Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 152.10 | ||
Character | \(\chi\) | \(=\) | 405.152 |
Dual form | 405.2.r.a.8.10 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{17}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.807333 | + | 0.565301i | 0.570871 | + | 0.399728i | 0.823064 | − | 0.567949i | \(-0.192263\pi\) |
−0.252193 | + | 0.967677i | \(0.581152\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.351818 | − | 0.966613i | −0.175909 | − | 0.483307i | ||||
\(5\) | 2.04189 | − | 0.911409i | 0.913163 | − | 0.407595i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.275357 | − | 0.590505i | −0.104075 | − | 0.223190i | 0.847374 | − | 0.530997i | \(-0.178183\pi\) |
−0.951449 | + | 0.307807i | \(0.900405\pi\) | |||||||
\(8\) | 0.772562 | − | 2.88324i | 0.273142 | − | 1.01938i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.16371 | + | 0.418474i | 0.684225 | + | 0.132333i | ||||
\(11\) | −0.890417 | − | 1.06116i | −0.268471 | − | 0.319951i | 0.614919 | − | 0.788591i | \(-0.289189\pi\) |
−0.883390 | + | 0.468639i | \(0.844744\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.93770 | − | 4.19546i | −0.814770 | − | 1.16361i | −0.984023 | − | 0.178040i | \(-0.943024\pi\) |
0.169253 | − | 0.985573i | \(-0.445864\pi\) | |||||||
\(14\) | 0.111508 | − | 0.632393i | 0.0298018 | − | 0.169014i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.677632 | − | 0.568601i | 0.169408 | − | 0.142150i | ||||
\(17\) | 1.18168 | + | 4.41009i | 0.286600 | + | 1.06961i | 0.947662 | + | 0.319274i | \(0.103439\pi\) |
−0.661063 | + | 0.750331i | \(0.729894\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.00652973 | − | 0.00376994i | 0.00149802 | − | 0.000864884i | −0.499251 | − | 0.866458i | \(-0.666391\pi\) |
0.500749 | + | 0.865593i | \(0.333058\pi\) | |||||||
\(20\) | −1.59936 | − | 1.65307i | −0.357627 | − | 0.369638i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.118990 | − | 1.36006i | −0.0253687 | − | 0.289966i | ||||
\(23\) | 6.70560 | + | 3.12687i | 1.39822 | + | 0.651998i | 0.968051 | − | 0.250752i | \(-0.0806780\pi\) |
0.430164 | + | 0.902751i | \(0.358456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.33867 | − | 3.72200i | 0.667733 | − | 0.744401i | ||||
\(26\) | − | 5.04782i | − | 0.989959i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.473914 | + | 0.473914i | −0.0895613 | + | 0.0895613i | ||||
\(29\) | 0.586508 | + | 3.32625i | 0.108912 | + | 0.617669i | 0.989586 | + | 0.143946i | \(0.0459791\pi\) |
−0.880674 | + | 0.473723i | \(0.842910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.73277 | − | 1.35862i | 0.670426 | − | 0.244015i | 0.0156946 | − | 0.999877i | \(-0.495004\pi\) |
0.654731 | + | 0.755862i | \(0.272782\pi\) | |||||||
\(32\) | −5.07868 | + | 0.444327i | −0.897792 | + | 0.0785466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.53902 | + | 4.22842i | −0.263940 | + | 0.725168i | ||||
\(35\) | −1.10044 | − | 0.954786i | −0.186008 | − | 0.161388i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.60572 | − | 0.430252i | 0.263979 | − | 0.0707331i | −0.124402 | − | 0.992232i | \(-0.539701\pi\) |
0.388381 | + | 0.921499i | \(0.373034\pi\) | |||||||
\(38\) | 0.00740282 | 0.000647662i | 0.00120090 | 0.000105065i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.05032 | − | 6.59139i | −0.166070 | − | 1.04219i | ||||
\(41\) | 1.90299 | + | 0.335548i | 0.297197 | + | 0.0524038i | 0.320258 | − | 0.947330i | \(-0.396230\pi\) |
−0.0230615 | + | 0.999734i | \(0.507341\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.929732 | + | 10.6269i | −0.141783 | + | 1.62058i | 0.508617 | + | 0.860993i | \(0.330157\pi\) |
−0.650400 | + | 0.759592i | \(0.725399\pi\) | |||||||
\(44\) | −0.712464 | + | 1.23402i | −0.107408 | + | 0.186036i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.64603 | + | 6.31511i | 0.537578 | + | 0.931113i | ||||
\(47\) | −6.61847 | + | 3.08624i | −0.965403 | + | 0.450175i | −0.840391 | − | 0.541980i | \(-0.817675\pi\) |
−0.125012 | + | 0.992155i | \(0.539897\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.22664 | − | 5.03711i | 0.603806 | − | 0.719587i | ||||
\(50\) | 4.79947 | − | 1.11755i | 0.678747 | − | 0.158045i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.02186 | + | 4.31566i | −0.419056 | + | 0.598474i | ||||
\(53\) | 1.18766 | + | 1.18766i | 0.163138 | + | 0.163138i | 0.783955 | − | 0.620817i | \(-0.213199\pi\) |
−0.620817 | + | 0.783955i | \(0.713199\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.78529 | − | 1.35524i | −0.375568 | − | 0.182740i | ||||
\(56\) | −1.91530 | + | 0.337719i | −0.255942 | + | 0.0451295i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.40682 | + | 3.01694i | −0.184725 | + | 0.396144i | ||||
\(59\) | 7.77643 | + | 6.52520i | 1.01240 | + | 0.849508i | 0.988654 | − | 0.150210i | \(-0.0479948\pi\) |
0.0237505 | + | 0.999718i | \(0.492439\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.02437 | − | 3.28460i | −1.15545 | − | 0.420550i | −0.307981 | − | 0.951392i | \(-0.599653\pi\) |
−0.847471 | + | 0.530842i | \(0.821876\pi\) | |||||||
\(62\) | 3.78162 | + | 1.01328i | 0.480266 | + | 0.128687i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.88351 | − | 3.39685i | −0.735439 | − | 0.424606i | ||||
\(65\) | −9.82225 | − | 5.88925i | −1.21830 | − | 0.730472i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.3176 | + | 8.62489i | −1.50484 | + | 1.05370i | −0.525658 | + | 0.850696i | \(0.676181\pi\) |
−0.979178 | + | 0.203002i | \(0.934930\pi\) | |||||||
\(68\) | 3.84712 | − | 2.69378i | 0.466532 | − | 0.326669i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.348682 | − | 1.39291i | −0.0416754 | − | 0.166485i | ||||
\(71\) | −5.41550 | − | 3.12664i | −0.642702 | − | 0.371064i | 0.142953 | − | 0.989730i | \(-0.454340\pi\) |
−0.785654 | + | 0.618666i | \(0.787674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1662 | + | 3.25991i | 1.42394 | + | 0.381544i | 0.886880 | − | 0.461999i | \(-0.152868\pi\) |
0.537061 | + | 0.843543i | \(0.319534\pi\) | |||||||
\(74\) | 1.53958 | + | 0.560360i | 0.178972 | + | 0.0651405i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.00594135 | − | 0.00498539i | −0.000681520 | − | 0.000571863i | ||||
\(77\) | −0.381436 | + | 0.817993i | −0.0434687 | + | 0.0932189i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.782046 | + | 0.137896i | −0.0879871 | + | 0.0155145i | −0.217468 | − | 0.976067i | \(-0.569780\pi\) |
0.129481 | + | 0.991582i | \(0.458669\pi\) | |||||||
\(80\) | 0.865425 | − | 1.77862i | 0.0967575 | − | 0.198856i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.34666 | + | 1.34666i | 0.148714 | + | 0.148714i | ||||
\(83\) | −5.32053 | + | 7.59850i | −0.584004 | + | 0.834044i | −0.997057 | − | 0.0766627i | \(-0.975574\pi\) |
0.413053 | + | 0.910707i | \(0.364462\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.43227 | + | 7.92795i | 0.697678 | + | 0.859907i | ||||
\(86\) | −6.75799 | + | 8.05386i | −0.728733 | + | 0.868470i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.74748 | + | 1.74748i | −0.399482 | + | 0.186282i | ||||
\(89\) | −5.89645 | − | 10.2130i | −0.625023 | − | 1.08257i | −0.988537 | − | 0.150982i | \(-0.951756\pi\) |
0.363514 | − | 0.931589i | \(-0.381577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.66853 | + | 2.88997i | −0.174909 | + | 0.302951i | ||||
\(92\) | 0.663323 | − | 7.58182i | 0.0691562 | − | 0.790459i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.08796 | − | 1.24980i | −0.731068 | − | 0.128907i | ||||
\(95\) | 0.00989706 | − | 0.0136491i | 0.00101542 | − | 0.00140037i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.18091 | − | 0.190805i | −0.221438 | − | 0.0193733i | −0.0241031 | − | 0.999709i | \(-0.507673\pi\) |
−0.197335 | + | 0.980336i | \(0.563229\pi\) | |||||||
\(98\) | 6.25979 | − | 1.67731i | 0.632334 | − | 0.169433i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.77234 | − | 1.91773i | −0.477234 | − | 0.191773i | ||||
\(101\) | −2.19882 | + | 6.04120i | −0.218790 | + | 0.601122i | −0.999724 | − | 0.0234923i | \(-0.992521\pi\) |
0.780934 | + | 0.624614i | \(0.214744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.32840 | − | 0.816129i | 0.919154 | − | 0.0804156i | 0.382250 | − | 0.924059i | \(-0.375149\pi\) |
0.536904 | + | 0.843643i | \(0.319594\pi\) | |||||||
\(104\) | −14.3661 | + | 5.22883i | −1.40871 | + | 0.512729i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.287452 | + | 1.63022i | 0.0279198 | + | 0.158341i | ||||
\(107\) | −2.45371 | + | 2.45371i | −0.237210 | + | 0.237210i | −0.815694 | − | 0.578484i | \(-0.803644\pi\) |
0.578484 | + | 0.815694i | \(0.303644\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.1343i | − | 1.06647i | −0.845967 | − | 0.533235i | \(-0.820976\pi\) | ||
0.845967 | − | 0.533235i | \(-0.179024\pi\) | |||||||
\(110\) | −1.48254 | − | 2.66865i | −0.141354 | − | 0.254446i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.522352 | − | 0.243577i | −0.0493576 | − | 0.0230158i | ||||
\(113\) | −0.776537 | − | 8.87586i | −0.0730505 | − | 0.834971i | −0.941019 | − | 0.338353i | \(-0.890130\pi\) |
