Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(178,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.178");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.v (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: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 472.4 | ||
Character | \(\chi\) | \(=\) | 735.472 |
Dual form | 735.2.v.a.313.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0611467 | + | 0.228203i | −0.0432372 | + | 0.161364i | −0.984169 | − | 0.177233i | \(-0.943285\pi\) |
0.940932 | + | 0.338596i | \(0.109952\pi\) | |||||||
\(3\) | 0.965926 | − | 0.258819i | 0.557678 | − | 0.149429i | ||||
\(4\) | 1.68371 | + | 0.972092i | 0.841857 | + | 0.486046i | ||||
\(5\) | 1.04485 | + | 1.97694i | 0.467272 | + | 0.884114i | ||||
\(6\) | 0.236253i | 0.0964497i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.658899 | + | 0.658899i | −0.232956 | + | 0.232956i | ||||
\(9\) | 0.866025 | − | 0.500000i | 0.288675 | − | 0.166667i | ||||
\(10\) | −0.515032 | + | 0.117555i | −0.162867 | + | 0.0371740i | ||||
\(11\) | −1.99301 | + | 3.45200i | −0.600915 | + | 1.04082i | 0.391767 | + | 0.920064i | \(0.371864\pi\) |
−0.992683 | + | 0.120752i | \(0.961470\pi\) | |||||||
\(12\) | 1.87794 | + | 0.503192i | 0.542114 | + | 0.145259i | ||||
\(13\) | −0.500437 | − | 0.500437i | −0.138796 | − | 0.138796i | 0.634295 | − | 0.773091i | \(-0.281291\pi\) |
−0.773091 | + | 0.634295i | \(0.781291\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.52092 | + | 1.63915i | 0.392699 | + | 0.423226i | ||||
\(16\) | 1.83411 | + | 3.17677i | 0.458528 | + | 0.794194i | ||||
\(17\) | 0.614336 | + | 2.29273i | 0.148998 | + | 0.556070i | 0.999545 | + | 0.0301697i | \(0.00960478\pi\) |
−0.850546 | + | 0.525900i | \(0.823729\pi\) | |||||||
\(18\) | 0.0611467 | + | 0.228203i | 0.0144124 | + | 0.0537879i | ||||
\(19\) | −3.60925 | − | 6.25141i | −0.828019 | − | 1.43417i | −0.899590 | − | 0.436735i | \(-0.856135\pi\) |
0.0715711 | − | 0.997435i | \(-0.477199\pi\) | |||||||
\(20\) | −0.162536 | + | 4.34429i | −0.0363441 | + | 0.971413i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.665888 | − | 0.665888i | −0.141968 | − | 0.141968i | ||||
\(23\) | 7.04878 | + | 1.88872i | 1.46977 | + | 0.393824i | 0.902853 | − | 0.429949i | \(-0.141468\pi\) |
0.566919 | + | 0.823773i | \(0.308135\pi\) | |||||||
\(24\) | −0.465912 | + | 0.806983i | −0.0951039 | + | 0.164725i | ||||
\(25\) | −2.81657 | + | 4.13121i | −0.563314 | + | 0.826243i | ||||
\(26\) | 0.144801 | − | 0.0836010i | 0.0283978 | − | 0.0163955i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.65191i | − | 0.678143i | −0.940761 | − | 0.339071i | \(-0.889887\pi\) | ||
0.940761 | − | 0.339071i | \(-0.110113\pi\) | |||||||
\(30\) | −0.467057 | + | 0.246849i | −0.0852725 | + | 0.0450683i | ||||
\(31\) | −4.27662 | − | 2.46911i | −0.768103 | − | 0.443465i | 0.0640944 | − | 0.997944i | \(-0.479584\pi\) |
−0.832198 | + | 0.554479i | \(0.812917\pi\) | |||||||
\(32\) | −2.63724 | + | 0.706647i | −0.466203 | + | 0.124919i | ||||
\(33\) | −1.03166 | + | 3.85020i | −0.179589 | + | 0.670234i | ||||
\(34\) | −0.560773 | −0.0961717 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.94418 | 0.324031 | ||||||||
\(37\) | 0.106980 | − | 0.399255i | 0.0175874 | − | 0.0656371i | −0.956574 | − | 0.291488i | \(-0.905850\pi\) |
0.974162 | + | 0.225851i | \(0.0725163\pi\) | |||||||
\(38\) | 1.64728 | − | 0.441387i | 0.267224 | − | 0.0716025i | ||||
\(39\) | −0.612908 | − | 0.353863i | −0.0981438 | − | 0.0566634i | ||||
\(40\) | −1.99105 | − | 0.614151i | −0.314813 | − | 0.0971058i | ||||
\(41\) | − | 7.63184i | − | 1.19189i | −0.803024 | − | 0.595947i | \(-0.796777\pi\) | ||
0.803024 | − | 0.595947i | \(-0.203223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.65191 | − | 3.65191i | 0.556911 | − | 0.556911i | −0.371516 | − | 0.928427i | \(-0.621162\pi\) |
0.928427 | + | 0.371516i | \(0.121162\pi\) | |||||||
\(44\) | −6.71132 | + | 3.87478i | −1.01177 | + | 0.584145i | ||||
\(45\) | 1.89334 | + | 1.18965i | 0.282242 | + | 0.177343i | ||||
\(46\) | −0.862019 | + | 1.49306i | −0.127098 | + | 0.220140i | ||||
\(47\) | −0.417052 | − | 0.111749i | −0.0608333 | − | 0.0163002i | 0.228274 | − | 0.973597i | \(-0.426692\pi\) |
−0.289107 | + | 0.957297i | \(0.593358\pi\) | |||||||
\(48\) | 2.59383 | + | 2.59383i | 0.374386 | + | 0.374386i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.770530 | − | 0.895358i | −0.108969 | − | 0.126623i | ||||
\(51\) | 1.18681 | + | 2.05561i | 0.166186 | + | 0.287843i | ||||
\(52\) | −0.356122 | − | 1.32906i | −0.0493852 | − | 0.184308i | ||||
\(53\) | 1.97527 | + | 7.37179i | 0.271324 | + | 1.01259i | 0.958265 | + | 0.285881i | \(0.0922861\pi\) |
−0.686942 | + | 0.726713i | \(0.741047\pi\) | |||||||
\(54\) | 0.118126 | + | 0.204601i | 0.0160750 | + | 0.0278426i | ||||
\(55\) | −8.90678 | − | 0.333235i | −1.20099 | − | 0.0449335i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.10425 | − | 5.10425i | −0.676075 | − | 0.676075i | ||||
\(58\) | 0.833375 | + | 0.223302i | 0.109428 | + | 0.0293210i | ||||
\(59\) | 3.05480 | − | 5.29106i | 0.397701 | − | 0.688838i | −0.595741 | − | 0.803176i | \(-0.703142\pi\) |
0.993442 | + | 0.114339i | \(0.0364750\pi\) | |||||||
\(60\) | 0.967387 | + | 4.23833i | 0.124889 | + | 0.547166i | ||||
\(61\) | 6.15784 | − | 3.55523i | 0.788431 | − | 0.455201i | −0.0509788 | − | 0.998700i | \(-0.516234\pi\) |
0.839410 | + | 0.543499i | \(0.182901\pi\) | |||||||
\(62\) | 0.824957 | − | 0.824957i | 0.104770 | − | 0.104770i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.69141i | 0.836426i | ||||||||
\(65\) | 0.466451 | − | 1.51222i | 0.0578561 | − | 0.187567i | ||||
\(66\) | −0.815543 | − | 0.470854i | −0.100386 | − | 0.0579581i | ||||
\(67\) | −1.28978 | + | 0.345596i | −0.157572 | + | 0.0422212i | −0.336743 | − | 0.941597i | \(-0.609325\pi\) |
0.179171 | + | 0.983818i | \(0.442659\pi\) | |||||||
\(68\) | −1.19438 | + | 4.45750i | −0.144840 | + | 0.540551i | ||||
\(69\) | 7.29744 | 0.878508 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.19297 | 0.141579 | 0.0707897 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707897 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(72\) | −0.241174 | + | 0.900073i | −0.0284226 | + | 0.106075i | ||||
\(73\) | 1.88918 | − | 0.506205i | 0.221112 | − | 0.0592469i | −0.146562 | − | 0.989201i | \(-0.546821\pi\) |
0.367674 | + | 0.929955i | \(0.380154\pi\) | |||||||
\(74\) | 0.0845694 | + | 0.0488262i | 0.00983100 | + | 0.00567593i | ||||
\(75\) | −1.65136 | + | 4.71943i | −0.190683 | + | 0.544953i | ||||
\(76\) | − | 14.0341i | − | 1.60982i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.118230 | − | 0.118230i | 0.0133869 | − | 0.0133869i | ||||
\(79\) | 7.48269 | − | 4.32013i | 0.841868 | − | 0.486053i | −0.0160304 | − | 0.999872i | \(-0.505103\pi\) |
0.857899 | + | 0.513819i | \(0.171770\pi\) | |||||||
\(80\) | −4.36391 | + | 6.94518i | −0.487900 | + | 0.776495i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.74161 | + | 0.466662i | 0.192328 | + | 0.0515342i | ||||
\(83\) | 11.9895 | + | 11.9895i | 1.31602 | + | 1.31602i | 0.916898 | + | 0.399122i | \(0.130685\pi\) |
0.399122 | + | 0.916898i | \(0.369315\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.89070 | + | 3.61007i | −0.422006 | + | 0.391567i | ||||
\(86\) | 0.610073 | + | 1.05668i | 0.0657859 | + | 0.113944i | ||||
\(87\) | −0.945184 | − | 3.52747i | −0.101334 | − | 0.378185i | ||||
\(88\) | −0.961324 | − | 3.58771i | −0.102477 | − | 0.382451i | ||||
\(89\) | 3.91290 | + | 6.77735i | 0.414767 | + | 0.718397i | 0.995404 | − | 0.0957652i | \(-0.0305298\pi\) |
−0.580637 | + | 0.814163i | \(0.697196\pi\) | |||||||
\(90\) | −0.387253 | + | 0.359321i | −0.0408201 | + | 0.0378758i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.0321 | + | 10.0321i | 1.04592 | + | 1.04592i | ||||
\(93\) | −4.76995 | − | 1.27810i | −0.494620 | − | 0.132533i | ||||
\(94\) | 0.0510027 | − | 0.0883393i | 0.00526053 | − | 0.00911150i | ||||
\(95\) | 8.58751 | − | 13.6671i | 0.881060 | − | 1.40221i | ||||
\(96\) | −2.36449 | + | 1.36514i | −0.241325 | + | 0.139329i | ||||
\(97\) | −7.43671 | + | 7.43671i | −0.755083 | + | 0.755083i | −0.975423 | − | 0.220340i | \(-0.929283\pi\) |
0.220340 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.98602i | 0.400610i | ||||||||
\(100\) | −8.75822 | + | 4.21782i | −0.875822 | + | 0.421782i | ||||
\(101\) | −5.47010 | − | 3.15816i | −0.544295 | − | 0.314249i | 0.202523 | − | 0.979278i | \(-0.435086\pi\) |
−0.746818 | + | 0.665028i | \(0.768419\pi\) | |||||||
\(102\) | −0.541665 | + | 0.145139i | −0.0536328 | + | 0.0143709i | ||||
\(103\) | 4.59031 | − | 17.1313i | 0.452296 | − | 1.68799i | −0.243620 | − | 0.969871i | \(-0.578335\pi\) |
0.695917 | − | 0.718122i | \(-0.254998\pi\) | |||||||
\(104\) | 0.659476 | 0.0646669 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.80304 | −0.175127 | ||||||||
\(107\) | 2.73794 | − | 10.2181i | 0.264687 | − | 0.987825i | −0.697755 | − | 0.716337i | \(-0.745817\pi\) |
0.962442 | − | 0.271488i | \(-0.0875159\pi\) | |||||||
\(108\) | 1.87794 | − | 0.503192i | 0.180705 | − | 0.0484197i | ||||
\(109\) | −0.578698 | − | 0.334112i | −0.0554293 | − | 0.0320021i | 0.472029 | − | 0.881583i | \(-0.343522\pi\) |
−0.527459 | + | 0.849581i | \(0.676855\pi\) | |||||||
\(110\) | 0.620666 | − | 2.01217i | 0.0591781 | − | 0.191853i | ||||
\(111\) | − | 0.413339i | − | 0.0392324i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.39653 | + | 3.39653i | −0.319518 | + | 0.319518i | −0.848582 | − | 0.529064i | \(-0.822543\pi\) |
0.529064 | + | 0.848582i | \(0.322543\pi\) | |||||||
\(114\) | 1.47691 | − | 0.852695i | 0.138325 | − | 0.0798622i | ||||
\(115\) | 3.63106 | + | 15.9084i | 0.338598 | + | 1.48347i | ||||
\(116\) | 3.54999 | − | 6.14877i | 0.329609 | − | 0.570899i | ||||
\(117\) | −0.683610 | − | 0.183173i | −0.0631998 | − | 0.0169343i | ||||
