Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (of order \(6\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 324.4 | ||
Character | \(\chi\) | \(=\) | 637.324 |
Dual form | 637.2.r.g.116.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.43372 | − | 0.827759i | −1.01379 | − | 0.585314i | −0.101493 | − | 0.994836i | \(-0.532362\pi\) |
−0.912300 | + | 0.409522i | \(0.865695\pi\) | |||||||
\(3\) | 0.247488 | + | 0.428663i | 0.142888 | + | 0.247488i | 0.928583 | − | 0.371125i | \(-0.121028\pi\) |
−0.785695 | + | 0.618614i | \(0.787695\pi\) | |||||||
\(4\) | 0.370370 | + | 0.641500i | 0.185185 | + | 0.320750i | ||||
\(5\) | 2.48886 | + | 1.43695i | 1.11305 | + | 0.642622i | 0.939619 | − | 0.342223i | \(-0.111180\pi\) |
0.173435 | + | 0.984845i | \(0.444513\pi\) | |||||||
\(6\) | − | 0.819443i | − | 0.334536i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.08473i | 0.737063i | ||||||||
\(9\) | 1.37750 | − | 2.38590i | 0.459166 | − | 0.795299i | ||||
\(10\) | −2.37889 | − | 4.12036i | −0.752271 | − | 1.30297i | ||||
\(11\) | −2.23554 | + | 1.29069i | −0.674040 | + | 0.389157i | −0.797606 | − | 0.603179i | \(-0.793900\pi\) |
0.123565 | + | 0.992336i | \(0.460567\pi\) | |||||||
\(12\) | −0.183325 | + | 0.317527i | −0.0529212 | + | 0.0916623i | ||||
\(13\) | 3.54562 | − | 0.654682i | 0.983377 | − | 0.181576i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.42251i | 0.367291i | ||||||||
\(16\) | 2.46639 | − | 4.27192i | 0.616598 | − | 1.06798i | ||||
\(17\) | −1.13792 | − | 1.97093i | −0.275986 | − | 0.478022i | 0.694397 | − | 0.719592i | \(-0.255671\pi\) |
−0.970383 | + | 0.241570i | \(0.922338\pi\) | |||||||
\(18\) | −3.94990 | + | 2.28047i | −0.931000 | + | 0.537513i | ||||
\(19\) | 3.80679 | + | 2.19785i | 0.873338 | + | 0.504222i | 0.868456 | − | 0.495766i | \(-0.165113\pi\) |
0.00488206 | + | 0.999988i | \(0.498446\pi\) | |||||||
\(20\) | 2.12881i | 0.476016i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.27352 | 0.911117 | ||||||||
\(23\) | −3.58463 | + | 6.20876i | −0.747447 | + | 1.29462i | 0.201595 | + | 0.979469i | \(0.435387\pi\) |
−0.949043 | + | 0.315148i | \(0.897946\pi\) | |||||||
\(24\) | −0.893645 | + | 0.515946i | −0.182414 | + | 0.105317i | ||||
\(25\) | 1.62963 | + | 2.82260i | 0.325926 | + | 0.564520i | ||||
\(26\) | −5.62534 | − | 1.99628i | −1.10322 | − | 0.391504i | ||||
\(27\) | 2.84859 | 0.548212 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.19574 | 1.15052 | 0.575260 | − | 0.817971i | \(-0.304901\pi\) | ||||
0.575260 | + | 0.817971i | \(0.304901\pi\) | |||||||
\(30\) | 1.17750 | − | 2.03948i | 0.214980 | − | 0.372357i | ||||
\(31\) | −5.93577 | + | 3.42702i | −1.06610 | + | 0.615511i | −0.927112 | − | 0.374784i | \(-0.877717\pi\) |
−0.138983 | + | 0.990295i | \(0.544383\pi\) | |||||||
\(32\) | −3.46138 | + | 1.99843i | −0.611891 | + | 0.353276i | ||||
\(33\) | −1.10654 | − | 0.638861i | −0.192624 | − | 0.111211i | ||||
\(34\) | 3.76769i | 0.646154i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.04074 | 0.340123 | ||||||||
\(37\) | 5.10298 | + | 2.94621i | 0.838925 | + | 0.484353i | 0.856899 | − | 0.515485i | \(-0.172388\pi\) |
−0.0179738 | + | 0.999838i | \(0.505722\pi\) | |||||||
\(38\) | −3.63859 | − | 6.30221i | −0.590256 | − | 1.02235i | ||||
\(39\) | 1.15814 | + | 1.35785i | 0.185450 | + | 0.217429i | ||||
\(40\) | −2.99564 | + | 5.18860i | −0.473653 | + | 0.820390i | ||||
\(41\) | − | 3.98014i | − | 0.621594i | −0.950476 | − | 0.310797i | \(-0.899404\pi\) | ||
0.950476 | − | 0.310797i | \(-0.100596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.31425 | 0.200422 | 0.100211 | − | 0.994966i | \(-0.468048\pi\) | ||||
0.100211 | + | 0.994966i | \(0.468048\pi\) | |||||||
\(44\) | −1.65595 | − | 0.956065i | −0.249644 | − | 0.144132i | ||||
\(45\) | 6.85682 | − | 3.95878i | 1.02215 | − | 0.590141i | ||||
\(46\) | 10.2787 | − | 5.93442i | 1.51551 | − | 0.874983i | ||||
\(47\) | 1.17094 | + | 0.676040i | 0.170799 | + | 0.0986106i | 0.582962 | − | 0.812499i | \(-0.301894\pi\) |
−0.412164 | + | 0.911110i | \(0.635227\pi\) | |||||||
\(48\) | 2.44161 | 0.352417 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 5.39576i | − | 0.763076i | ||||||
\(51\) | 0.563244 | − | 0.975567i | 0.0788699 | − | 0.136607i | ||||
\(52\) | 1.73317 | + | 2.03204i | 0.240347 | + | 0.281793i | ||||
\(53\) | 4.14389 | + | 7.17742i | 0.569207 | + | 0.985895i | 0.996645 | + | 0.0818503i | \(0.0260830\pi\) |
−0.427438 | + | 0.904045i | \(0.640584\pi\) | |||||||
\(54\) | −4.08408 | − | 2.35795i | −0.555773 | − | 0.320876i | ||||
\(55\) | −7.41860 | −1.00032 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.17577i | 0.288188i | ||||||||
\(58\) | −8.88296 | − | 5.12858i | −1.16639 | − | 0.673416i | ||||
\(59\) | 8.32324 | − | 4.80543i | 1.08359 | − | 0.625613i | 0.151730 | − | 0.988422i | \(-0.451515\pi\) |
0.931864 | + | 0.362809i | \(0.118182\pi\) | |||||||
\(60\) | −0.912540 | + | 0.526855i | −0.117808 | + | 0.0680167i | ||||
\(61\) | 4.77650 | − | 8.27315i | 0.611569 | − | 1.05927i | −0.379407 | − | 0.925230i | \(-0.623872\pi\) |
0.990976 | − | 0.134038i | \(-0.0427946\pi\) | |||||||
\(62\) | 11.3470 | 1.44107 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.24870 | −0.406087 | ||||||||
\(65\) | 9.76530 | + | 3.46545i | 1.21124 | + | 0.429836i | ||||
\(66\) | 1.05765 | + | 1.83190i | 0.130187 | + | 0.225491i | ||||
\(67\) | 13.7781 | − | 7.95477i | 1.68326 | − | 0.971830i | 0.723787 | − | 0.690024i | \(-0.242400\pi\) |
0.959471 | − | 0.281806i | \(-0.0909334\pi\) | |||||||
\(68\) | 0.842903 | − | 1.45995i | 0.102217 | − | 0.177045i | ||||
\(69\) | −3.54862 | −0.427204 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.79396i | 0.568938i | 0.958685 | + | 0.284469i | \(0.0918173\pi\) | ||||
−0.958685 | + | 0.284469i | \(0.908183\pi\) | |||||||
\(72\) | 4.97395 | + | 2.87171i | 0.586185 | + | 0.338434i | ||||
\(73\) | −4.94074 | + | 2.85253i | −0.578269 | + | 0.333864i | −0.760445 | − | 0.649402i | \(-0.775019\pi\) |
0.182176 | + | 0.983266i | \(0.441686\pi\) | |||||||
\(74\) | −4.87750 | − | 8.44808i | −0.566998 | − | 0.982069i | ||||
\(75\) | −0.806629 | + | 1.39712i | −0.0931415 | + | 0.161326i | ||||
\(76\) | 3.25607i | 0.373497i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.536475 | − | 2.90543i | −0.0607438 | − | 0.328975i | ||||
\(79\) | 1.00713 | − | 1.74440i | 0.113311 | − | 0.196260i | −0.803792 | − | 0.594910i | \(-0.797188\pi\) |
0.917103 | + | 0.398650i | \(0.130521\pi\) | |||||||
\(80\) | 12.2770 | − | 7.08815i | 1.37261 | − | 0.792479i | ||||
\(81\) | −3.42750 | − | 5.93661i | −0.380834 | − | 0.659623i | ||||
\(82\) | −3.29460 | + | 5.70641i | −0.363828 | + | 0.630168i | ||||
\(83\) | 3.11798i | 0.342243i | 0.985250 | + | 0.171122i | \(0.0547391\pi\) | ||||
−0.985250 | + | 0.171122i | \(0.945261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.54052i | − | 0.709419i | ||||||
\(86\) | −1.88427 | − | 1.08789i | −0.203187 | − | 0.117310i | ||||
\(87\) | 1.53337 | + | 2.65588i | 0.164395 | + | 0.284740i | ||||
\(88\) | −2.69074 | − | 4.66049i | −0.286833 | − | 0.496810i | ||||
\(89\) | −11.3089 | − | 6.52918i | −1.19874 | − | 0.692092i | −0.238464 | − | 0.971151i | \(-0.576644\pi\) |
−0.960274 | + | 0.279060i | \(0.909977\pi\) | |||||||
\(90\) | −13.1077 | −1.38167 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.31056 | −0.553664 | ||||||||
\(93\) | −2.93807 | − | 1.69629i | −0.304663 | − | 0.175898i | ||||
\(94\) | −1.11920 | − | 1.93850i | −0.115436 | − | 0.199942i | ||||
\(95\) | 6.31639 | + | 10.9403i | 0.648048 | + | 1.12245i | ||||
\(96\) | −1.71330 | − | 0.989176i | −0.174863 | − | 0.100957i | ||||
\(97\) | − | 14.0382i | − | 1.42536i | −0.701488 | − | 0.712682i | \(-0.747480\pi\) | ||
0.701488 | − | 0.712682i | \(-0.252520\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.11169i | 0.714752i | ||||||||
\(100\) | −1.20713 | + | 2.09081i | −0.120713 | + | 0.209081i | ||||
\(101\) | 8.72413 | + | 15.1106i | 0.868083 | + | 1.50356i | 0.863953 | + | 0.503573i | \(0.167981\pi\) |
0.00413039 | + | 0.999991i | \(0.498685\pi\) | |||||||
\(102\) | −1.61507 | + | 0.932461i | −0.159916 | + | 0.0923274i | ||||
\(103\) | 3.27849 | − | 5.67851i | 0.323039 | − | 0.559520i | −0.658074 | − | 0.752953i | \(-0.728629\pi\) |
0.981114 | + | 0.193433i | \(0.0619621\pi\) | |||||||
\(104\) | 1.36483 | + | 7.39164i | 0.133833 | + | 0.724810i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 13.7206i | − | 1.33266i | ||||||
\(107\) | −7.80102 | + | 13.5118i | −0.754153 | + | 1.30623i | 0.191642 | + | 0.981465i | \(0.438619\pi\) |
−0.945794 | + | 0.324766i | \(0.894715\pi\) | |||||||
\(108\) | 1.05503 | + | 1.82737i | 0.101521 | + | 0.175839i | ||||
\(109\) | −8.67508 | + | 5.00856i | −0.830922 | + | 0.479733i | −0.854168 | − | 0.519997i | \(-0.825933\pi\) |
0.0232461 | + | 0.999730i | \(0.492600\pi\) | |||||||
\(110\) | 10.6362 | + | 6.14082i | 1.01412 | + | 0.585504i | ||||
\(111\) | 2.91661i | 0.276832i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.95074 | −0.371654 | −0.185827 | − | 0.982582i | \(-0.559496\pi\) | ||||
−0.185827 | + | 0.982582i | \(0.559496\pi\) | |||||||
\(114\) | 1.80102 | − | 3.11945i | 0.168681 | − | 0.292163i | ||||
