Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(191,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 401.13 | ||
Character | \(\chi\) | \(=\) | 1110.401 |
Dual form | 1110.2.u.e.191.13 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | −0.544013 | + | 1.64440i | −0.314086 | + | 0.949394i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0.778090 | + | 1.54744i | 0.317654 | + | 0.631740i | ||||
\(7\) | −1.56844 | −0.592813 | −0.296407 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296407 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.40810 | − | 1.78915i | −0.802700 | − | 0.596384i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.64384 | −0.495638 | −0.247819 | − | 0.968806i | \(-0.579714\pi\) | ||||
−0.247819 | + | 0.968806i | \(0.579714\pi\) | |||||||
\(12\) | 1.64440 | + | 0.544013i | 0.474697 | + | 0.157043i | ||||
\(13\) | −0.629176 | + | 0.629176i | −0.174502 | + | 0.174502i | −0.788954 | − | 0.614452i | \(-0.789377\pi\) |
0.614452 | + | 0.788954i | \(0.289377\pi\) | |||||||
\(14\) | −1.10905 | + | 1.10905i | −0.296407 | + | 0.296407i | ||||
\(15\) | −1.54744 | + | 0.778090i | −0.399548 | + | 0.200902i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.46856 | − | 4.46856i | −1.08378 | − | 1.08378i | −0.996153 | − | 0.0876320i | \(-0.972070\pi\) |
−0.0876320 | − | 0.996153i | \(-0.527930\pi\) | |||||||
\(18\) | −2.96790 | + | 0.437662i | −0.699542 | + | 0.103158i | ||||
\(19\) | −4.49720 | + | 4.49720i | −1.03173 | + | 1.03173i | −0.0322497 | + | 0.999480i | \(0.510267\pi\) |
−0.999480 | + | 0.0322497i | \(0.989733\pi\) | |||||||
\(20\) | 0.707107 | − | 0.707107i | 0.158114 | − | 0.158114i | ||||
\(21\) | 0.853250 | − | 2.57914i | 0.186195 | − | 0.562814i | ||||
\(22\) | −1.16237 | + | 1.16237i | −0.247819 | + | 0.247819i | ||||
\(23\) | 1.08064 | + | 1.08064i | 0.225328 | + | 0.225328i | 0.810738 | − | 0.585410i | \(-0.199066\pi\) |
−0.585410 | + | 0.810738i | \(0.699066\pi\) | |||||||
\(24\) | 1.54744 | − | 0.778090i | 0.315870 | − | 0.158827i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0.889790i | 0.174502i | ||||||||
\(27\) | 4.25212 | − | 2.98655i | 0.818320 | − | 0.574763i | ||||
\(28\) | 1.56844i | 0.296407i | ||||||||
\(29\) | −0.289296 | + | 0.289296i | −0.0537209 | + | 0.0537209i | −0.733457 | − | 0.679736i | \(-0.762094\pi\) |
0.679736 | + | 0.733457i | \(0.262094\pi\) | |||||||
\(30\) | −0.544013 | + | 1.64440i | −0.0993228 | + | 0.300225i | ||||
\(31\) | −5.62866 | − | 5.62866i | −1.01094 | − | 1.01094i | −0.999940 | − | 0.0109977i | \(-0.996499\pi\) |
−0.0109977 | − | 0.999940i | \(-0.503501\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0.894273 | − | 2.70314i | 0.155673 | − | 0.470556i | ||||
\(34\) | −6.31950 | −1.08378 | ||||||||
\(35\) | −1.10905 | − | 1.10905i | −0.187464 | − | 0.187464i | ||||
\(36\) | −1.78915 | + | 2.40810i | −0.298192 | + | 0.401350i | ||||
\(37\) | −5.36910 | − | 2.85880i | −0.882675 | − | 0.469983i | ||||
\(38\) | 6.36001i | 1.03173i | ||||||||
\(39\) | −0.692337 | − | 1.37690i | −0.110863 | − | 0.220480i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | 10.6225 | 1.65896 | 0.829479 | − | 0.558537i | \(-0.188637\pi\) | ||||
0.829479 | + | 0.558537i | \(0.188637\pi\) | |||||||
\(42\) | −1.22039 | − | 2.42706i | −0.188310 | − | 0.374504i | ||||
\(43\) | −0.834374 | + | 0.834374i | −0.127241 | + | 0.127241i | −0.767859 | − | 0.640618i | \(-0.778678\pi\) |
0.640618 | + | 0.767859i | \(0.278678\pi\) | |||||||
\(44\) | 1.64384i | 0.247819i | ||||||||
\(45\) | −0.437662 | − | 2.96790i | −0.0652429 | − | 0.442429i | ||||
\(46\) | 1.52825 | 0.225328 | ||||||||
\(47\) | 13.1074i | 1.91191i | 0.293511 | + | 0.955956i | \(0.405176\pi\) | ||||
−0.293511 | + | 0.955956i | \(0.594824\pi\) | |||||||
\(48\) | 0.544013 | − | 1.64440i | 0.0785216 | − | 0.237349i | ||||
\(49\) | −4.54001 | −0.648572 | ||||||||
\(50\) | 0.707107 | + | 0.707107i | 0.100000 | + | 0.100000i | ||||
\(51\) | 9.77905 | − | 4.91714i | 1.36934 | − | 0.688537i | ||||
\(52\) | 0.629176 | + | 0.629176i | 0.0872511 | + | 0.0872511i | ||||
\(53\) | − | 4.14299i | − | 0.569084i | −0.958664 | − | 0.284542i | \(-0.908159\pi\) | ||
0.958664 | − | 0.284542i | \(-0.0918415\pi\) | |||||||
\(54\) | 0.894888 | − | 5.11851i | 0.121779 | − | 0.696541i | ||||
\(55\) | −1.16237 | − | 1.16237i | −0.156734 | − | 0.156734i | ||||
\(56\) | 1.10905 | + | 1.10905i | 0.148203 | + | 0.148203i | ||||
\(57\) | −4.94866 | − | 9.84174i | −0.655466 | − | 1.30357i | ||||
\(58\) | 0.409126i | 0.0537209i | ||||||||
\(59\) | −8.55319 | − | 8.55319i | −1.11353 | − | 1.11353i | −0.992669 | − | 0.120861i | \(-0.961435\pi\) |
−0.120861 | − | 0.992669i | \(-0.538565\pi\) | |||||||
\(60\) | 0.778090 | + | 1.54744i | 0.100451 | + | 0.199774i | ||||
\(61\) | −9.70779 | − | 9.70779i | −1.24296 | − | 1.24296i | −0.958769 | − | 0.284186i | \(-0.908277\pi\) |
−0.284186 | − | 0.958769i | \(-0.591723\pi\) | |||||||
\(62\) | −7.96013 | −1.01094 | ||||||||
\(63\) | 3.77695 | + | 2.80617i | 0.475851 | + | 0.353544i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.889790 | −0.110365 | ||||||||
\(66\) | −1.27906 | − | 2.54375i | −0.157441 | − | 0.313114i | ||||
\(67\) | 4.75260i | 0.580622i | 0.956932 | + | 0.290311i | \(0.0937588\pi\) | ||||
−0.956932 | + | 0.290311i | \(0.906241\pi\) | |||||||
\(68\) | −4.46856 | + | 4.46856i | −0.541892 | + | 0.541892i | ||||
\(69\) | −2.36488 | + | 1.18912i | −0.284698 | + | 0.143153i | ||||
\(70\) | −1.56844 | −0.187464 | ||||||||
\(71\) | − | 3.82480i | − | 0.453920i | −0.973904 | − | 0.226960i | \(-0.927121\pi\) | ||
0.973904 | − | 0.226960i | \(-0.0728786\pi\) | |||||||
\(72\) | 0.437662 | + | 2.96790i | 0.0515790 | + | 0.349771i | ||||
\(73\) | 12.7222i | 1.48902i | 0.667611 | + | 0.744510i | \(0.267317\pi\) | ||||
−0.667611 | + | 0.744510i | \(0.732683\pi\) | |||||||
\(74\) | −5.81801 | + | 1.77505i | −0.676329 | + | 0.206346i | ||||
\(75\) | −1.64440 | − | 0.544013i | −0.189879 | − | 0.0628173i | ||||
\(76\) | 4.49720 | + | 4.49720i | 0.515865 | + | 0.515865i | ||||
\(77\) | 2.57826 | 0.293821 | ||||||||
\(78\) | −1.46317 | − | 0.484058i | −0.165671 | − | 0.0548087i | ||||
\(79\) | −0.689395 | + | 0.689395i | −0.0775630 | + | 0.0775630i | −0.744824 | − | 0.667261i | \(-0.767467\pi\) |
0.667261 | + | 0.744824i | \(0.267467\pi\) | |||||||
\(80\) | −0.707107 | − | 0.707107i | −0.0790569 | − | 0.0790569i | ||||
\(81\) | 2.59788 | + | 8.61690i | 0.288653 | + | 0.957434i | ||||
\(82\) | 7.51125 | − | 7.51125i | 0.829479 | − | 0.829479i | ||||
\(83\) | − | 2.00378i | − | 0.219943i | −0.993935 | − | 0.109972i | \(-0.964924\pi\) | ||
0.993935 | − | 0.109972i | \(-0.0350760\pi\) | |||||||
\(84\) | −2.57914 | − | 0.853250i | −0.281407 | − | 0.0930973i | ||||
\(85\) | − | 6.31950i | − | 0.685446i | ||||||
\(86\) | 1.17998i | 0.127241i | ||||||||
\(87\) | −0.318337 | − | 0.633098i | −0.0341293 | − | 0.0678753i | ||||
\(88\) | 1.16237 | + | 1.16237i | 0.123909 | + | 0.123909i | ||||
\(89\) | 7.48295 | − | 7.48295i | 0.793191 | − | 0.793191i | −0.188820 | − | 0.982012i | \(-0.560466\pi\) |
0.982012 | + | 0.188820i | \(0.0604664\pi\) | |||||||
\(90\) | −2.40810 | − | 1.78915i | −0.253836 | − | 0.188593i | ||||
\(91\) | 0.986823 | − | 0.986823i | 0.103447 | − | 0.103447i | ||||
\(92\) | 1.08064 | − | 1.08064i | 0.112664 | − | 0.112664i | ||||
\(93\) | 12.3178 | − | 6.19370i | 1.27730 | − | 0.642257i | ||||
\(94\) | 9.26833 | + | 9.26833i | 0.955956 | + | 0.955956i | ||||
\(95\) | −6.36001 | −0.652523 | ||||||||
\(96\) | −0.778090 | − | 1.54744i | −0.0794135 | − | 0.157935i | ||||
\(97\) | 3.88735 | − | 3.88735i | 0.394701 | − | 0.394701i | −0.481658 | − | 0.876359i | \(-0.659965\pi\) |
0.876359 | + | 0.481658i | \(0.159965\pi\) | |||||||
\(98\) | −3.21027 | + | 3.21027i | −0.324286 | + | 0.324286i | ||||
\(99\) | 3.95854 | + | 2.94108i | 0.397848 | + | 0.295590i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.85174 | 0.482767 | 0.241383 | − | 0.970430i | \(-0.422399\pi\) | ||||
0.241383 | + | 0.970430i | \(0.422399\pi\) | |||||||
\(102\) | 3.43789 | − | 10.3918i | 0.340402 | − | 1.02894i | ||||
\(103\) | 7.40422 | + | 7.40422i | 0.729559 | + | 0.729559i | 0.970532 | − | 0.240973i | \(-0.0774664\pi\) |
−0.240973 | + | 0.970532i | \(0.577466\pi\) | |||||||
\(104\) | 0.889790 | 0.0872511 | ||||||||
\(105\) | 2.42706 | − | 1.22039i | 0.236857 | − | 0.119097i | ||||
\(106\) | −2.92954 | − | 2.92954i | −0.284542 | − | 0.284542i | ||||
\(107\) | 10.1894i | 0.985049i | 0.870299 | + | 0.492524i | \(0.163926\pi\) | ||||
−0.870299 | + | 0.492524i | \(0.836074\pi\) | |||||||
\(108\) | −2.98655 | − | 4.25212i | −0.287381 | − | 0.409160i | ||||
\(109\) | −9.85790 | + | 9.85790i | −0.944216 | + | 0.944216i | −0.998524 | − | 0.0543083i | \(-0.982705\pi\) |
0.0543083 | + | 0.998524i | \(0.482705\pi\) | |||||||
\(110\) | −1.64384 | −0.156734 | ||||||||
\(111\) | 7.62187 | − | 7.27373i | 0.723436 | − | 0.690392i | ||||
\(112\) | 1.56844 | 0.148203 | ||||||||
\(113\) | −13.0116 | + | 13.0116i | −1.22403 | + | 1.22403i | −0.257839 | + | 0.966188i | \(0.583010\pi\) |
−0.966188 | + | 0.257839i | \(0.916990\pi\) | |||||||
\(114\) | −10.4584 | − | 3.45993i | −0.979518 | − | 0.324052i | ||||
\(115\) | 1.52825i | 0.142510i | ||||||||
\(116\) | 0.289296 | + | 0.289296i | 0.0268604 | + | 0.0268604i | ||||
\(117\) | 2.64081 | − | 0.389427i | 0.244143 | − | 0.0360026i | ||||
\(118\) | −12.0960 | −1.11353 | ||||||||
\(119\) | 7.00865 | + | 7.00865i | 0.642482 | + | 0.642482i | ||||
\(120\) | 1.64440 | + | 0.544013i | 0.150112 | + | 0.0496614i | ||||