0.867969 | − | 0.496619i | \(-0.165425\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.5420 | + | 0.273199i | 1.54255 | + | 0.0254760i | ||||
\(116\) | 3.00885 | − | 1.73716i | 0.279365 | − | 0.161291i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.58947 | + | 9.66403i | 0.238380 | + | 0.889646i | ||||
\(119\) | 2.27880 | − | 1.91214i | 0.208897 | − | 0.175285i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.57692 | − | 8.94314i | 0.143356 | − | 0.813013i | ||||
\(122\) | −5.42888 | − | 7.75325i | −0.491508 | − | 0.701946i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.62652 | − | 3.13016i | −0.235868 | − | 0.281097i | ||||
\(125\) | 3.42494 | − | 10.6428i | 0.306336 | − | 0.951924i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.737710 | − | 2.75317i | 0.0654611 | − | 0.244304i | −0.925440 | − | 0.378893i | \(-0.876305\pi\) |
0.990902 | + | 0.134589i | \(0.0429714\pi\) | |||||||
\(128\) | 1.47937 | + | 3.17252i | 0.130759 | + | 0.280413i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.60063 | − | 10.3071i | −0.403502 | − | 0.903994i | ||||
\(131\) | −2.22104 | − | 6.10227i | −0.194053 | − | 0.533158i | 0.804060 | − | 0.594548i | \(-0.202669\pi\) |
−0.998114 | + | 0.0613901i | \(0.980447\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.00402417 | − | 0.00281776i | −0.000348940 | − | 0.000244330i | ||||
\(134\) | −14.8201 | −1.28026 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.6283 | 1.16862 | ||||||||
\(137\) | 15.1709 | + | 10.6228i | 1.29614 | + | 0.907567i | 0.998884 | − | 0.0472310i | \(-0.0150397\pi\) |
0.297256 | + | 0.954798i | \(0.403929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.75787 | + | 18.5671i | 0.573195 | + | 1.57484i | 0.799424 | + | 0.600767i | \(0.205138\pi\) |
−0.226229 | + | 0.974074i | \(0.572640\pi\) | |||||||
\(140\) | −0.535753 | + | 1.39961i | −0.0452794 | + | 0.118289i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.60462 | − | 5.58563i | −0.218575 | − | 0.468735i | ||||
\(143\) | −1.83628 | + | 6.85307i | −0.153557 | + | 0.573083i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.22916 | + | 6.25730i | 0.351213 | + | 0.519641i | ||||
\(146\) | 7.97931 | + | 9.50937i | 0.660373 | + | 0.787001i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.980811 | − | 1.40074i | −0.0806222 | − | 0.115140i | ||||
\(149\) | −2.60422 | + | 14.7692i | −0.213346 | + | 1.20994i | 0.670408 | + | 0.741992i | \(0.266119\pi\) |
−0.883754 | + | 0.467952i | \(0.844992\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.694966 | − | 0.583146i | 0.0565555 | − | 0.0474557i | −0.614072 | − | 0.789250i | \(-0.710469\pi\) |
0.670627 | + | 0.741794i | \(0.266025\pi\) | |||||||
\(152\) | −0.00582502 | − | 0.0217393i | −0.000472472 | − | 0.00176329i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.770358 | + | 0.444766i | −0.0620772 | + | 0.0358403i | ||||
\(155\) | 6.38367 | − | 6.17624i | 0.512749 | − | 0.496087i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.403811 | + | 4.61558i | 0.0322276 | + | 0.368363i | 0.995134 | + | 0.0985286i | \(0.0314136\pi\) |
−0.962907 | + | 0.269835i | \(0.913031\pi\) | |||||||
\(158\) | −0.709324 | − | 0.330763i | −0.0564308 | − | 0.0263141i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.96516 | + | 5.53602i | −0.787815 | + | 0.437661i | ||||
\(161\) | − | 4.82070i | − | 0.379924i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.94001 | + | 7.94001i | −0.621909 | + | 0.621909i | −0.946019 | − | 0.324110i | \(-0.894935\pi\) |
0.324110 | + | 0.946019i | \(0.394935\pi\) | |||||||
\(164\) | −0.345161 | − | 1.95751i | −0.0269526 | − | 0.152856i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.59088 | + | 3.12682i | −0.666782 | + | 0.242689i | ||||
\(167\) | −0.896457 | + | 0.0784299i | −0.0693700 | + | 0.00606908i | −0.121788 | − | 0.992556i | \(-0.538863\pi\) |
0.0524179 | + | 0.998625i | \(0.483307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.52560 | + | 12.4340i | −0.348123 | + | 0.956461i | ||||
\(170\) | 0.711306 | + | 10.0367i | 0.0545547 | + | 0.769777i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.5992 | − | 2.84004i | 0.808180 | − | 0.216551i | ||||
\(173\) | 13.3057 | + | 1.16409i | 1.01161 | + | 0.0885045i | 0.580891 | − | 0.813981i | \(-0.302704\pi\) |
0.430720 | + | 0.902486i | \(0.358260\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.11718 | − | 0.946619i | −0.235637 | − | 0.0715577i | ||||
\(176\) | −1.20675 | − | 0.212783i | −0.0909622 | − | 0.0160391i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.01299 | − | 11.5785i | 0.0759268 | − | 0.867847i | ||||
\(179\) | 3.72605 | − | 6.45370i | 0.278498 | − | 0.482372i | −0.692514 | − | 0.721405i | \(-0.743497\pi\) |
0.971012 | + | 0.239032i | \(0.0768302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.1147 | − | 22.7153i | −0.974806 | − | 1.68841i | −0.680574 | − | 0.732679i | \(-0.738270\pi\) |
−0.294232 | − | 0.955734i | \(-0.595064\pi\) | |||||||
\(182\) | −2.98076 | + | 1.38995i | −0.220949 | + | 0.103030i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.1960 | − | 16.9182i | 1.04655 | − | 1.24722i | ||||
\(185\) | 2.88658 | − | 2.34200i | 0.212226 | − | 0.172187i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.62762 | − | 5.18077i | 0.265278 | − | 0.378856i | ||||
\(188\) | 5.31170 | + | 5.31170i | 0.387396 | + | 0.387396i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.0157061 | − | 0.00542454i | 0.00113944 | − | 0.000393537i | ||||
\(191\) | 1.57094 | − | 0.276999i | 0.113669 | − | 0.0200430i | −0.116524 | − | 0.993188i | \(-0.537175\pi\) |
0.230193 | + | 0.973145i | \(0.426064\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.55560 | + | 7.62500i | −0.255937 | + | 0.548860i | −0.991729 | − | 0.128348i | \(-0.959032\pi\) |
0.735792 | + | 0.677208i | \(0.236810\pi\) | |||||||
\(194\) | −1.65286 | − | 1.38691i | −0.118668 | − | 0.0995745i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.35595 | − | 2.31338i | −0.453996 | − | 0.165241i | ||||
\(197\) | 10.9609 | + | 2.93696i | 0.780931 | + | 0.209250i | 0.627195 | − | 0.778862i | \(-0.284203\pi\) |
0.153736 | + | 0.988112i | \(0.450869\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.0022 | − | 12.1256i | −1.48881 | − | 0.859563i | −0.488889 | − | 0.872346i | \(-0.662598\pi\) |
−0.999918 | + | 0.0127826i | \(0.995931\pi\) | |||||||
\(200\) | −8.15210 | − | 12.5017i | −0.576441 | − | 0.884001i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.19027 | + | 3.63427i | −0.365186 | + | 0.255706i | ||||
\(203\) | 1.80267 | − | 1.26224i | 0.126522 | − | 0.0885920i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.19153 | − | 1.04925i | 0.292749 | − | 0.0732826i | ||||
\(206\) | 7.99248 | + | 4.61446i | 0.556863 | + | 0.321505i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.37622 | − | 1.17261i | −0.303436 | − | 0.0813055i | ||||
\(209\) | −0.00981468 | − | 0.00357225i | −0.000678896 | − | 0.000247098i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.98736 | + | 5.86309i | 0.481029 | + | 0.403632i | 0.850799 | − | 0.525492i | \(-0.176119\pi\) |
−0.369769 | + | 0.929124i | \(0.620563\pi\) | |||||||
\(212\) | 0.730167 | − | 1.56585i | 0.0501481 | − | 0.107543i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.36805 | + | 0.593878i | −0.230235 | + | 0.0405967i | ||||
\(215\) | 7.78703 | + | 22.5463i | 0.531071 | + | 1.53765i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.83011 | − | 1.83011i | −0.124236 | − | 0.124236i | ||||
\(218\) | 6.29421 | − | 8.98907i | 0.426298 | − | 0.608817i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.330076 | + | 3.16909i | −0.0222537 | + | 0.213660i | ||||
\(221\) | 15.0310 | − | 17.9132i | 1.01109 | − | 1.20497i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8136 | − | 6.90768i | 0.991990 | − | 0.462572i | 0.142282 | − | 0.989826i | \(-0.454556\pi\) |
0.849708 | + | 0.527254i | \(0.176778\pi\) | |||||||
\(224\) | 1.66083 | + | 2.87663i | 0.110969 | + | 0.192203i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.39061 | − | 7.60476i | 0.292059 | − | 0.505861i | ||||
\(227\) | −1.10129 | + | 12.5878i | −0.0730949 | + | 0.835479i | 0.867830 | + | 0.496862i | \(0.165515\pi\) |
−0.940924 | + | 0.338617i | \(0.890041\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.89322 | + | 1.56812i | 0.587681 | + | 0.103624i | 0.459579 | − | 0.888137i | \(-0.348000\pi\) |
0.128102 | + | 0.991761i | \(0.459112\pi\) | |||||||
\(230\) | 13.2005 | + | 9.57177i | 0.870413 | + | 0.631144i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0435 | + | 0.878692i | 0.659388 | + | 0.0576889i | ||||
\(233\) | −20.6198 | + | 5.52507i | −1.35085 | + | 0.361959i | −0.860449 | − | 0.509537i | \(-0.829817\pi\) |
−0.490402 | + | 0.871496i | \(0.663150\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.7014 | + | 12.3339i | −0.698081 | + | 0.804576i | ||||
\(236\) | 3.57145 | − | 9.81248i | 0.232482 | − | 0.638738i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.92068 | − | 0.255527i | 0.189320 | − | 0.0165633i | ||||
\(239\) | 5.43398 | − | 1.97781i | 0.351495 | − | 0.127934i | −0.160238 | − | 0.987078i | \(-0.551226\pi\) |