\(118\) | 1.02064 | + | 1.02064i | 0.0939578 | + | 0.0939578i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.08217 | − | 0.0779014i | −0.190075 | − | 0.00711139i | ||||
\(121\) | −2.44418 | − | 4.23345i | −0.222199 | − | 0.384859i | ||||
\(122\) | 0.434781 | + | 1.62263i | 0.0393633 | + | 0.146906i | ||||
\(123\) | −1.97527 | − | 7.37179i | −0.178104 | − | 0.664692i | ||||
\(124\) | −4.80040 | − | 8.31453i | −0.431088 | − | 0.746667i | ||||
\(125\) | −11.1101 | − | 1.25168i | −0.993713 | − | 0.111953i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.88837 | − | 5.88837i | −0.522508 | − | 0.522508i | 0.395820 | − | 0.918328i | \(-0.370460\pi\) |
−0.918328 | + | 0.395820i | \(0.870460\pi\) | |||||||
\(128\) | −6.80149 | − | 1.82245i | −0.601172 | − | 0.161084i | ||||
\(129\) | 2.58229 | − | 4.47266i | 0.227358 | − | 0.393796i | ||||
\(130\) | 0.316570 | + | 0.198912i | 0.0277650 | + | 0.0174458i | ||||
\(131\) | −16.2938 | + | 9.40722i | −1.42359 | + | 0.821913i | −0.996604 | − | 0.0823433i | \(-0.973760\pi\) |
−0.426991 | + | 0.904256i | \(0.640426\pi\) | |||||||
\(132\) | −5.47977 | + | 5.47977i | −0.476953 | + | 0.476953i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.315463i | − | 0.0272519i | ||||||
\(135\) | 2.13673 | + | 0.659085i | 0.183900 | + | 0.0567250i | ||||
\(136\) | −1.91547 | − | 1.10590i | −0.164250 | − | 0.0948297i | ||||
\(137\) | 1.10918 | − | 0.297204i | 0.0947637 | − | 0.0253919i | −0.211126 | − | 0.977459i | \(-0.567713\pi\) |
0.305889 | + | 0.952067i | \(0.401046\pi\) | |||||||
\(138\) | −0.446214 | + | 1.66529i | −0.0379843 | + | 0.141759i | ||||
\(139\) | 0.442439 | 0.0375272 | 0.0187636 | − | 0.999824i | \(-0.494027\pi\) | ||||
0.0187636 | + | 0.999824i | \(0.494027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.431764 | −0.0363611 | ||||||||
\(142\) | −0.0729461 | + | 0.272239i | −0.00612150 | + | 0.0228458i | ||||
\(143\) | 2.72489 | − | 0.730131i | 0.227866 | − | 0.0610566i | ||||
\(144\) | 3.17677 | + | 1.83411i | 0.264731 | + | 0.152843i | ||||
\(145\) | 7.21960 | − | 3.81570i | 0.599555 | − | 0.316877i | ||||
\(146\) | 0.462070i | 0.0382411i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.568236 | − | 0.568236i | 0.0467087 | − | 0.0467087i | ||||
\(149\) | −2.72031 | + | 1.57057i | −0.222856 | + | 0.128666i | −0.607272 | − | 0.794494i | \(-0.707736\pi\) |
0.384416 | + | 0.923160i | \(0.374403\pi\) | |||||||
\(150\) | −0.976010 | − | 0.665422i | −0.0796909 | − | 0.0543315i | ||||
\(151\) | 7.36197 | − | 12.7513i | 0.599109 | − | 1.03769i | −0.393844 | − | 0.919177i | \(-0.628855\pi\) |
0.992953 | − | 0.118509i | \(-0.0378116\pi\) | |||||||
\(152\) | 6.49718 | + | 1.74091i | 0.526991 | + | 0.141207i | ||||
\(153\) | 1.67840 | + | 1.67840i | 0.135690 | + | 0.135690i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.412839 | − | 11.0345i | 0.0331601 | − | 0.886309i | ||||
\(156\) | −0.687974 | − | 1.19161i | −0.0550820 | − | 0.0954049i | ||||
\(157\) | 2.91542 | + | 10.8805i | 0.232676 | + | 0.868358i | 0.979183 | + | 0.202980i | \(0.0650628\pi\) |
−0.746507 | + | 0.665378i | \(0.768271\pi\) | |||||||
\(158\) | 0.528324 | + | 1.97173i | 0.0420312 | + | 0.156862i | ||||
\(159\) | 3.81592 | + | 6.60937i | 0.302622 | + | 0.524157i | ||||
\(160\) | −4.15253 | − | 4.47533i | −0.328286 | − | 0.353806i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.167056 | + | 0.167056i | 0.0131251 | + | 0.0131251i | ||||
\(163\) | −14.2681 | − | 3.82312i | −1.11756 | − | 0.299450i | −0.347666 | − | 0.937619i | \(-0.613026\pi\) |
−0.769897 | + | 0.638169i | \(0.779692\pi\) | |||||||
\(164\) | 7.41885 | − | 12.8498i | 0.579315 | − | 1.00340i | ||||
\(165\) | −8.68954 | + | 1.98336i | −0.676480 | + | 0.154405i | ||||
\(166\) | −3.46916 | + | 2.00292i | −0.269259 | + | 0.155457i | ||||
\(167\) | −4.63621 | + | 4.63621i | −0.358761 | + | 0.358761i | −0.863356 | − | 0.504595i | \(-0.831642\pi\) |
0.504595 | + | 0.863356i | \(0.331642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.4991i | − | 0.961471i | ||||||
\(170\) | −0.585924 | − | 1.10861i | −0.0449383 | − | 0.0850267i | ||||
\(171\) | −6.25141 | − | 3.60925i | −0.478057 | − | 0.276006i | ||||
\(172\) | 9.69876 | − | 2.59878i | 0.739524 | − | 0.198155i | ||||
\(173\) | 0.909686 | − | 3.39499i | 0.0691621 | − | 0.258117i | −0.922684 | − | 0.385557i | \(-0.874009\pi\) |
0.991846 | + | 0.127440i | \(0.0406761\pi\) | |||||||
\(174\) | 0.862773 | 0.0654067 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.6216 | −1.10215 | ||||||||
\(177\) | 1.58128 | − | 5.90141i | 0.118856 | − | 0.443577i | ||||
\(178\) | −1.78587 | + | 0.478522i | −0.133857 | + | 0.0358667i | ||||
\(179\) | −19.1486 | − | 11.0554i | −1.43123 | − | 0.826321i | −0.434016 | − | 0.900905i | \(-0.642904\pi\) |
−0.997215 | + | 0.0745840i | \(0.976237\pi\) | |||||||
\(180\) | 2.03138 | + | 3.84353i | 0.151410 | + | 0.286480i | ||||
\(181\) | − | 8.48528i | − | 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.02786 | − | 5.02786i | 0.371670 | − | 0.371670i | ||||
\(184\) | −5.88891 | + | 3.39996i | −0.434136 | + | 0.250649i | ||||
\(185\) | 0.901080 | − | 0.205669i | 0.0662487 | − | 0.0151211i | ||||
\(186\) | 0.583333 | − | 1.01036i | 0.0427720 | − | 0.0740833i | ||||
\(187\) | −9.13889 | − | 2.44876i | −0.668302 | − | 0.179071i | ||||
\(188\) | −0.593566 | − | 0.593566i | −0.0432903 | − | 0.0432903i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.59376 | + | 2.79539i | 0.188171 | + | 0.202799i | ||||
\(191\) | −7.64492 | − | 13.2414i | −0.553167 | − | 0.958113i | −0.998044 | − | 0.0625216i | \(-0.980086\pi\) |
0.444877 | − | 0.895592i | \(-0.353248\pi\) | |||||||
\(192\) | 1.73186 | + | 6.46341i | 0.124987 | + | 0.466456i | ||||
\(193\) | −3.26783 | − | 12.1957i | −0.235223 | − | 0.877866i | −0.978048 | − | 0.208380i | \(-0.933181\pi\) |
0.742825 | − | 0.669486i | \(-0.233486\pi\) | |||||||
\(194\) | −1.24235 | − | 2.15181i | −0.0891952 | − | 0.154491i | ||||
\(195\) | 0.0591665 | − | 1.58142i | 0.00423700 | − | 0.113248i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.68715 | − | 2.68715i | −0.191451 | − | 0.191451i | 0.604872 | − | 0.796323i | \(-0.293224\pi\) |
−0.796323 | + | 0.604872i | \(0.793224\pi\) | |||||||
\(198\) | −0.909620 | − | 0.243732i | −0.0646439 | − | 0.0173213i | ||||
\(199\) | 0.308318 | − | 0.534023i | 0.0218561 | − | 0.0378559i | −0.854890 | − | 0.518809i | \(-0.826376\pi\) |
0.876747 | + | 0.480953i | \(0.159709\pi\) | |||||||
\(200\) | −0.866218 | − | 4.57789i | −0.0612509 | − | 0.323706i | ||||
\(201\) | −1.15639 | + | 0.667639i | −0.0815651 | + | 0.0470917i | ||||
\(202\) | 1.05518 | − | 1.05518i | 0.0742422 | − | 0.0742422i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.61474i | 0.323097i | ||||||||
\(205\) | 15.0877 | − | 7.97414i | 1.05377 | − | 0.556938i | ||||
\(206\) | 3.62871 | + | 2.09504i | 0.252825 | + | 0.145968i | ||||
\(207\) | 7.04878 | − | 1.88872i | 0.489924 | − | 0.131275i | ||||
\(208\) | 0.671919 | − | 2.50763i | 0.0465892 | − | 0.173873i | ||||
\(209\) | 28.7731 | 1.99028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.30849 | 0.640823 | 0.320411 | − | 0.947278i | \(-0.396179\pi\) | ||||
0.320411 | + | 0.947278i | \(0.396179\pi\) | |||||||
\(212\) | −3.84028 | + | 14.3321i | −0.263752 | + | 0.984334i | ||||
\(213\) | 1.15232 | − | 0.308763i | 0.0789557 | − | 0.0211561i | ||||
\(214\) | 2.16439 | + | 1.24961i | 0.147955 | + | 0.0854217i | ||||
\(215\) | 11.0353 | + | 3.40390i | 0.752602 | + | 0.232144i | ||||
\(216\) | 0.931824i | 0.0634026i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.111631 | − | 0.111631i | 0.00756058 | − | 0.00756058i | ||||
\(219\) | 1.69380 | − | 0.977914i | 0.114456 | − | 0.0660813i | ||||
\(220\) | −14.6725 | − | 9.21929i | −0.989222 | − | 0.621564i | ||||
\(221\) | 0.839933 | − | 1.45481i | 0.0565000 | − | 0.0978609i | ||||
\(222\) | 0.0943250 | + | 0.0252743i | 0.00633068 | + | 0.00169630i | ||||
\(223\) | 1.35505 | + | 1.35505i | 0.0907407 | + | 0.0907407i | 0.751020 | − | 0.660279i | \(-0.229562\pi\) |
−0.660279 | + | 0.751020i | \(0.729562\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.373614 | + | 4.98602i | −0.0249076 | + | 0.332401i | ||||
\(226\) | −0.567410 | − | 0.982782i | −0.0377435 | − | 0.0653737i | ||||
\(227\) | −1.52061 | − | 5.67498i | −0.100926 | − | 0.376662i | 0.896925 | − | 0.442183i | \(-0.145796\pi\) |
−0.997851 | + | 0.0655211i | \(0.979129\pi\) | |||||||
\(228\) | −3.63229 | − | 13.5559i | −0.240554 | − | 0.897761i | ||||
\(229\) | 6.49500 | + | 11.2497i | 0.429202 | + | 0.743399i | 0.996802 | − | 0.0799049i | \(-0.0254617\pi\) |
−0.567601 | + | 0.823304i | \(0.692128\pi\) | |||||||
\(230\) | −3.85237 | − | 0.144131i | −0.254018 | − | 0.00950374i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.40624 | + | 2.40624i | 0.157977 | + | 0.157977i | ||||
\(233\) | 22.4901 | + | 6.02620i | 1.47337 | + | 0.394790i | 0.904087 | − | 0.427349i | \(-0.140552\pi\) |
0.569288 | + | 0.822138i | \(0.307219\pi\) | |||||||
\(234\) | 0.0836010 | − | 0.144801i | 0.00546517 | − | 0.00946595i | ||||
\(235\) | −0.214837 | − | 0.941247i | −0.0140144 | − | 0.0614002i | ||||
\(236\) | 10.2868 | − | 5.93909i | 0.669614 | − | 0.386602i | ||||
\(237\) | 6.10959 | − | 6.10959i | 0.396861 | − | 0.396861i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.48048i | 0.354503i | 0.984166 | + | 0.177251i | \(0.0567205\pi\) | ||||
−0.984166 | + | 0.177251i | \(0.943279\pi\) | |||||||
\(240\) | −2.41767 | + | 7.83800i | −0.156060 | + | 0.505940i | ||||
\(241\) | −12.6879 | − | 7.32537i | −0.817300 | − | 0.471868i | 0.0321844 | − | 0.999482i | \(-0.489754\pi\) |
−0.849485 | + | 0.527613i | \(0.823087\pi\) | |||||||
\(242\) | 1.11554 | − | 0.298908i | 0.0717095 | − | 0.0192145i | ||||
\(243\) | 0.258819 | − | 0.965926i | 0.0166032 | − | 0.0619642i | ||||
