.0195472 | + | 0.0601491i | ||||
\(751\) | − | 12.4662i | − | 0.454898i | −0.973790 | − | 0.227449i | \(-0.926962\pi\) | ||
0.973790 | − | 0.227449i | \(-0.0730385\pi\) | |||||||
\(752\) | 10.4277i | 0.380259i | ||||||||
\(753\) | −11.7824 | − | 6.00264i | −0.429374 | − | 0.218748i | ||||
\(754\) | 8.19449 | − | 8.19449i | 0.298426 | − | 0.298426i | ||||
\(755\) | 6.25402 | + | 6.25402i | 0.227607 | + | 0.227607i | ||||
\(756\) | 10.6770 | + | 7.75465i | 0.388317 | + | 0.282034i | ||||
\(757\) | 16.0789 | + | 16.0789i | 0.584398 | + | 0.584398i | 0.936109 | − | 0.351710i | \(-0.114400\pi\) |
−0.351710 | + | 0.936109i | \(0.614400\pi\) | |||||||
\(758\) | 14.6734 | + | 14.6734i | 0.532963 | + | 0.532963i | ||||
\(759\) | −1.47813 | + | 2.90137i | −0.0536526 | + | 0.105313i | ||||
\(760\) | 2.49053 | − | 2.49053i | 0.0903411 | − | 0.0903411i | ||||
\(761\) | −29.9383 | −1.08526 | −0.542632 | − | 0.839971i | \(-0.682572\pi\) | ||||
−0.542632 | + | 0.839971i | \(0.682572\pi\) | |||||||
\(762\) | −22.0956 | − | 11.2568i | −0.800439 | − | 0.407790i | ||||
\(763\) | 4.50688 | + | 4.50688i | 0.163160 | + | 0.163160i | ||||
\(764\) | −6.53325 | − | 6.53325i | −0.236365 | − | 0.236365i | ||||
\(765\) | −12.0765 | − | 16.6182i | −0.436628 | − | 0.600832i | ||||
\(766\) | 22.4423 | 0.810874 | ||||||||
\(767\) | −18.6649 | −0.673952 | ||||||||
\(768\) | −1.64725 | + | 0.535321i | −0.0594400 | + | 0.0193167i | ||||
\(769\) | −27.9340 | + | 27.9340i | −1.00733 | + | 1.00733i | −0.00735452 | + | 0.999973i | \(0.502341\pi\) |
−0.999973 | + | 0.00735452i | \(0.997659\pi\) | |||||||
\(770\) | −3.94259 | −0.142081 | ||||||||
\(771\) | 14.3966 | − | 28.2586i | 0.518480 | − | 1.01771i | ||||
\(772\) | −1.18075 | + | 1.18075i | −0.0424961 | + | 0.0424961i | ||||
\(773\) | − | 1.29800i | − | 0.0466858i | −0.999728 | − | 0.0233429i | \(-0.992569\pi\) | ||
0.999728 | − | 0.0233429i | \(-0.00743094\pi\) | |||||||
\(774\) | −6.93392 | − | 9.54158i | −0.249235 | − | 0.342965i | ||||
\(775\) | −1.70231 | − | 1.70231i | −0.0611486 | − | 0.0611486i | ||||
\(776\) | 7.08991 | 0.254513 | ||||||||
\(777\) | 22.5245 | + | 14.4404i | 0.808061 | + | 0.518045i | ||||
\(778\) | −12.3267 | −0.441934 | ||||||||
\(779\) | −26.0986 | − | 26.0986i | −0.935081 | − | 0.935081i | ||||
\(780\) | 0.844532 | + | 2.59873i | 0.0302391 | + | 0.0930494i | ||||
\(781\) | − | 5.24148i | − | 0.187555i | ||||||
\(782\) | 5.86338 | − | 5.86338i | 0.209674 | − | 0.209674i | ||||
\(783\) | −37.6987 | + | 5.97707i | −1.34724 | + | 0.213603i | ||||
\(784\) | 0.550669 | 0.0196667 | ||||||||
\(785\) | 2.95524 | − | 2.95524i | 0.105477 | − | 0.105477i | ||||
\(786\) | −0.486495 | − | 1.49701i | −0.0173527 | − | 0.0533964i | ||||
