Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,2,Mod(43,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.j (of order \(4\), 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: | \(0.638803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.9 | ||
Root | \(1.41303 - 0.0578659i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.43 |
Dual form | 80.2.j.b.67.9 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29521 | − | 0.567819i | 0.915855 | − | 0.401509i | ||||
\(3\) | 1.96251i | 1.13306i | 0.824043 | + | 0.566528i | \(0.191714\pi\) | ||||
−0.824043 | + | 0.566528i | \(0.808286\pi\) | |||||||
\(4\) | 1.35516 | − | 1.47090i | 0.677582 | − | 0.735448i | ||||
\(5\) | −1.72581 | − | 1.42182i | −0.771805 | − | 0.635859i | ||||
\(6\) | 1.11435 | + | 2.54187i | 0.454932 | + | 1.03772i | ||||
\(7\) | −1.60205 | + | 1.60205i | −0.605517 | + | 0.605517i | −0.941771 | − | 0.336254i | \(-0.890840\pi\) |
0.336254 | + | 0.941771i | \(0.390840\pi\) | |||||||
\(8\) | 0.920026 | − | 2.67461i | 0.325278 | − | 0.945618i | ||||
\(9\) | −0.851447 | −0.283816 | ||||||||
\(10\) | −3.04263 | − | 0.861621i | −0.962165 | − | 0.272468i | ||||
\(11\) | 0.754587 | − | 0.754587i | 0.227517 | − | 0.227517i | −0.584138 | − | 0.811654i | \(-0.698567\pi\) |
0.811654 | + | 0.584138i | \(0.198567\pi\) | |||||||
\(12\) | 2.88665 | + | 2.65952i | 0.833303 | + | 0.767738i | ||||
\(13\) | −5.94580 | −1.64907 | −0.824534 | − | 0.565812i | \(-0.808563\pi\) | ||||
−0.824534 | + | 0.565812i | \(0.808563\pi\) | |||||||
\(14\) | −1.16532 | + | 2.98467i | −0.311446 | + | 0.797687i | ||||
\(15\) | 2.79034 | − | 3.38692i | 0.720464 | − | 0.874498i | ||||
\(16\) | −0.327065 | − | 3.98661i | −0.0817662 | − | 0.996652i | ||||
\(17\) | 1.95574 | − | 1.95574i | 0.474336 | − | 0.474336i | −0.428978 | − | 0.903315i | \(-0.641126\pi\) |
0.903315 | + | 0.428978i | \(0.141126\pi\) | |||||||
\(18\) | −1.10281 | + | 0.483468i | −0.259934 | + | 0.113954i | ||||
\(19\) | −0.780680 | + | 0.780680i | −0.179100 | + | 0.179100i | −0.790964 | − | 0.611863i | \(-0.790420\pi\) |
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(20\) | −4.43011 | + | 0.611680i | −0.990602 | + | 0.136776i | ||||
\(21\) | −3.14404 | − | 3.14404i | −0.686085 | − | 0.686085i | ||||
\(22\) | 0.548884 | − | 1.40582i | 0.117022 | − | 0.299722i | ||||
\(23\) | 4.93121 | + | 4.93121i | 1.02823 | + | 1.02823i | 0.999590 | + | 0.0286378i | \(0.00911693\pi\) |
0.0286378 | + | 0.999590i | \(0.490883\pi\) | |||||||
\(24\) | 5.24896 | + | 1.80556i | 1.07144 | + | 0.368558i | ||||
\(25\) | 0.956833 | + | 4.90759i | 0.191367 | + | 0.981519i | ||||
\(26\) | −7.70109 | + | 3.37614i | −1.51031 | + | 0.662115i | ||||
\(27\) | 4.21656i | 0.811477i | ||||||||
\(28\) | 0.185408 | + | 4.52748i | 0.0350388 | + | 0.855614i | ||||
\(29\) | 1.44802 | + | 1.44802i | 0.268891 | + | 0.268891i | 0.828653 | − | 0.559762i | \(-0.189108\pi\) |
−0.559762 | + | 0.828653i | \(0.689108\pi\) | |||||||
\(30\) | 1.69094 | − | 5.97120i | 0.308722 | − | 1.09019i | ||||
\(31\) | − | 3.60859i | − | 0.648121i | −0.946036 | − | 0.324061i | \(-0.894952\pi\) | ||
0.946036 | − | 0.324061i | \(-0.105048\pi\) | |||||||
\(32\) | −2.68729 | − | 4.97780i | −0.475050 | − | 0.879959i | ||||
\(33\) | 1.48089 | + | 1.48089i | 0.257789 | + | 0.257789i | ||||
\(34\) | 1.42260 | − | 3.64361i | 0.243973 | − | 0.624874i | ||||
\(35\) | 5.04266 | − | 0.486998i | 0.852365 | − | 0.0823177i | ||||
\(36\) | −1.15385 | + | 1.25239i | −0.192308 | + | 0.208732i | ||||
\(37\) | 10.2364 | 1.68285 | 0.841427 | − | 0.540371i | \(-0.181716\pi\) | ||||
0.841427 | + | 0.540371i | \(0.181716\pi\) | |||||||
\(38\) | −0.567864 | + | 1.45443i | −0.0921197 | + | 0.235940i | ||||
\(39\) | − | 11.6687i | − | 1.86849i | ||||||
\(40\) | −5.39062 | + | 3.30776i | −0.852331 | + | 0.523002i | ||||
\(41\) | − | 6.93334i | − | 1.08281i | −0.840763 | − | 0.541403i | \(-0.817893\pi\) | ||
0.840763 | − | 0.541403i | \(-0.182107\pi\) | |||||||
\(42\) | −5.85745 | − | 2.28696i | −0.903823 | − | 0.352885i | ||||
\(43\) | −9.91344 | −1.51179 | −0.755893 | − | 0.654695i | \(-0.772797\pi\) | ||||
−0.755893 | + | 0.654695i | \(0.772797\pi\) | |||||||
\(44\) | −0.0873298 | − | 2.13251i | −0.0131655 | − | 0.321488i | ||||
\(45\) | 1.46944 | + | 1.21061i | 0.219050 | + | 0.180467i | ||||
\(46\) | 9.18700 | + | 3.58694i | 1.35455 | + | 0.528865i | ||||
\(47\) | −0.104270 | − | 0.104270i | −0.0152093 | − | 0.0152093i | 0.699461 | − | 0.714671i | \(-0.253423\pi\) |
−0.714671 | + | 0.699461i | \(0.753423\pi\) | |||||||
\(48\) | 7.82376 | − | 0.641868i | 1.12926 | − | 0.0926457i | ||||
\(49\) | 1.86688i | 0.266698i | ||||||||
\(50\) | 4.02593 | + | 5.81308i | 0.569352 | + | 0.822094i | ||||
\(51\) | 3.83816 | + | 3.83816i | 0.537450 | + | 0.537450i | ||||
\(52\) | −8.05753 | + | 8.74565i | −1.11738 | + | 1.21280i | ||||
\(53\) | − | 4.03213i | − | 0.553856i | −0.960891 | − | 0.276928i | \(-0.910684\pi\) | ||
0.960891 | − | 0.276928i | \(-0.0893164\pi\) | |||||||
\(54\) | 2.39424 | + | 5.46135i | 0.325815 | + | 0.743195i | ||||
\(55\) | −2.37516 | + | 0.229383i | −0.320267 | + | 0.0309300i | ||||
\(56\) | 2.81093 | + | 5.75878i | 0.375627 | + | 0.769550i | ||||
\(57\) | −1.53209 | − | 1.53209i | −0.202931 | − | 0.202931i | ||||
\(58\) | 2.69771 | + | 1.05328i | 0.354227 | + | 0.138303i | ||||
\(59\) | 3.46736 | + | 3.46736i | 0.451412 | + | 0.451412i | 0.895823 | − | 0.444411i | \(-0.146587\pi\) |
−0.444411 | + | 0.895823i | \(0.646587\pi\) | |||||||
\(60\) | −1.20043 | − | 8.69413i | −0.154975 | − | 1.12241i | ||||
\(61\) | 0.680578 | − | 0.680578i | 0.0871391 | − | 0.0871391i | −0.662194 | − | 0.749333i | \(-0.730374\pi\) |
0.749333 | + | 0.662194i | \(0.230374\pi\) | |||||||
\(62\) | −2.04902 | − | 4.67390i | −0.260226 | − | 0.593585i | ||||
\(63\) | 1.36406 | − | 1.36406i | 0.171855 | − | 0.171855i | ||||
\(64\) | −6.30711 | − | 4.92142i | −0.788388 | − | 0.615178i | ||||
\(65\) | 10.2613 | + | 8.45388i | 1.27276 | + | 1.04857i | ||||
\(66\) | 2.75894 | + | 1.07719i | 0.339602 | + | 0.132593i | ||||
\(67\) | −9.04721 | −1.10529 | −0.552646 | − | 0.833416i | \(-0.686382\pi\) | ||||
−0.552646 | + | 0.833416i | \(0.686382\pi\) | |||||||
\(68\) | −0.226341 | − | 5.52703i | −0.0274479 | − | 0.670251i | ||||
\(69\) | −9.67754 | + | 9.67754i | −1.16504 | + | 1.16504i | ||||
\(70\) | 6.25480 | − | 3.49408i | 0.747592 | − | 0.417623i | ||||
\(71\) | −3.64007 | −0.431997 | −0.215998 | − | 0.976394i | \(-0.569301\pi\) | ||||
−0.215998 | + | 0.976394i | \(0.569301\pi\) | |||||||
\(72\) | −0.783353 | + | 2.27729i | −0.0923191 | + | 0.268381i | ||||
\(73\) | 2.94030 | − | 2.94030i | 0.344136 | − | 0.344136i | −0.513784 | − | 0.857920i | \(-0.671757\pi\) |
0.857920 | + | 0.513784i | \(0.171757\pi\) | |||||||
\(74\) | 13.2583 | − | 5.81242i | 1.54125 | − | 0.675681i | ||||
\(75\) | −9.63120 | + | 1.87779i | −1.11212 | + | 0.216829i | ||||
\(76\) | 0.0903496 | + | 2.20625i | 0.0103638 | + | 0.253074i | ||||
\(77\) | 2.41777i | 0.275530i | ||||||||
\(78\) | −6.62570 | − | 15.1135i | −0.750213 | − | 1.71126i | ||||
\(79\) | −10.7140 | −1.20542 | −0.602711 | − | 0.797960i | \(-0.705913\pi\) | ||||
−0.602711 | + | 0.797960i | \(0.705913\pi\) | |||||||
\(80\) | −5.10380 | + | 7.34515i | −0.570622 | + | 0.821213i | ||||
\(81\) | −10.8294 | −1.20326 | ||||||||
\(82\) | −3.93688 | − | 8.98016i | −0.434756 | − | 0.991693i | ||||
\(83\) | − | 4.23845i | − | 0.465230i | −0.972569 | − | 0.232615i | \(-0.925272\pi\) | ||
0.972569 | − | 0.232615i | \(-0.0747282\pi\) | |||||||
\(84\) | −8.88523 | + | 0.363865i | −0.969458 | + | 0.0397009i | ||||
\(85\) | −6.15595 | + | 0.594515i | −0.667707 | + | 0.0644842i | ||||
\(86\) | −12.8400 | + | 5.62904i | −1.38458 | + | 0.606995i | ||||
\(87\) | −2.84176 | + | 2.84176i | −0.304668 | + | 0.304668i | ||||
\(88\) | −1.32399 | − | 2.71247i | −0.141138 | − | 0.289150i | ||||
\(89\) | −0.0426256 | −0.00451831 | −0.00225915 | − | 0.999997i | \(-0.500719\pi\) | ||||
−0.00225915 | + | 0.999997i | \(0.500719\pi\) | |||||||
\(90\) | 2.59064 | + | 0.733625i | 0.273078 | + | 0.0773308i | ||||
\(91\) | 9.52546 | − | 9.52546i | 0.998539 | − | 0.998539i | ||||
\(92\) | 13.9359 | − | 0.570698i | 1.45292 | − | 0.0594993i | ||||
\(93\) | 7.08189 | 0.734358 | ||||||||
\(94\) | −0.194258 | − | 0.0758455i | −0.0200362 | − | 0.00782287i | ||||
\(95\) | 2.45730 | − | 0.237315i | 0.252113 | − | 0.0243480i | ||||
\(96\) | 9.76898 | − | 5.27383i | 0.997042 | − | 0.538258i | ||||
\(97\) | −1.91173 | + | 1.91173i | −0.194106 | + | 0.194106i | −0.797468 | − | 0.603362i | \(-0.793828\pi\) |
0.603362 | + | 0.797468i | \(0.293828\pi\) | |||||||
\(98\) | 1.06005 | + | 2.41802i | 0.107081 | + | 0.244257i | ||||
\(99\) | −0.642491 | + | 0.642491i | −0.0645728 | + | 0.0645728i | ||||
\(100\) | 8.51522 | + | 5.24319i | 0.851522 | + | 0.524319i | ||||
\(101\) | 4.96537 | + | 4.96537i | 0.494073 | + | 0.494073i | 0.909587 | − | 0.415514i | \(-0.136398\pi\) |
−0.415514 | + | 0.909587i | \(0.636398\pi\) | |||||||
\(102\) | 7.15062 | + | 2.79186i | 0.708017 | + | 0.276435i | ||||
\(103\) | 0.442220 | + | 0.442220i | 0.0435733 | + | 0.0435733i | 0.728558 | − | 0.684984i | \(-0.240191\pi\) |
−0.684984 | + | 0.728558i | \(0.740191\pi\) | |||||||
\(104\) | −5.47029 | + | 15.9027i | −0.536406 | + | 1.55939i | ||||
\(105\) | 0.955739 | + | 9.89627i | 0.0932706 | + | 0.965777i | ||||
\(106\) | −2.28952 | − | 5.22248i | −0.222378 | − | 0.507252i | ||||
\(107\) | − | 17.5924i | − | 1.70072i | −0.526204 | − | 0.850359i | \(-0.676385\pi\) | ||
0.526204 | − | 0.850359i | \(-0.323615\pi\) | |||||||
\(108\) | 6.20211 | + | 5.71412i | 0.596799 | + | 0.549842i | ||||
\(109\) | −0.345161 | − | 0.345161i | −0.0330605 | − | 0.0330605i | 0.690383 | − | 0.723444i | \(-0.257442\pi\) |
−0.723444 | + | 0.690383i | \(0.757442\pi\) | |||||||
\(110\) | −2.94610 | + | 1.64576i | −0.280900 | + | 0.156917i | ||||
\(111\) | 20.0890i | 1.90677i | ||||||||
\(112\) | 6.91071 | + | 5.86276i | 0.653001 | + | 0.553979i | ||||
\(113\) | −5.43662 | − | 5.43662i | −0.511435 | − | 0.511435i | 0.403531 | − | 0.914966i | \(-0.367783\pi\) |
−0.914966 | + | 0.403531i | \(0.867783\pi\) | |||||||
\(114\) | −2.85434 | − | 1.11444i | −0.267334 | − | 0.104377i | ||||
\(115\) | −1.49901 | − | 15.5216i | −0.139784 | − | 1.44740i | ||||