\(244\) | 13.8241 | 0.884995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.80304 | 0.114958 | ||||||||
\(247\) | −1.32223 | + | 4.93464i | −0.0841317 | + | 0.313984i | ||||
\(248\) | 4.44475 | − | 1.19097i | 0.282242 | − | 0.0756265i | ||||
\(249\) | 14.6841 | + | 8.47787i | 0.930567 | + | 0.537263i | ||||
\(250\) | 0.964979 | − | 2.45881i | 0.0610306 | − | 0.155509i | ||||
\(251\) | − | 21.1506i | − | 1.33501i | −0.744604 | − | 0.667507i | \(-0.767361\pi\) | ||
0.744604 | − | 0.667507i | \(-0.232639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.5681 | + | 20.5681i | −1.29311 | + | 1.29311i | ||||
\(254\) | 1.70380 | − | 0.983687i | 0.106906 | − | 0.0617220i | ||||
\(255\) | −2.82378 | + | 4.49405i | −0.176832 | + | 0.281428i | ||||
\(256\) | −5.85964 | + | 10.1492i | −0.366227 | + | 0.634324i | ||||
\(257\) | −12.8304 | − | 3.43788i | −0.800336 | − | 0.214449i | −0.164604 | − | 0.986360i | \(-0.552635\pi\) |
−0.635731 | + | 0.771910i | \(0.719301\pi\) | |||||||
\(258\) | 0.862773 | + | 0.862773i | 0.0537139 | + | 0.0537139i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.25538 | − | 2.09271i | 0.139873 | − | 0.129784i | ||||
\(261\) | −1.82596 | − | 3.16265i | −0.113024 | − | 0.195763i | ||||
\(262\) | −1.15044 | − | 4.29350i | −0.0710745 | − | 0.265254i | ||||
\(263\) | 5.62869 | + | 21.0066i | 0.347080 | + | 1.29532i | 0.890163 | + | 0.455642i | \(0.150590\pi\) |
−0.543083 | + | 0.839679i | \(0.682743\pi\) | |||||||
\(264\) | −1.85714 | − | 3.21665i | −0.114299 | − | 0.197971i | ||||
\(265\) | −12.5097 | + | 11.6074i | −0.768466 | + | 0.713037i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.53368 | + | 5.53368i | 0.338656 | + | 0.338656i | ||||
\(268\) | −2.50757 | − | 0.671902i | −0.153174 | − | 0.0410429i | ||||
\(269\) | −11.4926 | + | 19.9057i | −0.700714 | + | 1.21367i | 0.267501 | + | 0.963557i | \(0.413802\pi\) |
−0.968216 | + | 0.250116i | \(0.919531\pi\) | |||||||
\(270\) | −0.281059 | + | 0.447306i | −0.0171047 | + | 0.0272222i | ||||
\(271\) | −13.6483 | + | 7.87982i | −0.829072 | + | 0.478665i | −0.853535 | − | 0.521036i | \(-0.825546\pi\) |
0.0244625 | + | 0.999701i | \(0.492213\pi\) | |||||||
\(272\) | −6.15674 | + | 6.15674i | −0.373307 | + | 0.373307i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.271291i | 0.0163893i | ||||||||
\(275\) | −8.64748 | − | 17.9563i | −0.521463 | − | 1.08281i | ||||
\(276\) | 12.2868 | + | 7.09378i | 0.739578 | + | 0.426995i | ||||
\(277\) | −6.56746 | + | 1.75975i | −0.394600 | + | 0.105733i | −0.450662 | − | 0.892694i | \(-0.648812\pi\) |
0.0560621 | + | 0.998427i | \(0.482146\pi\) | |||||||
\(278\) | −0.0270537 | + | 0.100966i | −0.00162257 | + | 0.00605553i | ||||
\(279\) | −4.93821 | −0.295643 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.65658 | −0.576063 | −0.288032 | − | 0.957621i | \(-0.593001\pi\) | ||||
−0.288032 | + | 0.957621i | \(0.593001\pi\) | |||||||
\(282\) | 0.0264009 | − | 0.0985297i | 0.00157215 | − | 0.00586736i | ||||
\(283\) | 20.3668 | − | 5.45726i | 1.21068 | − | 0.324400i | 0.403650 | − | 0.914913i | \(-0.367741\pi\) |
0.807028 | + | 0.590513i | \(0.201075\pi\) | |||||||
\(284\) | 2.00862 | + | 1.15968i | 0.119190 | + | 0.0688141i | ||||
\(285\) | 4.75760 | − | 15.4240i | 0.281816 | − | 0.913637i | ||||
\(286\) | 0.666471i | 0.0394092i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.93060 | + | 1.93060i | −0.113761 | + | 0.113761i | ||||
\(289\) | 9.84321 | − | 5.68298i | 0.579012 | − | 0.334293i | ||||
\(290\) | 0.429299 | + | 1.88085i | 0.0252093 | + | 0.110447i | ||||
\(291\) | −5.25855 | + | 9.10807i | −0.308261 | + | 0.533924i | ||||
\(292\) | 3.67292 | + | 0.984157i | 0.214942 | + | 0.0575934i | ||||
\(293\) | −4.79236 | − | 4.79236i | −0.279973 | − | 0.279973i | 0.553125 | − | 0.833098i | \(-0.313435\pi\) |
−0.833098 | + | 0.553125i | \(0.813435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.6519 | + | 0.510768i | 0.794845 | + | 0.0297381i | ||||
\(296\) | 0.192580 | + | 0.333558i | 0.0111935 | + | 0.0193876i | ||||
\(297\) | 1.03166 | + | 3.85020i | 0.0598629 | + | 0.223411i | ||||
\(298\) | −0.192070 | − | 0.716817i | −0.0111263 | − | 0.0415241i | ||||
\(299\) | −2.58229 | − | 4.47266i | −0.149338 | − | 0.258660i | ||||
\(300\) | −7.36814 | + | 6.34089i | −0.425400 | + | 0.366091i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.45972 | + | 2.45972i | 0.141541 | + | 0.141541i | ||||
\(303\) | −6.10111 | − | 1.63479i | −0.350499 | − | 0.0939160i | ||||
\(304\) | 13.2395 | − | 22.9316i | 0.759340 | − | 1.31521i | ||||
\(305\) | 13.4625 | + | 8.45899i | 0.770861 | + | 0.484360i | ||||
\(306\) | −0.485643 | + | 0.280386i | −0.0277624 | + | 0.0160286i | ||||
\(307\) | −9.85063 | + | 9.85063i | −0.562205 | + | 0.562205i | −0.929933 | − | 0.367728i | \(-0.880136\pi\) |
0.367728 | + | 0.929933i | \(0.380136\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 17.7356i | − | 1.00894i | ||||||
\(310\) | 2.49285 | + | 0.768932i | 0.141584 | + | 0.0436724i | ||||
\(311\) | −23.6480 | − | 13.6532i | −1.34095 | − | 0.774200i | −0.354006 | − | 0.935243i | \(-0.615181\pi\) |
−0.986947 | + | 0.161043i | \(0.948514\pi\) | |||||||
\(312\) | 0.637004 | − | 0.170685i | 0.0360633 | − | 0.00966313i | ||||
\(313\) | −6.77439 | + | 25.2824i | −0.382911 | + | 1.42904i | 0.458523 | + | 0.888683i | \(0.348379\pi\) |
−0.841434 | + | 0.540361i | \(0.818288\pi\) | |||||||
\(314\) | −2.66123 | −0.150182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.7983 | 0.944977 | ||||||||
\(317\) | −8.00839 | + | 29.8877i | −0.449796 | + | 1.67866i | 0.253156 | + | 0.967425i | \(0.418531\pi\) |
−0.702952 | + | 0.711237i | \(0.748135\pi\) | |||||||
\(318\) | −1.74161 | + | 0.466662i | −0.0976644 | + | 0.0261691i | ||||
\(319\) | 12.6064 | + | 7.27830i | 0.705822 | + | 0.407506i | ||||
\(320\) | −13.2285 | + | 6.99153i | −0.739496 | + | 0.390839i | ||||
\(321\) | − | 10.5786i | − | 0.590440i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.1155 | − | 12.1155i | 0.674126 | − | 0.674126i | ||||
\(324\) | 1.68371 | − | 0.972092i | 0.0935396 | − | 0.0540051i | ||||
\(325\) | 3.47693 | − | 0.657897i | 0.192865 | − | 0.0364936i | ||||
\(326\) | 1.74489 | − | 3.02224i | 0.0966406 | − | 0.167386i | ||||
\(327\) | −0.645454 | − | 0.172949i | −0.0356937 | − | 0.00956410i | ||||
\(328\) | 5.02861 | + | 5.02861i | 0.277659 | + | 0.277659i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.0787277 | − | 2.10425i | 0.00433382 | − | 0.115835i | ||||
\(331\) | 8.34566 | + | 14.4551i | 0.458719 | + | 0.794524i | 0.998894 | − | 0.0470286i | \(-0.0149752\pi\) |
−0.540175 | + | 0.841553i | \(0.681642\pi\) | |||||||
\(332\) | 8.53199 | + | 31.8418i | 0.468254 | + | 1.74755i | ||||
\(333\) | −0.106980 | − | 0.399255i | −0.00586246 | − | 0.0218790i | ||||
\(334\) | −0.774506 | − | 1.34148i | −0.0423791 | − | 0.0734027i | ||||
\(335\) | −2.03085 | − | 2.18872i | −0.110957 | − | 0.119583i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.54028 | + | 2.54028i | 0.138378 | + | 0.138378i | 0.772903 | − | 0.634525i | \(-0.218804\pi\) |
−0.634525 | + | 0.772903i | \(0.718804\pi\) | |||||||
\(338\) | 2.85233 | + | 0.764280i | 0.155146 | + | 0.0415714i | ||||
\(339\) | −2.40171 | + | 4.15988i | −0.130443 | + | 0.225934i | ||||
\(340\) | −10.0602 | + | 2.29620i | −0.545589 | + | 0.124529i | ||||
\(341\) | 17.0467 | − | 9.84191i | 0.923130 | − | 0.532969i | ||||
\(342\) | 1.20589 | − | 1.20589i | 0.0652072 | − | 0.0652072i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 4.81248i | 0.259472i | ||||||||
\(345\) | 7.62474 | + | 14.4266i | 0.410502 | + | 0.776701i | ||||
\(346\) | 0.719122 | + | 0.415185i | 0.0386602 | + | 0.0223205i | ||||
\(347\) | −18.7118 | + | 5.01382i | −1.00450 | + | 0.269156i | −0.723331 | − | 0.690501i | \(-0.757390\pi\) |
−0.281173 | + | 0.959657i | \(0.590723\pi\) | |||||||
\(348\) | 1.83761 | − | 6.85806i | 0.0985063 | − | 0.367631i | ||||
\(349\) | −0.508601 | −0.0272248 | −0.0136124 | − | 0.999907i | \(-0.504333\pi\) | ||||
−0.0136124 | + | 0.999907i | \(0.504333\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.707725 | −0.0377756 | ||||||||
\(352\) | 2.81671 | − | 10.5121i | 0.150131 | − | 0.560297i | ||||
\(353\) | 14.9193 | − | 3.99763i | 0.794077 | − | 0.212772i | 0.161095 | − | 0.986939i | \(-0.448497\pi\) |
0.632982 | + | 0.774167i | \(0.281831\pi\) | |||||||
\(354\) | 1.25003 | + | 0.721704i | 0.0664382 | + | 0.0383581i | ||||
\(355\) | 1.24648 | + | 2.35843i | 0.0661561 | + | 0.125172i | ||||
\(356\) | 15.2148i | 0.806383i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.69375 | − | 3.69375i | 0.195221 | − | 0.195221i | ||||
\(359\) | −13.8443 | + | 7.99301i | −0.730674 | + | 0.421855i | −0.818669 | − | 0.574266i | \(-0.805288\pi\) |
0.0879945 | + | 0.996121i | \(0.471954\pi\) | |||||||
\(360\) | −2.03138 | + | 0.463657i | −0.107063 | + | 0.0244369i | ||||
\(361\) | −16.5534 | + | 28.6713i | −0.871231 | + | 1.50902i | ||||
\(362\) | 1.93636 | + | 0.518847i | 0.101773 | + | 0.0272700i | ||||
\(363\) | −3.45660 | − | 3.45660i | −0.181424 | − | 0.181424i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.97465 | + | 3.20589i | 0.155701 | + | 0.167804i | ||||
\(366\) | 0.839933 | + | 1.45481i | 0.0439040 | + | 0.0760440i | ||||
\(367\) | −0.150084 | − | 0.560120i | −0.00783431 | − | 0.0292380i | 0.961898 | − | 0.273408i | \(-0.0881510\pi\) |
−0.969732 | + | 0.244170i | \(0.921484\pi\) | |||||||
\(368\) | 6.92823 | + | 25.8565i | 0.361159 | + | 1.34786i | ||||
\(369\) | −3.81592 | − | 6.60937i | −0.198649 | − | 0.344070i | ||||
\(370\) | −0.00816384 | + | 0.218205i | −0.000424418 | + | 0.0113439i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.78879 | − | 6.78879i | −0.351982 | − | 0.351982i | ||||
\(373\) | 4.70591 | + | 1.26094i | 0.243663 | + | 0.0652892i | 0.378583 | − | 0.925567i | \(-0.376411\pi\) |
−0.134921 | + | 0.990856i | \(0.543078\pi\) | |||||||