\(115\) | −17.8433 | + | 10.3018i | −1.66390 | + | 0.960652i | ||||
\(116\) | 2.29472 | + | 3.97457i | 0.213059 | + | 0.369029i | ||||
\(117\) | 3.32208 | − | 9.36130i | 0.307126 | − | 0.865453i | ||||
\(118\) | −15.9109 | −1.46472 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.96555 | −0.270716 | ||||||||
\(121\) | −2.16824 | + | 3.75551i | −0.197113 | + | 0.341410i | ||||
\(122\) | −13.6963 | + | 7.90759i | −1.24001 | + | 0.715920i | ||||
\(123\) | 1.70614 | − | 0.985039i | 0.153837 | − | 0.0888180i | ||||
\(124\) | −4.39686 | − | 2.53853i | −0.394850 | − | 0.227967i | ||||
\(125\) | − | 5.00270i | − | 0.447455i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.37353 | −0.210616 | −0.105308 | − | 0.994440i | \(-0.533583\pi\) | ||||
−0.105308 | + | 0.994440i | \(0.533583\pi\) | |||||||
\(128\) | 11.5805 | + | 6.68600i | 1.02358 | + | 0.590964i | ||||
\(129\) | 0.325263 | + | 0.563372i | 0.0286378 | + | 0.0496021i | ||||
\(130\) | −11.1322 | − | 13.0518i | −0.976355 | − | 1.14472i | ||||
\(131\) | 1.06773 | − | 1.84936i | 0.0932878 | − | 0.161579i | −0.815605 | − | 0.578609i | \(-0.803596\pi\) |
0.908893 | + | 0.417030i | \(0.136929\pi\) | |||||||
\(132\) | − | 0.946460i | − | 0.0823788i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −26.3385 | −2.27530 | ||||||||
\(135\) | 7.08976 | + | 4.09327i | 0.610189 | + | 0.352293i | ||||
\(136\) | 4.10886 | − | 2.37225i | 0.352332 | − | 0.203419i | ||||
\(137\) | −0.371707 | + | 0.214605i | −0.0317570 | + | 0.0183349i | −0.515794 | − | 0.856712i | \(-0.672503\pi\) |
0.484037 | + | 0.875047i | \(0.339170\pi\) | |||||||
\(138\) | 5.08773 | + | 2.93740i | 0.433096 | + | 0.250048i | ||||
\(139\) | 19.4858 | 1.65276 | 0.826381 | − | 0.563112i | \(-0.190396\pi\) | ||||
0.826381 | + | 0.563112i | \(0.190396\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.669248i | 0.0563609i | ||||||||
\(142\) | 3.96824 | − | 6.87319i | 0.333007 | − | 0.576786i | ||||
\(143\) | −7.08137 | + | 6.03985i | −0.592174 | + | 0.505078i | ||||
\(144\) | −6.79491 | − | 11.7691i | −0.566242 | − | 0.980760i | ||||
\(145\) | 15.4204 | + | 8.90295i | 1.28059 | + | 0.739350i | ||||
\(146\) | 9.44485 | 0.781661 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.36475i | 0.358780i | ||||||||
\(149\) | −19.8323 | − | 11.4502i | −1.62473 | − | 0.938037i | −0.985631 | − | 0.168911i | \(-0.945975\pi\) |
−0.639097 | − | 0.769126i | \(-0.720692\pi\) | |||||||
\(150\) | 2.31296 | − | 1.33539i | 0.188853 | − | 0.109034i | ||||
\(151\) | −9.71744 | + | 5.61037i | −0.790794 | + | 0.456565i | −0.840242 | − | 0.542211i | \(-0.817587\pi\) |
0.0494478 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(152\) | −4.58192 | + | 7.93613i | −0.371643 | + | 0.643705i | ||||
\(153\) | −6.26993 | −0.506894 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.6978 | −1.58216 | ||||||||
\(156\) | −0.442119 | + | 1.24585i | −0.0353978 | + | 0.0997478i | ||||
\(157\) | −1.89400 | − | 3.28050i | −0.151157 | − | 0.261812i | 0.780496 | − | 0.625161i | \(-0.214967\pi\) |
−0.931653 | + | 0.363349i | \(0.881633\pi\) | |||||||
\(158\) | −2.88788 | + | 1.66732i | −0.229748 | + | 0.132645i | ||||
\(159\) | −2.05113 | + | 3.55266i | −0.162665 | + | 0.281744i | ||||
\(160\) | −11.4865 | −0.908091 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 11.3486i | 0.891629i | ||||||||
\(163\) | −16.9853 | − | 9.80649i | −1.33039 | − | 0.768103i | −0.345034 | − | 0.938590i | \(-0.612133\pi\) |
−0.985360 | + | 0.170487i | \(0.945466\pi\) | |||||||
\(164\) | 2.55326 | − | 1.47413i | 0.199376 | − | 0.115110i | ||||
\(165\) | −1.83602 | − | 3.18008i | −0.142934 | − | 0.247569i | ||||
\(166\) | 2.58094 | − | 4.47032i | 0.200320 | − | 0.346964i | ||||
\(167\) | 10.2922i | 0.796435i | 0.917291 | + | 0.398217i | \(0.130371\pi\) | ||||
−0.917291 | + | 0.398217i | \(0.869629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1428 | − | 4.64250i | 0.934060 | − | 0.357116i | ||||
\(170\) | −5.41397 | + | 9.37728i | −0.415233 | + | 0.719204i | ||||
\(171\) | 10.4877 | − | 6.05508i | 0.802015 | − | 0.463044i | ||||
\(172\) | 0.486761 | + | 0.843094i | 0.0371151 | + | 0.0642853i | ||||
\(173\) | −3.00220 | + | 5.19995i | −0.228253 | + | 0.395345i | −0.957290 | − | 0.289128i | \(-0.906635\pi\) |
0.729038 | + | 0.684474i | \(0.239968\pi\) | |||||||
\(174\) | − | 5.07706i | − | 0.384891i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.7334i | 0.959815i | ||||||||
\(177\) | 4.11981 | + | 2.37858i | 0.309664 | + | 0.178785i | ||||
\(178\) | 10.8092 | + | 18.7220i | 0.810182 | + | 1.40328i | ||||
\(179\) | −3.87565 | − | 6.71282i | −0.289680 | − | 0.501740i | 0.684054 | − | 0.729432i | \(-0.260215\pi\) |
−0.973733 | + | 0.227692i | \(0.926882\pi\) | |||||||
\(180\) | 5.07912 | + | 2.93243i | 0.378575 | + | 0.218570i | ||||
\(181\) | −19.9999 | −1.48658 | −0.743289 | − | 0.668970i | \(-0.766735\pi\) | ||||
−0.743289 | + | 0.668970i | \(0.766735\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.72852 | 0.349542 | ||||||||
\(184\) | −12.9436 | − | 7.47298i | −0.954213 | − | 0.550915i | ||||
\(185\) | 8.46708 | + | 14.6654i | 0.622512 | + | 1.07822i | ||||
\(186\) | 2.80825 | + | 4.86402i | 0.205911 | + | 0.356648i | ||||
\(187\) | 5.08773 | + | 2.93740i | 0.372052 | + | 0.214804i | ||||
\(188\) | 1.00154i | 0.0730448i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 20.9138i | − | 1.51725i | ||||||
\(191\) | −10.2418 | + | 17.7392i | −0.741068 | + | 1.28357i | 0.210942 | + | 0.977499i | \(0.432347\pi\) |
−0.952010 | + | 0.306068i | \(0.900986\pi\) | |||||||
\(192\) | −0.804015 | − | 1.39260i | −0.0580248 | − | 0.100502i | ||||
\(193\) | −10.7672 | + | 6.21647i | −0.775043 | + | 0.447471i | −0.834671 | − | 0.550750i | \(-0.814342\pi\) |
0.0596279 | + | 0.998221i | \(0.481009\pi\) | |||||||
\(194\) | −11.6202 | + | 20.1269i | −0.834285 | + | 1.44502i | ||||
\(195\) | 0.931292 | + | 5.04368i | 0.0666912 | + | 0.361185i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9805i | 1.35231i | 0.736761 | + | 0.676154i | \(0.236354\pi\) | ||||
−0.736761 | + | 0.676154i | \(0.763646\pi\) | |||||||
\(198\) | 5.88677 | − | 10.1962i | 0.418354 | − | 0.724611i | ||||
\(199\) | −6.40940 | − | 11.1014i | −0.454350 | − | 0.786958i | 0.544300 | − | 0.838891i | \(-0.316795\pi\) |
−0.998651 | + | 0.0519325i | \(0.983462\pi\) | |||||||
\(200\) | −5.88436 | + | 3.39734i | −0.416087 | + | 0.240228i | ||||
\(201\) | 6.81982 | + | 3.93743i | 0.481033 | + | 0.277725i | ||||
\(202\) | − | 28.8859i | − | 2.03241i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.834435 | 0.0584221 | ||||||||
\(205\) | 5.71925 | − | 9.90603i | 0.399450 | − | 0.691867i | ||||
\(206\) | −9.40088 | + | 5.42760i | −0.654990 | + | 0.378159i | ||||
\(207\) | 9.87565 | + | 17.1051i | 0.686405 | + | 1.18889i | ||||
\(208\) | 5.94813 | − | 16.7613i | 0.412429 | − | 1.16219i | ||||
\(209\) | −11.3470 | −0.784887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.86926 | −0.541743 | −0.270871 | − | 0.962616i | \(-0.587312\pi\) | ||||
−0.270871 | + | 0.962616i | \(0.587312\pi\) | |||||||
\(212\) | −3.06954 | + | 5.31660i | −0.210817 | + | 0.365146i | ||||
\(213\) | −2.05499 | + | 1.18645i | −0.140806 | + | 0.0812941i | ||||
\(214\) | 22.3690 | − | 12.9147i | 1.52911 | − | 0.882832i | ||||
\(215\) | 3.27100 | + | 1.88851i | 0.223080 | + | 0.128796i | ||||
\(216\) | 5.93854i | 0.404066i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.5835 | 1.12318 | ||||||||
\(219\) | −2.44555 | − | 1.41194i | −0.165255 | − | 0.0954100i | ||||
\(220\) | −2.74763 | − | 4.75903i | −0.185245 | − | 0.320854i | ||||
\(221\) | −5.32496 | − | 6.24320i | −0.358196 | − | 0.419963i | ||||
\(222\) | 2.41425 | − | 4.18160i | 0.162034 | − | 0.280651i | ||||
\(223\) | − | 7.77059i | − | 0.520357i | −0.965560 | − | 0.260179i | \(-0.916219\pi\) | ||
0.965560 | − | 0.260179i | \(-0.0837815\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.97925 | 0.598617 | ||||||||
\(226\) | 5.66426 | + | 3.27026i | 0.376781 | + | 0.217534i | ||||
\(227\) | 22.1210 | − | 12.7716i | 1.46822 | − | 0.847678i | 0.468855 | − | 0.883275i | \(-0.344667\pi\) |
0.999366 | + | 0.0355975i | \(0.0113334\pi\) | |||||||
\(228\) | −1.39576 | + | 0.805841i | −0.0924363 | + | 0.0533681i | ||||
\(229\) | −11.1705 | − | 6.44929i | −0.738167 | − | 0.426181i | 0.0832356 | − | 0.996530i | \(-0.473475\pi\) |
−0.821402 | + | 0.570349i | \(0.806808\pi\) | |||||||
\(230\) | 34.1098 | 2.24913 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.9164i | 0.848005i | ||||||||
\(233\) | 4.07139 | − | 7.05186i | 0.266726 | − | 0.461983i | −0.701289 | − | 0.712877i | \(-0.747392\pi\) |
0.968014 | + | 0.250895i | \(0.0807249\pi\) | |||||||
\(234\) | −12.5118 | + | 10.6716i | −0.817924 | + | 0.697625i | ||||
\(235\) | 1.94287 | + | 3.36514i | 0.126739 | + | 0.219518i | ||||
\(236\) | 6.16536 | + | 3.55957i | 0.401331 | + | 0.231708i | ||||
\(237\) | 0.997011 | 0.0647628 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 23.8122i | − | 1.54028i | −0.637875 | − | 0.770140i | \(-0.720186\pi\) | ||
0.637875 | − | 0.770140i | \(-0.279814\pi\) | |||||||
\(240\) | 6.07685 | + | 3.50847i | 0.392259 | + | 0.226471i | ||||
\(241\) | −0.249889 | + | 0.144273i | −0.0160967 | + | 0.00929346i | −0.508027 | − | 0.861341i | \(-0.669625\pi\) |
