Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(115,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("418.115");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.f (of order \(5\), degree \(4\), 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: | \(3.33774680449\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 267.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.267 |
Dual form | 418.2.f.b.191.1 |
$q$-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 \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(343\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 3.11803 | + | 2.26538i | 1.39443 | + | 1.01311i | 0.995363 | + | 0.0961876i | \(0.0306649\pi\) |
0.399064 | + | 0.916923i | \(0.369335\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.190983 | − | 0.587785i | 0.0721848 | − | 0.222162i | −0.908455 | − | 0.417983i | \(-0.862737\pi\) |
0.980640 | + | 0.195821i | \(0.0627372\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | 2.42705 | − | 1.76336i | 0.809017 | − | 0.587785i | ||||
\(10\) | −3.85410 | −1.21877 | ||||||||
\(11\) | 2.54508 | − | 2.12663i | 0.767372 | − | 0.641202i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 1.45309i | −0.554700 | + | 0.403013i | −0.829515 | − | 0.558484i | \(-0.811383\pi\) |
0.274815 | + | 0.961497i | \(0.411383\pi\) | |||||||
\(14\) | 0.190983 | + | 0.587785i | 0.0510424 | + | 0.157092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | −3.30902 | − | 2.40414i | −0.802555 | − | 0.583090i | 0.109108 | − | 0.994030i | \(-0.465201\pi\) |
−0.911662 | + | 0.410940i | \(0.865201\pi\) | |||||||
\(18\) | −0.927051 | + | 2.85317i | −0.218508 | + | 0.672499i | ||||
\(19\) | 0.309017 | + | 0.951057i | 0.0708934 | + | 0.218187i | ||||
\(20\) | 3.11803 | − | 2.26538i | 0.697214 | − | 0.506555i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.809017 | + | 3.21644i | −0.172483 | + | 0.685747i | ||||
\(23\) | 1.14590 | 0.238936 | 0.119468 | − | 0.992838i | \(-0.461881\pi\) | ||||
0.119468 | + | 0.992838i | \(0.461881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.04508 | + | 9.37181i | 0.609017 | + | 1.87436i | ||||
\(26\) | 0.763932 | − | 2.35114i | 0.149819 | − | 0.461097i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.500000 | − | 0.363271i | −0.0944911 | − | 0.0686518i | ||||
\(29\) | 0.381966 | − | 1.17557i | 0.0709293 | − | 0.218298i | −0.909308 | − | 0.416124i | \(-0.863388\pi\) |
0.980237 | + | 0.197826i | \(0.0633882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.61803 | − | 3.35520i | 0.829423 | − | 0.602611i | −0.0899727 | − | 0.995944i | \(-0.528678\pi\) |
0.919396 | + | 0.393333i | \(0.128678\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.09017 | 0.701458 | ||||||||
\(35\) | 1.92705 | − | 1.40008i | 0.325731 | − | 0.236657i | ||||
\(36\) | −0.927051 | − | 2.85317i | −0.154508 | − | 0.475528i | ||||
\(37\) | −2.85410 | + | 8.78402i | −0.469211 | + | 1.44408i | 0.384396 | + | 0.923168i | \(0.374410\pi\) |
−0.853608 | + | 0.520916i | \(0.825590\pi\) | |||||||
\(38\) | −0.809017 | − | 0.587785i | −0.131240 | − | 0.0953514i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.19098 | + | 3.66547i | −0.188311 | + | 0.579562i | ||||
\(41\) | 3.23607 | + | 9.95959i | 0.505389 | + | 1.55543i | 0.800116 | + | 0.599846i | \(0.204771\pi\) |
−0.294727 | + | 0.955582i | \(0.595229\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61803 | −0.246748 | −0.123374 | − | 0.992360i | \(-0.539371\pi\) | ||||
−0.123374 | + | 0.992360i | \(0.539371\pi\) | |||||||
\(44\) | −1.23607 | − | 3.07768i | −0.186344 | − | 0.463978i | ||||
\(45\) | 11.5623 | 1.72361 | ||||||||
\(46\) | −0.927051 | + | 0.673542i | −0.136686 | + | 0.0993083i | ||||
\(47\) | −3.59017 | − | 11.0494i | −0.523680 | − | 1.61172i | −0.766911 | − | 0.641753i | \(-0.778207\pi\) |
0.243231 | − | 0.969968i | \(-0.421793\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.35410 | + | 3.88998i | 0.764872 | + | 0.555712i | ||||
\(50\) | −7.97214 | − | 5.79210i | −1.12743 | − | 0.819126i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.763932 | + | 2.35114i | 0.105938 | + | 0.326045i | ||||
\(53\) | −1.61803 | + | 1.17557i | −0.222254 | + | 0.161477i | −0.693341 | − | 0.720610i | \(-0.743862\pi\) |
0.471087 | + | 0.882087i | \(0.343862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.7533 | − | 0.865300i | 1.71965 | − | 0.116677i | ||||
\(56\) | 0.618034 | 0.0825883 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.381966 | + | 1.17557i | 0.0501546 | + | 0.154360i | ||||
\(59\) | −3.09017 | + | 9.51057i | −0.402306 | + | 1.23817i | 0.520818 | + | 0.853668i | \(0.325627\pi\) |
−0.923124 | + | 0.384502i | \(0.874373\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.16312 | − | 5.93085i | −1.04518 | − | 0.759368i | −0.0738903 | − | 0.997266i | \(-0.523541\pi\) |
−0.971290 | + | 0.237898i | \(0.923541\pi\) | |||||||
\(62\) | −1.76393 | + | 5.42882i | −0.224020 | + | 0.689461i | ||||
\(63\) | −0.572949 | − | 1.76336i | −0.0721848 | − | 0.222162i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | −9.52786 | −1.18179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | −0.977356 | −0.488678 | − | 0.872464i | \(-0.662521\pi\) | ||||
−0.488678 | + | 0.872464i | \(0.662521\pi\) | |||||||
\(68\) | −3.30902 | + | 2.40414i | −0.401277 | + | 0.291545i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.736068 | + | 2.26538i | −0.0879770 | + | 0.270765i | ||||
\(71\) | −6.85410 | − | 4.97980i | −0.813432 | − | 0.590993i | 0.101391 | − | 0.994847i | \(-0.467671\pi\) |
−0.914824 | + | 0.403853i | \(0.867671\pi\) | |||||||
\(72\) | 2.42705 | + | 1.76336i | 0.286031 | + | 0.207813i | ||||
\(73\) | −2.61803 | + | 8.05748i | −0.306418 | + | 0.943057i | 0.672727 | + | 0.739891i | \(0.265123\pi\) |
−0.979144 | + | 0.203166i | \(0.934877\pi\) | |||||||
\(74\) | −2.85410 | − | 8.78402i | −0.331783 | − | 1.02112i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −0.763932 | − | 1.90211i | −0.0870581 | − | 0.216766i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.70820 | − | 7.05342i | 1.09226 | − | 0.793572i | 0.112479 | − | 0.993654i | \(-0.464121\pi\) |
0.979779 | + | 0.200082i | \(0.0641209\pi\) | |||||||
\(80\) | −1.19098 | − | 3.66547i | −0.133156 | − | 0.409812i | ||||
\(81\) | 2.78115 | − | 8.55951i | 0.309017 | − | 0.951057i | ||||
\(82\) | −8.47214 | − | 6.15537i | −0.935591 | − | 0.679747i | ||||
\(83\) | −3.11803 | − | 2.26538i | −0.342249 | − | 0.248658i | 0.403361 | − | 0.915041i | \(-0.367842\pi\) |
−0.745610 | + | 0.666383i | \(0.767842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.87132 | − | 14.9924i | −0.528369 | − | 1.62615i | ||||
\(86\) | 1.30902 | − | 0.951057i | 0.141155 | − | 0.102555i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.80902 | + | 1.76336i | 0.299442 | + | 0.187974i | ||||
\(89\) | −14.1803 | −1.50311 | −0.751557 | − | 0.659669i | \(-0.770697\pi\) | ||||
−0.751557 | + | 0.659669i | \(0.770697\pi\) | |||||||
\(90\) | −9.35410 | + | 6.79615i | −0.986009 | + | 0.716377i | ||||
\(91\) | 0.472136 | + | 1.45309i | 0.0494933 | + | 0.152325i | ||||
\(92\) | 0.354102 | − | 1.08981i | 0.0369177 | − | 0.113621i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.39919 | + | 6.82891i | 0.969452 | + | 0.704348i | ||||
\(95\) | −1.19098 | + | 3.66547i | −0.122192 | + | 0.376069i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.09017 | − | 4.42477i | 0.618363 | − | 0.449267i | −0.233986 | − | 0.972240i | \(-0.575177\pi\) |
0.852349 | + | 0.522973i | \(0.175177\pi\) | |||||||
\(98\) | −6.61803 | −0.668522 | ||||||||
\(99\) | 2.42705 | − | 9.64932i | 0.243928 | − | 0.969793i | ||||
\(100\) | 9.85410 | 0.985410 | ||||||||
\(101\) | −1.11803 | + | 0.812299i | −0.111249 | + | 0.0808268i | −0.642019 | − | 0.766689i | \(-0.721903\pi\) |
0.530770 | + | 0.847516i | \(0.321903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.29180 | − | 7.05342i | 0.225817 | − | 0.694994i | −0.772390 | − | 0.635148i | \(-0.780939\pi\) |
0.998208 | − | 0.0598462i | \(-0.0190610\pi\) | |||||||
\(104\) | −2.00000 | − | 1.45309i | −0.196116 | − | 0.142487i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.618034 | − | 1.90211i | 0.0600288 | − | 0.184750i | ||||
\(107\) | −2.85410 | − | 8.78402i | −0.275916 | − | 0.849184i | −0.988975 | − | 0.148079i | \(-0.952691\pi\) |
0.713059 | − | 0.701104i | \(-0.247309\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.70820 | 0.163616 | 0.0818081 | − | 0.996648i | \(-0.473931\pi\) | ||||
0.0818081 | + | 0.996648i | \(0.473931\pi\) | |||||||
\(110\) | −9.80902 | + | 8.19624i | −0.935253 | + | 0.781481i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.500000 | + | 0.363271i | −0.0472456 | + | 0.0343259i | ||||
\(113\) | −4.23607 | − | 13.0373i | −0.398496 | − | 1.22644i | −0.926205 | − | 0.377019i | \(-0.876949\pi\) |
0.527710 | − | 0.849425i | \(-0.323051\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.57295 | + | 2.59590i | 0.333179 | + | 0.242069i | ||||