\(374\) | 1.11763 | − | 1.93578i | 0.0577911 | − | 0.100097i | ||||
\(375\) | −11.0554 | + | 1.66647i | −0.570901 | + | 0.0860559i | ||||
\(376\) | 0.348426 | − | 0.201164i | 0.0179687 | − | 0.0103742i | ||||
\(377\) | −1.82755 | + | 1.82755i | −0.0941237 | + | 0.0941237i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 12.9179i | − | 0.663547i | −0.943359 | − | 0.331773i | \(-0.892353\pi\) | ||
0.943359 | − | 0.331773i | \(-0.107647\pi\) | |||||||
\(380\) | 27.7445 | − | 14.6636i | 1.42327 | − | 0.752224i | ||||
\(381\) | −7.21175 | − | 4.16371i | −0.369469 | − | 0.213313i | ||||
\(382\) | 3.48918 | − | 0.934923i | 0.178522 | − | 0.0478348i | ||||
\(383\) | 3.68844 | − | 13.7654i | 0.188470 | − | 0.703381i | −0.805391 | − | 0.592744i | \(-0.798044\pi\) |
0.993861 | − | 0.110636i | \(-0.0352889\pi\) | |||||||
\(384\) | −7.04142 | −0.359331 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.98291 | 0.151826 | ||||||||
\(387\) | 1.33669 | − | 4.98860i | 0.0679479 | − | 0.253585i | ||||
\(388\) | −19.7504 | + | 5.29212i | −1.00268 | + | 0.268666i | ||||
\(389\) | −21.0704 | − | 12.1650i | −1.06831 | − | 0.616791i | −0.140593 | − | 0.990068i | \(-0.544901\pi\) |
−0.927720 | + | 0.373277i | \(0.878234\pi\) | |||||||
\(390\) | 0.357265 | + | 0.110200i | 0.0180908 | + | 0.00558021i | ||||
\(391\) | 17.3213i | 0.875976i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.3038 | + | 13.3038i | −0.671089 | + | 0.671089i | ||||
\(394\) | 0.777524 | − | 0.448904i | 0.0391711 | − | 0.0226154i | ||||
\(395\) | 16.3589 | + | 10.2789i | 0.823108 | + | 0.517189i | ||||
\(396\) | −3.87478 | + | 6.71132i | −0.194715 | + | 0.337256i | ||||
\(397\) | 9.29762 | + | 2.49129i | 0.466634 | + | 0.125034i | 0.484472 | − | 0.874807i | \(-0.339012\pi\) |
−0.0178380 | + | 0.999841i | \(0.505678\pi\) | |||||||
\(398\) | 0.103013 | + | 0.103013i | 0.00516356 | + | 0.00516356i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.2898 | − | 1.37050i | −0.914492 | − | 0.0685249i | ||||
\(401\) | 4.41545 | + | 7.64778i | 0.220497 | + | 0.381912i | 0.954959 | − | 0.296738i | \(-0.0958987\pi\) |
−0.734462 | + | 0.678650i | \(0.762565\pi\) | |||||||
\(402\) | −0.0816479 | − | 0.304714i | −0.00407223 | − | 0.0151978i | ||||
\(403\) | 0.904546 | + | 3.37581i | 0.0450587 | + | 0.168161i | ||||
\(404\) | −6.14006 | − | 10.6349i | −0.305479 | − | 0.529105i | ||||
\(405\) | 2.23450 | + | 0.0836010i | 0.111033 | + | 0.00415417i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.16501 | + | 1.16501i | 0.0577476 | + | 0.0577476i | ||||
\(408\) | −2.13643 | − | 0.572453i | −0.105769 | − | 0.0283407i | ||||
\(409\) | −11.5992 | + | 20.0905i | −0.573546 | + | 0.993410i | 0.422652 | + | 0.906292i | \(0.361099\pi\) |
−0.996198 | + | 0.0871183i | \(0.972234\pi\) | |||||||
\(410\) | 0.897158 | + | 3.93064i | 0.0443075 | + | 0.194120i | ||||
\(411\) | 0.994464 | − | 0.574154i | 0.0490533 | − | 0.0283209i | ||||
\(412\) | 24.3819 | − | 24.3819i | 1.20121 | − | 1.20121i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.72404i | 0.0847319i | ||||||||
\(415\) | −11.1753 | + | 36.2298i | −0.548572 | + | 1.77845i | ||||
\(416\) | 1.67341 | + | 0.966143i | 0.0820456 | + | 0.0473690i | ||||
\(417\) | 0.427364 | − | 0.114512i | 0.0209281 | − | 0.00560766i | ||||
\(418\) | −1.75938 | + | 6.56610i | −0.0860541 | + | 0.321158i | ||||
\(419\) | −13.0393 | −0.637009 | −0.318505 | − | 0.947921i | \(-0.603181\pi\) | ||||
−0.318505 | + | 0.947921i | \(0.603181\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.3549 | −1.52814 | −0.764071 | − | 0.645132i | \(-0.776802\pi\) | ||||
−0.764071 | + | 0.645132i | \(0.776802\pi\) | |||||||
\(422\) | −0.569183 | + | 2.12422i | −0.0277074 | + | 0.103405i | ||||
\(423\) | −0.417052 | + | 0.111749i | −0.0202778 | + | 0.00543341i | ||||
\(424\) | −6.15877 | − | 3.55577i | −0.299096 | − | 0.172683i | ||||
\(425\) | −11.2021 | − | 3.91969i | −0.543382 | − | 0.190133i | ||||
\(426\) | 0.281842i | 0.0136553i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.5429 | − | 14.5429i | 0.702957 | − | 0.702957i | ||||
\(429\) | 2.44307 | − | 1.41050i | 0.117952 | − | 0.0680998i | ||||
\(430\) | −1.45155 | + | 2.31015i | −0.0700000 | + | 0.111405i | ||||
\(431\) | 11.2779 | − | 19.5339i | 0.543238 | − | 0.940915i | −0.455478 | − | 0.890247i | \(-0.650532\pi\) |
0.998716 | − | 0.0506681i | \(-0.0161351\pi\) | |||||||
\(432\) | 3.54323 | + | 0.949406i | 0.170474 | + | 0.0456783i | ||||
\(433\) | 19.9639 | + | 19.9639i | 0.959405 | + | 0.959405i | 0.999208 | − | 0.0398028i | \(-0.0126730\pi\) |
−0.0398028 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.98602 | − | 5.55426i | 0.287008 | − | 0.266306i | ||||
\(436\) | −0.649575 | − | 1.12510i | −0.0311090 | − | 0.0538824i | ||||
\(437\) | −13.6337 | − | 50.8816i | −0.652188 | − | 2.43400i | ||||
\(438\) | 0.119592 | + | 0.446325i | 0.00571435 | + | 0.0213262i | ||||
\(439\) | 15.0972 | + | 26.1490i | 0.720548 | + | 1.24803i | 0.960780 | + | 0.277310i | \(0.0894430\pi\) |
−0.240232 | + | 0.970715i | \(0.577224\pi\) | |||||||
\(440\) | 6.08824 | − | 5.64910i | 0.290246 | − | 0.269310i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.280632 | + | 0.280632i | 0.0133483 | + | 0.0133483i | ||||
\(443\) | 17.4063 | + | 4.66400i | 0.826997 | + | 0.221593i | 0.647403 | − | 0.762148i | \(-0.275855\pi\) |
0.179594 | + | 0.983741i | \(0.442522\pi\) | |||||||
\(444\) | 0.401803 | − | 0.695944i | 0.0190687 | − | 0.0330280i | ||||
\(445\) | −9.30999 | + | 14.8169i | −0.441336 | + | 0.702388i | ||||
\(446\) | −0.392082 | + | 0.226369i | −0.0185656 | + | 0.0107189i | ||||
\(447\) | −2.22112 | + | 2.22112i | −0.105056 | + | 0.105056i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4170i | 1.43547i | 0.696318 | + | 0.717734i | \(0.254820\pi\) | ||||
−0.696318 | + | 0.717734i | \(0.745180\pi\) | |||||||
\(450\) | −1.11498 | − | 0.390138i | −0.0525605 | − | 0.0183913i | ||||
\(451\) | 26.3451 | + | 15.2103i | 1.24054 | + | 0.716227i | ||||
\(452\) | −9.02051 | + | 2.41704i | −0.424289 | + | 0.113688i | ||||
\(453\) | 3.81084 | − | 14.2222i | 0.179049 | − | 0.668219i | ||||
\(454\) | 1.38802 | 0.0651432 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.72637 | 0.314991 | ||||||||
\(457\) | 0.481493 | − | 1.79696i | 0.0225233 | − | 0.0840581i | −0.953749 | − | 0.300603i | \(-0.902812\pi\) |
0.976273 | + | 0.216545i | \(0.0694788\pi\) | |||||||
\(458\) | −2.96435 | + | 0.794295i | −0.138515 | + | 0.0371150i | ||||
\(459\) | 2.05561 | + | 1.18681i | 0.0959476 | + | 0.0553954i | ||||
\(460\) | −9.35081 | + | 30.3150i | −0.435984 | + | 1.41344i | ||||
\(461\) | 1.29957i | 0.0605272i | 0.999542 | + | 0.0302636i | \(0.00963467\pi\) | ||||
−0.999542 | + | 0.0302636i | \(0.990365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.5240 | − | 16.5240i | 0.767934 | − | 0.767934i | −0.209809 | − | 0.977742i | \(-0.567284\pi\) |
0.977742 | + | 0.209809i | \(0.0672841\pi\) | |||||||
\(464\) | 11.6013 | − | 6.69801i | 0.538577 | − | 0.310947i | ||||
\(465\) | −2.45716 | − | 10.7653i | −0.113948 | − | 0.499230i | ||||
\(466\) | −2.75039 | + | 4.76381i | −0.127409 | + | 0.220679i | ||||
\(467\) | 27.4583 | + | 7.35742i | 1.27062 | + | 0.340461i | 0.830267 | − | 0.557365i | \(-0.188188\pi\) |
0.440350 | + | 0.897826i | \(0.354854\pi\) | |||||||
\(468\) | −0.972943 | − | 0.972943i | −0.0449743 | − | 0.0449743i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.227932 | + | 0.00852775i | 0.0105137 | + | 0.000393356i | ||||
\(471\) | 5.63216 | + | 9.75519i | 0.259516 | + | 0.449495i | ||||
\(472\) | 1.47347 | + | 5.49908i | 0.0678221 | + | 0.253116i | ||||
\(473\) | 5.32808 | + | 19.8847i | 0.244986 | + | 0.914298i | ||||
\(474\) | 1.02064 | + | 1.76781i | 0.0468797 | + | 0.0811980i | ||||
\(475\) | 35.9916 | + | 2.69693i | 1.65141 | + | 0.123744i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.39653 | + | 5.39653i | 0.247090 | + | 0.247090i | ||||
\(478\) | −1.25066 | − | 0.335113i | −0.0572038 | − | 0.0153277i | ||||
\(479\) | −5.54182 | + | 9.59872i | −0.253212 | + | 0.438577i | −0.964408 | − | 0.264417i | \(-0.914820\pi\) |
0.711196 | + | 0.702994i | \(0.248154\pi\) | |||||||
\(480\) | −5.16933 | − | 3.24808i | −0.235947 | − | 0.148254i | ||||
\(481\) | −0.253339 | + | 0.146265i | −0.0115513 | + | 0.00666912i | ||||
\(482\) | 2.44749 | − | 2.44749i | 0.111480 | − | 0.111480i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 9.50389i | − | 0.431995i | ||||||
\(485\) | −22.4722 | − | 6.93165i | −1.02041 | − | 0.314750i | ||||
\(486\) | 0.204601 | + | 0.118126i | 0.00928088 | + | 0.00535832i | ||||
\(487\) | 18.6489 | − | 4.99695i | 0.845060 | − | 0.226433i | 0.189787 | − | 0.981825i | \(-0.439220\pi\) |
0.655273 | + | 0.755392i | \(0.272554\pi\) | |||||||
\(488\) | −1.71486 | + | 6.39994i | −0.0776280 | + | 0.289712i | ||||
\(489\) | −14.7714 | −0.667986 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1155 | 1.44935 | 0.724677 | − | 0.689089i | \(-0.241989\pi\) | ||||
0.724677 | + | 0.689089i | \(0.241989\pi\) | |||||||
\(492\) | 3.84028 | − | 14.3321i | 0.173133 | − | 0.646142i | ||||
\(493\) | 8.37286 | − | 2.24350i | 0.377095 | − | 0.101042i | ||||
\(494\) | −1.04525 | − | 0.603474i | −0.0470279 | − | 0.0271516i | ||||
\(495\) | −7.88012 | + | 4.16480i | −0.354185 | + | 0.187194i | ||||
\(496\) | − | 18.1145i | − | 0.813364i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.83255 | + | 2.83255i | −0.126930 | + | 0.126930i | ||||
\(499\) | 3.70166 | − | 2.13715i | 0.165709 | − | 0.0956722i | −0.414852 | − | 0.909889i | \(-0.636167\pi\) |
0.580561 | + | 0.814217i | \(0.302833\pi\) | |||||||
\(500\) | −17.4894 | − | 12.9075i | −0.782150 | − | 0.577239i | ||||
\(501\) | −3.27830 | + | 5.67818i | −0.146463 | + | 0.253682i | ||||
\(502\) | 4.82662 | + | 1.29329i | 0.215423 | + | 0.0577223i | ||||
\(503\) | −17.5637 | − | 17.5637i | −0.783128 | − | 0.783128i | 0.197229 | − | 0.980357i | \(-0.436806\pi\) |
