Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(26,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.26");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 18 x^{16} - 45 x^{15} + 59 x^{14} - 147 x^{13} + 271 x^{12} + \cdots + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.10 | ||
Root | \(-0.310170 + 1.70405i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.26 |
Dual form | 525.2.t.i.101.10 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36764 | + | 1.36696i | 1.67417 | + | 0.966585i | 0.965260 | + | 0.261291i | \(0.0841483\pi\) |
0.708915 | + | 0.705294i | \(0.249185\pi\) | |||||||
\(3\) | −1.63084 | − | 0.583411i | −0.941565 | − | 0.336833i | ||||
\(4\) | 2.73715 | + | 4.74088i | 1.36857 | + | 2.37044i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.06374 | − | 3.61059i | −1.25077 | − | 1.47402i | ||||
\(7\) | −2.24882 | + | 1.39384i | −0.849975 | + | 0.526823i | ||||
\(8\) | 9.49844i | 3.35821i | ||||||||
\(9\) | 2.31926 | + | 1.90290i | 0.773088 | + | 0.634299i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.79388 | − | 1.03570i | 0.540876 | − | 0.312275i | −0.204558 | − | 0.978854i | \(-0.565576\pi\) |
0.745434 | + | 0.666579i | \(0.232242\pi\) | |||||||
\(12\) | −1.69796 | − | 9.32849i | −0.490160 | − | 2.69290i | ||||
\(13\) | 2.04106i | 0.566088i | 0.959107 | + | 0.283044i | \(0.0913443\pi\) | ||||
−0.959107 | + | 0.283044i | \(0.908656\pi\) | |||||||
\(14\) | −7.22973 | + | 0.226073i | −1.93223 | + | 0.0604206i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.50967 | + | 13.0071i | −1.87742 | + | 3.25178i | ||||
\(17\) | 1.05144 | + | 1.82114i | 0.255011 | + | 0.441692i | 0.964899 | − | 0.262623i | \(-0.0845875\pi\) |
−0.709887 | + | 0.704315i | \(0.751254\pi\) | |||||||
\(18\) | 2.89000 | + | 7.67571i | 0.681179 | + | 1.80918i | ||||
\(19\) | −2.41421 | − | 1.39384i | −0.553857 | − | 0.319769i | 0.196819 | − | 0.980440i | \(-0.436939\pi\) |
−0.750676 | + | 0.660670i | \(0.770272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.48065 | − | 0.961143i | 0.977757 | − | 0.209739i | ||||
\(22\) | 5.66303 | 1.20736 | ||||||||
\(23\) | −1.53909 | − | 0.888591i | −0.320921 | − | 0.185284i | 0.330882 | − | 0.943672i | \(-0.392654\pi\) |
−0.651803 | + | 0.758388i | \(0.725987\pi\) | |||||||
\(24\) | 5.54150 | − | 15.4904i | 1.13115 | − | 3.16197i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.79004 | + | 4.83250i | −0.547173 | + | 0.947731i | ||||
\(27\) | −2.67217 | − | 4.45640i | −0.514259 | − | 0.857635i | ||||
\(28\) | −12.7634 | − | 6.84624i | −2.41206 | − | 1.29382i | ||||
\(29\) | 2.79774i | 0.519528i | 0.965672 | + | 0.259764i | \(0.0836448\pi\) | ||||
−0.965672 | + | 0.259764i | \(0.916355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.04532 | − | 3.49027i | 1.08577 | − | 0.626870i | 0.153324 | − | 0.988176i | \(-0.451002\pi\) |
0.932447 | + | 0.361306i | \(0.117669\pi\) | |||||||
\(32\) | −19.1086 | + | 11.0324i | −3.37796 | + | 1.95027i | ||||
\(33\) | −3.52977 | + | 0.642485i | −0.614454 | + | 0.111842i | ||||
\(34\) | 5.74909i | 0.985961i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.67324 | + | 16.2039i | −0.445541 | + | 2.70064i | ||||
\(37\) | 3.03329 | − | 5.25381i | 0.498670 | − | 0.863722i | −0.501329 | − | 0.865257i | \(-0.667155\pi\) |
0.999999 | + | 0.00153522i | \(0.000488676\pi\) | |||||||
\(38\) | −3.81065 | − | 6.60024i | −0.618169 | − | 1.07070i | ||||
\(39\) | 1.19078 | − | 3.32864i | 0.190677 | − | 0.533009i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.7165 | 1.82981 | 0.914905 | − | 0.403670i | \(-0.132266\pi\) | ||||
0.914905 | + | 0.403670i | \(0.132266\pi\) | |||||||
\(42\) | 11.9224 | + | 3.84922i | 1.83967 | + | 0.593947i | ||||
\(43\) | 4.37014 | 0.666440 | 0.333220 | − | 0.942849i | \(-0.391865\pi\) | ||||
0.333220 | + | 0.942849i | \(0.391865\pi\) | |||||||
\(44\) | 9.82025 | + | 5.66973i | 1.48046 | + | 0.854743i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.42933 | − | 4.20773i | −0.358186 | − | 0.620396i | ||||
\(47\) | −1.47384 | + | 2.55277i | −0.214982 | + | 0.372360i | −0.953267 | − | 0.302129i | \(-0.902303\pi\) |
0.738285 | + | 0.674489i | \(0.235636\pi\) | |||||||
\(48\) | 19.8356 | − | 16.8313i | 2.86302 | − | 2.42939i | ||||
\(49\) | 3.11440 | − | 6.26901i | 0.444915 | − | 0.895573i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.652249 | − | 3.58341i | −0.0913331 | − | 0.501778i | ||||
\(52\) | −9.67643 | + | 5.58669i | −1.34188 | + | 0.774734i | ||||
\(53\) | 5.36432 | − | 3.09709i | 0.736846 | − | 0.425418i | −0.0840757 | − | 0.996459i | \(-0.526794\pi\) |
0.820921 | + | 0.571041i | \(0.193460\pi\) | |||||||
\(54\) | −0.235023 | − | 14.2039i | −0.0319825 | − | 1.93291i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.2393 | − | 21.3603i | −1.76918 | − | 2.85439i | ||||
\(57\) | 3.12400 | + | 3.68161i | 0.413783 | + | 0.487641i | ||||
\(58\) | −3.82440 | + | 6.62405i | −0.502168 | + | 0.869781i | ||||
\(59\) | −1.44301 | − | 2.49936i | −0.187864 | − | 0.325389i | 0.756674 | − | 0.653792i | \(-0.226823\pi\) |
−0.944538 | + | 0.328403i | \(0.893490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.30263 | − | 3.63883i | −0.806969 | − | 0.465904i | 0.0389331 | − | 0.999242i | \(-0.487604\pi\) |
−0.845902 | + | 0.533338i | \(0.820937\pi\) | |||||||
\(62\) | 19.0842 | 2.42369 | ||||||||
\(63\) | −7.86795 | − | 1.04659i | −0.991269 | − | 0.131858i | ||||
\(64\) | −30.2845 | −3.78556 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.23548 | − | 3.30387i | −1.13681 | − | 0.406679i | ||||
\(67\) | −3.70150 | − | 6.41119i | −0.452211 | − | 0.783252i | 0.546312 | − | 0.837581i | \(-0.316031\pi\) |
−0.998523 | + | 0.0543297i | \(0.982698\pi\) | |||||||
\(68\) | −5.75589 | + | 9.96949i | −0.698004 | + | 1.20898i | ||||
\(69\) | 1.99158 | + | 2.34707i | 0.239759 | + | 0.282554i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.80885i | − | 0.452027i | −0.974124 | − | 0.226014i | \(-0.927431\pi\) | ||
0.974124 | − | 0.226014i | \(-0.0725694\pi\) | |||||||
\(72\) | −18.0746 | + | 22.0294i | −2.13011 | + | 2.59619i | ||||
\(73\) | −5.81273 | + | 3.35598i | −0.680328 | + | 0.392788i | −0.799979 | − | 0.600028i | \(-0.795156\pi\) |
0.119651 | + | 0.992816i | \(0.461823\pi\) | |||||||
\(74\) | 14.3635 | − | 8.29276i | 1.66972 | − | 0.964014i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 15.2606i | − | 1.75051i | ||||||
\(77\) | −2.59052 | + | 4.82949i | −0.295218 | + | 0.550372i | ||||
\(78\) | 7.36944 | − | 6.25328i | 0.834425 | − | 0.708044i | ||||
\(79\) | 2.95787 | − | 5.12317i | 0.332786 | − | 0.576402i | −0.650271 | − | 0.759702i | \(-0.725345\pi\) |
0.983057 | + | 0.183300i | \(0.0586781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.75796 | + | 8.82664i | 0.195329 | + | 0.980738i | ||||
\(82\) | 27.7405 | + | 16.0160i | 3.06342 | + | 1.76867i | ||||
\(83\) | 5.96419 | 0.654655 | 0.327327 | − | 0.944911i | \(-0.393852\pi\) | ||||
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(84\) | 16.8209 | + | 18.6114i | 1.83531 | + | 2.03067i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.3469 | + | 5.97380i | 1.11574 | + | 0.644171i | ||||
\(87\) | 1.63224 | − | 4.56267i | 0.174994 | − | 0.489169i | ||||
\(88\) | 9.83752 | + | 17.0391i | 1.04868 | + | 1.81637i | ||||
\(89\) | −6.20912 | + | 10.7545i | −0.658166 | + | 1.13998i | 0.322924 | + | 0.946425i | \(0.395334\pi\) |
−0.981090 | + | 0.193552i | \(0.937999\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.84492 | − | 4.58998i | −0.298228 | − | 0.481161i | ||||
\(92\) | − | 9.72883i | − | 1.01430i | ||||||
\(93\) | −11.8952 | + | 2.16515i | −1.23347 | + | 0.224516i | ||||
\(94\) | −6.97906 | + | 4.02936i | −0.719835 | + | 0.415597i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 37.5995 | − | 6.84382i | 3.83748 | − | 0.698494i | ||||
\(97\) | − | 9.97170i | − | 1.01247i | −0.862395 | − | 0.506237i | \(-0.831036\pi\) | ||
0.862395 | − | 0.506237i | \(-0.168964\pi\) | |||||||
\(98\) | 15.9433 | − | 10.5855i | 1.61051 | − | 1.06930i | ||||
\(99\) | 6.13132 | + | 1.01152i | 0.616220 | + | 0.101661i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.06825 | + | 13.9746i | 0.802821 | + | 1.39053i | 0.917752 | + | 0.397153i | \(0.130002\pi\) |
−0.114931 | + | 0.993373i | \(0.536665\pi\) | |||||||
\(102\) | 3.35408 | − | 9.37583i | 0.332104 | − | 0.928345i | ||||
\(103\) | 0.453075 | + | 0.261583i | 0.0446428 | + | 0.0257745i | 0.522155 | − | 0.852850i | \(-0.325128\pi\) |
−0.477513 | + | 0.878625i | \(0.658461\pi\) | |||||||
\(104\) | −19.3869 | −1.90104 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.9344 | 1.64481 | ||||||||
\(107\) | −2.66952 | − | 1.54125i | −0.258073 | − | 0.148998i | 0.365382 | − | 0.930858i | \(-0.380938\pi\) |
−0.623455 | + | 0.781859i | \(0.714272\pi\) | |||||||
\(108\) | 13.8131 | − | 24.8663i | 1.32917 | − | 2.39276i | ||||
\(109\) | −6.77743 | − | 11.7389i | −0.649160 | − | 1.12438i | −0.983324 | − | 0.181864i | \(-0.941787\pi\) |
0.334163 | − | 0.942515i | \(-0.391546\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.01194 | + | 6.79846i | −0.760459 | + | 0.645281i | ||||
\(112\) | −1.24198 | − | 39.7180i | −0.117356 | − | 3.75300i | ||||
\(113\) | 11.0653i | 1.04093i | 0.853883 | + | 0.520466i | \(0.174242\pi\) | ||||
−0.853883 | + | 0.520466i | \(0.825758\pi\) | |||||||
