Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (of order \(12\), degree \(4\), 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: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 80.2 | ||
Character | \(\chi\) | \(=\) | 637.80 |
Dual form | 637.2.x.a.215.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.521585 | − | 1.94658i | −0.368816 | − | 1.37644i | −0.862173 | − | 0.506614i | \(-0.830897\pi\) |
0.493357 | − | 0.869827i | \(-0.335770\pi\) | |||||||
\(3\) | − | 1.44369i | − | 0.833512i | −0.909018 | − | 0.416756i | \(-0.863167\pi\) | ||
0.909018 | − | 0.416756i | \(-0.136833\pi\) | |||||||
\(4\) | −1.78508 | + | 1.03062i | −0.892539 | + | 0.515308i | ||||
\(5\) | −0.849184 | + | 3.16920i | −0.379766 | + | 1.41731i | 0.466487 | + | 0.884528i | \(0.345519\pi\) |
−0.846254 | + | 0.532780i | \(0.821147\pi\) | |||||||
\(6\) | −2.81025 | + | 0.753004i | −1.14728 | + | 0.307413i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.0872533 | + | 0.0872533i | 0.0308487 | + | 0.0308487i | ||||
\(9\) | 0.915773 | 0.305258 | ||||||||
\(10\) | 6.61202 | 2.09090 | ||||||||
\(11\) | 4.20434 | + | 4.20434i | 1.26766 | + | 1.26766i | 0.947296 | + | 0.320360i | \(0.103804\pi\) |
0.320360 | + | 0.947296i | \(0.396196\pi\) | |||||||
\(12\) | 1.48788 | + | 2.57709i | 0.429515 | + | 0.743942i | ||||
\(13\) | 2.81021 | − | 2.25892i | 0.779413 | − | 0.626511i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.57532 | + | 1.22595i | 1.18134 | + | 0.316540i | ||||
\(16\) | −1.93689 | + | 3.35480i | −0.484224 | + | 0.838700i | ||||
\(17\) | 0.314289 | + | 0.544364i | 0.0762262 | + | 0.132028i | 0.901619 | − | 0.432531i | \(-0.142380\pi\) |
−0.825393 | + | 0.564559i | \(0.809046\pi\) | |||||||
\(18\) | −0.477654 | − | 1.78263i | −0.112584 | − | 0.420169i | ||||
\(19\) | −0.521911 | − | 0.521911i | −0.119735 | − | 0.119735i | 0.644701 | − | 0.764435i | \(-0.276982\pi\) |
−0.764435 | + | 0.644701i | \(0.776982\pi\) | |||||||
\(20\) | −1.75036 | − | 6.53244i | −0.391393 | − | 1.46070i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.99117 | − | 10.3770i | 1.27732 | − | 2.21239i | ||||
\(23\) | 3.93752 | + | 2.27333i | 0.821029 | + | 0.474021i | 0.850771 | − | 0.525536i | \(-0.176135\pi\) |
−0.0297422 | + | 0.999558i | \(0.509469\pi\) | |||||||
\(24\) | 0.125966 | − | 0.125966i | 0.0257128 | − | 0.0257128i | ||||
\(25\) | −4.99256 | − | 2.88246i | −0.998513 | − | 0.576492i | ||||
\(26\) | −5.86293 | − | 4.29209i | −1.14982 | − | 0.841749i | ||||
\(27\) | − | 5.65314i | − | 1.08795i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.33622 | − | 2.31439i | −0.248129 | − | 0.429772i | 0.714878 | − | 0.699250i | \(-0.246482\pi\) |
−0.963007 | + | 0.269477i | \(0.913149\pi\) | |||||||
\(30\) | − | 9.54568i | − | 1.74279i | ||||||
\(31\) | 1.06713 | − | 0.285936i | 0.191662 | − | 0.0513556i | −0.161711 | − | 0.986838i | \(-0.551701\pi\) |
0.353373 | + | 0.935482i | \(0.385035\pi\) | |||||||
\(32\) | 7.77903 | + | 2.08438i | 1.37515 | + | 0.368471i | ||||
\(33\) | 6.06974 | − | 6.06974i | 1.05661 | − | 1.05661i | ||||
\(34\) | 0.895721 | − | 0.895721i | 0.153615 | − | 0.153615i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.63473 | + | 0.943810i | −0.272454 | + | 0.157302i | ||||
\(37\) | −2.44528 | + | 0.655210i | −0.402001 | + | 0.107716i | −0.454154 | − | 0.890923i | \(-0.650058\pi\) |
0.0521528 | + | 0.998639i | \(0.483392\pi\) | |||||||
\(38\) | −0.743721 | + | 1.28816i | −0.120648 | + | 0.208968i | ||||
\(39\) | −3.26116 | − | 4.05706i | −0.522204 | − | 0.649650i | ||||
\(40\) | −0.350617 | + | 0.202429i | −0.0554374 | + | 0.0320068i | ||||
\(41\) | −0.746755 | + | 2.78693i | −0.116624 | + | 0.435245i | −0.999403 | − | 0.0345422i | \(-0.989003\pi\) |
0.882780 | + | 0.469787i | \(0.155669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.49297 | + | 2.01667i | 0.532673 | + | 0.307539i | 0.742104 | − | 0.670285i | \(-0.233828\pi\) |
−0.209431 | + | 0.977823i | \(0.567161\pi\) | |||||||
\(44\) | −11.8381 | − | 3.17202i | −1.78467 | − | 0.478200i | ||||
\(45\) | −0.777660 | + | 2.90227i | −0.115927 | + | 0.432644i | ||||
\(46\) | 2.37147 | − | 8.85043i | 0.349654 | − | 1.30492i | ||||
\(47\) | 7.10802 | + | 1.90459i | 1.03681 | + | 0.277813i | 0.736791 | − | 0.676120i | \(-0.236340\pi\) |
0.300020 | + | 0.953933i | \(0.403007\pi\) | |||||||
\(48\) | 4.84328 | + | 2.79627i | 0.699067 | + | 0.403606i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00689 | + | 11.2219i | −0.425239 | + | 1.58701i | ||||
\(51\) | 0.785891 | − | 0.453734i | 0.110047 | − | 0.0635355i | ||||
\(52\) | −2.68838 | + | 6.92859i | −0.372811 | + | 0.960823i | ||||
\(53\) | 3.89042 | − | 6.73840i | 0.534390 | − | 0.925590i | −0.464803 | − | 0.885414i | \(-0.653875\pi\) |
0.999193 | − | 0.0401759i | \(-0.0127918\pi\) | |||||||
\(54\) | −11.0043 | + | 2.94859i | −1.49750 | + | 0.401253i | ||||
\(55\) | −16.8946 | + | 9.75412i | −2.27807 | + | 1.31525i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.753475 | + | 0.753475i | −0.0998002 | + | 0.0998002i | ||||
\(58\) | −3.80821 | + | 3.80821i | −0.500042 | + | 0.500042i | ||||
\(59\) | −0.919907 | − | 0.246488i | −0.119762 | − | 0.0320901i | 0.198440 | − | 0.980113i | \(-0.436412\pi\) |
−0.318202 | + | 0.948023i | \(0.603079\pi\) | |||||||
\(60\) | −9.43079 | + | 2.52697i | −1.21751 | + | 0.326231i | ||||
\(61\) | − | 1.08909i | − | 0.139443i | −0.997566 | − | 0.0697217i | \(-0.977789\pi\) | ||
0.997566 | − | 0.0697217i | \(-0.0222111\pi\) | |||||||
\(62\) | −1.11320 | − | 1.92811i | −0.141376 | − | 0.244870i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.48212i | − | 1.06026i | ||||||
\(65\) | 4.77256 | + | 10.8244i | 0.591963 | + | 1.34260i | ||||
\(66\) | −14.9811 | − | 8.64936i | −1.84405 | − | 1.06466i | ||||
\(67\) | −3.81608 | + | 3.81608i | −0.466208 | + | 0.466208i | −0.900684 | − | 0.434476i | \(-0.856934\pi\) |
0.434476 | + | 0.900684i | \(0.356934\pi\) | |||||||
\(68\) | −1.12206 | − | 0.647822i | −0.136070 | − | 0.0785599i | ||||
\(69\) | 3.28197 | − | 5.68453i | 0.395102 | − | 0.684338i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.590023 | + | 2.20200i | 0.0700229 | + | 0.261329i | 0.992059 | − | 0.125776i | \(-0.0401419\pi\) |
−0.922036 | + | 0.387105i | \(0.873475\pi\) | |||||||
\(72\) | 0.0799043 | + | 0.0799043i | 0.00941681 | + | 0.00941681i | ||||
\(73\) | 1.59300 | + | 5.94515i | 0.186446 | + | 0.695827i | 0.994316 | + | 0.106466i | \(0.0339537\pi\) |
−0.807870 | + | 0.589361i | \(0.799380\pi\) | |||||||
\(74\) | 2.55084 | + | 4.41818i | 0.296529 | + | 0.513603i | ||||
\(75\) | −4.16136 | + | 7.20769i | −0.480513 | + | 0.832273i | ||||
\(76\) | 1.46954 | + | 0.393762i | 0.168568 | + | 0.0451677i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.19643 | + | 8.46422i | −0.701608 | + | 0.958385i | ||||
\(79\) | −6.08299 | − | 10.5361i | −0.684390 | − | 1.18540i | −0.973628 | − | 0.228141i | \(-0.926735\pi\) |
0.289238 | − | 0.957257i | \(-0.406598\pi\) | |||||||
\(80\) | −8.98724 | − | 8.98724i | −1.00480 | − | 1.00480i | ||||
\(81\) | −5.41404 | −0.601560 | ||||||||
\(82\) | 5.81448 | 0.642102 | ||||||||
\(83\) | 3.59152 | + | 3.59152i | 0.394220 | + | 0.394220i | 0.876189 | − | 0.481968i | \(-0.160078\pi\) |
−0.481968 | + | 0.876189i | \(0.660078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.99209 | + | 0.533778i | −0.216072 | + | 0.0578963i | ||||
\(86\) | 2.10373 | − | 7.85121i | 0.226851 | − | 0.846618i | ||||
\(87\) | −3.34126 | + | 1.92908i | −0.358220 | + | 0.206819i | ||||
\(88\) | 0.733685i | 0.0782111i | ||||||||
\(89\) | −1.05715 | − | 3.94532i | −0.112057 | − | 0.418203i | 0.886993 | − | 0.461783i | \(-0.152790\pi\) |
−0.999050 | + | 0.0435803i | \(0.986124\pi\) | |||||||
\(90\) | 6.05511 | 0.638265 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.37170 | −0.977067 | ||||||||
\(93\) | −0.412802 | − | 1.54060i | −0.0428055 | − | 0.159752i | ||||
\(94\) | − | 14.8297i | − | 1.52957i | ||||||
\(95\) | 2.09724 | − | 1.21084i | 0.215172 | − | 0.124230i | ||||
\(96\) | 3.00919 | − | 11.2305i | 0.307125 | − | 1.14620i | ||||
\(97\) | 8.41780 | − | 2.25554i | 0.854698 | − | 0.229016i | 0.195239 | − | 0.980756i | \(-0.437452\pi\) |
0.659460 | + | 0.751740i | \(0.270785\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.85022 | + | 3.85022i | 0.386962 | + | 0.386962i | ||||
\(100\) | 11.8828 | 1.18828 | ||||||||
\(101\) | 17.1752 | 1.70899 | 0.854496 | − | 0.519458i | \(-0.173866\pi\) | ||||
0.854496 | + | 0.519458i | \(0.173866\pi\) | |||||||
\(102\) | −1.29314 | − | 1.29314i | −0.128040 | − | 0.128040i | ||||
\(103\) | −7.19481 | − | 12.4618i | −0.708926 | − | 1.22790i | −0.965256 | − | 0.261306i | \(-0.915847\pi\) |
0.256330 | − | 0.966589i | \(-0.417487\pi\) | |||||||
\(104\) | 0.442298 | + | 0.0481025i | 0.0433709 | + | 0.00471684i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.1460 | − | 4.05836i | −1.47111 | − | 0.394183i | ||||
\(107\) | −1.56036 | + | 2.70262i | −0.150846 | + | 0.261272i | −0.931539 | − | 0.363643i | \(-0.881533\pi\) |
0.780693 | + | 0.624915i | \(0.214866\pi\) | |||||||
\(108\) | 5.82622 | + | 10.0913i | 0.560628 | + | 0.971036i | ||||
\(109\) | 2.45900 | + | 9.17711i | 0.235529 | + | 0.879008i | 0.977909 | + | 0.209029i | \(0.0670302\pi\) |
−0.742380 | + | 0.669979i | \(0.766303\pi\) | |||||||
\(110\) | 27.7992 | + | 27.7992i | 2.65055 | + | 2.65055i | ||||
\(111\) | 0.945917 | + | 3.53021i | 0.0897825 | + | 0.335073i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.34080 | − | 2.32234i | 0.126132 | − | 0.218467i | −0.796043 | − | 0.605240i | \(-0.793077\pi\) |
0.922175 | + | 0.386773i | \(0.126410\pi\) | |||||||
\(114\) | 1.85970 | + | 1.07370i | 0.174177 | + | 0.100561i | ||||