\(121\) | −8.29778 | −0.754343 | ||||||||
\(122\) | −13.7289 | −1.24296 | ||||||||
\(123\) | −5.77879 | + | 17.4677i | −0.521056 | + | 1.57501i | ||||
\(124\) | −5.62866 | + | 5.62866i | −0.505469 | + | 0.505469i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 4.65497 | − | 0.686446i | 0.414697 | − | 0.0611534i | ||||
\(127\) | 11.4287 | 1.01414 | 0.507068 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507068 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −0.918134 | − | 1.82596i | −0.0808372 | − | 0.160766i | ||||
\(130\) | −0.629176 | + | 0.629176i | −0.0551824 | + | 0.0551824i | ||||
\(131\) | −3.48311 | + | 3.48311i | −0.304320 | + | 0.304320i | −0.842702 | − | 0.538381i | \(-0.819036\pi\) |
0.538381 | + | 0.842702i | \(0.319036\pi\) | |||||||
\(132\) | −2.70314 | − | 0.894273i | −0.235278 | − | 0.0778365i | ||||
\(133\) | 7.05358 | − | 7.05358i | 0.611623 | − | 0.611623i | ||||
\(134\) | 3.36059 | + | 3.36059i | 0.290311 | + | 0.290311i | ||||
\(135\) | 5.11851 | + | 0.894888i | 0.440531 | + | 0.0770197i | ||||
\(136\) | 6.31950i | 0.541892i | ||||||||
\(137\) | − | 4.49515i | − | 0.384047i | −0.981390 | − | 0.192023i | \(-0.938495\pi\) | ||
0.981390 | − | 0.192023i | \(-0.0615049\pi\) | |||||||
\(138\) | −0.831388 | + | 2.51305i | −0.0707725 | + | 0.213925i | ||||
\(139\) | − | 21.9294i | − | 1.86002i | −0.367529 | − | 0.930012i | \(-0.619796\pi\) | ||
0.367529 | − | 0.930012i | \(-0.380204\pi\) | |||||||
\(140\) | −1.10905 | + | 1.10905i | −0.0937320 | + | 0.0937320i | ||||
\(141\) | −21.5538 | − | 7.13060i | −1.81516 | − | 0.600505i | ||||
\(142\) | −2.70454 | − | 2.70454i | −0.226960 | − | 0.226960i | ||||
\(143\) | 1.03427 | − | 1.03427i | 0.0864898 | − | 0.0864898i | ||||
\(144\) | 2.40810 | + | 1.78915i | 0.200675 | + | 0.149096i | ||||
\(145\) | −0.409126 | −0.0339761 | ||||||||
\(146\) | 8.99595 | + | 8.99595i | 0.744510 | + | 0.744510i | ||||
\(147\) | 2.46983 | − | 7.46559i | 0.203708 | − | 0.615751i | ||||
\(148\) | −2.85880 | + | 5.36910i | −0.234992 | + | 0.441338i | ||||
\(149\) | − | 22.3567i | − | 1.83153i | −0.401716 | − | 0.915764i | \(-0.631586\pi\) | ||
0.401716 | − | 0.915764i | \(-0.368414\pi\) | |||||||
\(150\) | −1.54744 | + | 0.778090i | −0.126348 | + | 0.0635308i | ||||
\(151\) | 22.5415i | 1.83440i | 0.398426 | + | 0.917201i | \(0.369557\pi\) | ||||
−0.398426 | + | 0.917201i | \(0.630443\pi\) | |||||||
\(152\) | 6.36001 | 0.515865 | ||||||||
\(153\) | 2.76581 | + | 18.7557i | 0.223602 | + | 1.51631i | ||||
\(154\) | 1.82311 | − | 1.82311i | 0.146910 | − | 0.146910i | ||||
\(155\) | − | 7.96013i | − | 0.639373i | ||||||
\(156\) | −1.37690 | + | 0.692337i | −0.110240 | + | 0.0554313i | ||||
\(157\) | −2.37029 | −0.189170 | −0.0945848 | − | 0.995517i | \(-0.530152\pi\) | ||||
−0.0945848 | + | 0.995517i | \(0.530152\pi\) | |||||||
\(158\) | 0.974951i | 0.0775630i | ||||||||
\(159\) | 6.81273 | + | 2.25384i | 0.540285 | + | 0.178741i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −1.69491 | − | 1.69491i | −0.133577 | − | 0.133577i | ||||
\(162\) | 7.93005 | + | 4.25609i | 0.623043 | + | 0.334390i | ||||
\(163\) | 8.06627 | + | 8.06627i | 0.631799 | + | 0.631799i | 0.948519 | − | 0.316720i | \(-0.102582\pi\) |
−0.316720 | + | 0.948519i | \(0.602582\pi\) | |||||||
\(164\) | − | 10.6225i | − | 0.829479i | ||||||
\(165\) | 2.54375 | − | 1.27906i | 0.198031 | − | 0.0995746i | ||||
\(166\) | −1.41689 | − | 1.41689i | −0.109972 | − | 0.109972i | ||||
\(167\) | 5.21464 | + | 5.21464i | 0.403521 | + | 0.403521i | 0.879472 | − | 0.475951i | \(-0.157896\pi\) |
−0.475951 | + | 0.879472i | \(0.657896\pi\) | |||||||
\(168\) | −2.42706 | + | 1.22039i | −0.187252 | + | 0.0941548i | ||||
\(169\) | 12.2083i | 0.939098i | ||||||||
\(170\) | −4.46856 | − | 4.46856i | −0.342723 | − | 0.342723i | ||||
\(171\) | 18.8759 | − | 2.78354i | 1.44348 | − | 0.212862i | ||||
\(172\) | 0.834374 | + | 0.834374i | 0.0636204 | + | 0.0636204i | ||||
\(173\) | 18.5616 | 1.41121 | 0.705605 | − | 0.708606i | \(-0.250676\pi\) | ||||
0.705605 | + | 0.708606i | \(0.250676\pi\) | |||||||
\(174\) | −0.672766 | − | 0.222570i | −0.0510023 | − | 0.0168730i | ||||
\(175\) | − | 1.56844i | − | 0.118563i | ||||||
\(176\) | 1.64384 | 0.123909 | ||||||||
\(177\) | 18.7179 | − | 9.41181i | 1.40692 | − | 0.707435i | ||||
\(178\) | − | 10.5825i | − | 0.793191i | ||||||
\(179\) | −4.75163 | + | 4.75163i | −0.355153 | + | 0.355153i | −0.862023 | − | 0.506869i | \(-0.830803\pi\) |
0.506869 | + | 0.862023i | \(0.330803\pi\) | |||||||
\(180\) | −2.96790 | + | 0.437662i | −0.221214 | + | 0.0326214i | ||||
\(181\) | 1.37431 | 0.102152 | 0.0510759 | − | 0.998695i | \(-0.483735\pi\) | ||||
0.0510759 | + | 0.998695i | \(0.483735\pi\) | |||||||
\(182\) | − | 1.39558i | − | 0.103447i | ||||||
\(183\) | 21.2447 | − | 10.6823i | 1.57045 | − | 0.789660i | ||||
\(184\) | − | 1.52825i | − | 0.112664i | ||||||
\(185\) | −1.77505 | − | 5.81801i | −0.130505 | − | 0.427748i | ||||
\(186\) | 4.33042 | − | 13.0896i | 0.317522 | − | 0.959778i | ||||
\(187\) | 7.34562 | + | 7.34562i | 0.537165 | + | 0.537165i | ||||
\(188\) | 13.1074 | 0.955956 | ||||||||
\(189\) | −6.66917 | + | 4.68422i | −0.485111 | + | 0.340727i | ||||
\(190\) | −4.49720 | + | 4.49720i | −0.326262 | + | 0.326262i | ||||
\(191\) | 8.07560 | + | 8.07560i | 0.584330 | + | 0.584330i | 0.936090 | − | 0.351760i | \(-0.114417\pi\) |
−0.351760 | + | 0.936090i | \(0.614417\pi\) | |||||||
\(192\) | −1.64440 | − | 0.544013i | −0.118674 | − | 0.0392608i | ||||
\(193\) | −10.3501 | + | 10.3501i | −0.745016 | + | 0.745016i | −0.973539 | − | 0.228523i | \(-0.926611\pi\) |
0.228523 | + | 0.973539i | \(0.426611\pi\) | |||||||
\(194\) | − | 5.49755i | − | 0.394701i | ||||||
\(195\) | 0.484058 | − | 1.46317i | 0.0346641 | − | 0.104780i | ||||
\(196\) | 4.54001i | 0.324286i | ||||||||
\(197\) | − | 9.80467i | − | 0.698554i | −0.937020 | − | 0.349277i | \(-0.886427\pi\) | ||
0.937020 | − | 0.349277i | \(-0.113573\pi\) | |||||||
\(198\) | 4.87877 | − | 0.719449i | 0.346719 | − | 0.0511290i | ||||
\(199\) | 5.14958 | + | 5.14958i | 0.365044 | + | 0.365044i | 0.865666 | − | 0.500622i | \(-0.166895\pi\) |
−0.500622 | + | 0.865666i | \(0.666895\pi\) | |||||||
\(200\) | 0.707107 | − | 0.707107i | 0.0500000 | − | 0.0500000i | ||||
\(201\) | −7.81517 | − | 2.58548i | −0.551240 | − | 0.182366i | ||||
\(202\) | 3.43070 | − | 3.43070i | 0.241383 | − | 0.241383i | ||||
\(203\) | 0.453742 | − | 0.453742i | 0.0318464 | − | 0.0318464i | ||||
\(204\) | −4.91714 | − | 9.77905i | −0.344269 | − | 0.684671i | ||||
\(205\) | 7.51125 | + | 7.51125i | 0.524609 | + | 0.524609i | ||||
\(206\) | 10.4711 | 0.729559 | ||||||||
\(207\) | −0.668857 | − | 4.53570i | −0.0464888 | − | 0.315253i | ||||
\(208\) | 0.629176 | − | 0.629176i | 0.0436255 | − | 0.0436255i | ||||
\(209\) | 7.39270 | − | 7.39270i | 0.511364 | − | 0.511364i | ||||
\(210\) | 0.853250 | − | 2.57914i | 0.0588799 | − | 0.177977i | ||||
\(211\) | −0.591484 | −0.0407194 | −0.0203597 | − | 0.999793i | \(-0.506481\pi\) | ||||
−0.0203597 | + | 0.999793i | \(0.506481\pi\) | |||||||
\(212\) | −4.14299 | −0.284542 | ||||||||
\(213\) | 6.28949 | + | 2.08074i | 0.430949 | + | 0.142570i | ||||
\(214\) | 7.20501 | + | 7.20501i | 0.492524 | + | 0.492524i | ||||
\(215\) | −1.17998 | −0.0804742 | ||||||||
\(216\) | −5.11851 | − | 0.894888i | −0.348271 | − | 0.0608894i | ||||
\(217\) | 8.82820 | + | 8.82820i | 0.599297 | + | 0.599297i | ||||
\(218\) | 13.9412i | 0.944216i | ||||||||
\(219\) | −20.9204 | − | 6.92104i | −1.41367 | − | 0.467681i | ||||
\(220\) | −1.16237 | + | 1.16237i | −0.0783672 | + | 0.0783672i | ||||
\(221\) | 5.62302 | 0.378246 | ||||||||
\(222\) | 0.246175 | − | 10.5328i | 0.0165222 | − | 0.706914i | ||||
\(223\) | −0.315113 | −0.0211015 | −0.0105508 | − | 0.999944i | \(-0.503358\pi\) | ||||
−0.0105508 | + | 0.999944i | \(0.503358\pi\) | |||||||
\(224\) | 1.10905 | − | 1.10905i | 0.0741017 | − | 0.0741017i | ||||
\(225\) | 1.78915 | − | 2.40810i | 0.119277 | − | 0.160540i | ||||
\(226\) | 18.4012i | 1.22403i | ||||||||
\(227\) | −9.38302 | − | 9.38302i | −0.622773 | − | 0.622773i | 0.323467 | − | 0.946240i | \(-0.395152\pi\) |
−0.946240 | + | 0.323467i | \(0.895152\pi\) | |||||||
\(228\) | −9.84174 | + | 4.94866i | −0.651785 | + | 0.327733i | ||||
\(229\) | 25.4498 | 1.68177 | 0.840884 | − | 0.541216i | \(-0.182036\pi\) | ||||
0.840884 | + | 0.541216i | \(0.182036\pi\) | |||||||
\(230\) | 1.08064 | + | 1.08064i | 0.0712550 | + | 0.0712550i | ||||
\(231\) | −1.40261 | + | 4.23970i | −0.0922850 | + | 0.278952i | ||||
\(232\) | 0.409126 | 0.0268604 | ||||||||
\(233\) | 7.54603 | 0.494357 | 0.247178 | − | 0.968970i | \(-0.420497\pi\) | ||||
0.247178 | + | 0.968970i | \(0.420497\pi\) | |||||||
\(234\) | 1.59197 | − | 2.14270i | 0.104070 | − | 0.140073i | ||||
\(235\) | −9.26833 | + | 9.26833i | −0.604599 | + | 0.604599i | ||||
\(236\) | −8.55319 | + | 8.55319i | −0.556765 | + | 0.556765i | ||||
\(237\) | −0.758600 | − | 1.50868i | −0.0492764 | − | 0.0979993i | ||||
\(238\) | 9.91173 | 0.642482 | ||||||||
\(239\) | 2.13485 | + | 2.13485i | 0.138092 | + | 0.138092i | 0.772774 | − | 0.634682i | \(-0.218869\pi\) |
−0.634682 | + | 0.772774i | \(0.718869\pi\) | |||||||
\(240\) | 1.54744 | − | 0.778090i | 0.0998869 | − | 0.0502255i | ||||
\(241\) | 12.4422 | − | 12.4422i | 0.801472 | − | 0.801472i | −0.181854 | − | 0.983326i | \(-0.558210\pi\) |
0.983326 | + | 0.181854i | \(0.0582097\pi\) | |||||||
\(242\) | −5.86741 | + | 5.86741i | −0.377172 | + | 0.377172i | ||||