0.491930 | + | 0.870635i | \(0.336292\pi\) | |||||||
\(242\) | 6.21731 | − | 3.58957i | 0.399664 | − | 0.230746i | ||||
\(243\) | 5.96942 | − | 10.3393i | 0.382939 | − | 0.663269i | ||||
\(244\) | 7.07630 | 0.453013 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.26150 | −0.207946 | ||||||||
\(247\) | 14.9363 | + | 5.30050i | 0.950375 | + | 0.337263i | ||||
\(248\) | −7.14440 | − | 12.3745i | −0.453670 | − | 0.785779i | ||||
\(249\) | −1.33656 | + | 0.771665i | −0.0847012 | + | 0.0489023i | ||||
\(250\) | −4.14103 | + | 7.17247i | −0.261902 | + | 0.453627i | ||||
\(251\) | −7.61843 | −0.480871 | −0.240435 | − | 0.970665i | \(-0.577290\pi\) | ||||
−0.240435 | + | 0.970665i | \(0.577290\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 18.5066i | − | 1.16350i | ||||||
\(254\) | 3.40297 | + | 1.96471i | 0.213522 | + | 0.123277i | ||||
\(255\) | 2.80368 | − | 1.61870i | 0.175573 | − | 0.101367i | ||||
\(256\) | −7.82009 | − | 13.5448i | −0.488756 | − | 0.846550i | ||||
\(257\) | 5.82801 | − | 10.0944i | 0.363541 | − | 0.629672i | −0.625000 | − | 0.780625i | \(-0.714901\pi\) |
0.988541 | + | 0.150953i | \(0.0482343\pi\) | |||||||
\(258\) | − | 1.07696i | − | 0.0670484i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.39369 | + | 7.54793i | 0.0864331 | + | 0.468103i | ||||
\(261\) | 8.53463 | − | 14.7824i | 0.528280 | − | 0.915008i | ||||
\(262\) | −3.06165 | + | 1.76764i | −0.189149 | + | 0.109205i | ||||
\(263\) | 6.77638 | + | 11.7370i | 0.417850 | + | 0.723737i | 0.995723 | − | 0.0923895i | \(-0.0294505\pi\) |
−0.577873 | + | 0.816127i | \(0.696117\pi\) | |||||||
\(264\) | 1.33185 | − | 2.30684i | 0.0819698 | − | 0.141976i | ||||
\(265\) | 23.8182i | 1.46314i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.46359i | − | 0.395565i | ||||||
\(268\) | 10.2060 | + | 5.89241i | 0.623428 | + | 0.359936i | ||||
\(269\) | −8.91662 | − | 15.4440i | −0.543656 | − | 0.941640i | −0.998690 | − | 0.0511657i | \(-0.983706\pi\) |
0.455034 | − | 0.890474i | \(-0.349627\pi\) | |||||||
\(270\) | −6.77649 | − | 11.7372i | −0.412404 | − | 0.714304i | ||||
\(271\) | −26.3049 | − | 15.1872i | −1.59791 | − | 0.922555i | −0.991889 | − | 0.127107i | \(-0.959431\pi\) |
−0.606023 | − | 0.795447i | \(-0.707236\pi\) | |||||||
\(272\) | −11.2262 | −0.680690 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.710564 | 0.0429268 | ||||||||
\(275\) | −7.28620 | − | 4.20669i | −0.439375 | − | 0.253673i | ||||
\(276\) | −1.31430 | − | 2.27644i | −0.0791117 | − | 0.137025i | ||||
\(277\) | 2.60712 | + | 4.51567i | 0.156647 | + | 0.271320i | 0.933657 | − | 0.358167i | \(-0.116598\pi\) |
−0.777011 | + | 0.629487i | \(0.783265\pi\) | |||||||
\(278\) | −27.9372 | − | 16.1295i | −1.67556 | − | 0.967385i | ||||
\(279\) | 18.8829i | 1.13049i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.66255i | 0.0991794i | 0.998770 | + | 0.0495897i | \(0.0157914\pi\) | ||||
−0.998770 | + | 0.0495897i | \(0.984209\pi\) | |||||||
\(282\) | 0.553976 | − | 0.959515i | 0.0329888 | − | 0.0571383i | ||||
\(283\) | 6.89783 | + | 11.9474i | 0.410033 | + | 0.710198i | 0.994893 | − | 0.100936i | \(-0.0321838\pi\) |
−0.584860 | + | 0.811134i | \(0.698850\pi\) | |||||||
\(284\) | −3.07532 | + | 1.77554i | −0.182487 | + | 0.105359i | ||||
\(285\) | −3.12647 | + | 5.41520i | −0.185196 | + | 0.320769i | ||||
\(286\) | 15.1523 | − | 2.79780i | 0.895972 | − | 0.165437i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 11.0113i | 0.648849i | ||||||||
\(289\) | 5.91028 | − | 10.2369i | 0.347663 | − | 0.602171i | ||||
\(290\) | −14.7390 | − | 25.5287i | −0.865503 | − | 1.49910i | ||||
\(291\) | 6.01765 | − | 3.47429i | 0.352761 | − | 0.203667i | ||||
\(292\) | −3.65980 | − | 2.11299i | −0.214174 | − | 0.123653i | ||||
\(293\) | 12.8576i | 0.751149i | 0.926792 | + | 0.375574i | \(0.122555\pi\) | ||||
−0.926792 | + | 0.375574i | \(0.877445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.6206 | 1.60813 | ||||||||
\(296\) | −6.14204 | + | 10.6383i | −0.356999 | + | 0.618340i | ||||
\(297\) | −6.36814 | + | 3.67665i | −0.369517 | + | 0.213341i | ||||
\(298\) | 18.9560 | + | 32.8328i | 1.09809 | + | 1.90195i | ||||
\(299\) | −8.64496 | + | 24.3607i | −0.499951 | + | 1.40881i | ||||
\(300\) | −1.19500 | −0.0689936 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 18.5761 | 1.06894 | ||||||||
\(303\) | −4.31824 | + | 7.47941i | −0.248077 | + | 0.429681i | ||||
\(304\) | 18.7781 | − | 10.8415i | 1.07700 | − | 0.621805i | ||||
\(305\) | 23.7761 | − | 13.7272i | 1.36142 | − | 0.786015i | ||||
\(306\) | 8.98933 | + | 5.18999i | 0.513886 | + | 0.296692i | ||||
\(307\) | − | 20.9016i | − | 1.19292i | −0.802644 | − | 0.596458i | \(-0.796574\pi\) | ||
0.802644 | − | 0.596458i | \(-0.203426\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.24555 | 0.184633 | ||||||||
\(310\) | 28.2411 | + | 16.3050i | 1.60399 | + | 0.926062i | ||||
\(311\) | −8.56961 | − | 14.8430i | −0.485938 | − | 0.841669i | 0.513931 | − | 0.857831i | \(-0.328189\pi\) |
−0.999869 | + | 0.0161620i | \(0.994855\pi\) | |||||||
\(312\) | −2.83074 | + | 2.41440i | −0.160259 | + | 0.136688i | ||||
\(313\) | −1.27633 | + | 2.21067i | −0.0721424 | + | 0.124954i | −0.899840 | − | 0.436220i | \(-0.856317\pi\) |
0.827698 | + | 0.561174i | \(0.189650\pi\) | |||||||
\(314\) | 6.27109i | 0.353898i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.49204 | 0.0839339 | ||||||||
\(317\) | 23.6328 | + | 13.6444i | 1.32735 | + | 0.766345i | 0.984889 | − | 0.173188i | \(-0.0554068\pi\) |
0.342459 | + | 0.939533i | \(0.388740\pi\) | |||||||
\(318\) | 5.88149 | − | 3.39568i | 0.329818 | − | 0.190420i | ||||
\(319\) | −13.8508 | + | 7.99678i | −0.775497 | + | 0.447733i | ||||
\(320\) | −8.08557 | − | 4.66821i | −0.451997 | − | 0.260961i | ||||
\(321\) | −7.72264 | −0.431036 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.0039i | − | 0.556633i | ||||||
\(324\) | 2.53889 | − | 4.39748i | 0.141049 | − | 0.244305i | ||||
\(325\) | 7.62595 | + | 8.94097i | 0.423012 | + | 0.495956i | ||||
\(326\) | 16.2348 | + | 28.1195i | 0.899163 | + | 1.55740i | ||||
\(327\) | −4.29397 | − | 2.47912i | −0.237457 | − | 0.137096i | ||||
\(328\) | 8.29751 | 0.458154 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.07912i | 0.334645i | ||||||||
\(331\) | −8.39444 | − | 4.84653i | −0.461400 | − | 0.266390i | 0.251233 | − | 0.967927i | \(-0.419164\pi\) |
−0.712633 | + | 0.701537i | \(0.752497\pi\) | |||||||
\(332\) | −2.00018 | + | 1.15481i | −0.109774 | + | 0.0633783i | ||||
\(333\) | 14.0587 | − | 8.11679i | 0.770412 | − | 0.444798i | ||||
\(334\) | 8.51947 | − | 14.7561i | 0.466164 | − | 0.807421i | ||||
\(335\) | 45.7223 | 2.49808 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.31370 | 0.343929 | 0.171965 | − | 0.985103i | \(-0.444988\pi\) | ||||
0.171965 | + | 0.985103i | \(0.444988\pi\) | |||||||
\(338\) | −21.2522 | − | 3.39525i | −1.15597 | − | 0.184677i | ||||
\(339\) | −0.977762 | − | 1.69353i | −0.0531048 | − | 0.0919801i | ||||
\(340\) | 4.19574 | − | 2.42241i | 0.227546 | − | 0.131374i | ||||
\(341\) | 8.84643 | − | 15.3225i | 0.479061 | − | 0.829758i | ||||
\(342\) | −20.0486 | −1.08410 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.73986i | 0.147724i | ||||||||
\(345\) | −8.83203 | − | 5.09918i | −0.475501 | − | 0.274530i | ||||
\(346\) | 8.60862 | − | 4.97019i | 0.462802 | − | 0.267199i | ||||
\(347\) | −14.5600 | − | 25.2187i | −0.781622 | − | 1.35381i | −0.930997 | − | 0.365028i | \(-0.881059\pi\) |
0.149375 | − | 0.988781i | \(-0.452274\pi\) | |||||||
\(348\) | −1.13583 | + | 1.96732i | −0.0608870 | + | 0.105459i | ||||
\(349\) | 20.3297i | 1.08822i | 0.839013 | + | 0.544112i | \(0.183133\pi\) | ||||
−0.839013 | + | 0.544112i | \(0.816867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.1000 | − | 1.86492i | 0.539099 | − | 0.0995421i | ||||
\(352\) | 5.15870 | − | 8.93513i | 0.274960 | − | 0.476244i | ||||
\(353\) | 12.2958 | − | 7.09900i | 0.654441 | − | 0.377841i | −0.135715 | − | 0.990748i | \(-0.543333\pi\) |
0.790155 | + | 0.612907i | \(0.210000\pi\) | |||||||
\(354\) | −3.93777 | − | 6.82043i | −0.209290 | − | 0.362502i | ||||
\(355\) | −6.88866 | + | 11.9315i | −0.365612 | + | 0.633259i | ||||
\(356\) | − | 9.67285i | − | 0.512660i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.8324i | 0.678214i | ||||||||
\(359\) | −6.49661 | − | 3.75082i | −0.342878 | − | 0.197961i | 0.318666 | − | 0.947867i | \(-0.396765\pi\) |
−0.661544 | + | 0.749906i | \(0.730098\pi\) | |||||||
\(360\) | 8.25299 | + | 14.2946i | 0.434971 | + | 0.753391i | ||||
\(361\) | 0.161114 | + | 0.279058i | 0.00847971 | + | 0.0146873i | ||||
\(362\) | 28.6742 | + | 16.5551i | 1.50708 | + | 0.870115i | ||||
\(363\) | −2.14646 | −0.112660 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.3958 | −0.858193 | ||||||||
\(366\) | −6.77938 | − | 3.91407i | −0.354364 | − | 0.204592i | ||||
\(367\) | −14.2942 | − | 24.7582i | −0.746149 | − | 1.29237i | −0.949656 | − | 0.313294i | \(-0.898567\pi\) |
0.203507 | − | 0.979073i | \(-0.434766\pi\) | |||||||
\(368\) | 17.6822 | + | 30.6265i | 0.921749 | + | 1.59652i | ||||
\(369\) | −9.49621 | − | 5.48264i | −0.494353 | − | 0.285415i | ||||