\(115\) | −10.5483 | + | 10.5483i | −0.983633 | + | 0.983633i | ||||
\(116\) | 4.77050 | + | 2.75425i | 0.442930 | + | 0.255726i | ||||
\(117\) | 2.57352 | − | 2.06866i | 0.237922 | − | 0.191247i | ||||
\(118\) | 1.91924i | 0.176680i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.292243 | + | 0.506181i | 0.0266781 | + | 0.0462077i | ||||
\(121\) | 24.3529i | 2.21390i | ||||||||
\(122\) | −2.12000 | + | 0.568052i | −0.191936 | + | 0.0514290i | ||||
\(123\) | 4.02345 | + | 1.07808i | 0.362782 | + | 0.0972071i | ||||
\(124\) | −1.61022 | + | 1.61022i | −0.144602 | + | 0.144602i | ||||
\(125\) | 1.77462 | − | 1.77462i | 0.158727 | − | 0.158727i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.93218 | + | 2.84760i | −0.437661 | + | 0.252683i | −0.702605 | − | 0.711580i | \(-0.747980\pi\) |
0.264944 | + | 0.964264i | \(0.414646\pi\) | |||||||
\(128\) | −0.953075 | + | 0.255376i | −0.0842407 | + | 0.0225722i | ||||
\(129\) | 2.91143 | − | 5.04275i | 0.256337 | − | 0.443989i | ||||
\(130\) | 18.5812 | − | 14.9360i | 1.62968 | − | 1.30997i | ||||
\(131\) | −15.1645 | + | 8.75520i | −1.32492 | + | 0.764946i | −0.984510 | − | 0.175329i | \(-0.943901\pi\) |
−0.340415 | + | 0.940275i | \(0.610568\pi\) | |||||||
\(132\) | −4.57939 | + | 17.0905i | −0.398585 | + | 1.48754i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.41872 | + | 5.43790i | 0.813653 | + | 0.469763i | ||||
\(135\) | 17.9159 | + | 4.80056i | 1.54196 | + | 0.413166i | ||||
\(136\) | −0.0200748 | + | 0.0749203i | −0.00172140 | + | 0.00642437i | ||||
\(137\) | 3.79415 | − | 14.1600i | 0.324156 | − | 1.20977i | −0.591001 | − | 0.806671i | \(-0.701267\pi\) |
0.915157 | − | 0.403097i | \(-0.132066\pi\) | |||||||
\(138\) | −12.7772 | − | 3.42365i | −1.08767 | − | 0.291440i | ||||
\(139\) | 3.10457 | + | 1.79243i | 0.263327 | + | 0.152032i | 0.625851 | − | 0.779943i | \(-0.284752\pi\) |
−0.362525 | + | 0.931974i | \(0.618085\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.74963 | − | 10.2617i | 0.231560 | − | 0.864195i | ||||
\(142\) | 3.97862 | − | 2.29706i | 0.333878 | − | 0.192765i | ||||
\(143\) | 21.3123 | + | 2.31784i | 1.78223 | + | 0.193827i | ||||
\(144\) | −1.77376 | + | 3.07224i | −0.147813 | + | 0.256020i | ||||
\(145\) | 8.46946 | − | 2.26939i | 0.703351 | − | 0.188462i | ||||
\(146\) | 10.7418 | − | 6.20180i | 0.889001 | − | 0.513265i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.68974 | − | 3.68974i | 0.303295 | − | 0.303295i | ||||
\(149\) | 10.1485 | − | 10.1485i | 0.831400 | − | 0.831400i | −0.156308 | − | 0.987708i | \(-0.549959\pi\) |
0.987708 | + | 0.156308i | \(0.0499593\pi\) | |||||||
\(150\) | 16.2009 | + | 4.34101i | 1.32279 | + | 0.354442i | ||||
\(151\) | −22.9711 | + | 6.15509i | −1.86936 | + | 0.500894i | −0.869386 | + | 0.494134i | \(0.835485\pi\) |
−0.999977 | + | 0.00676075i | \(0.997848\pi\) | |||||||
\(152\) | − | 0.0910769i | − | 0.00738732i | ||||||
\(153\) | 0.287817 | + | 0.498514i | 0.0232687 | + | 0.0403025i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.62475i | 0.291147i | ||||||||
\(156\) | 10.0027 | + | 3.88117i | 0.800857 | + | 0.310742i | ||||
\(157\) | −6.58929 | − | 3.80433i | −0.525882 | − | 0.303618i | 0.213456 | − | 0.976953i | \(-0.431528\pi\) |
−0.739338 | + | 0.673334i | \(0.764861\pi\) | |||||||
\(158\) | −17.3365 | + | 17.3365i | −1.37922 | + | 1.37922i | ||||
\(159\) | −9.72812 | − | 5.61653i | −0.771490 | − | 0.445420i | ||||
\(160\) | −13.2116 | + | 22.8832i | −1.04447 | + | 1.80908i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 2.82388 | + | 10.5389i | 0.221865 | + | 0.828012i | ||||
\(163\) | −1.81864 | − | 1.81864i | −0.142447 | − | 0.142447i | 0.632287 | − | 0.774734i | \(-0.282116\pi\) |
−0.774734 | + | 0.632287i | \(0.782116\pi\) | |||||||
\(164\) | −1.53923 | − | 5.74450i | −0.120194 | − | 0.448570i | ||||
\(165\) | 14.0819 | + | 24.3905i | 1.09627 | + | 1.89880i | ||||
\(166\) | 5.11790 | − | 8.86446i | 0.397226 | − | 0.688016i | ||||
\(167\) | 3.28638 | + | 0.880582i | 0.254308 | + | 0.0681415i | 0.383720 | − | 0.923449i | \(-0.374643\pi\) |
−0.129413 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.79460 | − | 12.6961i | 0.214969 | − | 0.976621i | ||||
\(170\) | 2.07808 | + | 3.59935i | 0.159382 | + | 0.276057i | ||||
\(171\) | −0.477952 | − | 0.477952i | −0.0365499 | − | 0.0365499i | ||||
\(172\) | −8.31363 | −0.633908 | ||||||||
\(173\) | 14.0503 | 1.06823 | 0.534114 | − | 0.845412i | \(-0.320645\pi\) | ||||
0.534114 | + | 0.845412i | \(0.320645\pi\) | |||||||
\(174\) | 5.49785 | + | 5.49785i | 0.416791 | + | 0.416791i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −22.2481 | + | 5.96136i | −1.67701 | + | 0.449354i | ||||
\(177\) | −0.355852 | + | 1.32806i | −0.0267474 | + | 0.0998228i | ||||
\(178\) | −7.12850 | + | 4.11564i | −0.534303 | + | 0.308480i | ||||
\(179\) | 14.9624i | 1.11834i | 0.829053 | + | 0.559170i | \(0.188880\pi\) | ||||
−0.829053 | + | 0.559170i | \(0.811120\pi\) | |||||||
\(180\) | −1.60294 | − | 5.98224i | −0.119476 | − | 0.445890i | ||||
\(181\) | −15.4409 | −1.14772 | −0.573858 | − | 0.818955i | \(-0.694554\pi\) | ||||
−0.573858 | + | 0.818955i | \(0.694554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57230 | −0.116228 | ||||||||
\(184\) | 0.145206 | + | 0.541917i | 0.0107047 | + | 0.0399506i | ||||
\(185\) | − | 8.30596i | − | 0.610666i | ||||||
\(186\) | −2.78359 | + | 1.60710i | −0.204102 | + | 0.117839i | ||||
\(187\) | −0.967315 | + | 3.61007i | −0.0707371 | + | 0.263994i | ||||
\(188\) | −14.6513 | + | 3.92580i | −1.06855 | + | 0.286318i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.45089 | − | 3.45089i | −0.250354 | − | 0.250354i | ||||
\(191\) | −17.1549 | −1.24129 | −0.620643 | − | 0.784093i | \(-0.713128\pi\) | ||||
−0.620643 | + | 0.784093i | \(0.713128\pi\) | |||||||
\(192\) | −12.2455 | −0.883743 | ||||||||
\(193\) | −4.33644 | − | 4.33644i | −0.312144 | − | 0.312144i | 0.533596 | − | 0.845740i | \(-0.320840\pi\) |
−0.845740 | + | 0.533596i | \(0.820840\pi\) | |||||||
\(194\) | −8.78120 | − | 15.2095i | −0.630453 | − | 1.09198i | ||||
\(195\) | 15.6270 | − | 6.89008i | 1.11907 | − | 0.493409i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.7906 | + | 6.64263i | 1.76626 | + | 0.473268i | 0.987971 | − | 0.154640i | \(-0.0494219\pi\) |
0.778288 | + | 0.627908i | \(0.216089\pi\) | |||||||
\(198\) | 5.48655 | − | 9.50299i | 0.389912 | − | 0.675348i | ||||
\(199\) | −4.36369 | − | 7.55813i | −0.309334 | − | 0.535782i | 0.668883 | − | 0.743368i | \(-0.266773\pi\) |
−0.978217 | + | 0.207586i | \(0.933439\pi\) | |||||||
\(200\) | −0.184114 | − | 0.687122i | −0.0130188 | − | 0.0485869i | ||||
\(201\) | 5.50921 | + | 5.50921i | 0.388590 | + | 0.388590i | ||||
\(202\) | −8.95830 | − | 33.4328i | −0.630304 | − | 2.35233i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.935251 | + | 1.61990i | −0.0654806 | + | 0.113416i | ||||
\(205\) | −8.19819 | − | 4.73323i | −0.572586 | − | 0.330583i | ||||
\(206\) | −20.5052 | + | 20.5052i | −1.42866 | + | 1.42866i | ||||
\(207\) | 3.60587 | + | 2.08185i | 0.250625 | + | 0.144699i | ||||
\(208\) | 2.13513 | + | 13.8030i | 0.148044 | + | 0.957065i | ||||
\(209\) | − | 4.38858i | − | 0.303565i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.41370 | − | 9.37680i | −0.372694 | − | 0.645525i | 0.617285 | − | 0.786740i | \(-0.288233\pi\) |
−0.989979 | + | 0.141214i | \(0.954899\pi\) | |||||||
\(212\) | 16.0381i | 1.10150i | ||||||||
\(213\) | 3.17899 | − | 0.851808i | 0.217821 | − | 0.0583649i | ||||
\(214\) | 6.07473 | + | 1.62772i | 0.415260 | + | 0.111269i | ||||
\(215\) | −9.35739 | + | 9.35739i | −0.638168 | + | 0.638168i | ||||
\(216\) | 0.493256 | − | 0.493256i | 0.0335618 | − | 0.0335618i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.5814 | − | 9.57329i | 1.12304 | − | 0.648385i | ||||
\(219\) | 8.58292 | − | 2.29979i | 0.579980 | − | 0.155405i | ||||
\(220\) | 20.1055 | − | 34.8237i | 1.35551 | − | 2.34782i | ||||
\(221\) | 2.11289 | + | 0.819827i | 0.142128 | + | 0.0551476i | ||||
\(222\) | 6.37847 | − | 3.68261i | 0.428095 | − | 0.247161i | ||||
\(223\) | 2.01754 | − | 7.52957i | 0.135105 | − | 0.504217i | −0.864893 | − | 0.501957i | \(-0.832614\pi\) |
0.999997 | − | 0.00226068i | \(-0.000719598\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.57206 | − | 2.63968i | −0.304804 | − | 0.175979i | ||||
\(226\) | −5.21997 | − | 1.39869i | −0.347227 | − | 0.0930392i | ||||
\(227\) | −3.68960 | + | 13.7698i | −0.244888 | + | 0.913933i | 0.728552 | + | 0.684990i | \(0.240194\pi\) |
−0.973440 | + | 0.228943i | \(0.926473\pi\) | |||||||
\(228\) | 0.568469 | − | 2.12156i | 0.0376478 | − | 0.140503i | ||||
\(229\) | −11.0227 | − | 2.95351i | −0.728398 | − | 0.195174i | −0.124482 | − | 0.992222i | \(-0.539727\pi\) |
−0.603916 | + | 0.797048i | \(0.706394\pi\) | |||||||
\(230\) | 26.0349 | + | 15.0313i | 1.71669 | + | 0.991133i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0853493 | − | 0.318528i | 0.00560346 | − | 0.0209124i | ||||
\(233\) | −18.9544 | + | 10.9433i | −1.24175 | + | 0.716922i | −0.969450 | − | 0.245291i | \(-0.921117\pi\) |
−0.272297 | + | 0.962213i | \(0.587783\pi\) | |||||||
\(234\) | −5.36911 | − | 3.93058i | −0.350990 | − | 0.256950i | ||||
\(235\) | −12.0720 | + | 20.9094i | −0.787492 | + | 1.36398i | ||||
\(236\) | 1.89614 | − | 0.508069i | 0.123428 | − | 0.0330725i | ||||
\(237\) | −15.2107 | + | 8.78193i | −0.988044 | + | 0.570448i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.79044 | − | 3.79044i | 0.245183 | − | 0.245183i | −0.573807 | − | 0.818990i | \(-0.694534\pi\) |
0.818990 | + | 0.573807i | \(0.194534\pi\) | |||||||
\(240\) | −12.9747 | + | 12.9747i | −0.837516 | + | 0.837516i | ||||
