Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 373.5 | ||
Character | \(\chi\) | \(=\) | 784.373 |
Dual form | 784.2.x.o.557.5 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.805226 | − | 1.16259i | −0.569381 | − | 0.822074i | ||||
\(3\) | −1.16533 | − | 0.312249i | −0.672803 | − | 0.180277i | −0.0937859 | − | 0.995592i | \(-0.529897\pi\) |
−0.579017 | + | 0.815315i | \(0.696564\pi\) | |||||||
\(4\) | −0.703221 | + | 1.87229i | −0.351611 | + | 0.936146i | ||||
\(5\) | −0.980942 | + | 0.262843i | −0.438691 | + | 0.117547i | −0.471403 | − | 0.881918i | \(-0.656252\pi\) |
0.0327122 | + | 0.999465i | \(0.489586\pi\) | |||||||
\(6\) | 0.575337 | + | 1.60623i | 0.234880 | + | 0.655740i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.74296 | − | 0.690063i | 0.969782 | − | 0.243974i | ||||
\(9\) | −1.33758 | − | 0.772254i | −0.445861 | − | 0.257418i | ||||
\(10\) | 1.09546 | + | 0.928784i | 0.346414 | + | 0.293707i | ||||
\(11\) | 0.635020 | − | 2.36993i | 0.191466 | − | 0.714560i | −0.801688 | − | 0.597743i | \(-0.796064\pi\) |
0.993153 | − | 0.116817i | \(-0.0372690\pi\) | |||||||
\(12\) | 1.40411 | − | 1.96226i | 0.405330 | − | 0.566455i | ||||
\(13\) | 2.65786 | − | 2.65786i | 0.737157 | − | 0.737157i | −0.234870 | − | 0.972027i | \(-0.575466\pi\) |
0.972027 | + | 0.234870i | \(0.0754663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.22519 | 0.316343 | ||||||||
\(16\) | −3.01096 | − | 2.63327i | −0.752740 | − | 0.658318i | ||||
\(17\) | 0.509128 | + | 0.881836i | 0.123482 | + | 0.213877i | 0.921138 | − | 0.389235i | \(-0.127261\pi\) |
−0.797657 | + | 0.603112i | \(0.793927\pi\) | |||||||
\(18\) | 0.179244 | + | 2.17690i | 0.0422482 | + | 0.513100i | ||||
\(19\) | 0.0250951 | + | 0.0936561i | 0.00575721 | + | 0.0214862i | 0.968745 | − | 0.248060i | \(-0.0797930\pi\) |
−0.962987 | + | 0.269546i | \(0.913126\pi\) | |||||||
\(20\) | 0.197701 | − | 2.02145i | 0.0442073 | − | 0.452009i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.26658 | + | 1.17006i | −0.696438 | + | 0.249458i | ||||
\(23\) | 1.67238 | + | 0.965551i | 0.348716 | + | 0.201331i | 0.664120 | − | 0.747626i | \(-0.268807\pi\) |
−0.315404 | + | 0.948958i | \(0.602140\pi\) | |||||||
\(24\) | −3.41192 | − | 0.0523353i | −0.696455 | − | 0.0106829i | ||||
\(25\) | −3.43697 | + | 1.98433i | −0.687393 | + | 0.396867i | ||||
\(26\) | −5.23017 | − | 0.949817i | −1.02572 | − | 0.186274i | ||||
\(27\) | 3.87683 | + | 3.87683i | 0.746096 | + | 0.746096i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.05325 | + | 5.05325i | −0.938365 | + | 0.938365i | −0.998208 | − | 0.0598432i | \(-0.980940\pi\) |
0.0598432 | + | 0.998208i | \(0.480940\pi\) | |||||||
\(30\) | −0.986557 | − | 1.42439i | −0.180120 | − | 0.260058i | ||||
\(31\) | −4.28249 | − | 7.41749i | −0.769158 | − | 1.33222i | −0.938020 | − | 0.346581i | \(-0.887343\pi\) |
0.168862 | − | 0.985640i | \(-0.445991\pi\) | |||||||
\(32\) | −0.636906 | + | 5.62089i | −0.112590 | + | 0.993642i | ||||
\(33\) | −1.48001 | + | 2.56346i | −0.257637 | + | 0.446241i | ||||
\(34\) | 0.615248 | − | 1.30198i | 0.105514 | − | 0.223288i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.38650 | − | 1.96128i | 0.397751 | − | 0.326880i | ||||
\(37\) | −7.71428 | + | 2.06704i | −1.26822 | + | 0.339818i | −0.829349 | − | 0.558732i | \(-0.811288\pi\) |
−0.438871 | + | 0.898550i | \(0.644622\pi\) | |||||||
\(38\) | 0.0886762 | − | 0.104590i | 0.0143852 | − | 0.0169667i | ||||
\(39\) | −3.92719 | + | 2.26737i | −0.628854 | + | 0.363069i | ||||
\(40\) | −2.50930 | + | 1.39788i | −0.396756 | + | 0.221024i | ||||
\(41\) | 8.51782i | 1.33026i | 0.746728 | + | 0.665130i | \(0.231624\pi\) | ||||
−0.746728 | + | 0.665130i | \(0.768376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.47950 | − | 4.47950i | −0.683117 | − | 0.683117i | 0.277584 | − | 0.960701i | \(-0.410466\pi\) |
−0.960701 | + | 0.277584i | \(0.910466\pi\) | |||||||
\(44\) | 3.99064 | + | 2.85553i | 0.601611 | + | 0.430487i | ||||
\(45\) | 1.51507 | + | 0.405963i | 0.225854 | + | 0.0605174i | ||||
\(46\) | −0.224109 | − | 2.72178i | −0.0330431 | − | 0.401304i | ||||
\(47\) | −6.02995 | + | 10.4442i | −0.879559 | + | 1.52344i | −0.0277324 | + | 0.999615i | \(0.508829\pi\) |
−0.851826 | + | 0.523825i | \(0.824505\pi\) | |||||||
\(48\) | 2.68652 | + | 4.00880i | 0.387766 | + | 0.578620i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5.07450 | + | 2.39794i | 0.717642 | + | 0.339120i | ||||
\(51\) | −0.317949 | − | 1.18660i | −0.0445218 | − | 0.166158i | ||||
\(52\) | 3.10723 | + | 6.84535i | 0.430895 | + | 0.949279i | ||||
\(53\) | 0.381000 | − | 1.42191i | 0.0523344 | − | 0.195315i | −0.934809 | − | 0.355150i | \(-0.884430\pi\) |
0.987144 | + | 0.159836i | \(0.0510964\pi\) | |||||||
\(54\) | 1.38543 | − | 7.62888i | 0.188533 | − | 1.03816i | ||||
\(55\) | 2.49167i | 0.335977i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.116976i | − | 0.0154939i | ||||||
\(58\) | 9.94385 | + | 1.80584i | 1.30569 | + | 0.237118i | ||||
\(59\) | 1.86535 | − | 6.96158i | 0.242848 | − | 0.906320i | −0.731605 | − | 0.681729i | \(-0.761229\pi\) |
0.974453 | − | 0.224592i | \(-0.0721048\pi\) | |||||||
\(60\) | −0.861581 | + | 2.29392i | −0.111230 | + | 0.296144i | ||||
\(61\) | 1.18609 | + | 4.42654i | 0.151863 | + | 0.566760i | 0.999354 | + | 0.0359500i | \(0.0114457\pi\) |
−0.847491 | + | 0.530810i | \(0.821888\pi\) | |||||||
\(62\) | −5.17511 | + | 10.9515i | −0.657240 | + | 1.39085i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.04763 | − | 3.78563i | 0.880953 | − | 0.473203i | ||||
\(65\) | −1.90861 | + | 3.30580i | −0.236734 | + | 0.410034i | ||||
\(66\) | 4.17199 | − | 0.343519i | 0.513537 | − | 0.0422842i | ||||
\(67\) | −3.38700 | − | 0.907543i | −0.413787 | − | 0.110874i | 0.0459185 | − | 0.998945i | \(-0.485379\pi\) |
−0.459706 | + | 0.888071i | \(0.652045\pi\) | |||||||
\(68\) | −2.00908 | + | 0.333111i | −0.243637 | + | 0.0403957i | ||||
\(69\) | −1.64738 | − | 1.64738i | −0.198322 | − | 0.198322i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.43131i | 0.644578i | 0.946641 | + | 0.322289i | \(0.104452\pi\) | ||||
−0.946641 | + | 0.322289i | \(0.895548\pi\) | |||||||
\(72\) | −4.20184 | − | 1.19524i | −0.495191 | − | 0.140861i | ||||
\(73\) | −7.34303 | + | 4.23950i | −0.859436 | + | 0.496196i | −0.863824 | − | 0.503795i | \(-0.831937\pi\) |
0.00438712 | + | 0.999990i | \(0.498604\pi\) | |||||||
\(74\) | 8.61485 | + | 7.30410i | 1.00146 | + | 0.849084i | ||||
\(75\) | 4.62480 | − | 1.23921i | 0.534026 | − | 0.143092i | ||||
\(76\) | −0.192999 | − | 0.0188756i | −0.0221385 | − | 0.00216518i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.79829 | + | 2.73996i | 0.656527 | + | 0.310240i | ||||
\(79\) | −0.433595 | + | 0.751008i | −0.0487832 | + | 0.0844950i | −0.889386 | − | 0.457157i | \(-0.848868\pi\) |
0.840603 | + | 0.541652i | \(0.182201\pi\) | |||||||
\(80\) | 3.64571 | + | 1.79168i | 0.407603 | + | 0.200316i | ||||
\(81\) | −0.990483 | − | 1.71557i | −0.110054 | − | 0.190619i | ||||
\(82\) | 9.90271 | − | 6.85877i | 1.09357 | − | 0.757425i | ||||
\(83\) | 5.44318 | − | 5.44318i | 0.597466 | − | 0.597466i | −0.342171 | − | 0.939638i | \(-0.611162\pi\) |
0.939638 | + | 0.342171i | \(0.111162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.731209 | − | 0.731209i | −0.0793108 | − | 0.0793108i | ||||
\(86\) | −1.60080 | + | 8.81482i | −0.172619 | + | 0.950526i | ||||
\(87\) | 7.46657 | − | 4.31083i | 0.800500 | − | 0.462169i | ||||
\(88\) | 0.106434 | − | 6.93881i | 0.0113459 | − | 0.739680i | ||||
\(89\) | −3.93155 | − | 2.26988i | −0.416744 | − | 0.240607i | 0.276939 | − | 0.960887i | \(-0.410680\pi\) |
−0.693683 | + | 0.720280i | \(0.744013\pi\) | |||||||
\(90\) | −0.748010 | − | 2.08830i | −0.0788471 | − | 0.220126i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.98385 | + | 2.45219i | −0.311088 | + | 0.255659i | ||||
\(93\) | 2.67441 | + | 9.98102i | 0.277323 | + | 1.03498i | ||||
\(94\) | 16.9977 | − | 1.39958i | 1.75318 | − | 0.144356i | ||||
\(95\) | −0.0492336 | − | 0.0852752i | −0.00505126 | − | 0.00874905i | ||||
\(96\) | 2.49732 | − | 6.35131i | 0.254882 | − | 0.648228i | ||||
\(97\) | −16.4025 | −1.66542 | −0.832712 | − | 0.553706i | \(-0.813213\pi\) | ||||
−0.832712 | + | 0.553706i | \(0.813213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.67958 | + | 2.67958i | −0.269308 | + | 0.269308i | ||||
\(100\) | −1.29831 | − | 7.83043i | −0.129831 | − | 0.783043i | ||||
\(101\) | −2.38049 | + | 8.88412i | −0.236868 | + | 0.884003i | 0.740430 | + | 0.672134i | \(0.234622\pi\) |
−0.977298 | + | 0.211870i | \(0.932045\pi\) | |||||||
\(102\) | −1.12351 | + | 1.32513i | −0.111244 | + | 0.131207i | ||||
\(103\) | −6.69469 | − | 3.86518i | −0.659647 | − | 0.380848i | 0.132495 | − | 0.991184i | \(-0.457701\pi\) |
−0.792143 | + | 0.610336i | \(0.791034\pi\) | |||||||
\(104\) | 5.45630 | − | 9.12448i | 0.535034 | − | 0.894729i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.95989 | + | 0.702015i | −0.190361 | + | 0.0681857i | ||||
\(107\) | 18.2555 | − | 4.89154i | 1.76482 | − | 0.472883i | 0.777137 | − | 0.629332i | \(-0.216671\pi\) |
0.987686 | + | 0.156449i | \(0.0500046\pi\) | |||||||
\(108\) | −9.98483 | + | 4.53229i | −0.960791 | + | 0.436120i | ||||
\(109\) | 15.8026 | + | 4.23429i | 1.51361 | + | 0.405571i | 0.917633 | − | 0.397428i | \(-0.130097\pi\) |
0.595980 | + | 0.802999i | \(0.296764\pi\) | |||||||
\(110\) | 2.89679 | − | 2.00636i | 0.276198 | − | 0.191299i | ||||
\(111\) | 9.63510 | 0.914524 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.1152 | −1.89228 | −0.946138 | − | 0.323765i | \(-0.895051\pi\) | ||||
−0.946138 | + | 0.323765i | \(0.895051\pi\) | |||||||
\(114\) | −0.135995 | + | 0.0941922i | −0.0127371 | + | 0.00882191i | ||||
\(115\) | −1.89430 | − | 0.507576i | −0.176644 | − | 0.0473317i | ||||
\(116\) | −5.90761 | − | 13.0147i | −0.548508 | − | 1.20839i | ||||
\(117\) | −5.60765 | + | 1.50257i | −0.518428 | + | 0.138912i | ||||