\(370\) | − | 28.0348i | − | 1.45746i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 2.51303i | − | 0.130294i | ||||||
\(373\) | 3.95602 | − | 6.85203i | 0.204835 | − | 0.354784i | −0.745245 | − | 0.666791i | \(-0.767668\pi\) |
0.950080 | + | 0.312006i | \(0.101001\pi\) | |||||||
\(374\) | −4.86292 | − | 8.42283i | −0.251456 | − | 0.435534i | ||||
\(375\) | 2.14447 | − | 1.23811i | 0.110740 | − | 0.0639357i | ||||
\(376\) | −1.40936 | + | 2.44108i | −0.0726822 | + | 0.125889i | ||||
\(377\) | 21.9677 | − | 4.05624i | 1.13139 | − | 0.208907i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.78091i | 0.0914791i | 0.998953 | + | 0.0457395i | \(0.0145644\pi\) | ||||
−0.998953 | + | 0.0457395i | \(0.985436\pi\) | |||||||
\(380\) | −4.67880 | + | 8.10393i | −0.240018 | + | 0.415723i | ||||
\(381\) | −0.587421 | − | 1.01744i | −0.0300945 | − | 0.0521251i | ||||
\(382\) | 29.3676 | − | 16.9554i | 1.50258 | − | 0.867515i | ||||
\(383\) | −12.2973 | − | 7.09987i | −0.628364 | − | 0.362786i | 0.151754 | − | 0.988418i | \(-0.451508\pi\) |
−0.780118 | + | 0.625632i | \(0.784841\pi\) | |||||||
\(384\) | 6.61883i | 0.337766i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.5829 | 1.04764 | ||||||||
\(387\) | 1.81038 | − | 3.13568i | 0.0920270 | − | 0.159395i | ||||
\(388\) | 9.00550 | − | 5.19933i | 0.457185 | − | 0.263956i | ||||
\(389\) | −3.38749 | − | 5.86731i | −0.171753 | − | 0.297485i | 0.767280 | − | 0.641312i | \(-0.221610\pi\) |
−0.939033 | + | 0.343828i | \(0.888276\pi\) | |||||||
\(390\) | 2.83974 | − | 8.00211i | 0.143796 | − | 0.405202i | ||||
\(391\) | 16.3161 | 0.825140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.05700 | 0.0533187 | ||||||||
\(394\) | 15.7113 | − | 27.2128i | 0.791524 | − | 1.37096i | ||||
\(395\) | 5.01321 | − | 2.89438i | 0.252242 | − | 0.145632i | ||||
\(396\) | −4.56215 | + | 2.63396i | −0.229257 | + | 0.132361i | ||||
\(397\) | 25.1167 | + | 14.5011i | 1.26057 | + | 0.727792i | 0.973185 | − | 0.230023i | \(-0.0738801\pi\) |
0.287387 | + | 0.957815i | \(0.407213\pi\) | |||||||
\(398\) | 21.2218i | 1.06375i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.0772 | 0.803861 | ||||||||
\(401\) | −19.0183 | − | 10.9802i | −0.949728 | − | 0.548326i | −0.0567318 | − | 0.998389i | \(-0.518068\pi\) |
−0.892997 | + | 0.450064i | \(0.851401\pi\) | |||||||
\(402\) | −6.51848 | − | 11.2903i | −0.325112 | − | 0.563111i | ||||
\(403\) | −18.8023 | + | 16.0369i | −0.936612 | + | 0.798856i | ||||
\(404\) | −6.46231 | + | 11.1930i | −0.321512 | + | 0.556875i | ||||
\(405\) | − | 19.7006i | − | 0.978928i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.2105 | −0.753959 | ||||||||
\(408\) | 2.03379 | + | 1.17421i | 0.100688 | + | 0.0581321i | ||||
\(409\) | −3.46661 | + | 2.00145i | −0.171413 | + | 0.0989653i | −0.583252 | − | 0.812291i | \(-0.698220\pi\) |
0.411839 | + | 0.911257i | \(0.364887\pi\) | |||||||
\(410\) | −16.3996 | + | 9.46832i | −0.809919 | + | 0.467607i | ||||
\(411\) | −0.183986 | − | 0.106224i | −0.00907537 | − | 0.00523967i | ||||
\(412\) | 4.85702 | 0.239288 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 32.6986i | − | 1.60705i | ||||||
\(415\) | −4.48037 | + | 7.76024i | −0.219933 | + | 0.380935i | ||||
\(416\) | −10.9644 | + | 9.35176i | −0.537573 | + | 0.458508i | ||||
\(417\) | 4.82250 | + | 8.35282i | 0.236159 | + | 0.409039i | ||||
\(418\) | 16.2684 | + | 9.39256i | 0.795713 | + | 0.459405i | ||||
\(419\) | −1.75047 | −0.0855162 | −0.0427581 | − | 0.999085i | \(-0.513614\pi\) | ||||
−0.0427581 | + | 0.999085i | \(0.513614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2204i | 0.790533i | 0.918566 | + | 0.395267i | \(0.129348\pi\) | ||||
−0.918566 | + | 0.395267i | \(0.870652\pi\) | |||||||
\(422\) | 11.2823 | + | 6.51385i | 0.549215 | + | 0.317089i | ||||
\(423\) | 3.22593 | − | 1.86249i | 0.156850 | − | 0.0905573i | ||||
\(424\) | −14.9630 | + | 8.63888i | −0.726666 | + | 0.419541i | ||||
\(425\) | 3.70878 | − | 6.42379i | 0.179902 | − | 0.311600i | ||||
\(426\) | 3.92837 | 0.190330 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −11.5570 | −0.558631 | ||||||||
\(429\) | −4.34162 | − | 1.54072i | −0.209615 | − | 0.0743869i | ||||
\(430\) | −3.12647 | − | 5.41520i | −0.150772 | − | 0.261144i | ||||
\(431\) | −10.1149 | + | 5.83984i | −0.487217 | + | 0.281295i | −0.723419 | − | 0.690409i | \(-0.757431\pi\) |
0.236202 | + | 0.971704i | \(0.424097\pi\) | |||||||
\(432\) | 7.02574 | − | 12.1689i | 0.338026 | − | 0.585479i | ||||
\(433\) | −31.6289 | −1.51999 | −0.759994 | − | 0.649930i | \(-0.774798\pi\) | ||||
−0.759994 | + | 0.649930i | \(0.774798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.81351i | 0.422575i | ||||||||
\(436\) | −6.42598 | − | 3.71004i | −0.307749 | − | 0.177679i | ||||
\(437\) | −27.2919 | + | 15.7570i | −1.30555 | + | 0.753759i | ||||
\(438\) | 2.33749 | + | 4.04865i | 0.111690 | + | 0.193452i | ||||
\(439\) | −4.85769 | + | 8.41377i | −0.231845 | + | 0.401567i | −0.958351 | − | 0.285593i | \(-0.907810\pi\) |
0.726506 | + | 0.687160i | \(0.241143\pi\) | |||||||
\(440\) | − | 15.4658i | − | 0.737302i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.46664 | + | 13.3588i | 0.117326 | + | 0.635413i | ||||
\(443\) | −10.5582 | + | 18.2873i | −0.501633 | + | 0.868854i | 0.498365 | + | 0.866967i | \(0.333934\pi\) |
−0.999998 | + | 0.00188659i | \(0.999399\pi\) | |||||||
\(444\) | −1.87100 | + | 1.08022i | −0.0887939 | + | 0.0512652i | ||||
\(445\) | −18.7642 | − | 32.5005i | −0.889507 | − | 1.54067i | ||||
\(446\) | −6.43218 | + | 11.1409i | −0.304573 | + | 0.527535i | ||||
\(447\) | − | 11.3352i | − | 0.536135i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13.4710i | − | 0.635735i | −0.948135 | − | 0.317867i | \(-0.897033\pi\) | ||
0.948135 | − | 0.317867i | \(-0.102967\pi\) | |||||||
\(450\) | −12.8737 | − | 7.43266i | −0.606874 | − | 0.350379i | ||||
\(451\) | 5.13713 | + | 8.89776i | 0.241898 | + | 0.418979i | ||||
\(452\) | −1.46323 | − | 2.53440i | −0.0688248 | − | 0.119208i | ||||
\(453\) | −4.80991 | − | 2.77700i | −0.225989 | − | 0.130475i | ||||
\(454\) | −42.2871 | −1.98463 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.53589 | −0.212413 | ||||||||
\(457\) | 8.10237 | + | 4.67791i | 0.379013 | + | 0.218823i | 0.677389 | − | 0.735625i | \(-0.263112\pi\) |
−0.298376 | + | 0.954449i | \(0.596445\pi\) | |||||||
\(458\) | 10.6769 | + | 18.4929i | 0.498899 | + | 0.864119i | ||||
\(459\) | −3.24147 | − | 5.61439i | −0.151299 | − | 0.262057i | ||||
\(460\) | −13.2173 | − | 7.63099i | −0.616258 | − | 0.355797i | ||||
\(461\) | 8.14109i | 0.379168i | 0.981864 | + | 0.189584i | \(0.0607140\pi\) | ||||
−0.981864 | + | 0.189584i | \(0.939286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3018i | 1.12940i | 0.825296 | + | 0.564700i | \(0.191008\pi\) | ||||
−0.825296 | + | 0.564700i | \(0.808992\pi\) | |||||||
\(464\) | 15.2811 | − | 26.4677i | 0.709408 | − | 1.22873i | ||||
\(465\) | −4.87497 | − | 8.44369i | −0.226071 | − | 0.391567i | ||||
\(466\) | −11.6745 | + | 6.74026i | −0.540810 | + | 0.312237i | ||||
\(467\) | −16.3968 | + | 28.4000i | −0.758751 | + | 1.31420i | 0.184736 | + | 0.982788i | \(0.440857\pi\) |
−0.943488 | + | 0.331408i | \(0.892476\pi\) | |||||||
\(468\) | 7.23567 | − | 1.33603i | 0.334469 | − | 0.0617582i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 6.43290i | − | 0.296728i | ||||||
\(471\) | 0.937484 | − | 1.62377i | 0.0431970 | − | 0.0748194i | ||||
\(472\) | 10.0180 | + | 17.3517i | 0.461116 | + | 0.798677i | ||||
\(473\) | −2.93807 | + | 1.69629i | −0.135093 | + | 0.0779957i | ||||
\(474\) | −1.42944 | − | 0.825285i | −0.0656561 | − | 0.0379066i | ||||
\(475\) | 14.3267i | 0.657356i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.8328 | 1.04544 | ||||||||
\(478\) | −19.7107 | + | 34.1400i | −0.901548 | + | 1.56153i | ||||
\(479\) | −2.14868 | + | 1.24054i | −0.0981759 | + | 0.0566819i | −0.548284 | − | 0.836292i | \(-0.684719\pi\) |
0.450108 | + | 0.892974i | \(0.351385\pi\) | |||||||
\(480\) | −2.84279 | − | 4.92385i | −0.129755 | − | 0.224742i | ||||
\(481\) | 20.0220 | + | 7.10529i | 0.912926 | + | 0.323973i | ||||
\(482\) | 0.477694 | 0.0217584 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.21221 | −0.146009 | ||||||||
\(485\) | 20.1721 | − | 34.9392i | 0.915970 | − | 1.58651i | ||||
\(486\) | −17.1170 | + | 9.88248i | −0.776441 | + | 0.448279i | ||||
\(487\) | −19.8506 | + | 11.4608i | −0.899519 | + | 0.519337i | −0.877044 | − | 0.480410i | \(-0.840488\pi\) |
−0.0224747 | + | 0.999747i | \(0.507155\pi\) | |||||||
\(488\) | 17.2473 | + | 9.95771i | 0.780747 | + | 0.450764i | ||||
\(489\) | − | 9.70797i | − | 0.439010i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.8735 | −1.03227 | −0.516134 | − | 0.856508i | \(-0.672629\pi\) | ||||
−0.516134 | + | 0.856508i | \(0.672629\pi\) | |||||||
\(492\) | 1.26380 | + | 0.729658i | 0.0569767 | + | 0.0328955i | ||||
\(493\) | −7.05026 | − | 12.2114i | −0.317528 | − | 0.549974i | ||||
\(494\) | −17.0270 | − | 19.9631i | −0.766080 | − | 0.898183i | ||||
\(495\) | −10.2191 | + | 17.7000i | −0.459315 | + | 0.795557i | ||||
\(496\) | 33.8095i | 1.51809i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.55501 | 0.114493 | ||||||||