\(787\) | −3.84246 | −0.136969 | −0.0684844 | − | 0.997652i | \(-0.521816\pi\) | ||||
−0.0684844 | + | 0.997652i | \(0.521816\pi\) | |||||||
\(788\) | 3.07165 | 0.109423 | ||||||||
\(789\) | −12.1915 | + | 3.96199i | −0.434031 | + | 0.141051i | ||||
\(790\) | 6.52251 | + | 6.52251i | 0.232061 | + | 0.232061i | ||||
\(791\) | 28.9337 | + | 28.9337i | 1.02876 | + | 1.02876i | ||||
\(792\) | −0.728091 | + | 4.60016i | −0.0258716 | + | 0.163460i | ||||
\(793\) | −16.5403 | −0.587363 | ||||||||
\(794\) | 0.0671608 | − | 0.0671608i | 0.00238345 | − | 0.00238345i | ||||
\(795\) | −7.96570 | − | 4.05819i | −0.282514 | − | 0.143929i | ||||
\(796\) | −1.93640 | − | 1.93640i | −0.0686339 | − | 0.0686339i | ||||
\(797\) | −4.77954 | − | 4.77954i | −0.169300 | − | 0.169300i | 0.617372 | − | 0.786672i | \(-0.288198\pi\) |
−0.786672 | + | 0.617372i | \(0.788198\pi\) | |||||||
\(798\) | −4.78827 | − | 14.7341i | −0.169503 | − | 0.521582i | ||||
\(799\) | −50.4907 | − | 50.4907i | −1.78623 | − | 1.78623i | ||||
\(800\) | −0.707107 | + | 0.707107i | −0.0250000 | + | 0.0250000i | ||||
\(801\) | 44.2871 | + | 7.00954i | 1.56481 | + | 0.247670i | ||||
\(802\) | 5.50588i | 0.194420i | ||||||||
\(803\) | − | 0.745484i | − | 0.0263075i | ||||||
\(804\) | 3.27760 | − | 1.06515i | 0.115592 | − | 0.0375649i | ||||
\(805\) | 3.07526i | 0.108389i | ||||||||
\(806\) | −2.68559 | − | 2.68559i | −0.0945958 | − | 0.0945958i | ||||
\(807\) | −11.9866 | − | 36.8844i | −0.421950 | − | 1.29839i | ||||
\(808\) | 2.21150 | − | 2.21150i | 0.0778002 | − | 0.0778002i | ||||
\(809\) | 22.1315 | + | 22.1315i | 0.778101 | + | 0.778101i | 0.979508 | − | 0.201406i | \(-0.0645512\pi\) |
−0.201406 | + | 0.979508i | \(0.564551\pi\) | |||||||
\(810\) | 2.77933 | − | 8.56010i | 0.0976556 | − | 0.300771i | ||||
\(811\) | −53.7835 | −1.88859 | −0.944297 | − | 0.329094i | \(-0.893257\pi\) | ||||
−0.944297 | + | 0.329094i | \(0.893257\pi\) | |||||||
\(812\) | 13.1910 | − | 13.1910i | 0.462913 | − | 0.462913i | ||||
\(813\) | −30.4535 | + | 9.89675i | −1.06805 | + | 0.347094i | ||||
\(814\) | −0.932473 | + | 9.39719i | −0.0326832 | + | 0.329371i | ||||
\(815\) | − | 2.18852i | − | 0.0766607i | ||||||
\(816\) | 5.38394 | − | 10.5680i | 0.188476 | − | 0.369953i | ||||
\(817\) | 13.8478i | 0.484475i | ||||||||
\(818\) | 32.2541 | 1.12774 | ||||||||
\(819\) | 11.8716 | + | 1.87897i | 0.414826 | + | 0.0656566i | ||||
\(820\) | 7.40987 | + | 7.40987i | 0.258764 | + | 0.258764i | ||||
\(821\) | − | 8.80205i | − | 0.307194i | −0.988134 | − | 0.153597i | \(-0.950914\pi\) | ||
0.988134 | − | 0.153597i | \(-0.0490857\pi\) | |||||||
\(822\) | −17.9019 | + | 35.1390i | −0.624399 | + | 1.22561i | ||||
\(823\) | 32.0302 | 1.11650 | 0.558251 | − | 0.829672i | \(-0.311473\pi\) | ||||