−0.980357 | + | 0.197229i | \(0.936806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.528051 | − | 14.1139i | 0.0234980 | − | 0.628059i | ||||
\(506\) | −3.43603 | − | 5.95138i | −0.152750 | − | 0.264571i | ||||
\(507\) | −3.23501 | − | 12.0732i | −0.143672 | − | 0.536191i | ||||
\(508\) | −4.19029 | − | 15.6384i | −0.185914 | − | 0.693840i | ||||
\(509\) | −13.9581 | − | 24.1762i | −0.618682 | − | 1.07159i | −0.989726 | − | 0.142974i | \(-0.954333\pi\) |
0.371044 | − | 0.928615i | \(-0.379000\pi\) | |||||||
\(510\) | −0.852889 | − | 0.919189i | −0.0377666 | − | 0.0407024i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −11.9158 | − | 11.9158i | −0.526611 | − | 0.526611i | ||||
\(513\) | −6.97254 | − | 1.86829i | −0.307845 | − | 0.0824868i | ||||
\(514\) | 1.56907 | − | 2.71771i | 0.0692086 | − | 0.119873i | ||||
\(515\) | 38.6636 | − | 8.82487i | 1.70372 | − | 0.388870i | ||||
\(516\) | 8.69567 | − | 5.02045i | 0.382806 | − | 0.221013i | ||||
\(517\) | 1.21695 | − | 1.21695i | 0.0535212 | − | 0.0535212i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.51476i | − | 0.154281i | ||||||
\(520\) | 0.689054 | + | 1.30374i | 0.0302170 | + | 0.0571729i | ||||
\(521\) | 24.9975 | + | 14.4323i | 1.09516 | + | 0.632292i | 0.934946 | − | 0.354790i | \(-0.115448\pi\) |
0.160216 | + | 0.987082i | \(0.448781\pi\) | |||||||
\(522\) | 0.833375 | − | 0.223302i | 0.0364758 | − | 0.00977367i | ||||
\(523\) | 1.29832 | − | 4.84539i | 0.0567715 | − | 0.211874i | −0.931713 | − | 0.363195i | \(-0.881686\pi\) |
0.988485 | + | 0.151321i | \(0.0483526\pi\) | |||||||
\(524\) | −36.5788 | −1.59795 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.13793 | −0.224024 | ||||||||
\(527\) | 3.03372 | − | 11.3220i | 0.132151 | − | 0.493195i | ||||
\(528\) | −14.1234 | + | 3.78435i | −0.614642 | + | 0.164693i | ||||
\(529\) | 26.1995 | + | 15.1263i | 1.13911 | + | 0.657665i | ||||
\(530\) | −1.88391 | − | 3.56450i | −0.0818319 | − | 0.154832i | ||||
\(531\) | − | 6.10959i | − | 0.265134i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.81926 | + | 3.81926i | −0.165430 | + | 0.165430i | ||||
\(534\) | −1.60117 | + | 0.924434i | −0.0692892 | + | 0.0400042i | ||||
\(535\) | 23.0614 | − | 5.26370i | 0.997031 | − | 0.227570i | ||||
\(536\) | 0.622122 | − | 1.07755i | 0.0268716 | − | 0.0465430i | ||||
\(537\) | −21.3574 | − | 5.72271i | −0.921642 | − | 0.246953i | ||||
\(538\) | −3.83980 | − | 3.83980i | −0.165546 | − | 0.165546i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.95695 | + | 3.18681i | 0.127247 | + | 0.137138i | ||||
\(541\) | 2.04349 | + | 3.53943i | 0.0878565 | + | 0.152172i | 0.906605 | − | 0.421981i | \(-0.138665\pi\) |
−0.818748 | + | 0.574153i | \(0.805332\pi\) | |||||||
\(542\) | −0.963650 | − | 3.59639i | −0.0413923 | − | 0.154478i | ||||
\(543\) | −2.19615 | − | 8.19615i | −0.0942459 | − | 0.351731i | ||||
\(544\) | −3.24031 | − | 5.61238i | −0.138927 | − | 0.240629i | ||||
\(545\) | 0.0558641 | − | 1.49315i | 0.00239296 | − | 0.0639594i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.2200 | + | 28.2200i | 1.20660 | + | 1.20660i | 0.972121 | + | 0.234482i | \(0.0753392\pi\) |
0.234482 | + | 0.972121i | \(0.424661\pi\) | |||||||
\(548\) | 2.15645 | + | 0.577820i | 0.0921191 | + | 0.0246832i | ||||
\(549\) | 3.55523 | − | 6.15784i | 0.151734 | − | 0.262810i | ||||
\(550\) | 4.62645 | − | 0.875407i | 0.197272 | − | 0.0373275i | ||||
\(551\) | −22.8296 | + | 13.1807i | −0.972572 | + | 0.561515i | ||||
\(552\) | −4.80827 | + | 4.80827i | −0.204654 | + | 0.204654i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 1.60631i | − | 0.0682457i | ||||||
\(555\) | 0.817145 | − | 0.431878i | 0.0346859 | − | 0.0183322i | ||||
\(556\) | 0.744941 | + | 0.430092i | 0.0315925 | + | 0.0182400i | ||||
\(557\) | −38.4695 | + | 10.3079i | −1.63000 | + | 0.436758i | −0.953919 | − | 0.300065i | \(-0.902992\pi\) |
−0.676086 | + | 0.736823i | \(0.736325\pi\) | |||||||
\(558\) | 0.301955 | − | 1.12691i | 0.0127828 | − | 0.0477060i | ||||
\(559\) | −3.65510 | −0.154594 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.46128 | −0.399455 | ||||||||
\(562\) | 0.590468 | − | 2.20366i | 0.0249074 | − | 0.0929556i | ||||
\(563\) | −37.3806 | + | 10.0161i | −1.57541 | + | 0.422129i | −0.937500 | − | 0.347985i | \(-0.886866\pi\) |
−0.637906 | + | 0.770114i | \(0.720199\pi\) | |||||||
\(564\) | −0.726967 | − | 0.419715i | −0.0306108 | − | 0.0176732i | ||||
\(565\) | −10.2636 | − | 3.16586i | −0.431792 | − | 0.133189i | ||||
\(566\) | 4.98144i | 0.209386i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.786047 | + | 0.786047i | −0.0329818 | + | 0.0329818i | ||||
\(569\) | −15.3951 | + | 8.88837i | −0.645396 | + | 0.372620i | −0.786690 | − | 0.617348i | \(-0.788207\pi\) |
0.141294 | + | 0.989968i | \(0.454874\pi\) | |||||||
\(570\) | 3.22888 | + | 2.02882i | 0.135243 | + | 0.0849780i | ||||
\(571\) | 8.44331 | − | 14.6242i | 0.353342 | − | 0.612005i | −0.633491 | − | 0.773750i | \(-0.718379\pi\) |
0.986833 | + | 0.161744i | \(0.0517120\pi\) | |||||||
\(572\) | 5.29768 | + | 1.41951i | 0.221507 | + | 0.0593527i | ||||
\(573\) | −10.8116 | − | 10.8116i | −0.451659 | − | 0.451659i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −27.6561 | + | 23.8003i | −1.15334 | + | 0.992543i | ||||
\(576\) | 3.34571 | + | 5.79493i | 0.139404 | + | 0.241456i | ||||
\(577\) | −1.42632 | − | 5.32309i | −0.0593784 | − | 0.221603i | 0.929861 | − | 0.367912i | \(-0.119927\pi\) |
−0.989239 | + | 0.146309i | \(0.953261\pi\) | |||||||
\(578\) | 0.694991 | + | 2.59374i | 0.0289078 | + | 0.107885i | ||||
\(579\) | −6.31296 | − | 10.9344i | −0.262358 | − | 0.454417i | ||||
\(580\) | 15.8650 | + | 0.593566i | 0.658756 | + | 0.0246465i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.75694 | − | 1.75694i | −0.0728276 | − | 0.0728276i | ||||
\(583\) | −29.3841 | − | 7.87345i | −1.21697 | − | 0.326085i | ||||
\(584\) | −0.911244 | + | 1.57832i | −0.0377075 | + | 0.0653114i | ||||
\(585\) | −0.352150 | − | 1.54284i | −0.0145596 | − | 0.0637887i | ||||
\(586\) | 1.38667 | − | 0.800592i | 0.0572826 | − | 0.0330721i | ||||
\(587\) | 15.1058 | − | 15.1058i | 0.623484 | − | 0.623484i | −0.322937 | − | 0.946420i | \(-0.604670\pi\) |
0.946420 | + | 0.322937i | \(0.104670\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6465i | 1.46879i | ||||||||
\(590\) | −0.951328 | + | 3.08417i | −0.0391655 | + | 0.126973i | ||||
\(591\) | −3.29107 | − | 1.90010i | −0.135377 | − | 0.0781597i | ||||
\(592\) | 1.46456 | − | 0.392426i | 0.0601928 | − | 0.0161286i | ||||
\(593\) | 1.25558 | − | 4.68590i | 0.0515606 | − | 0.192427i | −0.935342 | − | 0.353745i | \(-0.884908\pi\) |
0.986902 | + | 0.161318i | \(0.0515746\pi\) | |||||||
\(594\) | −0.941708 | −0.0386388 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.10696 | −0.250151 | ||||||||
\(597\) | 0.159597 | − | 0.595625i | 0.00653188 | − | 0.0243773i | ||||
\(598\) | 1.17857 | − | 0.315797i | 0.0481953 | − | 0.0129139i | ||||
\(599\) | −8.74769 | − | 5.05048i | −0.357421 | − | 0.206357i | 0.310528 | − | 0.950564i | \(-0.399494\pi\) |
−0.667949 | + | 0.744207i | \(0.732827\pi\) | |||||||
\(600\) | −2.02155 | − | 4.19771i | −0.0825293 | − | 0.171371i | ||||
\(601\) | 38.4063i | 1.56663i | 0.621628 | + | 0.783313i | \(0.286472\pi\) | ||||
−0.621628 | + | 0.783313i | \(0.713528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.944185 | + | 0.944185i | −0.0384502 | + | 0.0384502i | ||||
\(604\) | 24.7909 | − | 14.3130i | 1.00873 | − | 0.582389i | ||||
\(605\) | 5.81546 | − | 9.25533i | 0.236432 | − | 0.376283i | ||||
\(606\) | 0.746125 | − | 1.29233i | 0.0303093 | − | 0.0524972i | ||||
\(607\) | 14.0606 | + | 3.76752i | 0.570702 | + | 0.152919i | 0.532618 | − | 0.846356i | \(-0.321208\pi\) |
0.0380833 | + | 0.999275i | \(0.487875\pi\) | |||||||
\(608\) | 13.9360 | + | 13.9360i | 0.565180 | + | 0.565180i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.75355 | + | 2.55494i | −0.111488 | + | 0.103447i | ||||
\(611\) | 0.152785 | + | 0.264632i | 0.00618103 | + | 0.0107059i | ||||
\(612\) | 1.19438 | + | 4.45750i | 0.0482801 | + | 0.180184i | ||||
\(613\) | −5.27642 | − | 19.6919i | −0.213113 | − | 0.795347i | −0.986822 | − | 0.161807i | \(-0.948268\pi\) |
0.773710 | − | 0.633540i | \(-0.218399\pi\) | |||||||
\(614\) | −1.64560 | − | 2.85027i | −0.0664112 | − | 0.115028i | ||||
\(615\) | 12.5097 | − | 11.6074i | 0.504440 | − | 0.468056i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4196 | − | 25.4196i | −1.02336 | − | 1.02336i | −0.999721 | − | 0.0236346i | \(-0.992476\pi\) |
−0.0236346 | − | 0.999721i | \(-0.507524\pi\) | |||||||
\(618\) | 4.04731 | + | 1.08447i | 0.162807 | + | 0.0436239i | ||||
\(619\) | −5.59953 | + | 9.69868i | −0.225064 | + | 0.389823i | −0.956339 | − | 0.292261i | \(-0.905593\pi\) |
0.731274 | + | 0.682083i | \(0.238926\pi\) | |||||||
\(620\) | 11.4216 | − | 18.1775i | 0.458703 | − | 0.730028i | ||||
\(621\) | 6.31977 | − | 3.64872i | 0.253603 | − | 0.146418i | ||||
\(622\) | 4.56168 | − | 4.56168i | 0.182907 | − | 0.182907i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 2.59609i | − | 0.103927i | ||||||
\(625\) | −9.13387 | − | 23.2717i | −0.365355 | − | 0.930868i | ||||
\(626\) | −5.35527 | − | 3.09186i | −0.214040 | − | 0.123576i | ||||
\(627\) | 27.7927 | − | 7.44703i | 1.10993 | − | 0.297406i | ||||
\(628\) | −5.66812 | + | 21.1537i | −0.226182 | + | 0.844124i | ||||
\(629\) | 0.981107 | 0.0391193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.2015 | 0.844020 | 0.422010 | − | 0.906591i | \(-0.361325\pi\) | ||||
0.422010 | + | 0.906591i | \(0.361325\pi\) | |||||||
\(632\) | −2.08381 | + | 7.77687i | −0.0828894 | + | 0.309347i | ||||
\(633\) | 8.99131 | − | 2.40921i | 0.357373 | − | 0.0957577i | ||||
\(634\) | −6.33077 | − | 3.65507i | −0.251427 | − | 0.145161i | ||||
