Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(81,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.ba (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: | \(3.57729801055\) |
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 | 81.4 | ||
Character | \(\chi\) | \(=\) | 448.81 |
Dual form | 448.2.ba.c.177.4 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.16533 | + | 0.312249i | −0.672803 | + | 0.180277i | −0.579017 | − | 0.815315i | \(-0.696564\pi\) |
−0.0937859 | + | 0.995592i | \(0.529897\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.980942 | + | 0.262843i | 0.438691 | + | 0.117547i | 0.471403 | − | 0.881918i | \(-0.343748\pi\) |
−0.0327122 | + | 0.999465i | \(0.510414\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60251 | + | 0.476386i | −0.983656 | + | 0.180057i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.33758 | + | 0.772254i | −0.445861 | + | 0.257418i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.635020 | − | 2.36993i | −0.191466 | − | 0.714560i | −0.993153 | − | 0.116817i | \(-0.962731\pi\) |
0.801688 | − | 0.597743i | \(-0.203936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.65786 | − | 2.65786i | −0.737157 | − | 0.737157i | 0.234870 | − | 0.972027i | \(-0.424534\pi\) |
−0.972027 | + | 0.234870i | \(0.924534\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.22519 | −0.316343 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.509128 | + | 0.881836i | −0.123482 | + | 0.213877i | −0.921138 | − | 0.389235i | \(-0.872739\pi\) |
0.797657 | + | 0.603112i | \(0.206073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0250951 | − | 0.0936561i | 0.00575721 | − | 0.0214862i | −0.962987 | − | 0.269546i | \(-0.913126\pi\) |
0.968745 | + | 0.248060i | \(0.0797930\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.88403 | − | 1.36778i | 0.629347 | − | 0.298474i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.67238 | + | 0.965551i | −0.348716 | + | 0.201331i | −0.664120 | − | 0.747626i | \(-0.731193\pi\) |
0.315404 | + | 0.948958i | \(0.397860\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.43697 | − | 1.98433i | −0.687393 | − | 0.396867i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.87683 | − | 3.87683i | 0.746096 | − | 0.746096i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.05325 | − | 5.05325i | −0.938365 | − | 0.938365i | 0.0598432 | − | 0.998208i | \(-0.480940\pi\) |
−0.998208 | + | 0.0598432i | \(0.980940\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.28249 | + | 7.41749i | −0.769158 | + | 1.33222i | 0.168862 | + | 0.985640i | \(0.445991\pi\) |
−0.938020 | + | 0.346581i | \(0.887343\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.48001 | + | 2.56346i | 0.257637 | + | 0.446241i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.67813 | − | 0.216743i | −0.452686 | − | 0.0366363i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.71428 | − | 2.06704i | −1.26822 | − | 0.339818i | −0.438871 | − | 0.898550i | \(-0.644622\pi\) |
−0.829349 | + | 0.558732i | \(0.811288\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.92719 | + | 2.26737i | 0.628854 | + | 0.363069i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | \(-0.589534\pi\) |
0.960701 | + | 0.277584i | \(0.0895338\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.51507 | + | 0.405963i | −0.225854 | + | 0.0605174i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.02995 | − | 10.4442i | −0.879559 | − | 1.52344i | −0.851826 | − | 0.523825i | \(-0.824505\pi\) |
−0.0277324 | − | 0.999615i | \(-0.508829\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.54611 | − | 2.47960i | 0.935159 | − | 0.354229i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.317949 | − | 1.18660i | 0.0445218 | − | 0.166158i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.381000 | + | 1.42191i | 0.0523344 | + | 0.195315i | 0.987144 | − | 0.159836i | \(-0.0510964\pi\) |
−0.934809 | + | 0.355150i | \(0.884430\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.49167i | − | 0.335977i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.116976i | 0.0154939i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.86535 | + | 6.96158i | 0.242848 | + | 0.906320i | 0.974453 | + | 0.224592i | \(0.0721048\pi\) |
−0.731605 | + | 0.681729i | \(0.761229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.18609 | + | 4.42654i | −0.151863 | + | 0.566760i | 0.847491 | + | 0.530810i | \(0.178112\pi\) |
−0.999354 | + | 0.0359500i | \(0.988554\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.11318 | − | 2.64701i | 0.392224 | − | 0.333491i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.90861 | − | 3.30580i | −0.236734 | − | 0.410034i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.38700 | − | 0.907543i | 0.413787 | − | 0.110874i | −0.0459185 | − | 0.998945i | \(-0.514621\pi\) |
0.459706 | + | 0.888071i | \(0.347955\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 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 | \(0.895548\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.34303 | + | 4.23950i | 0.859436 | + | 0.496196i | 0.863824 | − | 0.503795i | \(-0.168063\pi\) |
−0.00438712 | + | 0.999990i | \(0.501396\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.62480 | + | 1.23921i | 0.534026 | + | 0.143092i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.78165 | + | 5.86524i | 0.316998 | + | 0.668406i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.433595 | + | 0.751008i | 0.0487832 | + | 0.0844950i | 0.889386 | − | 0.457157i | \(-0.151132\pi\) |
−0.840603 | + | 0.541652i | \(0.817799\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.990483 | + | 1.71557i | −0.110054 | + | 0.190619i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.44318 | + | 5.44318i | 0.597466 | + | 0.597466i | 0.939638 | − | 0.342171i | \(-0.111162\pi\) |
−0.342171 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.731209 | + | 0.731209i | −0.0793108 | + | 0.0793108i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.46657 | + | 4.31083i | 0.800500 | + | 0.462169i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.93155 | − | 2.26988i | 0.416744 | − | 0.240607i | −0.276939 | − | 0.960887i | \(-0.589320\pi\) |
0.693683 | + | 0.720280i | \(0.255987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.18327 | + | 5.65093i | 0.857840 | + | 0.592379i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.67441 | − | 9.98102i | 0.277323 | − | 1.03498i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0492336 | − | 0.0852752i | 0.00505126 | − | 0.00874905i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.4025 | 1.66542 | 0.832712 | − | 0.553706i | \(-0.186787\pi\) | ||||
0.832712 | + | 0.553706i | \(0.186787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.67958 | + | 2.67958i | 0.269308 | + | 0.269308i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.38049 | + | 8.88412i | 0.236868 | + | 0.884003i | 0.977298 | + | 0.211870i | \(0.0679552\pi\) |
−0.740430 | + | 0.672134i | \(0.765378\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.69469 | + | 3.86518i | −0.659647 | + | 0.380848i | −0.792143 | − | 0.610336i | \(-0.791034\pi\) |
0.132495 | + | 0.991184i | \(0.457701\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.18858 | − | 0.583665i | 0.311173 | − | 0.0569599i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.2555 | − | 4.89154i | −1.76482 | − | 0.472883i | −0.777137 | − | 0.629332i | \(-0.783329\pi\) |
−0.987686 | + | 0.156449i | \(0.949995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8026 | − | 4.23429i | 1.51361 | − | 0.405571i | 0.595980 | − | 0.802999i | \(-0.296764\pi\) |
0.917633 | + | 0.397428i | \(0.130097\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 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 | 0 | ||||||||