0.558251 | + | 0.829672i | \(0.311473\pi\) | |||||||
\(824\) | − | 13.3627i | − | 0.465513i | ||||||
\(825\) | 0.831073 | + | 2.55731i | 0.0289342 | + | 0.0890343i | ||||
\(826\) | −30.0457 | −1.04542 | ||||||||
\(827\) | 35.6688 | − | 35.6688i | 1.24033 | − | 1.24033i | 0.280461 | − | 0.959865i | \(-0.409513\pi\) |
0.959865 | − | 0.280461i | \(-0.0904874\pi\) | |||||||
\(828\) | 3.58817 | + | 0.567919i | 0.124698 | + | 0.0197365i | ||||
\(829\) | 13.6682 | − | 13.6682i | 0.474716 | − | 0.474716i | −0.428721 | − | 0.903437i | \(-0.641036\pi\) |
0.903437 | + | 0.428721i | \(0.141036\pi\) | |||||||
\(830\) | 8.64749i | 0.300159i | ||||||||
\(831\) | −8.59148 | + | 16.8639i | −0.298035 | + | 0.585004i | ||||
\(832\) | −1.11554 | + | 1.11554i | −0.0386745 | + | 0.0386745i | ||||
\(833\) | −2.66633 | + | 2.66633i | −0.0923828 | + | 0.0923828i | ||||
\(834\) | −5.46757 | + | 10.7321i | −0.189327 | + | 0.371623i | ||||
\(835\) | − | 19.4831i | − | 0.674240i | ||||||
\(836\) | 3.86649 | − | 3.86649i | 0.133725 | − | 0.133725i | ||||
\(837\) | 1.95887 | + | 12.3550i | 0.0677084 | + | 0.427052i | ||||
\(838\) | 13.7606 | − | 13.7606i | 0.475350 | − | 0.475350i | ||||
\(839\) | −19.8742 | −0.686135 | −0.343067 | − | 0.939311i | \(-0.611466\pi\) | ||||
−0.343067 | + | 0.939311i | \(0.611466\pi\) | |||||||
\(840\) | 1.35948 | + | 4.18328i | 0.0469064 | + | 0.144337i | ||||
\(841\) | 24.9599i | 0.860685i | ||||||||
\(842\) | −19.9688 | −0.688171 | ||||||||
\(843\) | 4.39474 | − | 8.62631i | 0.151363 | − | 0.297106i | ||||
\(844\) | − | 24.0332i | − | 0.827257i | ||||||
\(845\) | −7.43249 | − | 7.43249i | −0.255685 | − | 0.255685i | ||||
\(846\) | 4.89046 | − | 30.8985i | 0.168137 | − | 1.06231i | ||||
\(847\) | 21.8143 | 0.749548 | ||||||||
\(848\) | − | 5.16143i | − | 0.177244i | ||||||
\(849\) | −4.64092 | + | 9.10951i | −0.159276 | + | 0.312638i | ||||
\(850\) | − | 6.84760i | − | 0.234871i | ||||||
\(851\) | 7.32990 | + | 0.727338i | 0.251266 | + | 0.0249328i | ||||
\(852\) | −5.56146 | + | 1.80736i | −0.190532 | + | 0.0619190i | ||||
\(853\) | 28.1221 | − | 28.1221i | 0.962882 | − | 0.962882i | −0.0364533 | − | 0.999335i | \(-0.511606\pi\) |
0.999335 | + | 0.0364533i | \(0.0116060\pi\) | |||||||
\(854\) | −26.6255 | −0.911107 | ||||||||
\(855\) | −8.54776 | + | 6.21171i | −0.292327 | + | 0.212436i | ||||
\(856\) | 1.36163 | + | 1.36163i | 0.0465397 | + | 0.0465397i | ||||
\(857\) | 14.2681 | − | 14.2681i | 0.487389 | − | 0.487389i | −0.420092 | − | 0.907481i | \(-0.638002\pi\) |
0.907481 | + | 0.420092i | \(0.138002\pi\) | |||||||
\(858\) | 1.31111 | + | 4.03446i | 0.0447607 | + | 0.137734i | ||||
\(859\) | 11.9927 | + | 11.9927i | 0.409185 | + | 0.409185i | 0.881454 | − | 0.472269i | \(-0.156565\pi\) |