\(243\) | −15.5829 | − | 0.415759i | −0.999644 | − | 0.0266710i | ||||
\(244\) | −9.70779 | + | 9.70779i | −0.621478 | + | 0.621478i | ||||
\(245\) | −3.21027 | − | 3.21027i | −0.205097 | − | 0.205097i | ||||
\(246\) | 8.26528 | + | 16.4377i | 0.526975 | + | 1.04803i | ||||
\(247\) | − | 5.65907i | − | 0.360078i | ||||||
\(248\) | 7.96013i | 0.505469i | ||||||||
\(249\) | 3.29501 | + | 1.09008i | 0.208813 | + | 0.0690812i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −1.93314 | + | 1.93314i | −0.122019 | + | 0.122019i | −0.765479 | − | 0.643460i | \(-0.777498\pi\) |
0.643460 | + | 0.765479i | \(0.277498\pi\) | |||||||
\(252\) | 2.80617 | − | 3.77695i | 0.176772 | − | 0.237925i | ||||
\(253\) | −1.77640 | − | 1.77640i | −0.111681 | − | 0.111681i | ||||
\(254\) | 8.08133 | − | 8.08133i | 0.507068 | − | 0.507068i | ||||
\(255\) | 10.3918 | + | 3.43789i | 0.650758 | + | 0.215289i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.00157497 | + | 0.00157497i | 9.82441e−5 | + | 9.82441e-5i | 0.707156 | − | 0.707058i | \(-0.249978\pi\) |
−0.707058 | + | 0.707156i | \(0.749978\pi\) | |||||||
\(258\) | −1.94036 | − | 0.641927i | −0.120802 | − | 0.0399646i | ||||
\(259\) | 8.42110 | + | 4.48384i | 0.523262 | + | 0.278612i | ||||
\(260\) | 0.889790i | 0.0551824i | ||||||||
\(261\) | 1.21425 | − | 0.179059i | 0.0751600 | − | 0.0110835i | ||||
\(262\) | 4.92586i | 0.304320i | ||||||||
\(263\) | −10.5582 | −0.651043 | −0.325522 | − | 0.945535i | \(-0.605540\pi\) | ||||
−0.325522 | + | 0.945535i | \(0.605540\pi\) | |||||||
\(264\) | −2.54375 | + | 1.27906i | −0.156557 | + | 0.0787207i | ||||
\(265\) | 2.92954 | − | 2.92954i | 0.179960 | − | 0.179960i | ||||
\(266\) | − | 9.97527i | − | 0.611623i | ||||||
\(267\) | 8.23413 | + | 16.3758i | 0.503921 | + | 1.00218i | ||||
\(268\) | 4.75260 | 0.290311 | ||||||||
\(269\) | − | 9.40474i | − | 0.573417i | −0.958018 | − | 0.286708i | \(-0.907439\pi\) | ||
0.958018 | − | 0.286708i | \(-0.0925611\pi\) | |||||||
\(270\) | 4.25212 | − | 2.98655i | 0.258776 | − | 0.181756i | ||||
\(271\) | −6.28538 | −0.381810 | −0.190905 | − | 0.981609i | \(-0.561142\pi\) | ||||
−0.190905 | + | 0.981609i | \(0.561142\pi\) | |||||||
\(272\) | 4.46856 | + | 4.46856i | 0.270946 | + | 0.270946i | ||||
\(273\) | 1.08589 | + | 2.15958i | 0.0657208 | + | 0.130703i | ||||
\(274\) | −3.17855 | − | 3.17855i | −0.192023 | − | 0.192023i | ||||
\(275\) | − | 1.64384i | − | 0.0991275i | ||||||
\(276\) | 1.18912 | + | 2.36488i | 0.0715764 | + | 0.142349i | ||||
\(277\) | −17.7788 | − | 17.7788i | −1.06822 | − | 1.06822i | −0.997496 | − | 0.0707289i | \(-0.977467\pi\) |
−0.0707289 | − | 0.997496i | \(-0.522533\pi\) | |||||||
\(278\) | −15.5064 | − | 15.5064i | −0.930012 | − | 0.930012i | ||||
\(279\) | 3.48385 | + | 23.6249i | 0.208573 | + | 1.41439i | ||||
\(280\) | 1.56844i | 0.0937320i | ||||||||
\(281\) | −15.9903 | − | 15.9903i | −0.953902 | − | 0.953902i | 0.0450817 | − | 0.998983i | \(-0.485645\pi\) |
−0.998983 | + | 0.0450817i | \(0.985645\pi\) | |||||||
\(282\) | −20.2829 | + | 10.1987i | −1.20783 | + | 0.607326i | ||||
\(283\) | 5.52382 | + | 5.52382i | 0.328357 | + | 0.328357i | 0.851962 | − | 0.523604i | \(-0.175413\pi\) |
−0.523604 | + | 0.851962i | \(0.675413\pi\) | |||||||
\(284\) | −3.82480 | −0.226960 | ||||||||
\(285\) | 3.45993 | − | 10.4584i | 0.204949 | − | 0.619502i | ||||
\(286\) | − | 1.46268i | − | 0.0864898i | ||||||
\(287\) | −16.6607 | −0.983453 | ||||||||
\(288\) | 2.96790 | − | 0.437662i | 0.174885 | − | 0.0257895i | ||||
\(289\) | 22.9361i | 1.34918i | ||||||||
\(290\) | −0.289296 | + | 0.289296i | −0.0169880 | + | 0.0169880i | ||||
\(291\) | 4.27759 | + | 8.50713i | 0.250757 | + | 0.498697i | ||||
\(292\) | 12.7222 | 0.744510 | ||||||||
\(293\) | − | 13.9882i | − | 0.817202i | −0.912713 | − | 0.408601i | \(-0.866017\pi\) | ||
0.912713 | − | 0.408601i | \(-0.133983\pi\) | |||||||
\(294\) | −3.53254 | − | 7.02540i | −0.206022 | − | 0.409729i | ||||
\(295\) | − | 12.0960i | − | 0.704258i | ||||||
\(296\) | 1.77505 | + | 5.81801i | 0.103173 | + | 0.338165i | ||||
\(297\) | −6.98982 | + | 4.90943i | −0.405590 | + | 0.284874i | ||||
\(298\) | −15.8085 | − | 15.8085i | −0.915764 | − | 0.915764i | ||||
\(299\) | −1.35982 | −0.0786405 | ||||||||
\(300\) | −0.544013 | + | 1.64440i | −0.0314086 | + | 0.0949394i | ||||
\(301\) | 1.30866 | − | 1.30866i | 0.0754301 | − | 0.0754301i | ||||
\(302\) | 15.9392 | + | 15.9392i | 0.917201 | + | 0.917201i | ||||
\(303\) | −2.63941 | + | 7.97821i | −0.151630 | + | 0.458336i | ||||
\(304\) | 4.49720 | − | 4.49720i | 0.257932 | − | 0.257932i | ||||
\(305\) | − | 13.7289i | − | 0.786114i | ||||||
\(306\) | 15.2180 | + | 11.3065i | 0.869954 | + | 0.646352i | ||||
\(307\) | 10.1886i | 0.581493i | 0.956800 | + | 0.290746i | \(0.0939036\pi\) | ||||
−0.956800 | + | 0.290746i | \(0.906096\pi\) | |||||||
\(308\) | − | 2.57826i | − | 0.146910i | ||||||
\(309\) | −16.2035 | + | 8.14750i | −0.921784 | + | 0.463495i | ||||
\(310\) | −5.62866 | − | 5.62866i | −0.319686 | − | 0.319686i | ||||
\(311\) | −10.4912 | + | 10.4912i | −0.594899 | + | 0.594899i | −0.938951 | − | 0.344052i | \(-0.888200\pi\) |
0.344052 | + | 0.938951i | \(0.388200\pi\) | |||||||
\(312\) | −0.484058 | + | 1.46317i | −0.0274044 | + | 0.0828357i | ||||
\(313\) | 24.4934 | − | 24.4934i | 1.38445 | − | 1.38445i | 0.547922 | − | 0.836529i | \(-0.315419\pi\) |
0.836529 | − | 0.547922i | \(-0.184581\pi\) | |||||||
\(314\) | −1.67605 | + | 1.67605i | −0.0945848 | + | 0.0945848i | ||||
\(315\) | 0.686446 | + | 4.65497i | 0.0386768 | + | 0.262278i | ||||
\(316\) | 0.689395 | + | 0.689395i | 0.0387815 | + | 0.0387815i | ||||
\(317\) | −18.8817 | −1.06050 | −0.530250 | − | 0.847841i | \(-0.677902\pi\) | ||||
−0.530250 | + | 0.847841i | \(0.677902\pi\) | |||||||
\(318\) | 6.41104 | − | 3.22362i | 0.359513 | − | 0.180772i | ||||
\(319\) | 0.475557 | − | 0.475557i | 0.0266261 | − | 0.0266261i | ||||
\(320\) | −0.707107 | + | 0.707107i | −0.0395285 | + | 0.0395285i | ||||
\(321\) | −16.7555 | − | 5.54318i | −0.935200 | − | 0.309390i | ||||
\(322\) | −2.39696 | −0.133577 | ||||||||
\(323\) | 40.1921 | 2.23635 | ||||||||
\(324\) | 8.61690 | − | 2.59788i | 0.478717 | − | 0.144327i | ||||
\(325\) | −0.629176 | − | 0.629176i | −0.0349004 | − | 0.0349004i | ||||
\(326\) | 11.4074 | 0.631799 | ||||||||
\(327\) | −10.8475 | − | 21.5732i | −0.599868 | − | 1.19300i | ||||
\(328\) | −7.51125 | − | 7.51125i | −0.414740 | − | 0.414740i | ||||
\(329\) | − | 20.5581i | − | 1.13341i | ||||||
\(330\) | 0.894273 | − | 2.70314i | 0.0492281 | − | 0.148803i | ||||
\(331\) | −16.7777 | + | 16.7777i | −0.922187 | + | 0.922187i | −0.997184 | − | 0.0749970i | \(-0.976105\pi\) |
0.0749970 | + | 0.997184i | \(0.476105\pi\) | |||||||
\(332\) | −2.00378 | −0.109972 | ||||||||
\(333\) | 7.81451 | + | 16.4904i | 0.428233 | + | 0.903669i | ||||
\(334\) | 7.37462 | 0.403521 | ||||||||
\(335\) | −3.36059 | + | 3.36059i | −0.183609 | + | 0.183609i | ||||
\(336\) | −0.853250 | + | 2.57914i | −0.0465486 | + | 0.140703i | ||||
\(337\) | 18.2617i | 0.994779i | 0.867527 | + | 0.497390i | \(0.165708\pi\) | ||||
−0.867527 | + | 0.497390i | \(0.834292\pi\) | |||||||
\(338\) | 8.63255 | + | 8.63255i | 0.469549 | + | 0.469549i | ||||
\(339\) | −14.3178 | − | 28.4747i | −0.777634 | − | 1.54653i | ||||
\(340\) | −6.31950 | −0.342723 | ||||||||
\(341\) | 9.25264 | + | 9.25264i | 0.501059 | + | 0.501059i | ||||
\(342\) | 11.3790 | − | 15.3155i | 0.615307 | − | 0.828169i | ||||
\(343\) | 18.0998 | 0.977296 | ||||||||
\(344\) | 1.17998 | 0.0636204 | ||||||||
\(345\) | −2.51305 | − | 0.831388i | −0.135298 | − | 0.0447604i | ||||
\(346\) | 13.1250 | − | 13.1250i | 0.705605 | − | 0.705605i | ||||
\(347\) | 8.03823 | − | 8.03823i | 0.431515 | − | 0.431515i | −0.457628 | − | 0.889144i | \(-0.651301\pi\) |
0.889144 | + | 0.457628i | \(0.151301\pi\) | |||||||
\(348\) | −0.633098 | + | 0.318337i | −0.0339376 | + | 0.0170647i | ||||
\(349\) | −8.68067 | −0.464665 | −0.232333 | − | 0.972636i | \(-0.574636\pi\) | ||||
−0.232333 | + | 0.972636i | \(0.574636\pi\) | |||||||
\(350\) | −1.10905 | − | 1.10905i | −0.0592813 | − | 0.0592813i | ||||
\(351\) | −0.796262 | + | 4.55440i | −0.0425013 | + | 0.243096i | ||||
\(352\) | 1.16237 | − | 1.16237i | 0.0619547 | − | 0.0619547i | ||||
\(353\) | 4.36437 | − | 4.36437i | 0.232292 | − | 0.232292i | −0.581357 | − | 0.813649i | \(-0.697478\pi\) |
0.813649 | + | 0.581357i | \(0.197478\pi\) | |||||||
\(354\) | 6.58041 | − | 19.8907i | 0.349745 | − | 1.05718i | ||||
\(355\) | 2.70454 | − | 2.70454i | 0.143542 | − | 0.143542i | ||||
\(356\) | −7.48295 | − | 7.48295i | −0.396596 | − | 0.396596i | ||||
\(357\) | −15.3378 | + | 7.71222i | −0.811764 | + | 0.408174i | ||||
\(358\) | 6.71982i | 0.355153i | ||||||||
\(359\) | − | 20.7643i | − | 1.09590i | −0.836511 | − | 0.547950i | \(-0.815409\pi\) | ||
0.836511 | − | 0.547950i | \(-0.184591\pi\) | |||||||
\(360\) | −1.78915 | + | 2.40810i | −0.0942965 | + | 0.126918i | ||||
\(361\) | − | 21.4497i | − | 1.12893i | ||||||
\(362\) | 0.971785 | − | 0.971785i | 0.0510759 | − | 0.0510759i | ||||
\(363\) | 4.51410 | − | 13.6449i | 0.236929 | − | 0.716169i | ||||
\(364\) | −0.986823 | − | 0.986823i | −0.0517236 | − | 0.0517236i | ||||
\(365\) | −8.99595 | + | 8.99595i | −0.470870 | + | 0.470870i | ||||
\(366\) | 7.46870 | − | 22.5758i | 0.390395 | − | 1.18005i | ||||
\(367\) | −22.0692 | −1.15200 | −0.576002 | − | 0.817448i | \(-0.695388\pi\) | ||||
−0.576002 | + | 0.817448i | \(0.695388\pi\) | |||||||
\(368\) | −1.08064 | − | 1.08064i | −0.0563320 | − | 0.0563320i | ||||