\(116\) | 4.09219 | − | 0.167582i | 0.379950 | − | 0.0155596i | ||||
\(117\) | 5.06253 | 0.468031 | ||||||||
\(118\) | 6.45981 | + | 2.52214i | 0.594673 | + | 0.232182i | ||||
\(119\) | 6.26638i | 0.574438i | ||||||||
\(120\) | −6.49151 | − | 10.5791i | −0.592591 | − | 0.965739i | ||||
\(121\) | 9.86120i | 0.896472i | ||||||||
\(122\) | 0.495050 | − | 1.26794i | 0.0448197 | − | 0.114794i | ||||
\(123\) | 13.6067 | 1.22688 | ||||||||
\(124\) | −5.30785 | − | 4.89023i | −0.476659 | − | 0.439155i | ||||
\(125\) | 5.32642 | − | 9.83002i | 0.476410 | − | 0.879223i | ||||
\(126\) | 0.992211 | − | 2.54129i | 0.0883932 | − | 0.226396i | ||||
\(127\) | 6.27150 | + | 6.27150i | 0.556505 | + | 0.556505i | 0.928311 | − | 0.371805i | \(-0.121261\pi\) |
−0.371805 | + | 0.928311i | \(0.621261\pi\) | |||||||
\(128\) | −10.9635 | − | 2.79301i | −0.969049 | − | 0.246869i | ||||
\(129\) | − | 19.4552i | − | 1.71294i | ||||||
\(130\) | 18.0909 | + | 5.12302i | 1.58667 | + | 0.449319i | ||||
\(131\) | 1.61521 | + | 1.61521i | 0.141122 | + | 0.141122i | 0.774138 | − | 0.633017i | \(-0.218184\pi\) |
−0.633017 | + | 0.774138i | \(0.718184\pi\) | |||||||
\(132\) | 4.18507 | − | 0.171386i | 0.364263 | − | 0.0149172i | ||||
\(133\) | − | 2.50138i | − | 0.216897i | ||||||
\(134\) | −11.7181 | + | 5.13718i | −1.01229 | + | 0.443785i | ||||
\(135\) | 5.99520 | − | 7.27697i | 0.515985 | − | 0.626302i | ||||
\(136\) | −3.43152 | − | 7.03018i | −0.294250 | − | 0.602833i | ||||
\(137\) | −6.83585 | − | 6.83585i | −0.584026 | − | 0.584026i | 0.351981 | − | 0.936007i | \(-0.385508\pi\) |
−0.936007 | + | 0.351981i | \(0.885508\pi\) | |||||||
\(138\) | −7.03941 | + | 18.0296i | −0.599234 | + | 1.53478i | ||||
\(139\) | 13.7427 | + | 13.7427i | 1.16564 | + | 1.16564i | 0.983220 | + | 0.182423i | \(0.0583940\pi\) |
0.182423 | + | 0.983220i | \(0.441606\pi\) | |||||||
\(140\) | 6.11730 | − | 8.07718i | 0.517006 | − | 0.682647i | ||||
\(141\) | 0.204631 | − | 0.204631i | 0.0172330 | − | 0.0172330i | ||||
\(142\) | −4.71467 | + | 2.06690i | −0.395647 | + | 0.173450i | ||||
\(143\) | −4.48662 | + | 4.48662i | −0.375190 | + | 0.375190i | ||||
\(144\) | 0.278479 | + | 3.39439i | 0.0232066 | + | 0.282865i | ||||
\(145\) | −0.440176 | − | 4.55784i | −0.0365547 | − | 0.378508i | ||||
\(146\) | 2.13876 | − | 5.47788i | 0.177005 | − | 0.453353i | ||||
\(147\) | −3.66378 | −0.302184 | ||||||||
\(148\) | 13.8720 | − | 15.0567i | 1.14027 | − | 1.23765i | ||||
\(149\) | 1.73811 | − | 1.73811i | 0.142391 | − | 0.142391i | −0.632318 | − | 0.774709i | \(-0.717896\pi\) |
0.774709 | + | 0.632318i | \(0.217896\pi\) | |||||||
\(150\) | −11.4082 | + | 7.90093i | −0.931478 | + | 0.645108i | ||||
\(151\) | 5.83522 | 0.474864 | 0.237432 | − | 0.971404i | \(-0.423694\pi\) | ||||
0.237432 | + | 0.971404i | \(0.423694\pi\) | |||||||
\(152\) | 1.36977 | + | 2.80626i | 0.111103 | + | 0.227618i | ||||
\(153\) | −1.66521 | + | 1.66521i | −0.134624 | + | 0.134624i | ||||
\(154\) | 1.37286 | + | 3.13153i | 0.110628 | + | 0.252346i | ||||
\(155\) | −5.13078 | + | 6.22773i | −0.412114 | + | 0.500223i | ||||
\(156\) | −17.1634 | − | 15.8130i | −1.37417 | − | 1.26605i | ||||
\(157\) | − | 3.14732i | − | 0.251183i | −0.992082 | − | 0.125592i | \(-0.959917\pi\) | ||
0.992082 | − | 0.125592i | \(-0.0400829\pi\) | |||||||
\(158\) | −13.8770 | + | 6.08363i | −1.10399 | + | 0.483987i | ||||
\(159\) | 7.91310 | 0.627550 | ||||||||
\(160\) | −2.43980 | + | 12.4116i | −0.192883 | + | 0.981222i | ||||
\(161\) | −15.8001 | −1.24522 | ||||||||
\(162\) | −14.0264 | + | 6.14913i | −1.10202 | + | 0.483121i | ||||
\(163\) | 7.82117i | 0.612601i | 0.951935 | + | 0.306301i | \(0.0990913\pi\) | ||||
−0.951935 | + | 0.306301i | \(0.900909\pi\) | |||||||
\(164\) | −10.1982 | − | 9.39580i | −0.796347 | − | 0.733689i | ||||
\(165\) | −0.450167 | − | 4.66128i | −0.0350454 | − | 0.362880i | ||||
\(166\) | −2.40667 | − | 5.48970i | −0.186794 | − | 0.426083i | ||||
\(167\) | −9.88460 | + | 9.88460i | −0.764893 | + | 0.764893i | −0.977203 | − | 0.212309i | \(-0.931902\pi\) |
0.212309 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(168\) | −11.3017 | + | 5.51649i | −0.871943 | + | 0.425606i | ||||
\(169\) | 22.3525 | 1.71942 | ||||||||
\(170\) | −7.63570 | + | 4.26549i | −0.585632 | + | 0.327148i | ||||
\(171\) | 0.664708 | − | 0.664708i | 0.0508315 | − | 0.0508315i | ||||
\(172\) | −13.4343 | + | 14.5816i | −1.02436 | + | 1.11184i | ||||
\(173\) | 3.49245 | 0.265526 | 0.132763 | − | 0.991148i | \(-0.457615\pi\) | ||||
0.132763 | + | 0.991148i | \(0.457615\pi\) | |||||||
\(174\) | −2.06708 | + | 5.29429i | −0.156705 | + | 0.401359i | ||||
\(175\) | −9.39509 | − | 6.32931i | −0.710202 | − | 0.478451i | ||||
\(176\) | −3.25504 | − | 2.76144i | −0.245358 | − | 0.208152i | ||||
\(177\) | −6.80473 | + | 6.80473i | −0.511475 | + | 0.511475i | ||||
\(178\) | −0.0552094 | + | 0.0242036i | −0.00413812 | + | 0.00181414i | ||||
\(179\) | 13.0809 | − | 13.0809i | 0.977713 | − | 0.977713i | −0.0220444 | − | 0.999757i | \(-0.507018\pi\) |
0.999757 | + | 0.0220444i | \(0.00701753\pi\) | |||||||
\(180\) | 3.77200 | − | 0.520813i | 0.281148 | − | 0.0388191i | ||||
\(181\) | 13.6393 | + | 13.6393i | 1.01380 | + | 1.01380i | 0.999903 | + | 0.0138952i | \(0.00442312\pi\) |
0.0138952 | + | 0.999903i | \(0.495577\pi\) | |||||||
\(182\) | 6.92878 | − | 17.7462i | 0.513595 | − | 1.31544i | ||||
\(183\) | 1.33564 | + | 1.33564i | 0.0987335 | + | 0.0987335i | ||||
\(184\) | 17.7259 | − | 8.65223i | 1.30677 | − | 0.637851i | ||||
\(185\) | −17.6661 | − | 14.5544i | −1.29884 | − | 1.07006i | ||||
\(186\) | 9.17257 | − | 4.02123i | 0.672565 | − | 0.294851i | ||||
\(187\) | − | 2.95155i | − | 0.215839i | ||||||
\(188\) | −0.294673 | + | 0.0120674i | −0.0214912 | + | 0.000880102i | ||||
\(189\) | −6.75513 | − | 6.75513i | −0.491363 | − | 0.491363i | ||||
\(190\) | 3.04797 | − | 1.70267i | 0.221123 | − | 0.123525i | ||||
\(191\) | 2.92523i | 0.211662i | 0.994384 | + | 0.105831i | \(0.0337503\pi\) | ||||
−0.994384 | + | 0.105831i | \(0.966250\pi\) | |||||||
\(192\) | 9.65835 | − | 12.3778i | 0.697031 | − | 0.893288i | ||||
\(193\) | 0.0830702 | + | 0.0830702i | 0.00597953 | + | 0.00597953i | 0.710090 | − | 0.704111i | \(-0.248654\pi\) |
−0.704111 | + | 0.710090i | \(0.748654\pi\) | |||||||
\(194\) | −1.39058 | + | 3.56161i | −0.0998379 | + | 0.255709i | ||||
\(195\) | −16.5908 | + | 20.1379i | −1.18809 | + | 1.44211i | ||||
\(196\) | 2.74599 | + | 2.52993i | 0.196142 | + | 0.180710i | ||||
\(197\) | 7.80487 | 0.556074 | 0.278037 | − | 0.960570i | \(-0.410316\pi\) | ||||
0.278037 | + | 0.960570i | \(0.410316\pi\) | |||||||
\(198\) | −0.467346 | + | 1.19698i | −0.0332128 | + | 0.0850659i | ||||
\(199\) | − | 10.9740i | − | 0.777924i | −0.921254 | − | 0.388962i | \(-0.872834\pi\) | ||
0.921254 | − | 0.388962i | \(-0.127166\pi\) | |||||||
\(200\) | 14.0062 | + | 1.95595i | 0.990389 | + | 0.138307i | ||||
\(201\) | − | 17.7552i | − | 1.25236i | ||||||
\(202\) | 9.25065 | + | 3.61179i | 0.650873 | + | 0.254125i | ||||
\(203\) | −4.63960 | −0.325636 | ||||||||
\(204\) | 10.8469 | − | 0.444197i | 0.759432 | − | 0.0311000i | ||||
\(205\) | −9.85799 | + | 11.9656i | −0.688512 | + | 0.835715i | ||||
\(206\) | 0.823871 | + | 0.321669i | 0.0574018 | + | 0.0224118i | ||||
\(207\) | −4.19866 | − | 4.19866i | −0.291827 | − | 0.291827i | ||||
\(208\) | 1.94466 | + | 23.7036i | 0.134838 | + | 1.64355i | ||||
\(209\) | 1.17818i | 0.0814966i | ||||||||
\(210\) | 6.85718 | + | 12.2751i | 0.473190 | + | 0.847063i | ||||
\(211\) | −8.92204 | − | 8.92204i | −0.614218 | − | 0.614218i | 0.329824 | − | 0.944042i | \(-0.393011\pi\) |
−0.944042 | + | 0.329824i | \(0.893011\pi\) | |||||||
\(212\) | −5.93085 | − | 5.46420i | −0.407332 | − | 0.375283i | ||||
\(213\) | − | 7.14367i | − | 0.489477i | ||||||
\(214\) | −9.98927 | − | 22.7859i | −0.682853 | − | 1.55761i | ||||
\(215\) | 17.1087 | + | 14.0952i | 1.16680 | + | 0.961283i | ||||
\(216\) | 11.2777 | + | 3.87934i | 0.767347 | + | 0.263956i | ||||
\(217\) | 5.78113 | + | 5.78113i | 0.392449 | + | 0.392449i | ||||
\(218\) | −0.643047 | − | 0.251069i | −0.0435527 | − | 0.0170045i | ||||
\(219\) | 5.77037 | + | 5.77037i | 0.389926 | + | 0.389926i | ||||
\(220\) | −2.88134 | + | 3.80447i | −0.194260 | + | 0.256497i | ||||
\(221\) | −11.6284 | + | 11.6284i | −0.782213 | + | 0.782213i | ||||
\(222\) | 11.4069 | + | 26.0196i | 0.765584 | + | 1.74632i | ||||
\(223\) | 13.1678 | − | 13.1678i | 0.881784 | − | 0.881784i | −0.111931 | − | 0.993716i | \(-0.535704\pi\) |
0.993716 | + | 0.111931i | \(0.0357037\pi\) | |||||||
\(224\) | 12.2798 | + | 3.66950i | 0.820481 | + | 0.245179i | ||||
\(225\) | −0.814693 | − | 4.17856i | −0.0543129 | − | 0.278570i | ||||
\(226\) | −10.1286 | − | 3.95458i | −0.673745 | − | 0.263055i | ||||
\(227\) | 19.3432 | 1.28385 | 0.641927 | − | 0.766766i | \(-0.278135\pi\) | ||||
0.641927 | + | 0.766766i | \(0.278135\pi\) | |||||||
\(228\) | −4.32979 | + | 0.177312i | −0.286747 | + | 0.0117428i | ||||
\(229\) | −13.2143 | + | 13.2143i | −0.873223 | + | 0.873223i | −0.992822 | − | 0.119599i | \(-0.961839\pi\) |
0.119599 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(230\) | −10.7550 | − | 19.2527i | −0.709165 | − | 1.26948i | ||||
\(231\) | −4.74490 | −0.312191 | ||||||||
\(232\) | 5.20511 | − | 2.54068i | 0.341732 | − | 0.166804i | ||||
\(233\) | −20.6884 | + | 20.6884i | −1.35534 | + | 1.35534i | −0.475769 | + | 0.879570i | \(0.657830\pi\) |
−0.879570 | + | 0.475769i | \(0.842170\pi\) | |||||||
\(234\) | 6.55707 | − | 2.87460i | 0.428649 | − | 0.187919i | ||||
\(235\) | 0.0316965 | + | 0.328204i | 0.00206765 | + | 0.0214096i | ||||
\(236\) | 9.79896 | − | 0.401284i | 0.637858 | − | 0.0261214i | ||||
\(237\) | − | 21.0264i | − | 1.36581i | ||||||
\(238\) | 3.55817 | + | 8.11630i | 0.230642 | + | 0.526102i | ||||
\(239\) | −14.1053 | −0.912395 | −0.456198 | − | 0.889878i | \(-0.650789\pi\) | ||||
−0.456198 | + | 0.889878i | \(0.650789\pi\) | |||||||
\(240\) | −14.4149 | − | 10.0163i | −0.930480 | − | 0.646547i | ||||
\(241\) | 12.8011 | 0.824592 | 0.412296 | − | 0.911050i | \(-0.364727\pi\) | ||||
0.412296 | + | 0.911050i | \(0.364727\pi\) | |||||||
\(242\) | 5.59937 | + | 12.7724i | 0.359941 | + | 0.821039i | ||||
\(243\) | − | 8.60310i | − | 0.551889i | ||||||