\(241\) | 15.0798 | + | 4.04063i | 0.971377 | + | 0.260280i | 0.709409 | − | 0.704797i | \(-0.248962\pi\) |
0.261968 | + | 0.965077i | \(0.415629\pi\) | |||||||
\(242\) | 47.4050 | − | 12.7021i | 3.04731 | − | 0.816523i | ||||
\(243\) | − | 9.14326i | − | 0.586541i | ||||||
\(244\) | 1.12243 | + | 1.94411i | 0.0718563 | + | 0.124459i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 8.39427i | − | 0.535199i | ||||||
\(247\) | −2.64563 | − | 0.287728i | −0.168338 | − | 0.0183077i | ||||
\(248\) | 0.118059 | + | 0.0681616i | 0.00749677 | + | 0.00432826i | ||||
\(249\) | 5.18502 | − | 5.18502i | 0.328587 | − | 0.328587i | ||||
\(250\) | −4.38005 | − | 2.52882i | −0.277019 | − | 0.159937i | ||||
\(251\) | −2.30694 | + | 3.99573i | −0.145612 | + | 0.252208i | −0.929601 | − | 0.368567i | \(-0.879849\pi\) |
0.783989 | + | 0.620775i | \(0.213182\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.99682 | + | 26.1125i | 0.439886 | + | 1.64168i | ||||
\(254\) | 8.11563 | + | 8.11563i | 0.509220 | + | 0.509220i | ||||
\(255\) | 0.770607 | + | 2.87595i | 0.0482573 | + | 0.180099i | ||||
\(256\) | −7.48790 | − | 12.9694i | −0.467994 | − | 0.810589i | ||||
\(257\) | −7.83278 | + | 13.5668i | −0.488596 | + | 0.846273i | −0.999914 | − | 0.0131189i | \(-0.995824\pi\) |
0.511318 | + | 0.859391i | \(0.329157\pi\) | |||||||
\(258\) | −11.3347 | − | 3.03712i | −0.705666 | − | 0.189083i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −19.6751 | − | 14.4036i | −1.22020 | − | 0.893276i | ||||
\(261\) | −1.22367 | − | 2.11946i | −0.0757434 | − | 0.131191i | ||||
\(262\) | 24.9523 | + | 24.9523i | 1.54156 | + | 1.54156i | ||||
\(263\) | −23.9108 | −1.47441 | −0.737203 | − | 0.675671i | \(-0.763854\pi\) | ||||
−0.737203 | + | 0.675671i | \(0.763854\pi\) | |||||||
\(264\) | 1.05921 | 0.0651899 | ||||||||
\(265\) | 18.0516 | + | 18.0516i | 1.10890 | + | 1.10890i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.69580 | + | 1.52618i | −0.348577 | + | 0.0934010i | ||||
\(268\) | 2.87909 | − | 10.7449i | 0.175868 | − | 0.656350i | ||||
\(269\) | −11.7207 | + | 6.76695i | −0.714624 | + | 0.412588i | −0.812771 | − | 0.582584i | \(-0.802042\pi\) |
0.0981467 | + | 0.995172i | \(0.468709\pi\) | |||||||
\(270\) | − | 37.3787i | − | 2.27480i | ||||||
\(271\) | 5.60453 | + | 20.9164i | 0.340451 | + | 1.27058i | 0.897838 | + | 0.440327i | \(0.145137\pi\) |
−0.557387 | + | 0.830253i | \(0.688196\pi\) | |||||||
\(272\) | −2.43498 | −0.147642 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −29.5425 | −1.78473 | ||||||||
\(275\) | −8.87160 | − | 33.1093i | −0.534978 | − | 1.99656i | ||||
\(276\) | 13.5298i | 0.814397i | ||||||||
\(277\) | 18.5473 | − | 10.7083i | 1.11440 | − | 0.643399i | 0.174434 | − | 0.984669i | \(-0.444190\pi\) |
0.939965 | + | 0.341270i | \(0.110857\pi\) | |||||||
\(278\) | 1.86981 | − | 6.97821i | 0.112143 | − | 0.418525i | ||||
\(279\) | 0.977247 | − | 0.261853i | 0.0585063 | − | 0.0156767i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.874765 | + | 0.874765i | 0.0521841 | + | 0.0521841i | 0.732717 | − | 0.680533i | \(-0.238252\pi\) |
−0.680533 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(282\) | −21.4095 | −1.27492 | ||||||||
\(283\) | −18.4612 | −1.09741 | −0.548703 | − | 0.836018i | \(-0.684878\pi\) | ||||
−0.548703 | + | 0.836018i | \(0.684878\pi\) | |||||||
\(284\) | −3.32265 | − | 3.32265i | −0.197163 | − | 0.197163i | ||||
\(285\) | −1.74807 | − | 3.02775i | −0.103547 | − | 0.179348i | ||||
\(286\) | −6.60433 | − | 42.6952i | −0.390522 | − | 2.52462i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.12383 | + | 1.90882i | 0.419775 | + | 0.112479i | ||||
\(289\) | 8.30245 | − | 14.3803i | 0.488379 | − | 0.845897i | ||||
\(290\) | −8.83509 | − | 15.3028i | −0.518814 | − | 0.898613i | ||||
\(291\) | −3.25629 | − | 12.1527i | −0.190887 | − | 0.712401i | ||||
\(292\) | −8.97079 | − | 8.97079i | −0.524976 | − | 0.524976i | ||||
\(293\) | −3.21602 | − | 12.0024i | −0.187882 | − | 0.701186i | −0.993995 | − | 0.109424i | \(-0.965099\pi\) |
0.806113 | − | 0.591762i | \(-0.201567\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.56234 | − | 2.70605i | 0.0909629 | − | 0.157552i | ||||
\(296\) | −0.270528 | − | 0.156189i | −0.0157241 | − | 0.00907832i | ||||
\(297\) | 23.7677 | − | 23.7677i | 1.37914 | − | 1.37914i | ||||
\(298\) | −25.0483 | − | 14.4616i | −1.45101 | − | 0.837739i | ||||
\(299\) | 16.2005 | − | 2.50599i | 0.936900 | − | 0.144925i | ||||
\(300\) | − | 17.1551i | − | 0.990448i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 23.9628 | + | 41.5048i | 1.37890 | + | 2.38833i | ||||
\(303\) | − | 24.7955i | − | 1.42447i | ||||||
\(304\) | 2.76179 | − | 0.740021i | 0.158400 | − | 0.0424431i | ||||
\(305\) | 3.45154 | + | 0.924836i | 0.197634 | + | 0.0529560i | ||||
\(306\) | 0.820277 | − | 0.820277i | 0.0468921 | − | 0.0468921i | ||||
\(307\) | 3.51390 | − | 3.51390i | 0.200549 | − | 0.200549i | −0.599686 | − | 0.800235i | \(-0.704708\pi\) |
0.800235 | + | 0.599686i | \(0.204708\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.9909 | + | 10.3870i | −1.02347 | + | 0.590898i | ||||
\(310\) | 7.05587 | − | 1.89061i | 0.400746 | − | 0.107380i | ||||
\(311\) | −9.18303 | + | 15.9055i | −0.520722 | + | 0.901916i | 0.478988 | + | 0.877821i | \(0.341004\pi\) |
−0.999710 | + | 0.0240949i | \(0.992330\pi\) | |||||||
\(312\) | 0.0694448 | − | 0.638540i | 0.00393154 | − | 0.0361502i | ||||
\(313\) | −7.78607 | + | 4.49529i | −0.440095 | + | 0.254089i | −0.703638 | − | 0.710559i | \(-0.748442\pi\) |
0.263543 | + | 0.964648i | \(0.415109\pi\) | |||||||
\(314\) | −3.96856 | + | 14.8109i | −0.223959 | + | 0.835825i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.7172 | + | 12.5385i | 1.22169 | + | 0.705343i | ||||
\(317\) | −13.9161 | − | 3.72880i | −0.781605 | − | 0.209430i | −0.154113 | − | 0.988053i | \(-0.549252\pi\) |
−0.627492 | + | 0.778623i | \(0.715919\pi\) | |||||||
\(318\) | −5.85900 | + | 21.8661i | −0.328556 | + | 1.22619i | ||||
\(319\) | 4.11259 | − | 15.3484i | 0.230261 | − | 0.859346i | ||||
\(320\) | 26.8815 | + | 7.20287i | 1.50272 | + | 0.402653i | ||||
\(321\) | 3.90173 | + | 2.25267i | 0.217773 | + | 0.125732i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.120079 | − | 0.448141i | 0.00668137 | − | 0.0249352i | ||||
\(324\) | 9.66448 | − | 5.57979i | 0.536916 | − | 0.309988i | ||||
\(325\) | −20.5414 | + | 3.17746i | −1.13943 | + | 0.176254i | ||||
\(326\) | −2.59156 | + | 4.48871i | −0.143533 | + | 0.248607i | ||||
\(327\) | 13.2489 | − | 3.55002i | 0.732663 | − | 0.196317i | ||||
\(328\) | −0.308326 | + | 0.178012i | −0.0170244 | + | 0.00982906i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 40.1333 | − | 40.1333i | 2.20926 | − | 2.20926i | ||||
\(331\) | 5.78697 | − | 5.78697i | 0.318081 | − | 0.318081i | −0.529949 | − | 0.848030i | \(-0.677789\pi\) |
0.848030 | + | 0.529949i | \(0.177789\pi\) | |||||||
\(332\) | −10.1126 | − | 2.70967i | −0.555001 | − | 0.148712i | ||||
\(333\) | −2.23932 | + | 0.600024i | −0.122714 | + | 0.0328811i | ||||
\(334\) | − | 6.85650i | − | 0.375171i | ||||||
\(335\) | −8.85335 | − | 15.3345i | −0.483710 | − | 0.837811i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.63832i | − | 0.0892447i | −0.999004 | − | 0.0446224i | \(-0.985792\pi\) | ||
0.999004 | − | 0.0446224i | \(-0.0142085\pi\) | |||||||
\(338\) | −26.1716 | + | 1.18217i | −1.42355 | + | 0.0643017i | ||||
\(339\) | −3.35273 | − | 1.93570i | −0.182095 | − | 0.105133i | ||||
\(340\) | 3.00591 | − | 3.00591i | 0.163018 | − | 0.163018i | ||||
\(341\) | 5.68874 | + | 3.28439i | 0.308062 | + | 0.177860i | ||||
\(342\) | −0.681080 | + | 1.17967i | −0.0368286 | + | 0.0637890i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.128812 | + | 0.480734i | 0.00694510 | + | 0.0259194i | ||||
\(345\) | 15.2284 | + | 15.2284i | 0.819870 | + | 0.819870i | ||||
\(346\) | −7.32845 | − | 27.3501i | −0.393980 | − | 1.47035i | ||||
\(347\) | 4.81567 | + | 8.34098i | 0.258519 | + | 0.447768i | 0.965845 | − | 0.259119i | \(-0.0834323\pi\) |
−0.707327 | + | 0.706887i | \(0.750099\pi\) | |||||||
\(348\) | 3.97627 | − | 6.88710i | 0.213150 | − | 0.369187i | ||||
\(349\) | −28.4665 | − | 7.62758i | −1.52378 | − | 0.408295i | −0.602794 | − | 0.797897i | \(-0.705946\pi\) |
−0.920983 | + | 0.389602i | \(0.872613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.7700 | − | 15.8865i | −0.681611 | − | 0.847961i | ||||
\(352\) | 23.9422 | + | 41.4691i | 1.27612 | + | 2.21031i | ||||
\(353\) | −11.3032 | − | 11.3032i | −0.601610 | − | 0.601610i | 0.339130 | − | 0.940740i | \(-0.389867\pi\) |
−0.940740 | + | 0.339130i | \(0.889867\pi\) | |||||||
\(354\) | 2.77078 | 0.147265 | ||||||||
\(355\) | −7.47960 | −0.396976 | ||||||||
\(356\) | 5.95319 | + | 5.95319i | 0.315519 | + | 0.315519i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 29.1255 | − | 7.80415i | 1.53933 | − | 0.412462i | ||||
\(359\) | −1.48737 | + | 5.55095i | −0.0785005 | + | 0.292968i | −0.994004 | − | 0.109342i | \(-0.965126\pi\) |
0.915504 | + | 0.402309i | \(0.131792\pi\) | |||||||
\(360\) | −0.321086 | + | 0.185379i | −0.0169227 | + | 0.00977033i | ||||
\(361\) | − | 18.4552i | − | 0.971327i | ||||||
\(362\) | 8.05376 | + | 30.0570i | 0.423296 | + | 1.57976i | ||||
\(363\) | 35.1580 | 1.84531 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.1941 | −1.05701 | ||||||||
\(366\) | 0.820088 | + | 3.06061i | 0.0428667 | + | 0.159981i | ||||
\(367\) | − | 25.4610i | − | 1.32905i | −0.747264 | − | 0.664527i | \(-0.768633\pi\) | ||
0.747264 | − | 0.664527i | \(-0.231367\pi\) | |||||||
\(368\) | −15.2531 | + | 8.80639i | −0.795123 | + | 0.459065i | ||||
\(369\) | −0.683858 | + | 2.55219i | −0.0356002 | + | 0.132862i | ||||