\(369\) | −25.5801 | − | 19.0053i | −1.33165 | − | 0.989376i | ||||
\(370\) | −5.36910 | − | 2.85880i | −0.279126 | − | 0.148622i | ||||
\(371\) | 6.49802i | 0.337360i | ||||||||
\(372\) | −6.19370 | − | 12.3178i | −0.321128 | − | 0.638650i | ||||
\(373\) | 12.9551i | 0.670787i | 0.942078 | + | 0.335394i | \(0.108869\pi\) | ||||
−0.942078 | + | 0.335394i | \(0.891131\pi\) | |||||||
\(374\) | 10.3883 | 0.537165 | ||||||||
\(375\) | −0.778090 | − | 1.54744i | −0.0401804 | − | 0.0799095i | ||||
\(376\) | 9.26833 | − | 9.26833i | 0.477978 | − | 0.477978i | ||||
\(377\) | − | 0.364036i | − | 0.0187488i | ||||||
\(378\) | −1.40357 | + | 8.02806i | −0.0721921 | + | 0.412919i | ||||
\(379\) | −9.36563 | −0.481080 | −0.240540 | − | 0.970639i | \(-0.577325\pi\) | ||||
−0.240540 | + | 0.970639i | \(0.577325\pi\) | |||||||
\(380\) | 6.36001i | 0.326262i | ||||||||
\(381\) | −6.21738 | + | 18.7934i | −0.318526 | + | 0.962814i | ||||
\(382\) | 11.4206 | 0.584330 | ||||||||
\(383\) | −1.18802 | − | 1.18802i | −0.0607051 | − | 0.0607051i | 0.676103 | − | 0.736808i | \(-0.263668\pi\) |
−0.736808 | + | 0.676103i | \(0.763668\pi\) | |||||||
\(384\) | −1.54744 | + | 0.778090i | −0.0789675 | + | 0.0397068i | ||||
\(385\) | 1.82311 | + | 1.82311i | 0.0929142 | + | 0.0929142i | ||||
\(386\) | 14.6372i | 0.745016i | ||||||||
\(387\) | 3.50208 | − | 0.516434i | 0.178021 | − | 0.0262518i | ||||
\(388\) | −3.88735 | − | 3.88735i | −0.197350 | − | 0.197350i | ||||
\(389\) | −22.0352 | − | 22.0352i | −1.11723 | − | 1.11723i | −0.992146 | − | 0.125085i | \(-0.960080\pi\) |
−0.125085 | − | 0.992146i | \(-0.539920\pi\) | |||||||
\(390\) | −0.692337 | − | 1.37690i | −0.0350578 | − | 0.0697219i | ||||
\(391\) | − | 9.65777i | − | 0.488414i | ||||||
\(392\) | 3.21027 | + | 3.21027i | 0.162143 | + | 0.162143i | ||||
\(393\) | −3.83276 | − | 7.62248i | −0.193337 | − | 0.384503i | ||||
\(394\) | −6.93295 | − | 6.93295i | −0.349277 | − | 0.349277i | ||||
\(395\) | −0.974951 | −0.0490551 | ||||||||
\(396\) | 2.94108 | − | 3.95854i | 0.147795 | − | 0.198924i | ||||
\(397\) | 19.3715i | 0.972229i | 0.873895 | + | 0.486115i | \(0.161586\pi\) | ||||
−0.873895 | + | 0.486115i | \(0.838414\pi\) | |||||||
\(398\) | 7.28261 | 0.365044 | ||||||||
\(399\) | 7.76166 | + | 15.4361i | 0.388569 | + | 0.772774i | ||||
\(400\) | − | 1.00000i | − | 0.0500000i | ||||||
\(401\) | −15.3652 | + | 15.3652i | −0.767300 | + | 0.767300i | −0.977630 | − | 0.210331i | \(-0.932546\pi\) |
0.210331 | + | 0.977630i | \(0.432546\pi\) | |||||||
\(402\) | −7.35437 | + | 3.69795i | −0.366803 | + | 0.184437i | ||||
\(403\) | 7.08284 | 0.352821 | ||||||||
\(404\) | − | 4.85174i | − | 0.241383i | ||||||
\(405\) | −4.25609 | + | 7.93005i | −0.211487 | + | 0.394047i | ||||
\(406\) | − | 0.641688i | − | 0.0318464i | ||||||
\(407\) | 8.82597 | + | 4.69942i | 0.437487 | + | 0.232942i | ||||
\(408\) | −10.3918 | − | 3.43789i | −0.514470 | − | 0.170201i | ||||
\(409\) | −14.2762 | − | 14.2762i | −0.705914 | − | 0.705914i | 0.259759 | − | 0.965673i | \(-0.416357\pi\) |
−0.965673 | + | 0.259759i | \(0.916357\pi\) | |||||||
\(410\) | 10.6225 | 0.524609 | ||||||||
\(411\) | 7.39182 | + | 2.44542i | 0.364612 | + | 0.120624i | ||||
\(412\) | 7.40422 | − | 7.40422i | 0.364780 | − | 0.364780i | ||||
\(413\) | 13.4151 | + | 13.4151i | 0.660115 | + | 0.660115i | ||||
\(414\) | −3.68018 | − | 2.73427i | −0.180871 | − | 0.134382i | ||||
\(415\) | 1.41689 | − | 1.41689i | 0.0695522 | − | 0.0695522i | ||||
\(416\) | − | 0.889790i | − | 0.0436255i | ||||||
\(417\) | 36.0606 | + | 11.9299i | 1.76590 | + | 0.584208i | ||||
\(418\) | − | 10.4549i | − | 0.511364i | ||||||
\(419\) | − | 0.599281i | − | 0.0292768i | −0.999893 | − | 0.0146384i | \(-0.995340\pi\) | ||
0.999893 | − | 0.0146384i | \(-0.00465972\pi\) | |||||||
\(420\) | −1.22039 | − | 2.42706i | −0.0595487 | − | 0.118429i | ||||
\(421\) | 2.61990 | + | 2.61990i | 0.127686 | + | 0.127686i | 0.768062 | − | 0.640376i | \(-0.221221\pi\) |
−0.640376 | + | 0.768062i | \(0.721221\pi\) | |||||||
\(422\) | −0.418242 | + | 0.418242i | −0.0203597 | + | 0.0203597i | ||||
\(423\) | 23.4511 | − | 31.5639i | 1.14023 | − | 1.53469i | ||||
\(424\) | −2.92954 | + | 2.92954i | −0.142271 | + | 0.142271i | ||||
\(425\) | 4.46856 | − | 4.46856i | 0.216757 | − | 0.216757i | ||||
\(426\) | 5.91865 | − | 2.97604i | 0.286759 | − | 0.144189i | ||||
\(427\) | 15.2261 | + | 15.2261i | 0.736840 | + | 0.736840i | ||||
\(428\) | 10.1894 | 0.492524 | ||||||||
\(429\) | 1.13809 | + | 2.26340i | 0.0549477 | + | 0.109278i | ||||
\(430\) | −0.834374 | + | 0.834374i | −0.0402371 | + | 0.0402371i | ||||
\(431\) | −26.5760 | + | 26.5760i | −1.28012 | + | 1.28012i | −0.339523 | + | 0.940598i | \(0.610266\pi\) |
−0.940598 | + | 0.339523i | \(0.889734\pi\) | |||||||
\(432\) | −4.25212 | + | 2.98655i | −0.204580 | + | 0.143691i | ||||
\(433\) | −35.9427 | −1.72730 | −0.863649 | − | 0.504094i | \(-0.831826\pi\) | ||||
−0.863649 | + | 0.504094i | \(0.831826\pi\) | |||||||
\(434\) | 12.4850 | 0.599297 | ||||||||
\(435\) | 0.222570 | − | 0.672766i | 0.0106714 | − | 0.0322567i | ||||
\(436\) | 9.85790 | + | 9.85790i | 0.472108 | + | 0.472108i | ||||
\(437\) | −9.71968 | −0.464955 | ||||||||
\(438\) | −19.6869 | + | 9.89902i | −0.940674 | + | 0.472993i | ||||
\(439\) | −18.6711 | − | 18.6711i | −0.891124 | − | 0.891124i | 0.103505 | − | 0.994629i | \(-0.466994\pi\) |
−0.994629 | + | 0.103505i | \(0.966994\pi\) | |||||||
\(440\) | 1.64384i | 0.0783672i | ||||||||
\(441\) | 10.9328 | + | 8.12276i | 0.520609 | + | 0.386798i | ||||
\(442\) | 3.97608 | − | 3.97608i | 0.189123 | − | 0.189123i | ||||
\(443\) | 11.8103 | 0.561123 | 0.280562 | − | 0.959836i | \(-0.409479\pi\) | ||||
0.280562 | + | 0.959836i | \(0.409479\pi\) | |||||||
\(444\) | −7.27373 | − | 7.62187i | −0.345196 | − | 0.361718i | ||||
\(445\) | 10.5825 | 0.501658 | ||||||||
\(446\) | −0.222819 | + | 0.222819i | −0.0105508 | + | 0.0105508i | ||||
\(447\) | 36.7633 | + | 12.1623i | 1.73884 | + | 0.575258i | ||||
\(448\) | − | 1.56844i | − | 0.0741017i | ||||||
\(449\) | 23.8504 | + | 23.8504i | 1.12557 | + | 1.12557i | 0.990889 | + | 0.134681i | \(0.0430009\pi\) |
0.134681 | + | 0.990889i | \(0.456999\pi\) | |||||||
\(450\) | −0.437662 | − | 2.96790i | −0.0206316 | − | 0.139908i | ||||
\(451\) | −17.4618 | −0.822242 | ||||||||
\(452\) | 13.0116 | + | 13.0116i | 0.612013 | + | 0.612013i | ||||
\(453\) | −37.0672 | − | 12.2629i | −1.74157 | − | 0.576160i | ||||
\(454\) | −13.2696 | −0.622773 | ||||||||
\(455\) | 1.39558 | 0.0654257 | ||||||||
\(456\) | −3.45993 | + | 10.4584i | −0.162026 | + | 0.489759i | ||||
\(457\) | 5.62384 | − | 5.62384i | 0.263072 | − | 0.263072i | −0.563229 | − | 0.826301i | \(-0.690441\pi\) |
0.826301 | + | 0.563229i | \(0.190441\pi\) | |||||||
\(458\) | 17.9957 | − | 17.9957i | 0.840884 | − | 0.840884i | ||||
\(459\) | −32.3464 | − | 5.65524i | −1.50980 | − | 0.263964i | ||||
\(460\) | 1.52825 | 0.0712550 | ||||||||
\(461\) | −16.5535 | − | 16.5535i | −0.770972 | − | 0.770972i | 0.207305 | − | 0.978276i | \(-0.433531\pi\) |
−0.978276 | + | 0.207305i | \(0.933531\pi\) | |||||||
\(462\) | 2.00612 | + | 3.98971i | 0.0933333 | + | 0.185618i | ||||
\(463\) | 1.55048 | − | 1.55048i | 0.0720571 | − | 0.0720571i | −0.670160 | − | 0.742217i | \(-0.733774\pi\) |
0.742217 | + | 0.670160i | \(0.233774\pi\) | |||||||
\(464\) | 0.289296 | − | 0.289296i | 0.0134302 | − | 0.0134302i | ||||
\(465\) | 13.0896 | + | 4.33042i | 0.607017 | + | 0.200818i | ||||
\(466\) | 5.33585 | − | 5.33585i | 0.247178 | − | 0.247178i | ||||
\(467\) | −14.2943 | − | 14.2943i | −0.661461 | − | 0.661461i | 0.294263 | − | 0.955724i | \(-0.404926\pi\) |
−0.955724 | + | 0.294263i | \(0.904926\pi\) | |||||||
\(468\) | −0.389427 | − | 2.64081i | −0.0180013 | − | 0.122071i | ||||
\(469\) | − | 7.45415i | − | 0.344201i | ||||||
\(470\) | 13.1074i | 0.604599i | ||||||||
\(471\) | 1.28947 | − | 3.89770i | 0.0594156 | − | 0.179597i | ||||
\(472\) | 12.0960i | 0.556765i | ||||||||
\(473\) | 1.37158 | − | 1.37158i | 0.0630654 | − | 0.0630654i | ||||
\(474\) | −1.60321 | − | 0.530387i | −0.0736379 | − | 0.0243615i | ||||
\(475\) | −4.49720 | − | 4.49720i | −0.206346 | − | 0.206346i | ||||
\(476\) | 7.00865 | − | 7.00865i | 0.321241 | − | 0.321241i | ||||
\(477\) | −7.41244 | + | 9.97673i | −0.339392 | + | 0.456803i | ||||
\(478\) | 3.01914 | 0.138092 | ||||||||
\(479\) | 2.65048 | + | 2.65048i | 0.121103 | + | 0.121103i | 0.765061 | − | 0.643958i | \(-0.222709\pi\) |
−0.643958 | + | 0.765061i | \(0.722709\pi\) | |||||||
\(480\) | 0.544013 | − | 1.64440i | 0.0248307 | − | 0.0750562i | ||||
\(481\) | 5.17680 | − | 1.57942i | 0.236042 | − | 0.0720156i | ||||
\(482\) | − | 17.5959i | − | 0.801472i | ||||||
\(483\) | 3.70916 | − | 1.86505i | 0.168773 | − | 0.0848629i | ||||
\(484\) | 8.29778i | 0.377172i | ||||||||
\(485\) | 5.49755 | 0.249631 | ||||||||
\(486\) | −11.3128 | + | 10.7248i | −0.513158 | + | 0.486487i | ||||
\(487\) | −5.77603 | + | 5.77603i | −0.261737 | + | 0.261737i | −0.825759 | − | 0.564023i | \(-0.809253\pi\) |
0.564023 | + | 0.825759i | \(0.309253\pi\) | |||||||
\(488\) | 13.7289i | 0.621478i | ||||||||
\(489\) | −17.6523 | + | 8.87601i | −0.798266 | + | 0.401387i | ||||
\(490\) | −4.54001 | −0.205097 | ||||||||
\(491\) | − | 0.605121i | − | 0.0273087i | −0.999907 | − | 0.0136544i | \(-0.995654\pi\) | ||
0.999907 | − | 0.0136544i | \(-0.00434645\pi\) | |||||||
\(492\) | 17.4677 | + | 5.77879i | 0.787503 | + | 0.260528i | ||||
\(493\) | 2.58547 | 0.116444 | ||||||||
