Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(79,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.e (of order \(3\), degree \(2\), not 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.2696112.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.2 | ||
Root | \(0.235342 + 0.407624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.508 |
Dual form | 637.2.e.j.79.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.235342 | − | 0.407624i | −0.166412 | − | 0.288234i | 0.770744 | − | 0.637145i | \(-0.219885\pi\) |
−0.937156 | + | 0.348911i | \(0.886551\pi\) | |||||||
\(3\) | −1.12457 | + | 1.94781i | −0.649271 | + | 1.12457i | 0.334026 | + | 0.942564i | \(0.391593\pi\) |
−0.983297 | + | 0.182007i | \(0.941741\pi\) | |||||||
\(4\) | 0.889229 | − | 1.54019i | 0.444614 | − | 0.770095i | ||||
\(5\) | −0.264658 | − | 0.458402i | −0.118359 | − | 0.205003i | 0.800759 | − | 0.598987i | \(-0.204430\pi\) |
−0.919117 | + | 0.393984i | \(0.871097\pi\) | |||||||
\(6\) | 1.05863 | 0.432185 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.77846 | −0.628780 | ||||||||
\(9\) | −1.02932 | − | 1.78283i | −0.343106 | − | 0.594276i | ||||
\(10\) | −0.124570 | + | 0.215762i | −0.0393926 | + | 0.0682299i | ||||
\(11\) | 1.12457 | − | 1.94781i | 0.339071 | − | 0.587288i | −0.645187 | − | 0.764024i | \(-0.723221\pi\) |
0.984258 | + | 0.176737i | \(0.0565541\pi\) | |||||||
\(12\) | 2.00000 | + | 3.46410i | 0.577350 | + | 1.00000i | ||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19051 | 0.307388 | ||||||||
\(16\) | −1.35991 | − | 2.35544i | −0.339978 | − | 0.588859i | ||||
\(17\) | 0.653887 | − | 1.13257i | 0.158591 | − | 0.274687i | −0.775770 | − | 0.631016i | \(-0.782638\pi\) |
0.934361 | + | 0.356328i | \(0.115972\pi\) | |||||||
\(18\) | −0.484482 | + | 0.839148i | −0.114194 | + | 0.197789i | ||||
\(19\) | 0.735342 | + | 1.27365i | 0.168699 | + | 0.292195i | 0.937963 | − | 0.346736i | \(-0.112710\pi\) |
−0.769264 | + | 0.638931i | \(0.779377\pi\) | |||||||
\(20\) | −0.941367 | −0.210496 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.05863 | −0.225701 | ||||||||
\(23\) | −2.91855 | − | 5.05507i | −0.608559 | − | 1.05405i | −0.991478 | − | 0.130273i | \(-0.958415\pi\) |
0.382919 | − | 0.923782i | \(-0.374919\pi\) | |||||||
\(24\) | 2.00000 | − | 3.46410i | 0.408248 | − | 0.707107i | ||||
\(25\) | 2.35991 | − | 4.08749i | 0.471982 | − | 0.817497i | ||||
\(26\) | −0.235342 | − | 0.407624i | −0.0461543 | − | 0.0799416i | ||||
\(27\) | −2.11727 | −0.407468 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.22154 | 0.969616 | 0.484808 | − | 0.874621i | \(-0.338889\pi\) | ||||
0.484808 | + | 0.874621i | \(0.338889\pi\) | |||||||
\(30\) | −0.280176 | − | 0.485279i | −0.0511529 | − | 0.0885994i | ||||
\(31\) | 3.51380 | − | 6.08608i | 0.631097 | − | 1.09309i | −0.356231 | − | 0.934398i | \(-0.615938\pi\) |
0.987328 | − | 0.158694i | \(-0.0507283\pi\) | |||||||
\(32\) | −2.41855 | + | 4.18904i | −0.427542 | + | 0.740525i | ||||
\(33\) | 2.52932 | + | 4.38090i | 0.440298 | + | 0.762618i | ||||
\(34\) | −0.615547 | −0.105566 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.66119 | −0.610198 | ||||||||
\(37\) | 1.18320 | + | 2.04937i | 0.194517 | + | 0.336914i | 0.946742 | − | 0.321992i | \(-0.104353\pi\) |
−0.752225 | + | 0.658907i | \(0.771019\pi\) | |||||||
\(38\) | 0.346113 | − | 0.599486i | 0.0561470 | − | 0.0972494i | ||||
\(39\) | −1.12457 | + | 1.94781i | −0.180075 | + | 0.311900i | ||||
\(40\) | 0.470683 | + | 0.815248i | 0.0744216 | + | 0.128902i | ||||
\(41\) | 6.49828 | 1.01486 | 0.507431 | − | 0.861693i | \(-0.330595\pi\) | ||||
0.507431 | + | 0.861693i | \(0.330595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3940 | 1.73757 | 0.868785 | − | 0.495190i | \(-0.164902\pi\) | ||||
0.868785 | + | 0.495190i | \(0.164902\pi\) | |||||||
\(44\) | −2.00000 | − | 3.46410i | −0.301511 | − | 0.522233i | ||||
\(45\) | −0.544834 | + | 0.943681i | −0.0812191 | + | 0.140676i | ||||
\(46\) | −1.37371 | + | 2.37934i | −0.202543 | + | 0.350814i | ||||
\(47\) | −4.29226 | − | 7.43441i | −0.626090 | − | 1.08442i | −0.988329 | − | 0.152334i | \(-0.951321\pi\) |
0.362239 | − | 0.932085i | \(-0.382012\pi\) | |||||||
\(48\) | 6.11727 | 0.882951 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.22154 | −0.314174 | ||||||||
\(51\) | 1.47068 | + | 2.54730i | 0.205937 | + | 0.356693i | ||||
\(52\) | 0.889229 | − | 1.54019i | 0.123314 | − | 0.213586i | ||||
\(53\) | −5.63837 | + | 9.76594i | −0.774490 | + | 1.34146i | 0.160591 | + | 0.987021i | \(0.448660\pi\) |
−0.935081 | + | 0.354434i | \(0.884673\pi\) | |||||||
\(54\) | 0.498281 | + | 0.863048i | 0.0678075 | + | 0.117446i | ||||
\(55\) | −1.19051 | −0.160528 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.30777 | −0.438125 | ||||||||
\(58\) | −1.22885 | − | 2.12843i | −0.161355 | − | 0.279476i | ||||
\(59\) | 6.08623 | − | 10.5417i | 0.792360 | − | 1.37241i | −0.132142 | − | 0.991231i | \(-0.542186\pi\) |
0.924502 | − | 0.381177i | \(-0.124481\pi\) | |||||||
\(60\) | 1.05863 | − | 1.83361i | 0.136669 | − | 0.236718i | ||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | −3.30777 | −0.420088 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.16291 | −0.395364 | ||||||||
\(65\) | −0.264658 | − | 0.458402i | −0.0328268 | − | 0.0568577i | ||||
\(66\) | 1.19051 | − | 2.06202i | 0.146541 | − | 0.253817i | ||||
\(67\) | 7.96896 | − | 13.8027i | 0.973564 | − | 1.68626i | 0.288969 | − | 0.957338i | \(-0.406687\pi\) |
0.684595 | − | 0.728924i | \(-0.259979\pi\) | |||||||
\(68\) | −1.16291 | − | 2.01422i | −0.141024 | − | 0.244260i | ||||
\(69\) | 13.1284 | 1.58048 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.19051 | 0.141287 | 0.0706436 | − | 0.997502i | \(-0.477495\pi\) | ||||
0.0706436 | + | 0.997502i | \(0.477495\pi\) | |||||||
\(72\) | 1.83060 | + | 3.17068i | 0.215738 | + | 0.373669i | ||||
\(73\) | −3.82157 | + | 6.61916i | −0.447281 | + | 0.774714i | −0.998208 | − | 0.0598398i | \(-0.980941\pi\) |
0.550927 | + | 0.834554i | \(0.314274\pi\) | |||||||
\(74\) | 0.556914 | − | 0.964604i | 0.0647400 | − | 0.112133i | ||||
\(75\) | 5.30777 | + | 9.19333i | 0.612889 | + | 1.06155i | ||||
\(76\) | 2.61555 | 0.300024 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.05863 | 0.119867 | ||||||||
\(79\) | 0.669405 | + | 1.15944i | 0.0753139 | + | 0.130448i | 0.901223 | − | 0.433356i | \(-0.142671\pi\) |
−0.825909 | + | 0.563804i | \(0.809337\pi\) | |||||||
\(80\) | −0.719824 | + | 1.24677i | −0.0804788 | + | 0.139393i | ||||
\(81\) | 5.46896 | − | 9.47252i | 0.607663 | − | 1.05250i | ||||
\(82\) | −1.52932 | − | 2.64885i | −0.168885 | − | 0.292517i | ||||
\(83\) | −16.3500 | −1.79464 | −0.897322 | − | 0.441377i | \(-0.854490\pi\) | ||||
−0.897322 | + | 0.441377i | \(0.854490\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.692226 | −0.0750825 | ||||||||
\(86\) | −2.68148 | − | 4.64447i | −0.289152 | − | 0.500826i | ||||
\(87\) | −5.87199 | + | 10.1706i | −0.629544 | + | 1.09040i | ||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | −3.45517 | − | 5.98452i | −0.366247 | − | 0.634358i | 0.622729 | − | 0.782438i | \(-0.286024\pi\) |
−0.988975 | + | 0.148080i | \(0.952691\pi\) | |||||||
\(90\) | 0.512889 | 0.0540632 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −10.3810 | −1.08230 | ||||||||
\(93\) | 7.90303 | + | 13.6884i | 0.819506 | + | 1.41943i | ||||
\(94\) | −2.02029 | + | 3.49925i | −0.208377 | + | 0.360920i | ||||
\(95\) | 0.389229 | − | 0.674164i | 0.0399340 | − | 0.0691677i | ||||
\(96\) | −5.43965 | − | 9.42175i | −0.555182 | − | 0.961603i | ||||
\(97\) | −3.47068 | −0.352395 | −0.176197 | − | 0.984355i | \(-0.556380\pi\) | ||||
−0.176197 | + | 0.984355i | \(0.556380\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.63016 | −0.465348 | ||||||||
\(100\) | −4.19700 | − | 7.26942i | −0.419700 | − | 0.726942i | ||||
\(101\) | −3.87543 | + | 6.71244i | −0.385620 | + | 0.667913i | −0.991855 | − | 0.127372i | \(-0.959346\pi\) |
0.606235 | + | 0.795285i | \(0.292679\pi\) | |||||||
\(102\) | 0.692226 | − | 1.19897i | 0.0685406 | − | 0.118716i | ||||
\(103\) | 8.49828 | + | 14.7195i | 0.837361 | + | 1.45035i | 0.892094 | + | 0.451850i | \(0.149236\pi\) |
−0.0547334 | + | 0.998501i | \(0.517431\pi\) | |||||||
\(104\) | −1.77846 | −0.174392 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.30777 | 0.515537 | ||||||||
\(107\) | 2.77846 | + | 4.81243i | 0.268604 | + | 0.465235i | 0.968501 | − | 0.249008i | \(-0.0801045\pi\) |
−0.699898 | + | 0.714243i | \(0.746771\pi\) | |||||||
\(108\) | −1.88273 | + | 3.26099i | −0.181166 | + | 0.313789i | ||||
\(109\) | −3.96166 | + | 6.86180i | −0.379458 | + | 0.657241i | −0.990984 | − | 0.133984i | \(-0.957223\pi\) |
0.611525 | + | 0.791225i | \(0.290556\pi\) | |||||||
\(110\) | 0.280176 | + | 0.485279i | 0.0267137 | + | 0.0462696i | ||||
\(111\) | −5.32238 | −0.505178 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.89229 | −0.930588 | −0.465294 | − | 0.885156i | \(-0.654051\pi\) | ||||
−0.465294 | + | 0.885156i | \(0.654051\pi\) | |||||||