\(244\) | −0.0787646 | − | 1.92335i | −0.00504238 | − | 0.123130i | ||||
\(245\) | 2.65438 | − | 3.22189i | 0.169582 | − | 0.205839i | ||||
\(246\) | 17.6237 | − | 7.72617i | 1.12364 | − | 0.492603i | ||||
\(247\) | 4.64177 | − | 4.64177i | 0.295349 | − | 0.295349i | ||||
\(248\) | −9.65157 | − | 3.31999i | −0.612876 | − | 0.210820i | ||||
\(249\) | 8.31800 | 0.527132 | ||||||||
\(250\) | 1.31719 | − | 15.7564i | 0.0833066 | − | 0.996524i | ||||
\(251\) | −6.84118 | + | 6.84118i | −0.431812 | + | 0.431812i | −0.889244 | − | 0.457433i | \(-0.848769\pi\) |
0.457433 | + | 0.889244i | \(0.348769\pi\) | |||||||
\(252\) | −0.157865 | − | 3.85491i | −0.00994457 | − | 0.242837i | ||||
\(253\) | 7.44205 | 0.467878 | ||||||||
\(254\) | 11.6840 | + | 4.56186i | 0.733120 | + | 0.286237i | ||||
\(255\) | −1.16674 | − | 12.0811i | −0.0730642 | − | 0.756549i | ||||
\(256\) | −15.7861 | + | 2.60776i | −0.986629 | + | 0.162985i | ||||
\(257\) | −6.66524 | + | 6.66524i | −0.415766 | + | 0.415766i | −0.883742 | − | 0.467975i | \(-0.844984\pi\) |
0.467975 | + | 0.883742i | \(0.344984\pi\) | |||||||
\(258\) | −11.0471 | − | 25.1987i | −0.687759 | − | 1.56880i | ||||
\(259\) | −16.3992 | + | 16.3992i | −1.01900 | + | 1.01900i | ||||
\(260\) | 26.3405 | − | 3.63693i | 1.63357 | − | 0.225553i | ||||
\(261\) | −1.23291 | − | 1.23291i | −0.0763154 | − | 0.0763154i | ||||
\(262\) | 3.00919 | + | 1.17490i | 0.185908 | + | 0.0725854i | ||||
\(263\) | −7.32015 | − | 7.32015i | −0.451380 | − | 0.451380i | 0.444432 | − | 0.895812i | \(-0.353405\pi\) |
−0.895812 | + | 0.444432i | \(0.853405\pi\) | |||||||
\(264\) | 5.32325 | − | 2.59834i | 0.327623 | − | 0.159917i | ||||
\(265\) | −5.73298 | + | 6.95869i | −0.352174 | + | 0.427469i | ||||
\(266\) | −1.42033 | − | 3.23982i | −0.0870859 | − | 0.198646i | ||||
\(267\) | − | 0.0836533i | − | 0.00511950i | ||||||
\(268\) | −12.2604 | + | 13.3075i | −0.748926 | + | 0.812885i | ||||
\(269\) | 15.9801 | + | 15.9801i | 0.974321 | + | 0.974321i | 0.999678 | − | 0.0253576i | \(-0.00807242\pi\) |
−0.0253576 | + | 0.999678i | \(0.508072\pi\) | |||||||
\(270\) | 3.63307 | − | 12.8294i | 0.221102 | − | 0.780774i | ||||
\(271\) | − | 3.59684i | − | 0.218492i | −0.994015 | − | 0.109246i | \(-0.965156\pi\) | ||
0.994015 | − | 0.109246i | \(-0.0348437\pi\) | |||||||
\(272\) | −8.43642 | − | 7.15711i | −0.511533 | − | 0.433963i | ||||
\(273\) | 18.6938 | + | 18.6938i | 1.13140 | + | 1.13140i | ||||
\(274\) | −12.7354 | − | 4.97237i | −0.769375 | − | 0.300392i | ||||
\(275\) | 4.42522 | + | 2.98119i | 0.266851 | + | 0.179773i | ||||
\(276\) | 1.12000 | + | 27.3493i | 0.0674161 | + | 1.64623i | ||||
\(277\) | −20.9416 | −1.25826 | −0.629131 | − | 0.777300i | \(-0.716589\pi\) | ||||
−0.629131 | + | 0.777300i | \(0.716589\pi\) | |||||||
\(278\) | 25.6032 | + | 9.99640i | 1.53558 | + | 0.599545i | ||||
\(279\) | 3.07252i | 0.183947i | ||||||||
\(280\) | 3.33684 | − | 13.9352i | 0.199415 | − | 0.832788i | ||||
\(281\) | − | 3.26699i | − | 0.194892i | −0.995241 | − | 0.0974462i | \(-0.968933\pi\) | ||
0.995241 | − | 0.0974462i | \(-0.0310674\pi\) | |||||||
\(282\) | 0.148848 | − | 0.381234i | 0.00886375 | − | 0.0227022i | ||||
\(283\) | 0.000151619 | 0 | 9.01279e−6 | 0 | 4.50640e−6 | − | 1.00000i | \(-0.499999\pi\) | ||
4.50640e−6 | 1.00000i | \(0.499999\pi\) | ||||||||
\(284\) | −4.93289 | + | 5.35416i | −0.292713 | + | 0.317711i | ||||
\(285\) | 0.465733 | + | 4.82247i | 0.0275877 | + | 0.285658i | ||||
\(286\) | −3.26355 | + | 8.35873i | −0.192978 | + | 0.494262i | ||||
\(287\) | 11.1075 | + | 11.1075i | 0.655657 | + | 0.655657i | ||||
\(288\) | 2.28809 | + | 4.23833i | 0.134827 | + | 0.249746i | ||||
\(289\) | 9.35017i | 0.550010i | ||||||||
\(290\) | −3.15815 | − | 5.65344i | −0.185453 | − | 0.331981i | ||||
\(291\) | −3.75178 | − | 3.75178i | −0.219933 | − | 0.219933i | ||||
\(292\) | −0.340287 | − | 8.30947i | −0.0199138 | − | 0.486275i | ||||
\(293\) | − | 11.0593i | − | 0.646091i | −0.946384 | − | 0.323045i | \(-0.895293\pi\) | ||
0.946384 | − | 0.323045i | \(-0.104707\pi\) | |||||||
\(294\) | −4.74538 | + | 2.08036i | −0.276756 | + | 0.121329i | ||||
\(295\) | −1.05402 | − | 10.9140i | −0.0613677 | − | 0.635436i | ||||
\(296\) | 9.41775 | − | 27.3784i | 0.547396 | − | 1.59134i | ||||
\(297\) | 3.18176 | + | 3.18176i | 0.184624 | + | 0.184624i | ||||
\(298\) | 1.26429 | − | 3.23815i | 0.0732384 | − | 0.187581i | ||||
\(299\) | −29.3200 | − | 29.3200i | −1.69562 | − | 1.69562i | ||||
\(300\) | −10.2898 | + | 16.7112i | −0.594083 | + | 0.964822i | ||||
\(301\) | 15.8818 | − | 15.8818i | 0.915413 | − | 0.915413i | ||||
\(302\) | 7.55787 | − | 3.31335i | 0.434906 | − | 0.190662i | ||||
\(303\) | −9.74459 | + | 9.74459i | −0.559812 | + | 0.559812i | ||||
\(304\) | 3.36760 | + | 2.85693i | 0.193145 | + | 0.163856i | ||||
\(305\) | −2.14221 | + | 0.206885i | −0.122663 | + | 0.0118462i | ||||
\(306\) | −1.21127 | + | 3.10234i | −0.0692435 | + | 0.177349i | ||||
\(307\) | 15.1317 | 0.863613 | 0.431806 | − | 0.901966i | \(-0.357876\pi\) | ||||
0.431806 | + | 0.901966i | \(0.357876\pi\) | |||||||
\(308\) | 3.55629 | + | 3.27647i | 0.202638 | + | 0.186694i | ||||
\(309\) | −0.867862 | + | 0.867862i | −0.0493709 | + | 0.0493709i | ||||
\(310\) | −3.10923 | + | 10.9796i | −0.176593 | + | 0.623600i | ||||
\(311\) | −27.1556 | −1.53985 | −0.769925 | − | 0.638134i | \(-0.779707\pi\) | ||||
−0.769925 | + | 0.638134i | \(0.779707\pi\) | |||||||
\(312\) | −31.2092 | − | 10.7355i | −1.76687 | − | 0.607778i | ||||
\(313\) | 13.6695 | − | 13.6695i | 0.772646 | − | 0.772646i | −0.205922 | − | 0.978568i | \(-0.566019\pi\) |
0.978568 | + | 0.205922i | \(0.0660194\pi\) | |||||||
\(314\) | −1.78711 | − | 4.07645i | −0.100852 | − | 0.230048i | ||||
\(315\) | −4.29356 | + | 0.414653i | −0.241915 | + | 0.0233631i | ||||
\(316\) | −14.5193 | + | 15.7592i | −0.816772 | + | 0.886525i | ||||
\(317\) | 25.8314i | 1.45084i | 0.688307 | + | 0.725419i | \(0.258354\pi\) | ||||
−0.688307 | + | 0.725419i | \(0.741646\pi\) | |||||||
\(318\) | 10.2492 | − | 4.49321i | 0.574745 | − | 0.251967i | ||||
\(319\) | 2.18532 | 0.122354 | ||||||||
\(320\) | 3.88746 | + | 17.4610i | 0.217316 | + | 0.976101i | ||||
\(321\) | 34.5252 | 1.92701 | ||||||||
\(322\) | −20.4645 | + | 8.97157i | −1.14044 | + | 0.499966i | ||||
\(323\) | 3.05361i | 0.169908i | ||||||||
\(324\) | −14.6756 | + | 15.9289i | −0.815310 | + | 0.884938i | ||||
\(325\) | −5.68914 | − | 29.1796i | −0.315576 | − | 1.61859i | ||||
\(326\) | 4.44101 | + | 10.1301i | 0.245965 | + | 0.561054i | ||||
\(327\) | 0.677383 | − | 0.677383i | 0.0374594 | − | 0.0374594i | ||||
\(328\) | −18.5440 | − | 6.37885i | −1.02392 | − | 0.352213i | ||||
\(329\) | 0.334091 | 0.0184190 | ||||||||
\(330\) | −3.22983 | − | 5.78175i | −0.177796 | − | 0.318275i | ||||
\(331\) | −13.6207 | + | 13.6207i | −0.748659 | + | 0.748659i | −0.974227 | − | 0.225568i | \(-0.927576\pi\) |
0.225568 | + | 0.974227i | \(0.427576\pi\) | |||||||
\(332\) | −6.23431 | − | 5.74379i | −0.342152 | − | 0.315231i | ||||
\(333\) | −8.71576 | −0.477621 | ||||||||
\(334\) | −7.19002 | + | 18.4153i | −0.393420 | + | 1.00764i | ||||
\(335\) | 15.6138 | + | 12.8635i | 0.853071 | + | 0.702810i | ||||
\(336\) | −11.5057 | + | 13.5623i | −0.627689 | + | 0.739886i | ||||
\(337\) | 16.0911 | − | 16.0911i | 0.876536 | − | 0.876536i | −0.116638 | − | 0.993174i | \(-0.537212\pi\) |
0.993174 | + | 0.116638i | \(0.0372119\pi\) | |||||||
\(338\) | 28.9513 | − | 12.6922i | 1.57474 | − | 0.690364i | ||||
\(339\) | 10.6694 | − | 10.6694i | 0.579484 | − | 0.579484i | ||||
\(340\) | −7.46785 | + | 9.86042i | −0.405001 | + | 0.534756i | ||||
\(341\) | −2.72299 | − | 2.72299i | −0.147458 | − | 0.147458i | ||||
\(342\) | 0.483506 | − | 1.23837i | 0.0261450 | − | 0.0669636i | ||||
\(343\) | −14.2052 | − | 14.2052i | −0.767007 | − | 0.767007i | ||||
\(344\) | −9.12062 | + | 26.5146i | −0.491751 | + | 1.42957i | ||||
\(345\) | 30.4614 | − | 2.94183i | 1.63998 | − | 0.158383i | ||||
\(346\) | 4.52347 | − | 1.98308i | 0.243183 | − | 0.106611i | ||||
\(347\) | − | 5.57562i | − | 0.299315i | −0.988738 | − | 0.149658i | \(-0.952183\pi\) | ||
0.988738 | − | 0.149658i | \(-0.0478171\pi\) | |||||||
\(348\) | 0.328882 | + | 8.03097i | 0.0176299 | + | 0.430505i | ||||
\(349\) | −15.0811 | − | 15.0811i | −0.807273 | − | 0.807273i | 0.176947 | − | 0.984220i | \(-0.443378\pi\) |
−0.984220 | + | 0.176947i | \(0.943378\pi\) | |||||||
\(350\) | −15.7626 | − | 2.86310i | −0.842544 | − | 0.153039i | ||||
\(351\) | − | 25.0708i | − | 1.33818i | ||||||
\(352\) | −5.78398 | − | 1.72839i | −0.308287 | − | 0.0921234i | ||||
\(353\) | 2.57880 | + | 2.57880i | 0.137256 | + | 0.137256i | 0.772397 | − | 0.635141i | \(-0.219058\pi\) |
−0.635141 | + | 0.772397i | \(0.719058\pi\) | |||||||
\(354\) | −4.94973 | + | 12.6774i | −0.263075 | + | 0.673798i | ||||
\(355\) | 6.28206 | + | 5.17554i | 0.333417 | + | 0.274689i | ||||
\(356\) | −0.0577647 | + | 0.0626979i | −0.00306152 | + | 0.00332298i | ||||
\(357\) | −12.2978 | −0.650870 | ||||||||
\(358\) | 9.51500 | − | 24.3702i | 0.502883 | − | 1.28800i | ||||
\(359\) | 5.77227i | 0.304649i | 0.988331 | + | 0.152324i | \(0.0486758\pi\) | ||||
−0.988331 | + | 0.152324i | \(0.951324\pi\) | |||||||
\(360\) | 4.58983 | − | 2.81638i | 0.241905 | − | 0.148436i | ||||
\(361\) | 17.7811i | 0.935846i | ||||||||
\(362\) | 25.4104 | + | 9.92115i | 1.33554 | + | 0.521444i | ||||
\(363\) | −19.3527 | −1.01575 | ||||||||
\(364\) | −1.10240 | − | 26.9195i | −0.0577814 | − | 1.41096i | ||||
\(365\) | −9.25499 | + | 0.893807i | −0.484428 | + | 0.0467840i | ||||
\(366\) | 2.48835 | + | 0.971540i | 0.130068 | + | 0.0507832i | ||||
\(367\) | −8.30496 | − | 8.30496i | −0.433516 | − | 0.433516i | 0.456307 | − | 0.889822i | \(-0.349172\pi\) |
−0.889822 | + | 0.456307i | \(0.849172\pi\) | |||||||
\(368\) | 18.0460 | − | 21.2716i | 0.940710 | − | 1.10886i | ||||
\(369\) | 5.90337i | 0.307317i | ||||||||
\(370\) | −31.1456 | − | 8.81990i | −1.61918 | − | 0.458525i | ||||
\(371\) | 6.45967 | + | 6.45967i | 0.335369 | + | 0.335369i | ||||
\(372\) | 9.59712 | − | 10.4167i | 0.497587 | − | 0.540082i | ||||
\(373\) | 16.0484i | 0.830953i | 0.909604 | + | 0.415477i | \(0.136385\pi\) | ||||
−0.909604 | + | 0.415477i | \(0.863615\pi\) | |||||||