−0.472269 | + | 0.881454i | \(0.656565\pi\) | |||||||
\(860\) | − | 3.93165i | − | 0.134068i | ||||||
\(861\) | 43.8372 | − | 14.2461i | 1.49397 | − | 0.485507i | ||||
\(862\) | 32.9451i | 1.12211i | ||||||||
\(863\) | 18.0730i | 0.615211i | 0.951514 | + | 0.307605i | \(0.0995277\pi\) | ||||
−0.951514 | + | 0.307605i | \(0.900472\pi\) | |||||||
\(864\) | 5.13205 | − | 0.813678i | 0.174596 | − | 0.0276819i | ||||
\(865\) | −15.8577 | + | 15.8577i | −0.539179 | + | 0.539179i | ||||
\(866\) | −4.61021 | − | 4.61021i | −0.156661 | − | 0.156661i | ||||
\(867\) | 16.0005 | + | 49.2357i | 0.543407 | + | 1.67213i | ||||
\(868\) | −4.32310 | − | 4.32310i | −0.146735 | − | 0.146735i | ||||
\(869\) | 10.1260 | + | 10.1260i | 0.343502 | + | 0.343502i | ||||
\(870\) | −11.3368 | − | 5.77560i | −0.384352 | − | 0.195811i | ||||
\(871\) | 2.21964 | − | 2.21964i | 0.0752097 | − | 0.0752097i | ||||
\(872\) | 2.50977 | 0.0849916 | ||||||||
\(873\) | −21.0082 | − | 3.32508i | −0.711020 | − | 0.112537i | ||||
\(874\) | −3.01590 | − | 3.01590i | −0.102014 | − | 0.102014i | ||||
\(875\) | 1.79574 | + | 1.79574i | 0.0607069 | + | 0.0607069i | ||||
\(876\) | −0.790993 | + | 0.257056i | −0.0267252 | + | 0.00868511i | ||||
\(877\) | −54.1088 | −1.82712 | −0.913562 | − | 0.406698i | \(-0.866680\pi\) | ||||
−0.913562 | + | 0.406698i | \(0.866680\pi\) | |||||||
\(878\) | −11.2830 | −0.380783 | ||||||||
\(879\) | −8.15153 | − | 25.0833i | −0.274944 | − | 0.846038i | ||||
\(880\) | −1.09777 | + | 1.09777i | −0.0370057 | + | 0.0370057i | ||||
\(881\) | 26.8290 | 0.903891 | 0.451946 | − | 0.892045i | \(-0.350730\pi\) | ||||
0.451946 | + | 0.892045i | \(0.350730\pi\) | |||||||
\(882\) | −1.63170 | − | 0.258257i | −0.0549420 | − | 0.00869596i | ||||
\(883\) | 32.1258 | − | 32.1258i | 1.08112 | − | 1.08112i | 0.0847128 | − | 0.996405i | \(-0.473003\pi\) |
0.996405 | − | 0.0847128i | \(-0.0269973\pi\) | |||||||
\(884\) | − | 10.8029i | − | 0.363341i | ||||||
\(885\) | 6.33343 | + | 19.4888i | 0.212896 | + | 0.655107i | ||||
\(886\) | −0.120564 | − | 0.120564i | −0.00405043 | − | 0.00405043i | ||||
\(887\) | 56.0728 | 1.88274 | 0.941370 | − | 0.337377i | \(-0.109540\pi\) | ||||
0.941370 | + | 0.337377i | \(0.109540\pi\) | |||||||
\(888\) | 10.2924 | − | 2.25092i | 0.345390 | − | 0.0755359i | ||||
\(889\) | −36.3588 | −1.21944 | ||||||||
\(890\) | 10.5685 | + | 10.5685i | 0.354257 | + | 0.354257i | ||||
\(891\) | 4.31484 | − | 13.2893i | 0.144552 | − | 0.445210i | ||||
\(892\) | − | 19.6653i | − | 0.658442i | ||||||
\(893\) | −25.9705 | + | 25.9705i | −0.869070 | + | 0.869070i | ||||
\(894\) | −12.0854 | + | 23.7222i | −0.404198 | + | 0.793387i | ||||
\(895\) | −8.16769 | −0.273016 | ||||||||