0.511733 | + | 0.859145i | \(0.329004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00297 | − | 22.7020i | −0.257854 | − | 1.46236i | −0.788639 | − | 0.614857i | \(-0.789214\pi\) |
0.530784 | − | 0.847507i | \(-0.321897\pi\) | |||||||
\(242\) | 6.32866 | − | 6.32866i | 0.406822 | − | 0.406822i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.87866i | 0.632416i | ||||||||
\(245\) | 4.03948 | − | 14.1374i | 0.258073 | − | 0.903208i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0349990 | − | 0.0163203i | −0.00222693 | − | 0.00103844i | ||||
\(248\) | −1.03342 | − | 11.8121i | −0.0656225 | − | 0.750069i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.78146 | − | 6.65619i | 0.555389 | − | 0.420974i | ||||
\(251\) | 2.17404 | − | 1.25518i | 0.137224 | − | 0.0792266i | −0.429816 | − | 0.902916i | \(-0.641422\pi\) |
0.567041 | + | 0.823690i | \(0.308088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.65268 | − | 9.89993i | −0.166772 | − | 0.622403i | ||||
\(254\) | 2.15195 | − | 1.80570i | 0.135025 | − | 0.113300i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.95851 | + | 16.7785i | −0.184907 | + | 1.04866i | ||||
\(257\) | −7.24292 | − | 10.3440i | −0.451801 | − | 0.645238i | 0.527045 | − | 0.849837i | \(-0.323300\pi\) |
−0.978846 | + | 0.204599i | \(0.934411\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.696213 | − | 0.829715i | −0.0432606 | − | 0.0515560i | ||||
\(260\) | −2.23698 | + | 11.5663i | −0.138732 | + | 0.717309i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.65649 | − | 6.18212i | 0.102339 | − | 0.381933i | ||||
\(263\) | −7.09675 | − | 15.2190i | −0.437604 | − | 0.938445i | −0.994188 | − | 0.107654i | \(-0.965666\pi\) |
0.556584 | − | 0.830791i | \(-0.312112\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.50752 | + | 1.34263i | 0.215465 | + | 0.0824772i | ||||
\(266\) | −0.00165597 | − | 0.00454974i | −0.000101534 | − | 0.000278962i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.6705 | + | 8.87198i | 0.773974 | + | 0.541942i | ||||
\(269\) | 3.27377 | 0.199605 | 0.0998027 | − | 0.995007i | \(-0.468179\pi\) | ||||
0.0998027 | + | 0.995007i | \(0.468179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.46872 | 0.514438 | 0.257219 | − | 0.966353i | \(-0.417194\pi\) | ||||
0.257219 | + | 0.966353i | \(0.417194\pi\) | |||||||
\(272\) | 3.30833 | + | 2.31652i | 0.200597 | + | 0.140459i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.24292 | + | 17.1523i | 0.377148 | + | 1.03621i | ||||
\(275\) | −6.92244 | − | 0.228717i | −0.417439 | − | 0.0137922i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.04261 | − | 2.23589i | −0.0626445 | − | 0.134342i | 0.872493 | − | 0.488627i | \(-0.162502\pi\) |
−0.935137 | + | 0.354285i | \(0.884724\pi\) | |||||||
\(278\) | −5.04014 | + | 18.8101i | −0.302288 | + | 1.12815i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.60304 | + | 2.43521i | −0.215323 | + | 0.145531i | ||||
\(281\) | 12.4917 | + | 14.8870i | 0.745190 | + | 0.888082i | 0.996816 | − | 0.0797423i | \(-0.0254097\pi\) |
−0.251626 | + | 0.967825i | \(0.580965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.8099 | − | 15.4382i | −0.642583 | − | 0.917703i | 0.357285 | − | 0.933996i | \(-0.383703\pi\) |
−0.999867 | + | 0.0162923i | \(0.994814\pi\) | |||||||
\(284\) | −1.11698 | + | 6.33470i | −0.0662805 | + | 0.375896i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.35653 | + | 4.49466i | −0.316738 | + | 0.265775i | ||||
\(287\) | −0.325858 | − | 1.21612i | −0.0192348 | − | 0.0717853i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.33013 | + | 1.92265i | −0.195890 | + | 0.113097i | ||||
\(290\) | −0.122916 | + | 7.44248i | −0.00721789 | + | 0.437037i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.12920 | − | 12.9069i | −0.0660817 | − | 0.755317i | ||||
\(293\) | −3.65580 | − | 1.70473i | −0.213574 | − | 0.0995913i | 0.312887 | − | 0.949790i | \(-0.398704\pi\) |
−0.526461 | + | 0.850199i | \(0.676482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.8258 | + | 6.23626i | 1.27075 | + | 0.363089i | ||||
\(296\) | − | 4.96208i | − | 0.288415i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.4515 | + | 10.4515i | −0.605441 | + | 0.605441i | ||||
\(299\) | −6.58033 | − | 37.3189i | −0.380551 | − | 2.15821i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.53123 | − | 2.37717i | 0.376454 | − | 0.137018i | ||||
\(302\) | 0.890722 | − | 0.0779280i | 0.0512553 | − | 0.00448426i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.00228116 | − | 0.00626744i | 0.000130834 | − | 0.000359462i | ||||
\(305\) | −21.4204 | + | 1.51808i | −1.22653 | + | 0.0869251i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.60536 | − | 2.30580i | 0.491134 | − | 0.131599i | −0.00474824 | − | 0.999989i | \(-0.501511\pi\) |
0.495882 | + | 0.868390i | \(0.334845\pi\) | |||||||
\(308\) | 0.924879 | + | 0.0809164i | 0.0526999 | + | 0.00461064i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.64518 | − | 1.37759i | 0.491013 | − | 0.0782417i | ||||
\(311\) | −26.8272 | − | 4.73035i | −1.52123 | − | 0.268234i | −0.650313 | − | 0.759666i | \(-0.725362\pi\) |
−0.870916 | + | 0.491433i | \(0.836473\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.36924 | − | 15.6505i | 0.0773941 | − | 0.884618i | −0.853921 | − | 0.520403i | \(-0.825782\pi\) |
0.931315 | − | 0.364215i | \(-0.118663\pi\) | |||||||
\(314\) | −2.28318 | + | 3.95459i | −0.128847 | + | 0.223170i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.408430 | + | 0.707422i | 0.0229760 | + | 0.0397956i | ||||
\(317\) | −12.8207 | + | 5.97838i | −0.720081 | + | 0.335779i | −0.747880 | − | 0.663834i | \(-0.768928\pi\) |
0.0277988 | + | 0.999614i | \(0.491150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00744 | − | 3.58413i | 0.168384 | − | 0.200673i | ||||
\(320\) | −15.1094 | − | 1.57372i | −0.844643 | − | 0.0879735i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.72514 | − | 3.89191i | 0.151866 | − | 0.216888i | ||||
\(323\) | 0.0243419 | + | 0.0243419i | 0.00135442 | + | 0.00135442i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.4235 | − | 3.07315i | −1.41024 | − | 0.170467i | ||||
\(326\) | −10.8987 | + | 1.92174i | −0.603624 | + | 0.106435i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.43764 | − | 5.22754i | 0.134596 | − | 0.288643i | ||||
\(329\) | 3.64488 | + | 3.05842i | 0.200949 | + | 0.168616i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8479 | + | 5.76816i | 0.871078 | + | 0.317047i | 0.738604 | − | 0.674140i | \(-0.235485\pi\) |
0.132475 | + | 0.991186i | \(0.457708\pi\) | |||||||
\(332\) | 9.21668 | + | 2.46960i | 0.505831 | + | 0.135537i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.768076 | − | 0.443449i | −0.0420273 | − | 0.0242645i | ||||
\(335\) | −17.2905 | + | 28.8375i | −0.944680 | + | 1.57556i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.0410 | + | 11.2321i | −0.873811 | + | 0.611849i | −0.922086 | − | 0.386985i | \(-0.873516\pi\) |
0.0482752 | + | 0.998834i | \(0.484628\pi\) | |||||||
\(338\) | −10.6826 | + | 7.48005i | −0.581058 | + | 0.406861i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.40027 | − | 9.00672i | 0.292871 | − | 0.488458i | ||||
\(341\) | −4.76543 | − | 2.75132i | −0.258063 | − | 0.148993i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.54371 | − | 2.28928i | −0.461317 | − | 0.123610i | ||||
\(344\) | 29.9216 | + | 10.8906i | 1.61326 | + | 0.587180i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.0840 | + | 8.46151i | 0.542121 | + | 0.454894i | ||||
\(347\) | −4.69183 | + | 10.0617i | −0.251871 | + | 0.540138i | −0.991069 | − | 0.133349i | \(-0.957427\pi\) |
0.739199 | + | 0.673488i | \(0.235205\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.91569 | + | 1.04309i | −0.316659 | + | 0.0558356i | −0.329719 | − | 0.944079i | \(-0.606954\pi\) |
0.0130596 | + | 0.999915i | \(0.495843\pi\) | |||||||
\(350\) | −1.98148 | − | 2.52638i | −0.105915 | − | 0.135041i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.99364 | + | 4.99364i | 0.266162 | + | 0.266162i | ||||
\(353\) | −6.60297 | + | 9.43001i | −0.351440 | + | 0.501909i | −0.955484 | − | 0.295042i | \(-0.904666\pi\) |
0.604044 | + | 0.796951i | \(0.293555\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.9075 | − | 1.44853i | −0.738135 | − | 0.0768802i | ||||
\(356\) | −7.79749 | + | 9.29269i | −0.413266 | + | 0.492512i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.65644 | − | 3.10395i | 0.351804 | − | 0.164049i | ||||
\(359\) | −7.64807 | − | 13.2468i | −0.403649 | − | 0.699141i | 0.590514 | − | 0.807028i | \(-0.298925\pi\) |
−0.994163 | + | 0.107886i | \(0.965592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49997 | + | 16.4544i | −0.499999 | + | 0.866023i | ||||
\(362\) | 2.25305 | − | 25.7525i | 0.118418 | − | 1.35352i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.38050 | + | 0.596074i | 0.177187 | + | 0.0312428i | ||||
\(365\) | 27.8131 | − | 4.43195i | 1.45581 | − | 0.231979i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.8423 | − | 1.12355i | −0.670361 | − | 0.0586490i | −0.253106 | − | 0.967439i | \(-0.581452\pi\) |