\(494\) | −4.00157 | − | 4.00157i | −0.180039 | − | 0.180039i | ||||
\(495\) | 0.719449 | + | 4.87877i | 0.0323368 | + | 0.219284i | ||||
\(496\) | 5.62866 | + | 5.62866i | 0.252734 | + | 0.252734i | ||||
\(497\) | 5.99895i | 0.269090i | ||||||||
\(498\) | 3.10073 | − | 1.55912i | 0.138947 | − | 0.0698659i | ||||
\(499\) | −11.7173 | − | 11.7173i | −0.524539 | − | 0.524539i | 0.394400 | − | 0.918939i | \(-0.370952\pi\) |
−0.918939 | + | 0.394400i | \(0.870952\pi\) | |||||||
\(500\) | 0.707107 | + | 0.707107i | 0.0316228 | + | 0.0316228i | ||||
\(501\) | −11.4118 | + | 5.73812i | −0.509841 | + | 0.256360i | ||||
\(502\) | 2.73388i | 0.122019i | ||||||||
\(503\) | 15.1330 | + | 15.1330i | 0.674748 | + | 0.674748i | 0.958807 | − | 0.284059i | \(-0.0916810\pi\) |
−0.284059 | + | 0.958807i | \(0.591681\pi\) | |||||||
\(504\) | −0.686446 | − | 4.65497i | −0.0305767 | − | 0.207349i | ||||
\(505\) | 3.43070 | + | 3.43070i | 0.152664 | + | 0.152664i | ||||
\(506\) | −2.51220 | −0.111681 | ||||||||
\(507\) | −20.0753 | − | 6.64147i | −0.891574 | − | 0.294958i | ||||
\(508\) | − | 11.4287i | − | 0.507068i | ||||||
\(509\) | −20.4200 | −0.905101 | −0.452551 | − | 0.891739i | \(-0.649486\pi\) | ||||
−0.452551 | + | 0.891739i | \(0.649486\pi\) | |||||||
\(510\) | 9.77905 | − | 4.91714i | 0.433024 | − | 0.217735i | ||||
\(511\) | − | 19.9540i | − | 0.882711i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −5.69149 | + | 32.5538i | −0.251286 | + | 1.43728i | ||||
\(514\) | 0.00222735 | 9.82441e−5 | ||||||||
\(515\) | 10.4711i | 0.461414i | ||||||||
\(516\) | −1.82596 | + | 0.918134i | −0.0803832 | + | 0.0404186i | ||||
\(517\) | − | 21.5465i | − | 0.947615i | ||||||
\(518\) | 9.12517 | − | 2.78406i | 0.400937 | − | 0.122325i | ||||
\(519\) | −10.0977 | + | 30.5226i | −0.443241 | + | 1.33979i | ||||
\(520\) | 0.629176 | + | 0.629176i | 0.0275912 | + | 0.0275912i | ||||
\(521\) | 27.5843 | 1.20849 | 0.604246 | − | 0.796798i | \(-0.293475\pi\) | ||||
0.604246 | + | 0.796798i | \(0.293475\pi\) | |||||||
\(522\) | 0.731988 | − | 0.985216i | 0.0320382 | − | 0.0431217i | ||||
\(523\) | 24.4745 | − | 24.4745i | 1.07019 | − | 1.07019i | 0.0728501 | − | 0.997343i | \(-0.476791\pi\) |
0.997343 | − | 0.0728501i | \(-0.0232095\pi\) | |||||||
\(524\) | 3.48311 | + | 3.48311i | 0.152160 | + | 0.152160i | ||||
\(525\) | 2.57914 | + | 0.853250i | 0.112563 | + | 0.0372389i | ||||
\(526\) | −7.46574 | + | 7.46574i | −0.325522 | + | 0.325522i | ||||
\(527\) | 50.3040i | 2.19128i | ||||||||
\(528\) | −0.894273 | + | 2.70314i | −0.0389182 | + | 0.117639i | ||||
\(529\) | − | 20.6645i | − | 0.898455i | ||||||
\(530\) | − | 4.14299i | − | 0.179960i | ||||||
\(531\) | 5.29398 | + | 35.8999i | 0.229739 | + | 1.55792i | ||||
\(532\) | −7.05358 | − | 7.05358i | −0.305811 | − | 0.305811i | ||||
\(533\) | −6.68344 | + | 6.68344i | −0.289492 | + | 0.289492i | ||||
\(534\) | 17.4018 | + | 5.75702i | 0.753051 | + | 0.249130i | ||||
\(535\) | −7.20501 | + | 7.20501i | −0.311500 | + | 0.311500i | ||||
\(536\) | 3.36059 | − | 3.36059i | 0.145156 | − | 0.145156i | ||||
\(537\) | −5.22862 | − | 10.3985i | −0.225632 | − | 0.448729i | ||||
\(538\) | −6.65015 | − | 6.65015i | −0.286708 | − | 0.286708i | ||||
\(539\) | 7.46306 | 0.321457 | ||||||||
\(540\) | 0.894888 | − | 5.11851i | 0.0385098 | − | 0.220266i | ||||
\(541\) | −25.8071 | + | 25.8071i | −1.10953 | + | 1.10953i | −0.116323 | + | 0.993211i | \(0.537111\pi\) |
−0.993211 | + | 0.116323i | \(0.962889\pi\) | |||||||
\(542\) | −4.44443 | + | 4.44443i | −0.190905 | + | 0.190905i | ||||
\(543\) | −0.747644 | + | 2.25992i | −0.0320845 | + | 0.0969823i | ||||
\(544\) | 6.31950 | 0.270946 | ||||||||
\(545\) | −13.9412 | −0.597175 | ||||||||
\(546\) | 2.29489 | + | 0.759213i | 0.0982122 | + | 0.0324913i | ||||
\(547\) | 11.6788 | + | 11.6788i | 0.499350 | + | 0.499350i | 0.911236 | − | 0.411886i | \(-0.135130\pi\) |
−0.411886 | + | 0.911236i | \(0.635130\pi\) | |||||||
\(548\) | −4.49515 | −0.192023 | ||||||||
\(549\) | 6.00862 | + | 40.7460i | 0.256442 | + | 1.73900i | ||||
\(550\) | −1.16237 | − | 1.16237i | −0.0495638 | − | 0.0495638i | ||||
\(551\) | − | 2.60204i | − | 0.110851i | ||||||
\(552\) | 2.51305 | + | 0.831388i | 0.106963 | + | 0.0353862i | ||||
\(553\) | 1.08127 | − | 1.08127i | 0.0459804 | − | 0.0459804i | ||||
\(554\) | −25.1430 | −1.06822 | ||||||||
\(555\) | 10.5328 | + | 0.246175i | 0.447091 | + | 0.0104495i | ||||
\(556\) | −21.9294 | −0.930012 | ||||||||
\(557\) | −14.2831 | + | 14.2831i | −0.605195 | + | 0.605195i | −0.941687 | − | 0.336491i | \(-0.890760\pi\) |
0.336491 | + | 0.941687i | \(0.390760\pi\) | |||||||
\(558\) | 19.1688 | + | 14.2419i | 0.811479 | + | 0.602906i | ||||
\(559\) | − | 1.04994i | − | 0.0444076i | ||||||
\(560\) | 1.10905 | + | 1.10905i | 0.0468660 | + | 0.0468660i | ||||
\(561\) | −16.0752 | + | 8.08301i | −0.678697 | + | 0.341265i | ||||
\(562\) | −22.6137 | −0.953902 | ||||||||
\(563\) | −28.5674 | − | 28.5674i | −1.20397 | − | 1.20397i | −0.972947 | − | 0.231027i | \(-0.925791\pi\) |
−0.231027 | − | 0.972947i | \(-0.574209\pi\) | |||||||
\(564\) | −7.13060 | + | 21.5538i | −0.300253 | + | 0.907579i | ||||
\(565\) | −18.4012 | −0.774143 | ||||||||
\(566\) | 7.81186 | 0.328357 | ||||||||
\(567\) | −4.07461 | − | 13.5151i | −0.171117 | − | 0.567579i | ||||
\(568\) | −2.70454 | + | 2.70454i | −0.113480 | + | 0.113480i | ||||
\(569\) | 28.2760 | − | 28.2760i | 1.18539 | − | 1.18539i | 0.207065 | − | 0.978327i | \(-0.433609\pi\) |
0.978327 | − | 0.207065i | \(-0.0663913\pi\) | |||||||
\(570\) | −4.94866 | − | 9.84174i | −0.207277 | − | 0.412225i | ||||
\(571\) | 4.49985 | 0.188313 | 0.0941563 | − | 0.995557i | \(-0.469985\pi\) | ||||
0.0941563 | + | 0.995557i | \(0.469985\pi\) | |||||||
\(572\) | −1.03427 | − | 1.03427i | −0.0432449 | − | 0.0432449i | ||||
\(573\) | −17.6727 | + | 8.88627i | −0.738289 | + | 0.371229i | ||||
\(574\) | −11.7809 | + | 11.7809i | −0.491726 | + | 0.491726i | ||||
\(575\) | −1.08064 | + | 1.08064i | −0.0450656 | + | 0.0450656i | ||||
\(576\) | 1.78915 | − | 2.40810i | 0.0745479 | − | 0.100337i | ||||
\(577\) | −18.3521 | + | 18.3521i | −0.764009 | + | 0.764009i | −0.977044 | − | 0.213036i | \(-0.931665\pi\) |
0.213036 | + | 0.977044i | \(0.431665\pi\) | |||||||
\(578\) | 16.2182 | + | 16.2182i | 0.674590 | + | 0.674590i | ||||
\(579\) | −11.3891 | − | 22.6503i | −0.473315 | − | 0.941313i | ||||
\(580\) | 0.409126i | 0.0169880i | ||||||||
\(581\) | 3.14280i | 0.130385i | ||||||||
\(582\) | 9.04017 | + | 2.99074i | 0.374727 | + | 0.123970i | ||||
\(583\) | 6.81043i | 0.282059i | ||||||||
\(584\) | 8.99595 | − | 8.99595i | 0.372255 | − | 0.372255i | ||||
\(585\) | 2.14270 | + | 1.59197i | 0.0885898 | + | 0.0658198i | ||||
\(586\) | −9.89119 | − | 9.89119i | −0.408601 | − | 0.408601i | ||||
\(587\) | −11.8937 | + | 11.8937i | −0.490908 | + | 0.490908i | −0.908592 | − | 0.417685i | \(-0.862842\pi\) |
0.417685 | + | 0.908592i | \(0.362842\pi\) | |||||||
\(588\) | −7.46559 | − | 2.46983i | −0.307876 | − | 0.101854i | ||||
\(589\) | 50.6265 | 2.08603 | ||||||||
\(590\) | −8.55319 | − | 8.55319i | −0.352129 | − | 0.352129i | ||||
\(591\) | 16.1228 | + | 5.33387i | 0.663203 | + | 0.219406i | ||||
\(592\) | 5.36910 | + | 2.85880i | 0.220669 | + | 0.117496i | ||||
\(593\) | − | 13.6712i | − | 0.561409i | −0.959794 | − | 0.280705i | \(-0.909432\pi\) | ||
0.959794 | − | 0.280705i | \(-0.0905681\pi\) | |||||||
\(594\) | −1.47106 | + | 8.41404i | −0.0603582 | + | 0.345232i | ||||
\(595\) | 9.91173i | 0.406341i | ||||||||
\(596\) | −22.3567 | −0.915764 | ||||||||
\(597\) | −11.2694 | + | 5.66653i | −0.461226 | + | 0.231915i | ||||
\(598\) | −0.961538 | + | 0.961538i | −0.0393202 | + | 0.0393202i | ||||
\(599\) | 16.0843i | 0.657186i | 0.944472 | + | 0.328593i | \(0.106574\pi\) | ||||
−0.944472 | + | 0.328593i | \(0.893426\pi\) | |||||||
\(600\) | 0.778090 | + | 1.54744i | 0.0317654 | + | 0.0631740i | ||||
\(601\) | −24.8780 | −1.01479 | −0.507397 | − | 0.861713i | \(-0.669392\pi\) | ||||
−0.507397 | + | 0.861713i | \(0.669392\pi\) | |||||||
\(602\) | − | 1.85073i | − | 0.0754301i | ||||||
\(603\) | 8.50312 | − | 11.4447i | 0.346274 | − | 0.466065i | ||||
\(604\) | 22.5415 | 0.917201 | ||||||||
\(605\) | −5.86741 | − | 5.86741i | −0.238544 | − | 0.238544i | ||||
\(606\) | 3.77510 | + | 7.50779i | 0.153353 | + | 0.304983i | ||||
\(607\) | 9.34830 | + | 9.34830i | 0.379436 | + | 0.379436i | 0.870899 | − | 0.491463i | \(-0.163538\pi\) |
−0.491463 | + | 0.870899i | \(0.663538\pi\) | |||||||
\(608\) | − | 6.36001i | − | 0.257932i | ||||||
\(609\) | 0.499291 | + | 0.992975i | 0.0202323 | + | 0.0402374i | ||||
\(610\) | −9.70779 | − | 9.70779i | −0.393057 | − | 0.393057i | ||||
\(611\) | −8.24687 | − | 8.24687i | −0.333633 | − | 0.333633i | ||||
\(612\) | 18.7557 | − | 2.76581i | 0.758153 | − | 0.111801i | ||||
\(613\) | 26.4265i | 1.06736i | 0.845688 | + | 0.533678i | \(0.179190\pi\) | ||||
−0.845688 | + | 0.533678i | \(0.820810\pi\) | |||||||
\(614\) | 7.20441 | + | 7.20441i | 0.290746 | + | 0.290746i | ||||
\(615\) | −16.4377 | + | 8.26528i | −0.662833 | + | 0.333288i | ||||
\(616\) | −1.82311 | − | 1.82311i | −0.0734551 | − | 0.0734551i | ||||
\(617\) | −14.1919 | −0.571346 | −0.285673 | − | 0.958327i | \(-0.592217\pi\) | ||||
−0.285673 | + | 0.958327i | \(0.592217\pi\) | |||||||
\(618\) | −5.69644 | + | 17.2187i | −0.229145 | + | 0.692639i | ||||
\(619\) | − | 44.4517i | − | 1.78666i | −0.449398 | − | 0.893332i | \(-0.648362\pi\) | ||
0.449398 | − | 0.893332i | \(-0.351638\pi\) | |||||||