\(374\) | −1.67595 | − | 3.82289i | −0.0866612 | − | 0.197677i | ||||
\(375\) | 19.2915 | + | 10.4532i | 0.996209 | + | 0.539799i | ||||
\(376\) | −0.374813 | + | 0.182951i | −0.0193295 | + | 0.00943496i | ||||
\(377\) | −8.60964 | − | 8.60964i | −0.443419 | − | 0.443419i | ||||
\(378\) | −12.5850 | − | 4.91365i | −0.647304 | − | 0.252731i | ||||
\(379\) | 8.91367 | + | 8.91367i | 0.457865 | + | 0.457865i | 0.897954 | − | 0.440089i | \(-0.145053\pi\) |
−0.440089 | + | 0.897954i | \(0.645053\pi\) | |||||||
\(380\) | 2.98097 | − | 3.93602i | 0.152921 | − | 0.201914i | ||||
\(381\) | −12.3079 | + | 12.3079i | −0.630552 | + | 0.630552i | ||||
\(382\) | 1.66100 | + | 3.78880i | 0.0849841 | + | 0.193852i | ||||
\(383\) | 24.8928 | − | 24.8928i | 1.27196 | − | 1.27196i | 0.326904 | − | 0.945057i | \(-0.393995\pi\) |
0.945057 | − | 0.326904i | \(-0.106005\pi\) | |||||||
\(384\) | 5.48131 | − | 21.5161i | 0.279717 | − | 1.09799i | ||||
\(385\) | 3.43764 | − | 4.17261i | 0.175199 | − | 0.212656i | ||||
\(386\) | 0.154763 | + | 0.0604250i | 0.00787721 | + | 0.00307555i | ||||
\(387\) | 8.44078 | 0.429069 | ||||||||
\(388\) | 0.221247 | + | 5.40265i | 0.0112321 | + | 0.274278i | ||||
\(389\) | 16.5819 | − | 16.5819i | 0.840738 | − | 0.840738i | −0.148217 | − | 0.988955i | \(-0.547353\pi\) |
0.988955 | + | 0.148217i | \(0.0473534\pi\) | |||||||
\(390\) | −10.0540 | + | 35.5035i | −0.509103 | + | 1.79779i | ||||
\(391\) | 19.2883 | 0.975452 | ||||||||
\(392\) | 4.99319 | + | 1.71758i | 0.252194 | + | 0.0867510i | ||||
\(393\) | −3.16987 | + | 3.16987i | −0.159899 | + | 0.159899i | ||||
\(394\) | 10.1090 | − | 4.43176i | 0.509284 | − | 0.223269i | ||||
\(395\) | 18.4904 | + | 15.2335i | 0.930351 | + | 0.766478i | ||||
\(396\) | 0.0743567 | + | 1.81572i | 0.00373656 | + | 0.0912432i | ||||
\(397\) | 8.62531i | 0.432892i | 0.976295 | + | 0.216446i | \(0.0694465\pi\) | ||||
−0.976295 | + | 0.216446i | \(0.930553\pi\) | |||||||
\(398\) | −6.23123 | − | 14.2137i | −0.312343 | − | 0.712466i | ||||
\(399\) | 4.90897 | 0.245756 | ||||||||
\(400\) | 19.2517 | − | 5.41962i | 0.962585 | − | 0.270981i | ||||
\(401\) | 19.7107 | 0.984307 | 0.492153 | − | 0.870508i | \(-0.336210\pi\) | ||||
0.492153 | + | 0.870508i | \(0.336210\pi\) | |||||||
\(402\) | −10.0818 | − | 22.9969i | −0.502833 | − | 1.14698i | ||||
\(403\) | 21.4559i | 1.06880i | ||||||||
\(404\) | 14.0324 | − | 0.574651i | 0.698139 | − | 0.0285900i | ||||
\(405\) | 18.6894 | + | 15.3975i | 0.928686 | + | 0.765107i | ||||
\(406\) | −6.00928 | + | 2.63445i | −0.298235 | + | 0.130746i | ||||
\(407\) | 7.72426 | − | 7.72426i | 0.382877 | − | 0.382877i | ||||
\(408\) | 13.7968 | − | 6.73438i | 0.683043 | − | 0.333402i | ||||
\(409\) | −26.7930 | −1.32483 | −0.662414 | − | 0.749138i | \(-0.730468\pi\) | ||||
−0.662414 | + | 0.749138i | \(0.730468\pi\) | |||||||
\(410\) | −5.97391 | + | 21.0956i | −0.295030 | + | 1.04184i | ||||
\(411\) | 13.4154 | − | 13.4154i | 0.661734 | − | 0.661734i | ||||
\(412\) | 1.24974 | − | 0.0511790i | 0.0615703 | − | 0.00252141i | ||||
\(413\) | −11.1098 | −0.546675 | ||||||||
\(414\) | −7.82225 | − | 3.05409i | −0.384443 | − | 0.150100i | ||||
\(415\) | −6.02633 | + | 7.31475i | −0.295821 | + | 0.359067i | ||||
\(416\) | 15.9781 | + | 29.5970i | 0.783390 | + | 1.45111i | ||||
\(417\) | −26.9702 | + | 26.9702i | −1.32074 | + | 1.32074i | ||||
\(418\) | 0.668995 | + | 1.52600i | 0.0327216 | + | 0.0746391i | ||||
\(419\) | −11.0752 | + | 11.0752i | −0.541061 | + | 0.541061i | −0.923840 | − | 0.382779i | \(-0.874967\pi\) |
0.382779 | + | 0.923840i | \(0.374967\pi\) | |||||||
\(420\) | 15.8516 | + | 12.0053i | 0.773477 | + | 0.585797i | ||||
\(421\) | −0.243092 | − | 0.243092i | −0.0118476 | − | 0.0118476i | 0.701158 | − | 0.713006i | \(-0.252667\pi\) |
−0.713006 | + | 0.701158i | \(0.752667\pi\) | |||||||
\(422\) | −16.6221 | − | 6.48985i | −0.809149 | − | 0.315921i | ||||
\(423\) | 0.0887804 | + | 0.0887804i | 0.00431665 | + | 0.00431665i | ||||
\(424\) | −10.7844 | − | 3.70967i | −0.523737 | − | 0.180157i | ||||
\(425\) | 11.4693 | + | 7.72666i | 0.556342 | + | 0.374798i | ||||
\(426\) | −4.05631 | − | 9.25259i | −0.196529 | − | 0.448290i | ||||
\(427\) | 2.18064i | 0.105528i | ||||||||
\(428\) | −25.8765 | − | 23.8405i | −1.25079 | − | 1.15237i | ||||
\(429\) | −8.80505 | − | 8.80505i | −0.425112 | − | 0.425112i | ||||
\(430\) | 30.1630 | + | 8.54163i | 1.45459 | + | 0.411914i | ||||
\(431\) | − | 20.7024i | − | 0.997200i | −0.866832 | − | 0.498600i | \(-0.833848\pi\) | ||
0.866832 | − | 0.498600i | \(-0.166152\pi\) | |||||||
\(432\) | 16.8098 | − | 1.37909i | 0.808760 | − | 0.0663514i | ||||
\(433\) | −5.68221 | − | 5.68221i | −0.273069 | − | 0.273069i | 0.557265 | − | 0.830335i | \(-0.311851\pi\) |
−0.830335 | + | 0.557265i | \(0.811851\pi\) | |||||||
\(434\) | 10.7704 | + | 4.20517i | 0.516998 | + | 0.201855i | ||||
\(435\) | 8.94480 | − | 0.863851i | 0.428871 | − | 0.0414185i | ||||
\(436\) | −0.975446 | + | 0.0399462i | −0.0467154 | + | 0.00191307i | ||||
\(437\) | −7.69939 | −0.368312 | ||||||||
\(438\) | 10.7504 | + | 4.19735i | 0.513674 | + | 0.200557i | ||||
\(439\) | 18.7902i | 0.896808i | 0.893831 | + | 0.448404i | \(0.148007\pi\) | ||||
−0.893831 | + | 0.448404i | \(0.851993\pi\) | |||||||
\(440\) | −1.57170 | + | 6.56368i | −0.0749279 | + | 0.312911i | ||||
\(441\) | − | 1.58955i | − | 0.0756930i | ||||||
\(442\) | −8.45848 | + | 21.6642i | −0.402329 | + | 1.03046i | ||||
\(443\) | 12.1641 | 0.577934 | 0.288967 | − | 0.957339i | \(-0.406688\pi\) | ||||
0.288967 | + | 0.957339i | \(0.406688\pi\) | |||||||
\(444\) | 29.5489 | + | 27.2239i | 1.40233 | + | 1.29199i | ||||
\(445\) | 0.0735637 | + | 0.0606062i | 0.00348725 | + | 0.00287301i | ||||
\(446\) | 9.57824 | − | 24.5321i | 0.453543 | − | 1.16163i | ||||
\(447\) | 3.41105 | + | 3.41105i | 0.161337 | + | 0.161337i | ||||
\(448\) | 17.9886 | − | 2.21993i | 0.849884 | − | 0.104882i | ||||
\(449\) | − | 27.2708i | − | 1.28699i | −0.765452 | − | 0.643493i | \(-0.777484\pi\) | ||
0.765452 | − | 0.643493i | \(-0.222516\pi\) | |||||||
\(450\) | −3.42787 | − | 4.94953i | −0.161591 | − | 0.233323i | ||||
\(451\) | −5.23181 | − | 5.23181i | −0.246356 | − | 0.246356i | ||||
\(452\) | −15.3642 | + | 0.629191i | −0.722672 | + | 0.0295946i | ||||
\(453\) | 11.4517i | 0.538047i | ||||||||
\(454\) | 25.0536 | − | 10.9834i | 1.17582 | − | 0.515479i | ||||
\(455\) | −29.9826 | + | 2.89559i | −1.40561 | + | 0.135748i | ||||
\(456\) | −5.50732 | + | 2.68819i | −0.257904 | + | 0.125886i | ||||
\(457\) | −19.7514 | − | 19.7514i | −0.923933 | − | 0.923933i | 0.0733714 | − | 0.997305i | \(-0.476624\pi\) |
−0.997305 | + | 0.0733714i | \(0.976624\pi\) | |||||||
\(458\) | −9.61200 | + | 24.6186i | −0.449139 | + | 1.15035i | ||||
\(459\) | 8.24649 | + | 8.24649i | 0.384913 | + | 0.384913i | ||||
\(460\) | −24.8621 | − | 18.8295i | −1.15920 | − | 0.877928i | ||||
\(461\) | 12.9262 | − | 12.9262i | 0.602035 | − | 0.602035i | −0.338818 | − | 0.940852i | \(-0.610027\pi\) |
0.940852 | + | 0.338818i | \(0.110027\pi\) | |||||||
\(462\) | −6.14566 | + | 2.69424i | −0.285922 | + | 0.125348i | ||||
\(463\) | −14.5647 | + | 14.5647i | −0.676879 | + | 0.676879i | −0.959293 | − | 0.282414i | \(-0.908865\pi\) |
0.282414 | + | 0.959293i | \(0.408865\pi\) | |||||||
\(464\) | 5.29909 | − | 6.24629i | 0.246004 | − | 0.289977i | ||||
\(465\) | −12.2220 | − | 10.0692i | −0.566781 | − | 0.466948i | ||||
\(466\) | −15.0486 | + | 38.5431i | −0.697114 | + | 1.78547i | ||||
\(467\) | −42.3556 | −1.95998 | −0.979991 | − | 0.199040i | \(-0.936218\pi\) | ||||
−0.979991 | + | 0.199040i | \(0.936218\pi\) | |||||||
\(468\) | 6.86056 | − | 7.44646i | 0.317130 | − | 0.344213i | ||||
\(469\) | 14.4941 | − | 14.4941i | 0.669274 | − | 0.669274i | ||||
\(470\) | 0.227414 | + | 0.407096i | 0.0104898 | + | 0.0187779i | ||||
\(471\) | 6.17665 | 0.284605 | ||||||||
\(472\) | 12.4639 | − | 6.08378i | 0.573698 | − | 0.280029i | ||||
\(473\) | −7.48056 | + | 7.48056i | −0.343956 | + | 0.343956i | ||||
\(474\) | −11.9392 | − | 27.2337i | −0.548385 | − | 1.25088i | ||||
\(475\) | −4.57824 | − | 3.08428i | −0.210064 | − | 0.141517i | ||||
\(476\) | 9.21718 | + | 8.49196i | 0.422469 | + | 0.389229i | ||||
\(477\) | 3.43315i | 0.157193i | ||||||||
\(478\) | −18.2694 | + | 8.00925i | −0.835622 | + | 0.366335i | ||||
\(479\) | −27.0905 | −1.23780 | −0.618899 | − | 0.785470i | \(-0.712421\pi\) | ||||
−0.618899 | + | 0.785470i | \(0.712421\pi\) | |||||||
\(480\) | −24.3579 | − | 4.78814i | −1.11178 | − | 0.218548i | ||||
\(481\) | −60.8636 | −2.77514 | ||||||||
\(482\) | 16.5802 | − | 7.26871i | 0.755207 | − | 0.331081i | ||||
\(483\) | − | 31.0078i | − | 1.41090i | ||||||
\(484\) | 14.5048 | + | 13.3635i | 0.659308 | + | 0.607433i | ||||
\(485\) | 6.01741 | − | 0.581136i | 0.273236 | − | 0.0263880i | ||||
\(486\) | −4.88500 | − | 11.1429i | −0.221588 | − | 0.505450i | ||||
\(487\) | 21.9674 | − | 21.9674i | 0.995436 | − | 0.995436i | −0.00455390 | − | 0.999990i | \(-0.501450\pi\) |
0.999990 | + | 0.00455390i | \(0.00144956\pi\) | |||||||
\(488\) | −1.19413 | − | 2.44643i | −0.0540559 | − | 0.110745i | ||||
\(489\) | −15.3491 | −0.694111 | ||||||||
\(490\) | 1.60855 | − | 5.68024i | 0.0726667 | − | 0.256607i | ||||
\(491\) | −6.11955 | + | 6.11955i | −0.276171 | + | 0.276171i | −0.831579 | − | 0.555407i | \(-0.812562\pi\) |
0.555407 | + | 0.831579i | \(0.312562\pi\) | |||||||
\(492\) | 18.4394 | − | 20.0141i | 0.831311 | − | 0.902305i | ||||
\(493\) | 5.66390 | 0.255089 | ||||||||
\(494\) | 3.37640 | − | 8.64777i | 0.151912 | − | 0.389082i | ||||
\(495\) | 2.02233 | − | 0.195308i | 0.0908968 | − | 0.00877842i | ||||
\(496\) | −14.3860 | + | 1.18024i | −0.645951 | + | 0.0529945i | ||||
\(497\) | 5.83157 | − | 5.83157i | 0.261581 | − | 0.261581i | ||||
\(498\) | 10.7736 | − | 4.72312i | 0.482776 | − | 0.211648i | ||||
\(499\) | −15.4115 | + | 15.4115i | −0.689914 | + | 0.689914i | −0.962213 | − | 0.272298i | \(-0.912216\pi\) |
0.272298 | + | 0.962213i | \(0.412216\pi\) | |||||||
\(500\) | −7.24075 | − | 21.1559i | −0.323816 | − | 0.946120i | ||||
\(501\) | −19.3986 | − | 19.3986i | −0.866667 | − | 0.866667i | ||||
\(502\) | −4.97625 | + | 12.7454i | −0.222101 | + | 0.568853i | ||||