−0.417255 | + | 0.908790i | \(0.637008\pi\) | |||||||
\(368\) | 6.32188 | − | 1.69394i | 0.329551 | − | 0.0883028i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.65437 | − | 0.258988i | 0.189982 | − | 0.0134641i | ||||
\(371\) | 0.374288 | − | 1.02835i | 0.0194321 | − | 0.0533892i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1018 | + | 1.40873i | −0.833720 | + | 0.0729411i | −0.496018 | − | 0.868312i | \(-0.665205\pi\) |
−0.337702 | + | 0.941253i | \(0.609650\pi\) | |||||||
\(374\) | 5.85739 | − | 2.13192i | 0.302878 | − | 0.110239i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.78520 | + | 21.4670i | 0.195207 | + | 1.10707i | ||||
\(377\) | 12.2322 | − | 12.2322i | 0.629989 | − | 0.629989i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.64380i | 0.495369i | 0.968841 | + | 0.247684i | \(0.0796696\pi\) | ||||
−0.968841 | + | 0.247684i | \(0.920330\pi\) | |||||||
\(380\) | −0.0166753 | − | 0.00476463i | −0.000855427 | − | 0.000244420i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.42486 | + | 0.664424i | 0.0729023 | + | 0.0339949i | ||||
\(383\) | 1.26741 | + | 14.4866i | 0.0647619 | + | 0.740232i | 0.957269 | + | 0.289199i | \(0.0933888\pi\) |
−0.892507 | + | 0.451033i | \(0.851056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0333266 | + | 2.01790i | −0.00169848 | + | 0.102842i | ||||
\(386\) | −7.18097 | + | 4.14594i | −0.365502 | + | 0.211023i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.582850 | + | 2.17522i | 0.0295897 | + | 0.110430i | ||||
\(389\) | 12.6045 | − | 10.5764i | 0.639073 | − | 0.536246i | −0.264660 | − | 0.964342i | \(-0.585260\pi\) |
0.903733 | + | 0.428096i | \(0.140815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.86593 | + | 33.2673i | −0.296653 | + | 1.68240i | ||||
\(392\) | −11.2579 | − | 16.0779i | −0.568608 | − | 0.812056i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.18883 | + | 8.56731i | 0.362168 | + | 0.431615i | ||||
\(395\) | −1.47118 | + | 0.994333i | −0.0740229 | + | 0.0500303i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.64123 | + | 21.0533i | −0.283125 | + | 1.05664i | 0.667073 | + | 0.744992i | \(0.267547\pi\) |
−0.950199 | + | 0.311645i | \(0.899120\pi\) | |||||||
\(398\) | −10.1012 | − | 21.6620i | −0.506325 | − | 1.08582i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.146054 | − | 4.42052i | 0.00730270 | − | 0.221026i | ||||
\(401\) | −9.14946 | − | 25.1379i | −0.456902 | − | 1.25533i | −0.927779 | − | 0.373130i | \(-0.878285\pi\) |
0.470877 | − | 0.882199i | \(-0.343938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.6658 | − | 11.6695i | −0.830182 | − | 0.581300i | ||||
\(404\) | 6.61309 | 0.329013 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.16890 | 0.107641 | ||||||||
\(407\) | −1.88633 | − | 1.32082i | −0.0935019 | − | 0.0654707i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.85481 | − | 18.8334i | −0.338949 | − | 0.931253i | −0.985694 | − | 0.168547i | \(-0.946092\pi\) |
0.646745 | − | 0.762706i | \(-0.276130\pi\) | |||||||
\(410\) | 3.97710 | + | 1.52238i | 0.196415 | + | 0.0751850i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.07078 | − | 8.72982i | −0.200553 | − | 0.430088i | ||||
\(413\) | 1.71187 | − | 6.38878i | 0.0842355 | − | 0.314371i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.93862 | + | 20.3645i | −0.193339 | + | 0.999655i | ||||
\(416\) | 16.7838 | + | 20.0021i | 0.822892 | + | 0.980684i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.00590432 | − | 0.00843224i | −0.000288790 | − | 0.000412435i | ||||
\(419\) | −0.389697 | + | 2.21008i | −0.0190379 | + | 0.107969i | −0.992846 | − | 0.119402i | \(-0.961902\pi\) |
0.973808 | + | 0.227372i | \(0.0730133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.9696 | + | 15.0783i | −0.875786 | + | 0.734872i | −0.965308 | − | 0.261113i | \(-0.915911\pi\) |
0.0895219 | + | 0.995985i | \(0.471466\pi\) | |||||||
\(422\) | 2.32672 | + | 8.68342i | 0.113263 | + | 0.422702i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.34185 | − | 2.50677i | 0.210859 | − | 0.121739i | ||||
\(425\) | 20.3596 | + | 10.3256i | 0.987587 | + | 0.500866i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.545349 | + | 6.23337i | 0.0263913 | + | 0.301654i | ||||
\(428\) | 3.23505 | + | 1.50853i | 0.156372 | + | 0.0729176i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.45874 | + | 22.6044i | −0.311468 | + | 1.09008i | ||||
\(431\) | 15.7591i | 0.759089i | 0.925173 | + | 0.379545i | \(0.123919\pi\) | ||||
−0.925173 | + | 0.379545i | \(0.876081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0286 | − | 14.0286i | 0.674170 | − | 0.674170i | −0.284505 | − | 0.958675i | \(-0.591829\pi\) |
0.958675 | + | 0.284505i | \(0.0918291\pi\) | |||||||
\(434\) | −0.442947 | − | 2.51208i | −0.0212621 | − | 0.120584i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.7625 | + | 3.91724i | −0.515432 | + | 0.187602i | ||||
\(437\) | 0.0555739 | − | 0.00486209i | 0.00265846 | − | 0.000232585i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.43394 | − | 3.93972i | 0.0684382 | − | 0.188033i | −0.900759 | − | 0.434320i | \(-0.856989\pi\) |
0.969197 | + | 0.246288i | \(0.0792108\pi\) | |||||||
\(440\) | −6.05928 | + | 6.98365i | −0.288865 | + | 0.332932i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 22.2614 | − | 5.96491i | 1.05886 | − | 0.283722i | ||||
\(443\) | −21.2489 | − | 1.85904i | −1.00957 | − | 0.0883257i | −0.429646 | − | 0.902998i | \(-0.641361\pi\) |
−0.579922 | + | 0.814672i | \(0.696917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.3481 | − | 15.4797i | −1.01200 | − | 0.733808i | ||||
\(446\) | 15.8644 | + | 2.79732i | 0.751201 | + | 0.132457i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.385789 | + | 4.40959i | −0.0182268 | + | 0.208333i | ||||
\(449\) | −9.32000 | + | 16.1427i | −0.439838 | + | 0.761822i | −0.997677 | − | 0.0681276i | \(-0.978297\pi\) |
0.557839 | + | 0.829949i | \(0.311631\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.33838 | − | 2.31815i | −0.0630221 | − | 0.109157i | ||||
\(452\) | −8.30633 | + | 3.87330i | −0.390697 | + | 0.182185i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.00497 | + | 9.53996i | −0.375692 | + | 0.447732i | ||||
\(455\) | −0.773008 | + | 7.42173i | −0.0362392 | + | 0.347936i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.19900 | − | 11.7094i | 0.383533 | − | 0.547742i | −0.580247 | − | 0.814441i | \(-0.697044\pi\) |
0.963780 | + | 0.266699i | \(0.0859328\pi\) | |||||||
\(458\) | 6.29334 | + | 6.29334i | 0.294068 | + | 0.294068i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.55570 | − | 16.0858i | −0.259036 | − | 0.750006i | ||||
\(461\) | −24.9949 | + | 4.40727i | −1.16413 | + | 0.205267i | −0.722135 | − | 0.691752i | \(-0.756839\pi\) |
−0.441992 | + | 0.897019i | \(0.645728\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.43841 | + | 11.6627i | −0.252744 | + | 0.542012i | −0.991213 | − | 0.132276i | \(-0.957772\pi\) |
0.738469 | + | 0.674288i | \(0.235549\pi\) | |||||||
\(464\) | 2.28875 | + | 1.92049i | 0.106252 | + | 0.0891563i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −19.7704 | − | 7.19584i | −0.915846 | − | 0.333341i | ||||
\(467\) | −26.2781 | − | 7.04119i | −1.21600 | − | 0.325828i | −0.406890 | − | 0.913477i | \(-0.633387\pi\) |
−0.809115 | + | 0.587650i | \(0.800053\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.48478 | + | 4.89869i | 0.391791 | + | 0.226200i | ||||
\(470\) | −15.6120 | + | 3.90808i | −0.720126 | + | 0.180266i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.8215 | − | 17.3802i | 1.14250 | − | 0.799988i | ||||
\(473\) | 12.1047 | − | 8.47577i | 0.556572 | − | 0.389716i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.00776886 | − | 0.0368902i | 0.000356460 | − | 0.00169264i | ||||
\(476\) | −2.65002 | − | 1.52999i | −0.121464 | − | 0.0701270i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.50508 | + | 1.47508i | 0.251797 | + | 0.0674687i | ||||
\(479\) | 17.2415 | + | 6.27539i | 0.787784 | + | 0.286730i | 0.704415 | − | 0.709789i | \(-0.251210\pi\) |
0.0833693 | + | 0.996519i | \(0.473432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.52224 | − | 5.47281i | −0.297388 | − | 0.249538i | ||||
\(482\) | 9.60172 | − | 20.5910i | 0.437346 | − | 0.937892i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.19935 | + | 1.62209i | −0.418152 | + | 0.0737315i | ||||
\(485\) | −4.62709 | + | 1.59810i | −0.210105 | + | 0.0725659i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.34114 | + | 4.34114i | 0.196716 | + | 0.196716i | 0.798591 | − | 0.601875i | \(-0.205579\pi\) |
−0.601875 | + | 0.798591i | \(0.705579\pi\) | |||||||
\(488\) | −16.4422 | + | 23.4819i | −0.744302 | + | 1.06297i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.2531 | − | 9.13011i | 0.508364 | − | 0.412456i | ||||
\(491\) | −17.5435 | + | 20.9075i | −0.791728 | + | 0.943544i | −0.999399 | − | 0.0346544i | \(-0.988967\pi\) |
0.207672 | + | 0.978199i | \(0.433411\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.9760 | + | 6.51712i | −0.629448 | + | 0.293516i | ||||