\(499\) | −7.34465 | − | 4.24044i | −0.328792 | − | 0.189828i | 0.326513 | − | 0.945193i | \(-0.394126\pi\) |
−0.655305 | + | 0.755365i | \(0.727460\pi\) | |||||||
\(500\) | 3.20923 | − | 1.85285i | 0.143521 | − | 0.0828620i | ||||
\(501\) | −4.41188 | + | 2.54720i | −0.197108 | + | 0.113801i | ||||
\(502\) | 10.9227 | + | 6.30622i | 0.487504 | + | 0.281460i | ||||
\(503\) | 9.36890 | 0.417739 | 0.208869 | − | 0.977944i | \(-0.433022\pi\) | ||||
0.208869 | + | 0.977944i | \(0.433022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.1444i | 2.23140i | ||||||||
\(506\) | −15.3190 | + | 26.5333i | −0.681012 | + | 1.17955i | ||||
\(507\) | 4.99527 | + | 4.05619i | 0.221848 | + | 0.180142i | ||||
\(508\) | −0.879083 | − | 1.52262i | −0.0390030 | − | 0.0675552i | ||||
\(509\) | −18.6544 | − | 10.7701i | −0.826840 | − | 0.477376i | 0.0259293 | − | 0.999664i | \(-0.491746\pi\) |
−0.852770 | + | 0.522287i | \(0.825079\pi\) | |||||||
\(510\) | −5.35958 | −0.237326 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 0.851388i | − | 0.0376264i | ||||||
\(513\) | 10.8440 | + | 6.26078i | 0.478774 | + | 0.276420i | ||||
\(514\) | −16.7115 | + | 9.64837i | −0.737111 | + | 0.425572i | ||||
\(515\) | 16.3194 | − | 9.42203i | 0.719120 | − | 0.415184i | ||||
\(516\) | −0.240935 | + | 0.417312i | −0.0106066 | + | 0.0183711i | ||||
\(517\) | −3.49023 | −0.153500 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.97203 | −0.130458 | ||||||||
\(520\) | −7.22451 | + | 20.3580i | −0.316816 | + | 0.892757i | ||||
\(521\) | 7.87350 | + | 13.6373i | 0.344944 | + | 0.597461i | 0.985344 | − | 0.170581i | \(-0.0545645\pi\) |
−0.640399 | + | 0.768042i | \(0.721231\pi\) | |||||||
\(522\) | −24.4725 | + | 14.1292i | −1.07113 | + | 0.618420i | ||||
\(523\) | 8.97018 | − | 15.5368i | 0.392238 | − | 0.679377i | −0.600506 | − | 0.799620i | \(-0.705034\pi\) |
0.992744 | + | 0.120243i | \(0.0383675\pi\) | |||||||
\(524\) | 1.58182 | 0.0691020 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 22.4369i | − | 0.978293i | ||||||
\(527\) | 13.5089 | + | 7.79934i | 0.588455 | + | 0.339745i | ||||
\(528\) | −5.45832 | + | 3.15136i | −0.237543 | + | 0.137146i | ||||
\(529\) | −14.1992 | − | 24.5937i | −0.617355 | − | 1.06929i | ||||
\(530\) | 19.7157 | − | 34.1486i | 0.856396 | − | 1.48332i | ||||
\(531\) | − | 26.4779i | − | 1.14904i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.60573 | − | 14.1121i | −0.112867 | − | 0.611261i | ||||
\(534\) | −5.35029 | + | 9.26698i | −0.231530 | + | 0.401021i | ||||
\(535\) | −38.8313 | + | 22.4193i | −1.67883 | + | 0.969270i | ||||
\(536\) | 16.5835 | + | 28.7235i | 0.716299 | + | 1.24067i | ||||
\(537\) | 1.91836 | − | 3.32269i | 0.0827832 | − | 0.143385i | ||||
\(538\) | 29.5232i | 1.27284i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.06410i | 0.260957i | ||||||||
\(541\) | 8.10237 | + | 4.67791i | 0.348348 | + | 0.201119i | 0.663958 | − | 0.747770i | \(-0.268876\pi\) |
−0.315609 | + | 0.948889i | \(0.602209\pi\) | |||||||
\(542\) | 25.1426 | + | 43.5483i | 1.07997 | + | 1.87056i | ||||
\(543\) | −4.94974 | − | 8.57319i | −0.212413 | − | 0.367911i | ||||
\(544\) | 7.87755 | + | 4.54810i | 0.337747 | + | 0.194998i | ||||
\(545\) | −28.7881 | −1.23315 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1634 | −1.41796 | −0.708981 | − | 0.705227i | \(-0.750845\pi\) | ||||
−0.708981 | + | 0.705227i | \(0.750845\pi\) | |||||||
\(548\) | −0.275338 | − | 0.158966i | −0.0117619 | − | 0.00679071i | ||||
\(549\) | −13.1593 | − | 22.7925i | −0.561624 | − | 0.972761i | ||||
\(550\) | 6.96425 | + | 12.0624i | 0.296957 | + | 0.514344i | ||||
\(551\) | 23.5859 | + | 13.6173i | 1.00479 | + | 0.580118i | ||||
\(552\) | − | 7.39790i | − | 0.314876i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 8.63228i | − | 0.366750i | ||||||
\(555\) | −4.19101 | + | 7.25904i | −0.177898 | + | 0.308129i | ||||
\(556\) | 7.21695 | + | 12.5001i | 0.306067 | + | 0.530123i | ||||
\(557\) | 9.65899 | − | 5.57662i | 0.409265 | − | 0.236289i | −0.281209 | − | 0.959647i | \(-0.590735\pi\) |
0.690474 | + | 0.723357i | \(0.257402\pi\) | |||||||
\(558\) | 15.6305 | − | 27.0727i | 0.661690 | − | 1.14608i | ||||
\(559\) | 4.65984 | − | 0.860419i | 0.197090 | − | 0.0363918i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.90789i | 0.122771i | ||||||||
\(562\) | 1.37619 | − | 2.38363i | 0.0580511 | − | 0.100547i | ||||
\(563\) | 9.58889 | + | 16.6085i | 0.404124 | + | 0.699963i | 0.994219 | − | 0.107371i | \(-0.0342432\pi\) |
−0.590095 | + | 0.807334i | \(0.700910\pi\) | |||||||
\(564\) | −0.429323 | + | 0.247869i | −0.0180777 | + | 0.0104372i | ||||
\(565\) | −9.83285 | − | 5.67700i | −0.413671 | − | 0.238833i | ||||
\(566\) | − | 22.8389i | − | 0.959993i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.99409 | −0.419343 | ||||||||
\(569\) | 6.73361 | − | 11.6630i | 0.282288 | − | 0.488937i | −0.689660 | − | 0.724133i | \(-0.742240\pi\) |
0.971948 | + | 0.235197i | \(0.0755734\pi\) | |||||||
\(570\) | 8.96497 | − | 5.17593i | 0.375501 | − | 0.216796i | ||||
\(571\) | 12.5804 | + | 21.7899i | 0.526473 | + | 0.911877i | 0.999524 | + | 0.0308427i | \(0.00981909\pi\) |
−0.473052 | + | 0.881035i | \(0.656848\pi\) | |||||||
\(572\) | −6.49729 | − | 2.30572i | −0.271665 | − | 0.0964068i | ||||
\(573\) | −10.1389 | −0.423557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3665 | −0.974450 | ||||||||
\(576\) | −4.47508 | + | 7.75106i | −0.186462 | + | 0.322961i | ||||
\(577\) | 18.7481 | − | 10.8242i | 0.780492 | − | 0.450617i | −0.0561126 | − | 0.998424i | \(-0.517871\pi\) |
0.836605 | + | 0.547807i | \(0.184537\pi\) | |||||||
\(578\) | −16.9474 | + | 9.78457i | −0.704918 | + | 0.406984i | ||||
\(579\) | −5.32953 | − | 3.07701i | −0.221488 | − | 0.127876i | ||||
\(580\) | 13.1895i | 0.547666i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.5035 | −0.476836 | ||||||||
\(583\) | −18.5276 | − | 10.6969i | −0.767337 | − | 0.443022i | ||||
\(584\) | −5.94676 | − | 10.3001i | −0.246079 | − | 0.426221i | ||||
\(585\) | 21.7199 | − | 18.5254i | 0.898007 | − | 0.765929i | ||||
\(586\) | 10.6430 | − | 18.4342i | 0.439658 | − | 0.761510i | ||||
\(587\) | − | 34.5576i | − | 1.42634i | −0.700989 | − | 0.713172i | \(-0.747258\pi\) | ||
0.700989 | − | 0.713172i | \(-0.252742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.1283 | −1.24142 | ||||||||
\(590\) | −39.6002 | − | 22.8632i | −1.63031 | − | 0.941262i | ||||
\(591\) | −8.13624 | + | 4.69746i | −0.334680 | + | 0.193228i | ||||
\(592\) | 25.1719 | − | 14.5330i | 1.03456 | − | 0.597303i | ||||
\(593\) | 1.09846 | + | 0.634194i | 0.0451082 | + | 0.0260432i | 0.522385 | − | 0.852710i | \(-0.325043\pi\) |
−0.477276 | + | 0.878753i | \(0.658376\pi\) | |||||||
\(594\) | 12.1735 | 0.499485 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 16.9632i | − | 0.694842i | ||||||
\(597\) | 3.17251 | − | 5.49494i | 0.129842 | − | 0.224893i | ||||
\(598\) | 32.5592 | − | 27.7705i | 1.33145 | − | 1.13562i | ||||
\(599\) | −8.75714 | − | 15.1678i | −0.357807 | − | 0.619740i | 0.629787 | − | 0.776768i | \(-0.283142\pi\) |
−0.987594 | + | 0.157028i | \(0.949809\pi\) | |||||||
\(600\) | −2.91262 | − | 1.68160i | −0.118907 | − | 0.0686511i | ||||
\(601\) | 9.02164 | 0.368000 | 0.184000 | − | 0.982926i | \(-0.441095\pi\) | ||||
0.184000 | + | 0.982926i | \(0.441095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 43.8307i | − | 1.78493i | ||||||
\(604\) | −7.19810 | − | 4.15582i | −0.292886 | − | 0.169098i | ||||
\(605\) | −10.7929 | + | 6.23130i | −0.438795 | + | 0.253338i | ||||
\(606\) | 12.3823 | − | 7.14893i | 0.502997 | − | 0.290405i | ||||
\(607\) | −7.91450 | + | 13.7083i | −0.321239 | + | 0.556403i | −0.980744 | − | 0.195297i | \(-0.937433\pi\) |
0.659505 | + | 0.751701i | \(0.270766\pi\) | |||||||
\(608\) | −17.5690 | −0.712517 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −45.4511 | −1.84026 | ||||||||
\(611\) | 4.59428 | + | 1.63039i | 0.185865 | + | 0.0659584i | ||||
\(612\) | −2.32219 | − | 4.02216i | −0.0938692 | − | 0.162586i | ||||
\(613\) | 15.1853 | − | 8.76721i | 0.613327 | − | 0.354104i | −0.160940 | − | 0.986964i | \(-0.551452\pi\) |
0.774266 | + | 0.632860i | \(0.218119\pi\) | |||||||
\(614\) | −17.3015 | + | 29.9670i | −0.698230 | + | 1.20937i | ||||
\(615\) | 5.66179 | 0.228306 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.01448i | − | 0.282392i | −0.989982 | − | 0.141196i | \(-0.954905\pi\) | ||
0.989982 | − | 0.141196i | \(-0.0450948\pi\) | |||||||
\(618\) | −4.65322 | − | 2.68654i | −0.187180 | − | 0.108068i | ||||
\(619\) | 33.6245 | − | 19.4131i | 1.35148 | − | 0.780280i | 0.363027 | − | 0.931779i | \(-0.381743\pi\) |
0.988457 | + | 0.151499i | \(0.0484099\pi\) | |||||||
\(620\) | −7.29546 | − | 12.6361i | −0.292993 | − | 0.507478i | ||||
\(621\) | −10.2111 | + | 17.6862i | −0.409759 | + | 0.709724i | ||||
\(622\) | 28.3743i | 1.13771i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.65703 | − | 1.59848i | 0.346558 | − | 0.0639904i | ||||
\(625\) | 15.3368 | − | 26.5641i | 0.613470 | − | 1.06256i | ||||
\(626\) | 3.65980 | − | 2.11299i | 0.146275 | − | 0.0844519i | ||||
\(627\) | −2.80825 | − | 4.86402i | −0.112151 | − | 0.194250i | ||||
\(628\) | 1.40296 | − | 2.42999i | 0.0559841 | − | 0.0969674i | ||||