\(118\) | −9.59547 | + | 3.43701i | −0.883335 | + | 0.316403i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.36065 | − | 0.845460i | 0.306784 | − | 0.0771796i | ||||
\(121\) | 4.31298 | + | 2.49010i | 0.392089 | + | 0.226373i | ||||
\(122\) | 4.19117 | − | 4.94330i | 0.379451 | − | 0.447545i | ||||
\(123\) | 2.65968 | − | 9.92606i | 0.239815 | − | 0.895003i | ||||
\(124\) | 16.8992 | − | 2.80194i | 1.51760 | − | 0.251621i | ||||
\(125\) | 6.44039 | − | 6.44039i | 0.576046 | − | 0.576046i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.988901 | −0.0877508 | −0.0438754 | − | 0.999037i | \(-0.513970\pi\) | ||||
−0.0438754 | + | 0.999037i | \(0.513970\pi\) | |||||||
\(128\) | −10.0761 | − | 5.14520i | −0.890606 | − | 0.454776i | ||||
\(129\) | 3.82137 | + | 6.61880i | 0.336453 | + | 0.582753i | ||||
\(130\) | 5.38015 | − | 0.442997i | 0.471870 | − | 0.0388534i | ||||
\(131\) | 2.03878 | + | 7.60883i | 0.178129 | + | 0.664786i | 0.995998 | + | 0.0893811i | \(0.0284889\pi\) |
−0.817869 | + | 0.575405i | \(0.804844\pi\) | |||||||
\(132\) | −3.75877 | − | 4.57370i | −0.327159 | − | 0.398089i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.67220 | + | 4.66846i | 0.144456 | + | 0.403293i | ||||
\(135\) | −4.82194 | − | 2.78395i | −0.415007 | − | 0.239604i | ||||
\(136\) | 2.00504 | + | 2.06751i | 0.171931 | + | 0.177287i | ||||
\(137\) | −9.57893 | + | 5.53040i | −0.818383 | + | 0.472494i | −0.849859 | − | 0.527011i | \(-0.823313\pi\) |
0.0314753 | + | 0.999505i | \(0.489979\pi\) | |||||||
\(138\) | −0.588712 | + | 3.24175i | −0.0501145 | + | 0.275956i | ||||
\(139\) | −12.4154 | − | 12.4154i | −1.05306 | − | 1.05306i | −0.998511 | − | 0.0545473i | \(-0.982628\pi\) |
−0.0545473 | − | 0.998511i | \(-0.517372\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2881 | − | 10.2881i | 0.866411 | − | 0.866411i | ||||
\(142\) | 6.31438 | − | 4.37344i | 0.529891 | − | 0.367011i | ||||
\(143\) | −4.61114 | − | 7.98672i | −0.385603 | − | 0.667883i | ||||
\(144\) | 1.99386 | + | 5.84745i | 0.166155 | + | 0.487287i | ||||
\(145\) | 3.62873 | − | 6.28515i | 0.301350 | − | 0.521954i | ||||
\(146\) | 10.8416 | + | 5.12316i | 0.897256 | + | 0.423996i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.55475 | − | 15.8970i | 0.127800 | − | 1.30672i | ||||
\(149\) | −5.06147 | + | 1.35622i | −0.414652 | + | 0.111106i | −0.460113 | − | 0.887861i | \(-0.652191\pi\) |
0.0454610 | + | 0.998966i | \(0.485524\pi\) | |||||||
\(150\) | −5.16471 | − | 4.37889i | −0.421696 | − | 0.357535i | ||||
\(151\) | 1.18073 | − | 0.681693i | 0.0960862 | − | 0.0554754i | −0.451187 | − | 0.892429i | \(-0.648999\pi\) |
0.547273 | + | 0.836954i | \(0.315666\pi\) | |||||||
\(152\) | 0.133463 | + | 0.239578i | 0.0108253 | + | 0.0194323i | ||||
\(153\) | − | 1.57271i | − | 0.127146i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.15051 | + | 6.15051i | 0.494021 | + | 0.494021i | ||||
\(156\) | −1.48349 | − | 8.94732i | −0.118774 | − | 0.716359i | ||||
\(157\) | −0.306970 | − | 0.0822524i | −0.0244989 | − | 0.00656446i | 0.246549 | − | 0.969130i | \(-0.420703\pi\) |
−0.271048 | + | 0.962566i | \(0.587370\pi\) | |||||||
\(158\) | 1.22226 | − | 0.100640i | 0.0972374 | − | 0.00800645i | ||||
\(159\) | −0.887981 | + | 1.53803i | −0.0704215 | + | 0.121974i | ||||
\(160\) | −0.852640 | − | 5.68117i | −0.0674071 | − | 0.449136i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.19693 | + | 2.53294i | −0.0940400 | + | 0.199007i | ||||
\(163\) | −3.84175 | − | 14.3376i | −0.300909 | − | 1.12301i | −0.936410 | − | 0.350907i | \(-0.885873\pi\) |
0.635501 | − | 0.772100i | \(-0.280794\pi\) | |||||||
\(164\) | −15.9478 | − | 5.98991i | −1.24532 | − | 0.467733i | ||||
\(165\) | 0.778022 | − | 2.90362i | 0.0605689 | − | 0.226046i | ||||
\(166\) | −10.7112 | − | 1.94518i | −0.831347 | − | 0.150975i | ||||
\(167\) | 14.5986i | 1.12967i | 0.825204 | + | 0.564836i | \(0.191060\pi\) | ||||
−0.825204 | + | 0.564836i | \(0.808940\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.12842i | − | 0.0868018i | ||||||
\(170\) | −0.261306 | + | 1.43888i | −0.0200413 | + | 0.110357i | ||||
\(171\) | 0.0387596 | − | 0.144653i | 0.00296402 | − | 0.0110619i | ||||
\(172\) | 11.5370 | − | 5.23685i | 0.879688 | − | 0.399306i | ||||
\(173\) | 3.19660 | + | 11.9299i | 0.243033 | + | 0.907011i | 0.974362 | + | 0.224986i | \(0.0722337\pi\) |
−0.731329 | + | 0.682025i | \(0.761100\pi\) | |||||||
\(174\) | −11.0240 | − | 5.20935i | −0.835727 | − | 0.394920i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.15268 | + | 5.46357i | −0.614531 | + | 0.411832i | ||||
\(177\) | −4.34749 | + | 7.53008i | −0.326777 | + | 0.565995i | ||||
\(178\) | 0.526851 | + | 6.39855i | 0.0394892 | + | 0.479591i | ||||
\(179\) | 0.455619 | + | 0.122083i | 0.0340545 | + | 0.00912489i | 0.275806 | − | 0.961213i | \(-0.411055\pi\) |
−0.241752 | + | 0.970338i | \(0.577722\pi\) | |||||||
\(180\) | −1.82551 | + | 2.55118i | −0.136066 | + | 0.190154i | ||||
\(181\) | −15.4654 | − | 15.4654i | −1.14953 | − | 1.14953i | −0.986645 | − | 0.162887i | \(-0.947919\pi\) |
−0.162887 | − | 0.986645i | \(-0.552081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.52873i | − | 0.408696i | ||||||
\(184\) | 5.25356 | + | 1.49441i | 0.387298 | + | 0.110170i | ||||
\(185\) | 7.02396 | − | 4.05528i | 0.516412 | − | 0.298150i | ||||
\(186\) | 9.45031 | − | 11.1462i | 0.692930 | − | 0.817280i | ||||
\(187\) | 2.41319 | − | 0.646613i | 0.176470 | − | 0.0472850i | ||||
\(188\) | −15.3142 | − | 18.6344i | −1.11690 | − | 1.35905i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0594956 | + | 0.125904i | −0.00431627 | + | 0.00913405i | ||||
\(191\) | −3.04108 | + | 5.26731i | −0.220045 | + | 0.381129i | −0.954821 | − | 0.297180i | \(-0.903954\pi\) |
0.734776 | + | 0.678309i | \(0.237287\pi\) | |||||||
\(192\) | −9.39486 | + | 2.21088i | −0.678016 | + | 0.159557i | ||||
\(193\) | −5.03089 | − | 8.71375i | −0.362131 | − | 0.627229i | 0.626180 | − | 0.779678i | \(-0.284617\pi\) |
−0.988311 | + | 0.152449i | \(0.951284\pi\) | |||||||
\(194\) | 13.2077 | + | 19.0694i | 0.948261 | + | 1.36910i | ||||
\(195\) | 3.25639 | − | 3.25639i | 0.233195 | − | 0.233195i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0837 | − | 10.0837i | −0.718432 | − | 0.718432i | 0.249852 | − | 0.968284i | \(-0.419618\pi\) |
−0.968284 | + | 0.249852i | \(0.919618\pi\) | |||||||
\(198\) | 5.27291 | + | 0.957578i | 0.374730 | + | 0.0680521i | ||||
\(199\) | −10.0980 | + | 5.83005i | −0.715825 | + | 0.413282i | −0.813214 | − | 0.581965i | \(-0.802284\pi\) |
0.0973893 | + | 0.995246i | \(0.468951\pi\) | |||||||
\(200\) | −8.05814 | + | 7.81466i | −0.569796 | + | 0.552580i | ||||
\(201\) | 3.66359 | + | 2.11517i | 0.258409 | + | 0.149193i | ||||
\(202\) | 12.2454 | − | 4.38620i | 0.861584 | − | 0.308612i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.44526 | + | 0.239150i | 0.171202 | + | 0.0167439i | ||||
\(205\) | −2.23885 | − | 8.35549i | −0.156368 | − | 0.583572i | ||||
\(206\) | 0.897128 | + | 10.8955i | 0.0625058 | + | 0.759126i | ||||
\(207\) | −1.49130 | − | 2.58301i | −0.103653 | − | 0.179532i | ||||
\(208\) | −15.0016 | + | 1.00384i | −1.04017 | + | 0.0696038i | ||||
\(209\) | 0.237894 | 0.0164555 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.53423 | − | 6.53423i | 0.449835 | − | 0.449835i | −0.445465 | − | 0.895300i | \(-0.646962\pi\) |
0.895300 | + | 0.445465i | \(0.146962\pi\) | |||||||
\(212\) | 2.39431 | + | 1.71326i | 0.164442 | + | 0.117667i | ||||
\(213\) | 1.69592 | − | 6.32927i | 0.116203 | − | 0.433674i | ||||
\(214\) | −20.3866 | − | 17.2848i | −1.39360 | − | 1.18156i | ||||
\(215\) | 5.57153 | + | 3.21672i | 0.379975 | + | 0.219379i | ||||
\(216\) | 13.3092 | + | 7.95872i | 0.905579 | + | 0.541522i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.80192 | − | 21.7815i | −0.528413 | − | 1.47523i | ||||
\(219\) | 9.88082 | − | 2.64756i | 0.667684 | − | 0.178905i | ||||
\(220\) | −4.66514 | − | 1.75220i | −0.314523 | − | 0.118133i | ||||
\(221\) | 3.69698 | + | 0.990604i | 0.248686 | + | 0.0666352i | ||||
\(222\) | −7.75844 | − | 11.2017i | −0.520712 | − | 0.751806i | ||||
\(223\) | 23.3350 | 1.56263 | 0.781315 | − | 0.624137i | \(-0.214549\pi\) | ||||
0.781315 | + | 0.624137i | \(0.214549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.12964 | 0.408643 | ||||||||
\(226\) | 16.1973 | + | 23.3856i | 1.07743 | + | 1.55559i | ||||
\(227\) | −15.1161 | − | 4.05036i | −1.00329 | − | 0.268832i | −0.280468 | − | 0.959863i | \(-0.590490\pi\) |
−0.722824 | + | 0.691032i | \(0.757156\pi\) | |||||||
\(228\) | 0.219013 | + | 0.0822601i | 0.0145045 | + | 0.00544781i | ||||
\(229\) | 25.8292 | − | 6.92092i | 1.70684 | − | 0.457347i | 0.732196 | − | 0.681094i | \(-0.238496\pi\) |
0.974647 | + | 0.223747i | \(0.0718290\pi\) | |||||||
\(230\) | 0.935237 | + | 2.61100i | 0.0616677 | + | 0.172164i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.3738 | + | 17.3479i | −0.681072 | + | 1.13895i | ||||
\(233\) | −11.0402 | − | 6.37405i | −0.723267 | − | 0.417578i | 0.0926872 | − | 0.995695i | \(-0.470454\pi\) |
−0.815954 | + | 0.578117i | \(0.803788\pi\) | |||||||
\(234\) | 6.26229 | + | 5.30948i | 0.409379 | + | 0.347092i | ||||
\(235\) | 3.16986 | − | 11.8301i | 0.206779 | − | 0.771708i | ||||
\(236\) | 11.7224 | + | 8.38801i | 0.763061 | + | 0.546013i | ||||
\(237\) | 0.739782 | − | 0.739782i | 0.0480540 | − | 0.0480540i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.9688 | 0.968253 | 0.484127 | − | 0.874998i | \(-0.339137\pi\) | ||||
0.484127 | + | 0.874998i | \(0.339137\pi\) | |||||||
\(240\) | −3.68901 | − | 3.22627i | −0.238124 | − | 0.208255i | ||||
\(241\) | 9.90526 | + | 17.1564i | 0.638054 | + | 1.10514i | 0.985859 | + | 0.167575i | \(0.0535937\pi\) |
−0.347805 | + | 0.937567i | \(0.613073\pi\) | |||||||
\(242\) | −0.577964 | − | 7.01931i | −0.0371530 | − | 0.451218i | ||||
\(243\) | −3.63850 | − | 13.5791i | −0.233410 | − | 0.871098i | ||||