\(494\) | −0.0190300 | − | 0.0329609i | −0.000856199 | − | 0.00148298i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.75694 | − | 3.04310i | 0.0788887 | − | 0.136639i | ||||
\(497\) | −0.355101 | + | 4.05882i | −0.0159284 | + | 0.182063i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.3225 | + | 7.63893i | 1.93938 | + | 0.341965i | 1.00000 | 0.000905893i | \(-0.000288355\pi\) | |
0.939382 | + | 0.342871i | \(0.111399\pi\) | |||||||
\(500\) | −11.4925 | + | 0.433752i | −0.513958 | + | 0.0193980i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.46473 | + | 0.215636i | 0.110006 | + | 0.00962432i | ||||
\(503\) | 4.03331 | − | 1.08072i | 0.179836 | − | 0.0481870i | −0.167777 | − | 0.985825i | \(-0.553659\pi\) |
0.347613 | + | 0.937638i | \(0.386992\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.01625 | + | 14.3395i | 0.0452226 | + | 0.638100i | ||||
\(506\) | 3.45484 | − | 9.49210i | 0.153586 | − | 0.421975i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.92079 | + | 0.255536i | −0.129589 | + | 0.0113376i | ||||
\(509\) | 1.50937 | − | 0.549366i | 0.0669017 | − | 0.0243502i | −0.308353 | − | 0.951272i | \(-0.599778\pi\) |
0.375254 | + | 0.926922i | \(0.377555\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.42504 | − | 8.08181i | −0.0630401 | − | 0.357518i | ||||
\(512\) | −6.92298 | + | 6.92298i | −0.305956 | + | 0.305956i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 12.4454i | − | 0.548945i | ||||||
\(515\) | 18.3038 | − | 10.1684i | 0.806561 | − | 0.448075i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.16819 | + | 4.27520i | 0.403216 | + | 0.188023i | ||||
\(518\) | −0.0930377 | − | 1.06343i | −0.00408784 | − | 0.0467242i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.5684 | + | 23.7701i | −1.07740 | + | 1.04239i | ||||
\(521\) | 28.3338 | − | 16.3586i | 1.24133 | − | 0.716681i | 0.271964 | − | 0.962308i | \(-0.412327\pi\) |
0.969365 | + | 0.245626i | \(0.0789936\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.7572 | − | 40.1466i | −0.470381 | − | 1.75549i | −0.638402 | − | 0.769703i | \(-0.720404\pi\) |
0.168021 | − | 0.985783i | \(-0.446262\pi\) | |||||||
\(524\) | −5.11713 | + | 4.29378i | −0.223543 | + | 0.187575i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.87389 | − | 16.2986i | 0.125307 | − | 0.710654i | ||||
\(527\) | 10.4026 | + | 14.8564i | 0.453144 | + | 0.647156i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.4037 | + | 24.3162i | 0.887116 | + | 1.05722i | ||||
\(530\) | 2.07275 | + | 3.06676i | 0.0900344 | + | 0.133211i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.00130790 | + | 0.00488116i | −5.67048e−5 | + | 0.000211625i | ||||
\(533\) | −4.18262 | − | 8.96966i | −0.181169 | − | 0.388519i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.77389 | + | 7.24656i | −0.119926 | + | 0.313296i | ||||
\(536\) | 15.3515 | + | 42.1779i | 0.663084 | + | 1.82181i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.64303 | + | 1.85067i | 0.113949 | + | 0.0797879i | ||||
\(539\) | −9.10864 | −0.392337 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5826 | 0.626954 | 0.313477 | − | 0.949596i | \(-0.398506\pi\) | ||||
0.313477 | + | 0.949596i | \(0.398506\pi\) | |||||||
\(542\) | 6.83708 | + | 4.78737i | 0.293678 | + | 0.205635i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.96090 | − | 21.8724i | −0.341321 | − | 0.937771i | ||||
\(545\) | −10.1479 | − | 22.7350i | −0.434687 | − | 0.973861i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.97161 | + | 12.8062i | 0.255327 | + | 0.547551i | 0.991632 | − | 0.129099i | \(-0.0412085\pi\) |
−0.736304 | + | 0.676651i | \(0.763431\pi\) | |||||||
\(548\) | 4.93072 | − | 18.4017i | 0.210630 | − | 0.786082i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.45942 | − | 4.09791i | −0.232790 | − | 0.174735i | ||||
\(551\) | 0.0163695 | + | 0.0195084i | 0.000697364 | + | 0.000831086i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.296770 | + | 0.423831i | 0.0126199 | + | 0.0180231i | ||||
\(554\) | 0.422214 | − | 2.39450i | 0.0179382 | − | 0.101732i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.5697 | − | 13.0645i | 0.660301 | − | 0.554058i | ||||
\(557\) | −6.98848 | − | 26.0814i | −0.296111 | − | 1.10510i | −0.940331 | − | 0.340262i | \(-0.889484\pi\) |
0.644220 | − | 0.764841i | \(-0.277182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.3160 | − | 27.3179i | 2.00125 | − | 1.15542i | ||||
\(560\) | −1.28859 | − | 0.0212816i | −0.0544527 | − | 0.000899314i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.66931 | + | 19.0803i | 0.0704155 | + | 0.804853i | ||||
\(563\) | −4.52364 | − | 2.10941i | −0.190649 | − | 0.0889009i | 0.324950 | − | 0.945731i | \(-0.394653\pi\) |
−0.515598 | + | 0.856830i | \(0.672430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.67515 | − | 17.4158i | −0.407037 | − | 0.732690i | ||||
\(566\) | − | 18.5746i | − | 0.780748i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.1987 | + | 13.1987i | −0.553804 | + | 0.553804i | ||||
\(569\) | 2.39518 | + | 13.5837i | 0.100411 | + | 0.569459i | 0.992954 | + | 0.118497i | \(0.0378077\pi\) |
−0.892543 | + | 0.450962i | \(0.851081\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.72552 | − | 1.71995i | 0.197757 | − | 0.0719776i | −0.241243 | − | 0.970465i | \(-0.577555\pi\) |
0.439000 | + | 0.898487i | \(0.355333\pi\) | |||||||
\(572\) | 7.27031 | − | 0.636069i | 0.303987 | − | 0.0265954i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.424397 | − | 1.16602i | 0.0177140 | − | 0.0486688i | ||||
\(575\) | 34.0260 | − | 14.5187i | 1.41898 | − | 0.605471i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.65137 | + | 0.710433i | −0.110378 | + | 0.0295757i | −0.313585 | − | 0.949560i | \(-0.601530\pi\) |
0.203207 | + | 0.979136i | \(0.434863\pi\) | |||||||
\(578\) | −3.77540 | − | 0.330305i | −0.157036 | − | 0.0137389i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.56050 | − | 6.28940i | 0.189364 | − | 0.261153i | ||||
\(581\) | 5.95200 | + | 1.04950i | 0.246930 | + | 0.0435405i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.202782 | − | 2.31781i | 0.00839837 | − | 0.0959938i | ||||
\(584\) | 18.7982 | − | 32.5595i | 0.777876 | − | 1.34732i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.98777 | − | 3.44291i | −0.0821138 | − | 0.142225i | ||||
\(587\) | −18.7722 | + | 8.75362i | −0.774811 | + | 0.361300i | −0.769468 | − | 0.638685i | \(-0.779479\pi\) |
−0.00534328 | + | 0.999986i | \(0.501701\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0192521 | − | 0.0229437i | 0.000793268 | − | 0.000945380i | ||||
\(590\) | 14.0953 | + | 17.3729i | 0.580295 | + | 0.715229i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.843448 | − | 1.20457i | 0.0346655 | − | 0.0495075i | ||||
\(593\) | −33.2020 | − | 33.2020i | −1.36344 | − | 1.36344i | −0.869487 | − | 0.493956i | \(-0.835550\pi\) |
−0.493956 | − | 0.869487i | \(-0.664450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.91032 | − | 5.98130i | 0.119312 | − | 0.245209i | ||||
\(596\) | 15.1924 | − | 2.67882i | 0.622303 | − | 0.109729i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 15.7839 | − | 33.8487i | 0.645452 | − | 1.38418i | ||||
\(599\) | 9.01503 | + | 7.56451i | 0.368344 | + | 0.309078i | 0.808106 | − | 0.589037i | \(-0.200493\pi\) |
−0.439762 | + | 0.898114i | \(0.644937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.4574 | + | 4.89809i | 0.548938 | + | 0.199797i | 0.601575 | − | 0.798817i | \(-0.294540\pi\) |
−0.0526366 | + | 0.998614i | \(0.516763\pi\) | |||||||
\(602\) | 6.61670 | + | 1.77294i | 0.269677 | + | 0.0722596i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.808178 | − | 0.466602i | −0.0328843 | − | 0.0189858i | ||||
\(605\) | −4.93096 | − | 19.6982i | −0.200472 | − | 0.800844i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.7167 | − | 11.7051i | 0.678509 | − | 0.475097i | −0.182819 | − | 0.983147i | \(-0.558522\pi\) |
0.861328 | + | 0.508049i | \(0.169633\pi\) | |||||||
\(608\) | −0.0314873 | + | 0.0220476i | −0.00127698 | + | 0.000894150i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.1516 | − | 10.8834i | −0.734936 | − | 0.440655i | ||||
\(611\) | 32.3913 | + | 18.7011i | 1.31041 | + | 0.756566i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.1941 | + | 8.62637i | 1.30031 | + | 0.348416i | 0.841566 | − | 0.540155i | \(-0.181634\pi\) |
0.458740 | + | 0.888571i | \(0.348301\pi\) | |||||||
\(614\) | 8.25087 | + | 3.00307i | 0.332978 | + | 0.121194i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.06379 | + | 1.73172i | 0.0831523 | + | 0.0697731i | ||||
\(617\) | 0.373483 | − | 0.800937i | 0.0150359 | − | 0.0322445i | −0.898646 | − | 0.438674i | \(-0.855448\pi\) |
0.913682 | + | 0.406429i | \(0.133226\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.2863 | + | 1.99007i | −0.453633 | + | 0.0799877i | −0.395796 | − | 0.918338i | \(-0.629531\pi\) |
−0.0578365 | + | 0.998326i | \(0.518420\pi\) | |||||||
\(620\) | −8.21593 | − | 3.99763i | −0.329960 | − | 0.160549i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.9844 | − | 18.9844i | −0.761204 | − | 0.761204i | ||||