\(116\) | −1.00000 | − | 0.726543i | −0.0928477 | − | 0.0674578i | ||||
\(117\) | −2.29180 | + | 7.05342i | −0.211877 | + | 0.652089i | ||||
\(118\) | −3.09017 | − | 9.51057i | −0.284473 | − | 0.875518i | ||||
\(119\) | −2.04508 | + | 1.48584i | −0.187473 | + | 0.136207i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.95492 | − | 10.8249i | 0.177720 | − | 0.984081i | ||||
\(122\) | 10.0902 | 0.913521 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.76393 | − | 5.42882i | −0.158406 | − | 0.487523i | ||||
\(125\) | −5.78115 | + | 17.7926i | −0.517082 | + | 1.59141i | ||||
\(126\) | 1.50000 | + | 1.08981i | 0.133631 | + | 0.0970883i | ||||
\(127\) | 4.23607 | + | 3.07768i | 0.375890 | + | 0.273100i | 0.759649 | − | 0.650333i | \(-0.225371\pi\) |
−0.383759 | + | 0.923433i | \(0.625371\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.70820 | − | 5.60034i | 0.676054 | − | 0.491182i | ||||
\(131\) | −6.32624 | −0.552726 | −0.276363 | − | 0.961053i | \(-0.589129\pi\) | ||||
−0.276363 | + | 0.961053i | \(0.589129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.618034 | 0.0535903 | ||||||||
\(134\) | 6.47214 | − | 4.70228i | 0.559107 | − | 0.406215i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.26393 | − | 3.88998i | 0.108381 | − | 0.333563i | ||||
\(137\) | 13.4443 | + | 9.76784i | 1.14862 | + | 0.834522i | 0.988297 | − | 0.152542i | \(-0.0487459\pi\) |
0.160325 | + | 0.987064i | \(0.448746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.97214 | + | 18.3803i | −0.506550 | + | 1.55900i | 0.291599 | + | 0.956541i | \(0.405813\pi\) |
−0.798149 | + | 0.602460i | \(0.794187\pi\) | |||||||
\(140\) | −0.736068 | − | 2.26538i | −0.0622091 | − | 0.191460i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.47214 | 0.710966 | ||||||||
\(143\) | −2.00000 | + | 7.95148i | −0.167248 | + | 0.664936i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 3.85410 | − | 2.80017i | 0.320066 | − | 0.232541i | ||||
\(146\) | −2.61803 | − | 8.05748i | −0.216670 | − | 0.666842i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.47214 | + | 5.42882i | 0.614206 | + | 0.446247i | ||||
\(149\) | −10.8541 | − | 7.88597i | −0.889203 | − | 0.646044i | 0.0464673 | − | 0.998920i | \(-0.485204\pi\) |
−0.935670 | + | 0.352876i | \(0.885204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.38197 | − | 13.4863i | −0.356599 | − | 1.09750i | −0.955076 | − | 0.296360i | \(-0.904227\pi\) |
0.598477 | − | 0.801140i | \(-0.295773\pi\) | |||||||
\(152\) | −0.809017 | + | 0.587785i | −0.0656199 | + | 0.0476757i | ||||
\(153\) | −12.2705 | −0.992012 | ||||||||
\(154\) | 1.73607 | + | 1.08981i | 0.139896 | + | 0.0878197i | ||||
\(155\) | 22.0000 | 1.76708 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.135255 | + | 0.416272i | 0.0107945 | + | 0.0332221i | 0.956309 | − | 0.292359i | \(-0.0944401\pi\) |
−0.945514 | + | 0.325581i | \(0.894440\pi\) | |||||||
\(158\) | −3.70820 | + | 11.4127i | −0.295009 | + | 0.907944i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.11803 | + | 2.26538i | 0.246502 | + | 0.179094i | ||||
\(161\) | 0.218847 | − | 0.673542i | 0.0172476 | − | 0.0530825i | ||||
\(162\) | 2.78115 | + | 8.55951i | 0.218508 | + | 0.672499i | ||||
\(163\) | −20.2984 | + | 14.7476i | −1.58989 | + | 1.15512i | −0.685795 | + | 0.727795i | \(0.740545\pi\) |
−0.904096 | + | 0.427329i | \(0.859455\pi\) | |||||||
\(164\) | 10.4721 | 0.817736 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.85410 | 0.299136 | ||||||||
\(167\) | −6.47214 | + | 4.70228i | −0.500829 | + | 0.363874i | −0.809334 | − | 0.587349i | \(-0.800171\pi\) |
0.308505 | + | 0.951223i | \(0.400171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.12868 | + | 6.55139i | −0.163744 | + | 0.503953i | ||||
\(170\) | 12.7533 | + | 9.26581i | 0.978133 | + | 0.710655i | ||||
\(171\) | 2.42705 | + | 1.76336i | 0.185601 | + | 0.134847i | ||||
\(172\) | −0.500000 | + | 1.53884i | −0.0381246 | + | 0.117336i | ||||
\(173\) | −6.00000 | − | 18.4661i | −0.456172 | − | 1.40395i | −0.869754 | − | 0.493485i | \(-0.835723\pi\) |
0.413583 | − | 0.910467i | \(-0.364277\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.09017 | 0.460374 | ||||||||
\(176\) | −3.30902 | + | 0.224514i | −0.249427 | + | 0.0169234i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 11.4721 | − | 8.33499i | 0.859873 | − | 0.624734i | ||||
\(179\) | 2.23607 | + | 6.88191i | 0.167132 | + | 0.514378i | 0.999187 | − | 0.0403143i | \(-0.0128359\pi\) |
−0.832055 | + | 0.554692i | \(0.812836\pi\) | |||||||
\(180\) | 3.57295 | − | 10.9964i | 0.266312 | − | 0.819624i | ||||
\(181\) | 10.2361 | + | 7.43694i | 0.760841 | + | 0.552783i | 0.899168 | − | 0.437603i | \(-0.144173\pi\) |
−0.138327 | + | 0.990387i | \(0.544173\pi\) | |||||||
\(182\) | −1.23607 | − | 0.898056i | −0.0916235 | − | 0.0665683i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.354102 | + | 1.08981i | 0.0261047 | + | 0.0803421i | ||||
\(185\) | −28.7984 | + | 20.9232i | −2.11730 | + | 1.53831i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.5344 | + | 0.918300i | −0.989736 | + | 0.0671528i | ||||
\(188\) | −11.6180 | −0.847332 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.19098 | − | 3.66547i | −0.0864030 | − | 0.265921i | ||||
\(191\) | 2.95492 | − | 9.09429i | 0.213810 | − | 0.658040i | −0.785426 | − | 0.618956i | \(-0.787556\pi\) |
0.999236 | − | 0.0390841i | \(-0.0124440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.61803 | − | 1.17557i | −0.116469 | − | 0.0846194i | 0.528026 | − | 0.849228i | \(-0.322932\pi\) |
−0.644495 | + | 0.764609i | \(0.722932\pi\) | |||||||
\(194\) | −2.32624 | + | 7.15942i | −0.167014 | + | 0.514017i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.35410 | − | 3.88998i | 0.382436 | − | 0.277856i | ||||
\(197\) | 7.52786 | 0.536338 | 0.268169 | − | 0.963372i | \(-0.413581\pi\) | ||||
0.268169 | + | 0.963372i | \(0.413581\pi\) | |||||||
\(198\) | 3.70820 | + | 9.23305i | 0.263531 | + | 0.656164i | ||||
\(199\) | 4.61803 | 0.327364 | 0.163682 | − | 0.986513i | \(-0.447663\pi\) | ||||
0.163682 | + | 0.986513i | \(0.447663\pi\) | |||||||
\(200\) | −7.97214 | + | 5.79210i | −0.563715 | + | 0.409563i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.427051 | − | 1.31433i | 0.0300472 | − | 0.0924758i | ||||
\(203\) | −0.618034 | − | 0.449028i | −0.0433775 | − | 0.0315156i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.4721 | + | 38.3853i | −0.871092 | + | 2.68094i | ||||
\(206\) | 2.29180 | + | 7.05342i | 0.159677 | + | 0.491435i | ||||
\(207\) | 2.78115 | − | 2.02063i | 0.193303 | − | 0.140443i | ||||
\(208\) | 2.47214 | 0.171412 | ||||||||
\(209\) | 2.80902 | + | 1.76336i | 0.194304 | + | 0.121974i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.8541 | − | 10.0656i | 0.953756 | − | 0.692944i | 0.00206355 | − | 0.999998i | \(-0.499343\pi\) |
0.951692 | + | 0.307054i | \(0.0993432\pi\) | |||||||
\(212\) | 0.618034 | + | 1.90211i | 0.0424467 | + | 0.130638i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.47214 | + | 5.42882i | 0.510785 | + | 0.371107i | ||||
\(215\) | −5.04508 | − | 3.66547i | −0.344072 | − | 0.249983i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.09017 | − | 3.35520i | −0.0740056 | − | 0.227766i | ||||
\(218\) | −1.38197 | + | 1.00406i | −0.0935985 | + | 0.0680033i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.11803 | − | 12.3965i | 0.210218 | − | 0.835771i | ||||
\(221\) | 10.1115 | 0.680170 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.38197 | + | 4.25325i | 0.0925433 | + | 0.284819i | 0.986606 | − | 0.163124i | \(-0.0521569\pi\) |
−0.894062 | + | 0.447943i | \(0.852157\pi\) | |||||||
\(224\) | 0.190983 | − | 0.587785i | 0.0127606 | − | 0.0392731i | ||||
\(225\) | 23.9164 | + | 17.3763i | 1.59443 | + | 1.15842i | ||||
\(226\) | 11.0902 | + | 8.05748i | 0.737707 | + | 0.535976i | ||||
\(227\) | 3.56231 | − | 10.9637i | 0.236439 | − | 0.727683i | −0.760489 | − | 0.649351i | \(-0.775041\pi\) |
0.996927 | − | 0.0783320i | \(-0.0249594\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.454915 | − | 0.330515i | 0.0300616 | − | 0.0218411i | −0.572653 | − | 0.819798i | \(-0.694086\pi\) |
0.602715 | + | 0.797957i | \(0.294086\pi\) | |||||||
\(230\) | −4.41641 | −0.291209 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.23607 | 0.0811518 | ||||||||
\(233\) | 7.20820 | − | 5.23707i | 0.472225 | − | 0.343092i | −0.326083 | − | 0.945341i | \(-0.605729\pi\) |
0.798308 | + | 0.602250i | \(0.205729\pi\) | |||||||
\(234\) | −2.29180 | − | 7.05342i | −0.149819 | − | 0.461097i | ||||
\(235\) | 13.8369 | − | 42.5855i | 0.902619 | − | 2.77797i | ||||
\(236\) | 8.09017 | + | 5.87785i | 0.526625 | + | 0.382616i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.781153 | − | 2.40414i | 0.0506346 | − | 0.155837i | ||||
\(239\) | 4.88197 | + | 15.0251i | 0.315788 | + | 0.971896i | 0.975429 | + | 0.220315i | \(0.0707085\pi\) |