\(115\) | −1.89430 | + | 0.507576i | −0.176644 | + | 0.0473317i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.60765 | + | 1.50257i | 0.518428 | + | 0.138912i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.904916 | − | 2.53753i | 0.0829535 | − | 0.232615i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.31298 | − | 2.49010i | 0.392089 | − | 0.226373i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.65968 | − | 9.92606i | −0.239815 | − | 0.895003i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.44039 | − | 6.44039i | −0.576046 | − | 0.576046i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.988901 | 0.0877508 | 0.0438754 | − | 0.999037i | \(-0.486030\pi\) | ||||
0.0438754 | + | 0.999037i | \(0.486030\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.82137 | + | 6.61880i | −0.336453 | + | 0.582753i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.03878 | − | 7.60883i | 0.178129 | − | 0.664786i | −0.817869 | − | 0.575405i | \(-0.804844\pi\) |
0.995998 | − | 0.0893811i | \(-0.0284889\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0206937 | + | 0.255696i | −0.00179437 | + | 0.0221716i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.82194 | − | 2.78395i | 0.415007 | − | 0.239604i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.57893 | − | 5.53040i | −0.818383 | − | 0.472494i | 0.0314753 | − | 0.999505i | \(-0.489979\pi\) |
−0.849859 | + | 0.527011i | \(0.823313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4154 | + | 12.4154i | −1.05306 | + | 1.05306i | −0.0545473 | + | 0.998511i | \(0.517372\pi\) |
−0.998511 | + | 0.0545473i | \(0.982628\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.2881 | + | 10.2881i | 0.866411 | + | 0.866411i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.61114 | + | 7.98672i | −0.385603 | + | 0.667883i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.62873 | − | 6.28515i | −0.301350 | − | 0.521954i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.85412 | + | 4.93357i | −0.565318 | + | 0.406914i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.06147 | − | 1.35622i | −0.414652 | − | 0.111106i | 0.0454610 | − | 0.998966i | \(-0.485524\pi\) |
−0.460113 | + | 0.887861i | \(0.652191\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.18073 | − | 0.681693i | −0.0960862 | − | 0.0554754i | 0.451187 | − | 0.892429i | \(-0.351001\pi\) |
−0.547273 | + | 0.836954i | \(0.684334\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.57271i | − | 0.127146i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.15051 | + | 6.15051i | −0.494021 | + | 0.494021i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.306970 | − | 0.0822524i | 0.0244989 | − | 0.00656446i | −0.246549 | − | 0.969130i | \(-0.579297\pi\) |
0.271048 | + | 0.962566i | \(0.412630\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.887981 | − | 1.53803i | −0.0704215 | − | 0.121974i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.89242 | − | 3.30955i | 0.306765 | − | 0.260829i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.84175 | − | 14.3376i | 0.300909 | − | 1.12301i | −0.635501 | − | 0.772100i | \(-0.719206\pi\) |
0.936410 | − | 0.350907i | \(-0.114127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.778022 | + | 2.90362i | 0.0605689 | + | 0.226046i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 14.5986i | − | 1.12967i | −0.825204 | − | 0.564836i | \(-0.808940\pi\) | ||
0.825204 | − | 0.564836i | \(-0.191060\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.12842i | 0.0868018i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0387596 | + | 0.144653i | 0.00296402 | + | 0.0110619i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.19660 | + | 11.9299i | −0.243033 | + | 0.907011i | 0.731329 | + | 0.682025i | \(0.238900\pi\) |
−0.974362 | + | 0.224986i | \(0.927766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.89005 | + | 3.52692i | 0.747617 | + | 0.266610i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.34749 | − | 7.53008i | −0.326777 | − | 0.565995i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.455619 | + | 0.122083i | −0.0340545 | + | 0.00912489i | −0.275806 | − | 0.961213i | \(-0.588945\pi\) |
0.241752 | + | 0.970338i | \(0.422278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4654 | − | 15.4654i | 1.14953 | − | 1.14953i | 0.162887 | − | 0.986645i | \(-0.447919\pi\) |
0.986645 | − | 0.162887i | \(-0.0520807\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.52873i | − | 0.408696i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.02396 | − | 4.05528i | −0.516412 | − | 0.298150i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.41319 | + | 0.646613i | 0.176470 | + | 0.0472850i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.24262 | + | 11.9364i | −0.599562 | + | 0.868242i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.04108 | + | 5.26731i | 0.220045 | + | 0.381129i | 0.954821 | − | 0.297180i | \(-0.0960463\pi\) |
−0.734776 | + | 0.678309i | \(0.762713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.03089 | + | 8.71375i | −0.362131 | + | 0.627229i | −0.988311 | − | 0.152449i | \(-0.951284\pi\) |
0.626180 | + | 0.779678i | \(0.284617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.25639 | + | 3.25639i | 0.233195 | + | 0.233195i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0837 | + | 10.0837i | −0.718432 | + | 0.718432i | −0.968284 | − | 0.249852i | \(-0.919618\pi\) |
0.249852 | + | 0.968284i | \(0.419618\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0980 | − | 5.83005i | −0.715825 | − | 0.413282i | 0.0973893 | − | 0.995246i | \(-0.468951\pi\) |
−0.813214 | + | 0.581965i | \(0.802284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.66359 | + | 2.11517i | −0.258409 | + | 0.149193i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5584 | + | 10.7438i | 1.09199 | + | 0.754069i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.23885 | + | 8.35549i | −0.156368 | + | 0.583572i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.49130 | − | 2.58301i | 0.103653 | − | 0.179532i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.237894 | −0.0164555 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.53423 | − | 6.53423i | −0.449835 | − | 0.449835i | 0.445465 | − | 0.895300i | \(-0.353038\pi\) |
−0.895300 | + | 0.445465i | \(0.853038\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.69592 | − | 6.32927i | −0.116203 | − | 0.433674i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.57153 | − | 3.21672i | 0.379975 | − | 0.219379i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.61163 | − | 21.3442i | 0.516711 | − | 1.44894i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.88082 | − | 2.64756i | −0.667684 | − | 0.178905i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.69698 | − | 0.990604i | 0.248686 | − | 0.0666352i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 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 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.1161 | + | 4.05036i | −1.00329 | + | 0.268832i | −0.722824 | − | 0.691032i | \(-0.757156\pi\) |
−0.280468 | + | 0.959863i | \(0.590490\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.8292 | − | 6.92092i | −1.70684 | − | 0.457347i | −0.732196 | − | 0.681094i | \(-0.761504\pi\) |
−0.974647 | + | 0.223747i | \(0.928171\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.07295 | − | 5.96637i | −0.333775 | − | 0.392558i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.0402 | + | 6.37405i | −0.723267 | + | 0.417578i | −0.815954 | − | 0.578117i | \(-0.803788\pi\) |
0.0926872 | + | 0.995695i | \(0.470454\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.16986 | − | 11.8301i | −0.206779 | − | 0.771708i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.739782 | − | 0.739782i | −0.0480540 | − | 0.0480540i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.9688 | −0.968253 | −0.484127 | − | 0.874998i | \(-0.660863\pi\) | ||||
−0.484127 | + | 0.874998i | \(0.660863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.90526 | + | 17.1564i | −0.638054 | + | 1.10514i | 0.347805 | + | 0.937567i | \(0.386927\pi\) |