\(244\) | −9.12186 | − | 0.892134i | −0.583967 | − | 0.0571130i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −13.6816 | + | 4.90061i | −0.872305 | + | 0.312452i | ||||
\(247\) | 0.315624 | + | 0.182226i | 0.0200827 | + | 0.0115947i | ||||
\(248\) | −16.8652 | − | 17.3907i | −1.07094 | − | 1.10431i | ||||
\(249\) | −8.04272 | + | 4.64346i | −0.509686 | + | 0.294268i | ||||
\(250\) | −12.6735 | − | 2.30155i | −0.801542 | − | 0.145563i | ||||
\(251\) | −9.23966 | − | 9.23966i | −0.583202 | − | 0.583202i | 0.352580 | − | 0.935782i | \(-0.385305\pi\) |
−0.935782 | + | 0.352580i | \(0.885305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.35028 | − | 3.35028i | 0.210630 | − | 0.210630i | ||||
\(254\) | 0.796289 | + | 1.14968i | 0.0499636 | + | 0.0721376i | ||||
\(255\) | 0.623780 | + | 1.08042i | 0.0390626 | + | 0.0676584i | ||||
\(256\) | 2.13176 | + | 15.8574i | 0.133235 | + | 0.991084i | ||||
\(257\) | 11.6109 | − | 20.1107i | 0.724271 | − | 1.25447i | −0.235003 | − | 0.971995i | \(-0.575510\pi\) |
0.959273 | − | 0.282479i | \(-0.0911568\pi\) | |||||||
\(258\) | 4.61788 | − | 9.77231i | 0.287496 | − | 0.608398i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.84726 | − | 5.89818i | −0.300614 | − | 0.365790i | ||||
\(261\) | 10.6615 | − | 2.85675i | 0.659933 | − | 0.176828i | ||||
\(262\) | 7.20425 | − | 8.49709i | 0.445080 | − | 0.524952i | ||||
\(263\) | −3.91454 | + | 2.26006i | −0.241381 | + | 0.139361i | −0.615811 | − | 0.787894i | \(-0.711172\pi\) |
0.374430 | + | 0.927255i | \(0.377838\pi\) | |||||||
\(264\) | −2.29067 | + | 8.05276i | −0.140981 | + | 0.495613i | ||||
\(265\) | 1.49496i | 0.0918345i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.87278 | + | 3.87278i | 0.237011 | + | 0.237011i | ||||
\(268\) | 4.08099 | − | 5.70325i | 0.249286 | − | 0.348381i | ||||
\(269\) | 0.385363 | + | 0.103258i | 0.0234960 | + | 0.00629574i | 0.270548 | − | 0.962707i | \(-0.412795\pi\) |
−0.247052 | + | 0.969002i | \(0.579462\pi\) | |||||||
\(270\) | 0.646168 | + | 7.84764i | 0.0393246 | + | 0.477592i | ||||
\(271\) | 5.31084 | − | 9.19864i | 0.322611 | − | 0.558778i | −0.658415 | − | 0.752655i | \(-0.728773\pi\) |
0.981026 | + | 0.193877i | \(0.0621063\pi\) | |||||||
\(272\) | 0.789149 | − | 3.99584i | 0.0478492 | − | 0.242284i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.1428 | + | 6.68313i | 0.854397 | + | 0.403742i | ||||
\(275\) | 2.52018 | + | 9.40545i | 0.151973 | + | 0.567170i | ||||
\(276\) | 4.24286 | − | 1.92591i | 0.255390 | − | 0.115926i | ||||
\(277\) | −2.98011 | + | 11.1219i | −0.179058 | + | 0.668252i | 0.816767 | + | 0.576967i | \(0.195764\pi\) |
−0.995825 | + | 0.0912848i | \(0.970903\pi\) | |||||||
\(278\) | −4.43678 | + | 24.4312i | −0.266100 | + | 1.46528i | ||||
\(279\) | 13.2287i | 0.791981i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6360i | 1.11173i | 0.831272 | + | 0.555866i | \(0.187613\pi\) | ||||
−0.831272 | + | 0.555866i | \(0.812387\pi\) | |||||||
\(282\) | −20.2450 | − | 3.67656i | −1.20557 | − | 0.218936i | ||||
\(283\) | −2.35222 | + | 8.77861i | −0.139825 | + | 0.521834i | 0.860106 | + | 0.510115i | \(0.170397\pi\) |
−0.999931 | + | 0.0117192i | \(0.996270\pi\) | |||||||
\(284\) | −10.1690 | − | 3.81942i | −0.603420 | − | 0.226641i | ||||
\(285\) | 0.0307463 | + | 0.114747i | 0.00182125 | + | 0.00679701i | ||||
\(286\) | −5.57226 | + | 11.7920i | −0.329495 | + | 0.697274i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.19267 | − | 7.02655i | 0.305981 | − | 0.414044i | ||||
\(289\) | 7.98158 | − | 13.8245i | 0.469505 | − | 0.813206i | ||||
\(290\) | −10.2290 | + | 0.842247i | −0.600667 | + | 0.0494585i | ||||
\(291\) | 19.1143 | + | 5.12167i | 1.12050 | + | 0.300238i | ||||
\(292\) | −2.77381 | − | 16.7296i | −0.162325 | − | 0.979026i | ||||
\(293\) | 12.0193 | + | 12.0193i | 0.702174 | + | 0.702174i | 0.964877 | − | 0.262703i | \(-0.0846138\pi\) |
−0.262703 | + | 0.964877i | \(0.584614\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.31920i | 0.426140i | ||||||||
\(296\) | −19.7336 | + | 10.9931i | −1.14699 | + | 0.638962i | ||||
\(297\) | 11.6497 | − | 6.72594i | 0.675982 | − | 0.390278i | ||||
\(298\) | 5.65235 | + | 4.79234i | 0.327432 | + | 0.277613i | ||||
\(299\) | 7.01125 | − | 1.87866i | 0.405471 | − | 0.108646i | ||||
\(300\) | −0.932092 | + | 9.53042i | −0.0538143 | + | 0.550239i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.74328 | − | 0.823782i | −0.100315 | − | 0.0474033i | ||||
\(303\) | 5.54812 | − | 9.60962i | 0.318731 | − | 0.552058i | ||||
\(304\) | 0.171062 | − | 0.348077i | 0.00981106 | − | 0.0199636i | ||||
\(305\) | −2.32697 | − | 4.03043i | −0.133242 | − | 0.230781i | ||||
\(306\) | −1.82841 | + | 1.26638i | −0.104523 | + | 0.0723944i | ||||
\(307\) | −17.8339 | + | 17.8339i | −1.01784 | + | 1.01784i | −0.0179975 | + | 0.999838i | \(0.505729\pi\) |
−0.999838 | + | 0.0179975i | \(0.994271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.59462 | + | 6.59462i | 0.375155 | + | 0.375155i | ||||
\(310\) | 2.19795 | − | 12.1031i | 0.124835 | − | 0.687407i | ||||
\(311\) | 5.66778 | − | 3.27229i | 0.321390 | − | 0.185555i | −0.330622 | − | 0.943763i | \(-0.607258\pi\) |
0.652012 | + | 0.758209i | \(0.273925\pi\) | |||||||
\(312\) | −9.20750 | + | 8.92930i | −0.521272 | + | 0.505522i | ||||
\(313\) | −16.6047 | − | 9.58671i | −0.938551 | − | 0.541873i | −0.0490453 | − | 0.998797i | \(-0.515618\pi\) |
−0.889506 | + | 0.456924i | \(0.848951\pi\) | |||||||
\(314\) | 0.151555 | + | 0.423112i | 0.00855274 | + | 0.0238776i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.10119 | − | 1.33994i | −0.0619470 | − | 0.0753776i | ||||
\(317\) | 4.87115 | + | 18.1794i | 0.273591 | + | 1.02106i | 0.956780 | + | 0.290814i | \(0.0939260\pi\) |
−0.683189 | + | 0.730242i | \(0.739407\pi\) | |||||||
\(318\) | 2.50312 | − | 0.206105i | 0.140368 | − | 0.0115578i | ||||
\(319\) | 8.76691 | + | 15.1847i | 0.490853 | + | 0.850182i | ||||
\(320\) | −5.91829 | + | 5.56590i | −0.330842 | + | 0.311143i | ||||
\(321\) | −22.8010 | −1.27263 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0698127 | + | 0.0698127i | −0.00388448 | + | 0.00388448i | ||||
\(324\) | 3.90857 | − | 0.648051i | 0.217143 | − | 0.0360028i | ||||
\(325\) | −3.86089 | + | 14.4090i | −0.214164 | + | 0.799270i | ||||
\(326\) | −13.5752 | + | 16.0114i | −0.751863 | + | 0.886788i | ||||
\(327\) | −17.0931 | − | 9.86868i | −0.945248 | − | 0.545739i | ||||
\(328\) | 5.87783 | + | 23.3640i | 0.324549 | + | 1.29006i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.00219 | + | 1.43355i | −0.220313 | + | 0.0789143i | ||||
\(331\) | −9.45985 | + | 2.53476i | −0.519960 | + | 0.139323i | −0.509248 | − | 0.860620i | \(-0.670076\pi\) |
−0.0107120 | + | 0.999943i | \(0.503410\pi\) | |||||||
\(332\) | 6.36346 | + | 14.0190i | 0.349240 | + | 0.769391i | ||||
\(333\) | 11.9148 | + | 3.19255i | 0.652926 | + | 0.174951i | ||||
\(334\) | 16.9721 | − | 11.7552i | 0.928673 | − | 0.643213i | ||||
\(335\) | 3.56099 | 0.194558 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.91600 | 0.267792 | 0.133896 | − | 0.990995i | \(-0.457251\pi\) | ||||
0.133896 | + | 0.990995i | \(0.457251\pi\) | |||||||
\(338\) | −1.31189 | + | 0.908636i | −0.0713575 | + | 0.0494233i | ||||
\(339\) | 23.4408 | + | 6.28094i | 1.27313 | + | 0.341134i | ||||
\(340\) | 1.88324 | − | 0.854836i | 0.102133 | − | 0.0463600i | ||||
\(341\) | −20.2984 | + | 5.43893i | −1.09922 | + | 0.294535i | ||||
\(342\) | −0.199382 | + | 0.0714167i | −0.0107813 | + | 0.00386178i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −15.3782 | − | 9.19593i | −0.829137 | − | 0.495811i | ||||
\(345\) | 2.04899 | + | 1.18299i | 0.110314 | + | 0.0636898i | ||||
\(346\) | 11.2955 | − | 13.3226i | 0.607252 | − | 0.716226i | ||||
\(347\) | 2.42076 | − | 9.03438i | 0.129953 | − | 0.484991i | −0.870015 | − | 0.493026i | \(-0.835891\pi\) |
0.999968 | + | 0.00803463i | \(0.00255753\pi\) | |||||||
\(348\) | 2.82048 | + | 17.0111i | 0.151193 | + | 0.911889i | ||||
\(349\) | 17.2061 | − | 17.2061i | 0.921021 | − | 0.921021i | −0.0760810 | − | 0.997102i | \(-0.524241\pi\) |
0.997102 | + | 0.0760810i | \(0.0242407\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.6081 | 1.09998 | ||||||||
\(352\) | 12.9166 | + | 5.07879i | 0.688459 | + | 0.270701i | ||||
\(353\) | −4.08472 | − | 7.07494i | −0.217408 | − | 0.376561i | 0.736607 | − | 0.676321i | \(-0.236427\pi\) |
−0.954015 | + | 0.299760i | \(0.903093\pi\) | |||||||
\(354\) | 12.2551 | − | 1.00907i | 0.651351 | − | 0.0536317i | ||||
\(355\) | −1.42758 | − | 5.32780i | −0.0757681 | − | 0.282771i | ||||
\(356\) | 7.01464 | − | 5.76479i | 0.371775 | − | 0.305533i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.224944 | − | 0.628001i | −0.0118887 | − | 0.0331909i | ||||
\(359\) | −10.0193 | − | 5.78465i | −0.528799 | − | 0.305302i | 0.211728 | − | 0.977329i | \(-0.432091\pi\) |
−0.740527 | + | 0.672027i | \(0.765424\pi\) | |||||||
\(360\) | 4.43592 | + | 0.0680425i | 0.233794 | + | 0.00358615i | ||||
\(361\) | 16.4463 | − | 9.49530i | 0.865597 | − | 0.499753i | ||||
\(362\) | −5.52673 | + | 30.4330i | −0.290478 | + | 1.59952i | ||||
\(363\) | −4.24851 | − | 4.24851i | −0.222989 | − | 0.222989i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.08876 | − | 6.08876i | 0.318700 | − | 0.318700i | ||||
\(366\) | −6.42764 | + | 4.45188i | −0.335978 | + | 0.232703i | ||||
\(367\) | 4.25356 | + | 7.36738i | 0.222034 | + | 0.384574i | 0.955425 | − | 0.295232i | \(-0.0953971\pi\) |
−0.733392 | + | 0.679807i | \(0.762064\pi\) | |||||||
\(368\) | −2.49292 | − | 7.31107i | −0.129952 | − | 0.381116i | ||||
\(369\) | 6.57792 | − | 11.3933i | 0.342433 | − | 0.593111i | ||||
\(370\) | −10.3705 | − | 4.90055i | −0.539136 | − | 0.254767i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −20.5681 | − | 2.01159i | −1.06641 | − | 0.104296i | ||||
\(373\) | −5.06649 | + | 1.35756i | −0.262333 | + | 0.0702919i | −0.387588 | − | 0.921833i | \(-0.626692\pi\) |
0.125255 | + | 0.992125i | \(0.460025\pi\) | |||||||
\(374\) | −2.69491 | − | 2.28488i | −0.139350 | − | 0.118148i | ||||