−0.659641 | + | 0.751581i | \(0.729292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.05573 | 0.583331 | 0.291665 | − | 0.956520i | \(-0.405791\pi\) | ||||
0.291665 | + | 0.956520i | \(0.405791\pi\) | |||||||
\(242\) | 4.78115 | + | 9.90659i | 0.307344 | + | 0.636820i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.16312 | + | 5.93085i | −0.522590 | + | 0.379684i | ||||
\(245\) | 7.88197 | + | 24.2582i | 0.503560 | + | 1.54980i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | − | 1.45309i | −0.127257 | − | 0.0924576i | ||||
\(248\) | 4.61803 | + | 3.35520i | 0.293245 | + | 0.213055i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.78115 | − | 17.7926i | −0.365632 | − | 1.12530i | ||||
\(251\) | 18.8713 | − | 13.7108i | 1.19115 | − | 0.865419i | 0.197762 | − | 0.980250i | \(-0.436633\pi\) |
0.993385 | + | 0.114831i | \(0.0366326\pi\) | |||||||
\(252\) | −1.85410 | −0.116797 | ||||||||
\(253\) | 2.91641 | − | 2.43690i | 0.183353 | − | 0.153206i | ||||
\(254\) | −5.23607 | −0.328540 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | −1.76393 | + | 5.42882i | −0.110031 | + | 0.338641i | −0.990878 | − | 0.134760i | \(-0.956974\pi\) |
0.880847 | + | 0.473401i | \(0.156974\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.61803 | + | 3.35520i | 0.286951 | + | 0.208482i | ||||
\(260\) | −2.94427 | + | 9.06154i | −0.182596 | + | 0.561973i | ||||
\(261\) | −1.14590 | − | 3.52671i | −0.0709293 | − | 0.218298i | ||||
\(262\) | 5.11803 | − | 3.71847i | 0.316193 | − | 0.229728i | ||||
\(263\) | −1.52786 | −0.0942121 | −0.0471061 | − | 0.998890i | \(-0.515000\pi\) | ||||
−0.0471061 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.70820 | −0.473511 | ||||||||
\(266\) | −0.500000 | + | 0.363271i | −0.0306570 | + | 0.0222736i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.47214 | + | 7.60845i | −0.151010 | + | 0.464760i | ||||
\(269\) | −13.2361 | − | 9.61657i | −0.807017 | − | 0.586332i | 0.105947 | − | 0.994372i | \(-0.466213\pi\) |
−0.912964 | + | 0.408039i | \(0.866213\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.35410 | + | 13.4005i | −0.264493 | + | 0.814025i | 0.727317 | + | 0.686302i | \(0.240767\pi\) |
−0.991810 | + | 0.127724i | \(0.959233\pi\) | |||||||
\(272\) | 1.26393 | + | 3.88998i | 0.0766371 | + | 0.235865i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.6180 | −1.00393 | ||||||||
\(275\) | 27.6803 | + | 17.3763i | 1.66919 | + | 1.04783i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.7984 | − | 12.9313i | 1.06940 | − | 0.776965i | 0.0935962 | − | 0.995610i | \(-0.470164\pi\) |
0.975804 | + | 0.218645i | \(0.0701637\pi\) | |||||||
\(278\) | −5.97214 | − | 18.3803i | −0.358185 | − | 1.10238i | ||||
\(279\) | 5.29180 | − | 16.2865i | 0.316812 | − | 0.975046i | ||||
\(280\) | 1.92705 | + | 1.40008i | 0.115163 | + | 0.0836711i | ||||
\(281\) | −17.0902 | − | 12.4167i | −1.01951 | − | 0.740720i | −0.0533309 | − | 0.998577i | \(-0.516984\pi\) |
−0.966183 | + | 0.257857i | \(0.916984\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.42705 | + | 25.9358i | 0.500936 | + | 1.54172i | 0.807497 | + | 0.589872i | \(0.200822\pi\) |
−0.306561 | + | 0.951851i | \(0.599178\pi\) | |||||||
\(284\) | −6.85410 | + | 4.97980i | −0.406716 | + | 0.295497i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.05573 | − | 7.60845i | −0.180689 | − | 0.449897i | ||||
\(287\) | 6.47214 | 0.382038 | ||||||||
\(288\) | 2.42705 | − | 1.76336i | 0.143015 | − | 0.103907i | ||||
\(289\) | −0.0835921 | − | 0.257270i | −0.00491718 | − | 0.0151335i | ||||
\(290\) | −1.47214 | + | 4.53077i | −0.0864468 | + | 0.266056i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.85410 | + | 4.97980i | 0.401106 | + | 0.291421i | ||||
\(293\) | −0.527864 | + | 1.62460i | −0.0308381 | + | 0.0949101i | −0.965291 | − | 0.261177i | \(-0.915889\pi\) |
0.934453 | + | 0.356087i | \(0.115889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.1803 | + | 22.6538i | −1.81539 | + | 1.31896i | ||||
\(296\) | −9.23607 | −0.536836 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.4164 | 0.777192 | ||||||||
\(299\) | −2.29180 | + | 1.66509i | −0.132538 | + | 0.0962945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.309017 | + | 0.951057i | −0.0178114 | + | 0.0548180i | ||||
\(302\) | 11.4721 | + | 8.33499i | 0.660147 | + | 0.479625i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.309017 | − | 0.951057i | 0.0177233 | − | 0.0545468i | ||||
\(305\) | −12.0172 | − | 36.9852i | −0.688104 | − | 2.11777i | ||||
\(306\) | 9.92705 | − | 7.21242i | 0.567492 | − | 0.412307i | ||||
\(307\) | −19.4164 | −1.10815 | −0.554076 | − | 0.832466i | \(-0.686928\pi\) | ||||
−0.554076 | + | 0.832466i | \(0.686928\pi\) | |||||||
\(308\) | −2.04508 | + | 0.138757i | −0.116530 | + | 0.00790643i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.7984 | + | 12.9313i | −1.01088 | + | 0.734447i | ||||
\(311\) | −10.2984 | − | 31.6951i | −0.583967 | − | 1.79727i | −0.603379 | − | 0.797455i | \(-0.706179\pi\) |
0.0194116 | − | 0.999812i | \(-0.493821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.836881 | + | 0.608030i | 0.0473033 | + | 0.0343679i | 0.611186 | − | 0.791487i | \(-0.290693\pi\) |
−0.563882 | + | 0.825855i | \(0.690693\pi\) | |||||||
\(314\) | −0.354102 | − | 0.257270i | −0.0199831 | − | 0.0145186i | ||||
\(315\) | 2.20820 | − | 6.79615i | 0.124418 | − | 0.382920i | ||||
\(316\) | −3.70820 | − | 11.4127i | −0.208603 | − | 0.642013i | ||||
\(317\) | −12.4721 | + | 9.06154i | −0.700505 | + | 0.508947i | −0.880097 | − | 0.474795i | \(-0.842522\pi\) |
0.179592 | + | 0.983741i | \(0.442522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.52786 | − | 3.80423i | −0.0855440 | − | 0.212996i | ||||
\(320\) | −3.85410 | −0.215451 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.218847 | + | 0.673542i | 0.0121959 | + | 0.0375350i | ||||
\(323\) | 1.26393 | − | 3.88998i | 0.0703271 | − | 0.216444i | ||||
\(324\) | −7.28115 | − | 5.29007i | −0.404508 | − | 0.293893i | ||||
\(325\) | −19.7082 | − | 14.3188i | −1.09321 | − | 0.794267i | ||||
\(326\) | 7.75329 | − | 23.8622i | 0.429415 | − | 1.32160i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.47214 | + | 6.15537i | −0.467795 | + | 0.339873i | ||||
\(329\) | −7.18034 | −0.395865 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4721 | −0.905390 | −0.452695 | − | 0.891665i | \(-0.649537\pi\) | ||||
−0.452695 | + | 0.891665i | \(0.649537\pi\) | |||||||
\(332\) | −3.11803 | + | 2.26538i | −0.171124 | + | 0.124329i | ||||
\(333\) | 8.56231 | + | 26.3521i | 0.469211 | + | 1.44408i | ||||
\(334\) | 2.47214 | − | 7.60845i | 0.135269 | − | 0.416316i | ||||
\(335\) | −24.9443 | − | 18.1231i | −1.36285 | − | 0.990169i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.52786 | + | 13.9353i | −0.246648 | + | 0.759106i | 0.748712 | + | 0.662895i | \(0.230672\pi\) |
−0.995361 | + | 0.0962111i | \(0.969328\pi\) | |||||||
\(338\) | −2.12868 | − | 6.55139i | −0.115785 | − | 0.356349i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.7639 | −0.854919 | ||||||||
\(341\) | 4.61803 | − | 18.3601i | 0.250081 | − | 0.994255i | ||||
\(342\) | −3.00000 | −0.162221 | ||||||||
\(343\) | 6.80902 | − | 4.94704i | 0.367652 | − | 0.267115i | ||||
\(344\) | −0.500000 | − | 1.53884i | −0.0269582 | − | 0.0829688i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.7082 | + | 11.4127i | 0.844478 | + | 0.613549i | ||||
\(347\) | −13.9271 | − | 10.1186i | −0.747643 | − | 0.543195i | 0.147452 | − | 0.989069i | \(-0.452893\pi\) |
−0.895095 | + | 0.445875i | \(0.852893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.66312 | + | 29.7400i | 0.517255 | + | 1.59195i | 0.779141 | + | 0.626848i | \(0.215655\pi\) |
−0.261887 | + | 0.965099i | \(0.584345\pi\) | |||||||
\(350\) | −4.92705 | + | 3.57971i | −0.263362 | + | 0.191344i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.54508 | − | 2.12663i | 0.135653 | − | 0.113350i | ||||
\(353\) | 8.32624 | 0.443161 | 0.221580 | − | 0.975142i | \(-0.428878\pi\) | ||||
0.221580 | + | 0.975142i | \(0.428878\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0902 | − | 31.0543i | −0.535531 | − | 1.64819i | ||||
\(356\) | −4.38197 | + | 13.4863i | −0.232244 | + | 0.714773i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.85410 | − | 4.25325i | −0.309399 | − | 0.224791i | ||||
\(359\) | 0.534442 | − | 1.64484i | 0.0282068 | − | 0.0868115i | −0.935962 | − | 0.352101i | \(-0.885467\pi\) |
0.964169 | + | 0.265289i | \(0.0854674\pi\) | |||||||
\(360\) | 3.57295 | + | 10.9964i | 0.188311 | + | 0.579562i | ||||
\(361\) | −0.809017 | + | 0.587785i | −0.0425798 | + | 0.0309361i | ||||
\(362\) | −12.6525 | −0.664999 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.52786 | 0.0800818 | ||||||||
\(365\) | −26.4164 | + | 19.1926i | −1.38270 | + | 1.00459i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.371323 | − | 1.14281i | 0.0193829 | − | 0.0596544i | −0.940897 | − | 0.338692i | \(-0.890015\pi\) |