\(623\) | −4.40717 | + | 6.29409i | −0.176569 | + | 0.252167i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.70661 | − | 24.8531i | −0.108264 | − | 0.994122i | ||||
\(626\) | 9.95267 | − | 11.8611i | 0.397789 | − | 0.474066i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.31941 | − | 2.01418i | 0.172363 | − | 0.0803744i | ||||
\(629\) | 3.79491 | + | 6.57297i | 0.151313 | + | 0.262082i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.493720 | − | 0.855149i | 0.0196547 | − | 0.0340429i | −0.856031 | − | 0.516925i | \(-0.827077\pi\) |
0.875685 | + | 0.482882i | \(0.160410\pi\) | |||||||
\(632\) | −0.206592 | + | 2.36136i | −0.00821780 | + | 0.0939299i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.7301 | − | 2.42099i | −0.545293 | − | 0.0961500i | ||||
\(635\) | −1.00294 | − | 6.29404i | −0.0398004 | − | 0.249771i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.5496 | − | 2.93521i | −1.32928 | − | 0.116297i | ||||
\(638\) | 4.45412 | − | 1.19348i | 0.176340 | − | 0.0472502i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.91217 | + | 5.12963i | 0.233699 | + | 0.202766i | ||||
\(641\) | 9.55555 | − | 26.2536i | 0.377421 | − | 1.03696i | −0.595000 | − | 0.803726i | \(-0.702848\pi\) |
0.972421 | − | 0.233231i | \(-0.0749298\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.9171 | + | 2.61741i | −1.17982 | + | 0.103221i | −0.660140 | − | 0.751142i | \(-0.729503\pi\) |
−0.519677 | + | 0.854363i | \(0.673948\pi\) | |||||||
\(644\) | −4.65975 | + | 1.69601i | −0.183620 | + | 0.0668322i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.00589152 | + | 0.0334124i | 0.000231799 | + | 0.00131460i | ||||
\(647\) | 22.0995 | − | 22.0995i | 0.868820 | − | 0.868820i | −0.123522 | − | 0.992342i | \(-0.539419\pi\) |
0.992342 | + | 0.123522i | \(0.0394188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.0622i | − | 0.551988i | ||||||
\(650\) | −18.7880 | − | 16.8530i | −0.736926 | − | 0.661028i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.4684 | + | 4.88147i | 0.409972 | + | 0.191173i | ||||
\(653\) | 0.292733 | + | 3.34596i | 0.0114555 | + | 0.130937i | 0.999769 | − | 0.0214986i | \(-0.00684375\pi\) |
−0.988313 | + | 0.152436i | \(0.951288\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.0968 | − | 10.4359i | −0.394515 | − | 0.407765i | ||||
\(656\) | 1.48032 | − | 0.854663i | 0.0577968 | − | 0.0333690i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.21371 | + | 4.52962i | 0.0473152 | + | 0.176583i | ||||
\(659\) | −19.8580 | + | 16.6629i | −0.773560 | + | 0.649094i | −0.941618 | − | 0.336683i | \(-0.890695\pi\) |
0.168058 | + | 0.985777i | \(0.446250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.41723 | − | 36.3939i | 0.249601 | − | 1.41556i | −0.559958 | − | 0.828521i | \(-0.689183\pi\) |
0.809559 | − | 0.587038i | \(-0.199706\pi\) | |||||||
\(662\) | 9.53378 | + | 13.6156i | 0.370541 | + | 0.529187i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.7979 | + | 21.2107i | 0.690692 | + | 0.823134i | ||||
\(665\) | −0.0107851 | − | 0.00208589i | −0.000418227 | − | 8.08875e-5i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.46788 | + | 24.1385i | −0.250437 | + | 0.934645i | ||||
\(668\) | 0.391202 | + | 0.838935i | 0.0151360 | + | 0.0324594i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −30.2610 | + | 13.5072i | −1.16909 | + | 0.521827i | ||||
\(671\) | 4.54997 | + | 12.5009i | 0.175650 | + | 0.482593i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.90829 | − | 3.43682i | −0.189201 | − | 0.132480i | 0.475138 | − | 0.879911i | \(-0.342398\pi\) |
−0.664339 | + | 0.747431i | \(0.731287\pi\) | |||||||
\(674\) | −19.2999 | −0.743406 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.6111 | 0.523502 | ||||||||
\(677\) | 28.2910 | + | 19.8096i | 1.08731 | + | 0.761345i | 0.972700 | − | 0.232066i | \(-0.0745484\pi\) |
0.114613 | + | 0.993410i | \(0.463437\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.487857 | + | 1.34038i | 0.0187222 | + | 0.0514389i | ||||
\(680\) | 27.8275 | − | 12.4209i | 1.06714 | − | 0.476321i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.29197 | − | 4.91514i | −0.0877639 | − | 0.188210i | ||||
\(683\) | 0.984841 | − | 3.67548i | 0.0376839 | − | 0.140638i | −0.944521 | − | 0.328451i | \(-0.893473\pi\) |
0.982205 | + | 0.187813i | \(0.0601399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6591 | + | 7.86371i | 1.55351 | + | 0.300457i | ||||
\(686\) | −5.60349 | − | 6.67798i | −0.213942 | − | 0.254966i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.41244 | + | 7.72977i | 0.206347 | + | 0.294695i | ||||
\(689\) | 1.49380 | − | 8.47177i | 0.0569093 | − | 0.322749i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.658559 | − | 0.552596i | 0.0250528 | − | 0.0210218i | −0.630175 | − | 0.776453i | \(-0.717017\pi\) |
0.655228 | + | 0.755431i | \(0.272573\pi\) | |||||||
\(692\) | −3.55595 | − | 13.2710i | −0.135177 | − | 0.504487i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.47573 | + | 5.47082i | −0.359694 | + | 0.207669i | ||||
\(695\) | 30.7211 | + | 31.7529i | 1.16532 | + | 1.20446i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.768927 | + | 8.78887i | 0.0291252 | + | 0.332902i | ||||
\(698\) | −5.36559 | − | 2.50202i | −0.203091 | − | 0.0947027i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.181668 | + | 3.34615i | 0.00686641 | + | 0.126473i | ||||
\(701\) | 28.2369i | 1.06649i | 0.845960 | + | 0.533246i | \(0.179028\pi\) | ||||
−0.845960 | + | 0.533246i | \(0.820972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.00886291 | − | 0.00886291i | 0.000334271 | − | 0.000334271i | ||||
\(704\) | 1.63419 | + | 9.26794i | 0.0615908 | + | 0.349299i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.6616 | + | 3.88050i | −0.401254 | + | 0.146045i | ||||
\(707\) | 4.17282 | − | 0.365074i | 0.156935 | − | 0.0137300i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.66301 | + | 7.31657i | −0.100012 | + | 0.274780i | −0.979600 | − | 0.200955i | \(-0.935596\pi\) |
0.879589 | + | 0.475735i | \(0.157818\pi\) | |||||||
\(710\) | −10.4092 | − | 9.03139i | −0.390649 | − | 0.338942i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −34.0018 | + | 9.11075i | −1.27427 | + | 0.341440i | ||||
\(713\) | 29.2787 | + | 2.56156i | 1.09650 | + | 0.0959310i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.49647 | + | 15.6668i | 0.0933628 | + | 0.585907i | ||||
\(716\) | −7.54913 | − | 1.33111i | −0.282124 | − | 0.0497461i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.31391 | − | 15.0181i | 0.0490347 | − | 0.560469i | ||||
\(719\) | 5.23184 | − | 9.06182i | 0.195115 | − | 0.337949i | −0.751823 | − | 0.659365i | \(-0.770825\pi\) |
0.946938 | + | 0.321416i | \(0.104159\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.05057 | − | 5.28374i | −0.113609 | − | 0.196777i | ||||
\(722\) | −16.9713 | + | 7.91387i | −0.631608 | + | 0.294524i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.3429 | + | 20.6685i | −0.644544 | + | 0.768138i | ||||
\(725\) | 14.3385 | + | 8.92226i | 0.532517 | + | 0.331364i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.3885 | − | 14.8363i | 0.385289 | − | 0.550250i | −0.578923 | − | 0.815382i | \(-0.696527\pi\) |
0.964212 | + | 0.265133i | \(0.0854157\pi\) | |||||||
\(728\) | 7.04345 | + | 7.04345i | 0.261048 | + | 0.261048i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24.9598 | + | 12.1447i | 0.923805 | + | 0.449496i | ||||
\(731\) | −47.9642 | + | 8.45739i | −1.77402 | + | 0.312808i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.7723 | − | 27.3902i | 0.471755 | − | 1.01168i | −0.516133 | − | 0.856509i | \(-0.672629\pi\) |
0.987887 | − | 0.155173i | \(-0.0495934\pi\) | |||||||
\(734\) | −9.73284 | − | 8.16683i | −0.359246 | − | 0.301443i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.4450 | − | 12.9009i | −1.30652 | − | 0.475534i | ||||
\(737\) | 20.1202 | + | 5.39119i | 0.741137 | + | 0.198587i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.17194 | − | 1.83132i | −0.116682 | − | 0.0673663i | 0.440523 | − | 0.897741i | \(-0.354793\pi\) |
−0.557205 | + | 0.830375i | \(0.688126\pi\) | |||||||
\(740\) | −3.27936 | − | 1.96625i | −0.120552 | − | 0.0722808i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.883502 | − | 0.618635i | 0.0324344 | − | 0.0227108i | ||||
\(743\) | −26.5204 | + | 18.5698i | −0.972939 | + | 0.681259i | −0.947947 | − | 0.318429i | \(-0.896845\pi\) |
−0.0249919 | + | 0.999688i | \(0.507956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.14329 | + | 32.5308i | 0.298347 | + | 1.19183i | ||||
\(746\) | −13.7959 | − | 7.96506i | −0.505103 | − | 0.291621i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.28407 | − | 1.68381i | −0.229768 | − | 0.0615662i | ||||
\(749\) | 2.12458 | + | 0.773283i | 0.0776303 | + | 0.0282551i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.4509 | − | 13.8040i | −0.600303 | − | 0.503714i | 0.291240 | − | 0.956650i | \(-0.405932\pi\) |
−0.891543 | + | 0.452936i | \(0.850377\pi\) | |||||||
\(752\) | −2.73005 | + | 5.85460i | −0.0995546 | + | 0.213495i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.7903 | − | 2.96058i | 0.611467 | − | 0.107818i | ||||