\(114\) | 0.778457 | + | 1.34833i | 0.0729092 | + | 0.126282i | ||||
\(115\) | −1.54483 | + | 2.67573i | −0.144057 | + | 0.249513i | ||||
\(116\) | 4.64315 | − | 8.04216i | 0.431105 | − | 0.746696i | ||||
\(117\) | −1.02932 | − | 1.78283i | −0.0951604 | − | 0.164823i | ||||
\(118\) | −5.72938 | −0.527432 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.11727 | −0.193279 | ||||||||
\(121\) | 2.97068 | + | 5.14537i | 0.270062 | + | 0.467761i | ||||
\(122\) | 0.470683 | − | 0.815248i | 0.0426137 | − | 0.0738090i | ||||
\(123\) | −7.30777 | + | 12.6574i | −0.658920 | + | 1.14128i | ||||
\(124\) | −6.24914 | − | 10.8238i | −0.561189 | − | 0.972009i | ||||
\(125\) | −5.14486 | −0.460171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.824101 | 0.0731271 | 0.0365635 | − | 0.999331i | \(-0.488359\pi\) | ||||
0.0365635 | + | 0.999331i | \(0.488359\pi\) | |||||||
\(128\) | 5.58145 | + | 9.66736i | 0.493336 | + | 0.854482i | ||||
\(129\) | −12.8134 | + | 22.1934i | −1.12815 | + | 1.95402i | ||||
\(130\) | −0.124570 | + | 0.215762i | −0.0109255 | + | 0.0189236i | ||||
\(131\) | −5.30777 | − | 9.19333i | −0.463742 | − | 0.803225i | 0.535401 | − | 0.844598i | \(-0.320160\pi\) |
−0.999144 | + | 0.0413724i | \(0.986827\pi\) | |||||||
\(132\) | 8.99656 | 0.783050 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.50172 | −0.648050 | ||||||||
\(135\) | 0.560352 | + | 0.970558i | 0.0482274 | + | 0.0835324i | ||||
\(136\) | −1.16291 | + | 2.01422i | −0.0997187 | + | 0.172718i | ||||
\(137\) | −5.68148 | + | 9.84062i | −0.485402 | + | 0.840741i | −0.999859 | − | 0.0167751i | \(-0.994660\pi\) |
0.514457 | + | 0.857516i | \(0.327993\pi\) | |||||||
\(138\) | −3.08967 | − | 5.35146i | −0.263010 | − | 0.455547i | ||||
\(139\) | −13.9233 | −1.18096 | −0.590480 | − | 0.807052i | \(-0.701062\pi\) | ||||
−0.590480 | + | 0.807052i | \(0.701062\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.3078 | 1.62601 | ||||||||
\(142\) | −0.280176 | − | 0.485279i | −0.0235119 | − | 0.0407237i | ||||
\(143\) | 1.12457 | − | 1.94781i | 0.0940413 | − | 0.162884i | ||||
\(144\) | −2.79956 | + | 4.84898i | −0.233297 | + | 0.404082i | ||||
\(145\) | −1.38192 | − | 2.39356i | −0.114763 | − | 0.198775i | ||||
\(146\) | 3.59750 | 0.297731 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.20855 | 0.345941 | ||||||||
\(149\) | −4.65389 | − | 8.06077i | −0.381261 | − | 0.660364i | 0.609982 | − | 0.792416i | \(-0.291177\pi\) |
−0.991243 | + | 0.132052i | \(0.957844\pi\) | |||||||
\(150\) | 2.49828 | − | 4.32715i | 0.203984 | − | 0.353310i | ||||
\(151\) | −3.53662 | + | 6.12561i | −0.287806 | + | 0.498495i | −0.973286 | − | 0.229597i | \(-0.926259\pi\) |
0.685480 | + | 0.728092i | \(0.259593\pi\) | |||||||
\(152\) | −1.30777 | − | 2.26513i | −0.106074 | − | 0.183726i | ||||
\(153\) | −2.69223 | −0.217654 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.71982 | −0.298783 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | 3.02029 | − | 5.23130i | 0.241046 | − | 0.417503i | −0.719967 | − | 0.694009i | \(-0.755843\pi\) |
0.961012 | + | 0.276505i | \(0.0891763\pi\) | |||||||
\(158\) | 0.315078 | − | 0.545730i | 0.0250662 | − | 0.0434160i | ||||
\(159\) | −12.6815 | − | 21.9650i | −1.00571 | − | 1.74194i | ||||
\(160\) | 2.56035 | 0.202414 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.14830 | −0.404489 | ||||||||
\(163\) | −3.19051 | − | 5.52612i | −0.249900 | − | 0.432839i | 0.713598 | − | 0.700555i | \(-0.247064\pi\) |
−0.963498 | + | 0.267716i | \(0.913731\pi\) | |||||||
\(164\) | 5.77846 | − | 10.0086i | 0.451222 | − | 0.781539i | ||||
\(165\) | 1.33881 | − | 2.31889i | 0.104226 | − | 0.180525i | ||||
\(166\) | 3.84783 | + | 6.66464i | 0.298650 | + | 0.517276i | ||||
\(167\) | −16.5845 | −1.28335 | −0.641674 | − | 0.766977i | \(-0.721760\pi\) | ||||
−0.641674 | + | 0.766977i | \(0.721760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.162910 | + | 0.282168i | 0.0124946 | + | 0.0216413i | ||||
\(171\) | 1.51380 | − | 2.62198i | 0.115763 | − | 0.200508i | ||||
\(172\) | 10.1319 | − | 17.5489i | 0.772548 | − | 1.33809i | ||||
\(173\) | 11.6504 | + | 20.1792i | 0.885767 | + | 1.53419i | 0.844832 | + | 0.535032i | \(0.179700\pi\) |
0.0409355 | + | 0.999162i | \(0.486966\pi\) | |||||||
\(174\) | 5.52770 | 0.419054 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.11727 | −0.461106 | ||||||||
\(177\) | 13.6888 | + | 23.7097i | 1.02891 | + | 1.78213i | ||||
\(178\) | −1.62629 | + | 2.81682i | −0.121896 | + | 0.211129i | ||||
\(179\) | −10.5211 | + | 18.2231i | −0.786384 | + | 1.36206i | 0.141785 | + | 0.989898i | \(0.454716\pi\) |
−0.928169 | + | 0.372160i | \(0.878617\pi\) | |||||||
\(180\) | 0.968964 | + | 1.67830i | 0.0722223 | + | 0.125093i | ||||
\(181\) | 16.7474 | 1.24483 | 0.622413 | − | 0.782689i | \(-0.286152\pi\) | ||||
0.622413 | + | 0.782689i | \(0.286152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.49828 | −0.332523 | ||||||||
\(184\) | 5.19051 | + | 8.99022i | 0.382649 | + | 0.662768i | ||||
\(185\) | 0.626289 | − | 1.08476i | 0.0460457 | − | 0.0797535i | ||||
\(186\) | 3.71982 | − | 6.44292i | 0.272751 | − | 0.472418i | ||||
\(187\) | −1.47068 | − | 2.54730i | −0.107547 | − | 0.186277i | ||||
\(188\) | −15.2672 | −1.11347 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.366407 | −0.0265819 | ||||||||
\(191\) | 3.71982 | + | 6.44292i | 0.269157 | + | 0.466194i | 0.968644 | − | 0.248451i | \(-0.0799216\pi\) |
−0.699487 | + | 0.714645i | \(0.746588\pi\) | |||||||
\(192\) | 3.55691 | − | 6.16076i | 0.256698 | − | 0.444614i | ||||
\(193\) | 0.750859 | − | 1.30053i | 0.0540480 | − | 0.0936140i | −0.837736 | − | 0.546076i | \(-0.816121\pi\) |
0.891784 | + | 0.452462i | \(0.149454\pi\) | |||||||
\(194\) | 0.816797 | + | 1.41473i | 0.0586426 | + | 0.101572i | ||||
\(195\) | 1.19051 | 0.0852540 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.9931 | 1.70944 | 0.854720 | − | 0.519090i | \(-0.173729\pi\) | ||||
0.854720 | + | 0.519090i | \(0.173729\pi\) | |||||||
\(198\) | 1.08967 | + | 1.88736i | 0.0774394 | + | 0.134129i | ||||
\(199\) | 1.00730 | − | 1.74470i | 0.0714059 | − | 0.123679i | −0.828112 | − | 0.560563i | \(-0.810585\pi\) |
0.899518 | + | 0.436884i | \(0.143918\pi\) | |||||||
\(200\) | −4.19700 | + | 7.26942i | −0.296773 | + | 0.514026i | ||||
\(201\) | 17.9233 | + | 31.0441i | 1.26421 | + | 2.18968i | ||||
\(202\) | 3.64820 | 0.256687 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 5.23109 | 0.366250 | ||||||||
\(205\) | −1.71982 | − | 2.97882i | −0.120118 | − | 0.208050i | ||||
\(206\) | 4.00000 | − | 6.92820i | 0.278693 | − | 0.482711i | ||||
\(207\) | −6.00821 | + | 10.4065i | −0.417600 | + | 0.723304i | ||||
\(208\) | −1.35991 | − | 2.35544i | −0.0942929 | − | 0.163320i | ||||
\(209\) | 3.30777 | 0.228803 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.1008 | 0.695370 | 0.347685 | − | 0.937611i | \(-0.386968\pi\) | ||||
0.347685 | + | 0.937611i | \(0.386968\pi\) | |||||||
\(212\) | 10.0276 | + | 17.3683i | 0.688698 | + | 1.19286i | ||||
\(213\) | −1.33881 | + | 2.31889i | −0.0917337 | + | 0.158887i | ||||
\(214\) | 1.30777 | − | 2.26513i | 0.0893976 | − | 0.154841i | ||||
\(215\) | −3.01552 | − | 5.22303i | −0.205657 | − | 0.356208i | ||||
\(216\) | 3.76547 | 0.256208 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.72938 | 0.252585 | ||||||||
\(219\) | −8.59525 | − | 14.8874i | −0.580813 | − | 1.00600i | ||||
\(220\) | −1.05863 | + | 1.83361i | −0.0713730 | + | 0.123622i | ||||
\(221\) | 0.653887 | − | 1.13257i | 0.0439852 | − | 0.0761846i | ||||
\(222\) | 1.25258 | + | 2.16953i | 0.0840676 | + | 0.145609i | ||||
\(223\) | 10.1414 | 0.679120 | 0.339560 | − | 0.940584i | \(-0.389722\pi\) | ||||
0.339560 | + | 0.940584i | \(0.389722\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.71639 | −0.647759 | ||||||||
\(226\) | 2.32807 | + | 4.03233i | 0.154861 | + | 0.268227i | ||||
\(227\) | 2.69223 | − | 4.66307i | 0.178689 | − | 0.309499i | −0.762743 | − | 0.646702i | \(-0.776148\pi\) |
0.941432 | + | 0.337203i | \(0.109481\pi\) | |||||||
\(228\) | −2.94137 | + | 5.09460i | −0.194797 | + | 0.337398i | ||||
\(229\) | −1.66119 | − | 2.87727i | −0.109775 | − | 0.190135i | 0.805904 | − | 0.592046i | \(-0.201680\pi\) |
−0.915679 | + | 0.401911i | \(0.868346\pi\) | |||||||
\(230\) | 1.45426 | 0.0958908 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.28629 | −0.609675 | ||||||||
\(233\) | −6.85991 | − | 11.8817i | −0.449408 | − | 0.778397i | 0.548940 | − | 0.835862i | \(-0.315032\pi\) |
−0.998348 | + | 0.0574648i | \(0.981698\pi\) | |||||||
\(234\) | −0.484482 | + | 0.839148i | −0.0316716 | + | 0.0548568i | ||||
\(235\) | −2.27196 | + | 3.93515i | −0.148206 | + | 0.256701i | ||||
\(236\) | −10.8241 | − | 18.7479i | −0.704589 | − | 1.22038i | ||||
\(237\) | −3.01117 | −0.195597 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.50172 | −0.226507 | −0.113254 | − | 0.993566i | \(-0.536127\pi\) | ||||
−0.113254 | + | 0.993566i | \(0.536127\pi\) | |||||||
\(240\) | −1.61899 | − | 2.80416i | −0.104505 | − | 0.181008i | ||||
\(241\) | −0.793975 | + | 1.37520i | −0.0511444 | + | 0.0885847i | −0.890464 | − | 0.455053i | \(-0.849620\pi\) |