\(114\) | 2.36390 | + | 12.9871i | 0.221399 | + | 1.21635i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.2638 | + | 7.65784i | −1.23151 | + | 0.711013i | ||||
\(117\) | −3.88393 | + | 4.73376i | −0.359069 | + | 0.437636i | ||||
\(118\) | − | 7.89013i | − | 0.726345i | ||||||
\(119\) | −4.90289 | − | 2.62989i | −0.449447 | − | 0.241082i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.35465 | + | 5.81043i | −0.304969 | + | 0.528221i | ||||
\(122\) | −9.94824 | − | 17.2309i | −0.900672 | − | 1.56001i | ||||
\(123\) | −19.1077 | − | 6.83554i | −1.72288 | − | 0.616340i | ||||
\(124\) | 33.0939 | + | 19.1068i | 2.97192 | + | 1.71584i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −17.1978 | − | 13.2331i | −1.53210 | − | 1.17890i | ||||
\(127\) | −4.98617 | −0.442451 | −0.221226 | − | 0.975223i | \(-0.571006\pi\) | ||||
−0.221226 | + | 0.975223i | \(0.571006\pi\) | |||||||
\(128\) | −33.4855 | − | 19.3329i | −2.95973 | − | 1.70880i | ||||
\(129\) | −7.12699 | − | 2.54959i | −0.627497 | − | 0.224479i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.85196 | − | 10.1359i | 0.511288 | − | 0.885577i | −0.488626 | − | 0.872493i | \(-0.662502\pi\) |
0.999914 | − | 0.0130842i | \(-0.00416493\pi\) | |||||||
\(132\) | −12.7075 | − | 14.9756i | −1.10604 | − | 1.30346i | ||||
\(133\) | 7.37192 | − | 0.230519i | 0.639226 | − | 0.0199886i | ||||
\(134\) | − | 20.2392i | − | 1.74840i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −17.2980 | + | 9.98702i | −1.48329 | + | 0.856380i | ||||
\(137\) | 10.9606 | − | 6.32808i | 0.936423 | − | 0.540644i | 0.0475860 | − | 0.998867i | \(-0.484847\pi\) |
0.888837 | + | 0.458223i | \(0.151514\pi\) | |||||||
\(138\) | 1.50701 | + | 8.27943i | 0.128285 | + | 0.704791i | ||||
\(139\) | 18.0304i | 1.52932i | 0.644434 | + | 0.764660i | \(0.277093\pi\) | ||||
−0.644434 | + | 0.764660i | \(0.722907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.89291 | − | 3.30330i | 0.327842 | − | 0.278188i | ||||
\(142\) | 5.20654 | − | 9.01798i | 0.436923 | − | 0.756772i | ||||
\(143\) | 2.11392 | + | 3.66143i | 0.176775 | + | 0.306184i | ||||
\(144\) | −42.1681 | + | 15.8768i | −3.51401 | + | 1.32307i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −18.3499 | −1.51865 | ||||||||
\(147\) | −8.73650 | + | 8.40676i | −0.720574 | + | 0.693378i | ||||
\(148\) | 33.2103 | 2.72987 | ||||||||
\(149\) | −12.6249 | − | 7.28898i | −1.03427 | − | 0.597136i | −0.116065 | − | 0.993242i | \(-0.537028\pi\) |
−0.918205 | + | 0.396105i | \(0.870362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.51450 | + | 6.08730i | 0.286006 | + | 0.495377i | 0.972853 | − | 0.231425i | \(-0.0743389\pi\) |
−0.686847 | + | 0.726802i | \(0.741006\pi\) | |||||||
\(152\) | 13.2393 | − | 22.9312i | 1.07385 | − | 1.85997i | ||||
\(153\) | −1.02689 | + | 6.22449i | −0.0830192 | + | 0.503220i | ||||
\(154\) | −12.7351 | + | 7.89337i | −1.02623 | + | 0.636066i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 19.0400 | − | 3.46564i | 1.52442 | − | 0.277474i | ||||
\(157\) | −18.9680 | + | 10.9512i | −1.51381 | + | 0.874000i | −0.513943 | + | 0.857824i | \(0.671816\pi\) |
−0.999869 | + | 0.0161753i | \(0.994851\pi\) | |||||||
\(158\) | 14.0063 | − | 8.08656i | 1.11428 | − | 0.643332i | ||||
\(159\) | −10.5552 | + | 1.92125i | −0.837082 | + | 0.152365i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.69969 | − | 0.146959i | 0.370387 | − | 0.0115820i | ||||
\(162\) | −7.90343 | + | 23.3014i | −0.620952 | + | 1.83073i | ||||
\(163\) | 4.04815 | − | 7.01159i | 0.317075 | − | 0.549190i | −0.662801 | − | 0.748795i | \(-0.730633\pi\) |
0.979876 | + | 0.199605i | \(0.0639659\pi\) | |||||||
\(164\) | 32.0698 | + | 55.5465i | 2.50423 | + | 4.33745i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.1211 | + | 8.15279i | 1.09601 | + | 0.632780i | ||||
\(167\) | 3.58777 | 0.277630 | 0.138815 | − | 0.990318i | \(-0.455671\pi\) | ||||
0.138815 | + | 0.990318i | \(0.455671\pi\) | |||||||
\(168\) | 9.12936 | + | 42.5592i | 0.704345 | + | 3.28351i | ||||
\(169\) | 8.83407 | 0.679544 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.94684 | − | 7.82668i | −0.225350 | − | 0.598521i | ||||
\(172\) | 11.9617 | + | 20.7183i | 0.912073 | + | 1.57976i | ||||
\(173\) | 6.50462 | − | 11.2663i | 0.494537 | − | 0.856563i | −0.505443 | − | 0.862860i | \(-0.668671\pi\) |
0.999980 | + | 0.00629680i | \(0.00200435\pi\) | |||||||
\(174\) | 10.1015 | − | 8.57156i | 0.765794 | − | 0.649808i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 31.1110i | 2.34508i | ||||||||
\(177\) | 0.895156 | + | 4.91792i | 0.0672840 | + | 0.369654i | ||||
\(178\) | −29.4020 | + | 16.9752i | −2.20377 | + | 1.27235i | ||||
\(179\) | −3.50400 | + | 2.02304i | −0.261902 | + | 0.151209i | −0.625202 | − | 0.780463i | \(-0.714983\pi\) |
0.363300 | + | 0.931672i | \(0.381650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.00970i | 0.669686i | 0.942274 | + | 0.334843i | \(0.108683\pi\) | ||||
−0.942274 | + | 0.334843i | \(0.891317\pi\) | |||||||
\(182\) | −0.461429 | − | 14.7563i | −0.0342034 | − | 1.09381i | ||||
\(183\) | 8.15564 | + | 9.61136i | 0.602882 | + | 0.710492i | ||||
\(184\) | 8.44023 | − | 14.6189i | 0.622222 | − | 1.07772i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −31.1232 | − | 11.1339i | −2.28206 | − | 0.816379i | ||||
\(187\) | 3.77232 | + | 2.17795i | 0.275859 | + | 0.159267i | ||||
\(188\) | −16.1365 | −1.17688 | ||||||||
\(189\) | 12.2208 | + | 6.29707i | 0.888929 | + | 0.458045i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.6067 | − | 13.0520i | −1.63576 | − | 0.944409i | −0.982269 | − | 0.187478i | \(-0.939969\pi\) |
−0.653495 | − | 0.756931i | \(-0.726698\pi\) | |||||||
\(192\) | 49.3891 | + | 17.6683i | 3.56435 | + | 1.27510i | ||||
\(193\) | −3.75401 | − | 6.50213i | −0.270219 | − | 0.468034i | 0.698699 | − | 0.715416i | \(-0.253763\pi\) |
−0.968918 | + | 0.247383i | \(0.920430\pi\) | |||||||
\(194\) | 13.6309 | − | 23.6094i | 0.978642 | − | 1.69506i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 38.2452 | − | 2.39419i | 2.73180 | − | 0.171014i | ||||
\(197\) | 20.7941i | 1.48152i | 0.671772 | + | 0.740758i | \(0.265534\pi\) | ||||
−0.671772 | + | 0.740758i | \(0.734466\pi\) | |||||||
\(198\) | 13.1341 | + | 10.7762i | 0.933396 | + | 0.765829i | ||||
\(199\) | −19.8822 | + | 11.4790i | −1.40941 | + | 0.813725i | −0.995332 | − | 0.0965149i | \(-0.969230\pi\) |
−0.414081 | + | 0.910240i | \(0.635897\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.29619 | + | 12.6151i | 0.161961 | + | 0.889801i | ||||
\(202\) | 44.1158i | 3.10398i | ||||||||
\(203\) | −3.89962 | − | 6.29163i | −0.273699 | − | 0.441586i | ||||
\(204\) | 15.2032 | − | 12.9006i | 1.06444 | − | 0.903220i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.715145 | + | 1.23867i | 0.0498265 | + | 0.0863021i | ||||
\(207\) | −1.87864 | − | 4.98960i | −0.130575 | − | 0.346801i | ||||
\(208\) | −26.5483 | − | 15.3277i | −1.84080 | − | 1.06278i | ||||
\(209\) | −5.77441 | −0.399424 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.9736 | −1.30620 | −0.653098 | − | 0.757273i | \(-0.726531\pi\) | ||||
−0.653098 | + | 0.757273i | \(0.726531\pi\) | |||||||
\(212\) | 29.3659 | + | 16.9544i | 2.01686 | + | 1.16443i | ||||
\(213\) | −2.22212 | + | 6.21161i | −0.152257 | + | 0.425613i | ||||
\(214\) | −4.21365 | − | 7.29826i | −0.288039 | − | 0.498899i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 42.3289 | − | 25.3814i | 2.88011 | − | 1.72699i | ||||
\(217\) | −8.72996 | + | 16.2752i | −0.592628 | + | 1.10483i | ||||
\(218\) | − | 37.0579i | − | 2.50988i | ||||||
\(219\) | 11.4375 | − | 2.08185i | 0.772877 | − | 0.140678i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.71707 | + | 2.14605i | −0.250037 | + | 0.144359i | ||||
\(222\) | −28.2626 | + | 5.14433i | −1.89686 | + | 0.345265i | ||||
\(223\) | − | 6.06277i | − | 0.405993i | −0.979179 | − | 0.202997i | \(-0.934932\pi\) | ||
0.979179 | − | 0.202997i | \(-0.0650681\pi\) | |||||||
\(224\) | 27.5945 | − | 51.4443i | 1.84374 | − | 3.43726i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.1257 | + | 26.1985i | −1.00615 | + | 1.74270i | ||||
\(227\) | −10.9025 | − | 18.8837i | −0.723626 | − | 1.25336i | −0.959537 | − | 0.281582i | \(-0.909141\pi\) |
0.235911 | − | 0.971775i | \(-0.424193\pi\) | |||||||
\(228\) | −8.90322 | + | 24.8876i | −0.589630 | + | 1.64822i | ||||
\(229\) | −7.94782 | − | 4.58868i | −0.525207 | − | 0.303228i | 0.213856 | − | 0.976865i | \(-0.431398\pi\) |
−0.739062 | + | 0.673637i | \(0.764731\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.04230 | − | 6.36478i | 0.463350 | − | 0.418772i | ||||
\(232\) | −26.5742 | −1.74468 | ||||||||
\(233\) | 15.7465 | + | 9.09122i | 1.03158 | + | 0.595586i | 0.917438 | − | 0.397878i | \(-0.130253\pi\) |
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(234\) | −15.6666 | + | 5.89866i | −1.02416 | + | 0.385608i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.89946 | − | 13.6823i | 0.514211 | − | 0.890640i | ||||
\(237\) | −7.81271 | + | 6.62941i | −0.507490 | + | 0.430627i | ||||
\(238\) | −8.01333 | − | 12.9287i | −0.519427 | − | 0.838042i | ||||
\(239\) | 13.1450i | 0.850278i | 0.905128 | + | 0.425139i | \(0.139775\pi\) | ||||