0.960280 | + | 0.279038i | \(0.0900155\pi\) | |||||||
\(368\) | −0.927051 | − | 0.673542i | −0.0483259 | − | 0.0351108i | ||||
\(369\) | 25.4164 | + | 18.4661i | 1.32313 | + | 0.961307i | ||||
\(370\) | 11.0000 | − | 33.8545i | 0.571863 | − | 1.76001i | ||||
\(371\) | 0.381966 | + | 1.17557i | 0.0198307 | + | 0.0610326i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.5967 | 1.32535 | 0.662675 | − | 0.748907i | \(-0.269421\pi\) | ||||
0.662675 | + | 0.748907i | \(0.269421\pi\) | |||||||
\(374\) | 10.4098 | − | 8.69827i | 0.538279 | − | 0.449777i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.39919 | − | 6.82891i | 0.484726 | − | 0.352174i | ||||
\(377\) | 0.944272 | + | 2.90617i | 0.0486325 | + | 0.149675i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23607 | − | 0.898056i | −0.0634925 | − | 0.0461300i | 0.555586 | − | 0.831459i | \(-0.312494\pi\) |
−0.619079 | + | 0.785329i | \(0.712494\pi\) | |||||||
\(380\) | 3.11803 | + | 2.26538i | 0.159952 | + | 0.116212i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.95492 | + | 9.09429i | 0.151187 | + | 0.465305i | ||||
\(383\) | −14.9443 | + | 10.8576i | −0.763617 | + | 0.554800i | −0.900017 | − | 0.435854i | \(-0.856446\pi\) |
0.136401 | + | 0.990654i | \(0.456446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.92705 | − | 7.66145i | 0.0982116 | − | 0.390464i | ||||
\(386\) | 2.00000 | 0.101797 | ||||||||
\(387\) | −3.92705 | + | 2.85317i | −0.199623 | + | 0.145035i | ||||
\(388\) | −2.32624 | − | 7.15942i | −0.118097 | − | 0.363465i | ||||
\(389\) | 2.35410 | − | 7.24518i | 0.119358 | − | 0.367345i | −0.873473 | − | 0.486872i | \(-0.838138\pi\) |
0.992831 | + | 0.119527i | \(0.0381378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.79180 | − | 2.75490i | −0.191759 | − | 0.139321i | ||||
\(392\) | −2.04508 | + | 6.29412i | −0.103292 | + | 0.317901i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.09017 | + | 4.42477i | −0.306818 | + | 0.222917i | ||||
\(395\) | 46.2492 | 2.32705 | ||||||||
\(396\) | −8.42705 | − | 5.29007i | −0.423475 | − | 0.265836i | ||||
\(397\) | 7.79837 | 0.391389 | 0.195695 | − | 0.980665i | \(-0.437304\pi\) | ||||
0.195695 | + | 0.980665i | \(0.437304\pi\) | |||||||
\(398\) | −3.73607 | + | 2.71441i | −0.187272 | + | 0.136061i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.04508 | − | 9.37181i | 0.152254 | − | 0.468590i | ||||
\(401\) | 2.76393 | + | 2.00811i | 0.138024 | + | 0.100280i | 0.654655 | − | 0.755928i | \(-0.272814\pi\) |
−0.516631 | + | 0.856208i | \(0.672814\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.36068 | + | 13.4208i | −0.217221 | + | 0.668537i | ||||
\(404\) | 0.427051 | + | 1.31433i | 0.0212466 | + | 0.0653903i | ||||
\(405\) | 28.0623 | − | 20.3885i | 1.39443 | − | 1.01311i | ||||
\(406\) | 0.763932 | 0.0379133 | ||||||||
\(407\) | 11.4164 | + | 28.4257i | 0.565890 | + | 1.40901i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.1803 | + | 13.9353i | −0.948407 | + | 0.689058i | −0.950430 | − | 0.310940i | \(-0.899356\pi\) |
0.00202274 | + | 0.999998i | \(0.499356\pi\) | |||||||
\(410\) | −12.4721 | − | 38.3853i | −0.615955 | − | 1.89571i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.00000 | − | 4.35926i | −0.295599 | − | 0.214765i | ||||
\(413\) | 5.00000 | + | 3.63271i | 0.246034 | + | 0.178754i | ||||
\(414\) | −1.06231 | + | 3.26944i | −0.0522095 | + | 0.160684i | ||||
\(415\) | −4.59017 | − | 14.1271i | −0.225323 | − | 0.693472i | ||||
\(416\) | −2.00000 | + | 1.45309i | −0.0980581 | + | 0.0712434i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.30902 | + | 0.224514i | −0.161849 | + | 0.0109813i | ||||
\(419\) | 12.6738 | 0.619154 | 0.309577 | − | 0.950874i | \(-0.399813\pi\) | ||||
0.309577 | + | 0.950874i | \(0.399813\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.65248 | − | 23.5519i | −0.372959 | − | 1.14785i | −0.944845 | − | 0.327517i | \(-0.893788\pi\) |
0.571887 | − | 0.820333i | \(-0.306212\pi\) | |||||||
\(422\) | −5.29180 | + | 16.2865i | −0.257601 | + | 0.792813i | ||||
\(423\) | −28.1976 | − | 20.4867i | −1.37101 | − | 0.996099i | ||||
\(424\) | −1.61803 | − | 1.17557i | −0.0785787 | − | 0.0570908i | ||||
\(425\) | 12.4549 | − | 38.3323i | 0.604152 | − | 1.85939i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.04508 | + | 3.66547i | −0.244149 | + | 0.177384i | ||||
\(428\) | −9.23607 | −0.446442 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.23607 | 0.300730 | ||||||||
\(431\) | 22.5623 | − | 16.3925i | 1.08679 | − | 0.789598i | 0.107934 | − | 0.994158i | \(-0.465576\pi\) |
0.978854 | + | 0.204560i | \(0.0655765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.2918 | + | 34.7526i | −0.542649 | + | 1.67010i | 0.183866 | + | 0.982951i | \(0.441139\pi\) |
−0.726515 | + | 0.687151i | \(0.758861\pi\) | |||||||
\(434\) | 2.85410 | + | 2.07363i | 0.137001 | + | 0.0995373i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.527864 | − | 1.62460i | 0.0252801 | − | 0.0778042i | ||||
\(437\) | 0.354102 | + | 1.08981i | 0.0169390 | + | 0.0521329i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.3607 | −1.73540 | −0.867700 | − | 0.497088i | \(-0.834403\pi\) | ||||
−0.867700 | + | 0.497088i | \(0.834403\pi\) | |||||||
\(440\) | 4.76393 | + | 11.8617i | 0.227112 | + | 0.565485i | ||||
\(441\) | 19.8541 | 0.945433 | ||||||||
\(442\) | −8.18034 | + | 5.94336i | −0.389099 | + | 0.282697i | ||||
\(443\) | −0.809017 | − | 2.48990i | −0.0384376 | − | 0.118299i | 0.929997 | − | 0.367568i | \(-0.119810\pi\) |
−0.968434 | + | 0.249269i | \(0.919810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −44.2148 | − | 32.1239i | −2.09598 | − | 1.52282i | ||||
\(446\) | −3.61803 | − | 2.62866i | −0.171319 | − | 0.124470i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.190983 | + | 0.587785i | 0.00902310 | + | 0.0277702i | ||||
\(449\) | 26.6525 | − | 19.3642i | 1.25781 | − | 0.913851i | 0.259160 | − | 0.965834i | \(-0.416554\pi\) |
0.998648 | + | 0.0519833i | \(0.0165543\pi\) | |||||||
\(450\) | −29.5623 | −1.39358 | ||||||||
\(451\) | 29.4164 | + | 18.4661i | 1.38516 | + | 0.869535i | ||||
\(452\) | −13.7082 | −0.644780 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.56231 | + | 10.9637i | 0.167187 | + | 0.514550i | ||||
\(455\) | −1.81966 | + | 5.60034i | −0.0853070 | + | 0.262548i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.9164 | + | 18.1028i | 1.16554 | + | 0.846815i | 0.990468 | − | 0.137741i | \(-0.0439841\pi\) |
0.175072 | + | 0.984556i | \(0.443984\pi\) | |||||||
\(458\) | −0.173762 | + | 0.534785i | −0.00811937 | + | 0.0249888i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.57295 | − | 2.59590i | 0.166590 | − | 0.121034i | ||||
\(461\) | 25.3820 | 1.18216 | 0.591078 | − | 0.806614i | \(-0.298703\pi\) | ||||
0.591078 | + | 0.806614i | \(0.298703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.8541 | −0.829750 | −0.414875 | − | 0.909878i | \(-0.636175\pi\) | ||||
−0.414875 | + | 0.909878i | \(0.636175\pi\) | |||||||
\(464\) | −1.00000 | + | 0.726543i | −0.0464238 | + | 0.0337289i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.75329 | + | 8.47375i | −0.127544 | + | 0.392539i | ||||
\(467\) | −3.35410 | − | 2.43690i | −0.155209 | − | 0.112766i | 0.507470 | − | 0.861669i | \(-0.330581\pi\) |
−0.662679 | + | 0.748903i | \(0.730581\pi\) | |||||||
\(468\) | 6.00000 | + | 4.35926i | 0.277350 | + | 0.201507i | ||||
\(469\) | −1.52786 | + | 4.70228i | −0.0705502 | + | 0.217131i | ||||
\(470\) | 13.8369 | + | 42.5855i | 0.638248 | + | 1.96432i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.0000 | −0.460287 | ||||||||
\(473\) | −4.11803 | + | 3.44095i | −0.189347 | + | 0.158215i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.97214 | + | 5.79210i | −0.365787 | + | 0.265760i | ||||
\(476\) | 0.781153 | + | 2.40414i | 0.0358041 | + | 0.110194i | ||||
\(477\) | −1.85410 | + | 5.70634i | −0.0848935 | + | 0.261275i | ||||
\(478\) | −12.7812 | − | 9.28605i | −0.584596 | − | 0.424734i | ||||
\(479\) | −13.3992 | − | 9.73508i | −0.612224 | − | 0.444807i | 0.237972 | − | 0.971272i | \(-0.423517\pi\) |
−0.850197 | + | 0.526465i | \(0.823517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.05573 | − | 21.7153i | −0.321714 | − | 0.990132i | ||||
\(482\) | −7.32624 | + | 5.32282i | −0.333701 | + | 0.242448i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.69098 | − | 5.20431i | −0.440499 | − | 0.236560i | ||||
\(485\) | 29.0132 | 1.31742 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.85410 | + | 24.1724i | 0.355903 | + | 1.09536i | 0.955484 | + | 0.295043i | \(0.0953341\pi\) |
−0.599581 | + | 0.800314i | \(0.704666\pi\) | |||||||
\(488\) | 3.11803 | − | 9.59632i | 0.141147 | − | 0.434405i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −20.6353 | − | 14.9924i | −0.932206 | − | 0.677287i | ||||
\(491\) | −10.9894 | + | 33.8218i | −0.495943 | + | 1.52635i | 0.319540 | + | 0.947573i | \(0.396472\pi\) |