0.839320 | + | 0.543638i | \(0.182954\pi\) | |||||||
\(242\) | 1.39825 | − | 2.42184i | 0.0898830 | − | 0.155682i | ||||
\(243\) | 9.12457 | + | 15.8042i | 0.585341 | + | 1.01384i | ||||
\(244\) | 3.55691 | 0.227708 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.87930 | 0.438608 | ||||||||
\(247\) | 0.735342 | + | 1.27365i | 0.0467887 | + | 0.0810404i | ||||
\(248\) | −6.24914 | + | 10.8238i | −0.396821 | + | 0.687314i | ||||
\(249\) | 18.3867 | − | 31.8467i | 1.16521 | − | 2.01820i | ||||
\(250\) | 1.21080 | + | 2.09717i | 0.0765778 | + | 0.132637i | ||||
\(251\) | −4.92676 | −0.310974 | −0.155487 | − | 0.987838i | \(-0.549695\pi\) | ||||
−0.155487 | + | 0.987838i | \(0.549695\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1284 | −0.825378 | ||||||||
\(254\) | −0.193945 | − | 0.335923i | −0.0121692 | − | 0.0210777i | ||||
\(255\) | 0.778457 | − | 1.34833i | 0.0487489 | − | 0.0844355i | ||||
\(256\) | −0.535811 | + | 0.928053i | −0.0334882 | + | 0.0580033i | ||||
\(257\) | 4.00730 | + | 6.94085i | 0.249969 | + | 0.432959i | 0.963517 | − | 0.267648i | \(-0.0862463\pi\) |
−0.713548 | + | 0.700606i | \(0.752913\pi\) | |||||||
\(258\) | 12.0621 | 0.750952 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.941367 | −0.0583811 | ||||||||
\(261\) | −5.37462 | − | 9.30912i | −0.332681 | − | 0.576220i | ||||
\(262\) | −2.49828 | + | 4.32715i | −0.154344 | + | 0.267332i | ||||
\(263\) | −0.801279 | + | 1.38786i | −0.0494090 | + | 0.0855788i | −0.889672 | − | 0.456600i | \(-0.849067\pi\) |
0.840263 | + | 0.542179i | \(0.182400\pi\) | |||||||
\(264\) | −4.49828 | − | 7.79125i | −0.276850 | − | 0.479518i | ||||
\(265\) | 5.96896 | 0.366671 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.5423 | 0.951174 | ||||||||
\(268\) | −14.1725 | − | 24.5474i | −0.865721 | − | 1.49947i | ||||
\(269\) | 5.91033 | − | 10.2370i | 0.360359 | − | 0.624161i | −0.627661 | − | 0.778487i | \(-0.715987\pi\) |
0.988020 | + | 0.154327i | \(0.0493208\pi\) | |||||||
\(270\) | 0.263748 | − | 0.456826i | 0.0160512 | − | 0.0278015i | ||||
\(271\) | −10.9414 | − | 18.9510i | −0.664641 | − | 1.15119i | −0.979383 | − | 0.202014i | \(-0.935251\pi\) |
0.314742 | − | 0.949177i | \(-0.398082\pi\) | |||||||
\(272\) | −3.55691 | −0.215670 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.34836 | 0.323106 | ||||||||
\(275\) | −5.30777 | − | 9.19333i | −0.320071 | − | 0.554379i | ||||
\(276\) | 11.6742 | − | 20.2203i | 0.702703 | − | 1.21712i | ||||
\(277\) | 5.10905 | − | 8.84914i | 0.306973 | − | 0.531693i | −0.670725 | − | 0.741706i | \(-0.734017\pi\) |
0.977699 | + | 0.210012i | \(0.0673505\pi\) | |||||||
\(278\) | 3.27674 | + | 5.67548i | 0.196526 | + | 0.340392i | ||||
\(279\) | −14.4672 | −0.866131 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.54231 | 0.0920063 | 0.0460031 | − | 0.998941i | \(-0.485352\pi\) | ||||
0.0460031 | + | 0.998941i | \(0.485352\pi\) | |||||||
\(282\) | −4.54392 | − | 7.87031i | −0.270587 | − | 0.468670i | ||||
\(283\) | −7.92332 | + | 13.7236i | −0.470993 | + | 0.815783i | −0.999449 | − | 0.0331771i | \(-0.989437\pi\) |
0.528457 | + | 0.848960i | \(0.322771\pi\) | |||||||
\(284\) | 1.05863 | − | 1.83361i | 0.0628183 | − | 0.108805i | ||||
\(285\) | 0.875430 | + | 1.51629i | 0.0518560 | + | 0.0898172i | ||||
\(286\) | −1.05863 | −0.0625983 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9.95779 | 0.586769 | ||||||||
\(289\) | 7.64486 | + | 13.2413i | 0.449698 | + | 0.778900i | ||||
\(290\) | −0.650449 | + | 1.12661i | −0.0381957 | + | 0.0661569i | ||||
\(291\) | 3.90303 | − | 6.76024i | 0.228800 | − | 0.396292i | ||||
\(292\) | 6.79650 | + | 11.7719i | 0.397735 | + | 0.688898i | ||||
\(293\) | 11.0828 | 0.647464 | 0.323732 | − | 0.946149i | \(-0.395062\pi\) | ||||
0.323732 | + | 0.946149i | \(0.395062\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.44309 | −0.375131 | ||||||||
\(296\) | −2.10428 | − | 3.64471i | −0.122309 | − | 0.211845i | ||||
\(297\) | −2.38101 | + | 4.12404i | −0.138160 | + | 0.239301i | ||||
\(298\) | −2.19051 | + | 3.79407i | −0.126893 | + | 0.219785i | ||||
\(299\) | −2.91855 | − | 5.05507i | −0.168784 | − | 0.292342i | ||||
\(300\) | 18.8793 | 1.09000 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.32926 | 0.191577 | ||||||||
\(303\) | −8.71639 | − | 15.0972i | −0.500743 | − | 0.867313i | ||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 0.529317 | − | 0.916803i | 0.0303086 | − | 0.0524960i | ||||
\(306\) | 0.633593 | + | 1.09742i | 0.0362201 | + | 0.0627351i | ||||
\(307\) | 20.4121 | 1.16498 | 0.582489 | − | 0.812839i | \(-0.302079\pi\) | ||||
0.582489 | + | 0.812839i | \(0.302079\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −38.2277 | −2.17470 | ||||||||
\(310\) | 0.875430 | + | 1.51629i | 0.0497211 | + | 0.0861194i | ||||
\(311\) | 0.961661 | − | 1.66564i | 0.0545308 | − | 0.0944501i | −0.837471 | − | 0.546481i | \(-0.815967\pi\) |
0.892002 | + | 0.452031i | \(0.149300\pi\) | |||||||
\(312\) | 2.00000 | − | 3.46410i | 0.113228 | − | 0.196116i | ||||
\(313\) | 7.18320 | + | 12.4417i | 0.406019 | + | 0.703245i | 0.994439 | − | 0.105310i | \(-0.0335835\pi\) |
−0.588421 | + | 0.808555i | \(0.700250\pi\) | |||||||
\(314\) | −2.84320 | −0.160451 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.38101 | 0.133943 | ||||||||
\(317\) | −7.77846 | − | 13.4727i | −0.436882 | − | 0.756701i | 0.560565 | − | 0.828110i | \(-0.310584\pi\) |
−0.997447 | + | 0.0714089i | \(0.977250\pi\) | |||||||
\(318\) | −5.96896 | + | 10.3385i | −0.334723 | + | 0.579757i | ||||
\(319\) | 5.87199 | − | 10.1706i | 0.328768 | − | 0.569444i | ||||
\(320\) | 0.837090 | + | 1.44988i | 0.0467948 | + | 0.0810509i | ||||
\(321\) | −12.4983 | −0.697586 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.92332 | 0.107016 | ||||||||
\(324\) | −9.72632 | − | 16.8465i | −0.540351 | − | 0.935915i | ||||
\(325\) | 2.35991 | − | 4.08749i | 0.130904 | − | 0.226733i | ||||
\(326\) | −1.50172 | + | 2.60105i | −0.0831725 | + | 0.144059i | ||||
\(327\) | −8.91033 | − | 15.4331i | −0.492742 | − | 0.853455i | ||||
\(328\) | −11.5569 | −0.638124 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.26031 | −0.0693778 | ||||||||
\(331\) | −15.7750 | − | 27.3231i | −0.867073 | − | 1.50182i | −0.864974 | − | 0.501818i | \(-0.832665\pi\) |
−0.00209996 | − | 0.999998i | \(-0.500668\pi\) | |||||||
\(332\) | −14.5389 | + | 25.1821i | −0.797924 | + | 1.38205i | ||||
\(333\) | 2.43578 | − | 4.21890i | 0.133480 | − | 0.231194i | ||||
\(334\) | 3.90303 | + | 6.76024i | 0.213564 | + | 0.369904i | ||||
\(335\) | −8.43621 | −0.460919 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.42666 | −0.459029 | −0.229515 | − | 0.973305i | \(-0.573714\pi\) | ||||
−0.229515 | + | 0.973305i | \(0.573714\pi\) | |||||||
\(338\) | −0.235342 | − | 0.407624i | −0.0128009 | − | 0.0221718i | ||||
\(339\) | 11.1246 | − | 19.2683i | 0.604204 | − | 1.04651i | ||||
\(340\) | −0.615547 | + | 1.06616i | −0.0333827 | + | 0.0578206i | ||||
\(341\) | −7.90303 | − | 13.6884i | −0.427973 | − | 0.741271i | ||||
\(342\) | −1.42504 | −0.0770573 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.2637 | −1.09255 | ||||||||
\(345\) | −3.47455 | − | 6.01810i | −0.187063 | − | 0.324003i | ||||
\(346\) | 5.48367 | − | 9.49800i | 0.294804 | − | 0.510616i | ||||
\(347\) | −9.67418 | + | 16.7562i | −0.519337 | + | 0.899518i | 0.480410 | + | 0.877044i | \(0.340488\pi\) |
−0.999747 | + | 0.0224745i | \(0.992846\pi\) | |||||||
\(348\) | 10.4431 | + | 18.0880i | 0.559808 | + | 0.969616i | ||||
\(349\) | 27.2553 | 1.45894 | 0.729470 | − | 0.684013i | \(-0.239767\pi\) | ||||
0.729470 | + | 0.684013i | \(0.239767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.11727 | −0.113011 | ||||||||
\(352\) | 5.43965 | + | 9.42175i | 0.289934 | + | 0.502181i | ||||
\(353\) | 12.8371 | − | 22.2345i | 0.683249 | − | 1.18342i | −0.290734 | − | 0.956804i | \(-0.593900\pi\) |
0.973984 | − | 0.226619i | \(-0.0727671\pi\) | |||||||
\(354\) | 6.44309 | − | 11.1598i | 0.342446 | − | 0.593134i | ||||
\(355\) | −0.315078 | − | 0.545730i | −0.0167226 | − | 0.0289644i | ||||
\(356\) | −12.2897 | −0.651354 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.90422 | 0.523454 | ||||||||
\(359\) | 11.7091 | + | 20.2807i | 0.617982 | + | 1.07038i | 0.989854 | + | 0.142092i | \(0.0453828\pi\) |
−0.371872 | + | 0.928284i | \(0.621284\pi\) | |||||||
\(360\) | 0.968964 | − | 1.67830i | 0.0510689 | − | 0.0884540i | ||||
\(361\) | 8.41855 | − | 14.5813i | 0.443081 | − | 0.767439i | ||||
\(362\) | −3.94137 | − | 6.82665i | −0.207154 | − | 0.358801i | ||||
\(363\) | −13.3630 | −0.701374 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.04564 | 0.211759 | ||||||||
\(366\) | 1.05863 | + | 1.83361i | 0.0553356 | + | 0.0958441i | ||||
\(367\) | 7.34268 | − | 12.7179i | 0.383285 | − | 0.663868i | −0.608245 | − | 0.793749i | \(-0.708126\pi\) |
0.991530 | + | 0.129881i | \(0.0414595\pi\) | |||||||
\(368\) | −7.93793 | + | 13.7489i | −0.413793 | + | 0.716711i | ||||
\(369\) | −6.68879 | − | 11.5853i | −0.348204 | − | 0.603108i | ||||