−0.905128 | + | 0.425139i | \(0.860225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0154860 | − | 0.00894087i | 0.000997544 | − | 0.000575932i | −0.499501 | − | 0.866313i | \(-0.666483\pi\) |
0.500499 | + | 0.865737i | \(0.333150\pi\) | |||||||
\(242\) | −15.8852 | + | 9.17135i | −1.02114 | + | 0.589556i | ||||
\(243\) | 2.28261 | − | 15.4204i | 0.146430 | − | 0.989221i | ||||
\(244\) | − | 39.8400i | − | 2.55050i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −35.8963 | − | 42.3035i | −2.28866 | − | 2.69717i | ||||
\(247\) | 2.84492 | − | 4.92754i | 0.181018 | − | 0.313532i | ||||
\(248\) | 33.1521 | + | 57.4211i | 2.10516 | + | 3.64624i | ||||
\(249\) | −9.72662 | − | 3.47957i | −0.616400 | − | 0.220509i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.38577 | −0.339947 | −0.169973 | − | 0.985449i | \(-0.554368\pi\) | ||||
−0.169973 | + | 0.985449i | \(0.554368\pi\) | |||||||
\(252\) | −16.5740 | − | 40.1657i | −1.04406 | − | 2.53020i | ||||
\(253\) | −3.68125 | −0.231438 | ||||||||
\(254\) | −11.8055 | − | 6.81589i | −0.740741 | − | 0.427667i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −22.5700 | − | 39.0923i | −1.41062 | − | 2.44327i | ||||
\(257\) | 10.8420 | − | 18.7790i | 0.676308 | − | 1.17140i | −0.299777 | − | 0.954009i | \(-0.596912\pi\) |
0.976085 | − | 0.217391i | \(-0.0697545\pi\) | |||||||
\(258\) | −13.3890 | − | 15.7788i | −0.833561 | − | 0.982346i | ||||
\(259\) | 0.501658 | + | 16.0428i | 0.0311715 | + | 0.996852i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.32382 | + | 6.48871i | −0.329536 | + | 0.401641i | ||||
\(262\) | 27.7107 | − | 15.9988i | 1.71197 | − | 0.988408i | ||||
\(263\) | 1.24114 | − | 0.716573i | 0.0765320 | − | 0.0441858i | −0.461246 | − | 0.887272i | \(-0.652597\pi\) |
0.537778 | + | 0.843087i | \(0.319264\pi\) | |||||||
\(264\) | −6.10261 | − | 33.5273i | −0.375590 | − | 2.06346i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 17.7692 | + | 9.53132i | 1.08950 | + | 0.584403i | ||||
\(267\) | 16.4004 | − | 13.9164i | 1.00369 | − | 0.851670i | ||||
\(268\) | 20.2631 | − | 35.0968i | 1.23777 | − | 2.14388i | ||||
\(269\) | −9.99414 | − | 17.3104i | −0.609354 | − | 1.05543i | −0.991347 | − | 0.131266i | \(-0.958096\pi\) |
0.381993 | − | 0.924165i | \(-0.375238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.6061 | − | 7.85550i | −0.826513 | − | 0.477187i | 0.0261443 | − | 0.999658i | \(-0.491677\pi\) |
−0.852657 | + | 0.522471i | \(0.825010\pi\) | |||||||
\(272\) | −31.5838 | −1.91505 | ||||||||
\(273\) | 1.96175 | + | 9.14527i | 0.118731 | + | 0.553497i | ||||
\(274\) | 34.6009 | 2.09032 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.67591 | + | 15.8661i | −0.341649 | + | 0.955029i | ||||
\(277\) | −1.09487 | − | 1.89637i | −0.0657844 | − | 0.113942i | 0.831257 | − | 0.555888i | \(-0.187622\pi\) |
−0.897042 | + | 0.441946i | \(0.854288\pi\) | |||||||
\(278\) | −24.6468 | + | 42.6896i | −1.47822 | + | 2.56035i | ||||
\(279\) | 20.6623 | + | 3.40878i | 1.23702 | + | 0.204078i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.0597482i | − | 0.00356428i | −0.999998 | − | 0.00178214i | \(-0.999433\pi\) | ||
0.999998 | − | 0.00178214i | \(-0.000567273\pi\) | |||||||
\(282\) | 13.7325 | − | 2.49957i | 0.817757 | − | 0.148847i | ||||
\(283\) | 13.8059 | − | 7.97086i | 0.820677 | − | 0.473818i | −0.0299727 | − | 0.999551i | \(-0.509542\pi\) |
0.850650 | + | 0.525733i | \(0.176209\pi\) | |||||||
\(284\) | 18.0573 | − | 10.4254i | 1.07150 | − | 0.618633i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.5586i | 0.683474i | ||||||||
\(287\) | −26.3483 | + | 16.3310i | −1.55529 | + | 0.963986i | ||||
\(288\) | −65.3114 | − | 10.7748i | −3.84851 | − | 0.634911i | ||||
\(289\) | 6.28895 | − | 10.8928i | 0.369939 | − | 0.640752i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.81760 | + | 16.2622i | −0.341034 | + | 0.953309i | ||||
\(292\) | −31.8206 | − | 18.3716i | −1.86216 | − | 1.07512i | ||||
\(293\) | 19.3670 | 1.13143 | 0.565715 | − | 0.824601i | \(-0.308600\pi\) | ||||
0.565715 | + | 0.824601i | \(0.308600\pi\) | |||||||
\(294\) | −32.1766 | + | 7.96176i | −1.87658 | + | 0.464339i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 49.9030 | + | 28.8115i | 2.90055 | + | 1.67464i | ||||
\(297\) | −9.40905 | − | 5.22670i | −0.545968 | − | 0.303284i | ||||
\(298\) | −19.9275 | − | 34.5154i | −1.15437 | − | 1.99942i | ||||
\(299\) | 1.81367 | − | 3.14137i | 0.104887 | − | 0.181670i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.82767 | + | 6.09129i | −0.566458 | + | 0.351096i | ||||
\(302\) | 19.2167i | 1.10580i | ||||||||
\(303\) | −5.00506 | − | 27.4974i | −0.287533 | − | 1.57969i | ||||
\(304\) | 36.2598 | − | 20.9346i | 2.07964 | − | 1.20068i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.9399 | + | 13.3336i | −0.625394 | + | 0.762234i | ||||
\(307\) | − | 17.7639i | − | 1.01384i | −0.861993 | − | 0.506921i | \(-0.830784\pi\) | ||
0.861993 | − | 0.506921i | \(-0.169216\pi\) | |||||||
\(308\) | −29.9867 | + | 0.937683i | −1.70865 | + | 0.0534294i | ||||
\(309\) | −0.586281 | − | 0.690928i | −0.0333523 | − | 0.0393055i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.58777 | + | 6.21419i | 0.203444 | + | 0.352375i | 0.949636 | − | 0.313356i | \(-0.101453\pi\) |
−0.746192 | + | 0.665731i | \(0.768120\pi\) | |||||||
\(312\) | 31.6169 | + | 11.3105i | 1.78995 | + | 0.640333i | ||||
\(313\) | 11.7724 | + | 6.79679i | 0.665414 | + | 0.384177i | 0.794337 | − | 0.607477i | \(-0.207818\pi\) |
−0.128922 | + | 0.991655i | \(0.541152\pi\) | |||||||
\(314\) | −59.8792 | −3.37918 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.3845 | 1.82177 | ||||||||
\(317\) | 2.78896 | + | 1.61021i | 0.156644 | + | 0.0904383i | 0.576273 | − | 0.817257i | \(-0.304507\pi\) |
−0.419629 | + | 0.907696i | \(0.637840\pi\) | |||||||
\(318\) | −27.6172 | − | 9.87970i | −1.54870 | − | 0.554026i | ||||
\(319\) | 2.89762 | + | 5.01883i | 0.162236 | + | 0.281000i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.45438 | + | 4.07096i | 0.192805 | + | 0.227219i | ||||
\(322\) | 11.3281 | + | 6.07633i | 0.631288 | + | 0.338621i | ||||
\(323\) | − | 5.86216i | − | 0.326179i | ||||||
\(324\) | −37.0343 | + | 32.4941i | −2.05746 | + | 1.80523i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.1691 | − | 11.0673i | 1.06168 | − | 0.612961i | ||||
\(327\) | 4.20431 | + | 23.0982i | 0.232499 | + | 1.27733i | ||||
\(328\) | 111.288i | 6.14488i | ||||||||
\(329\) | −0.243750 | − | 7.79503i | −0.0134384 | − | 0.429754i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.59353 | − | 2.76008i | 0.0875885 | − | 0.151708i | −0.818903 | − | 0.573932i | \(-0.805417\pi\) |
0.906491 | + | 0.422224i | \(0.138751\pi\) | |||||||
\(332\) | 16.3249 | + | 28.2755i | 0.895944 | + | 1.55182i | ||||
\(333\) | 17.0325 | − | 6.41293i | 0.933373 | − | 0.351426i | ||||
\(334\) | 8.49454 | + | 4.90433i | 0.464801 | + | 0.268353i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −21.1465 | + | 65.4982i | −1.15363 | + | 3.57322i | ||||
\(337\) | 33.9495 | 1.84935 | 0.924673 | − | 0.380763i | \(-0.124339\pi\) | ||||
0.924673 | + | 0.380763i | \(0.124339\pi\) | |||||||
\(338\) | 20.9159 | + | 12.0758i | 1.13768 | + | 0.656837i | ||||
\(339\) | 6.45559 | − | 18.0456i | 0.350620 | − | 0.980104i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.22973 | − | 12.5223i | 0.391512 | − | 0.678118i | ||||
\(342\) | 3.72168 | − | 22.5590i | 0.201246 | − | 1.21985i | ||||
\(343\) | 1.73427 | + | 18.4389i | 0.0936419 | + | 0.995606i | ||||
\(344\) | 41.5095i | 2.23804i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 30.8012 | − | 17.7831i | 1.65588 | − | 0.956024i | ||||
\(347\) | 24.2234 | − | 13.9854i | 1.30038 | − | 0.750773i | 0.319909 | − | 0.947448i | \(-0.396348\pi\) |
0.980469 | + | 0.196675i | \(0.0630144\pi\) | |||||||
\(348\) | 26.0987 | − | 4.75047i | 1.39904 | − | 0.254652i | ||||
\(349\) | − | 19.3368i | − | 1.03508i | −0.855660 | − | 0.517539i | \(-0.826848\pi\) | ||
0.855660 | − | 0.517539i | \(-0.173152\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.09579 | − | 5.45406i | 0.485497 | − | 0.291116i | ||||
\(352\) | −22.8524 | + | 39.5816i | −1.21804 | + | 2.10971i | ||||
\(353\) | −3.44352 | − | 5.96436i | −0.183280 | − | 0.317451i | 0.759715 | − | 0.650256i | \(-0.225338\pi\) |
−0.942996 | + | 0.332805i | \(0.892005\pi\) | |||||||
\(354\) | −4.60319 | + | 12.8675i | −0.244657 | + | 0.683901i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −67.9812 | −3.60300 | ||||||||
\(357\) | 6.46151 | + | 7.14932i | 0.341979 | + | 0.378382i | ||||
\(358\) | −11.0616 | −0.584625 | ||||||||
\(359\) | 18.0588 | + | 10.4263i | 0.953108 | + | 0.550277i | 0.894045 | − | 0.447977i | \(-0.147855\pi\) |
0.0590629 | + | 0.998254i | \(0.481189\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.61440 | − | 9.72443i | −0.295495 | − | 0.511812i | ||||
\(362\) | −12.3159 | + | 21.3317i | −0.647309 | + | 1.12117i | ||||
\(363\) | 8.86077 | − | 7.51873i | 0.465070 | − | 0.394631i | ||||
\(364\) | 13.9736 | − | 26.0509i | 0.732416 | − | 1.36544i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.17129 | + | 33.9047i | 0.322579 | + | 1.77222i | ||||
\(367\) | −20.7408 | + | 11.9747i | −1.08266 | + | 0.625075i | −0.931613 | − | 0.363451i | \(-0.881598\pi\) |
−0.151048 | + | 0.988526i | \(0.548265\pi\) | |||||||
\(368\) | 23.1160 | − | 13.3461i | 1.20501 | − | 0.695711i | ||||