\(755\) | 0.887563 | − | 1.82412i | 0.0323017 | − | 0.0663865i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3709 | + | 20.3709i | 0.740395 | + | 0.740395i | 0.972654 | − | 0.232259i | \(-0.0746118\pi\) |
−0.232259 | + | 0.972654i | \(0.574612\pi\) | |||||||
\(758\) | −5.45165 | + | 7.78576i | −0.198013 | + | 0.282792i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.0317075 | − | 0.0390804i | −0.00115015 | − | 0.00141759i | ||||
\(761\) | −20.6946 | + | 24.6629i | −0.750179 | + | 0.894028i | −0.997185 | − | 0.0749859i | \(-0.976109\pi\) |
0.247006 | + | 0.969014i | \(0.420553\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.57484 | + | 3.06590i | −0.238025 | + | 0.110993i | ||||
\(764\) | −0.820438 | − | 1.42104i | −0.0296824 | − | 0.0514114i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.16607 | + | 12.4120i | −0.258921 | + | 0.448464i | ||||
\(767\) | 4.53146 | − | 51.7948i | 0.163621 | − | 1.87020i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.27352 | − | 0.577210i | −0.118046 | − | 0.0208147i | 0.114313 | − | 0.993445i | \(-0.463533\pi\) |
−0.232359 | + | 0.972630i | \(0.574644\pi\) | |||||||
\(770\) | −1.16763 | + | 1.61028i | −0.0420783 | + | 0.0580304i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.62135 | + | 0.754271i | 0.310289 | + | 0.0271468i | ||||
\(773\) | 3.47814 | − | 0.931964i | 0.125100 | − | 0.0335204i | −0.195726 | − | 0.980659i | \(-0.562706\pi\) |
0.320826 | + | 0.947138i | \(0.396040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.40570 | − | 18.4294i | 0.266021 | − | 0.662002i | ||||
\(776\) | −2.23502 | + | 6.14068i | −0.0802327 | + | 0.220437i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.1549 | − | 1.41337i | 0.579181 | − | 0.0506718i | ||||
\(779\) | 0.0136910 | − | 0.00498312i | 0.000490531 | − | 0.000178539i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.50420 | + | 8.53071i | 0.0538243 | + | 0.305253i | ||||
\(782\) | −23.5418 | + | 23.5418i | −0.841853 | + | 0.841853i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 5.81658i | − | 0.207735i | ||||||
\(785\) | 5.03122 | + | 9.05649i | 0.179572 | + | 0.323240i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.8637 | − | 15.7909i | −1.20711 | − | 0.562886i | −0.288285 | − | 0.957545i | \(-0.593085\pi\) |
−0.918828 | + | 0.394659i | \(0.870863\pi\) | |||||||
\(788\) | −1.01734 | − | 11.6282i | −0.0362412 | − | 0.414238i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.74983 | − | 0.0288993i | −0.0622560 | − | 0.00102819i | ||||
\(791\) | −5.02741 | + | 2.90258i | −0.178754 | + | 0.103204i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7304 | + | 47.5106i | 0.452070 | + | 1.68715i | ||||
\(794\) | −16.4558 | + | 13.8081i | −0.583995 | + | 0.490030i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.33183 | + | 24.5670i | −0.153538 | + | 0.870756i | ||||
\(797\) | 11.3609 | + | 16.2250i | 0.402423 | + | 0.574719i | 0.968306 | − | 0.249766i | \(-0.0803537\pi\) |
−0.565884 | + | 0.824485i | \(0.691465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.4315 | − | 25.5411i | −0.758194 | − | 0.903580i | ||||
\(800\) | −15.3022 | + | 20.3863i | −0.541015 | + | 0.720765i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.82383 | − | 25.4669i | 0.240958 | − | 0.899267i | ||||
\(803\) | −7.37368 | − | 15.8129i | −0.260211 | − | 0.558025i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.39363 | − | 9.84336i | −0.154855 | − | 0.346933i | ||||
\(806\) | −6.85806 | − | 18.8424i | −0.241565 | − | 0.663694i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.7195 | + | 11.0069i | 0.553010 | + | 0.387222i | ||||
\(809\) | −0.320020 | −0.0112513 | −0.00562564 | − | 0.999984i | \(-0.501791\pi\) | ||||
−0.00562564 | + | 0.999984i | \(0.501791\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.9979 | −0.912910 | −0.456455 | − | 0.889747i | \(-0.650881\pi\) | ||||
−0.456455 | + | 0.889747i | \(0.650881\pi\) | |||||||
\(812\) | −1.85431 | − | 1.29840i | −0.0650736 | − | 0.0455650i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.776235 | − | 2.13269i | −0.0272070 | − | 0.0747506i | ||||
\(815\) | −8.97606 | + | 23.4493i | −0.314418 | + | 0.821391i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0339918 | + | 0.0728957i | 0.00118922 | + | 0.00255030i | ||||
\(818\) | 5.11244 | − | 19.0799i | 0.178752 | − | 0.667112i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.48887 | − | 3.68244i | −0.0869152 | − | 0.128596i | ||||
\(821\) | −3.59136 | − | 4.28001i | −0.125339 | − | 0.149373i | 0.699725 | − | 0.714412i | \(-0.253306\pi\) |
−0.825064 | + | 0.565039i | \(0.808861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.2514 | + | 30.3501i | 0.740776 | + | 1.05794i | 0.995849 | + | 0.0910165i | \(0.0290116\pi\) |
−0.255073 | + | 0.966922i | \(0.582100\pi\) | |||||||
\(824\) | 4.85367 | − | 27.5265i | 0.169086 | − | 0.958932i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.99363 | − | 4.19015i | 0.173750 | − | 0.145794i | ||||
\(827\) | 3.37514 | + | 12.5962i | 0.117365 | + | 0.438013i | 0.999453 | − | 0.0330724i | \(-0.0105292\pi\) |
−0.882088 | + | 0.471085i | \(0.843863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.2366 | + | 12.8383i | −0.772309 | + | 0.445893i | −0.833698 | − | 0.552221i | \(-0.813780\pi\) |
0.0613890 | + | 0.998114i | \(0.480447\pi\) | |||||||
\(830\) | −14.6919 | + | 14.2145i | −0.509962 | + | 0.493391i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.03262 | + | 34.6630i | 0.105137 | + | 1.20172i | ||||
\(833\) | 27.2087 | + | 12.6876i | 0.942725 | + | 0.439600i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.75899 | + | 0.977185i | −0.0608724 | + | 0.0338169i | ||||
\(836\) | 0.0107438i | 0.000371582i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.56397 | + | 1.56397i | −0.0540266 | + | 0.0540266i | ||||
\(839\) | −1.09940 | − | 6.23500i | −0.0379555 | − | 0.215256i | 0.959931 | − | 0.280236i | \(-0.0904128\pi\) |
−0.997887 | + | 0.0649800i | \(0.979302\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.5311 | − | 6.01684i | 0.570039 | − | 0.207477i | ||||
\(842\) | −23.0313 | + | 2.01497i | −0.793710 | + | 0.0694406i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.20906 | − | 8.81681i | 0.110460 | − | 0.303487i | ||||
\(845\) | 2.09165 | + | 29.5136i | 0.0719549 | + | 1.01530i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.71518 | + | 1.53138i | −0.196376 | + | 0.0526188i | ||||
\(848\) | 1.48010 | + | 0.129492i | 0.0508269 | + | 0.00444678i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 10.5999 | + | 19.8455i | 0.363574 | + | 0.680696i | ||||
\(851\) | 12.1127 | + | 2.13579i | 0.415218 | + | 0.0732141i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.29982 | + | 49.1472i | −0.147223 | + | 1.68277i | 0.459752 | + | 0.888047i | \(0.347938\pi\) |
−0.606975 | + | 0.794721i | \(0.707617\pi\) | |||||||
\(854\) | −3.08345 | + | 5.34069i | −0.105513 | + | 0.182755i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.17900 | + | 8.97029i | 0.177015 | + | 0.306598i | ||||
\(857\) | −50.2090 | + | 23.4128i | −1.71511 | + | 0.799768i | −0.720809 | + | 0.693134i | \(0.756229\pi\) |
−0.994298 | + | 0.106634i | \(0.965993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.5665 | + | 12.5926i | −0.360523 | + | 0.429655i | −0.915566 | − | 0.402167i | \(-0.868257\pi\) |
0.555043 | + | 0.831821i | \(0.312702\pi\) | |||||||
\(860\) | 19.0540 | − | 15.4593i | 0.649735 | − | 0.527156i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.90863 | + | 12.7228i | −0.303429 | + | 0.433342i | ||||
\(863\) | 13.7094 | + | 13.7094i | 0.466672 | + | 0.466672i | 0.900835 | − | 0.434162i | \(-0.142956\pi\) |
−0.434162 | + | 0.900835i | \(0.642956\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.2297 | − | 9.74994i | 0.959839 | − | 0.331508i | ||||
\(866\) | 19.2561 | − | 3.39537i | 0.654348 | − | 0.115379i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.12515 | + | 2.41288i | −0.0381899 | + | 0.0818985i | ||||
\(869\) | 0.842676 | + | 0.707089i | 0.0285858 | + | 0.0239864i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 72.3708 | + | 26.3408i | 2.45219 | + | 0.892525i | ||||
\(872\) | −32.1028 | − | 8.60192i | −1.08714 | − | 0.291298i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.0476152 | + | 0.0274906i | 0.00161061 | + | 0.000929885i | ||||
\(875\) | −7.22772 | + | 0.908134i | −0.244342 | + | 0.0307005i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0198 | − | 16.8189i | 0.811093 | − | 0.567933i | −0.0928040 | − | 0.995684i | \(-0.529583\pi\) |
0.903896 | + | 0.427751i | \(0.140694\pi\) | |||||||
\(878\) | 3.38479 | − | 2.37006i | 0.114231 | − | 0.0799856i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.65799 | + | 0.665364i | −0.0896008 | + | 0.0224294i | ||||
\(881\) | −24.7559 | − | 14.2928i | −0.834048 | − | 0.481538i | 0.0211883 | − | 0.999776i | \(-0.493255\pi\) |
−0.855237 | + | 0.518237i | \(0.826588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.2423 | − | 8.37134i | −1.05139 | − | 0.281718i | −0.308562 | − | 0.951204i | \(-0.599848\pi\) |
−0.742825 | + | 0.669486i | \(0.766514\pi\) | |||||||