\(629\) | − | 13.4102i | − | 0.534699i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.7484i | 0.507506i | 0.967269 | + | 0.253753i | \(0.0816650\pi\) | ||||
−0.967269 | + | 0.253753i | \(0.918335\pi\) | |||||||
\(632\) | 3.63660 | + | 2.09959i | 0.144656 | + | 0.0835172i | ||||
\(633\) | −1.94755 | − | 3.37326i | −0.0774082 | − | 0.134075i | ||||
\(634\) | −22.5885 | − | 39.1245i | −0.897105 | − | 1.55383i | ||||
\(635\) | −5.90739 | − | 3.41063i | −0.234427 | − | 0.135347i | ||||
\(636\) | −3.03871 | −0.120493 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.4776 | 1.04826 | ||||||||
\(639\) | 11.4379 | + | 6.60367i | 0.452476 | + | 0.261237i | ||||
\(640\) | 19.2148 | + | 33.2811i | 0.759533 | + | 1.31555i | ||||
\(641\) | −4.85715 | − | 8.41282i | −0.191846 | − | 0.332287i | 0.754016 | − | 0.656856i | \(-0.228114\pi\) |
−0.945862 | + | 0.324569i | \(0.894781\pi\) | |||||||
\(642\) | 11.0721 | + | 6.39249i | 0.436982 | + | 0.252291i | ||||
\(643\) | − | 0.458279i | − | 0.0180728i | −0.999959 | − | 0.00903639i | \(-0.997124\pi\) | ||
0.999959 | − | 0.00903639i | \(-0.00287641\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.86954i | 0.0736131i | ||||||||
\(646\) | −8.28084 | + | 14.3428i | −0.325805 | + | 0.564311i | ||||
\(647\) | 3.08861 | + | 5.34963i | 0.121426 | + | 0.210316i | 0.920330 | − | 0.391142i | \(-0.127920\pi\) |
−0.798904 | + | 0.601458i | \(0.794587\pi\) | |||||||
\(648\) | 12.3762 | − | 7.14541i | 0.486184 | − | 0.280698i | ||||
\(649\) | −12.4046 | + | 21.4854i | −0.486924 | + | 0.843377i | ||||
\(650\) | −3.53251 | − | 19.1313i | −0.138556 | − | 0.750392i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 14.5281i | − | 0.568965i | ||||||
\(653\) | −14.2193 | + | 24.6285i | −0.556443 | + | 0.963787i | 0.441347 | + | 0.897337i | \(0.354501\pi\) |
−0.997790 | + | 0.0664508i | \(0.978832\pi\) | |||||||
\(654\) | 4.10423 | + | 7.10874i | 0.160488 | + | 0.277974i | ||||
\(655\) | 5.31486 | − | 3.06854i | 0.207669 | − | 0.119898i | ||||
\(656\) | −17.0028 | − | 9.81659i | −0.663849 | − | 0.383274i | ||||
\(657\) | 15.7175i | 0.613196i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.9818 | −1.01211 | −0.506054 | − | 0.862502i | \(-0.668897\pi\) | ||||
−0.506054 | + | 0.862502i | \(0.668897\pi\) | |||||||
\(660\) | 1.36001 | − | 2.35561i | 0.0529384 | − | 0.0916920i | ||||
\(661\) | 32.2812 | − | 18.6376i | 1.25560 | − | 0.724918i | 0.283380 | − | 0.959008i | \(-0.408544\pi\) |
0.972215 | + | 0.234090i | \(0.0752109\pi\) | |||||||
\(662\) | 8.02353 | + | 13.8972i | 0.311843 | + | 0.540128i | ||||
\(663\) | 1.35836 | − | 3.82773i | 0.0527544 | − | 0.148657i | ||||
\(664\) | −6.50015 | −0.252255 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.8750 | −1.04139 | ||||||||
\(667\) | −22.2094 | + | 38.4679i | −0.859953 | + | 1.48948i | ||||
\(668\) | −6.60245 | + | 3.81192i | −0.255456 | + | 0.147488i | ||||
\(669\) | 3.33096 | − | 1.92313i | 0.128782 | − | 0.0743526i | ||||
\(670\) | −65.5530 | − | 37.8470i | −2.53253 | − | 1.46216i | ||||
\(671\) | 24.6599i | 0.951986i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.7078 | 1.60772 | 0.803859 | − | 0.594820i | \(-0.202777\pi\) | ||||
0.803859 | + | 0.594820i | \(0.202777\pi\) | |||||||
\(674\) | −9.05209 | − | 5.22623i | −0.348673 | − | 0.201307i | ||||
\(675\) | 4.64215 | + | 8.04044i | 0.178676 | + | 0.309477i | ||||
\(676\) | 7.47548 | + | 6.07015i | 0.287519 | + | 0.233467i | ||||
\(677\) | 9.10347 | − | 15.7677i | 0.349875 | − | 0.606001i | −0.636352 | − | 0.771399i | \(-0.719557\pi\) |
0.986227 | + | 0.165398i | \(0.0528908\pi\) | |||||||
\(678\) | 3.23741i | 0.124332i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13.6352 | 0.522886 | ||||||||
\(681\) | 10.9494 | + | 6.32162i | 0.419581 | + | 0.242245i | ||||
\(682\) | −25.3666 | + | 14.6454i | −0.971338 | + | 0.560802i | ||||
\(683\) | 23.6736 | − | 13.6680i | 0.905847 | − | 0.522991i | 0.0267542 | − | 0.999642i | \(-0.491483\pi\) |
0.879093 | + | 0.476651i | \(0.158150\pi\) | |||||||
\(684\) | 7.76866 | + | 4.48524i | 0.297042 | + | 0.171497i | ||||
\(685\) | −1.23350 | −0.0471297 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 6.38449i | − | 0.243584i | ||||||
\(688\) | 3.24147 | − | 5.61439i | 0.123580 | − | 0.214047i | ||||
\(689\) | 19.3916 | + | 22.7355i | 0.738760 | + | 0.866152i | ||||
\(690\) | 8.44178 | + | 14.6216i | 0.321373 | + | 0.556634i | ||||
\(691\) | 7.27098 | + | 4.19790i | 0.276601 | + | 0.159696i | 0.631884 | − | 0.775063i | \(-0.282282\pi\) |
−0.355283 | + | 0.934759i | \(0.615615\pi\) | |||||||
\(692\) | −4.44769 | −0.169076 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 48.2087i | 1.82998i | ||||||||
\(695\) | 48.4974 | + | 28.0000i | 1.83961 | + | 1.06210i | ||||
\(696\) | −5.53679 | + | 3.19667i | −0.209872 | + | 0.121169i | ||||
\(697\) | −7.84460 | + | 4.52908i | −0.297135 | + | 0.171551i | ||||
\(698\) | 16.8281 | − | 29.1471i | 0.636953 | − | 1.10323i | ||||
\(699\) | 4.03049 | 0.152447 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.4998 | 1.03865 | 0.519327 | − | 0.854576i | \(-0.326183\pi\) | ||||
0.519327 | + | 0.854576i | \(0.326183\pi\) | |||||||
\(702\) | −16.0243 | − | 5.68660i | −0.604798 | − | 0.214627i | ||||
\(703\) | 12.9507 | + | 22.4312i | 0.488443 | + | 0.846009i | ||||
\(704\) | 7.26259 | − | 4.19306i | 0.273719 | − | 0.158032i | ||||
\(705\) | −0.961674 | + | 1.66567i | −0.0362187 | + | 0.0627327i | ||||
\(706\) | −23.5050 | −0.884623 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.52381i | 0.132433i | ||||||||
\(709\) | 25.0991 | + | 14.4910i | 0.942618 | + | 0.544221i | 0.890780 | − | 0.454435i | \(-0.150159\pi\) |
0.0518380 | + | 0.998656i | \(0.483492\pi\) | |||||||
\(710\) | 19.7528 | − | 11.4043i | 0.741310 | − | 0.427996i | ||||
\(711\) | −2.77464 | − | 4.80581i | −0.104057 | − | 0.180232i | ||||
\(712\) | 13.6116 | − | 23.5759i | 0.510115 | − | 0.883545i | ||||
\(713\) | − | 49.1384i | − | 1.84025i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.3035 | + | 4.85683i | −0.983696 | + | 0.181635i | ||||
\(716\) | 2.87085 | − | 4.97246i | 0.107289 | − | 0.185829i | ||||
\(717\) | 10.2074 | − | 5.89323i | 0.381202 | − | 0.220087i | ||||
\(718\) | 6.20955 | + | 10.7552i | 0.231738 | + | 0.401382i | ||||
\(719\) | 8.77612 | − | 15.2007i | 0.327294 | − | 0.566890i | −0.654680 | − | 0.755906i | \(-0.727197\pi\) |
0.981974 | + | 0.189016i | \(0.0605299\pi\) | |||||||
\(720\) | − | 39.0557i | − | 1.45552i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 0.533456i | − | 0.0198532i | ||||||
\(723\) | −0.123689 | − | 0.0714119i | −0.00460005 | − | 0.00265584i | ||||
\(724\) | −7.40735 | − | 12.8299i | −0.275292 | − | 0.476820i | ||||
\(725\) | 10.0968 | + | 17.4881i | 0.374984 | + | 0.649492i | ||||
\(726\) | 3.07743 | + | 1.77675i | 0.114214 | + | 0.0659415i | ||||
\(727\) | 22.1403 | 0.821139 | 0.410569 | − | 0.911829i | \(-0.365330\pi\) | ||||
0.410569 | + | 0.911829i | \(0.365330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.6556 | −0.542799 | ||||||||
\(730\) | 23.5069 | + | 13.5717i | 0.870031 | + | 0.502313i | ||||
\(731\) | −1.49552 | − | 2.59031i | −0.0553137 | − | 0.0958061i | ||||
\(732\) | 1.75130 | + | 3.03334i | 0.0647300 | + | 0.112116i | ||||
\(733\) | 44.4629 | + | 25.6707i | 1.64228 | + | 0.948169i | 0.980022 | + | 0.198889i | \(0.0637334\pi\) |
0.662254 | + | 0.749279i | \(0.269600\pi\) | |||||||
\(734\) | 47.3285i | 1.74693i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 28.6545i | − | 1.05622i | ||||||
\(737\) | −20.5343 | + | 35.5664i | −0.756389 | + | 1.31010i | ||||
\(738\) | 9.07661 | + | 15.7212i | 0.334115 | + | 0.578704i | ||||
\(739\) | 19.7270 | − | 11.3894i | 0.725668 | − | 0.418965i | −0.0911674 | − | 0.995836i | \(-0.529060\pi\) |
0.816835 | + | 0.576871i | \(0.195726\pi\) | |||||||
\(740\) | −6.27191 | + | 10.8633i | −0.230560 | + | 0.399341i | ||||
\(741\) | 1.42444 | + | 7.71445i | 0.0523281 | + | 0.283398i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 27.6199i | − | 1.01328i | −0.862159 | − | 0.506638i | \(-0.830888\pi\) | ||
0.862159 | − | 0.506638i | \(-0.169112\pi\) | |||||||
\(744\) | 3.53631 | − | 6.12507i | 0.129647 | − | 0.224556i | ||||
\(745\) | −32.9067 | − | 56.9960i | −1.20561 | − | 2.08817i | ||||
\(746\) | −11.3437 | + | 6.54926i | −0.415321 | + | 0.239785i | ||||
\(747\) | 7.43919 | + | 4.29502i | 0.272186 | + | 0.157147i | ||||
\(748\) | 4.35170i | 0.159114i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.09943 | −0.149690 | ||||||||
\(751\) | 20.5586 | − | 35.6085i | 0.750194 | − | 1.29937i | −0.197534 | − | 0.980296i | \(-0.563293\pi\) |
0.947728 | − | 0.319078i | \(-0.103373\pi\) | |||||||
\(752\) | 5.77597 | − | 3.33476i | 0.210628 | − | 0.121606i | ||||
\(753\) | −1.88547 | − | 3.26573i | −0.0687104 | − | 0.119010i | ||||
\(754\) | −34.8532 | − | 12.3685i | −1.26928 | − | 0.450433i | ||||
\(755\) | −32.2472 | −1.17360 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.0143 | 0.509357 | 0.254678 | − | 0.967026i | \(-0.418030\pi\) | ||||
0.254678 | + | 0.967026i | \(0.418030\pi\) | |||||||
\(758\) | 1.47416 | − | 2.55332i | 0.0535440 | − | 0.0927409i | ||||
\(759\) | 7.93308 | − | 4.58016i | 0.287952 | − | 0.166249i | ||||