\(369\) | 27.1736 | + | 22.2953i | 1.41460 | + | 1.16065i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.74654 | + | 14.4418i | −0.402180 | + | 0.749782i | ||||
\(372\) | −42.8236 | − | 50.4673i | −2.22030 | − | 2.61661i | ||||
\(373\) | −1.99026 | + | 3.44723i | −0.103052 | + | 0.178491i | −0.912940 | − | 0.408093i | \(-0.866194\pi\) |
0.809889 | + | 0.586583i | \(0.199527\pi\) | |||||||
\(374\) | 5.95433 | + | 10.3132i | 0.307891 | + | 0.533283i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.2473 | − | 13.9992i | −1.25046 | − | 0.721954i | ||||
\(377\) | −5.71037 | −0.294099 | ||||||||
\(378\) | 20.3265 | + | 31.6145i | 1.04548 | + | 1.62607i | ||||
\(379\) | −13.9203 | −0.715038 | −0.357519 | − | 0.933906i | \(-0.616377\pi\) | ||||
−0.357519 | + | 0.933906i | \(0.616377\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.13164 | + | 2.90899i | 0.416596 | + | 0.149032i | ||||
\(382\) | −35.6830 | − | 61.8048i | −1.82570 | − | 3.16221i | ||||
\(383\) | −7.90064 | + | 13.6843i | −0.403704 | + | 0.699236i | −0.994170 | − | 0.107827i | \(-0.965611\pi\) |
0.590466 | + | 0.807063i | \(0.298944\pi\) | |||||||
\(384\) | 43.3304 | + | 51.0646i | 2.21120 | + | 2.60588i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 20.5263i | − | 1.04476i | ||||||
\(387\) | 10.1355 | + | 8.31593i | 0.515217 | + | 0.422723i | ||||
\(388\) | 47.2747 | − | 27.2940i | 2.40001 | − | 1.38564i | ||||
\(389\) | 21.7212 | − | 12.5407i | 1.10131 | − | 0.635841i | 0.164744 | − | 0.986336i | \(-0.447320\pi\) |
0.936564 | + | 0.350495i | \(0.113987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.73720i | − | 0.188998i | ||||||
\(392\) | 59.5458 | + | 29.5820i | 3.00752 | + | 1.49412i | ||||
\(393\) | −15.4570 | + | 13.1159i | −0.779702 | + | 0.661610i | ||||
\(394\) | −28.4246 | + | 49.2329i | −1.43201 | + | 2.48032i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 11.9868 | + | 31.8365i | 0.602361 | + | 1.59985i | ||||
\(397\) | 1.27064 | + | 0.733605i | 0.0637716 | + | 0.0368186i | 0.531547 | − | 0.847029i | \(-0.321611\pi\) |
−0.467775 | + | 0.883847i | \(0.654944\pi\) | |||||||
\(398\) | −62.7653 | −3.14614 | ||||||||
\(399\) | −12.1569 | − | 3.92492i | −0.608606 | − | 0.196492i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.5840 | − | 10.7295i | −0.928039 | − | 0.535804i | −0.0418482 | − | 0.999124i | \(-0.513325\pi\) |
−0.886191 | + | 0.463320i | \(0.846658\pi\) | |||||||
\(402\) | −11.8078 | + | 33.0068i | −0.588918 | + | 1.64623i | ||||
\(403\) | 7.12384 | + | 12.3389i | 0.354864 | + | 0.614642i | ||||
\(404\) | −44.1680 | + | 76.5012i | −2.19744 | + | 3.80608i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.632495 | − | 20.2269i | −0.0313902 | − | 1.00385i | ||||
\(407\) | − | 12.5663i | − | 0.622889i | ||||||
\(408\) | 34.0368 | − | 6.19535i | 1.68507 | − | 0.306715i | ||||
\(409\) | −6.02404 | + | 3.47798i | −0.297870 | + | 0.171975i | −0.641485 | − | 0.767135i | \(-0.721682\pi\) |
0.343616 | + | 0.939110i | \(0.388348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.5668 | + | 3.92556i | −1.06381 | + | 0.193634i | ||||
\(412\) | 2.86396i | 0.141097i | ||||||||
\(413\) | 6.72879 | + | 3.60930i | 0.331102 | + | 0.177602i | ||||
\(414\) | 2.37262 | − | 14.3816i | 0.116608 | − | 0.706817i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −22.5177 | − | 39.0019i | −1.10402 | − | 1.91222i | ||||
\(417\) | 10.5192 | − | 29.4047i | 0.515125 | − | 1.43995i | ||||
\(418\) | −13.6717 | − | 7.89337i | −0.668706 | − | 0.386077i | ||||
\(419\) | 34.8831 | 1.70415 | 0.852076 | − | 0.523419i | \(-0.175344\pi\) | ||||
0.852076 | + | 0.523419i | \(0.175344\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.6603 | −1.44555 | −0.722777 | − | 0.691082i | \(-0.757134\pi\) | ||||
−0.722777 | + | 0.691082i | \(0.757134\pi\) | |||||||
\(422\) | −44.9227 | − | 25.9361i | −2.18680 | − | 1.26255i | ||||
\(423\) | −8.27589 | + | 3.11597i | −0.402387 | + | 0.151504i | ||||
\(424\) | 29.4175 | + | 50.9526i | 1.42864 | + | 2.47448i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −13.7522 | + | 11.6693i | −0.666297 | + | 0.565380i | ||||
\(427\) | 19.2454 | − | 0.601804i | 0.931353 | − | 0.0291233i | ||||
\(428\) | − | 16.8745i | − | 0.815661i | ||||||
\(429\) | −1.31135 | − | 7.20448i | −0.0633127 | − | 0.347835i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.32938 | − | 4.23162i | 0.353044 | − | 0.203830i | −0.312981 | − | 0.949759i | \(-0.601328\pi\) |
0.666025 | + | 0.745929i | \(0.267994\pi\) | |||||||
\(432\) | 78.0321 | − | 1.29115i | 3.75432 | − | 0.0621203i | ||||
\(433\) | 10.6435i | 0.511495i | 0.966744 | + | 0.255748i | \(0.0823216\pi\) | ||||
−0.966744 | + | 0.255748i | \(0.917678\pi\) | |||||||
\(434\) | −42.9169 | + | 26.6004i | −2.06008 | + | 1.27686i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 37.1017 | − | 64.2620i | 1.77685 | − | 3.07759i | ||||
\(437\) | 2.47711 | + | 4.29049i | 0.118496 | + | 0.205242i | ||||
\(438\) | 29.9258 | + | 10.7056i | 1.42991 | + | 0.511531i | ||||
\(439\) | 10.9548 | + | 6.32477i | 0.522845 | + | 0.301865i | 0.738098 | − | 0.674694i | \(-0.235724\pi\) |
−0.215253 | + | 0.976558i | \(0.569058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.1524 | − | 8.61309i | 0.912019 | − | 0.410147i | ||||
\(442\) | −11.7342 | −0.558141 | ||||||||
\(443\) | −22.2838 | − | 12.8656i | −1.05874 | − | 0.611261i | −0.133654 | − | 0.991028i | \(-0.542671\pi\) |
−0.925082 | + | 0.379767i | \(0.876004\pi\) | |||||||
\(444\) | −54.1606 | − | 19.3752i | −2.57035 | − | 0.919508i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.28756 | − | 14.3545i | 0.392427 | − | 0.679704i | ||||
\(447\) | 16.3367 | + | 19.2526i | 0.772697 | + | 0.910618i | ||||
\(448\) | 68.1044 | − | 42.2118i | 3.21763 | − | 1.99432i | ||||
\(449\) | 35.6974i | 1.68466i | 0.538960 | + | 0.842331i | \(0.318817\pi\) | ||||
−0.538960 | + | 0.842331i | \(0.681183\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.0180 | − | 12.1348i | 0.989700 | − | 0.571404i | ||||
\(452\) | −52.4590 | + | 30.2872i | −2.46747 | + | 1.42459i | ||||
\(453\) | −2.18019 | − | 11.9778i | −0.102434 | − | 0.562766i | ||||
\(454\) | − | 59.6132i | − | 2.79778i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −34.9695 | + | 29.6731i | −1.63760 | + | 1.38957i | ||||
\(457\) | −5.55255 | + | 9.61730i | −0.259737 | + | 0.449878i | −0.966172 | − | 0.257900i | \(-0.916969\pi\) |
0.706434 | + | 0.707779i | \(0.250303\pi\) | |||||||
\(458\) | −12.5451 | − | 21.7287i | −0.586192 | − | 1.01531i | ||||
\(459\) | 5.30613 | − | 9.55204i | 0.247669 | − | 0.445851i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.8795 | 0.879304 | 0.439652 | − | 0.898168i | \(-0.355102\pi\) | ||||
0.439652 | + | 0.898168i | \(0.355102\pi\) | |||||||
\(462\) | 25.3740 | − | 5.44298i | 1.18051 | − | 0.253230i | ||||
\(463\) | −14.6440 | −0.680565 | −0.340282 | − | 0.940323i | \(-0.610523\pi\) | ||||
−0.340282 | + | 0.940323i | \(0.610523\pi\) | |||||||
\(464\) | −36.3906 | − | 21.0101i | −1.68939 | − | 0.975371i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.8546 | + | 43.0495i | 1.15137 | + | 1.99423i | ||||
\(467\) | −2.71213 | + | 4.69754i | −0.125502 | + | 0.217376i | −0.921929 | − | 0.387359i | \(-0.873388\pi\) |
0.796427 | + | 0.604735i | \(0.206721\pi\) | |||||||
\(468\) | −33.0731 | − | 5.45626i | −1.52880 | − | 0.252216i | ||||
\(469\) | 17.2602 | + | 9.25832i | 0.797003 | + | 0.427509i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.3228 | − | 6.79346i | 1.71974 | − | 0.313026i | ||||
\(472\) | 23.7401 | − | 13.7063i | 1.09272 | − | 0.630885i | ||||
\(473\) | 7.83952 | − | 4.52615i | 0.360462 | − | 0.208113i | ||||
\(474\) | −27.5598 | + | 5.01641i | −1.26586 | + | 0.230411i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.951932 | − | 30.4424i | −0.0436317 | − | 1.39533i | ||||
\(477\) | 18.3347 | + | 3.02478i | 0.839488 | + | 0.138495i | ||||
\(478\) | −17.9686 | + | 31.1226i | −0.821866 | + | 1.42351i | ||||
\(479\) | 1.85555 | + | 3.21391i | 0.0847823 | + | 0.146847i | 0.905298 | − | 0.424776i | \(-0.139647\pi\) |
−0.820516 | + | 0.571623i | \(0.806314\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.7234 | + | 6.19113i | 0.488943 | + | 0.282291i | ||||
\(482\) | 0.0488872 | 0.00222675 | ||||||||
\(483\) | −7.75016 | − | 2.50218i | −0.352645 | − | 0.113853i | ||||
\(484\) | −36.7288 | −1.66949 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 26.4835 | − | 33.3898i | 1.20132 | − | 1.51459i | ||||
\(487\) | −9.16240 | − | 15.8697i | −0.415188 | − | 0.719127i | 0.580260 | − | 0.814431i | \(-0.302951\pi\) |
−0.995448 | + | 0.0953043i | \(0.969618\pi\) | |||||||
\(488\) | 34.5632 | − | 59.8652i | 1.56460 | − | 2.70997i | ||||
\(489\) | −10.6925 | + | 9.07304i | −0.483532 | + | 0.410297i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.7134i | 1.65685i | 0.560098 | + | 0.828426i | \(0.310763\pi\) | ||||
−0.560098 | + | 0.828426i | \(0.689237\pi\) | |||||||
\(492\) | −19.8942 | − | 109.297i | −0.896899 | − | 4.92750i | ||||
\(493\) | −5.09510 | + | 2.94166i | −0.229472 | + | 0.132486i | ||||
\(494\) | 13.4715 | − | 7.77777i | 0.606111 | − | 0.349938i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 104.843i | 4.70759i | ||||||||
\(497\) | 5.30894 | + | 8.56542i | 0.238138 | + | 0.384212i | ||||
\(498\) | −18.2727 | − | 21.5343i | −0.818820 | − | 0.964973i | ||||