\(896\) | −1.79574 | + | 1.79574i | −0.0599913 | + | 0.0599913i | ||||
\(897\) | 3.14692 | − | 1.02268i | 0.105073 | − | 0.0341464i | ||||
\(898\) | −36.6657 | −1.22355 | ||||||||
\(899\) | 17.6843 | 0.589805 | ||||||||
\(900\) | 2.42686 | − | 1.76361i | 0.0808954 | − | 0.0587872i | ||||
\(901\) | 24.9916 | + | 24.9916i | 0.832590 | + | 0.832590i | ||||
\(902\) | 11.5036 | + | 11.5036i | 0.383030 | + | 0.383030i | ||||
\(903\) | −15.4094 | − | 7.85045i | −0.512793 | − | 0.261247i | ||||
\(904\) | 16.1124 | 0.535892 | ||||||||
\(905\) | 9.29009 | − | 9.29009i | 0.308813 | − | 0.308813i | ||||
\(906\) | 6.95402 | − | 13.6498i | 0.231032 | − | 0.453485i | ||||
\(907\) | 29.0323 | + | 29.0323i | 0.964003 | + | 0.964003i | 0.999374 | − | 0.0353712i | \(-0.0112613\pi\) |
−0.0353712 | + | 0.999374i | \(0.511261\pi\) | |||||||
\(908\) | 2.56107 | + | 2.56107i | 0.0849921 | + | 0.0849921i | ||||
\(909\) | −7.59009 | + | 5.51576i | −0.251747 | + | 0.182946i | ||||
\(910\) | 2.83298 | + | 2.83298i | 0.0939125 | + | 0.0939125i | ||||
\(911\) | 23.5290 | − | 23.5290i | 0.779551 | − | 0.779551i | −0.200203 | − | 0.979754i | \(-0.564160\pi\) |
0.979754 | + | 0.200203i | \(0.0641602\pi\) | |||||||
\(912\) | −5.43576 | − | 2.76929i | −0.179996 | − | 0.0917005i | ||||
\(913\) | 13.4250i | 0.444303i | ||||||||
\(914\) | − | 2.59170i | − | 0.0857259i | ||||||
\(915\) | 5.61249 | + | 17.2703i | 0.185543 | + | 0.570939i | ||||
\(916\) | 13.0356i | 0.430709i | ||||||||
\(917\) | −1.63195 | − | 1.63195i | −0.0538917 | − | 0.0538917i | ||||
\(918\) | −20.9095 | + | 28.7891i | −0.690116 | + | 0.950182i | ||||
\(919\) | −13.4771 | + | 13.4771i | −0.444568 | + | 0.444568i | −0.893544 | − | 0.448976i | \(-0.851789\pi\) |
0.448976 | + | 0.893544i | \(0.351789\pi\) | |||||||
\(920\) | 0.856269 | + | 0.856269i | 0.0282303 | + | 0.0282303i | ||||
\(921\) | −12.0679 | − | 37.1344i | −0.397650 | − | 1.22362i | ||||
\(922\) | 16.1738 | 0.532656 | ||||||||
\(923\) | −3.76631 | + | 3.76631i | −0.123970 | + | 0.123970i | ||||
\(924\) | 2.11055 | + | 6.49444i | 0.0694321 | + | 0.213651i | ||||
\(925\) | 4.70486 | − | 3.85543i | 0.154695 | − | 0.126766i | ||||
\(926\) | − | 20.7344i | − | 0.681376i | ||||||
\(927\) | −6.26695 | + | 39.5953i | −0.205834 | + | 1.30048i | ||||
\(928\) | − | 7.34574i | − | 0.241136i | ||||||
\(929\) | −48.7123 | −1.59820 | −0.799099 | − | 0.601200i | \(-0.794690\pi\) | ||||
−0.799099 | + | 0.601200i | \(0.794690\pi\) | |||||||
\(930\) | −1.89284 | + | 3.71540i | −0.0620688 | + | 0.121833i | ||||
\(931\) | 1.37146 | + | 1.37146i | 0.0449477 | + | 0.0449477i | ||||
\(932\) | − | 20.4916i | − | 0.671223i | ||||||
\(933\) | −13.3528 | − | 6.80269i | −0.437151 | − | 0.222710i | ||||