−0.815482 | + | 0.578782i | \(0.803528\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.09017 | + | 2.97168i | −0.184212 | + | 0.133838i | ||||
\(494\) | 2.47214 | 0.111227 | ||||||||
\(495\) | 29.4271 | − | 24.5887i | 1.32265 | − | 1.10518i | ||||
\(496\) | −5.70820 | −0.256306 | ||||||||
\(497\) | −4.23607 | + | 3.07768i | −0.190014 | + | 0.138053i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.19098 | + | 22.1316i | −0.321913 | + | 0.990745i | 0.650902 | + | 0.759161i | \(0.274391\pi\) |
−0.972815 | + | 0.231584i | \(0.925609\pi\) | |||||||
\(500\) | 15.1353 | + | 10.9964i | 0.676869 | + | 0.491774i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.20820 | + | 22.1846i | −0.321718 | + | 0.990146i | ||||
\(503\) | 8.47214 | + | 26.0746i | 0.377754 | + | 1.16261i | 0.941602 | + | 0.336728i | \(0.109320\pi\) |
−0.563848 | + | 0.825879i | \(0.690680\pi\) | |||||||
\(504\) | 1.50000 | − | 1.08981i | 0.0668153 | − | 0.0485442i | ||||
\(505\) | −5.32624 | −0.237014 | ||||||||
\(506\) | −0.927051 | + | 3.68571i | −0.0412124 | + | 0.163850i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.23607 | − | 3.07768i | 0.187945 | − | 0.136550i | ||||
\(509\) | 7.09017 | + | 21.8213i | 0.314266 | + | 0.967212i | 0.976055 | + | 0.217522i | \(0.0697974\pi\) |
−0.661789 | + | 0.749690i | \(0.730203\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.23607 | + | 3.07768i | 0.187393 | + | 0.136149i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.76393 | − | 5.42882i | −0.0778037 | − | 0.239455i | ||||
\(515\) | 23.1246 | − | 16.8010i | 1.01899 | − | 0.740341i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.6353 | − | 20.4867i | −1.43530 | − | 0.901005i | ||||
\(518\) | −5.70820 | −0.250804 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.94427 | − | 9.06154i | −0.129115 | − | 0.397375i | ||||
\(521\) | −1.76393 | + | 5.42882i | −0.0772793 | + | 0.237841i | −0.982232 | − | 0.187671i | \(-0.939906\pi\) |
0.904953 | + | 0.425512i | \(0.139906\pi\) | |||||||
\(522\) | 3.00000 | + | 2.17963i | 0.131306 | + | 0.0953997i | ||||
\(523\) | 19.1803 | + | 13.9353i | 0.838698 | + | 0.609350i | 0.922007 | − | 0.387174i | \(-0.126549\pi\) |
−0.0833089 | + | 0.996524i | \(0.526549\pi\) | |||||||
\(524\) | −1.95492 | + | 6.01661i | −0.0854009 | + | 0.262837i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.23607 | − | 0.898056i | 0.0538951 | − | 0.0391571i | ||||
\(527\) | −23.3475 | −1.01703 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.6869 | −0.942909 | ||||||||
\(530\) | 6.23607 | − | 4.53077i | 0.270877 | − | 0.196804i | ||||
\(531\) | 9.27051 | + | 28.5317i | 0.402306 | + | 1.23817i | ||||
\(532\) | 0.190983 | − | 0.587785i | 0.00828016 | − | 0.0254837i | ||||
\(533\) | −20.9443 | − | 15.2169i | −0.907197 | − | 0.659117i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0000 | − | 33.8545i | 0.475571 | − | 1.46366i | ||||
\(536\) | −2.47214 | − | 7.60845i | −0.106780 | − | 0.328635i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.3607 | 0.705359 | ||||||||
\(539\) | 21.8992 | − | 1.48584i | 0.943265 | − | 0.0639997i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.2533 | − | 18.3476i | 1.08572 | − | 0.788824i | 0.107052 | − | 0.994253i | \(-0.465859\pi\) |
0.978672 | + | 0.205429i | \(0.0658590\pi\) | |||||||
\(542\) | −4.35410 | − | 13.4005i | −0.187025 | − | 0.575603i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.30902 | − | 2.40414i | −0.141873 | − | 0.103077i | ||||
\(545\) | 5.32624 | + | 3.86974i | 0.228151 | + | 0.165761i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.27051 | + | 25.4540i | 0.353621 | + | 1.08833i | 0.956804 | + | 0.290732i | \(0.0938989\pi\) |
−0.603183 | + | 0.797603i | \(0.706101\pi\) | |||||||
\(548\) | 13.4443 | − | 9.76784i | 0.574311 | − | 0.417261i | ||||
\(549\) | −30.2705 | −1.29191 | ||||||||
\(550\) | −32.6074 | + | 2.21238i | −1.39038 | + | 0.0943364i | ||||
\(551\) | 1.23607 | 0.0526583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.29180 | − | 7.05342i | −0.0974571 | − | 0.299942i | ||||
\(554\) | −6.79837 | + | 20.9232i | −0.288835 | + | 0.888943i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.6353 | + | 11.3597i | 0.663083 | + | 0.481758i | ||||
\(557\) | −9.93363 | + | 30.5726i | −0.420901 | + | 1.29540i | 0.485963 | + | 0.873979i | \(0.338469\pi\) |
−0.906865 | + | 0.421422i | \(0.861531\pi\) | |||||||
\(558\) | 5.29180 | + | 16.2865i | 0.224020 | + | 0.689461i | ||||
\(559\) | 3.23607 | − | 2.35114i | 0.136871 | − | 0.0994427i | ||||
\(560\) | −2.38197 | −0.100656 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.1246 | 0.891088 | ||||||||
\(563\) | 8.85410 | − | 6.43288i | 0.373156 | − | 0.271114i | −0.385362 | − | 0.922765i | \(-0.625924\pi\) |
0.758518 | + | 0.651652i | \(0.225924\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.3262 | − | 50.2470i | 0.686850 | − | 2.11391i | ||||
\(566\) | −22.0623 | − | 16.0292i | −0.927348 | − | 0.673758i | ||||
\(567\) | −4.50000 | − | 3.26944i | −0.188982 | − | 0.137304i | ||||
\(568\) | 2.61803 | − | 8.05748i | 0.109850 | − | 0.338084i | ||||
\(569\) | 1.90983 | + | 5.87785i | 0.0800642 | + | 0.246412i | 0.983074 | − | 0.183207i | \(-0.0586478\pi\) |
−0.903010 | + | 0.429619i | \(0.858648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.5066 | 1.02557 | 0.512784 | − | 0.858518i | \(-0.328614\pi\) | ||||
0.512784 | + | 0.858518i | \(0.328614\pi\) | |||||||
\(572\) | 6.94427 | + | 4.35926i | 0.290355 | + | 0.182270i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.23607 | + | 3.80423i | −0.218549 | + | 0.158785i | ||||
\(575\) | 3.48936 | + | 10.7391i | 0.145516 | + | 0.447853i | ||||
\(576\) | −0.927051 | + | 2.85317i | −0.0386271 | + | 0.118882i | ||||
\(577\) | −26.2705 | − | 19.0866i | −1.09366 | − | 0.794587i | −0.113643 | − | 0.993522i | \(-0.536252\pi\) |
−0.980013 | + | 0.198934i | \(0.936252\pi\) | |||||||
\(578\) | 0.218847 | + | 0.159002i | 0.00910284 | + | 0.00661360i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.47214 | − | 4.53077i | −0.0611271 | − | 0.188130i | ||||
\(581\) | −1.92705 | + | 1.40008i | −0.0799475 | + | 0.0580853i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.61803 | + | 6.43288i | −0.0670121 | + | 0.266423i | ||||
\(584\) | −8.47214 | −0.350579 | ||||||||
\(585\) | −23.1246 | + | 16.8010i | −0.956085 | + | 0.694636i | ||||
\(586\) | −0.527864 | − | 1.62460i | −0.0218059 | − | 0.0671115i | ||||
\(587\) | 0.583592 | − | 1.79611i | 0.0240874 | − | 0.0741335i | −0.938290 | − | 0.345849i | \(-0.887591\pi\) |
0.962378 | + | 0.271715i | \(0.0875910\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.61803 | + | 3.35520i | 0.190283 | + | 0.138249i | ||||
\(590\) | 11.9098 | − | 36.6547i | 0.490320 | − | 1.50905i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.47214 | − | 5.42882i | 0.307103 | − | 0.223123i | ||||
\(593\) | 31.9098 | 1.31038 | 0.655190 | − | 0.755464i | \(-0.272589\pi\) | ||||
0.655190 | + | 0.755464i | \(0.272589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.74265 | −0.399410 | ||||||||
\(596\) | −10.8541 | + | 7.88597i | −0.444601 | + | 0.323022i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.875388 | − | 2.69417i | 0.0357973 | − | 0.110173i | ||||
\(599\) | −12.2361 | − | 8.89002i | −0.499952 | − | 0.363237i | 0.309047 | − | 0.951047i | \(-0.399990\pi\) |
−0.808999 | + | 0.587810i | \(0.799990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.81966 | − | 20.9888i | 0.278180 | − | 0.856149i | −0.710181 | − | 0.704019i | \(-0.751387\pi\) |
0.988361 | − | 0.152130i | \(-0.0486132\pi\) | |||||||
\(602\) | −0.309017 | − | 0.951057i | −0.0125946 | − | 0.0387622i | ||||
\(603\) | −19.4164 | + | 14.1068i | −0.790697 | + | 0.574475i | ||||
\(604\) | −14.1803 | −0.576990 | ||||||||
\(605\) | 30.6180 | − | 29.3238i | 1.24480 | − | 1.19218i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0344 | − | 10.9232i | 0.610229 | − | 0.443357i | −0.239266 | − | 0.970954i | \(-0.576907\pi\) |
0.849495 | + | 0.527597i | \(0.176907\pi\) | |||||||
\(608\) | 0.309017 | + | 0.951057i | 0.0125323 | + | 0.0385704i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 31.4615 | + | 22.8581i | 1.27384 | + | 0.925498i | ||||
\(611\) | 23.2361 | + | 16.8820i | 0.940031 | + | 0.682972i | ||||
\(612\) | −3.79180 | + | 11.6699i | −0.153274 | + | 0.471730i | ||||
\(613\) | −3.70163 | − | 11.3924i | −0.149507 | − | 0.460136i | 0.848056 | − | 0.529907i | \(-0.177773\pi\) |
−0.997563 | + | 0.0697709i | \(0.977773\pi\) | |||||||
\(614\) | 15.7082 | − | 11.4127i | 0.633932 | − | 0.460578i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.57295 | − | 1.31433i | 0.0633759 | − | 0.0529558i | ||||
\(617\) | 30.9443 | 1.24577 | 0.622885 | − | 0.782314i | \(-0.285961\pi\) | ||||
0.622885 | + | 0.782314i | \(0.285961\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.5557 | + | 44.7979i | 0.585044 | + | 1.80058i | 0.599093 | + | 0.800679i | \(0.295528\pi\) |