\(499\) | −0.535767 | + | 0.927975i | −0.0239842 | + | 0.0415419i | −0.877768 | − | 0.479085i | \(-0.840968\pi\) |
0.853784 | + | 0.520627i | \(0.174302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.85107 | − | 2.09314i | −0.261406 | − | 0.0935147i | ||||
\(502\) | −12.7516 | − | 7.36212i | −0.569131 | − | 0.328588i | ||||
\(503\) | −27.1662 | −1.21128 | −0.605640 | − | 0.795739i | \(-0.707083\pi\) | ||||
−0.605640 | + | 0.795739i | \(0.707083\pi\) | |||||||
\(504\) | 9.94099 | − | 74.7333i | 0.442807 | − | 3.32888i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.71588 | − | 5.03212i | −0.387468 | − | 0.223705i | ||||
\(507\) | −14.4069 | − | 5.15390i | −0.639834 | − | 0.228893i | ||||
\(508\) | −13.6479 | − | 23.6388i | −0.605527 | − | 1.04880i | ||||
\(509\) | 11.8003 | − | 20.4387i | 0.523037 | − | 0.905927i | −0.476603 | − | 0.879119i | \(-0.658132\pi\) |
0.999641 | − | 0.0268088i | \(-0.00853453\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.39408 | − | 15.6490i | 0.371332 | − | 0.692272i | ||||
\(512\) | − | 46.0773i | − | 2.03635i | ||||||
\(513\) | 0.239645 | + | 14.4833i | 0.0105806 | + | 0.639451i | ||||
\(514\) | 51.3401 | − | 29.6412i | 2.26452 | − | 1.30742i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.42033 | − | 40.7668i | −0.326662 | − | 1.79466i | ||||
\(517\) | 6.10583i | 0.268534i | ||||||||
\(518\) | −20.7421 | + | 38.6694i | −0.911356 | + | 1.69904i | ||||
\(519\) | −17.1809 | + | 14.5787i | −0.754157 | + | 0.639933i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.5487 | + | 21.7350i | 0.549770 | + | 0.952230i | 0.998290 | + | 0.0584568i | \(0.0186180\pi\) |
−0.448520 | + | 0.893773i | \(0.648049\pi\) | |||||||
\(522\) | −21.4747 | + | 8.08548i | −0.939922 | + | 0.353892i | ||||
\(523\) | 5.29103 | + | 3.05478i | 0.231361 | + | 0.133576i | 0.611200 | − | 0.791476i | \(-0.290687\pi\) |
−0.379839 | + | 0.925053i | \(0.624021\pi\) | |||||||
\(524\) | 64.0708 | 2.79895 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.91810 | 0.170837 | ||||||||
\(527\) | 12.7126 | + | 7.33960i | 0.553768 | + | 0.319718i | ||||
\(528\) | 18.1505 | − | 50.7370i | 0.789900 | − | 2.20805i | ||||
\(529\) | −9.92081 | − | 17.1833i | −0.431340 | − | 0.747102i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.40932 | − | 8.54258i | 0.0611592 | − | 0.370716i | ||||
\(532\) | 21.2709 | + | 34.3184i | 0.922211 | + | 1.48789i | ||||
\(533\) | 23.9141i | 1.03583i | ||||||||
\(534\) | 57.8533 | − | 10.5304i | 2.50356 | − | 0.455695i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 60.8963 | − | 35.1585i | 2.63032 | − | 1.51862i | ||||
\(537\) | 6.89472 | − | 1.25497i | 0.297529 | − | 0.0541560i | ||||
\(538\) | − | 54.6463i | − | 2.35597i | ||||||
\(539\) | −0.905929 | − | 14.4715i | −0.0390211 | − | 0.623330i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2979 | − | 19.5686i | 0.485737 | − | 0.841321i | −0.514129 | − | 0.857713i | \(-0.671885\pi\) |
0.999866 | + | 0.0163924i | \(0.00521808\pi\) | |||||||
\(542\) | −21.4763 | − | 37.1980i | −0.922485 | − | 1.59779i | ||||
\(543\) | 5.25636 | − | 14.6934i | 0.225572 | − | 0.630552i | ||||
\(544\) | −40.1831 | − | 23.1997i | −1.72284 | − | 0.994680i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.85648 | + | 24.3344i | −0.336226 | + | 1.04141i | ||||
\(547\) | 20.6880 | 0.884556 | 0.442278 | − | 0.896878i | \(-0.354170\pi\) | ||||
0.442278 | + | 0.896878i | \(0.354170\pi\) | |||||||
\(548\) | 60.0013 | + | 34.6418i | 2.56313 | + | 1.47982i | ||||
\(549\) | −7.69314 | − | 20.4327i | −0.328335 | − | 0.872044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.89962 | − | 6.75433i | 0.166129 | − | 0.287744i | ||||
\(552\) | −22.2935 | + | 18.9169i | −0.948874 | + | 0.805158i | ||||
\(553\) | 0.489184 | + | 15.6439i | 0.0208022 | + | 0.665246i | ||||
\(554\) | − | 5.98657i | − | 0.254345i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −85.4801 | + | 49.3520i | −3.62516 | + | 2.09299i | ||||
\(557\) | −4.08989 | + | 2.36130i | −0.173294 | + | 0.100051i | −0.584138 | − | 0.811654i | \(-0.698567\pi\) |
0.410844 | + | 0.911706i | \(0.365234\pi\) | |||||||
\(558\) | 44.2612 | + | 36.3153i | 1.87373 | + | 1.53735i | ||||
\(559\) | 8.91972i | 0.377264i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.88140 | − | 5.75269i | −0.206093 | − | 0.242879i | ||||
\(562\) | 0.0816733 | − | 0.141462i | 0.00344518 | − | 0.00596723i | ||||
\(563\) | −16.9161 | − | 29.2995i | −0.712927 | − | 1.23483i | −0.963754 | − | 0.266794i | \(-0.914036\pi\) |
0.250826 | − | 0.968032i | \(-0.419298\pi\) | |||||||
\(564\) | 26.3160 | + | 9.41422i | 1.10810 | + | 0.396410i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 43.5833 | 1.83194 | ||||||||
\(567\) | −16.2563 | − | 17.3992i | −0.682700 | − | 0.730699i | ||||
\(568\) | 36.1781 | 1.51800 | ||||||||
\(569\) | −21.5858 | − | 12.4626i | −0.904926 | − | 0.522459i | −0.0261307 | − | 0.999659i | \(-0.508319\pi\) |
−0.878795 | + | 0.477199i | \(0.841652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.10062 | − | 1.90633i | −0.0460596 | − | 0.0797776i | 0.842076 | − | 0.539358i | \(-0.181333\pi\) |
−0.888136 | + | 0.459581i | \(0.848000\pi\) | |||||||
\(572\) | −11.5723 | + | 20.0437i | −0.483860 | + | 0.838071i | ||||
\(573\) | 29.2532 | + | 34.4747i | 1.22207 | + | 1.44020i | ||||
\(574\) | −84.7071 | + | 2.64879i | −3.53561 | + | 0.110558i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −70.2377 | − | 57.6283i | −2.92657 | − | 2.40118i | ||||
\(577\) | −21.9455 | + | 12.6702i | −0.913602 | + | 0.527469i | −0.881588 | − | 0.472019i | \(-0.843525\pi\) |
−0.0320140 | + | 0.999487i | \(0.510192\pi\) | |||||||
\(578\) | 29.7800 | − | 17.1935i | 1.23868 | − | 0.715154i | ||||
\(579\) | 2.32876 | + | 12.7940i | 0.0967799 | + | 0.531702i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.4124 | + | 8.31314i | −0.556440 | + | 0.344887i | ||||
\(582\) | −36.0038 | + | 30.5507i | −1.49240 | + | 1.26637i | ||||
\(583\) | 6.41531 | − | 11.1116i | 0.265695 | − | 0.460197i | ||||
\(584\) | −31.8766 | − | 55.2118i | −1.31906 | − | 2.28468i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 45.8540 | + | 26.4738i | 1.89421 | + | 1.09362i | ||||
\(587\) | 21.7712 | 0.898593 | 0.449297 | − | 0.893383i | \(-0.351675\pi\) | ||||
0.449297 | + | 0.893383i | \(0.351675\pi\) | |||||||
\(588\) | −63.7685 | − | 18.4082i | −2.62977 | − | 0.759139i | ||||
\(589\) | −19.4595 | −0.801816 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.1315 | − | 33.9118i | 0.499023 | − | 1.39494i | ||||
\(592\) | 45.5580 | + | 78.9088i | 1.87242 | + | 3.24313i | ||||
\(593\) | −17.4071 | + | 30.1501i | −0.714826 | + | 1.23811i | 0.248201 | + | 0.968709i | \(0.420161\pi\) |
−0.963027 | + | 0.269406i | \(0.913173\pi\) | |||||||
\(594\) | −15.1326 | − | 25.2367i | −0.620897 | − | 1.03548i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 79.8041i | − | 3.26890i | ||||||
\(597\) | 39.1216 | − | 7.12088i | 1.60114 | − | 0.291438i | ||||
\(598\) | 8.58823 | − | 4.95842i | 0.351199 | − | 0.202765i | ||||
\(599\) | 5.38292 | − | 3.10783i | 0.219940 | − | 0.126982i | −0.385983 | − | 0.922506i | \(-0.626137\pi\) |
0.605922 | + | 0.795524i | \(0.292804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 29.5235i | − | 1.20429i | −0.798388 | − | 0.602144i | \(-0.794313\pi\) | ||
0.798388 | − | 0.602144i | \(-0.205687\pi\) | |||||||
\(602\) | −31.5949 | + | 0.987972i | −1.28771 | + | 0.0402667i | ||||
\(603\) | 3.61508 | − | 21.9128i | 0.147218 | − | 0.892359i | ||||
\(604\) | −19.2394 | + | 33.3237i | −0.782841 | + | 1.35592i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 25.7377 | − | 71.9458i | 1.04552 | − | 2.92260i | ||||
\(607\) | −16.1380 | − | 9.31727i | −0.655021 | − | 0.378176i | 0.135356 | − | 0.990797i | \(-0.456782\pi\) |
−0.790377 | + | 0.612621i | \(0.790115\pi\) | |||||||
\(608\) | 61.5096 | 2.49454 | ||||||||
\(609\) | 2.68903 | + | 12.5357i | 0.108965 | + | 0.507973i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.21036 | − | 3.00820i | −0.210788 | − | 0.121699i | ||||
\(612\) | −32.3203 | + | 12.1690i | −1.30647 | + | 0.491903i | ||||
\(613\) | 2.59472 | + | 4.49418i | 0.104800 | + | 0.181518i | 0.913656 | − | 0.406487i | \(-0.133247\pi\) |
−0.808857 | + | 0.588006i | \(0.799913\pi\) | |||||||
\(614\) | 24.2826 | − | 42.0586i | 0.979965 | − | 1.69735i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −45.8727 | − | 24.6059i | −1.84826 | − | 0.991401i | ||||
\(617\) | − | 8.86686i | − | 0.356966i | −0.983943 | − | 0.178483i | \(-0.942881\pi\) | ||
0.983943 | − | 0.178483i | \(-0.0571190\pi\) | |||||||
\(618\) | −0.443633 | − | 2.43729i | −0.0178455 | − | 0.0980422i | ||||
\(619\) | 20.2601 | − | 11.6972i | 0.814321 | − | 0.470148i | −0.0341335 | − | 0.999417i | \(-0.510867\pi\) |
0.848454 | + | 0.529269i | \(0.177534\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.152776 | + | 9.23325i | 0.00613071 | + | 0.370517i | ||||
\(622\) | 19.6173i | 0.786582i | ||||||||
\(623\) | −1.02689 | − | 32.8395i | −0.0411415 | − | 1.31569i | ||||
\(624\) | 34.3537 | + | 40.4856i | 1.37525 | + | 1.62072i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.5819 | + | 32.1847i | 0.742680 | + | 1.28636i | ||||
\(627\) | 9.41712 | + | 3.36885i | 0.376084 | + | 0.134539i | ||||