−0.985859 | + | 0.167575i | \(0.946406\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.63850 | + | 13.5791i | −0.233410 | + | 0.871098i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.07310 | − | 0.711747i | 0.451884 | − | 0.0454718i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.315624 | + | 0.182226i | −0.0200827 | + | 0.0115947i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.04272 | − | 4.64346i | −0.509686 | − | 0.294268i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.23966 | + | 9.23966i | −0.583202 | + | 0.583202i | −0.935782 | − | 0.352580i | \(-0.885305\pi\) |
0.352580 | + | 0.935782i | \(0.385305\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.35028 | + | 3.35028i | 0.210630 | + | 0.210630i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.623780 | − | 1.08042i | 0.0390626 | − | 0.0676584i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.6109 | − | 20.1107i | −0.724271 | − | 1.25447i | −0.959273 | − | 0.282479i | \(-0.908843\pi\) |
0.235003 | − | 0.971995i | \(-0.424490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.0612 | + | 1.70450i | 1.30868 | + | 0.105913i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.6615 | + | 2.85675i | 0.659933 | + | 0.176828i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.91454 | + | 2.26006i | 0.241381 | + | 0.139361i | 0.615811 | − | 0.787894i | \(-0.288828\pi\) |
−0.374430 | + | 0.927255i | \(0.622162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.49496i | 0.0918345i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.87278 | + | 3.87278i | −0.237011 | + | 0.237011i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.385363 | + | 0.103258i | −0.0234960 | + | 0.00629574i | −0.270548 | − | 0.962707i | \(-0.587205\pi\) |
0.247052 | + | 0.969002i | \(0.420538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.31084 | + | 9.19864i | 0.322611 | + | 0.558778i | 0.981026 | − | 0.193877i | \(-0.0621063\pi\) |
−0.658415 | + | 0.752655i | \(0.728773\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.3007 | − | 4.02998i | −0.683949 | − | 0.243906i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.52018 | + | 9.40545i | −0.151973 | + | 0.567170i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.98011 | − | 11.1219i | −0.179058 | − | 0.668252i | −0.995825 | − | 0.0912848i | \(-0.970903\pi\) |
0.816767 | − | 0.576967i | \(-0.195764\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 13.2287i | − | 0.791981i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.6360i | − | 1.11173i | −0.831272 | − | 0.555866i | \(-0.812387\pi\) | ||
0.831272 | − | 0.555866i | \(-0.187613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.35222 | − | 8.77861i | −0.139825 | − | 0.521834i | −0.999931 | − | 0.0117192i | \(-0.996270\pi\) |
0.860106 | − | 0.510115i | \(-0.170397\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0307463 | + | 0.114747i | −0.00182125 | + | 0.00679701i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.05777 | − | 22.1677i | −0.239523 | − | 1.30852i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.98158 | + | 13.8245i | 0.469505 | + | 0.813206i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.1143 | + | 5.12167i | −1.12050 | + | 0.300238i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.0193 | + | 12.0193i | −0.702174 | + | 0.702174i | −0.964877 | − | 0.262703i | \(-0.915386\pi\) |
0.262703 | + | 0.964877i | \(0.415386\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.31920i | 0.426140i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.6497 | − | 6.72594i | −0.675982 | − | 0.390278i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.01125 | + | 1.87866i | 0.405471 | + | 0.108646i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.52396 | + | 13.7919i | −0.548952 | + | 0.794952i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.54812 | − | 9.60962i | −0.318731 | − | 0.552058i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.32697 | + | 4.03043i | −0.133242 | + | 0.230781i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.8339 | − | 17.8339i | −1.01784 | − | 1.01784i | −0.999838 | − | 0.0179975i | \(-0.994271\pi\) |
−0.0179975 | − | 0.999838i | \(-0.505729\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.59462 | − | 6.59462i | 0.375155 | − | 0.375155i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.66778 | + | 3.27229i | 0.321390 | + | 0.185555i | 0.652012 | − | 0.758209i | \(-0.273925\pi\) |
−0.330622 | + | 0.943763i | \(0.607258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.6047 | − | 9.58671i | 0.938551 | − | 0.541873i | 0.0490453 | − | 0.998797i | \(-0.484382\pi\) |
0.889506 | + | 0.456924i | \(0.151049\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.74960 | − | 1.77828i | 0.211266 | − | 0.100195i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.87115 | − | 18.1794i | 0.273591 | − | 1.02106i | −0.683189 | − | 0.730242i | \(-0.739407\pi\) |
0.956780 | − | 0.290814i | \(-0.0939260\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.76691 | + | 15.1847i | −0.490853 | + | 0.850182i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.8010 | 1.27263 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0698127 | + | 0.0698127i | 0.00388448 | + | 0.00388448i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.86089 | + | 14.4090i | 0.214164 | + | 0.799270i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.0931 | + | 9.86868i | −0.945248 | + | 0.545739i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.6685 | + | 24.3085i | 1.13949 | + | 1.34017i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.45985 | + | 2.53476i | 0.519960 | + | 0.139323i | 0.509248 | − | 0.860620i | \(-0.329924\pi\) |
0.0107120 | + | 0.999943i | \(0.496590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.9148 | − | 3.19255i | 0.652926 | − | 0.174951i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.56099 | 0.194558 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.91600 | 0.267792 | 0.133896 | − | 0.990995i | \(-0.457251\pi\) | ||||
0.133896 | + | 0.990995i | \(0.457251\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.4408 | − | 6.28094i | 1.27313 | − | 0.341134i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.2984 | + | 5.43893i | 1.09922 | + | 0.294535i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8551 | + | 9.57166i | −0.856093 | + | 0.516821i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.04899 | − | 1.18299i | 0.110314 | − | 0.0636898i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.42076 | − | 9.03438i | −0.129953 | − | 0.484991i | 0.870015 | − | 0.493026i | \(-0.164109\pi\) |
−0.999968 | + | 0.00803463i | \(0.997442\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2061 | − | 17.2061i | −0.921021 | − | 0.921021i | 0.0760810 | − | 0.997102i | \(-0.475759\pi\) |
−0.997102 | + | 0.0760810i | \(0.975759\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.6081 | −1.09998 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.08472 | − | 7.07494i | 0.217408 | − | 0.376561i | −0.736607 | − | 0.676321i | \(-0.763573\pi\) |
0.954015 | + | 0.299760i | \(0.0969066\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.42758 | + | 5.32780i | −0.0757681 | + | 0.282771i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.262185 | + | 3.23961i | −0.0138763 | + | 0.171459i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0193 | − | 5.78465i | 0.528799 | − | 0.305302i | −0.211728 | − | 0.977329i | \(-0.567909\pi\) |
0.740527 | + | 0.672027i | \(0.234576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4463 | + | 9.49530i | 0.865597 | + | 0.499753i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.24851 | + | 4.24851i | −0.222989 | + | 0.222989i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.08876 | + | 6.08876i | 0.318700 | + | 0.318700i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.25356 | − | 7.36738i | 0.222034 | − | 0.384574i | −0.733392 | − | 0.679807i | \(-0.762064\pi\) |
0.955425 | + | 0.295232i | \(0.0953971\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.57792 | − | 11.3933i | −0.342433 | − | 0.593111i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.66894 | − | 3.51904i | −0.0866469 | − | 0.182699i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.06649 | − | 1.35756i | −0.262333 | − | 0.0702919i | 0.125255 | − | 0.992125i | \(-0.460025\pi\) |