−0.0140491 | + | 0.999901i | \(0.504472\pi\) | |||||||
\(620\) | 6.79837 | − | 20.9232i | 0.273029 | − | 0.840298i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.9615 | + | 19.5887i | 1.08106 | + | 0.785434i | ||||
\(623\) | −2.70820 | + | 8.33499i | −0.108502 | + | 0.333935i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.4721 | + | 13.4208i | −0.738885 | + | 0.536832i | ||||
\(626\) | −1.03444 | −0.0413446 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.437694 | 0.0174659 | ||||||||
\(629\) | 30.5623 | − | 22.2048i | 1.21860 | − | 0.885364i | ||||
\(630\) | 2.20820 | + | 6.79615i | 0.0879770 | + | 0.270765i | ||||
\(631\) | 5.41641 | − | 16.6700i | 0.215624 | − | 0.663622i | −0.783485 | − | 0.621411i | \(-0.786560\pi\) |
0.999109 | − | 0.0422110i | \(-0.0134402\pi\) | |||||||
\(632\) | 9.70820 | + | 7.05342i | 0.386172 | + | 0.280570i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.76393 | − | 14.6619i | 0.189200 | − | 0.582297i | ||||
\(635\) | 6.23607 | + | 19.1926i | 0.247471 | + | 0.761637i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.3607 | −0.648234 | ||||||||
\(638\) | 3.47214 | + | 2.17963i | 0.137463 | + | 0.0862923i | ||||
\(639\) | −25.4164 | −1.00546 | ||||||||
\(640\) | 3.11803 | − | 2.26538i | 0.123251 | − | 0.0895472i | ||||
\(641\) | −10.6525 | − | 32.7849i | −0.420747 | − | 1.29493i | −0.907008 | − | 0.421114i | \(-0.861639\pi\) |
0.486260 | − | 0.873814i | \(-0.338361\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4336 | + | 19.2052i | 1.04244 | + | 0.757377i | 0.970760 | − | 0.240050i | \(-0.0771639\pi\) |
0.0716801 | + | 0.997428i | \(0.477164\pi\) | |||||||
\(644\) | −0.572949 | − | 0.416272i | −0.0225774 | − | 0.0164034i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.26393 | + | 3.88998i | 0.0497287 | + | 0.153049i | ||||
\(647\) | −16.4721 | + | 11.9677i | −0.647586 | + | 0.470499i | −0.862448 | − | 0.506145i | \(-0.831070\pi\) |
0.214862 | + | 0.976644i | \(0.431070\pi\) | |||||||
\(648\) | 9.00000 | 0.353553 | ||||||||
\(649\) | 12.3607 | + | 30.7768i | 0.485199 | + | 1.20810i | ||||
\(650\) | 24.3607 | 0.955504 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.75329 | + | 23.8622i | 0.303642 | + | 0.934515i | ||||
\(653\) | −3.59017 | + | 11.0494i | −0.140494 | + | 0.432397i | −0.996404 | − | 0.0847283i | \(-0.972998\pi\) |
0.855910 | + | 0.517125i | \(0.172998\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.7254 | − | 14.3314i | −0.770736 | − | 0.559973i | ||||
\(656\) | 3.23607 | − | 9.95959i | 0.126347 | − | 0.388857i | ||||
\(657\) | 7.85410 | + | 24.1724i | 0.306418 | + | 0.943057i | ||||
\(658\) | 5.80902 | − | 4.22050i | 0.226459 | − | 0.164532i | ||||
\(659\) | 41.3050 | 1.60901 | 0.804506 | − | 0.593944i | \(-0.202430\pi\) | ||||
0.804506 | + | 0.593944i | \(0.202430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.94427 | −0.270101 | −0.135050 | − | 0.990839i | \(-0.543120\pi\) | ||||
−0.135050 | + | 0.990839i | \(0.543120\pi\) | |||||||
\(662\) | 13.3262 | − | 9.68208i | 0.517939 | − | 0.376305i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.19098 | − | 3.66547i | 0.0462191 | − | 0.142248i | ||||
\(665\) | 1.92705 | + | 1.40008i | 0.0747278 | + | 0.0542929i | ||||
\(666\) | −22.4164 | − | 16.2865i | −0.868618 | − | 0.631088i | ||||
\(667\) | 0.437694 | − | 1.34708i | 0.0169476 | − | 0.0521593i | ||||
\(668\) | 2.47214 | + | 7.60845i | 0.0956498 | + | 0.294380i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 30.8328 | 1.19118 | ||||||||
\(671\) | −33.3885 | + | 2.26538i | −1.28895 | + | 0.0874542i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.76393 | + | 2.73466i | −0.145089 | + | 0.105413i | −0.657962 | − | 0.753051i | \(-0.728581\pi\) |
0.512873 | + | 0.858465i | \(0.328581\pi\) | |||||||
\(674\) | −4.52786 | − | 13.9353i | −0.174407 | − | 0.536769i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.57295 | + | 4.04898i | 0.214344 | + | 0.155730i | ||||
\(677\) | −35.6525 | − | 25.9030i | −1.37024 | − | 0.995535i | −0.997719 | − | 0.0675095i | \(-0.978495\pi\) |
−0.372517 | − | 0.928025i | \(-0.621505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.43769 | − | 4.42477i | −0.0551736 | − | 0.169807i | ||||
\(680\) | 12.7533 | − | 9.26581i | 0.489066 | − | 0.355327i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.05573 | + | 17.5680i | 0.270178 | + | 0.672715i | ||||
\(683\) | 16.8328 | 0.644090 | 0.322045 | − | 0.946724i | \(-0.395630\pi\) | ||||
0.322045 | + | 0.946724i | \(0.395630\pi\) | |||||||
\(684\) | 2.42705 | − | 1.76336i | 0.0928006 | − | 0.0674236i | ||||
\(685\) | 19.7918 | + | 60.9129i | 0.756206 | + | 2.32736i | ||||
\(686\) | −2.60081 | + | 8.00448i | −0.0992995 | + | 0.305612i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.30902 | + | 0.951057i | 0.0499058 | + | 0.0362587i | ||||
\(689\) | 1.52786 | − | 4.70228i | 0.0582070 | − | 0.179143i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.2984 | + | 16.2007i | −0.848270 | + | 0.616304i | −0.924669 | − | 0.380773i | \(-0.875658\pi\) |
0.0763984 | + | 0.997077i | \(0.475658\pi\) | |||||||
\(692\) | −19.4164 | −0.738101 | ||||||||
\(693\) | −5.20820 | − | 3.26944i | −0.197843 | − | 0.124196i | ||||
\(694\) | 17.2148 | 0.653464 | ||||||||
\(695\) | −60.2599 | + | 43.7814i | −2.28579 | + | 1.66072i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.2361 | − | 40.7364i | 0.501352 | − | 1.54300i | ||||
\(698\) | −25.2984 | − | 18.3803i | −0.957558 | − | 0.695706i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.88197 | − | 5.79210i | 0.0711316 | − | 0.218921i | ||||
\(701\) | 2.29837 | + | 7.07367i | 0.0868084 | + | 0.267169i | 0.985032 | − | 0.172369i | \(-0.0551422\pi\) |
−0.898224 | + | 0.439538i | \(0.855142\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.23607 | −0.348345 | ||||||||
\(704\) | −0.809017 | + | 3.21644i | −0.0304910 | + | 0.121224i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.73607 | + | 4.89404i | −0.253515 | + | 0.184190i | ||||
\(707\) | 0.263932 | + | 0.812299i | 0.00992619 | + | 0.0305497i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1180 | + | 8.80427i | 0.455102 | + | 0.330651i | 0.791607 | − | 0.611031i | \(-0.209245\pi\) |
−0.336505 | + | 0.941682i | \(0.609245\pi\) | |||||||
\(710\) | 26.4164 | + | 19.1926i | 0.991390 | + | 0.720287i | ||||
\(711\) | 11.1246 | − | 34.2380i | 0.417206 | − | 1.28403i | ||||
\(712\) | −4.38197 | − | 13.4863i | −0.164221 | − | 0.505421i | ||||
\(713\) | 5.29180 | − | 3.84471i | 0.198179 | − | 0.143986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.2492 | + | 20.2622i | −0.906870 | + | 0.757764i | ||||
\(716\) | 7.23607 | 0.270425 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.534442 | + | 1.64484i | 0.0199452 | + | 0.0613850i | ||||
\(719\) | −16.0106 | + | 49.2757i | −0.597096 | + | 1.83767i | −0.0530939 | + | 0.998590i | \(0.516908\pi\) |
−0.544002 | + | 0.839084i | \(0.683092\pi\) | |||||||
\(720\) | −9.35410 | − | 6.79615i | −0.348607 | − | 0.253278i | ||||
\(721\) | −3.70820 | − | 2.69417i | −0.138101 | − | 0.100336i | ||||
\(722\) | 0.309017 | − | 0.951057i | 0.0115004 | − | 0.0353947i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.2361 | − | 7.43694i | 0.380420 | − | 0.276392i | ||||
\(725\) | 12.1803 | 0.452366 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9098 | −0.960942 | −0.480471 | − | 0.877011i | \(-0.659534\pi\) | ||||
−0.480471 | + | 0.877011i | \(0.659534\pi\) | |||||||
\(728\) | −1.23607 | + | 0.898056i | −0.0458117 | + | 0.0332842i | ||||
\(729\) | −8.34346 | − | 25.6785i | −0.309017 | − | 0.951057i | ||||
\(730\) | 10.0902 | − | 31.0543i | 0.373454 | − | 1.14937i | ||||
\(731\) | 5.35410 | + | 3.88998i | 0.198029 | + | 0.143876i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5729 | − | 35.6179i | 0.427457 | − | 1.31558i | −0.473166 | − | 0.880973i | \(-0.656889\pi\) |
0.900622 | − | 0.434603i | \(-0.143111\pi\) | |||||||
\(734\) | 0.371323 | + | 1.14281i | 0.0137058 | + | 0.0421820i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.14590 | 0.0422384 | ||||||||
\(737\) | −20.3607 | + | 17.0130i | −0.749995 | + | 0.626683i | ||||
\(738\) | −31.4164 | −1.15645 | ||||||||
\(739\) | 17.8262 | − | 12.9515i | 0.655749 | − | 0.476429i | −0.209476 | − | 0.977814i | \(-0.567176\pi\) |
0.865225 | + | 0.501384i | \(0.167176\pi\) | |||||||
\(740\) | 11.0000 | + | 33.8545i | 0.404368 | + | 1.24452i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.00000 | − | 0.726543i | −0.0367112 | − | 0.0266722i | ||||
\(743\) | −24.0344 | − | 17.4620i | −0.881738 | − | 0.640620i | 0.0519726 | − | 0.998649i | \(-0.483449\pi\) |
−0.933711 | + | 0.358028i | \(0.883449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9787 | − | 49.1774i | −0.585415 | − | 1.80172i | ||||
\(746\) | −20.7082 | + | 15.0454i | −0.758181 | + | 0.550851i | ||||
\(747\) | −11.5623 | −0.423043 | ||||||||