\(370\) | −0.589568 | −0.0306502 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 28.1104 | 1.45746 | ||||||||
\(373\) | 11.8337 | + | 20.4965i | 0.612723 | + | 1.06127i | 0.990779 | + | 0.135485i | \(0.0432593\pi\) |
−0.378056 | + | 0.925783i | \(0.623407\pi\) | |||||||
\(374\) | −0.692226 | + | 1.19897i | −0.0357942 | + | 0.0619973i | ||||
\(375\) | 5.78576 | − | 10.0212i | 0.298775 | − | 0.517494i | ||||
\(376\) | 7.63359 | + | 13.2218i | 0.393673 | + | 0.681861i | ||||
\(377\) | 5.22154 | 0.268923 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.7405 | −1.68177 | −0.840884 | − | 0.541215i | \(-0.817965\pi\) | ||||
−0.840884 | + | 0.541215i | \(0.817965\pi\) | |||||||
\(380\) | −0.692226 | − | 1.19897i | −0.0355105 | − | 0.0615059i | ||||
\(381\) | −0.926759 | + | 1.60519i | −0.0474793 | + | 0.0822366i | ||||
\(382\) | 1.75086 | − | 3.03258i | 0.0895818 | − | 0.155160i | ||||
\(383\) | 11.3078 | + | 19.5856i | 0.577800 | + | 1.00078i | 0.995731 | + | 0.0923006i | \(0.0294221\pi\) |
−0.417931 | + | 0.908479i | \(0.637245\pi\) | |||||||
\(384\) | −25.1070 | −1.28123 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.706834 | −0.0359769 | ||||||||
\(387\) | −11.7280 | − | 20.3136i | −0.596170 | − | 1.03260i | ||||
\(388\) | −3.08623 | + | 5.34551i | −0.156680 | + | 0.271377i | ||||
\(389\) | −19.0242 | + | 32.9508i | −0.964563 | + | 1.67067i | −0.253779 | + | 0.967262i | \(0.581674\pi\) |
−0.710784 | + | 0.703410i | \(0.751660\pi\) | |||||||
\(390\) | −0.280176 | − | 0.485279i | −0.0141873 | − | 0.0245731i | ||||
\(391\) | −7.63359 | −0.386047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.8759 | 1.20438 | ||||||||
\(394\) | −5.64658 | − | 9.78017i | −0.284471 | − | 0.492718i | ||||
\(395\) | 0.354327 | − | 0.613712i | 0.0178281 | − | 0.0308792i | ||||
\(396\) | −4.11727 | + | 7.13131i | −0.206900 | + | 0.358362i | ||||
\(397\) | 5.85261 | + | 10.1370i | 0.293734 | + | 0.508762i | 0.974690 | − | 0.223563i | \(-0.0717687\pi\) |
−0.680956 | + | 0.732325i | \(0.738435\pi\) | |||||||
\(398\) | −0.948243 | −0.0475311 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.8371 | −0.641855 | ||||||||
\(401\) | −1.77846 | − | 3.08038i | −0.0888119 | − | 0.153827i | 0.818197 | − | 0.574938i | \(-0.194974\pi\) |
−0.907009 | + | 0.421111i | \(0.861640\pi\) | |||||||
\(402\) | 8.43621 | − | 14.6119i | 0.420760 | − | 0.728778i | ||||
\(403\) | 3.51380 | − | 6.08608i | 0.175035 | − | 0.303169i | ||||
\(404\) | 6.89229 | + | 11.9378i | 0.342904 | + | 0.593927i | ||||
\(405\) | −5.78963 | −0.287689 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.32238 | 0.263821 | ||||||||
\(408\) | −2.61555 | − | 4.53026i | −0.129489 | − | 0.224281i | ||||
\(409\) | −2.63107 | + | 4.55714i | −0.130098 | + | 0.225336i | −0.923714 | − | 0.383083i | \(-0.874862\pi\) |
0.793616 | + | 0.608419i | \(0.208196\pi\) | |||||||
\(410\) | −0.809493 | + | 1.40208i | −0.0399780 | + | 0.0692439i | ||||
\(411\) | −12.7785 | − | 22.1329i | −0.630315 | − | 1.09174i | ||||
\(412\) | 30.2277 | 1.48921 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.65593 | 0.277974 | ||||||||
\(415\) | 4.32716 | + | 7.49486i | 0.212412 | + | 0.367908i | ||||
\(416\) | −2.41855 | + | 4.18904i | −0.118579 | + | 0.205385i | ||||
\(417\) | 15.6578 | − | 27.1200i | 0.766763 | − | 1.32807i | ||||
\(418\) | −0.778457 | − | 1.34833i | −0.0380756 | − | 0.0659488i | ||||
\(419\) | 26.0337 | 1.27183 | 0.635915 | − | 0.771759i | \(-0.280623\pi\) | ||||
0.635915 | + | 0.771759i | \(0.280623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.2423 | 1.08402 | 0.542011 | − | 0.840372i | \(-0.317663\pi\) | ||||
0.542011 | + | 0.840372i | \(0.317663\pi\) | |||||||
\(422\) | −2.37715 | − | 4.11734i | −0.115718 | − | 0.200429i | ||||
\(423\) | −8.83618 | + | 15.3047i | −0.429630 | + | 0.744141i | ||||
\(424\) | 10.0276 | − | 17.3683i | 0.486983 | − | 0.843480i | ||||
\(425\) | −3.08623 | − | 5.34551i | −0.149704 | − | 0.259295i | ||||
\(426\) | 1.26031 | 0.0610622 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9.88273 | 0.477700 | ||||||||
\(429\) | 2.52932 | + | 4.38090i | 0.122117 | + | 0.211512i | ||||
\(430\) | −1.41935 | + | 2.45839i | −0.0684473 | + | 0.118554i | ||||
\(431\) | −13.8371 | + | 23.9665i | −0.666509 | + | 1.15443i | 0.312365 | + | 0.949962i | \(0.398879\pi\) |
−0.978874 | + | 0.204465i | \(0.934454\pi\) | |||||||
\(432\) | 2.87930 | + | 4.98709i | 0.138530 | + | 0.239941i | ||||
\(433\) | −12.7880 | −0.614552 | −0.307276 | − | 0.951620i | \(-0.599418\pi\) | ||||
−0.307276 | + | 0.951620i | \(0.599418\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.21629 | 0.298048 | ||||||||
\(436\) | 7.04564 | + | 12.2034i | 0.337425 | + | 0.584437i | ||||
\(437\) | 4.29226 | − | 7.43441i | 0.205326 | − | 0.355636i | ||||
\(438\) | −4.04564 | + | 7.00726i | −0.193308 | + | 0.334820i | ||||
\(439\) | 9.08279 | + | 15.7319i | 0.433498 | + | 0.750841i | 0.997172 | − | 0.0751569i | \(-0.0239458\pi\) |
−0.563674 | + | 0.825998i | \(0.690612\pi\) | |||||||
\(440\) | 2.11727 | 0.100937 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.615547 | −0.0292786 | ||||||||
\(443\) | −0.0538572 | − | 0.0932834i | −0.00255883 | − | 0.00443203i | 0.864743 | − | 0.502214i | \(-0.167481\pi\) |
−0.867302 | + | 0.497782i | \(0.834148\pi\) | |||||||
\(444\) | −4.73281 | + | 8.19747i | −0.224609 | + | 0.389035i | ||||
\(445\) | −1.82888 | + | 3.16771i | −0.0866971 | + | 0.150164i | ||||
\(446\) | −2.38670 | − | 4.13389i | −0.113014 | − | 0.195745i | ||||
\(447\) | 20.9345 | 0.990167 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1725 | −1.04638 | −0.523192 | − | 0.852215i | \(-0.675259\pi\) | ||||
−0.523192 | + | 0.852215i | \(0.675259\pi\) | |||||||
\(450\) | 2.28667 | + | 3.96063i | 0.107795 | + | 0.186706i | ||||
\(451\) | 7.30777 | − | 12.6574i | 0.344110 | − | 0.596015i | ||||
\(452\) | −8.79650 | + | 15.2360i | −0.413753 | + | 0.716641i | ||||
\(453\) | −7.95436 | − | 13.7773i | −0.373728 | − | 0.647316i | ||||
\(454\) | −2.53437 | −0.118944 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.88273 | 0.275484 | ||||||||
\(457\) | −2.17977 | − | 3.77546i | −0.101965 | − | 0.176609i | 0.810529 | − | 0.585698i | \(-0.199180\pi\) |
−0.912494 | + | 0.409090i | \(0.865846\pi\) | |||||||
\(458\) | −0.781895 | + | 1.35428i | −0.0365356 | + | 0.0632814i | ||||
\(459\) | −1.38445 | + | 2.39794i | −0.0646207 | + | 0.111926i | ||||
\(460\) | 2.74742 | + | 4.75867i | 0.128099 | + | 0.221874i | ||||
\(461\) | 32.3810 | 1.50813 | 0.754067 | − | 0.656797i | \(-0.228089\pi\) | ||||
0.754067 | + | 0.656797i | \(0.228089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.36641 | 0.388820 | 0.194410 | − | 0.980920i | \(-0.437721\pi\) | ||||
0.194410 | + | 0.980920i | \(0.437721\pi\) | |||||||
\(464\) | −7.10084 | − | 12.2990i | −0.329648 | − | 0.570967i | ||||
\(465\) | 4.18320 | − | 7.24552i | 0.193991 | − | 0.336003i | ||||
\(466\) | −3.22885 | + | 5.59253i | −0.149573 | + | 0.259069i | ||||
\(467\) | 9.77115 | + | 16.9241i | 0.452155 | + | 0.783156i | 0.998520 | − | 0.0543919i | \(-0.0173220\pi\) |
−0.546365 | + | 0.837547i | \(0.683989\pi\) | |||||||
\(468\) | −3.66119 | −0.169239 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.13875 | 0.0986532 | ||||||||
\(471\) | 6.79307 | + | 11.7659i | 0.313008 | + | 0.542146i | ||||
\(472\) | −10.8241 | + | 18.7479i | −0.498220 | + | 0.862942i | ||||
\(473\) | 12.8134 | − | 22.1934i | 0.589159 | − | 1.02045i | ||||
\(474\) | 0.708654 | + | 1.22742i | 0.0325496 | + | 0.0563775i | ||||
\(475\) | 6.94137 | 0.318492 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.2147 | 1.06293 | ||||||||
\(478\) | 0.824101 | + | 1.42738i | 0.0376935 | + | 0.0652870i | ||||
\(479\) | 14.2612 | − | 24.7012i | 0.651612 | − | 1.12862i | −0.331120 | − | 0.943589i | \(-0.607426\pi\) |
0.982732 | − | 0.185036i | \(-0.0592402\pi\) | |||||||
\(480\) | −2.87930 | + | 4.98709i | −0.131421 | + | 0.227628i | ||||
\(481\) | 1.18320 | + | 2.04937i | 0.0539494 | + | 0.0934432i | ||||
\(482\) | 0.747422 | 0.0340441 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.5665 | 0.480294 | ||||||||
\(485\) | 0.918545 | + | 1.59097i | 0.0417090 | + | 0.0722421i | ||||
\(486\) | 4.29478 | − | 7.43878i | 0.194815 | − | 0.337430i | ||||
\(487\) | −12.4121 | + | 21.4983i | −0.562444 | + | 0.974181i | 0.434839 | + | 0.900508i | \(0.356805\pi\) |
−0.997282 | + | 0.0736727i | \(0.976528\pi\) | |||||||
\(488\) | −1.77846 | − | 3.08038i | −0.0805070 | − | 0.139442i | ||||
\(489\) | 14.3518 | 0.649011 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1690 | 1.31638 | 0.658190 | − | 0.752852i | \(-0.271322\pi\) | ||||
0.658190 | + | 0.752852i | \(0.271322\pi\) | |||||||
\(492\) | 12.9966 | + | 22.5107i | 0.585930 | + | 1.01486i | ||||
\(493\) | 3.41430 | − | 5.91374i | 0.153772 | − | 0.266341i | ||||
\(494\) | 0.346113 | − | 0.599486i | 0.0155724 | − | 0.0269721i | ||||
\(495\) | 1.22541 | + | 2.12247i | 0.0550780 | + | 0.0953980i | ||||
\(496\) | −19.1138 | −0.858236 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −17.3086 | −0.775618 | ||||||||