\(884\) | −22.6033 | − | 8.22694i | −0.760232 | − | 0.276702i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.1041 | − | 13.5129i | −0.541026 | − | 0.453975i | ||||
\(887\) | 9.85973 | − | 21.1443i | 0.331057 | − | 0.709955i | −0.668369 | − | 0.743830i | \(-0.733007\pi\) |
0.999426 | + | 0.0338753i | \(0.0107849\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.82889 | + | 0.322483i | −0.0613391 | + | 0.0108157i | ||||
\(890\) | −8.48435 | − | 24.5654i | −0.284396 | − | 0.823433i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.8887 | − | 11.8887i | −0.398064 | − | 0.398064i | ||||
\(893\) | −0.0315819 | + | 0.0451036i | −0.00105685 | + | 0.00150933i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.72623 | − | 16.5737i | 0.0577016 | − | 0.553999i | ||||
\(896\) | 1.46603 | − | 1.74715i | 0.0489767 | − | 0.0583681i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.6498 | + | 7.76395i | −0.555612 | + | 0.259086i | ||||
\(899\) | 6.70840 | + | 11.6193i | 0.223738 | + | 0.387525i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.83426 | + | 6.64113i | −0.127738 | + | 0.221248i | ||||
\(902\) | 0.229930 | − | 2.62811i | 0.00765582 | − | 0.0875064i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −26.1912 | − | 4.61821i | −0.871105 | − | 0.153599i | ||||
\(905\) | −47.4817 | − | 34.4294i | −1.57834 | − | 1.14447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.44305 | + | 0.738671i | 0.280347 | + | 0.0245272i | 0.226462 | − | 0.974020i | \(-0.427284\pi\) |
0.0538847 | + | 0.998547i | \(0.482840\pi\) | |||||||
\(908\) | 12.5549 | − | 3.36409i | 0.416650 | − | 0.111641i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.81958 | + | 5.55483i | −0.159768 | + | 0.184141i | ||||
\(911\) | 14.3752 | − | 39.4954i | 0.476270 | − | 1.30854i | −0.436366 | − | 0.899769i | \(-0.643735\pi\) |
0.912636 | − | 0.408773i | \(-0.134043\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.8007 | − | 1.11992i | 0.423641 | − | 0.0370638i | ||||
\(914\) | 13.2386 | − | 4.81847i | 0.437896 | − | 0.159381i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.61304 | − | 9.14800i | −0.0532963 | − | 0.302258i | ||||
\(917\) | −2.99184 | + | 2.99184i | −0.0987992 | + | 0.0987992i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.1112i | 1.62003i | 0.586409 | + | 0.810015i | \(0.300541\pi\) | ||||
−0.586409 | + | 0.810015i | \(0.699459\pi\) | |||||||
\(920\) | 13.5674 | − | 47.4835i | 0.447305 | − | 1.56548i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.6706 | − | 10.5715i | −0.746617 | − | 0.348153i | ||||
\(923\) | 2.79138 | + | 31.9057i | 0.0918795 | + | 1.05019i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.75958 | − | 7.41298i | 0.123614 | − | 0.243737i | ||||
\(926\) | −10.9835 | + | 6.34135i | −0.360942 | + | 0.208390i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.45662 | − | 16.6324i | −0.146296 | − | 0.545984i | ||||
\(929\) | −0.315673 | + | 0.264881i | −0.0103569 | + | 0.00869047i | −0.647951 | − | 0.761682i | \(-0.724374\pi\) |
0.637594 | + | 0.770372i | \(0.279930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.00860919 | − | 0.0488251i | 0.000282155 | − | 0.00160018i | ||||
\(932\) | 12.5950 | + | 17.9876i | 0.412564 | + | 0.589203i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.2348 | − | 20.5396i | −0.563939 | − | 0.672077i | ||||
\(935\) | 2.68541 | − | 13.8848i | 0.0878222 | − | 0.454083i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.474207 | + | 1.76977i | −0.0154917 | + | 0.0578157i | −0.973239 | − | 0.229795i | \(-0.926194\pi\) |
0.957747 | + | 0.287611i | \(0.0928610\pi\) | |||||||
\(938\) | 4.08081 | + | 8.75132i | 0.133243 | + | 0.285741i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.6871 | + | 6.00480i | 0.511656 | + | 0.195855i | ||||
\(941\) | −2.52471 | − | 6.93657i | −0.0823031 | − | 0.226126i | 0.891714 | − | 0.452598i | \(-0.149503\pi\) |
−0.974018 | + | 0.226473i | \(0.927281\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.7115 | + | 8.20046i | 0.381378 | + | 0.267044i | ||||
\(944\) | 8.97979 | 0.292267 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.5638 | 0.473511 | ||||||||
\(947\) | 37.0964 | + | 25.9752i | 1.20547 | + | 0.844080i | 0.991158 | − | 0.132685i | \(-0.0423598\pi\) |
0.214313 | + | 0.976765i | \(0.431249\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.0636 | − | 60.6193i | −0.716216 | − | 1.96779i | ||||
\(950\) | 0.0271261 | − | 0.0253910i | 0.000880088 | − | 0.000823792i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.75264 | − | 8.04757i | −0.121624 | − | 0.260823i | ||||
\(953\) | −15.2575 | + | 56.9417i | −0.494238 | + | 1.84452i | 0.0400176 | + | 0.999199i | \(0.487259\pi\) |
−0.534256 | + | 0.845323i | \(0.679408\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.95524 | − | 1.99737i | 0.0956293 | − | 0.0646335i | ||||
\(956\) | −3.82355 | − | 4.55672i | −0.123662 | − | 0.147375i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.3721 | + | 14.8130i | 0.335109 | + | 0.478585i | ||||
\(959\) | 2.09539 | − | 11.8836i | 0.0676638 | − | 0.383740i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.6596 | + | 9.78359i | −0.376117 | + | 0.315600i | ||||
\(962\) | −2.17184 | − | 8.10540i | −0.0700228 | − | 0.261329i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.5357 | + | 11.8563i | −0.661411 | + | 0.381866i | ||||
\(965\) | −0.310658 | + | 18.8101i | −0.0100004 | + | 0.605517i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.13774 | − | 35.8645i | −0.100903 | − | 1.15332i | −0.862772 | − | 0.505593i | \(-0.831274\pi\) |
0.761869 | − | 0.647731i | \(-0.224282\pi\) | |||||||
\(968\) | −24.5670 | − | 11.4558i | −0.789612 | − | 0.368202i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.63901 | − | 1.32550i | −0.148950 | − | 0.0425592i | ||||
\(971\) | − | 28.3419i | − | 0.909536i | −0.890610 | − | 0.454768i | \(-0.849722\pi\) | ||
0.890610 | − | 0.454768i | \(-0.150278\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.10313 | − | 9.10313i | 0.291833 | − | 0.291833i | ||||
\(974\) | 1.05070 | + | 5.95880i | 0.0336665 | + | 0.190932i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.98283 | + | 2.90551i | −0.255524 | + | 0.0930032i | ||||
\(977\) | −0.127935 | + | 0.0111928i | −0.00409300 | + | 0.000358091i | −0.0892021 | − | 0.996014i | \(-0.528432\pi\) |
0.0851091 | + | 0.996372i | \(0.472876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.58725 | + | 15.3509i | −0.178569 | + | 0.490615i | ||||
\(980\) | −15.0866 | + | 1.06920i | −0.481924 | + | 0.0341543i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.9825 | + | 6.96199i | −0.829135 | + | 0.222166i | ||||
\(983\) | 42.4506 | + | 3.71395i | 1.35396 | + | 0.118457i | 0.740921 | − | 0.671592i | \(-0.234389\pi\) |
0.613044 | + | 0.790049i | \(0.289945\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.0578 | − | 3.99289i | 0.798407 | − | 0.127224i | ||||
\(986\) | −14.9674 | − | 2.63916i | −0.476660 | − | 0.0840480i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.00346213 | + | 0.0395723i | −0.000110145 | + | 0.00125896i | ||||
\(989\) | −39.4634 | + | 68.3525i | −1.25486 | + | 2.17348i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.60146 | − | 16.6302i | −0.305001 | − | 0.528276i | 0.672261 | − | 0.740314i | \(-0.265323\pi\) |
−0.977261 | + | 0.212038i | \(0.931990\pi\) | |||||||
\(992\) | −18.3539 | + | 8.55855i | −0.582736 | + | 0.271734i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.58114 | + | 3.07608i | −0.0818688 | + | 0.0975674i | ||||
\(995\) | −53.9357 | − | 5.61766i | −1.70988 | − | 0.178092i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.0633 | + | 24.3689i | −0.540400 | + | 0.771771i | −0.992766 | − | 0.120061i | \(-0.961691\pi\) |
0.452367 | + | 0.891832i | \(0.350580\pi\) | |||||||
\(998\) | 30.6574 | + | 30.6574i | 0.970443 | + | 0.970443i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.2.r.a.152.10 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.122.7 | yes | 192 | ||
5.3 | odd | 4 | inner | 405.2.r.a.233.10 | 192 | ||
15.2 | even | 4 | 675.2.ba.b.68.10 | 192 | |||
15.8 | even | 4 | 135.2.q.a.68.7 | yes | 192 | ||
15.14 | odd | 2 | 675.2.ba.b.257.10 | 192 | |||
27.2 | odd | 18 | inner | 405.2.r.a.332.10 | 192 | ||
27.25 | even | 9 | 135.2.q.a.2.7 | ✓ | 192 | ||
135.52 | odd | 36 | 675.2.ba.b.218.10 | 192 | |||
135.79 | even | 18 | 675.2.ba.b.407.10 | 192 | |||
135.83 | even | 36 | inner | 405.2.r.a.8.10 | 192 | ||
135.133 | odd | 36 | 135.2.q.a.83.7 | yes | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.2.7 | ✓ | 192 | 27.25 | even | 9 | ||
135.2.q.a.68.7 | yes | 192 | 15.8 | even | 4 | ||
135.2.q.a.83.7 | yes | 192 | 135.133 | odd | 36 | ||
135.2.q.a.122.7 | yes | 192 | 3.2 | odd | 2 | ||
405.2.r.a.8.10 | 192 | 135.83 | even | 36 | inner | ||
405.2.r.a.152.10 | 192 | 1.1 | even | 1 | trivial | ||
405.2.r.a.233.10 | 192 | 5.3 | odd | 4 | inner | ||
405.2.r.a.332.10 | 192 | 27.2 | odd | 18 | inner | ||
675.2.ba.b.68.10 | 192 | 15.2 | even | 4 | |||
675.2.ba.b.218.10 | 192 | 135.52 | odd | 36 | |||
675.2.ba.b.257.10 | 192 | 15.14 | odd | 2 | |||
675.2.ba.b.407.10 | 192 | 135.79 | even | 18 |