−0.387588 | + | 0.921833i | \(0.626692\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.51618 | + | 5.49417i | 0.491414 | + | 0.283718i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.8616i | 1.38344i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.62966 | − | 3.62966i | 0.186443 | − | 0.186443i | −0.607713 | − | 0.794156i | \(-0.707913\pi\) |
0.794156 | + | 0.607713i | \(0.207913\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.15239 | + | 0.308783i | −0.0590390 | + | 0.0158194i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.48127 | − | 6.02973i | −0.177884 | − | 0.308105i | 0.763271 | − | 0.646078i | \(-0.223592\pi\) |
−0.941156 | + | 0.337973i | \(0.890259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.18700 | + | 6.48460i | 0.0604950 | + | 0.330486i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.53239 | + | 9.45101i | −0.128729 | + | 0.480422i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.41145 | − | 12.7317i | −0.172967 | − | 0.645523i | −0.996889 | − | 0.0788190i | \(-0.974885\pi\) |
0.823922 | − | 0.566704i | \(-0.191782\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.96636i | − | 0.0994429i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.50339i | 0.479383i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.227934 | + | 0.850663i | 0.0114686 | + | 0.0428015i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.61554 | − | 6.02928i | 0.0810817 | − | 0.302601i | −0.913462 | − | 0.406925i | \(-0.866601\pi\) |
0.994543 | + | 0.104324i | \(0.0332678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0557258 | − | 0.304431i | −0.00278978 | − | 0.0152406i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.95077 | + | 13.7711i | 0.397042 | + | 0.687697i | 0.993360 | − | 0.115051i | \(-0.0367033\pi\) |
−0.596317 | + | 0.802749i | \(0.703370\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.0969 | − | 8.33239i | 1.54905 | − | 0.415066i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.42253 | + | 1.42253i | −0.0706861 | + | 0.0706861i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.5949i | 0.971282i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.93864 | + | 2.85133i | 0.244200 | + | 0.140989i | 0.617106 | − | 0.786880i | \(-0.288305\pi\) |
−0.372906 | + | 0.927869i | \(0.621638\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.8895 | + | 3.45372i | 0.635791 | + | 0.170360i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.17099 | − | 17.2289i | −0.402068 | − | 0.847781i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.90874 | + | 6.77014i | 0.191873 | + | 0.332333i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5913 | − | 18.3447i | 0.518659 | − | 0.898343i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.57142 | + | 4.57142i | 0.223328 | + | 0.223328i | 0.809898 | − | 0.586570i | \(-0.199522\pi\) |
−0.586570 | + | 0.809898i | \(0.699522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.421252 | − | 0.421252i | 0.0205306 | − | 0.0205306i | −0.696767 | − | 0.717298i | \(-0.745379\pi\) |
0.717298 | + | 0.696767i | \(0.245379\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.1311 | + | 9.31331i | 0.784322 | + | 0.452829i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.49971 | − | 2.02056i | 0.169761 | − | 0.0980115i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.978062 | − | 12.0852i | 0.0473317 | − | 0.584841i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.87964 | − | 10.7470i | 0.139031 | − | 0.518869i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5518 | + | 18.2762i | −0.508262 | + | 0.880336i | 0.491692 | + | 0.870769i | \(0.336379\pi\) |
−0.999954 | + | 0.00956658i | \(0.996955\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9717 | −0.671436 | −0.335718 | − | 0.941962i | \(-0.608979\pi\) | ||||
−0.335718 | + | 0.941962i | \(0.608979\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.19120 | + | 6.19120i | 0.296845 | + | 0.296845i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0484611 | + | 0.180859i | 0.00231821 | + | 0.00865168i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.69322 | + | 2.70963i | −0.223995 | + | 0.129324i | −0.607799 | − | 0.794091i | \(-0.707947\pi\) |
0.383804 | + | 0.923415i | \(0.374614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.84109 | + | 8.37194i | −0.325766 | + | 0.398664i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.83698 | + | 1.56401i | 0.277323 | + | 0.0743085i | 0.394800 | − | 0.918767i | \(-0.370814\pi\) |
−0.117477 | + | 0.993076i | \(0.537481\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.45325 | − | 1.19324i | 0.211104 | − | 0.0565652i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.32175 | 0.299009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.4262 | 0.869587 | 0.434794 | − | 0.900530i | \(-0.356821\pi\) | ||||
0.434794 | + | 0.900530i | \(0.356821\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.1866 | − | 5.40898i | 0.950550 | − | 0.254699i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.58879 | + | 0.425716i | 0.0746480 | + | 0.0200019i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.54201 | + | 7.69415i | 0.306694 | + | 0.360707i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.1530 | + | 17.9862i | −1.45728 | + | 0.841358i | −0.998877 | − | 0.0473884i | \(-0.984910\pi\) |
−0.458399 | + | 0.888747i | \(0.651577\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.44492 | + | 5.39253i | 0.0674433 | + | 0.251702i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.903879 | − | 0.903879i | −0.0420978 | − | 0.0420978i | 0.685745 | − | 0.727842i | \(-0.259477\pi\) |
−0.727842 | + | 0.685745i | \(0.759477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5999 | 0.585565 | 0.292782 | − | 0.956179i | \(-0.405419\pi\) | ||||
0.292782 | + | 0.956179i | \(0.405419\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.24687 | − | 9.08785i | 0.243318 | − | 0.421439i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.14538 | − | 8.00668i | 0.0992765 | − | 0.370505i | −0.898357 | − | 0.439267i | \(-0.855238\pi\) |
0.997633 | + | 0.0687620i | \(0.0219049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.38235 | + | 3.97541i | −0.387061 | + | 0.183567i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.332038 | + | 0.191702i | −0.0152995 | + | 0.00883318i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.4606 | − | 7.77151i | −0.618921 | − | 0.357334i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.272096 | + | 0.272096i | −0.0124846 | + | 0.0124846i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.60770 | − | 1.60770i | −0.0736114 | − | 0.0736114i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.63918 | − | 8.03529i | 0.211969 | − | 0.367142i | −0.740361 | − | 0.672209i | \(-0.765346\pi\) |
0.952331 | + | 0.305067i | \(0.0986789\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.0096 | + | 25.9974i | 0.684378 | + | 1.18538i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.50254 | + | 5.07212i | −0.159371 | + | 0.230790i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0899 | + | 4.31128i | 0.730606 | + | 0.195765i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.5037 | + | 19.3434i | 1.51820 | + | 0.876533i | 0.999771 | + | 0.0214118i | \(0.00681612\pi\) |
0.518429 | + | 0.855121i | \(0.326517\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.9076i | 0.809810i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.8086 | − | 29.8086i | 1.34524 | − | 1.34524i | 0.454494 | − | 0.890750i | \(-0.349820\pi\) |
0.890750 | − | 0.454494i | \(-0.150180\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.02889 | − | 1.88338i | 0.316565 | − | 0.0848234i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.92420 | + | 3.33282i | 0.0864865 | + | 0.149799i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.58740 | − | 14.1350i | −0.116061 | − | 0.634044i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.89367 | − | 10.7993i | 0.129538 | − | 0.483444i | −0.870422 | − | 0.492306i | \(-0.836154\pi\) |