\(635\) | 5.48847 | − | 17.7934i | 0.217803 | − | 0.706110i | ||||
\(636\) | 14.8377i | 0.588353i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.43176 | + | 2.43176i | −0.0962745 | + | 0.0962745i | ||||
\(639\) | 1.03314 | − | 0.596485i | 0.0408705 | − | 0.0235966i | ||||
\(640\) | −3.50367 | − | 15.3503i | −0.138495 | − | 0.606774i | ||||
\(641\) | 14.9484 | − | 25.8915i | 0.590428 | − | 1.02265i | −0.403746 | − | 0.914871i | \(-0.632292\pi\) |
0.994175 | − | 0.107781i | \(-0.0343745\pi\) | |||||||
\(642\) | 2.41406 | + | 0.646846i | 0.0952755 | + | 0.0255290i | ||||
\(643\) | −11.2813 | − | 11.2813i | −0.444891 | − | 0.444891i | 0.448761 | − | 0.893652i | \(-0.351866\pi\) |
−0.893652 | + | 0.448761i | \(0.851866\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.5403 | + | 0.431764i | 0.454398 | + | 0.0170007i | ||||
\(646\) | 2.02397 | + | 3.50562i | 0.0796320 | + | 0.137927i | ||||
\(647\) | 9.60434 | + | 35.8439i | 0.377586 | + | 1.40917i | 0.849530 | + | 0.527540i | \(0.176886\pi\) |
−0.471944 | + | 0.881628i | \(0.656448\pi\) | |||||||
\(648\) | 0.241174 | + | 0.900073i | 0.00947420 | + | 0.0353582i | ||||
\(649\) | 12.1765 | + | 21.0903i | 0.477969 | + | 0.827866i | ||||
\(650\) | −0.0624689 | + | 0.833673i | −0.00245023 | + | 0.0326993i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.3069 | − | 20.3069i | −0.795281 | − | 0.795281i | ||||
\(653\) | 2.69982 | + | 0.723414i | 0.105652 | + | 0.0283094i | 0.311258 | − | 0.950326i | \(-0.399250\pi\) |
−0.205606 | + | 0.978635i | \(0.565916\pi\) | |||||||
\(654\) | 0.0789348 | − | 0.136719i | 0.00308659 | − | 0.00534614i | ||||
\(655\) | −35.6221 | − | 22.3827i | −1.39187 | − | 0.874563i | ||||
\(656\) | 24.2446 | − | 13.9976i | 0.946594 | − | 0.546516i | ||||
\(657\) | 1.38298 | − | 1.38298i | 0.0539552 | − | 0.0539552i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 15.1044i | − | 0.588385i | −0.955746 | − | 0.294193i | \(-0.904949\pi\) | ||
0.955746 | − | 0.294193i | \(-0.0950507\pi\) | |||||||
\(660\) | −16.5587 | − | 5.10762i | −0.644547 | − | 0.198814i | ||||
\(661\) | −0.953098 | − | 0.550272i | −0.0370712 | − | 0.0214031i | 0.481350 | − | 0.876529i | \(-0.340147\pi\) |
−0.518421 | + | 0.855125i | \(0.673480\pi\) | |||||||
\(662\) | −3.80900 | + | 1.02062i | −0.148041 | + | 0.0396675i | ||||
\(663\) | 0.434781 | − | 1.62263i | 0.0168855 | − | 0.0630176i | ||||
\(664\) | −15.7998 | −0.613150 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0976524 | 0.00378395 | ||||||||
\(667\) | 6.89742 | − | 25.7415i | 0.267069 | − | 0.996716i | ||||
\(668\) | −12.3129 | + | 3.29923i | −0.476399 | + | 0.127651i | ||||
\(669\) | 1.65959 | + | 0.958163i | 0.0641633 | + | 0.0370447i | ||||
\(670\) | 0.623651 | − | 0.329612i | 0.0240937 | − | 0.0127340i | ||||
\(671\) | 28.3425i | 1.09415i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.4381 | + | 11.4381i | −0.440906 | + | 0.440906i | −0.892316 | − | 0.451411i | \(-0.850921\pi\) |
0.451411 | + | 0.892316i | \(0.350921\pi\) | |||||||
\(674\) | −0.735028 | + | 0.424369i | −0.0283122 | + | 0.0163461i | ||||
\(675\) | 0.929594 | + | 4.91283i | 0.0357801 | + | 0.189095i | ||||
\(676\) | 12.1503 | − | 21.0449i | 0.467319 | − | 0.809421i | ||||
\(677\) | −33.6052 | − | 9.00447i | −1.29155 | − | 0.346070i | −0.453302 | − | 0.891357i | \(-0.649754\pi\) |
−0.838249 | + | 0.545287i | \(0.816421\pi\) | |||||||
\(678\) | −0.802438 | − | 0.802438i | −0.0308175 | − | 0.0308175i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.184908 | − | 4.94226i | 0.00709089 | − | 0.189527i | ||||
\(681\) | −2.93759 | − | 5.08805i | −0.112569 | − | 0.194974i | ||||
\(682\) | 1.20360 | + | 4.49190i | 0.0460882 | + | 0.172004i | ||||
\(683\) | −5.07507 | − | 18.9404i | −0.194192 | − | 0.724736i | −0.992474 | − | 0.122452i | \(-0.960924\pi\) |
0.798282 | − | 0.602284i | \(-0.205742\pi\) | |||||||
\(684\) | −7.01705 | − | 12.1539i | −0.268304 | − | 0.464715i | ||||
\(685\) | 1.74648 | + | 1.88225i | 0.0667297 | + | 0.0719170i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.18531 | + | 9.18531i | 0.350442 | + | 0.350442i | ||||
\(688\) | 18.2993 | + | 4.90328i | 0.697655 | + | 0.186936i | ||||
\(689\) | 2.70062 | − | 4.67762i | 0.102886 | − | 0.178203i | ||||
\(690\) | −3.75841 | + | 0.857847i | −0.143080 | + | 0.0326577i | ||||
\(691\) | 10.7439 | − | 6.20301i | 0.408718 | − | 0.235974i | −0.281521 | − | 0.959555i | \(-0.590839\pi\) |
0.690239 | + | 0.723582i | \(0.257505\pi\) | |||||||
\(692\) | 4.83190 | − | 4.83190i | 0.183681 | − | 0.183681i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 4.57667i | − | 0.173728i | ||||||
\(695\) | 0.462284 | + | 0.874675i | 0.0175354 | + | 0.0331783i | ||||
\(696\) | 2.94703 | + | 1.70147i | 0.111707 | + | 0.0644940i | ||||
\(697\) | 17.4978 | − | 4.68852i | 0.662776 | − | 0.177590i | ||||
\(698\) | 0.0310993 | − | 0.116064i | 0.00117713 | − | 0.00439309i | ||||
\(699\) | 23.2835 | 0.880661 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.45193 | 0.0548388 | 0.0274194 | − | 0.999624i | \(-0.491271\pi\) | ||||
0.0274194 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(702\) | 0.0432751 | − | 0.161505i | 0.00163331 | − | 0.00609560i | ||||
\(703\) | −2.88202 | + | 0.772235i | −0.108697 | + | 0.0291254i | ||||
\(704\) | −23.0987 | − | 13.3361i | −0.870566 | − | 0.502622i | ||||
\(705\) | −0.451129 | − | 0.853571i | −0.0169905 | − | 0.0321473i | ||||
\(706\) | 3.64907i | 0.137335i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.39914 | − | 8.39914i | 0.315659 | − | 0.315659i | ||||
\(709\) | −42.0269 | + | 24.2642i | −1.57835 | + | 0.911262i | −0.583262 | + | 0.812284i | \(0.698224\pi\) |
−0.995090 | + | 0.0989781i | \(0.968443\pi\) | |||||||
\(710\) | −0.614417 | + | 0.140239i | −0.0230587 | + | 0.00526308i | ||||
\(711\) | 4.32013 | − | 7.48269i | 0.162018 | − | 0.280623i | ||||
\(712\) | −7.04380 | − | 1.88738i | −0.263977 | − | 0.0707325i | ||||
\(713\) | −25.4815 | − | 25.4815i | −0.954290 | − | 0.954290i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.29052 | + | 4.62405i | 0.160457 | + | 0.172930i | ||||
\(716\) | −21.4938 | − | 37.2283i | −0.803261 | − | 1.39129i | ||||
\(717\) | 1.41845 | + | 5.29373i | 0.0529730 | + | 0.197698i | ||||
\(718\) | −0.977492 | − | 3.64805i | −0.0364797 | − | 0.136144i | ||||
\(719\) | 21.7936 | + | 37.7476i | 0.812764 | + | 1.40775i | 0.910922 | + | 0.412578i | \(0.135372\pi\) |
−0.0981578 | + | 0.995171i | \(0.531295\pi\) | |||||||
\(720\) | −0.306667 | + | 8.19666i | −0.0114288 | + | 0.305472i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.53068 | − | 5.53068i | −0.205831 | − | 0.205831i | ||||
\(723\) | −14.1515 | − | 3.79189i | −0.526301 | − | 0.141022i | ||||
\(724\) | 8.24848 | − | 14.2868i | 0.306552 | − | 0.530964i | ||||
\(725\) | 15.0868 | + | 10.2859i | 0.560311 | + | 0.382007i | ||||
\(726\) | 1.00016 | − | 0.577445i | 0.0371196 | − | 0.0214310i | ||||
\(727\) | −10.4498 | + | 10.4498i | −0.387563 | + | 0.387563i | −0.873817 | − | 0.486254i | \(-0.838363\pi\) |
0.486254 | + | 0.873817i | \(0.338363\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −0.913483 | + | 0.482794i | −0.0338095 | + | 0.0178690i | ||||
\(731\) | 10.6164 | + | 6.12936i | 0.392660 | + | 0.226703i | ||||
\(732\) | 13.3530 | − | 3.57793i | 0.493542 | − | 0.132244i | ||||
\(733\) | −6.90644 | + | 25.7752i | −0.255095 | + | 0.952028i | 0.712942 | + | 0.701223i | \(0.247362\pi\) |
−0.968037 | + | 0.250806i | \(0.919305\pi\) | |||||||
\(734\) | 0.136998 | 0.00505669 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.9240 | −0.734409 | ||||||||
\(737\) | 1.37755 | − | 5.14109i | 0.0507428 | − | 0.189375i | ||||
\(738\) | 1.74161 | − | 0.466662i | 0.0641094 | − | 0.0171781i | ||||
\(739\) | −18.1596 | − | 10.4845i | −0.668013 | − | 0.385677i | 0.127311 | − | 0.991863i | \(-0.459366\pi\) |
−0.795323 | + | 0.606186i | \(0.792699\pi\) | |||||||
\(740\) | 1.71709 | + | 0.529645i | 0.0631215 | + | 0.0194701i | ||||
\(741\) | 5.10872i | 0.187673i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.18724 | − | 9.18724i | 0.337047 | − | 0.337047i | −0.518208 | − | 0.855255i | \(-0.673401\pi\) |
0.855255 | + | 0.518208i | \(0.173401\pi\) | |||||||
\(744\) | 3.98506 | − | 2.30077i | 0.146099 | − | 0.0843504i | ||||
\(745\) | −5.94724 | − | 3.73687i | −0.217890 | − | 0.136908i | ||||
\(746\) | −0.575501 | + | 0.996797i | −0.0210706 | + | 0.0364953i | ||||
\(747\) | 16.3780 | + | 4.38847i | 0.599239 | + | 0.160566i | ||||
\(748\) | −13.0069 | − | 13.0069i | −0.475578 | − | 0.475578i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.295712 | − | 2.62478i | 0.0107979 | − | 0.0958434i | ||||
\(751\) | −5.59843 | − | 9.69676i | −0.204290 | − | 0.353840i | 0.745617 | − | 0.666375i | \(-0.232155\pi\) |
−0.949906 | + | 0.312535i | \(0.898822\pi\) | |||||||
\(752\) | −0.409919 | − | 1.52984i | −0.0149482 | − | 0.0557875i | ||||
\(753\) | −5.47418 | − | 20.4299i | −0.199490 | − | 0.744507i | ||||
\(754\) | −0.305303 | − | 0.528801i | −0.0111185 | − | 0.0192578i | ||||
\(755\) | 32.9007 | + | 1.23094i | 1.19738 | + | 0.0447984i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9324 | − | 13.9324i | −0.506383 | − | 0.506383i | 0.407031 | − | 0.913414i | \(-0.366564\pi\) |
−0.913414 | + | 0.407031i | \(0.866564\pi\) | |||||||
\(758\) | 2.94789 | + | 0.789886i | 0.107072 | + | 0.0286899i | ||||
\(759\) | −14.5439 | + | 25.1907i | −0.527909 | + | 0.914365i | ||||
\(760\) | 3.34691 | + | 14.6635i | 0.121405 | + | 0.531902i | ||||
\(761\) | 7.61085 | − | 4.39412i | 0.275893 | − | 0.159287i | −0.355670 | − | 0.934612i | \(-0.615747\pi\) |
0.631563 | + | 0.775325i | \(0.282414\pi\) | |||||||
\(762\) | 1.39114 | − | 1.39114i | 0.0503958 | − | 0.0503958i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 29.7263i | − | 1.07546i | ||||||
\(765\) | −1.56441 | + | 5.07177i | −0.0565615 | + | 0.183370i | ||||