\(503\) | 26.4312 | + | 26.4312i | 1.17851 | + | 1.17851i | 0.980124 | + | 0.198387i | \(0.0635704\pi\) |
0.198387 | + | 0.980124i | \(0.436430\pi\) | |||||||
\(504\) | −2.39336 | − | 4.90330i | −0.106609 | − | 0.218410i | ||||
\(505\) | −1.50940 | − | 15.6292i | −0.0671673 | − | 0.695488i | ||||
\(506\) | 9.63905 | − | 4.22574i | 0.428508 | − | 0.187857i | ||||
\(507\) | 43.8671i | 1.94820i | ||||||||
\(508\) | 17.7236 | − | 0.725812i | 0.786358 | − | 0.0322027i | ||||
\(509\) | 0.233714 | + | 0.233714i | 0.0103592 | + | 0.0103592i | 0.712267 | − | 0.701908i | \(-0.247668\pi\) |
−0.701908 | + | 0.712267i | \(0.747668\pi\) | |||||||
\(510\) | −8.37107 | − | 14.9851i | −0.370677 | − | 0.663553i | ||||
\(511\) | 9.42101i | 0.416761i | ||||||||
\(512\) | −18.9656 | + | 12.3412i | −0.838169 | + | 0.545410i | ||||
\(513\) | −3.29178 | − | 3.29178i | −0.145336 | − | 0.145336i | ||||
\(514\) | −4.84827 | + | 12.4176i | −0.213848 | + | 0.547716i | ||||
\(515\) | −0.134428 | − | 1.39195i | −0.00592362 | − | 0.0613365i | ||||
\(516\) | −28.6166 | − | 26.3650i | −1.25978 | − | 1.16066i | ||||
\(517\) | −0.157362 | −0.00692075 | ||||||||
\(518\) | −11.9287 | + | 30.5523i | −0.524118 | + | 1.34239i | ||||
\(519\) | 6.85397i | 0.300856i | ||||||||
\(520\) | 32.0515 | − | 19.6673i | 1.40555 | − | 0.862466i | ||||
\(521\) | − | 4.50147i | − | 0.197213i | −0.995127 | − | 0.0986064i | \(-0.968562\pi\) | ||
0.995127 | − | 0.0986064i | \(-0.0314385\pi\) | |||||||
\(522\) | −2.29696 | − | 0.896816i | −0.100535 | − | 0.0392526i | ||||
\(523\) | −12.6042 | −0.551141 | −0.275571 | − | 0.961281i | \(-0.588867\pi\) | ||||
−0.275571 | + | 0.961281i | \(0.588867\pi\) | |||||||
\(524\) | 4.56468 | − | 0.186931i | 0.199409 | − | 0.00816613i | ||||
\(525\) | 12.4213 | − | 18.4380i | 0.542111 | − | 0.804699i | ||||
\(526\) | −13.6377 | − | 5.32465i | −0.594632 | − | 0.232166i | ||||
\(527\) | −7.05746 | − | 7.05746i | −0.307428 | − | 0.307428i | ||||
\(528\) | 5.41936 | − | 6.38805i | 0.235847 | − | 0.278004i | ||||
\(529\) | 25.6336i | 1.11450i | ||||||||
\(530\) | −3.47417 | + | 12.2683i | −0.150908 | + | 0.532901i | ||||
\(531\) | −2.95227 | − | 2.95227i | −0.128118 | − | 0.128118i | ||||
\(532\) | −3.67926 | − | 3.38977i | −0.159516 | − | 0.146965i | ||||
\(533\) | 41.2242i | 1.78562i | ||||||||
\(534\) | −0.0474999 | − | 0.108349i | −0.00205552 | − | 0.00468872i | ||||
\(535\) | −25.0132 | + | 30.3610i | −1.08142 | + | 1.31262i | ||||
\(536\) | −8.32367 | + | 24.1978i | −0.359528 | + | 1.04519i | ||||
\(537\) | 25.6714 | + | 25.6714i | 1.10780 | + | 1.10780i | ||||
\(538\) | 29.7714 | + | 11.6238i | 1.28354 | + | 0.501139i | ||||
\(539\) | 1.40873 | + | 1.40873i | 0.0606782 | + | 0.0606782i | ||||
\(540\) | −2.57918 | − | 18.6798i | −0.110990 | − | 0.803851i | ||||
\(541\) | 14.5013 | − | 14.5013i | 0.623459 | − | 0.623459i | −0.322955 | − | 0.946414i | \(-0.604676\pi\) |
0.946414 | + | 0.322955i | \(0.104676\pi\) | |||||||
\(542\) | −2.04235 | − | 4.65868i | −0.0877266 | − | 0.200107i | ||||
\(543\) | −26.7672 | + | 26.7672i | −1.14869 | + | 1.14869i | ||||
\(544\) | −14.9909 | − | 4.47964i | −0.642730 | − | 0.192063i | ||||
\(545\) | 0.104924 | + | 1.08644i | 0.00449444 | + | 0.0465380i | ||||
\(546\) | 34.8272 | + | 13.5978i | 1.49047 | + | 0.581932i | ||||
\(547\) | 30.2936 | 1.29526 | 0.647630 | − | 0.761955i | \(-0.275760\pi\) | ||||
0.647630 | + | 0.761955i | \(0.275760\pi\) | |||||||
\(548\) | −19.3185 | + | 0.791125i | −0.825246 | + | 0.0337952i | ||||
\(549\) | −0.579476 | + | 0.579476i | −0.0247314 | + | 0.0247314i | ||||
\(550\) | 7.42439 | + | 1.34856i | 0.316577 | + | 0.0575029i | ||||
\(551\) | −2.26088 | −0.0963169 | ||||||||
\(552\) | 16.9801 | + | 34.7873i | 0.722721 | + | 1.48064i | ||||
\(553\) | 17.1644 | − | 17.1644i | 0.729904 | − | 0.729904i | ||||
\(554\) | −27.1239 | + | 11.8911i | −1.15239 | + | 0.505203i | ||||
\(555\) | 28.5631 | − | 34.6699i | 1.21244 | − | 1.47165i | ||||
\(556\) | 38.8378 | − | 1.59047i | 1.64709 | − | 0.0674510i | ||||
\(557\) | 9.72758i | 0.412171i | 0.978534 | + | 0.206085i | \(0.0660725\pi\) | ||||
−0.978534 | + | 0.206085i | \(0.933928\pi\) | |||||||
\(558\) | 1.74464 | + | 3.97958i | 0.0738563 | + | 0.168469i | ||||
\(559\) | 58.9433 | 2.49304 | ||||||||
\(560\) | −3.59075 | − | 19.9438i | −0.151737 | − | 0.842780i | ||||
\(561\) | 5.79245 | 0.244557 | ||||||||
\(562\) | −1.85506 | − | 4.23146i | −0.0782510 | − | 0.178493i | ||||
\(563\) | − | 17.7853i | − | 0.749562i | −0.927113 | − | 0.374781i | \(-0.877718\pi\) | ||
0.927113 | − | 0.374781i | \(-0.122282\pi\) | |||||||
\(564\) | −0.0236823 | − | 0.578299i | −0.000997205 | − | 0.0243508i | ||||
\(565\) | 1.65265 | + | 17.1125i | 0.0695276 | + | 0.719928i | ||||
\(566\) | 0.000196379 | 0 | 8.60919e-5i | 8.25441e−6 | 0 | 3.61871e-6i | ||||
\(567\) | 17.3492 | − | 17.3492i | 0.728597 | − | 0.728597i | ||||
\(568\) | −3.34896 | + | 9.73578i | −0.140519 | + | 0.408504i | ||||
\(569\) | −15.7897 | −0.661938 | −0.330969 | − | 0.943642i | \(-0.607376\pi\) | ||||
−0.330969 | + | 0.943642i | \(0.607376\pi\) | |||||||
\(570\) | 3.34151 | + | 5.98168i | 0.139961 | + | 0.250545i | ||||
\(571\) | 23.3108 | − | 23.3108i | 0.975528 | − | 0.975528i | −0.0241793 | − | 0.999708i | \(-0.507697\pi\) |
0.999708 | + | 0.0241793i | \(0.00769727\pi\) | |||||||
\(572\) | 0.519245 | + | 12.6795i | 0.0217107 | + | 0.530155i | ||||
\(573\) | −5.74079 | −0.239825 | ||||||||
\(574\) | 20.6937 | + | 8.07958i | 0.863739 | + | 0.337235i | ||||
\(575\) | −19.4820 | + | 28.9187i | −0.812456 | + | 1.20599i | ||||
\(576\) | 5.37017 | + | 4.19033i | 0.223757 | + | 0.174597i | ||||
\(577\) | 25.7383 | − | 25.7383i | 1.07150 | − | 1.07150i | 0.0742597 | − | 0.997239i | \(-0.476341\pi\) |
0.997239 | − | 0.0742597i | \(-0.0236594\pi\) | |||||||
\(578\) | 5.30920 | + | 12.1105i | 0.220834 | + | 0.503729i | ||||
\(579\) | −0.163026 | + | 0.163026i | −0.00677514 | + | 0.00677514i | ||||
\(580\) | −7.30061 | − | 5.52916i | −0.303141 | − | 0.229586i | ||||
\(581\) | 6.79020 | + | 6.79020i | 0.281705 | + | 0.281705i | ||||
\(582\) | −6.98969 | − | 2.72903i | −0.289732 | − | 0.113122i | ||||
\(583\) | −3.04260 | − | 3.04260i | −0.126011 | − | 0.126011i | ||||
\(584\) | −5.15902 | − | 10.5693i | −0.213482 | − | 0.437362i | ||||
\(585\) | −8.73697 | − | 7.19803i | −0.361229 | − | 0.297602i | ||||
\(586\) | −6.27967 | − | 14.3242i | −0.259411 | − | 0.591725i | ||||
\(587\) | − | 23.1327i | − | 0.954790i | −0.878689 | − | 0.477395i | \(-0.841581\pi\) | ||
0.878689 | − | 0.477395i | \(-0.158419\pi\) | |||||||
\(588\) | −4.96502 | + | 5.38904i | −0.204754 | + | 0.222240i | ||||
\(589\) | 2.81715 | + | 2.81715i | 0.116079 | + | 0.116079i | ||||
\(590\) | −7.56235 | − | 13.5374i | −0.311337 | − | 0.557328i | ||||
\(591\) | 15.3171i | 0.630063i | ||||||||
\(592\) | −3.34797 | − | 40.8085i | −0.137601 | − | 1.67722i | ||||
\(593\) | −25.5047 | − | 25.5047i | −1.04735 | − | 1.04735i | −0.998822 | − | 0.0485322i | \(-0.984546\pi\) |
−0.0485322 | − | 0.998822i | \(-0.515454\pi\) | |||||||
\(594\) | 5.92773 | + | 2.31440i | 0.243218 | + | 0.0949609i | ||||
\(595\) | 8.90969 | − | 10.8146i | 0.365261 | − | 0.443354i | ||||
\(596\) | −0.201154 | − | 4.91199i | −0.00823960 | − | 0.201203i | ||||
\(597\) | 21.5365 | 0.881432 | ||||||||
\(598\) | −54.6241 | − | 21.3272i | −2.23374 | − | 0.872135i | ||||
\(599\) | − | 11.0699i | − | 0.452304i | −0.974092 | − | 0.226152i | \(-0.927385\pi\) | ||
0.974092 | − | 0.226152i | \(-0.0726146\pi\) | |||||||
\(600\) | −3.83858 | + | 27.4874i | −0.156709 | + | 1.12217i | ||||
\(601\) | 13.7579i | 0.561197i | 0.959825 | + | 0.280599i | \(0.0905330\pi\) | ||||
−0.959825 | + | 0.280599i | \(0.909467\pi\) | |||||||
\(602\) | 11.5524 | − | 29.5884i | 0.470839 | − | 1.20593i | ||||
\(603\) | 7.70322 | 0.313700 | ||||||||
\(604\) | 7.90768 | − | 8.58300i | 0.321759 | − | 0.349237i | ||||
\(605\) | 14.0209 | − | 17.0185i | 0.570030 | − | 0.691902i | ||||
\(606\) | −7.08817 | + | 18.1545i | −0.287937 | + | 0.737476i | ||||
\(607\) | 18.4675 | + | 18.4675i | 0.749573 | + | 0.749573i | 0.974399 | − | 0.224826i | \(-0.0721813\pi\) |
−0.224826 | + | 0.974399i | \(0.572181\pi\) | |||||||
\(608\) | 5.98398 | + | 1.78815i | 0.242683 | + | 0.0725193i | ||||
\(609\) | − | 9.10526i | − | 0.368964i | ||||||
\(610\) | −2.65715 | + | 1.48435i | −0.107585 | + | 0.0600995i | ||||
\(611\) | 0.619968 | + | 0.619968i | 0.0250812 | + | 0.0250812i | ||||
\(612\) | 0.192718 | + | 4.70598i | 0.00779015 | + | 0.190228i | ||||
\(613\) | − | 11.6810i | − | 0.471790i | −0.971779 | − | 0.235895i | \(-0.924198\pi\) | ||
0.971779 | − | 0.235895i | \(-0.0758021\pi\) | |||||||
\(614\) | 19.5988 | − | 8.59208i | 0.790944 | − | 0.346748i | ||||
\(615\) | −23.4826 | − | 19.3464i | −0.946912 | − | 0.780122i | ||||
\(616\) | 6.46660 | + | 2.22441i | 0.260547 | + | 0.0896240i | ||||
\(617\) | 29.1000 | + | 29.1000i | 1.17152 | + | 1.17152i | 0.981847 | + | 0.189677i | \(0.0607441\pi\) |
0.189677 | + | 0.981847i | \(0.439256\pi\) | |||||||
\(618\) | −0.631279 | + | 1.61686i | −0.0253938 | + | 0.0650395i | ||||
\(619\) | −4.23279 | − | 4.23279i | −0.170130 | − | 0.170130i | 0.616906 | − | 0.787036i | \(-0.288386\pi\) |
−0.787036 | + | 0.616906i | \(0.788386\pi\) | |||||||
\(620\) | 2.20730 | + | 15.9864i | 0.0886474 | + | 0.642030i | ||||
\(621\) | −20.7927 | + | 20.7927i | −0.834383 | + | 0.834383i | ||||
\(622\) | −35.1723 | + | 15.4194i | −1.41028 | + | 0.618263i | ||||
\(623\) | 0.0682883 | − | 0.0682883i | 0.00273591 | − | 0.00273591i | ||||
\(624\) | −46.5185 | + | 3.81642i | −1.86223 | + | 0.152779i | ||||
\(625\) | −23.1689 | + | 9.39149i | −0.926758 | + | 0.375660i | ||||
\(626\) | 9.94314 | − | 25.4668i | 0.397408 | − | 1.01786i | ||||
\(627\) | −2.31220 | −0.0923402 | ||||||||
\(628\) | −4.62938 | − | 4.26513i | −0.184732 | − | 0.170197i | ||||
\(629\) | 20.0197 | − | 20.0197i | 0.798239 | − | 0.798239i | ||||
\(630\) | −5.32563 | + | 2.97503i | −0.212178 | + | 0.118528i | ||||
\(631\) | −1.33886 | −0.0532991 | −0.0266496 | − | 0.999645i | \(-0.508484\pi\) | ||||
−0.0266496 | + | 0.999645i | \(0.508484\pi\) | |||||||
\(632\) | −9.85718 | + | 28.6559i | −0.392097 | + | 1.13987i | ||||
\(633\) | 17.5096 | − | 17.5096i | 0.695944 | − | 0.695944i | ||||
\(634\) | 14.6676 | + | 33.4573i | 0.582524 | + | 1.32876i | ||||