\(760\) | −22.8076 | + | 13.1680i | −0.827318 | + | 0.477652i | ||||
\(761\) | −29.5876 | − | 17.0824i | −1.07255 | − | 0.619236i | −0.143672 | − | 0.989625i | \(-0.545891\pi\) |
−0.928877 | + | 0.370389i | \(0.879224\pi\) | |||||||
\(762\) | 1.94497i | 0.0704588i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.1730 | −0.548938 | ||||||||
\(765\) | −15.6050 | − | 9.00956i | −0.564200 | − | 0.325741i | ||||
\(766\) | 11.7540 | + | 20.3584i | 0.424688 | + | 0.735581i | ||||
\(767\) | 26.3650 | − | 22.4873i | 0.951985 | − | 0.811969i | ||||
\(768\) | 3.87076 | − | 6.70436i | 0.139674 | − | 0.241923i | ||||
\(769\) | 52.9061i | 1.90784i | 0.300059 | + | 0.953921i | \(0.402994\pi\) | ||||
−0.300059 | + | 0.953921i | \(0.597006\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.76946 | 0.207782 | ||||||||
\(772\) | −7.97572 | − | 4.60478i | −0.287052 | − | 0.165730i | ||||
\(773\) | −39.7621 | + | 22.9567i | −1.43014 | + | 0.825694i | −0.997131 | − | 0.0756940i | \(-0.975883\pi\) |
−0.433013 | + | 0.901388i | \(0.642549\pi\) | |||||||
\(774\) | −5.19117 | + | 2.99712i | −0.186593 | + | 0.107729i | ||||
\(775\) | −19.3462 | − | 11.1695i | −0.694937 | − | 0.401222i | ||||
\(776\) | 29.2658 | 1.05058 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.2161i | 0.402117i | ||||||||
\(779\) | 8.74777 | − | 15.1516i | 0.313421 | − | 0.542862i | ||||
\(780\) | −2.89059 | + | 2.46545i | −0.103500 | + | 0.0882773i | ||||
\(781\) | −6.18751 | − | 10.7171i | −0.221406 | − | 0.383487i | ||||
\(782\) | −23.3927 | − | 13.5058i | −0.836522 | − | 0.482966i | ||||
\(783\) | 17.6491 | 0.630728 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 10.8863i | − | 0.388548i | ||||||
\(786\) | −1.51545 | − | 0.874943i | −0.0540541 | − | 0.0312082i | ||||
\(787\) | 13.1525 | − | 7.59358i | 0.468835 | − | 0.270682i | −0.246917 | − | 0.969037i | \(-0.579417\pi\) |
0.715752 | + | 0.698355i | \(0.246084\pi\) | |||||||
\(788\) | −12.1760 | + | 7.02982i | −0.433752 | + | 0.250427i | ||||
\(789\) | −3.35415 | + | 5.80956i | −0.119411 | + | 0.206826i | ||||
\(790\) | −9.58340 | −0.340962 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.8259 | −0.526817 | ||||||||
\(793\) | 11.5194 | − | 32.4605i | 0.409065 | − | 1.15271i | ||||
\(794\) | −24.0069 | − | 41.5812i | −0.851973 | − | 1.47566i | ||||
\(795\) | −10.2100 | + | 5.89472i | −0.362110 | + | 0.209064i | ||||
\(796\) | 4.74770 | − | 8.22326i | 0.168278 | − | 0.291466i | ||||
\(797\) | −16.3006 | −0.577398 | −0.288699 | − | 0.957420i | \(-0.593223\pi\) | ||||
−0.288699 | + | 0.957420i | \(0.593223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.07712i | − | 0.108861i | ||||||
\(800\) | −11.2815 | − | 6.51340i | −0.398863 | − | 0.230283i | ||||
\(801\) | −31.1559 | + | 17.9879i | −1.10084 | + | 0.635570i | ||||
\(802\) | 18.1779 | + | 31.4851i | 0.641886 | + | 1.11178i | ||||
\(803\) | 7.36347 | − | 12.7539i | 0.259851 | − | 0.450076i | ||||
\(804\) | 5.83322i | 0.205722i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 40.2320 | − | 7.42866i | 1.41711 | − | 0.261663i | ||||
\(807\) | 4.41352 | − | 7.64444i | 0.155363 | − | 0.269097i | ||||
\(808\) | −31.5016 | + | 18.1874i | −1.10822 | + | 0.639832i | ||||
\(809\) | −5.19286 | − | 8.99430i | −0.182571 | − | 0.316223i | 0.760184 | − | 0.649708i | \(-0.225109\pi\) |
−0.942755 | + | 0.333485i | \(0.891775\pi\) | |||||||
\(810\) | −16.3073 | + | 28.2451i | −0.572981 | + | 0.992431i | ||||
\(811\) | 10.9705i | 0.385227i | 0.981275 | + | 0.192614i | \(0.0616964\pi\) | ||||
−0.981275 | + | 0.192614i | \(0.938304\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 15.0346i | − | 0.527286i | ||||||
\(814\) | 21.8077 | + | 12.5907i | 0.764359 | + | 0.441303i | ||||
\(815\) | −28.1828 | − | 48.8140i | −0.987200 | − | 1.70988i | ||||
\(816\) | −2.77836 | − | 4.81226i | −0.0972621 | − | 0.168463i | ||||
\(817\) | 5.00310 | + | 2.88854i | 0.175036 | + | 0.101057i | ||||
\(818\) | 6.62687 | 0.231703 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.47296 | 0.295888 | ||||||||
\(821\) | 34.8423 | + | 20.1162i | 1.21601 | + | 0.702061i | 0.964061 | − | 0.265681i | \(-0.0855966\pi\) |
0.251945 | + | 0.967742i | \(0.418930\pi\) | |||||||
\(822\) | 0.175856 | + | 0.304592i | 0.00613370 | + | 0.0106239i | ||||
\(823\) | −1.63250 | − | 2.82757i | −0.0569053 | − | 0.0985628i | 0.836169 | − | 0.548471i | \(-0.184790\pi\) |
−0.893075 | + | 0.449908i | \(0.851457\pi\) | |||||||
\(824\) | 11.8381 | + | 6.83476i | 0.412401 | + | 0.238100i | ||||
\(825\) | − | 4.16443i | − | 0.144987i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.0118i | 1.59999i | 0.600009 | + | 0.799993i | \(0.295164\pi\) | ||||
−0.600009 | + | 0.799993i | \(0.704836\pi\) | |||||||
\(828\) | −7.31529 | + | 12.6705i | −0.254224 | + | 0.440329i | ||||
\(829\) | 15.1933 | + | 26.3155i | 0.527683 | + | 0.913974i | 0.999479 | + | 0.0322667i | \(0.0102726\pi\) |
−0.471796 | + | 0.881708i | \(0.656394\pi\) | |||||||
\(830\) | 12.8472 | − | 7.41734i | 0.445933 | − | 0.257460i | ||||
\(831\) | −1.29047 | + | 2.23515i | −0.0447658 | + | 0.0775366i | ||||
\(832\) | −11.5186 | + | 2.12686i | −0.399337 | + | 0.0737358i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 15.9675i | − | 0.552909i | ||||||
\(835\) | −14.7893 | + | 25.6159i | −0.511807 | + | 0.886475i | ||||
\(836\) | −4.20258 | − | 7.27908i | −0.145349 | − | 0.251752i | ||||
\(837\) | −16.9086 | + | 9.76217i | −0.584446 | + | 0.337430i | ||||
\(838\) | 2.50969 | + | 1.44897i | 0.0866958 | + | 0.0500538i | ||||
\(839\) | 1.52007i | 0.0524787i | 0.999656 | + | 0.0262394i | \(0.00835321\pi\) | ||||
−0.999656 | + | 0.0262394i | \(0.991647\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.38720 | 0.323697 | ||||||||
\(842\) | 13.4266 | − | 23.2555i | 0.462710 | − | 0.801438i | ||||
\(843\) | −0.712673 | + | 0.411462i | −0.0245457 | + | 0.0141715i | ||||
\(844\) | −2.91454 | − | 5.04813i | −0.100323 | − | 0.173764i | ||||
\(845\) | 36.8928 | + | 5.89397i | 1.26915 | + | 0.202759i | ||||
\(846\) | −6.16677 | −0.212018 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 40.8818 | 1.40389 | ||||||||
\(849\) | −3.41426 | + | 5.91368i | −0.117177 | + | 0.202957i | ||||
\(850\) | −10.6347 | + | 6.13995i | −0.364767 | + | 0.210598i | ||||
\(851\) | −36.5846 | + | 21.1221i | −1.25410 | + | 0.724057i | ||||
\(852\) | −1.52221 | − | 0.878850i | −0.0521501 | − | 0.0301089i | ||||
\(853\) | − | 43.7939i | − | 1.49947i | −0.661736 | − | 0.749737i | \(-0.730180\pi\) | ||
0.661736 | − | 0.749737i | \(-0.269820\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 34.8033 | 1.19025 | ||||||||
\(856\) | −28.1683 | − | 16.2630i | −0.962774 | − | 0.555858i | ||||
\(857\) | 7.42605 | + | 12.8623i | 0.253669 | + | 0.439368i | 0.964533 | − | 0.263962i | \(-0.0850292\pi\) |
−0.710864 | + | 0.703329i | \(0.751696\pi\) | |||||||
\(858\) | 4.94932 | + | 5.80278i | 0.168967 | + | 0.198104i | ||||
\(859\) | −22.1784 | + | 38.4141i | −0.756717 | + | 1.31067i | 0.187799 | + | 0.982208i | \(0.439865\pi\) |
−0.944516 | + | 0.328465i | \(0.893469\pi\) | |||||||
\(860\) | 2.79780i | 0.0954040i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.3359 | 0.658584 | ||||||||
\(863\) | −22.3825 | − | 12.9226i | −0.761910 | − | 0.439889i | 0.0680712 | − | 0.997680i | \(-0.478315\pi\) |
−0.829981 | + | 0.557792i | \(0.811649\pi\) | |||||||
\(864\) | −9.86006 | + | 5.69271i | −0.335446 | + | 0.193670i | ||||
\(865\) | −14.9441 | + | 8.62799i | −0.508115 | + | 0.293360i | ||||
\(866\) | 45.3470 | + | 26.1811i | 1.54095 | + | 0.889670i | ||||
\(867\) | 5.85090 | 0.198707 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.19956i | 0.176383i | ||||||||
\(870\) | 7.29546 | − | 12.6361i | 0.247339 | − | 0.428404i | ||||
\(871\) | 43.6439 | − | 37.2248i | 1.47882 | − | 1.26131i | ||||
\(872\) | −10.4415 | − | 18.0852i | −0.353593 | − | 0.612442i | ||||
\(873\) | −33.4937 | − | 19.3376i | −1.13359 | − | 0.654479i | ||||
\(874\) | 52.1719 | 1.76474 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 2.09176i | − | 0.0706740i | ||||||
\(877\) | 1.18892 | + | 0.686420i | 0.0401468 | + | 0.0231788i | 0.519939 | − | 0.854203i | \(-0.325955\pi\) |
−0.479792 | + | 0.877382i | \(0.659288\pi\) | |||||||
\(878\) | 13.9291 | − | 8.04200i | 0.470086 | − | 0.271404i | ||||
\(879\) | −5.51157 | + | 3.18211i | −0.185901 | + | 0.107330i | ||||
\(880\) | −18.2972 | + | 31.6917i | −0.616798 | + | 1.06833i | ||||
\(881\) | −16.2514 | −0.547524 | −0.273762 | − | 0.961797i | \(-0.588268\pi\) | ||||
−0.273762 | + | 0.961797i | \(0.588268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.619110 | 0.0208347 | 0.0104174 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104174 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(884\) | 2.03281 | − | 5.72826i | 0.0683707 | − | 0.192662i | ||||
\(885\) | 6.83577 | + | 11.8399i | 0.229782 | + | 0.397994i | ||||
\(886\) | 30.2749 | − | 17.4792i | 1.01710 | − | 0.587226i | ||||
\(887\) | −15.9690 | + | 27.6591i | −0.536185 | + | 0.928700i | 0.462920 | + | 0.886400i | \(0.346802\pi\) |
−0.999105 | + | 0.0423000i | \(0.986531\pi\) | |||||||
\(888\) | −6.08034 | −0.204043 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 62.1288i | 2.08256i | ||||||||