\(375\) | −9.51618 | + | 5.49417i | −0.491414 | + | 0.283718i | ||||
\(376\) | −9.33275 | + | 32.8090i | −0.481300 | + | 1.69199i | ||||
\(377\) | 26.8616i | 1.38344i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.62966 | − | 3.62966i | −0.186443 | − | 0.186443i | 0.607713 | − | 0.794156i | \(-0.292087\pi\) |
−0.794156 | + | 0.607713i | \(0.792087\pi\) | |||||||
\(380\) | 0.194282 | − | 0.0322125i | 0.00996647 | − | 0.00165246i | ||||
\(381\) | 1.15239 | + | 0.308783i | 0.0590390 | + | 0.0158194i | ||||
\(382\) | 8.57247 | − | 0.705850i | 0.438605 | − | 0.0361144i | ||||
\(383\) | −3.48127 | + | 6.02973i | −0.177884 | + | 0.308105i | −0.941156 | − | 0.337973i | \(-0.890259\pi\) |
0.763271 | + | 0.646078i | \(0.223592\pi\) | |||||||
\(384\) | 10.1353 | + | 9.14209i | 0.517217 | + | 0.466530i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.07950 | + | 12.8654i | −0.309438 | + | 0.654831i | ||||
\(387\) | 2.53239 | + | 9.45101i | 0.128729 | + | 0.480422i | ||||
\(388\) | 11.5346 | − | 30.7103i | 0.585581 | − | 1.55908i | ||||
\(389\) | −3.41145 | + | 12.7317i | −0.172967 | + | 0.645523i | 0.823922 | + | 0.566704i | \(0.191782\pi\) |
−0.996889 | + | 0.0788190i | \(0.974885\pi\) | |||||||
\(390\) | −6.40797 | − | 1.16371i | −0.324480 | − | 0.0589267i | ||||
\(391\) | 1.96636i | 0.0994429i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 9.50339i | − | 0.479383i | ||||||
\(394\) | −3.60352 | + | 19.8428i | −0.181543 | + | 0.999665i | ||||
\(395\) | 0.227934 | − | 0.850663i | 0.0114686 | − | 0.0428015i | ||||
\(396\) | −3.13262 | − | 6.90129i | −0.157420 | − | 0.346803i | ||||
\(397\) | −1.61554 | − | 6.02928i | −0.0810817 | − | 0.302601i | 0.913462 | − | 0.406925i | \(-0.133399\pi\) |
−0.994543 | + | 0.104324i | \(0.966732\pi\) | |||||||
\(398\) | 14.9091 | + | 7.04524i | 0.747325 | + | 0.353146i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.5739 | + | 3.07572i | 0.778693 | + | 0.153786i | ||||
\(401\) | 7.95077 | − | 13.7711i | 0.397042 | − | 0.687697i | −0.596317 | − | 0.802749i | \(-0.703370\pi\) |
0.993360 | + | 0.115051i | \(0.0367033\pi\) | |||||||
\(402\) | −0.490942 | − | 5.96243i | −0.0244860 | − | 0.297379i | ||||
\(403\) | −31.0969 | − | 8.33239i | −1.54905 | − | 0.415066i | ||||
\(404\) | −14.9597 | − | 10.7045i | −0.744271 | − | 0.532568i | ||||
\(405\) | 1.42253 | + | 1.42253i | 0.0706861 | + | 0.0706861i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.5949i | 0.971282i | ||||||||
\(408\) | −1.69095 | − | 3.03540i | −0.0837146 | − | 0.150275i | ||||
\(409\) | −4.93864 | + | 2.85133i | −0.244200 | + | 0.140989i | −0.617106 | − | 0.786880i | \(-0.711695\pi\) |
0.372906 | + | 0.927869i | \(0.378362\pi\) | |||||||
\(410\) | −7.91121 | + | 9.33091i | −0.390707 | + | 0.460821i | ||||
\(411\) | 12.8895 | − | 3.45372i | 0.635791 | − | 0.170360i | ||||
\(412\) | 11.9446 | − | 9.81634i | 0.588468 | − | 0.483616i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.80214 | + | 3.81368i | −0.0885704 | + | 0.187432i | ||||
\(415\) | −3.90874 | + | 6.77014i | −0.191873 | + | 0.332333i | ||||
\(416\) | 13.2467 | + | 16.6323i | 0.649473 | + | 0.815467i | ||||
\(417\) | 10.5913 | + | 18.3447i | 0.518659 | + | 0.898343i | ||||
\(418\) | −0.191558 | − | 0.276573i | −0.00936943 | − | 0.0135276i | ||||
\(419\) | 4.57142 | − | 4.57142i | 0.223328 | − | 0.223328i | −0.586570 | − | 0.809898i | \(-0.699522\pi\) |
0.809898 | + | 0.586570i | \(0.199522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.421252 | + | 0.421252i | 0.0205306 | + | 0.0205306i | 0.717298 | − | 0.696767i | \(-0.245379\pi\) |
−0.696767 | + | 0.717298i | \(0.745379\pi\) | |||||||
\(422\) | −12.8581 | − | 2.33508i | −0.625925 | − | 0.113670i | ||||
\(423\) | 16.1311 | − | 9.31331i | 0.784322 | − | 0.452829i | ||||
\(424\) | 0.0638586 | − | 4.16316i | 0.00310125 | − | 0.202181i | ||||
\(425\) | −3.49971 | − | 2.02056i | −0.169761 | − | 0.0980115i | ||||
\(426\) | −8.72393 | + | 3.12483i | −0.422676 | + | 0.151399i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.67924 | + | 37.6194i | −0.177843 | + | 1.81840i | ||||
\(429\) | 2.87964 | + | 10.7470i | 0.139031 | + | 0.518869i | ||||
\(430\) | −0.746617 | − | 9.06758i | −0.0360051 | − | 0.437278i | ||||
\(431\) | 10.5518 | + | 18.2762i | 0.508262 | + | 0.880336i | 0.999954 | + | 0.00956658i | \(0.00304518\pi\) |
−0.491692 | + | 0.870769i | \(0.663621\pi\) | |||||||
\(432\) | −1.46423 | − | 21.8817i | −0.0704479 | − | 1.05279i | ||||
\(433\) | 13.9717 | 0.671436 | 0.335718 | − | 0.941962i | \(-0.391021\pi\) | ||||
0.335718 | + | 0.941962i | \(0.391021\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.19120 | + | 6.19120i | −0.296845 | + | 0.296845i | ||||
\(436\) | −19.0405 | + | 26.6094i | −0.911877 | + | 1.27436i | ||||
\(437\) | −0.0484611 | + | 0.180859i | −0.00231821 | + | 0.00865168i | ||||
\(438\) | −11.0343 | − | 9.35544i | −0.527240 | − | 0.447020i | ||||
\(439\) | −4.69322 | − | 2.70963i | −0.223995 | − | 0.129324i | 0.383804 | − | 0.923415i | \(-0.374614\pi\) |
−0.607799 | + | 0.794091i | \(0.707947\pi\) | |||||||
\(440\) | 1.71941 | + | 6.83455i | 0.0819696 | + | 0.325824i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.82525 | − | 5.09573i | −0.0868181 | − | 0.242379i | ||||
\(443\) | −5.83698 | + | 1.56401i | −0.277323 | + | 0.0743085i | −0.394800 | − | 0.918767i | \(-0.629186\pi\) |
0.117477 | + | 0.993076i | \(0.462519\pi\) | |||||||
\(444\) | −6.77561 | + | 18.0397i | −0.321556 | + | 0.856128i | ||||
\(445\) | 4.45325 | + | 1.19324i | 0.211104 | + | 0.0565652i | ||||
\(446\) | −18.7900 | − | 27.1290i | −0.889732 | − | 1.28460i | ||||
\(447\) | 6.32175 | 0.299009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.4262 | 0.869587 | 0.434794 | − | 0.900530i | \(-0.356821\pi\) | ||||
0.434794 | + | 0.900530i | \(0.356821\pi\) | |||||||
\(450\) | −4.93575 | − | 7.12625i | −0.232673 | − | 0.335934i | ||||
\(451\) | 20.1866 | + | 5.40898i | 0.950550 | + | 0.254699i | ||||
\(452\) | 14.1454 | − | 37.6615i | 0.665344 | − | 1.77145i | ||||
\(453\) | −1.58879 | + | 0.425716i | −0.0746480 | + | 0.0200019i | ||||
\(454\) | 7.46301 | + | 20.8353i | 0.350257 | + | 0.977848i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.0807208 | − | 0.320860i | −0.00378010 | − | 0.0150257i | ||||
\(457\) | −31.1530 | − | 17.9862i | −1.45728 | − | 0.841358i | −0.458399 | − | 0.888747i | \(-0.651577\pi\) |
−0.998877 | + | 0.0473884i | \(0.984910\pi\) | |||||||
\(458\) | −28.8445 | − | 24.4558i | −1.34782 | − | 1.14275i | ||||
\(459\) | −1.44492 | + | 5.39253i | −0.0674433 | + | 0.251702i | ||||
\(460\) | 2.28244 | − | 3.18974i | 0.106419 | − | 0.148723i | ||||
\(461\) | 0.903879 | − | 0.903879i | 0.0420978 | − | 0.0420978i | −0.685745 | − | 0.727842i | \(-0.740523\pi\) |
0.727842 | + | 0.685745i | \(0.240523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.5999 | −0.585565 | −0.292782 | − | 0.956179i | \(-0.594581\pi\) | ||||
−0.292782 | + | 0.956179i | \(0.594581\pi\) | |||||||
\(464\) | 28.5217 | − | 1.90855i | 1.32409 | − | 0.0886022i | ||||
\(465\) | −5.24687 | − | 9.08785i | −0.243318 | − | 0.421439i | ||||
\(466\) | 1.47945 | + | 17.9677i | 0.0685342 | + | 0.832340i | ||||
\(467\) | 2.14538 | + | 8.00668i | 0.0992765 | + | 0.370505i | 0.997633 | − | 0.0687620i | \(-0.0219049\pi\) |
−0.898357 | + | 0.439267i | \(0.855238\pi\) | |||||||
\(468\) | 1.13018 | − | 11.5558i | 0.0522424 | − | 0.534167i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.3059 | + | 5.84064i | −0.752137 | + | 0.269409i | ||||
\(471\) | 0.332038 | + | 0.191702i | 0.0152995 | + | 0.00883318i | ||||
\(472\) | 0.312647 | − | 20.3825i | 0.0143907 | − | 0.938181i | ||||
\(473\) | −13.4606 | + | 7.77151i | −0.618921 | + | 0.357334i | ||||
\(474\) | −1.45575 | − | 0.264370i | −0.0668650 | − | 0.0121429i | ||||
\(475\) | −0.272096 | − | 0.272096i | −0.0124846 | − | 0.0124846i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.60770 | + | 1.60770i | −0.0736114 | + | 0.0736114i | ||||
\(478\) | −12.0533 | − | 17.4026i | −0.551305 | − | 0.795975i | ||||
\(479\) | 4.63918 | + | 8.03529i | 0.211969 | + | 0.367142i | 0.952331 | − | 0.305067i | \(-0.0986789\pi\) |
−0.740361 | + | 0.672209i | \(0.765346\pi\) | |||||||
\(480\) | −0.780333 | + | 6.88667i | −0.0356172 | + | 0.314332i | ||||
\(481\) | −15.0096 | + | 25.9974i | −0.684378 | + | 1.18538i | ||||
\(482\) | 11.9699 | − | 25.3305i | 0.545212 | − | 1.15377i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.69517 | + | 6.32407i | −0.349781 | + | 0.287458i | ||||
\(485\) | 16.0899 | − | 4.31128i | 0.730606 | − | 0.195765i | ||||
\(486\) | −12.8570 | + | 15.1643i | −0.583207 | + | 0.687867i | ||||
\(487\) | −33.5037 | + | 19.3434i | −1.51820 | + | 0.876533i | −0.518429 | + | 0.855121i | \(0.673483\pi\) |
−0.999771 | + | 0.0214118i | \(0.993184\pi\) | |||||||
\(488\) | 6.30798 | + | 11.3233i | 0.285549 | + | 0.512583i | ||||
\(489\) | 17.9076i | 0.809810i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.8086 | − | 29.8086i | −1.34524 | − | 1.34524i | −0.890750 | − | 0.454494i | \(-0.849820\pi\) |
−0.454494 | − | 0.890750i | \(-0.650180\pi\) | |||||||
\(492\) | 16.7141 | + | 11.9599i | 0.753532 | + | 0.539195i | ||||
\(493\) | −7.02889 | − | 1.88338i | −0.316565 | − | 0.0848234i | ||||
\(494\) | −0.0422954 | − | 0.513673i | −0.00190296 | − | 0.0231113i | ||||
\(495\) | 1.92420 | − | 3.33282i | 0.0864865 | − | 0.149799i | ||||
\(496\) | −6.63786 | + | 33.6107i | −0.298049 | + | 1.50917i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 11.8746 | + | 5.61132i | 0.532115 | + | 0.251449i | ||||
\(499\) | −2.89367 | − | 10.7993i | −0.129538 | − | 0.483444i | 0.870422 | − | 0.492306i | \(-0.163846\pi\) |
−0.999961 | + | 0.00886191i | \(0.997179\pi\) | |||||||
\(500\) | 7.52928 | + | 16.5873i | 0.336720 | + | 0.741808i | ||||
\(501\) | 4.55839 | − | 17.0121i | 0.203654 | − | 0.760046i | ||||
\(502\) | −3.30190 | + | 18.1819i | −0.147371 | + | 0.811499i | ||||