\(370\) | −16.1682 | + | 4.33226i | −0.840546 | + | 0.225224i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.32465 | + | 2.32465i | 0.120527 | + | 0.120527i | ||||
\(373\) | 18.7156 | 0.969055 | 0.484528 | − | 0.874776i | \(-0.338991\pi\) | ||||
0.484528 | + | 0.874776i | \(0.338991\pi\) | |||||||
\(374\) | 7.53183 | 0.389462 | ||||||||
\(375\) | −2.56199 | − | 2.56199i | −0.132301 | − | 0.132301i | ||||
\(376\) | 0.454017 | + | 0.786380i | 0.0234141 | + | 0.0405545i | ||||
\(377\) | −8.98308 | − | 3.48554i | −0.462652 | − | 0.179515i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5112 | − | 5.49596i | −1.05359 | − | 0.282309i | −0.309856 | − | 0.950784i | \(-0.600281\pi\) |
−0.743735 | + | 0.668475i | \(0.766947\pi\) | |||||||
\(380\) | −2.49582 | + | 4.32289i | −0.128033 | + | 0.221760i | ||||
\(381\) | 4.11103 | + | 7.12052i | 0.210615 | + | 0.364795i | ||||
\(382\) | 8.94774 | + | 33.3934i | 0.457806 | + | 1.70856i | ||||
\(383\) | −22.9487 | − | 22.9487i | −1.17262 | − | 1.17262i | −0.981582 | − | 0.191039i | \(-0.938814\pi\) |
−0.191039 | − | 0.981582i | \(-0.561186\pi\) | |||||||
\(384\) | 0.368682 | + | 1.37594i | 0.0188142 | + | 0.0702157i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.17941 | + | 10.7031i | −0.314524 | + | 0.544771i | ||||
\(387\) | 3.19877 | + | 1.84681i | 0.162603 | + | 0.0938786i | ||||
\(388\) | −12.7018 | + | 12.7018i | −0.644838 | + | 0.644838i | ||||
\(389\) | −6.03084 | − | 3.48191i | −0.305776 | − | 0.176540i | 0.339259 | − | 0.940693i | \(-0.389824\pi\) |
−0.645035 | + | 0.764153i | \(0.723157\pi\) | |||||||
\(390\) | −21.5629 | − | 26.8254i | −1.09188 | − | 1.35836i | ||||
\(391\) | 2.85792i | 0.144531i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.6398 | + | 21.8927i | 0.637591 | + | 1.10434i | ||||
\(394\) | − | 51.7217i | − | 2.60570i | ||||||
\(395\) | 38.5564 | − | 10.3312i | 1.93998 | − | 0.519817i | ||||
\(396\) | −10.8410 | − | 2.90485i | −0.544783 | − | 0.145974i | ||||
\(397\) | 10.5642 | − | 10.5642i | 0.530203 | − | 0.530203i | −0.390430 | − | 0.920633i | \(-0.627674\pi\) |
0.920633 | + | 0.390430i | \(0.127674\pi\) | |||||||
\(398\) | −12.4365 | + | 12.4365i | −0.623384 | + | 0.623384i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.3401 | − | 11.1660i | 0.967007 | − | 0.558302i | ||||
\(401\) | −23.3513 | + | 6.25695i | −1.16611 | + | 0.312457i | −0.789402 | − | 0.613877i | \(-0.789609\pi\) |
−0.376704 | + | 0.926334i | \(0.622943\pi\) | |||||||
\(402\) | 7.85061 | − | 13.5977i | 0.391553 | − | 0.678190i | ||||
\(403\) | 2.35295 | − | 3.21409i | 0.117209 | − | 0.160105i | ||||
\(404\) | −30.6590 | + | 17.7010i | −1.52534 | + | 0.880657i | ||||
\(405\) | 4.59751 | − | 17.1582i | 0.228452 | − | 0.852595i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.0355 | − | 7.52605i | −0.646146 | − | 0.373052i | ||||
\(408\) | 0.108161 | + | 0.0289818i | 0.00535479 | + | 0.00143481i | ||||
\(409\) | −9.71416 | + | 36.2537i | −0.480334 | + | 1.79263i | 0.119875 | + | 0.992789i | \(0.461751\pi\) |
−0.600209 | + | 0.799843i | \(0.704916\pi\) | |||||||
\(410\) | −4.93756 | + | 18.4272i | −0.243849 | + | 0.910056i | ||||
\(411\) | −20.4425 | − | 5.47756i | −1.00836 | − | 0.270188i | ||||
\(412\) | 25.6866 | + | 14.8302i | 1.26549 | + | 0.730630i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.17172 | − | 8.10499i | 0.106734 | − | 0.398338i | ||||
\(415\) | −14.4321 | + | 8.33236i | −0.708443 | + | 0.409020i | ||||
\(416\) | 26.5692 | − | 11.7146i | 1.30266 | − | 0.574356i | ||||
\(417\) | 2.58770 | − | 4.48203i | 0.126720 | − | 0.219486i | ||||
\(418\) | −8.54273 | + | 2.28902i | −0.417839 | + | 0.111960i | ||||
\(419\) | 7.05130 | − | 4.07107i | 0.344478 | − | 0.198885i | −0.317772 | − | 0.948167i | \(-0.602935\pi\) |
0.662251 | + | 0.749282i | \(0.269601\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.46118 | − | 2.46118i | 0.119951 | − | 0.119951i | −0.644583 | − | 0.764534i | \(-0.722969\pi\) |
0.764534 | + | 0.644583i | \(0.222969\pi\) | |||||||
\(422\) | −15.4290 | + | 15.4290i | −0.751072 | + | 0.751072i | ||||
\(423\) | 6.50934 | + | 1.74417i | 0.316495 | + | 0.0848045i | ||||
\(424\) | 0.927399 | − | 0.248496i | 0.0450385 | − | 0.0120680i | ||||
\(425\) | − | 3.62370i | − | 0.175775i | ||||||
\(426\) | −3.31623 | − | 5.74387i | −0.160672 | − | 0.278292i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 6.43252i | − | 0.310927i | ||||||
\(429\) | 3.34623 | − | 30.7683i | 0.161557 | − | 1.48551i | ||||
\(430\) | 23.0956 | + | 13.3342i | 1.11377 | + | 0.643034i | ||||
\(431\) | −10.8313 | + | 10.8313i | −0.521724 | + | 0.521724i | −0.918092 | − | 0.396368i | \(-0.870271\pi\) |
0.396368 | + | 0.918092i | \(0.370271\pi\) | |||||||
\(432\) | 18.9652 | + | 10.9495i | 0.912462 | + | 0.526810i | ||||
\(433\) | −6.16396 | + | 10.6763i | −0.296221 | + | 0.513070i | −0.975268 | − | 0.221025i | \(-0.929060\pi\) |
0.679047 | + | 0.734095i | \(0.262393\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.27628 | − | 12.2272i | −0.157086 | − | 0.586251i | ||||
\(436\) | −13.8476 | − | 13.8476i | −0.663179 | − | 0.663179i | ||||
\(437\) | −0.868559 | − | 3.24151i | −0.0415488 | − | 0.155062i | ||||
\(438\) | −8.95345 | − | 15.5078i | −0.427812 | − | 0.740993i | ||||
\(439\) | 3.88598 | − | 6.73072i | 0.185468 | − | 0.321240i | −0.758266 | − | 0.651945i | \(-0.773953\pi\) |
0.943734 | + | 0.330705i | \(0.107287\pi\) | |||||||
\(440\) | −2.32519 | − | 0.623033i | −0.110849 | − | 0.0297019i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.493808 | − | 4.54053i | 0.0234881 | − | 0.215971i | ||||
\(443\) | −3.14950 | − | 5.45509i | −0.149637 | − | 0.259179i | 0.781456 | − | 0.623960i | \(-0.214477\pi\) |
−0.931093 | + | 0.364781i | \(0.881144\pi\) | |||||||
\(444\) | −5.32682 | − | 5.32682i | −0.252800 | − | 0.252800i | ||||
\(445\) | 13.4012 | 0.635278 | ||||||||
\(446\) | −15.7092 | −0.743854 | ||||||||
\(447\) | −14.6513 | − | 14.6513i | −0.692982 | − | 0.692982i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6362 | − | 3.92175i | 0.690723 | − | 0.185079i | 0.103651 | − | 0.994614i | \(-0.466947\pi\) |
0.587072 | + | 0.809535i | \(0.300281\pi\) | |||||||
\(450\) | −2.75363 | + | 10.2767i | −0.129808 | + | 0.484448i | ||||
\(451\) | −14.8568 | + | 8.57758i | −0.699579 | + | 0.403902i | ||||
\(452\) | 5.52741i | 0.259987i | ||||||||
\(453\) | 8.88602 | + | 33.1631i | 0.417501 | + | 1.55814i | ||||
\(454\) | 28.7285 | 1.34829 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.131486 | −0.00615742 | ||||||||
\(457\) | 4.02470 | + | 15.0204i | 0.188267 | + | 0.702623i | 0.993907 | + | 0.110218i | \(0.0351549\pi\) |
−0.805640 | + | 0.592405i | \(0.798178\pi\) | |||||||
\(458\) | 22.9970i | 1.07458i | ||||||||
\(459\) | 3.07737 | − | 1.77672i | 0.143639 | − | 0.0829302i | ||||
\(460\) | 7.95829 | − | 29.7008i | 0.371057 | − | 1.38480i | ||||
\(461\) | −29.6778 | + | 7.95214i | −1.38223 | + | 0.370368i | −0.871931 | − | 0.489628i | \(-0.837133\pi\) |
−0.510301 | + | 0.859996i | \(0.670466\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.11310 | − | 4.11310i | −0.191152 | − | 0.191152i | 0.605042 | − | 0.796194i | \(-0.293156\pi\) |
−0.796194 | + | 0.605042i | \(0.793156\pi\) | |||||||
\(464\) | 10.3524 | 0.480600 | ||||||||
\(465\) | 5.23300 | 0.242674 | ||||||||
\(466\) | 31.1885 | + | 31.1885i | 1.44478 | + | 1.44478i | ||||
\(467\) | 4.08246 | + | 7.07102i | 0.188913 | + | 0.327208i | 0.944888 | − | 0.327393i | \(-0.106170\pi\) |
−0.755975 | + | 0.654601i | \(0.772837\pi\) | |||||||
\(468\) | −2.46194 | + | 6.34502i | −0.113803 | + | 0.293299i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 46.9984 | + | 12.5932i | 2.16787 | + | 0.580880i | ||||
\(471\) | −5.49225 | + | 9.51285i | −0.253069 | + | 0.438329i | ||||
\(472\) | −0.0587580 | − | 0.101772i | −0.00270456 | − | 0.00468443i | ||||
\(473\) | 6.20688 | + | 23.1644i | 0.285393 | + | 1.06510i | ||||
\(474\) | 25.0284 | + | 25.0284i | 1.14959 | + | 1.14959i | ||||
\(475\) | 1.10129 | + | 4.11006i | 0.0505305 | + | 0.188583i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.56274 | − | 6.17084i | 0.163127 | − | 0.282544i | ||||
\(478\) | −9.35544 | − | 5.40136i | −0.427908 | − | 0.247053i | ||||
\(479\) | 25.8476 | − | 25.8476i | 1.18101 | − | 1.18101i | 0.201523 | − | 0.979484i | \(-0.435411\pi\) |
0.979484 | − | 0.201523i | \(-0.0645890\pi\) | |||||||
\(480\) | 33.0362 | + | 19.0735i | 1.50789 | + | 0.870580i | ||||
\(481\) | −5.39169 | + | 7.36496i | −0.245840 | + | 0.335813i | ||||
\(482\) | − | 31.4616i | − | 1.43304i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −25.0985 | − | 43.4719i | −1.14084 | − | 1.97599i | ||||
\(485\) | 28.5930i | 1.29834i | ||||||||
\(486\) | −17.7981 | + | 4.76899i | −0.807339 | + | 0.216326i | ||||
\(487\) | −16.2718 | − | 4.36001i | −0.737344 | − | 0.197571i | −0.129447 | − | 0.991586i | \(-0.541320\pi\) |
−0.607897 | + | 0.794016i | \(0.707987\pi\) | |||||||
\(488\) | 0.0950266 | − | 0.0950266i | 0.00430165 | − | 0.00430165i | ||||
\(489\) | −2.62555 | + | 2.62555i | −0.118731 | + | 0.118731i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.48030 | − | 4.89611i | 0.382711 | − | 0.220958i | −0.296286 | − | 0.955099i | \(-0.595748\pi\) |
0.678997 | + | 0.734141i | \(0.262415\pi\) | |||||||
\(492\) | −8.29325 | + | 2.22217i | −0.373889 | + | 0.100183i | ||||
\(493\) | 0.839916 | − | 1.45478i | 0.0378279 | − | 0.0655199i | ||||
\(494\) | 0.819837 | + | 5.30002i | 0.0368862 | + | 0.238459i | ||||
\(495\) | −15.4717 | + | 8.93256i | −0.695399 | + | 0.401489i | ||||
\(496\) | −1.10766 | + | 4.13383i | −0.0497352 | + | 0.185614i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −12.7975 | − | 7.38863i | −0.573469 | − | 0.331093i | ||||