\(499\) | 16.6504 | + | 28.8394i | 0.745376 | + | 1.29103i | 0.950019 | + | 0.312193i | \(0.101064\pi\) |
−0.204642 | + | 0.978837i | \(0.565603\pi\) | |||||||
\(500\) | −4.57496 | + | 7.92406i | −0.204598 | + | 0.354375i | ||||
\(501\) | 18.6504 | − | 32.3035i | 0.833241 | − | 1.44322i | ||||
\(502\) | 1.15947 | + | 2.00826i | 0.0517498 | + | 0.0896332i | ||||
\(503\) | −12.3258 | −0.549581 | −0.274791 | − | 0.961504i | \(-0.588609\pi\) | ||||
−0.274791 | + | 0.961504i | \(0.588609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.10266 | 0.182566 | ||||||||
\(506\) | 3.08967 | + | 5.35146i | 0.137353 | + | 0.237902i | ||||
\(507\) | −1.12457 | + | 1.94781i | −0.0499439 | + | 0.0865054i | ||||
\(508\) | 0.732814 | − | 1.26927i | 0.0325134 | − | 0.0563148i | ||||
\(509\) | −11.8526 | − | 20.5293i | −0.525358 | − | 0.909946i | −0.999564 | − | 0.0295323i | \(-0.990598\pi\) |
0.474206 | − | 0.880414i | \(-0.342735\pi\) | |||||||
\(510\) | −0.732814 | −0.0324495 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.8302 | 1.00896 | ||||||||
\(513\) | −1.55691 | − | 2.69665i | −0.0687394 | − | 0.119060i | ||||
\(514\) | 1.88617 | − | 3.26694i | 0.0831955 | − | 0.144099i | ||||
\(515\) | 4.49828 | − | 7.79125i | 0.198218 | − | 0.343324i | ||||
\(516\) | 22.7880 | + | 39.4700i | 1.00319 | + | 1.73757i | ||||
\(517\) | −19.3078 | −0.849155 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −52.4070 | −2.30041 | ||||||||
\(520\) | 0.470683 | + | 0.815248i | 0.0206408 | + | 0.0357510i | ||||
\(521\) | −21.9509 | + | 38.0201i | −0.961687 | + | 1.66569i | −0.243424 | + | 0.969920i | \(0.578270\pi\) |
−0.718264 | + | 0.695771i | \(0.755063\pi\) | |||||||
\(522\) | −2.52974 | + | 4.38165i | −0.110724 | + | 0.191779i | ||||
\(523\) | −18.7164 | − | 32.4177i | −0.818410 | − | 1.41753i | −0.906853 | − | 0.421447i | \(-0.861522\pi\) |
0.0884425 | − | 0.996081i | \(-0.471811\pi\) | |||||||
\(524\) | −18.8793 | −0.824746 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.754297 | 0.0328889 | ||||||||
\(527\) | −4.59525 | − | 7.95921i | −0.200172 | − | 0.346709i | ||||
\(528\) | 6.87930 | − | 11.9153i | 0.299383 | − | 0.518546i | ||||
\(529\) | −5.53581 | + | 9.58831i | −0.240687 | + | 0.416883i | ||||
\(530\) | −1.40475 | − | 2.43309i | −0.0610183 | − | 0.105687i | ||||
\(531\) | −25.0586 | −1.08745 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.49828 | 0.281472 | ||||||||
\(534\) | −3.65775 | − | 6.33541i | −0.158286 | − | 0.274160i | ||||
\(535\) | 1.47068 | − | 2.54730i | 0.0635832 | − | 0.110129i | ||||
\(536\) | −14.1725 | + | 24.5474i | −0.612157 | + | 1.06029i | ||||
\(537\) | −23.6634 | − | 40.9863i | −1.02115 | − | 1.76869i | ||||
\(538\) | −5.56379 | −0.239872 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.99312 | 0.0857704 | ||||||||
\(541\) | 17.4875 | + | 30.2893i | 0.751848 | + | 1.30224i | 0.946926 | + | 0.321451i | \(0.104171\pi\) |
−0.195078 | + | 0.980788i | \(0.562496\pi\) | |||||||
\(542\) | −5.14992 | + | 8.91992i | −0.221208 | + | 0.383144i | ||||
\(543\) | −18.8337 | + | 32.6208i | −0.808229 | + | 1.39989i | ||||
\(544\) | 3.16291 | + | 5.47832i | 0.135609 | + | 0.234881i | ||||
\(545\) | 4.19395 | 0.179649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.50783 | 0.278255 | 0.139127 | − | 0.990274i | \(-0.455570\pi\) | ||||
0.139127 | + | 0.990274i | \(0.455570\pi\) | |||||||
\(548\) | 10.1043 | + | 17.5011i | 0.431633 | + | 0.747611i | ||||
\(549\) | 2.05863 | − | 3.56566i | 0.0878603 | − | 0.152179i | ||||
\(550\) | −2.49828 | + | 4.32715i | −0.106527 | + | 0.184510i | ||||
\(551\) | 3.83962 | + | 6.65041i | 0.163573 | + | 0.283317i | ||||
\(552\) | −23.3484 | −0.993772 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.80949 | −0.204336 | ||||||||
\(555\) | 1.40861 | + | 2.43979i | 0.0597923 | + | 0.103563i | ||||
\(556\) | −12.3810 | + | 21.4445i | −0.525072 | + | 0.909451i | ||||
\(557\) | 21.7164 | − | 37.6139i | 0.920153 | − | 1.59375i | 0.120976 | − | 0.992655i | \(-0.461398\pi\) |
0.799177 | − | 0.601096i | \(-0.205269\pi\) | |||||||
\(558\) | 3.40475 | + | 5.89719i | 0.144134 | + | 0.249648i | ||||
\(559\) | 11.3940 | 0.481915 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.61555 | 0.279309 | ||||||||
\(562\) | −0.362969 | − | 0.628681i | −0.0153109 | − | 0.0265193i | ||||
\(563\) | 16.9414 | − | 29.3433i | 0.713993 | − | 1.23667i | −0.249353 | − | 0.968413i | \(-0.580218\pi\) |
0.963346 | − | 0.268260i | \(-0.0864487\pi\) | |||||||
\(564\) | 17.1690 | − | 29.7376i | 0.722946 | − | 1.25218i | ||||
\(565\) | 2.61808 | + | 4.53464i | 0.110143 | + | 0.190774i | ||||
\(566\) | 7.45875 | 0.313515 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.11727 | −0.0888385 | ||||||||
\(569\) | −9.60733 | − | 16.6404i | −0.402760 | − | 0.697601i | 0.591298 | − | 0.806453i | \(-0.298616\pi\) |
−0.994058 | + | 0.108852i | \(0.965283\pi\) | |||||||
\(570\) | 0.412050 | − | 0.713692i | 0.0172589 | − | 0.0298933i | ||||
\(571\) | −10.4134 | + | 18.0365i | −0.435787 | + | 0.754805i | −0.997359 | − | 0.0726226i | \(-0.976863\pi\) |
0.561573 | + | 0.827427i | \(0.310196\pi\) | |||||||
\(572\) | −2.00000 | − | 3.46410i | −0.0836242 | − | 0.144841i | ||||
\(573\) | −16.7328 | −0.699023 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.5500 | −1.14892 | ||||||||
\(576\) | 3.25564 | + | 5.63893i | 0.135651 | + | 0.234955i | ||||
\(577\) | −14.3224 | + | 24.8071i | −0.596249 | + | 1.03273i | 0.397121 | + | 0.917766i | \(0.370009\pi\) |
−0.993369 | + | 0.114966i | \(0.963324\pi\) | |||||||
\(578\) | 3.59831 | − | 6.23246i | 0.149670 | − | 0.259236i | ||||
\(579\) | 1.68879 | + | 2.92507i | 0.0701837 | + | 0.121562i | ||||
\(580\) | −4.91539 | −0.204100 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.67418 | −0.152300 | ||||||||
\(583\) | 12.6815 | + | 21.9650i | 0.525213 | + | 0.909696i | ||||
\(584\) | 6.79650 | − | 11.7719i | 0.281241 | − | 0.487124i | ||||
\(585\) | −0.544834 | + | 0.943681i | −0.0225261 | + | 0.0390164i | ||||
\(586\) | −2.60824 | − | 4.51761i | −0.107746 | − | 0.186621i | ||||
\(587\) | −4.32076 | −0.178337 | −0.0891685 | − | 0.996017i | \(-0.528421\pi\) | ||||
−0.0891685 | + | 0.996017i | \(0.528421\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.3354 | 0.425862 | ||||||||
\(590\) | 1.51633 | + | 2.62636i | 0.0624262 | + | 0.108125i | ||||
\(591\) | −26.9820 | + | 46.7341i | −1.10989 | + | 1.92238i | ||||
\(592\) | 3.21811 | − | 5.57392i | 0.132263 | − | 0.229087i | ||||
\(593\) | 7.98448 | + | 13.8295i | 0.327883 | + | 0.567911i | 0.982092 | − | 0.188404i | \(-0.0603314\pi\) |
−0.654208 | + | 0.756314i | \(0.726998\pi\) | |||||||
\(594\) | 2.24141 | 0.0919661 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.5535 | −0.678057 | ||||||||
\(597\) | 2.26557 | + | 3.92408i | 0.0927235 | + | 0.160602i | ||||
\(598\) | −1.37371 | + | 2.37934i | −0.0561752 | + | 0.0972983i | ||||
\(599\) | 8.43487 | − | 14.6096i | 0.344640 | − | 0.596933i | −0.640649 | − | 0.767834i | \(-0.721334\pi\) |
0.985288 | + | 0.170901i | \(0.0546678\pi\) | |||||||
\(600\) | −9.43965 | − | 16.3499i | −0.385372 | − | 0.667484i | ||||
\(601\) | −15.3415 | −0.625792 | −0.312896 | − | 0.949787i | \(-0.601299\pi\) | ||||
−0.312896 | + | 0.949787i | \(0.601299\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.8103 | −1.33614 | ||||||||
\(604\) | 6.28973 | + | 10.8941i | 0.255925 | + | 0.443276i | ||||
\(605\) | 1.57243 | − | 2.72353i | 0.0639285 | − | 0.110727i | ||||
\(606\) | −4.10266 | + | 7.10601i | −0.166659 | + | 0.288662i | ||||
\(607\) | −17.9176 | − | 31.0343i | −0.727254 | − | 1.25964i | −0.958039 | − | 0.286637i | \(-0.907463\pi\) |
0.230785 | − | 0.973005i | \(-0.425871\pi\) | |||||||
\(608\) | −7.11383 | −0.288504 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.498281 | −0.0201748 | ||||||||
\(611\) | −4.29226 | − | 7.43441i | −0.173646 | − | 0.300764i | ||||
\(612\) | −2.39400 | + | 4.14654i | −0.0967719 | + | 0.167614i | ||||
\(613\) | −9.83365 | + | 17.0324i | −0.397177 | + | 0.687932i | −0.993376 | − | 0.114905i | \(-0.963344\pi\) |
0.596199 | + | 0.802837i | \(0.296677\pi\) | |||||||
\(614\) | −4.80381 | − | 8.32044i | −0.193866 | − | 0.335786i | ||||
\(615\) | 7.73625 | 0.311956 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −41.4588 | −1.66907 | −0.834533 | − | 0.550958i | \(-0.814263\pi\) | ||||
−0.834533 | + | 0.550958i | \(0.814263\pi\) | |||||||
\(618\) | 8.99656 | + | 15.5825i | 0.361895 | + | 0.626820i | ||||
\(619\) | −5.43965 | + | 9.42175i | −0.218638 | + | 0.378692i | −0.954392 | − | 0.298557i | \(-0.903495\pi\) |
0.735754 | + | 0.677249i | \(0.236828\pi\) | |||||||
\(620\) | −3.30777 | + | 5.72923i | −0.132843 | + | 0.230091i | ||||
\(621\) | 6.17934 | + | 10.7029i | 0.247968 | + | 0.429494i | ||||
\(622\) | −0.905275 | −0.0362982 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.11727 | 0.244887 | ||||||||
\(625\) | −10.4379 | − | 18.0790i | −0.417517 | − | 0.723161i | ||||
\(626\) | 3.38101 | − | 5.85609i | 0.135133 | − | 0.234056i | ||||
\(627\) | −3.71982 | + | 6.44292i | −0.148555 | + | 0.257306i | ||||