\(503\) | − | 18.1532i | − | 0.809409i | −0.914448 | − | 0.404704i | \(-0.867374\pi\) | ||
0.914448 | − | 0.404704i | \(-0.132626\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 9.34050i | − | 0.415647i | ||||||
\(506\) | −6.59273 | − | 1.19726i | −0.293082 | − | 0.0532248i | ||||
\(507\) | −0.352349 | + | 1.31498i | −0.0156484 | + | 0.0584005i | ||||
\(508\) | 0.695416 | − | 1.85151i | 0.0308541 | − | 0.0821475i | ||||
\(509\) | −0.530258 | − | 1.97895i | −0.0235033 | − | 0.0877154i | 0.953178 | − | 0.302410i | \(-0.0977911\pi\) |
−0.976681 | + | 0.214694i | \(0.931124\pi\) | |||||||
\(510\) | 0.753798 | − | 1.59518i | 0.0333787 | − | 0.0706358i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.7190 | − | 15.2471i | 0.738883 | − | 0.673834i | ||||
\(513\) | −0.265799 | + | 0.460378i | −0.0117353 | + | 0.0203262i | ||||
\(514\) | −32.7299 | + | 2.69496i | −1.44366 | + | 0.118869i | ||||
\(515\) | 7.58304 | + | 2.03187i | 0.334149 | + | 0.0895348i | ||||
\(516\) | −15.0796 | + | 2.50024i | −0.663843 | + | 0.110067i | ||||
\(517\) | 20.9228 | + | 20.9228i | 0.920183 | + | 0.920183i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 14.9004i | − | 0.654053i | ||||||
\(520\) | −2.95401 | + | 10.3847i | −0.129542 | + | 0.455401i | ||||
\(521\) | 2.51905 | − | 1.45437i | 0.110361 | − | 0.0637172i | −0.443803 | − | 0.896124i | \(-0.646371\pi\) |
0.554165 | + | 0.832407i | \(0.313038\pi\) | |||||||
\(522\) | −11.9062 | − | 10.0946i | −0.521119 | − | 0.441831i | ||||
\(523\) | 16.0023 | − | 4.28781i | 0.699732 | − | 0.187493i | 0.108622 | − | 0.994083i | \(-0.465356\pi\) |
0.591111 | + | 0.806590i | \(0.298690\pi\) | |||||||
\(524\) | −15.6797 | − | 1.53350i | −0.684969 | − | 0.0669911i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.77962 | + | 2.73114i | 0.252003 | + | 0.119083i | ||||
\(527\) | 4.36067 | − | 7.55290i | 0.189954 | − | 0.329010i | ||||
\(528\) | 11.2065 | − | 3.82119i | 0.487702 | − | 0.166296i | ||||
\(529\) | −9.63542 | − | 16.6890i | −0.418931 | − | 0.725611i | ||||
\(530\) | 1.73802 | − | 1.20378i | 0.0754947 | − | 0.0522888i | ||||
\(531\) | −7.87117 | + | 7.87117i | −0.341580 | + | 0.341580i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.6392 | + | 22.6392i | 0.980611 | + | 0.980611i | ||||
\(534\) | 1.38398 | − | 7.62092i | 0.0598909 | − | 0.329789i | ||||
\(535\) | −16.6219 | + | 9.59663i | −0.718625 | + | 0.414899i | ||||
\(536\) | −9.91665 | − | 0.152111i | −0.428334 | − | 0.00657020i | ||||
\(537\) | −0.492826 | − | 0.284533i | −0.0212670 | − | 0.0122785i | ||||
\(538\) | −0.190258 | − | 0.531165i | −0.00820262 | − | 0.0229001i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.60326 | − | 7.07035i | 0.370225 | − | 0.304260i | ||||
\(541\) | 1.87978 | + | 7.01543i | 0.0808180 | + | 0.301617i | 0.994489 | − | 0.104837i | \(-0.0334320\pi\) |
−0.913671 | + | 0.406453i | \(0.866765\pi\) | |||||||
\(542\) | −14.9707 | + | 1.23267i | −0.643045 | + | 0.0529478i | ||||
\(543\) | 13.1932 | + | 22.8513i | 0.566174 | + | 0.980643i | ||||
\(544\) | −5.28096 | + | 2.30010i | −0.226419 | + | 0.0986161i | ||||
\(545\) | −16.6144 | −0.711682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2712 | − | 18.2712i | 0.781218 | − | 0.781218i | −0.198818 | − | 0.980036i | \(-0.563710\pi\) |
0.980036 | + | 0.198818i | \(0.0637103\pi\) | |||||||
\(548\) | −3.61842 | − | 21.8237i | −0.154571 | − | 0.932260i | ||||
\(549\) | 1.83192 | − | 6.83683i | 0.0781846 | − | 0.291789i | ||||
\(550\) | 8.90534 | − | 10.5034i | 0.379725 | − | 0.447868i | ||||
\(551\) | −0.600079 | − | 0.346456i | −0.0255642 | − | 0.0147595i | ||||
\(552\) | −5.65550 | − | 3.38190i | −0.240714 | − | 0.143943i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 15.3299 | − | 5.49103i | 0.651305 | − | 0.233291i | ||||
\(555\) | −9.45148 | + | 2.53252i | −0.401193 | + | 0.107499i | ||||
\(556\) | 31.9760 | − | 14.5145i | 1.35608 | − | 0.615550i | ||||
\(557\) | −4.78640 | − | 1.28251i | −0.202806 | − | 0.0543418i | 0.155986 | − | 0.987759i | \(-0.450145\pi\) |
−0.358792 | + | 0.933417i | \(0.616811\pi\) | |||||||
\(558\) | 15.3795 | − | 10.6521i | 0.651067 | − | 0.450939i | ||||
\(559\) | −23.8117 | −1.00713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.01407 | −0.127254 | ||||||||
\(562\) | 21.6660 | − | 15.0062i | 0.913925 | − | 0.632999i | ||||
\(563\) | −23.4858 | − | 6.29301i | −0.989809 | − | 0.265219i | −0.272639 | − | 0.962116i | \(-0.587896\pi\) |
−0.717170 | + | 0.696898i | \(0.754563\pi\) | |||||||
\(564\) | 12.0275 | + | 26.4970i | 0.506448 | + | 1.11573i | ||||
\(565\) | 19.7318 | − | 5.28712i | 0.830123 | − | 0.222431i | ||||
\(566\) | 12.1000 | − | 4.33410i | 0.508600 | − | 0.182176i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.74795 | + | 14.8979i | 0.157260 | + | 0.625100i | ||||
\(569\) | 2.33865 | + | 1.35022i | 0.0980412 | + | 0.0566041i | 0.548219 | − | 0.836335i | \(-0.315306\pi\) |
−0.450178 | + | 0.892939i | \(0.648639\pi\) | |||||||
\(570\) | 0.108645 | − | 0.128142i | 0.00455066 | − | 0.00536729i | ||||
\(571\) | −3.43500 | + | 12.8196i | −0.143750 | + | 0.536484i | 0.856058 | + | 0.516881i | \(0.172907\pi\) |
−0.999808 | + | 0.0196030i | \(0.993760\pi\) | |||||||
\(572\) | 18.1961 | − | 3.01696i | 0.760818 | − | 0.126146i | ||||
\(573\) | 5.18857 | − | 5.18857i | 0.216756 | − | 0.216756i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.66390 | −0.319607 | ||||||||
\(576\) | −12.3503 | − | 0.378970i | −0.514594 | − | 0.0157904i | ||||
\(577\) | −12.4461 | − | 21.5572i | −0.518137 | − | 0.897439i | −0.999778 | − | 0.0210709i | \(-0.993292\pi\) |
0.481641 | − | 0.876369i | \(-0.340041\pi\) | |||||||
\(578\) | −22.4992 | + | 1.85256i | −0.935842 | + | 0.0770565i | ||||
\(579\) | 3.14178 | + | 11.7253i | 0.130568 | + | 0.487286i | ||||
\(580\) | 9.21584 | + | 11.2139i | 0.382667 | + | 0.465632i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.43697 | − | 26.3462i | −0.391175 | − | 1.09209i | ||||
\(583\) | −3.12788 | − | 1.80589i | −0.129544 | − | 0.0747921i | ||||
\(584\) | −17.2161 | + | 16.6959i | −0.712407 | + | 0.690882i | ||||
\(585\) | 5.10584 | − | 2.94786i | 0.211101 | − | 0.121879i | ||||
\(586\) | 4.29523 | − | 23.6517i | 0.177434 | − | 0.977044i | ||||
\(587\) | −23.9315 | − | 23.9315i | −0.987758 | − | 0.987758i | 0.0121684 | − | 0.999926i | \(-0.496127\pi\) |
−0.999926 | + | 0.0121684i | \(0.996127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.587224 | − | 0.587224i | 0.0241961 | − | 0.0241961i | ||||
\(590\) | 8.50921 | − | 5.89361i | 0.350319 | − | 0.242636i | ||||
\(591\) | 8.60218 | + | 14.8994i | 0.353846 | + | 0.612880i | ||||
\(592\) | 28.6705 | + | 14.0900i | 1.17835 | + | 0.579097i | ||||
\(593\) | 0.895084 | − | 1.55033i | 0.0367567 | − | 0.0636645i | −0.847062 | − | 0.531494i | \(-0.821631\pi\) |
0.883819 | + | 0.467830i | \(0.154964\pi\) | |||||||
\(594\) | −17.2001 | − | 8.12786i | −0.705729 | − | 0.333490i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.02010 | − | 10.4303i | 0.0417849 | − | 0.427241i | ||||
\(597\) | 13.5879 | − | 3.64086i | 0.556114 | − | 0.149010i | ||||
\(598\) | −7.82975 | − | 6.63845i | −0.320182 | − | 0.271466i | ||||
\(599\) | 37.3788 | − | 21.5806i | 1.52726 | − | 0.881761i | 0.527779 | − | 0.849381i | \(-0.323025\pi\) |
0.999476 | − | 0.0323796i | \(-0.0103085\pi\) | |||||||
\(600\) | 11.8305 | − | 6.59051i | 0.482978 | − | 0.269056i | ||||
\(601\) | − | 27.6564i | − | 1.12813i | −0.825730 | − | 0.564065i | \(-0.809237\pi\) | ||
0.825730 | − | 0.564065i | \(-0.190763\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.82954 | + | 3.82954i | 0.155951 | + | 0.155951i | ||||
\(604\) | 0.446017 | + | 2.69005i | 0.0181482 | + | 0.109457i | ||||
\(605\) | −4.88529 | − | 1.30901i | −0.198615 | − | 0.0532188i | ||||
\(606\) | −15.6395 | + | 1.28775i | −0.635312 | + | 0.0523111i | ||||
\(607\) | −10.7968 | + | 18.7006i | −0.438228 | + | 0.759032i | −0.997553 | − | 0.0699158i | \(-0.977727\pi\) |
0.559325 | + | 0.828948i | \(0.311060\pi\) | |||||||
\(608\) | −0.542413 | + | 0.0814064i | −0.0219978 | + | 0.00330147i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.81199 | + | 5.95071i | −0.113854 | + | 0.240937i | ||||
\(611\) | 11.7324 | + | 43.7859i | 0.474642 | + | 1.77139i | ||||
\(612\) | 2.94457 | + | 1.10596i | 0.119027 | + | 0.0447058i | ||||
\(613\) | −2.56885 | + | 9.58708i | −0.103755 | + | 0.387219i | −0.998201 | − | 0.0599573i | \(-0.980904\pi\) |
0.894446 | + | 0.447176i | \(0.147570\pi\) | |||||||
\(614\) | 35.0938 | + | 6.37316i | 1.41627 | + | 0.257200i | ||||
\(615\) | 10.4360i | 0.420819i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.2458i | 0.573515i | 0.958003 | + | 0.286758i | \(0.0925774\pi\) | ||||
−0.958003 | + | 0.286758i | \(0.907423\pi\) | |||||||
\(618\) | 2.35666 | − | 12.9770i | 0.0947989 | − | 0.522011i | ||||
\(619\) | −9.45579 | + | 35.2895i | −0.380060 | + | 1.41840i | 0.465748 | + | 0.884917i | \(0.345785\pi\) |
−0.845808 | + | 0.533487i | \(0.820881\pi\) | |||||||
\(620\) | −15.8407 | + | 7.19038i | −0.636178 | + | 0.288773i | ||||
\(621\) | 2.74027 | + | 10.2268i | 0.109963 | + | 0.410388i | ||||
\(622\) | −8.36817 | − | 3.95435i | −0.335533 | − | 0.158555i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 17.7952 | + | 3.51442i | 0.712379 | + | 0.140689i | ||||
\(625\) | 5.29682 | − | 9.17437i | 0.211873 | − | 0.366975i | ||||
\(626\) | 2.22512 | + | 27.0239i | 0.0889338 | + | 1.08009i | ||||
\(627\) | −0.277225 | − | 0.0742821i | −0.0110713 | − | 0.00296654i | ||||
\(628\) | 0.369869 | − | 0.516897i | 0.0147594 | − | 0.0206264i | ||||
\(629\) | −5.75034 | − | 5.75034i | −0.229281 | − | 0.229281i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.87006i | − | 0.193874i | −0.995291 | − | 0.0969370i | \(-0.969095\pi\) | ||
0.995291 | − | 0.0969370i | \(-0.0309045\pi\) | |||||||
\(632\) | −0.671089 | + | 2.35919i | −0.0266945 | + | 0.0938436i | ||||
\(633\) | −9.65483 | + | 5.57422i | −0.383745 | + | 0.221555i | ||||
\(634\) | 17.2127 | − | 20.3016i | 0.683605 | − | 0.806282i | ||||