\(499\) | 2.84635 | + | 0.762677i | 0.127420 | + | 0.0341421i | 0.321966 | − | 0.946751i | \(-0.395656\pi\) |
−0.194545 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(500\) | −1.33888 | + | 4.99678i | −0.0598767 | + | 0.223463i | ||||
\(501\) | 1.27128 | − | 4.74449i | 0.0567968 | − | 0.211968i | ||||
\(502\) | 8.98127 | + | 2.40653i | 0.400854 | + | 0.107408i | ||||
\(503\) | −24.6898 | − | 14.2547i | −1.10086 | − | 0.635584i | −0.164416 | − | 0.986391i | \(-0.552574\pi\) |
−0.936448 | + | 0.350807i | \(0.885907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.5849 | + | 54.4314i | −0.649018 | + | 2.42217i | ||||
\(506\) | 47.1807 | − | 27.2398i | 2.09744 | − | 1.21096i | ||||
\(507\) | −18.3291 | − | 4.03452i | −0.814025 | − | 0.179179i | ||||
\(508\) | 5.86956 | − | 10.1664i | 0.260419 | − | 0.451060i | ||||
\(509\) | 18.6168 | − | 4.98837i | 0.825177 | − | 0.221106i | 0.178569 | − | 0.983927i | \(-0.442853\pi\) |
0.646609 | + | 0.762822i | \(0.276187\pi\) | |||||||
\(510\) | 5.19632 | − | 3.00010i | 0.230097 | − | 0.132847i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.7359 | + | 22.7359i | −1.00479 | + | 1.00479i | ||||
\(513\) | −2.95044 | + | 2.95044i | −0.130265 | + | 0.130265i | ||||
\(514\) | 30.4943 | + | 8.17093i | 1.34505 | + | 0.360404i | ||||
\(515\) | 45.6035 | − | 12.2194i | 2.00953 | − | 0.538452i | ||||
\(516\) | 12.0023i | 0.528370i | ||||||||
\(517\) | 21.8770 | + | 37.8921i | 0.962149 | + | 1.66649i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 20.2843i | − | 0.890381i | ||||||
\(520\) | −0.528039 | + | 1.36088i | −0.0231560 | + | 0.0596786i | ||||
\(521\) | −9.05428 | − | 5.22749i | −0.396675 | − | 0.229020i | 0.288373 | − | 0.957518i | \(-0.406886\pi\) |
−0.685048 | + | 0.728498i | \(0.740219\pi\) | |||||||
\(522\) | −3.48746 | + | 3.48746i | −0.152642 | + | 0.152642i | ||||
\(523\) | −15.9637 | − | 9.21666i | −0.698045 | − | 0.403016i | 0.108574 | − | 0.994088i | \(-0.465372\pi\) |
−0.806619 | + | 0.591072i | \(0.798705\pi\) | |||||||
\(524\) | 18.0465 | − | 31.2574i | 0.788365 | − | 1.36549i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.4715 | + | 46.5444i | 0.543785 | + | 2.02943i | ||||
\(527\) | 0.491040 | + | 0.491040i | 0.0213900 | + | 0.0213900i | ||||
\(528\) | 8.60632 | + | 32.1192i | 0.374542 | + | 1.39781i | ||||
\(529\) | −1.16397 | − | 2.01606i | −0.0506076 | − | 0.0876549i | ||||
\(530\) | 25.7235 | − | 44.5544i | 1.11736 | − | 1.93532i | ||||
\(531\) | −0.842426 | − | 0.225727i | −0.0365582 | − | 0.00979574i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.19689 | + | 9.51872i | 0.181788 | + | 0.412301i | ||||
\(534\) | 5.94169 | + | 10.2913i | 0.257122 | + | 0.445348i | ||||
\(535\) | −7.24010 | − | 7.24010i | −0.313017 | − | 0.313017i | ||||
\(536\) | −0.665931 | −0.0287638 | ||||||||
\(537\) | 21.6010 | 0.932151 | ||||||||
\(538\) | 19.2858 | + | 19.2858i | 0.831469 | + | 0.831469i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −36.9288 | + | 9.89505i | −1.58916 | + | 0.425815i | ||||
\(541\) | −10.8498 | + | 40.4921i | −0.466470 | + | 1.74089i | 0.185499 | + | 0.982644i | \(0.440610\pi\) |
−0.651969 | + | 0.758246i | \(0.726057\pi\) | |||||||
\(542\) | 37.7922 | − | 21.8193i | 1.62331 | − | 0.937221i | ||||
\(543\) | 22.2919i | 0.956635i | ||||||||
\(544\) | 1.31020 | + | 4.88972i | 0.0561743 | + | 0.209645i | ||||
\(545\) | −31.1722 | −1.33527 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.3151 | 1.68099 | 0.840496 | − | 0.541818i | \(-0.182264\pi\) | ||||
0.840496 | + | 0.541818i | \(0.182264\pi\) | |||||||
\(548\) | 7.82062 | + | 29.1870i | 0.334080 | + | 1.24680i | ||||
\(549\) | − | 0.997358i | − | 0.0425662i | ||||||
\(550\) | −59.8226 | + | 34.5386i | −2.55084 | + | 1.47273i | ||||
\(551\) | −0.510522 | + | 1.90529i | −0.0217490 | + | 0.0811683i | ||||
\(552\) | 0.782357 | − | 0.209632i | 0.0332993 | − | 0.00892253i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −30.5185 | − | 30.5185i | −1.29661 | − | 1.29661i | ||||
\(555\) | −11.9912 | −0.508998 | ||||||||
\(556\) | −7.38921 | −0.313372 | ||||||||
\(557\) | −30.1372 | − | 30.1372i | −1.27695 | − | 1.27695i | −0.942365 | − | 0.334587i | \(-0.891403\pi\) |
−0.334587 | − | 0.942365i | \(-0.608597\pi\) | |||||||
\(558\) | −1.01943 | − | 1.76571i | −0.0431561 | − | 0.0747486i | ||||
\(559\) | 14.3715 | − | 2.22306i | 0.607848 | − | 0.0940255i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.21180 | + | 1.39650i | 0.220042 | + | 0.0589602i | ||||
\(562\) | 1.24654 | − | 2.15907i | 0.0525820 | − | 0.0910747i | ||||
\(563\) | 18.6963 | + | 32.3829i | 0.787955 | + | 1.36478i | 0.927218 | + | 0.374523i | \(0.122193\pi\) |
−0.139263 | + | 0.990255i | \(0.544473\pi\) | |||||||
\(564\) | 5.66761 | + | 21.1518i | 0.238650 | + | 0.890652i | ||||
\(565\) | 6.22136 | + | 6.22136i | 0.261735 | + | 0.261735i | ||||
\(566\) | 9.62909 | + | 35.9363i | 0.404741 | + | 1.51051i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.140650 | + | 0.243613i | −0.00590155 | + | 0.0102218i | ||||
\(569\) | 26.9875 | + | 15.5812i | 1.13137 | + | 0.653199i | 0.944280 | − | 0.329143i | \(-0.106760\pi\) |
0.187094 | + | 0.982342i | \(0.440093\pi\) | |||||||
\(570\) | −4.98199 | + | 4.98199i | −0.208673 | + | 0.208673i | ||||
\(571\) | 16.5495 | + | 9.55483i | 0.692573 | + | 0.399857i | 0.804575 | − | 0.593851i | \(-0.202393\pi\) |
−0.112002 | + | 0.993708i | \(0.535726\pi\) | |||||||
\(572\) | −40.4330 | + | 17.8273i | −1.69059 | + | 0.745397i | ||||
\(573\) | 24.7663i | 1.03463i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.1055 | − | 22.6995i | −0.546539 | − | 0.946633i | ||||
\(576\) | − | 7.76770i | − | 0.323654i | ||||||
\(577\) | −19.2526 | + | 5.15872i | −0.801497 | + | 0.214760i | −0.636241 | − | 0.771490i | \(-0.719512\pi\) |
−0.165256 | + | 0.986251i | \(0.552845\pi\) | |||||||
\(578\) | −32.3228 | − | 8.66086i | −1.34445 | − | 0.360244i | ||||
\(579\) | −6.26045 | + | 6.26045i | −0.260176 | + | 0.260176i | ||||
\(580\) | −12.7798 | + | 12.7798i | −0.530652 | + | 0.530652i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.9577 | + | 12.6773i | −0.910176 | + | 0.525490i | ||||
\(583\) | 44.6871 | − | 11.9739i | 1.85075 | − | 0.495907i | ||||
\(584\) | −0.379740 | + | 0.657728i | −0.0157137 | + | 0.0272170i | ||||
\(585\) | 4.37058 | + | 9.91265i | 0.180701 | + | 0.409838i | ||||
\(586\) | −21.6861 | + | 12.5205i | −0.895847 | + | 0.517217i | ||||
\(587\) | −10.4047 | + | 38.8308i | −0.429447 | + | 1.60272i | 0.324569 | + | 0.945862i | \(0.394781\pi\) |
−0.754016 | + | 0.656856i | \(0.771886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.706179 | − | 0.407713i | −0.0290976 | − | 0.0167995i | ||||
\(590\) | −6.08244 | − | 1.62979i | −0.250410 | − | 0.0670972i | ||||
\(591\) | 9.58986 | − | 35.7898i | 0.394474 | − | 1.47220i | ||||
\(592\) | 2.53815 | − | 9.47249i | 0.104317 | − | 0.389317i | ||||
\(593\) | 6.94560 | + | 1.86107i | 0.285222 | + | 0.0764249i | 0.398594 | − | 0.917128i | \(-0.369498\pi\) |
−0.113372 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(594\) | −58.6627 | − | 33.8689i | −2.40696 | − | 1.38966i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.65669 | + | 28.5752i | −0.313630 | + | 1.17048i | ||||
\(597\) | −10.9116 | + | 6.29979i | −0.446580 | + | 0.257833i | ||||
\(598\) | −13.3281 | − | 30.2285i | −0.545025 | − | 1.23614i | ||||
\(599\) | 14.6877 | − | 25.4398i | 0.600123 | − | 1.03944i | −0.392679 | − | 0.919676i | \(-0.628452\pi\) |
0.992802 | − | 0.119768i | \(-0.0382150\pi\) | |||||||
\(600\) | −0.991988 | + | 0.265802i | −0.0404977 | + | 0.0108513i | ||||
\(601\) | 40.3495 | − | 23.2958i | 1.64589 | − | 0.950255i | 0.667208 | − | 0.744871i | \(-0.267489\pi\) |
0.978682 | − | 0.205384i | \(-0.0658442\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.49466 | + | 3.49466i | −0.142314 | + | 0.142314i | ||||
\(604\) | 34.6617 | − | 34.6617i | 1.41036 | − | 1.41036i | ||||
\(605\) | −77.1792 | − | 20.6801i | −3.13778 | − | 0.840766i | ||||
\(606\) | −48.2665 | + | 12.9330i | −1.96069 | + | 0.525366i | ||||
\(607\) | − | 21.4872i | − | 0.872140i | −0.899913 | − | 0.436070i | \(-0.856370\pi\) | ||
0.899913 | − | 0.436070i | \(-0.143630\pi\) | |||||||
\(608\) | −2.97210 | − | 5.14782i | −0.120534 | − | 0.208772i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 7.20107i | − | 0.291563i | ||||||
\(611\) | 24.2774 | − | 10.7041i | 0.982157 | − | 0.433043i | ||||
\(612\) | −1.02755 | − | 0.593258i | −0.0415364 | − | 0.0239810i | ||||
\(613\) | 20.2128 | − | 20.2128i | 0.816389 | − | 0.816389i | −0.169194 | − | 0.985583i | \(-0.554116\pi\) |
0.985583 | + | 0.169194i | \(0.0541165\pi\) | |||||||
\(614\) | −8.67288 | − | 5.00729i | −0.350009 | − | 0.202078i | ||||
\(615\) | −6.83329 | + | 11.8356i | −0.275545 | + | 0.477257i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.40928 | − | 20.1877i | −0.217769 | − | 0.812726i | −0.985173 | − | 0.171562i | \(-0.945119\pi\) |
0.767404 | − | 0.641164i | \(-0.221548\pi\) | |||||||
\(618\) | 29.6030 | + | 29.6030i | 1.19081 | + | 1.19081i | ||||
\(619\) | 1.16061 | + | 4.33146i | 0.0466489 | + | 0.174096i | 0.985320 | − | 0.170718i | \(-0.0546087\pi\) |
−0.938671 | + | 0.344814i | \(0.887942\pi\) | |||||||
\(620\) | −3.73572 | − | 6.47046i | −0.150030 | − | 0.259860i | ||||
\(621\) | 12.8514 | − | 22.2593i | 0.515711 | − | 0.893237i | ||||
\(622\) | 35.7510 | + | 9.57946i | 1.43349 | + | 0.384101i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 19.9272 | − | 3.08245i | 0.797725 | − | 0.123397i | ||||
\(625\) | −10.2952 | − | 17.8317i | −0.411806 | − | 0.713269i | ||||