\(748\) | −3.30902 | + | 13.1558i | −0.120990 | + | 0.481023i | ||||
\(749\) | −5.70820 | −0.208573 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.2705 | − | 31.6094i | −0.374776 | − | 1.15344i | −0.943629 | − | 0.331004i | \(-0.892613\pi\) |
0.568853 | − | 0.822439i | \(-0.307387\pi\) | |||||||
\(752\) | −3.59017 | + | 11.0494i | −0.130920 | + | 0.402930i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.47214 | − | 1.79611i | −0.0900299 | − | 0.0654105i | ||||
\(755\) | 16.8885 | − | 51.9776i | 0.614637 | − | 1.89166i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.2705 | − | 27.8052i | 1.39097 | − | 1.01060i | 0.395207 | − | 0.918592i | \(-0.370673\pi\) |
0.995759 | − | 0.0920032i | \(-0.0293270\pi\) | |||||||
\(758\) | 1.52786 | 0.0554945 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.85410 | −0.139803 | ||||||||
\(761\) | −4.38197 | + | 3.18368i | −0.158846 | + | 0.115408i | −0.664369 | − | 0.747405i | \(-0.731300\pi\) |
0.505523 | + | 0.862813i | \(0.331300\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.326238 | − | 1.00406i | 0.0118106 | − | 0.0363493i | ||||
\(764\) | −7.73607 | − | 5.62058i | −0.279881 | − | 0.203346i | ||||
\(765\) | −38.2599 | − | 27.7974i | −1.38329 | − | 1.00502i | ||||
\(766\) | 5.70820 | − | 17.5680i | 0.206246 | − | 0.634759i | ||||
\(767\) | −7.63932 | − | 23.5114i | −0.275840 | − | 0.848948i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.7426 | −1.14467 | −0.572335 | − | 0.820020i | \(-0.693962\pi\) | ||||
−0.572335 | + | 0.820020i | \(0.693962\pi\) | |||||||
\(770\) | 2.94427 | + | 7.33094i | 0.106104 | + | 0.264189i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.61803 | + | 1.17557i | −0.0582343 | + | 0.0423097i | ||||
\(773\) | 13.7082 | + | 42.1895i | 0.493050 | + | 1.51745i | 0.819974 | + | 0.572401i | \(0.193988\pi\) |
−0.326924 | + | 0.945051i | \(0.606012\pi\) | |||||||
\(774\) | 1.50000 | − | 4.61653i | 0.0539164 | − | 0.165938i | ||||
\(775\) | 45.5066 | + | 33.0625i | 1.63464 | + | 1.18764i | ||||
\(776\) | 6.09017 | + | 4.42477i | 0.218624 | + | 0.158840i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.35410 | + | 7.24518i | 0.0843986 | + | 0.259752i | ||||
\(779\) | −8.47214 | + | 6.15537i | −0.303546 | + | 0.220539i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0344 | + | 1.90211i | −1.00315 | + | 0.0680630i | ||||
\(782\) | 4.68692 | 0.167604 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.04508 | − | 6.29412i | −0.0730387 | − | 0.224790i | ||||
\(785\) | −0.521286 | + | 1.60435i | −0.0186055 | + | 0.0572619i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.5066 | + | 22.8909i | 1.12309 | + | 0.815971i | 0.984674 | − | 0.174403i | \(-0.0557996\pi\) |
0.138414 | + | 0.990374i | \(0.455800\pi\) | |||||||
\(788\) | 2.32624 | − | 7.15942i | 0.0828688 | − | 0.255044i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −37.4164 | + | 27.1846i | −1.33122 | + | 0.967185i | ||||
\(791\) | −8.47214 | −0.301234 | ||||||||
\(792\) | 9.92705 | − | 0.673542i | 0.352742 | − | 0.0239333i | ||||
\(793\) | 24.9443 | 0.885797 | ||||||||
\(794\) | −6.30902 | + | 4.58377i | −0.223899 | + | 0.162672i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.42705 | − | 4.39201i | 0.0505805 | − | 0.155671i | ||||
\(797\) | 10.8541 | + | 7.88597i | 0.384472 | + | 0.279335i | 0.763186 | − | 0.646178i | \(-0.223634\pi\) |
−0.378714 | + | 0.925514i | \(0.623634\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.6844 | + | 45.1940i | −0.519497 | + | 1.59885i | ||||
\(800\) | 3.04508 | + | 9.37181i | 0.107660 | + | 0.331343i | ||||
\(801\) | −34.4164 | + | 25.0050i | −1.21604 | + | 0.883508i | ||||
\(802\) | −3.41641 | −0.120638 | ||||||||
\(803\) | 10.4721 | + | 26.0746i | 0.369554 | + | 0.920151i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.20820 | − | 1.60435i | 0.0778290 | − | 0.0565461i | ||||
\(806\) | −4.36068 | − | 13.4208i | −0.153598 | − | 0.472727i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.11803 | − | 0.812299i | −0.0393323 | − | 0.0285766i | ||||
\(809\) | 37.3885 | + | 27.1644i | 1.31451 | + | 0.955048i | 0.999983 | + | 0.00580010i | \(0.00184624\pi\) |
0.314528 | + | 0.949248i | \(0.398154\pi\) | |||||||
\(810\) | −10.7188 | + | 32.9892i | −0.376622 | + | 1.15912i | ||||
\(811\) | 17.2361 | + | 53.0472i | 0.605240 | + | 1.86274i | 0.495131 | + | 0.868818i | \(0.335120\pi\) |
0.110109 | + | 0.993919i | \(0.464880\pi\) | |||||||
\(812\) | −0.618034 | + | 0.449028i | −0.0216887 | + | 0.0157578i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.9443 | − | 16.2865i | −0.909346 | − | 0.570841i | ||||
\(815\) | −96.7001 | −3.38726 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.500000 | − | 1.53884i | −0.0174928 | − | 0.0538373i | ||||
\(818\) | 7.32624 | − | 22.5478i | 0.256156 | − | 0.788367i | ||||
\(819\) | 3.70820 | + | 2.69417i | 0.129575 | + | 0.0941418i | ||||
\(820\) | 32.6525 | + | 23.7234i | 1.14027 | + | 0.828457i | ||||
\(821\) | −2.46556 | + | 7.58821i | −0.0860486 | + | 0.264830i | −0.984818 | − | 0.173592i | \(-0.944463\pi\) |
0.898769 | + | 0.438422i | \(0.144463\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.97214 | − | 5.79210i | 0.277891 | − | 0.201900i | −0.440106 | − | 0.897946i | \(-0.645059\pi\) |
0.717997 | + | 0.696046i | \(0.245059\pi\) | |||||||
\(824\) | 7.41641 | 0.258363 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.18034 | −0.215042 | ||||||||
\(827\) | 30.0344 | − | 21.8213i | 1.04440 | − | 0.758801i | 0.0732603 | − | 0.997313i | \(-0.476660\pi\) |
0.971140 | + | 0.238512i | \(0.0766596\pi\) | |||||||
\(828\) | −1.06231 | − | 3.26944i | −0.0369177 | − | 0.113621i | ||||
\(829\) | 4.34752 | − | 13.3803i | 0.150996 | − | 0.464717i | −0.846737 | − | 0.532011i | \(-0.821436\pi\) |
0.997733 | + | 0.0672938i | \(0.0214365\pi\) | |||||||
\(830\) | 12.0172 | + | 8.73102i | 0.417124 | + | 0.303058i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.763932 | − | 2.35114i | 0.0264846 | − | 0.0815111i | ||||
\(833\) | −8.36475 | − | 25.7440i | −0.289821 | − | 0.891978i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.8328 | −1.06701 | ||||||||
\(836\) | 2.54508 | − | 2.12663i | 0.0880236 | − | 0.0735509i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.2533 | + | 7.44945i | −0.354194 | + | 0.257337i | ||||
\(839\) | 7.76393 | + | 23.8949i | 0.268041 | + | 0.824944i | 0.990977 | + | 0.134030i | \(0.0427919\pi\) |
−0.722937 | + | 0.690914i | \(0.757208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2254 | + | 16.1477i | 0.766394 | + | 0.556818i | ||||
\(842\) | 20.0344 | + | 14.5559i | 0.690432 | + | 0.501629i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.29180 | − | 16.2865i | −0.182151 | − | 0.560604i | ||||
\(845\) | −21.4787 | + | 15.6052i | −0.738890 | + | 0.536835i | ||||
\(846\) | 34.8541 | 1.19831 | ||||||||
\(847\) | −5.98936 | − | 3.21644i | −0.205797 | − | 0.110518i | ||||
\(848\) | 2.00000 | 0.0686803 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.4549 | + | 38.3323i | 0.427200 | + | 1.31479i | ||||
\(851\) | −3.27051 | + | 10.0656i | −0.112112 | + | 0.345044i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.2533 | + | 9.62908i | 0.453784 | + | 0.329693i | 0.791088 | − | 0.611702i | \(-0.209515\pi\) |
−0.337304 | + | 0.941396i | \(0.609515\pi\) | |||||||
\(854\) | 1.92705 | − | 5.93085i | 0.0659423 | − | 0.202950i | ||||
\(855\) | 3.57295 | + | 10.9964i | 0.122192 | + | 0.376069i | ||||
\(856\) | 7.47214 | − | 5.42882i | 0.255392 | − | 0.185553i | ||||
\(857\) | 32.8328 | 1.12155 | 0.560774 | − | 0.827969i | \(-0.310504\pi\) | ||||
0.560774 | + | 0.827969i | \(0.310504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.6869 | −0.671709 | −0.335854 | − | 0.941914i | \(-0.609025\pi\) | ||||
−0.335854 | + | 0.941914i | \(0.609025\pi\) | |||||||
\(860\) | −5.04508 | + | 3.66547i | −0.172036 | + | 0.124991i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.61803 | + | 26.5236i | −0.293531 | + | 0.903397i | ||||
\(863\) | −6.76393 | − | 4.91428i | −0.230247 | − | 0.167284i | 0.466680 | − | 0.884426i | \(-0.345450\pi\) |
−0.696927 | + | 0.717142i | \(0.745450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.1246 | − | 71.1702i | 0.786260 | − | 2.41986i | ||||
\(866\) | −11.2918 | − | 34.7526i | −0.383711 | − | 1.18094i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.52786 | −0.119744 | ||||||||
\(869\) | 9.70820 | − | 38.5973i | 0.329328 | − | 1.30932i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.0000 | − | 11.6247i | 0.542139 | − | 0.393887i | ||||
\(872\) | 0.527864 | + | 1.62460i | 0.0178757 | + | 0.0550158i | ||||
\(873\) | 6.97871 | − | 21.4783i | 0.236194 | − | 0.726929i | ||||
\(874\) | −0.927051 | − | 0.673542i | −0.0313580 | − | 0.0227829i | ||||
\(875\) | 9.35410 | + | 6.79615i | 0.316226 | + | 0.229752i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.36068 | − | 16.4985i | −0.181017 | − | 0.557114i | 0.818840 | − | 0.574022i | \(-0.194618\pi\) |