\(635\) | 0.970054 | − | 0.259925i | 0.0384954 | − | 0.0103148i | ||||
\(636\) | −2.25519 | − | 2.74414i | −0.0894242 | − | 0.108812i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.5942 | − | 22.4195i | 0.419430 | − | 0.887595i | ||||
\(639\) | 4.19436 | − | 7.26484i | 0.165926 | − | 0.287393i | ||||
\(640\) | 11.2364 | + | 2.39873i | 0.444158 | + | 0.0948180i | ||||
\(641\) | −17.1939 | − | 29.7808i | −0.679120 | − | 1.17627i | −0.975246 | − | 0.221121i | \(-0.929028\pi\) |
0.296126 | − | 0.955149i | \(-0.404305\pi\) | |||||||
\(642\) | 18.3600 | + | 26.5082i | 0.724610 | + | 1.04619i | ||||
\(643\) | 11.9018 | − | 11.9018i | 0.469361 | − | 0.469361i | −0.432346 | − | 0.901708i | \(-0.642314\pi\) |
0.901708 | + | 0.432346i | \(0.142314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.48825 | − | 5.48825i | −0.216099 | − | 0.216099i | ||||
\(646\) | 0.137378 | + | 0.0249484i | 0.00540508 | + | 0.000981581i | ||||
\(647\) | 4.56190 | − | 2.63381i | 0.179347 | − | 0.103546i | −0.407639 | − | 0.913143i | \(-0.633648\pi\) |
0.586986 | + | 0.809597i | \(0.300314\pi\) | |||||||
\(648\) | −3.90070 | − | 4.02223i | −0.153234 | − | 0.158008i | ||||
\(649\) | −15.3139 | − | 8.84148i | −0.601123 | − | 0.347058i | ||||
\(650\) | 19.8607 | − | 7.11392i | 0.779000 | − | 0.279031i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.5458 | + | 2.88963i | 1.15710 | + | 0.113167i | ||||
\(653\) | −8.87812 | − | 33.1336i | −0.347427 | − | 1.29662i | −0.889751 | − | 0.456447i | \(-0.849122\pi\) |
0.542323 | − | 0.840170i | \(-0.317545\pi\) | |||||||
\(654\) | 2.29057 | + | 27.8187i | 0.0895684 | + | 1.08780i | ||||
\(655\) | −3.99985 | − | 6.92794i | −0.156287 | − | 0.270697i | ||||
\(656\) | 22.4297 | − | 25.6468i | 0.875734 | − | 1.00134i | ||||
\(657\) | 13.0959 | 0.510919 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.4817 | + | 14.4817i | −0.564126 | + | 0.564126i | −0.930477 | − | 0.366351i | \(-0.880607\pi\) |
0.366351 | + | 0.930477i | \(0.380607\pi\) | |||||||
\(660\) | 4.88930 | + | 3.49857i | 0.190316 | + | 0.136182i | ||||
\(661\) | 4.10893 | − | 15.3347i | 0.159819 | − | 0.596452i | −0.838826 | − | 0.544400i | \(-0.816757\pi\) |
0.998644 | − | 0.0520518i | \(-0.0165761\pi\) | |||||||
\(662\) | 10.5642 | + | 8.95685i | 0.410589 | + | 0.348118i | ||||
\(663\) | −3.99889 | − | 2.30876i | −0.155304 | − | 0.0896648i | ||||
\(664\) | 11.1743 | − | 18.6865i | 0.433646 | − | 0.725178i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.88246 | − | 16.4227i | −0.227941 | − | 0.636367i | ||||
\(667\) | −13.3301 | + | 3.57180i | −0.516145 | + | 0.138301i | ||||
\(668\) | −27.3328 | − | 10.2660i | −1.05754 | − | 0.397204i | ||||
\(669\) | −27.1930 | − | 7.28634i | −1.05134 | − | 0.281706i | ||||
\(670\) | −2.86740 | − | 4.13996i | −0.110777 | − | 0.159941i | ||||
\(671\) | 11.2438 | 0.434061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.09831 | −0.312167 | −0.156083 | − | 0.987744i | \(-0.549887\pi\) | ||||
−0.156083 | + | 0.987744i | \(0.549887\pi\) | |||||||
\(674\) | −3.95849 | − | 5.71528i | −0.152476 | − | 0.220145i | ||||
\(675\) | −21.0175 | − | 5.63161i | −0.808962 | − | 0.216761i | ||||
\(676\) | 2.11274 | + | 0.793531i | 0.0812592 | + | 0.0305204i | ||||
\(677\) | −21.8750 | + | 5.86138i | −0.840724 | + | 0.225271i | −0.653386 | − | 0.757025i | \(-0.726652\pi\) |
−0.187337 | + | 0.982296i | \(0.559986\pi\) | |||||||
\(678\) | −11.5730 | − | 32.3095i | −0.444458 | − | 1.24084i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.51026 | − | 1.50110i | −0.0962639 | − | 0.0575644i | ||||
\(681\) | 16.3505 | + | 9.43999i | 0.626554 | + | 0.361741i | ||||
\(682\) | 22.6680 | + | 19.2191i | 0.868003 | + | 0.735936i | ||||
\(683\) | 9.86156 | − | 36.8038i | 0.377342 | − | 1.40826i | −0.472550 | − | 0.881304i | \(-0.656666\pi\) |
0.849892 | − | 0.526956i | \(-0.176667\pi\) | |||||||
\(684\) | 0.243576 | + | 0.174292i | 0.00931335 | + | 0.00666423i | ||||
\(685\) | 7.94275 | − | 7.94275i | 0.303477 | − | 0.303477i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.2606 | −1.23082 | ||||||||
\(688\) | 1.69185 | + | 25.2833i | 0.0645012 | + | 0.963917i | ||||
\(689\) | −2.76660 | − | 4.79189i | −0.105399 | − | 0.182556i | ||||
\(690\) | −0.274577 | − | 3.33470i | −0.0104530 | − | 0.126950i | ||||
\(691\) | −6.40271 | − | 23.8952i | −0.243571 | − | 0.909018i | −0.974096 | − | 0.226133i | \(-0.927392\pi\) |
0.730526 | − | 0.682885i | \(-0.239275\pi\) | |||||||
\(692\) | −24.5841 | − | 2.40437i | −0.934548 | − | 0.0914004i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.4525 | + | 4.46038i | −0.472691 | + | 0.169314i | ||||
\(695\) | 15.4421 | + | 8.91547i | 0.585750 | + | 0.338183i | ||||
\(696\) | 17.5057 | − | 16.9768i | 0.663553 | − | 0.643504i | ||||
\(697\) | −7.51132 | + | 4.33666i | −0.284511 | + | 0.164263i | ||||
\(698\) | −33.8584 | − | 6.14879i | −1.28156 | − | 0.232735i | ||||
\(699\) | 10.8752 | + | 10.8752i | 0.411336 | + | 0.411336i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.6300 | + | 10.6300i | −0.401489 | + | 0.401489i | −0.878757 | − | 0.477269i | \(-0.841627\pi\) |
0.477269 | + | 0.878757i | \(0.341627\pi\) | |||||||
\(702\) | −16.5942 | − | 23.9588i | −0.626308 | − | 0.904265i | ||||
\(703\) | −0.387181 | − | 0.670617i | −0.0146028 | − | 0.0252928i | ||||
\(704\) | −4.49627 | − | 19.1063i | −0.169460 | − | 0.720096i | ||||
\(705\) | −7.38785 | + | 12.7961i | −0.278242 | + | 0.481930i | ||||
\(706\) | −4.93612 | + | 10.4458i | −0.185773 | + | 0.393132i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −11.0413 | − | 13.4351i | −0.414956 | − | 0.504921i | ||||
\(709\) | 3.42184 | − | 0.916878i | 0.128510 | − | 0.0344341i | −0.193991 | − | 0.981003i | \(-0.562143\pi\) |
0.322501 | + | 0.946569i | \(0.395477\pi\) | |||||||
\(710\) | −5.04452 | + | 5.94978i | −0.189317 | + | 0.223291i | ||||
\(711\) | 1.15994 | − | 0.669691i | 0.0435011 | − | 0.0251154i | ||||
\(712\) | −12.3504 | − | 3.51317i | −0.462852 | − | 0.131662i | ||||
\(713\) | − | 16.5398i | − | 0.619422i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.62251 | + | 6.62251i | 0.247668 | + | 0.247668i | ||||
\(716\) | −0.548975 | + | 0.767200i | −0.0205162 | + | 0.0286716i | ||||
\(717\) | −17.4436 | − | 4.67400i | −0.651444 | − | 0.174554i | ||||
\(718\) | 1.34265 | + | 16.3063i | 0.0501071 | + | 0.608545i | ||||
\(719\) | 8.10598 | − | 14.0400i | 0.302302 | − | 0.523603i | −0.674355 | − | 0.738407i | \(-0.735578\pi\) |
0.976657 | + | 0.214805i | \(0.0689115\pi\) | |||||||
\(720\) | −3.49282 | − | 5.21194i | −0.130170 | − | 0.194237i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −24.2821 | − | 11.4745i | −0.903688 | − | 0.427035i | ||||
\(723\) | −6.18582 | − | 23.0858i | −0.230053 | − | 0.858569i | ||||
\(724\) | 39.8313 | − | 18.0801i | 1.48032 | − | 0.671942i | ||||
\(725\) | 7.34051 | − | 27.3952i | 0.272620 | − | 1.01743i | ||||
\(726\) | −1.51825 | + | 8.36028i | −0.0563477 | + | 0.310279i | ||||
\(727\) | − | 14.2822i | − | 0.529699i | −0.964290 | − | 0.264849i | \(-0.914678\pi\) | ||
0.964290 | − | 0.264849i | \(-0.0853223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.9031i | 0.848263i | ||||||||
\(730\) | −11.9816 | − | 2.17589i | −0.443457 | − | 0.0805333i | ||||
\(731\) | 1.66954 | − | 6.23082i | 0.0617503 | − | 0.230455i | ||||
\(732\) | 10.3514 | + | 3.88792i | 0.382599 | + | 0.143702i | ||||
\(733\) | 8.91206 | + | 33.2603i | 0.329175 | + | 1.22850i | 0.910048 | + | 0.414502i | \(0.136044\pi\) |
−0.580874 | + | 0.813994i | \(0.697289\pi\) | |||||||
\(734\) | 5.14015 | − | 10.8775i | 0.189726 | − | 0.401497i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.49240 | + | 8.78531i | −0.239313 | + | 0.323831i | ||||
\(737\) | −4.30162 | + | 7.45062i | −0.158452 | + | 0.274447i | ||||
\(738\) | −18.5424 | + | 1.52677i | −0.682556 | + | 0.0562011i | ||||
\(739\) | 20.1534 | + | 5.40009i | 0.741356 | + | 0.198646i | 0.609681 | − | 0.792647i | \(-0.291298\pi\) |
0.131675 | + | 0.991293i | \(0.457964\pi\) | |||||||
\(740\) | 2.65328 | + | 16.0027i | 0.0975366 | + | 0.588270i | ||||
\(741\) | −0.310906 | − | 0.310906i | −0.0114214 | − | 0.0114214i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.1201i | − | 1.10500i | −0.833513 | − | 0.552500i | \(-0.813674\pi\) | ||
0.833513 | − | 0.552500i | \(-0.186326\pi\) | |||||||
\(744\) | 14.2233 | + | 25.5320i | 0.521452 | + | 0.936048i | ||||
\(745\) | 4.60854 | − | 2.66074i | 0.168844 | − | 0.0974820i | ||||
\(746\) | 5.65796 | + | 4.79710i | 0.207153 | + | 0.175634i | ||||
\(747\) | −11.4842 | + | 3.07719i | −0.420186 | + | 0.112588i | ||||
\(748\) | −0.486359 | + | 4.97291i | −0.0177831 | + | 0.181828i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.0501 | + | 6.63935i | 0.513039 | + | 0.242435i | ||||
\(751\) | −22.6093 | + | 39.1605i | −0.825026 | + | 1.42899i | 0.0768741 | + | 0.997041i | \(0.475506\pi\) |
−0.901900 | + | 0.431946i | \(0.857827\pi\) | |||||||
\(752\) | 45.6583 | − | 15.5685i | 1.66499 | − | 0.567725i | ||||
\(753\) | 7.88217 | + | 13.6523i | 0.287242 | + | 0.497518i | ||||
\(754\) | 31.2290 | − | 21.6297i | 1.13729 | − | 0.787707i | ||||
\(755\) | −0.979047 | + | 0.979047i | −0.0356312 | + | 0.0356312i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1353 | − | 10.1353i | −0.368375 | − | 0.368375i | 0.498509 | − | 0.866884i | \(-0.333881\pi\) |
−0.866884 | + | 0.498509i | \(0.833881\pi\) | |||||||
\(758\) | −1.29710 | + | 7.14250i | −0.0471128 | + | 0.259427i | ||||
\(759\) | −4.95030 | + | 2.85806i | −0.179684 | + | 0.103741i | ||||
\(760\) | −0.193891 | − | 0.199932i | −0.00703316 | − | 0.00725229i | ||||
\(761\) | 17.0843 | + | 9.86363i | 0.619306 | + | 0.357556i | 0.776599 | − | 0.629996i | \(-0.216943\pi\) |
−0.157293 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(762\) | −0.568951 | − | 1.58840i | −0.0206109 | − | 0.0575417i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.72339 | − | 9.39788i | −0.279422 | − | 0.340003i | ||||
\(765\) | 0.413374 | + | 1.54273i | 0.0149456 | + | 0.0557776i | ||||