\(626\) | 12.8115 | + | 12.8115i | 0.512052 | + | 0.512052i | ||||
\(627\) | −6.33573 | −0.253025 | ||||||||
\(628\) | 15.6832 | 0.625827 | ||||||||
\(629\) | −1.12520 | − | 1.12520i | −0.0448645 | − | 0.0448645i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.89598 | + | 2.65162i | −0.393953 | + | 0.105559i | −0.450357 | − | 0.892849i | \(-0.648703\pi\) |
0.0564039 | + | 0.998408i | \(0.482037\pi\) | |||||||
\(632\) | 0.388544 | − | 1.45007i | 0.0154555 | − | 0.0576806i | ||||
\(633\) | −13.5371 | + | 7.81567i | −0.538053 | + | 0.310645i | ||||
\(634\) | 29.0337i | 1.15307i | ||||||||
\(635\) | −4.83627 | − | 18.0492i | −0.191921 | − | 0.716260i | ||||
\(636\) | 23.1539 | 0.918114 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −32.0220 | −1.26776 | ||||||||
\(639\) | 0.540328 | + | 2.01653i | 0.0213750 | + | 0.0797727i | ||||
\(640\) | − | 3.23734i | − | 0.127967i | ||||||
\(641\) | 27.7522 | − | 16.0227i | 1.09615 | − | 0.632860i | 0.160940 | − | 0.986964i | \(-0.448547\pi\) |
0.935206 | + | 0.354104i | \(0.115214\pi\) | |||||||
\(642\) | 2.34991 | − | 8.77000i | 0.0927437 | − | 0.346124i | ||||
\(643\) | 44.5502 | − | 11.9372i | 1.75689 | − | 0.470757i | 0.770815 | − | 0.637059i | \(-0.219849\pi\) |
0.986075 | + | 0.166302i | \(0.0531826\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.5091 | + | 13.5091i | 0.531921 | + | 0.531921i | ||||
\(646\) | −0.934973 | −0.0367860 | ||||||||
\(647\) | −30.7013 | −1.20699 | −0.603496 | − | 0.797366i | \(-0.706226\pi\) | ||||
−0.603496 | + | 0.797366i | \(0.706226\pi\) | |||||||
\(648\) | −0.472393 | − | 0.472393i | −0.0185573 | − | 0.0185573i | ||||
\(649\) | −2.83128 | − | 4.90392i | −0.111137 | − | 0.192496i | ||||
\(650\) | 16.8993 | + | 38.3282i | 0.662844 | + | 1.50336i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.12074 | + | 1.37210i | 0.200544 | + | 0.0537355i | ||||
\(653\) | 7.67694 | − | 13.2969i | 0.300422 | − | 0.520346i | −0.675810 | − | 0.737076i | \(-0.736206\pi\) |
0.976232 | + | 0.216730i | \(0.0695392\pi\) | |||||||
\(654\) | −13.8208 | − | 23.9383i | −0.540436 | − | 0.936063i | ||||
\(655\) | −14.8696 | − | 55.4939i | −0.581001 | − | 2.16833i | ||||
\(656\) | −7.90320 | − | 7.90320i | −0.308568 | − | 0.308568i | ||||
\(657\) | 1.45883 | + | 5.44441i | 0.0569142 | + | 0.212407i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.71985 | − | 8.17502i | 0.183859 | − | 0.318454i | −0.759332 | − | 0.650703i | \(-0.774474\pi\) |
0.943192 | + | 0.332250i | \(0.107808\pi\) | |||||||
\(660\) | −50.2745 | − | 29.0260i | −1.95693 | − | 1.12984i | ||||
\(661\) | 5.84186 | − | 5.84186i | 0.227222 | − | 0.227222i | −0.584309 | − | 0.811531i | \(-0.698634\pi\) |
0.811531 | + | 0.584309i | \(0.198634\pi\) | |||||||
\(662\) | −14.2832 | − | 8.24641i | −0.555132 | − | 0.320506i | ||||
\(663\) | 1.18357 | − | 3.05035i | 0.0459662 | − | 0.118466i | ||||
\(664\) | 0.626743i | 0.0243224i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.33599 | + | 4.04605i | 0.0905178 | + | 0.156781i | ||||
\(667\) | − | 12.1506i | − | 0.470474i | ||||||
\(668\) | −6.77398 | + | 1.81508i | −0.262093 | + | 0.0702277i | ||||
\(669\) | −10.8703 | − | 2.91270i | −0.420271 | − | 0.112611i | ||||
\(670\) | −25.2320 | + | 25.2320i | −0.974797 | + | 0.974797i | ||||
\(671\) | 4.57890 | − | 4.57890i | 0.176766 | − | 0.176766i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.2566 | + | 15.7366i | −1.05067 | + | 0.606602i | −0.922836 | − | 0.385194i | \(-0.874134\pi\) |
−0.127830 | + | 0.991796i | \(0.540801\pi\) | |||||||
\(674\) | −3.18911 | + | 0.854521i | −0.122840 | + | 0.0329149i | ||||
\(675\) | −16.2950 | + | 28.2237i | −0.627193 | + | 1.08633i | ||||
\(676\) | 8.09619 | + | 25.5436i | 0.311392 | + | 0.982447i | ||||
\(677\) | 40.8799 | − | 23.6020i | 1.57114 | − | 0.907099i | 0.575112 | − | 0.818074i | \(-0.304958\pi\) |
0.996029 | − | 0.0890246i | \(-0.0283750\pi\) | |||||||
\(678\) | −2.01926 | + | 7.53599i | −0.0775493 | + | 0.289418i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.220390 | − | 0.127242i | −0.00845157 | − | 0.00487952i | ||||
\(681\) | 19.8792 | + | 5.32663i | 0.761774 | + | 0.204117i | ||||
\(682\) | 3.42618 | − | 12.7867i | 0.131195 | − | 0.489627i | ||||
\(683\) | −11.7625 | + | 43.8982i | −0.450079 | + | 1.67972i | 0.252087 | + | 0.967705i | \(0.418883\pi\) |
−0.702166 | + | 0.712013i | \(0.747784\pi\) | |||||||
\(684\) | 1.34577 | + | 0.360597i | 0.0514567 | + | 0.0137878i | ||||
\(685\) | 41.6538 | + | 24.0488i | 1.59151 | + | 0.918858i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.26394 | + | 15.9132i | −0.162680 | + | 0.607128i | ||||
\(688\) | −13.5310 | + | 7.81214i | −0.515866 | + | 0.297835i | ||||
\(689\) | −4.28858 | − | 27.7245i | −0.163382 | − | 1.05622i | ||||
\(690\) | 21.7004 | − | 37.5863i | 0.826121 | − | 1.43088i | ||||
\(691\) | 18.2526 | − | 4.89077i | 0.694361 | − | 0.186054i | 0.105658 | − | 0.994403i | \(-0.466305\pi\) |
0.588703 | + | 0.808349i | \(0.299639\pi\) | |||||||
\(692\) | −25.0810 | + | 14.4805i | −0.953435 | + | 0.550466i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.7246 | − | 13.7246i | 0.520980 | − | 0.520980i | ||||
\(695\) | −8.31690 | + | 8.31690i | −0.315478 | + | 0.315478i | ||||
\(696\) | −0.459854 | − | 0.123218i | −0.0174307 | − | 0.00467055i | ||||
\(697\) | −1.75180 | + | 0.469393i | −0.0663542 | + | 0.0177795i | ||||
\(698\) | 59.3908i | 2.24798i | ||||||||
\(699\) | 15.7987 | + | 27.3642i | 0.597563 | + | 1.03501i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.6032i | − | 1.19364i | −0.802377 | − | 0.596818i | \(-0.796431\pi\) | ||
0.802377 | − | 0.596818i | \(-0.203569\pi\) | |||||||
\(702\) | −24.2638 | + | 33.1440i | −0.915779 | + | 1.25094i | ||||
\(703\) | 1.61818 | + | 0.934256i | 0.0610308 | + | 0.0352361i | ||||
\(704\) | 35.6617 | − | 35.6617i | 1.34405 | − | 1.34405i | ||||
\(705\) | 30.1865 | + | 17.4282i | 1.13689 | + | 0.656384i | ||||
\(706\) | −16.1071 | + | 27.8982i | −0.606197 | + | 1.04996i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.733492 | − | 2.73743i | −0.0275663 | − | 0.102879i | ||||
\(709\) | −13.7245 | − | 13.7245i | −0.515433 | − | 0.515433i | 0.400753 | − | 0.916186i | \(-0.368748\pi\) |
−0.916186 | + | 0.400753i | \(0.868748\pi\) | |||||||
\(710\) | 3.90125 | + | 14.5597i | 0.146411 | + | 0.546414i | ||||
\(711\) | −5.57064 | − | 9.64864i | −0.208915 | − | 0.361852i | ||||
\(712\) | 0.252003 | − | 0.436482i | 0.00944421 | − | 0.0163578i | ||||
\(713\) | 4.85186 | + | 1.30005i | 0.181704 | + | 0.0486873i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.4438 | + | 65.5747i | −0.951543 | + | 2.45236i | ||||
\(716\) | −15.4205 | − | 26.7090i | −0.576290 | − | 0.998163i | ||||
\(717\) | −5.47220 | − | 5.47220i | −0.204363 | − | 0.204363i | ||||
\(718\) | 11.5812 | 0.432205 | ||||||||
\(719\) | −4.47081 | −0.166733 | −0.0833665 | − | 0.996519i | \(-0.526567\pi\) | ||||
−0.0833665 | + | 0.996519i | \(0.526567\pi\) | |||||||
\(720\) | −8.23028 | − | 8.23028i | −0.306724 | − | 0.306724i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −35.9246 | + | 9.62596i | −1.33697 | + | 0.358241i | ||||
\(723\) | 5.83339 | − | 21.7705i | 0.216946 | − | 0.809654i | ||||
\(724\) | 27.5633 | − | 15.9137i | 1.02438 | − | 0.591427i | ||||
\(725\) | 15.4064i | 0.572178i | ||||||||
\(726\) | −18.3379 | − | 68.4378i | −0.680582 | − | 2.53997i | ||||
\(727\) | −25.9080 | −0.960874 | −0.480437 | − | 0.877029i | \(-0.659522\pi\) | ||||
−0.480437 | + | 0.877029i | \(0.659522\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.4421 | −1.09045 | ||||||||
\(730\) | 10.5329 | + | 39.3095i | 0.389841 | + | 1.45491i | ||||
\(731\) | 2.53526i | 0.0937701i | ||||||||
\(732\) | 2.80668 | − | 1.62044i | 0.103738 | − | 0.0598931i | ||||
\(733\) | 12.4133 | − | 46.3272i | 0.458497 | − | 1.71114i | −0.219100 | − | 0.975703i | \(-0.570312\pi\) |
0.677597 | − | 0.735433i | \(-0.263021\pi\) | |||||||
\(734\) | −49.5619 | + | 13.2801i | −1.82936 | + | 0.490177i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.8916 | + | 25.8916i | 0.954376 | + | 0.954376i | ||||
\(737\) | −32.0882 | −1.18198 | ||||||||
\(738\) | 5.32474 | 0.196007 | ||||||||
\(739\) | −12.3488 | − | 12.3488i | −0.454258 | − | 0.454258i | 0.442507 | − | 0.896765i | \(-0.354089\pi\) |
−0.896765 | + | 0.442507i | \(0.854089\pi\) | |||||||
\(740\) | 8.56025 | + | 14.8268i | 0.314681 | + | 0.545043i | ||||
\(741\) | −0.415389 | + | 3.81946i | −0.0152597 | + | 0.140311i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.0523 | − | 8.85634i | −1.21257 | − | 0.324908i | −0.404801 | − | 0.914405i | \(-0.632659\pi\) |
−0.807770 | + | 0.589497i | \(0.799326\pi\) | |||||||
\(744\) | 0.0984038 | − | 0.170440i | 0.00360766 | − | 0.00624865i | ||||
\(745\) | 23.5447 | + | 40.7807i | 0.862612 | + | 1.49409i | ||||
\(746\) | −9.76176 | − | 36.4314i | −0.357403 | − | 1.33385i | ||||
\(747\) | 3.28901 | + | 3.28901i | 0.120339 | + | 0.120339i | ||||
\(748\) | −1.99386 | − | 7.44118i | −0.0729027 | − | 0.272077i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.65083 | + | 6.32342i | −0.133309 | + | 0.230899i | ||||
\(751\) | 4.81931 | + | 2.78243i | 0.175859 | + | 0.101532i | 0.585346 | − | 0.810784i | \(-0.300959\pi\) |
−0.409487 | + | 0.912316i | \(0.634292\pi\) | |||||||
\(752\) | −20.1570 | + | 20.1570i | −0.735050 | + | 0.735050i | ||||
\(753\) | 5.76857 | + | 3.33049i | 0.210219 | + | 0.121370i | ||||
\(754\) | −2.09945 | + | 19.3043i | −0.0764576 | + | 0.703021i | ||||
\(755\) | − | 78.0268i | − | 2.83969i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.89589 | − | 17.1402i | −0.359672 | − | 0.622971i | 0.628234 | − | 0.778025i | \(-0.283778\pi\) |
−0.987906 | + | 0.155054i | \(0.950445\pi\) | |||||||