−0.999857 | + | 0.0169082i | \(0.994618\pi\) | |||||||
\(878\) | 29.4164 | − | 21.3723i | 0.992756 | − | 0.721279i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.8262 | − | 6.79615i | −0.364952 | − | 0.229098i | ||||
\(881\) | −10.9443 | −0.368722 | −0.184361 | − | 0.982859i | \(-0.559022\pi\) | ||||
−0.184361 | + | 0.982859i | \(0.559022\pi\) | |||||||
\(882\) | −16.0623 | + | 11.6699i | −0.540846 | + | 0.392948i | ||||
\(883\) | −10.6976 | − | 32.9237i | −0.360002 | − | 1.10797i | −0.953052 | − | 0.302806i | \(-0.902077\pi\) |
0.593051 | − | 0.805165i | \(-0.297923\pi\) | |||||||
\(884\) | 3.12461 | − | 9.61657i | 0.105092 | − | 0.323440i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.11803 | + | 1.53884i | 0.0711567 | + | 0.0516984i | ||||
\(887\) | 12.0344 | − | 37.0382i | 0.404077 | − | 1.24362i | −0.517586 | − | 0.855631i | \(-0.673169\pi\) |
0.921663 | − | 0.387990i | \(-0.126831\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.61803 | − | 1.90211i | 0.0878060 | − | 0.0637948i | ||||
\(890\) | 54.6525 | 1.83196 | ||||||||
\(891\) | −11.1246 | − | 27.6992i | −0.372689 | − | 0.927957i | ||||
\(892\) | 4.47214 | 0.149738 | ||||||||
\(893\) | 9.39919 | − | 6.82891i | 0.314532 | − | 0.228521i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.61803 | + | 26.5236i | −0.288069 | + | 0.886586i | ||||
\(896\) | −0.500000 | − | 0.363271i | −0.0167038 | − | 0.0121360i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.1803 | + | 31.3319i | −0.339722 | + | 1.04556i | ||||
\(899\) | −2.18034 | − | 6.71040i | −0.0727184 | − | 0.223804i | ||||
\(900\) | 23.9164 | − | 17.3763i | 0.797214 | − | 0.579210i | ||||
\(901\) | 8.18034 | 0.272527 | ||||||||
\(902\) | −34.6525 | + | 2.35114i | −1.15380 | + | 0.0782844i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.0902 | − | 8.05748i | 0.368854 | − | 0.267988i | ||||
\(905\) | 15.0689 | + | 46.3773i | 0.500907 | + | 1.54163i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.1246 | − | 23.3399i | −1.06668 | − | 0.774989i | −0.0913676 | − | 0.995817i | \(-0.529124\pi\) |
−0.975313 | + | 0.220829i | \(0.929124\pi\) | |||||||
\(908\) | −9.32624 | − | 6.77591i | −0.309502 | − | 0.224866i | ||||
\(909\) | −1.28115 | + | 3.94298i | −0.0424932 | + | 0.130781i | ||||
\(910\) | −1.81966 | − | 5.60034i | −0.0603211 | − | 0.185649i | ||||
\(911\) | 9.70820 | − | 7.05342i | 0.321647 | − | 0.233690i | −0.415231 | − | 0.909716i | \(-0.636299\pi\) |
0.736878 | + | 0.676026i | \(0.236299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.7533 | + | 0.865300i | −0.422072 | + | 0.0286372i | ||||
\(914\) | −30.7984 | −1.01872 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.173762 | − | 0.534785i | −0.00574126 | − | 0.0176698i | ||||
\(917\) | −1.20820 | + | 3.71847i | −0.0398984 | + | 0.122795i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.73607 | + | 5.62058i | 0.255189 | + | 0.185406i | 0.708024 | − | 0.706189i | \(-0.249587\pi\) |
−0.452834 | + | 0.891595i | \(0.649587\pi\) | |||||||
\(920\) | −1.36475 | + | 4.20025i | −0.0449943 | + | 0.138478i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.5344 | + | 14.9191i | −0.676266 | + | 0.491336i | ||||
\(923\) | 20.9443 | 0.689389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −91.0132 | −2.99249 | ||||||||
\(926\) | 14.4443 | − | 10.4944i | 0.474668 | − | 0.344867i | ||||
\(927\) | −6.87539 | − | 21.1603i | −0.225817 | − | 0.694994i | ||||
\(928\) | 0.381966 | − | 1.17557i | 0.0125386 | − | 0.0385900i | ||||
\(929\) | −28.1074 | − | 20.4212i | −0.922174 | − | 0.669998i | 0.0218905 | − | 0.999760i | \(-0.493031\pi\) |
−0.944064 | + | 0.329762i | \(0.893031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.04508 | + | 6.29412i | −0.0670250 | + | 0.206282i | ||||
\(932\) | −2.75329 | − | 8.47375i | −0.0901870 | − | 0.277567i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.14590 | 0.135658 | ||||||||
\(935\) | −44.2812 | − | 27.7974i | −1.44815 | − | 0.909073i | ||||
\(936\) | −7.41641 | −0.242413 | ||||||||
\(937\) | 17.6353 | − | 12.8128i | 0.576119 | − | 0.418575i | −0.261204 | − | 0.965284i | \(-0.584120\pi\) |
0.837323 | + | 0.546709i | \(0.184120\pi\) | |||||||
\(938\) | −1.52786 | − | 4.70228i | −0.0498865 | − | 0.153535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −36.2254 | − | 26.3193i | −1.18154 | − | 0.858441i | ||||
\(941\) | 6.52786 | + | 4.74277i | 0.212802 | + | 0.154610i | 0.689081 | − | 0.724685i | \(-0.258015\pi\) |
−0.476278 | + | 0.879295i | \(0.658015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.70820 | + | 11.4127i | 0.120756 | + | 0.371648i | ||||
\(944\) | 8.09017 | − | 5.87785i | 0.263313 | − | 0.191308i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.30902 | − | 5.20431i | 0.0425598 | − | 0.169207i | ||||
\(947\) | −50.0344 | −1.62590 | −0.812950 | − | 0.582333i | \(-0.802140\pi\) | ||||
−0.812950 | + | 0.582333i | \(0.802140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.47214 | − | 19.9192i | −0.210094 | − | 0.646604i | ||||
\(950\) | 3.04508 | − | 9.37181i | 0.0987956 | − | 0.304062i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.04508 | − | 1.48584i | −0.0662816 | − | 0.0481564i | ||||
\(953\) | −6.47214 | + | 19.9192i | −0.209653 | + | 0.645246i | 0.789837 | + | 0.613317i | \(0.210165\pi\) |
−0.999490 | + | 0.0319290i | \(0.989835\pi\) | |||||||
\(954\) | −1.85410 | − | 5.70634i | −0.0600288 | − | 0.184750i | ||||
\(955\) | 29.8156 | − | 21.6623i | 0.964810 | − | 0.700975i | ||||
\(956\) | 15.7984 | 0.510956 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.5623 | 0.535104 | ||||||||
\(959\) | 8.30902 | − | 6.03685i | 0.268312 | − | 0.194940i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.489357 | − | 1.50609i | 0.0157857 | − | 0.0485834i | ||||
\(962\) | 18.4721 | + | 13.4208i | 0.595566 | + | 0.432704i | ||||
\(963\) | −22.4164 | − | 16.2865i | −0.722359 | − | 0.524824i | ||||
\(964\) | 2.79837 | − | 8.61251i | 0.0901296 | − | 0.277390i | ||||
\(965\) | −2.38197 | − | 7.33094i | −0.0766782 | − | 0.235991i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.201626 | −0.00648386 | −0.00324193 | − | 0.999995i | \(-0.501032\pi\) | ||||
−0.00324193 | + | 0.999995i | \(0.501032\pi\) | |||||||
\(968\) | 10.8992 | − | 1.48584i | 0.350313 | − | 0.0477567i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.4721 | + | 17.0535i | −0.753645 | + | 0.547555i | ||||
\(971\) | −7.90983 | − | 24.3440i | −0.253839 | − | 0.781235i | −0.994056 | − | 0.108867i | \(-0.965278\pi\) |
0.740218 | − | 0.672367i | \(-0.234722\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.66312 | + | 7.02067i | 0.309785 | + | 0.225072i | ||||
\(974\) | −20.5623 | − | 14.9394i | −0.658859 | − | 0.478689i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.11803 | + | 9.59632i | 0.0998058 | + | 0.307171i | ||||
\(977\) | 7.00000 | − | 5.08580i | 0.223950 | − | 0.162709i | −0.470153 | − | 0.882585i | \(-0.655801\pi\) |
0.694103 | + | 0.719876i | \(0.255801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.0902 | + | 30.1563i | −1.15345 | + | 0.963799i | ||||
\(980\) | 25.5066 | 0.814778 | ||||||||
\(981\) | 4.14590 | − | 3.01217i | 0.132368 | − | 0.0961712i | ||||
\(982\) | −10.9894 | − | 33.8218i | −0.350684 | − | 1.07930i | ||||
\(983\) | 5.72949 | − | 17.6336i | 0.182742 | − | 0.562423i | −0.817160 | − | 0.576411i | \(-0.804453\pi\) |
0.999902 | + | 0.0139880i | \(0.00445268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.4721 | + | 17.0535i | 0.747884 | + | 0.543370i | ||||
\(986\) | 1.56231 | − | 4.80828i | 0.0497540 | − | 0.153127i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.00000 | + | 1.45309i | −0.0636285 | + | 0.0462288i | ||||
\(989\) | −1.85410 | −0.0589570 | ||||||||
\(990\) | −9.35410 | + | 37.1895i | −0.297293 | + | 1.18196i | ||||
\(991\) | −39.7082 | −1.26137 | −0.630686 | − | 0.776038i | \(-0.717227\pi\) | ||||
−0.630686 | + | 0.776038i | \(0.717227\pi\) | |||||||
\(992\) | 4.61803 | − | 3.35520i | 0.146623 | − | 0.106528i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.61803 | − | 4.97980i | 0.0513209 | − | 0.157950i | ||||
\(995\) | 14.3992 | + | 10.4616i | 0.456485 | + | 0.331656i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.84346 | − | 5.67358i | 0.0583829 | − | 0.179684i | −0.917612 | − | 0.397477i | \(-0.869886\pi\) |
0.975995 | + | 0.217793i | \(0.0698858\pi\) | |||||||
\(998\) | −7.19098 | − | 22.1316i | −0.227627 | − | 0.700563i | ||||
\(999\) | 0 | 0 |
(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 | 418.2.f.b.267.1 | yes | 4 | |
11.2 | odd | 10 | 4598.2.a.z.1.1 | 2 | |||
11.4 | even | 5 | inner | 418.2.f.b.191.1 | ✓ | 4 | |
11.9 | even | 5 | 4598.2.a.bh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.b.191.1 | ✓ | 4 | 11.4 | even | 5 | inner | |
418.2.f.b.267.1 | yes | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.z.1.1 | 2 | 11.2 | odd | 10 | |||
4598.2.a.bh.1.1 | 2 | 11.9 | even | 5 |