\(620\) | −7.96013 | −0.319686 | ||||||||
\(621\) | 7.82236 | + | 1.36761i | 0.313901 | + | 0.0548804i | ||||
\(622\) | 14.8367i | 0.594899i | ||||||||
\(623\) | −11.7365 | + | 11.7365i | −0.470214 | + | 0.470214i | ||||
\(624\) | 0.692337 | + | 1.37690i | 0.0277157 | + | 0.0551200i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | − | 34.6390i | − | 1.38445i | ||||||
\(627\) | 8.13483 | + | 16.1783i | 0.324874 | + | 0.646099i | ||||
\(628\) | 2.37029i | 0.0945848i | ||||||||
\(629\) | 11.2175 | + | 36.7669i | 0.447269 | + | 1.46599i | ||||
\(630\) | 3.77695 | + | 2.80617i | 0.150477 | + | 0.111800i | ||||
\(631\) | 4.17746 | + | 4.17746i | 0.166302 | + | 0.166302i | 0.785352 | − | 0.619050i | \(-0.212482\pi\) |
−0.619050 | + | 0.785352i | \(0.712482\pi\) | |||||||
\(632\) | 0.974951 | 0.0387815 | ||||||||
\(633\) | 0.321775 | − | 0.972636i | 0.0127894 | − | 0.0386588i | ||||
\(634\) | −13.3514 | + | 13.3514i | −0.530250 | + | 0.530250i | ||||
\(635\) | 8.08133 | + | 8.08133i | 0.320698 | + | 0.320698i | ||||
\(636\) | 2.25384 | − | 6.81273i | 0.0893707 | − | 0.270142i | ||||
\(637\) | 2.85647 | − | 2.85647i | 0.113177 | − | 0.113177i | ||||
\(638\) | − | 0.672539i | − | 0.0266261i | ||||||
\(639\) | −6.84314 | + | 9.21049i | −0.270710 | + | 0.364361i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | − | 27.7886i | − | 1.09758i | −0.835960 | − | 0.548791i | \(-0.815088\pi\) | ||
0.835960 | − | 0.548791i | \(-0.184912\pi\) | |||||||
\(642\) | −15.7675 | + | 7.92829i | −0.622295 | + | 0.312905i | ||||
\(643\) | −3.14293 | − | 3.14293i | −0.123945 | − | 0.123945i | 0.642413 | − | 0.766358i | \(-0.277933\pi\) |
−0.766358 | + | 0.642413i | \(0.777933\pi\) | |||||||
\(644\) | −1.69491 | + | 1.69491i | −0.0667887 | + | 0.0667887i | ||||
\(645\) | 0.641927 | − | 1.94036i | 0.0252758 | − | 0.0764018i | ||||
\(646\) | 28.4201 | − | 28.4201i | 1.11817 | − | 1.11817i | ||||
\(647\) | −10.4437 | + | 10.4437i | −0.410582 | + | 0.410582i | −0.881941 | − | 0.471359i | \(-0.843764\pi\) |
0.471359 | + | 0.881941i | \(0.343764\pi\) | |||||||
\(648\) | 4.25609 | − | 7.93005i | 0.167195 | − | 0.311522i | ||||
\(649\) | 14.0601 | + | 14.0601i | 0.551908 | + | 0.551908i | ||||
\(650\) | −0.889790 | −0.0349004 | ||||||||
\(651\) | −19.3197 | + | 9.71442i | −0.757200 | + | 0.380738i | ||||
\(652\) | 8.06627 | − | 8.06627i | 0.315899 | − | 0.315899i | ||||
\(653\) | −7.10309 | + | 7.10309i | −0.277965 | + | 0.277965i | −0.832296 | − | 0.554331i | \(-0.812974\pi\) |
0.554331 | + | 0.832296i | \(0.312974\pi\) | |||||||
\(654\) | −22.9249 | − | 7.58419i | −0.896433 | − | 0.296565i | ||||
\(655\) | −4.92586 | −0.192469 | ||||||||
\(656\) | −10.6225 | −0.414740 | ||||||||
\(657\) | 22.7619 | − | 30.6363i | 0.888027 | − | 1.19524i | ||||
\(658\) | −14.5368 | − | 14.5368i | −0.566703 | − | 0.566703i | ||||
\(659\) | 9.05248 | 0.352635 | 0.176317 | − | 0.984333i | \(-0.443582\pi\) | ||||
0.176317 | + | 0.984333i | \(0.443582\pi\) | |||||||
\(660\) | −1.27906 | − | 2.54375i | −0.0497873 | − | 0.0990154i | ||||
\(661\) | −20.1666 | − | 20.1666i | −0.784391 | − | 0.784391i | 0.196177 | − | 0.980568i | \(-0.437147\pi\) |
−0.980568 | + | 0.196177i | \(0.937147\pi\) | |||||||
\(662\) | 23.7273i | 0.922187i | ||||||||
\(663\) | −3.05900 | + | 9.24650i | −0.118802 | + | 0.359104i | ||||
\(664\) | −1.41689 | + | 1.41689i | −0.0549858 | + | 0.0549858i | ||||
\(665\) | 9.97527 | 0.386824 | ||||||||
\(666\) | 17.1862 | + | 6.13478i | 0.665951 | + | 0.237718i | ||||
\(667\) | −0.625246 | −0.0242096 | ||||||||
\(668\) | 5.21464 | − | 5.21464i | 0.201761 | − | 0.201761i | ||||
\(669\) | 0.171426 | − | 0.518172i | 0.00662770 | − | 0.0200337i | ||||
\(670\) | 4.75260i | 0.183609i | ||||||||
\(671\) | 15.9581 | + | 15.9581i | 0.616055 | + | 0.616055i | ||||
\(672\) | 1.22039 | + | 2.42706i | 0.0470774 | + | 0.0936260i | ||||
\(673\) | −7.56707 | −0.291689 | −0.145845 | − | 0.989308i | \(-0.546590\pi\) | ||||
−0.145845 | + | 0.989308i | \(0.546590\pi\) | |||||||
\(674\) | 12.9130 | + | 12.9130i | 0.497390 | + | 0.497390i | ||||
\(675\) | 2.98655 | + | 4.25212i | 0.114953 | + | 0.163664i | ||||
\(676\) | 12.2083 | 0.469549 | ||||||||
\(677\) | 3.72965 | 0.143342 | 0.0716710 | − | 0.997428i | \(-0.477167\pi\) | ||||
0.0716710 | + | 0.997428i | \(0.477167\pi\) | |||||||
\(678\) | −30.2589 | − | 10.0105i | −1.16208 | − | 0.384450i | ||||
\(679\) | −6.09707 | + | 6.09707i | −0.233984 | + | 0.233984i | ||||
\(680\) | −4.46856 | + | 4.46856i | −0.171361 | + | 0.171361i | ||||
\(681\) | 20.5339 | − | 10.3249i | 0.786861 | − | 0.395653i | ||||
\(682\) | 13.0852 | 0.501059 | ||||||||
\(683\) | 9.79474 | + | 9.79474i | 0.374785 | + | 0.374785i | 0.869217 | − | 0.494431i | \(-0.164624\pi\) |
−0.494431 | + | 0.869217i | \(0.664624\pi\) | |||||||
\(684\) | −2.78354 | − | 18.8759i | −0.106431 | − | 0.721738i | ||||
\(685\) | 3.17855 | − | 3.17855i | 0.121446 | − | 0.121446i | ||||
\(686\) | 12.7985 | − | 12.7985i | 0.488648 | − | 0.488648i | ||||
\(687\) | −13.8450 | + | 41.8496i | −0.528220 | + | 1.59666i | ||||
\(688\) | 0.834374 | − | 0.834374i | 0.0318102 | − | 0.0318102i | ||||
\(689\) | 2.60667 | + | 2.60667i | 0.0993063 | + | 0.0993063i | ||||
\(690\) | −2.36488 | + | 1.18912i | −0.0900293 | + | 0.0452689i | ||||
\(691\) | − | 13.8014i | − | 0.525029i | −0.964928 | − | 0.262515i | \(-0.915448\pi\) | ||
0.964928 | − | 0.262515i | \(-0.0845518\pi\) | |||||||
\(692\) | − | 18.5616i | − | 0.705605i | ||||||
\(693\) | −6.20872 | − | 4.61290i | −0.235850 | − | 0.175230i | ||||
\(694\) | − | 11.3678i | − | 0.431515i | ||||||
\(695\) | 15.5064 | − | 15.5064i | 0.588191 | − | 0.588191i | ||||
\(696\) | −0.222570 | + | 0.672766i | −0.00843649 | + | 0.0255011i | ||||
\(697\) | −47.4674 | − | 47.4674i | −1.79795 | − | 1.79795i | ||||
\(698\) | −6.13816 | + | 6.13816i | −0.232333 | + | 0.232333i | ||||
\(699\) | −4.10514 | + | 12.4087i | −0.155271 | + | 0.469340i | ||||
\(700\) | −1.56844 | −0.0592813 | ||||||||
\(701\) | −5.58493 | − | 5.58493i | −0.210940 | − | 0.210940i | 0.593727 | − | 0.804667i | \(-0.297656\pi\) |
−0.804667 | + | 0.593727i | \(0.797656\pi\) | |||||||
\(702\) | 2.65741 | + | 3.78349i | 0.100297 | + | 0.142799i | ||||
\(703\) | 37.0026 | − | 11.2894i | 1.39558 | − | 0.425786i | ||||
\(704\) | − | 1.64384i | − | 0.0619547i | ||||||
\(705\) | −10.1987 | − | 20.2829i | −0.384107 | − | 0.763900i | ||||
\(706\) | − | 6.17215i | − | 0.232292i | ||||||
\(707\) | −7.60965 | −0.286190 | ||||||||
\(708\) | −9.41181 | − | 18.7179i | −0.353717 | − | 0.703462i | ||||
\(709\) | −13.9927 | + | 13.9927i | −0.525507 | + | 0.525507i | −0.919229 | − | 0.393722i | \(-0.871187\pi\) |
0.393722 | + | 0.919229i | \(0.371187\pi\) | |||||||
\(710\) | − | 3.82480i | − | 0.143542i | ||||||
\(711\) | 2.89356 | − | 0.426700i | 0.108517 | − | 0.0160025i | ||||
\(712\) | −10.5825 | −0.396596 | ||||||||
\(713\) | − | 12.1651i | − | 0.455585i | ||||||
\(714\) | −5.39211 | + | 16.2988i | −0.201795 | + | 0.609969i | ||||
\(715\) | 1.46268 | 0.0547010 | ||||||||
\(716\) | 4.75163 | + | 4.75163i | 0.177577 | + | 0.177577i | ||||
\(717\) | −4.67194 | + | 2.34916i | −0.174477 | + | 0.0877311i | ||||
\(718\) | −14.6826 | − | 14.6826i | −0.547950 | − | 0.547950i | ||||
\(719\) | − | 26.6215i | − | 0.992813i | −0.868090 | − | 0.496407i | \(-0.834653\pi\) | ||
0.868090 | − | 0.496407i | \(-0.165347\pi\) | |||||||
\(720\) | 0.437662 | + | 2.96790i | 0.0163107 | + | 0.110607i | ||||
\(721\) | −11.6130 | − | 11.6130i | −0.432492 | − | 0.432492i | ||||
\(722\) | −15.1672 | − | 15.1672i | −0.564466 | − | 0.564466i | ||||
\(723\) | 13.6912 | + | 27.2286i | 0.509182 | + | 1.01264i | ||||
\(724\) | − | 1.37431i | − | 0.0510759i | ||||||
\(725\) | −0.289296 | − | 0.289296i | −0.0107442 | − | 0.0107442i | ||||
\(726\) | −6.45642 | − | 12.8403i | −0.239620 | − | 0.476549i | ||||
\(727\) | −10.4677 | − | 10.4677i | −0.388226 | − | 0.388226i | 0.485828 | − | 0.874054i | \(-0.338518\pi\) |
−0.874054 | + | 0.485828i | \(0.838518\pi\) | |||||||
\(728\) | −1.39558 | −0.0517236 | ||||||||
\(729\) | 9.16099 | − | 25.3984i | 0.339296 | − | 0.940680i | ||||
\(730\) | 12.7222i | 0.470870i | ||||||||
\(731\) | 7.45690 | 0.275804 | ||||||||
\(732\) | −10.6823 | − | 21.2447i | −0.394830 | − | 0.785225i | ||||
\(733\) | − | 14.9277i | − | 0.551369i | −0.961248 | − | 0.275684i | \(-0.911096\pi\) | ||
0.961248 | − | 0.275684i | \(-0.0889044\pi\) | |||||||
\(734\) | −15.6053 | + | 15.6053i | −0.576002 | + | 0.576002i | ||||
\(735\) | 7.02540 | − | 3.53254i | 0.259136 | − | 0.130300i | ||||
\(736\) | −1.52825 | −0.0563320 | ||||||||
\(737\) | − | 7.81253i | − | 0.287778i | ||||||
\(738\) | −31.5266 | + | 4.64908i | −1.16051 | + | 0.171135i | ||||
\(739\) | − | 14.3573i | − | 0.528141i | −0.964503 | − | 0.264071i | \(-0.914935\pi\) | ||
0.964503 | − | 0.264071i | \(-0.0850652\pi\) | |||||||
\(740\) | −5.81801 | + | 1.77505i | −0.213874 | + | 0.0652523i | ||||
\(741\) | 9.30577 | + | 3.07861i | 0.341856 | + | 0.113096i | ||||
\(742\) | 4.59479 | + | 4.59479i | 0.168680 | + | 0.168680i | ||||
\(743\) | −34.5132 | −1.26617 | −0.633083 | − | 0.774084i | \(-0.718211\pi\) | ||||
−0.633083 | + | 0.774084i | \(0.718211\pi\) | |||||||
\(744\) | −13.0896 | − | 4.33042i | −0.479889 | − | 0.158761i | ||||
\(745\) | 15.8085 | − | 15.8085i | 0.579180 | − | 0.579180i | ||||
\(746\) | 9.16060 | + | 9.16060i | 0.335394 | + | 0.335394i | ||||
\(747\) | −3.58506 | + | 4.82530i | −0.131171 | + | 0.176548i | ||||
\(748\) | 7.34562 | − | 7.34562i | 0.268582 | − | 0.268582i | ||||