\(628\) | −5.37146 | − | 9.30365i | −0.214345 | − | 0.371256i | ||||
\(629\) | 3.09472 | 0.123395 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4396 | −1.25159 | −0.625796 | − | 0.779987i | \(-0.715226\pi\) | ||||
−0.625796 | + | 0.779987i | \(0.715226\pi\) | |||||||
\(632\) | −1.19051 | − | 2.06202i | −0.0473558 | − | 0.0820227i | ||||
\(633\) | −11.3591 | + | 19.6745i | −0.451484 | + | 0.781993i | ||||
\(634\) | −3.66119 | + | 6.34137i | −0.145404 | + | 0.251848i | ||||
\(635\) | −0.218105 | − | 0.377769i | −0.00865523 | − | 0.0149913i | ||||
\(636\) | −45.1070 | −1.78861 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.52770 | −0.218844 | ||||||||
\(639\) | −1.22541 | − | 2.12247i | −0.0484764 | − | 0.0839636i | ||||
\(640\) | 2.95436 | − | 5.11710i | 0.116781 | − | 0.202271i | ||||
\(641\) | −1.52110 | + | 2.63463i | −0.0600799 | + | 0.104062i | −0.894501 | − | 0.447066i | \(-0.852469\pi\) |
0.834421 | + | 0.551128i | \(0.185802\pi\) | |||||||
\(642\) | 2.94137 | + | 5.09460i | 0.116086 | + | 0.201068i | ||||
\(643\) | 8.02922 | 0.316641 | 0.158321 | − | 0.987388i | \(-0.449392\pi\) | ||||
0.158321 | + | 0.987388i | \(0.449392\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.5646 | 0.534107 | ||||||||
\(646\) | −0.452638 | − | 0.783991i | −0.0178088 | − | 0.0308457i | ||||
\(647\) | −3.53662 | + | 6.12561i | −0.139039 | + | 0.240822i | −0.927133 | − | 0.374732i | \(-0.877735\pi\) |
0.788094 | + | 0.615555i | \(0.211068\pi\) | |||||||
\(648\) | −9.72632 | + | 16.8465i | −0.382086 | + | 0.661792i | ||||
\(649\) | −13.6888 | − | 23.7097i | −0.537332 | − | 0.930686i | ||||
\(650\) | −2.22154 | −0.0871361 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.3484 | −0.444436 | ||||||||
\(653\) | 7.87930 | + | 13.6473i | 0.308341 | + | 0.534062i | 0.978000 | − | 0.208607i | \(-0.0668930\pi\) |
−0.669659 | + | 0.742669i | \(0.733560\pi\) | |||||||
\(654\) | −4.19395 | + | 7.26413i | −0.163996 | + | 0.284050i | ||||
\(655\) | −2.80949 | + | 4.86618i | −0.109776 | + | 0.190138i | ||||
\(656\) | −8.83709 | − | 15.3063i | −0.345030 | − | 0.597610i | ||||
\(657\) | 15.7344 | 0.613859 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.2181 | −0.475950 | −0.237975 | − | 0.971271i | \(-0.576484\pi\) | ||||
−0.237975 | + | 0.971271i | \(0.576484\pi\) | |||||||
\(660\) | −2.38101 | − | 4.12404i | −0.0926809 | − | 0.160528i | ||||
\(661\) | −1.86722 | + | 3.23411i | −0.0726263 | + | 0.125792i | −0.900052 | − | 0.435783i | \(-0.856471\pi\) |
0.827425 | + | 0.561576i | \(0.189805\pi\) | |||||||
\(662\) | −7.42504 | + | 12.8605i | −0.288582 | + | 0.499839i | ||||
\(663\) | 1.47068 | + | 2.54730i | 0.0571166 | + | 0.0989289i | ||||
\(664\) | 29.0777 | 1.12844 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.29296 | −0.0888506 | ||||||||
\(667\) | −15.2393 | − | 26.3953i | −0.590068 | − | 1.02203i | ||||
\(668\) | −14.7474 | + | 25.5433i | −0.570595 | + | 0.988299i | ||||
\(669\) | −11.4047 | + | 19.7536i | −0.440933 | + | 0.763718i | ||||
\(670\) | 1.98539 | + | 3.43880i | 0.0767024 | + | 0.132852i | ||||
\(671\) | 4.49828 | 0.173654 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.65775 | −0.218090 | −0.109045 | − | 0.994037i | \(-0.534779\pi\) | ||||
−0.109045 | + | 0.994037i | \(0.534779\pi\) | |||||||
\(674\) | 1.98314 | + | 3.43491i | 0.0763879 | + | 0.132308i | ||||
\(675\) | −4.99656 | + | 8.65430i | −0.192318 | + | 0.333104i | ||||
\(676\) | 0.889229 | − | 1.54019i | 0.0342011 | − | 0.0592380i | ||||
\(677\) | −4.69953 | − | 8.13983i | −0.180618 | − | 0.312839i | 0.761473 | − | 0.648196i | \(-0.224476\pi\) |
−0.942091 | + | 0.335357i | \(0.891143\pi\) | |||||||
\(678\) | −10.4723 | −0.402186 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.23109 | 0.0472103 | ||||||||
\(681\) | 6.05520 | + | 10.4879i | 0.232036 | + | 0.401897i | ||||
\(682\) | −3.71982 | + | 6.44292i | −0.142439 | + | 0.246712i | ||||
\(683\) | 10.3664 | − | 17.9551i | 0.396660 | − | 0.687034i | −0.596652 | − | 0.802500i | \(-0.703503\pi\) |
0.993311 | + | 0.115466i | \(0.0368360\pi\) | |||||||
\(684\) | −2.69223 | − | 4.66307i | −0.102940 | − | 0.178297i | ||||
\(685\) | 6.01461 | 0.229806 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.47250 | 0.285094 | ||||||||
\(688\) | −15.4948 | − | 26.8379i | −0.590735 | − | 1.02318i | ||||
\(689\) | −5.63837 | + | 9.76594i | −0.214805 | + | 0.372053i | ||||
\(690\) | −1.63541 | + | 2.83262i | −0.0622591 | + | 0.107836i | ||||
\(691\) | −8.04312 | − | 13.9311i | −0.305975 | − | 0.529963i | 0.671503 | − | 0.741002i | \(-0.265649\pi\) |
−0.977478 | + | 0.211038i | \(0.932316\pi\) | |||||||
\(692\) | 41.4396 | 1.57530 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.10695 | 0.345695 | ||||||||
\(695\) | 3.68492 | + | 6.38247i | 0.139777 | + | 0.242101i | ||||
\(696\) | 10.4431 | − | 18.0880i | 0.395844 | − | 0.685622i | ||||
\(697\) | 4.24914 | − | 7.35973i | 0.160948 | − | 0.278770i | ||||
\(698\) | −6.41430 | − | 11.1099i | −0.242785 | − | 0.420516i | ||||
\(699\) | 30.8578 | 1.16715 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.98013 | −0.263636 | −0.131818 | − | 0.991274i | \(-0.542081\pi\) | ||||
−0.131818 | + | 0.991274i | \(0.542081\pi\) | |||||||
\(702\) | 0.498281 | + | 0.863048i | 0.0188064 | + | 0.0325737i | ||||
\(703\) | −1.74012 | + | 3.01397i | −0.0656298 | + | 0.113674i | ||||
\(704\) | −3.55691 | + | 6.16076i | −0.134056 | + | 0.232192i | ||||
\(705\) | −5.10996 | − | 8.85071i | −0.192452 | − | 0.333337i | ||||
\(706\) | −12.0844 | −0.454803 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 48.6898 | 1.82988 | ||||||||
\(709\) | −4.19619 | − | 7.26802i | −0.157591 | − | 0.272956i | 0.776408 | − | 0.630230i | \(-0.217040\pi\) |
−0.934000 | + | 0.357274i | \(0.883706\pi\) | |||||||
\(710\) | −0.148302 | + | 0.256866i | −0.00556567 | + | 0.00964002i | ||||
\(711\) | 1.37806 | − | 2.38687i | 0.0516812 | − | 0.0895145i | ||||
\(712\) | 6.14486 | + | 10.6432i | 0.230289 | + | 0.398871i | ||||
\(713\) | −41.0207 | −1.53624 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.19051 | −0.0445225 | ||||||||
\(716\) | 18.7113 | + | 32.4090i | 0.699275 | + | 1.21118i | ||||
\(717\) | 3.93793 | − | 6.82069i | 0.147065 | − | 0.254723i | ||||
\(718\) | 5.51127 | − | 9.54580i | 0.205679 | − | 0.356246i | ||||
\(719\) | 2.58065 | + | 4.46981i | 0.0962418 | + | 0.166696i | 0.910126 | − | 0.414331i | \(-0.135984\pi\) |
−0.813884 | + | 0.581027i | \(0.802651\pi\) | |||||||
\(720\) | 2.96371 | 0.110451 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −7.92494 | −0.294936 | ||||||||
\(723\) | −1.78576 | − | 3.09303i | −0.0664132 | − | 0.115031i | ||||
\(724\) | 14.8923 | − | 25.7942i | 0.553467 | − | 0.958634i | ||||
\(725\) | 12.3224 | − | 21.3430i | 0.457642 | − | 0.792659i | ||||
\(726\) | 3.14486 | + | 5.44706i | 0.116717 | + | 0.202160i | ||||
\(727\) | −40.4362 | −1.49970 | −0.749848 | − | 0.661610i | \(-0.769873\pi\) | ||||
−0.749848 | + | 0.661610i | \(0.769873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.23109 | −0.304855 | ||||||||
\(730\) | −0.952109 | − | 1.64910i | −0.0352391 | − | 0.0610359i | ||||
\(731\) | 7.45039 | − | 12.9045i | 0.275563 | − | 0.477288i | ||||
\(732\) | −4.00000 | + | 6.92820i | −0.147844 | + | 0.256074i | ||||
\(733\) | 19.5656 | + | 33.8885i | 0.722670 | + | 1.25170i | 0.959926 | + | 0.280254i | \(0.0904188\pi\) |
−0.237255 | + | 0.971447i | \(0.576248\pi\) | |||||||
\(734\) | −6.91215 | −0.255132 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.2345 | 1.04074 | ||||||||
\(737\) | −17.9233 | − | 31.0441i | −0.660214 | − | 1.14352i | ||||
\(738\) | −3.14830 | + | 5.45302i | −0.115891 | + | 0.200728i | ||||
\(739\) | 3.56766 | − | 6.17936i | 0.131238 | − | 0.227311i | −0.792916 | − | 0.609331i | \(-0.791438\pi\) |
0.924154 | + | 0.382020i | \(0.124771\pi\) | |||||||
\(740\) | −1.11383 | − | 1.92921i | −0.0409451 | − | 0.0709191i | ||||
\(741\) | −3.30777 | −0.121514 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.8827 | 0.509308 | 0.254654 | − | 0.967032i | \(-0.418038\pi\) | ||||
0.254654 | + | 0.967032i | \(0.418038\pi\) | |||||||
\(744\) | −14.0552 | − | 24.3443i | −0.515288 | − | 0.892506i | ||||
\(745\) | −2.46338 | + | 4.26670i | −0.0902512 | + | 0.156320i | ||||
\(746\) | 5.56990 | − | 9.64736i | 0.203929 | − | 0.353215i | ||||
\(747\) | 16.8293 | + | 29.1492i | 0.615752 | + | 1.06651i | ||||
\(748\) | −5.23109 | −0.191268 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5.44652 | −0.198879 | ||||||||
\(751\) | 18.6625 | + | 32.3244i | 0.681005 | + | 1.17954i | 0.974674 | + | 0.223629i | \(0.0717903\pi\) |
−0.293669 | + | 0.955907i | \(0.594876\pi\) | |||||||
\(752\) | −11.6742 | + | 20.2203i | −0.425714 | + | 0.737358i | ||||
\(753\) | 5.54049 | − | 9.59640i | 0.201907 | − | 0.349712i | ||||
\(754\) | −1.22885 | − | 2.12843i | −0.0447520 | − | 0.0775127i | ||||
\(755\) | 3.74398 | 0.136258 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.10428 | −0.258209 | −0.129105 | − | 0.991631i | \(-0.541210\pi\) | ||||