\(766\) | 9.81330 | − | 0.808019i | 0.354569 | − | 0.0291949i | ||||
\(767\) | −13.5451 | − | 23.4607i | −0.489084 | − | 0.847118i | ||||
\(768\) | 2.46724 | − | 19.1447i | 0.0890290 | − | 0.690824i | ||||
\(769\) | 41.2736 | 1.48837 | 0.744183 | − | 0.667976i | \(-0.232839\pi\) | ||||
0.744183 | + | 0.667976i | \(0.232839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.8101 | + | 19.8101i | −0.713444 | + | 0.713444i | ||||
\(772\) | 19.8525 | − | 3.29160i | 0.714508 | − | 0.118467i | ||||
\(773\) | 13.8201 | − | 51.5773i | 0.497074 | − | 1.85511i | −0.0210159 | − | 0.999779i | \(-0.506690\pi\) |
0.518090 | − | 0.855326i | \(-0.326643\pi\) | |||||||
\(774\) | 8.94848 | − | 10.5543i | 0.321647 | − | 0.379368i | ||||
\(775\) | 29.4375 | + | 16.9958i | 1.05743 | + | 0.610506i | ||||
\(776\) | −44.9914 | + | 11.3188i | −1.61510 | + | 0.406320i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.5487 | − | 6.28579i | 0.629152 | − | 0.225356i | ||||
\(779\) | −0.797746 | + | 0.213755i | −0.0285822 | + | 0.00765858i | ||||
\(780\) | 3.80695 | + | 8.38687i | 0.136311 | + | 0.300298i | ||||
\(781\) | 12.8718 | + | 3.44899i | 0.460590 | + | 0.123415i | ||||
\(782\) | 2.28606 | − | 1.58336i | 0.0817494 | − | 0.0566209i | ||||
\(783\) | −39.1812 | −1.40022 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.322740 | 0.0115191 | ||||||||
\(786\) | −11.0485 | + | 7.65238i | −0.394088 | + | 0.272951i | ||||
\(787\) | −0.494375 | − | 0.132467i | −0.0176226 | − | 0.00472196i | 0.249997 | − | 0.968247i | \(-0.419570\pi\) |
−0.267620 | + | 0.963525i | \(0.586237\pi\) | |||||||
\(788\) | 25.9706 | − | 11.7885i | 0.925165 | − | 0.419949i | ||||
\(789\) | 5.26743 | − | 1.41140i | 0.187526 | − | 0.0502473i | ||||
\(790\) | −1.17251 | + | 0.419982i | −0.0417160 | + | 0.0149423i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.50089 | + | 9.19905i | −0.195466 | + | 0.326874i | ||||
\(793\) | 14.9176 | + | 8.61266i | 0.529739 | + | 0.305845i | ||||
\(794\) | −5.70869 | + | 6.73314i | −0.202594 | + | 0.238950i | ||||
\(795\) | 0.466799 | − | 1.74212i | 0.0165556 | − | 0.0617865i | ||||
\(796\) | −3.81447 | − | 23.0061i | −0.135200 | − | 0.815431i | ||||
\(797\) | −35.5605 | + | 35.5605i | −1.25962 | + | 1.25962i | −0.308341 | + | 0.951276i | \(0.599774\pi\) |
−0.951276 | + | 0.308341i | \(0.900226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.2801 | −0.434438 | ||||||||
\(800\) | −8.96468 | − | 20.5826i | −0.316949 | − | 0.727706i | ||||
\(801\) | 3.50586 | + | 6.07232i | 0.123873 | + | 0.214555i | ||||
\(802\) | −22.4123 | + | 1.84541i | −0.791406 | + | 0.0651638i | ||||
\(803\) | 5.38433 | + | 20.0946i | 0.190009 | + | 0.709123i | ||||
\(804\) | −6.53653 | + | 5.37187i | −0.230526 | + | 0.189451i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.3529 | + | 42.8623i | 0.540783 | + | 1.50976i | ||||
\(807\) | −0.416833 | − | 0.240659i | −0.0146732 | − | 0.00847158i | ||||
\(808\) | −0.398989 | + | 26.0115i | −0.0140364 | + | 0.915080i | ||||
\(809\) | −1.17802 | + | 0.680131i | −0.0414170 | + | 0.0239121i | −0.520566 | − | 0.853822i | \(-0.674279\pi\) |
0.479149 | + | 0.877734i | \(0.340946\pi\) | |||||||
\(810\) | 0.508358 | − | 2.79928i | 0.0178619 | − | 0.0983565i | ||||
\(811\) | −12.4370 | − | 12.4370i | −0.436722 | − | 0.436722i | 0.454186 | − | 0.890907i | \(-0.349930\pi\) |
−0.890907 | + | 0.454186i | \(0.849930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.06114 | + | 9.06114i | −0.317788 | + | 0.317788i | ||||
\(814\) | 22.7808 | − | 15.7783i | 0.798466 | − | 0.553030i | ||||
\(815\) | 7.53706 | + | 13.0546i | 0.264012 | + | 0.457282i | ||||
\(816\) | −2.16732 | + | 4.41006i | −0.0758713 | + | 0.154383i | ||||
\(817\) | 0.307119 | − | 0.531945i | 0.0107447 | − | 0.0186104i | ||||
\(818\) | 7.29164 | + | 3.44564i | 0.254946 | + | 0.120474i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 17.2183 | + | 1.68398i | 0.601290 | + | 0.0588072i | ||||
\(821\) | 5.33567 | − | 1.42969i | 0.186216 | − | 0.0498965i | −0.164506 | − | 0.986376i | \(-0.552603\pi\) |
0.350722 | + | 0.936480i | \(0.385936\pi\) | |||||||
\(822\) | −14.3942 | − | 12.2041i | −0.502055 | − | 0.425667i | ||||
\(823\) | 16.5082 | − | 9.53100i | 0.575439 | − | 0.332230i | −0.183880 | − | 0.982949i | \(-0.558866\pi\) |
0.759319 | + | 0.650719i | \(0.225532\pi\) | |||||||
\(824\) | −21.0305 | − | 5.98227i | −0.732631 | − | 0.208402i | ||||
\(825\) | − | 11.7474i | − | 0.408991i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.94521 | + | 3.94521i | 0.137188 | + | 0.137188i | 0.772366 | − | 0.635178i | \(-0.219073\pi\) |
−0.635178 | + | 0.772366i | \(0.719073\pi\) | |||||||
\(828\) | 5.88486 | − | 0.975725i | 0.204513 | − | 0.0339088i | ||||
\(829\) | −25.9036 | − | 6.94085i | −0.899669 | − | 0.241066i | −0.220795 | − | 0.975320i | \(-0.570865\pi\) |
−0.678874 | + | 0.734255i | \(0.737532\pi\) | |||||||
\(830\) | 11.0183 | − | 0.907238i | 0.382451 | − | 0.0314907i | ||||
\(831\) | 6.94562 | − | 12.0302i | 0.240941 | − | 0.417322i | ||||
\(832\) | 8.66994 | − | 28.7932i | 0.300576 | − | 0.998226i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.7989 | − | 27.0850i | 0.443190 | − | 0.937875i | ||||
\(835\) | −3.83713 | − | 14.3203i | −0.132789 | − | 0.495576i | ||||
\(836\) | −0.167292 | + | 0.445407i | −0.00578592 | + | 0.0154047i | ||||
\(837\) | 12.1539 | − | 45.3588i | 0.420099 | − | 1.56783i | ||||
\(838\) | −8.99570 | − | 1.63365i | −0.310751 | − | 0.0564335i | ||||
\(839\) | 5.34140i | 0.184406i | 0.995740 | + | 0.0922028i | \(0.0293908\pi\) | ||||
−0.995740 | + | 0.0922028i | \(0.970609\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 22.0706i | − | 0.761056i | ||||||
\(842\) | 0.150539 | − | 0.828947i | 0.00518793 | − | 0.0285674i | ||||
\(843\) | 5.81908 | − | 21.7171i | 0.200420 | − | 0.747976i | ||||
\(844\) | 7.63898 | + | 16.8290i | 0.262945 | + | 0.579278i | ||||
\(845\) | 0.296598 | + | 1.10692i | 0.0102033 | + | 0.0380791i | ||||
\(846\) | −23.8167 | − | 11.2545i | −0.818837 | − | 0.386939i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.89146 | + | 3.27804i | −0.167973 | + | 0.112568i | ||||
\(849\) | 5.48222 | − | 9.49549i | 0.188149 | − | 0.325884i | ||||
\(850\) | 0.468982 | + | 5.69573i | 0.0160859 | + | 0.195362i | ||||
\(851\) | −14.8971 | − | 3.99165i | −0.510664 | − | 0.136832i | ||||
\(852\) | 10.6576 | + | 7.62614i | 0.365125 | + | 0.261267i | ||||
\(853\) | −1.42841 | − | 1.42841i | −0.0489078 | − | 0.0489078i | 0.682230 | − | 0.731138i | \(-0.261010\pi\) |
−0.731138 | + | 0.682230i | \(0.761010\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.152084i | 0.00520115i | ||||||||
\(856\) | 46.6985 | − | 26.0147i | 1.59612 | − | 0.889164i | ||||
\(857\) | 22.1543 | − | 12.7908i | 0.756778 | − | 0.436926i | −0.0713599 | − | 0.997451i | \(-0.522734\pi\) |
0.828138 | + | 0.560525i | \(0.189401\pi\) | |||||||
\(858\) | 10.1755 | − | 12.0016i | 0.347387 | − | 0.409728i | ||||
\(859\) | −44.0264 | + | 11.7968i | −1.50216 | + | 0.402503i | −0.913823 | − | 0.406113i | \(-0.866884\pi\) |
−0.588337 | + | 0.808616i | \(0.700217\pi\) | |||||||
\(860\) | −9.94066 | + | 8.16946i | −0.338974 | + | 0.278576i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.7512 | − | 26.9839i | 0.434306 | − | 0.919075i | ||||
\(863\) | −19.7223 | + | 34.1601i | −0.671356 | + | 1.16282i | 0.306164 | + | 0.951979i | \(0.400954\pi\) |
−0.977520 | + | 0.210843i | \(0.932379\pi\) | |||||||
\(864\) | −24.2604 | + | 19.3220i | −0.825355 | + | 0.657349i | ||||
\(865\) | −6.27135 | − | 10.8623i | −0.213232 | − | 0.369329i | ||||
\(866\) | −11.2504 | − | 16.2433i | −0.382303 | − | 0.551970i | ||||
\(867\) | −13.6178 | + | 13.6178i | −0.462486 | + | 0.462486i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.50449 | + | 1.50449i | 0.0510364 | + | 0.0510364i | ||||
\(870\) | 12.1831 | + | 2.21250i | 0.413047 | + | 0.0750107i | ||||
\(871\) | −11.4143 | + | 6.59004i | −0.386758 | + | 0.223295i | ||||
\(872\) | 46.2677 | + | 0.709700i | 1.56682 | + | 0.0240335i | ||||
\(873\) | 21.9398 | + | 12.6669i | 0.742548 | + | 0.428710i | ||||
\(874\) | 0.249287 | − | 0.0892924i | 0.00843226 | − | 0.00302036i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.99140 | + | 20.3616i | −0.0672832 | + | 0.687955i | ||||
\(877\) | −2.72833 | − | 10.1823i | −0.0921292 | − | 0.343831i | 0.904439 | − | 0.426602i | \(-0.140290\pi\) |
−0.996569 | + | 0.0827714i | \(0.973623\pi\) | |||||||
\(878\) | 0.628918 | + | 7.63814i | 0.0212250 | + | 0.257775i | ||||
\(879\) | −10.2534 | − | 17.7594i | −0.345839 | − | 0.599011i | ||||
\(880\) | 6.56125 | − | 7.50232i | 0.221180 | − | 0.252903i | ||||
\(881\) | 15.4426 | 0.520274 | 0.260137 | − | 0.965572i | \(-0.416232\pi\) | ||||
0.260137 | + | 0.965572i | \(0.416232\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.0224 | − | 10.0224i | 0.337280 | − | 0.337280i | −0.518063 | − | 0.855343i | \(-0.673347\pi\) |
0.855343 | + | 0.518063i | \(0.173347\pi\) | |||||||
\(884\) | −4.45450 | + | 6.22522i | −0.149821 | + | 0.209377i | ||||
\(885\) | 2.28541 | − | 8.52927i | 0.0768233 | − | 0.286708i | ||||
\(886\) | 6.51839 | + | 5.52662i | 0.218990 | + | 0.185670i | ||||
\(887\) | 37.9027 | + | 21.8831i | 1.27265 | + | 0.734763i | 0.975485 | − | 0.220064i | \(-0.0706267\pi\) |
0.297162 | + | 0.954827i | \(0.403960\pi\) | |||||||
\(888\) | 26.4287 | − | 6.64883i | 0.886888 | − | 0.223120i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.19862 | − | 6.13812i | −0.0736979 | − | 0.205750i | ||||
\(891\) | −4.69474 | + | 1.25795i | −0.157280 | + | 0.0421430i | ||||
\(892\) | −16.4097 | + | 43.6900i | −0.549437 | + | 1.46285i | ||||
\(893\) | −1.12948 | − | 0.302644i | −0.0377967 | − | 0.0101276i | ||||
\(894\) | −5.09044 | − | 7.34959i | −0.170250 | − | 0.245807i | ||||
\(895\) | −0.479024 | −0.0160120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.75703 | −0.292389 | ||||||||
\(898\) | −14.8373 | − | 21.4221i | −0.495127 | − | 0.714865i | ||||