\(934\) | 11.2004 | 0.366490 | ||||||||
\(935\) | − | 10.6307i | − | 0.347662i | ||||||
\(936\) | 3.82866 | − | 2.78231i | 0.125144 | − | 0.0909426i | ||||
\(937\) | 24.3402 | 0.795161 | 0.397581 | − | 0.917567i | \(-0.369850\pi\) | ||||
0.397581 | + | 0.917567i | \(0.369850\pi\) | |||||||
\(938\) | 3.57305 | − | 3.57305i | 0.116664 | − | 0.116664i | ||||
\(939\) | −7.12986 | − | 3.63237i | −0.232674 | − | 0.118538i | ||||
\(940\) | 7.37349 | − | 7.37349i | 0.240497 | − | 0.240497i | ||||
\(941\) | 41.7533i | 1.36112i | 0.732694 | + | 0.680559i | \(0.238263\pi\) | ||||
−0.732694 | + | 0.680559i | \(0.761737\pi\) | |||||||
\(942\) | −6.45001 | − | 3.28601i | −0.210153 | − | 0.107064i | ||||
\(943\) | 8.97296 | − | 8.97296i | 0.292200 | − | 0.292200i | ||||
\(944\) | −8.36584 | + | 8.36584i | −0.272285 | + | 0.272285i | ||||
\(945\) | −2.06638 | − | 13.0331i | −0.0672193 | − | 0.423967i | ||||
\(946\) | − | 6.10379i | − | 0.198451i | ||||||
\(947\) | −34.4729 | + | 34.4729i | −1.12022 | + | 1.12022i | −0.128510 | + | 0.991708i | \(0.541019\pi\) |
−0.991708 | + | 0.128510i | \(0.958981\pi\) | |||||||
\(948\) | 7.25257 | − | 14.2358i | 0.235552 | − | 0.462359i | ||||
\(949\) | −0.535673 | + | 0.535673i | −0.0173887 | + | 0.0173887i | ||||
\(950\) | −3.52214 | −0.114273 | ||||||||
\(951\) | −49.4478 | + | 16.0695i | −1.60346 | + | 0.521089i | ||||
\(952\) | − | 17.3898i | − | 0.563608i | ||||||
\(953\) | −41.6524 | −1.34925 | −0.674627 | − | 0.738159i | \(-0.735695\pi\) | ||||
−0.674627 | + | 0.738159i | \(0.735695\pi\) | |||||||
\(954\) | −2.42065 | + | 15.2939i | −0.0783714 | + | 0.495159i | ||||
\(955\) | 9.23941i | 0.298980i | ||||||||
\(956\) | −16.0579 | − | 16.0579i | −0.519350 | − | 0.519350i | ||||
\(957\) | −17.6000 | − | 8.96648i | −0.568928 | − | 0.289845i | ||||
\(958\) | −26.3662 | −0.851853 | ||||||||
\(959\) | 57.8221i | 1.86717i | ||||||||
\(960\) | 1.54331 | + | 0.786252i | 0.0498101 | + | 0.0253762i | ||||
\(961\) | 25.2043i | 0.813042i | ||||||||
\(962\) | 7.42246 | − | 6.08239i | 0.239310 | − | 0.196104i | ||||
\(963\) | −3.39609 | − | 4.67327i | −0.109437 | − | 0.150594i | ||||
\(964\) | 8.01194 | − | 8.01194i | 0.258047 | − | 0.258047i | ||||
\(965\) | 1.66983 | 0.0537537 | ||||||||
\(966\) | 5.06573 | − | 1.64625i | 0.162987 | − | 0.0529673i | ||||
\(967\) | −17.9450 | − | 17.9450i | −0.577071 | − | 0.577071i | 0.357024 | − | 0.934095i | \(-0.383792\pi\) |
−0.934095 | + | 0.357024i | \(0.883792\pi\) | |||||||
\(968\) | 6.07392 | − | 6.07392i | 0.195223 | − | 0.195223i | ||||
\(969\) | 39.7288 | − | 12.9110i | 1.27627 | − | 0.414761i | ||||
\(970\) | −5.01332 | − | 5.01332i | −0.160968 | − | 0.160968i | ||||
\(971\) | − | 14.9163i | − | 0.478687i | −0.970935 | − | 0.239343i | \(-0.923068\pi\) | ||