0.999961 | + | 0.00886191i | \(0.00282087\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.55839 | + | 17.0121i | 0.203654 | + | 0.760046i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.1532i | 0.809409i | 0.914448 | + | 0.404704i | \(0.132626\pi\) | ||||
−0.914448 | + | 0.404704i | \(0.867374\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.34050i | 0.415647i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.352349 | − | 1.31498i | −0.0156484 | − | 0.0584005i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.530258 | − | 1.97895i | 0.0235033 | − | 0.0877154i | −0.953178 | − | 0.302410i | \(-0.902209\pi\) |
0.976681 | + | 0.214694i | \(0.0688756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.1299 | − | 7.53522i | −0.934733 | − | 0.333338i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.265799 | − | 0.460378i | −0.0117353 | − | 0.0203262i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.58304 | + | 2.03187i | −0.334149 | + | 0.0895348i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.9228 | + | 20.9228i | −0.920183 | + | 0.920183i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 14.9004i | − | 0.654053i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.51905 | − | 1.45437i | −0.110361 | − | 0.0637172i | 0.443803 | − | 0.896124i | \(-0.353629\pi\) |
−0.554165 | + | 0.832407i | \(0.686962\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0023 | + | 4.28781i | 0.699732 | + | 0.187493i | 0.591111 | − | 0.806590i | \(-0.298690\pi\) |
0.108622 | + | 0.994083i | \(0.465356\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.6264 | − | 1.02187i | −0.551063 | − | 0.0445980i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.36067 | − | 7.55290i | −0.189954 | − | 0.329010i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.63542 | + | 16.6890i | −0.418931 | + | 0.725611i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.87117 | − | 7.87117i | −0.341580 | − | 0.341580i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.6392 | − | 22.6392i | 0.980611 | − | 0.980611i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.6219 | − | 9.59663i | −0.718625 | − | 0.414899i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.492826 | − | 0.284533i | 0.0212670 | − | 0.0122785i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.0334 | − | 13.9392i | −0.432168 | − | 0.600404i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.87978 | − | 7.01543i | 0.0808180 | − | 0.301617i | −0.913671 | − | 0.406453i | \(-0.866765\pi\) |
0.994489 | + | 0.104837i | \(0.0334320\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.1932 | + | 22.8513i | −0.566174 | + | 0.980643i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.6144 | 0.711682 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.2712 | − | 18.2712i | −0.781218 | − | 0.781218i | 0.198818 | − | 0.980036i | \(-0.436290\pi\) |
−0.980036 | + | 0.198818i | \(0.936290\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.83192 | − | 6.83683i | −0.0781846 | − | 0.291789i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.600079 | + | 0.346456i | −0.0255642 | + | 0.0147595i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.48621 | − | 1.74795i | −0.0631999 | − | 0.0743303i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.45148 | + | 2.53252i | 0.401193 | + | 0.107499i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.78640 | + | 1.28251i | −0.202806 | + | 0.0543418i | −0.358792 | − | 0.933417i | \(-0.616811\pi\) |
0.155986 | + | 0.987759i | \(0.450145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.8117 | −1.00713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.01407 | −0.127254 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.4858 | + | 6.29301i | −0.989809 | + | 0.265219i | −0.717170 | − | 0.696898i | \(-0.754563\pi\) |
−0.272639 | + | 0.962116i | \(0.587896\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.7318 | − | 5.28712i | −0.830123 | − | 0.222431i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.76047 | − | 4.93663i | 0.0739327 | − | 0.207319i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.33865 | − | 1.35022i | 0.0980412 | − | 0.0566041i | −0.450178 | − | 0.892939i | \(-0.648639\pi\) |
0.548219 | + | 0.836335i | \(0.315306\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.43500 | + | 12.8196i | 0.143750 | + | 0.536484i | 0.999808 | + | 0.0196030i | \(0.00624022\pi\) |
−0.856058 | + | 0.516881i | \(0.827093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.18857 | − | 5.18857i | −0.216756 | − | 0.216756i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.66390 | 0.319607 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.4461 | − | 21.5572i | 0.518137 | − | 0.897439i | −0.481641 | − | 0.876369i | \(-0.659959\pi\) |
0.999778 | − | 0.0210709i | \(-0.00670757\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.14178 | − | 11.7253i | 0.130568 | − | 0.487286i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.7590 | − | 11.5729i | −0.695279 | − | 0.480123i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.12788 | − | 1.80589i | 0.129544 | − | 0.0747921i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.10584 | + | 2.94786i | 0.211101 | + | 0.121879i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.9315 | + | 23.9315i | −0.987758 | + | 0.987758i | −0.999926 | − | 0.0121684i | \(-0.996127\pi\) |
0.0121684 | + | 0.999926i | \(0.496127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.587224 | + | 0.587224i | 0.0241961 | + | 0.0241961i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.60218 | − | 14.8994i | 0.353846 | − | 0.612880i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.895084 | − | 1.55033i | −0.0367567 | − | 0.0636645i | 0.847062 | − | 0.531494i | \(-0.178369\pi\) |
−0.883819 | + | 0.467830i | \(0.845036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.55464 | − | 2.25132i | 0.0637341 | − | 0.0922950i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5879 | + | 3.64086i | 0.556114 | + | 0.149010i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.3788 | − | 21.5806i | −1.52726 | − | 0.881761i | −0.999476 | − | 0.0323796i | \(-0.989691\pi\) |
−0.527779 | − | 0.849381i | \(-0.676975\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 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 | 0 | ||||||||
\(605\) | 4.88529 | − | 1.30901i | 0.198615 | − | 0.0532188i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.7968 | − | 18.7006i | −0.438228 | − | 0.759032i | 0.559325 | − | 0.828948i | \(-0.311060\pi\) |
−0.997553 | + | 0.0699158i | \(0.977727\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.4854 | − | 7.66199i | −0.870634 | − | 0.310480i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.7324 | + | 43.7859i | −0.474642 | + | 1.77139i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.56885 | − | 9.58708i | −0.103755 | − | 0.387219i | 0.894446 | − | 0.447176i | \(-0.147570\pi\) |
−0.998201 | + | 0.0599573i | \(0.980904\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 10.4360i | − | 0.420819i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14.2458i | − | 0.573515i | −0.958003 | − | 0.286758i | \(-0.907423\pi\) | ||
0.958003 | − | 0.286758i | \(-0.0925774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.45579 | − | 35.2895i | −0.380060 | − | 1.41840i | −0.845808 | − | 0.533487i | \(-0.820881\pi\) |
0.465748 | − | 0.884917i | \(-0.345785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.74027 | + | 10.2268i | −0.109963 | + | 0.410388i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.15056 | + | 7.78033i | −0.366610 | + | 0.311712i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.29682 | + | 9.17437i | 0.211873 | + | 0.366975i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.277225 | − | 0.0742821i | 0.0110713 | − | 0.00296654i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 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 | 0 | ||||||||