\(749\) | − | 15.9815i | − | 0.583950i | ||||||
\(750\) | −1.64440 | − | 0.544013i | −0.0600450 | − | 0.0198646i | ||||
\(751\) | − | 26.5644i | − | 0.969350i | −0.874694 | − | 0.484675i | \(-0.838938\pi\) | ||
0.874694 | − | 0.484675i | \(-0.161062\pi\) | |||||||
\(752\) | − | 13.1074i | − | 0.477978i | ||||||
\(753\) | −2.12720 | − | 4.23051i | −0.0775196 | − | 0.154168i | ||||
\(754\) | −0.257412 | − | 0.257412i | −0.00937440 | − | 0.00937440i | ||||
\(755\) | −15.9392 | + | 15.9392i | −0.580089 | + | 0.580089i | ||||
\(756\) | 4.68422 | + | 6.66917i | 0.170363 | + | 0.242556i | ||||
\(757\) | 26.5621 | − | 26.5621i | 0.965417 | − | 0.965417i | −0.0340046 | − | 0.999422i | \(-0.510826\pi\) |
0.999422 | + | 0.0340046i | \(0.0108261\pi\) | |||||||
\(758\) | −6.62250 | + | 6.62250i | −0.240540 | + | 0.240540i | ||||
\(759\) | 3.88749 | − | 1.95472i | 0.141107 | − | 0.0709519i | ||||
\(760\) | 4.49720 | + | 4.49720i | 0.163131 | + | 0.163131i | ||||
\(761\) | 3.25195 | 0.117883 | 0.0589415 | − | 0.998261i | \(-0.481227\pi\) | ||||
0.0589415 | + | 0.998261i | \(0.481227\pi\) | |||||||
\(762\) | 8.89258 | + | 17.6853i | 0.322144 | + | 0.640670i | ||||
\(763\) | 15.4615 | − | 15.4615i | 0.559744 | − | 0.559744i | ||||
\(764\) | 8.07560 | − | 8.07560i | 0.292165 | − | 0.292165i | ||||
\(765\) | −11.3065 | + | 15.2180i | −0.408789 | + | 0.550207i | ||||
\(766\) | −1.68012 | −0.0607051 | ||||||||
\(767\) | 10.7629 | 0.388627 | ||||||||
\(768\) | −0.544013 | + | 1.64440i | −0.0196304 | + | 0.0593372i | ||||
\(769\) | 28.6343 | + | 28.6343i | 1.03258 | + | 1.03258i | 0.999451 | + | 0.0331270i | \(0.0105466\pi\) |
0.0331270 | + | 0.999451i | \(0.489453\pi\) | |||||||
\(770\) | 2.57826 | 0.0929142 | ||||||||
\(771\) | −0.00344669 | + | 0.00173308i | −0.000124130 | + | 6.24153e-5i | ||||
\(772\) | 10.3501 | + | 10.3501i | 0.372508 | + | 0.372508i | ||||
\(773\) | 14.0416i | 0.505041i | 0.967591 | + | 0.252521i | \(0.0812596\pi\) | ||||
−0.967591 | + | 0.252521i | \(0.918740\pi\) | |||||||
\(774\) | 2.11117 | − | 2.84152i | 0.0758844 | − | 0.102136i | ||||
\(775\) | 5.62866 | − | 5.62866i | 0.202187 | − | 0.202187i | ||||
\(776\) | −5.49755 | −0.197350 | ||||||||
\(777\) | −11.9544 | + | 11.4084i | −0.428862 | + | 0.409273i | ||||
\(778\) | −31.1625 | −1.11723 | ||||||||
\(779\) | −47.7716 | + | 47.7716i | −1.71160 | + | 1.71160i | ||||
\(780\) | −1.46317 | − | 0.484058i | −0.0523899 | − | 0.0173320i | ||||
\(781\) | 6.28737i | 0.224980i | ||||||||
\(782\) | −6.82907 | − | 6.82907i | −0.244207 | − | 0.244207i | ||||
\(783\) | −0.366122 | + | 2.09412i | −0.0130841 | + | 0.0748376i | ||||
\(784\) | 4.54001 | 0.162143 | ||||||||
\(785\) | −1.67605 | − | 1.67605i | −0.0598207 | − | 0.0598207i | ||||
\(786\) | −8.10008 | − | 2.67973i | −0.288920 | − | 0.0955829i | ||||
\(787\) | −8.86917 | −0.316152 | −0.158076 | − | 0.987427i | \(-0.550529\pi\) | ||||
−0.158076 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(788\) | −9.80467 | −0.349277 | ||||||||
\(789\) | 5.74378 | − | 17.3618i | 0.204484 | − | 0.618097i | ||||
\(790\) | −0.689395 | + | 0.689395i | −0.0245276 | + | 0.0245276i | ||||
\(791\) | 20.4078 | − | 20.4078i | 0.725619 | − | 0.725619i | ||||
\(792\) | −0.719449 | − | 4.87877i | −0.0255645 | − | 0.173360i | ||||
\(793\) | 12.2158 | 0.433797 | ||||||||
\(794\) | 13.6977 | + | 13.6977i | 0.486115 | + | 0.486115i | ||||
\(795\) | 3.22362 | + | 6.41104i | 0.114330 | + | 0.227376i | ||||
\(796\) | 5.14958 | − | 5.14958i | 0.182522 | − | 0.182522i | ||||
\(797\) | −15.5188 | + | 15.5188i | −0.549703 | + | 0.549703i | −0.926355 | − | 0.376652i | \(-0.877075\pi\) |
0.376652 | + | 0.926355i | \(0.377075\pi\) | |||||||
\(798\) | 16.4033 | + | 5.42668i | 0.580671 | + | 0.192102i | ||||
\(799\) | 58.5712 | − | 58.5712i | 2.07210 | − | 2.07210i | ||||
\(800\) | −0.707107 | − | 0.707107i | −0.0250000 | − | 0.0250000i | ||||
\(801\) | −31.4078 | + | 4.63156i | −1.10974 | + | 0.163648i | ||||
\(802\) | 21.7296i | 0.767300i | ||||||||
\(803\) | − | 20.9133i | − | 0.738015i | ||||||
\(804\) | −2.58548 | + | 7.81517i | −0.0911828 | + | 0.275620i | ||||
\(805\) | − | 2.39696i | − | 0.0844818i | ||||||
\(806\) | 5.00832 | − | 5.00832i | 0.176411 | − | 0.176411i | ||||
\(807\) | 15.4651 | + | 5.11630i | 0.544399 | + | 0.180102i | ||||
\(808\) | −3.43070 | − | 3.43070i | −0.120692 | − | 0.120692i | ||||
\(809\) | 13.9615 | − | 13.9615i | 0.490861 | − | 0.490861i | −0.417717 | − | 0.908577i | \(-0.637170\pi\) |
0.908577 | + | 0.417717i | \(0.137170\pi\) | |||||||
\(810\) | 2.59788 | + | 8.61690i | 0.0912802 | + | 0.302767i | ||||
\(811\) | 2.45176 | 0.0860930 | 0.0430465 | − | 0.999073i | \(-0.486294\pi\) | ||||
0.0430465 | + | 0.999073i | \(0.486294\pi\) | |||||||
\(812\) | −0.453742 | − | 0.453742i | −0.0159232 | − | 0.0159232i | ||||
\(813\) | 3.41933 | − | 10.3357i | 0.119921 | − | 0.362488i | ||||
\(814\) | 9.56389 | − | 2.91791i | 0.335214 | − | 0.102273i | ||||
\(815\) | 11.4074i | 0.399585i | ||||||||
\(816\) | −9.77905 | + | 4.91714i | −0.342335 | + | 0.172134i | ||||
\(817\) | − | 7.50470i | − | 0.262556i | ||||||
\(818\) | −20.1896 | −0.705914 | ||||||||
\(819\) | −4.14194 | + | 0.610792i | −0.144731 | + | 0.0213428i | ||||
\(820\) | 7.51125 | − | 7.51125i | 0.262304 | − | 0.262304i | ||||
\(821\) | 30.8973i | 1.07832i | 0.842202 | + | 0.539162i | \(0.181259\pi\) | ||||
−0.842202 | + | 0.539162i | \(0.818741\pi\) | |||||||
\(822\) | 6.95598 | − | 3.49763i | 0.242618 | − | 0.121994i | ||||
\(823\) | −48.7342 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(824\) | − | 10.4711i | − | 0.364780i | ||||||
\(825\) | 2.70314 | + | 0.894273i | 0.0941111 | + | 0.0311346i | ||||
\(826\) | 18.9719 | 0.660115 | ||||||||
\(827\) | −36.1060 | − | 36.1060i | −1.25553 | − | 1.25553i | −0.953205 | − | 0.302324i | \(-0.902237\pi\) |
−0.302324 | − | 0.953205i | \(-0.597763\pi\) | |||||||
\(828\) | −4.53570 | + | 0.668857i | −0.157626 | + | 0.0232444i | ||||
\(829\) | 6.67303 | + | 6.67303i | 0.231764 | + | 0.231764i | 0.813429 | − | 0.581665i | \(-0.197598\pi\) |
−0.581665 | + | 0.813429i | \(0.697598\pi\) | |||||||
\(830\) | − | 2.00378i | − | 0.0695522i | ||||||
\(831\) | 38.9074 | − | 19.5635i | 1.34968 | − | 0.678652i | ||||
\(832\) | −0.629176 | − | 0.629176i | −0.0218128 | − | 0.0218128i | ||||
\(833\) | 20.2873 | + | 20.2873i | 0.702913 | + | 0.702913i | ||||
\(834\) | 33.9344 | − | 17.0630i | 1.17505 | − | 0.590844i | ||||
\(835\) | 7.37462i | 0.255209i | ||||||||
\(836\) | −7.39270 | − | 7.39270i | −0.255682 | − | 0.255682i | ||||
\(837\) | −40.7440 | − | 7.12342i | −1.40832 | − | 0.246221i | ||||
\(838\) | −0.423756 | − | 0.423756i | −0.0146384 | − | 0.0146384i | ||||
\(839\) | 20.2839 | 0.700279 | 0.350140 | − | 0.936697i | \(-0.386134\pi\) | ||||
0.350140 | + | 0.936697i | \(0.386134\pi\) | |||||||
\(840\) | −2.57914 | − | 0.853250i | −0.0889886 | − | 0.0294399i | ||||
\(841\) | 28.8326i | 0.994228i | ||||||||
\(842\) | 3.70510 | 0.127686 | ||||||||
\(843\) | 34.9934 | − | 17.5955i | 1.20524 | − | 0.606021i | ||||
\(844\) | 0.591484i | 0.0203597i | ||||||||
\(845\) | −8.63255 | + | 8.63255i | −0.296969 | + | 0.296969i | ||||
\(846\) | −5.73662 | − | 38.9015i | −0.197229 | − | 1.33746i | ||||
\(847\) | 13.0145 | 0.447185 | ||||||||
\(848\) | 4.14299i | 0.142271i | ||||||||
\(849\) | −12.0884 | + | 6.07834i | −0.414873 | + | 0.208608i | ||||
\(850\) | − | 6.31950i | − | 0.216757i | ||||||
\(851\) | −2.71273 | − | 8.89136i | −0.0929910 | − | 0.304792i | ||||
\(852\) | 2.08074 | − | 6.28949i | 0.0712850 | − | 0.215474i | ||||
\(853\) | 40.0727 | + | 40.0727i | 1.37206 | + | 1.37206i | 0.857382 | + | 0.514680i | \(0.172089\pi\) |
0.514680 | + | 0.857382i | \(0.327911\pi\) | |||||||
\(854\) | 21.5329 | 0.736840 | ||||||||
\(855\) | 15.3155 | + | 11.3790i | 0.523780 | + | 0.389154i | ||||
\(856\) | 7.20501 | − | 7.20501i | 0.246262 | − | 0.246262i | ||||
\(857\) | −24.9268 | − | 24.9268i | −0.851485 | − | 0.851485i | 0.138831 | − | 0.990316i | \(-0.455665\pi\) |
−0.990316 | + | 0.138831i | \(0.955665\pi\) | |||||||
\(858\) | 2.40522 | + | 0.795715i | 0.0821130 | + | 0.0271653i | ||||
\(859\) | 17.6848 | − | 17.6848i | 0.603399 | − | 0.603399i | −0.337814 | − | 0.941213i | \(-0.609687\pi\) |
0.941213 | + | 0.337814i | \(0.109687\pi\) | |||||||
\(860\) | 1.17998i | 0.0402371i | ||||||||
\(861\) | 9.06367 | − | 27.3969i | 0.308889 | − | 0.933684i | ||||
\(862\) | 37.5841i | 1.28012i | ||||||||
\(863\) | − | 20.5644i | − | 0.700021i | −0.936746 | − | 0.350010i | \(-0.886178\pi\) | ||
0.936746 | − | 0.350010i | \(-0.113822\pi\) | |||||||
\(864\) | −0.894888 | + | 5.11851i | −0.0304447 | + | 0.174135i | ||||
\(865\) | 13.1250 | + | 13.1250i | 0.446263 | + | 0.446263i | ||||
\(866\) | −25.4153 | + | 25.4153i | −0.863649 | + | 0.863649i | ||||
\(867\) | −37.7160 | − | 12.4775i | −1.28090 | − | 0.423759i | ||||
\(868\) | 8.82820 | − | 8.82820i | 0.299648 | − | 0.299648i | ||||
\(869\) | 1.13326 | − | 1.13326i | 0.0384431 | − | 0.0384431i | ||||
\(870\) | −0.318337 | − | 0.633098i | −0.0107926 | − | 0.0214640i | ||||
\(871\) | −2.99022 | − | 2.99022i | −0.101320 | − | 0.101320i | ||||
\(872\) | 13.9412 | 0.472108 | ||||||||
\(873\) | −16.3162 | + | 2.40607i | −0.552219 | + | 0.0814331i | ||||
\(874\) | −6.87285 | + | 6.87285i | −0.232478 | + | 0.232478i | ||||
\(875\) | 1.10905 | − | 1.10905i | 0.0374928 | − | 0.0374928i | ||||
\(876\) | −6.92104 | + | 20.9204i | −0.233840 | + | 0.706834i | ||||
\(877\) | 25.7161 | 0.868372 | 0.434186 | − | 0.900823i | \(-0.357036\pi\) | ||||