\(758\) | 42.7934i | 1.55433i | ||||||||
\(759\) | 37.6982 | − | 10.1012i | 1.36836 | − | 0.366651i | ||||
\(760\) | 0.288641 | + | 0.0773410i | 0.0104701 | + | 0.00280545i | ||||
\(761\) | −23.9987 | + | 23.9987i | −0.869953 | + | 0.869953i | −0.992467 | − | 0.122514i | \(-0.960904\pi\) |
0.122514 | + | 0.992467i | \(0.460904\pi\) | |||||||
\(762\) | 11.7164 | − | 11.7164i | 0.424441 | − | 0.424441i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 30.6229 | − | 17.6801i | 1.10790 | − | 0.639644i | ||||
\(765\) | −1.82430 | + | 0.488820i | −0.0659577 | + | 0.0176733i | ||||
\(766\) | −32.7018 | + | 56.6411i | −1.18156 | + | 2.04653i | ||||
\(767\) | −3.14193 | + | 1.38531i | −0.113449 | + | 0.0500206i | ||||
\(768\) | −18.7238 | + | 10.8102i | −0.675635 | + | 0.390078i | ||||
\(769\) | 4.79803 | − | 17.9065i | 0.173021 | − | 0.645725i | −0.823859 | − | 0.566795i | \(-0.808183\pi\) |
0.996880 | − | 0.0789297i | \(-0.0251503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5862 | + | 11.3081i | 0.705378 | + | 0.407250i | ||||
\(772\) | 12.2101 | + | 3.27168i | 0.439451 | + | 0.117750i | ||||
\(773\) | 6.00148 | − | 22.3978i | 0.215858 | − | 0.805594i | −0.770005 | − | 0.638038i | \(-0.779746\pi\) |
0.985863 | − | 0.167555i | \(-0.0535873\pi\) | |||||||
\(774\) | 1.92654 | − | 7.18993i | 0.0692479 | − | 0.258437i | ||||
\(775\) | −6.15190 | − | 1.64840i | −0.220983 | − | 0.0592122i | ||||
\(776\) | 0.931285 | + | 0.537678i | 0.0334312 | + | 0.0193015i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.63222 | + | 13.5556i | −0.130221 | + | 0.485993i | ||||
\(779\) | 1.84427 | − | 1.06479i | 0.0660778 | − | 0.0381500i | ||||
\(780\) | −20.7943 | + | 28.4047i | −0.744556 | + | 1.01705i | ||||
\(781\) | −6.77729 | + | 11.7386i | −0.242510 | + | 0.420040i | ||||
\(782\) | 5.56318 | − | 1.49065i | 0.198939 | − | 0.0533055i | ||||
\(783\) | −13.0836 | + | 7.55382i | −0.467570 | + | 0.269952i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.6522 | − | 17.6522i | 0.630033 | − | 0.630033i | ||||
\(786\) | 36.0232 | − | 36.0232i | 1.28491 | − | 1.28491i | ||||
\(787\) | −15.1886 | − | 4.06976i | −0.541414 | − | 0.145071i | −0.0222599 | − | 0.999752i | \(-0.507086\pi\) |
−0.519154 | + | 0.854681i | \(0.673753\pi\) | |||||||
\(788\) | −51.0992 | + | 13.6920i | −1.82033 | + | 0.487757i | ||||
\(789\) | 34.5197i | 1.22894i | ||||||||
\(790\) | −40.2209 | − | 69.6646i | −1.43099 | − | 2.47856i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.671889i | 0.0238745i | ||||||||
\(793\) | −2.46016 | − | 3.06057i | −0.0873628 | − | 0.108684i | ||||
\(794\) | −26.0742 | − | 15.0540i | −0.925340 | − | 0.534245i | ||||
\(795\) | 26.0609 | − | 26.0609i | 0.924284 | − | 0.924284i | ||||
\(796\) | 15.5790 | + | 8.99457i | 0.552185 | + | 0.318804i | ||||
\(797\) | 10.8696 | − | 18.8267i | 0.385021 | − | 0.666876i | −0.606751 | − | 0.794892i | \(-0.707527\pi\) |
0.991772 | + | 0.128016i | \(0.0408608\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19718 | + | 4.46794i | 0.0423533 | + | 0.158064i | ||||
\(800\) | −32.8292 | − | 32.8292i | −1.16069 | − | 1.16069i | ||||
\(801\) | −0.968105 | − | 3.61302i | −0.0342063 | − | 0.127660i | ||||
\(802\) | 24.3593 | + | 42.1916i | 0.860158 | + | 1.48984i | ||||
\(803\) | −18.2979 | + | 31.6929i | −0.645720 | + | 1.11842i | ||||
\(804\) | −15.5123 | − | 4.15650i | −0.547075 | − | 0.146588i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.48376 | − | 2.90379i | −0.263604 | − | 0.102282i | ||||
\(807\) | 9.76935 | + | 16.9210i | 0.343897 | + | 0.595648i | ||||
\(808\) | 1.49859 | + | 1.49859i | 0.0527202 | + | 0.0527202i | ||||
\(809\) | 35.6805 | 1.25446 | 0.627229 | − | 0.778835i | \(-0.284189\pi\) | ||||
0.627229 | + | 0.778835i | \(0.284189\pi\) | |||||||
\(810\) | −35.7977 | −1.25780 | ||||||||
\(811\) | 0.747882 | + | 0.747882i | 0.0262617 | + | 0.0262617i | 0.720116 | − | 0.693854i | \(-0.244089\pi\) |
−0.693854 | + | 0.720116i | \(0.744089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.1967 | − | 8.09117i | 1.05904 | − | 0.283770i | ||||
\(814\) | −7.85095 | + | 29.3001i | −0.275176 | + | 1.02697i | ||||
\(815\) | 7.30800 | − | 4.21928i | 0.255988 | − | 0.147795i | ||||
\(816\) | 3.51534i | 0.123062i | ||||||||
\(817\) | −0.770499 | − | 2.87554i | −0.0269563 | − | 0.100602i | ||||
\(818\) | 75.6376 | 2.64461 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.5125 | 0.681407 | ||||||||
\(821\) | 2.86268 | + | 10.6837i | 0.0999084 | + | 0.372863i | 0.997718 | − | 0.0675209i | \(-0.0215089\pi\) |
−0.897809 | + | 0.440384i | \(0.854842\pi\) | |||||||
\(822\) | 42.6501i | 1.48759i | ||||||||
\(823\) | 20.4465 | − | 11.8048i | 0.712719 | − | 0.411488i | −0.0993482 | − | 0.995053i | \(-0.531676\pi\) |
0.812067 | + | 0.583564i | \(0.198342\pi\) | |||||||
\(824\) | 0.459560 | − | 1.71510i | 0.0160095 | − | 0.0597484i | ||||
\(825\) | −47.7994 | + | 12.8078i | −1.66416 | + | 0.445910i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.09240 | − | 1.09240i | −0.0379865 | − | 0.0379865i | 0.687858 | − | 0.725845i | \(-0.258551\pi\) |
−0.725845 | + | 0.687858i | \(0.758551\pi\) | |||||||
\(828\) | −8.58235 | −0.298257 | ||||||||
\(829\) | 38.2127 | 1.32718 | 0.663591 | − | 0.748095i | \(-0.269031\pi\) | ||||
0.663591 | + | 0.748095i | \(0.269031\pi\) | |||||||
\(830\) | 23.7472 | + | 23.7472i | 0.824277 | + | 0.824277i | ||||
\(831\) | −15.4594 | − | 26.7765i | −0.536280 | − | 0.928865i | ||||
\(832\) | −19.1604 | − | 23.8366i | −0.664267 | − | 0.826384i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −10.0743 | − | 2.69941i | −0.348846 | − | 0.0934729i | ||||
\(835\) | −5.58148 | + | 9.66740i | −0.193155 | + | 0.334554i | ||||
\(836\) | 4.52294 | + | 7.83396i | 0.156429 | + | 0.270943i | ||||
\(837\) | −1.61644 | − | 6.03263i | −0.0558722 | − | 0.208518i | ||||
\(838\) | −11.6025 | − | 11.6025i | −0.400802 | − | 0.400802i | ||||
\(839\) | 10.2082 | + | 38.0974i | 0.352425 | + | 1.31527i | 0.883694 | + | 0.468066i | \(0.155049\pi\) |
−0.531268 | + | 0.847204i | \(0.678284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.9291 | − | 18.9297i | 0.376864 | − | 0.652747i | ||||
\(842\) | −6.07460 | − | 3.50717i | −0.209345 | − | 0.120865i | ||||
\(843\) | 1.26288 | − | 1.26288i | 0.0434961 | − | 0.0434961i | ||||
\(844\) | 19.3277 | + | 11.1589i | 0.665288 | + | 0.384104i | ||||
\(845\) | 37.8632 | + | 19.6379i | 1.30253 | + | 0.675565i | ||||
\(846\) | − | 13.5807i | − | 0.466914i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.0707 | + | 26.1031i | 0.517528 | + | 0.896385i | ||||
\(849\) | 26.6522i | 0.914700i | ||||||||
\(850\) | −7.05382 | + | 1.89007i | −0.241944 | + | 0.0648288i | ||||
\(851\) | −11.1178 | − | 2.97901i | −0.381114 | − | 0.102119i | ||||
\(852\) | −4.79686 | + | 4.79686i | −0.164338 | + | 0.164338i | ||||
\(853\) | 2.18217 | − | 2.18217i | 0.0747162 | − | 0.0747162i | −0.668761 | − | 0.743477i | \(-0.733175\pi\) |
0.743477 | + | 0.668761i | \(0.233175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.92059 | − | 1.10886i | 0.0656829 | − | 0.0379220i | ||||
\(856\) | −0.371959 | + | 0.0996661i | −0.0127133 | + | 0.00340652i | ||||
\(857\) | 14.7330 | − | 25.5183i | 0.503270 | − | 0.871689i | −0.496723 | − | 0.867909i | \(-0.665464\pi\) |
0.999993 | − | 0.00377978i | \(-0.00120314\pi\) | |||||||
\(858\) | −61.6384 | + | 9.53458i | −2.10430 | + | 0.325505i | ||||
\(859\) | 44.5926 | − | 25.7455i | 1.52148 | − | 0.878426i | 0.521800 | − | 0.853068i | \(-0.325261\pi\) |
0.999678 | − | 0.0253585i | \(-0.00807272\pi\) | |||||||
\(860\) | 7.05980 | − | 26.3475i | 0.240737 | − | 0.898443i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 26.7334 | + | 15.4345i | 0.910543 | + | 0.525702i | ||||
\(863\) | −31.1185 | − | 8.33816i | −1.05928 | − | 0.283834i | −0.313201 | − | 0.949687i | \(-0.601401\pi\) |
−0.746083 | + | 0.665852i | \(0.768068\pi\) | |||||||
\(864\) | 11.7833 | − | 43.9760i | 0.400877 | − | 1.49609i | ||||
\(865\) | −11.9313 | + | 44.5283i | −0.405677 | + | 1.51401i | ||||
\(866\) | 23.9973 | + | 6.43005i | 0.815461 | + | 0.218502i | ||||
\(867\) | −20.7606 | − | 11.9861i | −0.705066 | − | 0.407070i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.7222 | − | 69.8721i | 0.635106 | − | 2.37025i | ||||
\(870\) | −22.0925 | + | 12.7551i | −0.749005 | + | 0.432438i | ||||
\(871\) | −2.10379 | + | 19.3442i | −0.0712843 | + | 0.655453i | ||||
\(872\) | −0.586177 | + | 1.01529i | −0.0198505 | + | 0.0343820i | ||||
\(873\) | 7.70880 | − | 2.06557i | 0.260903 | − | 0.0699088i | ||||
\(874\) | −5.85683 | + | 3.38144i | −0.198110 | + | 0.114379i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.9510 | + | 12.9510i | −0.437574 | + | 0.437574i | ||||
\(877\) | 17.5437 | − | 17.5437i | 0.592409 | − | 0.592409i | −0.345873 | − | 0.938281i | \(-0.612417\pi\) |
0.938281 | + | 0.345873i | \(0.112417\pi\) | |||||||
\(878\) | −15.1288 | − | 4.05374i | −0.510571 | − | 0.136807i | ||||
\(879\) | −17.3276 | + | 4.64293i | −0.584447 | + | 0.156602i | ||||
\(880\) | − | 75.5708i | − | 2.54749i | ||||||
\(881\) | 8.18440 | + | 14.1758i | 0.275740 | + | 0.477595i | 0.970321 | − | 0.241819i | \(-0.0777439\pi\) |
−0.694582 | + | 0.719414i | \(0.744411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.3555i | 0.449449i | 0.974422 | + | 0.224724i | \(0.0721482\pi\) | ||||
−0.974422 | + | 0.224724i | \(0.927852\pi\) | |||||||
\(884\) | −4.61660 | + | 0.714123i | −0.155273 | + | 0.0240185i | ||||
\(885\) | −3.90669 | − | 2.25553i | −0.131322 | − | 0.0758187i | ||||
\(886\) | −8.97605 | + | 8.97605i | −0.301556 | + | 0.301556i | ||||
\(887\) | −14.2827 | − | 8.24614i | −0.479567 | − | 0.276878i | 0.240669 | − | 0.970607i | \(-0.422633\pi\) |