\(635\) | −1.90644 | − | 19.7404i | −0.0756548 | − | 0.783373i | ||||
\(636\) | 10.7235 | − | 11.6393i | 0.425216 | − | 0.461530i | ||||
\(637\) | − | 11.1001i | − | 0.439803i | ||||||
\(638\) | 2.83045 | − | 1.24086i | 0.112059 | − | 0.0491263i | ||||
\(639\) | 3.09933 | 0.122608 | ||||||||
\(640\) | 14.9498 | + | 20.4084i | 0.590943 | + | 0.806713i | ||||
\(641\) | 24.5069 | 0.967965 | 0.483982 | − | 0.875078i | \(-0.339190\pi\) | ||||
0.483982 | + | 0.875078i | \(0.339190\pi\) | |||||||
\(642\) | 44.7175 | − | 19.6041i | 1.76486 | − | 0.773710i | ||||
\(643\) | − | 10.8979i | − | 0.429771i | −0.976639 | − | 0.214885i | \(-0.931062\pi\) | ||
0.976639 | − | 0.214885i | \(-0.0689378\pi\) | |||||||
\(644\) | −21.4117 | + | 23.2402i | −0.843738 | + | 0.915793i | ||||
\(645\) | −27.6619 | + | 33.5760i | −1.08919 | + | 1.32205i | ||||
\(646\) | 1.73390 | + | 3.95509i | 0.0682194 | + | 0.155611i | ||||
\(647\) | −11.6612 | + | 11.6612i | −0.458448 | + | 0.458448i | −0.898146 | − | 0.439698i | \(-0.855085\pi\) |
0.439698 | + | 0.898146i | \(0.355085\pi\) | |||||||
\(648\) | −9.96331 | + | 28.9644i | −0.391396 | + | 1.13783i | ||||
\(649\) | 5.23285 | 0.205407 | ||||||||
\(650\) | −23.9374 | − | 34.5634i | −0.938901 | − | 1.35569i | ||||
\(651\) | −11.3455 | + | 11.3455i | −0.444666 | + | 0.444666i | ||||
\(652\) | 11.5041 | + | 10.5990i | 0.450536 | + | 0.415087i | ||||
\(653\) | 5.28393 | 0.206776 | 0.103388 | − | 0.994641i | \(-0.467032\pi\) | ||||
0.103388 | + | 0.994641i | \(0.467032\pi\) | |||||||
\(654\) | 0.492726 | − | 1.26199i | 0.0192671 | − | 0.0493476i | ||||
\(655\) | −0.491000 | − | 5.08409i | −0.0191849 | − | 0.198652i | ||||
\(656\) | −27.6405 | + | 2.26765i | −1.07918 | + | 0.0885369i | ||||
\(657\) | −2.50351 | + | 2.50351i | −0.0976713 | + | 0.0976713i | ||||
\(658\) | 0.432720 | − | 0.189703i | 0.0168692 | − | 0.00739540i | ||||
\(659\) | 16.2902 | − | 16.2902i | 0.634578 | − | 0.634578i | −0.314635 | − | 0.949213i | \(-0.601882\pi\) |
0.949213 | + | 0.314635i | \(0.101882\pi\) | |||||||
\(660\) | −7.46631 | − | 5.65465i | −0.290626 | − | 0.220107i | ||||
\(661\) | −12.7924 | − | 12.7924i | −0.497566 | − | 0.497566i | 0.413114 | − | 0.910679i | \(-0.364441\pi\) |
−0.910679 | + | 0.413114i | \(0.864441\pi\) | |||||||
\(662\) | −9.90761 | + | 25.3757i | −0.385070 | + | 0.986256i | ||||
\(663\) | −22.8209 | − | 22.8209i | −0.886291 | − | 0.886291i | ||||
\(664\) | −11.3362 | − | 3.89948i | −0.439930 | − | 0.151329i | ||||
\(665\) | −3.55652 | + | 4.31690i | −0.137916 | + | 0.167402i | ||||
\(666\) | −11.2888 | + | 4.94897i | −0.437431 | + | 0.191769i | ||||
\(667\) | 14.2810i | 0.552962i | ||||||||
\(668\) | 1.14396 | + | 27.9344i | 0.0442613 | + | 1.08082i | ||||
\(669\) | 25.8420 | + | 25.8420i | 0.999111 | + | 0.999111i | ||||
\(670\) | 27.5273 | + | 7.79526i | 1.06347 | + | 0.301157i | ||||
\(671\) | − | 1.02711i | − | 0.0396512i | ||||||
\(672\) | −7.20144 | + | 24.0993i | −0.277802 | + | 0.929651i | ||||
\(673\) | 11.9553 | + | 11.9553i | 0.460841 | + | 0.460841i | 0.898931 | − | 0.438090i | \(-0.144345\pi\) |
−0.438090 | + | 0.898931i | \(0.644345\pi\) | |||||||
\(674\) | 11.7046 | − | 29.9782i | 0.450843 | − | 1.15472i | ||||
\(675\) | −20.6931 | + | 4.03454i | −0.796480 | + | 0.155290i | ||||
\(676\) | 30.2913 | − | 32.8782i | 1.16505 | − | 1.26455i | ||||
\(677\) | −3.18699 | −0.122486 | −0.0612430 | − | 0.998123i | \(-0.519506\pi\) | ||||
−0.0612430 | + | 0.998123i | \(0.519506\pi\) | |||||||
\(678\) | 7.76090 | − | 19.8775i | 0.298056 | − | 0.763391i | ||||
\(679\) | − | 6.12535i | − | 0.235069i | ||||||
\(680\) | −4.07353 | + | 17.0118i | −0.156213 | + | 0.652371i | ||||
\(681\) | 37.9613i | 1.45468i | ||||||||
\(682\) | −5.07303 | − | 1.98069i | −0.194256 | − | 0.0758447i | ||||
\(683\) | 35.1661 | 1.34559 | 0.672797 | − | 0.739827i | \(-0.265093\pi\) | ||||
0.672797 | + | 0.739827i | \(0.265093\pi\) | |||||||
\(684\) | −0.0769279 | − | 1.87850i | −0.00294141 | − | 0.0718264i | ||||
\(685\) | 2.07799 | + | 21.5167i | 0.0793961 | + | 0.822112i | ||||
\(686\) | −26.4647 | − | 10.3328i | −1.01043 | − | 0.394508i | ||||
\(687\) | −25.9331 | − | 25.9331i | −0.989410 | − | 0.989410i | ||||
\(688\) | 3.24234 | + | 39.5210i | 0.123613 | + | 1.50672i | ||||
\(689\) | 23.9743i | 0.913346i | ||||||||
\(690\) | 37.7836 | − | 21.1068i | 1.43840 | − | 0.803523i | ||||
\(691\) | 2.90121 | + | 2.90121i | 0.110367 | + | 0.110367i | 0.760134 | − | 0.649767i | \(-0.225133\pi\) |
−0.649767 | + | 0.760134i | \(0.725133\pi\) | |||||||
\(692\) | 4.73284 | − | 5.13703i | 0.179916 | − | 0.195280i | ||||
\(693\) | − | 2.05860i | − | 0.0781999i | ||||||
\(694\) | −3.16594 | − | 7.22163i | −0.120178 | − | 0.274129i | ||||
\(695\) | −4.17758 | − | 43.2571i | −0.158465 | − | 1.64083i | ||||
\(696\) | 4.98611 | + | 10.2151i | 0.188998 | + | 0.387202i | ||||
\(697\) | −13.5598 | − | 13.5598i | −0.513614 | − | 0.513614i | ||||
\(698\) | −28.0966 | − | 10.9699i | −1.06347 | − | 0.415218i | ||||
\(699\) | −40.6011 | − | 40.6011i | −1.53568 | − | 1.53568i | ||||
\(700\) | −22.0416 | + | 5.24195i | −0.833095 | + | 0.198127i | ||||
\(701\) | 15.7397 | − | 15.7397i | 0.594481 | − | 0.594481i | −0.344358 | − | 0.938839i | \(-0.611903\pi\) |
0.938839 | + | 0.344358i | \(0.111903\pi\) | |||||||
\(702\) | −14.2357 | − | 32.4721i | −0.537291 | − | 1.22558i | ||||
\(703\) | −7.99136 | + | 7.99136i | −0.301400 | + | 0.301400i | ||||
\(704\) | −8.47290 | + | 1.04562i | −0.319335 | + | 0.0394082i | ||||
\(705\) | −0.644103 | + | 0.0622047i | −0.0242583 | + | 0.00234276i | ||||
\(706\) | 4.80440 | + | 1.87581i | 0.180816 | + | 0.0705971i | ||||
\(707\) | −15.9095 | −0.598339 | ||||||||
\(708\) | 0.787524 | + | 19.2306i | 0.0295970 | + | 0.722729i | ||||
\(709\) | −1.95755 | + | 1.95755i | −0.0735172 | + | 0.0735172i | −0.742909 | − | 0.669392i | \(-0.766555\pi\) |
0.669392 | + | 0.742909i | \(0.266555\pi\) | |||||||
\(710\) | 11.0754 | + | 3.13636i | 0.415652 | + | 0.117705i | ||||
\(711\) | 9.12243 | 0.342118 | ||||||||
\(712\) | −0.0392167 | + | 0.114007i | −0.00146971 | + | 0.00427260i | ||||
\(713\) | 17.7947 | − | 17.7947i | 0.666416 | − | 0.666416i | ||||
\(714\) | −15.9283 | + | 6.98294i | −0.596103 | + | 0.261330i | ||||
\(715\) | 14.1222 | − | 1.36387i | 0.528142 | − | 0.0510057i | ||||
\(716\) | −1.51388 | − | 36.9674i | −0.0565762 | − | 1.38154i | ||||
\(717\) | − | 27.6818i | − | 1.03379i | ||||||
\(718\) | 3.27760 | + | 7.47633i | 0.122319 | + | 0.279014i | ||||
\(719\) | −0.0658604 | −0.00245618 | −0.00122809 | − | 0.999999i | \(-0.500391\pi\) | ||||
−0.00122809 | + | 0.999999i | \(0.500391\pi\) | |||||||
\(720\) | 4.34562 | − | 6.25401i | 0.161952 | − | 0.233073i | ||||
\(721\) | −1.41692 | −0.0527687 | ||||||||
\(722\) | 10.0964 | + | 23.0303i | 0.375750 | + | 0.857100i | ||||
\(723\) | 25.1223i | 0.934309i | ||||||||
\(724\) | 38.5454 | − | 1.57850i | 1.43253 | − | 0.0586644i | ||||
\(725\) | −5.72078 | + | 8.49181i | −0.212465 | + | 0.315378i | ||||
\(726\) | −25.0659 | + | 10.9888i | −0.930283 | + | 0.407834i | ||||
\(727\) | −16.2286 | + | 16.2286i | −0.601885 | + | 0.601885i | −0.940813 | − | 0.338927i | \(-0.889936\pi\) |
0.338927 | + | 0.940813i | \(0.389936\pi\) | |||||||
\(728\) | −16.7132 | − | 34.2406i | −0.619434 | − | 1.26904i | ||||
\(729\) | −15.6045 | −0.577943 | ||||||||
\(730\) | −11.4797 | + | 6.41283i | −0.424882 | + | 0.237350i | ||||
\(731\) | −19.3881 | + | 19.3881i | −0.717095 | + | 0.717095i | ||||
\(732\) | 3.77460 | − | 0.154576i | 0.139513 | − | 0.00571330i | ||||
\(733\) | −0.669106 | −0.0247140 | −0.0123570 | − | 0.999924i | \(-0.503933\pi\) | ||||
−0.0123570 | + | 0.999924i | \(0.503933\pi\) | |||||||
\(734\) | −15.4724 | − | 6.04100i | −0.571098 | − | 0.222977i | ||||
\(735\) | 6.32298 | + | 5.20925i | 0.233227 | + | 0.192146i | ||||
\(736\) | 11.2950 | − | 37.7981i | 0.416338 | − | 1.39326i | ||||
\(737\) | −6.82691 | + | 6.82691i | −0.251472 | + | 0.251472i | ||||
\(738\) | 3.35205 | + | 7.64614i | 0.123391 | + | 0.281458i | ||||
\(739\) | 23.4183 | − | 23.4183i | 0.861454 | − | 0.861454i | −0.130053 | − | 0.991507i | \(-0.541515\pi\) |
0.991507 | + | 0.130053i | \(0.0415147\pi\) | |||||||
\(740\) | −45.3484 | + | 6.26141i | −1.66704 | + | 0.230174i | ||||
\(741\) | 9.10952 | + | 9.10952i | 0.334647 | + | 0.334647i | ||||
\(742\) | 12.0346 | + | 4.69874i | 0.441804 | + | 0.172496i | ||||
\(743\) | 30.0968 | + | 30.0968i | 1.10414 | + | 1.10414i | 0.993905 | + | 0.110238i | \(0.0351614\pi\) |
0.110238 | + | 0.993905i | \(0.464839\pi\) | |||||||
\(744\) | 6.51552 | − | 18.9413i | 0.238871 | − | 0.694422i | ||||
\(745\) | −5.47092 | + | 0.528358i | −0.200439 | + | 0.0193575i | ||||
\(746\) | 9.11257 | + | 20.7861i | 0.333635 | + | 0.761033i | ||||
\(747\) | 3.60882i | 0.132040i | ||||||||
\(748\) | −4.34142 | − | 3.99983i | −0.158738 | − | 0.146248i | ||||
\(749\) | 28.1838 | + | 28.1838i | 1.02981 | + | 1.02981i | ||||
\(750\) | 30.9222 | + | 2.58501i | 1.12912 | + | 0.0943911i | ||||
\(751\) | 53.2724i | 1.94394i | 0.235107 | + | 0.971970i | \(0.424456\pi\) | ||||
−0.235107 | + | 0.971970i | \(0.575544\pi\) | |||||||
\(752\) | −0.381580 | + | 0.449786i | −0.0139148 | + | 0.0164020i | ||||
\(753\) | −13.4259 | − | 13.4259i | −0.489267 | − | 0.489267i | ||||
\(754\) | −16.0401 | − | 6.26262i | −0.584144 | − | 0.228071i | ||||
\(755\) | −10.0705 | − | 8.29666i | −0.366502 | − | 0.301946i | ||||
\(756\) | −19.0904 | + | 0.781783i | −0.694311 | + | 0.0284332i | ||||
\(757\) | −27.1717 | −0.987574 | −0.493787 | − | 0.869583i | \(-0.664388\pi\) | ||||
−0.493787 | + | 0.869583i | \(0.664388\pi\) | |||||||
\(758\) | 16.6065 | + | 6.48377i | 0.603174 | + | 0.235501i | ||||
\(759\) | 14.6051i | 0.530132i | ||||||||
\(760\) | 1.62605 | − | 6.79065i | 0.0589830 | − | 0.246323i | ||||
\(761\) | − | 12.9068i | − | 0.467870i | −0.972252 | − | 0.233935i | \(-0.924840\pi\) | ||
0.972252 | − | 0.233935i | \(-0.0751604\pi\) | |||||||
\(762\) | −8.95270 | + | 22.9300i | −0.324322 | + | 0.830666i | ||||
\(763\) | 1.10593 | 0.0400374 | ||||||||
\(764\) | 4.30270 | + | 3.96416i | 0.155666 | + | 0.143418i | ||||
\(765\) | 5.24147 | − | 0.506198i | 0.189506 | − | 0.0183016i | ||||
\(766\) | 18.1069 | − | 46.3761i | 0.654229 | − | 1.67564i | ||||