\(766\) | 2.91577 | + | 1.68342i | 0.105351 | + | 0.0608245i | ||||
\(767\) | −4.17658 | + | 1.11911i | −0.150808 | + | 0.0404088i | ||||
\(768\) | −3.03317 | + | 11.3199i | −0.109450 | + | 0.408473i | ||||
\(769\) | 11.2183 | 0.404543 | 0.202271 | − | 0.979330i | \(-0.435168\pi\) | ||||
0.202271 | + | 0.979330i | \(0.435168\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.2830 | −0.478374 | ||||||||
\(772\) | 6.35326 | − | 23.7107i | 0.228659 | − | 0.853366i | ||||
\(773\) | 29.3784 | − | 7.87192i | 1.05667 | − | 0.283133i | 0.311663 | − | 0.950193i | \(-0.399114\pi\) |
0.745005 | + | 0.667059i | \(0.232447\pi\) | |||||||
\(774\) | 1.05668 | + | 0.610073i | 0.0379815 | + | 0.0219286i | ||||
\(775\) | 22.2458 | − | 10.7132i | 0.799093 | − | 0.384830i | ||||
\(776\) | − | 9.80008i | − | 0.351802i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.06447 | − | 4.06447i | 0.145718 | − | 0.145718i | ||||
\(779\) | −47.7097 | + | 27.5452i | −1.70938 | + | 0.986910i | ||||
\(780\) | 1.63690 | − | 2.60514i | 0.0586105 | − | 0.0932788i | ||||
\(781\) | −2.37760 | + | 4.11813i | −0.0850773 | + | 0.147358i | ||||
\(782\) | −3.95276 | − | 1.05914i | −0.141351 | − | 0.0378748i | ||||
\(783\) | −2.58229 | − | 2.58229i | −0.0922835 | − | 0.0922835i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.4639 | + | 17.1321i | −0.659004 | + | 0.611471i | ||||
\(786\) | −2.22248 | − | 3.84945i | −0.0792733 | − | 0.137305i | ||||
\(787\) | −13.7140 | − | 51.1813i | −0.488851 | − | 1.82442i | −0.562055 | − | 0.827100i | \(-0.689989\pi\) |
0.0732040 | − | 0.997317i | \(-0.476678\pi\) | |||||||
\(788\) | −1.91223 | − | 7.13654i | −0.0681204 | − | 0.254229i | ||||
\(789\) | 10.8738 | + | 18.8340i | 0.387118 | + | 0.670507i | ||||
\(790\) | −3.34597 | + | 3.10463i | −0.119044 | + | 0.110458i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.62639 | − | 2.62639i | −0.0933246 | − | 0.0933246i | ||||
\(793\) | −4.86079 | − | 1.30244i | −0.172612 | − | 0.0462511i | ||||
\(794\) | −1.13704 | + | 1.96941i | −0.0403520 | + | 0.0698916i | ||||
\(795\) | −9.07924 | + | 14.4496i | −0.322007 | + | 0.512476i | ||||
\(796\) | 1.03824 | − | 0.599428i | 0.0367994 | − | 0.0212462i | ||||
\(797\) | −6.96365 | + | 6.96365i | −0.246665 | + | 0.246665i | −0.819601 | − | 0.572935i | \(-0.805805\pi\) |
0.572935 | + | 0.819601i | \(0.305805\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.02484i | − | 0.0362563i | ||||||
\(800\) | 4.50867 | − | 12.8853i | 0.159406 | − | 0.455566i | ||||
\(801\) | 6.77735 | + | 3.91290i | 0.239466 | + | 0.138256i | ||||
\(802\) | −2.01523 | + | 0.539980i | −0.0711604 | + | 0.0190674i | ||||
\(803\) | −2.01775 | + | 7.53033i | −0.0712047 | + | 0.265740i | ||||
\(804\) | −2.59603 | −0.0915549 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.825679 | −0.0290833 | ||||||||
\(807\) | −5.94899 | + | 22.2019i | −0.209414 | + | 0.781545i | ||||
\(808\) | 5.68516 | − | 1.52333i | 0.200003 | − | 0.0535907i | ||||
\(809\) | 36.5817 | + | 21.1205i | 1.28614 | + | 0.742556i | 0.977964 | − | 0.208772i | \(-0.0669466\pi\) |
0.308180 | + | 0.951328i | \(0.400280\pi\) | |||||||
\(810\) | −0.155711 | + | 0.504808i | −0.00547111 | + | 0.0177371i | ||||
\(811\) | 34.9480i | 1.22719i | 0.789620 | + | 0.613596i | \(0.210277\pi\) | ||||
−0.789620 | + | 0.613596i | \(0.789723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.1438 | + | 11.1438i | −0.390828 | + | 0.390828i | ||||
\(814\) | −0.337096 | + | 0.194622i | −0.0118152 | + | 0.00682151i | ||||
\(815\) | −7.34996 | − | 32.2017i | −0.257458 | − | 1.12798i | ||||
\(816\) | −4.35347 | + | 7.54044i | −0.152402 | + | 0.263968i | ||||
\(817\) | −36.0102 | − | 9.64891i | −1.25984 | − | 0.337573i | ||||
\(818\) | −3.87544 | − | 3.87544i | −0.135502 | − | 0.135502i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 33.1549 | + | 1.24045i | 1.15782 | + | 0.0433183i | ||||
\(821\) | 2.06708 | + | 3.58030i | 0.0721418 | + | 0.124953i | 0.899840 | − | 0.436221i | \(-0.143683\pi\) |
−0.827698 | + | 0.561174i | \(0.810350\pi\) | |||||||
\(822\) | 0.0702153 | + | 0.262047i | 0.00244904 | + | 0.00913994i | ||||
\(823\) | −2.09404 | − | 7.81506i | −0.0729936 | − | 0.272416i | 0.919777 | − | 0.392441i | \(-0.128369\pi\) |
−0.992771 | + | 0.120025i | \(0.961703\pi\) | |||||||
\(824\) | 8.26322 | + | 14.3123i | 0.287863 | + | 0.498593i | ||||
\(825\) | −13.0003 | − | 15.1064i | −0.452611 | − | 0.525936i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.0630 | + | 17.0630i | 0.593339 | + | 0.593339i | 0.938532 | − | 0.345193i | \(-0.112187\pi\) |
−0.345193 | + | 0.938532i | \(0.612187\pi\) | |||||||
\(828\) | 13.7041 | + | 3.67201i | 0.476252 | + | 0.127611i | ||||
\(829\) | −18.8573 | + | 32.6618i | −0.654940 | + | 1.13439i | 0.326968 | + | 0.945035i | \(0.393973\pi\) |
−0.981909 | + | 0.189355i | \(0.939360\pi\) | |||||||
\(830\) | −7.58440 | − | 4.76555i | −0.263258 | − | 0.165415i | ||||
\(831\) | −5.88822 | + | 3.39957i | −0.204260 | + | 0.117930i | ||||
\(832\) | 3.34863 | − | 3.34863i | 0.116093 | − | 0.116093i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.104527i | 0.00361949i | ||||||||
\(835\) | −14.0097 | − | 4.32135i | −0.484824 | − | 0.149546i | ||||
\(836\) | 48.4457 | + | 27.9701i | 1.67553 | + | 0.967367i | ||||
\(837\) | −4.76995 | + | 1.27810i | −0.164873 | + | 0.0441777i | ||||
\(838\) | 0.797307 | − | 2.97559i | 0.0275425 | − | 0.102790i | ||||
\(839\) | −22.3652 | −0.772133 | −0.386066 | − | 0.922471i | \(-0.626166\pi\) | ||||
−0.386066 | + | 0.922471i | \(0.626166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6636 | 0.540123 | ||||||||
\(842\) | 1.91725 | − | 7.15526i | 0.0660727 | − | 0.246587i | ||||
\(843\) | −9.32754 | + | 2.49931i | −0.321258 | + | 0.0860807i | ||||
\(844\) | 15.6728 | + | 9.04871i | 0.539481 | + | 0.311470i | ||||
\(845\) | 24.7100 | − | 13.0597i | 0.850050 | − | 0.449268i | ||||
\(846\) | − | 0.102005i | − | 0.00350702i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.7957 | + | 19.7957i | −0.679786 | + | 0.679786i | ||||
\(849\) | 18.2603 | − | 10.5426i | 0.626693 | − | 0.361822i | ||||
\(850\) | 1.57945 | − | 2.31667i | 0.0541749 | − | 0.0794612i | ||||
\(851\) | 1.50816 | − | 2.61220i | 0.0516989 | − | 0.0895452i | ||||
\(852\) | 2.24032 | + | 0.600293i | 0.0767522 | + | 0.0205657i | ||||
\(853\) | −24.1276 | − | 24.1276i | −0.826114 | − | 0.826114i | 0.160863 | − | 0.986977i | \(-0.448572\pi\) |
−0.986977 | + | 0.160863i | \(0.948572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.603474 | − | 16.1298i | 0.0206384 | − | 0.551627i | ||||
\(856\) | 4.92870 | + | 8.53675i | 0.168459 | + | 0.291780i | ||||
\(857\) | 0.560372 | + | 2.09134i | 0.0191419 | + | 0.0714387i | 0.974836 | − | 0.222923i | \(-0.0715597\pi\) |
−0.955694 | + | 0.294361i | \(0.904893\pi\) | |||||||
\(858\) | 0.172495 | + | 0.643761i | 0.00588889 | + | 0.0219777i | ||||
\(859\) | −20.9047 | − | 36.2081i | −0.713261 | − | 1.23540i | −0.963627 | − | 0.267253i | \(-0.913884\pi\) |
0.250366 | − | 0.968151i | \(-0.419449\pi\) | |||||||
\(860\) | 15.2714 | + | 16.4585i | 0.520750 | + | 0.561231i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.76808 | + | 3.76808i | 0.128341 | + | 0.128341i | ||||
\(863\) | 19.2128 | + | 5.14806i | 0.654011 | + | 0.175242i | 0.570542 | − | 0.821268i | \(-0.306733\pi\) |
0.0834696 | + | 0.996510i | \(0.473400\pi\) | |||||||
\(864\) | −1.36514 | + | 2.36449i | −0.0464429 | + | 0.0804415i | ||||
\(865\) | 7.66218 | − | 1.74887i | 0.260522 | − | 0.0594634i | ||||
\(866\) | −5.77654 | + | 3.33509i | −0.196295 | + | 0.113331i | ||||
\(867\) | 8.03695 | − | 8.03695i | 0.272949 | − | 0.272949i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.4403i | 1.16831i | ||||||||
\(870\) | 0.901470 | + | 1.70565i | 0.0305627 | + | 0.0578269i | ||||
\(871\) | 0.818403 | + | 0.472505i | 0.0277305 | + | 0.0160102i | ||||
\(872\) | 0.601450 | − | 0.161158i | 0.0203677 | − | 0.00545750i | ||||
\(873\) | −2.72202 | + | 10.1587i | −0.0921265 | + | 0.343821i | ||||
\(874\) | 12.4450 | 0.420958 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.80249 | 0.128474 | ||||||||
\(877\) | −14.4157 | + | 53.8001i | −0.486783 | + | 1.81670i | 0.0851110 | + | 0.996371i | \(0.472876\pi\) |
−0.571894 | + | 0.820328i | \(0.693791\pi\) | |||||||
\(878\) | −6.89042 | + | 1.84628i | −0.232540 | + | 0.0623090i | ||||
\(879\) | −5.86942 | − | 3.38871i | −0.197971 | − | 0.114298i | ||||
\(880\) | −15.2774 | − | 28.9060i | −0.515002 | − | 0.974422i | ||||
\(881\) | 25.7205i | 0.866546i | 0.901263 | + | 0.433273i | \(0.142641\pi\) | ||||
−0.901263 | + | 0.433273i | \(0.857359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.0968 | + | 25.0968i | −0.844574 | + | 0.844574i | −0.989450 | − | 0.144876i | \(-0.953722\pi\) |
0.144876 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(884\) | 2.82841 | − | 1.63299i | 0.0951298 | − | 0.0549232i | ||||
\(885\) | 13.3189 | − | 3.04001i | 0.447711 | − | 0.102189i | ||||
\(886\) | −2.12867 | + | 3.68697i | −0.0715142 | + | 0.123866i | ||||
\(887\) | −51.7651 | − | 13.8704i | −1.73810 | − | 0.465723i | −0.756077 | − | 0.654482i | \(-0.772887\pi\) |
−0.982023 | + | 0.188760i | \(0.939553\pi\) | |||||||
\(888\) | 0.272349 | + | 0.272349i | 0.00913942 | + | 0.00913942i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.81198 | − | 3.03057i | −0.0942577 | − | 0.101585i | ||||
\(891\) | 1.99301 | + | 3.45200i | 0.0667684 | + | 0.115646i | ||||
\(892\) | 0.964280 | + | 3.59874i | 0.0322865 | + | 0.120495i | ||||
\(893\) | 0.806659 | + | 3.01049i | 0.0269938 | + | 0.100742i | ||||
\(894\) | −0.371052 | − | 0.642680i | −0.0124098 | − | 0.0214944i | ||||
\(895\) | 1.84849 | − | 49.4068i | 0.0617882 | − | 1.65149i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.65191 | − | 3.65191i | −0.121934 | − | 0.121934i | ||||
\(898\) | −6.94124 | − | 1.85990i | −0.231632 | − | 0.0620656i | ||||