\(633\) | 9.65483 | + | 5.57422i | 0.383745 | + | 0.221555i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.970054 | + | 0.259925i | 0.0384954 | + | 0.0103148i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.9891 | − | 10.8082i | −0.950481 | − | 0.428237i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.19436 | − | 7.26484i | −0.165926 | − | 0.287393i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1939 | + | 29.7808i | −0.679120 | + | 1.17627i | 0.296126 | + | 0.955149i | \(0.404305\pi\) |
−0.975246 | + | 0.221121i | \(0.929028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.9018 | + | 11.9018i | 0.469361 | + | 0.469361i | 0.901708 | − | 0.432346i | \(-0.142314\pi\) |
−0.432346 | + | 0.901708i | \(0.642314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.48825 | + | 5.48825i | −0.216099 | + | 0.216099i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.56190 | + | 2.63381i | 0.179347 | + | 0.103546i | 0.586986 | − | 0.809597i | \(-0.300314\pi\) |
−0.407639 | + | 0.913143i | \(0.633648\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.3139 | − | 8.84148i | 0.601123 | − | 0.347058i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.20535 | + | 27.2497i | −0.0864343 | + | 1.06800i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.87812 | + | 33.1336i | −0.347427 | + | 1.29662i | 0.542323 | + | 0.840170i | \(0.317545\pi\) |
−0.889751 | + | 0.456447i | \(0.849122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.99985 | − | 6.92794i | 0.156287 | − | 0.270697i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.0959 | −0.510919 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.4817 | + | 14.4817i | 0.564126 | + | 0.564126i | 0.930477 | − | 0.366351i | \(-0.119393\pi\) |
−0.366351 | + | 0.930477i | \(0.619393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.10893 | − | 15.3347i | −0.159819 | − | 0.596452i | −0.998644 | − | 0.0520518i | \(-0.983424\pi\) |
0.838826 | − | 0.544400i | \(-0.183243\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.99889 | + | 2.30876i | −0.155304 | + | 0.0896648i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0875071 | + | 0.245384i | −0.00339338 | + | 0.00951557i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.3301 | + | 3.57180i | 0.516145 | + | 0.138301i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.1930 | + | 7.28634i | −1.05134 | + | 0.281706i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.2438 | 0.434061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.09831 | −0.312167 | −0.156083 | − | 0.987744i | \(-0.549887\pi\) | ||||
−0.156083 | + | 0.987744i | \(0.549887\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.0175 | + | 5.63161i | −0.808962 | + | 0.216761i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.8750 | + | 5.86138i | 0.840724 | + | 0.225271i | 0.653386 | − | 0.757025i | \(-0.273348\pi\) |
0.187337 | + | 0.982296i | \(0.440014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −42.6877 | + | 7.81394i | −1.63820 | + | 0.299871i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.3505 | − | 9.43999i | 0.626554 | − | 0.361741i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.86156 | − | 36.8038i | −0.377342 | − | 1.40826i | −0.849892 | − | 0.526956i | \(-0.823333\pi\) |
0.472550 | − | 0.881304i | \(-0.343334\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.94275 | − | 7.94275i | −0.303477 | − | 0.303477i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 32.2606 | 1.23082 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.76660 | − | 4.79189i | 0.105399 | − | 0.182556i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.40271 | + | 23.8952i | −0.243571 | + | 0.909018i | 0.730526 | + | 0.682885i | \(0.239275\pi\) |
−0.974096 | + | 0.226133i | \(0.927392\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.25014 | − | 5.69711i | −0.313397 | − | 0.216415i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.4421 | + | 8.91547i | −0.585750 | + | 0.338183i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.51132 | − | 4.33666i | −0.284511 | − | 0.164263i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.8752 | − | 10.8752i | 0.411336 | − | 0.411336i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.6300 | − | 10.6300i | −0.401489 | − | 0.401489i | 0.477269 | − | 0.878757i | \(-0.341627\pi\) |
−0.878757 | + | 0.477269i | \(0.841627\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.387181 | + | 0.670617i | −0.0146028 | + | 0.0252928i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.38785 | + | 12.7961i | 0.278242 | + | 0.481930i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.4275 | − | 21.9870i | −0.392168 | − | 0.826905i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.42184 | + | 0.916878i | 0.128510 | + | 0.0344341i | 0.322501 | − | 0.946569i | \(-0.395477\pi\) |
−0.193991 | + | 0.981003i | \(0.562143\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.15994 | − | 0.669691i | −0.0435011 | − | 0.0251154i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 16.5398i | − | 0.619422i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.62251 | + | 6.62251i | −0.247668 | + | 0.247668i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.4436 | − | 4.67400i | 0.651444 | − | 0.174554i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.10598 | + | 14.0400i | 0.302302 | + | 0.523603i | 0.976657 | − | 0.214805i | \(-0.0689115\pi\) |
−0.674355 | + | 0.738407i | \(0.735578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.5817 | − | 13.2484i | 0.580292 | − | 0.493397i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.18582 | − | 23.0858i | 0.230053 | − | 0.858569i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.34051 | + | 27.3952i | 0.272620 | + | 1.01743i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.2822i | 0.529699i | 0.964290 | + | 0.264849i | \(0.0853223\pi\) | ||||
−0.964290 | + | 0.264849i | \(0.914678\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 22.9031i | − | 0.848263i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.66954 | + | 6.23082i | 0.0617503 | + | 0.230455i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.91206 | + | 33.2603i | −0.329175 | + | 1.22850i | 0.580874 | + | 0.813994i | \(0.302711\pi\) |
−0.910048 | + | 0.414502i | \(0.863956\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.02025 | + | 3.03799i | −0.295831 | + | 0.112058i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.30162 | − | 7.45062i | −0.158452 | − | 0.274447i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1534 | + | 5.40009i | −0.741356 | + | 0.198646i | −0.609681 | − | 0.792647i | \(-0.708702\pi\) |
−0.131675 | + | 0.991293i | \(0.542036\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 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 | \(-0.186326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.60854 | − | 2.66074i | −0.168844 | − | 0.0974820i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.4842 | − | 3.07719i | −0.420186 | − | 0.112588i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 49.8403 | + | 4.03362i | 1.82112 | + | 0.147385i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.6093 | + | 39.1605i | 0.825026 | + | 1.42899i | 0.901900 | + | 0.431946i | \(0.142173\pi\) |
−0.0768741 | + | 0.997041i | \(0.524494\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.88217 | − | 13.6523i | 0.287242 | − | 0.497518i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.979047 | − | 0.979047i | −0.0356312 | − | 0.0356312i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1353 | + | 10.1353i | −0.368375 | + | 0.368375i | −0.866884 | − | 0.498509i | \(-0.833881\pi\) |
0.498509 | + | 0.866884i | \(0.333881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.95030 | − | 2.85806i | −0.179684 | − | 0.103741i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.0843 | + | 9.86363i | −0.619306 | + | 0.357556i | −0.776599 | − | 0.629996i | \(-0.783057\pi\) |
0.157293 | + | 0.987552i | \(0.449723\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.1092 | + | 18.5479i | −1.41585 | + | 0.671480i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.413374 | − | 1.54273i | 0.0149456 | − | 0.0557776i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.5451 | − | 23.4607i | 0.489084 | − | 0.847118i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.2736 | −1.48837 | −0.744183 | − | 0.667976i | \(-0.767161\pi\) | ||||