−0.129105 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(758\) | 7.70522 | + | 13.3458i | 0.279866 | + | 0.484742i | ||||
\(759\) | 14.7638 | − | 25.5717i | 0.535894 | − | 0.928195i | ||||
\(760\) | −0.692226 | + | 1.19897i | −0.0251097 | + | 0.0434913i | ||||
\(761\) | 12.9810 | + | 22.4838i | 0.470562 | + | 0.815038i | 0.999433 | − | 0.0336643i | \(-0.0107177\pi\) |
−0.528871 | + | 0.848702i | \(0.677384\pi\) | |||||||
\(762\) | 0.872420 | 0.0316044 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.2311 | 0.478684 | ||||||||
\(765\) | 0.712520 | + | 1.23412i | 0.0257612 | + | 0.0446197i | ||||
\(766\) | 5.32238 | − | 9.21864i | 0.192305 | − | 0.333083i | ||||
\(767\) | 6.08623 | − | 10.5417i | 0.219761 | − | 0.380637i | ||||
\(768\) | −1.20512 | − | 2.08732i | −0.0434859 | − | 0.0753197i | ||||
\(769\) | −21.4638 | −0.774005 | −0.387002 | − | 0.922079i | \(-0.626489\pi\) | ||||
−0.387002 | + | 0.922079i | \(0.626489\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0260 | −0.649190 | ||||||||
\(772\) | −1.33537 | − | 2.31293i | −0.0480611 | − | 0.0832442i | ||||
\(773\) | 20.2457 | − | 35.0666i | 0.728187 | − | 1.26126i | −0.229461 | − | 0.973318i | \(-0.573696\pi\) |
0.957649 | − | 0.287940i | \(-0.0929702\pi\) | |||||||
\(774\) | −5.52019 | + | 9.56125i | −0.198419 | + | 0.343672i | ||||
\(775\) | −16.5845 | − | 28.7252i | −0.595733 | − | 1.03184i | ||||
\(776\) | 6.17246 | 0.221578 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.9087 | 0.642058 | ||||||||
\(779\) | 4.77846 | + | 8.27653i | 0.171206 | + | 0.296537i | ||||
\(780\) | 1.05863 | − | 1.83361i | 0.0379051 | − | 0.0656536i | ||||
\(781\) | 1.33881 | − | 2.31889i | 0.0479064 | − | 0.0829762i | ||||
\(782\) | 1.79650 | + | 3.11163i | 0.0642428 | + | 0.111272i | ||||
\(783\) | −11.0554 | −0.395088 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.19738 | −0.114119 | ||||||||
\(786\) | −5.61899 | − | 9.73237i | −0.200423 | − | 0.347142i | ||||
\(787\) | 2.51036 | − | 4.34807i | 0.0894847 | − | 0.154992i | −0.817809 | − | 0.575490i | \(-0.804811\pi\) |
0.907293 | + | 0.420498i | \(0.138145\pi\) | |||||||
\(788\) | 21.3354 | − | 36.9539i | 0.760041 | − | 1.31643i | ||||
\(789\) | −1.80219 | − | 3.12148i | −0.0641596 | − | 0.111128i | ||||
\(790\) | −0.333552 | −0.0118672 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.23453 | 0.292601 | ||||||||
\(793\) | 1.00000 | + | 1.73205i | 0.0355110 | + | 0.0615069i | ||||
\(794\) | 2.75473 | − | 4.77132i | 0.0977616 | − | 0.169328i | ||||
\(795\) | −6.71252 | + | 11.6264i | −0.238069 | + | 0.412347i | ||||
\(796\) | −1.79145 | − | 3.10288i | −0.0634962 | − | 0.109979i | ||||
\(797\) | 19.7002 | 0.697815 | 0.348908 | − | 0.937157i | \(-0.386553\pi\) | ||||
0.348908 | + | 0.937157i | \(0.386553\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.2266 | −0.397169 | ||||||||
\(800\) | 11.4151 | + | 19.7715i | 0.403585 | + | 0.699030i | ||||
\(801\) | −7.11292 | + | 12.3199i | −0.251323 | + | 0.435304i | ||||
\(802\) | −0.837090 | + | 1.44988i | −0.0295587 | + | 0.0511971i | ||||
\(803\) | 8.59525 | + | 14.8874i | 0.303320 | + | 0.525366i | ||||
\(804\) | 63.7517 | 2.24835 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.30777 | −0.116511 | ||||||||
\(807\) | 13.2932 | + | 23.0244i | 0.467942 | + | 0.810499i | ||||
\(808\) | 6.89229 | − | 11.9378i | 0.242470 | − | 0.419970i | ||||
\(809\) | 1.28839 | − | 2.23156i | 0.0452974 | − | 0.0784574i | −0.842488 | − | 0.538715i | \(-0.818910\pi\) |
0.887785 | + | 0.460258i | \(0.152243\pi\) | |||||||
\(810\) | 1.36254 | + | 2.35999i | 0.0478748 | + | 0.0829216i | ||||
\(811\) | 41.2311 | 1.44782 | 0.723910 | − | 0.689895i | \(-0.242343\pi\) | ||||
0.723910 | + | 0.689895i | \(0.242343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 49.2173 | 1.72613 | ||||||||
\(814\) | −1.25258 | − | 2.16953i | −0.0439028 | − | 0.0760420i | ||||
\(815\) | −1.68879 | + | 2.92507i | −0.0591557 | + | 0.102461i | ||||
\(816\) | 4.00000 | − | 6.92820i | 0.140028 | − | 0.242536i | ||||
\(817\) | 8.37849 | + | 14.5120i | 0.293126 | + | 0.507709i | ||||
\(818\) | 2.47680 | 0.0865992 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.11727 | −0.213624 | ||||||||
\(821\) | −2.63359 | − | 4.56152i | −0.0919130 | − | 0.159198i | 0.816403 | − | 0.577483i | \(-0.195965\pi\) |
−0.908316 | + | 0.418284i | \(0.862632\pi\) | |||||||
\(822\) | −6.01461 | + | 10.4176i | −0.209784 | + | 0.363356i | ||||
\(823\) | −18.0096 | + | 31.1935i | −0.627774 | + | 1.08734i | 0.360224 | + | 0.932866i | \(0.382700\pi\) |
−0.987998 | + | 0.154470i | \(0.950633\pi\) | |||||||
\(824\) | −15.1138 | − | 26.1779i | −0.526515 | − | 0.911951i | ||||
\(825\) | 23.8759 | 0.831251 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.3157 | −0.567353 | −0.283676 | − | 0.958920i | \(-0.591554\pi\) | ||||
−0.283676 | + | 0.958920i | \(0.591554\pi\) | |||||||
\(828\) | 10.6854 | + | 18.5076i | 0.371342 | + | 0.643183i | ||||
\(829\) | 15.1978 | − | 26.3234i | 0.527842 | − | 0.914249i | −0.471631 | − | 0.881796i | \(-0.656335\pi\) |
0.999473 | − | 0.0324531i | \(-0.0103319\pi\) | |||||||
\(830\) | 2.03672 | − | 3.52770i | 0.0706956 | − | 0.122448i | ||||
\(831\) | 11.4910 | + | 19.9030i | 0.398618 | + | 0.690426i | ||||
\(832\) | −3.16291 | −0.109654 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.7397 | −0.510394 | ||||||||
\(835\) | 4.38923 | + | 7.60237i | 0.151896 | + | 0.263091i | ||||
\(836\) | 2.94137 | − | 5.09460i | 0.101729 | − | 0.176200i | ||||
\(837\) | −7.43965 | + | 12.8858i | −0.257152 | + | 0.445400i | ||||
\(838\) | −6.12682 | − | 10.6120i | −0.211647 | − | 0.366584i | ||||
\(839\) | 29.8398 | 1.03018 | 0.515092 | − | 0.857135i | \(-0.327758\pi\) | ||||
0.515092 | + | 0.857135i | \(0.327758\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.73549 | −0.0598445 | ||||||||
\(842\) | −5.23453 | − | 9.06648i | −0.180394 | − | 0.312451i | ||||
\(843\) | −1.73443 | + | 3.00412i | −0.0597370 | + | 0.103468i | ||||
\(844\) | 8.98195 | − | 15.5572i | 0.309172 | − | 0.535501i | ||||
\(845\) | −0.264658 | − | 0.458402i | −0.00910452 | − | 0.0157695i | ||||
\(846\) | 8.31809 | 0.285982 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 30.6707 | 1.05324 | ||||||||
\(849\) | −17.8207 | − | 30.8663i | −0.611604 | − | 1.05933i | ||||
\(850\) | −1.45264 | + | 2.51604i | −0.0498251 | + | 0.0862995i | ||||
\(851\) | 6.90647 | − | 11.9623i | 0.236751 | − | 0.410064i | ||||
\(852\) | 2.38101 | + | 4.12404i | 0.0815722 | + | 0.141287i | ||||
\(853\) | −0.203497 | −0.00696761 | −0.00348380 | − | 0.999994i | \(-0.501109\pi\) | ||||
−0.00348380 | + | 0.999994i | \(0.501109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.60256 | −0.0548063 | ||||||||
\(856\) | −4.94137 | − | 8.55870i | −0.168892 | − | 0.292530i | ||||
\(857\) | 6.30777 | − | 10.9254i | 0.215469 | − | 0.373204i | −0.737948 | − | 0.674857i | \(-0.764205\pi\) |
0.953418 | + | 0.301653i | \(0.0975385\pi\) | |||||||
\(858\) | 1.19051 | − | 2.06202i | 0.0406433 | − | 0.0703962i | ||||
\(859\) | 13.9836 | + | 24.2203i | 0.477113 | + | 0.826385i | 0.999656 | − | 0.0262286i | \(-0.00834979\pi\) |
−0.522543 | + | 0.852613i | \(0.675016\pi\) | |||||||
\(860\) | −10.7259 | −0.365751 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.0258 | 0.443660 | ||||||||
\(863\) | 1.38445 | + | 2.39794i | 0.0471273 | + | 0.0816269i | 0.888627 | − | 0.458631i | \(-0.151660\pi\) |
−0.841499 | + | 0.540258i | \(0.818327\pi\) | |||||||
\(864\) | 5.12070 | − | 8.86932i | 0.174210 | − | 0.301740i | ||||
\(865\) | 6.16678 | − | 10.6812i | 0.209677 | − | 0.363171i | ||||
\(866\) | 3.00955 | + | 5.21270i | 0.102269 | + | 0.177135i | ||||
\(867\) | −34.3887 | −1.16790 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.01117 | 0.102147 | ||||||||
\(870\) | −1.46295 | − | 2.53391i | −0.0495987 | − | 0.0859075i | ||||
\(871\) | 7.96896 | − | 13.8027i | 0.270018 | − | 0.467685i | ||||
\(872\) | 7.04564 | − | 12.2034i | 0.238596 | − | 0.413260i | ||||
\(873\) | 3.57243 | + | 6.18763i | 0.120909 | + | 0.209420i | ||||
\(874\) | −4.04059 | −0.136675 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −30.5726 | −1.03295 | ||||||||
\(877\) | −3.35567 | − | 5.81218i | −0.113313 | − | 0.196263i | 0.803791 | − | 0.594911i | \(-0.202813\pi\) |
−0.917104 | + | 0.398648i | \(0.869480\pi\) | |||||||
\(878\) | 4.27512 | − | 7.40473i | 0.144278 | − | 0.249897i | ||||
\(879\) | −12.4634 | + | 21.5872i | −0.420379 | + | 0.728118i | ||||
\(880\) | 1.61899 | + | 2.80416i | 0.0545760 | + | 0.0945284i | ||||
\(881\) | −18.3741 | −0.619040 | −0.309520 | − | 0.950893i | \(-0.600168\pi\) | ||||
−0.309520 | + | 0.950893i | \(0.600168\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.93105 | 0.334207 | 0.167103 | − | 0.985939i | \(-0.446559\pi\) | ||||
0.167103 | + | 0.985939i | \(0.446559\pi\) | |||||||
\(884\) | −1.16291 | − | 2.01422i | −0.0391129 | − | 0.0677455i | ||||
\(885\) | 7.24570 | − | 12.5499i | 0.243562 | − | 0.421861i | ||||
\(886\) | −0.0253497 | + | 0.0439070i | −0.000851640 | + | 0.00147508i | ||||
\(887\) | 25.6888 | + | 44.4943i | 0.862545 | + | 1.49397i | 0.869464 | + | 0.493996i | \(0.164464\pi\) |