\(891\) | 15.3246 | + | 8.84768i | 0.513395 | + | 0.296409i | ||||
\(892\) | 4.98483 | − | 2.87799i | 0.166905 | − | 0.0963624i | ||||
\(893\) | 2.97167 | + | 5.14709i | 0.0994432 | + | 0.172241i | ||||
\(894\) | −9.38279 | + | 16.2515i | −0.313807 | + | 0.543531i | ||||
\(895\) | − | 22.2764i | − | 0.744618i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.5820 | + | 2.32322i | −0.420102 | + | 0.0775700i | ||||
\(898\) | −11.1507 | + | 19.3136i | −0.372105 | + | 0.644504i | ||||
\(899\) | −36.7765 | + | 21.2329i | −1.22656 | + | 0.708157i | ||||
\(900\) | 3.32565 | + | 5.76019i | 0.110855 | + | 0.192006i | ||||
\(901\) | 9.43082 | − | 16.3347i | 0.314186 | − | 0.544187i | ||||
\(902\) | − | 17.0092i | − | 0.566345i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 8.23621i | − | 0.273932i | ||||||
\(905\) | −49.7769 | − | 28.7387i | −1.65464 | − | 0.955308i | ||||
\(906\) | 4.59738 | + | 7.96289i | 0.152738 | + | 0.264549i | ||||
\(907\) | 10.3518 | + | 17.9299i | 0.343728 | + | 0.595354i | 0.985122 | − | 0.171858i | \(-0.0549770\pi\) |
−0.641394 | + | 0.767211i | \(0.721644\pi\) | |||||||
\(908\) | 16.3859 | + | 9.46040i | 0.543785 | + | 0.313954i | ||||
\(909\) | 48.0699 | 1.59438 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.4143 | 1.30585 | 0.652926 | − | 0.757421i | \(-0.273541\pi\) | ||||
0.652926 | + | 0.757421i | \(0.273541\pi\) | |||||||
\(912\) | 9.29472 | + | 5.36631i | 0.307779 | + | 0.177696i | ||||
\(913\) | −4.02435 | − | 6.97037i | −0.133186 | − | 0.230686i | ||||
\(914\) | −7.74436 | − | 13.4136i | −0.256161 | − | 0.443683i | ||||
\(915\) | 11.7686 | + | 6.79463i | 0.389059 | + | 0.224623i | ||||
\(916\) | − | 9.55449i | − | 0.315689i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 10.7326i | 0.354229i | ||||||||
\(919\) | −7.10925 | + | 12.3136i | −0.234512 | + | 0.406187i | −0.959131 | − | 0.282963i | \(-0.908683\pi\) |
0.724618 | + | 0.689150i | \(0.242016\pi\) | |||||||
\(920\) | −21.4765 | − | 37.1985i | −0.708061 | − | 1.22640i | ||||
\(921\) | 8.95972 | − | 5.17290i | 0.295233 | − | 0.170453i | ||||
\(922\) | 6.73886 | − | 11.6721i | 0.221933 | − | 0.384399i | ||||
\(923\) | 3.13852 | + | 16.9975i | 0.103306 | + | 0.559480i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.2049i | 0.631454i | ||||||||
\(926\) | 20.1160 | − | 34.8420i | 0.661053 | − | 1.14498i | ||||
\(927\) | −9.03223 | − | 15.6443i | −0.296657 | − | 0.513826i | ||||
\(928\) | −21.4458 | + | 12.3817i | −0.703993 | + | 0.406451i | ||||
\(929\) | 24.8963 | + | 14.3739i | 0.816822 | + | 0.471593i | 0.849319 | − | 0.527879i | \(-0.177013\pi\) |
−0.0324972 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(930\) | 16.1412i | 0.529291i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.03168 | 0.197574 | ||||||||
\(933\) | 4.24176 | − | 7.34694i | 0.138869 | − | 0.240528i | ||||
\(934\) | 47.0167 | − | 27.1451i | 1.53843 | − | 0.888215i | ||||
\(935\) | 8.44178 | + | 14.6216i | 0.276076 | + | 0.478177i | ||||
\(936\) | 19.5158 | + | 6.92563i | 0.637893 | + | 0.226371i | ||||
\(937\) | 19.8495 | 0.648456 | 0.324228 | − | 0.945979i | \(-0.394895\pi\) | ||||
0.324228 | + | 0.945979i | \(0.394895\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.26351 | −0.0412330 | ||||||||
\(940\) | −1.43916 | + | 2.49270i | −0.0469402 | + | 0.0813028i | ||||
\(941\) | 39.1720 | − | 22.6160i | 1.27697 | − | 0.737260i | 0.300682 | − | 0.953725i | \(-0.402786\pi\) |
0.976291 | + | 0.216464i | \(0.0694525\pi\) | |||||||
\(942\) | −2.68818 | + | 1.55202i | −0.0875857 | + | 0.0505676i | ||||
\(943\) | 24.7118 | + | 14.2673i | 0.804726 | + | 0.464609i | ||||
\(944\) | − | 47.4083i | − | 1.54301i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.61649 | 0.182608 | ||||||||
\(947\) | −19.1474 | − | 11.0547i | −0.622206 | − | 0.359231i | 0.155521 | − | 0.987833i | \(-0.450294\pi\) |
−0.777727 | + | 0.628602i | \(0.783628\pi\) | |||||||
\(948\) | 0.369263 | + | 0.639582i | 0.0119931 | + | 0.0207727i | ||||
\(949\) | −15.6504 | + | 13.3486i | −0.508035 | + | 0.433314i | ||||
\(950\) | 11.8591 | − | 20.5406i | 0.384760 | − | 0.666424i | ||||
\(951\) | 13.5073i | 0.438004i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.3502 | −1.11271 | −0.556356 | − | 0.830944i | \(-0.687801\pi\) | ||||
−0.556356 | + | 0.830944i | \(0.687801\pi\) | |||||||
\(954\) | −32.7359 | − | 18.9001i | −1.05986 | − | 0.611912i | ||||
\(955\) | −50.9807 | + | 29.4337i | −1.64970 | + | 0.952453i | ||||
\(956\) | 15.2755 | − | 8.81931i | 0.494045 | − | 0.285237i | ||||
\(957\) | −6.85584 | − | 3.95822i | −0.221618 | − | 0.127951i | ||||
\(958\) | 4.10749 | 0.132707 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 4.62131i | − | 0.149152i | ||||||
\(961\) | 7.98890 | − | 13.8372i | 0.257706 | − | 0.446361i | ||||
\(962\) | −22.8245 | − | 26.7604i | −0.735893 | − | 0.862791i | ||||
\(963\) | 21.4918 | + | 37.2249i | 0.692563 | + | 1.19955i | ||||
\(964\) | −0.185102 | − | 0.106869i | −0.00596175 | − | 0.00344202i | ||||
\(965\) | −35.7309 | −1.15022 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.8805i | 0.767945i | 0.923344 | + | 0.383973i | \(0.125444\pi\) | ||||
−0.923344 | + | 0.383973i | \(0.874556\pi\) | |||||||
\(968\) | −7.82921 | − | 4.52020i | −0.251640 | − | 0.145285i | ||||
\(969\) | 4.28831 | − | 2.47585i | 0.137760 | − | 0.0795359i | ||||
\(970\) | −57.8424 | + | 33.3953i | −1.85721 | + | 1.07226i | ||||
\(971\) | 12.9689 | − | 22.4627i | 0.416190 | − | 0.720863i | −0.579362 | − | 0.815070i | \(-0.696698\pi\) |
0.995553 | + | 0.0942072i | \(0.0300316\pi\) | |||||||
\(972\) | 8.84358 | 0.283658 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37.9470 | 1.21590 | ||||||||
\(975\) | −1.94533 | + | 5.48175i | −0.0623003 | + | 0.175556i | ||||
\(976\) | −23.5615 | − | 40.8097i | −0.754184 | − | 1.30629i | ||||
\(977\) | −39.2285 | + | 22.6486i | −1.25503 | + | 0.724592i | −0.972104 | − | 0.234550i | \(-0.924638\pi\) |
−0.282926 | + | 0.959142i | \(0.591305\pi\) | |||||||
\(978\) | −8.03586 | + | 13.9185i | −0.256958 | + | 0.445065i | ||||
\(979\) | 33.7086 | 1.07733 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.5971i | 0.881109i | ||||||||
\(982\) | 32.7942 | + | 18.9338i | 1.04651 | + | 0.604200i | ||||
\(983\) | −1.75891 | + | 1.01551i | −0.0561004 | + | 0.0323896i | −0.527788 | − | 0.849376i | \(-0.676978\pi\) |
0.471687 | + | 0.881766i | \(0.343645\pi\) | |||||||
\(984\) | 2.05354 | + | 3.55683i | 0.0654644 | + | 0.113388i | ||||
\(985\) | −27.2740 | + | 47.2400i | −0.869022 | + | 1.50519i | ||||
\(986\) | 23.3437i | 0.743413i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.13169 | + | 11.5448i | 0.0678182 | + | 0.367289i | ||||
\(989\) | −4.71112 | + | 8.15990i | −0.149805 | + | 0.259470i | ||||
\(990\) | 29.3027 | − | 16.9179i | 0.931302 | − | 0.537687i | ||||
\(991\) | 13.4832 | + | 23.3536i | 0.428309 | + | 0.741853i | 0.996723 | − | 0.0808899i | \(-0.0257762\pi\) |
−0.568414 | + | 0.822743i | \(0.692443\pi\) | |||||||
\(992\) | 13.6973 | − | 23.7244i | 0.434890 | − | 0.753251i | ||||
\(993\) | − | 4.79785i | − | 0.152255i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 36.8399i | − | 1.16790i | ||||||
\(996\) | −0.990045 | − | 0.571603i | −0.0313708 | − | 0.0181119i | ||||
\(997\) | 3.32787 | + | 5.76404i | 0.105395 | + | 0.182549i | 0.913899 | − | 0.405941i | \(-0.133056\pi\) |
−0.808505 | + | 0.588490i | \(0.799723\pi\) | |||||||
\(998\) | 7.02012 | + | 12.1592i | 0.222218 | + | 0.384893i | ||||
\(999\) | 14.5363 | + | 8.39254i | 0.459908 | + | 0.265528i |
(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 | 637.2.r.g.324.4 | 32 | ||
7.2 | even | 3 | 637.2.c.g.246.13 | yes | 16 | ||
7.3 | odd | 6 | inner | 637.2.r.g.116.13 | 32 | ||
7.4 | even | 3 | inner | 637.2.r.g.116.14 | 32 | ||
7.5 | odd | 6 | 637.2.c.g.246.14 | yes | 16 | ||
7.6 | odd | 2 | inner | 637.2.r.g.324.3 | 32 | ||
13.12 | even | 2 | inner | 637.2.r.g.324.14 | 32 | ||
91.5 | even | 12 | 8281.2.a.cs.1.14 | 16 | |||
91.12 | odd | 6 | 637.2.c.g.246.4 | yes | 16 | ||
91.25 | even | 6 | inner | 637.2.r.g.116.4 | 32 | ||
91.38 | odd | 6 | inner | 637.2.r.g.116.3 | 32 | ||
91.44 | odd | 12 | 8281.2.a.cs.1.13 | 16 | |||
91.47 | even | 12 | 8281.2.a.cs.1.4 | 16 | |||
91.51 | even | 6 | 637.2.c.g.246.3 | ✓ | 16 | ||
91.86 | odd | 12 | 8281.2.a.cs.1.3 | 16 | |||
91.90 | odd | 2 | inner | 637.2.r.g.324.13 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.c.g.246.3 | ✓ | 16 | 91.51 | even | 6 | ||
637.2.c.g.246.4 | yes | 16 | 91.12 | odd | 6 | ||
637.2.c.g.246.13 | yes | 16 | 7.2 | even | 3 | ||
637.2.c.g.246.14 | yes | 16 | 7.5 | odd | 6 | ||
637.2.r.g.116.3 | 32 | 91.38 | odd | 6 | inner | ||
637.2.r.g.116.4 | 32 | 91.25 | even | 6 | inner | ||
637.2.r.g.116.13 | 32 | 7.3 | odd | 6 | inner | ||
637.2.r.g.116.14 | 32 | 7.4 | even | 3 | inner | ||
637.2.r.g.324.3 | 32 | 7.6 | odd | 2 | inner | ||
637.2.r.g.324.4 | 32 | 1.1 | even | 1 | trivial | ||
637.2.r.g.324.13 | 32 | 91.90 | odd | 2 | inner | ||
637.2.r.g.324.14 | 32 | 13.12 | even | 2 | inner | ||
8281.2.a.cs.1.3 | 16 | 91.86 | odd | 12 | |||
8281.2.a.cs.1.4 | 16 | 91.47 | even | 12 | |||
8281.2.a.cs.1.13 | 16 | 91.44 | odd | 12 | |||
8281.2.a.cs.1.14 | 16 | 91.5 | even | 12 |