\(628\) | −103.837 | − | 59.9501i | −4.14353 | − | 2.39227i | ||||
\(629\) | 12.7573 | 0.508666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.27702 | −0.329503 | −0.164752 | − | 0.986335i | \(-0.552682\pi\) | ||||
−0.164752 | + | 0.986335i | \(0.552682\pi\) | |||||||
\(632\) | 48.6621 | + | 28.0951i | 1.93568 | + | 1.11756i | ||||
\(633\) | 30.9429 | + | 11.0694i | 1.22987 | + | 0.439969i | ||||
\(634\) | 4.40217 | + | 7.62479i | 0.174833 | + | 0.302819i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −37.9996 | − | 44.7822i | −1.50678 | − | 1.77573i | ||||
\(637\) | 12.7954 | + | 6.35669i | 0.506973 | + | 0.251861i | ||||
\(638\) | 15.8437i | 0.627258i | ||||||||
\(639\) | 7.24785 | − | 8.83372i | 0.286720 | − | 0.349457i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.6157 | + | 20.5627i | −1.40673 | + | 0.812179i | −0.995072 | − | 0.0991572i | \(-0.968385\pi\) |
−0.411663 | + | 0.911336i | \(0.635052\pi\) | |||||||
\(642\) | 2.61389 | + | 14.3606i | 0.103162 | + | 0.566766i | ||||
\(643\) | − | 3.55349i | − | 0.140136i | −0.997542 | − | 0.0700680i | \(-0.977678\pi\) | ||
0.997542 | − | 0.0700680i | \(-0.0223216\pi\) | |||||||
\(644\) | 13.5605 | + | 21.8784i | 0.534357 | + | 0.862130i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.01333 | − | 13.8795i | 0.315280 | − | 0.546081i | ||||
\(647\) | 23.3627 | + | 40.4653i | 0.918481 | + | 1.59086i | 0.801724 | + | 0.597695i | \(0.203916\pi\) |
0.116757 | + | 0.993161i | \(0.462750\pi\) | |||||||
\(648\) | −83.8393 | + | 16.6979i | −3.29352 | + | 0.655954i | ||||
\(649\) | −5.17718 | − | 2.98905i | −0.203222 | − | 0.117330i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.7323 | − | 21.4491i | 0.930142 | − | 0.840655i | ||||
\(652\) | 44.3215 | 1.73576 | ||||||||
\(653\) | −1.64369 | − | 0.948985i | −0.0643226 | − | 0.0371367i | 0.467494 | − | 0.883996i | \(-0.345157\pi\) |
−0.531816 | + | 0.846860i | \(0.678490\pi\) | |||||||
\(654\) | −21.6200 | + | 60.4354i | −0.845408 | + | 2.36321i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −87.9870 | + | 152.398i | −3.43532 | + | 5.95014i | ||||
\(657\) | −19.8673 | − | 3.27763i | −0.775098 | − | 0.127872i | ||||
\(658\) | 10.0784 | − | 18.7890i | 0.392896 | − | 0.732472i | ||||
\(659\) | − | 2.32588i | − | 0.0906035i | −0.998973 | − | 0.0453017i | \(-0.985575\pi\) | ||
0.998973 | − | 0.0453017i | \(-0.0144249\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.03266 | + | 4.63766i | −0.312434 | + | 0.180384i | −0.648015 | − | 0.761627i | \(-0.724401\pi\) |
0.335581 | + | 0.942011i | \(0.391067\pi\) | |||||||
\(662\) | 7.54583 | − | 4.35659i | 0.293277 | − | 0.169324i | ||||
\(663\) | 7.31396 | − | 1.33128i | 0.284051 | − | 0.0517026i | ||||
\(664\) | 56.6505i | 2.19846i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 49.0930 | + | 8.09915i | 1.90231 | + | 0.313836i | ||||
\(667\) | 2.48605 | − | 4.30597i | 0.0962603 | − | 0.166728i | ||||
\(668\) | 9.82025 | + | 17.0092i | 0.379957 | + | 0.658105i | ||||
\(669\) | −3.53709 | + | 9.88740i | −0.136752 | + | 0.382269i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0749 | −0.581961 | ||||||||
\(672\) | −75.0153 | + | 67.7983i | −2.89378 | + | 2.61538i | ||||
\(673\) | −26.5356 | −1.02287 | −0.511436 | − | 0.859321i | \(-0.670886\pi\) | ||||
−0.511436 | + | 0.859321i | \(0.670886\pi\) | |||||||
\(674\) | 80.3801 | + | 46.4075i | 3.09613 | + | 1.78755i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.1802 | + | 41.8813i | 0.930006 | + | 1.61082i | ||||
\(677\) | 18.3673 | − | 31.8130i | 0.705911 | − | 1.22267i | −0.260450 | − | 0.965487i | \(-0.583871\pi\) |
0.966362 | − | 0.257187i | \(-0.0827957\pi\) | |||||||
\(678\) | 39.9521 | − | 33.9010i | 1.53435 | − | 1.30196i | ||||
\(679\) | 13.8990 | + | 22.4246i | 0.533394 | + | 0.860577i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.76327 | + | 37.1569i | 0.259169 | + | 1.42386i | ||||
\(682\) | 34.2348 | − | 19.7655i | 1.31092 | − | 0.756859i | ||||
\(683\) | −44.3300 | + | 25.5940i | −1.69624 | + | 0.979326i | −0.746976 | + | 0.664851i | \(0.768495\pi\) |
−0.949266 | + | 0.314475i | \(0.898171\pi\) | |||||||
\(684\) | 29.0394 | − | 35.3934i | 1.11035 | − | 1.35330i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −21.0990 | + | 46.0273i | −0.805565 | + | 1.75733i | ||||
\(687\) | 10.2845 | + | 12.1202i | 0.392379 | + | 0.462416i | ||||
\(688\) | −32.8183 | + | 56.8430i | −1.25119 | + | 2.16712i | ||||
\(689\) | 6.32135 | + | 10.9489i | 0.240824 | + | 0.417120i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.4415 | + | 8.91516i | 0.587423 | + | 0.339149i | 0.764078 | − | 0.645124i | \(-0.223194\pi\) |
−0.176655 | + | 0.984273i | \(0.556528\pi\) | |||||||
\(692\) | 71.2164 | 2.70724 | ||||||||
\(693\) | −15.1981 | + | 6.27137i | −0.577330 | + | 0.238229i | ||||
\(694\) | 76.4696 | 2.90275 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 43.3382 | + | 15.5037i | 1.64273 | + | 0.587666i | ||||
\(697\) | 12.3192 | + | 21.3374i | 0.466622 | + | 0.808213i | ||||
\(698\) | 26.4327 | − | 45.7827i | 1.00049 | − | 1.73290i | ||||
\(699\) | −20.3760 | − | 24.0130i | −0.770691 | − | 0.908254i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 42.3606i | − | 1.59994i | −0.600041 | − | 0.799970i | \(-0.704849\pi\) | ||
0.600041 | − | 0.799970i | \(-0.295151\pi\) | |||||||
\(702\) | 28.9910 | − | 0.479695i | 1.09420 | − | 0.0181049i | ||||
\(703\) | −14.6460 | + | 8.45586i | −0.552384 | + | 0.318919i | ||||
\(704\) | −54.3268 | + | 31.3656i | −2.04752 | + | 1.18214i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.8286i | − | 0.708624i | ||||||
\(707\) | −37.6225 | − | 20.1806i | −1.41494 | − | 0.758968i | ||||
\(708\) | −20.8651 | + | 17.7049i | −0.784159 | + | 0.665392i | ||||
\(709\) | 15.3029 | − | 26.5055i | 0.574714 | − | 0.995434i | −0.421359 | − | 0.906894i | \(-0.638447\pi\) |
0.996073 | − | 0.0885399i | \(-0.0282201\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.6089 | − | 6.25347i | 0.622884 | − | 0.234523i | ||||
\(712\) | −102.151 | − | 58.9770i | −3.82828 | − | 2.21026i | ||||
\(713\) | −12.4057 | −0.464596 | ||||||||
\(714\) | 5.52570 | + | 25.7596i | 0.206794 | + | 0.964030i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.1820 | − | 11.0747i | −0.716863 | − | 0.413881i | ||||
\(717\) | 7.66893 | − | 21.4373i | 0.286401 | − | 0.800592i | ||||
\(718\) | 28.5045 | + | 49.3713i | 1.06378 | + | 1.84252i | ||||
\(719\) | −11.4617 | + | 19.8522i | −0.427449 | + | 0.740364i | −0.996646 | − | 0.0818377i | \(-0.973921\pi\) |
0.569196 | + | 0.822202i | \(0.307254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.38349 | + | 0.0432616i | −0.0515238 | + | 0.00161115i | ||||
\(722\) | − | 30.6986i | − | 1.14248i | ||||||
\(723\) | −0.0304714 | + | 0.00554638i | −0.00113324 | + | 0.000206272i | ||||
\(724\) | −42.7139 | + | 24.6609i | −1.58745 | + | 0.916515i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.2569 | − | 5.68935i | 1.16005 | − | 0.211152i | ||||
\(727\) | − | 32.1534i | − | 1.19250i | −0.802798 | − | 0.596252i | \(-0.796656\pi\) | ||
0.802798 | − | 0.596252i | \(-0.203344\pi\) | |||||||
\(728\) | 43.5977 | − | 27.0223i | 1.61584 | − | 1.00151i | ||||
\(729\) | −12.7190 | + | 23.8165i | −0.471075 | + | 0.882093i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.59493 | + | 7.95866i | 0.169950 | + | 0.294362i | ||||
\(732\) | −23.2431 | + | 64.9726i | −0.859090 | + | 2.40146i | ||||
\(733\) | 11.8271 | + | 6.82836i | 0.436843 | + | 0.252211i | 0.702258 | − | 0.711923i | \(-0.252176\pi\) |
−0.265415 | + | 0.964134i | \(0.585509\pi\) | |||||||
\(734\) | −65.4757 | −2.41675 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 39.2131 | 1.44541 | ||||||||
\(737\) | −13.2801 | − | 7.66729i | −0.489180 | − | 0.282428i | ||||
\(738\) | 33.8607 | + | 89.9325i | 1.24643 | + | 3.31046i | ||||
\(739\) | 9.19147 | + | 15.9201i | 0.338114 | + | 0.585630i | 0.984078 | − | 0.177737i | \(-0.0568778\pi\) |
−0.645964 | + | 0.763368i | \(0.723544\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.51438 | + | 6.37626i | −0.276048 | + | 0.234238i | ||||
\(742\) | −38.0824 | + | 23.6038i | −1.39805 | + | 0.866524i | ||||
\(743\) | − | 10.0307i | − | 0.367992i | −0.982927 | − | 0.183996i | \(-0.941097\pi\) | ||
0.982927 | − | 0.183996i | \(-0.0589034\pi\) | |||||||
\(744\) | −20.5655 | − | 112.986i | −0.753970 | − | 4.14226i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.42443 | + | 5.44120i | −0.345053 | + | 0.199216i | ||||
\(747\) | 13.8325 | + | 11.3492i | 0.506105 | + | 0.415247i | ||||
\(748\) | 23.8455i | 0.871877i | ||||||||
\(749\) | 8.15155 | − | 0.254898i | 0.297851 | − | 0.00931378i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.6659 | + | 28.8661i | −0.608146 | + | 1.05334i | 0.383400 | + | 0.923582i | \(0.374753\pi\) |
−0.991546 | + | 0.129757i | \(0.958580\pi\) | |||||||
\(752\) | −22.1361 | − | 38.3409i | −0.807222 | − | 1.39815i | ||||
\(753\) | 8.78332 | + | 3.14212i | 0.320082 | + | 0.114505i | ||||
\(754\) | −13.5201 | − | 7.80583i | −0.492373 | − | 0.284272i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.59636 | + | 75.1732i | 0.130798 | + | 2.73402i | ||||
\(757\) | −7.30587 | −0.265536 | −0.132768 | − | 0.991147i | \(-0.542387\pi\) | ||||
−0.132768 | + | 0.991147i | \(0.542387\pi\) | |||||||
\(758\) | −32.9583 | − | 19.0285i | −1.19710 | − | 0.691145i | ||||