0.970935 | − | 0.239343i | \(-0.0769321\pi\) | |||||||
\(972\) | −15.5885 | + | 0.00415661i | −0.500000 | + | 0.000133323i | ||||
\(973\) | 17.6600i | 0.566153i | ||||||||
\(974\) | 12.5977i | 0.403657i | ||||||||
\(975\) | 1.24041 | − | 2.43475i | 0.0397248 | − | 0.0779745i | ||||
\(976\) | −7.41355 | + | 7.41355i | −0.237302 | + | 0.237302i | ||||
\(977\) | −7.77719 | − | 7.77719i | −0.248814 | − | 0.248814i | 0.571670 | − | 0.820484i | \(-0.306296\pi\) |
−0.820484 | + | 0.571670i | \(0.806296\pi\) | |||||||
\(978\) | −3.60505 | + | 1.17156i | −0.115277 | + | 0.0374625i | ||||
\(979\) | 16.4073 | + | 16.4073i | 0.524381 | + | 0.524381i | ||||
\(980\) | −0.389382 | − | 0.389382i | −0.0124383 | − | 0.0124383i | ||||
\(981\) | −7.43674 | − | 1.17705i | −0.237437 | − | 0.0375803i | ||||
\(982\) | 0.306040 | − | 0.306040i | 0.00976612 | − | 0.00976612i | ||||
\(983\) | 4.10130 | 0.130811 | 0.0654056 | − | 0.997859i | \(-0.479166\pi\) | ||||
0.0654056 | + | 0.997859i | \(0.479166\pi\) | |||||||
\(984\) | 8.23925 | − | 16.1726i | 0.262658 | − | 0.515563i | ||||
\(985\) | −2.17198 | − | 2.17198i | −0.0692052 | − | 0.0692052i | ||||
\(986\) | 35.5679 | + | 35.5679i | 1.13271 | + | 1.13271i | ||||
\(987\) | −14.1762 | − | 43.6220i | −0.451234 | − | 1.38850i | ||||
\(988\) | −5.55660 | −0.176779 | ||||||||
\(989\) | −4.76102 | −0.151392 | ||||||||
\(990\) | 3.76765 | − | 2.73797i | 0.119744 | − | 0.0870184i | ||||
\(991\) | 41.0764 | − | 41.0764i | 1.30484 | − | 1.30484i | 0.379744 | − | 0.925091i | \(-0.376012\pi\) |
0.925091 | − | 0.379744i | \(-0.123988\pi\) | |||||||
\(992\) | −2.40742 | −0.0764358 | ||||||||
\(993\) | −20.1191 | − | 10.2498i | −0.638459 | − | 0.325268i | ||||
\(994\) | −6.06278 | + | 6.06278i | −0.192300 | + | 0.192300i | ||||
\(995\) | 2.73848i | 0.0868158i | ||||||||
\(996\) | 14.2446 | − | 4.62918i | 0.451357 | − | 0.146681i | ||||
\(997\) | 4.48937 | + | 4.48937i | 0.142180 | + | 0.142180i | 0.774614 | − | 0.632434i | \(-0.217944\pi\) |
−0.632434 | + | 0.774614i | \(0.717944\pi\) | |||||||
\(998\) | −28.0543 | −0.888044 | ||||||||
\(999\) | −31.5532 | + | 1.84273i | −0.998299 | + | 0.0583014i |
(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.191.16 | yes | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.e.191.3 | ✓ | 40 | |
37.31 | odd | 4 | inner | 1110.2.u.e.401.3 | yes | 40 | |
111.68 | even | 4 | inner | 1110.2.u.e.401.16 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.e.191.3 | ✓ | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.e.191.16 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.u.e.401.3 | yes | 40 | 37.31 | odd | 4 | inner | |
1110.2.u.e.401.16 | yes | 40 | 111.68 | even | 4 | inner |