−0.720236 | + | 0.693729i | \(0.755967\pi\) | |||||||
\(888\) | −0.225488 | + | 0.390557i | −0.00756689 | + | 0.0131062i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.98987 | − | 26.0865i | −0.234301 | − | 0.874423i | ||||
\(891\) | −22.7625 | − | 22.7625i | −0.762571 | − | 0.762571i | ||||
\(892\) | 4.15862 | + | 15.5202i | 0.139241 | + | 0.519654i | ||||
\(893\) | −2.71573 | − | 4.70378i | −0.0908784 | − | 0.157406i | ||||
\(894\) | −20.8780 | + | 36.1618i | −0.698266 | + | 1.20943i | ||||
\(895\) | −47.4187 | − | 12.7058i | −1.58503 | − | 0.424708i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.61786 | − | 23.3884i | −0.120797 | − | 0.780917i | ||||
\(898\) | −15.2680 | − | 26.4450i | −0.509500 | − | 0.882480i | ||||
\(899\) | −2.08768 | − | 2.08768i | −0.0696281 | − | 0.0696281i | ||||
\(900\) | 10.8820 | 0.362732 | ||||||||
\(901\) | 4.89086 | 0.162938 | ||||||||
\(902\) | 24.4460 | + | 24.4460i | 0.813964 | + | 0.813964i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.319621 | − | 0.0856423i | 0.0106304 | − | 0.00284842i | ||||
\(905\) | 13.1122 | − | 48.9354i | 0.435864 | − | 1.62667i | ||||
\(906\) | 59.9198 | − | 34.5947i | 1.99070 | − | 1.14933i | ||||
\(907\) | − | 13.0225i | − | 0.432404i | −0.976349 | − | 0.216202i | \(-0.930633\pi\) | ||
0.976349 | − | 0.216202i | \(-0.0693670\pi\) | |||||||
\(908\) | −7.60512 | − | 28.3827i | −0.252385 | − | 0.941913i | ||||
\(909\) | 15.7285 | 0.521683 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.0374 | 0.962053 | 0.481026 | − | 0.876706i | \(-0.340264\pi\) | ||||
0.481026 | + | 0.876706i | \(0.340264\pi\) | |||||||
\(912\) | −1.06836 | − | 3.98716i | −0.0353768 | − | 0.132028i | ||||
\(913\) | 30.1999i | 0.999471i | ||||||||
\(914\) | 27.1392 | − | 15.6688i | 0.897683 | − | 0.518278i | ||||
\(915\) | 1.33517 | − | 4.98293i | 0.0441394 | − | 0.164731i | ||||
\(916\) | 22.7202 | − | 6.08787i | 0.750698 | − | 0.201149i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.06364 | − | 5.06364i | −0.167125 | − | 0.167125i | ||||
\(919\) | −15.4786 | −0.510591 | −0.255296 | − | 0.966863i | \(-0.582173\pi\) | ||||
−0.255296 | + | 0.966863i | \(0.582173\pi\) | |||||||
\(920\) | −1.84075 | −0.0606876 | ||||||||
\(921\) | −5.07296 | − | 5.07296i | −0.167160 | − | 0.167160i | ||||
\(922\) | 30.9590 | + | 53.6225i | 1.01958 | + | 1.76596i | ||||
\(923\) | 6.63222 | + | 4.85527i | 0.218302 | + | 0.159813i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0968 | + | 3.77723i | 0.463501 | + | 0.124195i | ||||
\(926\) | −5.86115 | + | 10.1518i | −0.192609 | + | 0.333609i | ||||
\(927\) | −6.58882 | − | 11.4122i | −0.216405 | − | 0.374825i | ||||
\(928\) | −5.57038 | − | 20.7889i | −0.182857 | − | 0.682430i | ||||
\(929\) | −31.9786 | − | 31.9786i | −1.04918 | − | 1.04918i | −0.998726 | − | 0.0504568i | \(-0.983932\pi\) |
−0.0504568 | − | 0.998726i | \(-0.516068\pi\) | |||||||
\(930\) | −2.72945 | − | 10.1865i | −0.0895023 | − | 0.334027i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 22.5568 | − | 39.0695i | 0.738871 | − | 1.27976i | ||||
\(933\) | 22.9625 | + | 13.2574i | 0.751758 | + | 0.434028i | ||||
\(934\) | 11.6350 | − | 11.6350i | 0.380708 | − | 0.380708i | ||||
\(935\) | −10.6196 | − | 6.13122i | −0.347298 | − | 0.200512i | ||||
\(936\) | 0.405045 | + | 0.0440510i | 0.0132393 | + | 0.00143985i | ||||
\(937\) | 26.8615i | 0.877526i | 0.898603 | + | 0.438763i | \(0.144583\pi\) | ||||
−0.898603 | + | 0.438763i | \(0.855417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.48978 | + | 11.2406i | 0.211786 | + | 0.366824i | ||||
\(940\) | − | 49.7665i | − | 1.62320i | ||||||
\(941\) | −1.40463 | + | 0.376369i | −0.0457896 | + | 0.0122693i | −0.281641 | − | 0.959520i | \(-0.590879\pi\) |
0.235852 | + | 0.971789i | \(0.424212\pi\) | |||||||
\(942\) | 21.3822 | + | 5.72935i | 0.696670 | + | 0.186672i | ||||
\(943\) | −9.27596 | + | 9.27596i | −0.302067 | + | 0.302067i | ||||
\(944\) | 2.60868 | − | 2.60868i | 0.0849054 | − | 0.0849054i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.8539 | − | 24.1644i | 1.36079 | − | 0.785652i | ||||
\(947\) | 37.4500 | − | 10.0347i | 1.21696 | − | 0.326084i | 0.407472 | − | 0.913218i | \(-0.366410\pi\) |
0.809490 | + | 0.587133i | \(0.199744\pi\) | |||||||
\(948\) | 18.1016 | − | 31.3529i | 0.587912 | − | 1.01829i | ||||
\(949\) | 17.9063 | + | 13.1087i | 0.581262 | + | 0.425526i | ||||
\(950\) | 7.42616 | − | 4.28749i | 0.240936 | − | 0.139105i | ||||
\(951\) | −5.38322 | + | 20.0904i | −0.174563 | + | 0.651477i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.6259 | + | 11.9084i | 0.668138 | + | 0.385750i | 0.795371 | − | 0.606123i | \(-0.207276\pi\) |
−0.127233 | + | 0.991873i | \(0.540609\pi\) | |||||||
\(954\) | −13.8703 | − | 3.71654i | −0.449068 | − | 0.120327i | ||||
\(955\) | 14.5677 | − | 54.3673i | 0.471399 | − | 1.75928i | ||||
\(956\) | −2.85975 | + | 10.6727i | −0.0924908 | + | 0.345180i | ||||
\(957\) | −22.1583 | − | 5.93729i | −0.716275 | − | 0.191925i | ||||
\(958\) | −63.7962 | − | 36.8327i | −2.06116 | − | 1.19001i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 10.3987 | − | 38.8084i | 0.335616 | − | 1.25254i | ||||
\(961\) | −25.7898 | + | 14.8897i | −0.831929 | + | 0.480314i | ||||
\(962\) | 17.1487 | + | 6.65391i | 0.552897 | + | 0.214531i | ||||
\(963\) | −1.42893 | + | 2.47499i | −0.0460468 | + | 0.0797553i | ||||
\(964\) | −31.0830 | + | 8.32866i | −1.00112 | + | 0.268248i | ||||
\(965\) | 17.4255 | − | 10.0606i | 0.560946 | − | 0.323862i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.04001 | − | 5.04001i | 0.162076 | − | 0.162076i | −0.621410 | − | 0.783486i | \(-0.713440\pi\) |
0.783486 | + | 0.621410i | \(0.213440\pi\) | |||||||
\(968\) | −2.12487 | + | 2.12487i | −0.0682960 | + | 0.0682960i | ||||
\(969\) | −0.646974 | − | 0.173356i | −0.0207838 | − | 0.00556900i | ||||
\(970\) | 55.6587 | − | 14.9137i | 1.78709 | − | 0.478850i | ||||
\(971\) | 16.7115i | 0.536296i | 0.963378 | + | 0.268148i | \(0.0864117\pi\) | ||||
−0.963378 | + | 0.268148i | \(0.913588\pi\) | |||||||
\(972\) | 9.42319 | + | 16.3214i | 0.302249 | + | 0.523510i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 33.9484i | 1.08778i | ||||||||
\(975\) | 4.58726 | + | 29.6553i | 0.146910 | + | 0.949730i | ||||
\(976\) | 3.65367 | + | 2.10945i | 0.116951 | + | 0.0675218i | ||||
\(977\) | −34.8162 | + | 34.8162i | −1.11387 | + | 1.11387i | −0.121248 | + | 0.992622i | \(0.538690\pi\) |
−0.992622 | + | 0.121248i | \(0.961310\pi\) | |||||||
\(978\) | 6.48029 | + | 3.74140i | 0.207217 | + | 0.119637i | ||||
\(979\) | 12.1429 | − | 21.0321i | 0.388088 | − | 0.672188i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.25189 | + | 8.40415i | 0.0718972 | + | 0.268324i | ||||
\(982\) | −13.9539 | − | 13.9539i | −0.445286 | − | 0.445286i | ||||
\(983\) | 9.14216 | + | 34.1190i | 0.291590 | + | 1.08823i | 0.943888 | + | 0.330265i | \(0.107138\pi\) |
−0.652298 | + | 0.757962i | \(0.726195\pi\) | |||||||
\(984\) | 0.256993 | + | 0.445125i | 0.00819264 | + | 0.0141901i | ||||
\(985\) | −42.1036 | + | 72.9255i | −1.34153 | + | 2.32360i | ||||
\(986\) | −3.26993 | − | 0.876175i | −0.104136 | − | 0.0279031i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.01920 | − | 2.21301i | 0.159682 | − | 0.0704054i | ||||
\(989\) | 9.16909 | + | 15.8813i | 0.291560 | + | 0.504997i | ||||
\(990\) | 25.4577 | + | 25.4577i | 0.809100 | + | 0.809100i | ||||
\(991\) | 6.83828 | 0.217225 | 0.108613 | − | 0.994084i | \(-0.465359\pi\) | ||||
0.108613 | + | 0.994084i | \(0.465359\pi\) | |||||||
\(992\) | 8.89722 | 0.282487 | ||||||||
\(993\) | −8.35456 | − | 8.35456i | −0.265124 | − | 0.265124i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27.6588 | − | 7.41114i | 0.876842 | − | 0.234949i | ||||
\(996\) | −3.91190 | + | 14.5994i | −0.123953 | + | 0.462600i | ||||
\(997\) | 42.8521 | − | 24.7407i | 1.35714 | − | 0.783545i | 0.367903 | − | 0.929864i | \(-0.380076\pi\) |
0.989237 | + | 0.146319i | \(0.0467425\pi\) | |||||||
\(998\) | − | 5.93845i | − | 0.187978i | ||||||
\(999\) | 3.70400 | + | 13.8235i | 0.117189 | + | 0.437356i |
(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.x.a.80.2 | 28 | ||
7.2 | even | 3 | 91.2.ba.a.54.2 | yes | 28 | ||
7.3 | odd | 6 | 637.2.bd.a.587.6 | 28 | |||
7.4 | even | 3 | 637.2.bd.b.587.6 | 28 | |||
7.5 | odd | 6 | 637.2.bb.a.509.2 | 28 | |||
7.6 | odd | 2 | 91.2.w.a.80.2 | yes | 28 | ||
13.7 | odd | 12 | 637.2.bb.a.423.2 | 28 | |||
21.2 | odd | 6 | 819.2.et.b.145.6 | 28 | |||
21.20 | even | 2 | 819.2.gh.b.262.6 | 28 | |||
91.20 | even | 12 | 91.2.ba.a.59.2 | yes | 28 | ||
91.33 | even | 12 | inner | 637.2.x.a.215.2 | 28 | ||
91.46 | odd | 12 | 637.2.bd.a.293.6 | 28 | |||
91.59 | even | 12 | 637.2.bd.b.293.6 | 28 | |||
91.72 | odd | 12 | 91.2.w.a.33.2 | ✓ | 28 | ||
273.20 | odd | 12 | 819.2.et.b.514.6 | 28 | |||
273.254 | even | 12 | 819.2.gh.b.397.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.33.2 | ✓ | 28 | 91.72 | odd | 12 | ||
91.2.w.a.80.2 | yes | 28 | 7.6 | odd | 2 | ||
91.2.ba.a.54.2 | yes | 28 | 7.2 | even | 3 | ||
91.2.ba.a.59.2 | yes | 28 | 91.20 | even | 12 | ||
637.2.x.a.80.2 | 28 | 1.1 | even | 1 | trivial | ||
637.2.x.a.215.2 | 28 | 91.33 | even | 12 | inner | ||
637.2.bb.a.423.2 | 28 | 13.7 | odd | 12 | |||
637.2.bb.a.509.2 | 28 | 7.5 | odd | 6 | |||
637.2.bd.a.293.6 | 28 | 91.46 | odd | 12 | |||
637.2.bd.a.587.6 | 28 | 7.3 | odd | 6 | |||
637.2.bd.b.293.6 | 28 | 91.59 | even | 12 | |||
637.2.bd.b.587.6 | 28 | 7.4 | even | 3 | |||
819.2.et.b.145.6 | 28 | 21.2 | odd | 6 | |||
819.2.et.b.514.6 | 28 | 273.20 | odd | 12 | |||
819.2.gh.b.262.6 | 28 | 21.20 | even | 2 | |||
819.2.gh.b.397.6 | 28 | 273.254 | even | 12 |