\(767\) | −20.6162 | − | 20.6162i | −0.744409 | − | 0.744409i | ||||
\(768\) | −5.11775 | − | 30.9803i | −0.184671 | − | 1.11791i | ||||
\(769\) | 34.4858i | 1.24359i | 0.783180 | + | 0.621795i | \(0.213596\pi\) | ||||
−0.783180 | + | 0.621795i | \(0.786404\pi\) | |||||||
\(770\) | 2.08320 | − | 7.35638i | 0.0750733 | − | 0.265106i | ||||
\(771\) | −13.0806 | − | 13.0806i | −0.471087 | − | 0.471087i | ||||
\(772\) | 0.234761 | − | 0.00961387i | 0.00844925 | − | 0.000346011i | ||||
\(773\) | 26.6789i | 0.959574i | 0.877385 | + | 0.479787i | \(0.159286\pi\) | ||||
−0.877385 | + | 0.479787i | \(0.840714\pi\) | |||||||
\(774\) | 10.9326 | − | 4.79283i | 0.392965 | − | 0.172275i | ||||
\(775\) | 17.7095 | − | 3.45281i | 0.636143 | − | 0.124029i | ||||
\(776\) | 3.35429 | + | 6.87196i | 0.120412 | + | 0.246689i | ||||
\(777\) | −32.1836 | − | 32.1836i | −1.15458 | − | 1.15458i | ||||
\(778\) | 12.0616 | − | 30.8927i | 0.432431 | − | 1.10756i | ||||
\(779\) | 5.41272 | + | 5.41272i | 0.193931 | + | 0.193931i | ||||
\(780\) | 7.13751 | + | 51.6936i | 0.255564 | + | 1.85093i | ||||
\(781\) | −2.74675 | + | 2.74675i | −0.0982864 | + | 0.0982864i | ||||
\(782\) | 24.9825 | − | 10.9523i | 0.893373 | − | 0.391652i | ||||
\(783\) | −6.10566 | + | 6.10566i | −0.218199 | + | 0.218199i | ||||
\(784\) | 7.44253 | − | 0.610593i | 0.265805 | − | 0.0218069i | ||||
\(785\) | −4.47493 | + | 5.43167i | −0.159717 | + | 0.193865i | ||||
\(786\) | −2.30575 | + | 5.90557i | −0.0822433 | + | 0.210645i | ||||
\(787\) | −33.2611 | −1.18563 | −0.592815 | − | 0.805338i | \(-0.701984\pi\) | ||||
−0.592815 | + | 0.805338i | \(0.701984\pi\) | |||||||
\(788\) | 10.5769 | − | 11.4802i | 0.376786 | − | 0.408963i | ||||
\(789\) | 14.3659 | − | 14.3659i | 0.511439 | − | 0.511439i | ||||
\(790\) | 32.5988 | + | 9.23142i | 1.15981 | + | 0.328439i | ||||
\(791\) | 17.4195 | 0.619365 | ||||||||
\(792\) | 1.12731 | + | 2.30952i | 0.0400571 | + | 0.0820653i | ||||
\(793\) | −4.04658 | + | 4.04658i | −0.143698 | + | 0.143698i | ||||
\(794\) | 4.89762 | + | 11.1716i | 0.173810 | + | 0.396466i | ||||
\(795\) | −13.6565 | − | 11.2510i | −0.484346 | − | 0.399033i | ||||
\(796\) | −16.1416 | − | 14.8715i | −0.572122 | − | 0.527107i | ||||
\(797\) | − | 15.9072i | − | 0.563461i | −0.959494 | − | 0.281730i | \(-0.909092\pi\) | ||
0.959494 | − | 0.281730i | \(-0.0909084\pi\) | |||||||
\(798\) | 6.35818 | − | 2.78741i | 0.225077 | − | 0.0986732i | ||||
\(799\) | −0.407850 | −0.0144287 | ||||||||
\(800\) | 21.8577 | − | 17.9510i | 0.772787 | − | 0.634665i | ||||
\(801\) | 0.0362935 | 0.00128237 | ||||||||
\(802\) | 25.5296 | − | 11.1921i | 0.901483 | − | 0.395208i | ||||
\(803\) | − | 4.43743i | − | 0.156593i | ||||||
\(804\) | −26.1161 | − | 24.0613i | −0.921044 | − | 0.848575i | ||||
\(805\) | 27.2679 | + | 22.4649i | 0.961067 | + | 0.791784i | ||||
\(806\) | 12.1831 | + | 27.7900i | 0.429131 | + | 0.978863i | ||||
\(807\) | −31.3610 | + | 31.3610i | −1.10396 | + | 1.10396i | ||||
\(808\) | 17.8487 | − | 8.71217i | 0.627915 | − | 0.306493i | ||||
\(809\) | 12.4922 | 0.439204 | 0.219602 | − | 0.975590i | \(-0.429524\pi\) | ||||
0.219602 | + | 0.975590i | \(0.429524\pi\) | |||||||
\(810\) | 32.9498 | + | 9.33082i | 1.15774 | + | 0.327851i | ||||
\(811\) | −35.4886 | + | 35.4886i | −1.24617 | + | 1.24617i | −0.288777 | + | 0.957396i | \(0.593249\pi\) |
−0.957396 | + | 0.288777i | \(0.906751\pi\) | |||||||
\(812\) | −6.28741 | + | 6.82436i | −0.220645 | + | 0.239488i | ||||
\(813\) | 7.05884 | 0.247564 | ||||||||
\(814\) | 5.61859 | − | 14.3906i | 0.196932 | − | 0.504389i | ||||
\(815\) | 11.1203 | − | 13.4978i | 0.389528 | − | 0.472809i | ||||
\(816\) | 14.0459 | − | 16.5566i | 0.491705 | − | 0.579595i | ||||
\(817\) | 7.73923 | − | 7.73923i | 0.270761 | − | 0.270761i | ||||
\(818\) | −34.7027 | + | 15.2136i | −1.21335 | + | 0.531930i | ||||
\(819\) | −8.11042 | + | 8.11042i | −0.283401 | + | 0.283401i | ||||
\(820\) | 4.24099 | + | 30.7154i | 0.148102 | + | 1.07263i | ||||
\(821\) | −15.9683 | − | 15.9683i | −0.557299 | − | 0.557299i | 0.371239 | − | 0.928537i | \(-0.378933\pi\) |
−0.928537 | + | 0.371239i | \(0.878933\pi\) | |||||||
\(822\) | 9.75833 | − | 24.9934i | 0.340361 | − | 0.871745i | ||||
\(823\) | −21.7278 | − | 21.7278i | −0.757384 | − | 0.757384i | 0.218462 | − | 0.975846i | \(-0.429896\pi\) |
−0.975846 | + | 0.218462i | \(0.929896\pi\) | |||||||
\(824\) | 1.58962 | − | 0.775914i | 0.0553771 | − | 0.0270302i | ||||
\(825\) | −5.85062 | + | 8.68454i | −0.203693 | + | 0.302357i | ||||
\(826\) | −14.3895 | + | 6.30833i | −0.500675 | + | 0.219495i | ||||
\(827\) | 39.2381i | 1.36444i | 0.731146 | + | 0.682221i | \(0.238986\pi\) | ||||
−0.731146 | + | 0.682221i | \(0.761014\pi\) | |||||||
\(828\) | −11.8657 | + | 0.485919i | −0.412360 | + | 0.0168869i | ||||
\(829\) | −18.6072 | − | 18.6072i | −0.646254 | − | 0.646254i | 0.305831 | − | 0.952086i | \(-0.401066\pi\) |
−0.952086 | + | 0.305831i | \(0.901066\pi\) | |||||||
\(830\) | −3.65193 | + | 12.8960i | −0.126760 | + | 0.447628i | ||||
\(831\) | − | 41.0982i | − | 1.42568i | ||||||
\(832\) | 37.5008 | + | 29.2618i | 1.30011 | + | 1.01447i | ||||
\(833\) | 3.65114 | + | 3.65114i | 0.126504 | + | 0.126504i | ||||
\(834\) | −19.6180 | + | 50.2465i | −0.679317 | + | 1.73989i | ||||
\(835\) | 31.1131 | − | 3.00477i | 1.07671 | − | 0.103984i | ||||
\(836\) | 1.73298 | + | 1.59663i | 0.0599365 | + | 0.0552206i | ||||
\(837\) | 15.2158 | 0.525935 | ||||||||
\(838\) | −8.05608 | + | 20.6335i | −0.278293 | + | 0.712774i | ||||
\(839\) | − | 12.5955i | − | 0.434845i | −0.976078 | − | 0.217422i | \(-0.930235\pi\) | ||
0.976078 | − | 0.217422i | \(-0.0697649\pi\) | |||||||
\(840\) | 27.3480 | + | 6.54859i | 0.943596 | + | 0.225948i | ||||
\(841\) | − | 24.8065i | − | 0.855396i | ||||||
\(842\) | −0.452889 | − | 0.176824i | −0.0156076 | − | 0.00609377i | ||||
\(843\) | 6.41151 | 0.220824 | ||||||||
\(844\) | −25.2142 | + | 1.03256i | −0.867909 | + | 0.0355423i | ||||
\(845\) | −38.5762 | − | 31.7814i | −1.32706 | − | 1.09331i | ||||
\(846\) | 0.165401 | + | 0.0645785i | 0.00568660 | + | 0.00222025i | ||||
\(847\) | −15.7981 | − | 15.7981i | −0.542829 | − | 0.542829i | ||||
\(848\) | −16.0745 | + | 1.31877i | −0.552002 | + | 0.0452867i | ||||
\(849\) | 0 | 0.000297553i | 0 | 1.02120e-5i | ||||||
\(850\) | 19.2425 | + | 3.49520i | 0.660014 | + | 0.119884i | ||||
\(851\) | 50.4778 | + | 50.4778i | 1.73036 | + | 1.73036i | ||||
\(852\) | −10.5076 | − | 9.68085i | −0.359984 | − | 0.331660i | ||||
\(853\) | − | 43.6914i | − | 1.49597i | −0.663718 | − | 0.747983i | \(-0.731022\pi\) | ||
0.663718 | − | 0.747983i | \(-0.268978\pi\) | |||||||
\(854\) | 1.23821 | + | 2.82439i | 0.0423706 | + | 0.0966488i | ||||
\(855\) | −2.09226 | + | 0.202061i | −0.0715537 | + | 0.00691035i | ||||
\(856\) | −47.0527 | − | 16.1854i | −1.60823 | − | 0.553206i | ||||
\(857\) | 28.9373 | + | 28.9373i | 0.988478 | + | 0.988478i | 0.999934 | − | 0.0114561i | \(-0.00364668\pi\) |
−0.0114561 | + | 0.999934i | \(0.503647\pi\) | |||||||
\(858\) | −16.4041 | − | 6.40475i | −0.560027 | − | 0.218655i | ||||
\(859\) | −28.1247 | − | 28.1247i | −0.959602 | − | 0.959602i | 0.0396134 | − | 0.999215i | \(-0.487387\pi\) |
−0.999215 | + | 0.0396134i | \(0.987387\pi\) | |||||||
\(860\) | 43.9176 | − | 6.06386i | 1.49758 | − | 0.206776i | ||||
\(861\) | −21.7987 | + | 21.7987i | −0.742896 | + | 0.742896i | ||||
\(862\) | −11.7552 | − | 26.8141i | −0.400384 | − | 0.913291i | ||||
\(863\) | 22.2144 | − | 22.2144i | 0.756186 | − | 0.756186i | −0.219440 | − | 0.975626i | \(-0.570423\pi\) |
0.975626 | + | 0.219440i | \(0.0704229\pi\) | |||||||
\(864\) | 20.9892 | − | 11.3311i | 0.714066 | − | 0.385492i | ||||
\(865\) | −6.02730 | − | 4.96565i | −0.204934 | − | 0.168837i | ||||
\(866\) | −10.5861 | − | 4.13322i | −0.359732 | − | 0.140452i | ||||
\(867\) | −18.3498 | −0.623192 | ||||||||
\(868\) | 16.3378 | − | 0.669061i | 0.554541 | − | 0.0227094i | ||||
\(869\) | −8.08466 | + | 8.08466i | −0.274253 | + | 0.274253i | ||||
\(870\) | 11.0949 | − | 6.19790i | 0.376153 | − | 0.210129i | ||||
\(871\) | 53.7929 | 1.82270 | ||||||||
\(872\) | −1.24073 | + | 0.605616i | −0.0420164 | + | 0.0205087i | ||||
\(873\) | 1.62773 | − | 1.62773i | 0.0550904 | − | 0.0550904i | ||||
\(874\) | −9.97237 | + | 4.37186i | −0.337320 | + | 0.147880i | ||||
\(875\) | 7.21497 | + | 24.2813i | 0.243911 | + | 0.820859i | ||||
\(876\) | 16.3074 | − | 0.667816i | 0.550976 | − | 0.0225634i | ||||
\(877\) | 5.13889i | 0.173528i | 0.996229 | + | 0.0867640i | \(0.0276526\pi\) | ||||
−0.996229 | + | 0.0867640i | \(0.972347\pi\) | |||||||
\(878\) | 10.6694 | + | 24.3374i | 0.360076 | + | 0.821346i | ||||
\(879\) | 21.7040 | 0.732057 | ||||||||
\(880\) | 1.69129 | + | 9.39382i | 0.0570135 | + | 0.316666i | ||||
\(881\) | −4.34528 | −0.146396 | −0.0731982 | − | 0.997317i | \(-0.523321\pi\) | ||||
−0.0731982 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(882\) | −0.902579 | − | 2.05881i | −0.0303914 | − | 0.0693239i | ||||
\(883\) | 35.4317i | 1.19237i | 0.802846 | + | 0.596186i | \(0.203318\pi\) | ||||
−0.802846 | + | 0.596186i | \(0.796682\pi\) | |||||||
\(884\) | 1.34578 | + | 32.8626i | 0.0452635 | + | 1.10529i | ||||
\(885\) | 21.4188 | − | 2.06853i | 0.719985 | − | 0.0695330i | ||||
\(886\) | 15.7551 | − | 6.90701i | 0.529304 | − | 0.232046i | ||||
\(887\) | 37.4644 | − | 37.4644i | 1.25793 | − | 1.25793i | 0.305855 | − | 0.952078i | \(-0.401058\pi\) |
0.952078 | − | 0.305855i | \(-0.0989422\pi\) | |||||||
\(888\) | 53.7304 | + | 18.4824i | 1.80307 | + | 0.620230i | ||||
\(889\) | −20.0945 | −0.673947 | ||||||||
\(890\) | 0.129694 | + | 0.0367271i | 0.00434736 | + | 0.00123110i | ||||
\(891\) | −8.17171 | + | 8.17171i | −0.273763 | + | 0.273763i | ||||
\(892\) | −1.52394 | − | 37.2131i | −0.0510253 | − | 1.24599i | ||||
\(893\) | 0.162803 | 0.00544799 | ||||||||
\(894\) | 6.35491 | + | 2.48119i | 0.212540 | + | 0.0829833i | ||||
\(895\) | −41.1739 | + | 3.97640i | −1.37629 | + | 0.132916i | ||||
\(896\) | 22.0386 | − | 13.0896i | 0.736259 | − | 0.437292i | ||||
\(897\) | 57.5407 | − | 57.5407i | 1.92123 | − | 1.92123i | ||||
\(898\) | −15.4849 | − | 35.3215i | −0.516736 | − | 1.17869i | ||||
\(899\) | 5.22531 | − | 5.22531i | 0.174274 | − | 0.174274i | ||||