−0.744183 | + | 0.667976i | \(0.767161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8101 | + | 19.8101i | 0.713444 | + | 0.713444i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.8201 | − | 51.5773i | −0.497074 | − | 1.85511i | −0.518090 | − | 0.855326i | \(-0.673357\pi\) |
0.0210159 | − | 0.999779i | \(-0.493310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.4375 | − | 16.9958i | 1.05743 | − | 0.610506i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −25.0754 | + | 4.59003i | −0.899577 | + | 0.164666i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.797746 | + | 0.213755i | 0.0285822 | + | 0.00765858i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.8718 | − | 3.44899i | 0.460590 | − | 0.123415i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.1812 | −1.40022 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.322740 | 0.0115191 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.494375 | + | 0.132467i | −0.0176226 | + | 0.00472196i | −0.267620 | − | 0.963525i | \(-0.586237\pi\) |
0.249997 | + | 0.968247i | \(0.419570\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.26743 | − | 1.41140i | −0.187526 | − | 0.0502473i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 52.3499 | − | 9.58259i | 1.86135 | − | 0.340718i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9176 | − | 8.61266i | 0.529739 | − | 0.305845i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.466799 | − | 1.74212i | −0.0165556 | − | 0.0617865i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.5605 | + | 35.5605i | 1.25962 | + | 1.25962i | 0.951276 | + | 0.308341i | \(0.0997736\pi\) |
0.308341 | + | 0.951276i | \(0.400226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.2801 | 0.434438 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.50586 | + | 6.07232i | −0.123873 | + | 0.214555i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.38433 | − | 20.0946i | 0.190009 | − | 0.709123i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.68813 | − | 2.22339i | 0.165235 | − | 0.0783641i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.416833 | − | 0.240659i | 0.0146732 | − | 0.00847158i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.17802 | − | 0.680131i | −0.0414170 | − | 0.0239121i | 0.479149 | − | 0.877734i | \(-0.340946\pi\) |
−0.520566 | + | 0.853822i | \(0.674279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.4370 | + | 12.4370i | −0.436722 | + | 0.436722i | −0.890907 | − | 0.454186i | \(-0.849930\pi\) |
0.454186 | + | 0.890907i | \(0.349930\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.06114 | − | 9.06114i | −0.317788 | − | 0.317788i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.53706 | − | 13.0546i | 0.264012 | − | 0.457282i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.307119 | − | 0.531945i | −0.0107447 | − | 0.0186104i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.3098 | − | 1.23903i | −0.534967 | − | 0.0432953i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.33567 | + | 1.42969i | 0.186216 | + | 0.0498965i | 0.350722 | − | 0.936480i | \(-0.385936\pi\) |
−0.164506 | + | 0.986376i | \(0.552603\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.5082 | − | 9.53100i | −0.575439 | − | 0.332230i | 0.183880 | − | 0.982949i | \(-0.441134\pi\) |
−0.759319 | + | 0.650719i | \(0.774468\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 11.7474i | − | 0.408991i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.94521 | + | 3.94521i | −0.137188 | + | 0.137188i | −0.772366 | − | 0.635178i | \(-0.780927\pi\) |
0.635178 | + | 0.772366i | \(0.280927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.9036 | − | 6.94085i | 0.899669 | − | 0.241066i | 0.220795 | − | 0.975320i | \(-0.429135\pi\) |
0.678874 | + | 0.734255i | \(0.262468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.94562 | + | 12.0302i | 0.240941 | + | 0.417322i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.14621 | + | 7.03503i | −0.0397138 | + | 0.243749i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.83713 | − | 14.3203i | 0.132789 | − | 0.495576i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.1539 | + | 45.3588i | 0.420099 | + | 1.56783i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 5.34140i | − | 0.184406i | −0.995740 | − | 0.0922028i | \(-0.970609\pi\) | ||
0.995740 | − | 0.0922028i | \(-0.0293908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.0706i | 0.761056i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.81908 | + | 21.7171i | 0.200420 | + | 0.747976i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.296598 | + | 1.10692i | −0.0102033 | + | 0.0380791i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.0383 | + | 8.53515i | −0.344921 | + | 0.293271i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.48222 | + | 9.49549i | 0.188149 | + | 0.325884i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.8971 | − | 3.99165i | 0.510664 | − | 0.136832i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.42841 | − | 1.42841i | 0.0489078 | − | 0.0489078i | −0.682230 | − | 0.731138i | \(-0.738990\pi\) |
0.731138 | + | 0.682230i | \(0.238990\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.152084i | 0.00520115i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.1543 | − | 12.7908i | −0.756778 | − | 0.436926i | 0.0713599 | − | 0.997451i | \(-0.477266\pi\) |
−0.828138 | + | 0.560525i | \(0.810599\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.0264 | − | 11.7968i | −1.50216 | − | 0.402503i | −0.588337 | − | 0.808616i | \(-0.700217\pi\) |
−0.913823 | + | 0.406113i | \(0.866884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6505 | + | 24.5656i | 0.397047 | + | 0.837194i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19.7223 | + | 34.1601i | 0.671356 | + | 1.16282i | 0.977520 | + | 0.210843i | \(0.0676210\pi\) |
−0.306164 | + | 0.951979i | \(0.599046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.27135 | + | 10.8623i | −0.213232 | + | 0.369329i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.6178 | − | 13.6178i | −0.462486 | − | 0.462486i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.50449 | − | 1.50449i | 0.0510364 | − | 0.0510364i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.4143 | − | 6.59004i | −0.386758 | − | 0.223295i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.9398 | + | 12.6669i | −0.742548 | + | 0.428710i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.8293 | + | 13.6931i | 0.670353 | + | 0.462910i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.72833 | + | 10.1823i | −0.0921292 | + | 0.343831i | −0.996569 | − | 0.0827714i | \(-0.973623\pi\) |
0.904439 | + | 0.426602i | \(0.140290\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.2534 | − | 17.7594i | 0.345839 | − | 0.599011i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.4426 | −0.520274 | −0.260137 | − | 0.965572i | \(-0.583768\pi\) | ||||
−0.260137 | + | 0.965572i | \(0.583768\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.0224 | − | 10.0224i | −0.337280 | − | 0.337280i | 0.518063 | − | 0.855343i | \(-0.326653\pi\) |
−0.855343 | + | 0.518063i | \(0.826653\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.28541 | − | 8.52927i | −0.0768233 | − | 0.286708i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.9027 | − | 21.8831i | 1.27265 | − | 0.734763i | 0.297162 | − | 0.954827i | \(-0.403960\pi\) |
0.975485 | + | 0.220064i | \(0.0706267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.57362 | + | 0.471099i | −0.0863166 | + | 0.0158001i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.69474 | + | 1.25795i | 0.157280 | + | 0.0421430i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.12948 | + | 0.302644i | −0.0377967 | + | 0.0101276i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.479024 | −0.0160120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.75703 | −0.292389 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.1229 | − | 15.8419i | 1.97186 | − | 0.528358i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.44787 | − | 0.387956i | −0.0482356 | − | 0.0129247i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.79204 | − | 19.0460i | 0.226025 | − | 0.633810i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.2356 | − | 11.1057i | 0.639413 | − | 0.369165i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5599 | + | 46.8743i | 0.417045 | + | 1.55643i | 0.780703 | + | 0.624902i | \(0.214861\pi\) |