\(759\) | 6.00353 | + | 2.14768i | 0.217914 | + | 0.0779560i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.12585 | − | 5.41414i | 0.113312 | − | 0.196262i | −0.803792 | − | 0.594911i | \(-0.797187\pi\) |
0.917104 | + | 0.398649i | \(0.130521\pi\) | |||||||
\(762\) | 15.2763 | + | 18.0030i | 0.553403 | + | 0.652182i | ||||
\(763\) | 31.6034 | + | 16.9519i | 1.14412 | + | 0.613701i | ||||
\(764\) | − | 142.901i | − | 5.16998i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.4118 | + | 21.5997i | −1.35174 | + | 0.780429i | ||||
\(767\) | 5.10135 | − | 2.94527i | 0.184199 | − | 0.106347i | ||||
\(768\) | 14.0010 | + | 76.9208i | 0.505219 | + | 2.77564i | ||||
\(769\) | − | 12.2298i | − | 0.441018i | −0.975385 | − | 0.220509i | \(-0.929228\pi\) | ||
0.975385 | − | 0.220509i | \(-0.0707718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.6375 | + | 24.3001i | −1.03135 | + | 0.875146i | ||||
\(772\) | 20.5505 | − | 35.5946i | 0.739630 | − | 1.28108i | ||||
\(773\) | −20.4185 | − | 35.3660i | −0.734404 | − | 1.27203i | −0.954984 | − | 0.296656i | \(-0.904128\pi\) |
0.220580 | − | 0.975369i | \(-0.429205\pi\) | |||||||
\(774\) | 12.6297 | + | 33.5440i | 0.453965 | + | 1.20571i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 94.7156 | 3.40009 | ||||||||
\(777\) | 8.54144 | − | 26.4559i | 0.306422 | − | 0.949101i | ||||
\(778\) | 68.5707 | 2.45838 | ||||||||
\(779\) | −28.2860 | − | 16.3310i | −1.01345 | − | 0.585117i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.94482 | − | 6.83263i | −0.141157 | − | 0.244491i | ||||
\(782\) | 5.10859 | − | 8.84834i | 0.182683 | − | 0.316416i | ||||
\(783\) | 12.4679 | − | 7.47605i | 0.445565 | − | 0.267172i | ||||
\(784\) | 58.1537 | + | 87.5877i | 2.07692 | + | 3.12813i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −54.5255 | + | 9.92468i | −1.94486 | + | 0.354002i | ||||
\(787\) | 38.0128 | − | 21.9467i | 1.35501 | − | 0.782316i | 0.366065 | − | 0.930589i | \(-0.380705\pi\) |
0.988946 | + | 0.148273i | \(0.0473714\pi\) | |||||||
\(788\) | −98.5822 | + | 56.9165i | −3.51185 | + | 2.02757i | ||||
\(789\) | −2.44215 | + | 0.444518i | −0.0869430 | + | 0.0158253i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.4232 | − | 24.8838i | −0.548387 | − | 0.884765i | ||||
\(792\) | −9.60785 | + | 58.2379i | −0.341400 | + | 2.06940i | ||||
\(793\) | 7.42706 | − | 12.8641i | 0.263743 | − | 0.456816i | ||||
\(794\) | 2.00561 | + | 3.47382i | 0.0711766 | + | 0.123281i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −108.841 | − | 62.8395i | −3.85777 | − | 2.22729i | ||||
\(797\) | −32.7354 | −1.15955 | −0.579773 | − | 0.814778i | \(-0.696859\pi\) | ||||
−0.579773 | + | 0.814778i | \(0.696859\pi\) | |||||||
\(798\) | −23.4180 | − | 25.9108i | −0.828986 | − | 0.917231i | ||||
\(799\) | −6.19862 | −0.219291 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34.8653 | + | 13.1272i | −1.23191 | + | 0.463828i | ||||
\(802\) | −29.3334 | − | 50.8070i | −1.03580 | − | 1.79406i | ||||
\(803\) | −6.95157 | + | 12.0405i | −0.245316 | + | 0.424899i | ||||
\(804\) | −53.5217 | + | 45.4154i | −1.88757 | + | 1.60168i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 38.9520i | 1.37203i | ||||||||
\(807\) | 6.19976 | + | 34.0611i | 0.218242 | + | 1.19901i | ||||
\(808\) | −132.737 | + | 76.6358i | −4.66967 | + | 2.69604i | ||||
\(809\) | −27.4680 | + | 15.8586i | −0.965722 | + | 0.557560i | −0.897929 | − | 0.440140i | \(-0.854929\pi\) |
−0.0677924 | + | 0.997699i | \(0.521596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.7354i | 0.903691i | 0.892096 | + | 0.451845i | \(0.149234\pi\) | ||||
−0.892096 | + | 0.451845i | \(0.850766\pi\) | |||||||
\(812\) | 19.1540 | − | 35.7087i | 0.672175 | − | 1.25313i | ||||
\(813\) | 17.6064 | + | 20.7490i | 0.617483 | + | 0.727699i | ||||
\(814\) | 17.1776 | − | 29.7525i | 0.602075 | − | 1.04282i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 51.5081 | + | 18.4264i | 1.80314 | + | 0.645051i | ||||
\(817\) | −10.5504 | − | 6.09129i | −0.369113 | − | 0.213107i | ||||
\(818\) | −19.0170 | −0.664914 | ||||||||
\(819\) | 2.13616 | − | 16.0590i | 0.0746434 | − | 0.561146i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3697 | − | 12.9152i | −0.780708 | − | 0.450742i | 0.0559731 | − | 0.998432i | \(-0.482174\pi\) |
−0.836681 | + | 0.547690i | \(0.815507\pi\) | |||||||
\(822\) | −56.4284 | − | 20.1865i | −1.96817 | − | 0.704086i | ||||
\(823\) | −19.0097 | − | 32.9258i | −0.662638 | − | 1.14772i | −0.979920 | − | 0.199392i | \(-0.936103\pi\) |
0.317282 | − | 0.948331i | \(-0.397230\pi\) | |||||||
\(824\) | −2.48463 | + | 4.30350i | −0.0865561 | + | 0.149920i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.9976 | + | 17.7435i | 0.382655 | + | 0.617375i | ||||
\(827\) | − | 2.97310i | − | 0.103385i | −0.998663 | − | 0.0516924i | \(-0.983538\pi\) | ||
0.998663 | − | 0.0516924i | \(-0.0164615\pi\) | |||||||
\(828\) | 18.5130 | − | 22.5637i | 0.643370 | − | 0.784143i | ||||
\(829\) | −5.17590 | + | 2.98831i | −0.179767 | + | 0.103788i | −0.587183 | − | 0.809454i | \(-0.699763\pi\) |
0.407416 | + | 0.913243i | \(0.366430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.679192 | + | 3.73143i | 0.0235609 | + | 0.129442i | ||||
\(832\) | − | 61.8125i | − | 2.14296i | ||||||
\(833\) | 14.6914 | − | 0.919696i | 0.509026 | − | 0.0318656i | ||||
\(834\) | 65.1006 | − | 55.2405i | 2.25425 | − | 1.91282i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15.8054 | − | 27.3758i | −0.546642 | − | 0.946811i | ||||
\(837\) | −31.7081 | − | 17.6138i | −1.09599 | − | 0.608821i | ||||
\(838\) | 82.5907 | + | 47.6837i | 2.85305 | + | 1.64721i | ||||
\(839\) | 44.9345 | 1.55131 | 0.775655 | − | 0.631157i | \(-0.217420\pi\) | ||||
0.775655 | + | 0.631157i | \(0.217420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1726 | 0.730090 | ||||||||
\(842\) | −70.2249 | − | 40.5444i | −2.42011 | − | 1.39725i | ||||
\(843\) | −0.0348578 | + | 0.0974396i | −0.00120057 | + | 0.00335600i | ||||
\(844\) | −51.9336 | − | 89.9516i | −1.78763 | − | 3.09626i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.8537 | − | 3.93529i | −0.820108 | − | 0.135298i | ||||
\(847\) | −0.554807 | − | 17.7425i | −0.0190634 | − | 0.609639i | ||||
\(848\) | 93.0325i | 3.19475i | ||||||||
\(849\) | −27.1655 | + | 4.94464i | −0.932318 | + | 0.169700i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.33698 | + | 5.39071i | −0.320068 | + | 0.184791i | ||||
\(852\) | −35.5308 | + | 6.46728i | −1.21727 | + | 0.221565i | ||||
\(853\) | − | 44.2981i | − | 1.51674i | −0.651826 | − | 0.758368i | \(-0.725997\pi\) | ||
0.651826 | − | 0.758368i | \(-0.274003\pi\) | |||||||
\(854\) | 46.3890 | + | 24.8829i | 1.58740 | + | 0.851474i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.6395 | − | 25.3563i | 0.500367 | − | 0.866661i | ||||
\(857\) | −7.37279 | − | 12.7700i | −0.251850 | − | 0.436216i | 0.712185 | − | 0.701991i | \(-0.247705\pi\) |
−0.964035 | + | 0.265775i | \(0.914372\pi\) | |||||||
\(858\) | 6.74341 | − | 18.8502i | 0.230216 | − | 0.643534i | ||||
\(859\) | 1.52877 | + | 0.882637i | 0.0521610 | + | 0.0301152i | 0.525854 | − | 0.850575i | \(-0.323746\pi\) |
−0.473693 | + | 0.880690i | \(0.657079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 52.4975 | − | 11.2612i | 1.78911 | − | 0.383782i | ||||
\(862\) | 23.1378 | 0.788076 | ||||||||
\(863\) | 18.7870 | + | 10.8467i | 0.639518 | + | 0.369226i | 0.784429 | − | 0.620219i | \(-0.212956\pi\) |
−0.144911 | + | 0.989445i | \(0.546290\pi\) | |||||||
\(864\) | 100.226 | + | 55.6754i | 3.40976 | + | 1.89411i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.5492 | + | 25.2000i | −0.494404 | + | 0.856332i | ||||
\(867\) | −16.6112 | + | 14.0953i | −0.564147 | + | 0.478702i | ||||
\(868\) | −101.054 | + | 3.15995i | −3.43000 | + | 0.107256i | ||||
\(869\) | − | 12.2538i | − | 0.415683i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.0856 | − | 7.55499i | 0.443390 | − | 0.255991i | ||||
\(872\) | 111.501 | − | 64.3750i | 3.77589 | − | 2.18001i | ||||
\(873\) | 18.9751 | − | 23.1270i | 0.642211 | − | 0.782730i | ||||
\(874\) | 13.5444i | 0.458147i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 41.1760 | + | 48.5256i | 1.39121 | + | 1.63953i | ||||
\(877\) | −15.7318 | + | 27.2482i | −0.531224 | + | 0.920107i | 0.468112 | + | 0.883669i | \(0.344934\pi\) |
−0.999336 | + | 0.0364380i | \(0.988399\pi\) | |||||||
\(878\) | 17.2914 | + | 29.9496i | 0.583556 | + | 1.01075i | ||||
\(879\) | −31.5844 | − | 11.2989i | −1.06531 | − | 0.381102i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8571 | 0.669004 | 0.334502 | − | 0.942395i | \(-0.391432\pi\) | ||||
0.334502 | + | 0.942395i | \(0.391432\pi\) | |||||||
\(882\) | 57.1198 | + | 5.78784i | 1.92332 | + | 0.194887i | ||||
\(883\) | 30.0998 | 1.01294 | 0.506469 | − | 0.862258i | \(-0.330951\pi\) | ||||
0.506469 | + | 0.862258i | \(0.330951\pi\) | |||||||
\(884\) | −20.3483 | − | 11.7481i | −0.684388 | − | 0.395132i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.1734 | − | 60.9221i | −1.18167 | − | 2.04672i | ||||
\(887\) | −14.7405 | + | 25.5312i | −0.494937 | + | 0.857255i | −0.999983 | − | 0.00583681i | \(-0.998142\pi\) |
0.505046 | + | 0.863092i | \(0.331475\pi\) | |||||||
\(888\) | −64.5748 | − | 76.1009i | −2.16699 | − | 2.55378i | ||||