0.434186 | + | 0.900823i | \(0.357036\pi\) | |||||||
\(878\) | −26.4049 | −0.891124 | ||||||||
\(879\) | 23.0023 | + | 7.60980i | 0.775847 | + | 0.256672i | ||||
\(880\) | 1.16237 | + | 1.16237i | 0.0391836 | + | 0.0391836i | ||||
\(881\) | −16.4414 | −0.553926 | −0.276963 | − | 0.960881i | \(-0.589328\pi\) | ||||
−0.276963 | + | 0.960881i | \(0.589328\pi\) | |||||||
\(882\) | 13.4743 | − | 1.98699i | 0.453703 | − | 0.0669055i | ||||
\(883\) | −21.5260 | − | 21.5260i | −0.724408 | − | 0.724408i | 0.245092 | − | 0.969500i | \(-0.421182\pi\) |
−0.969500 | + | 0.245092i | \(0.921182\pi\) | |||||||
\(884\) | − | 5.62302i | − | 0.189123i | ||||||
\(885\) | 19.8907 | + | 6.58041i | 0.668619 | + | 0.221198i | ||||
\(886\) | 8.35113 | − | 8.35113i | 0.280562 | − | 0.280562i | ||||
\(887\) | 8.59625 | 0.288634 | 0.144317 | − | 0.989532i | \(-0.453902\pi\) | ||||
0.144317 | + | 0.989532i | \(0.453902\pi\) | |||||||
\(888\) | −10.5328 | − | 0.246175i | −0.353457 | − | 0.00826109i | ||||
\(889\) | −17.9252 | −0.601193 | ||||||||
\(890\) | 7.48295 | − | 7.48295i | 0.250829 | − | 0.250829i | ||||
\(891\) | −4.27051 | − | 14.1648i | −0.143067 | − | 0.474540i | ||||
\(892\) | 0.315113i | 0.0105508i | ||||||||
\(893\) | −58.9467 | − | 58.9467i | −1.97258 | − | 1.97258i | ||||
\(894\) | 34.5956 | − | 17.3955i | 1.15705 | − | 0.581792i | ||||
\(895\) | −6.71982 | −0.224619 | ||||||||
\(896\) | −1.10905 | − | 1.10905i | −0.0370508 | − | 0.0370508i | ||||
\(897\) | 0.739761 | − | 2.23609i | 0.0246999 | − | 0.0746608i | ||||
\(898\) | 33.7296 | 1.12557 | ||||||||
\(899\) | 3.25669 | 0.108617 | ||||||||
\(900\) | −2.40810 | − | 1.78915i | −0.0802700 | − | 0.0596384i | ||||
\(901\) | −18.5132 | + | 18.5132i | −0.616764 | + | 0.616764i | ||||
\(902\) | −12.3473 | + | 12.3473i | −0.411121 | + | 0.411121i | ||||
\(903\) | 1.44003 | + | 2.86389i | 0.0479213 | + | 0.0953045i | ||||
\(904\) | 18.4012 | 0.612013 | ||||||||
\(905\) | 0.971785 | + | 0.971785i | 0.0323032 | + | 0.0323032i | ||||
\(906\) | −34.8817 | + | 17.5393i | −1.15887 | + | 0.582705i | ||||
\(907\) | −6.42906 | + | 6.42906i | −0.213474 | + | 0.213474i | −0.805741 | − | 0.592268i | \(-0.798233\pi\) |
0.592268 | + | 0.805741i | \(0.298233\pi\) | |||||||
\(908\) | −9.38302 | + | 9.38302i | −0.311386 | + | 0.311386i | ||||
\(909\) | −11.6835 | − | 8.68050i | −0.387517 | − | 0.287914i | ||||
\(910\) | 0.986823 | − | 0.986823i | 0.0327129 | − | 0.0327129i | ||||
\(911\) | 35.5905 | + | 35.5905i | 1.17917 | + | 1.17917i | 0.979957 | + | 0.199209i | \(0.0638373\pi\) |
0.199209 | + | 0.979957i | \(0.436163\pi\) | |||||||
\(912\) | 4.94866 | + | 9.84174i | 0.163867 | + | 0.325893i | ||||
\(913\) | 3.29390i | 0.109012i | ||||||||
\(914\) | − | 7.95330i | − | 0.263072i | ||||||
\(915\) | 22.5758 | + | 7.46870i | 0.746332 | + | 0.246908i | ||||
\(916\) | − | 25.4498i | − | 0.840884i | ||||||
\(917\) | 5.46303 | − | 5.46303i | 0.180405 | − | 0.180405i | ||||
\(918\) | −26.8712 | + | 18.8735i | −0.886883 | + | 0.622919i | ||||
\(919\) | −34.3198 | − | 34.3198i | −1.13210 | − | 1.13210i | −0.989827 | − | 0.142278i | \(-0.954557\pi\) |
−0.142278 | − | 0.989827i | \(-0.545443\pi\) | |||||||
\(920\) | 1.08064 | − | 1.08064i | 0.0356275 | − | 0.0356275i | ||||
\(921\) | −16.7541 | − | 5.54272i | −0.552066 | − | 0.182639i | ||||
\(922\) | −23.4101 | −0.770972 | ||||||||
\(923\) | 2.40647 | + | 2.40647i | 0.0792100 | + | 0.0792100i | ||||
\(924\) | 4.23970 | + | 1.40261i | 0.139476 | + | 0.0461425i | ||||
\(925\) | 2.85880 | − | 5.36910i | 0.0939967 | − | 0.176535i | ||||
\(926\) | − | 2.19272i | − | 0.0720571i | ||||||
\(927\) | −4.58283 | − | 31.0773i | −0.150520 | − | 1.02071i | ||||
\(928\) | − | 0.409126i | − | 0.0134302i | ||||||
\(929\) | 39.9456 | 1.31057 | 0.655287 | − | 0.755380i | \(-0.272548\pi\) | ||||
0.655287 | + | 0.755380i | \(0.272548\pi\) | |||||||
\(930\) | 12.3178 | − | 6.19370i | 0.403918 | − | 0.203099i | ||||
\(931\) | 20.4173 | − | 20.4173i | 0.669151 | − | 0.669151i | ||||
\(932\) | − | 7.54603i | − | 0.247178i | ||||||
\(933\) | −11.5443 | − | 22.9590i | −0.377944 | − | 0.751643i | ||||
\(934\) | −20.2152 | −0.661461 | ||||||||
\(935\) | 10.3883i | 0.339733i | ||||||||
\(936\) | −2.14270 | − | 1.59197i | −0.0700364 | − | 0.0520351i | ||||
\(937\) | 30.0452 | 0.981534 | 0.490767 | − | 0.871291i | \(-0.336717\pi\) | ||||
0.490767 | + | 0.871291i | \(0.336717\pi\) | |||||||
\(938\) | −5.27088 | − | 5.27088i | −0.172100 | − | 0.172100i | ||||
\(939\) | 26.9522 | + | 53.6018i | 0.879553 | + | 1.74923i | ||||
\(940\) | 9.26833 | + | 9.26833i | 0.302300 | + | 0.302300i | ||||
\(941\) | − | 9.31327i | − | 0.303604i | −0.988411 | − | 0.151802i | \(-0.951492\pi\) | ||
0.988411 | − | 0.151802i | \(-0.0485076\pi\) | |||||||
\(942\) | −1.84430 | − | 3.66788i | −0.0600905 | − | 0.119506i | ||||
\(943\) | 11.4791 | + | 11.4791i | 0.373810 | + | 0.373810i | ||||
\(944\) | 8.55319 | + | 8.55319i | 0.278383 | + | 0.278383i | ||||
\(945\) | −8.02806 | − | 1.40357i | −0.261153 | − | 0.0456583i | ||||
\(946\) | − | 1.93971i | − | 0.0630654i | ||||||
\(947\) | −28.7924 | − | 28.7924i | −0.935628 | − | 0.935628i | 0.0624214 | − | 0.998050i | \(-0.480118\pi\) |
−0.998050 | + | 0.0624214i | \(0.980118\pi\) | |||||||
\(948\) | −1.50868 | + | 0.758600i | −0.0489997 | + | 0.0246382i | ||||
\(949\) | −8.00450 | − | 8.00450i | −0.259837 | − | 0.259837i | ||||
\(950\) | −6.36001 | −0.206346 | ||||||||
\(951\) | 10.2719 | − | 31.0490i | 0.333089 | − | 1.00683i | ||||
\(952\) | − | 9.91173i | − | 0.321241i | ||||||
\(953\) | −0.610654 | −0.0197810 | −0.00989052 | − | 0.999951i | \(-0.503148\pi\) | ||||
−0.00989052 | + | 0.999951i | \(0.503148\pi\) | |||||||
\(954\) | 1.81323 | + | 12.2960i | 0.0587055 | + | 0.398098i | ||||
\(955\) | 11.4206i | 0.369562i | ||||||||
\(956\) | 2.13485 | − | 2.13485i | 0.0690461 | − | 0.0690461i | ||||
\(957\) | 0.523296 | + | 1.04072i | 0.0169158 | + | 0.0336415i | ||||
\(958\) | 3.74834 | 0.121103 | ||||||||
\(959\) | 7.05036i | 0.227668i | ||||||||
\(960\) | −0.778090 | − | 1.54744i | −0.0251128 | − | 0.0499435i | ||||
\(961\) | 32.3636i | 1.04399i | ||||||||
\(962\) | 2.54373 | − | 4.77737i | 0.0820131 | − | 0.154029i | ||||
\(963\) | 18.2304 | − | 24.5371i | 0.587467 | − | 0.790698i | ||||
\(964\) | −12.4422 | − | 12.4422i | −0.400736 | − | 0.400736i | ||||
\(965\) | −14.6372 | −0.471190 | ||||||||
\(966\) | 1.30398 | − | 3.94156i | 0.0419549 | − | 0.126818i | ||||
\(967\) | 8.52355 | − | 8.52355i | 0.274099 | − | 0.274099i | −0.556649 | − | 0.830748i | \(-0.687913\pi\) |
0.830748 | + | 0.556649i | \(0.187913\pi\) | |||||||
\(968\) | 5.86741 | + | 5.86741i | 0.188586 | + | 0.188586i | ||||
\(969\) | −21.8650 | + | 66.0918i | −0.702406 | + | 2.12317i | ||||
\(970\) | 3.88735 | − | 3.88735i | 0.124815 | − | 0.124815i | ||||
\(971\) | − | 56.8693i | − | 1.82502i | −0.409053 | − | 0.912511i | \(-0.634141\pi\) | ||
0.409053 | − | 0.912511i | \(-0.365859\pi\) | |||||||
\(972\) | −0.415759 | + | 15.5829i | −0.0133355 | + | 0.499822i | ||||
\(973\) | 34.3948i | 1.10265i | ||||||||
\(974\) | 8.16853i | 0.261737i | ||||||||
\(975\) | 1.37690 | − | 0.692337i | 0.0440960 | − | 0.0221725i | ||||
\(976\) | 9.70779 | + | 9.70779i | 0.310739 | + | 0.310739i | ||||
\(977\) | 37.9131 | − | 37.9131i | 1.21295 | − | 1.21295i | 0.242896 | − | 0.970052i | \(-0.421903\pi\) |
0.970052 | − | 0.242896i | \(-0.0780973\pi\) | |||||||
\(978\) | −6.20579 | + | 18.7584i | −0.198439 | + | 0.599826i | ||||
\(979\) | −12.3008 | + | 12.3008i | −0.393135 | + | 0.393135i | ||||
\(980\) | −3.21027 | + | 3.21027i | −0.102548 | + | 0.102548i | ||||
\(981\) | 41.3761 | − | 6.10153i | 1.32104 | − | 0.194807i | ||||
\(982\) | −0.427885 | − | 0.427885i | −0.0136544 | − | 0.0136544i | ||||
\(983\) | 31.8655 | 1.01635 | 0.508175 | − | 0.861254i | \(-0.330320\pi\) | ||||
0.508175 | + | 0.861254i | \(0.330320\pi\) | |||||||
\(984\) | 16.4377 | − | 8.26528i | 0.524016 | − | 0.263487i | ||||
\(985\) | 6.93295 | − | 6.93295i | 0.220902 | − | 0.220902i | ||||
\(986\) | 1.82820 | − | 1.82820i | 0.0582219 | − | 0.0582219i | ||||
\(987\) | 33.8058 | + | 11.1839i | 1.07605 | + | 0.355987i | ||||
\(988\) | −5.65907 | −0.180039 | ||||||||
\(989\) | −1.80331 | −0.0573419 | ||||||||
\(990\) | 3.95854 | + | 2.94108i | 0.125811 | + | 0.0934738i | ||||
\(991\) | 17.0198 | + | 17.0198i | 0.540652 | + | 0.540652i | 0.923720 | − | 0.383068i | \(-0.125133\pi\) |
−0.383068 | + | 0.923720i | \(0.625133\pi\) | |||||||
\(992\) | 7.96013 | 0.252734 | ||||||||
\(993\) | −18.4620 | − | 36.7166i | −0.585873 | − | 1.16517i | ||||
\(994\) | 4.24190 | + | 4.24190i | 0.134545 | + | 0.134545i | ||||
\(995\) | 7.28261i | 0.230874i | ||||||||
\(996\) | 1.09008 | − | 3.29501i | 0.0345406 | − | 0.104407i | ||||
\(997\) | 39.9508 | − | 39.9508i | 1.26526 | − | 1.26526i | 0.316745 | − | 0.948511i | \(-0.397410\pi\) |
0.948511 | − | 0.316745i | \(-0.102590\pi\) | |||||||
\(998\) | −16.5708 | −0.524539 | ||||||||
\(999\) | −31.3680 | + | 3.87918i | −0.992440 | + | 0.122732i |
(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 | 1110.2.u.e.401.13 | yes | 40 | |
3.2 | odd | 2 | inner | 1110.2.u.e.401.7 | yes | 40 | |
37.6 | odd | 4 | inner | 1110.2.u.e.191.7 | ✓ | 40 | |
111.80 | even | 4 | inner | 1110.2.u.e.191.13 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.u.e.191.7 | ✓ | 40 | 37.6 | odd | 4 | inner | |
1110.2.u.e.191.13 | yes | 40 | 111.80 | even | 4 | inner | |
1110.2.u.e.401.7 | yes | 40 | 3.2 | odd | 2 | inner | |
1110.2.u.e.401.13 | yes | 40 | 1.1 | even | 1 | trivial |