−0.00691915 | + | 0.999976i | \(0.502202\pi\) | |||||||
\(888\) | 9.46563 | 0.317646 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.72164 | 0.0577096 | ||||||||
\(891\) | −12.3005 | − | 21.3050i | −0.412081 | − | 0.713746i | ||||
\(892\) | 9.01805 | − | 15.6197i | 0.301947 | − | 0.522987i | ||||
\(893\) | 6.31255 | − | 10.9337i | 0.211241 | − | 0.365881i | ||||
\(894\) | −4.92676 | − | 8.53340i | −0.164775 | − | 0.285399i | ||||
\(895\) | 11.1380 | 0.372302 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.1284 | 0.438346 | ||||||||
\(898\) | 5.21811 | + | 9.03802i | 0.174130 | + | 0.301603i | ||||
\(899\) | 18.3475 | − | 31.7787i | 0.611922 | − | 1.05988i | ||||
\(900\) | −8.64009 | + | 14.9651i | −0.288003 | + | 0.498836i | ||||
\(901\) | 7.37371 | + | 12.7716i | 0.245654 | + | 0.425485i | ||||
\(902\) | −6.87930 | −0.229055 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.5930 | 0.585135 | ||||||||
\(905\) | −4.43234 | − | 7.67704i | −0.147336 | − | 0.255194i | ||||
\(906\) | −3.74398 | + | 6.48477i | −0.124386 | + | 0.215442i | ||||
\(907\) | −2.17112 | + | 3.76050i | −0.0720910 | + | 0.124865i | −0.899818 | − | 0.436266i | \(-0.856301\pi\) |
0.827727 | + | 0.561132i | \(0.189634\pi\) | |||||||
\(908\) | −4.78801 | − | 8.29307i | −0.158896 | − | 0.275215i | ||||
\(909\) | 15.9562 | 0.529233 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.4853 | 1.04315 | 0.521577 | − | 0.853204i | \(-0.325344\pi\) | ||||
0.521577 | + | 0.853204i | \(0.325344\pi\) | |||||||
\(912\) | 4.49828 | + | 7.79125i | 0.148953 | + | 0.257994i | ||||
\(913\) | −18.3867 | + | 31.8467i | −0.608511 | + | 1.05397i | ||||
\(914\) | −1.02598 | + | 1.77705i | −0.0339364 | + | 0.0587795i | ||||
\(915\) | 1.19051 | + | 2.06202i | 0.0393570 | + | 0.0681683i | ||||
\(916\) | −5.90871 | −0.195229 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.30328 | 0.0430146 | ||||||||
\(919\) | −21.7294 | − | 37.6364i | −0.716786 | − | 1.24151i | −0.962267 | − | 0.272108i | \(-0.912279\pi\) |
0.245481 | − | 0.969401i | \(-0.421054\pi\) | |||||||
\(920\) | 2.74742 | − | 4.75867i | 0.0905798 | − | 0.156889i | ||||
\(921\) | −22.9548 | + | 39.7589i | −0.756386 | + | 1.31010i | ||||
\(922\) | −7.62060 | − | 13.1993i | −0.250971 | − | 0.434695i | ||||
\(923\) | 1.19051 | 0.0391860 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1690 | 0.367235 | ||||||||
\(926\) | −1.96896 | − | 3.41035i | −0.0647042 | − | 0.112071i | ||||
\(927\) | 17.4948 | − | 30.3020i | 0.574606 | − | 0.995247i | ||||
\(928\) | −12.6285 | + | 21.8733i | −0.414552 | + | 0.718025i | ||||
\(929\) | −2.20259 | − | 3.81499i | −0.0722645 | − | 0.125166i | 0.827629 | − | 0.561276i | \(-0.189689\pi\) |
−0.899893 | + | 0.436110i | \(0.856356\pi\) | |||||||
\(930\) | −3.93793 | −0.129130 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −24.4001 | −0.799252 | ||||||||
\(933\) | 2.16291 | + | 3.74627i | 0.0708105 | + | 0.122647i | ||||
\(934\) | 4.59912 | − | 7.96591i | 0.150488 | − | 0.260653i | ||||
\(935\) | −0.778457 | + | 1.34833i | −0.0254583 | + | 0.0440950i | ||||
\(936\) | 1.83060 | + | 3.17068i | 0.0598349 | + | 0.103637i | ||||
\(937\) | −34.0990 | −1.11397 | −0.556983 | − | 0.830524i | \(-0.688041\pi\) | ||||
−0.556983 | + | 0.830524i | \(0.688041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.3121 | −1.05446 | ||||||||
\(940\) | 4.04059 | + | 6.99850i | 0.131789 | + | 0.228266i | ||||
\(941\) | −22.2336 | + | 38.5098i | −0.724795 | + | 1.25538i | 0.234263 | + | 0.972173i | \(0.424732\pi\) |
−0.959058 | + | 0.283209i | \(0.908601\pi\) | |||||||
\(942\) | 3.19738 | − | 5.53803i | 0.104176 | − | 0.180439i | ||||
\(943\) | −18.9655 | − | 32.8493i | −0.617603 | − | 1.06972i | ||||
\(944\) | −33.1070 | −1.07754 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0621 | −0.392172 | ||||||||
\(947\) | −28.9655 | − | 50.1698i | −0.941253 | − | 1.63030i | −0.763085 | − | 0.646298i | \(-0.776316\pi\) |
−0.178168 | − | 0.984000i | \(-0.557017\pi\) | |||||||
\(948\) | −2.67762 | + | 4.63777i | −0.0869650 | + | 0.150628i | ||||
\(949\) | −3.82157 | + | 6.61916i | −0.124053 | + | 0.214867i | ||||
\(950\) | −1.63359 | − | 2.82947i | −0.0530008 | − | 0.0918000i | ||||
\(951\) | 34.9897 | 1.13462 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.3060 | 1.14367 | 0.571836 | − | 0.820368i | \(-0.306231\pi\) | ||||
0.571836 | + | 0.820368i | \(0.306231\pi\) | |||||||
\(954\) | −5.46338 | − | 9.46285i | −0.176883 | − | 0.306371i | ||||
\(955\) | 1.96896 | − | 3.41035i | 0.0637142 | − | 0.110356i | ||||
\(956\) | −3.11383 | + | 5.39331i | −0.100708 | + | 0.174432i | ||||
\(957\) | 13.2069 | + | 22.8751i | 0.426920 | + | 0.739446i | ||||
\(958\) | −13.4250 | −0.433743 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.76547 | −0.121530 | ||||||||
\(961\) | −9.19356 | − | 15.9237i | −0.296567 | − | 0.513668i | ||||
\(962\) | 0.556914 | − | 0.964604i | 0.0179556 | − | 0.0311001i | ||||
\(963\) | 5.71982 | − | 9.90703i | 0.184319 | − | 0.319249i | ||||
\(964\) | 1.41205 | + | 2.44574i | 0.0454791 | + | 0.0787721i | ||||
\(965\) | −0.794885 | −0.0255882 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7148 | 0.762616 | 0.381308 | − | 0.924448i | \(-0.375474\pi\) | ||||
0.381308 | + | 0.924448i | \(0.375474\pi\) | |||||||
\(968\) | −5.28323 | − | 9.15083i | −0.169810 | − | 0.294119i | ||||
\(969\) | −2.16291 | + | 3.74627i | −0.0694827 | + | 0.120348i | ||||
\(970\) | 0.432344 | − | 0.748842i | 0.0138817 | − | 0.0240439i | ||||
\(971\) | 11.9690 | + | 20.7309i | 0.384102 | + | 0.665285i | 0.991644 | − | 0.129003i | \(-0.0411776\pi\) |
−0.607542 | + | 0.794288i | \(0.707844\pi\) | |||||||
\(972\) | 32.4553 | 1.04100 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.6843 | 0.374389 | ||||||||
\(975\) | 5.30777 | + | 9.19333i | 0.169985 | + | 0.294422i | ||||
\(976\) | 2.71982 | − | 4.71087i | 0.0870594 | − | 0.150791i | ||||
\(977\) | 8.09353 | − | 14.0184i | 0.258935 | − | 0.448489i | −0.707022 | − | 0.707192i | \(-0.749962\pi\) |
0.965957 | + | 0.258703i | \(0.0832951\pi\) | |||||||
\(978\) | −3.37758 | − | 5.85013i | −0.108003 | − | 0.187067i | ||||
\(979\) | −15.5423 | −0.496734 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.3112 | 0.520777 | ||||||||
\(982\) | −6.86469 | − | 11.8900i | −0.219061 | − | 0.379425i | ||||
\(983\) | −22.8622 | + | 39.5984i | −0.729190 | + | 1.26299i | 0.228036 | + | 0.973653i | \(0.426769\pi\) |
−0.957226 | + | 0.289341i | \(0.906564\pi\) | |||||||
\(984\) | 12.9966 | − | 22.5107i | 0.414315 | − | 0.717615i | ||||
\(985\) | −6.34998 | − | 10.9985i | −0.202327 | − | 0.350441i | ||||
\(986\) | −3.21411 | −0.102358 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.61555 | 0.0832116 | ||||||||
\(989\) | −33.2539 | − | 57.5975i | −1.05741 | − | 1.83149i | ||||
\(990\) | 0.576780 | − | 0.999012i | 0.0183313 | − | 0.0317507i | ||||
\(991\) | 2.70178 | − | 4.67962i | 0.0858248 | − | 0.148653i | −0.819918 | − | 0.572482i | \(-0.805981\pi\) |
0.905742 | + | 0.423829i | \(0.139314\pi\) | |||||||
\(992\) | 16.9966 | + | 29.4389i | 0.539641 | + | 0.934686i | ||||
\(993\) | 70.9605 | 2.25186 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.06637 | −0.0338061 | ||||||||
\(996\) | −32.7000 | − | 56.6380i | −1.03614 | − | 1.79464i | ||||
\(997\) | −3.02416 | + | 5.23800i | −0.0957761 | + | 0.165889i | −0.909932 | − | 0.414757i | \(-0.863867\pi\) |
0.814156 | + | 0.580646i | \(0.197200\pi\) | |||||||
\(998\) | 7.83709 | − | 13.5742i | 0.248079 | − | 0.429685i | ||||
\(999\) | −2.50516 | − | 4.33906i | −0.0792597 | − | 0.137282i |
(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 | 637.2.e.j.508.2 | 6 | ||
7.2 | even | 3 | inner | 637.2.e.j.79.2 | 6 | ||
7.3 | odd | 6 | 637.2.a.j.1.2 | 3 | |||
7.4 | even | 3 | 91.2.a.d.1.2 | ✓ | 3 | ||
7.5 | odd | 6 | 637.2.e.i.79.2 | 6 | |||
7.6 | odd | 2 | 637.2.e.i.508.2 | 6 | |||
21.11 | odd | 6 | 819.2.a.i.1.2 | 3 | |||
21.17 | even | 6 | 5733.2.a.x.1.2 | 3 | |||
28.11 | odd | 6 | 1456.2.a.t.1.1 | 3 | |||
35.4 | even | 6 | 2275.2.a.m.1.2 | 3 | |||
56.11 | odd | 6 | 5824.2.a.bs.1.3 | 3 | |||
56.53 | even | 6 | 5824.2.a.by.1.1 | 3 | |||
91.18 | odd | 12 | 1183.2.c.f.337.3 | 6 | |||
91.25 | even | 6 | 1183.2.a.i.1.2 | 3 | |||
91.38 | odd | 6 | 8281.2.a.bg.1.2 | 3 | |||
91.60 | odd | 12 | 1183.2.c.f.337.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.d.1.2 | ✓ | 3 | 7.4 | even | 3 | ||
637.2.a.j.1.2 | 3 | 7.3 | odd | 6 | |||
637.2.e.i.79.2 | 6 | 7.5 | odd | 6 | |||
637.2.e.i.508.2 | 6 | 7.6 | odd | 2 | |||
637.2.e.j.79.2 | 6 | 7.2 | even | 3 | inner | ||
637.2.e.j.508.2 | 6 | 1.1 | even | 1 | trivial | ||
819.2.a.i.1.2 | 3 | 21.11 | odd | 6 | |||
1183.2.a.i.1.2 | 3 | 91.25 | even | 6 | |||
1183.2.c.f.337.3 | 6 | 91.18 | odd | 12 | |||
1183.2.c.f.337.4 | 6 | 91.60 | odd | 12 | |||
1456.2.a.t.1.1 | 3 | 28.11 | odd | 6 | |||
2275.2.a.m.1.2 | 3 | 35.4 | even | 6 | |||
5733.2.a.x.1.2 | 3 | 21.17 | even | 6 | |||
5824.2.a.bs.1.3 | 3 | 56.11 | odd | 6 | |||
5824.2.a.by.1.1 | 3 | 56.53 | even | 6 | |||
8281.2.a.bg.1.2 | 3 | 91.38 | odd | 6 |