\(899\) | 59.1229 | + | 15.8419i | 1.97186 | + | 0.528358i | ||||
\(900\) | −4.31049 | + | 11.4765i | −0.143683 | + | 0.382549i | ||||
\(901\) | 1.44787 | − | 0.387956i | 0.0482356 | − | 0.0129247i | ||||
\(902\) | −9.96636 | − | 27.8242i | −0.331844 | − | 0.926443i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −55.1750 | + | 13.8807i | −1.83509 | + | 0.461666i | ||||
\(905\) | 19.2356 | + | 11.1057i | 0.639413 | + | 0.369165i | ||||
\(906\) | 1.77427 | + | 1.50431i | 0.0589462 | + | 0.0499775i | ||||
\(907\) | −12.5599 | + | 46.8743i | −0.417045 | + | 1.55643i | 0.363658 | + | 0.931533i | \(0.381528\pi\) |
−0.780703 | + | 0.624902i | \(0.785139\pi\) | |||||||
\(908\) | 18.2134 | − | 25.4535i | 0.604434 | − | 0.844705i | ||||
\(909\) | 10.0449 | − | 10.0449i | 0.333169 | − | 0.333169i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.2525 | −1.16797 | −0.583983 | − | 0.811766i | \(-0.698507\pi\) | ||||
−0.583983 | + | 0.811766i | \(0.698507\pi\) | |||||||
\(912\) | −0.308030 | + | 0.352210i | −0.0101999 | + | 0.0116628i | ||||
\(913\) | −9.44340 | − | 16.3564i | −0.312531 | − | 0.541319i | ||||
\(914\) | 4.17468 | + | 50.7010i | 0.138086 | + | 1.67704i | ||||
\(915\) | 1.45319 | + | 5.42336i | 0.0480409 | + | 0.179291i | ||||
\(916\) | −5.20567 | + | 53.2268i | −0.172000 | + | 1.75866i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7.43278 | − | 2.66236i | 0.245318 | − | 0.0878708i | ||||
\(919\) | −22.1228 | − | 12.7726i | −0.729763 | − | 0.421329i | 0.0885726 | − | 0.996070i | \(-0.471769\pi\) |
−0.818335 | + | 0.574741i | \(0.805103\pi\) | |||||||
\(920\) | −5.54624 | − | 0.0850736i | −0.182854 | − | 0.00280479i | ||||
\(921\) | 26.3510 | − | 15.2138i | 0.868295 | − | 0.501310i | ||||
\(922\) | −1.77867 | − | 0.323012i | −0.0585772 | − | 0.0106378i | ||||
\(923\) | 14.4357 | + | 14.4357i | 0.475156 | + | 0.475156i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4120 | − | 22.4120i | 0.736903 | − | 0.736903i | ||||
\(926\) | 10.1457 | + | 14.6484i | 0.333409 | + | 0.481377i | ||||
\(927\) | 5.96981 | + | 10.3400i | 0.196074 | + | 0.339610i | ||||
\(928\) | −25.1853 | − | 31.6222i | −0.826747 | − | 1.03805i | ||||
\(929\) | 1.98515 | − | 3.43838i | 0.0651306 | − | 0.112810i | −0.831621 | − | 0.555343i | \(-0.812587\pi\) |
0.896752 | + | 0.442534i | \(0.145920\pi\) | |||||||
\(930\) | −6.34051 | + | 13.4177i | −0.207913 | + | 0.439985i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 19.6978 | − | 16.1881i | 0.645222 | − | 0.530258i | ||||
\(933\) | −7.62660 | + | 2.04354i | −0.249684 | + | 0.0669025i | ||||
\(934\) | 7.58095 | − | 8.94139i | 0.248056 | − | 0.292571i | ||||
\(935\) | −2.19724 | + | 1.26858i | −0.0718576 | + | 0.0414870i | ||||
\(936\) | −14.3447 | + | 7.99110i | −0.468871 | + | 0.261197i | ||||
\(937\) | − | 18.3326i | − | 0.598899i | −0.954112 | − | 0.299450i | \(-0.903197\pi\) | ||
0.954112 | − | 0.299450i | \(-0.0968031\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.3565 | + | 16.3565i | 0.533773 | + | 0.533773i | ||||
\(940\) | 19.9202 | + | 14.2540i | 0.649726 | + | 0.464916i | ||||
\(941\) | 28.7932 | + | 7.71512i | 0.938632 | + | 0.251506i | 0.695531 | − | 0.718496i | \(-0.255169\pi\) |
0.243100 | + | 0.970001i | \(0.421836\pi\) | |||||||
\(942\) | −0.0444951 | − | 0.540387i | −0.00144973 | − | 0.0176068i | ||||
\(943\) | −8.22438 | + | 14.2451i | −0.267823 | + | 0.463883i | ||||
\(944\) | −23.9482 | + | 16.0491i | −0.779448 | + | 0.522352i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.8739 | + | 9.39136i | 0.646157 | + | 0.305339i | ||||
\(947\) | 7.28394 | + | 27.1840i | 0.236696 | + | 0.883362i | 0.977377 | + | 0.211505i | \(0.0678365\pi\) |
−0.740681 | + | 0.671857i | \(0.765497\pi\) | |||||||
\(948\) | 0.864858 | + | 1.90532i | 0.0280893 | + | 0.0618819i | ||||
\(949\) | −8.24874 | + | 30.7847i | −0.267765 | + | 0.999314i | ||||
\(950\) | −0.0972366 | + | 0.535434i | −0.00315477 | + | 0.0173718i | ||||
\(951\) | − | 22.7060i | − | 0.736291i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 9.54510i | − | 0.309196i | −0.987977 | − | 0.154598i | \(-0.950592\pi\) | ||
0.987977 | − | 0.154598i | \(-0.0494083\pi\) | |||||||
\(954\) | 3.16365 | + | 0.574530i | 0.102427 | + | 0.0186011i | ||||
\(955\) | 1.59865 | − | 5.96625i | 0.0517311 | − | 0.193063i | ||||
\(956\) | −10.5264 | + | 28.0260i | −0.340448 | + | 0.906427i | ||||
\(957\) | −5.47492 | − | 20.4327i | −0.176979 | − | 0.660495i | ||||
\(958\) | 5.60615 | − | 11.8637i | 0.181126 | − | 0.383298i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8.63470 | − | 4.63812i | 0.278684 | − | 0.149695i | ||||
\(961\) | −21.1794 | + | 36.6839i | −0.683208 | + | 1.18335i | ||||
\(962\) | 42.3103 | − | 3.48380i | 1.36414 | − | 0.112322i | ||||
\(963\) | −28.1957 | − | 7.55502i | −0.908595 | − | 0.243457i | ||||
\(964\) | −39.0874 | + | 6.48079i | −1.25892 | + | 0.208732i | ||||
\(965\) | 7.22535 | + | 7.22535i | 0.232592 | + | 0.232592i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.0255i | 1.73734i | 0.495388 | + | 0.868672i | \(0.335026\pi\) | ||||
−0.495388 | + | 0.868672i | \(0.664974\pi\) | |||||||
\(968\) | 13.5486 | + | 3.85401i | 0.435470 | + | 0.123873i | ||||
\(969\) | 0.103154 | − | 0.0595558i | 0.00331377 | − | 0.00191321i | ||||
\(970\) | −17.9683 | − | 15.2344i | −0.576927 | − | 0.489147i | ||||
\(971\) | 5.75433 | − | 1.54187i | 0.184665 | − | 0.0494809i | −0.165301 | − | 0.986243i | \(-0.552860\pi\) |
0.349966 | + | 0.936762i | \(0.386193\pi\) | |||||||
\(972\) | 27.9827 | + | 2.73675i | 0.897544 | + | 0.0877813i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 49.4665 | + | 23.3752i | 1.58501 | + | 0.748991i | ||||
\(975\) | 8.99842 | − | 15.5857i | 0.288180 | − | 0.499143i | ||||
\(976\) | 8.08502 | − | 16.4514i | 0.258795 | − | 0.526597i | ||||
\(977\) | 14.6499 | + | 25.3743i | 0.468690 | + | 0.811795i | 0.999360 | − | 0.0357835i | \(-0.0113927\pi\) |
−0.530669 | + | 0.847579i | \(0.678059\pi\) | |||||||
\(978\) | 20.8192 | − | 14.4197i | 0.665723 | − | 0.461090i | ||||
\(979\) | −7.87607 | + | 7.87607i | −0.251720 | + | 0.251720i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8673 | − | 17.8673i | −0.570460 | − | 0.570460i | ||||
\(982\) | −10.6525 | + | 58.6578i | −0.339934 | + | 1.87185i | ||||
\(983\) | −13.8442 | + | 7.99296i | −0.441562 | + | 0.254936i | −0.704260 | − | 0.709942i | \(-0.748721\pi\) |
0.262698 | + | 0.964878i | \(0.415388\pi\) | |||||||
\(984\) | 0.445783 | − | 29.0621i | 0.0142110 | − | 0.926466i | ||||
\(985\) | 12.5419 | + | 7.24108i | 0.399619 | + | 0.230720i | ||||
\(986\) | 3.47024 | + | 9.68825i | 0.110515 | + | 0.308537i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.563133 | + | 0.462795i | −0.0179156 | + | 0.0147235i | ||||
\(989\) | −3.16625 | − | 11.8166i | −0.100681 | − | 0.375746i | ||||
\(990\) | −5.42411 | + | 0.446617i | −0.172390 | + | 0.0141944i | ||||
\(991\) | −10.3826 | − | 17.9832i | −0.329814 | − | 0.571255i | 0.652661 | − | 0.757650i | \(-0.273653\pi\) |
−0.982475 | + | 0.186396i | \(0.940319\pi\) | |||||||
\(992\) | 44.4204 | − | 19.3471i | 1.41035 | − | 0.614272i | ||||
\(993\) | 11.8153 | 0.374948 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.37312 | − | 8.37312i | 0.265446 | − | 0.265446i | ||||
\(996\) | −3.03812 | − | 18.3237i | −0.0962664 | − | 0.580609i | ||||
\(997\) | −12.8681 | + | 48.0242i | −0.407535 | + | 1.52094i | 0.391796 | + | 0.920052i | \(0.371854\pi\) |
−0.799331 | + | 0.600890i | \(0.794813\pi\) | |||||||
\(998\) | −10.2251 | + | 12.0600i | −0.323670 | + | 0.381754i | ||||
\(999\) | −37.9205 | − | 21.8934i | −1.19975 | − | 0.692677i |
(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 | 784.2.x.o.373.5 | 48 | ||
7.2 | even | 3 | 784.2.m.k.197.5 | 24 | |||
7.3 | odd | 6 | 112.2.w.c.53.12 | yes | 48 | ||
7.4 | even | 3 | inner | 784.2.x.o.165.12 | 48 | ||
7.5 | odd | 6 | 784.2.m.j.197.5 | 24 | |||
7.6 | odd | 2 | 112.2.w.c.37.5 | ✓ | 48 | ||
16.13 | even | 4 | inner | 784.2.x.o.765.12 | 48 | ||
28.3 | even | 6 | 448.2.ba.c.305.9 | 48 | |||
28.27 | even | 2 | 448.2.ba.c.177.4 | 48 | |||
56.3 | even | 6 | 896.2.ba.e.865.4 | 48 | |||
56.13 | odd | 2 | 896.2.ba.f.737.4 | 48 | |||
56.27 | even | 2 | 896.2.ba.e.737.9 | 48 | |||
56.45 | odd | 6 | 896.2.ba.f.865.9 | 48 | |||
112.3 | even | 12 | 448.2.ba.c.81.4 | 48 | |||
112.13 | odd | 4 | 112.2.w.c.93.12 | yes | 48 | ||
112.27 | even | 4 | 896.2.ba.e.289.4 | 48 | |||
112.45 | odd | 12 | 112.2.w.c.109.5 | yes | 48 | ||
112.59 | even | 12 | 896.2.ba.e.417.9 | 48 | |||
112.61 | odd | 12 | 784.2.m.j.589.5 | 24 | |||
112.69 | odd | 4 | 896.2.ba.f.289.9 | 48 | |||
112.83 | even | 4 | 448.2.ba.c.401.9 | 48 | |||
112.93 | even | 12 | 784.2.m.k.589.5 | 24 | |||
112.101 | odd | 12 | 896.2.ba.f.417.4 | 48 | |||
112.109 | even | 12 | inner | 784.2.x.o.557.5 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.5 | ✓ | 48 | 7.6 | odd | 2 | ||
112.2.w.c.53.12 | yes | 48 | 7.3 | odd | 6 | ||
112.2.w.c.93.12 | yes | 48 | 112.13 | odd | 4 | ||
112.2.w.c.109.5 | yes | 48 | 112.45 | odd | 12 | ||
448.2.ba.c.81.4 | 48 | 112.3 | even | 12 | |||
448.2.ba.c.177.4 | 48 | 28.27 | even | 2 | |||
448.2.ba.c.305.9 | 48 | 28.3 | even | 6 | |||
448.2.ba.c.401.9 | 48 | 112.83 | even | 4 | |||
784.2.m.j.197.5 | 24 | 7.5 | odd | 6 | |||
784.2.m.j.589.5 | 24 | 112.61 | odd | 12 | |||
784.2.m.k.197.5 | 24 | 7.2 | even | 3 | |||
784.2.m.k.589.5 | 24 | 112.93 | even | 12 | |||
784.2.x.o.165.12 | 48 | 7.4 | even | 3 | inner | ||
784.2.x.o.373.5 | 48 | 1.1 | even | 1 | trivial | ||
784.2.x.o.557.5 | 48 | 112.109 | even | 12 | inner | ||
784.2.x.o.765.12 | 48 | 16.13 | even | 4 | inner | ||
896.2.ba.e.289.4 | 48 | 112.27 | even | 4 | |||
896.2.ba.e.417.9 | 48 | 112.59 | even | 12 | |||
896.2.ba.e.737.9 | 48 | 56.27 | even | 2 | |||
896.2.ba.e.865.4 | 48 | 56.3 | even | 6 | |||
896.2.ba.f.289.9 | 48 | 112.69 | odd | 4 | |||
896.2.ba.f.417.4 | 48 | 112.101 | odd | 12 | |||
896.2.ba.f.737.4 | 48 | 56.13 | odd | 2 | |||
896.2.ba.f.865.9 | 48 | 56.45 | odd | 6 |