\(899\) | −9.01695 | + | 15.6178i | −0.300732 | + | 0.520883i | ||||
\(900\) | −5.47593 | + | 8.03184i | −0.182531 | + | 0.267728i | ||||
\(901\) | −15.6881 | + | 9.05752i | −0.522646 | + | 0.301750i | ||||
\(902\) | −5.08195 | + | 5.08195i | −0.169211 | + | 0.169211i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 4.47594i | − | 0.148867i | ||||||
\(905\) | 16.7749 | − | 8.86586i | 0.557616 | − | 0.294711i | ||||
\(906\) | 3.01253 | + | 1.73929i | 0.100085 | + | 0.0577839i | ||||
\(907\) | 41.7950 | − | 11.1989i | 1.38778 | − | 0.371855i | 0.513840 | − | 0.857886i | \(-0.328222\pi\) |
0.873942 | + | 0.486031i | \(0.161556\pi\) | |||||||
\(908\) | 2.95634 | − | 11.0332i | 0.0981096 | − | 0.366150i | ||||
\(909\) | −6.31633 | −0.209499 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7843 | 0.688614 | 0.344307 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344307 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(912\) | 6.85329 | − | 25.5768i | 0.226935 | − | 0.846933i | ||||
\(913\) | −65.2830 | + | 17.4925i | −2.16055 | + | 0.578918i | ||||
\(914\) | 0.380628 | + | 0.219756i | 0.0125901 | + | 0.00726888i | ||||
\(915\) | 15.1931 | + | 4.68640i | 0.502269 | + | 0.154928i | ||||
\(916\) | 25.2550i | 0.834447i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.396526 | + | 0.396526i | −0.0130873 | + | 0.0130873i | ||||
\(919\) | 41.2267 | − | 23.8023i | 1.35994 | − | 0.785164i | 0.370328 | − | 0.928901i | \(-0.379245\pi\) |
0.989616 | + | 0.143737i | \(0.0459119\pi\) | |||||||
\(920\) | −12.8746 | − | 8.08955i | −0.424462 | − | 0.266705i | ||||
\(921\) | −6.96544 | + | 12.0645i | −0.229519 | + | 0.397539i | ||||
\(922\) | −0.296566 | − | 0.0794646i | −0.00976688 | − | 0.00261703i | ||||
\(923\) | −0.597007 | − | 0.597007i | −0.0196507 | − | 0.0196507i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34809 | + | 1.56649i | 0.0443249 | + | 0.0515057i | ||||
\(926\) | 2.76043 | + | 4.78120i | 0.0907132 | + | 0.157120i | ||||
\(927\) | −4.59031 | − | 17.1313i | −0.150765 | − | 0.562664i | ||||
\(928\) | 2.58061 | + | 9.63098i | 0.0847128 | + | 0.316152i | ||||
\(929\) | 20.3266 | + | 35.2067i | 0.666895 | + | 1.15510i | 0.978768 | + | 0.204972i | \(0.0657102\pi\) |
−0.311873 | + | 0.950124i | \(0.600956\pi\) | |||||||
\(930\) | 2.60692 | + | 0.0975344i | 0.0854843 | + | 0.00319828i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32.0088 | + | 32.0088i | 1.04848 | + | 1.04848i | ||||
\(933\) | −26.3759 | − | 7.06740i | −0.863508 | − | 0.231376i | ||||
\(934\) | −3.35797 | + | 5.81617i | −0.109876 | + | 0.190311i | ||||
\(935\) | −4.70774 | − | 20.6256i | −0.153960 | − | 0.674530i | ||||
\(936\) | 0.571123 | − | 0.329738i | 0.0186677 | − | 0.0107778i | ||||
\(937\) | 8.25994 | − | 8.25994i | 0.269841 | − | 0.269841i | −0.559195 | − | 0.829036i | \(-0.688890\pi\) |
0.829036 | + | 0.559195i | \(0.188890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.1742i | 0.854163i | ||||||||
\(940\) | 0.553255 | − | 1.79363i | 0.0180452 | − | 0.0585018i | ||||
\(941\) | −24.9263 | − | 14.3912i | −0.812575 | − | 0.469140i | 0.0352744 | − | 0.999378i | \(-0.488769\pi\) |
−0.847849 | + | 0.530237i | \(0.822103\pi\) | |||||||
\(942\) | −2.57055 | + | 0.688776i | −0.0837529 | + | 0.0224415i | ||||
\(943\) | 14.4144 | − | 53.7952i | 0.469397 | − | 1.75181i | ||||
\(944\) | 22.4113 | 0.729427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.86353 | −0.158127 | ||||||||
\(947\) | 1.56270 | − | 5.83206i | 0.0507808 | − | 0.189516i | −0.935876 | − | 0.352329i | \(-0.885390\pi\) |
0.986657 | + | 0.162812i | \(0.0520565\pi\) | |||||||
\(948\) | 16.2259 | − | 4.34771i | 0.526992 | − | 0.141207i | ||||
\(949\) | −1.19874 | − | 0.692094i | −0.0389128 | − | 0.0224663i | ||||
\(950\) | −2.81621 | + | 8.04847i | −0.0913700 | + | 0.261127i | ||||
\(951\) | 30.9421i | 1.00336i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.8382 | − | 31.8382i | 1.03134 | − | 1.03134i | 0.0318472 | − | 0.999493i | \(-0.489861\pi\) |
0.999493 | − | 0.0318472i | \(-0.0101390\pi\) | |||||||
\(954\) | −1.56148 | + | 0.901521i | −0.0505548 | + | 0.0291878i | ||||
\(955\) | 18.1896 | − | 28.9488i | 0.588602 | − | 0.936762i | ||||
\(956\) | −5.32753 | + | 9.22755i | −0.172305 | + | 0.298440i | ||||
\(957\) | 14.0606 | + | 3.76752i | 0.454514 | + | 0.121787i | ||||
\(958\) | −1.85159 | − | 1.85159i | −0.0598221 | − | 0.0598221i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −10.9682 | + | 10.1771i | −0.353998 | + | 0.328464i | ||||
\(961\) | −3.30703 | − | 5.72794i | −0.106678 | − | 0.184772i | ||||
\(962\) | −0.0178873 | − | 0.0667562i | −0.000576708 | − | 0.00215231i | ||||
\(963\) | −2.73794 | − | 10.2181i | −0.0882290 | − | 0.329275i | ||||
\(964\) | −14.2419 | − | 24.6676i | −0.458700 | − | 0.794491i | ||||
\(965\) | 20.6957 | − | 19.2030i | 0.666220 | − | 0.618166i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.5518 | − | 17.5518i | −0.564429 | − | 0.564429i | 0.366134 | − | 0.930562i | \(-0.380681\pi\) |
−0.930562 | + | 0.366134i | \(0.880681\pi\) | |||||||
\(968\) | 4.39989 | + | 1.17895i | 0.141418 | + | 0.0378928i | ||||
\(969\) | 8.56697 | − | 14.8384i | 0.275211 | − | 0.476679i | ||||
\(970\) | 2.95592 | − | 4.70436i | 0.0949089 | − | 0.151048i | ||||
\(971\) | −0.0805953 | + | 0.0465317i | −0.00258643 | + | 0.00149327i | −0.501293 | − | 0.865278i | \(-0.667142\pi\) |
0.498706 | + | 0.866771i | \(0.333809\pi\) | |||||||
\(972\) | 1.37475 | − | 1.37475i | 0.0440950 | − | 0.0440950i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.56126i | 0.146152i | ||||||||
\(975\) | 3.18818 | − | 1.53538i | 0.102104 | − | 0.0491714i | ||||
\(976\) | 22.5883 | + | 13.0414i | 0.723035 | + | 0.417445i | ||||
\(977\) | −7.10049 | + | 1.90257i | −0.227165 | + | 0.0608686i | −0.370606 | − | 0.928790i | \(-0.620850\pi\) |
0.143441 | + | 0.989659i | \(0.454183\pi\) | |||||||
\(978\) | 0.903223 | − | 3.37087i | 0.0288819 | − | 0.107789i | ||||
\(979\) | −31.1938 | −0.996959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.668223 | −0.0213347 | ||||||||
\(982\) | −1.96376 | + | 7.32884i | −0.0626660 | + | 0.233873i | ||||
\(983\) | −41.5189 | + | 11.1249i | −1.32425 | + | 0.354831i | −0.850567 | − | 0.525867i | \(-0.823741\pi\) |
−0.473679 | + | 0.880697i | \(0.657074\pi\) | |||||||
\(984\) | 6.15877 | + | 3.55577i | 0.196334 | + | 0.113354i | ||||
\(985\) | 2.50465 | − | 8.12000i | 0.0798049 | − | 0.258725i | ||||
\(986\) | 2.04789i | 0.0652181i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.02319 | + | 7.02319i | −0.223437 | + | 0.223437i | ||||
\(989\) | 32.6389 | − | 18.8441i | 1.03786 | − | 0.599208i | ||||
\(990\) | −0.468575 | − | 2.05293i | −0.0148923 | − | 0.0652463i | ||||
\(991\) | −17.1324 | + | 29.6742i | −0.544228 | + | 0.942631i | 0.454427 | + | 0.890784i | \(0.349844\pi\) |
−0.998655 | + | 0.0518468i | \(0.983489\pi\) | |||||||
\(992\) | 13.0233 | + | 3.48957i | 0.413489 | + | 0.110794i | ||||
\(993\) | 11.8025 | + | 11.8025i | 0.374542 | + | 0.374542i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.37788 | + | 0.0515514i | 0.0436817 | + | 0.00163429i | ||||
\(996\) | 16.4825 | + | 28.5486i | 0.522269 | + | 0.904597i | ||||
\(997\) | 7.75273 | + | 28.9336i | 0.245532 | + | 0.916336i | 0.973116 | + | 0.230318i | \(0.0739765\pi\) |
−0.727584 | + | 0.686019i | \(0.759357\pi\) | |||||||
\(998\) | 0.261360 | + | 0.975408i | 0.00827320 | + | 0.0308760i | ||||
\(999\) | −0.206669 | − | 0.357962i | −0.00653873 | − | 0.0113254i |
(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 | 735.2.v.a.472.4 | 32 | ||
5.3 | odd | 4 | inner | 735.2.v.a.178.6 | 32 | ||
7.2 | even | 3 | inner | 735.2.v.a.607.5 | 32 | ||
7.3 | odd | 6 | 105.2.m.a.97.4 | yes | 16 | ||
7.4 | even | 3 | 105.2.m.a.97.3 | yes | 16 | ||
7.5 | odd | 6 | inner | 735.2.v.a.607.6 | 32 | ||
7.6 | odd | 2 | inner | 735.2.v.a.472.3 | 32 | ||
21.11 | odd | 6 | 315.2.p.e.307.6 | 16 | |||
21.17 | even | 6 | 315.2.p.e.307.5 | 16 | |||
28.3 | even | 6 | 1680.2.cz.d.97.4 | 16 | |||
28.11 | odd | 6 | 1680.2.cz.d.97.5 | 16 | |||
35.3 | even | 12 | 105.2.m.a.13.3 | ✓ | 16 | ||
35.4 | even | 6 | 525.2.m.b.307.6 | 16 | |||
35.13 | even | 4 | inner | 735.2.v.a.178.5 | 32 | ||
35.17 | even | 12 | 525.2.m.b.118.6 | 16 | |||
35.18 | odd | 12 | 105.2.m.a.13.4 | yes | 16 | ||
35.23 | odd | 12 | inner | 735.2.v.a.313.3 | 32 | ||
35.24 | odd | 6 | 525.2.m.b.307.5 | 16 | |||
35.32 | odd | 12 | 525.2.m.b.118.5 | 16 | |||
35.33 | even | 12 | inner | 735.2.v.a.313.4 | 32 | ||
105.38 | odd | 12 | 315.2.p.e.118.6 | 16 | |||
105.53 | even | 12 | 315.2.p.e.118.5 | 16 | |||
140.3 | odd | 12 | 1680.2.cz.d.433.5 | 16 | |||
140.123 | even | 12 | 1680.2.cz.d.433.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.3 | ✓ | 16 | 35.3 | even | 12 | ||
105.2.m.a.13.4 | yes | 16 | 35.18 | odd | 12 | ||
105.2.m.a.97.3 | yes | 16 | 7.4 | even | 3 | ||
105.2.m.a.97.4 | yes | 16 | 7.3 | odd | 6 | ||
315.2.p.e.118.5 | 16 | 105.53 | even | 12 | |||
315.2.p.e.118.6 | 16 | 105.38 | odd | 12 | |||
315.2.p.e.307.5 | 16 | 21.17 | even | 6 | |||
315.2.p.e.307.6 | 16 | 21.11 | odd | 6 | |||
525.2.m.b.118.5 | 16 | 35.32 | odd | 12 | |||
525.2.m.b.118.6 | 16 | 35.17 | even | 12 | |||
525.2.m.b.307.5 | 16 | 35.24 | odd | 6 | |||
525.2.m.b.307.6 | 16 | 35.4 | even | 6 | |||
735.2.v.a.178.5 | 32 | 35.13 | even | 4 | inner | ||
735.2.v.a.178.6 | 32 | 5.3 | odd | 4 | inner | ||
735.2.v.a.313.3 | 32 | 35.23 | odd | 12 | inner | ||
735.2.v.a.313.4 | 32 | 35.33 | even | 12 | inner | ||
735.2.v.a.472.3 | 32 | 7.6 | odd | 2 | inner | ||
735.2.v.a.472.4 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.a.607.5 | 32 | 7.2 | even | 3 | inner | ||
735.2.v.a.607.6 | 32 | 7.5 | odd | 6 | inner | ||
1680.2.cz.d.97.4 | 16 | 28.3 | even | 6 | |||
1680.2.cz.d.97.5 | 16 | 28.11 | odd | 6 | |||
1680.2.cz.d.433.4 | 16 | 140.123 | even | 12 | |||
1680.2.cz.d.433.5 | 16 | 140.3 | odd | 12 |