−0.363658 | + | 0.931533i | \(0.618472\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0449 | − | 10.0449i | −0.333169 | − | 0.333169i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.2525 | 1.16797 | 0.583983 | − | 0.811766i | \(-0.301493\pi\) | ||||
0.583983 | + | 0.811766i | \(0.301493\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.44340 | − | 16.3564i | 0.312531 | − | 0.541319i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.45319 | − | 5.42336i | 0.0480409 | − | 0.179291i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.68120 | + | 20.7733i | −0.0555181 | + | 0.685994i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.1228 | − | 12.7726i | 0.729763 | − | 0.421329i | −0.0885726 | − | 0.996070i | \(-0.528231\pi\) |
0.818335 | + | 0.574741i | \(0.194897\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.3510 | + | 15.2138i | 0.868295 | + | 0.501310i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.4357 | − | 14.4357i | 0.475156 | − | 0.475156i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4120 | + | 22.4120i | 0.736903 | + | 0.736903i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.96981 | − | 10.3400i | 0.196074 | − | 0.339610i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.98515 | − | 3.43838i | −0.0651306 | − | 0.112810i | 0.831621 | − | 0.555343i | \(-0.187413\pi\) |
−0.896752 | + | 0.442534i | \(0.854080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0679545 | − | 0.675309i | −0.00222712 | − | 0.0221324i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.62660 | − | 2.04354i | −0.249684 | − | 0.0669025i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.19724 | + | 1.26858i | 0.0718576 | + | 0.0414870i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 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 | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.7932 | + | 7.71512i | −0.938632 | + | 0.251506i | −0.695531 | − | 0.718496i | \(-0.744831\pi\) |
−0.243100 | + | 0.970001i | \(0.578164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.22438 | − | 14.2451i | −0.267823 | − | 0.463883i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.2229 | + | 9.54236i | −0.365081 | + | 0.310413i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.28394 | + | 27.1840i | −0.236696 | + | 0.883362i | 0.740681 | + | 0.671857i | \(0.234503\pi\) |
−0.977377 | + | 0.211505i | \(0.932163\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.24874 | − | 30.7847i | −0.267765 | − | 0.999314i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.7060i | 0.736291i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.54510i | 0.309196i | 0.987977 | + | 0.154598i | \(0.0494083\pi\) | ||||
−0.987977 | + | 0.154598i | \(0.950592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.59865 | + | 5.96625i | 0.0517311 | + | 0.193063i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.47492 | − | 20.4327i | 0.176979 | − | 0.660495i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.5639 | + | 9.82964i | 0.890084 | + | 0.317416i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.1794 | − | 36.6839i | −0.683208 | − | 1.18335i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.1957 | − | 7.55502i | 0.908595 | − | 0.243457i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −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 | \(0.664974\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.103154 | − | 0.0595558i | −0.00331377 | − | 0.00191321i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.75433 | + | 1.54187i | 0.184665 | + | 0.0494809i | 0.349966 | − | 0.936762i | \(-0.386193\pi\) |
−0.165301 | + | 0.986243i | \(0.552860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.3966 | − | 38.2257i | 0.846237 | − | 1.22546i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.99842 | − | 15.5857i | −0.288180 | − | 0.499143i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.6499 | − | 25.3743i | 0.468690 | − | 0.811795i | −0.530669 | − | 0.847579i | \(-0.678059\pi\) |
0.999360 | + | 0.0357835i | \(0.0113927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.87607 | − | 7.87607i | −0.251720 | − | 0.251720i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.8673 | + | 17.8673i | −0.570460 | + | 0.570460i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.8442 | − | 7.99296i | −0.441562 | − | 0.254936i | 0.262698 | − | 0.964878i | \(-0.415388\pi\) |
−0.704260 | + | 0.709942i | \(0.748721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.5419 | + | 7.24108i | −0.399619 | + | 0.230720i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −31.6759 | − | 21.8737i | −1.00825 | − | 0.696247i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.16625 | + | 11.8166i | −0.100681 | + | 0.375746i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.3826 | − | 17.9832i | 0.329814 | − | 0.571255i | −0.652661 | − | 0.757650i | \(-0.726347\pi\) |
0.982475 | + | 0.186396i | \(0.0596806\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.8153 | −0.374948 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.37312 | − | 8.37312i | −0.265446 | − | 0.265446i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.8681 | + | 48.0242i | 0.407535 | + | 1.52094i | 0.799331 | + | 0.600890i | \(0.205187\pi\) |
−0.391796 | + | 0.920052i | \(0.628146\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −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 | 448.2.ba.c.81.4 | 48 | ||
4.3 | odd | 2 | 112.2.w.c.109.5 | yes | 48 | ||
7.2 | even | 3 | inner | 448.2.ba.c.401.9 | 48 | ||
8.3 | odd | 2 | 896.2.ba.f.417.4 | 48 | |||
8.5 | even | 2 | 896.2.ba.e.417.9 | 48 | |||
16.3 | odd | 4 | 896.2.ba.f.865.9 | 48 | |||
16.5 | even | 4 | inner | 448.2.ba.c.305.9 | 48 | ||
16.11 | odd | 4 | 112.2.w.c.53.12 | yes | 48 | ||
16.13 | even | 4 | 896.2.ba.e.865.4 | 48 | |||
28.3 | even | 6 | 784.2.m.k.589.5 | 24 | |||
28.11 | odd | 6 | 784.2.m.j.589.5 | 24 | |||
28.19 | even | 6 | 784.2.x.o.765.12 | 48 | |||
28.23 | odd | 6 | 112.2.w.c.93.12 | yes | 48 | ||
28.27 | even | 2 | 784.2.x.o.557.5 | 48 | |||
56.37 | even | 6 | 896.2.ba.e.289.4 | 48 | |||
56.51 | odd | 6 | 896.2.ba.f.289.9 | 48 | |||
112.11 | odd | 12 | 784.2.m.j.197.5 | 24 | |||
112.27 | even | 4 | 784.2.x.o.165.12 | 48 | |||
112.37 | even | 12 | inner | 448.2.ba.c.177.4 | 48 | ||
112.51 | odd | 12 | 896.2.ba.f.737.4 | 48 | |||
112.59 | even | 12 | 784.2.m.k.197.5 | 24 | |||
112.75 | even | 12 | 784.2.x.o.373.5 | 48 | |||
112.93 | even | 12 | 896.2.ba.e.737.9 | 48 | |||
112.107 | odd | 12 | 112.2.w.c.37.5 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.5 | ✓ | 48 | 112.107 | odd | 12 | ||
112.2.w.c.53.12 | yes | 48 | 16.11 | odd | 4 | ||
112.2.w.c.93.12 | yes | 48 | 28.23 | odd | 6 | ||
112.2.w.c.109.5 | yes | 48 | 4.3 | odd | 2 | ||
448.2.ba.c.81.4 | 48 | 1.1 | even | 1 | trivial | ||
448.2.ba.c.177.4 | 48 | 112.37 | even | 12 | inner | ||
448.2.ba.c.305.9 | 48 | 16.5 | even | 4 | inner | ||
448.2.ba.c.401.9 | 48 | 7.2 | even | 3 | inner | ||
784.2.m.j.197.5 | 24 | 112.11 | odd | 12 | |||
784.2.m.j.589.5 | 24 | 28.11 | odd | 6 | |||
784.2.m.k.197.5 | 24 | 112.59 | even | 12 | |||
784.2.m.k.589.5 | 24 | 28.3 | even | 6 | |||
784.2.x.o.165.12 | 48 | 112.27 | even | 4 | |||
784.2.x.o.373.5 | 48 | 112.75 | even | 12 | |||
784.2.x.o.557.5 | 48 | 28.27 | even | 2 | |||
784.2.x.o.765.12 | 48 | 28.19 | even | 6 | |||
896.2.ba.e.289.4 | 48 | 56.37 | even | 6 | |||
896.2.ba.e.417.9 | 48 | 8.5 | even | 2 | |||
896.2.ba.e.737.9 | 48 | 112.93 | even | 12 | |||
896.2.ba.e.865.4 | 48 | 16.13 | even | 4 | |||
896.2.ba.f.289.9 | 48 | 56.51 | odd | 6 | |||
896.2.ba.f.417.4 | 48 | 8.3 | odd | 2 | |||
896.2.ba.f.737.4 | 48 | 112.51 | odd | 12 | |||
896.2.ba.f.865.9 | 48 | 16.3 | odd | 4 |