\(889\) | 11.2130 | − | 6.94994i | 0.376072 | − | 0.233094i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.2953 | + | 14.0132i | 0.411909 | + | 0.469461i | ||||
\(892\) | 28.7429 | − | 16.5947i | 0.962383 | − | 0.555632i | ||||
\(893\) | 7.11632 | − | 4.10861i | 0.238139 | − | 0.137489i | ||||
\(894\) | 12.3618 | + | 67.9148i | 0.413440 | + | 2.27141i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 102.250 | − | 3.19735i | 3.41593 | − | 0.106816i | ||||
\(897\) | −4.79051 | + | 4.06494i | −0.159950 | + | 0.135725i | ||||
\(898\) | −48.7968 | + | 84.5185i | −1.62837 | + | 2.82042i | ||||
\(899\) | 9.76487 | + | 16.9133i | 0.325677 | + | 0.564089i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.2805 | + | 6.51280i | 0.375808 | + | 0.216973i | ||||
\(902\) | 66.3509 | 2.20924 | ||||||||
\(903\) | 19.5811 | − | 4.20033i | 0.651617 | − | 0.139778i | ||||
\(904\) | −105.103 | −3.49566 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.2112 | − | 31.3393i | 0.372469 | − | 1.04118i | ||||
\(907\) | 16.6945 | + | 28.9158i | 0.554333 | + | 0.960133i | 0.997955 | + | 0.0639189i | \(0.0203599\pi\) |
−0.443622 | + | 0.896214i | \(0.646307\pi\) | |||||||
\(908\) | 59.6837 | − | 103.375i | 1.98067 | − | 3.43062i | ||||
\(909\) | −7.87988 | + | 47.7639i | −0.261359 | + | 1.58423i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.1277i | 1.32949i | 0.747071 | + | 0.664744i | \(0.231460\pi\) | ||||
−0.747071 | + | 0.664744i | \(0.768540\pi\) | |||||||
\(912\) | −71.3473 | + | 12.9866i | −2.36255 | + | 0.430028i | ||||
\(913\) | 10.6991 | − | 6.17710i | 0.354087 | − | 0.204432i | ||||
\(914\) | −26.2929 | + | 15.1802i | −0.869692 | + | 0.502117i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 50.2396i | − | 1.65996i | ||||||
\(917\) | 0.967822 | + | 30.9506i | 0.0319603 | + | 1.02208i | ||||
\(918\) | 25.6202 | − | 15.3625i | 0.845594 | − | 0.507039i | ||||
\(919\) | −9.73901 | + | 16.8685i | −0.321260 | + | 0.556439i | −0.980748 | − | 0.195276i | \(-0.937440\pi\) |
0.659488 | + | 0.751715i | \(0.270773\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.3637 | + | 28.9701i | −0.341495 | + | 0.954597i | ||||
\(922\) | 44.6998 | + | 25.8074i | 1.47211 | + | 0.849922i | ||||
\(923\) | 7.77409 | 0.255887 | ||||||||
\(924\) | 49.4505 | + | 15.9654i | 1.62680 | + | 0.525222i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −34.6718 | − | 20.0177i | −1.13938 | − | 0.657824i | ||||
\(927\) | 0.553034 | + | 1.46883i | 0.0181640 | + | 0.0482428i | ||||
\(928\) | −30.8658 | − | 53.4611i | −1.01322 | − | 1.75495i | ||||
\(929\) | 22.2310 | − | 38.5053i | 0.729376 | − | 1.26332i | −0.227771 | − | 0.973715i | \(-0.573144\pi\) |
0.957147 | − | 0.289602i | \(-0.0935230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.2568 | + | 10.7937i | −0.532796 | + | 0.353749i | ||||
\(932\) | 99.5361i | 3.26041i | ||||||||
\(933\) | −2.22563 | − | 12.2275i | −0.0728640 | − | 0.400310i | ||||
\(934\) | −12.8427 | + | 7.41472i | −0.420225 | + | 0.242617i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −44.9633 | − | 36.8913i | −1.46967 | − | 1.20583i | ||||
\(937\) | 7.31878i | 0.239094i | 0.992829 | + | 0.119547i | \(0.0381443\pi\) | ||||
−0.992829 | + | 0.119547i | \(0.961856\pi\) | |||||||
\(938\) | 28.2103 | + | 45.5144i | 0.921098 | + | 1.48610i | ||||
\(939\) | −15.2335 | − | 17.9526i | −0.497127 | − | 0.585861i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.22911 | + | 7.32504i | 0.137865 | + | 0.238790i | 0.926688 | − | 0.375831i | \(-0.122643\pi\) |
−0.788823 | + | 0.614620i | \(0.789309\pi\) | |||||||
\(942\) | 97.6533 | + | 34.9342i | 3.18172 | + | 1.13822i | ||||
\(943\) | −18.0327 | − | 10.4112i | −0.587225 | − | 0.339035i | ||||
\(944\) | 43.3461 | 1.41079 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.7482 | 0.804635 | ||||||||
\(947\) | −16.0677 | − | 9.27668i | −0.522129 | − | 0.301452i | 0.215676 | − | 0.976465i | \(-0.430805\pi\) |
−0.737805 | + | 0.675013i | \(0.764138\pi\) | |||||||
\(948\) | −52.8138 | − | 18.8935i | −1.71531 | − | 0.613631i | ||||
\(949\) | −6.84976 | − | 11.8641i | −0.222353 | − | 0.385126i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.60893 | − | 4.25310i | −0.117028 | − | 0.137916i | ||||
\(952\) | 24.9799 | − | 46.5698i | 0.809602 | − | 1.50934i | ||||
\(953\) | 12.3994i | 0.401658i | 0.979626 | + | 0.200829i | \(0.0643635\pi\) | ||||
−0.979626 | + | 0.200829i | \(0.935637\pi\) | |||||||
\(954\) | 39.2752 | + | 32.2244i | 1.27158 | + | 1.04330i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −62.3188 | + | 35.9798i | −2.01553 | + | 1.16367i | ||||
\(957\) | −1.79751 | − | 9.87540i | −0.0581052 | − | 0.319226i | ||||
\(958\) | 10.1458i | 0.327797i | ||||||||
\(959\) | −15.8280 | + | 29.5080i | −0.511112 | + | 0.952863i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.86390 | − | 15.3527i | 0.285932 | − | 0.495249i | ||||
\(962\) | 16.9260 | + | 29.3167i | 0.545717 | + | 0.945210i | ||||
\(963\) | −3.25849 | − | 8.65440i | −0.105003 | − | 0.278884i | ||||
\(964\) | 0.0847752 | + | 0.0489450i | 0.00273043 | + | 0.00157641i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −14.9292 | − | 16.5184i | −0.480340 | − | 0.531471i | ||||
\(967\) | −55.9627 | −1.79964 | −0.899819 | − | 0.436263i | \(-0.856302\pi\) | ||||
−0.899819 | + | 0.436263i | \(0.856302\pi\) | |||||||
\(968\) | −55.1900 | − | 31.8640i | −1.77388 | − | 1.02415i | ||||
\(969\) | −3.42005 | + | 9.56023i | −0.109868 | + | 0.307119i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.9297 | − | 36.2512i | 0.671665 | − | 1.16336i | −0.305767 | − | 0.952106i | \(-0.598913\pi\) |
0.977432 | − | 0.211251i | \(-0.0677539\pi\) | |||||||
\(972\) | 79.3543 | − | 31.3864i | 2.54529 | − | 1.00672i | ||||
\(973\) | −25.1316 | − | 40.5472i | −0.805681 | − | 1.29988i | ||||
\(974\) | − | 50.0985i | − | 1.60526i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 94.6614 | − | 54.6528i | 3.03004 | − | 1.74939i | ||||
\(977\) | −15.9878 | + | 9.23058i | −0.511496 | + | 0.295312i | −0.733448 | − | 0.679745i | \(-0.762090\pi\) |
0.221952 | + | 0.975058i | \(0.428757\pi\) | |||||||
\(978\) | −37.7185 | + | 6.86548i | −1.20610 | + | 0.219534i | ||||
\(979\) | 25.7231i | 0.822115i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.61920 | − | 40.1223i | 0.211335 | − | 1.28101i | ||||
\(982\) | −50.1857 | + | 86.9241i | −1.60149 | + | 2.77386i | ||||
\(983\) | 19.4902 | + | 33.7581i | 0.621642 | + | 1.07672i | 0.989180 | + | 0.146707i | \(0.0468674\pi\) |
−0.367538 | + | 0.930008i | \(0.619799\pi\) | |||||||
\(984\) | 64.9269 | − | 181.493i | 2.06979 | − | 5.78580i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −16.0845 | −0.512234 | ||||||||
\(987\) | −4.15019 | + | 12.8546i | −0.132102 | + | 0.409167i | ||||
\(988\) | 31.1479 | 0.990945 | ||||||||
\(989\) | −6.72602 | − | 3.88327i | −0.213875 | − | 0.123481i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.60812 | + | 4.51739i | 0.0828495 | + | 0.143500i | 0.904473 | − | 0.426531i | \(-0.140265\pi\) |
−0.821623 | + | 0.570031i | \(0.806931\pi\) | |||||||
\(992\) | −77.0118 | + | 133.388i | −2.44513 | + | 4.23508i | ||||
\(993\) | −4.20906 | + | 3.57156i | −0.133570 | + | 0.113340i | ||||
\(994\) | 0.861078 | + | 27.5369i | 0.0273117 | + | 0.873419i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.1270 | − | 55.6369i | −0.320885 | − | 1.76292i | ||||
\(997\) | −28.5316 | + | 16.4727i | −0.903604 | + | 0.521696i | −0.878368 | − | 0.477985i | \(-0.841367\pi\) |
−0.0252363 | + | 0.999682i | \(0.508034\pi\) | |||||||
\(998\) | −2.53701 | + | 1.46474i | −0.0803075 | + | 0.0463656i | ||||
\(999\) | −31.5186 | + | 0.521517i | −0.997203 | + | 0.0165001i |
(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 | 525.2.t.i.26.10 | yes | 20 | |
3.2 | odd | 2 | inner | 525.2.t.i.26.1 | yes | 20 | |
5.2 | odd | 4 | 525.2.q.g.299.2 | 40 | |||
5.3 | odd | 4 | 525.2.q.g.299.19 | 40 | |||
5.4 | even | 2 | 525.2.t.h.26.1 | ✓ | 20 | ||
7.3 | odd | 6 | inner | 525.2.t.i.101.1 | yes | 20 | |
15.2 | even | 4 | 525.2.q.g.299.20 | 40 | |||
15.8 | even | 4 | 525.2.q.g.299.1 | 40 | |||
15.14 | odd | 2 | 525.2.t.h.26.10 | yes | 20 | ||
21.17 | even | 6 | inner | 525.2.t.i.101.10 | yes | 20 | |
35.3 | even | 12 | 525.2.q.g.374.20 | 40 | |||
35.17 | even | 12 | 525.2.q.g.374.1 | 40 | |||
35.24 | odd | 6 | 525.2.t.h.101.10 | yes | 20 | ||
105.17 | odd | 12 | 525.2.q.g.374.19 | 40 | |||
105.38 | odd | 12 | 525.2.q.g.374.2 | 40 | |||
105.59 | even | 6 | 525.2.t.h.101.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.q.g.299.1 | 40 | 15.8 | even | 4 | |||
525.2.q.g.299.2 | 40 | 5.2 | odd | 4 | |||
525.2.q.g.299.19 | 40 | 5.3 | odd | 4 | |||
525.2.q.g.299.20 | 40 | 15.2 | even | 4 | |||
525.2.q.g.374.1 | 40 | 35.17 | even | 12 | |||
525.2.q.g.374.2 | 40 | 105.38 | odd | 12 | |||
525.2.q.g.374.19 | 40 | 105.17 | odd | 12 | |||
525.2.q.g.374.20 | 40 | 35.3 | even | 12 | |||
525.2.t.h.26.1 | ✓ | 20 | 5.4 | even | 2 | ||
525.2.t.h.26.10 | yes | 20 | 15.14 | odd | 2 | ||
525.2.t.h.101.1 | yes | 20 | 105.59 | even | 6 | ||
525.2.t.h.101.10 | yes | 20 | 35.24 | odd | 6 | ||
525.2.t.i.26.1 | yes | 20 | 3.2 | odd | 2 | inner | |
525.2.t.i.26.10 | yes | 20 | 1.1 | even | 1 | trivial | |
525.2.t.i.101.1 | yes | 20 | 7.3 | odd | 6 | inner | |
525.2.t.i.101.10 | yes | 20 | 21.17 | even | 6 | inner |