\(900\) | −7.25026 | − | 4.46430i | −0.241675 | − | 0.148810i | ||||
\(901\) | −7.88580 | − | 7.88580i | −0.262714 | − | 0.262714i | ||||
\(902\) | −9.74703 | − | 3.80560i | −0.324541 | − | 0.126712i | ||||
\(903\) | 31.1682 | + | 31.1682i | 1.03721 | + | 1.03721i | ||||
\(904\) | −19.5427 | + | 9.53903i | −0.649980 | + | 0.317263i | ||||
\(905\) | −4.14613 | − | 42.9314i | −0.137822 | − | 1.42709i | ||||
\(906\) | 6.50248 | + | 14.8324i | 0.216031 | + | 0.492773i | ||||
\(907\) | − | 0.181405i | − | 0.00602345i | −0.999995 | − | 0.00301173i | \(-0.999041\pi\) | ||
0.999995 | − | 0.00301173i | \(-0.000958664\pi\) | |||||||
\(908\) | 26.2132 | − | 28.4518i | 0.869916 | − | 0.944208i | ||||
\(909\) | −4.22775 | − | 4.22775i | −0.140226 | − | 0.140226i | ||||
\(910\) | −37.1898 | + | 20.7751i | −1.23283 | + | 0.688689i | ||||
\(911\) | − | 23.4249i | − | 0.776101i | −0.921638 | − | 0.388050i | \(-0.873149\pi\) | ||
0.921638 | − | 0.388050i | \(-0.126851\pi\) | |||||||
\(912\) | −5.60676 | + | 6.60895i | −0.185658 | + | 0.218844i | ||||
\(913\) | −3.19828 | − | 3.19828i | −0.105848 | − | 0.105848i | ||||
\(914\) | −36.7976 | − | 14.3671i | −1.21716 | − | 0.475222i | ||||
\(915\) | −0.406015 | − | 4.20411i | −0.0134224 | − | 0.138984i | ||||
\(916\) | 1.52931 | + | 37.3443i | 0.0505299 | + | 1.23389i | ||||
\(917\) | −5.17529 | −0.170903 | ||||||||
\(918\) | 15.3635 | + | 5.99846i | 0.507071 | + | 0.197979i | ||||
\(919\) | 3.05885i | 0.100902i | 0.998727 | + | 0.0504511i | \(0.0160659\pi\) | ||||
−0.998727 | + | 0.0504511i | \(0.983934\pi\) | |||||||
\(920\) | −42.8935 | − | 10.2710i | −1.41416 | − | 0.338625i | ||||
\(921\) | 29.6962i | 0.978522i | ||||||||
\(922\) | 9.40249 | − | 24.0820i | 0.309654 | − | 0.793099i | ||||
\(923\) | 21.6431 | 0.712392 | ||||||||
\(924\) | −6.43011 | + | 6.97925i | −0.211535 | + | 0.229600i | ||||
\(925\) | 9.79453 | + | 50.2361i | 0.322042 | + | 1.65175i | ||||
\(926\) | −10.5943 | + | 27.1345i | −0.348150 | + | 0.891696i | ||||
\(927\) | −0.376527 | − | 0.376527i | −0.0123668 | − | 0.0123668i | ||||
\(928\) | 3.31670 | − | 11.0992i | 0.108876 | − | 0.364349i | ||||
\(929\) | 59.9772i | 1.96779i | 0.178752 | + | 0.983894i | \(0.442794\pi\) | ||||
−0.178752 | + | 0.983894i | \(0.557206\pi\) | |||||||
\(930\) | −21.5476 | − | 6.10190i | −0.706573 | − | 0.200089i | ||||
\(931\) | −1.45744 | − | 1.45744i | −0.0477657 | − | 0.0477657i | ||||
\(932\) | 2.39430 | + | 58.4665i | 0.0784280 | + | 1.91513i | ||||
\(933\) | − | 53.2931i | − | 1.74474i | ||||||
\(934\) | −54.8596 | + | 24.0503i | −1.79506 | + | 0.786950i | ||||
\(935\) | −4.19659 | + | 5.09381i | −0.137243 | + | 0.166586i | ||||
\(936\) | 4.65766 | − | 13.5403i | 0.152240 | − | 0.442579i | ||||
\(937\) | 23.7463 | + | 23.7463i | 0.775759 | + | 0.775759i | 0.979107 | − | 0.203347i | \(-0.0651821\pi\) |
−0.203347 | + | 0.979107i | \(0.565182\pi\) | |||||||
\(938\) | 10.5429 | − | 27.0029i | 0.344239 | − | 0.881677i | ||||
\(939\) | 26.8266 | + | 26.8266i | 0.875451 | + | 0.875451i | ||||
\(940\) | 0.525707 | + | 0.398147i | 0.0171467 | + | 0.0129861i | ||||
\(941\) | −35.2727 | + | 35.2727i | −1.14986 | + | 1.14986i | −0.163278 | + | 0.986580i | \(0.552207\pi\) |
−0.986580 | + | 0.163278i | \(0.947793\pi\) | |||||||
\(942\) | 8.00008 | − | 3.50722i | 0.260657 | − | 0.114271i | ||||
\(943\) | 34.1897 | − | 34.1897i | 1.11337 | − | 1.11337i | ||||
\(944\) | 12.6889 | − | 14.9570i | 0.412990 | − | 0.486810i | ||||
\(945\) | 2.05346 | + | 21.2627i | 0.0667989 | + | 0.691674i | ||||
\(946\) | −5.44133 | + | 13.9365i | −0.176913 | + | 0.453116i | ||||
\(947\) | −19.9140 | −0.647118 | −0.323559 | − | 0.946208i | \(-0.604879\pi\) | ||||
−0.323559 | + | 0.946208i | \(0.604879\pi\) | |||||||
\(948\) | −30.9276 | − | 28.4942i | −1.00448 | − | 0.925448i | ||||
\(949\) | −17.4824 | + | 17.4824i | −0.567504 | + | 0.567504i | ||||
\(950\) | −7.68112 | − | 1.39519i | −0.249208 | − | 0.0452661i | ||||
\(951\) | −50.6945 | −1.64388 | ||||||||
\(952\) | 16.7601 | + | 5.76523i | 0.543199 | + | 0.186852i | ||||
\(953\) | −23.1060 | + | 23.1060i | −0.748477 | + | 0.748477i | −0.974193 | − | 0.225716i | \(-0.927528\pi\) |
0.225716 | + | 0.974193i | \(0.427528\pi\) | |||||||
\(954\) | 1.94941 | + | 4.44667i | 0.0631144 | + | 0.143966i | ||||
\(955\) | 4.15916 | − | 5.04838i | 0.134587 | − | 0.163362i | ||||
\(956\) | −19.1150 | + | 20.7474i | −0.618222 | + | 0.671019i | ||||
\(957\) | 4.28871i | 0.138634i | ||||||||
\(958\) | −35.0881 | + | 15.3825i | −1.13364 | + | 0.496987i | ||||
\(959\) | 21.9027 | 0.707276 | ||||||||
\(960\) | −34.2675 | + | 7.62918i | −1.10598 | + | 0.246231i | ||||
\(961\) | 17.9781 | 0.579939 | ||||||||
\(962\) | −78.8314 | + | 34.5595i | −2.54163 | + | 1.11424i | ||||
\(963\) | 14.9790i | 0.482690i | ||||||||
\(964\) | 17.3476 | − | 18.8291i | 0.558728 | − | 0.606444i | ||||
\(965\) | −0.0252521 | − | 0.261475i | −0.000812894 | − | 0.00841717i | ||||
\(966\) | −17.6068 | − | 40.1617i | −0.566490 | − | 1.29218i | ||||
\(967\) | −41.7332 | + | 41.7332i | −1.34205 | + | 1.34205i | −0.448030 | + | 0.894018i | \(0.647874\pi\) |
−0.894018 | + | 0.448030i | \(0.852126\pi\) | |||||||
\(968\) | 26.3749 | + | 9.07255i | 0.847721 | + | 0.291603i | ||||
\(969\) | −5.99275 | −0.192515 | ||||||||
\(970\) | 7.46386 | − | 4.16949i | 0.239650 | − | 0.133874i | ||||
\(971\) | 33.5030 | − | 33.5030i | 1.07516 | − | 1.07516i | 0.0782268 | − | 0.996936i | \(-0.475074\pi\) |
0.996936 | − | 0.0782268i | \(-0.0249258\pi\) | |||||||
\(972\) | −12.6543 | − | 11.6586i | −0.405885 | − | 0.373950i | ||||
\(973\) | −44.0330 | −1.41163 | ||||||||
\(974\) | 15.9790 | − | 40.9259i | 0.511999 | − | 1.31135i | ||||
\(975\) | 57.2652 | − | 11.1650i | 1.83395 | − | 0.357566i | ||||
\(976\) | −2.93579 | − | 2.49060i | −0.0939723 | − | 0.0797223i | ||||
\(977\) | 9.16848 | − | 9.16848i | 0.293326 | − | 0.293326i | −0.545067 | − | 0.838393i | \(-0.683496\pi\) |
0.838393 | + | 0.545067i | \(0.183496\pi\) | |||||||
\(978\) | −19.8804 | + | 8.71552i | −0.635706 | + | 0.278692i | ||||
\(979\) | −0.0321648 | + | 0.0321648i | −0.00102799 | + | 0.00102799i | ||||
\(980\) | −1.14194 | − | 8.27050i | −0.0364778 | − | 0.264191i | ||||
\(981\) | 0.293887 | + | 0.293887i | 0.00938308 | + | 0.00938308i | ||||
\(982\) | −4.45134 | + | 11.4009i | −0.142048 | + | 0.363818i | ||||
\(983\) | −39.1183 | − | 39.1183i | −1.24768 | − | 1.24768i | −0.956742 | − | 0.290936i | \(-0.906033\pi\) |
−0.290936 | − | 0.956742i | \(-0.593967\pi\) | |||||||
\(984\) | 12.5186 | − | 36.3928i | 0.399077 | − | 1.16016i | ||||
\(985\) | −13.4697 | − | 11.0972i | −0.429181 | − | 0.353585i | ||||
\(986\) | 7.33597 | − | 3.21607i | 0.233625 | − | 0.102421i | ||||
\(987\) | 0.655657i | 0.0208698i | ||||||||
\(988\) | −0.537201 | − | 13.1179i | −0.0170906 | − | 0.417336i | ||||
\(989\) | −48.8852 | − | 48.8852i | −1.55446 | − | 1.55446i | ||||
\(990\) | 2.50845 | − | 1.40128i | 0.0797237 | − | 0.0445356i | ||||
\(991\) | − | 12.9925i | − | 0.412722i | −0.978476 | − | 0.206361i | \(-0.933838\pi\) | ||
0.978476 | − | 0.206361i | \(-0.0661621\pi\) | |||||||
\(992\) | −17.9628 | + | 9.69732i | −0.570320 | + | 0.307890i | ||||
\(993\) | −26.7307 | − | 26.7307i | −0.848273 | − | 0.848273i | ||||
\(994\) | 4.24186 | − | 10.8644i | 0.134544 | − | 0.344598i | ||||
\(995\) | −15.6031 | + | 18.9390i | −0.494650 | + | 0.600406i | ||||
\(996\) | 11.2722 | − | 12.2349i | 0.357175 | − | 0.387678i | ||||
\(997\) | −8.89509 | −0.281710 | −0.140855 | − | 0.990030i | \(-0.544985\pi\) | ||||
−0.140855 | + | 0.990030i | \(0.544985\pi\) | |||||||
\(998\) | −11.2103 | + | 28.7122i | −0.354855 | + | 0.908868i | ||||
\(999\) | 43.1624i | 1.36560i |
(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 | 80.2.j.b.43.9 | ✓ | 18 | |
3.2 | odd | 2 | 720.2.bd.g.523.1 | 18 | |||
4.3 | odd | 2 | 320.2.j.b.143.2 | 18 | |||
5.2 | odd | 4 | 80.2.s.b.27.6 | yes | 18 | ||
5.3 | odd | 4 | 400.2.s.d.107.4 | 18 | |||
5.4 | even | 2 | 400.2.j.d.43.1 | 18 | |||
8.3 | odd | 2 | 640.2.j.c.543.8 | 18 | |||
8.5 | even | 2 | 640.2.j.d.543.2 | 18 | |||
15.2 | even | 4 | 720.2.z.g.667.4 | 18 | |||
16.3 | odd | 4 | 80.2.s.b.3.6 | yes | 18 | ||
16.5 | even | 4 | 640.2.s.c.223.8 | 18 | |||
16.11 | odd | 4 | 640.2.s.d.223.2 | 18 | |||
16.13 | even | 4 | 320.2.s.b.303.2 | 18 | |||
20.3 | even | 4 | 1600.2.s.d.207.8 | 18 | |||
20.7 | even | 4 | 320.2.s.b.207.2 | 18 | |||
20.19 | odd | 2 | 1600.2.j.d.143.8 | 18 | |||
40.27 | even | 4 | 640.2.s.c.287.8 | 18 | |||
40.37 | odd | 4 | 640.2.s.d.287.2 | 18 | |||
48.35 | even | 4 | 720.2.z.g.163.4 | 18 | |||
80.3 | even | 4 | 400.2.j.d.307.1 | 18 | |||
80.13 | odd | 4 | 1600.2.j.d.1007.2 | 18 | |||
80.19 | odd | 4 | 400.2.s.d.243.4 | 18 | |||
80.27 | even | 4 | 640.2.j.d.607.8 | 18 | |||
80.29 | even | 4 | 1600.2.s.d.943.8 | 18 | |||
80.37 | odd | 4 | 640.2.j.c.607.2 | 18 | |||
80.67 | even | 4 | inner | 80.2.j.b.67.9 | yes | 18 | |
80.77 | odd | 4 | 320.2.j.b.47.8 | 18 | |||
240.227 | odd | 4 | 720.2.bd.g.307.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.9 | ✓ | 18 | 1.1 | even | 1 | trivial | |
80.2.j.b.67.9 | yes | 18 | 80.67 | even | 4 | inner | |
80.2.s.b.3.6 | yes | 18 | 16.3 | odd | 4 | ||
80.2.s.b.27.6 | yes | 18 | 5.2 | odd | 4 | ||
320.2.j.b.47.8 | 18 | 80.77 | odd | 4 | |||
320.2.j.b.143.2 | 18 | 4.3 | odd | 2 | |||
320.2.s.b.207.2 | 18 | 20.7 | even | 4 | |||
320.2.s.b.303.2 | 18 | 16.13 | even | 4 | |||
400.2.j.d.43.1 | 18 | 5.4 | even | 2 | |||
400.2.j.d.307.1 | 18 | 80.3 | even | 4 | |||
400.2.s.d.107.4 | 18 | 5.3 | odd | 4 | |||
400.2.s.d.243.4 | 18 | 80.19 | odd | 4 | |||
640.2.j.c.543.8 | 18 | 8.3 | odd | 2 | |||
640.2.j.c.607.2 | 18 | 80.37 | odd | 4 | |||
640.2.j.d.543.2 | 18 | 8.5 | even | 2 | |||
640.2.j.d.607.8 | 18 | 80.27 | even | 4 | |||
640.2.s.c.223.8 | 18 | 16.5 | even | 4 | |||
640.2.s.c.287.8 | 18 | 40.27 | even | 4 | |||
640.2.s.d.223.2 | 18 | 16.11 | odd | 4 | |||
640.2.s.d.287.2 | 18 | 40.37 | odd | 4 | |||
720.2.z.g.163.4 | 18 | 48.35 | even | 4 | |||
720.2.z.g.667.4 | 18 | 15.2 | even | 4 | |||
720.2.bd.g.307.1 | 18 | 240.227 | odd | 4 | |||
720.2.bd.g.523.1 | 18 | 3.2 | odd | 2 | |||
1600.2.j.d.143.8 | 18 | 20.19 | odd | 2 | |||
1600.2.j.d.1007.2 | 18 | 80.13 | odd | 4 | |||
1600.2.s.d.207.8 | 18 | 20.3 | even | 4 | |||
1600.2.s.d.943.8 | 18 | 80.29 | even | 4 |